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ABOUT THE EDITOR IN CHIEF Merrill Skolnik was Superintendent of the Radar Division at the U.S. Naval Research Labor...
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ABOUT THE EDITOR IN CHIEF Merrill Skolnik was Superintendent of the Radar Division at the U.S. Naval Research Laboratory for over 30 years. Before that he was involved in advances in radar while at the MIT Lincoln Laboratory, the Institute for Defense Analyses, and the Research Division of Electronic Communications, Inc. He is the author of the popular McGraw-Hill textbook Introduction to Radar Systems, now in its third edition, the editor of Radar Applications, as well as being a former editor of the Proceedings of the IEEE. He earned the Doctor of Engineering Degree from The Johns Hopkins University, where he also received the B.E and M.S.E degrees in electrical engineering. He is a member of the U.S. National Academy of Engineering, a Fellow of the IEEE, and the first recipient of the IEEE Dennis J. Picard Medal for Radar Technologies and Applications.
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RADAR HANDBOOK Merrill I. Skolnik Editor in Chief Third Edition
New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto
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Cataloging-in-Publication Data is on file with the Library of Congress McGraw-Hill books are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. To contact a representative, please visit the Contact Us pages at www.mhprofessional.com. Radar Handbook, Third Edition Copyright © 2008 by The McGraw-Hill Companies. All rights reserved. Printed in the United States of America. Except as permitted under the Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of publisher. 1 2 3 4 5 6 7 8 9 0 DOC DOC 0 1 9 8 ISBN 978-0-07-148547-0 MHID 0-07-148547-3 Sponsoring Editor Wendy Rinaldi Editorial Supervisor Janet Walden Project Editor LeeAnn Pickrell Acquisitions Coordinator Mandy Canales Copy Editor LeeAnn Pickrell Proofreader Susie Elkind Production Supervisor Jean Bodeaux Composition International Typesetting & Composition Illustration International Typesetting & Composition Art Director, Cover Jeff Weeks Cover Designer Mary McKeon Information has been obtained by McGraw-Hill from sources believed to be reliable. However, because of the possibility of human or mechanical error by our sources, McGraw-Hill, or others, McGraw-Hill does not guarantee the accuracy, adequacy, or completeness of any information and is not responsible for any errors or omissions or the results obtained from the use of such information.
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CONTENTS Contributors Preface Chapter 1 An Introduction and Overview of Radar Merrill Skolnik 1.1 Radar in Brief /
xiii xv 1.1 1.1
1.2 Types of Radars /
1.5
1.3 Information Available from a Radar /
1.7
1.4 The Radar Equation /
1.10
1.5 Radar Frequency Letter-band Nomenclature /
1.13
1.6 Effect of Operating Frequency on Radar /
1.14
1.7 Radar Nomenclature /
1.18
1.8 Some Past Advances in Radar /
1.19
1.9 Applications of Radar /
1.20
1.10 Conceptual Radar System Design /
1.22
Chapter 2 MTI Radar William W. Shrader and Vilhelm Gregers-Hansen 2.1 Preface /
2.1 2.1
2.2 Introduction to MTI Radar /
2.2
2.3 Clutter Filter Response to Moving Targets /
2.9
2.4 Clutter Characteristics /
2.10
2.5 Definitions /
2.19
2.6 Improvement Factor Calculations /
2.23
2.7 Optimum Design of Clutter Filters /
2.25
2.8 MTI Clutter Filter Design /
2.33
2.9 MTI Filter Design for Weather Radars /
2.46
2.10 Clutter Filter Bank Design /
2.52
2.11 Performance Degradation Caused by Receiver Limiting /
2.59
2.12 Radar System Stability Requirements /
2.65
2.13 Dynamic Range and A/D Conversion Considerations /
2.78
2.14 Adaptive MTI /
2.80
2.15 Radar Clutter Maps /
2.83
2.16 Sensitivity-velocity Control (SVC) /
2.87
2.17 Considerations Applicable to MTI Radar Systems /
2.91
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Chapter 3 Airborne MTI James K. Day and Fred M. Staudaher 3.1 Systems Using Airborne MTI Techniques /
3.1 3.1
3.2 Coverage Considerations /
3.2
3.3 Airborne MTI Performance Drivers /
3.3
3.4 Platform Motion and Altitude Effects on MTI Performance /
3.3
3.5 Platform-motion Compensation Abeam /
3.10
3.6 Scanning-motion Compensation /
3.14
3.7 Simultaneous Platform Motion and Scan Compensation /
3.18
3.8 Platform-motion Compensation, Forward Direction /
3.21
3.9 Space-time Adaptive Motion Compensation /
3.23
3.10 Effect of Multiple Spectra /
3.31
3.11 Example AMTI Radar System /
3.32
Chapter 4 Pulse Doppler Radar John P. Stralka and William G. Fedarko 4.1 Characteristics and Applications /
4.1 4.1
4.2 Pulse Doppler Clutter /
4.14
4.3 Dynamic-range and Stability Requirements /
4.24
4.4 Range and Doppler Ambiguity Resoluton /
4.31
4.5 Mode and Waveform Design /
4.35
4.6 Range Performance /
4.39
List of Abbreviations /
4.48
Chapter 5 Multifunctional Radar Systems for Fighter Aircraft David Lynch, Jr. and Carlo Kopp 5.1 Introduction /
5.1 5.1
5.2 Typical Missions and Modes /
5.10
5.3 A-A Mode Descriptions & Waveforms /
5.16
5.4 A-S Mode Descriptions & Waveforms /
5.28
Chapter 6 Radar Receivers Michael E. Yeomans 6.1 The Configuration of a Radar Receiver /
6.1 6.1
6.2 Noise and Dynamic-range Considerations /
6.4
6.3 Bandwidth Considerations /
6.9
6.4 Receiver Front End /
6.10
6.5 Local Oscillators /
6.14
6.6 Gain Control /
6.22
6.7 Filtering /
6.24
6.8 Limiters /
6.29
6.9 I/Q Demodulators /
6.31
6.10 Analog-to-Digital Converters /
6.35
6.11 Digital Receivers /
6.40
6.12 Diplex Operation /
6.46
6.13 Waveform Generation and Upconversion /
6.47
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Chapter 7 Automatic Detection, Tracking, and Sensor Integration W. G. Bath and G. V.Trunk 7.1 Introduction /
7.1 7.1
7.2 Automatic Detection /
7.1
7.3 Automatic Tracking /
7.22
7.4 Networked Radars /
7.46
7.5 Unlike-sensor Integration /
7.49
Chapter 8 Pulse Compression Radar Michael R. Ducoff and Byron W. Tietjen 8.1 Introduction / 8.2 Pulse Compression Waveform Types /
8.1 8.1 8.2
8.3 Factors Affecting Choice of Pulse Compression Systems /
8.26
8.4 Pulse Compression Implementation and Radar System Examples /
8.28
Appendix / Chapter 9 Tracking Radar Dean D. Howard 9.1 Introduction / 9.2 Monopulse (Simultaneous Lobing) /
8.36 9.1 9.1 9.3
9.3 Scanning and Lobing /
9.16
9.4 Servosystems for Tracking Radar /
9.17
9.5 Target Acquisition and Range Tracking /
9.20
9.6 Special Monopulse Techniques /
9.24
9.7 Sources of Error /
9.26
9.8 Target-caused Errors (Target Noise) /
9.26
9.9 Other External Causes of Error /
9.37
9.10 Internal Sources of Error /
9.42
9.11 Summary of Sources of Error /
9.43
9.12 Error Reduction Techniques /
9.46
Chapter 10 The Radar Transmitter Thomas A. Weil and Merrill Skolnik 10.1 Introduction /
10.1
10.2 Linear-beam Amplifiers /
10.1 10.4
10.3 Magnetron /
10.14
10.4 Crossed-field Amplifiers /
10.16
10.5 Gyrotrons /
10.17
10.6 Transmitter Spectrum Control /
10.19
10.7 Grid-controlled Tubes /
10.21
10.8 Modulators /
10.23
10.9 Which RF Power Source to Use? /
10.25
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Chapter 11 Solid id-State Transmitters Michael T. Borkowski 11.1 Introduction /
11.1 11.1
11.2 Advantages of Solid State /
11.1
11.3 Solid-state Devices /
11.5
11.4 Designing for the Solid-state Bottle Transmitter /
11.17
11.5 Designing for the Solid-state Phased Array Transmitter /
11.24
11.6 Solid-state System Examples /
11.37
Chapter 12 Reflector Antennas Michael E. Cooley and Daniel Davis 12.1 Introduction /
12.1 12.7
12.2 Basic Principles and Parameters /
12.3
12.3 Reflector Antenna Architectures /
12.16
12.4 Reflector Feeds /
12.25
12.5 Reflector Antenna Analysis /
12.37
12.6 Mechanical Design Considerations /
12.35
Acknowledgments / Chapter 13 Phased Array Radar Antennas Joe Frank and John D. Richards 13.1 Introduction / 13.2 Array Theory /
12.47 13.1 13.7 13.9
13.3 Planar Arrays and Beam Steering /
13.15
13.4 Aperture Matching and Mutual Coupling /
13.20
13.5 Low-sidelobe Phased Arrays /
13.28
13.6 Quantization Effects /
13.34
13.7 Bandwidth of Phased Arrays /
13.38
13.8 Feed Networks (Beamformers) /
13.46
13.9 Phase Shifters /
13.57
13.10 Solid-state Modules /
13.53
13.11 Multiple Simultaneous Receive Beams /
13.54
13.12 Digital Beamforming /
13.56
13.13 Radiation Pattern Nulling /
13.57
13.14 Calibration of Active Phased Array Antennas /
13.60
13.15 Phased Array Systems /
13.62
Chapter 14 Radar Cross Section Eugene F. Knott 14.1 Introduction /
14.1 14.1
14.2 The Concept of Echo Power /
14.4
14.3 RCS Prediction Techniques /
14.16
14.4 RCS Measurement Techniques /
14.27
14.5 Radar Echo Suppression /
14.36
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Chapter 15 Sea Clutter Lewis B. Wetzel 15.1 Introduction /
15.1 15.1
15.2 The Sea Surface /
15.3
15.3 Empirical Behavior of Sea Clutter /
15.7
15.4 Theories and Models of Sea Clutter /
15.27
15.5 Summary and Conclusions /
15.37
Chapter 16 Ground Echo Richard K. Moore 16.1 Introduction /
16.1 16.1
16.2 Parameters Affecting Ground Return /
16.4
16.3 Theoretical Models and Their Limitations /
16.7
16.4 Fading of Ground Echoes /
16.12
16.5 Measurement Techniques for Ground Return /
16.19
16.6 General Models for Scattering Coefficient (Clutter Models) /
16.29
16.7 Scattering Coefficient Data /
16.35
16.8 Polarimetry /
16.46
16.9 Scattering Coefficient Data Near Grazing /
16.52
16.10 Imaging Radar Interpretation /
16.55
Chapter 17 Synthetic Aperture Radar Roger Sullivan 17.1 Basic Principle of SAR /
17.1 17.1
17.2 Early History of SAR /
17.2
17.3 Types of SAR /
17.2
17.4 SAR Resolution /
17.6
17.5 Key Aspects of SAR /
17.10
17.6 SAR Image Quality /
17.16
17.7 Summary of Key SAR Equations /
17.21
17.8 Special SAR Applications /
17.22
Chapter 18 Space-Based Remote Sensing Radars R. Keith Raney 18.1 Perspective / 18.2 Synthetic Aperture Radar (SAR) /
18.1 18.1 18.5
18.3 Altimeters /
18.29
18.4 Planetary Radars /
18.43
18.5 Scatterometers /
18.53
18.6 Radar Sounders /
18.59
x
Chapter 19 Meteorological Radar R. Jeffrey Keeler and Robert J. Serafin 19.1 Introduction /
19.1 19.1
19.2 The Radar Equation for Meteorological Targets /
19.3
19.3 Design Considerations /
19.6
19.4 Signal Processing /
19.19
19.5 Operational Applications /
19.25
19.6 Research Applications /
19.33
Chapter 20 HF Over-the-Horizon Radar James M. Headrick and Stuart J. Anderson 20.1 Introduction /
20.1
20.2 The Radar Equation /
20.5
20.3 Factors Influencing Skywave Radar Design /
20.7
20.4 The Ionosphere and Radiowave Propagation /
20.13
20.5 Waveforms for HF Radar /
20.21
20.6 The Transmitting System /
20.23
20.7 Radar Cross Section /
20.26
20.8 Clutter: Echoes from the Environment /
20.29
20.9 Noise, Interference, and Spectrum Occupancy /
20.40
20.10 The Receiving System /
20.45
20.11 Signal Processing and Tracking /
20.49
20.12 Radar Resource Management /
20.54
20.13 Radar Performance Modeling /
20.55
Appendix: HF Surface Wave Radar /
20.70
Chapter 21 Ground Penetrating Radar David Daniels 21.1 Introduction / 21.2 Physics of Propagation in Materials /
20.1
21.1 21.1 21.6
21.3 Modeling /
21.13
21.4 Properties of Materials /
21.18
21.5 GPR Systems /
21.20
21.6 Modulation Techniques /
21.21
21.7 Antennas /
21.24
21.8 Signal and Image Processing /
21.30
21.9 Applications /
21.35
21.10 Licensing /
21.39
Chapter 22 Civil Marine Radar Andy Norris 22.1 Introduction /
22.1 22.1
22.2 The Challenges /
22.3
22.3 International Standards /
22.7
22.4 Technology /
22.10
22.5 Target Tracking /
22.17
xi
22.6 User Interface /
22.19
22.7 Integration with AIS /
22.23
22.8 Radar Beacons /
22.25
22.9 Validation Testing /
22.28
22.10 Vessel Tracking Services /
22.29
Appendix The Early Days of CMR /
22.31
List of Maritime Radar-related Abbreviations /
22.33
Acknowledgments /
22.34
Chapter 23 Bistatic Radar Nicholas J. Willis 23.1 Concept and Definitions /
23.1 23.1
23.2 Coordinate Systems /
23.3
23.3 Bistatic Radar Equation /
23.4
23.4 Applications /
23.9
23.5 Bistatic Doppler /
23.14
23.6 Target Location /
23.17
23.7 Target Cross Section /
23.19
23.8 Surface Clutter /
23.22
23.9 Unique Problems and Requirements /
23.26
Chapter 24 Electronic Counter-Countermeasures Alfonso Farina 24.1 Introduction /
24.1 24.1
24.2 Terminology /
24.2
24.3 Electronic Warfare Support Measures /
24.2
24.4 Electronic Countermeasures /
24.5
24.5 Objectives and Taxonomy of ECCM Techniques /
24.8
24.6 Antenna-related ECCM /
24.10
24.7 Transmitter-related ECCM /
24.31
24.8 Receiver-related ECCM /
24.32
24.9 Signal-processing-related ECCM /
24.33
24.10 Operational-deployment Techniques /
24.36
24.11 Application of ECCM Techniques /
24.37
24.12 ECCM and ECM Efficacy /
24.54
Acronym List /
24.56
Acknowledgments /
24.58
Chapter 25 Radar Digital Signal Processing James J. Alter and Jeffrey O. Coleman 25.1 Introduction /
25.1 25.1
25.2 Receive Channel Processing /
25.2
25.3 Transmit Channel Processing /
25.20
25.4 DSP Tools /
25.22
25.5 Design Considerations /
25.34
25.6 Summary /
25.37
Acknowledgments /
25.38
xii
Chapter 26 The Propagation Factor, Fp, in the Radar Equation Wayne L. Patterson 26.1 Introduction /
26.1 26.1
26.2 The Earth’s Atmosphere /
26.2
26.3 Refraction /
26.3
26.4 Standard Propagation /
26.4
26.5 Anomalous Propagation /
26.6
26.6 Propagation Modeling /
26.13
26.7 EM System Assessment Programs /
26.18
26.8 AREPS Radar System Assessment Model /
26.23
26.9 AREPS Radar Displays /
26.25
Index
1.1
xiii
CONTRIBUTORS James J. Alter Naval Research Laboratory (CHAPTER 25) Stuart J. Anderson Australian Defense Science and Technology Organisation (CHAPTER 20) W. G. Bath The Johns Hopkins University Applied Physics Laboratory (CHAPTER 7) Michael T. Borkowski Raytheon Company (CHAPTER 11) Jeffrey O. Coleman Naval Research Laboratory (CHAPTER 25) Michael E. Cooley Northrop Grumman, Electronic Systems (CHAPTER 12) David Daniels ERA Technology (CHAPTER 21) Daniel Davis Northrop Grumman Corporation (CHAPTER 12) James K. Day Lockheed Martin Corporation (CHAPTER 3) Michael R. Ducoff Lockheed Martin Corporation (CHAPTER 8) Alfonso Farina SELEX Sistemi Integrati (CHAPTER 24) William G. Fedarko Northrop Grumman Corporation (CHAPTER 4) Joe Frank The Johns Hopkins University Applied Physics Laboratory (CHAPTER 13) Vilhelm Gregers-Hansen Naval Research Laboratory (CHAPTER 2) James M. Headrick Naval Research Laboratory, retired (CHAPTER 20) Dean D. Howard Consultant to ITT Industries, Inc. (CHAPTER 9) R. Jeffrey Keeler National Center for Atmospheric Research (CHAPTER 19) Eugene F. Knott Tomorrow’s Research (CHAPTER 14) Carlo Kopp Monash University (CHAPTER 5) David Lynch, Jr. DL Sciences, Inc. (CHAPTER 5) Richard K. Moore The University of Kansas (CHAPTER 16) Andy Norris Consultant in Navigation Systems (CHAPTER 22) Wayne L. Patterson Space and Naval Warfare Systems Center (CHAPTER 26) Keith Raney The Johns Hopkins University Applied Physics Laboratory (CHAPTER 18) John D. Richards The Johns Hopkins University Applied Physics Laboratory (CHAPTER 13) Robert J. Serafin National Center for Atmospheric Research (CHAPTER 19) William W. Shrader Shrader Associates (CHAPTER 2) Merrill Skolnik (CHAPTERS 1 and 10) Fred M. Staudaher Naval Research Laboratory, retired (CHAPTER 3)
xiv
John P. Stralka Northrop Grumman Corporation (CHAPTER 4) Roger Sullivan Institute for Defense Analyses (CHAPTER 17) Byron W. Tietjen Lockheed Martin Corporation (CHAPTER 8) G. V. Trunk The Johns Hopkins University Applied Physics Laboratory (CHAPTER 7) Thomas A. Weil (CHAPTER 10) Lewis B. Wetzel Naval Research Laboratory, retired (CHAPTER 15) Nicholas J. Willis Technology Service Corporation, retired (CHAPTER 23) Michael E. Yeomans Raytheon Company (CHAPTER 6)
xv
PREFACE Radar is an important example of an electrical engineering system. In university engineering courses, the emphasis usually is on the basic tools of the electrical engineer such as circuit design, signals, solid state, digital processing, electronic devices, electromagnetics, automatic control, microwaves, and so forth. But in the real world of electrical engineering practice, these are only the techniques, piece parts, or subsystems that make up some type of system employed for a useful purpose. In addition to radar and other sensor systems, electrical engineering systems include communications, control, energy, information, industrial, military, navigation, entertainment, medical, and others. These are what the practice of electrical engineering is all about. Without them there would be little need for electrical engineers. However, the practicing engineer who is involved in producing a new type of electrical engineering system often has to depend on acquiring knowledge that was not usually covered in his or her engineering courses. The radar engineer, for example, has to understand the major components and subsystems that make up a radar, as well as how they fit together. The Radar Handbook attempts to help in this task. In addition to the radar system designer, it is hoped that those who are responsible for procuring new radar systems, those who utilize radars, those who maintain radar systems, and those who manage the engineers who do the above, also will find the Radar Handbook to be of help in fulfilling such tasks. The third edition of the Radar Handbook is evidence that the development and application of radar for both civilian and military purposes continue to grow in both utility and in improved technology. Some of the many advances in radar since the previous edition include the following: - The extensive use of digital methods for improved signal processing, data processing, decision making, flexible radar control, and multifunction radar - Doppler weather radar - Ground moving target indication, or GMTI - An extensive experimental database describing low-angle land clutter, as obtained by MIT Lincoln Laboratory, that replaced the previously widely used clutter model that dated back to World War II - The realization that microwave sea echo at low grazing angles is due chiefly to what are called “sea spikes” - The active-aperture phased array radar system using solid-state modules, also called active electronically scanned arrays (AESA), which is attractive for some multifunction radar applications that need to manage both power and spatial coverage - Planetary exploration with radar - Computer-based methods for predicting radar propagation performance in realistic environments
xvi
- Operational use of HF over-the-horizon radar - Improved methods for detecting moving targets in clutter, including space-time adaptive processing - Operational use of inverse synthetic aperture radar for target recognition - Interferometric synthetic aperture radar, or InSAR, to obtain the height of a resolved scatterer or to detect moving ground targets as well as provide a SAR image of a scene - High precision space-based altimeters, with accuracy of a few centimeters, to measure the Earth’s geoid - Ultrawideband radar for ground penetrating and similar applications - Improved high power, wide bandwidth klystron power sources based on clustered cavity resonators, as well as the multiple-beam klystron - The appearance of wide bandgap semiconductors that allow better performance because of high power and high operating temperatures - The availability of high-power millimeter-wave generators based on the gyroklystron - Nonlinear FM pulse compression with low sidelobe levels - The replacement, by the computer, of the operator as information extractor and decision maker The above are not listed in any particular order, nor should they be considered a complete enumeration of radar developments since the appearance of the previous edition. There were also some radar topics in previous editions of the Radar Handbook that are of lesser interest and so were not included in this edition. The chapter authors, who are experts in their particular field, were told to consider the reader of their chapter as being knowledgeable in the general subject of radar and even an expert in some other particular area of radar, but not necessarily knowledgeable about the subject of the particular chapter the author was writing. It should be expected that with a book in print as long as the Radar Handbook has been, not all chapter authors from the previous editions would be available to do the third edition. Many of the previous authors have retired or are no longer with us. Sixteen of the twenty-six chapters in this edition have authors or coauthors who were not involved in the previous editions. The hard work of preparing these chapters was done by the individual expert authors of the various chapters. Thus the value of the Radar Handbook is the result of the diligence and expertise of the authors who contributed their time, knowledge, and experience to make this handbook a useful addition to the desk of radar system engineers and all those people vital to the development, production, and employment of radar systems. I am deeply grateful to all the contributing authors for their fine work and the long hours they had to apply to their task. It is the chapter authors who make any handbook a success. My sincere thanks to them all. As stated in the Preface of the previous edition, readers who wish to reference or quote material from the Radar Handbook are asked to mention the names of the individual chapter authors who produced the material. MERRILL SKOLNIK Baltimore, Maryland
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£°£Ê , ,Ê Ê , 2ADAR IS AN ELECTROMAGNETIC SENSOR FOR THE DETECTION AND LOCATION OF REFLECTING OBJECTS )TS OPERATION CAN BE SUMMARIZED AS FOLLOWS 4HE RADAR RADIATES ELECTROMAGNETIC ENERGY FROM AN ANTENNA TO PROPAGATE IN SPACE 3OME OF THE RADIATED ENERGY IS INTERCEPTED BY A REFLECTING OBJECT USUALLY CALLED A TARGET LOCATED AT A DISTANCE FROM THE RADAR 4HE ENERGY INTERCEPTED BY THE TARGET IS RERADIATED IN MANY DIRECTIONS 3OME OF THE RERADIATED ECHO ENERGY IS RETURNED TO AND RECEIVED BY THE RADAR ANTENNA !FTER AMPLIFICATION BY A RECEIVER AND WITH THE AID OF PROPER SIGNAL PROCESSING A DECISION IS MADE AT THE OUTPUT OF THE RECEIVER AS TO WHETHER OR NOT A TARGET ECHO SIGNAL IS PRESENT !T THAT TIME THE TARGET LOCATION AND POSSIBLY OTHER INFORMATION ABOUT THE TARGET IS ACQUIRED
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! COMMON WAVEFORM RADIATED BY A RADAR IS A SERIES OF RELATIVELY NARROW RECTAN GULAR LIKE PULSES !N EXAMPLE OF A WAVEFORM FOR A MEDIUM RANGE RADAR THAT DETECTS AIRCRAFT MIGHT BE DESCRIBED AS A SHORT PULSE ONE MILLIONTH OF A SECOND IN DURATION ONE MICROSECOND THE TIME BETWEEN PULSES MIGHT BE ONE MILLISECOND SO THAT THE PULSE REPETITION FREQUENCY IS ONE KILOHERTZ THE PEAK POWER FROM THE RADAR TRANSMIT TER MIGHT BE ONE MILLION WATTS ONE MEGAWATT AND WITH THESE NUMBERS THE AVERAGE POWER FROM THE TRANSMITTER IS ONE KILOWATT !N AVERAGE POWER OF ONE KILOWATT MIGHT BE LESS THAN THE POWER OF THE ELECTRIC LIGHTING USUALLY FOUND IN A hTYPICALv CLASSROOM 7E ASSUME THIS EXAMPLE RADAR MIGHT OPERATE IN THE MIDDLE OF THE MICROWAVEo FRE QUENCY RANGE SUCH AS FROM TO '(Z WHICH IS A TYPICAL FREQUENCY BAND FOR CIVIL
4HIS CHAPTER IS A BRIEF OVERVIEW OF RADAR FOR THOSE NOT TOO FAMILIAR WITH THE SUBJECT &OR THOSE WHO ARE FAMILIAR WITH RADAR IT CAN BE CONSIDERED A REFRESHER o -ICROWAVES ARE LOOSELY DEFINED AS THOSE FREQUENCIES WHERE WAVEGUIDES ARE USED FOR TRANSMISSION LINES AND WHERE CAVITIES OR DISTRIBUTED CIRCUITS ARE USED FOR RESONANT CIRCUITS RATHER THAN LUMPED CONSTANT COMPONENTS -ICROWAVE RADARS MIGHT BE FROM ABOUT -(Z TO ABOUT '(Z BUT THESE LIMITS ARE NOT RIGID
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AIRPORT SURVEILLANCE RADARS )TS WAVELENGTH MIGHT BE ABOUT CM ROUNDING OFF FOR SIMPLICITY 7ITH THE PROPER ANTENNA SUCH A RADAR MIGHT DETECT AIRCRAFT OUT TO RANGESp OF TO NMI MORE OR LESS 4HE ECHO POWER RECEIVED BY A RADAR FROM A TARGET CAN VARY OVER A WIDE RANGE OF VALUES BUT WE ARBITRARILY ASSUME A hTYPICALv ECHO SIGNAL FOR ILLUSTRATIVE PURPOSES MIGHT HAVE A POWER OF PERHAPS WATTS )F THE RADIATED POWER IS WATTS ONE MEGAWATT THE RATIO OF ECHO SIGNAL POWER FROM A TARGET TO THE RADAR TRANSMITTER POWER IN THIS EXAMPLE IS n OR THE RECEIVED ECHO IS D" LESS THAN THE TRANSMITTED SIGNAL 4HAT IS QUITE A DIFFERENCE BETWEEN THE MAGNITUDE OF THE TRANSMITTED SIGNAL AND A DETECTABLE RECEIVED ECHO SIGNAL 3OME RADARS HAVE TO DETECT TARGETS AT RANGES AS SHORT AS THE DISTANCE FROM BEHIND HOME PLATE TO THE PITCHERS MOUND IN A BASEBALL PARK TO MEASURE THE SPEED OF A PITCHED BALL WHILE OTHER RADARS HAVE TO OPERATE OVER DISTANCES AS GREAT AS THE DISTANCES TO THE NEAREST PLANETS 4HUS A RADAR MIGHT BE SMALL ENOUGH TO HOLD IN THE PALM OF ONE HAND OR LARGE ENOUGH TO OCCUPY THE SPACE OF MANY FOOTBALL FIELDS 2ADAR TARGETS MIGHT BE AIRCRAFT SHIPS OR MISSILES BUT RADAR TARGETS CAN ALSO BE PEOPLE BIRDS INSECTS PRECIPITATION CLEAR AIR TURBULENCE IONIZED MEDIA LAND FEATURES VEGETATION MOUNTAINS ROADS RIVERS AIRFIELDS BUILDINGS FENCES AND POWER LINE POLES SEA ICE ICEBERGS BUOYS UNDERGROUND FEATURES METEORS AURORA SPACECRAFT AND PLANETS )N ADDITION TO MEASURING THE RANGE TO A TARGET AS WELL AS ITS ANGULAR DIREC TION A RADAR CAN ALSO FIND THE RELATIVE VELOCITY OF A TARGET EITHER BY DETERMINING THE RATE OF CHANGE OF THE RANGE MEASUREMENT WITH TIME OR BY EXTRACTING THE RADIAL VELOCITY FROM THE DOPPLER FREQUENCY SHIFT OF THE ECHO SIGNAL )F THE LOCATION OF A MOVING TARGET IS MEASURED OVER A PERIOD OF TIME THE TRACK OR TRAJECTORY OF THE TARGET CAN BE FOUND FROM WHICH THE ABSOLUTE VELOCITY OF THE TARGET AND ITS DIRECTION OF TRAVEL CAN BE DETERMINED AND A PREDICTION CAN BE MADE AS TO ITS FUTURE LOCATION 0ROPERLY DESIGNED RADARS CAN DETERMINE THE SIZE AND SHAPE OF A TARGET AND MIGHT EVEN BE ABLE TO RECOGNIZE ONE TYPE OR CLASS OF TARGET FROM ANOTHER "ASIC 0ARTS OF A 2ADAR &IGURE IS A VERY ELEMENTARY BASIC BLOCK DIAGRAM SHOWING THE SUBSYSTEMS USUALLY FOUND IN A RADAR 4HE TRANSMITTER WHICH IS SHOWN HERE AS A POWER AMPLIFIER GENERATES A SUITABLE WAVEFORM FOR THE PARTICULAR JOB THE RADAR IS TO PERFORM )T MIGHT HAVE AN AVERAGE POWER AS SMALL AS MILLIWATTS OR AS LARGE AS MEGA WATTS 4HE AVERAGE POWER IS A FAR BETTER INDICATION OF THE CAPABILITY OF A RADARS PERFOR MANCE THAN IS ITS PEAK POWER -OST RADARS USE A SHORT PULSE WAVEFORM SO THAT A SINGLE ANTENNA CAN BE USED ON A TIME SHARED BASIS FOR BOTH TRANSMITTING AND RECEIVING 4HE FUNCTION OF THE DUPLEXER IS TO ALLOW A SINGLE ANTENNA TO BE USED BY PROTECTING THE SENSITIVE RECEIVER FROM BURNING OUT WHILE THE TRANSMITTER IS ON AND BY DIRECTING THE RECEIVED ECHO SIGNAL TO THE RECEIVER RATHER THAN TO THE TRANSMITTER 4HE ANTENNA IS THE DEVICE THAT ALLOWS THE TRANSMITTED ENERGY TO BE PROPAGATED INTO SPACE AND THEN COLLECTS THE ECHO ENERGY ON RECEIVE )T IS ALMOST ALWAYS A DIRECTIVE ANTENNA ONE THAT DIRECTS THE RADIATED ENERGY INTO A NARROW BEAM TO CONCENTRATE THE POWER AS WELL AS TO ALLOW THE DETERMINATION OF THE DIRECTION TO THE TARGET !N ANTENNA THAT PRODUCES A NARROW DIRECTIVE BEAM ON TRANSMIT USUALLY HAS A LARGE AREA ON RECEIVE TO ALLOW THE COLLECTION OF WEAK ECHO SIGNALS FROM THE TARGET 4HE ANTENNA NOT ONLY CONCENTRATES THE ENERGY ON TRANSMIT AND COLLECTS THE ECHO ENERGY ON RECEIVE BUT IT ALSO ACTS AS A SPATIAL FILTER TO PROVIDE ANGLE RESOLUTION AND OTHER CAPABILITIES p )N RADAR RANGE IS THE TERM GENERALLY USED TO MEAN DISTANCE FROM THE RADAR TO THE TARGET 2ANGE IS ALSO USED HERE IN SOME OF ITS OTHER DICTIONARY DEFINITIONS
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&)'52% "LOCK DIAGRAM OF A SIMPLE RADAR EMPLOYING A POWER AMPLIFIER AS THE TRANSMITTER IN THE UPPER PORTION OF THE FIGURE AND A SUPERHETERODYNE RECEIVER IN THE LOWER PORTION OF THE FIGURE
4HE RECEIVER AMPLIFIES THE WEAK RECEIVED SIGNAL TO A LEVEL WHERE ITS PRESENCE CAN BE DETECTED "ECAUSE NOISE IS THE ULTIMATE LIMITATION ON THE ABILITY OF A RADAR TO MAKE A RELIABLE DETECTION DECISION AND EXTRACT INFORMATION ABOUT THE TARGET CARE IS TAKEN TO INSURE THAT THE RECEIVER PRODUCES VERY LITTLE NOISE OF ITS OWN !T THE MICROWAVE FREQUENCIES WHERE MOST RADARS ARE FOUND THE NOISE THAT AFFECTS RADAR PERFORMANCE IS USUALLY FROM THE FIRST STAGE OF THE RECEIVER SHOWN HERE IN &IGURE AS A LOW NOISE AMPLIFIER &OR MANY RADAR APPLICATIONS WHERE THE LIMITATION TO DETECTION IS THE UNWANTED RADAR ECHOES FROM THE ENVIRONMENT CALLED CLUTTER THE RECEIVER NEEDS TO HAVE A LARGE ENOUGH DYNAMIC RANGE SO AS TO AVOID HAVING THE CLUTTER ECHOES ADVERSELY AFFECT DETECTION OF WANTED MOVING TARGETS BY CAUSING THE RECEIVER TO SATURATE 4HE DYNAMIC RANGE OF A RECEIVER USUALLY EXPRESSED IN DECIBELS IS DEFINED AS THE RATIO OF THE MAXIMUM TO THE MINIMUM SIGNAL INPUT POWER LEVELS OVER WHICH THE RECEIVER CAN OPERATE WITH SOME SPECIFIED PERFORMANCE 4HE MAXIMUM SIGNAL LEVEL MIGHT BE SET BY THE NONLINEAR EFFECTS OF THE RECEIVER RESPONSE THAT CAN BE TOLERATED FOR EXAMPLE THE SIGNAL POWER AT WHICH THE RECEIVER BEGINS TO SATURATE AND THE MINIMUM SIGNAL MIGHT BE THE MINIMUM DETECTABLE SIGNAL 4HE SIGNAL PROCESSOR WHICH IS OFTEN IN THE )& PORTION OF THE RECEIVER MIGHT BE DESCRIBED AS BEING THE PART OF THE RECEIVER THAT SEPARATES THE DESIRED SIGNAL FROM THE UNDESIRED SIGNALS THAT CAN DEGRADE THE DETEC TION PROCESS 3IGNAL PROCESSING INCLUDES THE MATCHED FILTER THAT MAXIMIZES THE OUT PUT SIGNAL TO NOISE RATIO 3IGNAL PROCESSING ALSO INCLUDES THE DOPPLER PROCESSING THAT MAXIMIZES THE SIGNAL TO CLUTTER RATIO OF A MOVING TARGET WHEN CLUTTER IS LARGER THAN RECEIVER NOISE AND IT SEPARATES ONE MOVING TARGET FROM OTHER MOVING TARGETS OR FROM CLUTTER ECHOES 4HE DETECTION DECISION IS MADE AT THE OUTPUT OF THE RECEIVER SO A TARGET IS DECLARED TO BE PRESENT WHEN THE RECEIVER OUTPUT EXCEEDS A PREDETERMINED THRESHOLD )F THE THRESHOLD IS SET TOO LOW THE RECEIVER NOISE CAN CAUSE EXCESSIVE FALSE ALARMS )F THE THRESHOLD IS SET TOO HIGH DETECTIONS OF SOME TARGETS MIGHT BE MISSED THAT WOULD OTHERWISE HAVE BEEN DETECTED 4HE CRITERION FOR DETERMINING THE LEVEL OF THE DECISION THRESHOLD IS TO SET THE THRESHOLD SO IT PRODUCES AN ACCEPTABLE PREDETERMINED AVERAGE RATE OF FALSE ALARMS DUE TO RECEIVER NOISE !FTER THE DETECTION DECISION IS MADE THE TRACK OF A TARGET CAN BE DETERMINED WHERE A TRACK IS THE LOCUS OF TARGET LOCATIONS MEASURED OVER TIME 4HIS IS AN EXAMPLE OF DATA PROCESSING 4HE PROCESSED TARGET DETECTION INFORMATION OR ITS TRACK MIGHT BE DISPLAYED TO AN OPERATOR OR THE DETECTION INFORMATION MIGHT BE USED TO AUTOMATICALLY GUIDE A
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MISSILE TO A TARGET OR THE RADAR OUTPUT MIGHT BE FURTHER PROCESSED TO PROVIDE OTHER INFORMATION ABOUT THE NATURE OF THE TARGET 4HE RADAR CONTROL INSURES THAT THE VARIOUS PARTS OF A RADAR OPERATE IN A COORDINATED AND COOPERATIVE MANNER AS FOR EXAMPLE PROVIDING TIMING SIGNALS TO VARIOUS PARTS OF THE RADAR AS REQUIRED 4HE RADAR ENGINEER HAS AS RESOURCES TIME THAT ALLOWS GOOD DOPPLER PROCESSING BANDWIDTH FOR GOOD RANGE RESOLUTION SPACE THAT ALLOWS A LARGE ANTENNA AND ENERGY FOR LONG RANGE PERFORMANCE AND ACCURATE MEASUREMENTS %XTERNAL FACTORS AFFECTING RADAR PERFORMANCE INCLUDE THE TARGET CHARACTERISTICS EXTERNAL NOISE THAT MIGHT ENTER VIA THE ANTENNA UNWANTED CLUTTER ECHOES FROM LAND SEA BIRDS OR RAIN INTERFERENCE FROM OTHER ELECTROMAGNETIC RADIATORS AND PROPAGATION EFFECTS DUE TO THE EARTHS SURFACE AND ATMO SPHERE 4HESE FACTORS ARE MENTIONED TO EMPHASIZE THAT THEY CAN BE HIGHLY IMPORTANT IN THE DESIGN AND APPLICATION OF A RADAR 2ADAR 4RANSMITTERS 4HE RADAR TRANSMITTER MUST NOT ONLY BE ABLE TO GENERATE THE PEAK AND AVERAGE POWERS REQUIRED TO DETECT THE DESIRED TARGETS AT THE MAXIMUM RANGE BUT ALSO HAS TO GENERATE A SIGNAL WITH THE PROPER WAVEFORM AND THE STABILITY NEEDED FOR THE PARTICULAR APPLICATION 4RANSMITTERS MAY BE OSCILLATORS OR AMPLIFIERS BUT THE LATTER USUALLY OFFER MORE ADVANTAGES 4HERE HAVE BEEN MANY TYPES OF RADAR POWER SOURCES USED IN RADAR #HAPTER 4HE MAGNETRON POWER OSCILLATOR WAS AT ONE TIME VERY POPULAR BUT IT IS SELDOM USED EXCEPT FOR CIVIL MARINE RADAR #HAPTER "ECAUSE OF THE MAGNETRONS RELATIVELY LOW AVERAGE POWER ONE OR TWO KILOWATTS AND POOR STABILITY OTHER POWER SOURCES ARE USUALLY MORE APPROPRIATE FOR APPLICATIONS REQUIRING LONG RANGE DETECTION OF SMALL MOVING TARGETS IN THE PRESENCE OF LARGE CLUTTER ECHOES 4HE MAGNETRON POWER OSCIL LATOR IS AN EXAMPLE OF WHAT IS CALLED A CROSSED FIELD TUBE 4HERE IS ALSO A RELATED CROSSED FIELD AMPLIFIER #&! THAT HAS BEEN USED IN SOME RADARS IN THE PAST BUT IT ALSO SUFFERS LIMITATIONS FOR IMPORTANT RADAR APPLICATIONS ESPECIALLY FOR THOSE REQUIR ING DETECTION OF MOVING TARGETS IN CLUTTER 4HE HIGH POWER KLYSTRON AND THE TRAVELING WAVE TUBE 474 ARE EXAMPLES OF WHAT ARE CALLED LINEAR BEAM TUBES !T THE HIGH POWERS OFTEN EMPLOYED BY RADARS BOTH TUBES HAVE SUITABLY WIDE BANDWIDTHS AS WELL AS GOOD STABILITY AS NEEDED FOR DOPPLER PROCESSING AND BOTH HAVE BEEN POPULAR 4HE SOLID STATE AMPLIFIER SUCH AS THE TRANSISTOR HAS ALSO BEEN USED IN RADAR ESPE CIALLY IN PHASED ARRAYS !LTHOUGH AN INDIVIDUAL TRANSISTOR HAS RELATIVELY LOW POWER EACH OF THE MANY RADIATING ELEMENTS OF AN ARRAY ANTENNA CAN UTILIZE MULTIPLE TRANSISTORS TO ACHIEVE THE HIGH POWER NEEDED FOR MANY RADAR APPLICATIONS 7HEN SOLID STATE TRAN SISTOR AMPLIFIERS ARE USED THE RADAR DESIGNER HAS TO BE ABLE TO ACCOMMODATE THE HIGH DUTY CYCLE AT WHICH THESE DEVICES HAVE TO OPERATE THE LONG PULSES THEY MUST USE THAT REQUIRE PULSE COMPRESSION AND THE MULTIPLE PULSES OF DIFFERENT WIDTHS TO ALLOW DETEC TION AT SHORT AS WELL AS LONG RANGE 4HUS THE USE OF SOLID STATE TRANSMITTERS CAN HAVE AN EFFECT ON OTHER PARTS OF THE RADAR SYSTEM !T MILLIMETER WAVELENGTHS VERY HIGH POWER CAN BE OBTAINED WITH THE GYROTRON EITHER AS AN AMPLIFIER OR AS AN OSCILLATOR 4HE GRID CONTROL VACUUM TUBE WAS USED TO GOOD ADVANTAGE FOR A LONG TIME IN 5(& AND LOWER FREQUENCY RADARS BUT THERE HAS BEEN LESS INTEREST IN THE LOWER FREQUENCIES FOR RADAR !LTHOUGH NOT EVERYONE MIGHT AGREE SOME RADAR SYSTEM ENGINEERSIF GIVEN A CHOICEWOULD CONSIDER THE KLYSTRON AMPLIFIER AS THE PRIME CANDIDATE FOR A HIGH POWER MODERN RADAR IF THE APPLICATION WERE SUITABLE FOR ITS USE 2ADAR !NTENNAS 4HE ANTENNA IS WHAT CONNECTS THE RADAR TO THE OUTSIDE WORLD #HAPTERS AND )T PERFORMS SEVERAL PURPOSES CONCENTRATES THE RADIATED ENERGY
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ON TRANSMIT THAT IS IT IS DIRECTIVE AND HAS A NARROW BEAMWIDTH COLLECTS THE RECEIVED ECHO ENERGY FROM THE TARGET PROVIDES A MEASUREMENT OF THE ANGULAR DIRECTION TO THE TARGET PROVIDES SPATIAL RESOLUTION TO RESOLVE OR SEPARATE TARGETS IN ANGLE AND ALLOWS THE DESIRED VOLUME OF SPACE TO BE OBSERVED 4HE ANTENNA CAN BE A MECHANICALLY SCANNED PARABOLIC REFLECTOR A MECHANICALLY SCANNED PLANAR PHASED ARRAY OR A MECHANICALLY SCANNED END FIRE ANTENNA )T CAN BE AN ELECTRONICALLY SCANNED PHASED ARRAY USING A SINGLE TRANSMIT TER WITH EITHER A CORPORATE FEED OR A SPACE FEED CONFIGURATION TO DISTRIBUTE THE POWER TO EACH ANTENNA ELEMENT OR AN ELECTRONICALLY SCANNED PHASED ARRAY EMPLOYING AT EACH ANTENNA ELEMENT A SMALL SOLID STATE hMINIATUREv RADAR ALSO CALLED AN ACTIVE APERTURE PHASED ARRAY %ACH TYPE OF ANTENNA HAS ITS PARTICULAR ADVANTAGES AND LIMITATIONS 'ENERALLY THE LARGER THE ANTENNA THE BETTER BUT THERE CAN BE PRACTICAL CONSTRAINTS THAT LIMIT ITS SIZE
£°ÓÊ /9* -Ê"Ê, ,!LTHOUGH THERE IS NO SINGLE WAY TO CHARACTERIZE A RADAR HERE WE DO SO BY MEANS OF WHAT MIGHT BE THE MAJOR FEATURE THAT DISTINGUISHES ONE TYPE OF RADAR FROM ANOTHER 0ULSE RADAR 4HIS IS A RADAR THAT RADIATES A REPETITIVE SERIES OF ALMOST RECTANGULAR PULSES )T MIGHT BE CALLED THE CANONICAL FORM OF A RADAR THE ONE USUALLY THOUGHT OF AS A RADAR WHEN NOTHING ELSE IS SAID TO DEFINE A RADAR (IGH RESOLUTION RADAR (IGH RESOLUTION CAN BE OBTAINED IN THE RANGE ANGLE OR DOP PLER VELOCITY COORDINATES BUT HIGH RESOLUTION USUALLY IMPLIES THAT THE RADAR HAS HIGH RANGE RESOLUTION 3OME HIGH RESOLUTION RADARS HAVE RANGE RESOLUTIONS IN TERMS OF FRACTIONS OF A METER BUT IT CAN BE AS SMALL AS A FEW CENTIMETERS 0ULSE COMPRESSION RADAR 4HIS IS A RADAR THAT USES A LONG PULSE WITH INTERNAL MODU LATION USUALLY FREQUENCY OR PHASE MODULATION TO OBTAIN THE ENERGY OF A LONG PULSE WITH THE RESOLUTION OF A SHORT PULSE #ONTINUOUS WAVE #7 RADAR 4HIS RADAR EMPLOYS A CONTINUOUS SINE WAVE )T ALMOST ALWAYS USES THE DOPPLER FREQUENCY SHIFT FOR DETECTING MOVING TARGETS OR FOR MEASUR ING THE RELATIVE VELOCITY OF A TARGET &- #7 RADAR 4HIS #7 RADAR USES FREQUENCY MODULATION OF THE WAVEFORM TO ALLOW A RANGE MEASUREMENT 3URVEILLANCE RADAR !LTHOUGH A DICTIONARY MIGHT NOT DEFINE SURVEILLANCE THIS WAY A SURVEILLANCE RADAR IS ONE THAT DETECTS THE PRESENCE OF A TARGET SUCH AS AN AIRCRAFT OR A SHIP AND DETERMINES ITS LOCATION IN RANGE AND ANGLE )T CAN ALSO OBSERVE THE TARGET OVER A PERIOD OF TIME SO AS TO OBTAIN ITS TRACK -OVING TARGET INDICATION -4) 4HIS IS A PULSE RADAR THAT DETECTS MOVING TARGETS IN CLUTTER BY USING A LOW PULSE REPETITION FREQUENCY 02& THAT USUALLY HAS NO RANGE AMBIGUITIES )T DOES HAVE AMBIGUITIES IN THE DOPPLER DOMAIN THAT RESULT IN SO CALLED BLIND SPEEDS 0ULSE DOPPLER RADAR 4HERE ARE TWO TYPES OF PULSE DOPPLER RADARS THAT EMPLOY EITHER A HIGH OR MEDIUM 02& PULSE RADAR 4HEY BOTH USE THE DOPPLER FREQUENCY SHIFT TO EXTRACT MOVING TARGETS IN CLUTTER ! HIGH 02& PULSE DOPPLER RADAR HAS NO AMBIGUI TIES BLIND SPEEDS IN DOPPLER BUT IT DOES HAVE RANGE AMBIGUITIES ! MEDIUM 02& PULSE DOPPLER RADAR HAS AMBIGUITIES IN BOTH RANGE AND DOPPLER
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4RACKING RADAR 4HIS IS A RADAR THAT PROVIDES THE TRACK OR TRAJECTORY OF A TARGET 4RACKING RADARS CAN BE FURTHER DELINEATED AS 344 !$4 473 AND PHASED ARRAY TRACKERS AS DESCRIBED BELOW 3INGLE 4ARGET 4RACKER 344 4RACKS A SINGLE TARGET AT A DATA RATE HIGH ENOUGH TO PROVIDE ACCURATE TRACKING OF A MANEUVERING TARGET ! REVISIT TIME OF S DATA RATE OF MEASUREMENTS PER SECOND MIGHT BE hTYPICALv )T MIGHT EMPLOY THE MONOPULSE TRACKING METHOD FOR ACCURATE TRACKING INFORMATION IN THE ANGLE COORDINATE !UTOMATIC DETECTION AND TRACKING !$4 4HIS IS TRACKING PERFORMED BY A SUR VEILLANCE RADAR )T CAN HAVE A VERY LARGE NUMBER OF TARGETS IN TRACK BY USING THE MEASUREMENTS OF TARGET LOCATIONS OBTAINED OVER MULTIPLE SCANS OF THE ANTENNA )TS DATA RATE IS NOT AS HIGH AS THE 344 2EVISIT TIMES MIGHT RANGE FROM ONE TO SECONDS DEPENDING ON THE APPLICATION 4RACK WHILE SCAN 473 5SUALLY A RADAR THAT PROVIDES SURVEILLANCE OVER A NAR ROW REGION OF ANGLE IN ONE OR TWO DIMENSIONS SO AS TO PROVIDE AT A RAPID UPDATE RATE LOCATION INFORMATION ON ALL TARGETS WITHIN A LIMITED ANGULAR REGION OF OBSERVATION )T HAS BEEN USED IN THE PAST FOR GROUND BASED RADARS THAT GUIDE AIRCRAFT TO A LANDING IN SOME TYPES OF WEAPON CONTROL RADARS AND IN SOME MILITARY AIRBORNE RADARS 0HASED ARRAY TRACKER !N ELECTRONICALLY SCANNED PHASED ARRAY CAN ALMOST hCON TINUOUSLYv TRACK MORE THAN ONE TARGET AT A HIGH DATA RATE )T CAN ALSO SIMULTA NEOUSLY PROVIDE THE LOWER DATA RATE TRACKING OF MULTIPLE TARGETS SIMILAR TO THAT PERFORMED BY !$4 )MAGING RADAR 4HIS RADAR PRODUCES A TWO DIMENSIONAL IMAGE OF A TARGET OR A SCENE SUCH AS A PORTION OF THE SURFACE OF THE EARTH AND WHAT IS ON IT 4HESE RADARS USUALLY ARE ON MOVING PLATFORMS 3IDELOOKING AIRBORNE RADAR 3,!2 4HIS AIRBORNE SIDELOOKING IMAGING RADAR PRO VIDES HIGH RESOLUTION IN RANGE AND OBTAINS SUITABLE RESOLUTION IN ANGLE BY USING A NARROW BEAMWIDTH ANTENNA 3YNTHETIC APERTURE RADAR 3!2 3!2 IS A COHERENT IMAGING RADAR ON A MOVING VEHICLE THAT USES THE PHASE INFORMATION OF THE ECHO SIGNAL TO OBTAIN AN IMAGE OF A SCENE WITH HIGH RESOLUTION IN BOTH RANGE AND CROSS RANGE (IGH RANGE RESOLUTION IS OFTEN OBTAINED USING PULSE COMPRESSION )NVERSE SYNTHETIC APERTURE RADAR )3!2 )3!2 IS A COHERENT IMAGING RADAR THAT USES HIGH RESOLUTION IN RANGE AND THE RELATIVE MOTION OF THE TARGET TO OBTAIN HIGH RESOLU TION IN THE DOPPLER DOMAIN THAT ALLOWS RESOLUTION IN THE CROSS RANGE DIMENSION TO BE OBTAINED )T CAN BE ON A MOVING VEHICLE OR IT CAN BE STATIONARY 7EAPON CONTROL RADAR 4HIS NAME IS USUALLY APPLIED TO A SINGLE TARGET TRACKER USED FOR DEFENDING AGAINST AIR ATTACK 'UIDANCE RADAR 4HIS IS USUALLY A RADAR ON A MISSILE THAT ALLOWS THE MISSILE TO hHOME IN v OR GUIDE ITSELF TO A TARGET 7EATHER METEOROLOGICAL OBSERVATION 3UCH RADARS DETECT RECOGNIZE AND MEASURE PRECIPITATION RATE WIND SPEED AND DIRECTION AND OBSERVE OTHER WEATHER EFFECTS
#OHERENT IMPLIES THAT THE PHASE OF THE RADAR SIGNAL IS USED AS AN IMPORTANT PART OF THE RADAR PROCESS
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IMPORTANT FOR METEOROLOGICAL PURPOSES 4HESE MAY BE SPECIAL RADARS OR ANOTHER FUNCTION OF SURVEILLANCE RADARS $OPPLER WEATHER RADAR 4HIS IS A WEATHER OBSERVATION RADAR THAT EMPLOYS THE DOP PLER FREQUENCY SHIFT CAUSED BY MOVING WEATHER EFFECTS TO DETERMINE THE WIND THE WIND SHEAR WHEN THE WIND BLOWS IN DIFFERENT DIRECTIONS WHICH CAN INDICATE A DANGEROUS WEATHER CONDITION SUCH AS A TORNADO OR A DOWNBURST OF WIND AS WELL AS OTHER METEOROLOGICAL EFFECTS 4ARGET RECOGNITION )N SOME CASES IT MIGHT BE IMPORTANT TO RECOGNIZE THE TYPE OF TARGET BEING OBSERVED BY RADAR EG AN AUTOMOBILE RATHER THAN A BIRD OR TO RECOGNIZE THE PAR TICULAR TYPE OF TARGET AN AUTOMOBILE RATHER THAN A TRUCK OR A STARLING RATHER THAN A SPAR ROW OR TO RECOGNIZE ONE CLASS OF TARGET FROM ANOTHER A CRUISE SHIP RATHER THAN A TANKER 7HEN USED FOR MILITARY PURPOSES IT IS USUALLY CALLED A NONCOOPERATIVE TARGET RECOG NITION .#42 RADAR AS COMPARED TO A COOPERATIVE RECOGNITION SYSTEM SUCH AS )&& IDENTIFICATION FRIEND OR FOE WHICH IS NOT A RADAR 7HEN TARGET RECOGNITION INVOLVES SOME PART OF THE NATURAL ENVIRONMENT THE RADAR IS USUALLY KNOWN AS A REMOTE SENS ING OF THE ENVIRONMENT RADAR -ULTIFUNCTION RADAR )F EACH OF THE ABOVE RADARS WERE THOUGHT OF AS PROVIDING SOME RADAR FUNCTION THEN A MULTIFUNCTION RADAR IS ONE DESIGNED TO PERFORM MORE THAN ONE SUCH FUNCTIONUSUALLY PERFORMING ONE FUNCTION AT A TIME ON A TIME SHARED BASIS 4HERE ARE MANY OTHER WAYS TO DESCRIBE RADARS INCLUDING LAND SEA AIRBORNE SPACE BORNE MOBILE TRANSPORTABLE AIR TRAFFIC CONTROL MILITARY GROUND PENETRATING ULTRA WIDEBAND OVER THE HORIZON INSTRUMENTATION LASER OR LIDAR BY THE FREQUENCY BAND AT WHICH THEY OPERATE 5(& , 3 AND SO ON BY THEIR APPLICATION AND SO FORTH
£°ÎÊ ", /" Ê6 Ê," ÊÊ, , $ETECTION OF TARGETS IS OF LITTLE VALUE UNLESS SOME INFORMATION ABOUT THE TARGET IS OBTAINED AS WELL ,IKEWISE TARGET INFORMATION WITHOUT TARGET DETECTION IS MEANINGLESS 2ANGE 0ROBABLY THE MOST DISTINGUISHING FEATURE OF A CONVENTIONAL RADAR IS ITS ABILITY TO DETERMINE THE RANGE TO A TARGET BY MEASURING THE TIME IT TAKES FOR THE RADAR SIGNAL TO PROPAGATE AT THE SPEED OF LIGHT OUT TO THE TARGET AND BACK TO THE RADAR .O OTHER SENSOR CAN MEASURE THE DISTANCE TO A REMOTE TARGET AT LONG RANGE WITH THE ACCURACY OF RADAR BASICALLY LIMITED AT LONG RANGES BY THE ACCURACY OF THE KNOWLEDGE OF THE VELOCITY OF PROPAGATION !T MODEST RANGES THE PRECISION CAN BE A FEW CENTIMETERS 4O MEASURE RANGE SOME SORT OF TIMING MARK MUST BE INTRODUCED ON THE TRANSMITTED WAVEFORM ! TIMING MARK CAN BE A SHORT PULSE AN AMPLITUDE MODULATION OF THE SIGNAL BUT IT CAN ALSO BE A DISTINCTIVE MODULATION OF THE FREQUENCY OR PHASE 4HE ACCURACY OF A RANGE MEASUREMENT DEPENDS ON THE RADAR SIGNAL BANDWIDTH THE WIDER THE BANDWIDTH THE GREATER THE ACCURACY 4HUS BANDWIDTH IS THE BASIC MEASURE OF RANGE ACCURACY 2ADIAL 6ELOCITY 4HE RADIAL VELOCITY OF A TARGET IS OBTAINED FROM THE RATE OF CHANGE OF RANGE OVER A PERIOD OF TIME )T CAN ALSO BE OBTAINED FROM THE MEASUREMENT OF THE DOP PLER FREQUENCY SHIFT !N ACCURATE MEASUREMENT OF RADIAL VELOCITY REQUIRES TIME (ENCE TIME IS THE BASIC PARAMETER DESCRIBING THE QUALITY OF A RADIAL VELOCITY MEASUREMENT 4HE SPEED OF A MOVING TARGET AND ITS DIRECTION OF TRAVEL CAN BE OBTAINED FROM ITS TRACK WHICH CAN BE FOUND FROM THE RADAR MEASUREMENTS OF THE TARGET LOCATION OVER A PERIOD OF TIME
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!NGULAR $IRECTION /NE METHOD FOR DETERMINING THE DIRECTION TO A TARGET IS BY DETERMINING THE ANGLE WHERE THE MAGNITUDE OF THE ECHO SIGNAL FROM A SCANNING ANTENNA IS MAXIMUM 4HIS USUALLY REQUIRES AN ANTENNA WITH A NARROW BEAMWIDTH A HIGH GAIN ANTENNA !N AIR SURVEILLANCE RADAR WITH A ROTATING ANTENNA BEAM DETERMINES ANGLE IN THIS MANNER 4HE ANGLE TO A TARGET IN ONE ANGULAR DIMENSION CAN ALSO BE DETERMINED BY USING TWO ANTENNA BEAMS SLIGHTLY DISPLACED IN ANGLE AND COMPARING THE ECHO AMPLI TUDE RECEIVED IN EACH BEAM &OUR BEAMS ARE NEEDED TO OBTAIN THE ANGLE MEASUREMENT IN BOTH AZIMUTH AND ELEVATION 4HE MONOPULSE TRACKING RADAR DISCUSSED IN #HAPTER IS A GOOD EXAMPLE 4HE ACCURACY OF AN ANGLE MEASUREMENT DEPENDS ON THE ELECTRICAL SIZE OF THE ANTENNA IE THE SIZE OF THE ANTENNA GIVEN IN WAVELENGTHS 3IZE AND 3HAPE )F THE RADAR HAS SUFFICIENT RESOLUTION CAPABILITY IN RANGE OR ANGLE IT CAN PROVIDE A MEASUREMENT OF THE TARGET EXTENT IN THE DIMENSION OF HIGH RESOLU TION 2ANGE IS USUALLY THE COORDINATE WHERE RESOLUTION IS OBTAINED 2ESOLUTION IN CROSS RANGE GIVEN BY THE RANGE MULTIPLIED BY THE ANTENNA BEAMWIDTH CAN BE OBTAINED WITH VERY NARROW BEAMWIDTH ANTENNAS (OWEVER THE ANGULAR WIDTH OF AN ANTENNA BEAM IS LIMITED SO THE CROSS RANGE RESOLUTION OBTAINED BY THIS METHOD IS NOT AS GOOD AS THE RANGE RESOLUTION 6ERY GOOD RESOLUTION IN THE CROSS RANGE DIMENSION CAN BE OBTAINED BY EMPLOYING THE DOPPLER FREQUENCY DOMAIN BASED ON 3!2 SYNTHETIC APERTURE RADAR OR )3!2 INVERSE SYNTHETIC APERTURE RADAR SYSTEMS AS DISCUSSED IN #HAPTER 4HERE NEEDS TO BE RELATIVE MOTION BETWEEN THE TARGET AND THE RADAR IN ORDER TO OBTAIN THE CROSS RANGE RESOLUTION BY 3!2 OR )3!2 7ITH SUFFICIENT RESOLUTION IN BOTH RANGE AND CROSS RANGE NOT ONLY CAN THE SIZE BE OBTAINED IN TWO ORTHOGONAL COORDINATES BUT THE TARGET SHAPE CAN SOMETIMES BE DISCERNED 4HE )MPORTANCE OF "ANDWIDTH IN 2ADAR "ANDWIDTH BASICALLY REPRESENTS INFOR MATION HENCE IT IS VERY IMPORTANT IN MANY RADAR APPLICATIONS 4HERE ARE TWO TYPES OF BANDWIDTH ENCOUNTERED IN RADAR /NE IS THE SIGNAL BANDWIDTH WHICH IS THE BANDWIDTH DETERMINED BY THE SIGNAL PULSE WIDTH OR BY ANY INTERNAL MODULATION OF THE SIGNAL 4HE OTHER IS TUNABLE BANDWIDTH 'ENERALLY THE SIGNAL BANDWIDTH OF A SIMPLE PULSE OF SINE WAVE OF DURATION S IS S 0ULSE COMPRESSION WAVEFORMS DISCUSSED IN #HAPTER CAN HAVE MUCH GREATER BANDWIDTH THAN THE RECIPROCAL OF THEIR PULSE WIDTH ,ARGE BAND WIDTH IS NEEDED FOR RESOLVING TARGETS IN RANGE FOR ACCURATE MEASUREMENT OF RANGE TO A TARGET AND FOR PROVIDING A LIMITED CAPABILITY TO RECOGNIZE ONE TYPE OF TARGET FROM ANOTHER (IGH RANGE RESOLUTION ALSO CAN BE USEFUL FOR REDUCING THE DEGRADING EFFECTS OF WHAT IS KNOWN AS GLINT IN A TRACKING RADAR FOR MEASURING THE ALTITUDE OF AN AIRCRAFT BASED ON THE DIFFERENCE IN TIME DELAY RANGE BETWEEN THE TWO WAY DIRECT SIGNAL FROM RADAR TO TARGET AND THE TWO WAY SURFACE SCATTERED SIGNAL FROM RADAR TO SURFACE TO TARGET ALSO CALLED MULTIPATH HEIGHT FINDING AND IN INCREASING THE TARGET SIGNAL TO CLUTTER RATIO )N MILITARY SYSTEMS HIGH RANGE RESOLUTION MAY BE EMPLOYED FOR COUNTING THE NUMBER OF AIRCRAFT FLYING IN CLOSE FORMATION AND FOR RECOGNIZING AND THWARTING SOME TYPES OF DECEPTION COUNTERMEASURES 4UNABLE BANDWIDTH OFFERS THE ABILITY TO CHANGE TUNE THE RADAR SIGNAL FREQUENCY OVER A WIDE RANGE OF THE AVAILABLE SPECTRUM 4HIS CAN BE USED FOR REDUCING MUTUAL INTER FERENCE AMONG RADARS THAT OPERATE IN THE SAME FREQUENCY BAND AS WELL AS IN ATTEMPTING TO MAKE HOSTILE ELECTRONIC COUNTERMEASURES LESS EFFECTIVE 4HE HIGHER THE OPERATING FREQUENCY THE EASIER IT IS TO OBTAIN WIDE SIGNAL AND WIDE TUNABLE BANDWIDTH ! LIMITATION ON THE AVAILABILITY OF BANDWIDTH IN A RADAR IS THE CONTROL OF THE SPECTRUM BY GOVERNMENT REGULATING AGENCIES IN THE 5NITED 3TATES THE &EDERAL #OMMUNICATION
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#OMMISSION AND INTERNATIONALLY THE )NTERNATIONAL 4ELECOMMUNICATIONS 5NION !FTER THE SUCCESS OF RADAR IN 7ORLD 7AR )) RADAR WAS ALLOWED TO OPERATE OVER ABOUT ONE THIRD OF THE MICROWAVE SPECTRUM 4HIS SPECTRUM SPACE HAS BEEN REDUCED CONSIDERABLY OVER THE YEARS WITH THE ADVENT OF MANY COMMERCIAL USERS OF THE SPECTRUM IN THE AGE OF hWIRELESSv AND OTHER SERVICES REQUIRING THE ELECTROMAGNETIC SPECTRUM 4HUS THE RADAR ENGINEER IS INCREASINGLY EXPERIENCING SMALLER AVAILABLE SPECTRUM SPACE AND BANDWIDTH ALLOCATIONS THAT CAN BE VITAL FOR THE SUCCESS OF MANY RADAR APPLICATIONS 3IGNAL TO .OISE 2ATIO 4HE ACCURACY OF ALL RADAR MEASUREMENTS AS WELL AS THE RELIABLE DETECTION OF TARGETS DEPENDS ON THE RATIO %.O WHERE % IS THE TOTAL ENERGY OF THE RECEIVED SIGNAL THAT IS PROCESSED BY THE RADAR AND .O IS THE NOISE POWER PER UNIT BANDWIDTH OF THE RECEIVER 4HUS %.O IS AN IMPORTANT MEASURE OF THE CAPABILITY OF A RADAR /PERATION WITH -ORE 4HAN /NE &REQUENCY 4HERE MAY BE IMPORTANT BENEFITS WHEN A RADAR IS ABLE TO OPERATE AT MORE THAN ONE FREQUENCY &REQUENCY AGILITY USUALLY REFERS TO THE USE OF MULTIPLE FREQUENCIES ON A PULSE TO PULSE BASIS &REQUENCY DIVERSITY USUALLY RELATES TO THE USE OF MULTIPLE FREQUENCIES THAT ARE WIDELY SEPARATED SOMETIMES IN MORE THAN ONE RADAR BAND &REQUENCY DIVERSITY MIGHT OPERATE AT EACH FREQUENCY SIMUL TANEOUSLY OR ALMOST SIMULTANEOUSLY )T HAS BEEN USED IN ALMOST ALL CIVILIAN AIR TRAFFIC CONTROL RADARS 0ULSE TO PULSE FREQUENCY AGILITY HOWEVER IS NOT COMPATIBLE WITH THE USE OF DOPPLER PROCESSING TO DETECT MOVING TARGETS IN CLUTTER BUT FREQUENCY DIVERSITY CAN BE COMPATIBLE 4HE FREQUENCY RANGE IN BOTH AGILITY AND IN DIVERSITY OPERATIONS IS MUCH GREATER THAN THE INHERENT BANDWIDTH OF A PULSE OF WIDTH S %LEVATION .ULL &ILLING /PERATION OF A RADAR AT A SINGLE FREQUENCY CAN RESULT IN A LOBED STRUCTURE TO THE ELEVATION PATTERN OF AN ANTENNA DUE TO THE INTERFERENCE BETWEEN THE DIRECT SIGNAL RADAR TO TARGET AND THE SURFACE SCATTERED SIGNAL RADAR TO EARTHS SUR FACE TO TARGET "Y A LOBED STRUCTURE WE MEAN THAT THERE WILL BE REDUCED COVERAGE AT SOME ELEVATION ANGLES NULLS AND INCREASED SIGNAL STRENGTH AT OTHER ANGLES LOBES ! CHANGE IN FREQUENCY WILL CHANGE THE LOCATION OF THE NULLS AND LOBES SO THAT BY OPERATING OVER A WIDE FREQUENCY RANGE THE NULLS IN ELEVATION CAN BE FILLED IN AND THE RADAR WILL BE LESS LIKELY TO LOSE A TARGET ECHO SIGNAL &OR EXAMPLE MEASUREMENTS WITH A WIDEBAND EXPERIMENTAL RADAR KNOWN AS 3ENRAD WHICH COULD OPERATE FROM TO -(Z SHOWED THAT WHEN ONLY A SINGLE FREQUENCY WAS USED THE BLIP SCAN RATIO THE EXPERI MENTALLY MEASURED SINGLE SCAN PROBABILITY OF DETECTION WAS FOUND TO BE UNDER A PARTICULAR SET OF OBSERVATIONS 7HEN THE RADAR OPERATED AT FOUR DIFFERENT WIDELY SEPA RATED FREQUENCIES THE BLIP SCAN RATIO WAS A HIGHLY SIGNIFICANT INCREASE DUE TO FREQUENCY DIVERSITY )NCREASED 4ARGET $ETECTABILITY 4HE RADAR CROSS SECTION OF A COMPLEX TARGET SUCH AS AN AIRCRAFT CAN VARY GREATLY WITH A CHANGE IN FREQUENCY !T SOME FREQUENCIES THE RADAR CROSS SECTION WILL BE SMALL AND AT OTHERS IT WILL BE LARGE )F A RADAR OPERATES AT A SINGLE FREQUENCY IT MIGHT RESULT IN A SMALL TARGET ECHO AND THEREFORE A MISSED DETEC TION "Y OPERATING AT A NUMBER OF DIFFERENT FREQUENCIES THE CROSS SECTION WILL VARY AND CAN BE SMALL OR LARGE BUT A SUCCESSFUL DETECTION BECOMES MORE LIKELY THAN IF ONLY A SINGLE FREQUENCY WERE USED 4HIS IS ONE REASON THAT ALMOST ALL AIR TRAFFIC CONTROL RADARS OPERATE WITH TWO FREQUENCIES SPACED WIDE ENOUGH APART IN FREQUENCY TO INSURE THAT TARGET ECHOES ARE DECORRELATED AND THEREFORE INCREASE THE LIKELIHOOD OF DETECTION
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2EDUCED %FFECTIVENESS OF (OSTILE #OUNTERMEASURES !NY MILITARY RADAR THAT IS SUC CESSFUL CAN EXPECT A HOSTILE ADVERSARY TO EMPLOY COUNTERMEASURES TO REDUCE ITS EFFEC TIVENESS /PERATING OVER A WIDE RANGE OF FREQUENCIES MAKES COUNTERMEASURES MORE DIFFICULT THAN IF OPERATION IS AT ONLY ONE FREQUENCY !GAINST NOISE JAMMING CHANGING FREQUENCY IN AN UNPREDICTABLE MANNER OVER A WIDE RANGE OF FREQUENCIES CAUSES THE JAM MER TO HAVE TO SPREAD ITS POWER OVER A WIDE FREQUENCY RANGE AND WILL THEREFORE REDUCE THE HOSTILE JAMMING SIGNAL STRENGTH OVER THE BANDWIDTH OF THE RADAR SIGNAL &REQUENCY DIVERSITY OVER A WIDE BAND ALSO MAKES IT MORE DIFFICULT BUT NOT IMPOSSIBLE FOR A HOSTILE INTERCEPT RECEIVER OR AN ANTIRADIATION MISSILE TO DETECT AND LOCATE A RADAR SIGNAL 4HE $OPPLER 3HIFT IN 2ADAR 4HE IMPORTANCE OF THE DOPPLER FREQUENCY SHIFT BEGAN TO BE APPRECIATED FOR PULSE RADAR SHORTLY AFTER 7ORLD 7AR )) AND BECAME AN INCREASINGLY IMPORTANT FACTOR IN MANY RADAR APPLICATIONS -ODERN RADAR WOULD BE MUCH LESS INTERESTING OR USEFUL IF THE DOPPLER EFFECT DIDNT EXIST 4HE DOPPLER FREQUENCY SHIFT FD CAN BE WRITTEN AS
FD VR L V COS Q L
WHERE VR V COS P IS THE RELATIVE VELOCITY OF THE TARGET RELATIVE TO THE RADAR IN MS V IS THE ABSOLUTE VELOCITY OF THE TARGET IN MS K IS THE RADAR WAVELENGTH IN M AND P IS THE ANGLE BETWEEN THE TARGETS DIRECTION AND THE RADAR BEAM 4O AN ACCURACY OF ABOUT PER CENT THE DOPPLER FREQUENCY IN HERTZ IS APPROXIMATELY EQUAL TO VR KT DIVIDED BY K M 4HE DOPPLER FREQUENCY SHIFT IS WIDELY USED TO SEPARATE MOVING TARGETS FROM STATIONARY CLUTTER AS DISCUSSED IN #HAPTERS THROUGH 3UCH RADARS ARE KNOWN AS -4) MOVING TARGET INDICATION !-4) AIRBORNE -4) AND PULSE DOPPLER !LL MODERN AIR TRAFFIC CONTROL RADARS ALL IMPORTANT MILITARY GROUND BASED AND AIRBORNE AIR SURVEILLANCE RADARS AND ALL MILITARY AIRBORNE FIGHTER RADARS TAKE ADVANTAGE OF THE DOPPLER EFFECT 9ET IN 77)) NONE OF THESE PULSE RADAR APPLICATIONS USED DOPPLER 4HE #7 CONTINUOUS WAVE RADAR ALSO EMPLOYS THE DOPPLER EFFECT FOR DETECTING MOVING TARGETS BUT #7 RADAR FOR THIS PURPOSE IS NOT AS POPULAR AS IT ONCE WAS 4HE (& /4( RADAR #HAPTER COULD NOT DO ITS JOB OF DETECTING MOVING TARGETS IN THE PRESENCE OF LARGE CLUTTER ECHOES FROM THE EARTHS SURFACE WITHOUT THE USE OF DOPPLER !NOTHER SIGNIFICANT APPLICATION OF RADAR THAT DEPENDS ON THE DOPPLER SHIFT IS OBSER VATION OF THE WEATHER AS IN THE .EXRAD RADARS OF THE 53 .ATIONAL 7EATHER 3ERVICE #HAPTER MENTIONED EARLIER IN THIS CHAPTER "OTH THE 3!2 AND )3!2 CAN BE DESCRIBED IN TERMS OF THEIR USE OF THE DOPPLER FRE QUENCY SHIFT #HAPTER 4HE AIRBORNE DOPPLER NAVIGATOR RADAR IS ALSO BASED ON THE DOPPLER SHIFT 4HE USE OF DOPPLER IN A RADAR GENERALLY PLACES GREATER DEMANDS ON THE STABILITY OF THE RADAR TRANSMITTER AND IT INCREASES THE COMPLEXITY OF THE SIGNAL PROCESS ING YET THESE REQUIREMENTS ARE WILLINGLY ACCEPTED IN ORDER TO ACHIEVE THE SIGNIFICANT BENEFITS OFFERED BY DOPPLER )T SHOULD ALSO BE MENTIONED THAT THE DOPPLER SHIFT IS THE KEY CAPABILITY OF A RADAR THAT CAN MEASURE SPEED AS BY ITS DILIGENT USE BY TRAFFIC POLICE FOR MAINTAINING VEHICLE SPEED LIMITS AND IN OTHER VELOCITY MEASURING APPLICATIONS
£°{Ê / Ê, ,Ê +1/" 4HE RADAR RANGE EQUATION OR RADAR EQUATION FOR SHORT NOT ONLY SERVES THE VERY USEFUL PURPOSE OF ESTIMATING THE RANGE OF A RADAR AS A FUNCTION OF THE RADAR CHARACTERISTICS
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BUT ALSO IS QUITE USEFUL AS A GUIDE FOR DESIGNING A RADAR SYSTEM 4HE SIMPLE FORM OF THE RADAR EQUATION MAY BE WRITTEN AS
0R
0T 'T S r r !E P 2 P 2
4HE RIGHT HAND SIDE HAS BEEN WRITTEN AS THE PRODUCT OF THREE FACTORS TO REPRESENT THE PHYSICAL PROCESSES THAT TAKE PLACE 4HE FIRST FACTOR ON THE RIGHT IS THE POWER DENSITY AT A DISTANCE 2 FROM A RADAR THAT RADIATES A POWER 0T FROM AN ANTENNA OF GAIN 'T 4HE NUMERATOR R OF THE SECOND FACTOR IS THE RADAR CROSS SECTION OF THE TARGET )T HAS THE UNIT OF AREA FOR EXAMPLE SQUARE METERS AND IS A MEASURE OF THE ENERGY REDIRECTED BY THE TARGET BACK IN THE DIRECTION OF THE RADAR 4HE DENOMINATOR OF THE SECOND FACTOR ACCOUNTS FOR THE DIVERGENCE OF THE ECHO SIGNAL ON ITS RETURN PATH BACK TO THE RADAR 4HE PRODUCT OF THE FIRST TWO FACTORS REPRESENTS THE POWER PER UNIT AREA RETURNED TO THE RADAR ANTENNA .OTE THAT THE RADAR CROSS SECTION OF A TARGET R IS DEFINED BY THIS EQUATION 4HE RECEIVING ANTENNA OF EFFECTIVE AREA !E COLLECTS A PORTION 0R OF THE ECHO POWER RETURNED TO THE RADAR )F THE MAXIMUM RADAR RANGE 2MAX IS DEFINED AS OCCURRING WHEN THE RECEIVED SIGNAL IS EQUAL TO THE MINIMUM DETECTABLE SIGNAL OF THE RADAR 3MIN THE SIMPLE FORM OF THE RADAR EQUATION BECOMES
2MAX
0T 'T !E S P 3MIN
'ENERALLY MOST RADARS USE THE SAME ANTENNA FOR BOTH TRANSMITTING AND RECEIVING &ROM ANTENNA THEORY THERE IS A RELATION BETWEEN THE GAIN 'T OF THE ANTENNA ON TRANSMIT AND ITS EFFECTIVE AREA !E ON RECEIVE WHICH IS 'T P !E L WHERE K IS THE WAVELENGTH OF THE RADAR SIGNAL 3UBSTITUTING THIS INTO %Q PROVIDES TWO OTHER USEFUL FORMS OF THE RADAR EQUATION NOT SHOWN HERE ONE THAT REPRESENTS THE ANTENNA ONLY BY ITS GAIN AND THE OTHER THAT REPRESENTS THE ANTENNA ONLY BY ITS EFFECTIVE AREA 4HE SIMPLE FORM OF THE RADAR EQUATION IS INSTRUCTIVE BUT NOT VERY USEFUL SINCE IT LEAVES OUT MANY THINGS 4HE MINIMUM DETECTABLE SIGNAL 3MIN IS LIMITED BY RECEIVER NOISE AND CAN BE EXPRESSED AS
3MIN K4O "&N 3 .
)N THIS EXPRESSION K4O " IS THE SO CALLED THERMAL NOISE FROM AN IDEAL OHMIC CONDUC TOR WHERE K "OLTZMANNS CONSTANT 4O IS THE STANDARD TEMPERATURE OF + AND " RECEIVER BANDWIDTH USUALLY THAT OF THE )& STAGE OF THE SUPERHETERODYNE RECEIVER 4HE PRODUCT K4O IS EQUAL TO r 7(Z 4O ACCOUNT FOR THE ADDITIONAL NOISE INTRODUCED BY A PRACTICAL NONIDEAL RECEIVER THE THERMAL NOISE EXPRESSION IS MULTIPLIED BY THE NOISE FIGURE &N OF THE RECEIVER DEFINED AS THE NOISE OUT OF A PRACTICAL RECEIVER TO THE NOISE OUT OF AN IDEAL RECEIVER &OR A RECEIVED SIGNAL TO BE DETECTABLE IT HAS TO BE LARGER THAN THE RECEIVER NOISE BY A FACTOR DENOTED HERE AS 3. 4HIS VALUE OF SIGNAL TO NOISE RATIO 3. IS THAT REQUIRED IF ONLY ONE PULSE IS PRESENT )T HAS TO BE LARGE ENOUGH TO OBTAIN THE REQUIRED PROBABILITY OF FALSE ALARM DUE TO NOISE CROSSING THE RECEIVER THRESHOLD AND THE REQUIRED PROBABILITY OF DETECTION AS CAN BE FOUND IN VARIOUS RADAR TEXTS 2ADARS HOWEVER GENERALLY PROCESS MORE THAN ONE PULSE BEFORE MAKING A DETECTION DECISION 7E ASSUME THE RADAR WAVEFORM IS A REPETITIVE SERIES OF RECTANGULAR LIKE PULSES 4HESE PULSES ARE INTEGRATED ADDED TOGETHER BEFORE A DETECTION DECISION
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IS MADE 4O ACCOUNT FOR THESE ADDED SIGNALS THE NUMERATOR OF THE RADAR EQUATION IS MULTIPLIED BY A FACTOR N%IN WHERE %IN IS THE EFFICIENCY IN ADDING TOGETHER N PULSES 4HIS VALUE CAN ALSO BE FOUND IN STANDARD TEXTS 4HE POWER 0T IS THE PEAK POWER OF A RADAR PULSE 4HE AVERAGE POWER 0AV IS A BETTER MEASURE OF THE ABILITY OF A RADAR TO DETECT TARGETS SO IT IS SOMETIMES INSERTED INTO THE RADAR EQUATION USING 0T 0AV FPS WHERE FP IS THE PULSE REPETITION FREQUENCY OF THE PULSE RADAR AND S IS THE PULSE DURATION 4HE SURFACE OF THE EARTH AND THE EARTHS ATMOSPHERE CAN DRASTICALLY AFFECT THE PROPAGATION OF ELECTROMAGNETIC WAVES AND CHANGE THE COVERAGE AND CAPABILITIES OF A RADAR )N THE RADAR EQUATION THESE PROPAGATION EFFECTS ARE ACCOUNTED FOR BY A FACTOR & IN THE NUMERATOR OF THE RADAR EQUATION AS DISCUSSED IN #HAPTER 7ITH THE ABOVE SUBSTITUTED INTO THE SIMPLE FORM OF THE RADAR EQUATION WE GET
2MAX
0AV '!ES N%I N & P K4O &N F P 3 . ,S
)N THE ABOVE EQUATION IT WAS ASSUMED IN ITS DERIVATION THAT "S y WHICH IS GENERALLY APPLICABLE IN RADAR ! FACTOR ,S GREATER THAN UNITY CALLED THE SYSTEM LOSSES HAS BEEN INSERTED TO ACCOUNT FOR THE MANY WAYS THAT LOSS CAN OCCUR IN A RADAR 4HIS LOSS FACTOR CAN BE QUITE LARGE )F THE SYSTEM LOSS IS IGNORED IT MIGHT RESULT IN A VERY LARGE ERROR IN THE ESTIMATED RANGE PREDICTED BY THE RADAR EQUATION ! LOSS OF FROM D" TO MAY BE D" IS NOT UNUSUAL WHEN ALL RADAR SYSTEM LOSS FACTORS ARE TAKEN INTO ACCOUNT %QUATION APPLIES FOR A RADAR THAT OBSERVES A TARGET LONG ENOUGH TO RECEIVE N PULSES -ORE FUNDAMENTALLY IT APPLIES FOR A RADAR WHERE THE TIME ON TARGET TO IS EQUAL TO NFP !N EXAMPLE IS A TRACKING RADAR THAT CONTINUOUSLY OBSERVES A SINGLE TARGET FOR A TIME TO 4HIS EQUATION HOWEVER NEEDS TO BE MODIFIED FOR A SURVEILLANCE RADAR THAT OBSERVES AN ANGULAR VOLUME 7 WITH A REVISIT TIME TS !IR TRAFFIC CONTROL RADARS MIGHT HAVE A REVISIT TIME OF FROM TO S 4HUS A SURVEILLANCE RADAR HAS THE ADDITIONAL CONSTRAINT THAT IT MUST COVER AN ANGULAR VOLUME 7 IN A GIVEN TIME TS 4HE REVISIT TIME TS IS EQUAL TO TO77O WHERE TO NFP AND 7O THE SOLID BEAMWIDTH OF THE ANTENNA STERADIANS IS APPROXIMATELY RELATED TO THE ANTENNA GAIN ' BY ' O 7O 4HEREFORE WHEN NFP IN %Q IS REPLACED WITH ITS EQUAL O TS '7 THE RADAR EQUATION FOR A SURVEILLANCE RADAR IS OBTAINED AS
2MAX
0AV !ES %I N & T r S P K4O &N 3 . ,S 7
4HE RADAR DESIGNER HAS LITTLE CONTROL OVER THE REVISIT TIME TS OR THE ANGULAR COVERAGE 7 WHICH ARE DETERMINED MAINLY BY THE JOB THE RADAR HAS TO PERFORM 4HE RADAR CROSS SECTION ALSO IS DETERMINED BY THE RADAR APPLICATION )F A LARGE RANGE IS REQUIRED OF A SURVEILLANCE RADAR THE RADAR MUST HAVE THE NECESSARY VALUE OF THE PRODUCT 0AV !E &OR THIS REASON A COMMON MEASURE OF THE CAPABILITY OF A SURVEILLANCE RADAR IS ITS POWER APERTURE PRODUCT .OTE THAT THE RADAR FREQUENCY DOES NOT APPEAR EXPLICITLY IN THE SURVEILLANCE RADAR EQUATION 4HE CHOICE OF FREQUENCY HOWEVER WILL ENTER IMPLICITLY IN OTHER WAYS *UST AS THE RADAR EQUATION FOR A SURVEILLANCE RADAR IS DIFFERENT FROM THE CONVENTIONAL RADAR EQUATION OF %Q OR THE SIMPLE RADAR EQUATION OF %Q EACH PARTICULAR APPLICA TION OF A RADAR GENERALLY HAS TO EMPLOY A RADAR EQUATION TAILORED TO THAT SPECIFIC APPLICA TION 7HEN THE RADAR ECHOES FROM LAND SEA OR WEATHER CLUTTER ARE GREATER THAN THE RECEIVER NOISE THE RADAR EQUATION HAS TO BE MODIFIED TO ACCOUNT FOR CLUTTER BEING THE LIMITATION TO
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DETECTION RATHER THAN RECEIVER NOISE )T CAN HAPPEN THAT THE DETECTION CAPABILITY OF A RADAR MIGHT BE LIMITED BY CLUTTER IN SOME REGIONS OF ITS COVERAGE AND BE LIMITED BY RECEIVER NOISE IN OTHER REGIONS 4HIS CAN RESULT IN TWO DIFFERENT SETS OF RADAR CHARACTERISTICS ONE OPTIMIZED FOR NOISE AND THE OTHER OPTIMIZED FOR CLUTTER AND COMPROMISES USUALLY HAVE TO BE MADE IN RADAR DESIGN ! DIFFERENT TYPE OF RADAR EQUATION IS ALSO REQUIRED WHEN THE RADAR CAPABILITY IS LIMITED BY HOSTILE NOISE JAMMING
£°xÊ , ,Ê, +1 9Ê // , Ê " /1, )T IS NOT ALWAYS CONVENIENT TO USE THE EXACT NUMERICAL FREQUENCY RANGE OVER WHICH A PARTICULAR TYPE OF RADAR OPERATES 7ITH MANY MILITARY RADARS THE EXACT OPERATING FRE QUENCY RANGE OF A RADAR IS USUALLY NOT DISCLOSED 4HUS THE USE OF LETTERS TO DESIGNATE RADAR OPERATING BANDS HAS BEEN VERY HELPFUL 4HE )%%% )NSTITUTE OF %LECTRICAL AND %LECTRONIC %NGINEERS HAS OFFICIALLY STANDARDIZED THE RADAR LETTER BAND NOMENCLATURE AS SUMMARIZED IN 4ABLE #OMMENTS ON THE TABLE 4HE )NTERNATIONAL 4ELECOMMUNICATIONS 5NION )45 ASSIGNS SPECIFIC PORTIONS OF THE ELECTROMAGNETIC SPECTRUM FOR RADIOLOCATION RADAR USE AS SHOWN IN THE THIRD COLUMN WHICH APPLIES TO )45 2EGION THAT INCLUDES .ORTH AND 3OUTH !MERICA 3LIGHT DIFFERENCES OCCUR IN THE OTHER TWO )45 2EGIONS 4HUS AN , BAND RADAR CAN ONLY OPERATE WITHIN THE FREQUENCY RANGE FROM -(Z TO -(Z AND EVEN WITHIN THIS RANGE THERE MAY BE RESTRICTIONS 3OME OF THE INDICATED )45 BANDS ARE RESTRICTED IN THEIR USAGE FOR EXAMPLE THE BAND BETWEEN AND '(Z IS RESERVED
4!",% )%%% 3TANDARD ,ETTER $ESIGNATIONS FOR 2ADAR &REQUENCY "ANDS
"AND $ESIGNATION
.OMINAL &REQUENCY 2ANGE
(& 6(&
-(Zn -(Z n -(Z
5(&
n -(Z
, 3
n '(Z n '(Z
#
n '(Z
8 +U
n '(Z n '(Z
+
n '(Z
+A 6 7
n '(Z n '(Z n '(Z
3PECIFIC &REQUENCY 2ANGES FOR 2ADAR "ASED ON )45 &REQUENCY !SSIGNMENTS FOR 2EGION n -(Z n -(Z n -(Z n -(Z n -(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z n '(Z
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WITH FEW EXCEPTIONS FOR AIRBORNE RADAR ALTIMETERS 4HERE ARE NO OFFICIAL )45 ALLOCATIONS FOR RADAR IN THE (& BAND BUT MOST (& RADARS SHARE FREQUENCIES WITH OTHER ELECTROMAG NETIC SERVICES 4HE LETTER BAND DESIGNATION FOR MILLIMETER WAVE RADARS IS MM AND THERE ARE SEVERAL FREQUENCY BANDS ALLOCATED TO RADAR IN THIS REGION BUT THEY HAVE NOT BEEN LISTED HERE !LTHOUGH THE OFFICIAL )45 DESCRIPTION OF MILLIMETER WAVES IS FROM TO '(Z IN REALITY THE TECHNOLOGY OF RADARS AT +A BAND IS MUCH CLOSER TO THE TECHNOLOGY OF MICROWAVE FREQUENCIES THAN TO THE TECHNOLOGY OF 7 BAND 4HE MILLIMETER WAVE RADAR FREQUENCIES ARE OFTEN CONSIDERED BY THOSE WHO WORK IN THIS FIELD TO HAVE A LOWER BOUND OF '(Z RATHER THAN THE hLEGALv LOWER BOUND OF '(Z IN RECOGNITION OF THE SIGNIFICANT DIFFERENCE IN TECHNOLOGY AND APPLICATIONS THAT IS CHARACTERISTIC OF MILLIMETER WAVE RADAR -ICROWAVES HAVE NOT BEEN DEFINED IN THIS STANDARD BUT THIS TERM GENERALLY APPLIES TO RADARS THAT OPERATE FROM 5(& TO +A BAND 4HE REASON THAT THESE LETTER DESIGNATIONS MIGHT NOT BE EASY FOR THE NON RADAR ENGINEER TO RECOGNIZE IS THAT THEY WERE ORIGINALLY SELECTED TO DESCRIBE THE RADAR BANDS USED IN 7ORLD 7AR )) 3ECRECY WAS IMPORTANT AT THAT TIME SO THE LETTERS SELECTED TO DESIGNATE THE VARIOUS BANDS MADE IT HARD TO GUESS THE FREQUENCIES TO WHICH THEY APPLY 4HOSE WHO WORK AROUND RADAR HOWEVER SELDOM HAVE A PROBLEM WITH THE USAGE OF THE RADAR LETTER BANDS /THER LETTER BANDS HAVE BEEN USED FOR DESCRIBING THE ELECTROMAGNETIC SPECTRUM BUT THEY ARE NOT SUITABLE FOR RADAR AND SHOULD NEVER BE USED FOR RADAR /NE SUCH DESIGNATION USES THE LETTERS ! " # ETC ORIGINALLY DEVISED FOR CONDUCTING ELECTRONIC COUNTERMEASURE EXERCISES 4HE )%%% 3TANDARD MENTIONED PREVIOUSLY STATES THAT THESE hARE NOT CONSISTENT WITH RADAR PRACTICE AND SHALL NOT BE USED TO DESCRIBE RADAR FREQUENCY BANDSv 4HUS THERE MAY BE $ BAND JAMMERS BUT NEVER $ BAND RADARS
£°ÈÊ /Ê"Ê"* ,/ ÊÊ , +1 9Ê" Ê, , 2ADARS HAVE BEEN OPERATED AT FREQUENCIES AS LOW AS -(Z JUST ABOVE THE !- BROAD CAST BAND AND AS HIGH AS SEVERAL HUNDRED '(Z MILLIMETER WAVE REGION -ORE USU ALLY RADAR FREQUENCIES MIGHT BE FROM ABOUT -(Z TO OVER '(Z 4HIS IS A VERY LARGE EXTENT OF FREQUENCIES SO IT SHOULD BE EXPECTED THAT RADAR TECHNOLOGY CAPABILITIES AND APPLICATIONS WILL VARY CONSIDERABLY DEPENDING ON THE FREQUENCY RANGE AT WHICH A RADAR OPERATES 2ADARS AT A PARTICULAR FREQUENCY BAND USUALLY HAVE DIFFERENT CAPABILI TIES AND CHARACTERISTICS THAN RADARS IN OTHER FREQUENCY BANDS 'ENERALLY LONG RANGE IS EASIER TO ACHIEVE AT THE LOWER FREQUENCIES BECAUSE IT IS EASIER TO OBTAIN HIGH POWER TRANSMITTERS AND PHYSICALLY LARGE ANTENNAS AT THE LOWER FREQUENCIES /N THE OTHER HAND AT THE HIGHER RADAR FREQUENCIES IT IS EASIER TO ACHIEVE ACCURATE MEASUREMENTS OF RANGE AND LOCATION BECAUSE THE HIGHER FREQUENCIES PROVIDE WIDER BANDWIDTH WHICH DETERMINES RANGE ACCURACY AND RANGE RESOLUTION AS WELL AS NARROWER BEAM ANTENNAS FOR A GIVEN PHYSICAL SIZE ANTENNA WHICH DETERMINES ANGLE ACCURACY AND ANGLE RESOLU TION )N THE FOLLOWING THE APPLICATIONS USUALLY FOUND IN THE VARIOUS RADAR BANDS ARE BRIEFLY INDICATED 4HE DIFFERENCES BETWEEN ADJACENT BANDS HOWEVER ARE SELDOM SHARP IN PRACTICE AND OVERLAP IN CHARACTERISTICS BETWEEN ADJACENT BANDS IS LIKELY
4HE WAVELENGTHS OF +A BAND RANGE FROM MM TO MM WHICH QUALIFIES THEM UNDER THE hLEGALv DEFINITION OF MILLIMETERS BUT JUST BARELY
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(& TO -(Z 4HE MAJOR USE OF THE (& BAND FOR RADAR #HAPTER IS TO DETECT TARGETS AT LONG RANGES NOMINALLY OUT TO NMI BY TAKING ADVANTAGE OF THE REFRACTION OF (& ENERGY BY THE IONOSPHERE THAT LIES HIGH ABOVE THE SURFACE OF THE EARTH 2ADIO AMATEURS REFER TO THIS AS SHORT WAVE PROPAGATION AND USE IT TO COMMUNICATE OVER LONG DISTANCES 4HE TARGETS FOR SUCH (& RADARS MIGHT BE AIRCRAFT SHIPS AND BALLISTIC MISSILES AS WELL AS THE ECHO FROM THE SEA SURFACE ITSELF THAT PROVIDES INFORMATION ABOUT THE DIRECTION AND SPEED OF THE WINDS THAT DRIVE THE SEA 6(& TO -(Z !T THE BEGINNING OF RADAR DEVELOPMENT IN THE S RADARS WERE IN THIS FREQUENCY BAND BECAUSE THESE FREQUENCIES REPRESENTED THE FRONTIER OF RADIO TECHNOLOGY AT THAT TIME )T IS A GOOD FREQUENCY FOR LONG RANGE AIR SURVEILLANCE OR DETECTION OF BALLISTIC MISSILES !T THESE FREQUENCIES THE REFLECTION COEFFICIENT ON SCATTERING FROM THE EARTHS SURFACE CAN BE VERY LARGE ESPECIALLY OVER WATER SO THE CONSTRUCTIVE INTERFERENCE BETWEEN THE DIRECT SIGNAL AND THE SURFACE REFLECTED SIGNAL CAN INCREASE SIGNIFICANTLY THE RANGE OF A 6(& RADAR 3OMETIMES THIS EFFECT CAN ALMOST DOU BLE THE RADARS RANGE (OWEVER WHEN THERE IS CONSTRUCTIVE INTERFERENCE THAT INCREASES THE RANGE THERE CAN BE DESTRUCTIVE INTERFERENCE THAT DECREASES THE RANGE DUE TO THE DEEP NULLS IN THE ANTENNA PATTERN IN THE ELEVATION PLANE ,IKEWISE THE DESTRUCTIVE INTERFER ENCE CAN RESULT IN POOR LOW ALTITUDE COVERAGE $ETECTION OF MOVING TARGETS IN CLUTTER IS OFTEN BETTER AT THE LOWER FREQUENCIES WHEN THE RADAR TAKES ADVANTAGE OF THE DOPPLER FREQUENCY SHIFT BECAUSE DOPPLER AMBIGUITIES THAT CAUSE BLIND SPEEDS ARE FAR FEWER AT LOW FREQUENCIES 6(& RADARS ARE NOT BOTHERED BY ECHOES FROM RAIN BUT THEY CAN BE AFFECTED BY MULTIPLE TIME AROUND ECHOES FROM METEOR IONIZATION AND AURORA 4HE RADAR CROSS SECTION OF AIRCRAFT AT 6(& IS GENERALLY LARGER THAN THE RADAR CROSS SECTION AT HIGHER FREQUENCIES 6(& RADARS FREQUENTLY COST LESS COMPARED TO RADARS WITH THE SAME RANGE PERFORMANCE THAT OPERATE AT HIGHER FREQUENCIES !LTHOUGH THERE ARE MANY ATTRACTIVE ADVANTAGES OF 6(& RADARS FOR LONG RANGE SUR VEILLANCE THEY ALSO HAVE SOME SERIOUS LIMITATIONS $EEP NULLS IN ELEVATION AND POOR LOW ALTITUDE COVERAGE HAVE BEEN MENTIONED 4HE AVAILABLE SPECTRAL WIDTHS ASSIGNED TO RADAR AT 6(& ARE SMALL SO RANGE RESOLUTION IS OFTEN POOR 4HE ANTENNA BEAMWIDTHS ARE USUALLY WIDER THAN AT MICROWAVE FREQUENCIES SO THERE IS POOR RESOLUTION AND ACCURACY IN ANGLE 4HE 6(& BAND IS CROWDED WITH IMPORTANT CIVILIAN SERVICES SUCH AS 46 AND &- BROADCAST FURTHER REDUCING THE AVAILABILITY OF SPECTRUM SPACE FOR RADAR %XTERNAL NOISE LEVELS THAT CAN ENTER THE RADAR VIA THE ANTENNA ARE HIGHER AT 6(& THAN AT MICROWAVE FREQUENCIES 0ERHAPS THE CHIEF LIMITATION OF OPERATING RADARS AT 6(& IS THE DIFFICULTY OF OBTAINING SUITABLE SPECTRUM SPACE AT THESE CROWDED FREQUENCIES )N SPITE OF ITS LIMITATIONS THE 6(& AIR SURVEILLANCE RADAR WAS WIDELY USED BY THE 3OVIET 5NION BECAUSE IT WAS A LARGE COUNTRY AND THE LOWER COST OF 6(& RADARS MADE THEM ATTRACTIVE FOR PROVIDING AIR SURVEILLANCE OVER THE LARGE EXPANSE OF THAT COUNTRY 4HEY HAVE SAID THEY PRODUCED A LARGE NUMBER OF 6(& AIR SURVEILLANCE RADARS SOME WERE OF VERY LARGE SIZE AND LONG RANGE AND MOST WERE READILY TRANSPORTABLE )T IS INTERESTING TO NOTE THAT 6(& AIRBORNE INTERCEPT RADARS WERE WIDELY USED BY THE 'ERMANS IN 7ORLD 7AR )) &OR EXAMPLE THE ,ICHTENSTEIN 3. AIRBORNE RADAR OPER ATED FROM ABOUT TO OVER -(Z IN VARIOUS MODELS 2ADARS AT SUCH FREQUENCIES WERE NOT AFFECTED BY THE COUNTERMEASURE CALLED CHAFF ALSO KNOWN AS WINDOW 5(& TO -(Z -ANY OF THE CHARACTERISTICS OF RADAR OPERATING IN THE 6(& REGION ALSO APPLY TO SOME EXTENT AT 5(& 5(& IS A GOOD FREQUENCY FOR !IRBORNE -OVING 4ARGET )NDICATION !-4) RADAR IN AN !IRBORNE %ARLY 7ARNING 2ADAR !%7 AS DISCUSSED IN #HAPTER )T IS ALSO A GOOD FREQUENCY FOR THE OPERATION OF LONG RANGE
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RADARS FOR THE DETECTION AND TRACKING OF SATELLITES AND BALLISTIC MISSILES !T THE UPPER PORTION OF THIS BAND THERE CAN BE FOUND LONG RANGE SHIPBOARD AIR SURVEILLANCE RADARS AND RADARS CALLED WIND PROFILERS THAT MEASURE THE SPEED AND DIRECTION OF THE WIND 'ROUND 0ENETRATING 2ADAR '02 DISCUSSED IN #HAPTER IS AN EXAMPLE OF WHAT IS CALLED AN ULTRAWIDEBAND 57" RADAR )TS WIDE SIGNAL BANDWIDTH SOMETIMES COV ERS BOTH THE 6(& AND 5(& BANDS 3UCH A RADARS SIGNAL BANDWIDTH MIGHT EXTEND FOR INSTANCE FROM TO -(Z ! WIDE BANDWIDTH IS NEEDED IN ORDER TO OBTAIN GOOD RANGE RESOLUTION 4HE LOWER FREQUENCIES ARE NEEDED TO ALLOW THE PROPAGATION OF RADAR ENERGY INTO THE GROUND %VEN SO THE LOSS IN PROPAGATING THROUGH TYPICAL SOIL IS SO HIGH THAT THE RANGES OF A SIMPLE MOBILE '02 MIGHT BE ONLY A FEW METERS 3UCH RANGES ARE SUITABLE FOR LOCATING BURIED POWER LINES AND PIPE LINES AS WELL AS BURIED OBJECTS )F A RADAR IS TO SEE TARGETS LOCATED ON THE SURFACE BUT WITHIN FOLIAGE SIMILAR FREQUENCIES ARE NEEDED AS FOR THE '02 , BAND TO '(Z 4HIS IS THE PREFERRED FREQUENCY BAND FOR THE OPERATION OF LONG RANGE OUT TO NMI AIR SURVEILLANCE RADARS 4HE !IR 2OUTE 3URVEILLANCE 2ADAR !232 USED FOR LONG RANGE AIR TRAFFIC CONTROL IS A GOOD EXAMPLE !S ONE GOES UP IN FREQUENCY THE EFFECT OF RAIN ON PERFORMANCE BEGINS TO BECOME SIGNIFICANT SO THE RADAR DESIGNER MIGHT HAVE TO WORRY ABOUT REDUCING THE EFFECT OF RAIN AT , BAND AND HIGHER FREQUENCIES 4HIS FREQUENCY BAND HAS ALSO BEEN ATTRACTIVE FOR THE LONG RANGE DETECTION OF SATELLITES AND DEFENSE AGAINST INTERCONTINENTAL BALLISTIC MISSILES 3 BAND TO '(Z 4HE !IRPORT 3URVEILLANCE 2ADAR !32 THAT MONITORS AIR TRAFFIC WITHIN THE REGION OF AN AIRPORT IS AT 3 BAND )TS RANGE IS TYPICALLY TO NMI )F A $ RADAR IS WANTED ONE THAT DETERMINES RANGE AZIMUTH ANGLE AND ELEVATION ANGLE IT CAN BE ACHIEVED AT 3 BAND )T WAS SAID PREVIOUSLY THAT LONG RANGE SURVEILLANCE IS BETTER PERFORMED AT LOW FRE QUENCIES AND THE ACCURATE MEASUREMENT OF TARGET LOCATION IS BETTER PERFORMED AT HIGH FREQUENCIES )F ONLY A SINGLE RADAR OPERATING WITHIN A SINGLE FREQUENCY BAND CAN BE USED THEN 3 BAND IS A GOOD COMPROMISE )T IS ALSO SOMETIMES ACCEPTABLE TO USE # BAND AS THE CHOICE FOR A RADAR THAT PERFORMS BOTH FUNCTIONS 4HE !7!#3 AIRBORNE AIR SURVEILLANCE RADAR ALSO OPERATES AT 3 BAND 5SUALLY MOST RADAR APPLICATIONS ARE BEST OPERATED IN A PARTICULAR FREQUENCY BAND AT WHICH THE RADARS PERFORMANCE IS OPTIMUM (OWEVER IN THE EXAMPLE OF AIRBORNE AIR SURVEILLANCE RADARS !7!#3 IS FOUND AT 3 BAND AND THE 53 .AVYS % !%7 RADAR AT 5(& )N SPITE OF SUCH A DIFFERENCE IN FREQUENCY IT HAS BEEN SAID THAT BOTH RADARS HAVE COMPARABLE PERFORMANCE 4HIS IS AN EXCEPTION TO THE OBSERVATION ABOUT THERE BEING AN OPTIMUM FREQUENCY BAND FOR EACH APPLICATION 4HE .EXRAD WEATHER RADAR OPERATES AT 3 BAND )T IS A GOOD FREQUENCY FOR THE OBSER VATION OF WEATHER BECAUSE A LOWER FREQUENCY WOULD PRODUCE A MUCH WEAKER RADAR ECHO SIGNAL FROM RAIN SINCE THE RADAR ECHO FROM RAIN VARIES AS THE FOURTH POWER OF THE FREQUENCY AND A HIGHER FREQUENCY WOULD PRODUCE ATTENUATION OF THE SIGNAL AS IT PROPAGATES THROUGH THE RAIN AND WOULD NOT ALLOW AN ACCURATE MEASUREMENT OF RAINFALL RATE 4HERE ARE WEATHER RADARS AT HIGHER FREQUENCIES BUT THESE ARE USUALLY OF SHORTER RANGE THAN .EXRAD AND MIGHT BE USED FOR A MORE SPECIFIC WEATHER RADAR APPLICATION THAN THE ACCURATE METEOROLOGICAL MEASUREMENTS PROVIDED BY .EXRAD # BAND TO '(Z 4HIS BAND LIES BETWEEN 3 AND 8 BANDS AND HAS PROPERTIES IN BETWEEN THE TWO /FTEN EITHER 3 OR 8 BAND MIGHT BE PREFERRED TO THE USE OF # BAND ALTHOUGH THERE HAVE BEEN IMPORTANT APPLICATIONS IN THE PAST FOR # BAND
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8 BAND TO '(Z 4HIS IS A RELATIVELY POPULAR RADAR BAND FOR MILITARY APPLICATIONS )T IS WIDELY USED IN MILITARY AIRBORNE RADARS FOR PERFORMING THE ROLES OF INTERCEPTOR FIGHTER AND ATTACK OF GROUND TARGETS AS DISCUSSED IN #HAPTER )T IS ALSO POPULAR FOR IMAGING RADARS BASED ON 3!2 AND )3!2 8 BAND IS A SUITABLE FREQUENCY FOR CIVIL MARINE RADARS AIRBORNE WEATHER AVOIDANCE RADAR AIRBORNE DOPPLER NAVIGATION RADARS AND THE POLICE SPEED METER -ISSILE GUIDANCE SYSTEMS ARE SOMETIMES AT 8 BAND 2ADARS AT 8 BAND ARE GENERALLY OF A CONVENIENT SIZE AND ARE THEREFORE OF INTEREST FOR APPLICATIONS WHERE MOBILITY AND LIGHT WEIGHT ARE IMPORTANT AND VERY LONG RANGE IS NOT A MAJOR REQUIREMENT 4HE RELATIVELY WIDE RANGE OF FREQUENCIES AVAILABLE AT 8 BAND AND THE ABILITY TO OBTAIN NARROW BEAMWIDTHS WITH RELATIVELY SMALL ANTENNAS IN THIS BAND ARE IMPORTANT CONSIDERATIONS FOR HIGH RESOLUTION APPLICATIONS "ECAUSE OF THE HIGH FRE QUENCY OF 8 BAND RAIN CAN SOMETIMES BE A SERIOUS FACTOR IN REDUCING THE PERFORMANCE OF 8 BAND SYSTEMS +U + AND +A "ANDS TO '(Z !S ONE GOES TO HIGHER RADAR FREQUENCY THE PHYSICAL SIZE OF ANTENNAS DECREASE AND IN GENERAL IT IS MORE DIFFICULT TO GENERATE LARGE TRANSMITTER POWER 4HUS THE RANGE PERFORMANCE OF RADARS AT FREQUENCIES ABOVE 8 BAND IS GENERALLY LESS THAN THAT OF 8 BAND -ILITARY AIRBORNE RADARS ARE FOUND AT +U BAND AS WELL AS AT 8 BAND 4HESE FREQUENCY BANDS ARE ATTRACTIVE WHEN A RADAR OF SMALLER SIZE HAS TO BE USED FOR AN APPLICATION NOT REQUIRING LONG RANGE 4HE !IRPORT 3URFACE $ETECTION %QUIPMENT !3$% GENERALLY FOUND ON TOP OF THE CONTROL TOWER AT MAJOR AIRPORTS HAS BEEN AT +U BAND PRIMARILY BECAUSE OF ITS BETTER RESOLUTION THAN 8 BAND )N THE ORIGINAL + BAND THERE IS A WATER VAPOR ABSORPTION LINE AT '(Z WHICH CAUSES ATTENUATION THAT CAN BE A SERIOUS PROBLEM IN SOME APPLICATIONS 4HIS WAS DISCOVERED AFTER THE DEVELOPMENT OF + BAND RADARS BEGAN DURING 7ORLD 7AR )) WHICH IS WHY BOTH +U AND +A BANDS WERE LATER INTRODUCED 4HE RADAR ECHO FROM RAIN CAN LIMIT THE CAPABIL ITY OF RADARS AT THESE FREQUENCIES -ILLIMETER 7AVE 2ADAR !LTHOUGH THIS FREQUENCY REGION IS OF LARGE EXTENT MOST OF THE INTEREST IN MILLIMETER WAVE RADAR HAS BEEN IN THE VICINITY OF '(Z WHERE THERE IS A MINIMUM CALLED A WINDOW IN THE ATMOSPHERIC ATTENUATION ! WINDOW IS A REGION OF LOW ATTENUATION RELATIVE TO ADJACENT FREQUENCIES 4HE WIN DOW AT '(Z IS ABOUT AS WIDE AS THE ENTIRE MICROWAVE SPECTRUM !S MENTIONED PREVIOUSLY FOR RADAR PURPOSES THE MILLIMETER WAVE REGION IN PRACTICE GENERALLY STARTS AT '(Z OR EVEN AT HIGHER FREQUENCIES 4HE TECHNOLOGY OF MILLIMETER WAVE RADARS AND THE PROPAGATION EFFECTS OF THE ENVIRONMENT ARE NOT ONLY DIFFERENT FROM MICROWAVE RADARS BUT THEY ARE USUALLY MUCH MORE RESTRICTING 5NLIKE WHAT IS EXPERI ENCED AT MICROWAVES THE MILLIMETER RADAR SIGNAL CAN BE HIGHLY ATTENUATED EVEN WHEN PROPAGATING IN THE CLEAR ATMOSPHERE !TTENUATION VARIES OVER THE MILLIMETER WAVE REGION 4HE ATTENUATION IN THE '(Z WINDOW IS ACTUALLY HIGHER THAN THE ATTENU ATION OF THE ATMOSPHERIC WATER VAPOR ABSORPTION LINE AT '(Z 4HE ONE WAY ATTENUATION IN THE OXYGEN ABSORPTION LINE AT '(Z IS ABOUT D" PER KM WHICH ESSENTIALLY PRECLUDES ITS APPLICATION !TTENUATION IN RAIN CAN ALSO BE A LIMITATION IN THE MILLIMETER WAVE REGION )NTEREST IN MILLIMETER RADAR HAS BEEN MAINLY BECAUSE OF ITS CHALLENGES AS A FRONTIER TO BE EXPLORED AND PUT TO PRODUCTIVE USE )TS GOOD FEATURES ARE THAT IT IS A GREAT PLACE FOR EMPLOYING WIDE BANDWIDTH SIGNALS THERE IS PLENTY OF SPECTRUM SPACE RADARS CAN HAVE HIGH RANGE RESOLUTION AND NARROW BEAMWIDTHS WITH SMALL ANTENNAS HOSTILE ELECTRONIC COUNTERMEASURES TO MILITARY RADARS ARE DIFFICULT TO EMPLOY AND IT IS EASIER TO HAVE
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A MILITARY RADAR WITH LOW PROBABILITY OF INTERCEPT AT THESE FREQUENCIES THAN AT LOWER FREQUENCIES )N THE PAST MILLIMETER WAVE TRANSMITTERS WERE NOT CAPABLE OF AN AVERAGE POWER MORE THAN A FEW HUNDRED WATTSAND WERE USUALLY MUCH LESS !DVANCES IN GYROTRONS #HAPTER CAN PRODUCE AVERAGE POWER MANY ORDERS OF MAGNITUDE GREATER THAN MORE CONVENTIONAL MILLIMETER WAVE POWER SOURCES 4HUS AVAILABILITY OF HIGH POWER IS NOT A LIMITATION AS IT ONCE WAS ,ASER 2ADAR ,ASERS CAN PRODUCE USABLE POWER AT OPTICAL FREQUENCIES AND IN THE INFRARED REGION OF THE SPECTRUM 4HEY CAN UTILIZE WIDE BANDWIDTH VERY SHORT PULSES AND CAN HAVE VERY NARROW BEAMWIDTHS !NTENNA APERTURES HOWEVER ARE MUCH SMALLER THAN AT MICROWAVES !TTENUATION IN THE ATMOSPHERE AND RAIN IS VERY HIGH AND PER FORMANCE IN BAD WEATHER IS QUITE LIMITED 2ECEIVER NOISE IS DETERMINED BY QUANTUM EFFECTS RATHER THAN THERMAL NOISE &OR SEVERAL REASONS LASER RADAR HAS HAD ONLY LIMITED APPLICATION
£°ÇÊ , ,Ê " /1, -ILITARY ELECTRONIC EQUIPMENT INCLUDING RADAR IS IDENTIFIED BY THE *OINT %LECTRONICS 4YPE $ESIGNATION 3YSTEM *%4$3 AS DESCRIBED IN 53 -ILITARY 3TANDARD -), 34$ $ 4HE LETTER PORTION OF THE DESIGNATION CONSISTS OF THE LETTERS !. A SLANT BAR AND THREE ADDITIONAL LETTERS APPROPRIATELY SELECTED TO INDICATE WHERE THE EQUIPMENT IS INSTALLED THE TYPE OF EQUIPMENT AND ITS PURPOSE &OLLOWING THE THREE LETTERS ARE A DASH AND A NUMERAL 4HE NUMERAL IS ASSIGNED IN SEQUENCE FOR THAT PARTICULAR COMBINATION OF LETTERS 4ABLE SHOWS THE LETTERS THAT HAVE BEEN USED FOR RADAR DESIGNATIONS ! SUFFIX LETTER ! " # x FOLLOWS THE ORIGINAL DESIGNATION FOR EACH MODIFICATION OF THE EQUIPMENT WHERE INTERCHANGEABILITY HAS BEEN MAINTAINED 4HE LETTER 6 IN PAREN THESES ADDED TO THE DESIGNATION INDICATES VARIABLE SYSTEMS THOSE WHOSE FUNCTIONS MAY BE VARIED THROUGH THE ADDITION OR DELETION OF SETS GROUPS UNITS OR COMBINATIONS THEREOF 7HEN THE DESIGNATION IS FOLLOWED BY A DASH THE LETTER 4 AND A NUMBER THE EQUIPMENT IS DESIGNED FOR TRAINING )N ADDITION TO THE 5NITED 3TATES THESE DESIGNA TIONS CAN ALSO BE USED BY #ANADA !USTRALIA .EW :EALAND AND THE 5NITED +INGDOM 3PECIAL BLOCKS OF NUMBERS ARE RESERVED FOR THESE COUNTRIES &URTHER INFORMATION CAN BE FOUND ON THE )NTERNET UNDER -), 34$ $ 4HE 53 &EDERAL !VIATION !GENCY &!! USES THE FOLLOWING TO DESIGNATE THEIR AIR TRAFFIC CONTROL RADARS !32 !232 !3$% 4$72
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!IRPORT 3URVEILLANCE 2ADAR !IR 2OUTE 3URVEILLANCE 2ADAR !IRPORT 3URFACE $ETECTION %QUIPMENT 4ERMINAL $OPPLER 7EATHER 2ADAR
4HE NUMERAL FOLLOWING THE LETTER DESIGNATION INDICATES THE PARTICULAR RADAR MODEL IN SEQUENCE 7EATHER RADARS DEVELOPED BY THE 5 3 7EATHER 3ERVICE ./!! EMPLOY THE DES IGNATION 732 4HE NUMBER FOLLOWING THE DESIGNATION IS THE YEAR THE RADAR WENT INTO SERVICE 4HUS 732 $ IS THE .EXRAD DOPPLER RADAR THAT FIRST ENTERED SERVICE IN 4HE LETTER $ INDICATES IT IS A DOPPLER WEATHER RADAR
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4!",% *%4$3 ,ETTER $ESIGNATIONS THAT 0ERTAIN TO 2ADAR
)NSTALLATION FIRST LETTER ! 0ILOTED AIRCRAFT " 5NDERWATER MOBILE SUBMARINE $ 0ILOTLESS CARRIER & &IXED GROUND
4YPE OF %QUIPMENT SECOND LETTER , #OUNTERMEASURES 0 2ADAR 3 3PECIAL OR COMBINATION 7 !RMAMENT PECULIAR TO ARMAMENT NOT OTHERWISE COVERED
' 'ENERAL GROUND USE + !MPHIBIOUS - -OBILE GROUND 0 0ORTABLE 3 7ATER SHIP 4 4RANSPORTABLE GROUND 5 'ENERAL UTILITY
0URPOSE THIRD LETTER " "OMBING $ $IRECTION FINDER RECONNAISSANCE AND SURVEILLANCE ' &IRE CONTROL . .AVIGATION
1 3PECIAL OR COMBINATION 2 2ECEIVING 3 $ETECTINGRANGE AND BEARING SEARCH 4 4RANSMITTING 7 !UTOMATIC FLIGHT OR REMOTE CONTROL 8 )DENTIFICATION AND RECOGNITION 9 3URVEILLANCE AND CONTROL BOTH FIRE CONTROL AND AIR CONTROL
6 6EHICULAR GROUND 7 7ATER SURFACE AND UNDERWATER COMBINED : 0ILOTED PILOTLESS AIRBORNE VEHICLES COMBINED
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-Ê Ê, , ! BRIEF LISTING OF SOME OF THE MAJOR ADVANCES IN TECHNOLOGY AND CAPABILITY OF RADAR IN THE TWENTIETH CENTURY IS GIVEN IN SOMEWHAT CHRONOLOGICAL BUT NOT EXACT ORDER AS FOLLOWS 4HE DEVELOPMENT OF 6(& RADAR FOR DEPLOYMENT ON SURFACE SHIP AND AIRCRAFT FOR MILITARY AIR DEFENSE PRIOR TO AND DURING 7ORLD 7AR )) 4HE INVENTION OF THE MICROWAVE MAGNETRON AND THE APPLICATION OF WAVEGUIDE TECH NOLOGY EARLY IN 77)) TO OBTAIN RADARS THAT COULD OPERATE AT MICROWAVE FREQUENCIES SO THAT SMALLER AND MORE MOBILE RADARS COULD BE EMPLOYED 4HE MORE THAN DIFFERENT RADAR MODELS DEVELOPED AT THE -)4 2ADIATION ,ABORATORY IN ITS FIVE YEARS OF EXISTENCE DURING 77)) THAT PROVIDED THE FOUNDATION FOR MICROWAVE RADAR -ARCUMS THEORY OF RADAR DETECTION 4HE INVENTION AND DEVELOPMENT OF THE KLYSTRON AND 474 AMPLIFIER TUBES THAT PRO VIDED HIGH POWER WITH GOOD STABILITY
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4HE USE OF THE DOPPLER FREQUENCY SHIFT TO DETECT MOVING TARGETS IN THE PRESENCE OF MUCH LARGER ECHOES FROM CLUTTER 4HE DEVELOPMENT OF RADARS SUITABLE FOR AIR TRAFFIC CONTROL 0ULSE COMPRESSION -ONOPULSE TRACKING RADAR WITH GOOD TRACKING ACCURACY AND BETTER RESISTANCE TO ELEC TRONIC COUNTERMEASURES THAN PRIOR TRACKING RADARS 3YNTHETIC APERTURE RADAR WHICH PROVIDED IMAGES OF THE GROUND AND WHAT IS ON IT !IRBORNE -4) !-4) FOR LONG RANGE AIRBORNE AIR SURVEILLANCE IN THE PRESENCE OF CLUTTER 3TABLE COMPONENTS AND SUBSYSTEMS AND ULTRALOW SIDELOBE ANTENNAS THAT ALLOWED HIGH 02& PULSE DOPPLER RADAR !7!#3 WITH LARGE REJECTION OF UNWANTED CLUTTER (& OVER THE HORIZON RADAR THAT EXTENDED THE RANGE OF DETECTION OF AIRCRAFT AND SHIPS BY AN ORDER OF MAGNITUDE $IGITAL PROCESSING WHICH HAS HAD A VERY MAJOR EFFECT ON IMPROVING RADAR CAPABILI TIES EVER SINCE THE EARLY S !UTOMATIC DETECTION AND TRACKING FOR SURVEILLANCE RADARS 3ERIAL PRODUCTION OF ELECTRONICALLY SCANNED PHASED ARRAY RADARS )NVERSE SYNTHETIC APERTURE RADAR )3!2 THAT PROVIDED AN IMAGE OF A TARGET AS NEEDED FOR NONCOOPERATIVE TARGET RECOGNITION OF SHIPS $OPPLER WEATHER RADAR 3PACE RADARS SUITABLE FOR THE OBSERVATION OF PLANETS SUCH AS 6ENUS !CCURATE COMPUTER CALCULATION OF THE RADAR CROSS SECTION OF COMPLEX TARGETS -ULTIFUNCTION AIRBORNE MILITARY RADAR THAT ARE RELATIVELY SMALL AND LIGHTWEIGHT THAT FIT IN THE NOSE OF A FIGHTER AIRCRAFT AND CAN PERFORM A LARGE NUMBER OF DIFFERENT AIR TO AIR AND AIR TO GROUND FUNCTIONS
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)T IS ALWAYS A MATTER OF OPINION WHAT THE MAJOR ADVANCES IN RADAR HAVE BEEN /THERS MIGHT HAVE A DIFFERENT LIST .OT EVERY MAJOR RADAR ACCOMPLISHMENT HAS BEEN INCLUDED IN THIS LISTING )T COULD HAVE BEEN MUCH LONGER AND COULD HAVE INCLUDED MULTIPLE EXAM PLES FROM EACH OF THE OTHER CHAPTERS IN THIS BOOK BUT THIS LISTING IS SUFFICIENT TO INDICATE THE TYPE OF ADVANCES THAT HAVE BEEN IMPORTANT FOR IMPROVED RADAR CAPABILITIES
£°Ê ** /" -Ê"Ê, , -ILITARY !PPLICATIONS 2ADAR WAS INVENTED IN THE S BECAUSE OF THE NEED FOR DEFENSE AGAINST HEAVY MILITARY BOMBER AIRCRAFT 4HE MILITARY NEED FOR RADAR HAS PROBABLY BEEN ITS MOST IMPORTANT APPLICATION AND THE SOURCE OF MOST OF ITS MAJOR DEVELOPMENTS INCLUDING THOSE FOR CIVILIAN PURPOSES 4HE CHIEF USE OF MILITARY RADAR HAS BEEN FOR AIR DEFENSE OPERATING FROM LAND SEA OR AIR )T HAS NOT BEEN PRACTICAL TO PERFORM SUCCESSFUL AIR DEFENSE WITHOUT RADAR )N AIR DEFENSE RADAR IS USED FOR LONG RANGE AIR SURVEILLANCE SHORT RANGE DETECTION OF LOW ALTITUDE hPOP UPv TARGETS WEAPON CONTROL MISSILE GUIDANCE NONCOOPERATIVE TARGET RECOGNITION AND BATTLE DAMAGE ASSESSMENT 4HE PROXIMITY FUZE IN MANY WEAPONS IS
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ALSO AN EXAMPLE OF A RADAR !N EXCELLENT MEASURE OF THE SUCCESS OF RADAR FOR MILITARY AIR DEFENSE IS THE LARGE AMOUNTS OF MONEY THAT HAVE BEEN SPENT ON METHODS TO COUNTER ITS EFFECTIVENESS 4HESE INCLUDE ELECTRONIC COUNTERMEASURES AND OTHER ASPECTS OF ELEC TRONIC WARFARE ANTIRADIATION MISSILES TO HOME ON RADAR SIGNALS AND LOW CROSS SECTION AIRCRAFT AND SHIPS 2ADAR IS ALSO USED BY THE MILITARY FOR RECONNAISSANCE TARGETING OVER LAND OR SEA AS WELL AS SURVEILLANCE OVER THE SEA /N THE BATTLEFIELD RADAR IS ASKED TO PERFORM THE FUNCTIONS OF AIR SURVEILLANCE INCLUD ING SURVEILLANCE OF AIRCRAFT HELICOPTERS MISSILES AND UNMANNED AIRBORNE VEHICLES CONTROL OF WEAPONS TO AN AIR INTERCEPT HOSTILE WEAPONS LOCATION MORTARS ARTILLERY AND ROCKETS DETECTION OF INTRUDING PERSONNEL AND CONTROL OF AIR TRAFFIC 4HE USE OF RADAR FOR BALLISTIC MISSILE DEFENSE HAS BEEN OF INTEREST EVER SINCE THE THREAT OF BALLISTIC MISSILES AROSE IN THE LATE S 4HE LONGER RANGES HIGH SUPERSONIC SPEEDS AND THE SMALLER TARGET SIZE OF BALLISTIC MISSILES MAKE THE PROBLEM CHALLENGING 4HERE IS NO NATURAL CLUTTER PROBLEM IN SPACE AS THERE IS FOR DEFENSE AGAINST AIRCRAFT BUT BALLISTIC MISSILES CAN APPEAR IN THE PRESENCE OF A LARGE NUMBER OF EXTRANEOUS CON FUSION TARGETS AND OTHER COUNTERMEASURES THAT AN ATTACKER CAN LAUNCH TO ACCOMPANY THE REENTRY VEHICLE CARRYING A WARHEAD 4HE BASIC BALLISTIC MISSILE DEFENSE PROBLEM BECOMES MORE OF A TARGET RECOGNITION PROBLEM RATHER THAN DETECTION AND TRACKING 4HE NEED FOR WARNING OF THE APPROACH OF BALLISTIC MISSILES HAS RESULTED IN A NUMBER OF DIFFERENT TYPES OF RADARS FOR PERFORMING SUCH A FUNCTION 3IMILARLY RADARS HAVE BEEN DEPLOYED THAT ARE CAPABLE OF DETECTING AND TRACKING SATELLITES ! RELATED TASK FOR RADAR THAT IS NOT MILITARY IS THE DETECTION AND INTERCEPTION OF DRUG TRAFFIC 4HERE ARE SEVERAL TYPES OF RADARS THAT CAN CONTRIBUTE TO THIS NEED INCLUDING THE LONG RANGE (& OVER THE HORIZON RADAR 2EMOTE 3ENSING OF THE %NVIRONMENT 4HE MAJOR APPLICATION IN THIS CATEGORY HAS BEEN WEATHER OBSERVATION RADAR SUCH AS THE .EXRAD SYSTEM WHOSE OUTPUT IS OFTEN SEEN ON THE TELEVISION WEATHER REPORT 4HERE ALSO EXIST VERTICAL LOOKING WIND PROFILER RADARS THAT DETERMINE WIND SPEED AND DIRECTION AS A FUNCTION OF ALTITUDE BY DETECTING THE VERY WEAK RADAR ECHO FROM THE CLEAR AIR ,OCATED AROUND AIRPORTS ARE THE 4ERMINAL $OPPLER 7EATHER 2ADAR 4$72 SYSTEMS THAT WARN OF DANGEROUS WIND SHEAR PRODUCED BY THE WEATHER EFFECT KNOWN AS THE DOWNBURST WHICH CAN ACCOMPANY SEVERE STORMS 4HERE IS USUALLY A SPECIALLY DESIGNED WEATHER AVOIDANCE RADAR IN THE NOSE OF SMALL AS WELL AS LARGE AIRCRAFT TO WARN OF DANGEROUS OR UNCOMFORTABLE WEATHER IN FLIGHT !NOTHER SUCCESSFUL REMOTE SENSING RADAR WAS THE DOWNWARD LOOKING SPACEBORNE ALTIMETER RADAR THAT MEASURED WORLDWIDE THE GEOID THE MEAN SEA LEVEL WHICH IS NOT THE SAME ALL OVER THE WORLD WITH EXCEPTIONALLY HIGH ACCURACY 4HERE HAVE BEEN ATTEMPTS IN THE PAST TO USE RADAR FOR DETERMINING SOIL MOISTURE AND FOR ASSESSING THE STATUS OF AGRICULTURE CROPS BUT THESE HAVE NOT PROVIDED SUFFICIENT ACCURACY )MAGING RADARS IN SATELLITES OR AIRCRAFT HAVE BEEN USED TO HELP SHIPS EFFICIENTLY NAVIGATE NORTH ERN SEAS COATED WITH ICE BECAUSE RADAR CAN TELL WHICH TYPES OF ICE ARE EASIER FOR A SHIP TO PENETRATE !IR 4RAFFIC #ONTROL 4HE HIGH DEGREE OF SAFETY IN MODERN AIR TRAVEL IS DUE IN PART TO THE SUCCESSFUL APPLICATIONS OF RADAR FOR THE EFFECTIVE EFFICIENT AND SAFE CONTROL OF AIR TRAFFIC -AJOR AIRPORTS EMPLOY AN !IRPORT 3URVEILLANCE 2ADAR !32 FOR OBSERVING THE AIR TRAFFIC IN THE VICINITY OF THE AIRPORT 3UCH RADARS ALSO PROVIDE INFORMATION ABOUT NEARBY WEATHER SO AIRCRAFT CAN BE ROUTED AROUND UNCOMFORTABLE WEATHER -AJOR AIRPORTS ALSO HAVE A RADAR CALLED !IRPORT 3URFACE $ETECTION %QUIPMENT !3$% FOR OBSERVING
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AND SAFELY CONTROLLING AIRCRAFT AND AIRPORT VEHICLE TRAFFIC ON THE GROUND &OR CONTROL OF AIR TRAFFIC EN ROUTE FROM ONE TERMINAL TO ANOTHER LONG RANGE !IR 2OUTE 3URVEILLANCE 2ADARS !232 ARE FOUND WORLDWIDE 4HE !IR 4RAFFIC #ONTROL 2ADAR "EACON 3YSTEM !4#2"3 IS NOT A RADAR BUT IS A COOPERATIVE SYSTEM USED TO IDENTIFY AIRCRAFT IN FLIGHT )T USES RADAR LIKE TECHNOLOGY AND WAS ORIGINALLY BASED ON THE MILITARY )&& )DENTIFICATION &RIEND OR &OE SYSTEM /THER !PPLICATIONS ! HIGHLY SIGNIFICANT APPLICATION OF RADAR THAT PROVIDED INFORMATION NOT AVAILABLE BY ANY OTHER METHOD WAS THE EXPLORATION OF THE SURFACE OF THE PLANET 6ENUS BY AN IMAGING RADAR THAT COULD SEE UNDER THE EVER PRESENT CLOUDS THAT MASK THE PLANET /NE OF THE WIDEST USED AND LEAST EXPENSIVE OF RADARS HAS BEEN THE CIVIL MARINE RADAR FOUND THROUGHOUT THE WORLD FOR THE SAFE NAVIGATION OF BOATS AND SHIPS 3OME READERS HAVE UNDOUBTEDLY BEEN CONFRONTED BY THE HIGHWAY POLICE USING THE #7 DOPPLER RADAR TO MEASURE THE SPEED OF A VEHICLE 'ROUND PENETRATING RADAR HAS BEEN USED TO FIND BURIED UTILITY LINES AS WELL AS BY THE POLICE FOR LOCATING BURIED OBJECTS AND BODIES !RCHEOLOGISTS HAVE USED IT TO DETERMINE WHERE TO BEGIN TO LOOK FOR BURIED ARTIFACTS 2ADAR HAS BEEN HELPFUL TO BOTH THE ORNITHOLOGIST AND ENTOMOLOGIST FOR BETTER UNDERSTANDING THE MOVEMENTS OF BIRDS AND INSECTS )T HAS ALSO BEEN DEM ONSTRATED THAT RADAR CAN DETECT THE GAS SEEPAGE THAT IS OFTEN FOUND OVER UNDERGROUND OIL AND GAS DEPOSITS
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*/1 Ê, ,Ê-9-/ Ê - 4HERE ARE VARIOUS ASPECTS TO RADAR SYSTEM DESIGN "UT BEFORE A NEW RADAR THAT HAS NOT EXISTED PREVIOUSLY CAN BE MANUFACTURED A CONCEPTUAL DESIGN HAS TO BE PERFORMED TO GUIDE THE ACTUAL DEVELOPMENT ! CONCEPTUAL DESIGN IS BASED ON THE REQUIREMENTS FOR THE RADAR THAT WILL SATISFY THE CUSTOMER OR USER OF THE RADAR 4HE RESULT OF A CONCEPTUAL DESIGN EFFORT IS TO PROVIDE A LIST OF THE RADAR CHARACTERISTICS AS FOUND IN THE RADAR EQUA TION AND RELATED EQUATIONS AND THE GENERAL CHARACTERISTICS OF THE SUBSYSTEMS TRANSMIT TER ANTENNA RECEIVER SIGNAL PROCESSING AND SO FORTH THAT MIGHT BE EMPLOYED 4HE RADAR EQUATION IS USED AS AN IMPORTANT GUIDE FOR DETERMINING THE VARIOUS TRADEOFFS AND OPTIONS AVAILABLE TO THE RADAR SYSTEM DESIGNER SO AS TO DETERMINE A SUITABLE CONCEPT TO MEET THE DESIRED NEED 4HIS SECTION BRIEFLY SUMMARIZES HOW A RADAR SYSTEMS ENGINEER MIGHT BEGIN TO APPROACH THE CONCEPTUAL DESIGN OF A NEW RADAR 4HERE ARE NO FIRMLY ESTABLISHED PROCEDURES TO CARRY OUT A CONCEPTUAL DESIGN %VERY RADAR COMPANY AND EVERY RADAR DESIGN ENGINEER DEVELOPS HIS OR HER OWN STYLE 7HAT IS DESCRIBED HERE IS A BRIEF SUMMARY OF ONE APPROACH TO CONCEPTUAL RADAR DESIGN 'ENERAL 'UIDELINE )T SHOULD BE MENTIONED THAT THERE ARE AT LEAST TWO WAYS BY WHICH A NEW RADAR SYSTEM MIGHT BE PRODUCED FOR SOME PARTICULAR RADAR APPLICATION /NE METHOD IS BASED ON EXPLOITING THE ADVANTAGES OF SOME NEW INVENTION NEW TECHNIQUE NEW DEVICE OR NEW KNOWLEDGE 4HE INVENTION OF THE MICROWAVE MAGNETRON EARLY IN 7ORLD 7AR )) IS AN EXAMPLE !FTER THE MAGNETRON APPEARED RADAR DESIGN WAS DIFFERENT FROM WHAT IT HAD BEEN BEFORE 4HE OTHER AND PROBABLY MORE COMMON METHOD FOR CON CEPTUAL RADAR SYSTEM DESIGN IS TO START WITH WHAT THE NEW RADAR HAS TO DO EXAMINE THE VARIOUS APPROACHES AVAILABLE TO ACHIEVE THE DESIRED CAPABILITY CAREFULLY EVALUATE EACH APPROACH AND THEN SELECT THE ONE THAT BEST MEETS THE NEEDS WITHIN THE OPERATIONAL AND FISCAL CONSTRAINTS IMPOSED )N BRIEF IT MIGHT CONSIST OF THE FOLLOWING STEPS
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$ESCRIPTION OF THE NEED OR PROBLEM TO BE SOLVED 4HIS IS FROM THE VIEWPOINT OF THE CUSTOMER OR THE USER OF THE RADAR )NTERACTION BETWEEN THE CUSTOMER AND THE SYSTEMS ENGINEER 4HIS IS FOR THE PURPOSE OF EXPLORING THE TRADEOFFS WHICH THE CUSTOMER MIGHT NOT BE AWARE OF THAT MIGHT ALLOW THE CUSTOMER TO BETTER OBTAIN WHAT IS WANTED WITH OUT EXCESSIVE COST OR RISK 5NFORTUNATELY INTERACTION BETWEEN THE POTENTIAL USER OF THE RADAR AND THE RADAR SYSTEMS ENGINEER IS NOT ALWAYS DONE IN COMPETITIVE PROCUREMENTS )DENTIFICATION AND EXPLORATION OF POSSIBLE SOLUTIONS 4HIS INCLUDES UNDERSTANDING THE ADVANTAGES AND LIMITATIONS OF THE VARIOUS POS SIBLE SOLUTIONS 3ELECTION OF THE OPTIMUM OR NEAR OPTIMUM SOLUTION )N MANY ENGINEERING ENDEAVORS OPTIMUM DOES NOT MEAN THE BEST SINCE THE BEST MIGHT NOT BE AFFORDABLE OR ACHIEVABLE IN THE REQUIRED TIME /PTIMUM AS USED HERE MEANS THE BEST UNDER A GIVEN SET OF ASSUMPTIONS %NGINEERING OFTEN INVOLVES ACHIEV ING A NEAR OPTIMUM NOT THE OPTIMUM 3ELECTING THE PREFERRED SOLUTION SHOULD BE BASED ON A WELL DEFINED CRITERION $ETAILED DESCRIPTION OF THE SELECTED APPROACH 4HIS IS IN TERMS OF THE CHARACTERISTICS OF THE RADAR AND THE TYPE OF SUBSYSTEMS TO BE EMPLOYED !NALYSIS AND EVALUATION OF THE PROPOSED DESIGN 4HIS IS TO VERIFY THE CORRECTNESS OF THE SELECTED APPROACH
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!S ONE PROCEEDS THROUGH THIS PROCESS ONE MIGHT REACH A hDEAD ENDv AND HAVE TO START OVERSOMETIMES MORE THAN ONCE (AVING TO START OVER IS NOT UNUSUAL DURING A NEW DESIGN EFFORT /NE CANNOT DEVISE A UNIQUE SET OF GUIDELINES FOR PERFORMING THE DESIGN OF A RADAR )F THAT WERE POSSIBLE RADAR DESIGN COULD BE DONE ENTIRELY BY COMPUTER "ECAUSE OF THE USUAL LACK OF COMPLETE INFORMATION MOST ENGINEERING DESIGN REQUIRES AT SOME POINT THE JUDGMENT AND EXPERIENCE OF THE DESIGN ENGINEER IN ORDER TO SUCCEED 4HE 2ADAR %QUATION IN #ONCEPTUAL $ESIGN 4HE RADAR EQUATION IS THE BASIS FOR CONCEPTUAL RADAR SYSTEM DESIGN 3OME PARAMETERS OF THE RADAR EQUATION ARE DETER MINED BY WHAT THE RADAR IS REQUIRED TO DO /THERS MAY BE DECIDED UPON UNILATERALLY BY THE CUSTOMERBUT THAT SHOULD BE DONE WITH CAUTION 4HE CUSTOMER USUALLY SHOULD BE THE ONE WHO STATES THE NATURE OF THE RADAR TARGET THE ENVIRONMENT IN WHICH THE RADAR IS TO OPERATE RESTRICTIONS ON SIZE AND WEIGHT THE USE TO WHICH THE RADAR INFORMATION IS TO BE PUT AND ANY OTHER CONSTRAINTS THAT HAVE TO BE IMPOSED &ROM THIS INFORMATION THE RADAR SYSTEMS ENGINEER DETERMINES WHAT IS THE RADAR CROSS SECTION OF THE TARGET THE RANGE AND ANGLE ACCURACIES NEEDED TO MEET THE RADAR USERS NEEDS AS WELL AS THE ANTENNA REVISIT TIME 3OME PARAMETERS SUCH AS ANTENNA GAIN MIGHT BE AFFECTED BY MORE THAN ONE NEED OR REQUIREMENT &OR INSTANCE A PARTICULAR ANTENNA BEAMWIDTH MIGHT BE INFLUENCED BY THE TRACKING ACCURACY RESOLUTION OF NEARBY TARGETS THE MAXI MUM SIZE THE ANTENNA CAN BE FOR A PARTICULAR APPLICATION THE NEED FOR A DESIRED RADAR RANGE AND THE CHOICE OF RADAR FREQUENCY 4HE RADAR FREQUENCY IS USUALLY AFFECTED BY MANY THINGS INCLUDING THE AVAILABILITY OF ALLOWED FREQUENCIES AT WHICH TO OPERATE 4HE RADAR FREQUENCY MIGHT BE THE LAST PARAMETER OF THE RADAR TO BE SELECTEDAFTER MANY OTHER COMPROMISES HAVE BEEN MADE
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4HIS CHAPTER ADDRESSES SURFACE BASED RADARS EG RADARS SITED ON LAND OR INSTALLED ONBOARD SHIPS &OR AIRBORNE RADAR RAPID PLATFORM MOTION HAS A SIGNIFICANT EFFECT ON DESIGN AND PERFORMANCE AS DISCUSSED IN #HAPTERS AND OF THIS (ANDBOOK 4HE FUNDAMENTAL THEORY OF MOVING TARGET INDICATION -4) RADAR AS PRESENTED IN THE PREVIOUS EDITIONS OF THE 2ADAR (ANDBOOK HAS NOT MATERIALLY CHANGED 4HE PERFORMANCE OF -4) RADAR HOWEVER HAS BEEN GREATLY IMPROVED DUE PRIMARILY TO FOUR ADVANCES INCREASED STABILITY OF RADAR SUBSYSTEMS SUCH AS TRANSMITTERS OSCILLATORS AND RECEIVERS INCREASED DYNAMIC RANGE OF RECEIVERS AND ANALOG TO DIGITAL CONVERTERS !$ FASTER AND MORE POWERFUL DIGITAL PROCESSING AND BETTER AWARENESS OF THE LIMITA TIONS AND THEREFORE REQUISITE SOLUTIONS OF ADAPTING -4) SYSTEMS TO THE ENVIRONMENT 4HESE FOUR ADVANCES HAVE MADE IT PRACTICAL TO USE SOPHISTICATED TECHNIQUES THAT WERE CONSIDERED AND SOMETIMES TRIED MANY YEARS AGO BUT WERE IMPRACTICAL TO IMPLEMENT %XAMPLES OF EARLY CONCEPTS THAT WERE WELL AHEAD OF THE AVAILABLE TECHNOLOGY WERE THE VELOCITY INDICAT ING COHERENT INTEGRATOR 6)#) AND THE COHERENT MEMORY FILTER #-& !LTHOUGH THESE IMPROVEMENTS HAVE ENABLED MUCH IMPROVED -4) CAPABILITIES THERE ARE STILL NO PERFECT SOLUTIONS TO ALL -4) RADAR PROBLEMS AND THE DESIGN OF AN -4) SYSTEM IS STILL AS MUCH OF AN ART AS IT IS A SCIENCE %XAMPLES OF CURRENT PROBLEMS INCLUDE THE FACT THAT WHEN RECEIVERS ARE BUILT WITH INCREASED DYNAMIC RANGE SYSTEM INSTABILITY LIMITATIONS WILL CAUSE INCREASED CLUTTER RESIDUE RELATIVE TO SYSTEM NOISE THAT CAN CAUSE FALSE DETECTIONS #LUTTER MAPS WHICH ARE USED TO PREVENT FALSE DETECTIONS FROM CLUTTER RESIDUE WORK QUITE WELL ON FIXED RADAR SYSTEMS BUT ARE DIFFICULT TO IMPLEMENT ON FOR EXAMPLE SHIPBOARD RADARS BECAUSE AS THE SHIP MOVES THE ASPECT AND RANGE TO EACH CLUTTER PATCH CHANGES CREATING INCREASED RESIDUES AFTER THE CLUTTER MAP ! DECREASE IN THE RESOLUTION OF THE CLUTTER MAP TO COUNTER THE RAPIDLY CHANGING CLUTTER RESIDUE WILL PRECLUDE MUCH OF THE INTERCLUTTER VISIBILITY SEE LATER IN THIS CHAPTER WHICH IS ONE OF THE LEAST APPRECIATED SECRETS OF SUCCESSFUL -4) OPERATION -4) RADAR MUST WORK IN THE ENVIRONMENT THAT CONTAINS STRONG FIXED CLUTTER BIRDS BATS AND INSECTS WEATHER AUTOMOBILES AND DUCTING 4HE DUCTING ALSO REFERRED TO AS ANOMA LOUS PROPAGATION CAUSES RADAR RETURNS FROM CLUTTER ON THE SURFACE OF THE %ARTH TO APPEAR Ó°£
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AT GREATLY EXTENDED RANGES WHICH EXACERBATES THE PROBLEMS WITH BIRDS AND AUTOMOBILES AND CAN ALSO CAUSE THE DETECTION OF FIXED CLUTTER HUNDREDS OF KILOMETERS AWAY 4HE CLUTTER MODELS CONTAINED IN THIS CHAPTER ARE APPROXIMATIONS OF THE TYPES OF CLUTTER THAT MUST BE ADDRESSED 4HE EXACT QUANTITATIVE DATA SUCH AS PRECISE SPECTRUM AND AMPLITUDE OF EACH TYPE OF CLUTTER OR THE EXACT NUMBER OF BIRDS OR POINT REFLECTORS EG WATER TOWERS OR OIL WELL DERRICKS PER UNIT AREA IS NOT IMPORTANT BECAUSE THE -4) RADAR DESIGNER MUST CREATE A ROBUST SYSTEM THAT WILL FUNCTION WELL NO MATTER THE ACTUAL DEVIATION FROM THE CLUTTER MODELS OF REAL CLUTTER ENCOUNTERED -4) RADARS MAY USE ROTATING ANTENNAS OR FIXED APERTURES WITH ELECTRONIC BEAM SCAN NING PHASED ARRAYS 4HE ROTATING ANTENNA MAY USE A CONTINUOUS WAVEFORM PROCESSED THROUGH EITHER A FINITE IMPULSE RESPONSE &)2 FILTER OR AN INFINITE IMPULSE RESPONSE ))2 FILTER OR MAY USE A BATCH WAVEFORM CONSISTING OF COHERENT PROCESSING INTERVALS #0)S THAT ARE PROCESSED IN &)2 FILTERS IN GROUPS OF . PULSES 4HE TERM -4) FILTER USED OFTEN IN THIS CHAPTER IS A GENERIC NOMENCLATURE THAT INCLUDES BOTH &)2 AND ))2 FILTERS 4HE FINITE TIME ON TARGET DICTATES THE NEED FOR A BATCH PROCESSING APPROACH 4HERE ARE MANY DIFFERENT COMBINATIONS OF SUCCESSFUL -4) TECHNIQUES BUT ANY SPE CIFIC -4) RADAR SYSTEM MUST BE A TOTAL CONCEPT BASED ON THE PARAMETERS OF THE ANTENNA TRANSMITTER WAVEFORM SIGNAL PROCESSING AND THE OPERATIONAL ENVIRONMENT ! NUMBER OF PLAN POSITION INDICATOR 00) PHOTOGRAPHS TAKEN YEARS AGO ARE INCLUDED IN THIS CHAPTER TO PROVIDE A BETTER UNDERSTANDING OF THE ENVIRONMENT THAT IS DIFFICULT TO APPRECIATE WITH MANY MODERN RADARS 4HESE PHOTOGRAPHS SHOW -4) OPERA TION BIRDS INSECTS AND DUCTING BETTER THAN CAN BE DESCRIBED IN WORDS !TTENTION IS ESPECIALLY DIRECTED TO THE FINAL SECTION IN THIS CHAPTER h#ONSIDERATIONS !PPLICABLE TO -4) 2ADAR 3YSTEMS v WHICH PROVIDES INSIGHT INTO BOTH HARDWARE AND ENVIRONMENTAL LESSONS LEARNED DURING MANY DECADES OF -4) SYSTEM DEVELOPMENT
Ó°ÓÊ /," 1 /" Ê/"Ê /Ê, , 4HE PURPOSE OF -4) RADAR IS TO REJECT RETURNS FROM FIXED OR SLOW MOVING UNWANTED TARGETS SUCH AS BUILDINGS HILLS TREES SEA AND RAIN AND RETAIN FOR DETECTION OR DISPLAY SIGNALS FROM MOVING TARGETS SUCH AS AIRCRAFT &IGURE SHOWS A PAIR OF PHOTOGRAPHS OF A 00) WHICH ILLUSTRATES THE EFFECTIVENESS OF SUCH AN -4) SYSTEM 4HE DISTANCE FROM THE CENTER TO THE EDGE OF THE 00) IS NMI 4HE RANGE MARKS ARE AT NMI INTERVALS 4HE PICTURE ON THE LEFT IS THE NORMAL VIDEO DISPLAY SHOWING MAINLY THE FIXED TARGET RETURNS 4HE PICTURE ON THE RIGHT SHOWS THE EFFECTIVENESS OF THE -4) CLUTTER REJECTION 4HE CAMERA SHUTTER WAS LEFT OPEN FOR THREE SCANS OF THE ANTENNA THUS AIRCRAFT SHOW UP AS A SUCCESSION OF THREE RETURNS -4) RADAR UTILIZES THE DOPPLER SHIFT IMPARTED ON THE REFLECTED SIGNAL BY A MOVING TARGET TO DISTINGUISH MOVING TARGETS FROM FIXED TARGETS )N A PULSE RADAR SYSTEM THIS DOPPLER SHIFT APPEARS AS A CHANGE OF PHASE OF RECEIVED SIG NALS BETWEEN CONSECUTIVE RADAR PULSES #ONSIDER A RADAR THAT TRANSMITS A PULSE OF RADIO FREQUENCY 2& ENERGY THAT IS REFLECTED BY BOTH A BUILDING FIXED TARGET AND AN AIRPLANE MOVING TARGET APPROACHING THE RADAR 4HE REFLECTED PULSES RETURN TO THE RADAR A CERTAIN TIME LATER 4HE RADAR THEN TRANSMITS A SECOND PULSE 4HE REFLECTION FROM THE BUILDING OCCURS IN EXACTLY THE SAME AMOUNT OF TIME BUT THE REFLECTION FROM THE MOVING AIRCRAFT OCCURS IN LESS TIME BECAUSE THE AIRCRAFT HAS MOVED CLOSER TO THE RADAR IN THE INTERVAL BETWEEN TRANSMITTED PULSES 4HE PRECISE TIME THAT IT TAKES THE REFLECTED SIGNAL TO REACH THE RADAR IS NOT OF FUNDAMENTAL IMPORTANCE 7HAT IS SIGNIFICANT IS WHETHER THE TIME CHANGES BETWEEN PULSES 4HE TIME CHANGE WHICH IS OF THE ORDER OF A FEW NANOSECONDS FOR AN AIRCRAFT TARGET IS DETERMINED BY COMPARING THE PHASE OF THE RECEIVED SIGNAL WITH
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&)'52% A .ORMAL VIDEO AND B -4) VIDEO 4HESE 00) PHOTOGRAPHS SHOW HOW EFFECTIVE AN -4) SYSTEM CAN BE !IRCRAFT APPEAR AS THREE CONSECUTIVE BLIPS IN THE RIGHT HAND PICTURE BECAUSE THE CAMERA SHUTTER WAS OPEN FOR THREE REVOLUTIONS OF THE ANTENNA 4HE 00) RANGE IS NMI
THE PHASE OF A REFERENCE OSCILLATOR IN THE RADAR )F THE TARGET MOVES BETWEEN PULSES THE PHASE OF THE RECEIVED PULSE CHANGES &IGURE SHOWS A SIMPLIFIED BLOCK DIAGRAM OF A COHERENT -4) SYSTEM 4HE 2& OSCILLATOR FEEDS THE PULSED AMPLIFIER WHICH TRANSMITS THE PULSES 4HE 2& OSCILLATOR
&)'52% 3IMPLIFIED BLOCK DIAGRAM OF A COHERENT -4) SYSTEM
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IS ALSO USED AS A PHASE REFERENCE FOR DETERMINING THE PHASE OF REFLECTED SIGNALS 4HE PHASE INFORMATION IS STORED IN A PULSE REPETITION INTERVAL 02) MEMORY FOR THE PERIOD 4 BETWEEN TRANSMITTED PULSES AND IS SUBTRACTED FROM THE PHASE INFORMATION FROM THE CURRENT RECEIVED PULSE 4HERE IS AN OUTPUT FROM THE SUBTRACTOR ONLY WHEN A REFLECTION HAS OCCURRED FROM A MOVING TARGET -OVING 4ARGET )NDICATOR -4) "LOCK $IAGRAM ! MORE COMPLETE BLOCK DIA GRAM OF AN -4) RADAR IS SHOWN IN &IGURE 4HIS BLOCK DIAGRAM IS REPRESENTATIVE OF A MODERN AIR TRAFFIC CONTROL RADAR OPERATING AT , OR 3 BAND WITH A TYPICAL INTERPULSE PERIOD OF n MS AND A #7 PULSE LENGTH OF A FEW MS WHEN THE TRANSMITTER EMPLOYS A VACUUM TUBE AMPLIFIER SUCH AS FOR EXAMPLE A KLYSTRON OR TENS OF MS FOR A PULSE COMPRESSION WAVEFORM WHEN A SOLID STATE TRANSMITTER IS USED 4HE RECEIVED SIGNALS ARE AMPLIFIED IN A LOW NOISE AMPLIFIER ,.! AND SUBSEQUENTLY DOWNCONVERTED THROUGH ONE OR MORE INTERMEDIATE FREQUENCIES )& BY MIXING WITH STABLE LOCAL OSCILLATORS ! BANDPASS )& LIMITER AT THE RECEIVER OUTPUT PROTECTS THE !$ CONVERTER FROM DAMAGE BUT ALSO PREVENTS LIMITING FROM TAKING PLACE IN THE !$ CONVERTER )N EARLY -4) SYSTEMS THE )& LIM ITER SERVED THE PURPOSE OF DELIBERATELY RESTRICTING THE DYNAMIC RANGE TO REDUCE CLUTTER RESIDUES AT THE -4) OUTPUT 4HE RECEIVED SIGNALS ARE THEN CONVERTED INTO IN PHASE AND QUADRATURE COMPONENTS ) 1 THROUGH THE !$ CONVERTER EITHER USING A PAIR OF PHASE DETECTORS OR THROUGH DIRECT SAMPLING AS DISCUSSED IN 3ECTION 4HE IN PHASE ) AND QUADRATURE 1 OUTPUTS ARE A FUNCTION OF THE AMPLITUDE AND PHASE OF THE )& SIGNAL AND
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HAVE IN THE PAST BEEN REFERRED TO AS BIPOLAR VIDEOS BUT A MORE CORRECT TERMINOLOGY IS THAT OF THE COMPLEX ENVELOPE OF THE RECEIVED SIGNALS !N EXAMPLE OF SUCH A BIPOLAR VIDEO EITHER ) OR 1 RECEIVED FROM A SINGLE TRANSMITTED PULSE AND INCLUDING BOTH CLUT TER AND POINT TARGETS IS SKETCHED IN &IGURE )F THE POINT TARGETS ARE MOVING THE SUPER IMPOSED BIPOLAR VIDEO FROM SEVERAL TRANSMITTED PULSES WOULD APPEAR AS IN &IGURE 4HE REMAINDER OF THE BLOCK DIAGRAM IN &IGURE SHOWS THE REMAINING PROCESS ING REQUIRED SO THAT THE MOVING TARGETS CAN BE DISPLAYED ON A 00) OR SENT TO AN AUTO MATIC TARGET EXTRACTOR 4HE IN PHASE AND QUADRATURE OUTPUTS FROM THE !$ CONVERTER ARE STORED IN A 02) MEMORY AND ALSO SUBTRACTED FROM THE OUTPUT FROM THE PREVIOUS TRANS MITTED PULSE 4HIS IMPLEMENTATION REPRESENTS THE MOST BASIC TWO PULSE -4) CANCELER IMPLEMENTED AS A FINITE IMPULSE RESPONSE &)2 FILTER !S DISCUSSED IN 3ECTION -4) CANCELERS USED IN PRACTICAL RADARS USE HIGHER ORDER FILTERS AND THESE ARE SOMETIMES IMPLEMENTED AS INFINITE IMPULSE RESPONSE ))2 FILTERS 4HE OUTPUT OF THE SUBTRACTORS IS AGAIN A BIPOLAR SIGNAL THAT CONTAINS MOVING TAR GETS SYSTEM NOISE AND A SMALL AMOUNT OF CLUTTER RESIDUE IF THE CLUTTER CANCELLATION IS NOT PERFECT 4HE MAGNITUDES OF THE IN PHASE AND QUADRATURE SIGNALS ARE THEN COM PUTED ) 1 AND CONVERTED TO ANALOG VIDEO IN A DIGITAL TO ANALOG $! CON VERTER FOR DISPLAY ON A 00) 4HE DIGITAL SIGNAL MAY ALSO BE SENT TO AUTOMATIC TARGET DETECTION CIRCUITRY 4HE DYNAMIC RANGE PEAK SIGNAL TO RMS NOISE IS LIMITED TO ABOUT D" FOR A 00) DISPLAY ! KEY DISTINCTION SOMETIMES LOST IN THE COMPLEXITIES OF THE SYSTEMS THAT FOLLOW IS THAT AN -4) RADAR SYSTEM ELIMINATES FIXED CLUTTER BECAUSE THE PHASE OF SIGNALS RETURNED FROM CONSECUTIVE TRANSMITTED PULSES DO NOT APPRECIABLY CHANGE 4HE FIXED CLUTTER IS REMOVED AFTER AS FEW AS TWO TRANSMITTED PULSES BY THE SUBTRACTION PROCESS DESCRIBED
&)'52% "IPOLAR VIDEO FROM CONSECUTIVE TRANSMITTED PULSES
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ABOVE EVEN IF EACH TRANSMITTED PULSE HAS FREQUENCY MODULATION OR OTHER ARTIFACTS AS LONG AS THE ARTIFACTS ARE IDENTICAL PULSE TO PULSE 4HE POINT BEING MADE HERE IS THAT -4) SYSTEM OPERATION DOES NOT DEPEND ON THE FREQUENCY RESOLUTION OF TARGETS FROM CLUTTER 4O PROVIDE FREQUENCY RESOLUTION WOULD REQUIRE MUCH LONGER DWELL TIMES ON TARGET THAN TWO PULSES SEPARATED BY A SINGLE 02) 3UCH EXTENDED DWELL TIMES IS ONE OF THE FUNDA MENTAL CHARACTERISTICS OF THE MOVING TARGET DETECTOR -OVING 4ARGET $ETECTOR -4$ "LOCK $IAGRAM 0ROGRESS IN DIGITAL SIGNAL PROCESSING TECHNOLOGY BY THE MID S MADE IT PRACTICAL FOR THE FIRST TIME TO IMPROVE THE PERFORMANCE OF THE CLASSICAL -4) BY IMPLEMENTING A PARALLEL BANK OF &)2 FILTERS TO INCREASE THE OUTPUT SIGNAL TO CLUTTER RATIO AND REPLACING THE )& LIMITER USED IN THE PAST WITH A HIGH RESOLUTION CLUTTER MAP FOR EFFECTIVE FALSE ALARM CONTROL !LTHOUGH THESE CONCEPTS HAD BEEN EXPLORED MANY YEARS EARLIER USING THE 6ELOCITY )NDICATING #OHERENT )NTEGRATOR 6)#) OR THE #OHERENT -EMORY &ILTER #-& TO IMPLEMENT A DOPPLER FILTER BANK AND STORAGE TUBES OR MAGNETIC DRUM MEMORY TO IMPLEMENT CLUT TER MAPS IT WAS THE WORK AT THE -)4 ,INCOLN ,ABORATORY TO IMPROVE THE PERFORMANCE OF AIRPORT SURVEILLANCE RADARS THAT RESULTED IN ONE OF THE FIRST WORKING EXAMPLES OF WHAT HAS BECOME KNOWN AS THE -OVING 4ARGET $ETECTION -4$ RADAR 4HE THEORY AND EXPECTED BENEFITS OF THIS APPROACH WERE DESCRIBED IN TWO REPORTS IN WHICH PROVIDED THE MATHEMATICAL FOUNDATION FOR THE UNDERSTANDING AND THE PRACTICAL IMPLE MENTATION OF THE -4$ CONCEPT 4HE PREDICTED SUBCLUTTER VISIBILITY IMPROVEMENT FOR THE !32 AIRPORT SURVEILLANCE RADAR WHEN THE THREE PULSE -4) PROCESSOR WAS REPLACED BY THE SECOND GENERATION -4$ )) PROCESSOR IS SHOWN IN &IGURE
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0ART OF THIS IMPROVEMENT WAS DUE TO THE USE OF DOPPLER FILTER DESIGNS UTILIZING EIGHT PULSES INSTEAD OF JUST THREE FOR THE -4) AND PART WAS THE RESULT OF ALLOWING A LARGER DYNAMIC RANGE INTO THE -4$ PROCESSOR AND RELYING ON A CLUTTER MAP TO SUPPRESS RESIDUES IN REGIONS WHERE THE CLUTTER LEVEL EXCEEDS THE MAXIMUM CLUTTER SUPPRESSION OF THE RADAR 4HE BLOCK DIAGRAM OF THE -4$ )) SIGNAL PROCESSOR IS SHOWN IN &IGURE 0ARALLEL PROCESSING CHANNELS ARE PROVIDED FOR MOVING TARGETS THROUGH THE TWO PULSE -4) CAN CELER AND THE SEVEN PULSE DOPPLER FILTER BANK AND FOR NONMOVING hZERO DOPPLERv TARGETS THROUGH THE 6ELOCITY &ILTER ! HIGH RESOLUTION CLUTTER MAP IS BUILT FROM THE h 6ELOCITY &ILTERv OUTPUT AND THE CLUTTER MAP CONTENT IS USED FOR THRESHOLDING IN THE TWO PROCESSING CHANNELS )N THE MOVING TARGET CHANNEL THE THRESHOLD OBTAINED FROM THE CLUTTER MAP CONTENT IS SCALED DOWN BY THE EXPECTED CLUTTER ATTENUATION )N ADDITION TO THE CLUTTER MAP THRESHOLDING CONVENTIONAL CONSTANT FALSE ALARM RATE THRESHOLDING IS UTILIZED AGAINST MOVING CLUTTER RAIN AND INTERFERENCE $ETECTION OUTPUTS NAMED 0RIMITIVE 4ARGET /UTPUTS ARE OBTAINED THROUGH THIS PROCESSING FOR EACH INDIVIDUAL PRO CESSED #0) &IGURE SHOWS THE ADDITIONAL PROCESSING REQUIRED TO GENERATE CENTROIDED 4ARGET 2EPORTS AND THE PROCESSING OF THESE 4ARGET 2EPORTS TO OBTAIN TRACK OUTPUTS FOR DISPLAY TO THE AIR TRAFFIC CONTROL SYSTEM 4HE -4$ RADAR TRANSMITS A GROUP OF . PULSES AT A CONSTANT PULSE REPETITION FRE QUENCY 02& AND AT A FIXED RADAR FREQUENCY 4HIS SET OF PULSES IS USUALLY REFERRED TO AS THE COHERENT PROCESSING INTERVAL #0) OR PULSE BATCH 3OMETIMES ONE OR TWO ADDITIONAL FILL PULSES ARE ADDED TO THE #0) IN ORDER TO SUPPRESS RANGE AMBIGUOUS CLUTTER RETURNS AS MIGHT OCCUR DURING PERIODS OF ANOMALOUS PROPAGATION 4HE RETURNS RECEIVED DURING ONE #0) ARE PROCESSED IN THE BANK OF . PULSE FINITE IMPULSE RESPONSE &)2 FILTERS 4HEN THE RADAR MAY CHANGE ITS 02& ANDOR 2& FREQUENCY AND TRANSMIT ANOTHER #0) OF . PULSES 3INCE MOST SEARCH RADARS ARE AMBIGUOUS IN DOPPLER THE USE OF DIFFERENT
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&)'52% 0ROCESSING OF 0RIMITIVE 4ARGET DETECTIONS AND 2ADAR 4ARGET 2EPORTS IN -4$ ))
02&S ON SUCCESSIVE COHERENT DWELLS WILL CAUSE THE TARGET RESPONSE TO FALL AT DIFFERENT FREQUENCIES OF THE FILTER PASSBAND ON THE SUCCESSIVE OPPORTUNITIES DURING THE TIME ON TARGET THUS ELIMINATING BLIND SPEEDS %ACH DOPPLER FILTER IS DESIGNED TO RESPOND TO TARGETS IN NONOVERLAPPING PORTIONS OF THE DOPPLER FREQUENCY BAND AND TO SUPPRESS SOURCES OF CLUTTER AT ALL OTHER DOPPLER FREQUENCIES 4HIS APPROACH MAXIMIZES THE COHERENT SIGNAL INTEGRATION IN EACH DOPPLER FILTER AND PROVIDES CLUTTER ATTENUATION OVER A LARGER RANGE OF DOPPLER FREQUENCIES THAN ACHIEVABLE WITH A SINGLE -4) FILTER 4HUS ONE OR MORE CLUTTER FILTERS MAY SUPPRESS MULTIPLE CLUTTER SOURCES LOCATED AT DIFFERENT DOPPLER FREQUENCIES !N EXAMPLE OF THE USE OF AN -4$ DOPPLER FILTER BANK AGAINST SIMULTANEOUS LAND AND WEATHER CLUTTER 7X IS ILLUSTRATED IN &IGURE )T CAN BE SEEN THAT FILTERS AND WILL PROVIDE SIGNIFICANT SUPPRESSION OF BOTH CLUTTER SOURCES 4HE OUTPUT OF EACH DOPPLER FILTER IS ENVELOPE DETECTED AND PROCESSED THROUGH A CELL AVERAGING CONSTANT FALSE ALARM RATE #! #&!2 PROCESSOR TO SUPPRESS RESIDUES DUE TO RANGE EXTENDED CLUTTER THAT MAY NOT HAVE BEEN FULLY SUPPRESSED BY THE FILTER !S WILL BE DISCUSSED LATER IN THIS CHAPTER THE CONVENTIONAL -4) DETECTION SYSTEM OFTEN RELIES ON A CAREFULLY CONTROLLED DYNAMIC RANGE IN THE )& SECTION OF THE RADAR RECEIVER TO ENSURE THAT CLUTTER RESIDUES AT THE -4) OUTPUT ARE SUPPRESSED TO THE LEVEL OF THE RECEIVER NOISE OR BELOW 4HIS LIMITED DYNAMIC RANGE HOWEVER HAS THE UNDESIRABLE EFFECT OF CAUSING ADDITIONAL CLUTTER SPECTRAL BROADENING AND THE ACHIEVABLE CLUTTER SUP PRESSION IS CONSEQUENTLY REDUCED
-4) 2!$!2
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&)'52% 3UPPRESSION OF MULTIPLE CLUTTER SOURCES BY USING A DOPPLER FILTER BANK
)N THE -4$ ONE OR MORE HIGH RESOLUTION CLUTTER MAPS ARE USED TO SUPPRESS THE CLUTTER RESIDUES AFTER DOPPLER FILTERING TO THE RECEIVER NOISE LEVEL OR ALTERNATIVELY TO RAISE THE DETECTION THRESHOLD ABOVE THE LEVEL OF THE RESIDUES 4HIS IN TURN ELIMINATES THE NEED TO RESTRICT THE )& DYNAMIC RANGE WHICH CAN THEN BE SET TO THE MAXIMUM VALUE SUPPORTED BY THE !$ CONVERTERS 4HUS A SYSTEM CONCEPT IS OBTAINED THAT PROVIDES A CLUTTER SUPPRESSION CAPABILITY THAT IS LIMITED ONLY BY THE RADAR SYSTEM STABILITY THE DYNAMIC RANGE OF THE RECEIVER PROCESSOR AND THE SPECTRUM WIDTH OF THE RETURNS FROM CLUTTER 4HE CONCEPT OF A HIGH RESOLUTION DIGITAL CLUTTER MAP TO SUPPRESS CLUTTER RESIDUES IS RELATED TO EARLIER EFFORTS TO CONSTRUCT ANALOG AREA -4) SYSTEMS USING FOR EXAMPLE STORAGE TUBES !LSO INCLUDED IN THE -4$ IMPLEMENTATION ARE hxAREA THRESHOLDS MAINTAINED TO CONTROL EXCESSIVE FALSE ALARMS PARTICULARLY FROM BIRD FLOCKS %ACH AREA OF ABOUT SQUARE NAUTICAL MILES IS DIVIDED INTO SEVERAL VELOCITY REGIONS 4HE THRESHOLD IN EACH REGION IS ADJUSTED ON EACH SCAN TO ACHIEVE THE DESIRED LIMIT ON FALSE ALARMS WITHOUT RAISING THE THRESHOLD SO HIGH THAT SMALL AIRCRAFT ARE PREVENTED FROM BEING PLACED IN TRACK STATUSv )N SUBSEQUENT SECTIONS SPECIFIC ASPECTS OF THE DESIGN OF AN -4$ SYSTEM WILL BE DISCUSSED 4HUS 3ECTION WILL DISCUSS THE DESIGN AND PERFORMANCE OF DOPPLER FILTER BANKS AND A DETAILED DISCUSSION OF CLUTTER MAPS WILL FOLLOW IN 3ECTION 3INCE THE ORIGINAL WORK AT ,INCOLN ,ABORATORY TO DEVELOP THE -4$ CONCEPT A NUMBER OF -4$ SYSTEMS HAVE BEEN DEVELOPED THAT VARY IN DETAIL FROM THE ORIGINAL CONCEPT !LSO THE USE OF CLUTTER MAPS TO INHIBIT EXCESSIVE CLUTTER RESIDUE INSTEAD OF CONTROL LING CLUTTER RESIDUE WITH INTENTIONALLY RESTRICTED DYNAMIC RANGE HAS BEEN ADOPTED IN NEWER -4) SYSTEMS
Ó°ÎÊ 1// ,Ê / ,Ê, -*" - ÊÊ /"Ê "6 Ê/, /4HE RESPONSE OF AN -4) SYSTEM TO A MOVING TARGET VARIES AS A FUNCTION OF THE TARGETS RADIAL VELOCITY &OR THE -4) SYSTEM DESCRIBED ABOVE THE RESPONSE NORMALIZED FOR UNITY NOISE POWER GAIN IS SHOWN IN &IGURE .OTE THAT THERE IS ZERO RESPONSE TO STATIONARY TARGETS AND ALSO TO TARGETS AT o o o KNOTS 4HESE SPEEDS KNOWN AS BLIND SPEEDS ARE WHERE THE TARGETS MOVE WAVELENGTHS BETWEEN CONSECUTIVE TRANSMITTED PULSES 4HIS RESULTS IN THE RECEIVED SIGNAL BEING
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&)'52% -4) SYSTEM RESPONSE FOR -(Z RADAR OPERATING AT PPS
SHIFTED PRECISELY OR MULTIPLES THEREOF BETWEEN PULSES WHICH RESULTS IN NO CHANGE IN THE PHASE DETECTOR OUTPUT 4HE BLIND SPEEDS CAN BE CALCULATED
6" K
L FR
K o
WHERE 6" IS THE BLIND SPEED IN METERS PER SECOND K IS THE TRANSMITTED WAVELENGTH IN METERS AND FR IS THE 02& IN HERTZ ! CONVENIENT SET OF UNITS FOR THIS EQUATION IS
6" KNOTS K
FR F'(Z
K o
WHERE FR IS THE 02& PULSE REPETITION FREQUENCY IN HERTZ AND F'(Z IS THE TRANSMITTED FREQUENCY IN GIGAHERTZ .OTE FROM THE VELOCITY RESPONSE CURVE THAT THE RESPONSE TO TARGETS AT VELOCITIES MIDWAY BETWEEN THE BLIND SPEEDS IS GREATER THAN THE RESPONSE FOR A NORMAL RECEIVER 4HE ABSCISSA OF THE VELOCITY RESPONSE CURVE CAN ALSO BE LABELED IN TERMS OF DOPPLER FREQUENCY 4HE DOPPLER FREQUENCY OF THE TARGET CAN BE CALCULATED FROM
FD
62 L
WHERE FD IS THE DOPPLER FREQUENCY IN HERTZ 62 IS THE TARGET RADIAL VELOCITY IN METERS PER SECOND AND K IS THE TRANSMITTED WAVELENGTH IN METERS )T CAN BE SEEN FROM &IGURE THAT THE DOPPLER FREQUENCIES FOR WHICH THE SYSTEM IS BLIND OCCUR AT MUL TIPLES OF THE PULSE REPETITION FREQUENCY
Ó°{Ê 1// ,Ê , / ,-/ 4HE CLUTTER SUPPRESSION NEEDED FROM AN -4) OR -4$ RADAR DEPENDS ON THE CHARACTER ISTICS OF THE CLUTTER ENVIRONMENT THE SPECIFIC RADAR TARGET DETECTION REQUIREMENTS AND THE MAJOR RADAR DESIGN CHARACTERISTICS SUCH AS RANGE AND ANGLE RESOLUTION AS WELL AS OPERATING FREQUENCY 4HE ABILITY OF A RADAR TO SUPPRESS CLUTTER IS DETERMINED BY RADAR
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WAVEFORM AND PROCESSING AVAILABLE DYNAMIC RANGE AND THE OVERALL RADAR SYSTEM STA BILITY )N THIS SECTION SOME OF THE KEY CHARACTERISTICS OF RADAR CLUTTER AND ITS INFLUENCE ON -4) RADAR DESIGN WILL BE SUMMARIZED 3PECTRAL #HARACTERISTICS 4HE SPECTRAL CHARACTERISTICS OF CLUTTER AS DISCUSSED IN MOST REFERENCES IMPLICITLY ASSUMES THAT THE RADAR TRANSMITS A CONTINUOUS CONSTANT 02& WAVEFORM 4HE SPECTRUM OF THE OUTPUT OF A PULSED TRANSMITTER USING A SIMPLE RECTANGULAR PULSE OF LENGTH S IS SHOWN IN &IGURE 4HE SPECTRAL WIDTH OF THE SIN 5 5 ENVELOPE IS DETERMINED BY THE TRANSMITTED PULSE WIDTH THE FIRST NULLS OCCURRING AT A FREQUENCY OF F o S 4HE INDIVIDUAL SPECTRAL LINES ARE SEPARATED BY A FREQUENCY EQUAL TO THE 02& 4HESE SPECTRAL LINES FALL AT PRECISELY THE SAME FREQUENCIES AS THE NULLS OF THE -4) FILTER RESPONSE SHOWN IN &IGURE 4HUS A CANCELER WILL IN THEORY FULLY REJECT CLUTTER WITH THIS IDEAL LINE SPECTRUM )N PRACTICE HOWEVER THE SPECTRAL LINES OF THE CLUTTER RETURNS ARE BROADENED BY MOTION OF THE CLUTTER SUCH AS WINDBLOWN TREES OR WAVES ON THE SEA SURFACE AS WELL AS BY THE MOTION OF THE ANTENNA IN A SCANNING RADAR OR DUE TO PLATFORM MOTION 4HIS SPECTRAL SPREAD PREVENTS PERFECT CANCELLATION OF CLUTTER IN AN -4) SYSTEM /FTEN IN THE PAST THE ASSUMPTION HAS BEEN MADE THAT THE RETURNS FROM CLUTTER HAVE A GAUSSIAN POWER SPECTRAL DENSITY WHICH MAY BE CHARACTERIZED BY ITS STANDARD DEVIATION RV AND MEAN VELOCITY MV BOTH IN UNITS OF MS 5SING THIS GAUSSIAN MODEL EACH OF THE SPECTRAL LINES IN &IGURE WILL BE CONVOLVED WITH THE SPECTRUM
3' F
¤ F M F ³ EXP ¥ S F ´µ PS F ¦
4HIS SPECTRUM IS NORMALIZED TO HAVE UNIT POWER AND THE VELOCITY PARAMETERS HAVE BEEN CONVERTED TO (Z USING THE DOPPLER EQUATION MF
MV L
S V SF L
&)'52% 0ULSE TRANSMITTER SPECTRUM
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WHERE K IS THE RADAR WAVELENGTH )NSTEAD OF THE STANDARD DEVIATION S F THE POWER SPEC TRUM CAN BE DEFINED BY ITS D" WIDTH " AS FOLLOWS
3' F
¤ LN F ³ LN EXP ¥ ´µ " ¦ P "
WHERE
" LN S F S F
4HE EARLY EXPERIMENTAL RESULTS THAT LED TO THE GENERAL ADOPTION OF THE GAUSSIAN MODEL WERE OBTAINED WITH RADAR EQUIPMENT OF LIMITED STABILITY AND THE SPECTRAL SHAPE WAS SOMETIMES DERIVED FROM VIDEO SPECTRA COMPUTED USING SQUARE LAW DETECTED RETURNS "Y THE MID S NEW EXPERIMENTAL RESULTS WERE OBTAINED WHICH SHOWED THAT THE SPECTRUM FALL OFF WAS SLOWER THAN PREDICTED BY THE GAUSSIAN MODEL 4HIS LED TO NEW MODELS BASED ON POLYNOMIAL REPRESENTATIONS OF THE SPECTRUM USING AN EQUATION OF THE FORM
¤P³ N SIN ¥ ´ ¦ Nµ 30/,9 F P "
¤ \ F \³ ¥ ¦ " ´µ
N
4HE SPECTRUM SHAPE IS DETERMINED BY THE INTEGER N WHICH MUST BE OR LARGER IN ORDER FOR THE TWO FIRST SPECTRAL MOMENTS TO EXIST ! TYPICAL VALUE USED FOR THIS SPECTRUM IS N WHICH RESULTS IN
30/,9 F
P "
¤ \ F \³ ¥ ´ ¦ " µ
4HE RELATIONSHIP BETWEEN THE STANDARD DEVIATION OF THIS SPECTRUM AND ITS D" WIDTH IS GIVEN BY " S F
! POTENTIAL ISSUE WITH THIS MODEL IS THAT THE SKIRTS OF THE SPECTRUM CORRESPOND TO VERY LARGE RADIAL VELOCITY COMPONENTS OF THE CLUTTER INTERNAL MOTION $URING THE S AN EXTENSIVE MEASUREMENT PROGRAM CONDUCTED AT THE -)4 ,INCOLN ,ABORATORY OBTAINED MORE ACCURATE DATA ON LAND CLUTTER SPECTRA USING A VERY STABLE RADAR EQUIPMENT AND DATA WAS COLLECTED UNDER WELL CONTROLLED CONDITIONS 4HESE NEW RESULTS LED TO THE FOLLOWING EXPONENTIAL MODEL FOR LAND CLUTTER SPECTRA
3%80 F
LN ¤ LN ³ EXP ¥ \ F \´ " " ¦ µ
(ERE THE D" SPECTRUM WIDTH CAN BE EXPRESSED IN TERMS OF THE STANDARD DEVIATION BY
" LN S F S F
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"ILLINGSLEY USED THE PARAMETERS G VC AND A RESPECTIVELY FOR THE GAUSSIAN THE POLYNOMIAL AND THE EXPONENTIAL SPECTRUM MODELS )N ADDITION THE EXPONENT N IS NEEDED FOR THE POLYNOMIAL MODEL 4HESE PARAMETERS WERE CHOSEN TO SIMPLIFY THE FUNCTIONAL DESCRIPTION OF THE SPECTRUM SHAPE )N TERMS OF THE STANDARD DEVIATION OF THE SPECTRAL WIDTH IN MS THESE PARAMETERS CAN BE DEFINED AS FOLLOWS G
S V
VC LN S V
B
SV
GAUSSIAN SPECTRRUM
POLYNOMIAL SPECTRUM WITH N
EXPONENTIAL SPECTRUM
!SSUMING A VALUE OF S V MS CORRESPONDING TO WINDY CONDITION THE THREE CLUTTER SPECTRUM MODELS ARE COMPARED IN &IGURE !S NOTED IN "ILLINGSLEY ALL THREE MODELS ARE IN REASONABLE AGREEMENT FOR THE UPPER n D" OF THEIR RANGE BUT DIFFER APPRECIABLY AT THE LOWER VALUES OF CLUTTER SPECTRAL DENSITY %STIMATED VALUES OF THE SPECTRAL SPREAD OF LAND CLUTTER FROM FORESTED REGIONS AND FOR DIFFERENT WIND SPEEDS ARE SHOWN IN 4ABLE 4HE VALUES IN THE TABLE ARE BASED ON "ILLINGSLEYS PARAMETER A BUT COLUMNS HAVE BEEN ADDED WITH THE CORRESPONDING RMS SPECTRAL SPREAD IN MS !N EXAMPLE OF A MEASURED LAND CLUTTER SPECTRUM IS SHOWN IN &IGURE 4HE SPECTRAL SHAPE PARAMETER A CAN BE ESTIMATED AS THE SLOPE OF THE UPPER SKIRT OF THE SPECTRUM IN D" PER MS DIVIDED BY LN 4HESE VALUES OF A WERE ADDED IN THIS FIGURE
&)'52% #OMPARISON OF GAUSSIAN EXPONENTIAL AND POLYNOMIAL SPECTRA FOR AN RMS SPECTRAL SPREAD OF RV MS
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4!",% -EASURED 3PECTRAL 3PREAD FOR $IFFERENT 7IND #ONDITIONS AFTER *""ILLINGSLEY
Ú 7ILLIAM !NDREW 0UBLISHING )NC
7IND #ONDITIONS ,IGHT AIR "REEZY 7INDY 'ALE FORCE EST
7IND 3PEED MPH n n n n
%XPONENTIAL AC 3HAPE 0ARAMETER A MS 4YPICAL
2-3 3PECTRAL 7IDTH R V MS
7ORST #ASE
4YPICAL
7ORST #ASE
4HE VALUES OF RMS SPECTRAL SPREAD OF LAND CLUTTER AS DERIVED FROM THE DATA IN "ILLINGSLEY AGREE QUITE WELL WITH PREVIOUS STUDIES )T CAN PROBABLY SAFELY BE STATED THAT THE POLYNOMIAL MODEL OF LAND CLUTTER SPECTRA IS FAR TOO PESSIMISTIC AT SPECTRAL VALUES BELOW n D" AND SHOULD BE AVOIDED FOR RADAR ANALYSIS REQUIRING A LARGE CLUTTER ATTENUATION VALUE 4HE CASE FOR THE EXPONENTIAL MODEL AS PRESENTED BY "ILLINGSLEY IS QUITE CONVINC ING AND THIS MODEL HAS BEEN WIDELY ACCEPTED AS BEING THE MOST ACCURATE FOR RADAR PERFORMANCE PREDICTIONS
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! COMPARISON BETWEEN THE GAUSSIAN AND THE EXPONENTIAL MODELS ON A LINEAR SCALE AS SHOWN IN &IGURE INDICATES THAT THE DIFFERENCE IN SPECTRAL WIDTH AT EVEN VERY LOW LEVELS n D" IS NO MORE THAN ABOUT A FACTOR OF &OR MANY ANALYSES THIS WOULD MOST LIKELY BE INSIGNIFICANT COMPARED TO THE ADDED CLUTTER SPECTRAL SPREADING CAUSED BY SCANNING MODULATION 4HUS IN MANY CASES THE SIMPLE GAUSSIAN MODEL CAN CONTINUE TO BE USED IN -4) AND -4$ PERFORMANCE ANALYSIS )N CASE OF DOUBT THE SPECTRAL SPREAD OF THE GAUSSIAN MODEL COULD BE DOUBLED TO ASSESS THE AVAILABLE MARGIN .ATHANSON AND 2EILLY HAVE SHOWN THAT THE CLUTTER SPECTRAL WIDTH OF RAIN IS PRI MARILY DUE TO A TURBULENCE AND WIND SHEAR CHANGE IN WIND VELOCITY WITH ALTITUDE -EASUREMENTS SHOW A TYPICAL AVERAGE VALUE OF R VT MS FOR TURBULENCE AND R VS MSKM FOR WIND SHEAR ! CONVENIENT EQUATION IS S VS 2 Q EL MS FOR THE EFFECT OF WIND SHEAR PROVIDED THE RAIN FILLS THE VERTICAL BEAM (ERE 2 IS THE RANGE TO THE WEATHER IN NAUTICAL MILES AND Q EL IS THE ONE WAY HALF POWER VERTI CAL BEAMWIDTH IN DEGREES 4HUS FOR EXAMPLE R VS OF RAIN VIEWED AT NMI WITH A VERTICAL BEAMWIDTH OF WOULD BE R VS MS 4HE TOTAL SPECTRAL SPREAD IS THEN S V S VT S VS MS 2AIN AND CHAFF ALSO HAVE AN AVERAGE VELOC ITY IN ADDITION TO THE SPECTRAL SPREAD NOTED ABOVE WHICH MUST BE TAKEN INTO ACCOUNT WHEN DESIGNING AN -4) SYSTEM 4HE CLUTTER SPECTRAL WIDTH IN METERS PER SECOND IS INDEPENDENT OF THE RADAR FREQUENCY 4HE STANDARD DEVIATION OF THE CLUTTER POWER SPECTRUM R F IN HERTZ IS S V (Z L WHERE K IS THE TRANSMITTED WAVELENGTH IN METERS AND R V IS THE CLUTTER STANDARD DEVIATION IN METERS PER SECOND
SF
&)'52% #OMPARISON OF GAUSSIAN AND EXPONENTIAL SPECTRA ON LINEAR VELOCITY SCALE
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!NTENNA SCANNING ALSO CAUSES A SPREAD OF THE CLUTTER POWER SPECTRUM DUE TO THE AMPLITUDE MODULATION OF THE ECHO SIGNALS BY THE TWO WAY ANTENNA PATTERN 4HE RESULT ING CLUTTER STANDARD DEVIATION IS LN FR F R (Z P N N WHERE FR IS THE 02& AND N IS THE NUMBER OF HITS BETWEEN THE ONE WAY D" POINTS OF THE ANTENNA PATTERN 4HIS EQUATION WAS DERIVED FROM A GAUSSIAN BEAM SHAPE BUT IS ESSEN TIALLY INDEPENDENT OF THE ACTUAL BEAM SHAPE OR APERTURE ILLUMINATION FUNCTION USED 4HE CLUTTER SPECTRAL SPREAD DUE TO SCANNING NORMALIZED TO THE 02& IS
SF
S F4
N
WHERE 4 02& IS THE INTERPULSE PERIOD 4HE COMBINED SPECTRAL EFFECTS OF INTERNAL CLUTTER MOTION AND ANTENNA SCANNING MODU LATION MUST BE OBTAINED AS THE CONVOLUTION OF THE INDIVIDUAL SPECTRA 7HEN BOTH SPECTRA ARE GAUSSIAN IN SHAPE THE RESULTING SPECTRUM REMAINS GAUSSIAN WITH A STANDARD DEVIATION THAT IS THE SQUARE ROOT OF THE SUM OF THE SQUARES OF THE INDIVIDUAL STANDARD DEVIATIONS "Y INTEGRATING THE TWO SIDED TAILS OF THE GAUSSIAN AND EXPONENTIAL SPECTRA OUTSIDE A MULTIPLE K OF THE STANDARD DEVIATION OF THE SPECTRA A ROUGH BUT CONSERVATIVE ESTIMATE CAN BE FOUND OF HOW WIDE THE -4) NOTCH MUST BE TO ACHIEVE A REQUIRED IMPROVEMENT FACTOR ) 3UCH A CURVE IS SHOWN IN &IGURE BASED ON THE CLUTTER SPECTRA SHOWN IN &IGURE !LTHOUGH THIS APPROACH WOULD ONLY BE STRICTLY CORRECT FOR AN IDEAL -4) FILTER WITH A STEP FUNCTION PASSBAND IT CAN SERVE AS A PRELIMINARY GUIDELINE FOR THE -4) FILTER DESIGN
&)'52% #LUTTER POWER IN TWO SIDED TAILS OF SPECTRUM VS MULTIPLE OF STANDARD DEVIATION
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!MPLITUDE #HARACTERISTICS 4O PREDICT THE PERFORMANCE OF AN -4) SYSTEM THE POWER OF THE CLUTTER RETURNS WITH WHICH A TARGET MUST COMPETE SHOULD BE KNOWN 4HE AMPLITUDE OF THE CLUTTER RETURNS DEPENDS ON THE SIZE OF THE RESOLUTION CELL OF THE RADAR THE FREQUENCY OF THE RADAR AND THE REFLECTIVITY OF THE CLUTTER 4HE EXPECTED RADAR CROSS SECTION OF CLUTTER CAN BE EXPRESSED AS THE PRODUCT OF A REFLECTIVITY FACTOR AND THE VOLUME OR AREA OF THE RESOLUTION CELL &OR SURFACE CLUTTER AS VIEWED BY A SURFACE BASED RADAR
S !C S 2 P AZ
C T S
WHERE S IS THE AVERAGE RADAR CROSS SECTION IN SQUARE METERS !C IS THE AREA OF CLUTTER ILLUMINATED IN SQUARE METERS 2 IS THE RANGE TO CLUTTER IN METERS PAZ IS THE ONE WAY HALF POWER AZIMUTHAL BEAMWIDTH IN RADIANS C IS THE SPEED OF PROPAGATION MILLION MS S IS THE HALF POWER RADAR PULSE LENGTH AFTER THE MATCHED FILTER IN SECONDS AND R IS THE AVERAGE CLUTTER REFLECTIVITY FACTOR IN SQUARE METERS PER SQUARE METER &OR VOLUMETRIC CLUTTER SUCH AS CHAFF OR RAIN THE AVERAGE CROSS SECTION IS C T H WHERE 6C IS THE VOLUME OF CLUTTER ILLUMINATED M AND G IS THE CLUTTER REFLECTIVITY FACTOR MM 4HE VOLUME 6C IS COMPUTED FROM THE HEIGHT EXTENT OF CLUTTER ( METERS THE AZIMUTH EXTENT OF THE CLUTTER 2 P AZ AND THE RADAR RANGE RESOLUTION CELL S )F THE CLUTTER COMPLETELY FILLS THE VERTICAL BEAM THEN ( 2 P EL WHERE P EL IS THE ELEVATION BEAM WIDTH 2 IS THE RANGE TO THE CLUTTER METERS AND C IS THE SPEED OF PROPAGATION )T SHOULD BE NOTED THAT FOR LAND CLUTTER R CAN VARY CONSIDERABLY FROM ONE RESOLU TION CELL TO THE NEXT ! TYPICAL DISTRIBUTION OF R TAKEN FROM "ARTON IS SHOWN IN &IGURE 4YPICAL VALUES FOR R AND G FROM THE SAME REFERENCE ARE GIVEN IN 4ABLE !DDITIONAL RESULTS FOR CLUTTER REFLECTIVITY ARE FOUND IN "ILLINGSLEY
S 6C H 2 P AZ P EL (
4!",% 4YPICAL 6ALUES OF #LUTTER 2EFLECTIVITY
#LUTTER 0ARAMETERS FOR 4YPICAL #ONDITIONS #LUTTER ,AND EXCLUDING POINT CLUTTER
2EFLECTIVITY K M G M n L WORST PERCENT R M
S
#ONDITIONS
3EA STATE 3EA "EAUFORT SCALE R D" +" FT WAVES +" ANGLE % SIN % D" K D" ROUGH % #HAFF FOR FIXED WEIGHT PER UNIT G r K VOLUME G r R K 2AIN MATCHED R MMH FOR RATE R MMH POLARIZATION 0OINT CLUTTER
&ROM "ARTON
"AND K M
,
3
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R D"
n
n
n
n
R M
R D"
n
n
n
n
G Mn r n r n r n
n
G Mn r n r n r n r n
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"ECAUSE OF THE IMPRECISION IN PREDICTING R AND G THESE EQUATIONS DO NOT INCLUDE AN ANTENNA BEAM SHAPE FACTOR &OR THE MEASUREMENT OF THE REFLECTIVITY OF RAIN REFER ENCES ON RADAR METEOROLOGY PRESENT MORE PRECISE EQUATIONS )N ADDITION TO DISTRIBUTED CLUTTER TARGETS THERE ARE MANY TARGETS THAT APPEAR AS POINTS SUCH AS RADIO TOWERS WATER TANKS AND BUILDINGS 4HESE POINT TARGETS TYPICALLY HAVE A RADAR CROSS SECTION OF TO M WITH TYPICAL DENSITIES AS SHOWN LATER IN &IGURE 4HIS GRAPH IS FROM "ILLINGSLEY AND THE ADDITIONAL POINTS INDICATED BY AN ASTERISK ARE FROM 7ARD &IGURE A SHOWS A 00) DISPLAY OF ALL CLUTTER OBSERVED WITH A SURVEILLANCE RADAR WITH A BY MS RESOLUTION CELL IN THE MOUNTAINOUS REGION OF ,AKEHEAD /NTARIO #ANADA 4HE 00) RANGE IS SET FOR NMI #LUTTER THAT EXCEEDS THE MINIMUM DISCERNIBLE SIGNAL -$3 LEVEL OF THE RADAR BY D" IS SHOWN IN &IGURE B
&)'52% 00) DISPLAY NMI RANGE OF A ALL CLUTTER AT A MOUNTAINOUS SITE AND B CLUTTER THAT EXCEEDS THE SYSTEM NOISE LEVEL BY D"
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.OTE THAT THE CLUTTER IN &IGURE B IS VERY SPOTTY IN CHARACTER INCLUDING THE STRONG FIXED POINT TARGETS AND RETURNS FROM EXTENDED TARGETS )T IS SIGNIFICANT THAT THE EXTENDED TARGETS ARE NO LONGER VERY EXTENDED 4HE FACE OF A MOUNTAIN AT MI FROM TO OCLOCK IS ONLY A LINE )F THE -4) SYSTEM WERE INCAPABLE OF DISPLAYING AN AIR CRAFT WHILE IT WAS OVER THE MOUNTAIN FACE IT WOULD DISPLAY THE AIRCRAFT ON THE NEXT SCAN OF THE ANTENNA BECAUSE THE AIRCRAFT WOULD HAVE MOVED EITHER FARTHER OR NEARER 4HE 00) DOES NOT HAVE A RESOLUTION THAT APPROACHES THE RESOLUTION OF THE SIGNAL PROCESSING CIRCUITS OF THIS RADAR 4HUS THE APPARENT EXTENDED CLUTTER HAS MANY WEAK AREAS NOT VISIBLE IN THESE PHOTOGRAPHS WHERE TARGETS COULD BE DETECTED BY VIRTUE OF AN -4) RADARS INTERCLUTTER VISIBILITY DEFINED IN 3ECTION
Ó°xÊ /" 4HE )%%% 3TANDARD 2ADAR $EFINITIONS PROVIDE USEFUL DEFINITIONS FOR MANY OF THE QUANTITIES NEEDED TO QUANTIFY -4) AND -4$ PERFORMANCE BUT IN SOME CASES THE VAGUENESS OF THE ORIGINAL DEFINITION AND THE LACK OF DISTINCTION BETWEEN PERFORMANCE AGAINST DISTRIBUTED CLUTTER VERSUS POINT CLUTTER RETURNS HAVE LED TO AMBIGUOUS INTERPRE TATIONS OF SEVERAL TERMS )N THIS SECTION THE MAJOR DEFINITIONS WILL BE REVIEWED AND ANNOTATED TO ATTEMPT TO CLARIFY SOME OF THESE POTENTIAL AMBIGUITIES &OR EACH TERM THE )%%% DEFINITION WHEN AVAILABLE WILL BE QUOTED ALONG WITH A SUBSEQUENT DISCUSSION )MPROVEMENT &ACTOR 4HE )%%% DEFINITION OF )MPROVEMENT &ACTOR READS MOVING TARGET INDICATION -4) IMPROVEMENT FACTOR 4HE SIGNAL TO CLUTTER POWER RATIO AT THE OUTPUT OF THE CLUTTER FILTER DIVIDED BY THE SIGNAL TO CLUTTER POWER RATIO AT THE INPUT TO THE CLUTTER FILTER AVERAGED UNIFORMLY OVER ALL TARGET RADIAL VELOCITIES OF INTEREST 3YNONYM CLUTTER IMPROVEMENT FACTOR
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4HIS DEFINITION ASSUMES THAT CLUTTER IS DISTRIBUTED HOMOGENEOUSLY ACROSS MANY RANGE CELLS )N THIS CASE THE ABOVE DEFINITION IS EQUALLY VALID BEFORE AND AFTER PULSE COMPRESSION !GAINST POINT CLUTTER THIS DEFINITION ONLY APPLIES AFTER PULSE COMPRESSION AND MAY RESULT IN A DIFFERENT VALUE OF THE IMPROVEMENT FACTOR 4HE REAL DIFFICULTY WITH THIS DEFINITION IS HOWEVER THE LACK OF A PRECISE DEFINITION OF THE DOPPLER VELOCITY INTER VAL WHICH IS TO BE USED FOR THE REQUIRED hUNIFORMv AVERAGING /RIGINALLY THIS AVERAG ING WAS ASSUMED TO INVOLVE MULTIPLE 02& INTERVALS BASED ON CLASSICAL LOW 02& RADARS USING A SINGLE -4) FILTER )T WAS FOR THIS REASON THAT THE -4) )MPROVEMENT &ACTOR DEFI NITION ) PROVIDED IN THE ND EDITION OF THIS 2ADAR (ANDBOOK USED THE NOISE GAIN OF THE DOPPLER -4) FILTER AS THE NORMALIZING FACTOR 4HE INCREASED USE OF PULSE DOPPLER FILTER BANKS IN MODERN RADAR HAS HOWEVER LED TO A USE OF THE )%%% DEFINITION WHERE THE AVERAGING OF THE SIGNAL TO CLUTTER RATIO IMPROVEMENT IS PERFORMED ONLY ACROSS A NARROW REGION AROUND THE PEAK OF THE DOPPLER FILTER RESPONSE )N THIS CASE THE COHERENT INTEGRATION GAIN OF THE DOPPLER FILTER IS AUTOMATICALLY ADDED TO THE CONVENTIONAL -4) IMPROVEMENT FACTOR VALUE AND MUCH BETTER RADAR PERFORMANCE IS INDICATED 3INCE A DEFINITION OF CLUTTER SUPPRESSION IS OFTEN NEEDED WHICH QUANTIFIES THE INHER ENT RADAR STABILITY LIMITATIONS APART FROM ANY ADDITIONAL COHERENT GAIN IT IS SOMETIMES PREFERABLE TO USE THE )%%% DEFINITION OF CLUTTER ATTENUATION )N THIS CHAPTER IMPROVEMENT FACTOR AND CLUTTER ATTENUATION WILL BE USED SYNONYMOUSLY 7HEN THE COHERENT GAIN OF THE DOPPLER FILTER IS INCLUDED THE TERM SIGNAL TO CLUTTER RATIO IMPROVEMENT WILL BE USED #LUTTER !TTENUATION 4HE )%%% DEFINITION READS CLUTTER ATTENUATION #! )N MOVING TARGET INDICATION -4) OR DOPPLER RADAR THE RATIO OF THE CLUTTER TO NOISE RATIO AT THE INPUT TO THE PROCESSOR TO THE CLUTTER TO NOISE RATIO AT THE OUT PUT .OTE )N -4) A SINGLE VALUE OF #! WILL BE OBTAINED WHILE IN DOPPLER RADAR THE VALUE WILL GENERALLY VARY OVER THE DIFFERENT TARGET DOPPLER FILTERS )N -4) #! WILL BE EQUAL TO -4) IMPROVEMENT FACTOR IF THE TARGETS ARE ASSUMED UNIFORMLY DISTRIBUTED IN VELOCITY 3EE ALSO -4) IMPROVEMENT FACTOR
(ERE IT WILL BE ASSUMED THAT hPROCESSORv REFERS TO THE -4) FILTER OR A SINGLE DOPPLER FILTER IN A PULSE DOPPLER FILTER BANK "ASED ON THIS DEFINITION THE CLUTTER ATTENUATION IS GIVEN BY
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0#). 0./54 0#/54 0.).
WHERE 0#). AND 0#/54 ARE THE CLUTTER POWER AT THE INPUT AND OUTPUT OF THE -4) FILTER RESPECTIVELY AND 0.). AND 0./54 ARE THE CORRESPONDING NOISE POWERS !S NOTED IN THE )%%% DEFINITION THE VALUE OF #! WILL MOST LIKELY DIFFER FROM FILTER TO FILTER IN A DOPPLER FILTER BANK DUE TO SPECIFIC CLUTTER AND FILTER RESPONSE CHARACTERISTICS )N THE DISCUSSION ABOVE THE ASSUMPTION WAS IMPLICITLY MADE THAT CLUTTER RETURNS ARE STATIONARY AND DISTRIBUTED IN RANGE 4HE ABOVE DEFINITIONS WILL BE EQUALLY VALID BEFORE AND AFTER PULSE COMPRESSION &OR A SINGLE PIECE OF POINT CLUTTER AS OFTEN USED IN ACTUAL RADAR STABILITY MEASUREMENTS THE DEFINITION OF CLUTTER ATTENUATION WOULD HAVE TO BE CHANGED AS FOLLOWS TO PROVIDE IDENTICAL RESULTS CLUTTER ATTENUATION #! POINT CLUTTER )N MOVING TARGET INDICATION -4) OR $OPPLER RADAR THE RATIO OF THE TOTAL ENERGY IN THE RECEIVED POINT CLUTTER RETURN AT THE INPUT TO THE PROCESSOR TO THE TOTAL ENERGY IN THE POINT CLUTTER RESIDUE AT THE OUTPUT OF THE PROCESSOR MULTIPLIED BY THE NOISE GAIN OF PROCESSOR
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4HE CLUTTER ATTENUATION AGAINST POINT CLUTTER BASED ON THIS DEFINITION WILL BE THE SAME BEFORE OR AFTER PULSE COMPRESSION AND WILL ALSO BE IDENTICAL TO THE VALUE OF #! OBTAINED AGAINST DISTRIBUTED CLUTTER WITH IDENTICAL SPECTRAL CHARACTERISTICS &OR THE PRACTICAL MEASUREMENT OF #! AGAINST A SINGLE PIECE OF POINT CLUTTER IE CORNER REFLECTOR THE TOTAL ENERGY MUST BE INTEGRATED PER THE ABOVE DEFINITION AT THE INPUT AND OUTPUT OF EACH DOPPLER FILTER 4HE CALCULATION OF THE ENERGY IS BEST PERFORMED PRIOR TO PULSE COMPRESSION SINCE THE PRECISE DURATION OF THE UNCOMPRESSED PULSE AND THEREFORE THE INTEGRATION WINDOW IS ACCURATELY KNOWN )F DONE AFTER PULSE COMPRES SION UNCERTAINTIES IN THE INTEGRATION OF ENERGY MAY ARISE DUE TO THE TRANSIENT RESPONSE OF THE PULSE COMPRESSION FILTER 3IGNAL TO #LUTTER 2ATIO )MPROVEMENT )3#2 &OR A SYSTEM EMPLOYING MUL TIPLE DOPPLER FILTERS SUCH AS THE -4$ EACH DOPPLER FILTER WILL ALSO HAVE A COHER ENT GAIN '# F WHICH AT THE FILTER PEAK HAS A VALUE '# MAX 4HE COHERENT GAIN OF A DOPPLER FILTER IS EQUAL TO THE INCREASE IN SIGNAL TO THERMAL NOISE RATIO BETWEEN THE INPUT AND THE OUTPUT OF THE FILTER DUE TO THE COHERENT SUMMATION OF INDIVIDUAL TARGET RETURNS !GAIN THESE COHERENT GAIN VALUES WOULD USUALLY DIFFER FROM FILTER TO FILTER DUE TO POTENTIALLY DIFFERENT DOPPLER FILTER CHARACTERISTICS 4HESE COHERENT GAIN VALUES WILL INCLUDE THE FILTER MISMATCH LOSS BUT NOT THE STRADDLING LOSSES BETWEEN ADJACENT FILTERS 4HE PRODUCT OF THE CLUTTER ATTENUATION #!I AND THE COHERENT GAIN '#MAX I FOR THE ITH DOPPLER FILTER BECOMES THE DEFINITION OF THE SIGNAL TO CLUTTER RATIO 3#2 IMPROVEMENT )3#2 I #!I '# MAX I
4HIS QUANTITY WAS NOT INCLUDED IN THE )%%% $ICTIONARY BUT THE FOLLOWING DEFINI TION IS COMMONLY USED SIGNAL TO CLUTTER RATIO IMPROVEMENT )3#2 4HE RATIO OF THE SIGNAL TO CLUTTER RATIO OBTAINED AT THE OUTPUT OF THE DOPPLER FILTER BANK TO THE SIGNAL TO CLUTTER RATIO AT THE INPUT TO THE FILTER BANK COMPUTED AS A FUNCTION OF TARGET DOPPLER FREQUENCY
4HIS DEFINITION DOES NOT INCLUDE ANY DOPPLER AVERAGING ACROSS THE INDIVIDUAL FILTERS AND THE DEFINITION DOES NOT PROVIDE A SINGLE FIGURE OF MERIT FOR A RADAR DOP PLER PROCESSOR BECAUSE EACH FILTER MAY HAVE DIFFERENT VALUES OF CLUTTER ATTENUATION AND COHERENT GAIN 3INCE EACH DOPPLER FILTER HAS A COHERENT GAIN THAT IS A FUNCTION OF TARGET DOPPLER AN AVERAGE VALUE OF SIGNAL TO CLUTTER IMPROVEMENT CAN BE DEFINED BY AVERAGING ALL FILTERS OVER ITS RESPECTIVE RANGE OF TARGET DOPPLERS
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F § F ¶ ¨¯ #! '# F DF ¯ #! '# F DF · · F ¨¨ F · F . F ¨ F. · ¨ #!. '# . F DF · ¯ ¨ · F . © ¸
4HE SPECIFIC FREQUENCIES COULD LOGICALLY BE CHOSEN AS THE CROSSOVER BETWEEN INDI VIDUAL DOPPLER FILTERS 4HIS CALCULATION WILL NOW INCLUDE THE EFFECT OF A TARGET DOPPLER
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STRADDLING LOSS AND WOULD REPRESENT A SINGLE FIGURE OF MERIT FOR A DOPPLER PROCESSOR 4O SIMPLIFY THIS CALCULATION THE AVERAGE SIGNAL TO CLUTTER IMPROVEMENT MAY BE DEFINED AS THE FINITE SUM
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£ #!I '# MAX I
I
TO WHICH THE DOPPLER STRADDLING LOSS WOULD HAVE TO BE ADDED 3UBCLUTTER 6ISIBILITY 3#6 4HE )%%% DEFINITION OF SUBCLUTTER VISIBILITY IS 3UBCLUTTER VISIBILITY 4HE RATIO BY WHICH THE TARGET ECHO POWER MAY BE WEAKER THAN COINCIDENT CLUTTER ECHO POWER AND STILL BE DETECTED WITH SPECIFIED DETECTION AND FALSE ALARM PROBABILITIES .OTE 4ARGET AND CLUTTER POWERS ARE MEASURED ON A SINGLE PULSE RETURN AND ALL TARGET VELOCITIES ARE ASSUMED EQUALLY LIKELY
4HE SUBCLUTTER VISIBILITY 3#6 OF A RADAR SYSTEM IS A MEASURE OF ITS ABILITY TO DETECT MOVING TARGET SIGNALS SUPERIMPOSED ON CLUTTER SIGNALS ! RADAR WITH D" 3#6 CAN DETECT AN AIRCRAFT FLYING OVER CLUTTER WHOSE SIGNAL RETURN IS TIMES STRONGER .OTE THAT IT IS IMPLICITLY ASSUMED IN THE ABOVE DEFINITION THAT SIGNAL AND CLUTTER ARE BOTH OBSERVED AFTER PULSE COMPRESSION 4HE 3#6 OF TWO RADARS CANNOT NECESSARILY BE USED TO COMPARE THEIR PERFORMANCE WHILE OPERATING IN THE SAME ENVIRONMENT BECAUSE THE TARGET TO CLUTTER RATIO SEEN BY EACH RADAR IS PROPORTIONAL TO THE SIZE OF THE RADAR RESOLUTION CELL AND MAY BE A FUNCTION OF FREQUENCY 4HUS A RADAR WITH A MS PULSE LENGTH AND A BEAMWIDTH WOULD NEED D" MORE SUBCLUTTER VISIBILITY THAN A RADAR WITH A MS PULSE AND A BEAMWIDTH FOR EQUAL PERFORMANCE IN A DISTRIBUTED CLUTTER ENVIRONMENT 4HE SUBCLUTTER VISIBILITY OF A RADAR WHEN EXPRESSED IN DECIBELS IS LESS THAN THE IMPROVEMENT FACTOR BY THE CLUTTER VISIBILITY FACTOR 6OC SEE DEFINITION BELOW )NTERCLUTTER 6ISIBILITY )#6 4HE )%%% DEFINITION IS INTERCLUTTER VISIBILITY 4HE ABILITY OF A RADAR TO DETECT MOVING TARGETS THAT OCCUR IN RESOLUTION CELLS AMONG PATCHES OF STRONG CLUTTER USUALLY APPLIED TO MOVING TARGET INDICATION -4) OR PULSED $OPPLER RADARS .OTE 4HE HIGHER THE RADAR RANGE ANDOR ANGLE RESOLUTION THE BETTER THE INTERCLUTTER VISIBILITY
4HE INTERCLUTTER VISIBILITY )#6 OF A RADAR IS A MEASURE OF ITS CAPABILITY TO DETECT TARGETS BETWEEN POINTS OF STRONG CLUTTER BY VIRTUE OF THE ABILITY OF THE RADAR TO RESOLVE THE AREAS OF STRONG AND WEAK CLUTTER ! RADAR WITH HIGH RESOLUTION MAKES AVAILABLE REGIONS BETWEEN POINTS OF STRONG CLUTTER WHERE THE TARGET TO CLUTTER RATIO WILL BE SUF FICIENT FOR TARGET DETECTION EVEN THOUGH THE 3#6 OF THE RADAR BASED ON AVERAGE CLUTTER MAY BE RELATIVELY LOW 4O ACHIEVE )#6 A MECHANISM MUST BE FURNISHED TO PROVIDE #&!2 OPERATION AGAINST THE RESIDUE FROM STRONG CLUTTER 4HIS #&!2 IS PROVIDED IN OLDER -4) SYSTEM BY )& LIMITING AND IN THE -4$ IMPLEMENTATION THROUGH THE USE OF HIGH RESOLUTION CLUTTER MAPS ! QUANTITATIVE DEFINITION OF INTERCLUTTER VISIBILITY HAS NOT YET BEEN FORMULATED &ILTER -ISMATCH ,OSS 4HE )%%% DEFINITION IS FILTER MISMATCH LOSS 4HE LOSS IN OUTPUT SIGNAL TO NOISE RATIO OF A FILTER RELATIVE TO THE SIGNAL TO NOISE RATIO FROM A MATCHED FILTER
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4HE MAXIMUM SIGNAL TO NOISE RATIO AVAILABLE FROM AN . PULSE FILTER IS . TIMES THE SIGNAL TO NOISE RATIO OF A SINGLE PULSE ASSUMING ALL PULSES HAVE EQUAL AMPLI TUDE 7HEN WEIGHTING IS APPLIED TO REJECT CLUTTER AND CONTROL THE FILTER SIDELOBES THE PEAK OUTPUT SIGNAL TO NOISE RATIO IS REDUCED 4HE FILTER MISMATCH LOSS IS THE AMOUNT BY WHICH THE PEAK OUTPUT SIGNAL TO NOISE RATIO IS REDUCED BY THE USE OF WEIGHTING ! THREE PULSE -4) FILTER USING BINOMIAL WEIGHTS HAS A FILTER MISMATCH LOSS OF D" 4HE MISMATCH LOSS FOR THE BINOMIAL WEIGHTED FOUR PULSE CANCELER IS D" #LUTTER 6ISIBILITY &ACTOR 6OC 4HE )%%% DEFINITION IS CLUTTER DETECTABILITY FACTOR 4HE PREDETECTION SIGNAL TO CLUTTER RATIO THAT PROVIDES STATED PROBABILITY OF DETECTION FOR A GIVEN FALSE ALARM PROBABILITY IN AN AUTOMATIC DETECTION CIRCUIT .OTE )N -4) SYSTEMS IT IS THE RATIO AFTER CANCELLATION OR DOPPLER FILTERING
4HE CLUTTER VISIBILITY FACTOR IS THE RATIO BY WHICH THE TARGET SIGNAL MUST EXCEED THE CLUTTER RESIDUE SO THAT TARGET DETECTION CAN OCCUR WITHOUT HAVING THE CLUTTER RESIDUE RESULT IN FALSE TARGET DETECTIONS 4HE SYSTEM MUST PROVIDE A THRESHOLD THAT THE TARGETS WILL CROSS AND THE CLUTTER RESIDUE WILL NOT CROSS
Ó°ÈÊ *,"6 /Ê /",Ê 1 /" 5SING "ARTONS APPROACH THE MAXIMUM IMPROVEMENT FACTOR ) AGAINST ZERO MEAN CLUTTER WITH A GAUSSIAN SHAPED SPECTRUM FOR DIFFERENT IMPLEMENTATIONS OF THE FINITE IMPULSE RESPONSE BINOMIAL WEIGHT -4) CANCELER SEE 3ECTION IS
¤ F ³ ) y ¥ R ´ ¦ PS F µ
¤ F ³ ) y ¥ R ´ ¦ PS F µ
) y
¤ FR ³ ¥¦ PS F ´µ
WHERE ) IS THE -4) IMPROVEMENT FACTOR FOR THE SINGLE DELAY COHERENT CANCELER ) IS THE -4) IMPROVEMENT FACTOR FOR THE DUAL DELAY COHERENT CANCELER ) IS THE -4) IMPROVE MENT FACTOR FOR THE TRIPLE DELAY COHERENT CANCELER RF IS THE RMS FREQUENCY SPREAD OF THE GAUSSIAN CLUTTER POWER SPECTRUM IN HERTZ AND FR IS THE RADAR REPETITION FREQUENCY IN HERTZ 7HEN THE VALUES OF RF FOR SCANNING MODULATION IN %Q ARE SUBSTITUTED IN THE ABOVE EQUATIONS FOR ) THE LIMITATION ON ) DUE TO SCANNING IS
N N ) y N ) y ) y
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&)'52% 4HEORETICAL -4) IMPROVEMENT FACTOR DUE TO SCAN MODULATION GAUSSIAN ANTENNA PATTERN N NUMBER OF PULSES WITHIN THE ONE WAY HALF POWER BEAMWIDTH
4HESE RELATIONSHIPS ARE SHOWN GRAPHICALLY IN &IGURE 4HIS DERIVATION ASSUMES A LINEAR SYSTEM 4HAT IS IT IS ASSUMED THAT THE VOLTAGE ENVELOPE OF THE ECHO SIGNALS AS THE ANTENNA SCANS PAST A POINT TARGET IS IDENTICAL TO THE TWO WAY ANTENNA VOLTAGE PATTERN 4HIS ASSUMPTION OF A LINEAR SYSTEM MAY BE UNREALISTIC FOR SOME PRACTICAL -4) SYSTEMS WITH RELATIVELY FEW HITS PER BEAMWIDTH HOWEVER AS DISCUSSED IN 3ECTION 4HE SCANNING LIMITATION DOES NOT APPLY TO A SYSTEM THAT CAN STEP SCAN SUCH AS A PHASED ARRAY .OTE HOWEVER THAT SUFFICIENT PULSES MUST BE TRANSMITTED TO INITIAL IZE THE FILTER BEFORE USEFUL OUTPUTS MAY BE OBTAINED &OR EXAMPLE WITH A THREE PULSE BINOMIAL WEIGHT CANCELER THE FIRST TWO TRANSMITTED PULSES INITIALIZE THE CANCELER AND A USEFUL OUTPUT IS NOT AVAILABLE UNTIL AFTER THE THIRD PULSE HAS BEEN TRANSMITTED &EEDBACK OR INFINITE IMPULSE RESPONSE ))2 FILTERS WOULD NOT BE USED WITH A STEP SCAN SYSTEM BECAUSE OF THE LONG TRANSIENT SETTLING TIME OF THE FILTERS 4HE LIMITATION ON ) DUE TO INTERNAL CLUTTER FLUCTUATIONS CAN BE DETERMINED BY SUB STITUTING THE APPROPRIATE VALUE OF RF INTO %QS TO "Y LETTING RF RVK WHERE RV IS THE RMS VELOCITY SPREAD OF THE CLUTTER THE LIMITATION ON ) CAN BE PLOTTED FOR DIFFERENT TYPES OF CLUTTER AS A FUNCTION OF THE WAVELENGTH K AND THE PULSE REPETITION FREQUENCY FR 4HIS IS DONE FOR ONE TWO AND THREE DELAY BINOMIAL WEIGHT CANCELERS IN &IGURE &IGURE AND &IGURE 4HE VALUES OF 6" GIVEN ARE THE FIRST BLIND SPEED OF THE RADAR OR WHERE THE FIRST BLIND SPEED 6" WOULD BE FOR A STAGGERED 02& SYSTEM IF STAGGERING WERE NOT USED 4HE IMPROVEMENT FACTOR SHOWN IN THESE FIGURES FOR RAIN AND CHAFF IS BASED ON THE ASSUMPTION THAT THE AVERAGE VELOCITY OF THE RAIN AND CHAFF HAS BEEN COMPENSATED FOR SO THAT THE RETURNS ARE CENTERED IN THE CANCELER REJECTION NOTCH 5NLESS SUCH COMPENSATION IS PROVIDED THE -4) OFFERS LITTLE OR NO IMPROVEMENT FOR RAIN AND CHAFF 4WO FURTHER LIMITATIONS ON ) ARE THE EFFECT OF PULSE TO PULSE REPETITION PERIOD STAG GERING COMBINED WITH CLUTTER SPECTRAL SPREAD FROM SCANNING AND INTERNAL CLUTTER MOTION
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&)'52% -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE RMS VELOCITY SPREAD OF CLUTTER FOR A TWO PULSE BINOMIAL WEIGHT CANCELER
4HESE LIMITATIONS PLOTTED IN &IGURE AND &IGURE APPLY TO ALL CANCELERS WHETHER SINGLE OR MULTIPLE 4HE DERIVATION OF THESE LIMITATIONS AND A MEANS OF AVOIDING THEM BY THE USE OF TIME VARYING WEIGHTS ARE GIVEN IN h3TAGGER $ESIGN 0ROCEDURESv IN 3ECTION
Ó°ÇÊ "*/ 1 Ê - Ê"Ê 1// ,Ê / ,4HE STATISTICAL THEORY OF DETECTION OF SIGNALS IN GAUSSIAN NOISE PROVIDES THE REQUIRED FRAMEWORK FOR THE OPTIMUM DESIGN OF RADAR CLUTTER FILTERS 3UCH THEORETICAL RESULTS ARE IMPORTANT TO THE DESIGNER OF A PRACTICAL -4) OR -4$ SYSTEM IN THAT THEY ESTAB LISH UPPER BOUNDS ON THE ACHIEVABLE PERFORMANCE IN A PRECISELY SPECIFIED CLUTTER ENVIRONMENT )T SHOULD BE NOTED HOWEVER THAT OWING TO THE EXTREME VARIABILITY OF THE CHARACTERISTICS OF REAL CLUTTER RETURNS POWER LEVEL DOPPLER SHIFT SPECTRUM SHAPE SPECTRAL WIDTH ETC ANY ATTEMPT TO ACTUALLY APPROXIMATE THE PERFORMANCE OF SUCH OPTIMUM FILTERS FOR THE DETECTION OF TARGETS IN CLUTTER REQUIRES THE USE OF ADAPTIVE METHODS 4HE ADAPTIVE METHODS MUST ESTIMATE THE UNKNOWN CLUTTER STATISTICS AND
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&)'52% -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE RMS VELOCITY SPREAD OF CLUTTER FOR A THREE PULSE BINOMIAL WEIGHT CANCELER
SUBSEQUENTLY IMPLEMENT THE CORRESPONDING OPTIMUM FILTER !N EXAMPLE OF SUCH AN ADAPTIVE -4) SYSTEM IS DISCUSSED IN 3ECTION &OR A SINGLE RADAR PULSE WITH A DURATION OF A FEW MICROSECONDS THE DOPPLER SHIFT DUE TO AIRCRAFT TARGET MOTION IS A SMALL FRACTION OF THE SIGNAL BANDWIDTH AND CONVEN TIONAL -4) AND PULSE DOPPLER PROCESSING ARE NOT APPLICABLE )T IS WELL KNOWN THAT THE CLASSICAL SINGLE PULSE hMATCHEDv FILTER PROVIDES OPTIMUM RADAR DETECTION PERFORMANCE WHEN USED IN A WHITE NOISE BACKGROUND !GAINST CLUTTER RETURNS THAT HAVE THE SAME SPECTRUM AS THE TRANSMITTED RADAR PULSE THE MATCHED FILTER IS NO LONGER OPTIMUM BUT THE POTENTIAL IMPROVEMENT IN THE OUTPUT SIGNAL TO CLUTTER RATIO BY DESIGNING A MODIFIED OPTIMIZED FILTER IS USUALLY INSIGNIFICANT 7HEN THE DURATION OF THE TRANSMITTED RADAR SIGNAL WHETHER #7 OR A REPETITIVE TRAIN OF . IDENTICAL PULSES IS COMPARABLE WITH OR GREATER THAN THE RECIPROCAL OF ANTICIPATED TARGET DOPPLER SHIFTS THE DIFFERENCE BETWEEN A CONVENTIONAL WHITE NOISE MATCHED FIL TER OR COHERENT INTEGRATOR AND A FILTER OPTIMIZED TO REJECT THE ACCOMPANYING CLUTTER BECOMES SIGNIFICANT 4HE CHARACTERISTICS OF THE CLUTTER ARE CHARACTERIZED BY THE COVARI ANCE MATRIX &# OF THE . CLUTTER RETURNS )F THE POWER SPECTRUM OF THE CLUTTER IS DENOTED
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&)'52% -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE RMS VELOCITY SPREAD OF CLUTTER FOR A FOUR PULSE BINOMIAL WEIGHT CANCELER
3# F AND THE CORRESPONDING AUTOCORRELATION FUNCTION IS 2# TI n TJ THEN THE ELEMENTS OF &# ARE GIVEN BY
& IJ 2# TI T J
WHERE TI IS THE TRANSMISSION TIME OF THE ITH PULSE &OR EXAMPLE FOR A GAUSSIAN SHAPED CLUTTER SPECTRUM WE HAVE
3# F 0#
§ F FD ¶ EXP ¨ · P S F ¨© S F ·¸
WHERE 0# IS THE TOTAL CLUTTER POWER RF IS THE STANDARD DEVIATION OF THE CLUTTER SPECTRAL WIDTH AND FD IS THE AVERAGE DOPPLER SHIFT OF THE CLUTTER 4HE CORRESPONDING AUTOCOR RELATION FUNCTION IS
2# T 0# EXP PS F T EXP J P FDT
WHERE S IS THE SEPARATION IN TIME OF TWO CONSECUTIVE CLUTTER RETURNS
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&)'52% !PPROXIMATE -4) IMPROVEMENT FACTOR LIMITATION DUE TO PULSE TO PULSE REPETITION PERIOD STAGGERING AND SCANNING ALL CANCELER FIGURATIONS )D" LOG ;N F = F MAXIMUM PERIOD MINIMUM PERIOD
&OR TWO PULSES SEPARATED IN TIME BY THE INTERPULSE PERIOD 4 THE COMPLEX CORRELATION COEFFICIENT BETWEEN TWO CLUTTER RETURNS IS
R4 EXP PS F 4 EXP J P FD4
4HE SECOND FACTOR IN THIS EXPRESSION REPRESENTS THE PHASE SHIFT CAUSED BY THE DOPPLER SHIFT OF THE CLUTTER RETURNS &OR A KNOWN TARGET DOPPLER SHIFT THE RECEIVED TARGET RETURN CAN BE REPRESENTED BY AN . DIMENSIONAL VECTOR
S !3 F
WHERE !3 IS THE SIGNAL AMPLITUDE AND THE ELEMENTS OF THE VECTOR F ARE FI EXP ;JOFSTI= /N THE BASIS OF THIS DESCRIPTION OF SIGNAL AND CLUTTER IT HAS BEEN SHOWN THAT THE OPTI MUM DOPPLER FILTER WILL HAVE WEIGHTS GIVEN BY
W /04 & # S
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&)'52% !PPROXIMATE -4) IMPROVEMENT FACTOR LIMITATION DUE TO PULSE TO PULSE STAGGERING AND INTERNAL CLUTTER MOTION ALL CANCELER CONFIGURATIONS )D" LOG ;K F FR RV = F MAXIMUM PERIODMINIMUM PERIOD
AND THE CORRESPONDING SIGNAL TO CLUTTER IMPROVEMENT IS
)3#2
W4OPT S S4 W OPT W4OPT & # W OPT
WHERE THE ASTERISK DENOTES COMPLEX CONJUGATION AND SUPERSCRIPT 4 IS THE TRANSPOSITION OPERATOR !N EXAMPLE WHERE THE OPTIMUM PERFORMANCE IS DETERMINED FOR THE CASE OF CLUTTER AT ZERO DOPPLER HAVING A GAUSSIAN SHAPED SPECTRUM WITH A NORMALIZED WIDTH OF RF4 IS SHOWN IN &IGURE )N THIS CASE A COHERENT PROCESSING INTERVAL OF #0) NINE PULSES WAS ASSUMED AND THE LIMITATION DUE TO THERMAL NOISE WAS IGNORED BY SETTING THE CLUTTER LEVEL AT D" ABOVE NOISE )T SHOULD BE KEPT IN MIND THAT %Q FOR THE OPTIMUM WEIGHTS WILL YIELD A DIF FERENT RESULT FOR EACH DIFFERENT TARGET DOPPLER SHIFT SO THAT A LARGE NUMBER OF PARALLEL FILTERS WOULD BE NEEDED TO APPROXIMATE THE OPTIMUM PERFORMANCE EVEN WHEN THE CLUTTER CHARACTERISTICS ARE KNOWN EXACTLY !S AN EXAMPLE THE RESPONSE OF THE OPTIMUM FILTER DESIGNED FOR ONE PARTICULAR TARGET DOPPLER FREQUENCY LABELED AS POINT ! IN &IGURE IS SHOWN IN A BROKEN LINE !T APPROXIMATELY o FROM THE DESIGN DOPPLER THE PERFOR MANCE STARTS TO FALL SIGNIFICANTLY BELOW THE OPTIMUM
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&)'52% /PTIMUM SIGNAL TO CLUTTER RATIO IMPROVEMENT )3#2 FOR GAUSSIAN SHAPED CLUTTER SPECTRUM AND A #0) OF NINE PULSES CLUTTER TO NOISE RATIO D"
!LSO SHOWN IN &IGURE IS A HORIZONTAL LINE LABELED hAVERAGE 3#2 IMPROVE MENTv 4HIS INDICATES THE LEVEL CORRESPONDING TO THE AVERAGE OF THE OPTIMUM 3#2 CURVE ACROSS ONE DOPPLER INTERVAL AND MAY BE CONSIDERED AS A FIGURE OF MERIT FOR A MULTIPLE FILTER DOPPLER PROCESSOR SOMEWHAT ANALOGOUS TO THE -4) IMPROVEMENT FAC TOR DEFINED FOR A SINGLE DOPPLER FILTER )N &IGURE THE OPTIMUM AVERAGE )3#2 HAS BEEN COMPUTED FOR SEVERAL DIFFERENT VALUES OF THE #0) AS A FUNCTION OF THE NORMALIZED SPECTRUM WIDTH 4HESE RESULTS MAY BE USED AS A POINT OF REFERENCE FOR PRACTICAL DOPPLER
&)'52% 2EFERENCE CURVE OF OPTIMUM AVERAGE 3#2 IMPROVEMENT FOR A GAUSSIAN SHAPED CLUTTER SPECTRUM
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PROCESSOR DESIGNS AS DISCUSSED IN 3ECTION .OTE THAT FOR RF4 y THE AVERAGE 3#2 IMPROVEMENT IS DUE ONLY TO THE COHERENT INTEGRATION OF ALL THE PULSES IN THE #0) !N -4) FILTER CAN ALSO BE DESIGNED BASED ON THE CRITERION OF MAXIMIZING THE SIGNAL TO CLUTTER IMPROVEMENT AT A SPECIFIC TARGET DOPPLER (OWEVER SUCH A DESIGN WILL USUALLY PROVIDE SUBOPTIMUM PERFORMANCE AT ALL OTHER TARGET DOPPLERS 4HE SINGLE EXCEPTION IS THE TWO PULSE -4) CANCELER WHICH PROVIDES OPTIMUM PERFORMANCE FOR ALL TARGET DOPPLERS ! MORE ATTRACTIVE APPROACH FOR DESIGNING AN OPTIMUM -4) FILTER IS TO MAXIMIZE ITS IMPROVEMENT FACTOR OR CLUTTER ATTENUATION 4O DESIGN AN OPTIMUM -4) FILTER USING IMPROVEMENT FACTOR AS THE CRITERION THE COVARIANCE MATRIX OF THE CLUTTER RETURNS AS GIVEN BY %Q IS AGAIN THE STARTING POINT !S SHOWN BY #APON THE WEIGHTS OF THE OPTI MUM -4) FILTER ARE FOUND AS THE EIGENVECTOR CORRESPONDING TO THE SMALLEST EIGENVALUE OF THE CLUTTER COVARIANCE MATRIX AND THE -4) IMPROVEMENT FACTOR IS EQUAL TO THE INVERSE OF THE SMALLEST EIGENVALUE 4HE OPTIMUM IMPROVEMENT FACTOR FOR THE THREE MODELS FOR THE SPECTRUM OF LAND CLUTTER INTRODUCED IN 3ECTION HAVE BEEN COMPUTED BASED ON THIS ABOVE APPROACH &OR THE GAUSSIAN CLUTTER SPECTRUM THE OPTIMUM IMPROVEMENT FACTOR IS SHOWN IN &IGURE AS A FUNCTION OF THE RMS RELATIVE SPECTRUM WIDTH ASSUMING ZERO MEAN FOR THE SPECTRUM #ALCULATIONS ARE SHOWN FOR -4) CANCELERS OF ORDER . THROUGH &OR THE POLYNOMIAL CLUTTER SPECTRUM THE OPTIMUM IMPROVEMENT FACTOR IS SHOWN IN &IGURE AGAIN AS A FUNCTION OF THE 2-3 RELATIVE SPECTRUM WIDTH ASSUMING ZERO MEAN FOR THE SPECTRUM &INALLY FOR THE EXPONENTIAL CLUTTER SPECTRUM MODEL THE OPTIMUM IMPROVEMENT FAC TOR IS SHOWN IN &IGURE AGAIN AS A FUNCTION OF THE 2-3 RELATIVE SPECTRUM WIDTH ASSUMING ZERO MEAN FOR THE SPECTRUM
&)'52% /PTIMUM IMPROVEMENT FACTOR FOR GAUSSIAN SPECTRUM MODEL
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&)'52% /PTIMUM IMPROVEMENT FACTOR FOR POLYNOMIAL CLUTTER SPECTRUM MODEL
&)'52% /PTIMUM IMPROVEMENT FACTOR FOR "ILLINGSLEYS EXPONENTIAL SPECTRUM MODEL
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&)'52% #OMPARISON OF -4) IMPROVEMENT FACTOR OF BINOMIAL WEIGHT -4) AND OPTIMUM -4) AGAINST A GAUSSIAN SHAPED CLUTTER SPECTRUM
)N &IGURE THE IMPROVEMENT FACTOR OF AN -4) USING THE OPTIMUM WEIGHTS IS COMPARED WITH THE BINOMIAL COEFFICIENT -4) FOR DIFFERENT VALUES OF THE RELATIVE CLUTTER SPECTRAL SPREAD AND SHOWN AS A FUNCTION OF THE NUMBER OF PULSES IN THE #0) 4HESE RESULTS AGAIN ASSUME A GAUSSIAN SHAPED CLUTTER SPECTRUM &OR TYPICAL NUMBERS OF PULSES IN THE -4) THREE TO FIVE THE BINOMIAL COEFFICIENTS ARE REMARKABLY ROBUST AND PROVIDE A PERFORMANCE WHICH IS WITHIN A FEW DECIBELS OF THE OPTIMUM !GAIN IT SHOULD BE NOTED THAT ANY ATTEMPT TO IMPLEMENT AN -4) CANCELER WHICH PERFORMS CLOSE TO THE OPTIMUM WOULD REQUIRE THE USE OF ADAPTIVE TECHNIQUES THAT ESTIMATE THE CLUTTER CHARACTERISTICS IN REAL TIME )F THE ESTIMATE IS IN ERROR THE ACTUAL PERFORMANCE MAY FALL BELOW THAT OF THE BINOMIAL WEIGHT -4) CANCELER
Ó°nÊ /Ê 1// ,Ê / ,Ê - 4HE -4) BLOCK DIAGRAMS INTRODUCED BY &IGURES AND AND WHOSE RESPONSE WAS DISCUSSED IN DETAIL IN 3ECTION CONSIDERED A SINGLE DELAY CANCELER )T IS POSSIBLE TO UTILIZE MORE THAN ONE DELAY AND TO INTRODUCE FEEDBACK ANDOR FEEDFORWARD PATHS AROUND THE DELAYS TO CHANGE THE -4) SYSTEM RESPONSE TO TARGETS OF DIFFERENT VELOCITIES &ILTERS WITH ONLY FEEDFORWARD PATHS ARE CALLED FINITE IMPULSE RESPONSE &)2 FILTERS AND FILTERS THAT INCORPORATE FEEDBACK ARE CALLED INFINITE IMPULSE RESPONSE ))2 FILTERS OR RECURSIVE FILTERS -ULTIPLE DELAY CANCELERS HAVE WIDER CLUTTER REJECTION NOTCHES THAN SINGLE DELAY CANCELERS 4HE WIDER REJECTION NOTCH ENCOMPASSES MORE OF THE CLUTTER SPECTRUM AND THUS INCREASES THE -4) IMPROVEMENT FACTOR ATTAINABLE WITH A GIVEN CLUTTER SPECTRAL DISTRIBUTION
$ELAY IS USED HERE TO REPRESENT AN INTERPULSE MEMORY FOR AN -4) FILTER !N &)2 FILTER WITH ONE DELAY IS A TWO PULSE FILTER &OR FEEDBACK ))2 FILTERS IT IS INAPPROPRIATE TO CALL THEM TWO PULSE OR THREE PULSE ETC FILTERS BECAUSE THEY REQUIRE A NUMBER OF PULSES TO REACH STEADY STATE
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&)'52% $IRECT &ORM OR CANONICAL FORM OF ANY -4) FILTER DESIGN
! GENERAL BLOCK DIAGRAM MODEL APPLICABLE TO ANY -4) FILTER IS SHOWN IN &IGURE 4HIS MODEL HAS BEEN DENOTED THE h$IRECT &ORM v OR THE CANONICAL FORM IN THE TERMINOL OGY SURVEY PRESENTED IN 2ABINER ET AL )T CAN BE SHOWN THAT AN -4) FILTER AS SHOWN IN &IGURE CAN BE DIVIDED INTO A CASCADE OF SECOND ORDER SECTIONS AS SHOWN IN &IGURE 7HEN A NUMBER OF SINGLE DELAY FEEDFORWARD CANCELERS ARE CASCADED IN SERIES THE OVERALL FILTER VOLTAGE RESPONSE IS KN SINN O FD4 WHERE K IS THE TARGET AMPLITUDE N IS THE NUMBER OF DELAYS FD IS THE DOPPLER FREQUENCY AND 4 IS THE INTERPULSE PERIOD 4HE CASCADED SINGLE DELAY CANCELERS CAN BE REARRANGED AS A TRANSVERSAL FILTER AND THE WEIGHTS FOR EACH PULSE ARE THE BINOMIAL COEFFICIENTS WITH ALTERNATING SIGN FOR TWO PULSES FOR THREE PULSES FOR FOUR PULSES AND SO ON #HANGES OF THE BINOMIAL FEEDFORWARD COEFFICIENTS ANDOR THE ADDITION OF FEEDBACK MODIFY THE
&)'52% -4) SHOWN AS CASCADED FORM OF SECOND ORDER SECTION A IS FOR EVEN ORDER AND B IS FOR ODD ORDER WITH FIRST ORDER SECTION AT END
-4) 2!$!2
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&)'52% .TH ORDER &)2 -4) CANCELER BLOCK DIAGRAM
FILTER CHARACTERISTICS 7ITHIN THIS CHAPTER REFERENCE TO BINOMIAL WEIGHT CANCELERS REFERS TO CANCELERS WITH THE N SINN O FD4 TRANSFER FUNCTION 4HE BLOCK DIAGRAM OF THIS TYPE OF -4) CANCELER IS SHOWN IN &IGURE &IGURE TO &IGURE REPRESENT TYPICAL VELOCITY RESPONSE CURVES OBTAINABLE FROM ONE TWO AND THREE DELAY CANCELERS 3HOWN ALSO ARE THE CANCELER CONFIGURATIONS ASSUMED WITH CORRESPONDING : PLANE POLE ZERO DIAGRAMS 4HE : PLANE IS THE COMB FILTER EQUIVALENT OF THE 3 PLANE WITH THE LEFT HAND SIDE OF THE 3 PLANE TRANSFORMED TO THE INSIDE OF THE UNIT CIRCLE CENTERED AT : :ERO FREQUENCY IS AT : J 4HE STABILITY REQUIREMENT IS THAT THE POLES OF THE : TRANSFER FUNCTION LIE WITHIN THE UNIT CIRCLE :EROS MAY BE ANYWHERE
&)'52% /NE DELAY CANCELER
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2!$!2 (!.$"//+
&)'52% 4WO DELAY CANCELER
4HESE VELOCITY RESPONSE CURVES ARE CALCULATED FOR A SCANNING RADAR SYSTEM WITH HITS PER ONE WAY D" BEAMWIDTH !N ANTENNA BEAM SHAPE OF SIN 5 5 TERMI NATED AT THE FIRST NULLS WAS ASSUMED 4HE SHAPE OF THESE CURVES EXCEPT VERY NEAR THE BLIND SPEEDS IS ESSENTIALLY INDEPENDENT OF THE NUMBER OF HITS PER BEAMWIDTH OR THE ASSUMED BEAM SHAPE 4HE ORDINATE LABELED hRESPONSEv REPRESENTS THE SINGLE PULSE SIGNAL TO NOISE OUTPUT OF THE -4) RECEIVER RELATIVE TO THE SIGNAL TO NOISE RESPONSE OF A NORMAL LINEAR RECEIVER FOR THE SAME TARGET 4HUS ALL THE RESPONSE CURVES ARE NORMALIZED WITH RESPECT TO THE NOISE POWER GAIN FOR THE GIVEN CANCELER CONFIGURATION 4HE INTERSECTION AT THE ORDINATE REPRESENTS THE NEGATIVE DECIBEL VALUE OF ) THE -4) IMPROVEMENT FACTOR FOR A POINT CLUTTER TARGET PROCESSED IN A LINEAR SYSTEM
-4) 2!$!2
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&)'52% 4HREE DELAY CANCELER
"ECAUSE THESE CURVES SHOW THE SIGNAL TO NOISE RESPONSE FOR EACH OUTPUT PULSE FROM THE -4) CANCELER THE INHERENT LOSS INCURRED IN A SCANNING RADAR WITH -4) PROCESSING DUE TO THE REDUCTION OF THE EFFECTIVE NUMBER OF INDEPENDENT PULSES INTEGRATED IS NOT APPARENT 4HIS LOSS IS D" FOR A PULSE CANCELER AND D" FOR A PULSE CANCELER ASSUMING A LARGE NUMBER OF PULSES )F QUADRATURE -4) CHANNELS SEE 3ECTION ARE NOT EMPLOYED THERE IS AN ADDITIONAL LOSS OF TO D" 4HE ABSCISSA OF THESE CURVES 66" REPRESENTS THE RATIO OF TARGET VELOCITY 6 TO THE BLIND SPEED 6" K FR WHERE K IS THE RADAR WAVELENGTH AND FR IS THE AVERAGE 02& OF THE RADAR 4HE ABSCISSA CAN ALSO BE INTERPRETED AS THE RATIO OF THE TARGET DOPPLER FRE QUENCY TO THE AVERAGE 02& OF THE RADAR 4HE CANCELER CONFIGURATIONS SHOWN ARE NOT THE MOST GENERAL FEEDFORWARD FEEDBACK NETWORKS POSSIBLE 0AIRS OF DELAYS ARE REQUIRED TO LOCATE ZEROS AND POLES ELSEWHERE
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2!$!2 (!.$"//+
THAN ON THE REAL AXIS OF THE : PLANE )N THE CONFIGURATIONS SHOWN THE ZEROS ARE CON STRAINED TO THE UNIT CIRCLE 4O MOVE THE ZEROS OFF OF THE UNIT CIRCLE WHICH MAY BE DONE TO CONTROL THE FLATNESS OF THE FILTER PASSBAND RESPONSE REQUIRES A CONFIGURATION SIMILAR TO THE ELLIPTIC FILTER CONFIGURATION SHOWN IN &IGURE LATER IN THIS CHAPTER 4HE TRIPLE CANCELER CONFIGURATION SHOWN IS SUCH THAT TWO OF THE ZEROS CAN BE MOVED AROUND THE UNIT CIRCLE IN THE : PLANE -OVING THE ZEROS CAN PROVIDE A OR D" INCREASE IN THE -4) IMPROVEMENT FACTOR FOR SPECIFIC CLUTTER SPECTRAL SPREADS AS COMPARED WITH KEEPING ALL THREE ZEROS AT THE ORIGIN .OTE THE WIDTH OF THE REJECTION NOTCHES FOR THE DIFFERENT BINOMIAL WEIGHT CANCELER CONFIGURATIONS )F THE D" RESPONSE RELATIVE TO AVERAGE RESPONSE IS USED AS THE MEA SURING POINT THE REJECTION IS OF ALL TARGET DOPPLERS FOR THE SINGLE CANCELER FOR THE DUAL CANCELER AND FOR THE TRIPLE CANCELER #ONSIDER THE DUAL CANCELER %LIMINATING OF THE DOPPLERS MEANS LIMITING THE SYSTEM TO A LONG TERM AVERAGE OF SINGLE SCAN PROBABILITY OF DETECTION &EEDBACK CAN BE USED TO NARROW THE REJECTION NOTCH WITHOUT MUCH DEGRADATION OF ) )F FEEDBACK IS USED TO INCREASE THE IMPROVEMENT FACTOR THE SINGLE SCAN PROBABILITY OF DETECTION BECOMES WORSE &IGURE SHOWS THE IMPROVEMENT FACTOR LIMITATION DUE TO SCANNING FOR CANCELERS WITH FEEDBACK 4HESE CURVES WERE CALCULATED ASSUMING A SIN 5 5 ANTENNA PATTERN TERMINATED AT THE FIRST NULLS 4HE NO FEEDBACK CURVES SHOWN IN &IGURE ARE ALMOST INDISTINGUISHABLE FROM THE THEORETICAL CURVES DERIVED FOR A GAUSSIAN PATTERN SHOWN IN &IGURE /NE OF THE CURVES SHOWING THE EFFECT OF FEEDBACK ON THE TRIPLE CANCELER IS NOT STRAIGHT BECAUSE TWO OF THE THREE ZEROS ARE NOT AT THE ORIGIN BUT HAVE BEEN MOVED ALONG THE UNIT CIRCLE THE OPTIMUM AMOUNT FOR HITS PER BEAMWIDTH 4HUS AT HITS PER BEAMWIDTH THESE TWO ZEROS ARE TOO FAR REMOVED FROM THE ORIGIN TO BE VERY EFFECTIVE
&)'52% )MPROVEMENT FACTOR LIMITATION DUE TO SCANNING FOR CANCELERS WITH FEEDBACK
-4) 2!$!2
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)N THEORY IT IS POSSIBLE TO SYNTHESIZE ALMOST ANY VELOCITY RESPONSE CURVE WITH DIGI TAL FILTERS !S MENTIONED EARLIER FOR EACH PAIR OF POLES AND PAIR OF ZEROS ON THE : PLANE TWO DELAY SECTIONS ARE REQUIRED 4HE ZEROS ARE CONTROLLED BY THE FEEDFORWARD PATHS AND THE POLES BY THE FEEDBACK PATHS 6ELOCITY RESPONSE SHAPING CAN BE ACCOMPLISHED BY THE USE OF FEEDFORWARD ONLY WITHOUT THE USE OF FEEDBACK 4HE PRINCIPAL ADVANTAGE OF NOT USING FEEDBACK IS THE EXCELLENT TRANSIENT RESPONSE OF THE CANCELER AN IMPORTANT CONSIDERATION IN A PHASED ARRAY OR WHEN PULSE INTERFERENCE NOISE IS PRESENT )F A PHASED ARRAY RADAR SHOULD USE A FEEDBACK CANCELER MANY PULSES WOULD HAVE TO BE GATED OUT AFTER THE BEAM HAS BEEN REPOSITIONED BEFORE THE CANCELER TRANSIENT RESPONSE HAS SETTLED TO A TOLERABLE LEVEL !N INITIALIZATION TECHNIQUE HAS BEEN PROPOSED TO ALLEVIATE THIS PROBLEM BUT IT PRO VIDES ONLY PARTIAL REDUCTION IN THE TRANSIENT SETTLING TIME )F FEEDFORWARD ONLY IS USED ONLY THREE OR FOUR PULSES HAVE TO BE GATED OUT AFTER MOVING THE BEAM 4HE DISADVAN TAGE OF USING FEEDFORWARD FOR VELOCITY RESPONSE SHAPING IS THAT AN ADDITIONAL DELAY AND THEREFORE AN ADDITIONAL TRANSMIT PULSE MUST BE PROVIDED FOR EACH ZERO USED TO SHAPE THE RESPONSE &IGURE SHOWS THE VELOCITY RESPONSE AND : PLANE DIAGRAM OF A FEEDFORWARD ONLY SHAPED RESPONSE FOUR PULSE CANCELER !LSO SHOWN ARE THE VELOCITY RESPONSES OF A FIVE PULSE FEEDFORWARD CANCELER AND A THREE PULSE FEEDBACK CANCELER &OR THE CANCELERS SHOWN THE IMPROVEMENT FACTOR CAPABILITY OF THE THREE PULSE CANCELER IS ABOUT D" BETTER THAN THE SHAPED RESPONSE FOUR PULSE FEEDFORWARD CANCELER INDE PENDENT OF CLUTTER SPECTRAL SPREAD 4HE FIVE PULSE CANCELER RESPONSE SHOWN IS A LINEAR PHASE -4) FILTER DESCRIBED BY :VEREV 4HE FOUR ZEROS ARE LOCATED ON THE : PLANE REAL AXIS AT AND -UCH OF THE LITERATURE ON FILTER SYNTHESIS DESCRIBES LINEAR PHASE FILTERS BUT FOR -4) APPLICATIONS LINEAR PHASE IS OF NO IMPORTANCE !LMOST IDENTICAL FILTER RESPONSES CAN BE OBTAINED WITH NONLINEAR PHASE FILTERS THAT REQUIRE FEWER PULSES AS SHOWN IN &IGURE "ECAUSE ONLY A FIXED NUMBER OF PULSES IS AVAILABLE DURING THE TIME ON TARGET NONE SHOULD BE WASTED 4HUS ONE SHOULD CHOOSE THE NONLINEAR PHASE FILTER THAT USES FEWER PULSES 3TAGGER $ESIGN 0ROCEDURES 4HE INTERVAL BETWEEN RADAR PULSES MAY BE CHANGED TO MODIFY THE TARGET VELOCITIES TO WHICH THE -4) SYSTEM IS BLIND 4HE INTERVAL MAY BE CHANGED ON A PULSE TO PULSE DWELL TO DWELL EACH DWELL BEING A FRACTION OF THE BEAMWIDTH OR SCAN TO SCAN BASIS %ACH APPROACH HAS ADVANTAGES 4HE ADVANTAGES OF THE SCAN TO SCAN METHOD ARE THAT IT IS EASIER TO BUILD A STABLE TRANSMITTER AND MUL TIPLE TIME AROUND CLUTTER IS CANCELED IN A POWER AMPLIFIER -4) SYSTEM 4HE TRANSMIT TER STABILIZATION NECESSARY FOR GOOD OPERATION OF AN UNSTAGGERED -4) IS A SIGNIFICANT CHALLENGE 4O STABILIZE THE TRANSMITTER SUFFICIENTLY FOR PULSE TO PULSE OR DWELL TO DWELL STAGGER OPERATION IS CONSIDERABLY MORE DIFFICULT 4YPICALLY PULSE TO PULSE STAGGERING IS USED WITH -4) PROCESSING WHEREAS DWELL TO DWELL STAGGERING IS USED WITH -4$ FILTER BANK PROCESSING &OR MANY -4) APPLICATIONS PULSE TO PULSE OR DWELL TO DWELL STAGGERING IS PREF ERABLE TO SCAN TO SCAN STAGGERINGo &OR EXAMPLE IF A BINOMIAL WEIGHTED THREE PULSE CANCELER THAT HAS WIDE REJECTION NOTCHES IS EMPLOYED AND IF SCAN TO SCAN PULSE STAGGERING IS USED OF THE DESIRED TARGETS WOULD BE MISSING ON EACH SCAN OWING TO DOPPLER CONSIDERATION ALONE 4HIS MIGHT BE INTOLERABLE FOR SOME APPLICATIONS o 4HE CHOICE BETWEEN PULSE TO PULSE STAGGERING AND DWELL TO DWELL -4$ OPERATION IS A SYSTEM CONCEPT DECISION BOTH APPROACHES HAVE THEIR ADVANTAGES &OR EXAMPLE PULSE TO PULSE STAGGERING WILL NOT PROVIDE CANCELING OF CLUTTER IN THE AMBIGUOUS RANGE INTERVALS 7ITH DWELL TO DWELL STAGGERING AN EXTRA TRANSMITTER PULSE ALSO KNOWN AS A FILL PULSE WILL ENABLE CANCELING OF SECOND RANGE INTERVAL CLUTTER
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&)'52% 3HAPED VELOCITY RESPONSE FEEDFORWARD CANCELERS COMPARED WITH THREE PULSE FEEDBACK CANCELER 3EE TEXT FOR FIVE PULSE CANCELER PARAMETERS
7ITH PULSE TO PULSE STAGGERING GOOD RESPONSE CAN BE OBTAINED ON ALL DOPPLERS OF INTEREST ON EACH SCAN )N ADDITION BETTER VELOCITY RESPONSE CAN BE OBTAINED AT SOME DOPPLERS THAN EITHER PULSE INTERVAL WILL GIVE ON A SCAN TO SCAN BASIS 4HIS IS SO BECAUSE PULSE TO PULSE STAGGERING PRODUCES DOPPLER COMPONENTS IN THE PASSBAND OF THE -4) FILTER 0ULSE TO PULSE STAGGERING MAY DEGRADE THE IMPROVEMENT FACTOR ATTAINABLE AS SHOWN IN &IGURE AND &IGURE BUT THIS DEGRADATION MAY NOT BE SIGNIFICANT OR IT CAN BE ELIMINATED BY THE USE OF TIME VARYING WEIGHTS AS DESCRIBED BELOW /NE FURTHER ADVANTAGE OF PULSE TO PULSE STAGGERING IS THAT IT MAY PERMIT ELIMINATING THE USE OF FEEDBACK IN THE CANCELERS USED TO NARROW THE BLIND SPEED NOTCHES WHICH ELIMINATES THE TRANSIENT SETTLING PROBLEM OF THE FEEDBACK FILTERS 4HE OPTIMUM CHOICE OF THE STAGGER RATIO DEPENDS ON THE VELOCITY RANGE OVER WHICH THERE MUST BE NO BLIND SPEEDS AND ON THE PERMISSIBLE DEPTH OF THE FIRST NULL
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&)'52% 6ELOCITY RESPONSE CURVE DUAL CANCELER NO FEEDBACK PULSE INTERVAL RATIO
IN THE VELOCITY RESPONSE CURVE &OR MANY APPLICATIONS A FOUR PERIOD STAGGER RATIO IS BEST AND A GOOD SET OF STAGGER RATIOS CAN BE OBTAINED BY ADDING THE FIRST BLIND SPEED IN 66" TO THE NUMBERS OR 4HUS IN &IGURE p WHERE THE FIRST BLIND SPEED OCCURS AT ABOUT 66" THE STAGGER RATIO IS e ALTERNATING THE LONG AND SHORT PERIODS KEEPS THE TRANSMITTER DUTY CYCLE AS NEARLY CONSTANT AS POSSIBLE AS WELL AS ENSURING GOOD RESPONSE AT THE FIRST NULL WHERE 6 6" &IGURES AND SHOW TWO OTHER PERIOD VELOCITY RESPONSE CURVES )F USING FOUR INTERPULSE PERIODS MAKES THE FIRST NULL TO BE TOO DEEP THEN FIVE INTERPULSE PERIODS MAY BE USED WITH THE STAGGER RATIO OBTAINED BY ADDING THE FIRST BLIND SPEED TO THE NUMBER &IGURE SHOWS A VELOCITY RESPONSE CURVE FOR FIVE PULSE INTERVALS 4HE DEPTH OF THE FIRST NULL CAN BE PREDICTED FROM &IGURE WHICH IS DISCUSSED LATER &OR A RADAR SYSTEM WITH RELATIVELY FEW HITS PER BEAMWIDTH IT IS NOT ADVANTAGEOUS TO USE MORE THAN FOUR OR FIVE DIFFERENT INTERVALS BECAUSE THEN THE RESPONSE TO AN INDIVIDUAL TARGET WILL DEPEND ON WHICH PART OF THE PULSE SEQUENCE OCCURS AS THE PEAK OF THE BEAM PASSES THE TARGET 2ANDOM VARIATION OF THE PULSE INTERVALS IS NOT DESIRABLE UNLESS USED AS AN ELECTRONIC COUNTER COUNTERMEASURE FEATURE BECAUSE IT PERMITS THE NULLS TO BE DEEPER THAN THE OPTIMUM CHOICE OF FOUR OR FIVE PULSE INTERVALS 7HEN THE RATIO OF PULSE INTERVALS IS EXPRESSED AS A SET OF RELATIVELY PRIME INTEGERS IE A SET OF INTEGERS WITH NO COMMON DIVISOR OTHER THAN THE FIRST TRUE BLIND SPEED OCCURS AT
2 2 2 ! 2. 6 6" .
p !LL VELOCITY RESPONSE CURVES PLOTTED HEREIN PRESENT THE AVERAGE POWER RESPONSE OF THE OUTPUT PULSES OF THE CANCELER FOR THE DURATION OF THE TIME ON TARGET FOR A SCANNING RADAR )F STAGGERING WERE USED WITH BATCH PROCESSING SUCH AS IN A PHASED ARRAY THESE CURVES WOULD NOT APPLY FOR A SINGLE OUTPUT &OR EXAMPLE IF THE STAGGER RATIO WAS AND A THREE PULSE &)2 FILTER IS USED IT WOULD BE NECESSARY TO TRANSMIT SIX PULSES WITH INTERPULSE SPACINGS OF AND SUM THE POWER OUTPUT FROM THE FILTER AFTER THE LAST FOUR PULSES WERE TRANSMITTED TO GET THE EQUIVALENT RESPONSE SHOWN IN THESE CURVES e .OTE THAT THE FIRST DIFFERENCES BETWEEN ALL COMBINATIONS OF THE INTEGERS AND ARE 4HIS hPERFECT DIFFERENCE SETv FOR THE STAGGER SEQUENCE IS THE KEY TO THE RELATIVE FLATNESS OF THE RESPONSE CURVES
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&)'52% 6ELOCITY RESPONSE CURVE THREE PULSE BINOMIAL CANCELER PULSE INTERVAL RATIO
&)'52% 6ELOCITY RESPONSE CURVE THREE PULSE BINOMIAL CANCELER PULSE INTERVAL RATIO
&)'52% 6ELOCITY RESPONSE CURVE THREE PULSE BINOMIAL CANCELER PULSE INTERVAL RATIO 4HIS RESPONSE CURVE CONTINUES TO 66" WITH NO DIPS BELOW D" 4HE FIRST BLIND SPEED IS AT 66"
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WHERE 2 2 2 2. ARE THE SET OF INTEGERS AND 6" IS THE BLIND SPEED CORRESPOND ING TO THE AVERAGE INTERPULSE PERIOD 4HE VELOCITY RESPONSE CURVE IS SYMMETRICAL ABOUT ONE HALF OF THE VALUE FROM %Q &EEDBACK AND 0ULSE TO 0ULSE 3TAGGERING 7HEN PULSE TO PULSE STAGGERING IS EMPLOYED THE EFFECT OF FEEDBACK IS REDUCED 3TAGGERING CAUSES A MODULATION OF THE SIGNAL DOPPLER AT OR NEAR THE MAXIMUM RESPONSE FREQUENCY OF THE CANCELER 4HE AMOUNT OF THIS MODULATION IS PROPORTIONAL TO THE ABSOLUTE TARGET DOPPLER SO THAT FOR AN AIRCRAFT FLYING AT 6" THE CANCELER RESPONSE IS ESSENTIALLY INDEPENDENT OF THE FEEDBACK EMPLOYED &IGURE SHOWS A PLOT OF THE EFFECTS OF FEEDBACK ON A DUAL CANCELER SYS TEM WITH HITS PER BEAMWIDTH AND A RATIO OF STAGGER INTERVALS OF 4HE FEED BACK VALUES EMPLOYED ARE SEVERAL OF THOSE USED FOR THE UNSTAGGERED VELOCITY RESPONSE PLOT IN &IGURE )F SCAN TO SCAN PULSE INTERVAL STAGGERING HAD BEEN USED INSTEAD OF PULSE TO PULSE THE NO FEEDBACK RMS RESPONSE FOR THREE SCANS AT A TARGET VELOCITY OF 6" WOULD BE D" 4HE COMPOSITE RESPONSE FOR PULSE TO PULSE STAGGERING HOWEVER IS ONLY D" AT 6" THUS ILLUSTRATING THE ADVANTAGE OF PULSE TO PULSE STAGGERING )MPROVEMENT &ACTOR ,IMITATIONS #AUSED BY 3TAGGERING 7HEN PULSE TO PULSE STAGGERING IS USED IT LIMITS THE ATTAINABLE IMPROVEMENT FACTOR OWING TO THE UNEQUAL TIME SPACING OF THE RECEIVED CLUTTER SAMPLES 4HE CURVES IN &IGURE AND &IGURE WHICH HAVE BEEN REFERRED TO SEVERAL TIMES GIVE THE APPROXIMATE LIMITATION ON ) CAUSED BY PULSE TO PULSE STAGGERING AND EITHER ANTENNA SCANNING OR INTERNAL CLUTTER MOTION 4HEY HAVE BEEN DERIVED AS EXPLAINED BELOW ! TWO DELAY CANCELER WILL PERFECTLY CANCEL A LINEAR WAVEFORM 6T C AT IF IT IS SAMPLED AT EQUAL TIME INTERVALS INDEPENDENT OF THE CONSTANT C OR THE SLOPE A !DDITIONAL DELAY CANCELERS PERFECTLY CANCEL ADDITIONAL WAVEFORM DERIVATIVES EG A THREE DELAY CANCELER WILL PERFECTLY CANCEL 6T C AT BT ! STAGGER SYSTEM WITH TWO PULSE INTERVALS SAMPLES THE LINEAR WAVEFORM AT UNEQUAL INTERVALS AND THEREFORE
&)'52% %FFECT OF FEEDBACK ON THE VELOCITY RESPONSE CURVE DUAL CANCELER PULSE INTERVAL RATIO
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THERE WILL BE A VOLTAGE RESIDUE FROM THE CANCELERS THAT IS PROPORTIONAL TO THE SLOPE A AND INVERSELY PROPORTIONAL TO F WHERE F IS THE RATIO OF THE INTERVALS 4HE APPAR ENT DOPPLER FREQUENCY OF THE RESIDUE WILL BE AT ONE HALF THE AVERAGE REPETITION RATE OF THE SYSTEM AND THUS WILL BE AT THE FREQUENCY OF MAXIMUM RESPONSE OF A BINOMIAL WEIGHT CANCELER 4HE RATE OF CHANGE OF PHASE OR AMPLITUDE OF CLUTTER SIGNALS IN A SCANNING RADAR IS INVERSELY PROPORTIONAL TO THE HITS PER BEAMWIDTH N 4HUS WITH THE USE OF A COMPUTER SIMULATION TO DETERMINE THE PROPORTIONALITY CONSTANT THE LIMITATION ON ) DUE TO STAG GERING IS APPROXIMATELY ¤ N ³ ) y LOG ¥ D" ¦ G ´µ
WHICH IS PLOTTED IN &IGURE 4HESE CURVES WHICH APPLY TO ALL MULTIPLE DELAY CANCELERS GIVE ANSWERS THAT ARE FAIRLY CLOSE TO THE ACTUAL LIMITATION THAT WILL BE EXPERIENCED FOR MOST PRACTICAL STAGGER RATIOS !N EXAMPLE OF THE ACCURACY IS AS FOLLOWS ! SYSTEM WITH HITS PER BEAM WIDTH A FOUR PULSE BINOMIAL WEIGHT CANCELER AND A PULSE INTERVAL RATIO HAS AN IMPROVEMENT FACTOR LIMITATION OF D" DUE TO STAGGERING 4HE CURVE GIVES A LIMITA TION OF D" FOR THIS CASE "UT IF THE SEQUENCE OF PULSE INTERVALS WERE TO BE CHANGED FROM TO THE ACTUAL LIMITATION WOULD BE D" WHICH IS D" LESS THAN THAT INDICATED BY THE CURVE 4HIS OCCURS BECAUSE THE PRIMARY MODULATION WITH A PULSE INTERVAL RATIO LOOKS LIKE A TARGET AT MAXIMUM RESPONSE SPEED WHEREAS THE PRIMARY MODULATION WITH A PULSE INTERVAL RATIO LOOKS LIKE A TARGET AT ONE HALF THE SPEED OF MAXIMUM RESPONSE "ECAUSE IT IS DESIRABLE TO AVERAGE THE TRANSMITTER DUTY CYCLE OVER AS SHORT A PERIOD AS POSSIBLE THE PULSE INTERVAL RATIO WOULD PROBABLY BE CHOSEN FOR A PRACTICAL SYSTEM /NCE %Q FOR THE LIMITATION ON ) DUE TO SCANNING AND STAGGERING IS OBTAINED IT IS POSSIBLE TO DETERMINE THE LIMITATION ON ) DUE TO INTERNAL CLUTTER MOTION AND STAG GERING )F
N
N L FR LF r R P SV SV
FROM %QS AND IS SUBSTITUTED INTO %Q
¤ L FR ³ ¤ L FR ³ ) LOG ¥ r ´µ LOG ¥¦ G S ´µ SV ¦G V
WHERE K IS THE WAVELENGTH FR IS THE AVERAGE PULSE REPETITION FREQUENCY AND RV IS THE RMS VELOCITY SPREAD OF SCATTERING ELEMENTS 4HIS IS PLOTTED IN &IGURE FOR RAIN AND FOR WOODED HILLS WITH A KNOT WIND 4HIS LIMITATION ON THE -4) IMPROVEMENT FACTOR IS INDEPENDENT OF THE TYPE OF CANCELER EMPLOYED 4IME 6ARYING 7EIGHTS 4HE IMPROVEMENT FACTOR LIMITATION CAUSED BY PULSE TO PULSE STAGGERING CAN BE AVOIDED BY THE USE OF TIME VARYING WEIGHTS IN THE CANCELER FORWARD PATHS INSTEAD OF BINOMIAL WEIGHTS 4HE USE OF TIME VARYING WEIGHTS HAS NO APPRECIABLE EFFECT ON THE -4) VELOCITY RESPONSE CURVE 7HETHER THE ADDED COMPLEX ITY OF UTILIZING TIME VARYING WEIGHTS IS DESIRABLE DEPENDS ON WHETHER THE STAGGER
-4) 2!$!2
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LIMITATION IS PREDOMINANT &OR TWO DELAY CANCELERS THE STAGGER LIMITATION IS OFTEN COMPARABLE WITH THE BASIC CANCELER CAPABILITY WITHOUT STAGGERING &OR THREE DELAY CANCELERS THE STAGGER LIMITATION USUALLY PREDOMINATES #ONSIDER THE TRANSMITTER PULSE TRAIN AND THE CANCELER CONFIGURATIONS SHOWN IN &IGURE $URING THE INTERVAL 4. WHEN THE RETURNS FROM TRANSMITTED PULSE 0. ARE BEING RECEIVED THE TWO DELAY CANCELER WEIGHTS SHOULD BE !
#
4. 4.
" # AND THE THREE DELAY CANCELER WEIGHTS SHOULD BE !
#
4. 4. 4.
" # $ 4HESE WEIGHTS HAVE BEEN DERIVED BY ASSUMING THAT THE CANCELERS SHOULD PERFECTLY CANCEL A LINEAR WAVEFORM 6T C AT SAMPLED AT THE STAGGER RATE INDEPENDENT OF THE VALUES OF THE CONSTANT C OR THE SLOPE A !S MENTIONED AT THE BEGINNING OF THIS SECTION A MULTIPLE DELAY CANCELER WITH BINOMIAL WEIGHTS IN AN UNSTAGGERED SYSTEM WILL PERFECTLY CANCEL 6T C AT 4HE CHOICE OF ! IN BOTH CASES IS ARBITRARY )N THE THREE DELAY CANCELER SETTING $ ELIMINATES THE OPPORTUNITY FOR A SECOND ORDER CORRECTION TO CANCEL THE QUADRATIC TERM BT WHICH COULD BE OBTAINED IF $ WERE ALSO TIME VARYING #OMPUTER CALCULATIONS HAVE SHOWN THAT IT IS UNNECESSARY TO VARY $ IN MOST PRACTICAL SYSTEMS
&)'52% 5SE OF TIME VARYING WEIGHTS A PULSE TRAIN B TWO DELAY CANCELER AND C THREE DELAY CANCELER
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2!$!2 (!.$"//+
&)'52% !PPROXIMATE DEPTH OF NULLS IN THE VELOCITY RESPONSE CURVE FOR PULSE TO PULSE STAGGERED -4)
$EPTH OF &IRST .ULL IN 6ELOCITY 2ESPONSE 7HEN SELECTING SYSTEM PARAMETERS IT IS USEFUL TO KNOW THE DEPTH OF THE FIRST FEW NULLS TO BE EXPECTED IN THE VELOCITY RESPONSE CURVE !S DISCUSSED EARLIER THE NULL DEPTHS ARE ESSENTIALLY UNAFFECTED BY FEEDBACK 4HEY ARE ALSO ESSENTIALLY INDEPENDENT OF THE TYPE OF CANCELER EMPLOYED WHETHER SINGLE DUAL OR TRIPLE OR OF THE NUMBER OF HITS PER BEAMWIDTH &IGURE SHOWS APPROXIMATELY WHAT NULL DEPTHS CAN BE EXPECTED VERSUS THE RATIO OF MAXIMUM TO MINIMUM INTERPULSE PERIOD
Ó°Ê /Ê / ,Ê - Ê",Ê7 / ,Ê, ,-4) FILTERS ARE USED AT THE LOWER ELEVATION ANGLES IN WEATHER RADARS TO PREVENT WEATHER ESTIMATES FROM BEING CONTAMINATED WITH GROUND CLUTTER RETURNS )T IS HOWEVER ALSO VERY IMPORTANT TO PRESERVE AN ACCURATE MEASUREMENT OF WEATHER INTENSITY AND PRECIPI TATION RATE 4O MEET THIS DUAL OBJECTIVE -4) FILTERS WITH NARROW FIXED CLUTTER REJECTION NOTCHES AND FLAT PASSBANDS ARE NEEDED 5SE OF A VERY NARROW CLUTTER NOTCH EVEN PERMITS MEASURING WEATHER PRECIPITATION RATES WITH A MEAN RADIAL VELOCITY OF ZERO ALBEIT WITH SOME BIAS 3UCH MEASUREMENT IS POSSIBLE BECAUSE WEATHER USUALLY HAS A WIDE SPEC TRAL SPREADTYPICALLY TO MSWHEREAS FIXED CLUTTER HAS A MUCH NARROWER SPECTRAL SPREADTYPICALLY LESS THAN MS
"IAS AS USED HEREIN REFERS TO THE ERROR IN MEASURING RADAR REFLECTIVITY DUE TO THE CLUTTER NOTCH AND LACK OF FLATNESS OF THE -4) FILTERS 7HEN WEATHER HAS A WIDE SPECTRAL SPREAD AND THE CLUTTER NOTCH OF THE FILTERS IS NARROW THERE IS MINIMAL MEASUREMENT ERROR INDUCED BY THE -4) FILTERS #ONVERSELY WHEN THE WEATHER SPECTRAL WIDTH IS NARROW AND THE RADIAL VELOCITY OF THE WEATHER IS NEAR ZERO SIGNIFICANT ERROR IN THE WEATHER REFLECTIVITY MEASUREMENT WILL EXIST 4HERE ARE OTHER CAUSES OF ERROR BETWEEN RADAR ESTIMATES OF PRECIPITATION RATES AND RAIN GAUGE MEASUREMENTS THAT ARE NOT ADDRESSED HEREIN SUCH AS THE SPATIAL AND TEMPORAL DISTRIBUTION OF RAIN
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%XAMPLES OF WEATHER RADAR APPLICATIONS FOR WHICH -4) FILTERS ARE USED 7EATHER $OPPLER 2ADARS .%82!$732 2ADARS WITH ROTATING ANTENNAS THAT MEASURE PRECIPITATION RATE DOPPLER VELOCITY AND TURBULENCE -EASURES TOTAL RAINFALL AND PROVIDES TORNADO WARNINGS 4ERMINAL $OPPLER 7EATHER 2ADARS 4$72 2ADARS WITH ROTATING ANTENNAS DESIGNED TO DETECT SEVERE WIND SHEAR IN AIRCRAFT APPROACH AND DEPARTURE PATHS CLOSE TO AIRPORTS !IRPORT 3URVEILLANCE 2ADARS 2ADARS WITH ROTATING ANTENNAS DESIGNED FOR AIR TRAFFIC CONTROL FUNCTIONS IN THE TERMINAL AREA BUT WITH A SECONDARY FUNCTION OF DETECTING AND MONITORING SEVERE WEATHER AND WIND SHEAR IN AIRCRAFT APPROACH AND DEPARTURE PATHS 0HASED !RRAY 2ADARS 2ADARS WITH FIXED ELECTRONICALLY SCANNED ANTENNAS DESIGNED FOR MANY FUNCTIONS SUCH AS MISSILE DETECTION AND AIR TRAFFIC CONTROL AND USED CON CURRENTLY FOR MEASURING PRECIPITATION RATES !S AN EXAMPLE THE DESIGN OF ELLIPTIC -4) FILTERS AS USED IN THE 4$72 WILL BE DESCRIBED 4$72 IS A # BAND RADAR USED AT AIRPORTS FOR DETECTION OF DOWNBURSTS MICROBURSTS AND PREDICTION OF WIND DIRECTION %LLIPTIC FILTERS ARE INFINITE IMPULSE RESPONSE ))2 FILTERS THAT HAVE THE SHARPEST POSSIBLE TRANSITION FROM REJECTION NOTCH TO PASSBAND FOR A SPECIFIED LEVEL OF THE CLUTTER REJECTION NOTCH WIDTH AND DEPTH RIPPLE IN THE PASSBAND AND NUMBER OF DELAY SECTIONS SEE /PPENHEIM AND 3CHAFER 4HE ELLIP TIC FILTERS CAN BE FOLLOWED WITH PULSE PAIR PROCESSING FOR ESTIMATION OF WEATHER MEAN VELOCITY AND SPECTRAL WIDTH TURBULENCE 4HERE ARE TWO DRAWBACKS OF ELLIPTIC FILTERS &IRST THE LONG TRANSIENT SETTLING TIME &OR A SCANNING WEATHER RADAR IT TAKES ABOUT FOUR BEAMWIDTHS OF SCANNING AFTER THE TRANSMITTER STARTS PULSING BEFORE CLUTTER ATTENUATION REACHES TO D" 3ECOND IF THE INPUT CLUTTER SIGNAL REACHES THE LIMIT LEVEL IN THE )& RECEIVER THERE WILL BE A SIGNIFICANT TRANSIENT INCREASE OF CLUTTER RESIDUE /NE OF THE ELLIPTIC FILTERS EMPLOYED IN THE ORIGINAL 4$72 RADAR IS USED AS AN EXAMPLE 4$72 OPERATES AT # BAND '(Z 4HE ANTENNA ROTATES AT RPM AND HAS A ONE WAY BEAMWIDTH 4HE 02& IS (Z 4HE ELLIPTIC FILTER DESIGNED FOR THESE PARAMETERS HAS AN IMPROVEMENT FACTOR OF D" ("7 HITS PER ONE WAY D" BEAMWIDTH ARE 4HE SPECIFICATIONS FOR THE ELLIPTIC FILTER FOR THE ABOVE PARAMETERS ARE NORMALIZED STOPBAND EDGE RF4 PASSBAND EDGE RF4 STOP BAND ATTENUATION D" BELOW PEAK FILTER RESPONSE AND PASSBAND RIPPLE D" 4O MEET THESE REQUIREMENTS THE FILTER REQUIRES DELAY SECTIONS WHICH CAN BE IMPLE MENTED AS TWO CASCADED DELAY SECTIONS AS SHOWN IN &IGURE
&)'52% &OUR DELAY ELLIPTIC FILTER USED IN 4$72
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4HE FILTER COEFFICIENTS ARE A A B B
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4HE CALCULATED IMPROVEMENT FACTOR FOR THIS FILTER AGAINST LAND CLUTTER WITH ("7 IS D" AND THE BIAS FOR WEATHER RETURNS WITH SPECTRAL SPREADS OF AND MSEC IS n D" AND n D" RESPECTIVELY WHEN THE RADIAL VELOCITY OF THE WEATHER RETURNS IS V MS &IGURE SHOWS THE ELLIPTIC FILTER #7 RESPONSE AND ITS RESPONSE FOR WEATHER WITH MS AND MS RMS SPECTRAL SPREAD 4HE UNAMBIGUOUS DOPPLER INTERVAL CORRESPONDING TO FD4 IS MS FOR THE PARAMETERS USED TO CALCULATE THIS RESPONSE &IGURE SHOWS THE TIME DOMAIN RESPONSES FOR THIS FILTER AS THE ANTENNA SCANS PAST A POINT OF CLUTTER SUCH AS A WATER TOWER 4HIS FIGURE SHOWS THE INPUT TO THE ELLIPTIC FILTER AND THE RESIDUE OUTPUT ! GAUSSIAN ANTENNA PATTERN IS ASSUMED IN THIS FIGURE 4HE CALCULATED IMPROVEMENT FACTOR FOR THE SEQUENCE SHOWN TOTAL CLUTTER POWER INTO THE FILTER DIVIDED BY TOTAL RESIDUE POWER OUT OF THE FILTER NORMALIZED BY THE NOISE GAIN OF THE FILTER IS D" ! SINX X ANTENNA PATTERN IS ASSUMED FOR THE FOLLOWING THREE FIGURES BUT THE LESSONS TO BE GAINED FROM THESE FIGURES IS ESSENTIALLY INDEPENDENT OF THE ASSUMED BEAM SHAPE &IGURE SHOWS THE FILTER RESPONSE IF THE TRANSMITTER STARTS RADIATING JUST AS A NULL OF THE ANTENNA PATTERN PASSES THE POINT OF CLUTTER 4HE INDIVIDUAL SAMPLES OF RESIDUE ARE OR MORE D" BELOW THE PEAK CLUTTER RETURN 4HE IMPROVEMENT FACTOR FOR THIS SEQUENCE IS D"
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&)'52% 4IME DOMAIN CLUTTER INPUT AND OUTPUT RESIDUE AS ANTENNA SCANS PAST A POINT TARGET
&IGURE SHOWS THE RESIDUE IF THE TRANSMITTER STARTS RADIATING AS THE PEAK OF THE BEAM PASSES THE POINT CLUTTER &ORTY NINE PULSES AFTER THE TRANSMITTER STARTS RADIATING THE RESIDUE HAS DECAYED ONLY D" )T WOULD TAKE AT LEAST ANOTHER PULSES FOR THE RESIDUE TO DECAY TO D" &OR THIS REASON WHEN THE TRANSMITTER STARTS PULSING A SET TLING TIME OF AT LEAST PULSES MUST BE ALLOWED BEFORE USEFUL DATA IS COLLECTED
&)'52% #LUTTER INPUT AND RESIDUE FROM ELLIPTIC FILTER 2ADAR STARTS RADIATING AT PULSE NUMBER
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&)'52% #LUTTER INPUT AND RESIDUE FROM ELLIPTIC FILTER 2ADAR STARTS RADIATING AT PULSE NUMBER
&IGURE SHOWS THE EFFECT OF THE RETURNED SIGNAL IF THE POINT CLUTTER EXCEEDS THE )& LIMIT LEVEL BY D" 7HEN THE SIGNAL REACHES THE LIMIT LEVEL THERE IS A STEP INCREASE OF RESIDUE OF ABOUT D" 4$72 USES CLUTTER MAPS TO NORMALIZE THE RESIDUE FROM THE STRONG POINTS OF CLUTTER THAT EXCEED THE LIMIT LEVEL 4HE WEATHER MODE OF !IRPORT 3URVEILLANCE 2ADARS IS DEMONSTRATED BY FIVE PULSE FINITE IMPULSE RESPONSE &)2 FILTERS USED IN THE !32 AN 3 BAND RADAR USED FOR AIR TRAFFIC CONTROL AT AIRPORTS 4HE DESIGN OF THE FILTERS IS PRIMARILY FOR -OVING 4ARGET $ETECTOR -4$ DETECTION OF AIRCRAFT BUT SPECIAL ATTENTION IS GIVEN TO PROVIDING FLAT PASSBAND RESPONSE FOR ACCURATE WEATHER REFLECTIVITY ESTIMATION 4HE FILTER BANK FOR ("7 IS PICTURED IN &IGURE AND THE COEFFICIENTS ARE SHOWN IN 4ABLE
&)'52% %FFECT OF LIMITING ON ELLIPTIC FILTER RESPONSE
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4!",% !32 #OEFFICIENTS OF !32 0ULSE ,OW 02& &IR &ILTERS
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3ELECTION OF FILTERS IS BASED ON CLUTTER AMPLITUDE INFORMATION STORED IN A CLUTTER MAP 4HE FILTERS ARE SELECTED ON A RANGE CELL BY #0) BASIS 4HESE &)2 CLUTTER FILTERS HAVE THE NARROWEST REJECTION NOTCHES THAT CAN BE OBTAINED WITH FIVE PULSES AND THE INDICATED LEVEL OF FIXED CLUTTER REJECTION (OWEVER THE NOTCHES ARE SIGNIFICANTLY WIDER THAN THOSE OF THE ELLIPTIC FILTERS THUS THEY WILL HAVE GREATER BIAS FOR MEASUREMENT OF WEATHER INTENSITY WHEN THE WEATHER RADIAL VELOCITY IS ZERO &OR PHASED ARRAY RADARS &)2 FILTERS SIMILAR TO THOSE DESCRIBED FOR THE !32 ARE APPLICABLE 4HE FILTERS CAN BE DESIGNED IF THE TIME BUDGET OF THE PHASED ARRAY RADAR ALLOWS TO UTILIZE MORE THAN THE FIVE PULSES PER COHERENT PROCESSING INTERVAL #0) USED BY THE !32 RADAR 5SING MORE PULSES MAKES POSSIBLE NARROWER REJECTION NOTCHES AND THUS LESS BIAS FOR ESTIMATES OF PRECIPITATION WITH ZERO RADIAL VELOCITY
&)'52% 2ESPONSE OF !32 &)2 FILTERS LOW 02& FR PPS FILTERS OPERATING AGAINST FIXED CLUTTER WITH ("7 4HE UNAMBIGUOUS DOPPLER INTERVAL F 4 IS MS FOR THE PARAMETERS USED TO CALCULATE THIS RESPONSE
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Ó°£äÊ 1// ,Ê / ,Ê Ê - !S DISCUSSED IN 3ECTION THE -4$ USES A WAVEFORM CONSISTING OF COHERENT PRO CESSING INTERVALS #0)S OF . PULSES ALL AT THE SAME 02& AND 2& FREQUENCY 4HE 02& AND POSSIBLY THE 2& ARE CHANGED FROM ONE #0) TO THE NEXT 7ITH THIS CONSTRAINT ONLY FINITE IMPULSE RESPONSE &)2 FILTER DESIGNS ARE REALISTIC CANDIDATES FOR THE FILTER BANK DESIGN &EEDBACK FILTERS REQUIRE A NUMBER OF PULSES TO SETTLE AFTER EITHER THE 02& OR THE 2& IS CHANGED AND THUS WOULD NOT BE PRACTICAL 4HE NUMBER OF PULSES AVAILABLE DURING THE TIME WHEN A SURVEILLANCE RADAR BEAM ILLUMINATES A POTENTIAL TARGET POSITION IS DETERMINED BY SYSTEM PARAMETERS AND REQUIRE MENTS SUCH AS BEAMWIDTH 02& VOLUME TO BE SCANNED AND THE REQUIRED DATA UPDATE RATE 'IVEN THE CONSTRAINT ON THE NUMBER OF PULSES ON TARGET ONE MUST DECIDE HOW MANY #0)S SHOULD OCCUR DURING THE TIME ON TARGET AND HOW MANY PULSES PER #0) 4HE COMPROMISE IS USUALLY DIFFICULT /NE WISHES TO USE MORE PULSES PER #0) TO ENABLE THE USE OF BETTER FILTERS BUT ONE ALSO WISHES TO HAVE AS MANY #0)S AS POSSIBLE -ULTIPLE #0)S AT DIFFERENT 02&S AND PERHAPS AT DIFFERENT 2& FREQUENCIES IMPROVE DETECTION AND CAN PROVIDE INFORMATION FOR TRUE RADIAL VELOCITY DETERMINATION 4HE DESIGN OF THE INDIVIDUAL FILTERS IN THE DOPPLER FILTER BANK IS A COMPROMISE BETWEEN THE FREQUENCY SIDELOBE REQUIREMENT AND THE DEGRADATION IN THE COHERENT INTEGRATION GAIN OF THE FILTER 4HE NUMBER OF DOPPLER FILTERS REQUIRED FOR A GIVEN LENGTH OF THE #0) MUST BE BALANCED BETWEEN HARDWARE COMPLEXITY AND THE STRADDLING LOSS AT THE CROSSOVER BETWEEN FILTERS &INALLY THE REQUIREMENT OF PROVIDING A HIGH DEGREE OF CLUTTER SUPPRESSION AT ZERO DOPPLER LAND CLUTTER SOMETIMES INTRODUCES SPECIAL DESIGN CONSTRAINTS 7HEN THE NUMBER OF PULSES IN A #0) IS LARGE q THE SYSTEMATIC DESIGN PRO CEDURE AND EFFICIENT IMPLEMENTATION OF THE FAST &OURIER TRANSFORM &&4 ALGORITHM IS PARTICULARLY ATTRACTIVE 4HROUGH THE USE OF APPROPRIATE WEIGHTING FUNCTIONS OF THE TIME DOMAIN RETURNS IN A SINGLE #0) THE RESULTING FREQUENCY SIDELOBES CAN BE READILY CONTROLLED &URTHER THE NUMBER OF FILTERS EQUAL TO THE ORDER OF THE TRANSFORM NEEDED TO COVER THE TOTAL DOPPLER SPACE EQUAL TO THE RADAR 02& CAN BE CHOSEN INDEPENDENTLY OF THE #0) AS DISCUSSED BELOW !S THE #0) BECOMES SMALLER a IT BECOMES IMPORTANT TO CONSIDER SPECIAL DESIGNS OF THE INDIVIDUAL FILTERS TO MATCH THE SPECIFIC CLUTTER SUPPRESSION REQUIREMENTS AT DIFFERENT DOPPLER FREQUENCIES IN ORDER TO ACHIEVE BETTER OVERALL PERFORMANCE 7HILE SOME SYSTEMATIC PROCEDURES ARE AVAILABLE FOR DESIGNING &)2 FILTERS SUBJECT TO SPECIFIC PASSBAND AND STOPBAND CONSTRAINTS THE STRAIGHTFORWARD APPROACH FOR SMALL #0)S IS TO USE AN EMPIRICAL APPROACH IN WHICH THE ZEROS OF EACH FILTER ARE ADJUSTED UNTIL THE DESIRED RESPONSE IS OBTAINED !N EXAMPLE OF SUCH FILTER DESIGNS IS PRESENTED NEXT %MPIRICAL &ILTER $ESIGN !N EXAMPLE OF AN EMPIRICAL FILTER DESIGN FOR A SIX PULSE #0) FOLLOWS 4HE SIX PULSES PER #0) MAY BE DRIVEN BY SYSTEM CONSIDERATIONS SUCH AS TIME ON TARGET "ECAUSE THE FILTER WILL USE SIX PULSES ONLY FIVE ZEROS ARE AVAILABLE FOR THE FILTER DESIGN THE NUMBER OF ZEROS AVAILABLE IS THE NUMBER OF PULSES MINUS ONE 4HE FILTER DESIGN PROCESS CONSISTS OF PLACING THE ZEROS TO OBTAIN A FILTER BANK RESPONSE THAT CONFORMS TO THE SPECIFIED CONSTRAINTS 4HE EXAMPLE THAT FOLLOWS WAS PRODUCED WITH AN INTERACTIVE COMPUTER PROGRAM WITH WHICH THE ZEROS COULD BE MOVED UNTIL THE DESIRED RESPONSE WAS OBTAINED 4HE ASSUMED FILTER REQUIREMENTS ARE AS FOLLOWS L
0ROVIDE A RESPONSE OF D" IN THE CLUTTER REJECTION NOTCH RELATIVE TO THE PEAK TARGET RESPONSE OF THE MOVING TARGET FILTERS
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0ROVIDE A RESPONSE OF D" FOR CHAFF REJECTION AT VELOCITIES BETWEEN o OF THE AMBIGUOUS DOPPLER FREQUENCY RANGE )N THIS DESIGN ONLY FIVE FILTERS WILL BE IMPLEMENTED 4HREE OF THE FIVE FILTERS WILL REJECT FIXED CLUTTER AND RESPOND TO MOVING TARGETS 4WO FILTERS WILL RESPOND TO TARGETS AT ZERO DOPPLER AND ITS AMBIGUITIES 7ITH GOOD FIXED CLUTTER REJECTION FILTERS IT TAKES TWO OR MORE COHERENT FILTERS TO COVER THE GAP IN RESPONSE AT ZERO VELOCITY
7ITH THE ABOVE CONSIDERATIONS A FILTER BANK CAN BE CONSTRUCTED &IGURE A SHOWS THE FILTER DESIGNED TO RESPOND TO TARGETS IN THE MIDDLE OF THE DOPPLER PASSBAND 4HE SIDELOBES NEAR ZERO VELOCITY ARE D" DOWN FROM THE PEAK THUS PROVIDING GOOD CLUTTER REJECTION FOR CLUTTER WITHIN OF ZERO DOPPLER 4HE D" SIDELOBE PROVIDES CHAFF REJECTION TO o "ECAUSE OF THE CONSTRAINT OF HAVING ONLY FIVE ZEROS AVAILABLE THIS FILTER COULD NOT PROVIDE D" REJECTION TO o &IGURE B SHOWS THE FILTER THAT RESPONDS TO TARGETS AS NEAR AS POSSIBLE TO ZERO DOPPLER WHILE HAVING A ZERO DOPPLER RESPONSE OF D" 4WO ZEROS ARE PLACED NEAR PROVIDING D" RESPONSE TO CLUTTER AT 4HE FILTER SIDELOBES BETWEEN AND DOPPLER PROVIDE THE SPECIFIED CHAFF REJECTION OF D" ! MIRROR IMAGE OF THIS FILTER IS USED FOR THE THIRD MOVING DOPPLER FILTER 4HE MIRROR IMAGE FILTER HAS COEFFICIENTS THAT ARE COMPLEX CONJUGATES OF THE ORIGINAL FILTER COEFFICIENTS &IGURE C SHOWS THE FIRST FILTER DESIGNED FOR RESPONSE AT ZERO DOPPLER #ONSIDERATIONS HERE ARE THAT THE DOPPLER STRADDLING LOSS OF THE FILTER BANK BE MINIMIZED
&)'52% 3IX PULSE FILTERS FOR TARGETS AT A F 4 B &T F 4 AND C COMBINED RESPONSE OF COMPLETE BANK OF FIVE SIX PULSE FILTERS
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THIS DICTATES THE LOCATION OF THE PEAK THAT THE RESPONSE TO CHAFF AT DOPPLER BE DOWN D" AND THAT THE MISMATCH LOSS BE MINIMIZED -INIMIZING THE MISMATCH LOSS IS ACCOMPLISHED BY PERMITTING THE FILTER SIDELOBES BETWEEN AND TO RISE AS HIGH AS NEEDED LOWER SIDELOBES IN THIS RANGE INCREASE THE MISMATCH LOSS 4HE SECOND ZERO DOPPLER FILTER IS THE MIRROR IMAGE OF THIS ONE &IGURE D SHOWS THE COMPOSITE RESPONSE OF THE FILTER BANK .OTE THAT THE FILTER PEAKS ARE FAIRLY EVENLY DISTRIBUTED 4HE DIP BETWEEN THE FIRST ZERO DOPPLER FILTER AND THE FIRST MOVING DOPPLER FILTER IS LARGER THAN THE OTHERS PRIMARILY BECAUSE UNDER THE CONSTRAINTS IT IS IMPOSSIBLE TO MOVE THE FIRST DOPPLER FILTER NEARER TO ZERO VELOCITY #HEBYSHEV &ILTER "ANK &OR A LARGER NUMBER OF PULSES IN THE #0) A MORE SYSTEM ATIC APPROACH TO FILTER DESIGN IS DESIRABLE )F A DOPPLER FILTER DESIGN CRITERION IS CHOSEN THAT REQUIRES THE FILTER SIDELOBES OUTSIDE THE MAIN RESPONSE TO BE BELOW A SPECIFIED LEVEL IE PROVIDING A CONSTANT LEVEL OF CLUTTER SUPPRESSION WHILE SIMULTANEOUSLY MINIMIZ ING THE WIDTH OF THE FILTER RESPONSE A FILTER DESIGN BASED ON THE $OLPH #HEBYSHEV DIS TRIBUTION PROVIDES THE OPTIMUM SOLUTION 0ROPERTIES AND DESIGN PROCEDURES BASED ON THE $OLPH #HEBYSHEV DISTRIBUTION CAN BE FOUND IN THE ANTENNA LITERATURE !N EXAMPLE OF A FILTER DESIGN FOR A #0) OF PULSES AND A SIDELOBE REQUIREMENT OF D" IS SHOWN IN &IGURE 4HE PEAK FILTER RESPONSE CAN BE LOCATED ARBITRARILY IN FREQUENCY BY ADDING A LINEAR PHASE TERM TO THE FILTER COEFFICIENTS 4HE TOTAL NUMBER OF FILTERS IMPLEMENTED TO COVER ALL DOPPLER FREQUENCIES IS A DESIGN OPTION TRADING STRADDLING LOSS AT THE FILTER CROSSOVER FREQUENCIES AGAINST IMPLEMENTA TION COMPLEXITY !N EXAMPLE OF A COMPLETE DOPPLER FILTER BANK IMPLEMENTED WITH NINE UNIFORMLY SPACED FILTERS IS SHOWN IN &IGURE 4HE PERFORMANCE OF THIS DOPPLER FILTER BANK AGAINST THE CLUTTER MODEL CONSIDERED IN &IGURE IS SHOWN IN &IGURE 4HIS GRAPH SHOWS THE SIGNAL TO CLUTTER RATIO IMPROVEMENT AGAINST CLUTTER AT ZERO DOPPLER AS A FUNCTION OF TARGET DOPPLER FREQUENCY /NLY THE RESPONSE OF THE FILTER PROVIDING THE GREATEST IMPROVEMENT IS PLOTTED AT EACH TARGET DOPPLER &OR COMPARISON THE OPTIMUM CURVE FROM &IGURE IS SHOWN BY A BROKEN LINE AND THUS PROVIDES A DIRECT ASSESSMENT OF HOW WELL THE #HEBYSHEV FILTER DESIGN PERFORMS AGAINST A GIVEN CLUTTER MODEL !LSO SHOWN IS THE AVERAGE 3#2 IMPROVEMENT FOR BOTH THE OPTIMUM AND THE #HEBYSHEV FILTER BANK
&)'52% #HEBYSHEV &)2 FILTER DESIGN WITH D" DOPPLER SIDELOBES
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&)'52% $OPPLER FILTER BANK OF D" #HEBYSHEV FILTERS #0) PULSES
&INALLY &IGURE SHOWS THE AVERAGE 3#2 IMPROVEMENT OF THE D" #HEBYSHEV DOPPLER FILTER BANK AS WELL AS THE OPTIMUM CURVE FROM &IGURE AS A FUNCTION OF THE RELATIVE SPECTRUM SPREAD OF THE CLUTTER /WING TO THE FINITE NUMBER OF FILTERS IMPLEMENTED IN THE FILTER BANK THE AVERAGE 3#2 IMPROVEMENT WILL CHANGE BY A SMALL AMOUNT IF A DOPPLER SHIFT IS INTRODUCED INTO THE CLUTTER RETURNS 4HIS EFFECT IS ILLUSTRATED BY THE CROSS HATCHED REGION WHICH SHOWS UPPER AND LOWER LIMITS ON THE AVERAGE 3#2 IMPROVEMENT FOR ALL POSSIBLE CLUTTER DOPPLER SHIFTS &OR A SMALLER NUMBER OF FILTERS IN THE DOPPLER FILTER BANK THIS VARIATION WOULD BE GREATER &AST &OURIER 4RANSFORM &ILTER "ANK &OR A LARGE NUMBER OF PARALLEL DOPPLER FILTERS HARDWARE IMPLEMENTATION CAN BE SIMPLIFIED SIGNIFICANTLY THROUGH THE USE OF THE &&4 ALGORITHM 4HE USE OF THIS ALGORITHM CONSTRAINS ALL FILTERS IN THE FILTER BANK TO
&)'52% 3#2 IMPROVEMENT OF D" #HEBYSHEV DOPPLER FILTER BANK COMPARED WITH THE OPTIMUM
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&)'52% !VERAGE 3#2 IMPROVEMENT FOR THE D" #HEBYSHEV FILTER BANK SHOWN IN &IGURE #0) PULSES /PTIMUM IS FROM &IGURE
HAVE IDENTICAL RESPONSES AND THE FILTERS WILL BE UNIFORMLY SPACED ALONG THE DOPPLER AXIS 4HE NUMBER OF FILTERS IMPLEMENTED FOR A GIVEN SIZE OF THE #0) CAN HOWEVER BE VARIED &OR EXAMPLE A GREATER NUMBER OF FILTERS CAN BE REALIZED BY EXTENDING THE RECEIVED DATA WITH EXTRA ZERO VALUES ALSO KNOWN AS ZERO PADDING AFTER THE RECEIVED RETURNS HAVE BEEN APPROPRIATELY WEIGHTED IN ACCORDANCE WITH THE DESIRED FILTER RESPONSE EG #HEBYSHEV &ILTER "ANK $ESIGNS 5SING #ONSTRAINED /PTIMIZATION 4ECHNIQUES &OR A GREATER NUMBERS OF PULSES IN THE #0) AND WHEN THE ECONOMY OF THE &&4 IMPLEMENTA TION OF A DOPPLER FILTER BANK CAN BE REPLACED BY A &)2 IMPLEMENTATION MORE DESIRABLE &)2 FILTER RESPONSES CAN BE REALIZED THROUGH THE USE OF APPROPRIATE NUMERICAL DIGITAL FILTER DESIGN TECHNIQUES 4HE GOAL IS SIMILAR TO THAT PURSUED WITH THE EMPIRICAL FILTER DESIGNS DISCUSSED EARLIER BUT FILTERS WITH A LARGE NUMBER OF TAPS CAN BE DESIGNED TO EXACTING SPECIFICATIONS !S AN EXAMPLE CONSIDER THE DESIGN OF A DOPPLER FILTER BANK FOR AN 3 BAND '(Z RADAR USING A #0) OF . PULSES USING A 02& OF K(Z !SSUME THAT THE RADAR REQUIRE MENTS CALL FOR A SUPPRESSION OF STATIONARY LAND CLUTTER BY D" AND A SUPPRESSION OF MOVING CLUTTER RAIN BY D" &OR THE FILTER DESIGN A CLUTTER ATTENUATION D" BELOW THESE REQUIREMENTS WILL BE NEEDED TO KEEP THE SENSITIVITY LOSS DUE TO THE CLUTTER RESIDUE BELOW D" AND ALSO BECAUSE EACH DOPPLER FILTER WILL HAVE A COHERENT GAIN OF AROUND LOG D" THIS MUST BE ADDED TO THE FILTER DESIGN SPECIFICATION AS WELL 4HE TOTAL 3 BAND DOPPLER SPACE FOR THE ABOVE RADAR PARAMETERS IS MS AND ASSUMING THAT THE LAND CLUTTER SUPPRESSION REGION HAS TO BE o MS AND THAT THE MOVING CLUTTER SUPPRES SION REGION HAS TO BE o MS THE CONSTRAINT FOR ALL DOPPLER FILTER DESIGNS NORMALIZED TO THEIR PEAK IS AS SHOWN IN &IGURE 5SING A SIGNAL PROCESSING TOOLBOX DEVELOPED BY $R $AN 0 3CHOLNIK OF THE .AVAL 2ESEARCH ,ABORATORY A DOPPLER FILTER BANK MEETING THE ABOVE CONSTRAINTS WAS DESIGNED 4HE FIRST FILTER WHICH HAS ITS PEAK LOCATED AS CLOSE AS POSSIBLE TO THE LEFT EDGE OF THE CONSTRAINT BOX IS SHOWN IN &IGURE WITH THE ABSCISSA NORMALIZED TO THE TOTAL AVAIL ABLE DOPPLER SPACE
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4HE MISMATCH LOSS OF THIS FILTER IS ,M D" WHICH IS WELL BELOW THAT OF A D" $OLPH #HEBYSHEV FILTER BANK ,M D" &OR THE REMAINING FILTERS A RELATIVE SPAC ING OF $ WAS USED BUT THIS COULD BE REDUCED IN ORDER TO MINIMIZE DOPPLER STRADDLING LOSSES 4HE THIRD FILTER IN THE FILTER BANK IS SHOWN IN &IGURE
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4HE MISMATCH LOSS HAS NOW BEEN REDUCED TO D" &INALLY THE COMPLETE DOPPLER FILTER BANK IS SHOWN IN &IGURE 4HIS FILTER BANK COULD BE AUGMENTED WITH ADDI TIONAL FILTERS AROUND ZERO DOPPLER BUT THESE WOULD NOT MEET THE DESIGN CONSTRAINTS DISCUSSED ABOVE 4HE MAIN BENEFIT OF A CUSTOMIZED DOPPLER FILTER BANK DESIGN AS
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6 ,Ê / %LSEWHERE IN THIS CHAPTER 3ECTIONS AND PARTICULARLY )& BANDPASS LIMITERS HAVE BEEN DISCUSSED AS A MEANS OF PREVENTING RECEIVED CLUTTER SIGNALS FROM EXCEED ING THE RANGE OF THE !$ CONVERTERS NORMALIZING -4) CLUTTER RESIDUE CAUSED BY SYSTEM INSTABILITIES AND NORMALIZING RESIDUE DUE TO THE SPECTRAL SPREAD OF hFIXED CLUTTERv CAUSED BY EITHER SCANNING OR WIND BLOWN MOTION 4HERE ARE OCCASIONAL CLUTTER RESIDUE SPIKES WHEN CLUTTER EXCEEDS THE LIMIT LEVEL AND IN THE PAST THE ENERGY FROM THESE SPIKES OF RESIDUE HAS BEEN SUPPRESSED BY FURTHER REDUCTION OF THE LIMIT LEVEL 7HEN LIMITERS HAVE BEEN USED TO NORMALIZE THE ENERGY OF CLUTTER RESIDUE SPIKES THE AVERAGE IMPROVEMENT FACTOR OF THE -4) SYSTEMS DRASTICALLY DETERIORATES 4HE EQUA TIONS FOR ) IMPROVEMENT FACTOR OF A SCANNING RADAR IN 3ECTION ARE BASED ON LINEAR THEORY &IELD MEASUREMENTS HOWEVER HAVE SHOWN THAT MANY SCANNING MULTIPLE DELAY -4) RADAR SYSTEMS FALL CONSIDERABLY SHORT OF THE PREDICTED PERFORMANCE 4HIS OCCURS BECAUSE THE )& BANDPASS LIMITERS HAVE BEEN USED TO SUPPRESS THE ENERGY OF THE RESIDUE SPIKES THAT ARE CAUSED BY THE LIMITING ACTION ,ATER IN THIS SECTION IT IS SHOWN THAT THE USE OF A BINARY DETECTION SCHEME INSTEAD OF A DRASTIC REDUCTION OF THE LIMIT LEVEL CAN BE USED TO MAINTAIN A CLUTTER REJECTION PERFORMANCE CLOSE TO LINEAR THEORY PREDICTION IN THE RESOLUTION CELLS WHERE CLUTTER LIMITING OCCUR !N EXAMPLE OF HOW LIMITING THE DYNAMIC RANGE ADJUSTS THE RESIDUE IS SHOWN IN THE -4) 00) PHOTOGRAPHS SHOWN IN &IGURE 4HE RANGE RINGS ARE AT MI INTERVALS
&)'52% %FFECT OF LIMITERS A D" IMPROVEMENT FACTOR D" INPUT DYNAMIC RANGE AND B D" IMPROVEMENT FACTOR D" INPUT DYNAMIC RANGE
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! NUMBER OF BIRDS ARE SHOWN ON THE DISPLAY 4HE RESIDUE FROM CLUTTER IN THE LEFT PHOTO GRAPH IS SOLID OUT TO NMI AND THEN DECREASES UNTIL IT IS ALMOST ENTIRELY GONE AT NMI 4HE -4) IMPROVEMENT FACTOR IN BOTH PICTURES IS D" BUT THE INPUT DYNAMIC RANGE PEAK SIGNAL TO RMS NOISE TO THE CANCELER WAS CHANGED FROM TO D" BETWEEN THE TWO PICTURES !N AIRCRAFT FLYING OVER THE CLUTTER IN THE FIRST MI IN THE LEFT HAND PICTURE COULD NOT BE DETECTED NO MATTER HOW LARGE ITS RADAR CROSS SECTION )N THE RIGHT HAND PIC TURE THE AIRCRAFT COULD BE DETECTED IF THE TARGET TO CLUTTER CROSS SECTION RATIO WERE SUF FICIENT !LTHOUGH THIS EXAMPLE IS FROM MANY YEARS AGO THE PRINCIPLE IS STILL THE SAME EVEN THOUGH CURRENT -4) IMPROVEMENT FACTORS ARE BETTER BY TENS OF D"S 2ESTRICTION OF THE )& DYNAMIC RANGE IS STILL A VERY EFFICIENT WAY OF NORMALIZING CLUTTER RESIDUE DUE TO SYSTEM INSTABILITIES OR CLUTTER SPECTRAL SPREAD TO SYSTEM NOISE 4HIS IS TRUE WHETHER OR NOT THE RADAR USES PULSE COMPRESSION 0RIOR TO THE DEVELOPMENT OF MODERN CLUTTER MAPS FOR CONTROLLING FALSE ALARMS CAUSED BY CLUTTER RESIDUE OR THE MORE RECENT SUGGESTION THAT BINARY INTEGRATION CAN MITIGATE IMPULSE LIKE RESIDUE THE USE OF )& LIMITING WAS ESSENTIAL FOR FALSE ALARM CONTROL IN AN -4) RADAR 3UCH LIMITING HOWEVER SERIOUSLY AFFECTS THE MEAN IMPROVE MENT FACTOR OBTAINABLE WITH A SCANNING LIMITED MULTIPLE DELAY CANCELER BECAUSE OF THE INCREASED SPECTRAL SPREAD OF THE CLUTTER THAT EXCEEDS THE LIMIT LEVEL 0ART OF THE ADDITIONAL CLUTTER SPECTRAL COMPONENTS COMES FROM THE SHARP DISCONTINUITY IN THE ENVELOPE OF RETURNS AS THE CLUTTER REACHES THE LIMIT LEVEL ! TIME DOMAIN EXAMPLE OF THIS PHENOMENON IS SHOWN IN &IGURE FOR A RADAR WITH . HITS PER BEAM WIDTH /N THE LEFT IS A POINT TARGET THAT DOES NOT EXCEED THE LIMIT LEVEL ON THE RIGHT IS A POINT TARGET THAT EXCEEDS THE LIMIT LEVEL BY D" .OTE THAT FOR THIS EXAMPLE ) DEGRADES BY D" FOR THE DUAL CANCELER AND BY D" FOR THE TRIPLE CANCELER 4HE EXACT RESULT OF THIS CALCULATION DEPENDS ON THE ASSUMED SHAPE OF THE ANTENNA PATTERN FOR THIS EXAMPLE A SINU PATTERN TERMINATED AT THE FIRST NULLS WAS ASSUMED U 4HERE IS A COMPARABLE IMPROVEMENT FACTOR DEGRADATION DUE TO SPECTRAL SPREADING OF LIMITED DISTRIBUTED CLUTTER &IGURES AND SHOW THE EXPECTED MEAN IMPROVEMENT FACTOR FOR TWO THREE AND FOUR PULSE CANCELERS AS A FUNCTION OF R, THE RATIO OF THE RMS CLUTTER AMPLITUDE TO THE LIMIT LEVEL (ITS PER ONE WAY HALF POWER BEAMWIDTH ARE INDICATED BY . !N EXAMPLE OF CLUTTER RESIDUE FROM SIMULATED HARD LIMITED DISTRIBUTED CLUTTER IS TAKEN FROM (ALL AND 3HRADER &IGURE SHOWS A POLAR PLOT OF PART OF A LINEAR CLUT TER SEQUENCE FOR A SCANNING RADAR WITH . HITS PER BEAMWIDTH 4HIS LINEAR CLUTTER SEQUENCE IS CONSECUTIVE COMPLEX VOLTAGE RETURNS FROM ONE RANGE CELL OF DISTRIBUTED CLUTTER &IGURE SHOWS THE PHASE AND AMPLITUDE OF THIS SEQUENCE )F THIS CLUTTER SEQUENCE WERE D" STRONGER AND PASSED THROUGH A 6 )& LIMITER ONLY THE PHASE INFORMATION WOULD REMAIN %ACH PULSE WOULD HAVE A 6 AMPLITUDE 7HEN THE RESULTING LIMITED CLUTTER SEQUENCE IS PASSED THROUGH A THREE PULSE CANCELER COEFFICIENTS n THE OUTPUT RESIDUE APPEARS AS IN &IGURE A 4HE CORRESPOND ING PULSE TO PULSE IMPROVEMENT FACTOR IS SHOWN &IGURE B 4HE EXPECTED THREE PULSE CANCELER IMPROVEMENT FACTOR FROM EQUATION FOR A LINEAR SYSTEM WITH . IS ) N D" )N &IGURE B IT IS SEEN THAT THIS LEVEL OF ) IS ACHIEVED FOR MOST OF THE PULSES WITH ONLY TWO PULSES HAVING VERY LOW VALUES OF ) 4HE STATISTICS FOR THE DISTRIBUTION OF ) FOR THE THREE PULSE CANCELER FOR HARD LIMITED DISTRIBUTED CLUTTER ARE SHOWN IN &IGURE .OTE THAT FOR . LESS THAT OF THE HARD LIMITED SAMPLES HAVE AN IMPROVEMENT FACTOR LESS THAN D" WHEREAS ALMOST OF THE SAMPLES EXCEED THE ) EXPECTED FOR A LINEAR SYSTEM
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&)'52% )MPROVEMENT FACTOR RESTRICTION CAUSED BY A LIMITER
4HE TIME DOMAIN ILLUSTRATION SHOWN PREVIOUSLY IN &IGURE LEADS TO THE CONCLU SION OF (ALL AND 3HRADER THAT USING AN - OUT OF . BINARY DETECTOR AT THE OUTPUT OF AN -4) FILTER WILL PRECLUDE FALSE ALARMS FROM THE CLUTTER RESIDUES CAUSED BY LIMITING &IGURE SHOWS IN ADDITION TO CLUTTER RESIDUE THE RETURNS FROM A TARGET THAT WAS SUPERIMPOSED ON THE DISTRIBUTED CLUTTER PRIOR TO THE CLUTTER PLUS TARGET SEQUENCE PASS ING THROUGH THE )& LIMITING PROCESS /NE CAN SEE THAT MANY OF THE INDIVIDUAL PULSE RETURNS FROM THE TARGET EXCEED THE DETECTION THRESHOLD WHEREAS ONLY FOUR OF THE CLUTTER RESIDUE PULSES EXCEED THE THRESHOLD 4O SUMMARIZE 4HE -4) IMPROVEMENT FACTOR IN A MAJORITY OF LIMITING CLUTTER CELLS EXCEEDS THE AVERAGE IMPROVEMENT FACTOR OBTAINED WITH LINEAR PROCESSING CELLS WITH POOR -4) IMPROVEMENT FACTOR CAN BE REJECTED WITH BINARY DETECTION PROCESSING AND THEREFORE EXCELLENT -4) PERFORMANCE CAN BE OBTAINED EVEN IN REGIONS OF CLUTTER THAT EXCEED THE )& DYNAMIC RANGE
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&)'52% -EAN IMPROVEMENT FACTOR RESTRICTION VERSUS AMOUNT OF LIMITING AND CLUTTER SPECTRAL SPREAD FOR A TWO PULSE CANCELER AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% AND ( 2 7ARD AND 7 7 3HRADER Ú )%%%
&)'52% -EAN IMPROVEMENT FACTOR RESTRICTION VERSUS AMOUNT OF LIMITING AND CLUTTER SPECTRAL SPREAD FOR A THREE PULSE CANCELER AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% AND ( 2 7ARD AND 7 7 3HRADER Ú )%%%
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&)'52% -EAN IMPROVEMENT FACTOR RESTRICTION VERSUS AMOUNT OF LIMITING AND CLUTTER SPECTRAL SPREAD FOR A FOUR PULSE CANCELER AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% AND ( 2 7ARD AND 7 7 3HRADER Ú )%%%
.OTE THAT THIS DISCUSSION OF BINARY DETECTION IS ADDRESSED TO THE SPECTRAL DISTRIBUTION OF REAL CLUTTER THAT WHEN VIEWED IN THE TIME DOMAIN BEFORE LIMITING HAS A SMOOTHLY VARYING CHANGE OF THE AMPLITUDE AND PHASE OF THE CLUTTER VECTOR 4HIS IS DISTINCT FROM CLUTTER VARIATIONS DUE TO SYSTEM INSTABILITIES THAT ARE NOISE LIKE WHEREIN THE SYSTEM DYNAMIC RANGE SHOULD BE LIMITED TO PREVENT THE INSTABILITY RESIDUE FROM EXCEEDING THE SYSTEM NOISE LEVEL
&)'52% 0OLAR REPRESENTATION OF A LINEAR CLUTTER SEQUENCE FOR HITS PER BEAMWIDTH AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%%
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&)'52% ,INEAR CLUTTER SEQUENCE AMPLITUDE AND PHASE FOR HITS PER BEAMWIDTH AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%%
&)'52% A 4HREE PULSE CANCELER RESIDUE AND B IMPROVEMENT FACTOR FOR HARD LIMITED CLUTTER SEQUENCE FOR . HITS PER BEAMWIDTH AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%%
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&)'52% !FTER -4) PROCESSING OF THE HARD LIMITED DISTRIBUTED CLUTTER SEQUENCE . AND A TARGET SUPERIMPOSED ON THE CLUTTER SEQUENCE THE RESIDUE SPIKES ARE DISTINCTLY DIFFERENT FROM THE TARGET RETURNS ! BINARY - OF . DETECTOR WILL REJECT THE RESIDUE AND KEEP THE TARGET AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%%
Ó°£ÓÊ , ,Ê-9-/ Ê-/ /9Ê , +1, /3YSTEM )NSTABILITIES .OT ONLY DO THE ANTENNA MOTION AND CLUTTER SPECTRUM AFFECT THE IMPROVEMENT FACTOR THAT IS ATTAINABLE BUT SYSTEM INSTABILITIES ALSO PLACE A LIMIT ON -4) PERFORMANCE 4HESE INSTABILITIES COME FROM THE STALO AND COHO FROM THE TRANS MITTER PULSE TO PULSE FREQUENCY CHANGE IF A PULSED OSCILLATOR AND FROM PULSE TO PULSE
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PHASE CHANGE IF A POWER AMPLIFIER FROM THE INABILITY TO LOCK THE COHO PERFECTLY TO THE PHASE OF THE REFERENCE PULSE FROM TIME JITTER AND AMPLITUDE JITTER ON THE PULSES AND FROM QUANTIZATION NOISE OF THE !$ CONVERTER 0HASE INSTABILITIES WILL BE CONSIDERED FIRST )F THE PHASES OF CONSECUTIVE RECEIVED PULSES RELATIVE TO THE PHASE OF THE COHO DIFFER BY SAY RAD A LIMITATION OF D" IS IMPOSED ON ) 4HE RAD CLUTTER VECTOR CHANGE WOULD BE EQUIVALENT TO A TARGET VECTOR D" WEAKER THAN THE CLUTTER BEING SUPERIMPOSED ON THE CLUTTER AS SHOWN IN &IGURE )N THE POWER AMPLIFIER -4) SYSTEM SHOWN IN &IGURE PULSE TO PULSE PHASE CHANGES IN THE TRANSMITTED PULSE CAN BE INTRODUCED BY THE PULSED AMPLIFIER 4HE MOST COMMON CAUSE OF A POWER AMPLIFIER INTRODUCING PHASE CHANGES IS RIPPLE ON THE HIGH VOLTAGE POWER SUPPLY /THER CAUSES OF PHASE INSTABILITY INCLUDE AC VOLTAGE ON A TRANSMITTER TUBE FILAMENT AND UNEVEN POWER SUPPLY LOADING SUCH AS THAT CAUSED BY PULSE TO PULSE STAGGER )N THE PULSED OSCILLATOR SYSTEM SHOWN IN &IGURE PULSE TO PULSE FREQUENCY CHANGES RESULT IN PHASE RUN OUT DURING THE TRANSMITTED PULSE 0HASE RUN OUT IS THE CHANGE OF THE TRANSMITTED PULSE PHASE DURING THE PULSE DURATION WITH RESPECT TO THE PHASE OF THE REFERENCE OSCILLATOR )F THE COHO LOCKED PERFECTLY TO THE END OF THE TRANS MITTED PULSE A TOTAL PHASE RUN OUT OF RAD DURING THE TRANSMITTED PULSE WOULD THEN PLACE AN AVERAGE LIMITATION OF D" ON THE IMPROVEMENT FACTOR ATTAINABLE 0ULSE TO PULSE FREQUENCY CHANGE IN MICROWAVE OSCILLATORS IS PRIMARILY CAUSED BY HIGH VOLTAGE POWER SUPPLY RIPPLE )N THE PULSED OSCILLATOR SYSTEM A PULSE TO PULSE PHASE DIFFERENCE OF RAD IN LOCKING THE COHO RESULTS IN ) LIMITATION OF D" !S NOTED ELSEWHERE FREQUENCY CHANGE DURING A PULSE FROM A PULSED OSCILLATOR DOES NOT LIMIT ) IF IT REPEATS PRECISELY PULSE TO PULSE 4HE LIMITATIONS ON THE IMPROVEMENT FACTOR THAT ARE DUE TO EQUIPMENT INSTABILITIES IN THE FORM OF FREQUENCY CHANGES OF THE STALO AND COHO BETWEEN CONSECUTIVE TRANSMITTED PULSES ARE A FUNCTION OF THE RANGE OF THE CLUTTER 4HESE CHANGES ARE CHARACTERIZED IN TWO WAYS !LL OSCILLATORS HAVE A NOISE SPECTRUM )N ADDITION CAVITY OSCILLATORS USED BECAUSE THEY ARE READILY TUNABLE ARE MICROPHONIC AND THUS THEIR FREQUENCY MAY VARY AT AN AUDIO RATE 4HE LIMITATION ON THE IMPROVEMENT FACTOR DUE TO FREQUENCY CHANGES IS THE DIFFERENCE IN THE NUMBER OF RADIANS THAT THE OSCILLATOR RUNS THROUGH BETWEEN THE TIME OF TRANSMISSION AND THE TIME OF RECEPTION OF CONSECUTIVE PULSES 4HUS THE IMPROVEMENT FACTOR WILL BE LIMITED TO D" IF O$F 4 RAD WHERE $ F IS THE OSCILLATOR FREQUENCY CHANGE BETWEEN TRANSMITTED PULSES AND 4 IS THE TRANSIT TIME OF THE PULSE TO AND FROM THE TARGET
&)'52% 0HASE INSTABILITY
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&)'52% 0OWER AMPLIFIER SIMPLIFIED BLOCK DIAGRAM
4O EVALUATE THE EFFECTS OF OSCILLATOR PHASE NOISE ON -4) PERFORMANCE THERE ARE FOUR STEPS &IRST DETERMINE THE SINGLE SIDEBAND POWER SPECTRAL DENSITY OF THE PHASE NOISE AS A FUNCTION OF FREQUENCY FROM THE CARRIER 3ECOND INCREASE THIS SPECTRAL DENSITY BY D" 4HIS ACCOUNTS FOR A D" INCREASE BECAUSE BOTH SIDEBANDS OF NOISE AFFECT CLUT TER RESIDUE AND A D" INCREASE BECAUSE THE OSCILLATOR CONTRIBUTES NOISE DURING BOTH TRANSMITTING AND RECEIVING 4HIRD ADJUST THE OSCILLATOR PHASE NOISE SPECTRAL DENSITY DETERMINED ABOVE DUE TO THE FOLLOWING THREE EFFECTS A THE SELF CANCELLATION OF PHASE NOISE BASED ON CORRELATION RESULTING FROM THE TWO WAY RANGE DELAY OF THE CLUTTER OF INTEREST B NOISE REJECTION DUE TO THE FREQUENCY RESPONSE OF THE CLUTTER FILTERS AND C NOISE REJECTION DUE TO THE FREQUENCY RESPONSE OF THE RECEIVER PASSBAND &INALLY AS THE FOURTH STEP INTEGRATE THE ADJUSTED SPECTRAL DENSITY OF THE PHASE NOISE ACROSS THE ENTIRE PASSBAND 4HE RESULT IS THE LIMITATION ON ) DUE TO THE OSCILLATOR NOISE 2ATHER THAN PERFORMING THIS INTEGRATION OF THE RESIDUAL NOISE NUMERICALLY A MUCH SIMPLER ANALYSIS CAN BE CARRIED OUT IF BOTH THE OSCILLATOR PHASE NOISE CHARACTERISTIC AND ALL OF THE ADJUSTMENTS TO PHASE NOISE ARE APPROXIMATED BY STRAIGHT LINES ON A DECIBEL VERSUS LOG FREQUENCY PLOT 4HIS PROCEDURE BECOMES PARTICULARLY SIMPLE WHEN A -4) &)2 FILTER USING BINOMIAL COEFFICIENTS IS ASSUMED 4HE LOCATIONS ALONG THE FREQUENCY AXIS WHERE THE STRAIGHT LINES INTERSECT ARE CALLED BREAK FREQUENCIES 4HIS SIMPLIFIED PROCEDURE WHICH IS SIMILAR TO THAT PRESENTED IN 6IGNERI ET AL IS DESCRIBED IN THE FOLLOWING PARAGRAPHS 4HE FIRST OF THE THREE ADJUSTMENTSOSCILLATOR NOISE SELF CANCELLATION DUE TO THE RANGE OF THE CLUTTER OF INTERESTREDUCES NOISE AT THE LOW FREQUENCIES BY D" PER DECADE BELOW THE BREAK FREQUENCY OF F 42 P (ERE 42 2 C IS THE TIME
&)'52% 0ULSED OSCILLATOR SIMPLIFIED BLOCK DIAGRAM
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&)'52% 3TRAIGHT LINE APPROXIMATION TO TWO DELAY BINOMIAL -4)
DELAY OF THE CLUTTER RETURN 2 IS THE CLUTTER RANGE AND C IS THE SPEED OF LIGHT &OR THE SECOND ADJUSTMENT DUE TO THE FREQUENCY RESPONSE OF THE CLUTTER FILTERS WHICH AS STATED PREVIOUSLY ARE ASSUMED TO BE &)2 CANCELERS WITH BINOMIAL WEIGHTS IT IS NOTED THAT THE RESPONSE AT VERY LOW FREQUENCIES FALL OFF AT D" PER DECADE FOR ONE DELAY D" PER DECADE FOR TWO DELAYS D" PER DECADE FOR THREE DELAYS ETC !S AN EXAMPLE THE APPROXIMATION USED FOR A TWO DELAY -4) FILTER IS SHOWN IN &IGURE 4HE -4) RESPONSE HAS A PEAK VALUE OF y D" RESULTING IN AN AVERAGE NOISE GAIN OF UNITY AND THE STRAIGHT LINE APPROXIMATION FOLLOWS THE LOW FREQUENCY ASYMPTOTE UP TO THE D" LEVEL WHICH OCCURS AT F 4 AND STAYS CONSTANT AT THE D" LEVEL AT ALL HIGHER FREQUENCIES 4HE JUSTIFICATION FOR THE D" APPROXIMATION AT THE HIGHER FREQUEN CIES IS THAT THE OSCILLATOR SPECTRAL DENSITY IS MORE NEARLY CONSTANT AND THE AVERAGE OVER ONE PERIOD OF THE -4) RESPONSE IS UNITY &OR OTHER BINOMIAL COEFFICIENT -4) CANCELERS THE BREAK FREQUENCIES FOR THE START OF THE RESPONSE FALLOFF ARE F 4 FOR ONE DELAY FOR TWO DELAYS FOR THREE DELAYS AND FOR FOUR DELAYS &OR EXAMPLE CONSIDER AN OSCILLATOR WITH SINGLE SIDEBAND PHASE NOISE SPECTRAL DENSITY AS SHOWN IN &IGURE !LL OSCILLATOR NOISE CONTRIBUTIONS ARE ASSUMED TO BE COMBINED INTO THIS ONE CURVE 4HE SINGLE SIDEBAND NOISE IS INCREASED BY D" BECAUSE BOTH SIDEBANDS AFFECT SYSTEM STABILITY AND THE POWER INTEGRATION IS ONLY CARRIED OUT FOR POSITIVE FREQUENCIES AND BY AN ADDITIONAL D" BECAUSE THE OSCILLATOR INTRODUCES NOISE IN BOTH THE UPCONVERSION TO THE TRANSMITTED SIGNAL AND IN THE RECEIVER DOWNCON VERSION PROCESS &IGURE SHOWS THE SPECTRAL MODIFICATIONS DUE TO THE SYSTEM RESPONSES A 4HE FIRST MODIFICATION ACCOUNTS FOR CORRELATION DUE TO THE RANGE TO THE CLUTTER OF INTEREST ;ASSUMED CLUTTER RANGE IS y NMI KM THUS THE BREAK FREQUENCY IS (Z= B 3ECOND A THREE PULSE BINOMIAL WEIGHTED CANCELER IS ASSUMED WITH THE RADAR OPERAT ING AT A 02& OF (Z 4HUS THE BREAK FREQUENCY IS r (Z C 4HIRD THE RECEIVER PASSBAND IS ASSUMED TO EXTEND FROM K(Z TO K(Z WITH RESPECT TO THE )& CENTER FREQUENCY -(: TOTAL PASSBAND AT THE D" POINTS AND DETERMINED BY A TWO POLE FILTER 4HUS THE RECEIVER PASSBAND RESPONSE FALLS OFF AT D" PER DECADE FROM THE BREAK FREQUENCY AT K(Z AS SHOWN
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&)'52% 3INGLE SIDEBAND PHASE NOISE SPECTRAL DENSITY OF A MICROWAVE OSCILLATOR AND THE EFFECTIVE NOISE DENSITY
4HE ADJUSTED PHASE NOISE SPECTRAL DENSITY IS SHOWN IN &IGURE 4HE TOTAL NOISE POWER WITH RESPECT TO THE CARRIER IS DETERMINED BY INTEGRATION OF THE NOISE POWER UNDER THE CURVE 4HE EQUATION FOR THE POWER SPECTRAL DENSITY OF ANY ONE SEGMENT AS A FUNC TION OF FREQUENCY IS
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&)'52% !DJUSTMENTS BASED ON SYSTEM PARAMETERS SEE TEXT TO THE PHASE NOISE OF A MICROWAVE OSCILLATOR
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&)'52% #OMPOSITE ADJUSTMENTS AND ADJUSTED PHASE NOISE SPECTRAL DENSITY
D"C(Z VALUES IN &IGURE CORRESPOND TO LOG 3 &URTHER DENOTING THE PHASE NOISE SPECTRAL DENSITY RELATIVE TO THE CARRIER AT THE END OF THE SEGMENT AS 3 (Zn THE SLOPE IS DEFINED BY
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4HE SLOPE IN D"DECADE IS EQUAL TO A 4HE NOISE POWER CONTRIBUTION CORRESPOND ING TO THIS SEGMENT IS FOUND AS ª 3 A A ALL A w F A A §© F F ¶¸ 0 « 3 ;LNN F LN F = A ¬ FA
4ABLE GIVES THE INTEGRATION FOR THE EXAMPLE 7HEN THE INTEGRATED POWERS FOR ALL SEGMENTS HAVE BEEN CALCULATED THEY ARE SUMMED AND THEN CONVERTED BACK TO D"C 4HE FINAL ANSWER D"C IS THE LIMIT ON ) THAT RESULTS FROM OSCILLATOR NOISE 4HE LIMIT ON )3#2 D" IS ) D" PLUS TARGET INTEGRATION GAIN D" 4!",% )NTEGRATION OF THE 0HASE .OISE 3PECTRAL $ENSITY OF &IGURE WITH !DJUSTMENTS OF
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4IME JITTER OF THE TRANSMITTED PULSES RESULTS IN DEGRADATION OF -4) SYSTEMS 4IME JITTER RESULTS IN FAILURE OF THE LEADING AND TRAILING EDGES OF THE PULSES TO CANCEL THE AMPLITUDE OF EACH UNCANCELLED PART BEING $TS WHERE $T IS THE TIME JITTER AND S IS THE TRANSMITTED PULSE LENGTH 4HE TOTAL RESIDUE POWER IS $TS AND THEREFORE THE LIMITA TION ON THE IMPROVEMENT FACTOR DUE TO TIME JITTER IS ) LOG;T $ T = D" 4HIS LIMIT ON THE IMPROVEMENT FACTOR IS BASED ON A #7 TRANSMITTER PULSE AND ON THE ASSUMP TION THAT THE RECEIVER BANDWIDTH IS MATCHED TO THE DURATION OF THE TRANSMITTED PULSE )N A PULSE COMPRESSION SYSTEM THE RECEIVER BANDWIDTH IS WIDER BY THE TIME BANDWIDTH "S PRODUCT THUS THE CLUTTER RESIDUE POWER AT EACH END OF THE PULSE INCREASES IN PROPORTION TO THE "S PRODUCT 4HE LIMIT ON ) FOR A CHIRP PULSE COMPRESSION SYSTEM IS THEN ) LOG;T $ T " T = &OR PULSE COMPRESSION SYSTEMS EMPLOYING PHASE CODED WAVEFORMS THE FACTOR IN THE PRECEDING EQUATION SHOULD BE MULTIPLIED BY THE NUMBER OF SUBPULSES IN THE WAVEFORM 4HUS FOR EXAMPLE THE LIMIT ON ) FOR A PULSE "ARKER CODE IS
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) LOG
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) LOG
T D" *"T
4HE LIMITATIONS ON THE ATTAINABLE -4) IMPROVEMENT FACTOR ARE SUMMARIZED IN 4ABLE 4HIS DISCUSSION HAS ASSUMED THAT THE PEAK TO PEAK VALUES OF THESE INSTA BILITIES OCCUR ON A PULSE TO PULSE BASIS WHICH IS OFTEN THE CASE IN PULSE TO PULSE STAGGERED -4) OPERATION )F IT IS KNOWN THAT THE INSTABILITIES ARE RANDOM THE PEAK
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4!",% )NSTABILITY ,IMITATIONS
0ULSE TO 0ULSE )NSTABILITY
,IMIT ON )MPROVEMENT &ACTOR
/SCILLATOR PHASE NOISE 3EE DISCUSSION IN TEXT 4RANSMITTER FREQUENCY ) LOG ;O $F S = 3TALO OR COHO FREQUENCY ) LOG ;O $F 4 = 4RANSMITTER PHASE SHIFT ) LOG $E #OHO LOCKING ) LOG $E 0ULSE TIMING ) LOG ;T $T "T = 0ULSE WIDTH ) LOG ;T $07 "T = 0ULSE AMPLITUDE ) LOG !$! !$ JITTER ) LOG ;T * "T = !$ JITTER WITH PULSE COMPRESSION FOLLOWING !$ ) LOG ;T *"T = WHERE $F INTERPULSE FREQUENCY CHANGE S TRANSMITTED PULSE LENGTH 4 TRANSMISSION TIME TO AND FROM TARGET $E INTERPULSE PHASE CHANGE $T TIME JITTER * !$ SAMPLING TIME JITTER "S TIME BANDWIDTH PRODUCT OF PULSE COMPRESSION SYSTEM "S UNITY FOR #7 PULSES $07 PULSE WIDTH JITTER ! PULSE AMPLITUDE 6 $! INTERPULSE AMPLITUDE CHANGE
VALUES SHOWN IN THESE EQUATIONS CAN BE REPLACED BY THE RMS PULSE TO PULSE VALUES WHICH GIVES RESULTS ESSENTIALLY IDENTICAL TO 3TEINBERGS RESULTS )F THE INSTABILITIES OCCUR AT SOME KNOWN FREQUENCY EG HIGH VOLTAGE POWER SUP PLY RIPPLE THE RELATIVE EFFECT OF THE INSTABILITY CAN BE DETERMINED BY LOCATING THE RESPONSE ON THE VELOCITY RESPONSE CURVE FOR THE -4) SYSTEM FOR A TARGET AT AN EQUIVA LENT DOPPLER FREQUENCY )F FOR INSTANCE THE RESPONSE IS D" DOWN FROM THE MAXIMUM RESPONSE THE LIMITATION ON ) IS ABOUT D" LESS SEVERE THAN INDICATED IN THE EQUATIONS IN 4ABLE )F ALL SOURCES OF INSTABILITY ARE INDEPENDENT AS WOULD USUALLY BE THE CASE THEIR INDIVIDUAL POWER RESIDUES CAN BE ADDED TO DETERMINE THE TOTAL LIMITATION ON -4) PERFORMANCE )NTRAPULSE FREQUENCY OR PHASE VARIATIONS DO NOT INTERFERE WITH GOOD -4) OPERATION PROVIDED THEY REPEAT PRECISELY FROM PULSE TO PULSE 4HE ONLY CONCERN IS A LOSS OF SEN SITIVITY IF PHASE RUN OUT DURING THE TRANSMITTED PULSE OR MISTUNING OF THE COHO OR STALO PERMITS THE RECEIVED PULSES TO BE SIGNIFICANTLY DETUNED FROM THE INTENDED )& FREQUENCY )F A RAD PHASE RUN OUT DURING THE PULSE IS PERMITTED THE SYSTEM DETUNING MAY BE AS LARGE AS OS (Z WITH NO DEGRADATION OF -4) PERFORMANCE 4O GIVE AN EXAMPLE OF INTERPULSE STABILITY REQUIREMENTS CONSIDER A -(Z RADAR TRANSMITTING A #7 PULSE OF DURATION S MS AND THE REQUIREMENT THAT NO SINGLE SYSTEM INSTABILITY WILL LIMIT THE -4) IMPROVEMENT FACTOR ATTAINABLE AT A RANGE OF NMI TO LESS THAN D" A VOLTAGE RATIO OF 4HE RMS PULSE TO PULSE TRANSMITTER FREQUENCY CHANGE IF A PULSED OSCILLATOR MUST BE LESS THAN
$F
(Z PT
WHICH IS A STABILITY OF ABOUT PARTS IN
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4HE RMS PULSE TO PULSE TRANSMITTER PHASE SHIFT CHANGE IF A POWER AMPLIFIER MUST BE LESS THAN
$F
RAD
4HE STALO OR COHO FREQUENCY CHANGE IN THE INTERPULSE PERIOD MUST BE LESS THAN
$F
(Z P r r
WHICH IS A STABILITY OF PART IN FOR THE STALO AT ABOUT '(Z AND PART IN FOR THE COHO ASSUMING A -(Z )& FREQUENCY 4HE COHO LOCKING IF A PULSED OSCILLATOR SYSTEM MUST BE WITHIN
$F
RAD
4HE PULSE TIMING JITTER MUST BE LESS THAN
$T
T
r r S
4HE PULSE WIDTH JITTER MUST BE LESS THAN
$07
r T r S
4HE PULSE AMPLITUDE CHANGE MUST BE LESS THAN
$! PERCENT !
4HE !$ SAMPLING TIME JITTER MUST BE LESS THAN
*
r T r S
/F THE ABOVE REQUIREMENTS OSCILLATOR PHASE NOISE MAY DOMINATE (OWEVER IN SYSTEMS WITH LARGE BANDWIDTHS SHORT COMPRESSED PULSES THE TIMING JITTER REQUIRE MENTS BECOME SIGNIFICANT AND MAY REQUIRE SPECIAL CLOCK REGENERATION CIRCUITRY AT KEY SYSTEM LOCATIONS %FFECT OF 1UANTIZATION .OISE ON )MPROVEMENT &ACTOR 1UANTIZATION NOISE INTRODUCED IN THE !$ CONVERTER LIMITS THE ATTAINABLE -4) IMPROVEMENT FACTOR #ONSIDER A CONVENTIONAL VIDEO -4) SYSTEM AS SHOWN IN &IGURE "ECAUSE THE PEAK SIGNAL LEVEL IS CONTROLLED BY THE LINEAR LIMITING AMPLIFIER THE PEAK EXCURSION OF THE PHASE DETECTOR OUTPUT IS KNOWN AND THE !$ CONVERTER IS DESIGNED TO COVER THIS EXCURSION )F THE !$ CONVERTER USES . BITS AND THE PHASE DETECTOR OUTPUT IS FROM TO THE QUANTIZATION INTERVAL IS . 4HE RMS VALUE OF THE SIGNAL LEVEL DEVIATION
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&)'52% $IGITAL -4) CONSIDERATION
INTRODUCED BY THE !$ CONVERTER IS ; . = 4HE LIMIT ON THE -4) IMPROVE MENT FACTOR THAT THIS IMPOSES ON A SIGNAL REACHING THE FULL EXCURSION OF THE PHASE DETEC TOR IS FOUND BY SUBSTITUTING IN THE FOLLOWING EQUATION FROM 4ABLE ) LOG
ª ¹ ! LOG « . LOG ; . =
º $! ¬; = »
"ECAUSE TWO QUADRATURE CHANNELS CONTRIBUTE INDEPENDENT !$ NOISE THE AVERAGE LIMIT ON THE IMPROVEMENT FACTOR OF A FULL RANGE SIGNAL IS § ¶ ) LOG ¨ . LOG ; . = · © ¸
)F THE SIGNAL DOES NOT REACH THE FULL EXCURSION OF THE !$ CONVERTER WHICH IS NORMALLY THE CASE THEN THE QUANTIZATION LIMIT ON ) IS PROPORTIONATELY MORE SEVERE &OR EXAMPLE IF THE SYSTEM IS DESIGNED SO THAT THE MEAN LEVEL OF THE STRONGEST CLUTTER OF INTEREST IS D" BELOW THE !$ CONVERTER PEAK THE LIMIT ON ) WOULD BE LOG ; . = 4HIS IS TABULATED IN 4ABLE 4HIS DISCUSSION OF !$ QUANTIZATION NOISE HAS ASSUMED PERFECT !$ CONVERTERS -ANY !$ CONVERTERS PARTICULARLY UNDER HIGH SLEW RATE CONDITIONS ARE LESS THAN PER FECT 4HIS IN TURN LEADS TO SYSTEM LIMITATIONS MORE SEVERE THAN PREDICTED HERE SEE 3ECTION
4!",% 4YPICAL ,IMITATION ON ) $UE TO !$ 1UANTIZATION
.UMBER OF "ITS .
,IMIT ON -4) )MPROVEMENT &ACTOR ) D"
-4) 2!$!2
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0ULSE #OMPRESSION #ONSIDERATIONSo 7HEN AN -4) SYSTEM IS USED WITH PULSE COMPRESSION THE SYSTEM TARGET DETECTION CAPABILITY IN CLUTTER MAY BE AS GOOD AS A SYSTEM TRANSMITTING THE EQUIVALENT SHORT PULSE OR THE PERFORMANCE MAY BE NO BETTER THAN A SYSTEM TRANSMITTING THE SAME LENGTH #7 PULSE 4HE KIND OF CLUTTER ENVIRONMENT THE SYSTEM INSTABILITIES AND THE SIGNAL PROCESSING UTILIZED DETERMINE WHERE THE SYSTEM PERFORMANCE WILL FALL BETWEEN THE ABOVE TWO EXTREMES 5NLESS PROVISION IS INCORPO RATED FOR COPING WITH SYSTEM INSTABILITIES AND CLUTTER SPECTRAL SPREAD THE -4) PULSE COMPRESSION SYSTEM MAY FAIL TO WORK AT ALL IN A CLUTTER ENVIRONMENT )DEALLY A PULSE COMPRESSION RECEIVER COUPLED WITH AN -4) WOULD APPEAR AS IN &IGURE Ap )F THE PULSE COMPRESSION SYSTEM WAS PERFECT THE COMPRESSED PULSE WOULD LOOK AS IF THE RADAR HAD TRANSMITTED AND RECEIVED A SHORT PULSE AND -4) PRO CESSING COULD PROCEED AS IF THE PULSE COMPRESSION HAD NOT EXISTED )N PRACTICE THE COMPRESSED PULSE WILL HAVE TIME SIDELOBES FROM THREE BASIC CAUSES 4HE FIRST IS WAVE FORM AND SYSTEM DESIGN WHICH INCLUDES COMPONENTS THAT MAY BE NONLINEAR WITH FREQUENCY ETC 4HESE SIDELOBES WILL BE STABLE 4HAT IS THEY SHOULD REPEAT PRECISELY ON A PULSE TO PULSE BASIS AND THUS WILL CANCEL IN THE -4) CANCELER )T IS ASSUMED THAT THE RADAR SYSTEM IS FULLY COHERENT AS REQUIRED BY RULE IN 3ECTION 4HE SECOND CAUSE OF PULSE COMPRESSION SIDELOBES IS SYSTEM INSTABILITIES SUCH AS NOISE ON LOCAL OSCIL LATORS TRANSMITTER TIME JITTER TRANSMITTER TUBE NOISE AND !$ CONVERTER JITTER 4HESE SIDELOBES ARE NOISE LIKE AND ARE PROPORTIONAL TO THE CLUTTER AMPLITUDE 4HEY WILL NOT CANCEL IN THE -4) CANCELER 4HE THIRD SOURCE OF SIDELOBES IS HIGH FREQUENCY RIPPLE IN THE TRANSMITTER POWER SUPPLY )F THE TRANSMITTER POWER SUPPLY INCORPORATES HIGH FREQUENCY AC DC ANDOR DC DC CONVERTERS AND IF THE CONVERTER FREQUENCY COMPONENTS ARE NOT SUFFICIENTLY FILTERED THERE WILL BE DISCRETE TIME SIDELOBES OFFSET FROM THE CLUTTER IN RANGE AS PREDICTED BY PAIRED ECHO THEORY 4HE PAIRED ECHO SIDELOBES WILL ALSO HAVE A DOPPLER FREQUENCY EQUAL TO THE CONVERTER FREQUENCY 4HIS FREQUENCY FCONV WILL ALIAS INTO THE 02& FR DOPPLER INTERVAL AT THE FREQUENCY FDOP ; FDOP MODULO FCONV FR = 4HESE SIDELOBES WILL NOT CANCEL UNLESS THE HIGH FREQUENCY CONVERTERS ARE SYNCHRONIZED TO A MULTIPLE OF THE 02& IN WHICH CASE FDOP !SSUME THAT THE NOISE LIKE COMPONENT OF THE SIDELOBES IS DOWN D" FROM THE PEAK TRANSMITTED SIGNALS 4HIS NOISE LIKE COMPONENT WILL NOT CANCEL IN THE -4) SYS TEM AND THEREFORE FOR EACH CLUTTER AREA THAT EXCEEDS THE SYSTEM THRESHOLD BY D" OR MORE THE RESIDUE WILL EXCEED THE DETECTION THRESHOLD )F THE CLUTTER EXCEEDS THE THRESHOLD BY D" THE RESIDUE FROM THE -4) SYSTEM WILL EXCEED THE DETECTION THRESHOLD BY D" ELIMINATING THE EFFECTIVENESS OF THE -4) &IGURE B SHOWS A SKETCH OF THIS EFFECT 4O ENSURE THAT THE NOISE LIKE PULSE COMPRESSION SIDELOBES WILL NOT EXCEED THE SYSTEM NOISE AFTER THE -4) CANCELER THE SYSTEM STABILITY BUDGET MUST ENSURE THAT THE INSTABILITY SIDELOBE LEVEL IS LOWER THAN THE DYNAMIC RANGE OF THE RECEIVING SYSTEM 4HE RECEIVING SYSTEM DYNAMIC RANGE IS ULTIMATELY DETERMINED IN A WELL DESIGNED SYSTEM BY THE )&
o !LL SIGNAL PROCESSING FOLLOWING THE !$ DETECTOR IS DONE DIGITALLY )T IS MORE MEANINGFUL HOWEVER TO DESCRIBE AND DEPICT THE PROCESSING IN AN ANALOG MANNER p 4HE )& BANDPASS LIMITER ;2ADAR (ANDBOOK ND %D PP n= SHOWN IN THIS AND SUBSEQUENT DIAGRAMS HAS AN AMPLITUDE OUTPUT CHARACTERISTIC THAT IS LINEAR FOR INPUT SIGNAL VOLTAGES FROM NOISE LEVEL TO WITHIN D" OF THE LIMITER OUTPUT MAXIMUM VOLTAGE AND THEN TRANSITIONS SMOOTHLY TO THE MAXIMUM OUTPUT VOLTAGE 4HE PHASE OF THE INPUT SIGNAL IS PRECISELY PRESERVED 4HESE LIMITER CHARACTERISTICS EXIST WHETHER THE FILTER IS IMPLEMENTED IN ANALOG CIRCUITRY OR A DIGITAL ALGORITHM
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&)'52% 0ULSE COMPRESSION WITH -4) A IDEAL BUT DIFFICULT TO ACHIEVE COMBINATION AND B EFFECT OF OSCILLATOR ON TRANSMITTER INSTABILITIES
BANDPASS LIMITER THAT PRECEDES THE !$ CONVERTER )F SYSTEM INSTABILITIES CANNOT BE CON TROLLED TO BE LESS THAN THE SYSTEM DYNAMIC RANGE THEN THE SYSTEM DYNAMIC RANGE SHOULD BE DECREASED !N ALTERNATIVE TO DECREASING THE DYNAMIC RANGE IS TO DEPEND ON A CELL AVERAGING CONSTANT FALSE ALARM RATE #! #&!2 PROCESSOR AFTER THE SIGNAL PROCESSING TO PROVIDE A THRESHOLD THAT RIDES OVER THE RESIDUE NOISE BUT THE EFFICACY OF THIS METHOD DEPENDS ON THE RESIDUE NOISE BEING COMPLETELY NOISE LIKE WHICH IS UNLIKELY !FTER ADDRESSING THE UNSTABLE PULSE COMPRESSION SIDELOBES IT IS STILL NECESSARY TO CONTROL DETECTIONS FROM RESIDUE CAUSED BY THE SPECTRAL SPREAD OF THE CLUTTER OR BY LOW FREQUENCY TRANSMITTER POWER SUPPLY RIPPLE 4HIS CAN BE ACCOMPLISHED BY LIMITING THE MAXIMUM SIGNAL AMPLITUDE AT THE INPUT TO THE CANCELER 4HE PROCESS DESCRIBED ABOVE IS DEPICTED IN &IGURE /NE APPROACH THAT HAS BEEN SUCCESSFUL IN ACHIEVING THE MAXIMUM -4) SYSTEM PERFORMANCE ATTAINABLE WITHIN THE LIMITS IMPOSED BY SYSTEM AND CLUTTER INSTABILITIES
&)'52% 0RACTICAL -4) PULSE COMPRESSION COMBINATION
-4) 2!$!2
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IS SHOWN IN &IGURE 4RANSMITTER NOISE WILL BE USED IN THE FOLLOWING DISCUSSION TO REPRESENT ALL POSSIBLE SYSTEM INSTABILITIES THAT CREATE NOISE LIKE PULSE COMPRESSION TIME SIDELOBES ,IMITER IS SET TO LIMIT THE SYSTEM DYNAMIC RANGE TO THE RANGE BETWEEN PEAK CLUTTER AND CLUTTER INSTABILITY NOISE ,IMITER IS SET SO THAT THE DYNAMIC RANGE AT ITS OUTPUT IS EQUAL TO THE EXPECTED -4) IMPROVEMENT FACTOR AS LIMITED BY CLUTTER SPECTRAL SPREAD OR LOW FREQUENCY TRANSMITTER POWER SUPPLY RIPPLE 4HESE LIMITER SETTINGS CAUSE THE RESIDUE DUE TO TRANSMITTER NOISE AND THE RESIDUE DUE TO OTHER INSTABILITIES SUCH AS QUAN TIZATION NOISE AND INTERNAL CLUTTER MOTION EACH TO BE EQUAL TO FRONT END THERMAL NOISE AT THE CANCELER OUTPUT 4HIS ALLOWS MAXIMUM SENSITIVITY WITHOUT AN EXCESSIVE FALSE ALARM RATE ,IMITER IS A VERY EFFICIENT CONSTANT FALSE ALARM RATE DEVICE AGAINST SYSTEM INSTABILITIES BECAUSE IT SUPPRESSES THE INSTABILITY NOISE IN DIRECT PROPORTION TO THE CLUTTER SIGNAL STRENGTH BUT DOES NOT SUPPRESS AT ANY TIME WHEN THE CLUTTER SIGNAL IS NOT STRONG !LTHOUGH THE LIMITERS CAUSE PARTIAL OR COMPLETE SUPPRESSION OF SOME DESIRED TARGETS IN THE CLUTTER AREAS NO TARGETS ARE SUPPRESSED THAT COULD OTHERWISE HAVE BEEN DETECTED IN THE PRESENCE OF CLUTTER RESIDUE AT THE SYSTEM OUTPUT IF THE LIMITERS HAD NOT BEEN USED !S A SPECIFIC EXAMPLE CONSIDER A SYSTEM WITH A PULSE COMPRESSION RATIO OF ABOUT D" AND SYSTEM INSTABILITY NOISE APPROXIMATELY D" BELOW THE CARRIER POWER !SSUME THAT THE -4) CANCELER IMPROVEMENT FACTOR IS D" LIMITED BY CLUTTER SPEC TRAL SPREAD 7ITH THE ABOVE SYSTEM PARAMETERS A RECEIVER SYSTEM THAT WILL PROVIDE THE MAXIMUM OBTAINABLE PERFORMANCE IS SHOWN IN &IGURE !T THE OUTPUT OF THE PULSE COMPRESSION NETWORK THE SYSTEM INSTABILITY NOISE WILL BE EQUAL TO OR LESS THAN THERMAL NOISE FOR EITHER DISTRIBUTED CLUTTER OR POINT CLUTTER AND THE PEAK CLUTTER SIGNALS WILL VARY FROM ABOUT D" ABOVE THERMAL NOISE FOR EVENLY DISTRIBUTED CLUTTER TO D" ABOVE THERMAL NOISE FOR STRONG POINT CLUTTER "ECAUSE THE -4) CANCELER IS EXPECTED TO ATTENUATE CLUTTER BY D" THE SECOND LIM ITER IS PROVIDED TO PREVENT THE RESIDUE FROM STRONG CLUTTER FROM EXCEEDING THE THRESHOLD 7ITHOUT THE SECOND LIMITER A STRONG POINT REFLECTOR THAT WAS D" ABOVE NOISE AT THE CANCELER INPUT WOULD HAVE A RESIDUE D" ABOVE NOISE AT THE CANCELER OUTPUT 4HIS WOULD BE INDISTINGUISHABLE FROM AN AIRCRAFT TARGET )T THE TRANSMITTER NOISE WERE D" LESS THAN ASSUMED ABOVE THE FIRST LIMITER WOULD BE SET D" ABOVE THERMAL NOISE AND MUCH LESS TARGET SUPPRESSION WOULD OCCUR 4HUS TARGET DETECTABILITY WOULD IMPROVE IN AND NEAR THE STRONG CLUTTER AREAS EVEN THOUGH THE -4) IMPROVEMENT FACTOR WAS STILL LIMITED TO D" BY INTERNAL CLUTTER MOTION )N SUMMARY THE NOISE LIKE PULSE COMPRESSION SIDELOBES AND THE DURATION OF THE UNCOMPRESSED PULSE DICTATE HOW EFFECTIVE A PULSE COMPRESSION -4) SYSTEM CAN BE 3YSTEMS HAVE BEEN BUILT IN WHICH TRANSMITTER NOISE AND LONG UNCOMPRESSED PULSES COMBINED TO MAKE THE SYSTEMS INCAPABLE OF DETECTING AIRCRAFT TARGETS IN OR NEAR LAND CLUTTER 3OME EXISTING PULSE COMPRESSION SYSTEMS HAVE NOT DELIBERATELY PROVIDED THE
&)'52% -4) WITH PULSE COMPRESSION
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TWO SEPARATE LIMITERS DESCRIBED ABOVE BUT THE SYSTEMS WORK BECAUSE DYNAMIC RANGE IS SUFFICIENTLY RESTRICTED BY CIRCUIT COMPONENTS /THER SYSTEMS SUCH AS THOSE THAT DELIB ERATELY HARD LIMIT BEFORE PULSE COMPRESSION FOR #&!2 REASONS DO NOT HAVE CLUTTER RESIDUE PROBLEMS BUT SUFFER FROM SIGNIFICANT TARGET SUPPRESSION IN THE CLUTTER AREAS !N ALTERNATIVE TO THE USE OF LIMITERS IS THE USE OF CLUTTER MAPS IN CONJUNCTION WITH THE #! #&!2 #LUTTER MAPS WORK WELL FOR STATIONARY RADARS OPERATING AT FIXED FREQUENCIES BUT ARE LESS EFFECTIVE FOR OTHER RADARS 4HE #! #&!2 IS USEFUL EVEN FOR A SYSTEM WITH )& LIMITERS BECAUSE THERE WILL BE SMALL VARIATIONS ON THE ORDER OF A FEW D" IN THE COMBINATION OF CLUTTER RESIDUE AND SYSTEM NOISE 4O REEMPHASIZE HOWEVER WITHOUT THE LIMITERS THERE MAY BE TENS OF D"S DIFFERENCE BETWEEN CLUTTER RESIDUE AND SYSTEM NOISE
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" - ,/" 4HE ACCURATE CONVERSION OF THE RADAR )& SIGNAL INTO A DIGITAL REPRESENTATION OF THE COMPLEX ENVELOPE IS AN IMPORTANT STEP IN THE IMPLEMENTATION OF A MODERN DIGITAL SIG NAL PROCESSOR 4HIS ANALOG TO DIGITAL !$ CONVERSION MUST PRESERVE THE LINEARITY OF AMPLITUDE AND PHASE OVER THE REQUIRED DYNAMIC RANGE HAVE A SMALL EFFECT ON OVERALL RADAR SYSTEM NOISE TEMPERATURE AND BE FREE FROM UNDESIRED SPURIOUS RESPONSES !DVANCES IN !$ CONVERTER TECHNOLOGY IS NOW MAKING IT POSSIBLE TO DIRECTLY CON VERT AN ANALOG )& SIGNAL INTO A CORRESPONDING DIGITAL COMPLEX REPRESENTATION RATHER THAN GOING THROUGH THE INTERMEDIATE STEP OF FIRST DOWNCONVERTING THE )& SIGNAL INTO BASEBAND IN PHASE ) AND QUADRATURE 1 COMPONENTS AND SUBSEQUENTLY USING A SEPA RATE !$ CONVERTER IN EACH OF THESE TWO CHANNELS ! FLOW CHART OF A DIRECT )& !$ CONVERTER IS ILLUSTRATED IN &IGURE ALONG WITH SPECTRAL REPRESENTATIONS OF THE SIGNAL THROUGHOUT THE CONVERSION PROCESS 4HE )& INPUT CENTERED AT THE FREQUENCY F)& IS FIRST PASSED THROUGH A BANDPASS FILTER TO ENSURE THAT NEGLIGIBLE ALIASING WILL OCCUR DURING THE SUBSEQUENT !$ CONVERSION PROCESS /N THE RIGHT IN &IGURE THE TOP GRAPH SHOWS THE POSITIVE AND NEGATIVE PARTS OF THE SIGNAL SPECTRUM AT THE )& FILTER OUTPUT 4HE POSITIVE PART OF THIS SPECTRUM CORRESPONDS TO THE COMPLEX ENVELOPE WHICH NEEDS TO BE TRANSLATED INTO THE DIGITAL ) AND 1 REPRESENTATION 4HIS FILTER OUTPUT BECOMES THE INPUT TO THE !$ CONVERTER OPERATING AT A SAMPLING RATE OF F!$ 4HE SPECTRUM OF THE !$ CONVERTER OUTPUT IS AGAIN SHOWN AND IT IS OBTAINED SIMPLY BY REPLICATING THE ORIGINAL )& SPECTRUM FROM MINUS INFINITY TO PLUS INFINITY WITH A PERIOD OF F!$ )N THIS EXAMPLE AN !$ CONVERSION RATE OF F!$ F)& IS ASSUMED 4HE OPTIMUM CHOICE OF THE !$ CONVERTER SAMPLING RATE ENSURES THAT THE NEGATIVE PART OF THE SPECTRUM HAS THE SMALLEST POSSIBLE OVERLAP WITH THE POSITIVE PART OF THE SPECTRUM 4HE SMALLEST POSSIBLE OVERLAP OCCURS WHEN THE !$ SAMPLING RATE IS RELATED TO THE RADAR )& FREQUENCY AS FOLLOWS
F!$
F)& -
WHERE - IS AN INTEGER GREATER THAN 4HUS OPTIMUM SAMPLING RATES ARE F)& F)& F)& F)& x ETC 4HE CORRESPONDING MAXIMUM UNALIASED OR .YQUIST BANDWIDTH IS ".1 F!$ 4HIS VALUE IS THEREFORE THE MAXIMUM ALLOWABLE CUTOFF BANDWIDTH OF THE )& BANDPASS FILTER AT THE INPUT TO THE !$ CONVERTER )T IS NOT STRICTLY NECESSARY TO USE
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&)'52% )MPLEMENTATION OF !$ CONVERSION USING DIRECT SAMPLING OF THE )& SIGNAL
AN !$ CONVERTER SAMPLING RATE AS GIVEN BY %Q BUT OTHER VALUES WILL RESULT IN AN AVAILABLE .YQUIST BANDWIDTH LESS THAN F!$ 4HIS IS SHOWN IN &IGURE WHERE THE NORMALIZED .YQUIST BANDWIDTH IS SHOWN AS A FUNCTION OF THE RELATIVE !$ CONVERTER SAMPLING RATE &ROM THIS FIGURE IT IS SEEN THAT THE DIRECT CONVERSION APPROACH WILL FAIL WHENEVER A VALUE OF - WHICH IS LOCATED HALFWAY BETWEEN THE OPTIMUM VALUES IS USED !T THE !$ CONVERTER OUTPUT THE SIGNAL SAMPLES ARE STILL REAL VALUED 4O BE ABLE TO EXTRACT THE COMPLEX ENVELOPE CORRESPONDING TO THE POSITIVE PART OF THE SPECTRUM ! F F)& IT IS NECESSARY TO SHIFT THE SPECTRUM AT THE !$ CONVERTER OUTPUT DOWN IN FREQUENCY BY PTHE AMOUNT F)& 4HIS CORRESPONDS TO A MULTIPLICATION BY THE TIME SERIES UI E JI %QUIVALENTLY THE COMPLEX ENVELOPE SPECTRUM BELOW ZERO FREQUENCY CAN BE SHIFTED UP TO ZERO FREQUENCY BY MULTIPLICATION WITH THE TIME SERIES P UI E JI 4HIS RESULTS IN THE SPECTRUM SHOWN WHERE THE DESIRED SPECTRUM CORRE SPONDING TO THE COMPLEX ENVELOPE IS CENTERED AT ZERO FREQUENCY BUT THE SIGNAL STILL CONTAINS THE UNWANTED NEGATIVE SPECTRAL COMPONENTS LIGHT SHADING !S A RESULT OF THIS FREQUENCY TRANSLATION THE SIGNAL HAS NOW BECOME COMPLEX ! DIGITAL &)2 BAND PASS FILTER WITH A NEARLY RECTANGULAR RESPONSE IS THEN APPLIED TO REJECT THE NEGATIVE FREQUENCY COMPONENTS AS SHOWN IN THE FINAL GRAPH ON THE RIGHT 4HE DESIRED SAMPLED COMPLEX ENVELOPE REPRESENTATION HAS NOW BEEN REALIZED BUT AT THE ORIGINAL SAMPLING RATE OF F!$ )F DESIRED THE OVERSAMPLING CAN FINALLY BE REMOVED THROUGH DECIMATION BY A FACTOR OF AS SHOWN IN THE LAST STEP IN THE FIGURE
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"$ ! "' &)'52% !VAILABLE .YQUIST BANDWIDTH VS !$ CONVERTER SAMPLING RATE
!$ CONVERTERS ARE TYPICALLY CHARACTERIZED BY THEIR SIGNAL TO NOISE RATIO 3.2 PERFORMANCE REFERRED TO A BANDWIDTH EQUAL TO THE !$ SAMPLING RATE /FTEN THIS 3.2 IS NOT AS HIGH AS ONE WOULD EXPECT BASED ON THE NUMBER OF BITS USED BY THE !$ CONVERTER 3OMETIMES THE ACTUAL PERFORMANCE OF AN !$ CONVERTER IS CHARACTERIZED BY AN EFFECTIVE NUMBER OF BITS SMALLER THAN THE ACTUAL NUMBER OF BITS AND CORRESPOND ING TO THE ACHIEVABLE 3.2 4HE 3.2 OF AN !$ CONVERTER SETS AN UPPER LIMIT ON THE ACHIEVABLE IMPROVEMENT FACTOR
Ó°£{Ê */6 Ê / 7HEN THE DOPPLER FREQUENCY OF THE RETURNS FROM CLUTTER IS UNKNOWN AT THE RADAR INPUT SPECIAL TECHNIQUES ARE REQUIRED TO GUARANTEE SATISFACTORY CLUTTER SUPPRESSION !S DIS CUSSED IN 3ECTION THE DOPPLER FILTER BANK WILL USUALLY BE EFFECTIVE AGAINST MOVING CLUTTER 4HIS REQUIRES THAT THE INDIVIDUAL FILTERS BE DESIGNED WITH A LOW SIDELOBE LEVEL IN THE REGIONS WHERE CLUTTER MAY APPEAR AND THAT EACH FILTER BE FOLLOWED BY APPROPRI ATE #&!2 PROCESSING CIRCUITS TO REJECT UNWANTED CLUTTER RESIDUE 7HEN CLUTTER SUP PRESSION IS TO BE IMPLEMENTED WITH A SINGLE -4) FILTER IT IS NECESSARY TO USE ADAPTIVE TECHNIQUES TO ENSURE THAT THE CLUTTER FALLS IN THE -4) REJECTION NOTCH !N EXAMPLE OF SUCH AN ADAPTIVE -4) IS 4!##!2 ORIGINALLY DEVELOPED FOR AIRBORNE RADARS )N MANY APPLICATIONS THE ADAPTIVE -4) WILL FURTHER HAVE TO TAKE INTO ACCOUNT THE SITUATION WHERE MULTIPLE CLUTTER SOURCES WITH DIFFERENT RADIAL VELOCITIES ARE PRESENT AT THE SAME RANGE AND BEARING 5SUALLY THE DOPPLER SHIFT OF CLUTTER RETURNS IS CAUSED BY THE WIND FIELD AND EARLY ATTEMPTS OF COMPENSATING IN THE -4) HAVE VARIED THE COHO FREQUENCY SINUSOIDALLY AS A FUNCTION OF AZIMUTH BASED ON THE AVERAGE WIND SPEED AND DIRECTION 4HIS APPROACH IS
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UNSATISFACTORY BECAUSE THE WIND FIELD RARELY IS HOMOGENEOUS OVER A LARGE GEOGRAPHICAL AREA AND BECAUSE THE WIND VELOCITY USUALLY IS A FUNCTION OF ALTITUDE DUE TO WIND SHEAR IMPORTANT FOR RAIN CLUTTER AND CHAFF !GAINST A SINGLE CLUTTER SOURCE AN IMPLEMENTA TION IS REQUIRED THAT PERMITS THE -4) CLUTTER NOTCH TO BE SHIFTED AS A FUNCTION OF RANGE !N EXAMPLE OF SUCH AN ADAPTIVE -4) IMPLEMENTATION IS SHOWN IN &IGURE 4HE PHASE ERROR CIRCUIT COMPARES THE CLUTTER RETURN FROM ONE SWEEP TO THE NEXT 4HROUGH A CLOSED LOOP WHICH INCLUDES A SMOOTHING TIME CONSTANT THE ERROR SIGNAL CONTROLS A PHASE SHIFTER AT THE COHO OUTPUT SUCH THAT THE DOPPLER SHIFT FROM PULSE TO PULSE IS REMOVED )T SHOULD BE NOTED THAT SINCE THE FIRST SWEEP ENTERING THE -4) IS TAKEN AS A REFERENCE ANY PHASE SHIFT RUN OUT AS A FUNCTION OF RANGE WILL INCREASE PROPORTIONALLY TO THE NUMBER OF SWEEPS 5LTIMATELY THIS RUN OUT WILL EXCEED THE SPEED OF RESPONSE OF THE CLOSED LOOP AND THE -4) MUST BE RESET 4HIS TYPE OF CLOSED LOOP ADAPTIVE -4) MUST THEREFORE BE OPERATED FOR A FINITE SET BATCH OF PULSES TO ENSURE THAT THIS WILL NOT HAPPEN 3UCH BATCH MODE OPERATION IS ALSO REQUIRED IF A COMBINATION OF -4) OPERATION AND FREQUENCY AGILITY IS DESIRED )F A BIMODAL CLUTTER SITUATION IS CAUSED BY THE SIMULTANEOUS PRESENCE OF RETURNS FROM LAND CLUTTER AND WEATHER OR CHAFF AN ADAPTIVE -4) CAN BE IMPLEMENTED FOLLOWING A FIXED CLUTTER NOTCH -4) SECTION AS ILLUSTRATED IN &IGURE 4HE NUMBER OF ZEROS USED IN THE FIXED ZERO DOPPLER CLUTTER NOTCH SECTION OF THE -4) IS DETERMINED BY THE REQUIRED IMPROVEMENT FACTOR AND THE SPECTRAL SPREAD OF THE LAND CLUTTER 4YPICALLY THE FIXED NOTCH -4) WOULD USE TWO OR THREE ZEROS &OR THE ADAPTIVE PORTION OF THE -4) A FULLY DIGITAL IMPLEMENTATION IS SHOWN IN WHICH THE PULSE TO PULSE PHASE SHIFT OF THE CLUTTER OUTPUT FROM THE FIRST CANCELER IS MEASURED AND AVERAGED OVER A GIVEN NUMBER OF RANGE CELLS 4HIS ESTIMATED PHASE SHIFT IS ADDED TO THE PHASE SHIFT WHICH IS APPLIED TO THE DATA ON THE PREVIOUS SWEEP AND THIS NEW PHASE SHIFT IS APPLIED TO THE CURRENT DATA 4HE RANGE AVERAGING MUST BE PERFORMED SEPARATELY ON THE ) AND 1 COMPONENTS OF THE MEASURED PHASE IN EACH RANGE CELL DUE TO THE O AMBIGUITY OF THE PHASE REPRESENTA TION ITSELF 4HE ACCUMULATION OF THE APPLIED PHASE SHIFT FROM SWEEP TO SWEEP HOWEVER MUST BE PERFORMED DIRECTLY ON THE PHASE AND IS COMPUTED MODULO O 4HE NUMBER OF ZEROS OF THE ADAPTIVE -4) SECTION IS AGAIN DETERMINED BY THE REQUIRED IMPROVEMENT FACTOR AND THE EXPECTED SPECTRAL SPREAD OF THE CLUTTER 4HE PHASE SHIFT IS APPLIED TO THE INPUT DATA IN THE FORM OF A COMPLEX MULTIPLY WHICH AGAIN REQUIRES THE TRANSFORMATION OF THE PHASE ANGLE INTO RECTANGULAR COORDINATES 4HIS TRANSFORMATION CAN EASILY BE PERFORMED BY A TABLE LOOKUP OPERATION IN A READ ONLY MEMORY
&)'52% "LOCK DIAGRAM OF CLOSED LOOP ADAPTIVE DIGITAL -4)
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&)'52% /PEN LOOP ADAPTIVE -4) FOR CANCELLATION OF SIMULTANEOUS FIXED AND MOVING CLUTTER
7HEN DOPPLER SHIFTS ARE INTRODUCED BY DIGITAL MEANS AS DESCRIBED ABOVE THE ACCU RACY OF THE ) AND 1 REPRESENTATION OF THE ORIGINAL INPUT DATA BECOMES AN IMPORTANT CONSIDERATION !NY DC OFFSET AMPLITUDE IMBALANCE QUADRATURE PHASE ERROR OR NONLIN EARITY WILL RESULT IN THE GENERATION OF UNDESIRED SIDEBANDS THAT WILL APPEAR AS RESIDUE AT THE CANCELER OUTPUT ! DISCUSSION OF !$ CONVERSION CONSIDERATIONS WAS PRESENTED IN 3ECTION )N THE ADAPTIVE -4) IMPLEMENTATION DESCRIBED ABOVE THE NUMBER OF ZEROS ALLO CATED TO EACH OF THE TWO CANCELERS WAS FIXED BASED ON AN A PRIORI ASSESSMENT OF THE CLUTTER SUPPRESSION REQUIREMENT 4HE ONLY VARIATION POSSIBLE WOULD BE TO COMPLETELY BYPASS ONE OR BOTH OF THE -4) CANCELERS IF NO LAND CLUTTER OR WEATHER OR CHAFF RETURNS ARE RECEIVED ON A GIVEN RADIAL ! MORE CAPABLE SYSTEM CAN BE IMPLEMENTED IF THE NUM BER OF ZEROS CAN BE ALLOCATED DYNAMICALLY TO EITHER CLUTTER SOURCE AS A FUNCTION OF RANGE 4HIS LEADS TO A FULLY ADAPTIVE -4) IMPLEMENTATION USING A MORE COMPLEX ADAPTATION ALGORITHM AS DISCUSSED BELOW 3UCH AN ADAPTIVE -4) MAY PROVIDE A PERFORMANCE CLOSE TO THE OPTIMUM DISCUSSED IN 3ECTION )N ORDER TO ILLUSTRATE THE DIFFERENCE IN PERFORMANCE BETWEEN SUCH CANDIDATE -4) IMPLEMENTATIONS A SPECIFIC EXAMPLE IS CONSIDERED NEXT &OR THIS EXAMPLE LAND CLUTTER RETURNS ARE PRESENT AT ZERO DOPPLER WITH A NORMALIZED SPECTRAL SPREAD OF RF4 AND CHAFF RETURNS ARE PRESENT AT A NORMALIZED DOPPLER OFFSET OF FD4 WITH A NORMALIZED SPECTRAL SPREAD OF RF4 4HE POWER RATIO OF THE LAND CLUTTER TO THAT OF THE CHAFF IS DENOTED 1 D" 4HERMAL NOISE IS NOT CONSIDERED IN THIS EXAMPLE )N BOTH CASES THE TOTAL NUMBER OF FILTER ZEROS IS ASSUMED TO BE EQUAL TO &OR THE ADAPTIVE -4) WITH A FIXED ALLOCATION OF ZEROS TWO ZEROS ARE LOCATED AT ZERO DOPPLER AND THE REMAINING ZERO IS CENTERED ON THE CHAFF RETURNS )N THE OPTIMUM -4) THE ZERO LOCATIONS ARE CHOSEN SO THAT THAT OVERALL IMPROVEMENT FACTOR IS MAXIMIZED 4HE RESULTS OF THIS COMPARISON ARE PRESENTED IN &IGURE WHICH SHOWS THE IMPROVEMENT FACTOR FOR THE OPTIMUM AND THE ADAPTIVE -4) AS A FUNCTION OF THE POWER RATIO 1 D" 7HEN 1 IS SMALL SO THAT CHAFF RETURNS DOMINATE A SIGNIFICANT PERFORMANCE IMPROVEMENT CAN BE REALIZED BY USING ALL -4) FILTER ZEROS TO CANCEL THE CHAFF RETURNS 4HE PERFORMANCE DIFFERENCE FOR LARGE VALUES OF 1 IS A RESULT OF AN ASSUMPTION MADE THAT THE LOCATION OF THE THIRD ZERO REMAINS FIXED AT THE CHAFF DOPPLER FREQUENCY )N REALITY THE ADAPTIVE -4) WOULD MOVE
-4) 2!$!2
&)'52% )MPROVEMENT FACTOR COMPARISON OF OPTIMUM AND ADAPTIVE -4) AGAINST FIXED AND MOVING CLUTTER OF RATIO 1
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&)'52% ,OCATION OF THE THREE FILTER ZEROS FOR AN OPTIMUM -4) USED AGAINST FIXED AND MOV ING CLUTTER
ITS THIRD ZERO TO THE LAND CLUTTER AS THE LAND CLUTTER RESIDUE STARTS TO DOMINATE THE OUTPUT OF THE FIRST CANCELER 4HE ZERO LOCATIONS OF THE OPTIMUM -4) ARE SHOWN IN &IGURE AND CAN BE SEEN TO MOVE BETWEEN THE LAND CLUTTER AT ZERO DOPPLER TOWARD THE DOPPLER OF THE CHAFF RETURNS AS THE RELATIVE LEVEL OF THE LAND CLUTTER BECOMES SMALL
Ó°£xÊ , ,Ê 1// ,Ê *)N MANY -4) RADAR APPLICATIONS THE CLUTTER TO NOISE RATIO IN THE RECEIVER WILL EXCEED THE IMPROVEMENT FACTOR LIMIT OF THE SYSTEM EVEN WHEN TECHNIQUES SUCH AS SENSITIVITY TIME CONTROL 34# IMPROVED RADAR RESOLUTION AND REDUCED ANTENNA GAIN CLOSE TO THE HORIZON ARE USED TO REDUCE THE LEVEL OF CLUTTER RETURNS 4HE RESULTING CLUTTER RESIDUES AFTER THE -4) CANCELER MUST THEREFORE BE FURTHER SUPPRESSED TO PREVENT SATURATION OF THE 00) DISPLAY ANDOR AN EXCESSIVE FALSE ALARM RATE IN AN AUTOMATIC TARGET DETECTION !4$ SYSTEM !GAINST SPATIALLY HOMOGENEOUS SOURCES OF CLUTTER SUCH AS RAIN SEA CLUTTER OR CORRI DOR CHAFF A CELL AVERAGING CONSTANT FALSE ALARM RATE #! #&!2 PROCESSOR FOLLOWING THE -4) FILTER WILL USUALLY PROVIDE GOOD SUPPRESSION OF THE CLUTTER RESIDUES 3PECIAL FEATURES ARE SOMETIMES ADDED TO THE #! #&!2 SUCH AS GREATEST OF SELECTION OR TWO PARAMETER SCALE AND SHAPE NORMALIZATION LOGIC IN ORDER TO IMPROVE ITS EFFECTIVENESS AT CLUTTER BOUNDARIES IF THE PROBABILITY DISTRIBUTION OF THE CLUTTER AMPLITUDE IS NON GAUSSIAN (OWEVER WHEN THE CLUTTER RETURNS ARE SIGNIFICANTLY NONHOMOGENEOUS AS IS THE CASE FOR TYPICAL LAND CLUTTER RETURNS THE PERFORMANCE OF THE CELL AVERAGING #&!2 WILL NOT BE SATISFACTORY AND OTHER MEANS MUST BE IMPLEMENTED TO SUPPRESS THE OUTPUT RESIDUES TO THE NOISE LEVEL 4HE TRADITIONAL SOLUTION TO THIS PROBLEM HAS BEEN TO DELIBERATELY REDUCE THE RECEIVER DYNAMIC RANGE PRIOR TO THE -4) FILTER TO THE SAME VALUE AS THE MAXIMUM SYSTEM IMPROVEMENT FACTOR 4HEORETICALLY THEN THE OUTPUT RESIDUE SHOULD BE AT OR BELOW THE NORMAL RECEIVER NOISE LEVEL AND NO FALSE ALARMS WOULD BE GENERATED )N PRACTICE THE INTRODUCTION OF )& LIMITING AGAINST THE GROUND CLUTTER RETURNS WILL RESULT IN AN ADDITIONAL
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IMPROVEMENT FACTOR RESTRICTION AS DISCUSSED IN 3ECTION #ONSEQUENTLY FOR THE LIMITED )& DYNAMIC RANGE TO HAVE THE DESIRED EFFECT ON THE OUTPUT RESIDUES THE LIMIT LEVEL MUST BE SET TO D" BELOW THE IMPROVEMENT FACTOR LIMIT OF THE LINEAR SYSTEM 4HE NET RESULT IS THAT SOME OF THE CLUTTER SUPPRESSION CAPABILITY OF THE -4) RADAR MUST BE SACRIFICED IN EXCHANGE FOR CONTROL OF THE OUTPUT FALSE ALARM RATE 3INCE RETURNS FROM LAND CLUTTER SCATTERERS USUALLY ARE SPATIALLY FIXED AND THEREFORE APPEAR AT THE SAME RANGE AND BEARING FROM SCAN TO SCAN IT HAS LONG BEEN RECOGNIZED THAT A SUITABLE MEMORY CIRCUIT COULD BE USED TO STORE THE CLUTTER RESIDUES AND REMOVE THEM FROM THE OUTPUT RESIDUE ON SUBSEQUENT SCANS BY EITHER SUBTRACTION OR GAIN NOR MALIZATION 4HIS WAS THE BASIC PRINCIPLE OF THE SO CALLED AREA -4) AND MANY ATTEMPTS HAVE BEEN MADE TO IMPLEMENT AN EFFECTIVE VERSION OF THIS CIRCUIT OVER AN EXTENDED SPAN OF TIME 4HE MAIN HINDRANCE TO ITS SUCCESS HAS BEEN THE LACK OF APPROPRIATE MEMORY TECHNOLOGY SINCE THE STORAGE TUBE LONG THE ONLY VIABLE CANDIDATE LACKS IN RESOLUTION REGISTRATION ACCURACY SIMULTANEOUS READ AND WRITE CAPABILITY AND STABILITY 4HE DEVEL OPMENT OF HIGH CAPACITY SEMICONDUCTOR MEMORIES IS THE TECHNOLOGICAL BREAKTHROUGH THAT HAS MADE THE DESIGN OF A WORKING AREA -4) A REALITY 4HE AREA -4) IS BETTER KNOWN TODAY AS A CLUTTER MAP BUT BOTH TERMS ARE USED 4HE CLUTTER MAP MAY BE CONSIDERED AS A TYPE OF #&!2 WHERE THE REFERENCE SAMPLES WHICH ARE NEEDED TO ESTIMATE THE LEVEL OF THE CLUTTER OR CLUTTER RESIDUE ARE COLLECTED IN THE CELL UNDER TEST ON A NUMBER OF PREVIOUS SCANS 3INCE AIRCRAFT TARGETS USUALLY MOVE SEVERAL RESOLUTION CELLS FROM ONE SCAN TO THE NEXT IT IS UNLIKELY THAT THE REFERENCE SAMPLES WILL BE CONTAMINATED BY A TARGET RETURN !LTERNATIVELY BY MAKING THE AVERAG ING TIME IN TERMS OF PAST SCANS LONG THE EFFECT OF AN OCCASIONAL TARGET RETURN CAN BE MINIMIZED !LTHOUGH THE PRIMARY PURPOSE OF THE CLUTTER MAP IS TO PREVENT FALSE ALARMS DUE TO DISCRETE CLUTTER OR CLUTTER RESIDUES THAT ARE AT A FIXED LOCATION IT MAY ALSO BE NECESSARY TO CONSIDER SLOWLY MOVING POINT CLUTTER IN THE CLUTTER MAP DESIGN EITHER TO SUPPRESS BIRD RETURNS OR BECAUSE THE RADAR IS ON A MOVING PLATFORM EG A SHIP 4HE MEMORY OF A CLUTTER MAP IS USUALLY ORGANIZED IN A UNIFORM GRID OF RANGE AND AZIMUTH CELLS AS ILLUSTRATED IN &IGURE %ACH MAP CELL WILL TYPICALLY HAVE TO BITS OF MEMORY SO THAT IT WILL HANDLE THE FULL DYNAMIC RANGE OF SIGNALS AT ITS INPUT WHICH MAKES IT POSSIBLE TO DETECT A STRONG TARGET FLYING OVER A POINT OF CLUTTER SOME TIMES REFERRED TO AS SUPERCLUTTER VISIBILITY 4HE DIMENSIONS OF EACH CELL ARE A COMPRO MISE BETWEEN THE REQUIRED MEMORY AND SEVERAL PERFORMANCE CHARACTERISTICS 4HESE ARE THE MINIMUM TARGET VELOCITY THAT WILL NOT BE SUPPRESSED BY THE MAP SO CALLED CUTOFF VELOCITY ITS TRANSIENT RESPONSE AND THE LOSS IN SENSITIVITY CAUSED BY THE CLUTTER MAP SIMILAR TO A #&!2 LOSS 4HE MINIMUM CELL SIZE WILL BE CONSTRAINED BY THE SIZE OF THE RADAR RESOLUTION CELL
&)'52% #LUTTER MAP CELL DEFINITION
-4) 2!$!2
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%ACH MAP CELL IS UPDATED BY THE RADAR RETURNS OR RESIDUES FALLING WITHIN ITS BORDERS OR IN ITS VICINITY ON SEVERAL PREVIOUS SCANS 4O SAVE MEMORY THE CELLS ARE USUALLY UPDATED BY USING A SIMPLE RECURSIVE SINGLE POLE FILTER OF THE FORM
YI A YI A XI
WHERE YI IS THE CLUTTER MAP AMPLITUDE FROM THE PREVIOUS SCAN YI IS THE UPDATED CLUTTER MAP AMPLITUDE XI IS THE RADAR OUTPUT ON THE PRESENT SCAN AND THE CONSTANT @ DETERMINES THE MEMORY OF THE RECURSIVE FILTER 4HE TEST FOR DETECTING A TARGET BASED ON THE OUTPUT XI IS
XI q K4 YI
WHERE THE THRESHOLD CONSTANT K4 IS SELECTED TO GIVE THE REQUIRED FALSE ALARM RATE !LTERNATIVELY THE RADAR OUTPUT CAN BE NORMALIZED ON THE BASIS OF THE CLUTTER MAP XI CONTENT TO OBTAIN AN OUTPUT ZI Y I WHICH CAN BE PROCESSED FURTHER IF REQUIRED !NALOGOUSLY TO THE IMPLEMENTATION OF THE CELL AVERAGING #&!2 PROCESSOR THE AMPLI TUDE XI CAN BE OBTAINED USING A LINEAR SQUARE LAW OR LOGARITHMIC DETECTOR 4HE LOSS IN DETECTABILITY DUE TO THE CLUTTER MAP IS ANALOGOUS TO THE #&!2 LOSS ANA LYZED IN THE LITERATURE FOR MANY DIFFERENT CONDITIONS !N ANALYSIS OF THE CLUTTER MAP LOSS FOR SINGLE HIT DETECTION USING A SQUARE LAW DETECTOR HAS BEEN PRESENTED BY .ITZBERG 4HESE AND OTHER RESULTS CAN BE SUMMARIZED INTO A SINGLE UNIVERSAL CURVE OF CLUTTER MAP LOSS ,#- AS A FUNCTION OF THE CLUTTER MAP RATIO X,EFF AS SHOWN IN &IGURE WHERE X DEFINES THE REQUIRED FALSE ALARM PROBABILITY ACCORDING TO 0F X AND ,EFF IS THE EFFECTIVE NUMBER OF PAST OBSERVATIONS AVERAGED IN THE CLUTTER MAP DEFINED AS
,EFF
A A
&OR EXAMPLE FOR 0F AND @ THE CLUTTER MAP LOSS IS ,#- D" SINCE X AND ,EFF FOR THIS CASE !LSO SHOWN IN &IGURE IS THE CURVE FOR THE CONVEN TIONAL #! #&!2 WHERE ALL REFERENCE SAMPLES ARE EQUALLY WEIGHTED )F MORE THAN ONE NOISE ANDOR CLUTTER AMPLITUDE IS USED TO UPDATE THE CLUTTER MAP CONTENT ON EACH SCAN THE VALUE OF ,EFF SHOULD BE INCREASED PROPORTIONALLY )T SHOULD ALSO BE NOTED THAT MOST RADARS BASE THEIR TARGET DETECTION ON MULTIPLE HITS USING SOME FORM OF VIDEO INTEGRA TION AND THAT A CLUTTER MAP LOSS BASED ON THE SINGLE HIT RESULTS OF &IGURE COULD BE MUCH TOO LARGE !N ANALYSIS OF THE PERFORMANCE OF TYPICAL IMPLEMENTATIONS OF CLUTTER MAPS HAS BEEN DISCUSSED IN +HOURY AND (OYLE &ROM THIS REFERENCE A TYPICAL TRANSIENT RESPONSE CURVE IS SHOWN IN &IGURE FOR A SINGLE POINT CLUTTER SOURCE D" ABOVE THERMAL NOISE THAT FLUCTUATES FROM SCAN TO SCAN ACCORDING TO A 2AYLEIGH PROBABILITY DENSITY FUNCTION A FILTERING CONSTANT OF @ AND ASSUMING FOUR RETURNS NONCOHERENTLY INTEGRATED IN EACH CLUTTER MAP CELL 4HE ABSCISSA IS IN RADAR SCANS AND THE ORDINATE IS PROBABILITY OF DETECTION OF THE POINT CLUTTER SOURCE 3INCE THE CLUTTER POINT HAS THE SAME AMPLITUDE STATISTICS AS THERMAL NOISE THE OUTPUT FALSE ALARM RATE APPROACHES 0F ASYMPTOTICALLY !GAINST A SLOWLY MOVING SOURCE OF CLUTTER EG BIRDS THE PROBABILITY OF DETECTION MAY INCREASE AS THE CLUTTER SOURCE CROSSES THE BOUNDARY BETWEEN TWO CLUTTER MAP CELLS 4O PREVENT THIS A SPREADING TECHNIQUE CAN BE USED THROUGH WHICH EACH CLUTTER MAP CELL WILL BE UPDATEDNOT ONLY WITH RADAR RETURNS FALLING WITHIN ITS BOUNDARIES BUT ALSO
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&)'52% 5NIVERSAL CURVE FOR DETERMINING DETECTABILITY LOSS CAUSED BY THE CLUTTER MAP
BY USING RADAR RETURNS IN ADJACENT CELLS IN RANGE AND AZIMUTH 4HROUGH THE USE OF SUCH SPREADING AN ADDITIONAL DEGREE OF CONTROL OVER THE CLUTTER MAP VELOCITY RESPONSE CAN BE ACHIEVED !N EXAMPLE OF THE VELOCITY RESPONSE OF A CLUTTER MAP INCLUDING SUCH SPREADING IS SHOWN IN &IGURE 4HE RANGE EXTENT OF THE CLUTTER MAP CELL IS MS THE RADAR RESO LUTION CELL IS MS N PULSES ARE NONCOHERENTLY INTEGRATED THE FILTERING CONSTANT IS @ THE UPDATE INTERVAL IS S AND THE 3.2 D" /N EACH SCAN THE CLUTTER MAP CELL IS UPDATED WITH THE RADAR AMPLITUDES IN THE FIVE RANGE CELLS FALLING WITHIN THE CLUTTER MAP CELL AND WITH THE AMPLITUDE FROM ONE ADDITIONAL RADAR RESOLUTION CELL BEFORE AND AFTER THE CLUTTER MAP CELL
&)'52% 4RANSIENT RESPONSE OF CLUTTER MAP DUE TO 3WERLING #ASE POINT CLUTTER MODEL
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&)'52% 6ELOCITY RESPONSE OF CLUTTER MAP
)T IS SEEN FROM &IGURE THAT THE VELOCITY RESPONSE CHARACTERISTIC OF THE CLUTTER MAP FROM STOPBAND TO PASSBAND IS SOMEWHAT GRADUAL IN THIS PARTICULAR IMPLEMENTATION 4HIS IS PARTLY DUE TO THE LARGE SIZE OF THE CLUTTER MAP CELL RELATIVE TO THE RADAR RESOLU TION ! FINER GRAIN MAP WITH ADDITIONAL SPREADING WOULD HAVE A MUCH BETTER VELOCITY RESPONSE CHARACTERISTIC ! POTENTIAL PROBLEM WITH THE TYPE OF AMPLITUDE CLUTTER MAP DESCRIBED IN THIS SEC TION IS THE FACT THAT A LARGE TARGET FLYING IN FRONT OF A SMALLER TARGET MAY CAUSE ENOUGH BUILDUP IN THE MAP TO SUPPRESS THE SMALL TARGET /NE WAY TO OVERCOME THIS PROBLEM IN A SYSTEM THAT INCLUDES AUTOMATIC TRACKING WOULD BE TO USE THE TRACK PREDICTION GATE TO INHIBIT UPDATING OF THE CLUTTER MAP WITH NEW TARGET AMPLITUDES
Ó°£ÈÊ - -/6/96 " /9Ê " /," Ê-6 ® )N THE MID S SEVERAL RADAR RESEARCHERS HAD REALIZED THAT SIGNAL PROCESSING ALGO RITHMS TO ESTIMATE THE UNAMBIGUOUS RADIAL VELOCITY OF A TARGET USING MULTIPLE 02& DWELLS DURING THE TIME OF TARGET WERE BECOMING PRACTICAL 4HESE RADIAL VELOCITY ESTI MATES COULD BE USED FOR IMPROVED FALSE ALARM CONTROL AGAINST SLOW MOVING TARGETS SUCH AS BIRDS 7HEN SUCH RADIAL VELOCITY MEASUREMENTS ARE PAIRED WITH CORRE SPONDING CROSS SECTION ESTIMATES A POWERFUL DISCRIMINANT FOR DISTINGUISHING BETWEEN SLOW MOVING BIRDS AND LOW CROSS SECTION MISSILES BECOMES POSSIBLE USING THE SO CALLED SENSITIVITY VELOCITY CONTROL 36# ALGORITHM 4HE 36# #ONCEPT 3ENSITIVITY VELOCITY CONTROL 36# IS USED WHEN A RADAR MUST DETECT AIRCRAFT AND MISSILE TARGETS IN THE PRESENCE OF RETURNS FROM UNWANTED TARGETS SUCH AS LARGE BIRDS OR BIRD FLOCKS 4HE CRITERIA TO ACCEPT OR REJECT TARGETS IS BASED ON A COMBINATION OF THE RADIAL VELOCITY AND APPARENT 2#3 RADAR CROSS SECTION OF THE TARGET RETURNS 4HE DESIRED TARGETS MAY HAVE AN 2#3 SMALLER THAN A SINGLE BIRD OR POSSIBLY
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A BIRD FLOCK IN A SINGLE RADAR RESOLUTION CELL 4HUS DISCRIMINATION REQUIRES A PARAME TER IN ADDITION TO THE TARGET 2#3 4HE AVAILABLE PARAMETER IS TARGET RADIAL VELOCITY "IRDS TYPICALLY FLY AT KNOTS OR LESS WHEREAS TARGETS OF CONCERN USUALLY HAVE AIRSPEEDS OF KNOTS OR MORE )F THE RADAR CAN MAKE UNAMBIGUOUS RADAR DOPPLER MEASUREMENTS OF EG o KNOTS WITH A SINGLE #0) COHERENT PROCESSING INTERVAL THE RADAR CAN DETERMINE THE TRUE RADIAL VELOCITY OF EACH RADAR ECHO FROM RETURNS OF THREE OR MORE CONSECUTIVE #0)S AT DIFFERENT 02&S 4HE ACCEPTANCE CRITERIA OF THE 36# ALGORITHM RELATES TO THE TYPE OF TARGET AIRCRAFT MISSILE BIRD ETC BEING ACCEPTED OR REJECTED )N GENERAL THE CRITERIA ACCEPTS LARGE TAR GETS HAVING LOW TO HIGH RADIAL VELOCITIES 4HE SMALLER THE APPARENT RADAR CROSS SECTION OF THE TARGET THE HIGHER THE TRUE RADIAL VELOCITY MUST BE FOR ACCEPTANCE 4HE TRUE RADIAL VELOCITY VERSUS APPARENT RADAR CROSS SECTION PROFILE IS INTENDED TO ACCEPT AIRCRAFT AND MISSILES BUT REJECT BIRDS 4HEREFORE THREATENING TARGETS THAT HAVE HIGH RADIAL VELOCI TIES BUT VERY SMALL 2#3 CAN BE INSTANTLY IDENTIFIED WHEREAS RETURNS FROM BIRDS WITH THEIR SLOW RADIAL VELOCITIES CAN BE CENSORED ! TYPICAL 3#6 ACCEPTREJECT ALGORITHM IS DEPICTED IN &IGURE 4O OBTAIN THE DOPPLER SPACE OF o KNOTS AMBIGUOUS RANGE 02&S MUST BE USED 4HIS REQUIRES APPROXIMATE 02&S OF (Z AT , BAND (Z AT 3 BAND AND (Z AT 8 BAND UNAMBIGUOUS RANGES RESPECTIVELY NMI NMI AND NMI 4HE TRADEOFF FOR SELECTING 02&S IS THAT IN A DENSE TARGET ENVIRONMENT WHEN TRY ING TO RESOLVE TRUE RADIAL VELOCITY USING DIFFERENT 02&S hGHOSTSve MAY BE CREATED
e h'HOSTSv OCCUR WHEN TARGETS OR NOISE PEAKS AT DIFFERENT UNAMBIGUOUS RANGES FOLD INTO THE SAME BUT INCORRECT TRUE RANGE CELL 4HE VELOCITY RESOLUTION ALGORITHM THEN GIVES AN INCORRECT RESULT AND THE GHOSTS MAY BE DECLARED AS THREATENING TARGETS
-4) 2!$!2
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)N ADDITION TO THE hGHOSTv PROBLEM MULTIPLE RANGE AMBIGUITIES LEAD TO TARGETS HAVING TO COMPETE WITH CLUTTER AT ALL RANGES )N PARTICULAR TARGETS AT LONG DISTANCES HAVE TO COMPETE WITH STRONG CLUTTER RETURNS IN THE FIRST OR SEVERAL RANGE INTERVALS "ECAUSE OF THE GHOSTING PROBLEM IN ORDER TO MINIMIZE RANGE AMBIGUITIES WHILE RETAINING ADEQUATE DOPPLER SPACE 2& FREQUENCIES OF -(Z OR LOWER ARE BEST SUITED FOR THE 36# UNWANTED TARGET DISCRIMINATION TECHNIQUE 2ANGE AND 2ANGE 2ATE !MBIGUITY 2ESOLUTION 4O APPLY THE 36# ALGORITHM TRUE RANGE AND RADIAL VELOCITY RANGE RATE MUST BE DETERMINED FROM THE RANGE AMBIG UOUS AND DOPPLER AMBIGUOUS WAVEFORM 4HIS REQUIRES MULTIPLE DETECTIONS FROM THE SAME TARGET !SSUME A DOPPLER FILTER BANK OF N PULSE &)2 FILTERS AND ASSUME A PROCESS ING DWELL THAT CONSISTS OF THREE #0)S 4HE #0)S MUST USE DIFFERENT 02&S AND MAY ALSO EMPLOY DIFFERENT 2& FREQUENCIES 4HE DIFFERENT 2& FREQUENCIES CHANGE TARGET 2#3 STATISTICS FROM 3WERLING TO 3WERLING AND THUS LESS RADAR ENERGY IS REQUIRED FOR HIGH PROBABILITY OF DETECTION 4HE #0)S MUST HAVE SUFFICIENT TRANSMITTED PULSES SO THAT N RETURNS ENOUGH TO FILL AN N PULSE FILTER WILL BE RECEIVED FROM THE MOST DISTANT TARGET OF INTEREST AND THE MOST DISTANT CLUTTER AND ONE ADDITIONAL PULSE TO ENABLE VELOCITY DETERMINATION MORE ON THIS LATER 4RUE 2ANGE $ETERMINATION 4HE MOST STRAIGHTFORWARD WAY TO DETECT A TARGET AND SIMULTANEOUSLY DETERMINE ITS TRUE RANGE IS TO DETERMINE ON EACH #0) ALL hPRIMITIVEv DETECTIONS AT THE OUTPUT OF THE DOPPLER FILTER BANK &OR THIS IT IS ASSUMED THAT EACH DOPPLER FILTER OUTPUT IS PROCESSED THROUGH AN APPROPRIATE CLUTTER MAP THRESHOLD AND CELL AVERAGING #&!2 TO CONTROL THE FALSE ALARM RATE &OR EACH PEAK DETECTION ADJACENT AMPLITUDES WILL BE USED TO OBTAIN AN ACCURATE AMBIGUOUS RANGE ESTIMATE DENOTED R}I WHERE THE SUBSCRIPT REFERS TO THE #0) NUMBER !LSO FROM THE SPECIFIC DOPPLER FILTER CORRESPONDING TO THE PEAK DETECTION DESCRIBED ABOVE THE PHASE PI OF THE RETURN IS SAVED )N ADDITION A CORRESPONDING PHASE P I OBTAINED FROM AN IDENTICAL SECOND DOP PLER FILTER BANK TRAILING OR LEADING THE DETECTION FILTER BANK BY ONE PULSE REPETITION INTERVAL 02) IS SAVED 4HIS EXPLAINS WHY A #0) OF N PULSES IS NEEDED TO IMPLEMENT THE 36# CONCEPT &OR EACH PRIMITIVE DETECTION IN A #0) CALCULATE THE SET OF ALL POSSIBLE TARGET RANGES OUT TO THE MAXIMUM INSTRUMENTED RANGE 2MAX
2} I R}I M 202) I
M MMAX
WHERE MMAX INT 2MAX 202) I
I
WHERE 202) I IS THE AMBIGUOUS RANGE INTERVAL CORRESPONDING TO THE ITH #0) !FTER THE PRIMITIVE DETECTIONS FROM ALL #0)S IN THE PROCESSING DWELL HAVE BEEN PROCESSED THE VALUES OF 2} I FROM ALL #0)S ARE SORTED INTO A SINGLE LIST ! FINAL RANGE DETECTION AND ITS TRUE RANGE IS THEN FOUND AS A CLUSTER OF THREE PRIMITIVE DETECTIONS HAVING POSSIBLE RANGES WITHIN AN ERROR WINDOW OF TWO TO THREE TIMES THE STANDARD DEVIATION OF THE AMBIGUOUS RANGE ESTIMATE 4RUE 2ADIAL 6ELOCITY $ETERMINATION &OR EACH TRUE TARGET DETECTION AN UNAM BIGUOUS RADIAL VELOCITY ESTIMATE MUST NEXT BE DETERMINED USING A SIMILAR PROCE DURE TO THAT DESCRIBED ABOVE FOR RANGE &OR THIS AN ACCURATE ESTIMATE F}D I OF THE AMBIGUOUS TARGET RADIAL VELOCITY MUST BE OBTAINED AT THE RANGE CORRESPONDING TO THE AMBIGUOUS PRIMITIVE TARGET DETECTION ON EACH #0) 4HIS FREQUENCY ESTIMATION PROBLEM HAS BEEN STUDIED BY MANY AUTHORS WITH THE BEST APPROACH BEING DEFINED
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BY THE MAXIMUM LIKELIHOOD ESTIMATE &OR A SINGLE PULSE SIGNAL TO NOISE RATIO 3 AND N PULSES IN A #0) THE #RAMER 2AO LOWER BOUND FOR THE ACCURACY OF THE DOPPLER FREQUENCY ESTIMATE IS
SF 02& P 3 N N
3 N N
3INCE THE MAXIMUM LIKELIHOOD ESTIMATION PROCEDURE TENDS TO REQUIRE A TEDIOUS COMPUTATIONAL BURDEN A SIMPLIFIED APPROACH FOR ESTIMATING THE DOPPLER FREQUENCY IS HIGHLY DESIRABLE /NE SUCH APPROACH USING PHASE MEASUREMENTS OF THE DOPPLER FILTER OUTPUT AT TIMES SEPARATED BY ONE INTERPULSE PERIOD WAS PRESENTED IN -C-AHON AND "ARRETT 4HE NORMALIZED DOPPLER FREQUENCY ESTIMATE IS FD I Q Q I I 02& P
AND THE CORRESPONDING RADIAL VELOCITY IS
V}I
FD I L
)N MOST CASES OF INTEREST THE ACCURACY OF THIS ESTIMATE OF DOPPLER FREQUENCY IS AS GOOD AS THE MAXIMUM LIKELIHOOD PROCEDURE %XPRESSED IN TERMS OF THE NUMERATOR OF %Q WHICH WILL BE DENOTED BY K A SIMULATION OF THE PHASE DIFFERENCE ESTIMA TOR USING DIFFERENT WEIGHTING FUNCTIONS FOR THE DOPPLER FILTER BANK ARE SUMMARIZED IN &IGURE )T IS NOTED THAT THE PERFORMANCE OF THE PHASE DIFFERENCE ESTIMATION PROCEDURE IS BEST WHEN MODERATE 4AYLOR WEIGHTING FUNCTIONS ARE USED &OR UNIFORM WEIGHTING THE PROCEDURE WOULD BE SUBSTANTIALLY INFERIOR TO THE MAXIMUM LIKELIHOOD APPROACH 4HE INCREASE IN THE CONSTANT K FOR THE MORE SEVERE WEIGHTING CASES IS THE RESULT OF THE 3.2 LOSS RESULTING FROM THE USE OF WEIGHTING 5SING AN APPROACH SIMILAR TO THAT USED TO RESOLVE THE RANGE AMBIGUITY ALL POSSIBLE RADIAL VELOCITIES ARE THEN ENUMERATED TO THE MAXIMUM NEGATIVE AND POSITIVE RADIAL VELOCITY OF INTEREST ON EACH OF THE #0)S
6}I V}I M 6" I
M MMAX MMAX MMAX
WHERE MMAX INT6MAX 6" I
I
)N THIS EQUATION 6" I 02&I L IS THE BLIND VELOCITY FOR THE ITH #0) 4HE POS SIBLE TARGET RADIAL VELOCITIES FOR ALL #0)S ARE THEN SORTED INTO A SINGLE LIST AND THE MOST LIKELY TRUE RADIAL VELOCITY IS FOUND WHERE AT LEAST TWO POSSIBLE VELOCITIES FALL WITHIN AN INTERVAL LESS THAN TWO OR THREE TIMES THE STANDARD DEVIATION OF THE DOPPLER FREQUENCY ESTIMATE 4HE TIGHTNESS OF THE CLUSTER OF NEARLY IDENTICAL VELOCITIES IN CONJUNCTION WITH THE NUMBER OF #0)S CONTRIBUTING TO THE CLUSTER CAN BE UTILIZED AS A MEASURE OF RELIABILITY OF THE UNAMBIGUOUS RADIAL VELOCITY ESTIMATE
4HIS APPROACH WAS FIRST BROUGHT TO THE ATTENTION OF THE AUTHORS BY $R "EN #ANTRELL OF THE 53 .AVAL 2ESEARCH ,ABORATORY
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!& &)'52% 0ERFORMANCE OF PHASE DIFFERENCE DOPPLER FREQUENCY ESTIMATOR FOR DIFFERENT WEIGHTING FUNCTIONS OF THE DOPPLER FILTER BANK
#OMMENTS 4HE ABOVE PROCEDURE FOR DETERMINING TRUE RANGE AND TRUE RADIAL VELOC ITY HAS BEEN DESCRIBED FOR A DWELL OF THREE #0)S AND THE ASSUMPTION THAT EACH TARGET WILL HAVE A RETURN FOR EACH OF THE THREE #0)S )N PRACTICE THIS ASSUMPTION IS NOT ALWAYS VALID AND THE ACTUAL IMPLEMENTATION MAY CHOOSE FOR EXAMPLE TO HAVE THE DWELL CON SIST OF FOUR OR FIVE #0)S WITH THE RANGE AND VELOCITY DETERMINATIONS BEING BASED ON THE BEST GROUPING OF THREE RETURNS 4HE ACTUAL IMPLEMENTATION MUST BE BASED ON THE PARAMETERS OF THE SYSTEM AND PERMISSIBLE TIME ALLOCATED FOR EACH DWELL 4HE 02&S OF THE #0)S SHOULD BE SELECTED TO MINIMIZE THE CHANCE OF FALSE RADIAL VELOCITY DETERMINATIONS /NE METHOD OF SELECTING 02&S IS SIMILAR TO SELECTING PULSE INTERVAL RATIOS FOR STAGGERED 02& OPERATION AS DESCRIBED IN 3ECTION &OR EXAM PLE IF OPERATING AT AN AVERAGE 2& FREQUENCY OF -(Z AT AN AVERAGE 02& OF (Z AMBIGUOUS VELOCITY OF KNOTS AND COVERING A VELOCITY RANGE OF INTEREST OF o KNOTS THERE ARE APPROXIMATELY DOPPLER AMBIGUITIES TO COVER 5SING THE FACTORS OF n n AS USED IN 02& STAGGER SELECTION THE INTERPULSE PERIODS OF THE FOUR DIFFERENT 02&S WOULD BE IN THE RATIO OF 4HE AVERAGE OF THESE RATIOS IS 4HE 02&S ARE CALCULATED AS q q q AND q 4HE 02&S WOULD BE ABOUT AND (Z
Ó°£ÇÊ " - ,/" -Ê** ÊÊ /"Ê /Ê, ,Ê-9-/ -4) RADAR SYSTEM DESIGN ENCOMPASSES MUCH MORE THAN SIGNAL PROCESSOR DESIGN 4HE ENTIRE RADAR SYSTEMTRANSMITTER ANTENNA AND OPERATIONAL PARAMETERSMUST BE KEYED TO FUNCTION AS PART OF AN -4) RADAR &OR EXAMPLE EXCELLENT -4) CONCEPTS WILL NOT PERFORM SATISFACTORILY UNLESS THE RADAR LOCAL OSCILLATOR IS EXTREMELY STABLE AND THE
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TRANSMITTER HAS VERY LITTLE PULSE TO PULSE FREQUENCY OR PHASE JITTER )N ADDITION THE SYSTEM MUST SUCCESSFULLY OPERATE IN AN ENVIRONMENT THAT COMPRISES MANY UNWANTED TARGETS SUCH AS BIRDS INSECTS AND AUTOMOBILES (ARDWARE #ONSIDERATIONS )N THIS SECTION RULES AND FACTS RELATING TO -4) RADAR DESIGN AS DEVELOPED DURING MANY YEARS OF WORK IN THE FIELD WILL BE SUMMARIZED 4HE RULES ARE AS FOLLOWS /PERATE AT CONSTANT DUTY CYCLE 3YNCHRONIZE AC DC AND DC DC POWER CONDITIONERSo TO HARMONICS OF THE 02& $ESIGN THE SYSTEM TO BE FULLY COHERENTp 0ROVIDE )& ,IMITERS PRIOR TO !$ CONVERTERS "E WARY OF VIBRATION AND ACOUSTIC NOISE 4HE FACTS ARE AS FOLLOWS 4HE BASIC -4) CONCEPT DOES NOT REQUIRE A LONG TIME ON TARGET TO RESOLVE TARGETS FROM FIXED CLUTTER )NSTEAD -4) SYSTEMS REJECT FIXED CLUTTER THROUGH A SUBTRACTION PROCESS WHILE RETAINING MOVING TARGETS 4RANSMITTER INTRAPULSE ANOMALIES HAVE NO AFFECT ON -4) PERFORMANCE IF THEY REPEAT PRECISELY PULSE TO PULSE 2ULE /PERATE AT CONSTANT DUTY CYCLE 4HE TRANSMITTER WHETHER THE TRANSMITTER IS A SINGLE LARGE TUBE OR A DISTRIBUTED FUNCTION AS IN AN ACTIVE PHASED ARRAY WITH MANY TRANSMIT RECEIVE ELEMENTS SHOULD BE OPERATED AT CONSTANT DUTY CYCLE 4HIS PERMITS THE TRANSMITTER POWER SUPPLY TRANSIENT EFFECTS TO BE IDENTICAL PULSE TO PULSE AND ALSO PARTICULARLY APPLICABLE TO SOLID STATE TRANSMIT DEVICES PERMITS THE DEVICE HEATING AND COOLING TO BE IDENTICAL FROM PULSE TO PULSE 3OMETIMES CONSTANT DUTY CYCLE OPERATION IS NOT POSSIBLE BUT THERE ARE VARIOUS TECHNIQUES THAT CAN BE USED TO APPROACH THIS DESIRED CONDITION #ONSIDER AN -4$ WAVEFORM WHERE A #0) CONSISTING OF N PULSES IS TRANSMIT TED WITH A CONSTANT 02) 4HE NEXT #0) USES A DIFFERENT 02) #ONSTANT DUTY CYCLE CAN BE MAINTAINED BY CHANGING THE TRANSMITTED PULSE LENGTH IN PROPORTION TO THE CHANGE IN THE 02) )F PULSE COMPRESSION IS USED THE RANGE RESOLUTION OF THE COMPRESSED PULSE CAN BE MAINTAINED BY CHANGING THE PULSE COMPRESSION WAVEFORM )F IT IS NECESSARY TO UTILIZE PRECISELY THE SAME WAVEFORM AND 2& PULSE LENGTH FROM #0) TO #0) WITH FOR EXAMPLE A KLYSTRON TRANSMITTER THE BEAM PULSE OF THE KLYSTRON CAN BE VARIED TO MAINTAIN CON STANT BEAM DUTY CYCLE WHILE THE 2& PULSE LENGTH IS MAINTAINED CONSTANT 4HIS WASTES PART OF THE BEAM PULSE ENERGY FOR THE LONGER 02)S BUT THE AVERAGE POWER LOADING ON THE POWER SUPPLY REMAINS CONSTANT 4HE SAME TECHNIQUE CAN BE UTILIZED WITH SOLID STATE DEVICES BY CHANGING THE DRAIN VOLTAGE PULSE DURATION WHILE HOLDING THE 2& PULSE CONSTANT ! SECOND ORDER CORRECTION THAT HAS BEEN UTILIZED WHEN CHANGING BETWEEN #0)S WITH DIFFERENT 02)S IS TO HAVE A TRANSITION 02) THAT IS THE AVERAGE OF THE TWO 02)S 7ITH PHASED ARRAY RADARS IF THE BEAM TRANSITION TIME BETWEEN #0)S TAKES LONGER THAN A 02) IT IS IMPORTANT TO KEEP THE TRANSMITTER PULSING AT A CONSTANT DUTY CYCLE DURING THE TRANSITION TIME )F CONSTANT DUTY CYCLE CANNOT BE MAINTAINED OR WHEN STARTING TO RADIATE o 0OWER CONDITIONERS ACCEPT EITHER AC OR DC INPUT AND PROVIDE A REGULATED DC OUTPUT p h&ULLY COHERENTv IS DESCRIBED UNDER RULE
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AFTER DEAD TIME THE TRANSMITTER POWER SUPPLY AND HEATING EFFECTS MUST BE ALLOWED TO SETTLE BEFORE GOOD -4) PERFORMANCE CAN BE EXPECTED 4HE DURATION OF THE SETTLING TIME DEPENDS ON THE SYSTEM PARAMETERS AND THE REQUIREMENTS 2ULE 3YNCHRONIZE AC DC AND DC DC POWER CONDITIONERS TO HARMONICS OF THE 02& 7HEN AC DC ANDOR DC DC POWER CONDITIONERS ARE USED FOR VOLTAGES APPLIED TO TRANSMITTING DEVICES THE FREQUENCY AND ITS HARMONICS OF THE CONVERTER MUST BE ATTEN UATED SUFFICIENTLY SO THAT THEY DO NOT MODULATE THE PHASE OF THE TRANSMITTED PULSES )F THE POWER CONDITIONER FREQUENCIES CANNOT BE SUFFICIENTLY ATTENUATED THEIR FREQUENCY SHOULD BE SYNCHRONIZED TO A MULTIPLE OF THE 02& OF THE #0) SO THAT MODULATIONS REPEAT PRECISELY PULSE TO PULSE AND THUS WILL CANCEL LIKE STATIONARY CLUTTER 2ULE $ESIGN THE SYSTEM TO BE FULLY COHERENT !LL FREQUENCIES AND TIMING SIGNALS SHOULD BE GENERATED FROM A SINGLE MASTER OSCILLATOR $OING THIS MAKES THE ENTIRE SYS TEM COHERENT AND MIXER PRODUCTS WILL BE IDENTICAL PULSE TO PULSE AND WILL THEREFORE CANCEL IN THE -4) FILTERS 7HEN THIS COHERENCE OF ALL FREQUENCIES IS NOT MAINTAINED CLUTTER RESIDUE WILL OCCUR AND MUST BE QUANTIFIED TO DETERMINE IF IT IS AT AN ACCEPTABLE LEVEL /NE OF THE PROMINENT PLACES IN WHICH RESIDUE CAUSED BY UNSYNCHRONIZED LOCAL OSCILLATORS HAS SHOWN UP IS IN PULSE COMPRESSION SIDELOBES )F THE PULSE COMPRESSION SIDELOBES FROM FIXED CLUTTER RETURNS VARY FROM PULSE TO PULSE THEY DO NOT CANCEL 4HIS COHERENCY ISSUE HAS BEEN FURTHER DISCUSSED BY 4AYLOR 2ULE 0ROVIDE )& ,IMITERS PRIOR TO !$ CONVERTERS -4) RADARS REQUIRE THAT )& BANDPASS LIMITERS EXIST PRIOR TO AN !$ ANALOGDIGITAL CONVERTER 4HE LIMITER PREVENTS ANY CLUTTER RETURN FROM EXCEEDING THE DYNAMIC RANGE OF THE !$ 4HIS REQUIREMENT EXISTS FOR EITHER QUADRATURE ) 1 IN PHASE QUADRATURE SAMPLING OR DIRECT SAMPLING WITH THE ) AND 1 DATA CONSTRUCTED AFTER THE !$ 4HE LIMITER MUST BE DESIGNED TO MINIMIZE THE CONVERSION OF AMPLITUDE TO PHASE NO MATTER HOW MUCH THE SIGNAL LEVEL EXCEEDS THE LIMIT LEVEL )F CLUTTER SATURATES THE !$ THE ) 1 DATA IS SIGNIFICANTLY COR RUPTED 7HEN LIMITERS PREVENT !$ SATURATION THE SIGNALS ARE LIMITED IN A CONTROLLED MANNER THAT STILL ENABLES GOOD CLUTTER REJECTION ABOUT OF THE TIME 2ULE "E WARY OF VIBRATION AND ACOUSTIC NOISE -ANY 2& DEVICES ARE SUSCEPTIBLE TO BOTH VIBRATION AND ACOUSTIC NOISE !N AIR CONDITIONER FAN BLOWING ON WAVEGUIDE HAS CAUSED DEGRADATION OF IMPROVEMENT FACTOR DUE TO PHASE MODULATION OF SIGNALS 6IBRATIONS CAN CAUSE PHASE MODULATION OF AN OSCILLATOR !COUSTIC NOISE CAN ORIGINATE FROM COOLING FANS AND VIBRATIONS CAN COME FROM SHIPBOARD OR AIRBORNE RADAR PLAT FORMS #OMPONENTS SUCH AS KLYSTRONS AND SOLID STATE MODULES CAN HAVE UNEXPECTED SUSCEPTIBILITY TO VIBRATION 2& CONNECTORS MUST BE SECURE 3HOCK MOUNTS CAN BE USED TO ISOLATE COMPONENTS FROM THE CABINET STRUCTURE )T IS RECOMMENDED THAT ALL 2& COM PONENTS IN THEIR OPERATIONAL CONFIGURATION BE TESTED FOR PHASE STABILITY IN THE VIBRATION ENVIRONMENT IN WHICH THEY WILL BE USED &ACT 4HE BASIC -4) CONCEPT DOES NOT REQUIRE SUFFICIENT TIME ON TARGET TO RESOLVE TARGETS FROM FIXED CLUTTER USING A LINEAR TIME INVARIANT FILTER )NSTEAD -4) SYSTEMS REJECT FIXED CLUTTER THROUGH A SUBTRACTION PROCESS WHILE RETAINING MOVING TARGETS !N -4) SYSTEM USING A TWO PULSE CANCELER REQUIRES THE TRANSMITTER TO TRANSMIT ONLY TWO SUC CESSIVE IDENTICAL PULSES FOR THE SYSTEM TO BE ABLE TO REJECT STABLE FIXED CLUTTER 4HE RADAR RETURNS FROM THE SECOND PULSE ARE SUBTRACTED FROM THE RETURNS FROM THE FIRST PULSE
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4HE RESULT FROM THIS SUBTRACTION PROCESS IS THAT THE FIXED CLUTTER IS REMOVED AND MOVING TARGETS ARE RETAINED 4HE OUTPUT FROM THE FIRST PULSE IS NOT USED MAKING THIS TYPE OF -4) FILTER TIME VARIANT /F COURSE THE CLUTTER FILTERS MAY BE MORE COMPLEX THAN A TWO PULSE CANCELER e BUT THE PRINCIPLE STILL REMAINS THAT FIXED CLUTTER IS REJECTED BY THE ZEROS IN THE CANCELER TRANSFER CHARACTERISTIC 4HIS ENABLES PHASED ARRAY RADARS TO HAVE GOOD CLUT TER REJECTION WITH SHORT DWELLS
&ACT 4RANSMITTER INTRAPULSE ANOMALIES HAVE NO AFFECT ON -4) PERFORMANCE IF THEY REPEAT PRECISELY PULSE TO PULSE 4RANSMITTED PULSES SHOULD BE IDENTICAL )T DOES NOT MATTER IF THERE IS INTRAPULSE AMPLITUDE OR FREQUENCY MODULATION OF THE TRANSMITTED PULSE AS LONG AS IT REPEATS PRECISELY FROM PULSE TO PULSE )F THE VOLTAGE OF THE TRANS MITTER POWER SUPPLY VARIES PULSE TO PULSE THE TRANSMITTED PULSES WILL NOT BE IDENTI CAL AND THE RESULTING VARIATIONS MUST BE QUANTIFIED TO DETERMINE IF THE LIMITATIONS ON IMPROVEMENT FACTOR FALL WITHIN THE STABILITY BUDGET FOR THE SYSTEM (OWEVER IF THE ONLY DIFFERENCE BETWEEN PULSES IS ABSOLUTE PHASE NOT INTRAPULSE VARIATIONS PULSE TO PULSE SOME MITIGATION IS POSSIBLE /NE METHOD OF COMPENSATING FOR SMALL VARIATIONS IN THE PHASE OF TRANSMITTER PULSES FOLLOWS ,INCOLN ,ABORATORY CHANGED THE ORIGINAL 4$72 WAVEFORM TO AN -4$ TYPE WAVEFORM 4HE ORIGINAL 4$72 WAVEFORM WAS CONSTANT 02& DURING EACH ANTENNA ROTATION AND PROCESSING WAS DONE WITH ELLIPTIC FILTERS 4HEY THEN MODIFIED THE SYSTEM hxTO ACHIEVE D" CLUTTER SUPPRESSION USING A NEARBY WATER TOWER FOR A TARGETv 4HE 4$72 USES A KLYSTRON TRANSMITTER TUBE 4YPICAL PHASE PUSHING FOR A KLYSTRON DUE TO MODULATOR VOLTAGE CHANGE IS FOR DELTA %% 4HE STABILITY BUDGET ALLOCATED A D" LIMIT ON IMPROVEMENT FACTOR TO THE TRANSMITTER AND THIS REQUIRED THAT THE RMS PULSE TO PULSE POWER SUPPLY VOLTAGE VARIATION BE LESS THAN PART IN 4HE TRANSMITTER POWER SUPPLY COULD NOT MEET THIS REQUIREMENT WHEN THE RADAR CHANGED 02& FROM #0) TO #0) AS REQUIRED BY AN -4$ WAVEFORM 4HEREFORE THE ACTUAL PHASE OF EACH TRANSMITTED PULSE WAS MEASURED AND THIS MEASURED VALUE WAS USED TO CORRECT THE PHASE OF THE RECEIVED SIGNALS FOR THAT 02) 4HIS TECHNIQUE CAUSES SMALL PERTURBATIONS IN PHASE FROM WEATHER SIGNALS RECEIVED FROM AMBIGUOUS RANGES BUT DOES NOT INTERFERE WITH VELOCITY ESTIMATES )T DOES DEGRADE THE IMPROVEMENT FACTOR OF CLUTTER SIGNALS RECEIVED FROM AMBIGUOUS RANGES BUT FOR THE 4$72 OPERATION THAT DEGRADATION WAS DEEMED ACCEPTABLE %NVIRONMENTAL #ONSIDERATIONS 4HIS DISCUSSION CONTAINS ESSENTIAL INFORMA TION FOR THOSE DESIGNING A MODERN SURVEILLANCE RADAR TO DETECT MAN MADE AIRBORNE TARGETS 4HE LAWS OF PHYSICS COMBINED WITH THE ENVIRONMENT MAKE IT IMPOSSIBLE TO DESIGN AN -4) SURVEILLANCE RADAR THAT DOES NOT HAVE COMPROMISES 4HE PROBLEMS ARE RELATED TO THE UNWANTED RETURNS FROM BIRDS INSECTS AUTOMOBILES LONG RANGE FIXED CLUTTER AND SHORT AND LONG RANGE WEATHER 4HE CURRENT STATE OF THE ART OF RADAR CAN AMELIORATE THESE PROBLEMS BUT NOT WITHOUT SOME UNDESIRABLE SIDE EFFECTS -ANY UNWANTED POINT TARGET RETURNS HAVE CHARACTERISTICS SIMILAR TO THE RETURNS FROM WANTED TARGETS AND THE UNWANTED RETURNS MAY OUTNUMBER RETURNS FROM DESIRED TAR GETS BY THE THOUSANDS
e 4HE CLUTTER FILTERS MUST BE DESIGNED BASED ON SYSTEM PARAMETERS TO REJECT THE RADIAL SPEED OF THE hFIXEDv CLUTTER 3EE 3ECTIONS AND
)T HAS BEEN OBSERVED THAT SOME PHASED ARRAY RADARS HAVE POOR CLUTTER REJECTION WHICH IS OFTEN CAUSED BY FAILURE TO FOLLOW RULE
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4HE PROBLEMS ARE EXACERBATED WHEN ANOMALOUS OR DUCTED PROPAGATION OCCURS ANOMALOUS PROPAGATION AS USED HEREIN IS WHEN THE RADAR ENERGY FOLLOWS THE CURVATURE OF THE %ARTH THUS CAUSING DETECTION OF BOTH FIXED AND MOVING CLUTTER AT LONG RANGES &IGURE FROM 3HRADER SHOWS 00) PHOTOGRAPHS TAKEN WITH AN !232 RADAR MOUNTED ON A FT TOWER IN FLAT COUNTRY NEAR !TLANTIC #ITY .EW *ERSEY 7ITH NORMAL PROPAGATION THE EXPECTED LINE OF SIGHT IS ABOUT NMI BUT THE CLUTTER ACTUALLY GOES OUT TO NMI 4HE BRIDGES ACROSS THE INTRACOASTAL WATERWAY CAN BE SEEN /N OCCASION THE UNWANTED LONG RANGE CLUTTER AND WEATHER RETURNS COME FROM AMBIGUOUS RANGES
&)'52% !NOMALOUS PROPAGATION DUCTING A NMI MAXIMUM RANGE AND B NMI MAXIMUM RANGE
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4HE RADAR SYSTEM MUST HAVE FEATURES TO COPE WITH THESE SITUATIONS &OR EXAMPLE IF PULSE TO PULSE STAGGERING IS USED THE AMBIGUOUS RANGE CLUTTER WILL NOT CANCEL AND EITHER THE 02) MUST BE INCREASED OR THE 02) MUST BE MADE CONSTANT OVER THE AZIMUTH ANGLES FROM WHICH THE AMBIGUOUS RANGE CLUTTER IS RECEIVED !ND BE FOREWARNED OF A PITFALL INTO WHICH MANY RADAR DESIGNERS HAVE FALLEN &OR EXAMPLE WHEN PRESENTED WITH THE REQUIREMENT TO TRACK TARGETS THE DESIGNER MAY NOT REALIZE THAT RADAR RETURNS FROM THE TARGETS OF INTEREST MAY BE EMBEDDED IN SIMILAR RETURNS FROM THOUSANDS OF UNWANTED TARGETS ! TYPICAL LONG RANGE AIR TRAFFIC CONTROL RADAR HAS SUFFICIENT SENSITIVITY TO DETECT A SINGLE LARGE BIRD SUCH AS A CROW SEAGULL OR VULTURE APPROXIMATE 2#3 OF SQUARE METER AT A RANGE OF MILES )F THERE ARE MANY SUCH BIRDS IN THE RESOLUTION CELL OF THE RADAR THEN THE COMPOSITE 2#3 INCREASES 4EN LARGE BIRDS IN A RESOLUTION CELL WILL HAVE AN 2#3 OF SQUARE METER 7HEN MULTIPATH REFLECTIONS OCCUR SUCH AS OVER THE OCEAN WHEN THE RADAR BEAM IS CENTERED AT THE HORIZON THERE CAN BE UP TO A D" ENHANCEMENT OF THE 2#3 OF THE BIRDS GIVING AN APPARENT 2#3 GREATER THAN ONE SQUARE METER TO THE FLOCK OF BIRDS )F THERE IS BIRD OR BIRD FLOCK PER SQUARE MILE THERE WILL BE ABOUT BIRD RETURNS WITHIN MILES OF THE RADAR 4ECHNIQUES USED TO COUNTER UNWANTED TARGETS ARE AS FOLLOWS 3ENSITIVITY TIME CONTROL 34# USED FOR ELIMINATING LOW 2#3 TARGETS IN LOW 02& RADARSTHAT IS RADARS THAT HAVE NO RANGE AMBIGUITIES UNDER NORMAL OPERATION %NHANCED HIGH ANGLE GAIN ANTENNAS 4WO BEAM ANTENNASBEAM LIFTED ABOVE THE HORIZON FOR SHORT RANGE RECEPTION AND THEN LOWERED TO HORIZON FOR LONG RANGE -4$ TECHNIQUES USING CLUTTER MAPS !LSO COUNTING DETECTIONS IN SMALL RANGE AZIMUTH SECTORS AND INCREASING DETECTION THRESHOLDS IN EACH SECTOR IF TOO MANY DETECTIONS OCCUR 02&S HIGH ENOUGH SO THAT ALL TARGETS WITH RADIAL VELOCITIES BELOW KNOTS CAN BE CENSORED 3ENSITIVITY VELOCITY CONTROL 36# WHICH CENSORS RADIALLY SLOW SMALL TARGETS WHILE ACCEPTING RADIALLY FAST TARGETS AND LARGE TARGETS #OMBINATIONS OF TECHNIQUES THROUGH ARE USED IN MOST AIR TRAFFIC CONTROL RADARS WHERE THE SMALLEST TARGETS OF INTEREST HAVE AN 2#3 OF ONE SQUARE METER OR GREATER 4ECHNIQUES AND ARE USED WHEN THE DESIRED TARGETS MAY HAVE RADAR CROSS SECTIONS SIMILAR TO OR SMALLER THAN A BIRD 4ECHNIQUE 34# IS THE TRADITIONAL METHOD OF SUPPRESSING BIRDS AND INSECTS IN A RADAR WITH AN UNAMBIGUOUS RANGE 02& A 02& LOW ENOUGH SO THAT THE RANGE TO TARGETS AND CLUTTER IS UNAMBIGUOUS 34# DECREASES THE SENSITIVITY OF THE RADAR AT SHORT RANGE AND THEN INCREASES SENSITIVITY USUALLY USING A FOURTH POWER LAW AS RANGE INCREASES 4HIS HAS THE EFFECT OF NOT PERMITTING DETECTION OF TARGETS WITH APPARENT RADAR CROSS SEC TIONS OF SAY LESS THAN SQUARE METER &IGURE SHOWS HOW EFFECTIVE 34# CAN BE AGAINST BIRDS 4HESE 00) PHOTOS WERE TAKEN WITH AN , BAND !232 AIR ROUTE SURVEIL LANCE RADAR IN /KLAHOMA .OTE THAT THE MAJORITY OF RETURNS FROM BIRDS WERE ELIMI NATED BUT NOT &IGURE SHOWS THE EFFECT OF 34# AGAINST BATS AND INSECTSo o $AYTIME BIRD RETURNS AND NIGHTTIME BAT AND INSECT RETURNS CAN OFTEN BE SEEN IN REAL TIMETHE EXTENT DEPENDS ON THE WEATHER AND TIME OF YEARON THE .%82!$ 732 $ WEATHER RADAR IMAGES ON THE ./!! )NTERNET SITES
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&)'52% 34# CAN GREATLY REDUCE THE NUMBER OF BIRDS DISPLAYED 2ANGE NMI A "IRDS SEEN WITH -4) AND B BIRDS SEEN WITH -4) AND 34#
&)'52% )NSECTS WITH AND WITHOUT 34# AND RANGE MILES A BATS AND INSECTS SEEN WITH -4) AND B BATS AND INSECTS SEEN WITH -4) AND 34#
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4HE TYPICAL DOPPLER RADAR IMAGES PRESENTED BY 46 WEATHER FORECASTERS OFTEN HAVE THE BIRDS AND BATS AND INSECTS REMOVED BY HUMAN INTERVENTION 4ECHNIQUE 34# WORKS QUITE WELL FOR UNWANTED BIOLOGICAL RETURNS NEAR THE PEAK OF THE RADAR BEAM BUT WHEN USED WITH A COSECANT SQUARED ANTENNA BEAM IT SOLVES ONE PROBLEM BUT CREATES ANOTHER IT ALSO DECREASES SENSITIVITY TO DESIRED TARGETS AT HIGH ELEVATION ANGLES WHERE THE ANTENNA GAIN IS LOW 4HE SOLUTION TO THIS PROBLEM IS TO BOOST THE ANTENNA GAIN AT HIGH ELEVATION ANGLES TO BE CONSIDERABLY HIGHER THAN THE REQUIRE MENT FOR THE COSECANT SQUARED PATTERN .OT ONLY DOES THIS COMPENSATE FOR THE USE OF 34# BUT ALSO ENHANCES THE TARGET TO CLUTTER SIGNAL RATIO FOR TARGETS AT HIGH ELEVATION ANGLES THUS IMPROVING -4) PERFORMANCE 4HE PENALTY FOR THIS SOLUTION IS A LOSS IN THE PEAK ANTENNA GAIN THAT CAN BE ACHIEVED !N ILLUSTRATION OF THIS APPROACH IS PROVIDED IN &IGURE WHICH SHOWS BOTH THE !232 ANTENNA PATTERN AND THE CORRESPONDING FREE SPACE COVERAGE
&)'52% !NTENNA ELEVATION PATTERN FOR THE !232 ANTENNA A COMPARED WITH THE COSECANT SQUARED PATTERN AND B FREE SPACE COVERAGE DIAGRAM
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o KNOTS RESULTING IN A TOTAL REJECTION INTERVAL OF KNOTS 4O KEEP THIS REJECTION OF VELOCITIES TO NO MORE THAN OF THE DOPPLER SPACE AVAILABLE THE AMBIGUOUS VELOCITY MUST BE ABOUT KNOTS 4HIS REQUIRES 02&S OF (Z AT , BAND (Z AT 3 BAND AND AT 8 BAND UNAMBIGUOUS RANGES RESPECTIVELY NMI NMI AND NMI 4HE MAIN CHALLENGE WITH THIS TECH NIQUE IS THAT FIXED CLUTTER RETURNS FROM MANY RANGE AMBIGUITIES AS WELL AS ALL TARGETS OF INTEREST FOLD INTO THE FIRST RANGE INTERVAL 4HUS EXCELLENT CLUTTER REJECTION MUST BE PROVIDED TO PREVENT FOLDED CLUTTER FROM SUPPRESSING TARGETS OF INTEREST WHICH MAY BE AT ANY TRUE RANGE 4ECHNIQUE 36# AS DESCRIBED IN 3ECTION IS USED WHEN IT IS NECESSARY TO DISTINGUISH VERY LOW 2#3 TARGETS FROM LOW VELOCITY CLUTTER SUCH AS BIRDS INSECTS AND SEA 3OMEWHAT LOWER 02&S CAN BE USED THAN THOSE USED FOR TECHNIQUE BECAUSE THE
&)'52% 4WO BEAM ANTENNA
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"( #!$ % '
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&)'52% %XAMPLE OF COVERAGE OBTAINED WITH A TWO BEAM ANTENNA
LOGIC PERMITS RETAINING MANY OF THE TARGETS WITH SMALLER RADIAL VELOCITIES IF THEIR 2#3 IS LARGE ENOUGH 36# STILL REJECTS BIRD CLUTTER BUT RETAINS FOR EXAMPLE THE FAST INCOM ING THREATENING LOW 2#3 MISSILE WHILE ALSO RETAINING THE LARGER CROSS SECTION AIRCRAFT WITH LOWER RADIAL VELOCITIES
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ΰ£Ê -9-/ -Ê1- ÊÊ , ", Ê /Ê/ +1 !IRBORNE SEARCH RADARS WERE INITIALLY DEVELOPED FOR THE DETECTION OF SHIPS BY LONG RANGE PATROL AIRCRAFT $URING THE LATTER PART OF 7ORLD 7AR )) AIRBORNE EARLY WARNING !%7 RADARS WERE DEVELOPED BY THE 53 .AVY TO DETECT LOW FLYING AIRCRAFT APPROACHING A TASK FORCE BELOW THE RADAR COVERAGE OF THE SHIPS ANTENNA 4HE ADVANTAGE OF THE AIR BORNE PLATFORM IN EXTENDING THE MAXIMUM DETECTION RANGE FOR AIR AND SURFACE TARGETS IS APPARENT WHEN ONE CONSIDERS THAT THE RADAR HORIZON IS NMI FOR A FT ANTENNA MAST COMPARED WITH APPROXIMATELY NMI FOR A FT AIRCRAFT ALTITUDE 4HE AIRCRAFT CARRIERnBASED % $ AIRCRAFT &IGURE USES !%7 RADAR AS THE PRIMARY SENSOR IN ITS AIRBORNE TACTICAL DATA SYSTEM 4HESE RADARS WITH THEIR EXTENSIVE FIELD OF VIEW ARE REQUIRED TO DETECT SMALL AIRBORNE TARGETS AGAINST A BACKGROUND OF SEA AND LAND CLUTTER "ECAUSE THEIR PRIMARY MISSION IS TO DETECT LOW FLYING AIRCRAFT THEY CANNOT ELEVATE THEIR ANTENNA BEAM TO ELIMINATE THE CLUTTER 4HESE CONSIDERATIONS HAVE LED TO THE DEVELOPMENT OF AIRBORNE -4) !-4) RADAR SYSTEMS SIMILAR TO THOSE USED IN SURFACE RADARS n DISCUSSED IN THE PRECEDING CHAPTER 4HE MISSION REQUIREMENTS FOR AN !%7 RADAR DRIVE THE NEED FOR AZIMUTHAL COV ERAGE AND LONG RANGE DETECTION CAPABILITY 4HE AZIMUTHAL COVERAGE REQUIREMENT IS BECAUSE THE !%7 RADAR SYSTEM IS GENERALLY REQUIRED TO PROVIDE THE FIRST DETECTION OF AIRBORNE TARGETS WITHOUT ANY A PRIORI KNOWLEDGE OF THE LOCATION OF THESE TARGETS !%7 SYSTEMS HAVE GENERALLY BEEN DEVELOPED AT LOWER FREQUENCIESTHIS CAN BE UNDERSTOOD BY REVIEWING THE SURVEILLANCE RADAR RANGE EQUATION 2MAX
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3ECTIONS THROUGH AND WERE TAKEN PRIMARILY FROM THE SECOND EDITION OF THE 2ADAR (ANDBOOK #HAPTER AUTHORED BY &RED 3TAUDAHER WITH REVISIONS MADE BY *AMES $AY 4HE REMAINING SECTIONS OF THE CHAPTER WERE AUTHORED BY *AMES $AY
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&)'52% % $ AIRBORNE EARLY WARNING !%7 AIRCRAFT SHOWING ROTODOME HOUSING THE ANTENNA
WHERE TS IS THE SCAN TIME AND 7 IS THE SURVEILLANCE VOLUME COVERAGE REQUIREMENT PROD UCT OF THE AZIMUTH AND ELEVATION ANGLES !S LONG AS THE BEAMWIDTHS OF THE RADAR IN AZIMUTH AND ELEVATION ARE SMALLER THAN THE REGION TO BE SURVEILLED THIS EQUATION IS NOT DIRECTLY DEPENDENT UPON FREQUENCY (OWEVER KEY PARAMETERS IN THIS EQUATION ARE DEPENDENT UPON FREQUENCY 0ARTICULARLY PROPAGATION LOSSES FOR LOW ALTITUDE TARGETS AND TARGET 2#3 FOR SOME TARGET TYPES ARE GENERALLY ADVANTAGEOUS FOR LOWER FREQUENCIES 4HE RESULT IS THAT !%7 SYSTEMS HAVE BEEN DEVELOPED AT 5(& , BAND AND 3 BAND FREQUENCIES !IRBORNE -4) RADAR SYSTEMS HAVE ALSO BEEN UTILIZED TO ACQUIRE AND TRACK TARGETS IN INTERCEPTOR FIRE CONTROL SYSTEMS )N THIS APPLICATION THE SYSTEMS HAVE TO DISCRIMINATE AGAINST CLUTTER ONLY IN THE VICINITY OF A PRESCRIBED TARGET 4HIS ALLOWS THE SYSTEM TO BE OPTIMIZED AT THE RANGE AND ANGULAR SECTOR WHERE THE TARGET IS LOCATED -4) IS ALSO USED TO DETECT MOVING GROUND VEHICLES BY RECONNAISSANCE AND TACTICAL FIGHTER AIRCRAFT 4HE ENVIRONMENT OF HIGH PLATFORM ALTITUDE MOBILITY AND SPEED COUPLED WITH RESTRICTIONS ON SIZE WEIGHT AND POWER CONSUMPTION PRESENT A UNIQUE SET OF PROBLEMS TO THE DESIGNER OF AIRBORNE -4) SYSTEMS 4HIS CHAPTER WILL BE DEVOTED TO CONSIDER ATIONS UNIQUE TO THE AIRBORNE ENVIRONMENT
ΰÓÊ "6 , Ê " - ,/" 3EARCH RADARS GENERALLY REQUIRE n AZIMUTHAL COVERAGE 4HIS COVERAGE IS DIFFICULT TO OBTAIN ON AN AIRCRAFT SINCE MOUNTING AN ANTENNA IN THE CLEAR PRESENTS MAJOR DRAG STABILITY AND STRUCTURAL PROBLEMS 7HEN EXTENSIVE VERTICAL COVERAGE IS REQUIRED THE AIRCRAFTS PLANFORM AND VERTICAL STABILIZER DISTORT AND SHADOW THE ANTENNA PATTERN !NALYSIS OF TACTICAL REQUIREMENTS MAY SHOW THAT ONLY A LIMITED COVERAGE SECTOR IS REQUIRED (OWEVER THIS SECTOR USUALLY HAS TO BE CAPABLE OF BEING POSITIONED OVER THE FULL n RELATIVE TO THE AIRCRAFTS HEADING BECAUSE OF THE REQUIREMENTS FOR COVERAGE
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&)'52% "OEING 7EDGETAIL AIRCRAFT SHOWING ANTENNAS MOUNTED ABOVE THE FUSELAGE
WHILE REVERSING COURSE LARGE CRAB ANGLES WHEN HIGH WINDS ARE ENCOUNTERED THE NEED TO POSITION GROUND TRACK IN RELATION TO WIND NONTYPICAL OPERATING SITUATIONS AND OPERA TIONS REQUIREMENTS FOR COVERAGE WHILE PROCEEDING TO AND FROM THE STATION (OWEVER IN THE S AND S A NUMBER OF SYSTEMS HAVE BEEN DEVELOPED THAT PRO VIDE PHASED ARRAY PERFORMANCE IN AN AIRBORNE PLATFORM 4HE -ULTI 2OLE %LECTRONICALLY 3CANNED !RRAY -%3! RADAR DEVELOPED BY .ORTHROP 'RUMMAN ON A "OEING FOR THE !USTRALIAN 7EDGETAIL PROGRAM IS AN EXAMPLE SEE &IGURE !N ALTERNATE SOLU TION THAT COMBINES MECHANICAL SCANNING IN CONJUNCTION WITH ELECTRONIC SCANNING IS IN DEVELOPMENT WITH THE !.!09 RADAR FOR THE % $ AIRCRAFT FOLLOW UP TO THE 53 .AVYS % # AIRCRAFT
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Ê ,6 ,4HE PERFORMANCE OF AIRBORNE -4) SYSTEMS ARE PRIMARILY DETERMINED BY MOTION EFFECTS INDUCED ON THE CLUTTER ECHOES PLATFORM MOTION ANTENNA SCANNING MOTION AND CLUTTER INTER NAL MOTION THE PROCESSING TECHNIQUES USED TO ENHANCE TARGET DETECTION AND MAXIMIZE CLUT TER CANCELLATION AND THE HARDWARE STABILITY LIMITATIONS OF THE RADAR 4HIS CHAPTER WILL DISCUSS THE MOTION EFFECTS AS WELL AS THE PERFORMANCE OF VARIOUS PROCESSING TECHNIQUES
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-4) DISCRIMINATES BETWEEN AIRBORNE MOVING TARGETS AND STATIONARY LAND OR SEA CLUTTER (OWEVER IN THE AIRBORNE CASE THE CLUTTER MOVES WITH RESPECT TO THE MOVING AIRBORNE PLATFORM )T IS POSSIBLE TO COMPENSATE FOR THE MEAN CLUTTER RADIAL VELOCITY BY USING
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&)'52% $EFINING GEOMETRY @¼ ANTENNA POINTING ANGLE @ LINE OF SIGHT ANGLE P ANGLE FROM ANTENNA CENTERLINE 6G AIRCRAFT GROUND SPEED 6R RADIAL VELOCITY OF POINT TARGET 6" RADIAL VELOCITY ALONG ANTENNA CENTERLINE BORESIGHT X ANTENNA AZIMUTH ANGLE X AZIMUTH ANGLE 2 GROUND RANGE TO POINT TARGET AND ( AIRCRAFT HEIGHT
TECHNIQUES SUCH AS TIME AVERAGED CLUTTER COHERENT AIRBORNE RADAR 4!##!2 4HIS TECHNIQUE ATTEMPTS TO CENTER THE LARGEST RETURN FROM MAIN BEAM CLUTTER AT ZERO DOPPLER FREQUENCY SUCH THAT A SIMPLE -4) FILTER ALSO CENTERED AT ZERO DOPPLER FREQUENCY WILL CANCEL THE MAIN BEAM CLUTTER !S SHOWN IN &IGURE THE APPARENT RADIAL VELOCITY OF THE CLUTTER IS 6R 6G COS @ WHERE 6G IS THE GROUND SPEED OF THE PLATFORM AND A IS THE ANGLE SUBTENDED BETWEEN THE LINE OF SIGHT TO A POINT ON THE %ARTHS SURFACE AND THE AIRCRAFTS VELOCITY VECTOR &IGURE SHOWS THE LOCI OF CONSTANT RADIAL VELOCITY ALONG THE SURFACE )N ORDER TO NORMALIZE THE FIGURE A FLAT EARTH IS ASSUMED AND THE NORMALIZED RADIAL VELOCITY 6N 6R6G IS PRESENTED AS A FUNCTION OF AZIMUTH ANGLE X AND NORMALIZED GROUND RANGE 2( WHERE ( IS THE AIRCRAFTS ALTITUDE )NSTEAD OF A SINGLE CLUTTER DOPPLER FREQUENCY CORRESPONDING TO A CONSTANT RADIAL VELOCITY 6" IN &IGURE DETERMINED BY THE ANTENNA POINTING ANGLE @ THE RADIAL SEES A CONTINUUM OF VELOCITIES 4HIS RESULTS IN A FREQUENCY SPECTRUM AT A PARTICULAR RANGE WHOSE SHAPE IS DETERMINED BY THE ANTENNA PATTERN THAT INTERSECTS THE SURFACE THE REFLECTIVITY OF THE CLUTTER AND THE VELOCITY DISTRIBUTION WITHIN THE BEAM &URTHERMORE SINCE 6R VARIES AS A FUNCTION OF RANGE AT A PARTICULAR AZIMUTH X THE CENTER FREQUENCY AND SPECTRUM SHAPE VARY AS A FUNCTION OF RANGE AND AZIMUTH ANGLE X 7HEN THE ANTENNA IS POINTING AHEAD THE PREDOMINANT EFFECT IS THE VARIATION OF THE CEN TER FREQUENCY CORRESPONDING TO THE CHANGE IN @ WITH RANGE 7HEN THE ANTENNA IS POINTING
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&)'52% ,OCI OF CONSTANT NORMALIZED RADIAL VELOCITY 6R6G AS A FUNC TION OF AIRCRAFT RANGE TO HEIGHT RATIO 2( AND AZIMUTH ANGLE X
ABEAM THE PREDOMINANT EFFECT IS THE VELOCITY SPREAD ACROSS THE ANTENNA BEAMWIDTH 4HESE ARE CLASSIFIED AS THE SLANT RANGE EFFECT AND THE PLATFORM MOTION EFFECT RESPECTIVELY %FFECT OF 3LANT 2ANGE ON $OPPLER /FFSET 4HE ANTENNA BORESIGHT VELOCITY 6" IS THE GROUND VELOCITY COMPONENT ALONG THE ANTENNA CENTERLINE BORESIGHT AND IS GIVEN AS n6G COS @ )F THE CLUTTER SURFACE WERE COPLANAR WITH THE AIRCRAFT THIS COMPONENT WOULD BE EQUAL TO 6G COS X AND WOULD BE INDEPENDENT OF RANGE 4HE RATIO OF THE ACTUAL BORESIGHT VELOCITY TO THE COPLANAR BORESIGHT VELOCITY IS DEFINED AS THE NORMAL IZED BORESIGHT VELOCITY RATIO 6"2
COS A COS F COSY
WHERE E IS THE DEPRESSION ANGLE OF THE ANTENNA CENTERLINE FROM THE HORIZONTAL &IGURE SHOWS THE VARIATION OF THE NORMALIZED BORESIGHT VELOCITY RATIO AS A FUNCTION OF SLANT RANGE FOR A CURVED EARTH AND DIFFERENT AIRCRAFT ALTITUDES 4HE VARIATION IS FAIRLY RAPID FOR SLANT RANGES LESS THAN NMI )T IS DESIRABLE TO CENTER THE CLUTTER SPECTRUM IN THE NOTCH IE MINIMUM RESPONSE REGION OF THE !-4) FILTER IN ORDER TO OBTAIN MAXIMUM CLUTTER REJECTION 4HIS CAN BE ACCOMPLISHED BY OFFSETTING THE )& OR 2& FREQUENCY OF THE RADAR SIGNAL BY AN AMOUNT EQUAL TO THE AVERAGE DOPPLER FREQUENCY OF THE CLUTTER SPECTRUM "ECAUSE THE CLUTTER CENTER FREQUENCY VARIES WITH RANGE AND AZIMUTH WHEN THE RADAR IS MOVING IT IS NECES SARY FOR THE FILTER NOTCH TO TRACK THE DOPPLER OFFSET FREQUENCY USING AN OPEN OR CLOSED LOOP CONTROL SYSTEM SUCH AS 4!##!2 DESCRIBED BELOW !N EXAMPLE OF A RECEIVED CLUTTER SPECTRUM GIVEN AN ANTENNA RESPONSE IS SHOWN IN &IGURE A 4HE 4!##!2 FREQUENCY OFFSET THEN SHIFTS MAIN BEAM CLUTTER TO ZERO DOPPLER AS SHOWN IN &IGURE B
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4!##!2 4HE -)4 ,INCOLN ,ABORATORY ORIGINALLY DEVELOPED 4!##!2 TO SOLVE THE !-4) RADAR PROBLEM 4HE REQUIREMENTS AND THUS THE IMPLEMENTATION OF 4!##!2 CHANGE DEPENDING UPON THE TYPE OF CLUTTER CANCELLATION PROCESSING EMPLOYED !FTER MANY OTHER APPROACHES IT WAS RECOGNIZED THAT IF ONE USED THE CLUTTER RETURN RATHER THAN THE TRANSMIT PULSE TO PHASE LOCK THE RADAR TO THE CLUTTER FILTER ONE COULD CENTER THE CLUT TER IN THE FILTER STOPBAND 4HE CLUTTER PHASE VARIES FROM RANGE CELL TO RANGE CELL OWING TO THE DISTRIBUTION OF THE LOCATION OF THE SCATTERERS IN AZIMUTH (ENCE IT IS NECESSARY TO AVERAGE THE RETURN FOR AS LONG AN INTERVAL AS POSSIBLE 4!##!2 IS USED TO DESCRIBE THE CENTERING OF THE RETURNED CLUTTER SPECTRUM TO THE ZERO FILTER FREQUENCY 3INCE THE TECHNIQUE COMPENSATES FOR DRIFT IN THE VARIOUS SYSTEM ELEMENTS AND BIASES IN THE MEAN DOPPLER FREQUENCY DUE TO OCEAN CURRENTS CHAFF OR WEATHER CLUTTER IT IS USED IN SHIP BOARD AND LAND BASED RADARS AS WELL AS AIRBORNE RADAR ! FUNCTIONAL BLOCK DIAGRAM OF AN AIRBORNE RADAR EMPLOYING 4!##!2 IS SHOWN IN &IGURE 4HE CLUTTER ERROR SIGNAL IS OBTAINED BY MEASURING THE PULSE TO PULSE PHASE SHIFT VD4P OF THE CLUTTER RETURN 4HIS PROVIDES A VERY SENSITIVE ERROR SIGNAL 4HE AVER AGED ERROR SIGNAL CONTROLS A VOLTAGE CONTROLLED COHERENT MASTER OSCILLATOR #/-/ WHICH DETERMINES THE TRANSMITTED FREQUENCY OF THE RADAR 4HE #/-/ IS SLAVED TO
&)'52% #LUTTER 0OWER 3PECTRAL $ENSITY 03$ RESPONSE THROUGH ANTENNA PATTERN A WITHOUT 4!##!2 FREQUENCY OFFSET AND B WITH 4!##!2 FREQUENCY OFFSET
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&)'52% "LOCK DIAGRAM OF A RADAR ILLUSTRATING THE SIGNAL FLOW PATH OF THE 4!##!2 CONTROL LOOP
THE SYSTEM REFERENCE OSCILLATOR FREQUENCY VIA THE AUTOMATIC FREQUENCY CONTROL !&# LOOP SHOWN IN &IGURE 4HIS PROVIDES A STABLE REFERENCE IN THE ABSENCE OF CLUTTER !N INPUT FROM THE AIRCRAFT INERTIAL NAVIGATION SYSTEM AND THE ANTENNA SERVO PROVIDE A PREDICTED DOPPLER OFFSET 4HESE INPUTS ALLOW THE 4!##!2 SYSTEM TO PROVIDE A NARROW BANDWIDTH CORRECTION SIGNAL "ECAUSE OF THE NOISY NATURE OF THE CLUTTER SIGNAL THE NEED TO HAVE THE CONTROL SYSTEM BRIDGE REGIONS OF WEAK CLUTTER RETURN AND THE REQUIREMENT NOT TO RESPOND TO THE DOP PLER SHIFT OF A TRUE TARGET THE CONTROL SYSTEM USUALLY TRACKS THE AZIMUTH VARIATION OF A SPECIFIC RADAR RANGE INTERVAL 4HE MAXIMUM RANGE OF THIS INTERVAL IS CHOSEN SO THAT CLUTTER WILL BE THE DOMINANT SIGNAL WITHIN THE INTERVAL 4HE MINIMUM RANGE IS CHOSEN TO EXCLUDE SIGNALS WHOSE AVERAGE FREQUENCY DIFFERS SUBSTANTIALLY FROM THE FREQUENCY IN THE REGION OF INTEREST !LTERNATE APPROACHES TO PROVIDING THIS FREQUENCY OFFSET CAN BE IMPLEMENTED WITH DIGITAL EXCITERS OR ON RECEIVE &OR SOME APPLICATIONS IT MAY BE NECESSARY TO USE MULTIPLE CONTROL LOOPS EACH ONE COVERING A SPECIFIC RANGE INTERVAL OR TO VARY THE OFFSET FRE QUENCY IN RANGE 4HIS IS POSSIBLE IF THE FREQUENCY OFFSET IS IMPLEMENTED ON RECEIVE BUT NOT ON TRANSMIT !T ANY PARTICULAR RANGE THE FILTER NOTCH IS EFFECTIVELY AT ONE FREQUENCY AND THE CENTER FREQUENCY OF THE CLUTTER SPECTRUM AT ANOTHER 4HE DIFFERENCE BETWEEN THESE FREQUENCIES RESULTS IN A DOPPLER OFFSET ERROR AS SHOWN IN &IGURE 4HE CLUTTER SPECTRUM WILL EXTEND INTO MORE OF THE FILTER PASSBAND AND THE CLUTTER IMPROVEMENT FACTOR WILL BE DEGRADED 4HE REQUIRED ACCURACY FOR THE 4!##!2 CONTROL LOOP CAN BE RELAXED IF THE -4) FILTER IS AN ADAPTIVE FILTER SUCH AS WITH SPACE TIME ADAPTIVE PROCESS ING DISCUSSED LATER IN THIS CHAPTER 4HIS IS BECAUSE THE ADAPTIVE FILTER WILL ADJUST TO THE RECEIVED SIGNALS AND OPTIMIZE CLUTTER CANCELLATION 7ITHOUT ADAPTIVE ADJUSTMENT &IGURE SHOWS THE IMPROVEMENT FACTOR FOR SINGLE AND DOUBLE DELAY CANCELERS AS A FUNCTION OF THE RATIO OF THE NOTCH OFFSET ERROR TO THE PULSE REPETITION FREQUENCY 02& FOR DIFFERENT CLUTTER SPECTRAL WIDTHS &ORTUNATELY THE PLATFORM MOTION SPECTRUM IS NARROW IN THE FORWARD SECTOR OF COVERAGE WHERE OFFSET ERROR IS MAXIMUM !N OFFSET ERROR OF ONE HUNDREDTH OF THE 02& WOULD YIELD A D" IMPROVEMENT FACTOR FOR A DOUBLE CANCELER WITH AN INPUT CLUTTER SPECTRUM WHOSE WIDTH
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WAS OF THE 02& )F THE RADAR FREQUENCY WERE '(Z 02& K(Z AND GROUND SPEED KT THE NOTCH WOULD HAVE TO BE HELD WITHIN KT OR 6G "ECAUSE OF THESE REQUIREMENTS AND THE WIDTH OF THE PLATFORM MOTION SPECTRUM STAG GER 02& SYSTEMS MUST BE CHOSEN PRIMARILY ON THE BASIS OF MAINTAINING THE STOPBAND RATHER THAN FLATTENING THE PASSBAND 3IMILARLY HIGHER ORDER DELAY LINE FILTERS WITH OR WITHOUT FEEDBACK ARE SYNTHESIZED ON THE BASIS OF STOPBAND REJECTION 4HE LIMITING CASE IS THE NARROWBAND FILTER BANK WHERE EACH INDIVIDUAL FILTER CONSISTS OF A SMALL PASSBAND THE BALANCE BEING STOPBAND )MPROVEMENT FACTOR IS AN IMPORTANT METRIC BUT IN ADDITION TO THIS AVERAGE METRIC DEFINED ACROSS ALL DOPPLER FREQUENCIES IT IS OFTEN IMPORTANT TO CHARACTERIZE THE PERFOR MANCE AS A FUNCTION OF DOPPLER FREQUENCY PARTICULARLY WITH COHERENT DOPPLER FILTERING IMBEDDED IN THE PROCESSING CHAIN 7ITH PERFORMANCE CHARACTERIZED VERSUS DOPPLER
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FREQUENCY THE RADAR DESIGN CAN THEN BE EVALUATED THROUGH THE COMPLETE DETECTION CHAIN AND OPTIMIZED IN CONJUNCTION WITH ANY MULTIPLE 02& STAGGER WAVEFORMS UTILIZED TO BRIDGE -4) BLIND REGIONS 0LATFORM -OTION %FFECT 4O AN AIRBORNE RADAR A CLUTTER SCATTERER APPEARS TO HAVE A RADIAL VELOCITY THAT DIFFERS FROM THE ANTENNA BORESIGHT RADIAL VELOCITY AT THE SAME RANGE BY 6E 6R 6" 6G COS A 6G COS A
6G ;COS A COSA Q = 6X SIN Q 6Y SIN
Q
FOR SMALL VALUES OF P AND DEPRESSION ANGLE E WHERE 6X IS THE HORIZONTAL COMPONENT OF VELOCITY PERPENDICULAR TO THE ANTENNA BORESIGHT AND 6Y IS THE COMPONENT ALONG THE ANTENNA BORESIGHT P IS THE AZIMUTHAL ANGLE FROM THE ANTENNA BORESIGHT OR THE INTERSEC TION OF THE VERTICAL PLANE CONTAINING THE BORESIGHT WITH THE GROUND 4HE CORRESPONDING DOPPLER FREQUENCY WHEN @ IS A FEW BEAMWIDTHS FROM GROUND TRACK IS FD
6X 6 SIN Q y X Q L L
4HIS PHENOMENON RESULTS IN A PLATFORM MOTION CLUTTER POWER SPECTRUM THAT IS WEIGHTED BY THE ANTENNAS TWO WAY POWER PATTERN IN AZIMUTH 4HE TRUE SPECTRUM MAY BE APPROX IMATED BY A GAUSSIAN SPECTRUM
( F E
¤ F ³
¥ DS ´ ¦ PMµ
E
¤6 Q ³
¥ X LS ´ ¦ PMµ
y ' Q
'P THE TWO WAY POWER PATTERN OF THE ANTENNA IS WHEN P PA WHERE PA IS THE HALF POWER BEAMWIDTH WHICH CAN BE APPROXIMATED BY KA A BEING THE EFFECTIVE HORIZONTAL APERTURE WIDTH 4HUS
E
¤6 ³
¥ X AS ´ ¦ PMµ
OR
S PM
6X A
WHERE 6X AND A ARE IN CONSISTENT UNITS 4HIS VALUE IS LOWER THAN ONES DERIVED BY OTHER AUTHORS (OWEVER IT AGREES WITH MORE EXACT ANALYSIS OF ANTENNA RADIATION PATTERNS AND EXPERIMENTAL DATA ANALYZED BY & 3TAUDAHER ! MORE EXACT VALUE OF THE PARAMETER RPM MAY BE OBTAINED BY MATCHING A TWO WAY POWER PATTERN OF INTEREST WITH THE GAUSSIAN APPROXIMATION AT A SPECIFIC POINT ON THE PAT TERN DETERMINING THE STANDARD DEVIATION OF P BY USING STATISTICAL TECHNIQUES OR FITTING
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&)'52% %FFECT OF PLATFORM MOTION ON THE -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE FRACTION OF THE HORIZONTAL ANTENNA APERTURE DISPLACED PER INTERPULSE PERIOD 6X4PA
THE PATTERN AND USING NUMERICAL METHODS 4HE CALCULATION OF THE IMPROVEMENT FACTOR CAN BE PERFORMED BY AVERAGING THE RESULTANT RESIDUE POWER OBTAINED BY SUMMING THE SIGNAL PHASORS AT SPECIFIC VALUES OF P FROM NULL TO NULL OF THE ANTENNA PATTERN &IGURE SHOWS THE EFFECT OF PLATFORM MOTION ON THE -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE APERTURE DISPLACED IN THE PLANE OF THE APERTURE PER INTERPULSE PERIOD 4P ! DISPLACEMENT REDUCES THE DOUBLE DELAY IMPROVEMENT FACTOR TO D" 4HIS COR RESPONDS TO A SPEED OF KT IF THE SYSTEM HAS A 02& OF (Z AND A FT ANTENNA APERTURE &OR A SINGLE DELAY SYSTEM THE DISPLACEMENT HAS TO BE HELD TO FOR A D" PERFORMANCE LIMIT
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" * -/" Ê 4HE DELETERIOUS EFFECTS OF PLATFORM MOTION CAN BE REDUCED BY PHYSICALLY OR ELECTRONI CALLY DISPLACING THE ANTENNA PHASE CENTER ALONG THE PLANE OF THE APERTURE 4HIS IS REFERRED TO AS THE DISPLACED PHASE CENTER ANTENNA $0#! TECHNIQUEn )N ADDITION SOME FORMS OF SPACE TIME ADAPTIVE PROCESSING ARE EXPRESSLY DEVELOPED TO IMPROVE CLUTTER CANCELLA TION WITH AN ADAPTIVE FILTER ELECTRONICALLY DISPLACING THE ANTENNA PHASE CENTER %LECTRONICALLY $ISPLACED 0HASE #ENTER !NTENNA &IGURE A SHOWS THE PULSE TO PULSE PHASE ADVANCE OF AN ELEMENTAL SCATTERER AS SEEN BY THE RADAR RECEIVER
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&)'52% 0HASOR DIAGRAM SHOWING THE RETURN FROM A POINT SCATTERER DUE TO PLATFORM MOTION
4HE AMPLITUDE % OF THE RECEIVED SIGNAL IS PROPORTIONAL TO THE TWO WAY ANTENNA FIELD INTENSITY 4HE PHASE ADVANCE IS
H P FD4P
P 6X4P SIN Q L
WHERE FD DOPPLER SHIFT OF SCATTERER %Q 4P INTERPULSE PERIOD &IGURE B SHOWS A METHOD OF CORRECTING FOR THE PHASE ADVANCE G !N IDEALIZED CORRECTION SIGNAL %C IS APPLIED LEADING THE RECEIVED SIGNAL BY n AND LAGGING THE NEXT RECEIVED SIGNAL BY n &OR EXACT COMPENSATION THE FOLLOWING RELATION WOULD HOLD
%C % TAN H £ Q TAN
P 6X4P SIN Q L
4HIS ASSUMES A TWO LOBE ANTENNA PATTERN SIMILAR TO THAT IN A MONOPULSE TRACKING RADAR 4WO RECEIVERS ARE USED ONE SUPPLYING A SUM SIGNAL 3P AND THE OTHER A DIFFERENCE SIGNAL $P 4HE DIFFERENCE SIGNAL IS USED TO COMPENSATE FOR THE EFFECTS OF PLATFORM MOTION )F THE SYSTEM IS DESIGNED TO TRANSMIT THE SUM PATTERN 3P AND RECEIVE BOTH 3P AND A DIFFERENCE PATTERN $P THEN AT THE DESIGN SPEED THE RECEIVED SIGNAL 3P $P CAN BE APPLIED AS THE CORRECTION SIGNAL 4HE ACTUAL CORRECTION SIGNAL USED TO APPROXIMATE %C IS K 3P $P WHERE K IS THE RATIO OF THE AMPLIFICATION IN THE SUM AND DIFFERENCE CHANNELS OF THE RECEIVER ! UNIFORMLY ILLUMINATED MONOPULSE ARRAY HAS THE DIFFERENCE SIGNAL $ IN QUADRA TURE WITH THE SUM AND HAS THE AMPLITUDE RELATIONSHIP
¤ P7 ³ $Q £Q TAN ¥ SIN Q´ ¦ L µ
WHERE 7 IS THE DISTANCE BETWEEN THE PHASE CENTERS OF THE TWO HALVES OF THE ANTENNA (ENCE A CHOICE OF 7 6X4P AND K WOULD IDEALLY RESULT IN PERFECT CANCELLATION )N PRACTICE A SUM PATTERN IS CHOSEN BASED ON THE DESIRED BEAMWIDTH GAIN AND SIDELOBES FOR THE DETECTION SYSTEM REQUIREMENTS 4HEN THE DIFFERENCE PATTERN $P IS SYNTHESIZED INDEPENDENTLY BASED ON THE RELATIONSHIP REQUIRED AT DESIGN RADAR PLATFORM
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SPEED AND ALLOWABLE SIDELOBES 4HE TWO PATTERNS MAY BE REALIZED BY COMBINING THE ELEMENTS IN SEPARATE CORPORATE FEED STRUCTURES &IGURE SHOWS THE IDEALIZED IMPROVEMENT FACTOR AS A FUNCTION OF NORMALIZED APERTURE MOVEMENT FOR A DOUBLE DELAY CANCELER 4HE IMPROVEMENT FACTOR SHOWN IS THE IMPROVEMENT FACTOR FOR A POINT SCATTERER AVERAGED OVER THE NULL TO NULL ANTENNA BEAMWIDTH )N ONE CASE THE GAIN RATIO K IS OPTIMIZED AT EACH VALUE OF PULSE TO PULSE DISPLACEMENT )N THE OTHER COMPENSATED CASE THE OPTIMUM GAIN RATIO K IS APPROXIMATED BY THE LINEAR FUNCTION OF INTERPULSE PLATFORM MOTION K6X ! BLOCK DIAGRAM OF THE DOUBLE DELAY SYSTEM IS SHOWN IN &IGURE ! SINGLE DELAY SYSTEM WOULD NOT HAVE THE SECOND DELAY LINE AND SUBTRACTOR 4HE NORMALLY REQUIRED CIRCUITRY FOR MAINTAINING COHERENCE GAIN AND PHASE BALANCE AND TIMING IS NOT SHOWN 4HE SPEED CONTROL 6X IS BIPOLAR AND MUST BE CAPABLE OF REVERSING THE SIGN OF THE $P SIGNAL IN EACH CHANNEL WHEN THE ANTENNA POINTING ANGLE CHANGES FROM THE PORT TO THE STARBOARD SIDE OF THE AIRCRAFT
&)'52% -4) IMPROVEMENT FACTOR FOR $0#! COMPENSATION AS A FUNCTION OF THE FRACTION OF THE HORIZONTAL PHASE CENTER SEPARATION 7 THAT THE HORIZONTAL ANTENNA APERTURE IS DISPLACED PER INTERPULSE PERIOD 6X4P7 7 A WHERE A IS THE HORIZONTAL APERTURE LENGTH
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&)'52% 3IMPLIFIED DOUBLE DELAY $0#! MECHANIZATION
4HE HYBRID AMPLIFIER SHOWN HAS TWO INPUT TERMINALS THAT RECEIVE 3P AND J$P AND AMPLIFY THE $P CHANNEL BY K6X RELATIVE TO THE 3P CHANNEL 4HE OUTPUT TER MINALS PRODUCE THE SUM AND DIFFERENCE OF THE TWO AMPLIFIED INPUT SIGNALS "ECAUSE $0#! COMPENSATES FOR THE COMPLEX SIGNAL BOTH AMPLITUDE AND PHASE INFORMATION MUST BE RETAINED 4HEREFORE THESE OPERATIONS USUALLY OCCUR AT 2& OR )& $IGITAL COMPENSATION CAN BE USED IF SYNCHRONOUS DETECTION AND ANALOG TO DIGITAL !$ CONVERSION ARE PERFORMED AND THE COMPONENTS ARE TREATED AS COMPLEX PHASORS &URTHERMORE THE OPERATIONS MUST BE LINEAR UNTIL THE SUM SIGNAL AND DIFFERENCE SIG NALS HAVE BEEN PROCESSED BY THE HYBRID AMPLIFIER !FTER THIS SINGLE PULSE COMBINA TION THE ACTUAL DOUBLE CANCELLATION CAN BE PERFORMED BY ANY CONVENTIONAL -4) PROCESSING TECHNIQUES 0OWER IN THE !NTENNA 3IDELOBES !IRBORNE SYSTEMS ARE LIMITED IN THEIR ABILITY TO REJECT CLUTTER DUE TO THE POWER RETURNED BY THE ANTENNA SIDELOBES 4HE FULL n AZIMUTHAL PATTERN SEES VELOCITIES FROM 6G TO 6G 4HE COMPENSATION CIRCUITS OFFSET THE VELOCITY BY AN AMOUNT CORRESPONDING TO THE ANTENNA BORESIGHT VELOCITY 6" BUT THE TOTAL RANGE OF DOPPLER FREQUENCIES CORRESPONDING TO 6G IS OBTAINED BECAUSE OF ECHOES RECEIVED VIA THE SIDELOBES &OR AIRBORNE SYSTEMS WITH LOW 02&S THESE DOPPLER FRE QUENCIES CAN COVER SEVERAL MULTIPLES OF THE 02& SO THAT THE SIDELOBE POWER IS FOLDED INTO THE FILTER 4HIS LIMITATION IS A FUNCTION OF THE ANTENNA POINTING ANGLE THE -4) FILTER RESPONSE AND THE SIDELOBE PATTERN )F THE SIDELOBES ARE RELATIVELY WELL DISTRIBUTED IN AZIMUTH A MEASURE OF PERFORMANCE CAN BE OBTAINED BY AVERAGING THE POWER RETURNED BY THE SIDELOBES 4HE LIMITING IMPROVEMENT FACTOR DUE TO SIDELOBES IS P
)SL LIMIT
+ ¯ ' Q DQ
P
¯SL ' Q DQ
WHERE THE LOWER INTEGRAL IS TAKEN OUTSIDE THE MAIN BEAM REGION -AIN BEAM EFFECTS WOULD BE INCLUDED IN THE PLATFORM MOTION IMPROVEMENT FACTOR 4HE CONSTANT + IS THE NOISE NORMALIZATION FACTOR FOR THE -4) FILTER + FOR SINGLE DELAY AND FOR DOUBLE DELAY 'P IS THE TWO WAY POWER OF THE ANTENNA IN THE PLANE OF THE GROUND SURFACE 4HE $0#! PERFORMANCE DESCRIBED IN THE PRECEDING SUBSECTION CAN BE ANALYZED ON THE BASIS OF RADIATION PATTERNS OR THE EQUIVALENT APERTURE DISTRIBUTION FUNCTION )F THE RADIATION PATTERN IS USED THE COMPOSITE PERFORMANCE MAY BE OBTAINED EITHER BY APPLY ING THE PATTERN FUNCTIONS OVER THE ENTIRE n PATTERN OR BY COMBINING THE IMPROVEMENT
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FACTORS FOR THE $0#! MAIN BEAM AND THE SIDELOBE REGIONS IN THE SAME MANNER AS PARAL LEL IMPEDANCES ARE COMBINED ) TOTAL ) SL ) $0#!
)F THE APERTURE DISTRIBUTION IS USED THE SIDELOBE EFFECTS ARE INHERENT IN THE ANALYSIS #ARE MUST BE TAKEN HOWEVERIF THE ARRAY OR REFLECTOR FUNCTION IS USED WITHOUT CON SIDERING THE WEIGHTING OF THE ELEMENTAL PATTERN OR THE FEED DISTRIBUTION THE INHERENT SIDELOBE PATTERN CAN OBSCURE THE MAIN BEAM COMPENSATION RESULTS !GAIN THE PERFORMANCE VERSUS DOPPLER FREQUENCY IS IMPORTANT FOR EVALUATING OVERALL RADAR DETECTION PERFORMANCE !NTENNA SIDELOBE LIMITED PERFORMANCE CAN BE APPROXIMATED BY PERFORMING THE LOWER INTEGRAL OF %Q OVER THOSE ANGLES THAT MAP INTO A GIVEN DOPPLER FILTERS PASSBAND 4HE NOISE NORMALIZATION TERM K MUST ALSO BE MODIFIED TO REFLECT THE CASCADED NOISE GAIN OF THE -4) AND DOPPLER FILTER BANK AS .
.
.
I
I
I
. G K £ 7I £ 7I 7I COS P K . £ 7I 7I COS P K .
K .
FOR THREE PULSE -4) AND CASCADED . PULSE DOPPLER FILTER BANK WHERE 7I ARE THE DOP PLER FILTER WEIGHTS OR .
.
I
I
. G K £ 7I £ 7I 7I COSP K .
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FOR TWO PULSE -4) AND CASCADED . PULSE DOPPLER FILTER BANK
ΰÈÊ -
"/" Ê " * -/"
&IGURE A SHOWS A TYPICAL ANTENNA MAIN BEAM RADIATION PATTERN AND THE RESPONSE OF A POINT SCATTERER FOR TWO SUCCESSIVE PULSES WHEN THE ANTENNA IS SCANNING )T IS SEEN THAT THE SIGNALS RETURNED WOULD DIFFER BY $'P 4HIS RESULTS IN IMPERFECT CANCELLATION DUE TO SCANNING 4HE AVERAGE EFFECT ON THE IMPROVEMENT FACTOR CAN BE OBTAINED BY INTEGRAT ING THIS DIFFERENTIAL EFFECT $'P OVER THE MAIN BEAMS
)SCAN
Q
Q
\ ' Q \ DQ
Q
¯ Q \ 'Q 4PQ 'Q \ DQ
FOR SINGLE DELAY CANCELLATION
)SCAN
¯
¯
Q
Q
A
\ ' Q \ DQ
Q
¯ Q \ 'Q 4PQ 'Q 'Q 4PQ \ DQ
WHERE P NULL OF MAIN BEAM 'P TWO WAY VOLTAGE PATTERN
FOR DOUBLE DELAY CANCELLATIONN B
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&)'52% !NTENNA SCANNING EFFECTS A AS SEEN BY THE ANTENNA RADIATION PATTERN DUE TO THE APPARENT CHANGE IN AZIMUTH OF THE SCATTERER Q Q Q 4P B AS SEEN BY THE APERTURE ILLUMINATION FUNCTION DUE TO THE APPARENT MOTION V XQ OF THE SCATTERER RELATIVE TO THE ANTENNA AT POSITION X AND C STEP SCAN COMPENSATION OF TWO RECEIVED PHASORS
)N ORDER TO TREAT SCANNING MOTION IN THE FREQUENCY DOMAIN THE APPARENT CLUTTER VELOCITY SEEN BY THE SCANNING ANTENNA IS EXAMINED TO DETERMINE THE DOPPLER FREQUENCY %ACH ELEMENT OF AN ARRAY OR INCREMENTAL SECTION OF A CONTINUOUS APERTURE CAN BE CON SIDERED AS RECEIVING A DOPPLER SHIFTED SIGNAL DUE TO THE RELATIVE MOTION OF THE CLUTTER 4HE POWER RECEIVED BY THE ELEMENT IS PROPORTIONAL TO THE TWO WAY APERTURE POWER DISTRIBUTION FUNCTION &X AT THE ELEMENT )N ADDITION TO THE VELOCITY SEEN BY ALL ELEMENTS BECAUSE OF THE MOTION OF THE PLAT FORM EACH ELEMENT SEES AN APPARENT CLUTTER VELOCITY DUE TO ITS ROTATIONAL MOTION AS ILLUSTRATED IN &IGURE B 4HE APPARENT VELOCITY VARIES LINEARLY ALONG THE APERTURE (ENCE THE TWO WAY APERTURE DISTRIBUTION IS MAPPED INTO THE FREQUENCY DOMAIN 4HE RESULTING POWER SPECTRUM DUE TO THE ANTENNA SCANNING IS
¤L F³ ( F & ¥ ´ ¦ Q µ
a F a
AQ L
WHERE Q ANTENNA ROTATION RATE A HORIZONTAL ANTENNA APERTURE 4HIS SPECTRUM CAN BE APPROXIMATED BY A GAUSSIAN DISTRIBUTION WITH STANDARD DEVIATION
S C
FR AQ Q y N QA L
WHERE K AND A ARE IN THE SAME UNITS PA IS THE ONE WAY HALF POWER BEAMWIDTH AND N IS THE NUMBER OF HITS PER BEAMWIDTH 4HE APPROXIMATION PA y KA IS REPRESENTATIVE OF AN ANTENNA DISTRIBUTION YIELDING ACCEPTABLE SIDELOBE LEVELS )T CAN BE SEEN THAT THE ANTENNA PATTERN PULSE TO PULSE DIFFERENTIAL GAIN IS
$' Q
D' Q D' Q $Q Q 4P DQ DQ
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4HIS SUGGESTS THAT A CORRECTION SIGNAL IN THE REVERSE SENSE TO $'P BE APPLIED AS SHOWN IN &IGURE C (ALF THE CORRECTION IS ADDED TO ONE PULSE AND HALF SUBTRACTED FROM THE OTHER SO THAT #ORRECTION SIGNAL
$' Q Q4P D £ Q DQ
D £Q Q4P £Q DQ
WHERE 3P WAS SUBSTITUTED FOR 'P 4HE RADAR TRANSMITS A SUM PATTERN 3P AND RECEIVES ON THE DIFFERENCE PATTERN $P SO THAT THE RECEIVED SIGNAL IS PROPORTIONAL TO THE PRODUCT OF THE TWO )F THE SIGNAL RECEIVED ON THE DIFFERENCE PATTERN IS USED AS THE CORRECTION WE HAVE
%C $P 3P
"Y COMPARING %QS AND WE SEE THAT FOR %C TO APPROXIMATE THE CORRECTION SIGNAL THE DIFFERENCE PATTERNS SHOULD BE
D £Q $Q Q4P DQ
4HE DERIVATIVE OF THE SUM PATTERN IS SIMILAR TO A DIFFERENCE PATTERN IN THAT IT IS POSITIVE AT THE MAIN BEAM NULL P DECREASES TO ZERO ON THE ANTENNA CENTERLINE AND THEN GOES NEGATIVE UNTIL P 2EFERRING TO &IGURE ONE OBSERVES THAT THE MECHANIZATION FOR SCAN COMPENSA TION IS FUNDAMENTALLY SIMILAR TO THE $0#! MECHANIZATION EXCEPT THAT THE DIFFERENCE SIGNAL IS APPLIED IN PHASE WITH THE SUM SIGNAL AND AMPLIFIED BY AN AMOUNT DETERMINED BY THE ANTENNA ROTATION PER INTERPULSE PERIOD 4HE SIGNALS REQUIRED IF THE TRANSMISSION SIGNAL 3P THAT APPEARS IN EACH CHANNEL IS NEGLECTED ARE 3Q o LQ4P $Q WHERE L IS THE RATIO OF THE AMPLIFICATION IN THE TWO CHANNELS CHOSEN TO MAXIMIZE THE CLUTTER REJECTION 4HE REQUIRED DIFFERENCE PATTERN SLOPE IS DETERMINED BY THE DERIVATIVE OF THE SCAN PATTERN WHICH DIFFERS FROM THE $0#! CRITERION 4HIS TECHNIQUE IS KNOWN AS STEP SCAN COMPENSATION BECAUSE THE SYSTEM ELEC TRONICALLY POINTS THE ANTENNA SLIGHTLY AHEAD OF AND BEHIND OF BORESIGHT EACH PULSE SO THAT A LEADING AND LAGGING PAIR ARE TAKEN FROM SUCCESSIVE RETURNS TO OBTAIN THE EFFECT OF THE ANTENNA REMAINING STATIONARY &IGURE SHOWS THE IMPROVEMENT OBTAINED BY $ICKEY AND 3ANTA FOR SINGLE DELAY CANCELLATION #OMPENSATION 0ATTERN 3ELECTION 3ELECTION OF THE COMPENSATION PATTERN DEPENDS ON THE LEVEL OF SYSTEM PERFORMANCE REQUIRED THE TYPE OF -4) FILTERING USED THE PLATFORM VELOCITY SCAN RATE AND THE CHARACTERISTICS REQUIRED BY NORMAL RADAR PARAMETERS SUCH AS RESOLUTION DISTORTION GAIN SIDELOBES ETC &OR INSTANCE AN EXPONENTIAL PATTERN AND ITS CORRESPONDING DIFFERENCE PATTERN ARE EXCELLENT FOR SINGLE DELAY CANCELLATION $0#! BUT ARE UNSATISFACTORY WHEN DOUBLE DELAY CANCELLATION IS USED 4HIS IS BECAUSE THE SINGLE DELAY CANCELER REQUIRES THE BEST MATCH BETWEEN THE ACTUAL PATTERN AND THE REQUIRED PATTERN NEAR BORESIGHT WHEREAS DOUBLE CANCELLATION REQUIRES THE BEST MATCH
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&)'52% -4) IMPROVEMENT FACTOR FOR A STEP SCAN COMPENSATION OF A SINGLE DELAY CANCELER AS A FUNCTION OF THE NUMBER OF HITS PER BEAMWIDTH 4HE ANTENNA PATTERN IS SIN X X
ON THE BEAM SHOULDER 3TEP SCAN COMPENSATION USUALLY REQUIRES THE DIFFERENCE PATTERN PEAKS TO BE NEAR THE NULLS OF THE SUM PATTERN TO MATCH 'RISSETTI ET AL HAVE SHOWN THAT FOR STEP SCAN COMPENSATION THE IMPROVEMENT FACTOR FOR SINGLE DELAY CANCELLATION INCREASES AS A FUNCTION OF THE NUMBER OF HITS AT D" DECADE FOR THE FIRST DERIVATIVE
TYPE STEP SCAN COMPENSATION AT THE RATE OF D" DECADE AND WITH FIRST AND SECOND DERIVATIVE COMPENSATION AT THE RATE OF D"DECADE (ENCE FOR A GROUND BASED SYSTEM THAT IS LIMITED BY SCAN RATE ONE SHOULD IMPROVE THE COMPENSATION PATTERN RATHER THAN USE A HIGHER ORDER -4) CANCELER (OWEVER AIRBORNE SYSTEMS ARE PRIMARILY LIMITED BY PLATFORM MOTION AND REQUIRE BOTH BETTER CANCELERS AND COMPENSATION FOR OPERATION IN A LAND CLUTTER ENVIRONMENT )N THE SEA CLUTTER ENVIRON MENT THE SYSTEM IS USUALLY DOMINATED BY THE SPECTRAL WIDTH OF THE VELOCITY SPECTRUM OR PLATFORM MOTION RATHER THAN SCANNING 4HE APPLICABILITY OF $0#! OR STEP SCAN COMPEN SATION IN THE LATTER CASE IS DEPENDENT ON THE PARTICULAR SYSTEM PARAMETERS
4HE COMPENSATION REQUIRED BY $'P CAN BE DETERMINED FROM A 4AYLORS SERIES EXPANSION OF 'P )N THE PRE CEDING DISCUSSION WE USED THE FIRST DERIVATIVE 5SING HIGHER ORDER TERMS GIVES AN IMPROVED CORRECTION SIGNAL
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ΰÇÊ - 1 / "1-Ê* /", Ê "/" ÊÊ Ê- Ê " * -/" )N !-4) SYSTEMS HAVING MANY HITS PER SCAN SCANNING IS A SECONDARY LIMITATION FOR AN UNCOMPENSATED DOUBLE CANCELER (OWEVER THE PERFORMANCE OF A $0#! SYSTEM IS SIGNIFICANTLY REDUCED WHEN IT IS SCANNED 4HIS IS DUE TO THE SCANNING MODULATION ON THE DIFFERENCE PATTERN USED FOR PLATFORM MOTION COMPENSATION 3INCE THE $0#! APPLIES THE DIFFERENCE PATTERN IN QUADRATURE TO THE SUM PATTERN TO COMPENSATE FOR PHASE ERROR AND STEP SCAN APPLIES THE DIFFERENCE PATTERN IN PHASE TO COM PENSATE FOR AMPLITUDE ERROR IT IS POSSIBLE TO COMBINE THE TWO TECHNIQUES BY PROPERLY SCALING AND APPLYING THE DIFFERENCE PATTERN BOTH IN PHASE AND IN QUADRATURE 4HE SCALING FACTORS ARE CHOSEN TO MAXIMIZE THE IMPROVEMENT FACTOR UNDER CONDITIONS OF SCANNING AND PLATFORM MOTION 4HE RELATIONSHIPS FOR A DOUBLE DELAY THREE PULSE !-4) ARE SHOWN IN THE PHASOR DIAGRAM IN &IGURE 4HE PHASE ADVANCE BETWEEN THE FIRST PAIR OF PULSES FIRST AND SECOND PULSE FOR THE THREE PULSE -4) RECEIVED BY THE SUM PATTERN 3 IS H
P 4P L
§ ¤ W R 4P ³ W 4P ¤ ³¶ ¨6X ¥SIN Q SIN ´ 6Y ¥ COS R COS Q ´ · ¦ µ ·¸ µ ¨© ¦
AND THE PHASE ADVANCE BETWEEN THE SECOND PAIR OF PULSES SECOND AND THIRD PULSE FOR THE THREE PULSE -4) IS H
P 4P § ¤ W R 4P ³ W 4P ¤ ³¶ 6X ¥SIN Q SIN 6Y ¥ COS R COS Q ´ · ¨ ´ L ¨ ¦ µ ¦ µ ·¸ ©
&)'52% 0HASOR DIAGRAM FOR SIMULTANEOUS SCANNING AND MOTION COMPENSATION
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WHERE P IS THE DIRECTION OF THE CLUTTER CELL WITH RESPECT TO THE ANTENNA POINTING ANGLE WHEN THE SECOND PULSE IS RECEIVED AND VR IS THE ANTENNA SCAN RATE 4HE SUBSCRIPTS ON THE RECEIVED SIGNALS 3I AND $I INDICATE THE PULSE RECEPTION SEQUENCE 4HE DIFFERENCE PATTERN $ IS USED TO GENERATE AN IN PHASE CORRECTION FOR SCAN NING MOTION AND A QUADRATURE CORRECTION FOR PLATFORM MOTION 4HIS PROCESS YIELDS THE SET OF RESULTANT SIGNALS 2IJ WHERE THE SUBSCRIPT I DENOTES THE PULSE PAIR AND THE SUBSCRIPT J DENOTES THE COMPONENT OF THE PAIR "ECAUSE G DOES NOT EQUAL G DIF FERENT WEIGHTING CONSTANTS ARE REQUIRED FOR EACH PULSE PAIR 4HE VALUES OF K FOR THE QUADRATURE CORRECTION OF THE FIRST PULSE PAIR K FOR THE QUADRATURE CORRECTION FOR THE SECOND PULSE PAIR L FOR THE IN PHASE CORRECTION FOR THE FIRST PULSE PAIR AND L FOR THE SECOND PULSE PAIR ARE OPTIMIZED BY MINIMIZING THE INTEGRATED RESIDUE POWER OVER THE SIGNIFICANT PORTION OF THE ANTENNA PATTERN USUALLY CHOSEN BETWEEN THE FIRST NULLS OF THE MAIN BEAM &IGURE SHOWS THE SUM AND DIFFERENCE MAIN BEAM PATTERNS FOR AN APERTURE WAVELENGTHS LONG &IGURE SHOWS THE RESIDUE FOR THE CASE WHEN THE FRACTION OF THE HORIZONTAL APERTURE WIDTH A TRAVELED PER INTERPULSE PERIOD 4P 6N 6X4PA IS EQUAL TO AND WHEN THE NUMBER OF WAVELENGTHS THAT THE APERTURE TIP ROTATES PER INTERPULSE PERIOD 7N AVR4PK IS EQUAL TO 4HE CORRESPONDING IMPROVEMENT FACTOR IS D" 4HE IMPROVEMENT FACTOR IS SHOWN IN &IGURE FOR A RANGE OF NORMALIZED PLATFORM MOTION 6N AS A FUNCTION OF NORMALIZED SCANNING DISPLACEMENTS 7N 4HE NONSCANNING CASE IS SHOWN AS 7N 4HE IMPROVEMENT FACTORS WERE COMPUTED FOR THE WAVE LENGTH APERTURE PATTERNS SHOWN IN &IGURE !NDREWS HAS DEVELOPED AN OPTIMIZATION PROCEDURE FOR PLATFORM MOTION COMPEN SATION THAT ROTATES THE PHASORS DIRECTLY RATHER THAN BY USING A QUADRATURE CORRECTION 4HE PROCEDURE DETERMINES THE ANTENNA FEED COEFFICIENTS FOR TWO COMPENSATION PATTERNS ONE OF WHICH #P IS ADDED TO THE SUM PATTERN 3P AND FED TO THE UNDELAYED CANCELER
&)'52% 3UM AND DIFFERENCE PATTERNS USED TO DETERMINE $0#! PERFORMANCE
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&)'52% $0#! CLUTTER RESIDUE VERSUS ANGLE FOR NORMALIZED DISPLACEMENT 6N AND NORMALIZED SCANNING MOTION 7N
PATH AND THE OTHER #P WHICH IS ADDED TO THE SUM PATTERN AND FED TO THE DELAYED PATH AS SHOWN IN &IGURE 4HE PROCEDURE WAS DEVELOPED FOR A SINGLE DELAY CANCELER AND A NONSCANNING ANTENNA !NDREWS USED THE PROCEDURE TO MINIMIZE THE RESIDUE POWER OVER THE FULL ANTENNA PATTERN WHICH INCLUDES THE MAIN BEAM AND SIDELOBE REGIONS
&)'52% $0#! IMPROVEMENT FACTOR VERSUS NORMALIZED PLATFORM MOTION 6N AS A FUNCTION OF NORMAL IZED SCANNING MOTION 7N
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&)'52% /PTIMIZED $0#! PHASE COMPENSATION
ΰnÊ * /", "/" Ê " * -/" ]Ê ",7, Ê , /" 4HE PREVIOUS SECTIONS DISCUSSED THE COMPENSATION FOR THE COMPONENT OF PLATFORM MOTION PARALLEL TO THE ANTENNA APERTURE 4!##!2 REMOVES THE AVERAGE COMPONENT OF PLATFORM MOTION PERPENDICULAR TO THE APERTURE 4HE FORMER 7HEELER ,ABORATORIES DEVELOPED THE #OINCIDENT 0HASE #ENTER 4ECHNIQUE #0#4 TO REMOVE THE SPECTRAL SPREAD DUE TO THE VELOCITY COMPONENT PERPENDICULAR TO THE APERTURE AND DUE TO THE COMPONENT PARALLEL TO THE APERTURE 2EMOVAL OF THE COMPONENT PARALLEL TO THE APERTURE USES THE $0#! PATTERN SYNTHESIS TECHNIQUE DESCRIBED IN !NDERSON WHICH CREATES TWO SIMILARLY SHAPED ILLUMINATION FUNCTIONS WHOSE PHASE CENTERS ARE PHYSICALLY DISPLACED 2EMOVAL OF THE COMPONENT PERPENDICULAR TO THE APERTURE IS ACCOMPLISHED BY A NOVEL EXTENSION OF THIS CONCEPT 4HE FIRST TERM OF %Q FOR SPECTRAL WIDTH DUE TO PLATFORM MOTION APPROACHES ZERO AS THE ANTENNA POINTS AHEAD (OWEVER THE SECOND TERM OF %Q DOMINATES AS THE ANTENNA APPROACHES WITHIN A FEW BEAMWIDTHS OF THE AIRCRAFTS GROUND TRACK )N THIS REGION
FD y
6Y Q 6YQ SIN y L L
WHICH YIELDS A SINGLE SIDED SPECTRUM THAT IS SIGNIFICANTLY NARROWER THAN THE SPECTRUM ABEAM &OR MODERATE PLATFORM SPEEDS AND LOWER FREQUENCY 5(& RADARS THIS EFFECT IS NEGLIGIBLE AND COMPENSATION IS NOT REQUIRED
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7HEN IT IS NECESSARY TO COMPENSATE FOR THIS EFFECT THE PHASE CENTER OF THE ANTENNA MUST BE DISPLACED AHEAD OF THE APERTURE AND BEHIND THE APERTURE FOR ALTERNATE RECEIVE PULSES SO THAT THE PHASE CENTERS ARE COINCIDENT FOR A MOVING PLATFORM 4HIS TECHNIQUE CAN BE EXTENDED TO MORE THAN TWO PULSES BY USING THE NECESSARY PHASE CENTER DIS PLACEMENTS FOR EACH PULSE )N ORDER TO MAINTAIN THE EFFECTIVE 02& THE DISPLACEMENT MUST COMPENSATE FOR THE TWO WAY TRANSMISSION PATH 4O ACCOMPLISH THIS DISPLACEMENT NEAR FIELD ANTENNA PRINCIPLES ARE UTILIZED ! DESIRED APERTURE DISTRIBUTION FUNCTION IS SPECIFIED 4HE NEAR FIELD AMPLITUDE AND PHASE ARE CALCULATED AT A GIVEN DISTANCE FROM THE ORIGIN )F THIS FIELD IS USED AS THE ACTUAL ILLUMINATION FUNCTION A VIRTUAL APERTURE IS CREATED WITH THE DESIRED DISTRIBUTION FUNCTION AT THE SAME DISTANCE BEHIND THE PHYSICAL ANTENNA &IGURE A SHOWS THE PHASE AND AMPLITUDE DISTRIBUTION REQUIRED TO FORM A UNIFORM VIRTUAL DISTRIBUTION DISPLACED BEHIND THE PHYSICAL APERTURE )T CAN BE SHOWN THAT IF THE PHASE OF THE ILLUMINATION FUNCTION IS REVERSED E` E THE DESIRED VIRTUAL DISTRIBUTION FUNCTION IS DISPLACED AHEAD OF THE APERTURE AS SHOWN IN &IGURE B )N PRACTICE PERFORMANCE IS LIMITED BY THE ABILITY TO PRODUCE THE REQUIRED ILLUMINA TION FUNCTION !S THE DISPLACEMENT INCREASES A LARGER PHYSICAL APERTURE SIZE IS REQUIRED TO PRODUCE THE DESIRED VIRTUAL APERTURE SIZE OWING TO BEAM SPREADING 4HIS CAN BE SEEN IN &IGURE 4HE EFFECTIVENESS OF THE CORRECTION VARIES WITH ELEVATION ANGLE SINCE THE
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TO THE ANTENNA ELEMENTS 4EMPORAL ADAPTIVE ARRAY PROCESSING COMBINES AN ARRAY OF SIGNALS RECEIVED AT THE SAME SPATIAL LOCATION EG THE OUTPUT OF A REFLECTOR ANTENNA THAT ARE SAMPLED AT DIFFERENT INSTANCES OF TIME SUCH AS SEVERAL INTERPULSE PERIODS FOR AN ADAPTIVE -4) 3PACE TIME ADAPTIVE ARRAY PROCESSING COMBINES A TWO DIMENSIONAL ARRAY OF SIGNALS SAMPLED AT DIFFERENT INSTANCES OF TIME AND AT DIFFERENT SPATIAL LOCATIONS 34!0 IS A FAIRLY BROAD TOPIC THAT HAS APPLICABILITY BEYOND THIS CHAPTER ON AIRBORNE -4) RADAR 4HE PRIMARY MOTIVATION FOR 34!0 IS TO IMPROVE CLUTTER CANCELLATION PERFOR MANCE AND TO BETTER INTEGRATE A RADARS SPATIAL PROCESSING ANTENNA SIDELOBE CONTROL AND SIDELOBE JAMMING CANCELLATION WITH ITS TEMPORAL CLUTTER CANCELLATION PROCESSING 4HE APPLICABILITY OF 34!0 TO IMPROVING CLUTTER CANCELLATION MUST BE ASSESSED SPE CIFICALLY IN THE CONTEXT OF THE KEY PERFORMANCE LIMITERS TO AIRBORNE -4) RADAR CLUT TER CANCELLATION AS DESCRIBED AT THE START OF THIS CHAPTER 34!0 CAN IMPROVE A RADARS MOTION COMPENSATION PERFORMANCE AND IS MORE ROBUST THAN NONADAPTIVE TECHNIQUES IN ADDRESSING GENERALLY NON DISPERSIVE ERRORS IN THE RADAR FRONT END 34!0 WILL NOT DIRECTLY ADDRESS CLUTTER INTERNAL MOTION EFFECTS ANTENNA SCANNING MOTION EFFECTS OR OTHER HARDWARE STABILITY IMPACTS TO CLUTTER CANCELLATION PERFORMANCE 2ADAR DESIGNERS NEED TO ASSESS THE KEY LIMITATIONS IN A SPECIFIC APPLICATION BEFORE JUMPING TO THE CON CLUSION THAT 34!0 WILL IMPROVE PERFORMANCE 34!0S ABILITY TO INTEGRATE CLUTTER CANCELLATION TEMPORAL AND SPATIAL INTERFERENCE CANCELLATION CAN BE QUITE IMPORTANT TO MANY RADAR SYSTEMS WHETHER THEY TYPICALLY HAVE TO DEAL WITH INTENTIONAL JAMMING INTERFERENCE OR UNINTENTIONAL OR CASUAL ELECTROMAGNETIC INTERFERENCE %-) 34!0 GETS AWAY FROM CASCADED SOLUTIONS SUCH AS ANALOG SIDELOBE CANCELLERS FOLLOWED BY DIGITAL $0#! ANDOR -4) FILTERSTHAT DO NOT GENERALLY CREATE AN OPTIMUM INTERFERENCE CANCELLATION SOLUTION /PTIMAL !DAPTIVE 7EIGHTS -C'UFFIN 4HE OPTIMAL LINEAR ESTIMATE IS DETER MINED BY REQUIRING THE ADAPTED ESTIMATION ERROR BE ORTHOGONAL TO THE OBSERVED VEC TOR R 3TEADY STATE CONDITIONS ARE ASSUMED IN THIS DERIVATION THUS THE CONDITION FOR ORTHOGONALITY IS
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FREEDOM IN 34!0 WHILE STILL PROCESSING THE FULL APERTURE SPATIALLY 4HIS IS SIMILAR TO A CONVENTIONAL -4) OR $0#! ARCHITECTURE CASCADED WITH DOPPLER FILTERING 7E CALL THIS ARCHITECTURE A PRE DOPPLER ELEMENTAL LEVEL 34!0 ARCHITECTURE &OR A THREE PULSE VERSION OF THIS ARCHITECTURE THERE ARE - DEGREES OF FREEDOM )N THIS ARCHITECTURE PLATFORM MOTION COMPENSATION TAKES THE GENERAL FORM OF ADJUSTING THE ANTENNAS PHASE CENTER OVER THE THREE TEMPORALLY SEPARATED BEAMS ! BASIC BLOCK DIAGRAM OF A RADAR INCORPORATING PRE DOPPLER ELEMENTAL LEVEL SPACE TIME ADAPTIVE ARRAY PROCESSING IS SHOWN IN &IGURE !N INDIVIDUAL DUPLEXER IS PLACED BETWEEN EACH TRANSMITTERS CHANNELIZED OUTPUT AND ITS CORRESPONDING ANTENNA ELEMENT 0ROVISION COULD BE INCLUDED FOR ELECTRONIC BEAM STEERING USING HIGH POWER PHASE SHIFTERS OR TRANSMIT MODULES WITH LOW POWER BEAM STEERING /N RECEIVE EACH DUPLEXER OUTPUT IS SENT TO ITS OWN DIGITAL RECEIVER 4HE DIGITAL RECEIVER OUTPUTS ARE PASSED THROUGH 02) DELAYS TO YIELD TEMPORALLY DISPLACED DATA SAMPLES ! FULL COMPLEMENT OF ELEMENTS AND TIME DELAYED SIGNALS ARE SAMPLED AND USED TO GENERATE THE ADAPTIVE WEIGHTS 6ARIOUS ALGORITHMS ARE POSSIBLE TO GENERATE THE ESTIMATE OF THE ADAPTIVE WEIGHTS FROM %Q 4HE FAIRLY SIMPLE ,EAST -EAN 3QUARED ALGORITHM GENERALLY YIELDS FAIRLY SLOW CONVERGENCE RATES /THER ALGORITHMS CAN SPEED UP THE ADAPTATION RATE BUT A MORE COMPLEX MECHANIZATION IS REQUIRED %XAMPLES INCLUDE A 2ECURSIVE ,EAST 3QUARED ALGORITHM 1 2 DECOMPOSITION WITH 'RAM 3CHMIDT ORTHOGONALIZATION OR A (OUSEHOLDER 4RANSFORMATION 4HE ADAPTIVE WEIGHTS ARE THEN APPLIED TO THE RECEIVED SIGNALS AND BEAMFORMED TO GENERATE THREE SUM CHANNEL DETEC TION BEAMS UNDELAYED ONE 02) DELAYED AND TWO 02) DELAYED BEAMS 4HESE BEAMS ARE IN TURN ADDED TOGETHER TO FORM THE FINAL 34!0 WEIGHTED DETECTION BEAM ! SIMPLISTIC VIEW OF HOW THESE THREE BEAMS PERFORM MOTION COMPENSATION IS ILLUS TRATED IN &IGURE FOR THE CASE WHERE THE APERTURE IS PARALLEL WITH THE RADARS PLATFORM VELOCITY VECTOR 4HE FIRST PULSE RETURNS PHASE CENTER IS ADVANCED BY APERTURE WEIGHT ING THE SECOND PULSE RETURNS PHASE CENTER IS ESSENTIALLY UNCHANGED FROM THE QUIESCENT WEIGHTS AND THE THIRD PULSE RETURNS PHASE CENTER IS RETARDED BY APERTURE WEIGHTING 'IVEN IDEAL ANTENNA PATTERNS AND AN APERTURE LARGE ENOUGH TO ADJUST THE PHASE CENTERS
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MUST ALSO SPAN THE SPATIAL DIRECTIONS OF THAT INTERFERENCE !N EXAMPLE OF A SIMPLE TRANSFORMATION OF THIS TYPE WOULD BE SIDELOBE CANCELER ARCHITECTURE WHERE THE BEAM TRANSFORMATION WOULD GENERATE A SUM CHANNEL MAIN BEAM AND SELECT ELEMENTS FROM THE APERTURE AS SIDELOBE CANCELLERS 0OST $OPPLER %LEMENT !NTENNA 34!0 4HE SECOND TYPE OF TRANSFORMATION LEADS TO WHAT ARE CALLED POST DOPPLER 34!0 ARCHITECTURES !S THE NAME IMPLIES THE ANTENNA ELEMENT SIGNALS ARE FIRST DOPPLER FILTERED AND THEN PROCESSED THROUGH 34!0 4HE MOTIVATION FOR THIS TYPE OF ARCHITECTURE IS THAT THE RESULTANT 34!0 SOLUTIONS CAN INDEPENDENTLY ADDRESS A SUBSET OF THE CLUTTER INTERFERENCE PROBLEM ISOLATED TO CLUTTER THAT REMAINS IN A SINGLE DOPPLER FILTER 4HIS TECHNIQUE MAY BE MORE EFFECTIVE FOR RADAR SYSTEMS WHERE THE CLUTTER ENVIRONMENT AND WAVEFORM SELECTION LEAD TO UNAMBIGUOUS CLUTTER RETURNS WITHIN THE RADARS 02& 4WO EXAMPLE CONDITIONS THE FIRST WITH AMBIGU OUS DOPPLER CLUTTER AND THE SECOND WITH UNAMBIGUOUS DOPPLER CLUTTER ARE SHOWN IN &IGURE 4HE FIGURE SHOWS THOSE ANTENNA ANGLES WHERE THE CLUTTER DOPPLER RESPONSE REMAINS AFTER FILTERING THROUGH A SINGLE DOPPLER FILTER &IGURE A SHOWS THE RESPONSE FOR AN AMBIGUOUS 02& OF (Z AND &IGURE B SHOWS THE RESPONSE FOR AN UNAM BIGUOUS 02& OF (Z FOR A 5(& RADAR 4HIS FIGURE HIGHLIGHTS THAT EVEN WITH DOP PLER PROCESSING A GIVEN DOPPLER FILTER MAY STILL INCLUDE CLUTTER RETURNS FROM A NUMBER OF DISCONTIGUOUS ANGULAR INTERVALS 4HE ADVANTAGES OF THIS TRANSFORMATION FROM 02) TO DOPPLER SPACE ON OVERALL 34!0 PERFORMANCE VERSUS A PRE DOPPLER ARCHITECTURE ARE MORE DRAMATIC IN THE UNAMBIGUOUS DOPPLER CLUTTER CASE 02) STAGGERED DOPPLER FILTER OUTPUTS ARE REQUIRED TO MAINTAIN A SET OF TEMPORAL DEGREES OF FREEDOM IN THIS ARCHITECTURE 4HE BLOCK DIAGRAM IS MODIFIED TO THAT SHOWN IN &IGURE WITH MULTIPLE DOPPLER FILTER BANKS ON EACH ANTENNA ELEMENT AND 02) DELAY 0OST $OPPLER "EAM 3PACE 34!0 4HE FINAL CATEGORY RESULTS FROM IMPLEMENT ING BOTH DOPPLER AND SPATIAL TRANSFORMATIONS PRIOR TO 34!0 PROCESSING 4HE APPROPRIATE ARCHITECTURE SOLUTION DEPENDS UPON THE RADAR DESIGN CONSTRAINTS 4HE NUMBER OF ANTENNA ELEMENTS AND BEAMFORMING REQUIREMENTS ARE KEY DRIVERS IN THE
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MECHANICALLY SCANNED WITH AN OPERATOR SELECTABLE SCAN RATE AZIMUTH ELECTRONI CALLY SCANNED WITH THE MECHANICAL BORESITE PROVIDED AS AN INPUT TO THE RADAR AND MECHANICALLY SCANNED WITH ADDITIONAL ELECTRONIC SCANNING WITHIN AN OPERATOR SELECT ABLE AZIMUTH REGION 4HE TRANSMIT WAVEFORM INCLUDES 4!##!2 MODULATION TO CENTER MAINBEAM CLUTTER AT ZERO DOPPLER FREQUENCY (OWEVER BECAUSE THE RADAR IMPLEMENTS ADAPTIVE CLUTTER CANCELLATION 34!0 THE REQUIREMENTS ON 4!##!2 ARE SIGNIFICANTLY LESS COMPLEX THAN FOR LEGACY RADAR SYSTEMS 4HERE IS NO NEED TO INCLUDE CLOSED LOOP ADJUSTMENTS TO THE 4!##!2 MODULATION FREQUENCY 4HE OPTIMIZATION OF THE !-4) CLUTTER CANCELLA TION FILTER IS ACHIEVED IN THE 34!0 PROCESSING AS OPPOSED TO ADJUSTING THE LOCATION OF MAIN BEAM CLUTTER TO FIT A FIXED !-4) FILTER )N ORDER TO IMPLEMENT 34!0 AND ELECTRONIC SCANNING IN THIS RADAR ALL ELEMENTS OF THE PHASED ARRAY ANTENNA ARE PROCESSED ON TRANSMIT AND RECEIVE 4HE SOLID STATE TRANSMITTER PROVIDES LOW POWER PHASE SHIFT CONTROL FOR ELECTRONIC STEERING FOLLOWED BY POWER AMPLIFICATION IN EACH OF CHANNELS 4HESE ARE CONNECTED TO THE ELEMENTS OF THE PHASED ARRAY THROUGH AN CHANNEL ROTARY COUPLER 4HE TRANSMITRECEIVE ISOLA TION ON ALL CHANNELS IS PROVIDED THROUGH CIRCULATORS 4HE CHANNELS ARE PROCESSED SEPARATELY THROUGH RECEIVERS FINALLY FEEDING THE 34!0 SUBSYSTEM WITH DIGITAL BASEBAND SIGNALS 4HE RADAR PERFORMS PLATFORM MOTION COMPENSATION ELECTRONICALLY AS PART OF THE 34!0 ARCHITECTURE 4HE RADAR IMPLEMENTS AN ELEMENT SPACE PRE DOPPLER 34!0 ARCHI TECTURE !DAPTIVE WEIGHTS ARE GENERATED AND APPLIED TO THE RECEIVE CHANNELS FORM ING THREE BEAMS 3UM $ELTAAZ AND /MNI BY WEIGHTING AND SUMMING THE RECEIVE CHANNELS OVER THREE PULSES TO PROVIDE SIMULTANEOUS CLUTTER AND JAMMING CANCELLATION 4HE ADAPTIVE WEIGHT ALGORITHM IS MATCHED TO THE RADARS OPERATING PARAMETERS AND IS AUGMENTED WITH ADAPTIVE KNOWLEDGEnAIDED SAMPLING SCHEMES TO MAXIMIZE PERFOR MANCE IN A COMPLEX HETEROGENEOUS CLUTTER AND JAMMING INTERFERENCE ENVIRONMENT $OPPLER FILTERING IS PERFORMED AFTER DIGITAL BEAMFORMING /THER FUNCTIONS DISCUSSED IN THIS CHAPTER ARE NOT REQUIRED FOR THIS RADAR APPLICATION BECAUSE THEY DO NOT LIMIT PERFORMANCE %XAMPLES INCLUDE SCANNING MOTION COMPENSA TION AND MULTIPLE SPECTRA !-4) CLUTTER CANCELLATION
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2 # %MERSON h3OME PULSED DOPPLER -4) AND !-4) TECHNIQUES v 2AND #ORPORATION 2EPT 2 $$# $OC !$ -ARCH 2EPRINTED IN 2EFERENCE 4 3 'EORGE h&LUCTUATIONS OF GROUND CLUTTER RETURN IN AIRBORNE RADAR EQUIPMENT v 0ROC )%% ,ONDON VOL PT )6 PP n !PRIL & 2 $ICKEY *R h4HEORETICAL PERFORMANCE OF AIRBORNE MOVING TARGET INDICATORS v )2% 4RANS VOL 0'!% PP n *UNE 2 3 "ERKOWITZ ED -ODERN 2ADAR !NALYSIS %VALUATION AND 3YSTEM $ESIGN .EW 9ORK *OHN 7ILEY 3ONS $ + "ARTON 2ADAR 3YSTEMS !NALYSIS %NGLEWOOD #LIFFS .* 0RENTICE (ALL $ # 3CHLERER ED -4) 2ADAR .ORWOOD -! !RTECH (OUSE )NC & 2 $ICKEY *R AND - - 3ANTA h&INAL REPORT ON ANTICLUTTER TECHNIQUES v 'ENERAL %LECTRIC #OMPANY 2EPT 2%-( -ARCH $ " !NDERSON h! MICROWAVE TECHNIQUE TO REDUCE PLATFORM MOTION AND SCANNING NOISE IN AIRBORNE MOVING TARGET RADAR v )2% 7%3#/. #ONV 2EC VOL PT PP n
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h&INAL ENGINEERING REPORT ON DISPLACED PHASE CENTER ANTENNA v VOL -ARCH VOLS AND !PRIL 'ENERAL %LECTRIC #OMPANY 3CHENECTADY .9 ( 5RKOWITZ h4HE EFFECT OF ANTENNA PATTERNS ON PERFORMANCE OF DUAL ANTENNA RADAR MOVING TARGET INDICATORS v )%%% 4RANS VOL !.% PP n $ECEMBER ' . 4SANDOULIS h4OLERANCE CONTROL IN AN ARRAY ANTENNA v -ICROWAVE * PP n /CTOBER + ' 3HROEDER h"EAM PATTERNS FOR PHASE MONOPULSE ARRAYS v -ICROWAVES PP n -ARCH 2 3 'RISSETTI - - 3ANTA AND ' - +IRKPATRICK h%FFECT OF INTERNAL FLUCTUATIONS AND SCANNING ON CLUTTER ATTENUATION IN -4) 2ADAR v )2% 4RANS VOL !.% PP n -ARCH ' ! !NDREWS h!IRBORNE RADAR MOTION COMPENSATION TECHNIQUES /PTIMUM ARRAY CORRECTION PATTERNS v .AVAL 2ES ,AB 2EPT -ARCH ! 2 ,OPEZ AND 7 7 'ANZ h#0#4 ANTENNAS FOR !-4) RADAR VOL 4HEORETICAL STUDY v !IR &ORCE !VIONICS ,AB 2EPT 7, !$ *UNE .OT READILY AVAILABLE , % "RENNAN * $ -ALLETT AND ) 3 2EED h!DAPTIVE ARRAYS IN AIRBORNE -4) RADAR v )%%% 4RANS VOL !0 PP n 3EPTEMBER ! , -C'UFFIN h! BRIEF ASSESSMENT OF ADAPTIVE ANTENNAS WITH EMPHASIS ON AIRBORNE RADAR v 'ENERAL %LECTRIC #OMPANY !IRCRAFT %QUIPMENT $IVISION !UGUST " 7IDROW AND 3 $ 3TEARNS !DAPTIVE 3IGNAL 0ROCESSING .EW *ERSEY 0RENTICE (ALL )NC 3 0 !PPLEBAUM h!DAPTIVE ARRAYS v )%%% 4RANS VOL !0 PP n 3EPTEMBER , % "RENNAN % , 0UGH AND ) 3 2EED h#ONTROL LOOP NOISE IN ADAPTIVE ARRAY ANTENNAS v )%%% 4RANS VOL !%3 -ARCH * 7ARD h3PACE TIME ADAPTIVE PROCESSING FOR AIRBORNE RADAR v -)4 ,INCOLN ,ABORATORY 4ECHNICAL 2EPORT $ECEMBER , % "RENNAN AND & - 3TAUDAHER h3UBCLUTTER VISIBILITY DEMONSTRATION v 4ECHNICAL 2EPORT 2, 42 !DAPTIVE 3ENSORS )NCORPORATED -ARCH 2 ! -ONZINGO AND 4 7 -ILLER )NTRODUCTION TO !DAPTIVE !RRAYS .EW 9ORK *OHN 7ILEY 3ONS
#HAPTER
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Ê*°Ê-ÌÀ>>Ê 7>Ê°Êi`>À .ORTHROP 'RUMMAN #ORPORATION
{°£Ê , / ,-/ -Ê Ê** /" 4HE PRIMARY BENEFIT OF PULSE DOPPLER RADAR IS ITS ABILITY TO DETECT SMALL AMPLITUDE MOV ING TARGET RETURNS AGAINST AN OVERWHELMINGLY LARGE AMPLITUDE CLUTTER BACKGROUND .OMENCLATURE 2ADARS THAT RELY ON THE DOPPLER EFFECT TO ENHANCE TARGET DETEC TION ARE CALLED DOPPLER RADARS 4HE DOPPLER EFFECT MANIFESTS ITSELF WHEN THERE IS A RELATIVE RANGE RATE OR RADIAL VELOCITY BETWEEN THE RADAR AND THE TARGET 7HEN THE RADARS TRANSMIT SIGNAL IS REFLECTED FROM SUCH A TARGET THE CARRIER FREQUENCY OF THE RETURN SIGNAL WILL BE SHIFTED !SSUMING A MONOSTATIC RADAR IE COLLOCATED TRANSMIT TER AND RECEIVER THE ROUNDTRIP DISTANCE IS TWICE THE DISTANCE BETWEEN THE TRANSMITTER AND THE TARGET 4HE DOPPLER FREQUENCY SHIFT FD IS A FUNCTION OF THE CARRIER WAVELENGTH K AND THE RELATIVE RADIAL VELOCITY RANGE RATE BETWEEN THE RADAR AND THE TARGET 6RELATIVE AND IS WRITTEN AS FD 6RELATIVEK WHERE K CF IS THE WAVELENGTH C IS THE SPEED OF LIGHT AND F IS THE CARRIER FREQUENCY 7HEN THE TARGET IS MOVING AWAY FROM THE RADAR THE RELATIVE RADIAL VELOCITY OR RANGE RATE IS DEFINED TO BE POSITIVE AND RESULTS IN A NEGATIVE DOPPLER SHIFT $OPPLER RADARS CAN BE EITHER CONTINUOUS WAVE #7 o OR PULSED RADARS #7 RADARS SIMPLY OBSERVE THE DOPPLER SHIFT BETWEEN THE CARRIER FREQUENCY OF THE RETURN SIGNAL RELATIVE TO THE TRANSMIT SIGNAL 0ULSED SYSTEMS MEASURE DOPPLER BY USING A COHERENT TRAIN OF PULSES WHERE THERE IS A FIXED OR DETERMINISTIC PHASE RELATIONSHIP OF THE CARRIER FREQUENCY BETWEEN EACH SUCCESSIVE RADIO FREQUENCY 2& PULSE #OHERENCE CONCEN TRATES THE ENERGY IN THE FREQUENCY SPECTRUM OF THE PULSE TRAIN AROUND DISTINCT SPECTRAL LINES SEPARATED BY THE PULSE REPETITION FREQUENCY 02& 4HIS SEPARATION INTO SPECTRAL LINES ALLOWS FOR DISCRIMINATION OF DOPPLER SHIFTS $OPPLER RADARS USING PULSED TRANSMISSIONS ARE MORE COMPLEX THAN #7 RADARS BUT THEY OFFER SIGNIFICANT ADVANTAGES -OST IMPORTANT IS THE TIME GATING OF THE RECEIVER
$AVID ( -OONEY AND 7ILLIAM ! 3KILLMAN WROTE THIS CHAPTER FOR THE FIRST EDITION 7ILLIAM ( ,ONG JOINED THE AUTHORS FOR THE SECOND EDITION *OHN 0 3TRALKA AND 7ILLIAM ' &EDARKO UPDATED THE MATERIAL FOR THIS EDITION o 4O ASSIST THE READER ABBREVIATIONS USED THROUGHOUT THIS CHAPTER ARE DEFINED IN A LIST AT THE END OF THE CHAPTER
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4IME GATING ALLOWS THE BLANKING OF DIRECT TRANSMITTER LEAKAGE INTO THE RECEIVER 4HIS PERMITS THE USE OF A SINGLE ANTENNA FOR TRANSMIT AND RECEIVE WHICH OTHERWISE WOULD NOT BE FEASIBLE FOR #7 RADAR DUE TO EXCESSIVE TRANSMITRECEIVE ISOLATION REQUIREMENTS 0ULSED RADARS CAN ALSO USE RANGE GATING A SPECIFIC FORM OF TIME GATING WHICH DIVIDES THE INTERPULSE PERIOD INTO CELLS OR RANGE GATES 4HE DURATION OF EACH CELL IS TYPICALLY LESS THAN OR EQUAL TO THE INVERSE OF THE TRANSMIT PULSE BANDWIDTH 2ANGE GATING HELPS ELIMINATE EXCESS RECEIVER NOISE FROM COMPETING WITH TARGET RETURNS AND ALLOWS RANGE MEASUREMENT WITH PULSE DELAY RANGING IE MEASURING THE TIME BETWEEN TRANSMISSION OF A PULSE AND RECEPTION OF THE TARGET ECHO 0ULSED TRANSMISSION DOPPLER RADARS HAVE HISTORICALLY BEEN CATEGORIZED AS MOVING TARGET INDICATION -4) OR PULSE DOPPLER -4) TYPICALLY ELIMINATES CLUTTER BY PASSING THE RECEIVED RETURNS FROM MULTIPLE COHERENT PULSES THROUGH A FILTER WITH A STOPBAND PLACED IN SPECTRAL REGIONS OF HEAVY CLUTTER CONCENTRATIONS -OVING TARGETS WITH DOP PLER FREQUENCIES OUTSIDE THE STOPBAND ARE PASSED ONTO DETECTION PROCESSING 0ULSE DOPPLER RADARS ON THE OTHER HAND RESOLVE AND ENHANCE TARGETS WITHIN A PARTICULAR DOPPLER BAND WHILE REJECTING CLUTTER AND OTHER RETURNS OUTSIDE THE DOPPLER BAND OF INTEREST 4HIS IS TYPICALLY ACCOMPLISHED WITH A CONTIGUOUS BANK OF DOPPLER FILTERS FORMED BETWEEN TWO OF THE COHERENT PULSE TRAINS SPECTRAL LINES ONE OF WHICH IS THE CENTRAL LINE 2ANGE GATING PRECEDES THE DOPPLER FILTER BANK 4HE BANDWIDTH OF EACH DOPPLER FILTER IS INVERSELY PROPORTIONAL TO THE DURATION OF THE COHERENT PULSE TRAIN THAT IS PROCESSED TO FORM THE DOPPLER FILTER BANK 4HIS PROCESS FORMS A MATCHED FILTER TO THE ENTIRE PULSE TRAIN -4) AND PULSE DOPPLER RADARS SHARE THE FOLLOWING CHARACTERISTICS L
L
#OHERENT TRANSMISSION AND RECEPTION THAT IS EACH TRANSMITTED PULSE AND THE RECEIVER LOCAL OSCILLATOR ARE SYNCHRONIZED TO A FREE RUNNING HIGHLY STABLE OSCILLATOR #OHERENT PROCESSING TO REJECT MAIN BEAM CLUTTER ENHANCE TARGET DETECTION AND AID IN TARGET DISCRIMINATION OR CLASSIFICATION
-4) RADARS CAN ALSO BE IMPLEMENTED USING A DOPPLER FILTER BANK BLURRING THE HISTORIC DELINEATION BETWEEN -4) AND PULSE DOPPLER RADARS !S A RESULT THIS BOOK WILL DEFINE -4) RADARS AS THOSE RADARS WHOSE 02& IS SUFFICIENTLY LOW ENOUGH TO PROVIDE AN UNAM BIGUOUS RANGE MEASUREMENT VIA PULSE DELAY RANGING OVER THE RADARS INSTRUMENTED RANGE 4HE UNAMBIGUOUS RANGE 2U IS GIVEN BY CF2 WHERE C IS THE SPEED OF LIGHT AND F2 IS THE 02& 2ADARS WITH 02&S THAT RESULT IN RANGE AMBIGUITIES WITHIN THE RANGE COVERAGE OF INTEREST WILL BE REFERRED TO AS PULSE DOPPLER RADARS AND WILL BE THE FOCUS OF THIS CHAPTER !PPLICATIONS 0ULSE DOPPLER IS APPLIED PRINCIPALLY TO RADAR SYSTEMS REQUIRING THE DETECTION OF MOVING TARGETS IN A SEVERE CLUTTER ENVIRONMENT 4ABLE LISTS TYPI CAL APPLICATIONS AND REQUIREMENTSn 4HIS CHAPTER WILL DEAL PRINCIPALLY WITH AIRBORNE APPLICATIONS ALTHOUGH THE BASIC PRINCIPLES CAN ALSO BE APPLIED TO THE SURFACE BASED CASE /NLY MONOSTATIC RADARS WILL BE CONSIDERED 02&S 0ULSED RADARS THAT EMPLOY DOPPLER ARE DIVIDED INTO THREE BROAD 02& CAT EGORIES LOW MEDIUM AND HIGH ! LOW 02& RADAR IS ONE IN WHICH THE RANGES OF INTEREST ARE UNAMBIGUOUS WHILE THE RADIAL VELOCITIES DOPPLER FREQUENCIES ARE USUALLY HIGHLY AMBIGUOUS !S DISCUSSED PREVIOUSLY THIS TYPE OF RADAR IS CALLED MOVING TARGET INDICA TION -4) -4) RADARS ARE GENERALLY NOT CATEGORIZED AS PULSE DOPPLER RADARS ALTHOUGH THE PRINCIPLES OF OPERATION ARE SIMILAR
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4!",% 0ULSE $OPPLER !PPLICATIONS AND 2EQUIREMENTS
2ADAR !PPLICATION
2EQUIREMENTS
!IRBORNE OR SPACEBORNE SURVEILLANCE
,ONG DETECTION RANGE ACCURATE RANGE DATA
!IRBORNE INTERCEPTOR OR FIRE CONTROL
-EDIUM DETECTION RANGE ACCURATE RANGE VELOCITY AND ANGLE DATA
'ROUND BASED SURVEILLANCE
-EDIUM DETECTION RANGE ACCURATE RANGE DATA
"ATTLEFIELD SURVEILLANCE SLOW MOVING TARGET DETECTION
-EDIUM DETECTION RANGE ACCURATE RANGE VELOCITY DATA
-ISSILE SEEKER
3HORT DETECTION RANGE ACCURATE VELOCITY AND ANGLE RATE DATA MAY NOT NEED TRUE RANGE INFORMATION
3URFACE BASED WEAPON CONTROL
3HORT RANGE ACCURATE RANGE VELOCITY DATA
-ETEOROLOGICAL
'OOD VELOCITY RESOLUTION
-ISSILE WARNING
3HORT DETECTION RANGE VERY LOW FALSE ALARM RATE
4HE CONVERSE OF A LOW 02& RADAR IS A HIGH 02& RADAR THAT CAN MEASURE DOPPLER UNAMBIGUOUSLY OVER THE SPAN OF RADIAL VELOCITIES OF INTEREST BUT IS USUALLY HIGHLY AMBIGUOUS IN RANGE ! MEDIUM 02& RADAR HAS BOTH RANGE AND DOPPLER AMBIGUI TIESn ! BLEND OF MEDIUM AND HIGH 02& KNOWN AS HIGH MEDIUM 02& WHICH WILL BE DISCUSSED LATER IS CHARACTERIZED AS HAVING ONLY A SINGLE AMBIGUITY FOR THE RADIAL VELOCITIES OF INTEREST &OR THIS CHAPTER A PULSE DOPPLER RADAR IS CHARACTERIZED AS HAVING A 02& ANYWHERE WITHIN THE MEDIUM TO HIGH 02& REGIME THAT RESULTS IN AMBIGUOUS RANGE MEASUREMENTS DURING A COHERENT PROCESSING INTERVAL ! COMPARISON OF -4) AND PULSE DOPPLER RADARS IS SHOWN IN 4ABLE 0REVIOUSLY UNDEFINED TERMS WILL BE DEFINED THROUGHOUT THE CHAPTER 4HE TABLE ASSUMES AN AIRBORNE RADAR APPLICATION DESIGNED TO DETECT OTHER AIRCRAFT 3UCH AN APPLICATION IS COMMONLY REFERRED TO AS AIR TO AIR 4!",% #OMPARISON OF -4) AND 0ULSE $OPPLER 2ADARS FOR !IR TO !IR
!DVANTAGES
$ISADVANTAGES
,OW 02& -4) RANGE UNAMBIGUOUS DOPPLER AMBIGUOUS
#AN SORT CLUTTER FROM TARGETS ON BASIS OF RANGE &RONT END SENSITIVITY TIME CONTROL 34# SUPPRESSES SIDELOBE DETECTIONS AT SHORT RANGES AND REDUCES DYNAMIC RANGE REQUIREMENTS
-ULTIPLE BLIND SPEEDS 5SUALLY DOES NOT MEASURE RADIAL TARGET VELOCITY 0OOR GROUND MOVING TARGET REJECTION
-EDIUM 02& 0ULSE $OPPLER RANGE AMBIGUOUS DOPPLER AMBIGUOUS
0ERFORMANCE AT ALL TARGET ASPECTS 'OOD GROUND MOVING TARGET REJECTION -EASURES RADIAL VELOCITY ,ESS RANGE ECLIPSING THAN IN HIGH 02&
3IDELOBE CLUTTER CAN LIMIT PERFORMANCE !MBIGUITY RESOLUTION REQUIRED ,OW ANTENNA SIDELOBES NECESSARY 2EJECTION OF SIDELOBE RETURNS OF DISCRETE GROUND TARGETS NEEDED
(IGH 02& 0ULSE $OPPLER RANGE AMBIGUOUS DOPPLER UNAMBIGUOUS
!LLOWS THERMAL NOISE LIMITED DETECTION OF TARGETS WITH HIGH RADIAL VELOCITIES 3INGLE DOPPLER BLIND ZONE AT ZERO VELOCITY 'OOD GROUND MOVING TARGET REJECTION -EASURES RADIAL VELOCITY
,IMITED LOW RADIAL VELOCITY TARGET DETECTION 2ANGE ECLIPSING ,ARGE NUMBER OF RANGE AMBIGUITIES PRECLUDE PULSE DELAY RANGING (IGH STABILITY REQUIREMENTS DUE TO RANGE FOLDING
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4!",% 4YPICAL 6ALUES FOR AN 8 BAND '(Z !IRBORNE &IRE #ONTROL 2ADAR
0ULSE $OPPLER 7AVEFORM -EDIUM 02& (IGH MEDIUM 02& (IGH 02&
02&
4RANSMIT $UTY #YCLE
K(Z K(Z K(Z
4ABLE PROVIDES THE SPAN OF 02&S AND CORRESPONDING TRANSMIT DUTY CYCLES RATIO OF TRANSMIT PULSE WIDTH TO INTERPULSE PERIOD FOR THE VARIOUS PULSE DOPPLER WAVEFORMS USED IN A 8 BAND AIRBORNE FIRE CONTROL RADAR +EEP IN MIND THAT THE OPERATING FREQUENCY OF THE RADAR ALONG WITH ITS REQUIRED RANGE AND RADIAL VELOCITY COVERAGE DETERMINES WHETHER A 02& IS CONSIDERED MEDIUM HIGH MEDIUM OR HIGH !LSO MODERN MULTI FUNCTION RADARS ARE TYPICALLY CAPABLE OF UTILIZING WAVEFORMS FROM THE VARIOUS 02& CATEGORIES IN ORDER TO CARRY OUT THEIR DIVERSE MISSIONS 0ULSE $OPPLER 3PECTRUM 4HE TRANSMITTED SPECTRUM OF A PULSE DOPPLER RADAR CON SISTS OF DISCRETE LINES AT THE CARRIER FREQUENCY F AND AT SIDEBAND FREQUENCIES F o IF2 WHERE F2 IS THE 02& AND I IS AN INTEGER 4HE ENVELOPE OF THE SPECTRUM IS DETERMINED BY THE PULSE SHAPE &OR THE RECTANGULAR PULSES USUALLY EMPLOYED A SINX X SPECTRUM IS OBTAINED 5SING A CONSTANT VELOCITY AIRBORNE RADAR THE RECEIVED SPECTRUM FROM A STATIONARY TARGET HAS LINES THAT ARE DOPPLER SHIFTED PROPORTIONALLY TO THE RADIAL VELOCITY BETWEEN THE RADAR PLATFORM AND THE TARGET 4HE TWO WAY DOPPLER SHIFT IS GIVEN BY FD 62K COSX WHERE K IS THE RADAR WAVELENGTH 62 IS THE RADAR PLATFORM SPEED AND X IS THE ANGLE BETWEEN THE VELOCITY VECTOR AND THE LINE OF SIGHT TO THE TARGET .OTE THAT THE RELATIVE RADIAL VELOCITY RANGE RATE TO THE STATIONARY TARGET IS 6RELATIVE 62 COSX WHICH MAKES THE LATER EQUATION FOR DOPPLER SHIFT CONSISTENT WITH THE ONE PRESENTED AT THE BEGINNING OF THE CHAPTER )LLUSTRATED IN &IGURE IS THE RECEIVED PULSED SPECTRUM WITH RETURNS FROM DISTRIBUTED CLUTTER SUCH AS THE GROUND OR WEATHER AND FROM DISCRETE TARGETS SUCH AS AIRCRAFT AUTOMOBILES TANKS ETC &IGURE SHOWS THE UNFOLDED SPECTRUM IE NO SPECTRAL FOLDOVER FROM ADJACENT 02& LINES IN THE CASE OF HORIZONTAL MOTION OF THE RADAR PLATFORM WITH A SPEED 62 4HE CLUTTER FREE REGION IS DEFINED AS THAT PORTION OF THE SPECTRUM IN WHICH NO GROUND CLUTTER CAN EXIST ! CLUTTER FREE REGION USUALLY DOES NOT EXIST WITH MEDIUM 02&S DUE TO DOPPLER FOLDING 4HE SIDELOBE CLUTTER REGION 62K IN WIDTH CONTAINS GROUND CLUTTER POWER FROM THE SIDELOBES OF THE ANTENNA ALTHOUGH THIS CLUTTER POWER MAY BE BELOW THE NOISE LEVEL IN PART OF THE REGION 4HE MAIN BEAM CLUTTER REGION LOCATED AT F 62K COSX CONTAINS THE STRONG RETURN FROM THE MAIN BEAM OF THE ANTENNA
&)'52% #LUTTER AND TARGET FREQUENCY SPECTRUM FROM A HORIZONTALLY MOVING PLATFORM
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STRIKING THE GROUND AT A SCAN ANGLE OF X MEASURED FROM THE VELOCITY VECTOR 2AIN AND CHAFF CLUTTER MAY ALSO BE LARGE WHEN THE MAIN BEAM ILLUMINATES A RAIN OR CHAFF CLOUD -OTION DUE TO WINDS MAY DISPLACE ANDOR SPREAD THE RETURN IN FREQUENCY !LTITUDE LINE CLUTTER IS DUE TO THE RADAR RETURN FROM GROUND CLUTTER AT NEAR NORMAL INCIDENCE DIRECTLY BELOW THE RADAR PLATFORM AND IS AT ZERO DOPPLER IF THERE IS NO VERTICAL COMPONENT OF PLATFORM VELOCITY ! DISCRETE TARGET RETURN IN THE MAIN BEAM IS SHOWN AT F4 F 62 K COSX 64 K COSX4 WHERE THE TARGET SPEED IS 64 WITH AN ANGLE X4 BETWEEN THE TARGET VELOCITY VECTOR AND THE RADAR TARGET LINE OF SIGHT 4HE COMPONENTS OF THE SPECTRUM SHOWN IN &IGURE WILL ALSO VARY WITH RANGE AS DISCUSSED LATER .OTE THAT THE DIRECTION OF 64 COSX4 IS ASSUMED TO BE THE OPPOSITE OF 62 COSX RESULTING IN A RELATIVE RANGE RATE OF 6RELATIVE 64 COSX4 62 COSX WHICH IS CONSISTENT WITH THE DEFINITION FOR DOPPLER SHIFT STATED AT THE BEGINNING OF THE CHAPTER &IGURE ILLUSTRATES THE VARIOUS CLUTTER DOPPLER FREQUENCY REGIONS AS A FUNCTION OF THE ANTENNA MAIN BEAM AZIMUTH AND RELATIVE RADAR AND TARGET VELOCITIES AGAIN FOR AN UNFOLDED SPECTRUM 4HE ORDINATE IS THE RADIAL OR LINE OF SIGHT COMPONENT OF TARGET VELOCITY IN UNITS OF RADAR PLATFORM VELOCITY SO THE MAIN BEAM CLUTTER REGION IS AT ZERO VELOCITY AND THE SIDELOBE CLUTTER REGION FREQUENCY BOUNDARIES VARY SINU SOIDALLY WITH ANTENNA AZIMUTH 4HUS THE FIGURE SHOWS THE DOPPLER REGIONS IN WHICH THE TARGET BECOMES CLEAR OF SIDELOBE CLUTTER &OR EXAMPLE IF THE ANTENNA MAIN BEAM AZIMUTH ANGLE IS AT ZERO ANY HEAD ON TARGET 64 COSX4 IS CLEAR OF SIDELOBE CLUTTER WHEREAS IF THE RADAR IS IN TRAIL BEHIND THE TARGET X4 AND X THE TARGETS RADIAL VELOCITY HAS TO BE GREATER THAN TWICE THAT OF THE RADAR TO BECOME CLEAR OF SIDELOBE CLUTTER 4HE SIDELOBE CLEAR AND CLUTTER REGIONS CAN ALSO BE EXPRESSED IN TERMS OF THE ASPECT ANGLE WITH RESPECT TO THE TARGET AS SHOWN IN &IGURE (ERE COLLISION GEOMETRY IS ASSUMED IN WHICH THE RADAR AND TARGET AIRCRAFT FLY STRAIGHT LINE PATHS TOWARD AN INTERCEPT POINT THE LOOK ANGLE OF THE RADAR X AND THE ASPECT ANGLE OF THE TARGET X4 ARE CONSTANT FOR A GIVEN SET OF RADAR AND TARGET SPEEDS 62 AND 64 RESPECTIVELY 4HE CENTER OF THE DIAGRAM IS THE TARGET AND THE ANGLE TO THE RADAR ON THE CIRCUMFERENCE IS THE ASPECT ANGLE 4HE ASPECT ANGLE AND LOOK ANGLES SATISFY THE EQUATION 62 SINX 64 SINX4
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./4% 7 IDTH OF ALTITUDE LINE AND MAIN BEAM CLUTTER REGIONS VARIES WITH CONDITIONS AZIMUTH IS MEASURED FROM RADAR PLATFORM VELOCITY VECTOR TO THE ANTENNA BORESIGHT OR TO THE LINE OF SIGHT TO THE TARGET HORIZONTAL MOTION CASE &)'52% #LUTTER AND CLUTTER FREE REGIONS AS A FUNCTION OF TARGET VELOCITY AND AZIMUTH
WHICH IS DEFINED AS A COLLISION COURSE 4HE TARGET ASPECT ANGLE IS ZERO FOR A HEAD ON CONDITION AND FOR A TAIL CHASE 4HE ASPECT ANGLE CORRESPONDING TO THE BOUNDARY BETWEEN THE SIDELOBE CLUTTER REGION AND THE SIDELOBE CLEAR REGION IS A FUNCTION OF THE RELATIVE RADAR TARGET VELOCITY RATIO AND IS SHOWN IN &IGURE FOR FOUR CASES #ASE IS WHERE THE RADAR AND TARGET SPEEDS ARE EQUAL AND THE TARGET CAN BE SEEN CLEAR OF SIDELOBE CLUTTER IN A HEAD ON ASPECT OUT TO ON EITHER SIDE OF THE TARGETS VELOCITY VECTOR 3IMILARLY #ASES THROUGH SHOW CONDITIONS WHERE THE TARGETS SPEED IS AND TIMES THE RADARS SPEED IN WHICH CASE THE TARGET CAN BE SEEN CLEAR OF SIDELOBE CLUT TER OVER A REGION OF UP TO o RELATIVE TO THE TARGETS VELOCITY VECTOR !GAIN THESE CONDITIONS ARE FOR AN ASSUMED COLLISION COURSE !S IS EVIDENT THE ASPECT ANGLE OF THE TARGET CLEAR OF SIDELOBE CLUTTER IS ALWAYS FORWARD OF THE BEAM ASPECT !MBIGUITIES AND 02& 3ELECTION 0ULSE DOPPLER RADARS ARE AMBIGUOUS IN RANGE AND POSSIBLY DOPPLER !S MENTIONED EARLIER THE UNAMBIGUOUS RANGE 2U IS GIVEN BY CF2 WHERE C IS THE SPEED OF LIGHT AND F2 IS THE 02& )F THE AIRBORNE TARGET RADIAL VELOCITY TO BE OBSERVED IS BETWEEN 64 MAX OPENING FOR OPENING TARGETS POSITIVE RANGE RATE AND 64 MAX CLOSING FOR CLOSING TARGETS NEGATIVE RANGE RATE THEN THE MINIMUM VALUE OF 02& F2 MIN WHICH IS UNAMBIGUOUS IN VELOCITY IN BOTH MAGNITUDE AND SENSE IE POSITIVE AND NEGATIVE IS
F2 MIN 64 MAX CLOSING 64 MAX OPENING 6G L
WHERE 6G IS THE UPPER LIMIT FOR GROUND MOVING TARGET REJECTION 6 REFERS TO THE SPEED OR THE MAGNITUDE OF THE RANGE RATE
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&)'52% 3IDELOBE CLUTTER CLEAR REGIONS VERSUS TARGET ASPECT ANGLE .OTE THE TARGET IS AT THE CENTER OF THE PLOT WITH THE RADAR PLATFORM ON THE CIRCUMFERENCE
(OWEVER SOME PULSE DOPPLER RADARS EMPLOY A 02& THAT IS UNAMBIGUOUS IN VELOC ITY MAGNITUDE ONLY IE F2 MIN ;MAX64 MAX CLOSING 64 MAX OPENING 6G= K AND RELY ON DETECTIONS IN MULTIPLE 02&S DURING THE TIME ON TARGET TO RESOLVE THE SIGN AMBIGUITY IN DOPPLER 4HESE RADARS CAN BE DESCRIBED AS HIGH MEDIUM 02& AND CAN BE CONSIDERED TO BE IN THE HIGH 02& CATEGORY IF THE OLDER DEFINITION OF HIGH 02& NO VELOCITY AMBI GUITY IS EXTENDED TO ALLOW ONE VELOCITY AMBIGUITY THAT OF DOPPLER SENSE 4HE LOWER 02& EASES THE MEASUREMENT OF TRUE RANGE WHILE RETAINING THE HIGH 02& ADVANTAGE OF A SINGLE BLIND SPEED REGION NEAR ZERO DOPPLER (IGH MEDIUM 02& IS BECOMING MORE PREVALENT IN MODERN AIRBORNE RADARS FOR AIR TO AIR SEARCH 4HE CHOICE BETWEEN HIGH AND MEDIUM 02& INVOLVES A NUMBER OF CONSIDERATIONS SUCH AS TRANSMITTER DUTY CYCLE LIMIT PULSE COMPRESSION AVAILABILITY SIGNAL PROCESSING CAPABILITY MEASUREMENT ACCURACY REQUIREMENTS ETC BUT OFTEN DEPENDS ON THE NEED FOR ALL ASPECT TARGET DETECTABILITY !LL ASPECT COVERAGE REQUIRES GOOD PERFOR MANCE IN TAIL CHASE WHERE THE TARGET DOPPLER IS IN THE SIDELOBE CLUTTER REGION NEAR THE ALTITUDE LINE )N A HIGH 02& RADAR THE RANGE FOLDOVER MAY LEAVE LITTLE CLEAR REGION IN THE RANGE DIMENSION THUS DEGRADING TARGET DETECTABILITY "Y USING A LOWER OR MEDIUM 02& THE CLEAR REGION IN RANGE IS INCREASED AT THE EXPENSE OF VELOCITY FOLDOVER FOR HIGH DOPPLER TARGETS THAT ARE IN THE CLUTTER FREE REGION IN HIGH 02& !S AN EXAMPLE &IGURE SHOWS THE CLUTTER PLUS NOISE TO NOISE RATIO IN RANGE DOPPLER COORDINATES FOR TWO DIFFERENT 8 BAND WAVEFORMS AT SIMILAR ALTITUDES AND AIRCRAFT VELOCITIES 4HE RANGE DIMENSION REPRESENTS THE UNAMBIGUOUS RANGE INTERVAL 2U AND THE FREQUENCY DIMENSION REPRESENTS THE 02& INTERVAL WITH THE MAIN BEAM CLUTTER ALTITUDE LINE AND SIDELOBE CLUTTER REGIONS CLEARLY DISCERNIBLE )N BOTH WAVEFORMS THE MAIN BEAM CLUTTER RETURN IS POSITIONED TO $# THROUGH CLUTTER POSITIONING VIA AN
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OFFSET APPLIED TO THE TRANSMIT FREQUENCY 4HE MEDIUM 02& SPECTRUM 02& K(Z CONTAINS A RANGE DOPPLER REGION IN WHICH THE SIDELOBE CLUTTER IS BELOW THERMAL NOISE AND IN WHICH GOOD TAIL ASPECT TARGET DETECTABILITY CAN BE ACHIEVED 4HE K(Z HIGH MEDIUM 02& WAVEFORM HAS A MUCH MORE SEVERE CLUTTER FOLDING AND TAIL ASPECT TARGETS WOULD COMPETE WITH SIDELOBE CLUTTER AT NEARLY ALL RANGES BUT THE CLUTTER FREE REGION IS MUCH LARGER "ECAUSE THE CLUTTER IS FOLDED IN BOTH RANGE AND DOPPLER WITH MEDIUM 02& A NUM BER OF 02&S MAY BE REQUIRED TO OBTAIN A SATISFACTORY PROBABILITY OF SUFFICIENT DETECTIONS TO RESOLVE THE RANGE AND DOPPLER AMBIGUITIES 4HE MULTIPLE 02&S MOVE THE RELATIVE LOCATION OF THE CLEAR REGIONS SO THAT ALL ASPECT TARGET COVERAGE IS ACHIEVED 3INCE THE SIDELOBE CLUTTER GENERALLY COVERS THE DOPPLER REGION OF INTEREST THE RATIO OF THE REGION WITH SIDELOBE CLUTTER BELOW NOISE RELATIVE TO THE TOTAL RANGE DOPPLER SPACE IS A FUNCTION OF THE RADAR ALTITUDE SPEED AND ANTENNA SIDELOBE LEVEL )F A HIGH 02& WAVEFORM IS USED THE CLEAR RANGE REGION DISAPPEARS BECAUSE THE SIDELOBE CLUTTER FOLDS IN RANGE INTO THE UNAMBIGUOUS RANGE INTERVAL ASSUMING THE TAR GET DOPPLER IS SUCH THAT IT STILL COMPETES WITH THE SIDELOBE CLUTTER (OWEVER IN THOSE DOPPLER REGIONS FREE OF SIDELOBE CLUTTER AS SHOWN IN &IGURE AND &IGURE TARGET DETECTABILITY IS LIMITED ONLY BY THERMAL NOISE INDEPENDENT OF RADAR ALTITUDE SPEED AND SIDELOBE LEVEL 4HIS REQUIRES SYSTEM STABILITY SIDEBANDS TO BE WELL BELOW NOISE FOR THE WORST CASE MAIN BEAM CLUTTER 4HUS ALTHOUGH MEDIUM 02& PROVIDES ALL ASPECT TARGET COVERAGE THE TARGET IS POTENTIALLY COMPETING WITH SIDELOBE CLUTTER AT ALL ASPECTS WHEREAS WITH HIGH 02& A TARGET CAN BECOME CLEAR OF SIDELOBE CLUTTER AT ASPECT ANGLES FORWARD OF THE BEAM ASPECT &OR TARGETS WITH SUFFICIENT RADIAL VELOCITY HIGH 02& IS TYPICALLY MORE EFFICIENT THAN MEDIUM 02& 4HE TRANSMIT PULSE WIDTH IS USUALLY LIMITED BY THE TRANSMITTERS ABILITY TO PRESERVE THE PULSE AMPLITUDE AND PHASE CHARACTERISTICS OVER THE DURATION OF THE TRANSMIT PULSE &OR A FIXED TRANSMIT PULSE WIDTH AND PEAK POWER A WAVEFORM WITH A HIGHER 02& WILL HAVE A HIGHER TRANSMIT DUTY CYCLE RESULTING IN A HIGHER AVERAGE TRANSMIT POWER &OR A GIVEN COHERENT PROCESSING TIME MORE ENERGY IS PLACED ON THE TARGET WHICH IMPROVES DETECTABILITY &OR THIS REASON HIGH 02& IS USED FOR LONG RANGE SEARCH OF HIGH SPEED CLOSING TARGETS
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2ANGE 'ATING 2ANGE GATING DIVIDES THE TIME BETWEEN TRANSMIT PULSES INTO MUL TIPLE CELLS OR RANGE GATES 2ANGE GATING ELIMINATES EXCESS RECEIVER NOISE AND CLUTTER FROM COMPETING WITH THE SIGNAL AND PERMITS TARGET TRACKING AND RANGE MEASUREMENT 4HE RANGE GATE IS TYPICALLY MATCHED TO THE BANDWIDTH OF THE TRANSMIT PULSE )N A SURVEIL LANCE RADAR A NUMBER OF RECEIVER GATES ARE USED TO DETECT TARGETS THAT MAY APPEAR AT ANY RANGE WITHIN THE INTERPULSE PERIOD &IGURE ILLUSTRATES THE GENERAL CASE WHERE THE GATE SPACING SS THE GATE WIDTH SG AND THE TRANSMITTED PULSE ST ARE ALL UNEQUAL 3ELECTING ST SG MAXIMIZES TARGET RETURN SIGNAL TO NOISE RATIO AND AS A RESULT RANGE PERFORMANCE 3ELECTING SG SS CREATES OVERLAPPED RANGE GATES AND REDUCES THE RANGE GATE STRADDLE LOSS 3ECTION BUT CAN INCREASE THE POSSIBILITY OF RANGE GHOSTS UNLESS CONTIGUOUS DETECTIONS FROM STRADDLED TARGET RETURNS ARE hCLUMPEDv PRIOR TO THE AMBIGUITY RESOLU TION 3ECTION 7ITH RANGE GATING THE RANGE MEASUREMENT ACCURACY IS ON THE ORDER OF THE RANGE GATE SIZE MMS BUT THIS CAN BE IMPROVED TO A FRACTION OF THE GATE WIDTH BY AMPLITUDE CENTROIDING 4IMELINE $EFINITIONS 0ULSE DOPPLER RADAR WORKS ON SEVERAL DIFFERENT TIME SCALES 6ARIOUS ORGANIZATIONS HAVE THEIR OWN NOMENCLATURE FOR TIME BASED PARAMETERS 4HEREFORE THE TIMELINE DEFINITIONS USED THROUGHOUT THIS CHAPTER ARE DEFINED HERE &IGURE ILLUSTRATES THE DIFFERENT TIME SCALES 3TARTING AT THE LOWEST LEVEL A SERIES OF COHERENT PULSES ARE TRANSMITTED AT A PULSE REPETITION FREQUENCY 02& 4HE TIME BETWEEN THE PULSES IS THE INTERPULSE PERIOD )00 WHICH IS SIMPLY THE INVERSE OF THE 02& 4HE RECEIVE PORTION OF THE )00 IS BROKEN UP INTO RANGE GATES 4HE TRANSMIT DUTY CYCLE IS THE TRANSMIT PULSE WIDTH DIVIDED BY THE )00 4HE TRAIN OF PULSES IS CALLED THE COHERENT PROCESSING INTERVAL #0) 4HE COHERENT PROCESSING FORMS A BANK OF DOPPLER
&)'52% %XAMPLE OF RANGE GATES WITH OVERLAP EQUALLY SPACED IN THE INTERPULSE PERIOD SB REPRESENTS THE EXTRA BLANKING TIME AFTER THE TRANSMIT PULSE TO ALLOW FOR RECEIVERPROTECTOR RECOVERY
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FILTERS FOR EACH RANGE GATE RESULTING IN A RANGE DOPPLER MAP FOR A #0) SIMILAR TO THAT SHOWN IN &IGURE 3EVERAL #0)S WITH THE SAME 02& BUT POSSIBLY DIFFERENT TRANSMIT CARRIER FREQUEN CIES CAN BE NONCOHERENTLY COMBINED VIA POSTDETECTION INTEGRATION 0$) )F FREQUENCY MODULATION &- RANGING IS USED ALL THE #0)S THAT ARE NONCOHERENTLY INTEGRATED MUST HAVE THE SAME &- SLOPE 4HE GROUPING OF #0)S IS A LOOK $ETECTIONS ARE DETERMINED FOR THE RANGE DOPPLER CELLS IN A LOOK -ULTIPLE LOOKS WITH DIFFERENT 02&S OR FREQUENCY MODULATIONS ARE USED TO RESOLVE RANGE ANDOR DOPPLER AMBIGUITIES 4HIS GROUP OF LOOKS IS A DWELL ! DWELL IS ASSOCIATED WITH A PARTICULAR ANTENNA LINE OF SIGHT OR BEAM POSITION 4ARGET REPORTS ARE GENERATED FOR EACH DWELL ! BAR REFERS TO A LINE OF BEAM POSITIONS AT A CONSTANT ELEVATION )N SEARCH A MULTI BAR RASTER SCANS THE BEAM OVER AN ASSIGNED AREA OR VOLUME TO CREATE A FRAME ! FRAME MAY HAVE MULTIPLE BARS 4YPICALLY THE ANTENNA WILL VISIT EVERY BEAM POSITION ONCE DURING A SEARCH FRAME "ASIC #ONFIGURATION &IGURE SHOWS A REPRESENTATIVE CONFIGURATION OF A PULSE DOPPLER RADAR UTILIZING DIGITAL SIGNAL PROCESSING UNDER THE CONTROL OF A MISSION PROCESSOR )NCLUDED ARE THE ANTENNA RECEIVEREXCITER SIGNAL PROCESSOR AND DATA PROCESSOR 4HE RADARS CONTROL PROCESSOR RECEIVES INPUTS FROM THE ON BOARD SYSTEMS SUCH AS THE INER TIAL NAVIGATION SYSTEM ).3 AND OPERATOR CONTROLS VIA THE MISSION PROCESSOR AND PERFORMS AS A MASTER CONTROLLER FOR THE RADAR HARDWARE #OHERENT PROCESSING REQUIRES THAT ALL FREQUENCY DOWN CONVERSIONS INCLUDING THE FINAL CONVERSION TO BASEBAND RETAIN THE COHERENT PHASE RELATIONSHIP BETWEEN TRANSMIT TED AND RECEIVED PULSES !LL THE LOCAL OSCILLATORS ARE PHASE REFERENCED TO THE SAME MASTER OSCILLATOR WHICH IS ALSO USED TO PRODUCE THE TRANSMITTED WAVEFORM 4HE IN PHASE ) AND QUADRATURE 1 COMPONENTS AT BASEBAND REPRESENT THE REAL AND IMAGINARY PARTS RESPECTIVELY OF A COMPLEX NUMBER WHOSE COMPLEX ARGUMENT IN PHASOR NOTATION IS THE PHASE DIFFERENCE BETWEEN THE TRANSMITTED AND RECEIVED PULSES 4HE COMPLEX MODULUS OR MAGNITUDE IS PROPORTIONAL TO THE RECEIVED ECHO STRENGTH
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&)'52% 4YPICAL PULSE DOPPLER RADAR CONFIGURATION
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-ASTER /SCILLATOR 4HE MASTER OSCILLATOR PROVIDES A FREE RUNNING STABLE REFERENCE SINUSOID ON WHICH THE SYSTEM SYNCHRONIZATION IS BASED 3YNCHRONIZER 4HE SYNCHRONIZER DISTRIBUTES PRECISELY TIMED STROBES AND CLOCKS FOR THE VARIOUS COMPONENTS OF THE RADAR SYSTEM TO ENSURE THE TIME ALIGNMENT OF TRANSMIT WAVEFORMS AND THE RECEPTION OF THEIR CORRESPONDING RETURNS 4HESE LOW JITTER TIMING SIGNALS ARE USED TO ENABLE AND DISABLE THE TRANSMIT POWER AMPLIFIER TO CREATE THE TRANS MIT PULSE TRAIN BLANK THE RECEIVER DURING TRANSMISSION AND FORM THE RANGE GATES 2EFERENCE 'ENERATOR 4HE REFERENCE GENERATOR OUTPUTS FIXED FREQUENCY CLOCKS AND LOCAL OSCILLATORS ,/S 3YNTHESIZER 4HE SYNTHESIZER GENERATES THE TRANSMIT CARRIER FREQUENCY AND THE FIRST LOCAL OSCILLATOR ,/ FREQUENCY &REQUENCY AGILITY IS PROVIDED TO THE TRANSMIT AND ,/ SIGNALS #LUTTER /FFSET 'ENERATOR 4HE CLUTTER OFFSET GENERATOR SHIFTS THE TRANSMIT CARRIER SLIGHTLY SO THAT ON RECEIVE THE MAIN BEAM CLUTTER IS POSITIONED AT ZERO DOPPLER FRE QUENCY OR $# DIRECT CURRENT AFTER BASEBANDING 4HE SAME EFFECT COULD BE OBTAINED BY SHIFTING THE RECEIVER ,/ FREQUENCY 7ITH THE CLUTTER AT $# THE SPURIOUS SIGNALS CAUSED BY CERTAIN RECEIVER NONLINEARITIES SUCH AS MIXER INTERMODULATION PRODUCTS AND VIDEO HARMONICS ALSO FALL NEAR $# AND CAN BE FILTERED OUT ALONG WITH THE MAIN BEAM CLUTTER 4HE FREQUENCY SHIFT APPLIED IS A FUNCTION OF THE ANTENNA MAIN BEAM LINE OF SIGHT RELATIVE TO THE PLATFORMS VELOCITY VECTOR 4HIS PROCESS IS KNOWN AS CLUTTER POSITIONING /UTPUT 'ENERATOR 4HE OUTPUT GENERATES THE PULSED RADIO FREQUENCY 2& TRANSMIT SIGNAL WHICH IS THE TRANSMIT DRIVE SIGNAL THAT IS AMPLIFIED BY THE POWER AMPLIFIER PRIOR TO BEING FED TO THE TRANSMIT ANTENNA !NTENNA 4HE ANTENNA CAN BE MECHANICALLY OR ELECTRONICALLY SCANNED -ODERN PULSE DOPPLER RADARS HAVE MIGRATED TO THE USE OF ACTIVE ELECTRONICALLY SCANNED ARRAYS !%3!S !%3!S CONTAIN TRANSMITRECEIVE 42 MODULES EACH COMPRISING A TRANS MIT POWER AMPLIFIER AND A RECEIVE LOW NOISE AMPLIFIER ,.! ALONG WITH AN ATTENUATOR AND PHASE SHIFTER AT EACH ANTENNA ELEMENT )F THE SAME ANTENNA IS USED FOR TRANSMIT AND RECEIVE A DUPLEXER MUST BE INCLUDED 4HIS DUPLEXER IS USUALLY A PASSIVE DEVICE SUCH AS A CIRCULATOR WHICH EFFECTIVELY SWITCHES THE ANTENNA BETWEEN THE TRANSMITTER AND RECEIVER #ONSIDERABLE POWER MAY BE COUPLED TO THE RECEIVER SINCE TYPICALLY NO MORE THAN TO D" OF ISOLATION MAY BE EXPECTED FROM FERRITE CIRCULATORS !NTENNAS MAY FORM VARIOUS BEAMS 4HE TRANSMIT BEAM CAN BE FORMED WITH UNIFORM APERTURE ILLUMINATION TO MAXIMIZE THE AMOUNT OF ENERGY ON TARGET WHEREAS THE RECEIVE SUM 3 BEAM IS TYPICALLY FORMED WITH A LOW SIDELOBE TAPER TO MINIMIZE THE RETURNS FROM GROUND CLUTTER 4HE 3 BEAM IS USED FOR TARGET DETECTION AND ACTING AS A SPATIAL FILTER IS THE FIRST LINE OF DEFENSE AGAINST CLUTTER AND INTERFERENCE IN THE SIDELOBE REGION 4O FACILITATE TARGET TRACKING ANGLE MEASUREMENTS WITH ACCURACIES FINER THAN THE ANTENNA BEAMWIDTH ARE USUALLY REQUIRED ! TECHNIQUE TO OBTAIN SUCH ANGLE MEASUREMENTS OF A TARGET ON A SINGLE PULSE IS CALLED MONOPULSE -ONOPULSE CAN BE CHARACTERIZED AS AMPLITUDE OR PHASE WITH PHASE BEING PREFERABLE DUE TO ITS ADVANTAGE IN ANGLE ACCURACY FOR A GIVEN SIGNAL TO NOISE RATIO 0HASE MONOPULSE USES A DELTA OR DIFFERENCE BEAM
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WHICH IS ESSENTIALLY FORMED BY DIVIDING THE APERTURE INTO TWO HALVES AND SUBTRACTING THE CORRESPONDING PHASE CENTERS -ONOPULSE BEAMS DELTA AZIMUTH $!: AND DELTA ELEVATION $%, ARE FORMED TO PROVIDE PHASE MONOPULSE AZIMUTH AND ELEVATION ANGLE MEASUREMENTS 3ELF CALIBRATION ROUTINES CONTROLLED BY THE CONTROL PROCESSOR ENSURE THAT THE PHASE AND AMPLITUDE MATCH OF THE RECEIVER CHANNELS ENABLES ACCURATE MONO PULSE MEASUREMENTS ! GUARD BEAM WITH A NEAR OMNIDIRECTIONAL PATTERN IS FORMED FOR SIDELOBE DETECTION BLANKING AS DISCUSSED IN 3ECTION 2ECEIVER0ROTECTOR 20 4HE RECEIVERPROTECTOR IS A LOW LOSS FAST RESPONSE HIGH POWER SWITCH THAT PREVENTS THE TRANSMITTER OUTPUT FROM THE ANTENNAS DUPLEXER FROM DAMAGING THE SENSITIVE RECEIVER FRONT END &AST RECOVERY IS REQUIRED TO MINIMIZE DESENSITIZATION IN THE RANGE GATES FOLLOWING THE TRANSMITTED PULSE 20S CAN BE IMPLE MENTED WITH A GAS DISCHARGE TUBE IN WHICH A GAS IS IONIZED BY HIGH POWER 2& ! DIODE LIMITER CAN BE USED INSTEAD OF OR IN CONJUNCTION WITH THE GAS DISCHARGE TUBE 4HE 20 CAN BE REFLECTIVE OR ABSORPTIVE BUT MUST HAVE LOW INSERTION LOSS TO MINIMIZE IMPACT ON RECEIVE CHAIN NOISE FIGURE #LUTTER !UTOMATIC 'AIN #ONTROL #!'# 4HE #!'# ATTENUATOR IS USED BOTH FOR SUPPRESSING TRANSMITTER LEAKAGE FROM THE 20 INTO THE RECEIVER SO THE RECEIVER IS NOT DRIVEN INTO SATURATION WHICH COULD LENGTHEN RECOVERY TIME AFTER THE TRANSMITTER IS TURNED OFF AND FOR CONTROLLING THE INPUT SIGNAL LEVELS INTO THE RECEIVER 4HE RECEIVED LEVELS ARE KEPT BELOW SATURATION LEVELS TYPICALLY WITH A CLUTTER !'# IN SEARCH AND A TARGET !'# IN SINGLE TARGET TRACK TO PREVENT SPURIOUS SIGNALS WHICH DEGRADE PERFOR MANCE FROM BEING GENERATED .OISE !UTOMATIC 'AIN #ONTROL .!'# 4HE .!'# ATTENUATOR IS USED TO SET THE THERMAL NOISE LEVEL IN THE RECEIVER TO SUPPORT THE REQUIRED DYNAMIC RANGE AS DISCUSSED IN 3ECTION 4HE ATTENUATION IS COMMANDED BASED ON MEASUREMENTS OF THE NOISE DURING PERIODIC CALIBRATION $IGITAL 0REPROCESSING 4HE ADVENT OF HIGH SPEED HIGH DYNAMIC RANGE ANALOG TO DIGITAL CONVERTERS !$S ALLOWS )& SAMPLING AND DIGITAL BASEBANDING 4HE DIGITAL )& SAMPLED OUTPUT OF THE RECEIVER IS DOWNCONVERTED TO BASEBAND $# VIA A DIGITAL PRODUCT DETECTOR $0$ 3UPERIOR )1 IMAGE REJECTION IS AN ADVANTAGE OF A $0$ 4HE ) AND 1 SIGNALS ARE PASSED THROUGH THE DIGITAL PORTION OF THE PULSE MATCHED FILTER 4HE COMBINATION OF THE )& MATCHED FILTER AND THE DIGITAL MATCHED FILTER FORM THE RECEIVERS SINGLE PULSE MATCHED FILTER $IGITAL 3IGNAL 0ROCESSING &OLLOWING DIGITAL PREPROCESSING IS A DOPPLER FIL TER BANK FOR MAIN BEAM CLUTTER REJECTION AND COHERENT INTEGRATION 2& INTERFERENCE 2&) THAT IS PULSED AND ASYNCHRONOUS TO THE RADAR TIMING CAN OFTEN BE DETECTED PRIOR TO THE COHERENT INTEGRATION 2ANGE )00 CELLS WHERE 2&) IS DETECTED ARE THEN hREPAIREDv TO PREVENT CORRUPTION OF THE OUTPUT SPECTRUM 4HE FILTER BANK IS USUALLY REALIZED BY USING THE FAST &OURIER TRANSFORM &&4 HOWEVER THE DISCRETE &OURIER TRANSFORM $&4 CAN BE USED WHEN THE NUMBER OF FILTERS IS SMALL !PPROPRIATE WEIGHTING IS EMPLOYED TO REDUCE THE FILTER SIDELOBES 4HE AMOUNT OF WEIGHTING CAN BE CHOSEN ADAPTIVELY BY SENSING THE PEAK SIGNAL LEVELS USUALLY MAIN BEAM CLUTTER AND SELECTING THE DOPPLER WEIGHTING DYNAMICALLY )F PULSE COMPRESSION MODULATION IS USED ON THE TRANSMIT PULSE TO INCREASE ENERGY ON TARGET PULSE COMPRESSION CAN BE PERFORMED DIGITALLY EITHER BEFORE OR AFTER THE DOPPLER
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FILTER BANK 4HE ADVANTAGE OF PULSE COMPRESSION AFTER THE FILTER BANK IS THAT THE EFFECTS OF DOPPLER ON PULSE COMPRESSION CAN BE LARGELY REMOVED BY TAILORING THE PULSE COMPRES SION TO THE DOPPLER OFFSET OF EACH DOPPLER FILTER (OWEVER THIS INCREASES THE TOTAL AMOUNT OF SIGNAL PROCESSING REQUIRED 4HE ENVELOPE AT THE OUTPUT OF THE &&4 IS FORMED WITH A LINEAR ) 1 OR SQUARE LAW ) 1 DETECTOR (ISTORICALLY LINEAR DETECTORS WERE USED TO MANAGE DYNAMIC RANGE IN FIXED POINT PROCESSORS 3QUARE LAW DETECTORS ARE PREFERRED FOR SOME MODERN FLOATING POINT PROCESSORS 0OSTDETECTION INTEGRATION 0$) MAY BE USED WHERE EACH RANGE GATE DOPPLER FILTER OUTPUT IS LINEARLY SUMMED OVER SEVERAL #0)S &OR EACH RANGE DOPPLER CELL IN THE 3 CHANNEL THE 0$) OUTPUT IS COMPARED WITH A DETECTION THRESHOLD DETERMINED BY A CONSTANT FALSE ALARM RATE #&!2 PROCESSn #ELLS WITH AMPLITUDES GREATER THAN THE #&!2 THRESHOLD ARE LABELED AS DETECTIONS 3IMILAR PROCESSING IS DONE IN THE $!: AND $%, CHANNELS WITH EXCEPTIONS AS SHOWN IN &IGURE &OR THOSE RANGE DOPPLER CELLS WITH DECLARED DETECTIONS THE IMAGINARY PART OF THE $!:3 AND $%,3 RATIOS ARE USED FOR PHASE COMPARISON MONOPULSE TO ESTIMATE THE AZIMUTH AND ELEVATION ANGLES RESPECTIVELY RELATIVE TO THE CENTER OF THE 3 MAIN BEAM 4HE ANGLE ESTIMATES ARE COMPUTED FOR EACH COHERENT LOOK AND THEN AVERAGED OVER THE NUMBER OF #0)S NONCOHERENTLY INTEGRATED VIA 0$) 4HE GUARD CHANNEL IS PROCESSED SIMILAR TO THE 3 CHANNEL 4HE GUARD CHANNELS PUR POSE IS TO BLANK SIDELOBE DETECTIONS AS DESCRIBED IN 3ECTION 0OSTPROCESSING &OLLOWING THE #&!2 IS DETECTION EDITING WHICH CONTAINS THE SIDE LOBE DISCRETE REJECTION LOGIC &OLLOWING DETECTION EDITING RANGE AND VELOCITY AMBI GUITY RESOLVERS WORK OVER SEVERAL LOOKS WITHIN A DWELL 4HE FINAL DETECTION OUTPUTS ALONG WITH THEIR CORRESPONDING UNAMBIGUOUS RANGE VELOCITY AND ANGLE MEASUREMENTS AND THEIR ESTIMATED ACCURACIES ARE PASSED TO THE MISSION PROCESSOR FOR TRACKING AND OPERATOR DISPLAY
{°ÓÊ *1 - Ê "** ,Ê 1// , 'ENERAL #LUTTER RETURNS FROM VARIOUS SCATTERERS HAVE A STRONG INFLUENCE ON THE DESIGN OF A PULSE DOPPLER RADAR AS WELL AS AN EFFECT ON THE PROBABILITY OF DETECTION OF POINT TARGETS #LUTTER SCATTERERS INCLUDE TERRAIN BOTH LAND AND SEA WEATHER RAIN SNOW ETC AND CHAFF 3INCE THE ANTENNAS GENERALLY USED IN PULSE DOPPLER RADARS HAVE A SINGLE RELATIVELY HIGH GAIN MAIN BEAM MAIN BEAM CLUTTER MAY BE THE LARGEST SIGNAL HANDLED BY THE RADAR WHEN IN A DOWN LOOK CONDITION 4HE NARROW BEAM LIMITS THE FREQUENCY EXTENT OF THIS CLUTTER TO A RELATIVELY SMALL PORTION OF THE DOPPLER SPECTRUM 4HE REMAINDER OF THE ANTENNA PAT TERN CONSISTS OF SIDELOBES WHICH RESULT IN SIDELOBE CLUTTER 4HIS CLUTTER IS GENERALLY MUCH SMALLER THAN THE MAIN BEAM CLUTTER BUT COVERS MUCH MORE OF THE FREQUENCY DOMAIN 4HE SIDELOBE CLUTTER FROM THE GROUND DIRECTLY BELOW THE RADAR THE ALTITUDE LINE IS FREQUENTLY LARGE OWING TO A HIGH REFLECTION COEFFICIENT AT STEEP GRAZING ANGLES THE LARGE GEOMETRIC AREA AND THE SHORT RANGE 2ANGE PERFORMANCE IS DEGRADED FOR TARGETS IN THE SIDELOBE CLUTTER REGION WHEREVER THE CLUTTER IS NEAR OR ABOVE THE RECEIVER NOISE LEVEL -ULTIPLE 02&S MAY BE USED TO MOVE THE TARGET WITH RESPECT TO THE SIDELOBE CLUTTER IN THE RANGE DOPPLER MAP THUS AVOIDING COMPLETELY BLIND RANGES OR BLIND FREQUENCIES DUE TO HIGH CLUTTER LEVELS 4HIS RELATIVE MOTION OCCURS DUE TO THE RANGE AND DOPPLER FOLDOVER FROM RANGE ANDOR DOPPLER AMBIGUITIES )F ONE 02& FOLDS SIDELOBE CLUTTER AND A TARGET TO THE SAME APPARENT RANGE AND DOPPLER A SUFFICIENT CHANGE OF 02& WILL SEPARATE THEM
05,3% $/00,%2 2!$!2
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'ROUND #LUTTER IN A 3TATIONARY 2ADAR 7HEN THE RADAR IS FIXED WITH RESPECT TO THE GROUND BOTH STATIONARY MAIN BEAM AND SIDELOBE CLUTTER RETURNS OCCUR AT ZERO DOPPLER OFFSET FROM THE TRANSMIT CARRIER FREQUENCY 4HE SIDELOBE CLUTTER IS USUALLY SMALL COMPARED WITH MAIN BEAM CLUTTER AS LONG AS SOME PART OF THE MAIN BEAM STRIKES THE GROUND 4HE CLUTTER CAN BE CALCULATED AS IN A PULSED RADAR THEN FOLDED IN RANGE AS A FUNCTION OF THE 02& 'ROUND #LUTTER IN A -OVING 2ADAR 7HEN THE RADAR IS MOVING WITH A VELOCITY 62 THE CLUTTER IS SPREAD OVER THE FREQUENCY DOMAIN AS ILLUSTRATED IN &IGURE FOR THE SPECIAL CASE OF HORIZONTAL MOTION 4HE FOLDOVER IN RANGE AND DOPPLER IS ILLUSTRATED IN &IGURE FOR A MEDIUM 02& RADAR WHERE THE CLUTTER IS AMBIGUOUS IN BOTH RANGE AND DOPPLER 4HE RADAR PLATFORM IS MOVING TO THE RIGHT AT KT WITH A DIVE ANGLE OF 4HE NARROW ANNULI ISO RANGE CONTOURS DEFINE THE GROUND AREA THAT CONTRIBUTES TO CLUTTER IN THE SELECTED RANGE GATE 4HE FIVE NARROW HYPERBOLIC BANDS ISO DOPPLER CONTOURS DEFINE THE AREA THAT CONTRIBUTES TO CLUTTER IN THE SELECTED DOPPLER FILTER 4HE SHADED INTERSECTIONS REPRESENT THE AREA OR CLUTTER PATCHES THAT CONTRIBUTES TO THE RANGE GATE DOPPLER FILTER CELL %ACH CLUTTER PATCH CONTRIBUTES CLUTTER POWER AS A FUNCTION OF THE ANTENNA GAIN IN THE DIRECTION OF THE CLUTTER PATCH AND THE REFLECTIVITY OF THE CLUTTER PATCH 4HE MAIN BEAM ILLUMINATES THE ELLIPTICAL AREA TO THE LEFT OF THE GROUND TRACK 3INCE THIS AREA LIES ENTIRELY WITHIN THE FILTER AREA THE MAIN BEAM CLUTTER FALLS WITHIN THIS FILTER AND ALL OTHER FILTERS RECEIVE SIDELOBE CLUTTER &OUR RANGE ANNULI ARE INTERSECTED BY THE MAIN BEAM ELLIPSE SO THE MAIN BEAM CLUTTER IN THIS RANGE GATE IS THE VECTOR SUM OF THE SIGNALS RECEIVED FROM ALL FOUR CLUTTER PATCHES /WING TO THIS HIGH DEGREE OF RANGE FOLDOVER ALL RANGE GATES WILL HAVE APPROXIMATELY EQUAL CLUTTER
&)'52% 0LAN VIEW OF RANGE GATE AND DOPPLER FILTER AREAS 2ADAR ALTITUDE FT VELOCITY KT TO RIGHT DIVE ANGLE RADAR WAVELENGTH CM 02& K(Z RANGE GATE WIDTH MS RANGE GATE DOPPLER FILTER AT K(Z BANDWIDTH K(Z BEAMWIDTH CIRCULAR MAIN BEAM AZIMUTH DEPRESSION ANGLE
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)F THE MAIN BEAM WERE SCANNED IN AZIMUTH WITH THE SAME RADAR PLATFORM KINEMATICS THE MAIN BEAM CLUTTER WOULD SCAN IN DOPPLER FREQUENCY SO THAT IT WOULD APPEAR IN THE SELECTED FILTER TEN TIMES TWICE FOR EACH HYPERBOLIC BAND )N BETWEEN THE FILTER WOULD RECEIVE SIDELOBE CLUTTER FROM ALL DARKENED INTERSECTIONS 7ITH THE USE OF THE PROPER CLUTTER OFFSET WHICH WOULD VARY AS A FUNCTION OF MAIN BEAM AZIMUTH ON THE TRANSMIT FREQUENCY AS DESCRIBED IN 3ECTION THE DOPPLER OF THE MAIN BEAM CLUTTER RETURN WILL BE ZERO OR $# #LUTTER 2ETURN 'ENERAL %QUATIONS 4HE CLUTTER TO NOISE RATIO FROM A SINGLE CLUTTER PATCH WITH INCREMENTAL AREA D! AT A RANGE 2 IS # .
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WHERE 0AV AVERAGE TRANSMIT POWER '4 TRANSMIT GAIN IN PATCH DIRECTION '2 RECEIVE GAIN IN PATCH DIRECTION K OPERATING WAVELENGTH R CLUTTER BACKSCATTER COEFFICIENT ,# LOSSES APPLICABLE TO CLUTTER K "OLTZMANNS CONSTANT r 7(Z+ 4S SYSTEM NOISE TEMPERATURE + "N DOPPLER FILTER BANDWIDTH ,# REFERS TO LOSSES THAT APPLY TO DISTRIBUTED SURFACE CLUTTER AS OPPOSED TO DISCRETE RESOLVABLE TARGETS 4HESE LOSSES WILL BE DISCUSSED IN 3ECTION 4HE CLUTTER TO NOISE RATIO FROM EACH RADAR RESOLUTION CELL IS THE INTEGRAL OF %Q OVER THE DOPPLER AND RANGE EXTENT OF EACH OF THE AMBIGUOUS CELL POSITIONS ON THE GROUNDn 5NDER CERTAIN SIMPLIFIED CONDITIONS THE INTEGRATION CAN BE CLOSED FORM BUT IN GENERAL NUMERIC INTEGRATION IS REQUIRED -AIN BEAM #LUTTER 4HE NET MAIN BEAM CLUTTER TO NOISE POWER IN A SINGLE RANGE GATE IN THE RECEIVER CAN BE APPROXIMATED FROM %Q BY SUBSTITUTING THE RANGE GATES CS INTERSECTED AREA COS @ 2PAZ WITHIN THE MAIN BEAM ON THE GROUND FOR D! AND SUM MING OVER ALL AMBIGUITIES OF THAT RANGE GATE THAT ARE WITHIN THE MAIN BEAM '4 '2S # 0AV L QAZ CT £ . P ,# K4S "N 2 COSA
4HE SUMMATION LIMITS ARE THE LOWER AND UPPER EDGES IN THE ELEVATION DIMENSION OF THE SMALLER OF THE TRANSMIT AND RECEIVE BEAMS WHERE PAZ AZIMUTH HALF POWER BEAMWIDTH RADIANS S COMPRESSED PULSE WIDTH @ GRAZING ANGLE AT CLUTTER PATCH 4HE REMAINING TERMS ARE AS DEFINED FOLLOWING %Q )F THE MAIN BEAM IS POINTED BELOW THE HORIZON THE MAIN BEAM CLUTTER SPECTRAL WIDTH $F DUE TO PLATFORM MOTION MEASURED D" DOWN FROM THE PEAK IS APPROXIMATELY $F
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WHERE 62 RADAR GROUND SPEED K 2& WAVELENGTH P" D" ONE WAY ANTENNA AZIMUTH BEAMWIDTH RADIANS E MAIN BEAM DEPRESSION ANGLE RELATIVE TO LOCAL HORIZONTAL RADIANS P MAIN BEAM AZIMUTH ANGLE RELATIVE TO THE HORIZONTAL VELOCITY RADIANS S COMPRESSED PULSE WIDTH H RADAR ALTITUDE 7HEN THE MAGNITUDE OF THE MAIN BEAM AZIMUTH ANGLE IS GREATER THAN HALF OF THE AZI MUTH BEAMWIDTH \ Q \ q Q " THE MAIN BEAM CLUTTER POWER SPECTRAL DENSITY CAN BE MODELED WITH A GAUSSIAN SHAPE WITH A STANDARD DEVIATION RC $F -AIN BEAM #LUTTER &ILTERING )N A PULSE DOPPLER RADAR UTILIZING DIGITAL SIGNAL PROCESSING MAIN BEAM CLUTTER IS REJECTED BY EITHER A COMBINATION OF A DELAY LINE CLUT TER CANCELER -4) FILTER FOLLOWED BY A DOPPLER FILTER BANK OR BY A FILTER BANK WITH LOW FILTER SIDELOBES WHICH ARE ACHIEVED VIA WEIGHTING )N EITHER CASE THE FILTERS AROUND THE MAIN BEAM CLUTTER ARE BLANKED TO MINIMIZE FALSE ALARMS ON MAIN BEAM CLUTTER 4HIS BLANKED REGION IN DOPPLER IS KNOWN AS THE MAIN BEAM CLUTTER NOTCH 4HE CHOICE BETWEEN THESE OPTIONS IS A TRADE OFF OF QUANTIZATION NOISE AND COM PLEXITY VERSUS THE FILTER WEIGHTING LOSS )F A CANCELER IS USED FILTER WEIGHTING CAN BE RELAXED OVER THAT WITH A FILTER BANK ALONE SINCE THE CANCELER REDUCES THE DYNAMIC RANGE REQUIREMENTS INTO THE DOPPLER FILTER BANK IF THE MAIN BEAM CLUTTER IS THE LARGEST SIGNAL 7ITHOUT A CANCELER HEAVIER WEIGHTING IS NEEDED TO REDUCE SIDELOBES TO A LEVEL SO THAT THE FILTER RESPONSE TO MAIN BEAM CLUTTER IS BELOW THE THERMAL NOISE LEVEL 4HIS WEIGHTING INCREASES THE FILTER NOISE BANDWIDTH AND HENCE INCREASES THE LOSS IN SIGNAL TO NOISE RATIO #HOOSING THE PROPER WEIGHTING IS A COMPROMISE BETWEEN REJECTING MAIN BEAM CLUTTER AND MAXIMIZING TARGET SIGNAL TO NOISE RATIO 4O DYNAMICALLY MAKE THIS COM PROMISE THE FILTER WEIGHTING CAN BE ADAPTIVE TO THE MAIN BEAM CLUTTER LEVEL BY MEA SURING THE PEAK RETURN LEVEL USUALLY MAIN BEAM CLUTTER OVER THE )00S AND SELECTING OR COMPUTING THE BEST WEIGHTING TO APPLY ACROSS THE #0) !NOTHER TECHNIQUE THAT IS APPLICABLE TO HIGH MEDIUM AND HIGH 02& IS TO GENERATE A HYBRID FILTER WEIGHT ING BY CONVOLVING TWO WEIGHTING FUNCTIONS 4HE RESULT IS A FILTER WITH SIGNIFICANTLY LESS WEIGHTING LOSS AND LOW FAR OUT SIDELOBES BUT AT A COST OF RELATIVELY HIGH NEAR IN SIDELOBES 4O EVALUATE THE EFFECT OF MAIN BEAM CLUTTER ON TARGET DETECTION PERFORMANCE THE CLUTTER TO NOISE RATIO MUST BE KNOWN FOR EACH FILTER WHERE TARGETS ARE TO BE DETECTED ! GENERAL MEASURE THAT CAN BE EASILY APPLIED TO SPECIFIC CLUTTER LEVELS IS THE IMPROVEMENT FACTOR ) 7HEN USING A DOPPLER FILTER BANK AS OPPOSED TO AN -4) FILTER THE IMPROVEMENT FACTOR IS DEFINED FOR EACH DOPPLER FILTER AS THE RATIO OF THE SIGNAL TO CLUTTER POWER AT THE OUTPUT OF THE DOPPLER FILTER TO THE SIGNAL TO CLUTTER POWER AT THE INPUT 4HE SIGNAL IS ASSUMED TO BE AT THE CENTER OF THE DOPPLER FILTER )NCORPORATING THE EFFECT OF FILTER WEIGHTING THE IMPROVEMENT FACTOR FOR A DOPPLER FILTER IS GIVEN BY
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)00 WEIGHT a I a . NUMBER OF )00S IN #0) STANDARD DEVIATION OF CLUTTER SPECTRUM FILTER NUMBER + IS THE $# FILTER INTERPULSE PERIOD
#LUTTER TRANSIENT 3UPPRESSION 7HEN THE 02& IS CHANGED FOR MULTIPLE 02& RANGING THE SLOPE IS CHANGED IN LINEAR &- RANGING OR THE 2& CARRIER IS CHANGED THE TRANSIENT CHANGE IN THE CLUTTER RETURN MAY CAUSE DEGRADATION UNLESS IT IS PROPERLY HANDLED 3INCE THE CLUTTER IS USUALLY AMBIGUOUS IN RANGE IN A PULSE DOPPLER RADAR THE CLUTTER POWER INCREASES AT EACH INTERPULSE PERIOD )00 AS CLUTTER RETURN IS RECEIVED FROM THE FARTHER AMBIGUITIES UNTIL THE HORIZON IS REACHED 4HIS PHENOMENON IS CALLED SPACE CHARGING .OTE THAT ALTHOUGH AN INCREASING NUMBER OF CLUTTER RETURNS ARE RECEIVED DURING THE CHARGING PERIOD THE VECTOR SUM MAY ACTUALLY DECREASE OWING TO THE RANDOM PHASE RELATIONS OF THE RETURNS FROM DIFFERENT PATCHES )F A CLUTTER CANCELER -4) FILTER IS USED THE OUTPUT CANNOT BEGIN TO SETTLE TO ITS STEADY STATE VALUE UNTIL SPACE CHARGING IS COMPLETE 3OME SETTLING TIME MUST BE ALLOWED BEFORE SIGNALS ARE PASSED TO THE FILTER BANK 4HEREFORE THE COHERENT INTEGRA TION TIME AVAILABLE DURING EACH #0) IS REDUCED FROM THE TOTAL #0) TIME BY THE SUM OF THE SPACE CHARGE TIME AND THE TRANSIENT SETTLING TIME 4HE CANCELER SETTLING TIME CAN BE ELIMINATED BY PRECHARGING THE CANCELER WITH THE STEADY STATE INPUT VALUE 4HIS IS DONE BY CHANGING THE CANCELER GAINS SO THAT ALL DELAY LINES ACHIEVE THEIR STEADY STATE VALUES ON THE FIRST )00 OF DATA )F NO CANCELER IS USED SIGNALS CAN BE PASSED TO THE FILTER BANK AFTER THE SPACE CHARGE IS COMPLETE SO THAT THE COHERENT INTEGRATION TIME IS THE TOTAL #0) TIME MINUS THE SPACE CHARGE TIME !LTITUDE LINE #LUTTER "LANKING 4HE REFLECTION FROM THE EARTH DIRECTLY BENEATH AN AIRBORNE PULSE RADAR IS CALLED ALTITUDE LINE CLUTTER "ECAUSE OF SPECULAR REFLEC TION OVER SMOOTH TERRAIN THE LARGE GEOMETRIC AREA AND RELATIVELY SHORT RANGE THIS SIGNAL CAN BE LARGE )T LIES WITHIN THE SIDELOBE CLUTTER REGION OF THE PULSE DOPPLER SPECTRUM "ECAUSE IT CAN BE MUCH LARGER THAN DIFFUSE SIDELOBE CLUTTER AND USUALLY HAS A RELATIVELY NARROW SPECTRAL WIDTH ALTITUDE LINE CLUTTER IS OFTEN REMOVED EITHER BY A SPECIAL #&!2 THAT PREVENTS DETECTION OF THE ALTITUDE LINE OR BY A TRACKER BLANKER THAT REMOVES THESE REPORTS FROM THE FINAL OUTPUT )N THE CASE OF THE TRACKER BLANKER A CLOSED LOOP TRACKER IS USED TO POSITION RANGE AND VELOCITY GATES AROUND THE ALTITUDE RETURN AND BLANK THE AFFECTED RANGE DOPPLER REGION .OTE THAT AT VERY LOW ALTITUDES THE ANGLES THAT SUBTEND THE FIRST RANGE GATE ON THE GROUND CAN BE QUITE BIG AND THE SPECTRAL WIDTH WIDENS 3IDELOBE #LUTTER 4HE ENTIRE CLUTTER SPECTRUM CAN BE CALCULATED FOR EACH RANGE GATE BY %Q IF THE ANTENNA PATTERN IS KNOWN IN THE LOWER HEMISPHERE )N PRELIMINARY SYSTEM DESIGN THE EXACT GAIN FUNCTION MAY NOT BE KNOWN SO ONE USEFUL APPROXIMATION IS THAT THE SIDELOBE RADIATION IS ISOTROPIC WITH A CONSTANT GAIN OF '3, 3IDELOBE $ISCRETES !N INHERENT CHARACTERISTIC OF AIRBORNE PULSE DOPPLER RADARS IS THAT ECHOES FROM LARGE RESOLVABLE OBJECTS ON THE GROUND DISCRETES SUCH AS BUILD INGS MAY BE RECEIVED THROUGH THE ANTENNA SIDELOBES AND APPEAR AS THOUGH THEY WERE
05,3% $/00,%2 2!$!2
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SMALLER MOVING TARGETS IN THE MAIN BEAM 4HIS IS A PARTICULARLY SEVERE PROBLEM IN A MEDIUM 02& RADAR WHERE ALL ASPECT TARGET PERFORMANCE IS USUALLY DESIRED SINCE THESE RETURNS COMPETE WITH TARGETS OF INTEREST )N A HIGH 02& RADAR THERE IS LITTLE IF ANY RANGE REGION CLEAR OF SIDELOBE CLUTTER SUCH THAT THE SIDELOBE CLUTTER PORTION OF THE DOP PLER SPECTRUM IS OFTEN NOT PROCESSED SINCE TARGET DETECTABILITY IS SEVERELY DEGRADED IN THIS REGION &URTHER IN A HIGH 02& RADAR ESPECIALLY AT HIGHER ALTITUDES THE RELATIVE AMPLITUDES OF THE DISTRIBUTED SIDELOBE CLUTTER AND THE DISCRETE RETURNS ARE SUCH THAT THE DISCRETES ARE NOT VISIBLE IN THE SIDELOBE CLUTTER 4HE APPARENT RADAR CROSS SECTION 2#3 RAPP OF A SIDELOBE DISCRETE WITH AN 2#3 OF R IS RAPP R '3, WHERE '3, IS THE SIDELOBE GAIN RELATIVE TO THE MAIN BEAM 4HE LARGER SIZE DISCRETES APPEAR WITH A LOWER DENSITY THAN THE SMALLER ONES AND A MODEL COMMONLY ASSUMED AT THE HIGHER RADAR FREQUENCIES IS SHOWN IN 4ABLE 4HUS AS A PRACTICAL MATTER M DISCRETES ARE RARELY PRESENT M ARE SOMETIMES PRESENT AND M ARE OFTEN PRESENT 4WO MECHANIZATIONS FOR DETECTING AND ELIMINATING FALSE REPORTS FROM SIDELOBE DIS CRETES ARE THE GUARD CHANNEL AND POSTDETECTION SENSITIVITY TIME CONTROL 34# 4HESE ARE DISCUSSED IN THE PARAGRAPHS THAT FOLLOW 'UARD #HANNEL 4HE GUARD CHANNEL MECHANIZATION COMPARES THE OUTPUTS OF TWO PARALLEL RECEIVING CHANNELS ONE CONNECTED TO THE MAIN ANTENNA AND THE SEC OND TO A GUARD ANTENNA THE 3 AND 'UARD CHANNEL IN &IGURE RESPECTIVELY TO DETERMINE WHETHER A RECEIVED SIGNAL IS IN THE MAIN BEAM OR THE SIDELOBESn 4HE GUARD CHANNEL USES A BROAD BEAM ANTENNA THAT IDEALLY HAS A PATTERN ABOVE THE MAIN ANTENNA SIDELOBES 4HE RETURNS FROM BOTH CHANNELS ARE COMPARED FOR EACH RANGE DOPPLER CELL THAT HAD A DETECTION IN THE MAIN CHANNEL &OR THESE RANGE DOPPLER CELLS WHEN THE GUARD CHANNEL RETURN IS GREATER THAN THAT OF THE MAIN CHANNEL THE DETECTION IS REJECTED BLANKED )F THE MAIN CHANNEL RETURN IS HIGHER THE DETECTION IS PASSED ON ! BLOCK DIAGRAM OF A GUARD CHANNEL MECHANIZATION IS SHOWN IN &IGURE !FTER THE #&!2 WHICH IDEALLY WOULD BE IDENTICAL IN BOTH CHANNELS THERE ARE THREE THRESH OLDS THE MAIN CHANNEL GUARD CHANNEL AND MAIN TO GUARD RATIO THRESHOLDS 4HE DETEC TION LOGIC OF THESE THRESHOLDS IS ALSO SHOWN IN &IGURE 4HE BLANKING THAT OCCURS BECAUSE OF THE MAINGUARD COMPARISON AFFECTS THE DETECTABILITY IN THE MAIN CHANNEL THE EXTENT OF WHICH IS A FUNCTION OF THE THRESH OLD SETTINGS 4HE THRESHOLD SETTINGS ARE A TRADEOFF BETWEEN FALSE ALARMS DUE TO SIDELOBE RETURNS AND DETECTABILITY LOSS IN THE MAIN CHANNEL !N EXAMPLE IS SHOWN IN &IGURE FOR A NONFLUCTUATING TARGET WHERE THE ORDINATE IS THE PROBABILITY OF DETECTION IN THE FINAL OUTPUT OF THE SIDELOBE BLANKER AND THE ABSCISSA IS THE SIGNAL TO NOISE RATIO 3.2 IN THE MAIN CHANNEL 4HE QUANTITY " IS THE RATIO OF THE GUARD CHANNEL 3.2 TO THE MAIN CHANNEL 3.2 AND IS ILLUSTRATED IN &IGURE
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" IS SMALL FOR A TARGET IN THE MAIN BEAM AND LARGE D" OR SO FOR A TARGET AT THE SIDELOBE PEAKS )N THE EXAMPLE SHOWN THERE IS A D" DETECTABILITY LOSS DUE TO THE GUARD BLANKING FOR TARGETS IN THE MAIN BEAM )DEALLY THE GUARD ANTENNA GAIN PATTERN EXCEEDS THAT OF THE MAIN ANTENNA AT ALL ANGLES IN SPACE EXCEPT FOR THE MAIN BEAM TO MINIMIZE DETECTIONS THROUGH THE SIDELOBES )F NOT HOWEVER AS ILLUSTRATED IN &IGURE AND &IGURE RETURNS THROUGH THE SIDELOBE PEAKS OF THE MAIN PATTERN ABOVE THE GUARD PATTERN HAVE A SIGNIFICANT PROBABILITY OF DETECTION IN THE MAIN CHANNEL AND WOULD REPRESENT FALSE DETECTIONS 0OSTDETECTION 34# )N THE AMBIGUITY RESOLUTION AS THE OUTPUT RETURNS ARE RANGE CORRELATED THEY ARE SUBJECTED TO POSTDETECTION 34# OR 2#3 THRESHOLDING APPLIED INSIDE THE RANGE CORRELATION PROCESS 4ARGET RETURNS THAT RANGE CORRELATE INSIDE THE 34# RANGE BUT FALL BELOW THE 34# THRESHOLD ARE LIKELY SIDELOBE DISCRETES AND ARE BLANKED OR REMOVED FROM THE CORRELATION PROCESS AND KEPT FROM GHOSTING WITH OTHER TARGETS 4HE BASIC LOGIC IS SHOWN IN &IGURE "ASICALLY THE #&!2 OUTPUT DATA IS CORRELATED RESOLVED IN RANGE THREE TIMES %ACH CORRELATOR CALCULATES UNAMBIGUOUS RANGE USING - OUT OF THE . SETS OF DETECTION DATA EG THREE DETECTIONS REQUIRED OUT OF EIGHT 02&S .O DOPPLER CORRELATION IS USED SINCE THE DOPPLER IS AMBIGUOUS 4HE RESULTS OF THE FIRST TWO CORRELATIONS ARE USED TO BLANK ALL OUTPUTS THAT ARE LIKELY TO BE SIDELOBE DISCRETES FROM THE FINAL RANGE CORRELATOR (ERE THREE RANGE CORRELA TORS ARE USED IN WHICH THE FIRST THE ! CORRELATOR RESOLVES THE RANGE AMBIGUITIES WITHIN SOME NOMINAL RANGE SAY NM BEYOND WHICH SIDELOBE DISCRETES ARE NOT LIKELY TO BE DETECTED ! SECOND CORRELATOR THE " CORRELATOR RESOLVES THE RANGE AMBIGUITIES OUT TO THE SAME RANGE BUT BEFORE A TARGET CAN ENTER THE " CORRELATOR ITS AMPLITUDE IS THRESHOLDED BY A RANGE VARYING THRESHOLD THE 34# THRESHOLD ! RANGE GATE BY RANGE GATE COMPARISON IS MADE OF THE CORRELATIONS IN THE ! AND " CORRELATORS AND IF A RANGE GATE CORRELATES IN ! AND NOT IN " THAT GATE IS BLANKED OUT OF THE THIRD CORRELATOR THE # CORRELATOR 4HE # CORRELATOR RESOLVES THE RANGE AMBIGUITIES WITHIN THE MAXIMUM RANGE OF INTEREST !N ALTERNATIVE MECHANIZATION IS TO REPLACE THE RANGE VARYING 34# WITH AN EQUIVALENT 2#3 THRESHOLD INSIDE THE RANGE CORRELATION PROCESS 4HE 2#3 IS COMPUTED FOR EACH POSSIBLE UNFOLDED RANGE STARTING FROM THE SHORTEST RANGE AND COMPARED TO THE 2#3 THRESHOLD $ETECTIONS THAT RANGE CORRELATE BUT ARE BELOW THE 2#3 THRESHOLD ARE PREVENTED FROM COR RELATING WITH OTHER DETECTS AND ALL OF THEIR UNFOLDED RANGES ARE ALSO PREVENTED FROM CORRELATING 4HE PRINCIPLE BEHIND THE POSTDETECTION 34# APPROACH IS ILLUSTRATED IN &IGURE WHERE THE RETURN OF A TARGET IN THE MAIN BEAM AND A LARGE DISCRETE TARGET IN THE SIDE LOBES IS PLOTTED VERSUS UNAMBIGUOUS RANGE THAT IS AFTER THE RANGE AMBIGUITIES HAVE BEEN RESOLVED !LSO SHOWN ARE THE NORMAL #&!2 THRESHOLD AND THE 34# THRESHOLD VERSUS RANGE ! DISCRETE RETURN IN THE SIDELOBES IS BELOW THE 34# THRESHOLD AND A RETURN IN THE MAIN BEAM IS ABOVE THE THRESHOLD SUCH THAT THE SIDELOBE DISCRETE CAN BE RECOGNIZED AND BLANKED WITHOUT BLANKING THE TARGET IN THE MAIN BEAM 4HE 34# ONSET RANGE REPRESENTS THE RANGE AT WHICH A LARGE DISCRETE TARGET IN THE SIDELOBES EXCEEDS THE #&!2 THRESHOLD
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{°ÎÊ 9 , Ê Ê-/ /9Ê , +1, /$OPPLER PROCESSING SEPARATES MOVING TARGETS FROM CLUTTER AND ALLOWS THEM TO BE DETECTED WHILE ONLY COMPETING AGAINST THERMAL NOISE ASSUMING THAT THE TARGETS HAVE SUFFICIENT RADIAL VELOCITY 62K AND THE 02& IS HIGH ENOUGH FOR AN UNAMBIGUOUS CLUTTER SPECTRUM #OHERENCE THE CONSISTENCY OF PHASE OF A SIGNALS CARRIER FREQUENCY FROM ONE PULSE TO THE NEXT IS CRUCIAL FOR DOPPLER PROCESSING 7ITHOUT CAREFUL SYSTEM DESIGN AMPLITUDE AND PHASE INSTABILITIES DURING THE COHERENT INTEGRATION TIME WILL BROADEN THE MAIN BEAM CLUTTER SPECTRUM AND RAISE THE NOISE FLOOR THAT CLUTTER FREE TAR GETS MUST COMPETE WITH FOR DETECTION .ONLINEARITIES IN THE SYSTEM CAN ALSO CAUSE DISCRETE SPURIOUS SPECTRAL SIGNALS THAT CAN BE MISTAKEN AS TARGETS 4HE INSTANTANEOUS DYNAMIC RANGE OF THE SYSTEM GOVERNS THE SYSTEM LINEARITY AND HENCE SENSITIVITY IN A STRONG CLUTTER ENVIRONMENT 4HE DRIVING FACTOR UPON STABILITY REQUIREMENTS IS WHEN THE MAIN BEAM CLUTTER LEVEL IS AT THE SATURATION POINT OF THE RECEIVER $YNAMIC 2ANGE $YNAMIC RANGE AS DISCUSSED HERE CAN BE REFERRED TO AS INSTAN TANEOUS DYNAMIC RANGE AND IS THE LINEAR REGION ABOVE THERMAL NOISE OVER WHICH THE RECEIVER AND SIGNAL PROCESSOR OPERATE BEFORE ANY SATURATION CLIPPING OR GAIN LIMITING OCCURS )F SATURATIONS OCCUR SPURIOUS SIGNALS THAT DEGRADE PERFORMANCE MAY BE GENER ATED &OR EXAMPLE IF MAIN BEAM CLUTTER SATURATES SPURIOUS FREQUENCIES CAN APPEAR IN THE DOPPLER PASSBAND NORMALLY CLEAR OF MAIN BEAM CLUTTER AND THIS MAY GENERATE FALSE TARGET REPORTS !N AUTOMATIC GAIN CONTROL !'# FUNCTION IS OFTEN EMPLOYED TO PREVENT SATURATIONS ON EITHER MAIN BEAM CLUTTER IN SEARCH OR THE TARGET IN 3INGLE 4ARGET 4RACK MODE (OWEVER THE USE OF !'# DEGRADES THE SYSTEMS SENSITIVITY SO LARGE
05,3% $/00,%2 2!$!2
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INSTANTANEOUS DYNAMIC RANGE IS PREFERABLE )F SATURATIONS OCCUR IN A RANGE GATE DURING AN INTEGRATION PERIOD AN OPTION IN A MULTIPLE RANGE GATED SYSTEM IS SIMPLY TO BLANK DETECTION REPORTS FROM THAT GATE 7HEN A -4) FILTER IS NOT USED THE DOPPLER FILTER BANK FOR EACH RANGE GATE CAN BE EXAMINED TO DETERMINE IF THERE ARE ANY DETECTIONS DUE TO SPURIOUS SIGNALS FROM LARGE CLUTTER WITH SUBSEQUENT EDITING OF THESE DETECTIONS IF THE MEASURED CLUTTER TO NOISE RATIO EXCEEDS THE DYNAMIC RANGE 3IMILAR LOGIC CAN BE APPLIED TO SATURATED RANGE GATES TO DETERMINE IF THE LARGEST SIGNAL IN THE FILTER BANK IS IN THE PASSBAND OR REPRESENTS SATURATED CLUTTER RETURNS 3ATURATED RETURNS WITH THE PEAK SIGNAL IN THE DOPPLER PASSBAND CAN REPRESENT VALID TARGETS AT SHORT RANGES AND NEED NOT BE SUBJECTED TO THE SIDELOBE BLANKING LOGIC 4HE MOST STRESSING DYNAMIC RANGE REQUIREMENT IS DUE TO MAIN BEAM CLUTTER WHEN SEARCHING FOR A SMALL LOW FLYING TARGETS (ERE FULL SENSITIVITY MUST BE MAINTAINED IN THE PRESENCE OF THE CLUTTER TO MAXIMIZE THE PROBABILITY OF DETECTING THE TARGET 4HE DYNAMIC RANGE REQUIREMENT OF A PULSE DOPPLER RADAR AS DETERMINED BY MAIN BEAM CLUTTER IS A FUNCTION NOT ONLY OF THE BASIC RADAR PARAMETERS SUCH AS POWER ANTENNA GAIN ETC BUT OF RADAR ALTITUDE ABOVE THE TERRAIN AND THE RADAR CROSS SECTION 2#3 OF LOW FLYING TARGETS !S AN EXAMPLE &IGURE SHOWS THE MAXIMUM CLUTTER TO NOISE RATIO #.MAX THAT APPEARS IN THE AMBIGUOUS RANGE INTERVAL IE AFTER RANGE FOLDING FOR A MEDIUM 02& RADAR AS A FUNCTION OF RADAR ALTITUDE AND THE RANGE OF THE INTERSECTION OF THE PEAK OF THE MAIN BEAM WITH THE GROUND .OTE THAT THE CLUTTER TO NOISE RATIO IS A RMS POWER RATIO MEASURED AT THE !$ CONVERTER ! PEAK POWER RATIO WOULD BE D" HIGHER
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4HE AMPLITUDE OF CLUTTER RETURNS FLUCTUATE OVER TIME AND ARE MODELED AS A STOCHASTIC PROCESS 4HE CLUTTER TO NOISE RATIO REPRESENTS THE MEAN VALUE OF THIS PROCESS OVER TIME &IGURE ASSUMES A PENCIL BEAM ANTENNA PATTERN AND A CONSTANT GAMMA MODEL FOR CLUTTER REFLECTIVITY 4HE ANTENNA BEAM IS POINTED AT THE GROUND CORRESPONDING TO THE RANGE OF THE TARGET !T LONGER RANGES SMALL LOOK DOWN ANGLES CLUTTER DECREASES WITH INCREASING RADAR ALTITUDE SINCE RANGE FOLDING IS LESS SEVERE OWING TO LESS OF THE MAIN BEAM INTERSECTING THE GROUND !T SHORTER RANGES CLUTTER INCREASES WITH RADAR ALTITUDE SINCE THE CLUTTER PATCH SIZE ON THE GROUND INCREASES 7HILE &IGURE IS FOR A MEDIUM 02& RADAR SIMILAR CURVES RESULT FOR A HIGH 02& RADAR !LSO SHOWN IN &IGURE IS THE SINGLE SCAN PROBABILITY OF DETECTION 0D VERSUS RANGE FOR A GIVEN 2#3 TARGET IN A RECEIVER WITH UNLIMITED DYNAMIC RANGE )F IT IS DESIRED TO HAVE THE LOW FLYING TARGET REACH AT LEAST SAY AN 0D BEFORE ANY GAIN LIMITING IE THE USE OF !'# OCCURS THE DYNAMIC RANGE REQUIREMENT IS DRIVEN BY THE MAIN BEAM CLUTTER LEVELS #.MAX OF D" AT FT D" AT FT AND D" AT FT FOR THIS EXAMPLE 4HE HIGHER THE DESIRED PROBABILITY OF DETECTION OR THE LOWER THE RADAR ALTITUDE THE MORE DYNAMIC RANGE IS REQUIRED &URTHER IF THE SPECIFIED TARGET 2#3 IS REDUCED THE DYNAMIC RANGE REQUIREMENT FOR THE SAME DESIRED 0D INCREASES AS THE 0D VERSUS RANGE CURVE IN &IGURE SHIFTS TO THE LEFT )N A PULSE DOPPLER RADAR USING DIGITAL SIGNAL PROCESSING THE !$ CONVERTERS ARE USUALLY SELECTED TO HAVE A DYNAMIC RANGE THAT MEETS OR EXCEEDS THE USABLE DYNAMIC RANGE SET BY THE MAXIMUM CLUTTER TO NOISE RATIO #.MAX AND THE SYSTEM STABILITY 4HE PEAK DYNAMIC RANGE DEFINED AS THE MAXIMUM PEAK SINUSOIDAL SIGNAL LEVEL RELATIVE TO THE RMS THERMAL NOISE LEVEL THAT CAN BE PROCESSED LINEARLY IS RELATED TO THE NUMBER OF AMPLITUDE BITS IN THE !$ CONVERTER BY
¤ . !$ AMP ³ § 3MAX ¶ LOG ¥ ;NOISE= ´ ¨ . · QUANTA µ ¦ © ¸ D"
WHERE ;3MAX.=D" MAXIMUM INPUT PEAK SINUSOIDAL LEVEL RELATIVE TO RMS NOISE D" .!$ AMP N UMBER OF AMPLITUDE BITS NOT INCLUDING SIGN BIT IN THE !$ CONVERTER ;NOISE=QUANTA RMS THERMAL NOISE VOLTAGE LEVEL AT THE !$ CONVERTER QUANTA 4HE RMS THERMAL NOISE VOLTAGE LEVEL AT THE !$ CONVERTER IS GIVEN IN TERMS OF QUANTA ! SINGLE QUANTA REFERS TO A UNIT QUANTIZATION LEVEL OF THE !$ CONVERTER &ROM THE RELATIONSHIP DESCRIBED ABOVE AND ASSUMING THE !$ CONVERTER LIMITS THE DYNAMIC RANGE THE !$ CONVERTER SIZE CAN NOW BE DETERMINED !DDITIONAL MARGIN TO ALLOW FOR MAIN BEAM CLUTTER FLUCTUATIONS ABOVE THE MEAN VALUE ALSO NEEDS TO BE CON SIDERED 3INCE MAIN BEAM CLUTTER TIME FLUCTUATION STATISTICS ARE HIGHLY DEPENDENT ON THE TYPE OF CLUTTER BEING OBSERVED SUCH AS SEA CLUTTER OR CLUTTER FROM AN URBAN AREA AND ARE GENERALLY UNKNOWN A VALUE OF TO D" ABOVE THE RMS VALUE IS OFTEN ASSUMED FOR THE MAXIMUM PEAK LEVEL THIS ALSO INCLUDES THE D" DIFFERENCE BETWEEN THE RMS AND PEAK VALUES OF A SINUSOIDAL SIGNAL 4HUS THE REQUIRED NUMBER OF AMPLITUDE BITS IN THE !$ CONVERTER AS DETERMINED BY THE MAIN BEAM CLUTTER IS §;# . = § ¶¶ MAX D" ;FLUCT?MARGIN=D" LOG ©;NOISE=QUANTA ¸ . !$ AMP q #%), ¨ · ¨ · © ¸
05,3% $/00,%2 2!$!2
{°ÓÇ
WHERE #%),X IS THE SMALLEST INTEGER q X 4HE INSTANTANEOUS DYNAMIC RANGE SUPPORTED BY AN !$ CONVERTER IMPROVES ABOUT D" PER BIT &OR THE EXAMPLE CITED IN &IGURE WHERE THE MAXIMUM #. IS D" AT A FT RADAR ALTITUDE AND WITH A FLUCTUATION MARGIN OF D" AND THERMAL NOISE AT QUANTA D" THE !$ CONVERTER REQUIRES AT LEAST AMPLITUDE BITS PLUS A SIGN BIT FOR A TOTAL OF BITS TO ACHIEVE THE PEAK !$ DYNAMIC RANGE OF D" 4HE UPPER PORTION OF &IGURE ILLUSTRATES THIS CASE 4HE LOWER PORTION OF &IGURE WILL BE USED IN THE STABILITY DISCUSSION TO FOLLOW 3TABILITY 4O ACHIEVE THE THEORETICAL CLUTTER REJECTION AND TARGET DETECTION AND TRACKING PERFORMANCE OF A PULSE DOPPLER SYSTEM THE REFERENCE FREQUENCIES TIMING SIG NALS AND SIGNAL PROCESSING CIRCUITRY MUST BE EXTREMELY STABLEn )N MOST CASES THE MAJOR CONCERN IS WITH SHORT TERM RATHER THAN LONG TERM STABILITY ,ONG TERM STABILITY MAINLY AFFECTS VELOCITY OR RANGE ACCURACY OR SPURIOUS SIGNALS DUE TO 02& HARMONICS BUT IS RELATIVELY EASY TO MAKE ADEQUATE 3HORT TERM STABILITY REFERS TO VARIATIONS WITHIN THE ROUND TRIP RADAR ECHO TIME OR DURING THE SIGNAL COHERENT INTEGRATION TIME 4HE MOST SEVERE STABILITY REQUIREMENTS RELATE TO THE GENERATION OF SPURIOUS MODULATION SIDEBANDS ON THE MAIN BEAM CLUTTER WHICH RAISE THE SYSTEM NOISE FLOOR OR CAN APPEAR AS TARGETS AT THE DETECTORS 4HUS THE MAXIMUM RATIO OF MAIN BEAM CLUTTER TO SYSTEM NOISE MEASURED AT THE RECEIVER OUTPUT #. INCLUDING THE FLUCTUATION MARGIN AS DISCUSSED ABOVE IS THE PREDOMINANT PARAMETER THAT DETERMINES STABILITY REQUIREMENTS 4ARGET RETURNS COMPETE WITH CLUTTER RETURNS AND NOISE FOR DETECTION 3UPPOSE DESIRED TARGETS HAVE SUFFICIENT RADIAL SPEED SO THAT THEY LIE IN THE CLUTTER FREE REGION OF DOPPLER FREQUENCY WHEN A PULSE DOPPLER WAVEFORM IS USED 4HESE TARGETS NOW HAVE TO COMPETE ONLY WITH SYSTEM NOISE 4HIS NOISE CAN BE BOTH ADDITIVE AND MULTIPLICATIVE !DDITIVE NOISE TENDS TO MASK MULTIPLICATIVE NOISE IN LOW PERFORMANCE RADARS !DDITIVE NOISE SOURCES CAN BE EXTERNAL TO THE RADAR SUCH AS ATMOSPHERIC NOISE SKY TEMPERATURE GROUND NOISE BLACK BODY RADIATION AND JAMMERS OR THEY CAN BE INTERNAL SUCH AS THERMAL NOISE 4HERMAL NOISE IS ALSO KNOWN AS *OHNSON NOISE AND
'
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&)'52% $YNAMIC RANGE AND STABILITY LEVELS
{°Ón
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GAUSSIAN NOISE THE LATTER TERM ARISING FROM THE GAUSSIAN STATISTICS OF ITS VOLTAGE PROB ABILITY DENSITY FUNCTION 4HERMAL NOISE IS ALWAYS PRESENT IN THE RADAR RECEIVER AND IS THE ULTIMATE LIMIT ON RADAR SENSITIVITY 4HE ABSOLUTE LEVEL OF ADDITIVE NOISE SOURCES IS DETERMINED BY THE SOURCE AND ITS RELATION TO THE RADAR 0ROPER SYSTEM DESIGN CAN REDUCE THERMAL NOISE TO A LEVEL WHERE MULTIPLICATIVE NOISE CAN BECOME SIGNIFICANT IN LIMITING THE RADAR SENSITIVITY -ULTIPLICATIVE NOISE IS CHARACTERIZED BY EITHER A TIME VARYING AMPLITUDE AMPLI TUDE MODULATION !- OR A TIME VARYING PHASE PHASE MODULATION 0- OR FREQUENCY MODULATION &- 4HE ABSOLUTE LEVEL DEPENDS ON THE STRENGTH OF THE SIGNAL CARRIER ON WHICH THE NOISE SOURCE IS RIDING -ULTIPLICATIVE NOISE SOURCES ARE FREQUENCY INSTA BILITIES POWER SUPPLY RIPPLE AND NOISE F NOISE TIMING JITTER AND UNWANTED MIXER PRODUCTS DISCRETES OR SPURS -ULTIPLICATIVE NOISE MODULATES RADAR RETURNS BY VARYING THEIR AMPLITUDE OR PHASE AND IS PRESENT ON ALL RADAR RETURNS BEING MOST APPARENT ON LARGE RETURNS SUCH AS MAIN BEAM CLUTTER 4HE RESULT IN THE SPECTRAL DOMAIN IS SPURIOUS MODULATION SIDEBANDS 2ANDOM MULTIPLICATIVE NOISE BROADENS THE SPECTRUM OF THE CAR RIER FREQUENCY $ISCRETE MULTIPLICATIVE NOISE SOURCES GENERATE DISCRETE SPECTRAL LINES THAT CAN CAUSE FALSE ALARMS 3YSTEM STABILITY IS CHARACTERIZED BY THE OVERALL TWO WAY TRANSMIT AND RECEIVE COMPOSITE SYSTEM FREQUENCY RESPONSE WHICH IS THE RETURN OF A NONFLUCTUATING TARGET AS A FUNCTION OF DOPPLER FREQUENCY 3YSTEM FREQUENCY RESPONSE SHOULD BE DEFINED BY THE DOPPLER PASSBAND 4HE FOCUS OF THIS SECTION WILL BE THE STABILITY REQUIREMENTS FOR DOPPLER FREQUENCIES SEPARATED ENOUGH FROM THE CARRIER TO BE OUTSIDE THE GROUND MOV ING TARGET NOTCH 4HE CONCERN IN THIS REGION IS WHITE PHASE NOISE WHICH DETERMINES THE PHASE NOISE FLOOR ,OW FREQUENCY IE CLOSER TO THE CARRIER STABILITY IS MORE APPLICABLE TO AIR TO GROUND PULSE DOPPLER MODES SUCH AS '-4) AND 3!2 4HE LOCATION OF AN INSTABILITY SOURCE WITHIN THE SYSTEM WILL DETERMINE WHETHER IT IS IMPARTED UPON A RETURN SIGNAL VIA THE TRANSMIT PATH RECEIVE PATH OR BOTH )NSTABILITIES EITHER ON TRANSMIT OR RECEIVE ARE CALLED INDEPENDENT 4HOSE IMPOSED ON BOTH TRANSMIT AND RECEIVE ARE COMMON !MPLITUDE INSTABILITIES CAUSED BY !- TEND TO BE CONSIDERED INDEPENDENT SINCE THE ,/S DRIVE THE MIXERS IN THE RECEIVER INTO COMPRESSION !LSO TRANSMITTERS WORK MOST EFFICIENTLY WHEN DRIVEN INTO COMPRESSION IE WHERE THE POWER AMPLIFIER IS SATU RATED AND PROVIDES A CONSTANT OUTPUT POWER LEVEL REGARDLESS OF SMALL DEVIATIONS ON THE INPUT )NSTABILITIES DUE TO 0- OF WHICH &- IS A SPECIAL CASE TEND TO DOMINATE THOSE DUE TO !- !S SUCH THE FOCUS WILL BE ON PHASE DISTURBANCES RANDOM PHASE NOISE AND DISCRETE SINUSOIDAL SIGNALS SPURIOUS SIGNALS 2ANDOM 0HASE .OISE 2ANDOM PHASE NOISE RIDING ON A LARGE SIGNAL CAN MASK WEAK TARGET RETURNS 4HE OBJECT IS TO SPECIFY SYSTEM PHASE NOISE SO THAT IT IS WELL BELOW THE THERMAL NOISE WHEN A LARGE SIGNAL AT THE !$ SATURATION LEVEL IS PRESENT IN THE RECEIVER ! SIGNAL AT !$ SATURATION IS THE LARGEST SIGNAL THAT CAN BE LINEARLY PROCESSED BY THE RADAR RECEIVER 4HEN THE RADAR SENSITIVITY IS LIMITED BY THERMAL NOISE ALWAYS PRESENT PLUS A SMALL INCREASE IN THE TOTAL NOISE LEVEL CAUSED BY THE PHASE NOISE 4HE PHASE NOISE OF OSCILLATORS AND OTHER COMPONENTS IS TYPICALLY SPECIFIED AS THE MULTIPLICATIVE NOISE THAT RIDES ON A CONTINUOUS WAVEFORM OR #7 PHASE NOISE )N PULSE DOPPLER RADAR TRANSMIT GATING INTERRUPTS THE CONTINUOUS WAVEFORM TO PRODUCE A PULSED WAVEFORM 'ATED PHASE NOISE IS THE RESULT OF GATING #7 PHASE NOISE 4HE SPECTRUM OF A PULSED GATED SIGNAL IS DIFFERENT FROM #7 4HE RESULTING NOISE THE GATED NOISE CAN BE MUCH DIFFERENT FROM THE #7 NOISE ESPECIALLY FOR LOW DUTY CYCLE WAVEFORMS AND NOISE CLOSE TO THE CARRIER )T IS PREFERABLE TO MAKE NOISE MEASUREMENTS ON EQUIPMENT
05,3% $/00,%2 2!$!2
{°Ó
UNDER THE SAME GATING CONDITIONS THAT WILL BE USED IN THE RADAR SYSTEM 3OME DEVICES SUCH AS HIGH POWER TRANSMITTERS CANNOT OPERATE CONTINUOUSLY AND ONLY GATED NOISE MEASUREMENTS ARE POSSIBLE 4HE GATED PHASE NOISE SPECTRUM IS THE SUMMATION OF THE #7 PHASE NOISE SPECTRUM REPLICAS CENTERED AT FREQUENCIES o NF2 WHERE F2 IS THE 02& AND N IS AN INTEGER 4HE TOTAL GATED PHASE NOISE IN THE 02& BANDWIDTH F2 EQUALS THE TOTAL #7 PHASE NOISE IN THE TRANSMIT PULSE BANDWIDTH )N TERMS OF STABILITY REQUIREMENTS THE SYSTEM REQUIREMENTS ARE DERIVED USING GATED PHASE NOISE WHICH IN TURN IS CONVERTED TO A #7 VALUE FOR SPECIFYING COMPONENTS SUCH AS OSCILLATORS 4HE #7 PHASE NOISE FLOOR IS SMALLER BY A FACTOR OF THE RATIO OF THE 02& TO THE TRANSMIT BANDWIDTH WHEN THE #7 PHASE NOISE IS ASSUMED TO BE WHITE 3ENSITIVITY LOSS DUE TO PHASE NOISE IS QUANTIFIED BY THE INCREASE IN THE SYSTEM NOISE FLOOR IN THE hCLUTTER FREEv DOPPLER FILTERS DUE TO THE PHASE NOISE SIDEBANDS ON A LARGE SIGNAL SUCH AS MAIN BEAM CLUTTER 3ENSITIVITY LOSS IS THE AMOUNT BY WHICH THE TOTAL NOISE THERMAL PLUS PHASE EXCEEDS THE THERMAL NOISE LEVEL AS SHOWN IN %Q ! GATED PHASE NOISE TO THERMAL NOISE RATIO OF D" RESULTS IN AN APPROXIMATELY D" SENSITIVITY LOSS 4HIS ASSUMES A WORST CASE SCENARIO WITH THE MAIN BEAM CLUTTER RETURN AT THE !$ SATURATION LEVEL #!'# DISCUSSED IN 3ECTION IS TYPICALLY USED TO REGU LATE THE MEAN CLUTTER TO A LEVEL BELOW !$ SATURATION TYPICALLY BY THE AMOUNT OF THE EXPECTED CLUTTER FLUCTUATION LEVEL 7ITH #!'# SENSITIVITY LOSS WILL BE LESS THAN OR EQUAL TO THE CALCULATED WORST CASE VALUE
¤ 'ATED 0HASE .OISE 0OWER $ENSITY³ ;3ENSITIVITY ,OSS=D" LOG ¥ 4HERMAL .OISE 0OWER $ENSIITY ´µ ¦
4ABLE CONTAINS A CALCULATION OF THE PHASE NOISE FLOOR REQUIREMENTS FOR AN K(Z 02& WAVEFORM #LUTTER LEVELS THAT REQUIRE A BIT SIGN PLUS AMPLITUDE BITS !$ CONVERTER ARE ASSUMED AS SHOWN IN &IGURE 4HE TRANSMIT PULSE DURATION IS MS RESULTING IN A TRANSMIT PULSE BANDWIDTH OF APPROXIMATELY -(Z SINCE NO PULSE COMPRESSION IS USED 4HE RMS THERMAL NOISE POWER IS THE THERMAL NOISE FLOOR WITHIN THE RECEIVE PORTION OF )00 4HIS POWER LEVEL IS GIVEN IN DECIBELS WITH RESPECT TO THE CARRIER AMPLITUDE D"C 4HE THERMAL NOISE DENSITY IS OBTAINED BY DIVIDING THIS POWER BY THE 02& BANDWIDTH 4HE MAXIMUM GATED PHASE NOISE FLOOR IS SET TO BE D" BELOW THE THERMAL NOISE FLOOR FOR AT MOST A D" SENSITIVITY LOSS 4HE #7 PHASE NOISE FLOOR IS THEN OBTAINED BY MULTIPLYING BY THE 02& TO TRANSMIT BANDWIDTH RATIO 4!",% #7 0HASE .OISE $ENSITY &LOOR #ALCULATION
0ARAMETER 4HERMAL .OISE 0OWER AT !$ 02& "ANDWIDTH
6ALUE ;D"=
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4HERMAL .OISE $ENSITY &LOOR AT !$ 0HASE .OISE TO 4HERMAL .OISE 2ATIO
D"C(Z D"
'ATED 0HASE .OISE $ENSITY &LOOR 02& TO 4RANSMIT "ANDWIDTH 2ATIO
D"C(Z D"
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#OMMENT BIT !$ SIGN BITS THERMAL NOISE SET AT QUANTA K(Z 02& WAVEFORM -ARGIN FOR AT MOST D" SENSITIVITY LOSS -(Z TRANSMIT PULSE BANDWIDTH MS PULSE WIDTH W NO 0#
{°Îä
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4!",% .OTIONAL 3UBSYSTEM 0HASE .OISE !LLOCATION
!LLOCATION 3UBSYSTEM
!DJUSTMENT FOR #OMMON 3OURCE ;D"=
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4RANSMITTER !%XCITER 02ECIVER 3YNCHRONIZER 3YSTEM
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4HE SYSTEM LEVEL #7 PHASE NOISE FLOOR REQUIREMENT D"C(Z IS ALLOCATED TO THE CONTRIBUTING HARDWARE UNITS 4HE PERCENTAGES ARE BASED ON EXPERIENCE AND NEGO TIATIONS WITH THE SUBSYSTEM DESIGNERS ! POSSIBLE ALLOCATION IS PROVIDED IN 4ABLE $ISCRETES 3OME SOURCES OF DISCRETE SIDEBANDS ARE RIPPLE ON POWER SUPPLIES AND THE PICKUP OF DIGITAL CLOCKS )T IS DESIRABLE TO KEEP THE INTEGRATED DISCRETE SIDEBANDS BELOW NOISE AT THE #&!2 INPUT TO PREVENT DETECTING THESE DISCRETES AND PRODUCING FALSE ALARMS !LL COHERENT AND POSTDETECTION INTEGRATION MUST BE ACCOUNTED FOR WHEN WE SPECIFY DISCRETE PHASE NOISE REQUIREMENTS #OMMON DISCRETES ARE AFFECTED BY THE TIME DELAY BETWEEN THE PORTION IMPARTED ON THE TRANSMIT AND THAT ON RECEIVE 4HE TIME DELAY CHANGES THE CORRELATION BETWEEN THE PHASE OF THE SPURIOUS MODULATING FREQUENCY FROM THE TRANSMIT PATH WITH THE PHASE FROM THE RECEIVE PATH 4HIS CAN RELIEVE THE COMMON DISCRETE LEVEL REQUIREMENT FOR LOW 02& OR -4) WAVEFORMS THAT ARE RANGE UNAMBIGUOUS (OWEVER FOR HIGHLY RANGE AMBIGUOUS MEDIUM 02& AND HIGH 02& WAVEFORMS THE ASSUMPTION IS MADE THAT THE NOISE COMMON TO TRANSMIT AND RECEIVE ADDS NONCOHERENTLY IN THE DOWNCONVERSION PROCESS !S A RESULT THE COMMON DISCRETE POWER INCREASES BY D" 4ABLE PROVIDES THE CALCULATION FOR THE SYSTEM REQUIREMENTS FOR INDEPENDENT AND COMMON DISCRETE LEVELS !S IN 4ABLE A MAXIMUM CLUTTER LEVEL REQUIRING A BIT !$ IS ASSUMED AND THE RMS THERMAL NOISE LEVEL AT THE !$ CONVERTER IS SET TO QUANTA 4O FORM THE DOPPLER FILTERS PULSES ARE COHERENTLY INTEGRATED 4!",% $ISCRETE ,EVEL 2EQUIREMENT #ALCULATION
0ARAMETER 4HERMAL .OISE 0OWER AT !$ .UMBER OF 0ULSES #OHERENTLY )NTEGRATED 4OTAL $OPPER &ILTER 7EIGHTING )NTEGRATION .UMBER OF #0)S 'AIN .ONCOHERENTLY )NTEGRATED 4HERMAL .OISE 0OWER AT #&!2 $ISCRETE TO 4HERMAL .OISE -ARGIN )NDEPENDENT $ISCRETE 2EQUIREMENT #OMMON $ISCRETE 2EQUIREMENT
6ALUE ;D"= 5NITS
#OMMENT
D"C BIT !$ SIGN BITS THERMAL NOISE SET AT QUANTA
D"
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D"C %FFECTIVE NOISE LEVEL AFTER INTEGRATION
D"
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05,3% $/00,%2 2!$!2
{°Î£
4O REDUCE DOPPLER FILTER SIDELOBES A D" $OLPH #HEBYSHEV WEIGHTING IS APPLIED WHICH REDUCES THE COHERENT INTEGRATION 3.2 GAIN BY ABOUT D" &OR DETECTION THREE #0)S ARE INTEGRATED NONCOHERENTLY VIA 0$) FOR AN APPROXIMATE INTEGRATION GAIN IN D" OF LOG.0$) OR D" 4HIS RESULTS IN A THERMAL NOISE LEVEL OF D"C AT THE DETECTOR ! DISCRETE TO THERMAL NOISE MARGIN OF D" IS USED TO PROVIDE A LOW 0&! DUE TO DISCRETES 4HE COMMON DISCRETE REQUIREMENT IS MADE D" MORE STRINGENT RELATIVE TO THE INDEPENDENT REQUIREMENT AS DISCUSSED ABOVE
{°{Ê , Ê Ê "** ,Ê 1/9Ê, -" 1/" -EDIUM AND HIGH MEDIUM 02& WAVEFORMS USUALLY USE MULTIPLE DISCRETE 02& RANGING TO RESOLVE RANGE AMBIGUITIES WHILE LINEAR &- RANGING IS COMMONLY EMPLOYED WHEN HIGH 02& WAVEFORMS ARE USED -ULTIPLE $ISCRETE 02& 2ANGING 4HE TECHNIQUES FOR CALCULATING TRUE RANGE FROM SEVERAL AMBIGUOUS MEASUREMENTS GENERALLY INVOLVE SEQUENTIAL MEASUREMENT OF THE AMBIGUOUS RANGE IN EACH 02& FOLLOWED BY AN UNFOLDING AND CORRELATION PROCESS 4HE UNFOLDING CREATES A VECTOR OF POSSIBLE RANGES FOR EACH VALID DETECTION BY ADDING A SET OF INTEGERS ; x += TIMES THE UNAMBIGUOUS RANGE INTERVAL
2UNFOLD 2AMBIGUOUS
C ; F2
+=
WHERE THE UNAMBIGUOUS RANGE INTERVAL CF2 WITH C SPEED OF LIGHT AND F2 02& 4HE SET OF INTEGERS ;x+= ARE REFERRED TO AS THE RANGE AMBIGUITY NUMBERS WITH + DETER MINED BY THE MAXIMUM RANGE OF INTEREST + #%),;2MAX F2 C= 2ANGE CORRELATION OCCURS WHEN THE UNFOLDED DETECTIONS ARE SCANNED AND A CORRELATION WINDOW IS APPLIED ACROSS LOOKS AS SHOWN IN &IGURE )N THIS EXAMPLE THE CORRELATED TARGET RANGE HAS AN AMBIGUITY NUMBER OF TH TIME AROUND ECHO ON 02& AND AN AMBIGUITY
! " # !% # $ $"
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NUMBER OF ON 02&S AND 4HE )00 LENGTHS OFTEN EXPRESSED IN RANGE GATES PER )00 ARE USUALLY KEPT RELATIVELY PRIME NO COMMON FACTORS EXCEPT THE NUMBER TO PERMIT UNAMBIGUOUS RANGING AT THE MAXIMUM POSSIBLE RANGE 4HE LOGIC FOR CORRELATION REQUIRES AT LEAST - DETECTIONS ACROSS THE . 02&S IN A DWELL TO DECLARE A TARGET REPORT WITH - TYPICALLY q FOR MEDIUM AND HIGH MEDIUM 02& WAVEFORMS 2ANGE GHOSTS OCCUR IF THE CORRELATED RANGE DOES NOT REPRESENT THE TRUE TARGET RANGE AND TYPICALLY OCCUR WHEN THERE IS MORE THAN ONE DETECTION PER LOOK 2ANGE GHOSTS CAN ALSO OCCUR IF A TARGET DETECTION ON A SINGLE LOOK CORRELATED WITH OTHER DISSIMILAR TARGETS OR IF MULTIPLE RANGE CORRELATIONS OCCURRED ON A SET OF DETECTIONS CORRESPONDING TO A SINGLE UNIQUE TARGET IE MULTIPLE UNFOLDED RANGES FELL WITHIN THE CORRELATION WINDOW /NE METHOD FOR EFFICIENTLY SCANNING AND CORRELATING THE UNFOLDED DETECTIONS INVOLVES COARSE BINNING AS SHOWN IN &IGURE (ERE AMBIGUOUS DETECTIONS ARE FIRST AMPLITUDE CENTROIDED AND THEN UNFOLDED AS DISCUSSED PREVIOUSLY BUT WITH THE RESULTS STORED IN AN ARRAY WHOSE ELEMENTS ARE THE COARSE BINS 4HESE BINS HAVE A SIZE LESS THAN OR EQUAL TO THE SHORTEST )00 AND CORRELATION INVOLVES SCANNING IDENTICAL BINS ACROSS ALL OF THE 02&S IN THE DWELL AND APPLYING A CORRELATION WINDOW )N THE EXAMPLE SHOWN IN &IGURE THE BINS ARE SET TO NINE RANGE GATES SHORTEST )00 LENGTH AND THE FIFTH COARSE BIN CONTAINS DETECTIONS ACROSS THE THREE 02&S THAT FALL WITHIN THE CORRELA TION WINDOW OF o RANGE GATES "LANK OR EMPTY BINS OCCUR WHEN THE UNFOLDED RANGE FALLS OUTSIDE A PARTICULAR COARSE BIN INTERVAL +EY ADVANTAGES TO THIS APPROACH ARE THE ABILITY TO CHANGE THE RANGE CORRELATION WINDOW DYNAMICALLY AND PERFORM MOTION COM PENSATION EASILY FOR THE RANGE CHANGE ACROSS THE DWELL DUE TO RADAR PLATFORM MOTION ANDOR THE TARGETS MOTION IF THE UNAMBIGUOUS DOPPLER HAS BEEN RESOLVED PRIOR TO THIS PROCESS !DDITIONALLY THE RANGE GATE SIZES DO NOT NEED TO STAY THE SAME ACROSS THE SET OF 02&S USED IN THE DWELL IN THIS CASE THE AMBIGUOUS RANGE GATE MEASUREMENTS ON EACH LOOK ARE FIRST CONVERTED TO COMMON DISTANCE UNITS EG METERS PRIOR TO THE UNFOLDING AND SCANNINGCORRELATION PROCESSES
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&)'52% 2ANGE CORRELATION USING COARSE BINNING ON UNFOLDED CENTROIDED AMBIGUOUS DETECTIONS )N THIS EXAMPLE RANGE GATE SIZE IS THE SAME FOR ALL THREE 02&S
05,3% $/00,%2 2!$!2
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!DDITIONAL CRITERIA CAN BE USED TO REJECT RANGE GHOSTS SUCH AS SELECTING THE CORRE LATED RANGE WITH THE HIGHEST - OF . VALUE SELECTING THE DETECTIONS BASED ON THE MINI MUM VARIANCE ACROSS THE - DETECTIONS OR USING MAXIMUM LIKELIHOOD TECHNIQUES 4HE COMPUTED RADAR CROSS SECTION 2#3 OF CORRELATIONS CAN ALSO BE USED IN THE CORRELATION PROCESS TO REJECT SIDELOBE DISCRETE DETECTIONS AS DESCRIBED IN 3ECTION POSTDETECTION 34# 4HE GHOSTING PROBLEM CAN BE MITIGATED FURTHER BY A COMBINATION OF DOPPLER ANDOR MONOPULSE BINNING 2ESOLVING THE DOPPLER AMBIGUITIES FIRST PRIOR TO RANGE CORRELA TION WILL REDUCE THE SET OF DETECTIONS TO THOSE WITHIN THE DOPPLER CORRELATION WINDOW &OR CASES WHERE THIS IS NOT FEASIBLE GENERALLY THE LOWER MEDIUM 02&S UTILIZING BOTH RANGE AND DOPPLER CORRELATION WILL REDUCE GHOSTS 5SING MONOPULSE MEASUREMENTS TO SEGREGATE AND BIN TARGETS THAT ARE DISTINGUISHABLE IN ANGLE CAN ALSO REDUCE GHOSTING WHEN THERE ARE A SIGNIFICANT NUMBER OF DETECTIONS IN A DWELL ! TYPICAL MEDIUM OR HIGH MEDIUM 02& PULSE DOPPLER WAVEFORM CYCLES THROUGH . UNIQUE 02&S IN A PROCESSING DWELL . TYPICALLY BEING TO 4HE MEDIUM 02&S GENERALLY COVER NEARLY AN OCTAVE IN FREQUENCY FOR GOOD DOPPLER VISIBILITY AND GROUND MOVING TARGET REJECTION (OWEVER HIGH MEDIUM 02&S HAVE INHERENTLY GOOD DOPPLER VISIBILITY SINCE THEY ARE AMBIGUOUS IN SIGN ONLY SO THE SPAN OF THE 02&S IN A SET OF . 02&S IS USUALLY MUCH LESS THAN AN OCTAVE !DDITIONAL CONSTRAINTS ON 02& SELECTION FOR BOTH WAVEFORMS INCLUDE GOOD VISIBILITY IN SIDELOBE CLUTTER WHERE SOME 02&S MAY BE OBSCURED BY CLUTTER IN PORTIONS OF THE AMBIGUOUS RANGE INTERVAL AND MINIMIZATION OF GHOSTS IN THE AMBIGUITY RESOLUTION PROCESSING $OPPLER !MBIGUITY 2ESOLUTION 2ESOLUTION OF THE UNAMBIGUOUS DOPPLER VELOCITY IS NEEDED FOR MEDIUM 02& WAVEFORMS AND IT IS GENERALLY DONE WITH A SIMILAR UNFOLDING AND CORRELATION TECHNIQUE AS DESCRIBED PREVIOUSLY FOR RANGE AMBIGUITIES !S SHOWN IN &IGURE VELOCITY UNFOLDING OF DETECTIONS INVOLVES ADDING A SET OF SIGNED INTEGERS
! # !$
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&)'52% $OPPLER VELOCITY CORRELATION PERFORMED ON TWO DETECTIONS ACROSS TWO LOOKS !MBIGUOUS DETECTIONS ARE UNFOLDED OUT TO A MAXIMUM POSITIVE AND NEGATIVE VELOCITY
{°Î{
2!$!2 (!.$"//+
TIMES THE 02& VELOCITY FIRST BLIND SPEED TO EACH MEASURED AMBIGUOUS RADIAL VELOCITY AS FOLLOWS
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F2 L ¤ &CENTROID ; * ¥¦ . &&4
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WHERE F2K IS THE FIRST BLIND SPEED 02& VELOCITY &CENTROID IS THE AMPLITUDE CEN TROIDED DOPPLER FILTER NUMBER .&&4 IS THE NUMBER OF FILTERS IN THE DOPPLER FILTER BANK AND ; * x x += REPRESENTS THE SET OF DOPPLER AMBIGUITY NUMBERS COVERING THE MAXIMUM NEGATIVE AND POSITIVE DOPPLER VELOCITIES FOR THE TARGETS OF INTEREST &OR CASES WHERE THERE ARE ONLY A FEW AMBIGUITIES IN DOPPLER DOPPLER CORRELATION MAY BE PERFORMED PRIOR TO OR IN CONJUNCTION WITH RANGE CORRELATION TO MINIMIZE GHOSTING (IGH 02& 2ANGING 2ANGE AMBIGUITY RESOLUTION IN HIGH 02& IS PERFORMED BY MODULATING THE TRANSMITTED SIGNAL AND OBSERVING THE PHASE SHIFT OF THE MODULATION ON THE RETURN ECHO -ODULATION METHODS INCLUDE VARYING THE 02& EITHER CONTINU OUSLY OR IN DISCRETE STEPS VARYING THE 2& CARRIER WITH EITHER LINEAR OR SINUSOIDAL &- OR SOME FORM OF PULSE MODULATION SUCH AS PULSE WIDTH MODULATION 07- PULSE POSITION MODULATION 00- OR PULSE AMPLITUDE MODULATION 0!- /F THESE MODULATION TECHNIQUES 07- AND 00- MAY HAVE LARGE ERRORS BECAUSE OF CLIPPING OF THE RECEIVED MODULATION BY ECLIPSING OR STRADDLING DISCUSSED IN 3ECTION AND 0!- IS DIFFICULT TO MECHANIZE IN BOTH THE TRANSMITTER AND THE RECEIVER #ONSEQUENTLY THEY WILL NOT BE FURTHER CONSIDERED HERE ,INEAR #ARRIER &- ,INEAR FREQUENCY MODULATION &- OF THE CARRIER CAN BE USED TO MEASURE RANGE 4HE MODULATION AND DEMODULATION TO OBTAIN RANGE ARE THE SAME AS USED IN FREQUENCY MODULATED CONTINUOUS WAVE &- #7 RADAR BUT THE TRANSMISSION REMAINS PULSED 3UPPOSE THE DWELL TIME IS DIVIDED INTO TWO LOOKS )N THE FIRST LOOK NO &- IS APPLIED AND THE DOPPLER SHIFT OF THE TARGET IS MEASURED )N THE SECOND LOOK THE TRANSMITTER FREQUENCY IS VARIED LINEARLY AT A RATE F IN ONE DIRECTION IE INCREASING OR DECREASING IN FREQUENCY $URING THE ROUNDTRIP TIME TO THE TARGET THE LOCAL OSCILLATOR HAS CHANGED FREQUENCY SO THE TARGET RETURN HAS A FREQUENCY SHIFT IN ADDITION TO THE DOPPLER SHIFT THAT IS PROPORTIONAL TO RANGE 4HE DIFFERENCE IN THE FREQUENCY $F OF THE TARGET RETURN BETWEEN THE TWO LOOKS IS FOUND AND THE TARGET RANGE CALCULATED FROM
2
C$F F
4HE PROBLEM WITH ONLY TWO &- SEGMENTS DURING A DWELL IS THAT WITH MORE THAN A SINGLE TARGET IN THE ANTENNA BEAMWIDTH RANGE GHOSTS RESULT &OR EXAMPLE WITH TWO TAR GETS PRESENT AT DIFFERENT DOPPLERS THE TWO FREQUENCIES OBSERVED DURING THE &- PERIOD CANNOT BE UNAMBIGUOUSLY PAIRED WITH THE TWO FREQUENCIES OBSERVED DURING THE NO &- PERIOD 4O MITIGATE THIS PROBLEM A THREE SEGMENT SCHEME IS USED WITH THE FOLLOWING SEGMENTS NO &- &- UP AND &- DOWN 4HE RANGE IS FOUND BY SELECTING RETURNS FROM EACH OF THE THREE SEGMENTS THAT SATISFY THE RELATIONS
F F F
F F F
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4!",% 4HREE SLOPE &- 2ANGING %XAMPLE
4HERE ARE TWO TARGETS ! AND " &- SLOPE -(ZS 4ARGET
!
"
2ANGE NMI $OPPLER FREQUENCY K(Z &- SHIFT K(Z
/BSERVED &REQUENCIES F NO &- K(Z F &- UP K(Z F &- DOWN K(Z
0OSSIBLE SETS THAT SATISFY THE RELATIONS SHOWN IN %Q AND %Q ARE F
F
F
F
F F
4ARGET
2ANGE NMI
9ES .O .O 9ES
WHERE F F AND F ARE THE FREQUENCIES OBSERVED DURING THE NO &- &- UP AND &- DOWN SEGMENTS RESPECTIVELY 4HE RANGE THEN IS FOUND FROM %Q WHERE
$F F F
OR F F OR
F F
!N EXAMPLE IS SHOWN IN 4ABLE )F MORE THAN TWO TARGETS ARE ENCOUNTERED DURING A DWELL TIME GHOSTS AGAIN RESULT AS ONLY . SIMULTANEOUSLY DETECTED TARGETS CAN BE RESOLVED GHOST FREE WHERE . IS THE NUMBER OF &- SLOPES (OWEVER THIS PROBLEM IS NOT SEVERE IN PRACTICE SINCE MULTIPLE TARGETS IN A SINGLE BEAMWIDTH ARE USUALLY A TRANSIENT PHENOMENON 4HE ACCURACY OF THE RANGE MEASUREMENT IMPROVES AS THE &- SLOPE INCREASES SINCE THE OBSERVED FREQUENCY DIFFERENCES CAN BE MORE ACCURATELY MEASURED 4HE &- SLOPE IS HOWEVER LIMITED BY CLUTTER SPREADING CONSIDERATIONS SINCE DURING THE &- PERIODS THE CLUTTER IS SMEARED IN FREQUENCY AND CAN APPEAR IN FREQUENCY REGIONS NORMALLY CLEAR OF CLUTTER ! NO &- &- UP DOUBLE &- UP SCHEME IS RECOMMENDED TO PREVENT DESIRED TARGETS FROM COMPETING WITH MAIN BEAM CLUTTER 2ANGE ACCURACIES ON THE ORDER OF OR MILES CAN BE REASONABLY ACHIEVED
{°xÊ " Ê Ê76 ", Ê - -ODERN MULTIFUNCTION PULSE DOPPLER RADARS UTILIZE VARIOUS MODES TO ACCOMPLISH TASKS SUCH AS SEARCH AND TRACK %ACH MODE USES CERTAIN WAVEFORMS OPTIMIZED FOR THE DETEC TION AND MEASUREMENT OF VARIOUS TARGET CHARACTERISTICS &OR EXAMPLE THE RADAR OPERATOR MIGHT SELECT A SEARCH MODE AND SPECIFY A SEARCH VOLUME THAT THE RADAR WILL RASTER SCAN AS SHOWN IN &IGURE 6ALID DETECTIONS IN SEARCH ARE THEN CONVERTED TO TRACKS IN THE RADAR COMPUTER 4HESE TRACKS NEED TO BE UPDATED BY A TRACK MODE ON A REGULAR BASIS DEPENDING ON THE TRACK ACCURACY REQUIRED (IGH TRACK ACCURACY IS NEEDED FOR THREATENING TARGETS OR THOSE THAT NEED A FIRE CONTROL
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SOLUTION IN ORDER TO ENGAGE AS OPPOSED TO NONTHREATENING TARGETS WHERE A GENERAL SITU ATIONAL AWARENESS IS SUFFICIENT AND HIGH ACCURACY IS NOT REQUIRED 3EARCH 4HE TWO PRIMARY SEARCH MODES ARE !UTONOMOUS 3EARCH AND #UED 3EARCH )N !UTONOMOUS 3EARCH THE OPERATOR SELECTS A RANGE AZIMUTH AND ELEVATION COVERAGE AND THE RADAR SEARCHES EACH BEAM POSITION THAT COVERS THIS VOLUME ONCE PER FRAME 4HE TIME IT TAKES TO COMPLETE A FRAME IS KNOWN AS THE REVISIT OR FRAME TIME 4HE FRAME TIME SHOULD BE MINIMIZED TO ENHANCE THE CUMULATIVE PROBABILITY OF DETECTION OF TARGETS -ODERN RADAR SYSTEMS CAN TAKE ADVANTAGE OF ON AND OFF BOARD CUES TO INCREASE THE PROBABILITY OF ACQUIRING A TARGET USING #UED 3EARCH ! #UED 3EARCH MODE ADJUSTS THE SEARCH VOLUME AND WAVEFORM SELECTION ACCORDING TO THE ACCURACY OF THE CUES PARAMETERS 2ADARS WITH ELECTRONICALLY SCANNED ARRAY %3! ANTENNAS CAN INTERLEAVE OTHER FUNC TIONS TRACK UPDATES #UED 3EARCH CALIBRATIONS ETC WITH !UTONOMOUS 3EARCH 4HE RADAR COMPUTERS RESOURCE MANAGER MUST ENSURE THAT THE MAXIMUM FRAME TIME IS NOT EXCEEDED WITH THE INCLUSION OF THESE OTHER FUNCTIONS DURING A SEARCH FRAME &OR AIRBORNE PULSE DOPPLER RADARS !UTONOMOUS 3EARCH CAN HAVE TWO SUBMODES &ORWARD ASPECT AND !LL ASPECT 3EARCH &ORWARD ASPECT 3EARCH IS DESIGNED TO DETECT HEAD ON ENGAGEMENT TARGETS WITH HIGH CLOSING SPEEDS THAT ARE NOT COMPETING AGAINST MAIN BEAM OR SIDELOBE CLUTTER &ORWARD ASPECT 3EARCH USES HIGH DUTY HIGH 02& WAVE FORMS TO MAXIMIZE THE ENERGY ON TARGET AND PROVIDE LONG DETECTION RANGE &ORWARD ASPECT 3EARCH WAVEFORMS INCLUDE 6ELOCITY 3EARCH 63 (IGH 02& 2ANGE 7HILE 3EARCH (273 AND !LERT#ONFIRM !LL ASPECT 3EARCH CAN BE EITHER A SINGLE HIGH MEDIUM 02& WAVEFORM THAT HAS ACCEPTABLE PERFORMANCE FOR TARGETS THAT ARE COMPETING WITH SIDELOBE CLUTTER OR THE COMBINATION OF &ORWARD ASPECT 3EARCH HIGH 02& WAVEFORMS INTERLEAVED WITH MEDIUM 02& WAVEFORMS DESIGNED TO DETECT TARGETS COMPETING WITH SIDELOBE CLUT TER SUCH AS -EDIUM 02& 2ANGE 7HILE 3EARCH -273 6ELOCITY 3EARCH 63 IS A HIGH 02& SEARCH WAVEFORM THAT MEASURES DOPPLER FRE QUENCY UNAMBIGUOUSLY WITH THE POSSIBLE EXCEPTION OF SENSE BUT DOES NOT MEASURE RANGE 4HIS IS THE CLASSIC HIGH 02& WAVEFORM 4HE TRANSMIT DUTY CYCLE IS MAXIMIZED TO INCREASE DETECTION RANGE 4HE RECEIVER MAY BE RANGE GATED TO MATCH THE BANDWIDTH OF THE TRANSMIT WAVEFORM BUT RANGE MEASUREMENT IS NOT ATTEMPTED ! 63 DWELL WILL CONSIST OF A SINGLE LOOK AT A GIVEN 02& 4HE COHERENT INTEGRATION TIME IS MAXIMIZED WITHIN THE LIMITS OF THE MAXIMUM EXPECTED TARGET RADIAL ACCELERATION 63 IS OPTIMIZED FOR 3WERLING ) AND ))) TARGET AMPLITUDE FLUCTUATION STATISTICS AND THE CUMULATIVE PROBABILITY OF DETECTION OF INCOMING TARGETS OVER SEVERAL SEARCH FRAMES (IGH 02& 2ANGE 7HILE 3EARCH ,IKE 63 (273 IS A HIGH 02& WAVEFORM (OWEVER LINEAR CARRIER &- RANGING IS USED TO OBTAIN A RANGE MEASUREMENT AS DESCRIBED IN 3ECTION 4HIS RANGE MEASUREMENT COMES AT THE EXPENSE OF FRAME TIME WITH THE ADDITION OF VARIOUS &- SLOPES FOR EACH DWELL 4HE ACCURACY OF THIS RANGE MEASUREMENT IS DEPENDENT UPON THE LINEAR &- RANGING SLOPES !LERT#ONFIRM 4HE BEAM AGILITY OF %3! BASED RADARS ALLOWS THE USE OF SEQUEN TIAL DETECTION TECHNIQUES ! SIMPLIFICATION OF SUCH TECHNIQUES IS KNOWN AS !LERT #ONFIRM 4HE GOAL OF !LERT#ONFIRM IS TO PROVIDE HIGH SENSITIVITY WHILE MANAGING FALSE ALARMS AND MINIMIZING THE SEARCH FRAME TIME "Y TRANSMITTING A LONGER #ONFIRM DWELL FOR RANGING ONLY AT BEAM POSITIONS WHERE A SHORTER DWELL !LERT HAS DETECTED
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TARGETS !LERT#ONFIRM PROVIDES THE RANGE MEASUREMENT OF CLASSIC (273 WAVEFORMS WITHOUT THE FRAME TIME EXPENSE OF TRANSMITTING LINEAR &- RANGING DWELLS EVERY BEAM POSITION 4HE #ONFIRM DWELL CAN ALSO BE USED TO CONTROL FALSE ALARMS PERMITTING THE !LERT DWELL TO BE MORE SENSITIVE THAN CLASSIC 63 4HE !LERT PHASE IS USED TO SEARCH EACH BEAM POSITION OF THE FRAME FOR THE PRESENCE OF A TARGET ! 63 WAVEFORM IS USED WITH A LOW DETECTION THRESHOLD AND A CORRESPONDING FALSE ALARM TIME ON THE ORDER OF A FEW SECONDS 4HE LOWER DETECTION THRESHOLD INCREASES SENSITIVITY 7HEN AN !LERT DWELL DECLARES A DETECTION A #ONFIRM DWELL IS SCHEDULED FOR THAT !LERT DWELLS BEAM POSITION )F MONOPULSE MEASUREMENTS ARE AVAILABLE ON THE !LERT DETECTION THE #ONFIRM BEAM CAN BE CENTERED ON THE DETECTION TO DECREASE BEAM SHAPE LOSS 4HE #ONFIRM DWELL IS TYPICALLY A (273 WAVEFORM AND ONLY EXAMINES DOPPLER FILTERS WITHIN A WINDOW CENTERED ABOUT THE FILTER OF THE !LERT DETECTION CUE 4HE #ONFIRM DWELL MUST PRODUCE A DETECTION CORRESPONDING TO THE !LERT DETECTION IN ORDER FOR A VALID DETECTION DECLARATION 4HE #ONFIRM DWELL IS USED TO MANAGE FALSE ALERTS AND PROVIDE A RANGE MEASUREMENT FOR TARGET DETECTIONS 4HE !LERT AND #ONFIRM DETEC TION THRESHOLDS ARE DESIGNED TO ACHIEVE OVERALL FALSE ALARM TIME EQUAL TO CONVENTIONAL SEARCH ONE EVERY FEW MINUTES !LONG WITH USING THE SAME 02& IN !LERT AND #ONFIRM THE TIME BETWEEN THESE DWELLS OR LATENCY SHOULD BE MINIMIZED TO PREVENT A VALID !LERT DETECTION FROM BEING ECLIPSED DURING THE #ONFIRMATION DWELL ,OW LATENCY ALSO ALLOWS THE USE OF #ORRELATED !LERT#ONFIRM (ERE A 3WERLING ) TARGET 2#3 FLUCTUATION MODEL IS ASSUMED 4HIS IMPLIES THAT WHEN THE SAME 2& CAR RIER FREQUENCY IS USED FOR !LERT AND #ONFIRM THE TARGET 2#3 WILL BE RELATIVELY CONSTANT BETWEEN THE TWO DWELLS PROVIDING ADDITIONAL RANGE ENHANCEMENT IN TERMS OF THE CUMULATIVE PROBABILITY OF DETECTION -EDIUM 02& 2ANGE 7HILE 3EARCH ! MEDIUM 02& WAVEFORM IS USED TO DETECT TARGETS COMPETING WITH SIDELOBE CLUTTER THAT WOULD BE UNDETECTABLE IN (273 -273 ALLOWS THE DETECTION OF NOSE ASPECT TARGETS AT WIDE SCAN ANGLES THAT ARE CROSSING THE RADAR LINE OF SIGHT SUCH THAT THEIR LOW CLOSING VELOCITY PLACES THEM IN SIDELOBE CLUT TER AND TAIL ASPECT TARGETS IN LEAD PURSUIT ENGAGEMENTS AN ATTACK GEOMETRY WHERE THE NOSE OF THE ATTACKING AIRCRAFT IS POINTED AHEAD OF THE TARGETS PRESENT POSITION -273 PROVIDES COMPLETE SITUATIONAL AWARENESS PERCEPTION OF THE SURROUNDING TACTICAL ENVI RONMENT BUT DOES NOT HAVE THE MAXIMUM DETECTION RANGE PROVIDED BY THE HIGHER DUTY CYCLE OF (273 FOR THERMAL NOISE LIMITED TARGETS 4HE -273 WAVEFORM USES - OF . DETECTION PROCESSING A TYPICAL WAVEFORM MIGHT BE OF %ACH -273 DWELL IS MADE UP OF . LOOKS EACH WITH A DIFFERENT 02& $ETECTION IS REQUIRED ON AT LEAST - LOOKS TO RESOLVE TARGET RANGE AND RANGE RATE UNAM BIGUOUSLY 4HE DETECTION THRESHOLDS ARE SET TO PROVIDE APPROXIMATELY ONE FALSE ALARM PER MINUTE 4HE EFFECTIVENESS OF -273 IS DEPENDENT ON THE ABILITY TO DETECT TARGETS AT THE REQUIRED RANGES WHILE SIMULTANEOUSLY REJECTING DISCRETE CLUTTER DETECTIONS ,OW TWO WAY ANTENNA SIDELOBES ALONG WITH THE COMBINATION OF TECHNIQUES DISCUSSED IN 3ECTION SUCH AS GUARD CHANNEL BLANKING AND POSTDETECTION 34# ARE USED TO MITIGATE SIDELOBE CLUTTER DISCRETE FALSE ALARMS -273 ALSO USES PULSE COMPRESSION TO DECREASE THE AMOUNT OF SIDELOBE CLUTTER THAT TARGETS MUST COMPETE WITH 4HE LOWER 02& REDUCES ECLIPSING AND THE AMOUNT OF CLUT TER RANGE FOLDING 4RANSMIT CARRIER FREQUENCY DIVERSITY DWELL TO DWELL FORCES 3WERLING ) AND ))) TARGET FLUCTUATION STATISTICS AND IMPROVES CUMULATIVE PROBABILITY OF DETEC TION PERFORMANCE &REQUENCY DIVERSITY LOOK TO LOOK WITHIN A DWELL PRODUCES 3WERLING )) AND )6 STATISTICS AND IS BETTER SUITED FOR HIGH SINGLE SCAN PROBABILITY OF DETECTION
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-273 CAN ALSO BE IMPLEMENTED WITH A HIGH MEDIUM 02& WHICH IS CHARACTERIZED BY THE WAVEFORMS DOPPLER COVERAGE BEING UNAMBIGUOUS IN DOPPLER MAGNITUDE BUT NOT DOPPLER SENSE FOR THE MAXIMUM TARGET DOPPLER OF INTEREST 4HE RESULTING SINGLE BLIND SPEED DUE TO MAIN BEAM CLUTTER PERMITS AS WIDE OF A CLUTTER REJECTION NOTCH AS REQUIRED TO REJECT MAIN BEAM CLUTTER OR GROUND MOVING TARGETS AND STILL NOT RESULT IN DOPPLER BLIND SPEEDS FOR TARGETS OF INTEREST - OF . RANGING PROVIDES BETTER RANGE MEASUREMENT ACCURACY THAN LINEAR &- RANGING USED IN (273 4HE 02&S USED IN A DWELL MUST BE CHOSEN TO RESOLVE THE HIGH NUMBER OF RANGE AMBIGUITIES WITHIN THE INSTRUMENTED RANGE 4RACK 4ARGET TRACKING IS DONE BY MAKING RANGE RANGE RATE AND AZIMUTH AND ELEVA TION ANGLE MEASUREMENTS ON TARGETS 2ANGE MEASUREMENTS ARE OBTAINED USING RANGE GAT ING AND CENTROIDING ON THE TARGET RETURN WITH RANGE AMBIGUITIES BEING RESOLVED WITHIN THE TRACKER 2ANGE RATE IE DOPPLER MEASUREMENTS ARE FORMED WITH A CENTROID ON THE TARGETS DOPPLER RETURN IN THE FILTER BANK !NGLE MEASUREMENTS CAN BE OBTAINED USING MONOPULSE SEQUENTIAL LOBING OR CONICAL SCAN WITH MONOPULSE BEING THE PROMINENT CHOICE IN MOD ERN RADARS 4HE TRACKER CREATES WINDOWS OR GROUPS OF CONTIGUOUS RANGE DOPPLER CELLS AROUND EACH OF THESE MEASUREMENTS IN ORDER TO ASSOCIATE DETECTIONS WITH EXISTING TRACKS 4HE TRACKER USUALLY IMPLEMENTED WITH A NINE STATE POSITION VELOCITY AND ACCELERATION +ALMAN FILTER ESTIMATES TARGET MOTION IN AN INERTIAL COORDINATE SYSTEM -ULTIPLE 4ARGET 4RACKING -44 CAN BE ACCOMPLISHED IN SEVERAL WAYS /NE METHOD 4RACK 7HILE 3CAN OR 473 IS TO USE THE NORMAL SEARCH MODE WITH &- OR MULTIPLE 02& RANGING AND STORE THE RANGE ANGLE AND DOPPLER OF THE REPORTED DETEC TIONS IN THE RADAR COMPUTER 4HESE DETECTIONS ARE THEN USED TO FORM AND UPDATE TRACK FILES 4HE ANTENNA SCANS IN A NORMAL SEARCH PATTERN AND A SCAN TO SCAN CORRELATION IS MADE ON THE DETECTIONS THAT UPDATE THE TRACK FILES !LTHOUGH TRACKING ACCURACIES ARE LESS THAN CAN BE ACHIEVED IN A DEDICATED SINGLE TARGET TRACK MULTIPLE TARGETS CAN BE TRACKED SIMULTANEOUSLY OVER A LARGE VOLUME OF SPACE ! SECOND METHOD OF -ULTIPLE 4ARGET 4RACKING 0AUSE 7HILE 3CAN PARTICULARLY APPLICABLE TO %3! BASED RADARS IS TO SCAN IN A NORMAL SEARCH PATTERN PAUSE ON EACH SEARCH DETECTION AND ENTER A 3INGLE 4ARGET 4RACK MODE FOR A BRIEF PERIOD 4HE ADVANTAGE IS THAT THE RESULTING RANGE ANGLE AND DOPPLER MEASUREMENTS ARE MORE ACCURATE THAN THOSE MADE WITH A SCANNING ANTENNA BUT THE TIME TO SEARCH A VOLUME IN SPACE IS INCREASED 4RANSITION TO 4RACK OR 4RACK !CQUISITION IS USED TO CONFIRM SEARCH TARGET DETEC TIONS AND PROVIDE IMPROVED RANGE ACCURACY WHEN NEEDED )F THE TARGET IS SUCCESSFULLY ACQUIRED A TRACK FILE IN THE RADAR COMPUTER IS INITIATED 4HE 4RACK !CQUISITION WAVE FORMS PARAMETERS DEPEND UPON THE TYPE OF SEARCH WAVEFORM THAT PRODUCED THE TARGET DETECTION 4HE 4RACK !CQUISITION WAVEFORMS THRESHOLDS ARE SET TO REJECT FALSE ALARMS AND REDUCE THE FALSE TRACK INITIATION RATE TO LESS THAN ONE PER HOUR &OR 4RACK !CQUISITION A SEARCH DETECTION FROM 63 WOULD REQUIRE A (273 WAVE FORM TO OBTAIN A RANGE MEASUREMENT (273 AND !LERT#ONFIRM WAVEFORMS ARE FOLLOWED BY RANGE GATED HIGH 02& DWELLS USING - ON . RANGING TO ACHIEVE THE NECESSARY RANGE ACCURACY FOR SINGLE 02& TRACK UPDATES 4HE UNAMBIGUOUS (273 RANGE MEASUREMENT OF THE SEARCH DETECTION IS USED TO HELP RESOLVE THE RANGE AMBIGUITY &OR -273 DETECTIONS ANOTHER -273 DWELL IS USED FOR 4RACK !CQUISITION /NCE THE TRACK FILE IS INITIATED SEVERAL RAPID TRACK UPDATES ARE USED TO FIRMLY ESTABLISH THE TRACK 7HEN DOING 3INGLE 4ARGET 4RACK UPDATES A SINGLE 02& WAVEFORM CAN BE USED 4HE RANGE ANDOR DOPPLER AMBIGUITIES ARE RESOLVED IN SEARCH AND IF NECESSARY IN THE 4RANSITION TO 4RACK PHASE "Y USING THE UNAMBIGUOUS RANGE AND VELOCITY PREDICTIONS
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OF THE TARGET PROVIDED BY THE TRACKER A SINGLE 02& CAN BE CHOSEN SUCH THAT RANGE AND DOPPLER ECLIPSING IS AVOIDED WITH HIGH PROBABILITY 4HE LENGTH OF THE DWELL IS ADAPTED TO PROVIDE SUFFICIENT ENERGY ON TARGET SO THAT ITS RETURN SIGNAL TO NOISE RATIO WILL PRO VIDE THE NECESSARY MEASUREMENT ACCURACIES REQUIRED BY THE TRACKER 4HIS ADAPTIVE TRACK UPDATE WAVEFORM ALLOWS THE SEARCH REVISIT TIME TO BE MAINTAINED WHILE TRACKING MULTIPLE TARGETS
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4HE RADAR RANGE EQUATION IS USED TO DETERMINE THE PERFORMANCE OF PULSE DOPPLER RADAR 4HE RADAR RANGE EQUATION MUST INCLUDE LOSSES BOTH SYSTEM AND ENVIRONMENTAL THAT WILL DEGRADE THE STRENGTH OF RETURN SIGNALS AT THE DETECTOR 0ROBABILITY OF DETECTION 0D DEPENDS ON TARGET SIGNAL TO NOISE RATIO AND PROBABILITY OF FALSE ALARM 0&! WHICH ITSELF IS A FUNCTION OF WAVEFORM 4HE FALSE ALARM PROBABILITY DETERMINES THE DETECTION THRESHOLD AND IS REFERENCED TO AN INDIVIDUAL RANGE DOPPLER CELL 4HIS PER CELL PROBABIL ITY IS DERIVED FROM THE SPECIFIED FALSE REPORT TIME FOR THE SYSTEM 2ADAR 2ANGE %QUATION )N THE DOPPLER REGION WHERE THE SIGNAL DOES NOT FALL IN CLUTTER PERFORMANCE IS LIMITED ONLY BY SYSTEM NOISE 4HE SIGNAL TO NOISE POWER RATIO IN THE RANGE DOPPLER CELL AT THE DETECTOR PRIOR TO POSTDETECTION INTEGRATION FOR A TARGET AT RANGE 2 IS GIVEN BY
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WHERE 2O RANGE AT WHICH 3.2 IS EQUAL TO R4 TARGET RADAR CROSS SECTION ,4 LOSSES APPLICABLE TO THE TARGET 4HE REMAINING TERMS ARE AS DEFINED FOLLOWING %Q 4HE NET LOSS ,4 USED TO COM PUTE 3.2 FOR A TARGET IS GENERALLY HIGHER THAN THE NET LOSS ,# USED TO COMPUTE #.2 IN %Q ,4 INCLUDES LOSSES SUCH AS ECLIPSING AND RANGE GATE STRADDLE DOPPLER FILTER STRADDLE #&!2 AND GUARD BLANKING THAT ARE APPLICABLE TO RESOLVABLE TARGETS BUT NOT TO DISTRIBUTED CLUTTER 4HE TARGET 3.2 REPRESENTS THE ENVELOPE ) 1 FOR A LINEAR DETECTOR OR ) 1 FOR A SQUARE LAW DETECTOR OF THE TARGET RETURN COMPARED TO THAT OF JUST NOISE 4HE ENVE LOPE IS MEASURED AFTER THE ENTIRE COHERENT MATCHED FILTER PROCESS IE TRANSMIT PULSE MATCHED FILTER PULSE COMPRESSION AND COHERENT DOPPLER FILTERING 4HEREFORE 3.2 IS ASSOCIATED WITH A SINGLE #0) ,OSSES 3OME OF THE LOSSES INHERENT IN BUT NOT NECESSARILY UNIQUE TO PULSE DOP PLER RADARS THAT EMPLOY DIGITAL SIGNAL PROCESSING ARE DISCUSSED BELOW 3OME OF THE LOSSES MAY BE INCORPORATED INTO THE OTHER VARIABLES IN THE RADAR RANGE EQUATION #ARE MUST BE TAKEN TO ACCOUNT FOR ALL OF THE SYSTEM LOSSES WHILE AVOIDING REDUNDANCIES
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-OST FRONT END LOSSES ARE APPLICABLE TO BOTH TARGETS AND CLUTTER ,OSSES APPLICABLE ONLY TO TARGETS WILL BE INDICATED 2& 4RANSMIT ,OSS 4HIS LOSS ACCOUNTS FOR 2& OHMIC LOSSES BETWEEN THE TRANSMIT TER OR 2& POWER AMPLIFIER AND THE ANTENNA RADIATOR WHICH CAN INCLUDE LOSSES FROM CONNECTORS CIRCULATORS AND RADIATING ELEMENTS 2ADOME ,OSS -OST RADARS REQUIRE A RADOME TO PROTECT THE ANTENNA FROM ENVIRON MENTAL ELEMENTS AND TO CONFORM TO THE PLATFORMS SHAPE 2ADOMES WILL HAVE A LOSS THAT MAY DEPEND ON THE SCAN ANGLE OF THE ANTENNA 4HIS LOSS MUST BE ACCOUNTED FOR ON TRANSMIT AND RECEIVE IE A TWO WAY LOSS 0ROPAGATION ,OSS 0ROPAGATION THROUGH THE ATMOSPHERE RESULTS IN A LOSS ESPE CIALLY AT HIGHER RADAR CARRIER FREQUENCIES 4HIS LOSS IS A FUNCTION OF RANGE ALTITUDE AND WEATHER )T IS ALSO A TWO WAY LOSS 0ROPAGATION LOSS IS MORE OF A ENVIRONMENTAL LOSS THAN A SYSTEM LOSS BUT CAN BE GROUPED WITH THE OTHER LOSSES THAT MAKE UP NET LOSS IN THE RADAR RANGE EQUATION 3CAN ,OSS "ROADSIDE ELECTRONICALLY SCANNED ARRAY ANTENNAS ARE SUBJECT TO REDUC TION IN GAIN WHEN THE MAIN BEAM IS SCANNED OFF BROADSIDE 4HE PROJECTED AREA OF THE %3! APERTURE DECREASES AS BEAM SCANS FROM BROADSIDE 0ROJECTED AREA DROPS AS COSINE OF SCAN CONE ANGLE -UTUAL COUPLING BETWEEN RADIATING ELEMENTS FURTHER REDUCES THE EFFECTIVE AREA 3CAN LOSS MUST BE ACCOUNTED FOR ON TRANSMIT AND RECEIVE "EAMSHAPE ,OSS 4HIS TARGET SPECIFIC LOSS ACCOUNTS FOR THE LOSS IN GAIN WHEN THE TARGET IS NOT LOCATED AT THE PEAK OF THE BEAM "EAMSHAPE LOSS IS DEFINED AS THE INCREASE IN THE POWER OR THE 3.2 REQUIRED TO ACHIEVE THE SAME PROBABILITY OF DETECTION ON A TAR GET SPREAD UNIFORMLY OVER THE SPECIFIED BEAM COVERAGE AS WOULD OCCUR WITH A TARGET AT BEAM CENTER "EAMSHAPE LOSS IS USED PRIMARILY IN SEARCH DETECTION RANGE PERFORMANCE CALCULATIONS 2& 2ECEIVE ,OSS 4HIS LOSS IS SIMILAR TO 2& 4RANSMIT ,OSS EXCEPT IT ACCOUNTS FOR OHMIC LOSSES FROM THE ANTENNA FACE TO THE FIRST LOW NOISE AMPLIFIER 4HIS LOSS MAY BE INCLUDED IN THE RECEIVE SYSTEM NOISE FIGURE OR SYSTEM TEMPERATURE VALUE )& -ATCHED &ILTER ,OSS 4HE MATCHED FILTER FOR A PULSE DOPPLER WAVEFORM INCLUDES THE ANALOG )& MATCHED FILTER IN THE RECEIVER AND ANY SUBSEQUENT DIGITAL INTEGRATION OF !$ SAMPLES TO MATCH THE DURATION OF THE TRANSMIT PULSE )& MATCHED FILTER LOSS QUANTI FIES HOW WELL THE ANALOG )& MATCHED FILTER COMPARES TO THE IDEAL MATCHED FILTER FOR THAT POINT IN THE RECEPTION CHAIN 1UANTIZATION .OISE ,OSS 4HIS LOSS IS DUE TO THE NOISE ADDED BY THE !$ CONVER SION PROCESS AND TO TRUNCATION DUE TO FINITE WORD LENGTHS IN THE SIGNAL PROCESSOR THAT FOLLOW 4HIS LOSS CAN ALSO BE INCORPORATED INTO THE RECEIVER NOISE FIGURE VALUE 0ULSE #OMPRESSION -ISMATCH ,OSS 4HIS IS CAUSED BY THE INTENTIONAL MISMATCH ING OF THE PULSE COMPRESSION FILTER TO REDUCE TIME RANGE SIDELOBES %CLIPSING AND 2ANGE 'ATE 3TRADDLE ,OSS 4HE LARGE AMOUNT OF RANGE AMBIGUITY INHERENT IN PULSE DOPPLER WAVEFORMS RESULTS IN THE POSSIBLE ECLIPSING OF TARGET RETURNS
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WHEN THE RECEIVER IS BLANKED DURING PULSE TRANSMISSION )N A MULTIPLE RANGE GATE SYS TEM THE RETURNS MAY ALSO STRADDLE GATES REDUCING THE PULSE MATCHED FILTER OUTPUT OF A SINGLE GATE "ECAUSE OF ECLIPSING AND RANGE GATE STRADDLE THE VALUE OF 2O GIVEN BY %Q MAY FALL ANYWHERE BETWEEN ZERO AND A MAXIMUM VALUE DEPENDING ON THE EXACT LOCATION OF THE TARGET RETURN WITHIN THE INTERPULSE PERIOD &IGURE ILLUSTRATES THE EFFECT OF ECLIPSING AND RANGE GATE STRADDLE ON THE OUTPUT OF THE PULSE MATCHED FILTER OVER THE )00 %ACH RANGE GATE IS ASSUMED TO BE MATCHED TO THE TRANSMIT PULSE BANDWIDTH WHICH FOR UNMODULATED PULSES IE NO PULSE COMPRESSION MODULATION IS THE INVERSE OF THE PULSE DURATION 4HEREFORE REFERRING TO &IGURE THE GATE WIDTH SG EQUALS THE TRANSMITTED PULSE ST )N &IGURE THE )00 IS SG 4HE PLOTS ON THE LEFT REPRESENT A RANGE GATE SPACING OF SS EQUAL TO SG 2ANGE GATE STRADDLE LOSS CAN BE REDUCED BY THE USE OF OVERLAPPING GATES AT THE EXPENSE OF EXTRA HARDWARE AND PROCESS ING 4HE RIGHTMOST PLOTS REPRESENT THE USE OF RANGE GATE OVERLAP SS SG 4HE MAXIMUM PULSE MATCHED FILTER OUTPUT AS A FUNCTION OF RETURN DELAY IS SHOWN IN TERMS OF RELATIVE VOLTAGE AND POWER 4HE hVOLTAGEv PLOT SHOWS THE CUMULATIVE EFFECT OF CONVOLV ING THE RETURN PULSE WITH THE MATCHED FILTER OF EACH RANGE GATE &OR A SINGLE RANGE GATE THIS IS SIMPLY THE CONVOLUTION OF TWO RECTANGULAR PULSES WHICH RESULTS IN A TRIANGULAR RESPONSE 4O COMPUTE LOSS THE MATCHED FILTER OUTPUT IN TERMS OF POWER IE VOLTAGE SQUARED MUST BE USED 7HEN THE 02& IS HIGH SO THAT MANY RANGE AMBIGUITIES OCCUR THE TARGET RANGE DELAY MAY BE CONSIDERED TO BE RANDOM FROM FRAME TO FRAME WITH A UNIFORM DISTRIBUTION OVER THE )00 ! MEASURE OF PERFORMANCE REDUCTION DUE TO ECLIPSING AND RANGE GATE STRADDLE IS FOUND BY 5SING THE UNECLIPSED DETECTION CURVE 0D VS 3. FOR THE WAVEFORM AND SELECT ING A PARTICULAR 3.2 OF INTEREST 3. ALONG WITH ITS CORRESPONDING PROBABILITY OF DETECTION 0D 2EDUCE 3. BY A FACTOR RELATED TO THE RELATIVE OUTPUT hPOWERv OF THE MATCHED FILTER AS A FUNCTION OF AMBIGUOUS RANGE WITHIN THE )00 3EE THE THIRD ROW OF PLOTS IN &IGURE 7ITH THE REDUCED 3.2 DETERMINE THE NEW 0D AS A FUNCTION OF AMBIGUOUS RANGE WITHIN THE )00 FROM THE UNECLIPSED DETECTION CURVE !VERAGE THESE NEW 0D VALUES ACROSS THE )00 4HE RESULT WILL BE A NEW DETECTION CURVE INCLUDING THE AVERAGE EFFECT OF ECLIPSING AND RANGE GATE STRADDLE &OR A FIXED 0D THE DIFFERENCE IN 3.2 BETWEEN THE UNECLIPSED AND THE ECLIPSED DETECTION CURVES IS THE AVERAGE ECLIPSING AND RANGE GATE STRADDLE LOSS 4HIS DIFFERENCE REPRESENTS THE AVERAGE INCREASE IN SIGNAL TO NOISE RATIO REQUIRED TO OBTAIN THE SAME PROBABILITY OF DETECTION WITH ECLIPSING AND STRADDLE AS IN THE CASE WHERE THE TRANSMIT PULSE IS RECEIVED BY A MATCHED GATE WITH NO STRADDLE 3INCE THE DETECTION CURVE CHANGES SHAPE THE LOSS DEPENDS ON THE PROBABILITY OF DETECTION SELECTED WHICH IS DEPICTED IN &IGURE &OR ACCURATE RESULTS ECLIPSING AND RANGE GATE STRADDLE LOSS MUST BE COMPUTED TOGETHER ! LESS ACCURATE APPROXIMATION COMPARES THE AVERAGE SIGNAL TO NOISE RATIO OVER THE INTERPULSE PERIOD WITH THE SIGNAL TO NOISE RATIO OF THE MATCHED CASE )N THE CASE OF . CONTINUOUS RANGE GATES SPANNING THE DURATION OF THE )00 EACH OF WHICH ARE MATCHED TO THE TRANSMIT PULSE WIDTH THE APPROXIMATE AVERAGE ECLIPSING AND STRADDLE LOSS IS
APPROXIMATE ECLIPSING AND RANGE GATE STRADDLLE LOSS
. .
4IME .ORMALIZED BY 2ANGE 'ATE $URATION
.O 2' /VERLAP TT TG TS TB )00 TG
4IME .ORMALIZED BY 2ANGE 'ATE $URATION
2' /VERLAP TT TG TS TB )00 TG
&)'52% #ONCEPT OF ECLIPSING AND RANGE GATE STRADDLE LOSS 4HE TOP ROW OF PLOTS SHOWS THE TRANSMIT PULSE FOR A SINGLE )00 OF A PULSE DOPPLER WAVEFORM WITH A DUTY CYCLE OF 4HE SECOND ROW OF PLOTS SHOWS THE RELATIVE VOLTAGE OF THE MAXIMUM PULSE MATCHED FILTER -& OUTPUT AS A FUNCTION OF RANGE AMBIGUOUS TARGET RETURN WITHIN THE )00 4HE THIRD ROW OF PLOTS SHOWS THE OUTPUT IN TERMS OF RELATIVE POWER
4RANSMIT 0ULSE
-& /UTPUT h6OLTAGEv
-& /UTPUT h0OWERv
4RANSMIT 0ULSE -& /UTPUT h6OLTAGEv -& /UTPUT h0OWERv
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&327 ' /&* #0%3,!#0)'2
0.$#$*+*27.('2'%2*.-
5.%+*/1*-)#-& 20#&&+' 5%+*/1*-)#-& 20#&&+'//0.6 5%+*/1*-)#-& 20#&&+' 5%+*/1*-)#-& 20#&&+' 4'0+#/
"-'%+*/1'& *)-#+2. .*1' #2*.& &)'52% #OMPARISON OF DETECTION PERFORMANCE WITH AND WITHOUT ECLIPSING AND RANGE GATE STRADDLE LOSS 4HE APPROXIMATE PERFORMANCE USING %Q IS ALSO PROVIDED 4HE PERFORMANCE WITH ECLIPSING AND RANGE GATE STRADDLE LOSS WITH THE USE OF OVERLAPPED RANGE GATES IS SHOWN
%Q ASSUMES AN UNMODULATED RECTANGULAR TRANSMIT PULSE SHAPE WITH THE RECEIVE GATE MATCHED TO THE TRANSMIT PULSE WIDTH 4HERE IS NO RANGE GATE OVERLAP 4HE FIRST GATE OF THE . RANGE GATES ARE BLANKED FOR THE TRANSMIT PULSE !S SHOWN IN &IGURE THIS APPROXIMATION IS ONLY VALID FOR A 0D NEAR 4HERE ARE SEVERAL OTHER DETAILS THAT HAVE NOT BEEN INCLUDED IN &IGURE !S SHOWN IN &IGURE A PORTION OF THE FIRST VALID RECEIVE RANGE GATE AND POSSIBLY A PORTION OF THE LAST RANGE GATE IN THE )00 IS TYPICALLY BLANKED TO AVOID RECEIVING TRANSIENTS OF THE TRANSMIT TO RECEIVE AND RECEIVE TO TRANSMIT SWITCHING !LSO IF PULSE COMPRES SION MODULATION IS USED ON THE TRANSMIT PULSE THE RANGE GATE DURATION WILL BE REDUCED TO MATCH THE TRANSMIT PULSE BANDWIDTH !LL OF THESE EFFECTS SHOULD BE INCLUDED WHEN COMPUTING THE ECLIPSING AND RANGE GATE STRADDLE LOSS $OPPLER &ILTER 7EIGHTING ,OSS 4HIS LOSS RESULTS FROM THE INCREASED NOISE BAND WIDTH OF THE DOPPLER FILTERS THAT OCCURS BECAUSE OF FILTER SIDELOBE WEIGHTING 4HE LOSS CAN ALSO BE ACCOUNTED FOR BY AN INCREASE OF THE DOPPLER FILTER NOISE BANDWIDTH INSTEAD OF AS A SEPARATE LOSS $OPPLER &ILTER 3TRADDLE ,OSS 4HIS LOSS IS DUE TO A TARGET NOT ALWAYS BEING IN THE CENTER OF A DOPPLER FILTER )T IS COMPUTED BY ASSUMING A UNIFORMLY DISTRIBUTED TARGET DOP PLER OVER ONE FILTER SPACING AND IS A FUNCTION OF THE DOPPLER FILTER SIDELOBE WEIGHTING 4HIS LOSS CAN BE REDUCED AT THE EXPENSE OF INCREASED PROCESSING BY ZERO PADDING THE COLLECTED DATA AND PERFORMING A HIGHER POINT &&4 TO FORM HIGHLY OVERLAPPED DOPPLER FILTERS
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#&!2 ,OSS 4HIS LOSS IS CAUSED BY AN IMPERFECT ESTIMATE OF THE DETECTION THRESH OLD COMPARED WITH THE IDEAL THRESHOLD 4HE FLUCTUATION IN THE ESTIMATE NECESSITATES THAT THE MEAN THRESHOLD BE SET HIGHER THAN THE IDEAL HENCE A LOSS )T IS ONLY APPLICABLE TO TARGETS 'UARD "LANKING ,OSS 4HIS TARGET SPECIFIC LOSS IS THE DETECTABILITY LOSS IN THE MAIN CHANNEL CAUSED BY SPURIOUS BLANKING FROM THE GUARD CHANNEL 3EE &IGURE 0ROBABILITY OF &ALSE !LARM 2ADAR DETECTION PERFORMANCE IS DETERMINED BY THE DETECTION THRESHOLD WHICH IN TURN IS SET TO PROVIDE A SPECIFIED PROBABILITY OF FALSE ALARMn !S DESCRIBED IN 3ECTION PULSE DOPPLER RADARS OFTEN EMPLOY A MULTILOOK DETECTION CRITERION TO RESOLVE RANGE AMBIGUITIES 4HIS CAN BE ACCOM PLISHED WITH LINEAR &- RANGING AS IN THE (273 WAVEFORM OR - OF . RANGING USED BY -273 4HESE AMBIGUITY RESOLUTION TECHNIQUES DICTATE HOW THE PROBABILITY OF FALSE ALARM PER RANGE DOPPLER CELL IS COMPUTED 4HESE CALCULATIONS ASSUME A NOISE LIMITED ENVIRONMENT &OR (273 DIFFERENT LINEAR &- SLOPES ARE APPLIED TO LOOKS THROUGH M OF A M LOOK DWELL WHERE M IS TYPICALLY 4HE 02& IS HIGH ENOUGH FOR AT MOST ONLY A DOPPLER SIGN AMBIGUITY $ETECTIONS IN LOOKS THROUGH M MUST CORRELATE IN DOPPLER WITH DETECTIONS IN THE FIRST LOOK WHICH HAS NO SLOPE ! DOPPLER CORRELATION WINDOW IS SET EQUAL TO THE MAXIMUM DOPPLER OFFSET DUE TO LINEAR &- RANGING FROM A TARGET AT THE MAXIMUM INSTRUMENTED RANGE &OR DOPPLER ONLY CORRELATION THE 0&! PER RANGE DOPPLER CELL TO PROVIDE A SPECIFIED FALSE REPORT TIME IS
0&!
³ ¤ ´ 4D LN ¥ ´ ¥ . R ¥ ¤ M³ ´ M ¥¦ ¥¦ N´µ . F . &- 4&2 µ´
M
WHERE .R NUMBER OF INDEPENDENT RANGE SAMPLES PROCESSED PER )00 .F N UMBER OF INDEPENDENT DOPPLER FILTERS VISIBLE IN THE DOPPLER PASSBAND NUMBER OF UNBLANKED FILTERS&&4 WEIGHTING FACTOR 4D TOTAL DWELL TIME OF THE MULTIPLE 02&S INCLUDING POSTDETECTION INTEGRATION IF ANY SPACE CHANGE AND ANY DEAD TIME N NUMBER OF LOOKS IN A DWELL TIME M NUMBER OF DETECTIONS REQUIRED FOR A TARGET REPORT FOR A TYPICAL (273 DWELL N AND M ¤ M³ ¥¦ N´µ BINOMIAL COEFFICIENT N;MN M = 4&2 FALSE REPORT TIME PER -ARCUMS DEFINITION WHERE THE PROBABILITY IS THAT AT LEAST ONE FALSE REPORT WILL OCCUR IN THE FALSE REPORT TIME THIS CAN BE RELATED TO THE AVERAGE TIME 4!6' BETWEEN FALSE REPORTS BY 4&2 y 4!6' LN .&- K&- MAX2MAXC NUMBER OF INDEPENDENT DOPPLER FILTERS IN THE DOPPLER CORRELATION WINDOW K&- MAX STEEPEST LINEAR &- SLOPE MAGNITUDE 2MAX MAXIMUM INSTRUMENTED RANGE
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!LERT#ONFIRM INCREASES SENSITIVITY BY ALLOWING MORE FALSE ALARMS IN !LERT AND RELY ING ON #ONFIRM TO REJECT THOSE FALSE ALERTS 4HE !LERT#ONFIRM COMBINATION IS DESIGNED TO PROVIDE THE SAME FALSE REPORT TIME 4&2 AS A CONVENTIONAL WAVEFORM ! SPECIFIED FRACTIONAL INCREASE & IN FRAME TIME ACCOUNTS FOR THE EXECUTION OF #ONFIRM DWELLS TO REJECT FALSE !LERT DETECTIONS & IS ON THE ORDER OF n 7HEN USING A 63 !LERT AND A LOOK (273 #ONFIRM THE PROBABILITY OF FALSE ALARM PER RANGE DOPPLER CELL 0&! A AND 0&! C FOR !LERT AND #ONFIRM RESPECTIVELY IS
0&! A
4D A LN . R A . F A4&2 A
0&! C
& ³ ¤ 4D C LN r . R C ¥¦ . F CUE . && ´µ 4&2
WHERE 4D A TOTAL !LERT DWELL TIME .R A NUMBER OF INDEPENDENT RANGE SAMPLES PROCESSED PER )00 IN !LERT .F A NUMBER OF INDEPENDENT DOPPLER FILTERS VISIBLE IN THE !LERT DOPPLER PASSBAND 4&2 A 4D C & !LERT FALSE REPORT TIME 4D C TOTAL #ONFIRM DWELL TIME & FRACTIONAL INCREASE IN FRAME TIME ALLOCATED TO #ONFIRM n .R C NUMBER OF INDEPENDENT RANGE SAMPLES PROCESSED PER )00 IN #ONFIRM .F CUE NUMBER OF INDEPENDENT DOPPLER FILTERS IN THE #ONFIRM WINDOW CENTERED ABOUT THE DOPPLER OF THE !LERT DETECTION CUE .&- NUMBER OF INDEPENDENT DOPPLER FILTERS IN #ONFIRM LINEAR &- RANGING DOPPLER CORRELATION WINDOW 4&2 OVERALL !LERT#ONFIRM FALSE REPORT TIME 4HE - OF . RANGING USED IN -273 REQUIRES CORRELATION IN RANGE AND CAN BE VIEWED AS A BINARY DETECTOR -273 IS TYPICALLY A MEDIUM 02& WAVEFORM WITH RANGE AND DOP PLER AMBIGUITIES $OPPLER IS USED FOR CLUTTER MITIGATION IN EACH LOOK AND THE DOPPLER AMBIGUITY MAY NOT NEED TO BE RESOLVED SINCE THE TRACKER CAN DETERMINE RANGE RATE FROM SUCCESSIVE DWELLS ! TYPICAL -273 - OF . CORRELATION WOULD BE THREE DETECTIONS OUT OF EIGHT LOOKS IE M AND N &OR RANGE ONLY CORRELATION THE 0&! IN EACH RANGE DOPPLER CELL IS GIVEN BY M
0&!
§ ¶ ¨¨ 4D LN ·· . F ¨¤ M³ · ¨¥¦ N´µ . RU4&2 · © ¸
WHERE .RU NUMBER OF INDEPENDENT RANGE SAMPLES IN THE OUTPUT UNAMBIGUOUS RANGE INTERVAL DISPLAY RANGERANGE GATE SIZE
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&OR BETTER FALSE ALARM REJECTION DOPPLER CORRELATION CAN BE USED FOR -273 )N THE CASE WHERE BOTH RANGE AND DOPPLER CORRELATION ARE USED THE REQUIRED 0&! IS M
0&!
§ ¶ ¨ · 4D LN · ¨ ¨¤ M³ M · ¨¥¦ N´µ . FU . RU4&27 · © ¸
WHERE .FU NUMBER OF INDEPENDENT DOPPLER FILTERS IN THE UNAMBIGUOUS DOPPLER REGION 7 WIDTH IN DOPPLER FILTERS OF THE CORRELATION WINDOW APPLIED TO DETECTIONS FOLLOWING INITIAL DETECTION 0ROBABILITY OF $ETECTION 5SING THE 0&! PER RANGE DOPPLER CELL THE PROBABILITY OF DETECTION 0D OF A GIVEN LOOK CAN BE DETERMINED FOR A GIVEN TARGET 3.2 THE NUM BER OF #0)S NONCOHERENTLY INTEGRATED .PDI AND THE TARGET 2#3 FLUCTUATION MODEL ASSUMED 4HE INVERSE PROBLEM OF DETERMINING THE REQUIRED 3.2 FOR A GIVEN 0D CAN BE SOLVED VIA APPROXIMATIONS 5NIVERSAL DETECTION EQUATIONS HAVE BEEN PUBLISHED THAT PROVIDE REASONABLY ACCURATE RESULTS AND ARE REPRODUCED HERE !GAIN THE ASSUMPTION THAT TARGETS ARE IN A GAUSSIAN NOISE LIMITED ENVIRONMENT IS MADE &OR A SINGLE LOOK WITH .PDI #0)S NONCOHERENTLY INTEGRATED AND A SPECIFIED 0&! PER RANGE DOPPLER CELL THE 0D AS A FUNCTION OF 3.2 FOR A -ARCUM NONFLUCTUATING TARGET CAN BE APPROXIMATED AS 0D 3.2 0&! . PDI
¤ ERFC ¥ LN; 0&! 0&! = ¦
. PDI . PDI ³
. PDI 3.2
´ µ
WHERE ERFCq IS THE COMPLEMENTARY ERROR FUNCTION 4HE REQUIRED 3.2 AS A FUNCTION OF 0D FOR A -ARCUM TARGET IS APPROXIMATED AS
3.2 REQD 0D 0&! . PDI
H H . PDI . PDI
. PDI
WHERE
H LN; 0&! 0&! = SIGN 0D LN; 0D 0D =
&OR 3WERLING FLUCTUATING TARGET MODELS THE 0D AND REQUIRED 3.2 CAN BE APPROXI MATED RESPECTIVELY AS
§ ¶ ¨ + 0 . . N · E M &! PDI PDI 0D 3.2 0&! . PDI NE + M ¨ NE · . PDI ¨ · 3.2 ¨© ·¸ NE
§ + M 0D NE . PDI NE ¶ NE 3.2 0D 0&! . PDI NE ¨
· + M 0D NE ¨© ·¸ . PDI
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WHERE ª . PDI NE « ¬ . PDI
FOR 3WERLING ) TARGGET CHI SQUARED DISTRIBUTION WITH DEGRESSS OF FREEDOM FOR 3WERLING )) TARGET CHI SSQUARED DISTRIBUTION WITH . PDI DEGRESS OF FREEDOM FOR 3WERLING ))) TARGET CHI SQUARRED DISTRIBUTION WITH DEGRESS OF FREEDOM FOR 3WERLING )6 TARGET CHI SQUARED DISTRIIBUTION WITH . PDI DEGRESS OF FREEDOM
¤ D X³ + M X D 0 ¥ ´ CHI SQUARED DISTRIBUTION SURVIVAL FUNCTION ¦ µ + M P D INVERSE CHI SQUARED DISTRIBUTION SURVIVAL FUNCTION X
G A X 0A X ' A
¯ TA E T DT REGULARIZED LOWER INCOMPLETE GAMMA FUNCTION c ¯ TA E T DT
4HE INTEGRAL OF THE CHI SQUARED DISTRIBUTION +MX D AND ITS INVERSE + M P D ARE OFTEN INCLUDED IN MATHEMATICAL COMPUTATION SOFTWARE PACKAGES 7HEN - OF . DETECTION IE BINARY DETECTION IS USED WITHIN A DWELL THE PROBABIL ITY OF DETECTION FOR EACH LOOK 0D LOOK IS USED TO COMPUTE THE PROBABILITY OF DETECTION FOR A DWELL 0D DWELL 7HEN A DWELL REQUIRES M DETECTIONS OUT OF N LOOKS FOR A TARGET DECLARATION THE 0D DWELL IS N
0D DWELL
¤ K³
£ ¥¦N´µ 0DK LOOK 0D LOOK N K
K M
&OR !LERT#ONFIRM DETECTION PERFORMANCE THE 0D FOR THE !LERT DWELL AND THE 0D FOR THE #ONFIRM DWELL ARE INDIVIDUALLY COMPUTED AS A FUNCTION OF 3.2 #ARE MUST BE TAKEN TO NORMALIZE THE 3.2 TO ACCOUNT FOR DIFFERENCES IN DOPPLER FILTER BANDWIDTH BETWEEN THE !LERT AND #ONFIRM WAVEFORMS 4HE MULTIPLICATION OF NORMALIZED PROB ABILITY OF DETECTION CURVE FOR THE !LERT DWELL WITH THAT OF THE #ONFIRM DWELL RESULTS IN AN ESTIMATE OF THE COMPOSITE 0D VS 3. CURVE FOR !LERT#ONFIRM -ORE ACCURATE RESULTS MUST INCLUDE THE EFFECTS OF LATENCY BETWEEN THE !LERT AND #ONFIRM DWELLS 3EARCH DETECTION PERFORMANCE IS OFTEN CHARACTERIZED BY THE CUMULATIVE PROBABIL ITY OF DETECTION 0D CUM WHICH IS DEFINED AS THE PROBABILITY THAT THE RADAR WILL DETECT A CLOSING TARGET AT LEAST ONCE BY THE TIME THE TARGET HAS CLOSED TO A SPECIFIED RANGE 0D CUM IS ONLY DEFINED FOR CLOSING TARGETS 4HE CUMULATIVE PROBABILITY OF DETECTION FOR THE KTH SCAN OR FRAME IS K
0D CUM ;K = ; 0D SS ;I== I
0D CUM ;K = 0D SS ;K = 0D CUM ;K =
WHERE 0D SS;K= IS THE SINGLE SCAN PROBABILITY OF DETECTION ON THE KTH SCAN 4HE ACCUMULA TION OF SINGLE SCAN PROBABILITY OF DETECTIONS IS STARTED AT A RANGE WHERE THE TARGETS 0D SS IS APPROXIMATELY 4HERE IS AN OPTIMAL SEARCH FRAME TIME FOR CUMULATIVE DETECTION PERFORMANCE ! BALANCE MUST BE ACHIEVED ! SHORT FRAME TIME LIMITS THE AMOUNT OF ENERGY PLACED ON TARGET PER DWELL AND LOWERS THE SINGLE SCAN 0D ! LONG FRAME TIME ALLOWS THE TARGET TO CLOSE IN RANGE MORE BETWEEN REVISITS THUS LOWERING THE BENEFIT OF THE ACCUMULATION &IGURE ILLUSTRATES THE DIFFERENCE BETWEEN SINGLE SCAN AND CUMULATIVE PROBABILITY OF DETECTION
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$ $ #%
!# "" !
&)'52% 3INGLE SCAN VS CUMULATIVE 0D AS A FUNCTION OF RANGE FOR A FIXED RADIAL VELOCITY MOVING TARGET
#LUTTER LIMITED #ASE 4HE FOREGOING DISCUSSION ASSUMED THAT THE TARGET FELL IN THE NOISE LIMITED IE CLUTTER FREE PART OF THE DOPPLER BAND )F THE TARGET FALLS IN THE SIDELOBE CLUTTER REGION THE RANGE PERFORMANCE WILL BE DEGRADED SINCE THE TOTAL INTERFERENCE POWER SYSTEM NOISE PLUS CLUTTER AGAINST WHICH THE TARGET MUST COMPETE IS INCREASED 4HE FOREGOING DISCUSSION CAN BE APPLIED TO THE SIDELOBE CLUT TER REGION HOWEVER BY INTERPRETING 2O AS THE RANGE WHERE THE SIGNAL IS EQUAL TO SIDELOBE CLUTTER PLUS SYSTEM NOISEn 4HE #&!2 LOSS MAY ALSO BE HIGHER OWING TO THE INCREASED VARIABILITY OF THE THRESHOLD WHEN THE CLUTTER VARIES OVER THE TARGET DETECTION REGION -ORE ACCURATE CALCULATIONS OF DETECTION PERFORMANCE IN THE SIDE LOBE CLUTTER LIMITED CASE SHOULD INCLUDE THE PROPER CLUTTER 2#3 FLUCTUATION MODELS AND #&!2 TECHNIQUES
-/Ê"Ê , 6/" !%3! !$ !'# !- #!'# #&!2 #.2 #0) #7 $!: $%, D"C $# $&4
ACTIVE ELECTRONICALLY SCANNED ARRAY ANALOG TO DIGITAL AUTOMATIC GAIN CONTROL AMPLITUDE MODULATION CLUTTER AUTOMATIC GAIN CONTROL CONSTANT FALSE ALARM RATE CLUTTER TO NOISE POWER RATIO COHERENT PROCESSING INTERVAL CONTINUOUS WAVE DELTA AZIMUTH ANTENNA BEAM USED FOR MONOPULSE ANGLE ESTIMATION DELTA ELEVATION ANTENNA BEAM USED FOR MONOPULSE ANGLE ESTIMATION DECIBELS WITH RESPECT TO THE CARRIER DIRECT CURRENT DISCRETE &OURIER TRANSFORM
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$0$ DIGITAL PRODUCT DETECTOR %3! ELECTRONICALLY SCANNED ARRAY &&4 FAST &OURIER TRANSFORM &- FREQUENCY MODULATION &- #7 FREQUENCY MODULATED CONTINUOUS WAVE (273 HIGH 02& RANGE WHILE SEARCH ) INPHASE )& INTERMEDIATE FREQUENCY ).3 INERTIAL NAVIGATION SYSTEM )00 INTERPULSE PERIOD ,.! LOW NOISE AMPLIFIER ,/ LOCAL OSCILLATOR -& MATCHED FILTER -273 MEDIUM 02& RANGE WHILE SEARCH -4) MOVING TARGET INDICATION -44 MULTIPLE TARGET TRACKING .!'# NOISE AUTOMATIC GAIN CONTROL 0!- PULSE AMPLITUDE MODULATION 0D PROBABILITY OF DETECTION 0# PULSE COMPRESSION 0$) POSTDETECTION INTEGRATION NONCOHERENT INTEGRATION 0&! PROBABILITY OF FALSE ALARM 0- PHASE MODULATION 00- PULSE POSITION MODULATION 02& PULSE REPETITION FREQUENCY 07- PULSE WIDTH MODULATION 1 QUADRATURE 2#3 RADAR CROSS SECTION 2&) RADIO FREQUENCY INTERFERENCE RMS ROOT MEAN SQUARE 2& RADIO FREQUENCY 20 RECEIVER PROTECTOR 273 RANGE WHILE SEARCH 3 SUM RECEIVE ANTENNA BEAM PRIMARY BEAM USED FOR DETECTION 3," SIDELOBE BLANKER 3.2 SIGNAL TO NOISE POWER RATIO 34# SENSITIVITY TIME CONTROL 473 TRACK WHILE SCAN 42 TRANSMITRECEIVE 63 VELOCITY SEARCH
, ,
)%%% 3TANDARD 2ADAR $EFINITIONS )%%% 3TD n P $ # 3CHLEHER -4) AND 0ULSED $OPPLER 2ADAR .ORWOOD -! !RTECH (OUSE )NC PP IXnX & % .ATHANSON 2ADAR $ESIGN 0RINCIPLES ND %D .EW 9ORK -C'RAW (ILL PP n - ) 3KOLNIK )NTRODUCTION TO 2ADAR 3YSTEMS #HAPTER RD %D .EW 9ORK -C'RAW (ILL ' 7 3TIMSON )NTRODUCTION TO !IRBORNE 2ADAR #HAPTER 0ART 8 ND %D 2ALEIGH .# 3CI4ECH 0UBLISHING )NC
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0 ,ACOMME * (ARDANGE * -ARCHAIS AND % .ORMANT !IR AND 3PACEBORNE 2ADAR 3YSTEMS !N )NTRODUCTION #HAPTER .ORWICH .9 7ILLIAM !NDREW 0UBLISHING ,,# 3 ! (OVANESSIAN 2ADAR 3YSTEM $ESIGN AND !NALYSIS #HAPTER .ORWOOD -! !RTECH (OUSE )NC - ) 3KOLNIK 2ADAR !PPLICATIONS .EW 9ORK )%%% 0RESS 2 * $OVIAK $ 3 :RNIC AND $ 3 3IRMANS h$OPPLER WEATHER RADAR v IN 0ROCEEDINGS OF THE )%%% VOL NO PP n 0 -AHAPATRA !VIATION 7EATHER 3URVEILLANCE 3YSTEMS !DVANCED 2ADAR AND 3URFACE 3ENSORS FOR &LIGHT 3AFETY AND !IR 4RAFFIC -ANAGEMENT ,ONDON 5+ 4HE )NSTITUTION OF %LECTRICAL %NGINEERS + # /VERMAN + ! ,EAHY 4 7 ,AWRENCE AND 2 * &RITSCH h4HE FUTURE OF SURFACE SURVEILLANCE REVOLUTIONIZING THE VIEW OF THE BATTLEFIELD v IN 2ECORD OF THE )%%% )NTERNATIONAL 2ADAR #ONFERENCE -AY n PP n $EFENSE 3CIENCE "OARD &UTURE $O$ !IRBORNE (IGH &REQUENCY 2ADAR .EEDS2ESOURCES /FFICE OF THE 5NDER 3ECRETARY OF $EFENSE FOR !CQUISITION AND 4ECHNOLOGY 7ASHINGTON $# !PRIL - ) 3KOLNIK )NTRODUCTION TO 2ADAR 3YSTEMS RD %D .EW 9ORK -C'RAW (ILL PP n ' 7 3TIMSON )NTRODUCTION TO !IRBORNE 2ADAR ND %D 2ALEIGH .# 3CI4ECH 0UBLISHING )NC PP n & # 7ILLIAMS AND - % 2ADANT h!IRBORNE RADAR AND THE THREE 02&S v -ICROWAVE *OURNAL *ULY AND REPRINTED IN - ) 3KOLNIK 2ADAR !PPLICATIONS .EW 9ORK )%%% 0RESS PP n $ # 3CHLEHER -4) AND 0ULSED $OPPLER 2ADAR !RTECH (OUSE )NC PP n ' -ORRIS AND , (ARKNESS !IRBORNE 0ULSED $OPPLER 2ADAR ND %D .ORWOOD -! !RTECH (OUSE )NC P 7 ( ,ONG AND + ! (ARRIGER h-EDIUM 02& FOR THE !.!0' RADAR v IN 0ROCEEDINGS OF THE )%%% VOL ISSUE &EBRUARY PP n " #ANTRELL h!$# SPURIOUS SIGNAL MITIGATION IN RADAR BY MODIFYING THE ,/ v IN 0ROCEEDINGS OF THE )%%% 2ADAR #ONFERENCE !PRIL n PP n ( (OMMEL AND ( &ELDLE h#URRENT STATUS OF AIRBORNE ACTIVE PHASED ARRAY !%3! RADAR SYSTEMS AND FUTURE TRENDS v IN )%%% -44 3 )NTERNATIONAL -ICROWAVE 3YMPOSIUM $IGEST *UNE n PP n 3 - 3HERMAN -ONOPULSE 0RINCIPLES AND 4ECHNIQUES .ORWOOD -! !RTECH (OUSE )NC , % 0ELLON h! DOUBLE .YQUIST DIGITAL PRODUCT DETECTOR FOR QUADRATURE SAMPLING v )%%% 4RANSACTIONS ON 3IGNAL 0ROCESSING VOL ISSUE PP n *ULY ' -INKLER #&!2 4HE 0RINCIPLES OF !UTOMATIC 2ADAR $ETECTION IN #LUTTER "ALTIMORE -$ -AGELLAN "OOK #OMPANY 2 .ITZBERG 2ADAR 3IGNAL 0ROCESSING AND !DAPTIVE 3YSTEMS #HAPTER .ORWOOD -! !RTECH (OUSE )NC - 7EISS h!NALYSIS OF SOME MODIFIED CELL AVERAGING #&!2 PROCESSORS IN MULTIPLE TARGET SITUA TIONS v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 NO PP n *ANUARY 0 0 'ANDHI AND 3 ! +ASSAM h!NALYSIS OF #&!2 PROCESSORS IN NONHOMOGENEOUS BACKGROUND v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL NO *ULY * &ARRELL AND 2 4AYLOR h$OPPLER RADAR CLUTTER v )%%% 4RANSACTIONS ON !ERONAUTICAL .AVIGATIONAL %LECTRONICS VOL !.% PP n 3EPTEMBER AND REPRINTED IN $ + "ARTON #7 AND $OPPLER 2ADARS 3ECTION 6) 6OL .ORWOOD -! !RTECH (OUSE )NC PP n , (ELGOSTAM AND " 2ONNERSTAM h'ROUND CLUTTER CALCULATION FOR AIRBORNE DOPPLER RADAR v )%%% 4RANSACTIONS ON -ILITARY %LECTRONICS VOL -), PP n *ULYn/CTOBER
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! , &RIEDLANDER AND , * 'REENSTEIN h! GENERALIZED CLUTTER COMPUTATION PROCEDURE FOR AIRBORNE PULSE DOPPLER RADARS v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 PP n *ANUARY AND REPRINTED IN $ + "ARTON #7 AND $OPPLER 2ADARS 3ECTION 6) 6OL .ORWOOD -! !RTECH (OUSE )NC PP n - " 2INGEL h!N ADVANCED COMPUTER CALCULATION OF GROUND CLUTTER IN AN AIRBORNE PULSE DOPPLER RADAR v IN .!%#/. 2ECORD PP n AND REPRINTED IN $ + "ARTON #7 AND $OPPLER 2ADARS 3ECTION 6) 6OL .ORWOOD -! !RTECH (OUSE )NC PP n 2 , -ITCHELL 2ADAR 3IGNAL 3IMULATION #HAPTER .ORWOOD -! !RTECH (OUSE )NC * + *AO AND 7 " 'OGGINS h%FFICIENT CLOSED FORM COMPUTATION OF AIRBORNE PULSE DOPPLER CLUT TER v IN 0ROCEEDINGS OF THE )%%% )NTERNATIONAL 2ADAR #ONFERENCE 7ASHINGTON $# PP n 7 ! 3KILLMAN 3)'#,54 3URFACE AND 6OLUMETRIC #LUTTER TO .OISE *AMMER AND 4ARGET 3IGNAL TO .OISE 2ADAR #ALCULATION 3OFTWARE AND 5SERS -ANUAL .ORWOOD -! !RTECH (OUSE )NC PP n $ # 3CHLEHER -4) AND $OPPLER 2ADAR .ORWOOD -! !RTECH (OUSE )NC PP n & * (ARRIS h/N THE USE OF WINDOWS FOR HARMONIC ANALYSIS WITH THE DISCRETE &OURIER TRANSFORM v IN 0ROCEEDINGS OF THE )%%% VOL NO *ANUARY PP n 7 ! 3KILLMAN 2ADAR #ALCULATIONS 5SING THE 4) 0ROGRAMMABLE #ALCULATOR .ORWOOD -! !RTECH (OUSE )NC P 2 % :IEMER AND * ! :IEGLER h-4) IMPROVEMENT FACTORS FOR WEIGHTED $&4S v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 PP n -AY ( 2 7ARD h$OPPLER PROCESSOR REJECTION OF AMBIGUOUS CLUTTER v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 *ULY AND REPRINTED IN $ + "ARTON #7 AND $OPPLER 2ADARS 3ECTION )6n 6OL .ORWOOD -! !RTECH (OUSE )NC PP n 2 ( &LETCHER AND $ 7 "URLAGE h!N INITIALIZATION TECHNIQUE FOR IMPROVED -4) PERFORMANCE IN PHASED ARRAY RADAR v IN 0ROCEEDINGS OF THE )%%% VOL $ECEMBER PP n $ ( (ARVEY AND 4 , 7OOD h$ESIGN FOR SIDELOBE BLANKING SYSTEMS v IN 0ROCEEDINGS OF THE )%%% )NTERNATIONAL 2ADAR #ONFERENCE 7ASHINGTON $# PP n , -AISEL h0ERFORMANCE OF SIDELOBE BLANKING SYSTEMS v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 PP n -ARCH ( - &INN 2 3 *OHNSON AND 0 : 0EEBLES h&LUCTUATING TARGET DETECTION IN CLUTTER USING SID ELOBE BLANKING LOGIC v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 PP n -AY ! &ARINA !NTENNA BASED 3IGNAL 0ROCESSING 4ECHNIQUES FOR 2ADAR 3YSTEMS #HAPTER .ORWOOD -! !RTECH (OUSE )NC PP n $ ! 3HNIDMAN AND 3 3 4OUMODGE h3IDELOBE BLANKING WITH INTEGRATION AND TARGET FLUCTUA TION v )%%% 4RANSACTIONS ON !EROSPACE AND %LECTRONIC 3YSTEMS VOL NO PP n *ULY $ ( -OONEY h0OST $ETECTION 34# IN A -EDIUM 02& 0ULSE $OPPLER 2ADAR v 53 0ATENT *UNE & % .ATHANSON 2ADAR $ESIGN 0RINCIPLES ND %D .EW 9ORK -C'RAW (ILL )NC PP n * " 4SUI $IGITAL 4ECHNIQUES FOR 7IDEBAND 2ECEIVERS ND %D 2ALEIGH .# 3CI4ECH 0UBLISHING #OMPANY PP n , 0 'OETZ AND 7 ! 3KILLMAN h-ASTER OSCILLATOR REQUIREMENTS FOR COHERENT RADAR SETS v IN )%%% .!3! 3YMPOSIUM ON 3HORT 4ERM &REQUENCY 3TABILITY .!3! 30 .OVEMBER 2 3 2AVEN h2EQUIREMENTS FOR MASTER OSCILLATORS FOR COHERENT RADAR v IN 0ROCEEDINGS OF THE )%%% VOL &EBRUARY PP n AND REPRINTED IN $ + "ARTON #7 AND $OPPLER 2ADARS 3ECTION 6 ) 6OL !RTECH (OUSE )NC .ORWOOD -! PP n 2 3 2AVEN #ORRECTION TO h2EQUIREMENTS FOR MASTER OSCILLATORS FOR COHERENT RADAR v IN 0ROCEEDINGS OF THE )%%% VOL ISSUE !UGUST P
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x°£Ê /," 1 /" )N SPITE OF MORE THAN A HALF CENTURY OF IMPROVEMENTS IN RADAR PERFORMANCE AND RELIABILITY THE EFFORT REQUIRED FOR DEPLOYMENT OPERATION AND MAINTENANCE OF MOST RADARS IS SUBSTANTIAL &URTHERMORE THE POWER APERTURE PRODUCT IS NEVER AS LARGE AS DESIRED 4HE FORWARD PROJECTED AREA AS WELL AS AVIONICS WEIGHT IS VERY COSTLY IN MOST FIGHTER AIRCRAFT PARAMETERS 4HESE PARAMETERS HAVE MOTIVATED USERS BUYERS AND DESIGNERS TO WANT MORE FUNCTIONS IN A SINGLE RADAR AND ITS COMPLEMENTARY PROCESSING SUITE !S A RESULT MOST MODERN FIGHTER RADARS ARE MULTIFUNCTIONALPROVIDING RADAR NAVIGATION LANDING AIDS DATA LINK AND %LECTRONIC #OUNTER -EASURES %#- FUNC TIONS 4HE PRIMARY ENABLER FOR MULTIFUNCTIONAL RADAR IS SOFTWARE DEFINED SIGNAL AND DATA PROCESSING FIRST INTRODUCED IN THE MID Sn 3OFTWARE PROGRAMMABILITY ALLOWS MANY RADAR SYSTEM MODES TO BE PERFORMED USING THE SAME 2& HARDWARE )N ADDITION MODERN NAVIGATION AIDS WORK SO WELL THAT EACH RADAR MODE IS DEFINED BY ITS EARTH SITUATION GEOMETRY WITH ALMOST ALL WAVEFORM PARAMETERS SET BY LOCAL EARTH CONDITIONS 4HE MODERN RADAR OFTEN IS NET CENTRIC USING AND PROVIDING DATA TO A COMMUNICATIONS NETWORK AND WHERE SUITABLY EQUIPPED HAS ITS OWN )NTERNET PROTOCOL )0 ADDRESS -ULTIFUNCTIONALITY IS NOT DEPENDENT ON ANTENNA TYPE )N FACT THE MECHANICALLY SCANNED !.!0' AND RADARS HAVE DEMONSTRATED MULTIFUNCTIONALITY IN COMBAT (OWEVER MULTIFUNCTIONALITY IS FACILITATED BY !CTIVE %LECTRONICALLY 3CANNED !NTENNA !%3! ARRAYS 4HE MULTIFUNCTIONAL !%3! RADAR IN THE &! %& FIGHTER IS SHOWN WITH A PROTECTIVE COVER OVER THE ARRAY IN &IGURE 4HE !%3! IS SHAPED AND CANTED UPWARD TO AID IN SOME MODES AND TO MINIMIZE REFLECTIONS TO ENEMY RADARS
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4HIS CHAPTER ADDRESSES WHAT SIGNALS ARE EMITTED AND WHY THEY ARE NEEDED IN A -ULTIFUNCTIONAL &IGHTER !IRCRAFT 2ADAR -&!2 4HE WHY BEGINS WITH TYPICAL MIS SIONS WHICH SHOWS THE GEOMETRY THAT GIVES RISE TO EACH RADAR MODE AND WAVEFORM LISTS REPRESENTATIVE RADAR MODES AND SHOWS TYPICAL MODERN AIRBORNE RADAR MODE INTER LEAVING AND TIMING 4HE ANSWER TO WHAT IS PROVIDED BY TYPICAL WAVEFORM VARIATIONS AND A FEW EXAMPLES 4HE EXAMPLES ARE NOT FROM ANY SINGLE RADAR BUT ARE A COMPOSITE OF MODERN RADARS 4HE GENERAL -&!2 IDEA IS ILLUSTRATED IN &IGURE )T SHOWS TIME MULTIPLEXED OPERATIONS FOR AIR TO AIR ! ! AIR TO SURFACE ! 3 ELECTRONIC WARFARE %7 AND COMMUNICATION FROM THE SAME RADIO FREQUENCY 2& HARDWARE AND PROCESS ING COMPLEX OFTEN OVER MOST OF THE MICROWAVE BAND 3OMETIMES MULTIPLE FUNCTIONS CAN BE PERFORMED SIMULTANEOUSLY IF A COMMON WAVEFORM IS USED 4HE ANTENNA APERTURE USUALLY HAS MULTIPLE PHASE CENTERS ENABLING MEASUREMENT FOR 3PACE 4IME !DAPTIVE 0ROCESSING 34!0 $ISPLACED 0HASE #ENTER !NTENNA $0#!
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PROCESSING CONVENTIONAL MONOPULSE ANGLE TRACKING JAMMER NULLING AND OUT OF BAND ANGLE OF ARRIVAL !/! ESTIMATION 4HE OPTIMUM PLACEMENT OF PHASE CENTERS IS AN IMPORTANT DESIGN TRADEOFF ! PHASE CENTER IS AN ANTENNA APERTURE CHANNEL WHICH IS OFF SET IN SPACE AND PROVIDES A PARTIALLY OR FULLY INDEPENDENT MEASUREMENT OF AN INCOMING ELECTROMAGNETIC WAVEFRONT &OR EXAMPLE A ONE DIMENSIONAL PHASE MONOPULSE HAS TWO PHASE CENTERS A TWO DIMENSIONAL PHASE MONOPULSE HAS FOUR PHASE CENTERS $0#! HAS TWO OR MORE PHASE CENTERS A RADAR WITH A GUARD HORN FOR SIDELOBE SUPPRESSION HAS TWO PHASE CENTERS AND AN ADAPTIVE ARRAY MAY HAVE MANY PHASE CENTERSn 34!0 IS AN EXTENSION OF THE CLASSIC THEORY FOR A MATCHED FILTER IN THE PRESENCE OF NONnWHITE NOISE WHICH INCLUDES BOTH TIME AND SPACE /VERALL WEAPON SYSTEM REQUIREMENTS USUALLY FAVOR 8 OR +U BAND FOR THE OPERATING FREQUENCY OF A -&!2 )N ADDITION THE -&!2 APERTURES AND ASSOCIATED TRANSMITTER ARE USUALLY THE LARGEST ON AN AIRCRAFT AND HENCE CAN CREATE THE HIGHEST %FFECTIVE 2ADIATED 0OWER %20 FOR JAMMING ADVERSARY RADARS AND DATA LINKS WHERE THESE ARE IN BAND -ULTIFUNCTIONAL 2ADAR !RCHITECTURE !N EXAMPLE -&!2 BLOCK DIAGRAM IS SHOWN IN &IGURE 4HE MODERN INTEGRATED AVIONIC SUITE CONCEPT BLURS THE BOUNDARIES BETWEEN TRADITIONAL RADAR FUNCTIONS AND OTHER SENSORS COUNTERMEASURES WEAPONS AND COMMUNICATIONS SEE &IGURES AND LATER IN THE CHAPTER 4HERE IS A MICROWAVE AND 2& SUITE AN ELECTRO OPTICAL INFRARED ULTRAVIOLET %/ SUITE A STORES MANAGEMENT SUITE A CONTROLS AND DISPLAYS SUITE A MULTIPLY REDUNDANT VEHICLE MANAGEMENT SUITE AND A MULTIPLY REDUNDANT PROCESSOR COMPLEX %ACH MICROWAVE ANDOR 2& APERTURE MAY HAVE SOME EMBEDDED SIGNAL CONDITIONING BUT THEN MAY BE MULTIPLEXED TO STANDARDIZED COMMON DESIGN 2& FILTER FREQUENCY REF ERENCE ANALOG TO DIGITAL CONVERSION !$ INPUT OUTPUT )/ AND CONTROL MODULES ! SIMILAR DESIGN CONCEPT IS USED FOR THE ELECTRO OPTICAL %/ SENSORS STORES MANAGEMENT
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VEHICLE MANAGEMENT PILOT VEHICLE INTERFACE AND INTEGRATED CORE PROCESSING SUITE 4HERE IS SUBSTANTIAL DATA TRAFFIC BETWEEN THE CORE PROCESSING AND THE SENSORS TO PROVIDE POINT ING CUEING TRACKING AND MULTISENSOR FUSION OF DETECTIONS 4HE AIM OF THIS APPROACH IS TO PROVIDE A SHARED POOL OF COMPUTATIONAL RESOURCES WHICH MAY BE FLEXIBLY ALLOCATED BETWEEN SENSORS AND FUNCTIONS 4HE SENSORS MAY CONTAIN DEDICATED MOTION SENSING BUT LONG TERM NAVIGATION IS PRO VIDED BY THE VEHICLE MANAGEMENT GLOBAL POSITIONING SYSTEM AND INERTIAL NAVIGATION SYS TEM '03).3 4HE ON RADAR MOTION SENSING MUST SENSE POSITION TO A FRACTION OF THE TRANSMITTED WAVELENGTH OVER THE COHERENT PROCESSING INTERVAL 4HIS IS USUALLY DONE WITH INERTIAL SENSORS SUCH AS ACCELEROMETERS AND GYROS WITH VERY HIGH SAMPLING RATES !N INERTIAL NAVIGATION SYSTEM ESTIMATES THE POSITION OF THE AIRCRAFT IN A WORLDWIDE COORDINATE SPACE BY INTEGRATING THE OUTPUTS OF THE GYROS AND ACCELEROMETERS TYPICALLY USING +ALMAN FILTERING TECHNIQUES !CCUMULATED ERRORS IN SUCH A SYSTEM CAN BE CORRECTED BY USING '03 UPDATES AS WELL AS KNOWN REFERENCE POINTS MEASURED WITH THE RADAR OR %/ SENSORS 4HERE MAY BE DOZENS OR HUNDREDS OF STORED PROGRAM DEVICES DISTRIBUTED THROUGHOUT THE AVIONICS 4HESE LOWER LEVEL FUNCTIONAL SUITES ARE CONNECTED BY STANDARDIZED BUS SES WHICH MAY BE FIBER OPTIC OR WIRED 4HE PROGRAMMABLE DEVICES ARE CONTROLLED BY SOFTWARE OPERATING ENVIRONMENTS INVOKING PROGRAMS 4HE ARCHITECTURE OBJECTIVE IS TO HAVE STANDARD INTERFACES FEW UNIQUE ASSEMBLIES AND SINGLE LEVEL MAINTENANCE 4HE SUITE OF MICROWAVE AND 2& APERTURES IN A FIGHTER AIRCRAFT MIGHT APPEAR AS SHOWN IN &IGURE !S MANY AS APERTURES MAY BE DISTRIBUTED THROUGHOUT THE VEHI CLE PERFORMING RADAR DATA LINK NAVIGATION MISSILE WARNING DIRECTION FINDING JAM MING OR OTHER FUNCTIONS OVER A FREQUENCY RANGE COVERING SEVERAL DECADES 4HERE ARE APERTURES DISTRIBUTED OVER THE AIRCRAFT THAT POINT FORWARD AND AFT RIGHT AND LEFT AS WELL AS UP AND DOWN 3OME APERTURES WILL BE SHARED FOR COMMUNICATIONS RADIO NAVIGATION AND IDENTIFICATION #.) AS WELL AS IDENTIFICATION FRIEND OR FOE )&& DUE TO COMPATIBLE FREQUENCIES AND GEOMETRIES $ATA LINKS SUCH AS *4)$3,INK AND ,INK CAN SHARE APERTURES WITH '03 AND , BAND SATELLITE COMMUNICATIONS , 3!4#/- %7 APERTURES MUST BE BROADBAND BY NATURE AND CAN BE SHARED WITH RADAR WARNING RECEIVERS 272 RADAR AUXILIARIES AND SOME TYPES OF #.)S
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4HE APERTURES ARE SIGNAL CONDITIONED CONTROLLED AND INTERFACED THROUGH BUSSES IN THE AIRCRAFT WITH REMAINING PROCESSING PERFORMED EITHER IN A COMMON PROCESSOR COMPLEX AS SHOWN IN &IGURE OR IN FEDERATED PROCESSORS DISTRIBUTED THROUGHOUT THE AIRCRAFT /NE IMPORTANT CLASS OF STANDARDIZED MODULES CONTAINS BASIC TIMING AND PROGRAMMABLE EVENT GENERATORS 0%' THAT CREATE ACCURATE TIMING FOR 0ULSE 2EPETITION &REQUENCIES 02&S ANALOG TO DIGITAL CONVERSION !$ SAMPLING PULSE AND CHIP WIDTHS BLANK ING GATES BEAM REPOINTING COMMANDS AND OTHER SYNCHRONIZED REAL TIME INTERRUPTS ! SECOND CLASS CONTAINS 2& AND INTERMEDIATE FREQUENCY )& AMPLIFICATION AND MIXING ! THIRD CLASS CONTAINS LOW NOISE FREQUENCY SYNTHESIZERS WHICH MAY INCLUDE $IRECT $IGITAL FREQUENCY 3YNTHESIS $$3 !$ CONVERTERS AND CONTROL INTERFACE MODULES ARE THE FINAL CLASS "USSING PROTOCOLS AND SPEEDS MUST HAVE ADEQUATE RESERVES TO INSURE FAIL SAFE REAL TIME OPERATION 4HE FUNCTIONAL BLOCK DIAGRAM AND OPERATION OF A SPECIFIC SENSOR MODE IS THEN OVER LAID ON THIS HARDWARE AND SOFTWARE INFRASTRUCTURE ! SPECIFIC MODE IS IMPLEMENTED IN AN APPLICATIONS PROGRAM IN THE SAME SENSE THAT WORD PROCESSING IS ON A PERSONAL COMPUTER 0# #ARRYING THE ANALOGY FURTHER COMMON EXPERIENCE WITH THE UNRELIABILITY OF 0# HARDWARE AND SOFTWARE REQUIRES THAT A SYSTEM OF THE TYPE DEPICTED IN &IGURE MUST BE REDUNDANT ERROR CHECKING TRUSTED FAIL SAFE IN THE PRESENCE OF FAULTS AND EMBODY STRICT PROGRAM EXECUTION SECURITY 4HIS IS A VERY CHALLENGING SYSTEM ENGINEERING TASK %XHAUSTIVE MATHEMATICAL ASSURANCE AND SYSTEM TESTING IS REQUIRED WHICH IS COMPLETELY DIFFERENT FROM CURRENT COMMERCIAL PERSONAL COMPUTER PRACTICE ! NOTIONAL -&!2 INTEGRATED CORE PROCESSING COMPLEX WITH ITS CORRESPONDING INTER FACES SIMILAR TO THAT SHOWN IN &IGURE IS SHOWN IN &IGURE WHERE THERE ARE MULTIPLE REDUNDANT PROCESSING ARRAYS THAT CONTAIN STANDARDIZED MODULES CONNECTED IN A NON BLOCKING SWITCHED NETWORK )NTERNAL AND EXTERNAL BUSSES CONNECT THE INDIVIDUAL PROCESSING ARRAYS TO EACH OTHER AS WELL AS TO THE OTHER SUITES SENSORS CONTROLS AND DISPLAYS 5SUALLY THERE ARE BOTH PARALLEL ELECTRICAL SIGNAL BUSSES AS WELL AS SERIAL FIBER OPTIC BUSSES DEPENDING ON SPEED AND TOTAL LENGTH IN THE AIRCRAFT 4HE SIGNAL AND DATA PROCESSOR COMPLEX CONTAINS MULTIPLE PROCESSOR AND MEMORY ENTITIES WHICH MIGHT BE
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ON A SINGLE CHIP OR ON SEPARATE CHIPS DEPENDING ON YIELD COMPLEXITY SPEED CACHE SIZE AND SO ON %ACH PROCESSOR ARRAY MAY CONSIST OF PROGRAMMABLE SIGNAL PROCESSORS 030 GENERAL PURPOSE PROCESSORS '00 BULK MEMORY "- INPUT OUTPUT )/ AND A MASTER CONTROL UNIT -#5 4HE 030S PERFORM SIGNAL PROCESSING ON ARRAYS OF SENSOR DATA 4HE '00S PERFORM PROCESSING IN WHICH THERE ARE LARGE NUMBERS OF CONDITIONAL BRANCHES 4HE -#5 ISSUES PROGRAMS TO 030S '00S AND "- AS WELL AS MANAGES OVERALL EXECUTION AND CONTROL 4YPICAL PROCESSING SPEED IS -)03 MILLIONS OF INSTRUCTIONS PER SECOND PER CHIP BUT MIGHT BE ')03 BILLIONS OF INSTRUCTIONS PER SECOND IN THE NEAR FUTURE #LOCK FREQUENCIES ARE LIMITED BY ON CHIP SIGNAL PROPAGA TION BUT ARE UP TO '(Z GIGAHERTZ AND COULD BE '(Z IN THE NEAR FUTURE 3ENSOR PROCESSING HAS ARRIVED AT THE POINT WHERE THE CONCEPTION OF SUCCESSFUL ALGORITHMS IS MORE IMPORTANT THAN THE COMPUTATIONAL HORSEPOWER NECESSARY TO CARRY THEM OUT -&!2 3OFTWARE 3TRUCTURE )MPROPER OPERATION OF MANY FIGHTER SYSTEMS CAN BE HAZARDOUS !S PREVIOUSLY MENTIONED THE SOFTWARE MUST BE EXHAUSTIVELY TESTED ERROR CHECKED MATHEMATICALLY TRUSTED FAILSAFE IN THE PRESENCE OF FAULTS AND EMBODY STRICT PROGRAM EXECUTION SECURITY /NE OF THE MOST IMPORTANT ASPECTS IS RIGID ADHERENCE TO A STRUCTURED PROGRAM ARCHITECTURE !N OBJECT BASED HIERARCHI CAL STRUCTURE WHERE EACH LEVEL IS SUBORDINATE TO THE LEVEL ABOVE AND SUBPROGRAMS ARE CALLED IN STRICT SEQUENCE IS NECESSARY )T ALSO REQUIRES AMONG OTHER THINGS THAT SUBPROGRAMS NEVER CALL THEMSELVES RECURSIVE CODE OR ANY OTHERS AT THEIR EXECUTION LEVEL 3UBPROGRAMS OBJECTS ARE CALLED RECEIVE EXECUTION PARAMETERS FROM THE LEVEL ABOVE THE PARENT AND RETURN RESULTS BACK TO THE CALLING LEVEL !N EXAMPLE OF SUCH A SOFTWARE STRUCTURE IS SHOWN IN &IGURES AND 4HE SOFTWARE WOULD BE EXECUTED IN THE HARDWARE SHOWN IN &IGURE
&)'52% -&!2 STRUCTURED SOFTWARE
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&)'52% -&!2 PRIORITY SCHEDULING
!N -&!2 CAN SUPPORT MANY ACTIVITIES OR MODES CONCURRENTLY BY INTERLEAVING THEIR RESPECTIVE DATA COLLECTIONS 3URVEILLANCE TRACK UPDATES AND GROUND MAPS ARE EXAMPLES OF SUCH ACTIVITIES 4HE SOFTWARE NEEDED TO SUPPORT EACH ACTIVITY IS MAPPED TO A SPECIFIC CLIENT MODULE AS SHOWN IN &IGURE %ACH CLIENT MODULE IS RESPONSIBLE FOR MAINTAINING ITS OWN OBJECT DATABASE AND FOR REQUESTING USE OF THE APERTURE 2EQUESTS ARE MADE BY SUBMITTING ANTENNA JOB REQUESTS THAT SPECIFY BOTH THE WAVEFORM TO BE USED HOW TO DO IT AND THE PRIORITY AND URGENCY OF THE REQUEST ! SCHEDULER EXECUTES DURING EACH DATA COLLECTION INTERVAL AND DECIDES WHAT TO DO NEXT BASED ON THE PRIORITIES AND URGENCIES OF THE ANTENNA JOB REQUESTS THAT HAVE BEEN RECEIVED 4HIS KEEPS THE APERTURE BUSY AND RESPONSIVE TO THE LATEST ACTIVITY REQUESTS &OLLOWING THE SELECTION OF THE ANTENNA JOB BY THE SCHEDULER THE FRONT END TRANSMIT AND RECEIVE HARDWARE IS CONFIGURED AND IN PHASE AND QUADRITURE )1 DATA IS COLLECTED AND SENT TO THE SIGNAL PROCESSORS 4HERE THE DATA IS PROCESSED IN A MANNER DEFINED BY THE SENSOR MODE AND THE SIGNAL PROCESSING RESULTS ARE RETURNED TO THE CLIENT THAT REQUESTED THEM 4HIS TYPICALLY RESULTS IN DATABASE UPDATES ANDOR NEW ANTENNA JOB REQUESTS FROM THE CLIENT .EW ACTIVITIES CAN BE ADDED AT ANY TIME USING THIS MODULAR APPROACH !LTHOUGH THIS STRUCTURE IS COMPLEX AND THE SOFTWARE ENCOMPASSES MILLIONS OF LINES OF CODE MODERN -&!2 SOFTWARE INTEGRITY CAN BE MAINTAINED WITH STRICT CONTROL OF INTERFACES FORMAL CONFIGURATION MANAGEMENT PROCESSES AND FORMAL VERIFICATION AND VALIDATION SOFTWARE TOOLS )N ADDITION MOST SUBPROGRAMS ARE DRIVEN BY READ ONLY TABLES AS SHOWN IN &IGURE SO THAT THE EVOLUTION OF AIRCRAFT TACTICS CAPABILITIES AND HARDWARE DO NOT REQUIRE REWRITES OF VALIDATED SUBPROGRAMS 3OFTWARE VERSIONS BUILDS ARE UPDATED EVERY YEAR THROUGHOUT THE LIFETIME OF THE SYSTEM WHICH MAY BE DECADES %ACH SUBPROGRAM MUST HAVE TABLE DRIVEN ERROR CHECKING AS WELL -ANY LOWER LEVELS ARE NOT SHOWN IN &IGURES AND THERE MAY BE SEVERAL THOUSAND SUBPROGRAMS IN ALL 2ANGE $OPPLER 3ITUATION -ODERN RADARS HAVE THE LUXURY OF INTERLEAVING MOST OF THE MODES SUGGESTED IN &IGURE IN REAL TIME AND SELECTING THE BEST AVAILABLE TIME OR AIRCRAFT POSITION TO INVOKE EACH MODE AS THE MISSION REQUIRES 4HE GEOMETRY THAT MUST BE SOLVED EACH TIME IS SHOWN IN &IGURE 4HE FIGHTER AIRCRAFT PULSE DOPPLER GEOMETRY IS CENTERED AROUND THE AIRCRAFT TRAVELING AT A VELOCITY 6A AND AT AN ALTITUDE H ABOVE THE %ARTHS SURFACE 4HE RADAR PULSE REPETITION FREQUENCY
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2!$!2 (!.$"//+
&)'52% 3TRIKE FIGHTER PULSE DOPPLER GEOMETRY
02& GIVES RISE TO A SERIES OF RANGE AND DOPPLER X Y Z AMBIGUITIES AS SHOWN IN &IGURE WHICH INTERCEPT THE %ARTHS SURFACE AS RANGE hRINGSv AND ISO DOPPLER hHYPERBOLASv BECAUSE THE %ARTH IS A ROUGH GEOID CONSTANT RANGE AND DOPPLER CONTOURS ARE NOT ACTUALLY RINGS OR HYPERBOLAS 4HE RADAR ANTENNA PATTERN INTERCEPTS THE LIMB OF THE %ARTH USUALLY IN BOTH THE MAIN BEAM AND SIDELOBES ! TARGET IN THE MAIN BEAM AT RANGE 2T AND VELOCITY 6T MAY HAVE TO BE OBSERVED IN THE PRESENCE OF BOTH RANGE AND DOPPLER AMBIGUITIES /NLY THE TARGETS LINE OF SIGHT VELOCITY 6TLOS IS OBSERV ABLE ON A SHORT TERM BASIS 4HE RADAR DESIGNERS PROBLEM IS TO SELECT THE BEST WAVEFORM IN THIS TARGET CLUTTER GEOMETRY (ISTORICALLY THESE WAVEFORMS WERE SELECTED AHEAD OF TIME AND BUILT INTO THE RADAR HARDWARE AND SOFTWARE -OST MODERN AIRBORNE RADARS SOLVE THIS GEOMETRY IN REAL TIME AND CONTINUOUSLY SELECT THE BEST AVAILABLE FREQUENCY 02& PULSEWIDTH TRANSMIT POWER SCAN PATTERN ETC 5NFORTUNATELY THE SPECIFICS OF THE WAVEFORM ARE UNPREDICTABLE EVEN TO THE RADAR WITHOUT EXACT KNOWLEDGE OF THE AIRCRAFT TARGET EARTH VELOCITY GEOMETRY SET AND MODE OF OPERATION REQUESTED BY THE OPERATOR OR MISSION SOFTWARE 4HIS MAKES TESTING QUITE DIFFICULT FORTUNATELY TEST EQUIPMENT HAS COME A LONG WAY (ARDWARE IN THE LOOP TEST ING USING REAL TIME SIMULATION OF THE ENTIRE GEOMETRY AND EXTERNAL WORLD IN THE RADAR INTEGRATION LABORATORY IS COMMONLY EMPLOYED !CTIVE %LECTRONICALLY 3CANNED !RRAY !%3! !LTHOUGH MULTIFUNCTIONAL RADARS HAVE BEEN DEPLOYED WITH MECHANICALLY SCANNED AND ELECTRONICALLY SCANNED ANTENNAS FULLY MULTIFUNCTIONAL RADARS USE !CTIVE %LECTRONICALLY 3CANNED !RRAYS !%3! WHICH CONTAIN A TRANSMIT RECEIVE CHANNEL 42 FOR EACH RADIATOR 4HE ADVANTAGES OF !%3! ARE FAST ADAPTIVE BEAM SHAPING AND AGILITY IMPROVED POWER EFFICIENCY IMPROVED MODE INTERLEAVING SIMULTANEOUS MULTIPLE WEAPON SUPPORT AND REDUCED OBSERVABIL ITYn 0ERHAPS HALF THE COST AND COMPLEXITY OF AN !%3! IS IN THE 42 CHANNELS 4HAT SAID HOWEVER THE FEED NETWORK BEAM STEERING CONTROLLER "3# !%3! POWER SUPPLY AND COOLING SUBSYSTEM AIR OR LIQUID ARE EQUALLY IMPORTANT
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! MAJOR ENABLER FOR !%3!S IS THE STATE OF THE ART IN MICROWAVE INTEGRATED CIRCUITS 4HIS HAS FOLLOWED THE DRAMATIC COST AND PERFORMANCE GAINS AVAILABLE IN MOST SEMICON DUCTOR TECHNOLOGIES %ACH 42 CHANNEL HAS SELF DIAGNOSIS FEATURES WHICH CAN DETECT FAILURE AND COMMUNICATE THAT TO THE BEAM STEERING CONTROLLER FOR FAILURE COMPENSATION !%3!S CAN ACCOMMODATE UP TO FAILURES WITH VERY LITTLE DEGRADATION IF PROPERLY COMPENSATED IN THE "3# &ROM AN -&!2 POINT OF VIEW THE IMPORTANT PARAMETERS ARE VOLUMETRIC DENSITIES HIGH ENOUGH TO SUPPORT LESS THAN WAVELENGTH SPACING RADIATED POWER DENSITIES HIGH ENOUGH TO SUPPORT WATTS PER SQ CM RADIATED TO PRIME POWER EFFICIENCIES GREATER THAN BANDWIDTH OF SEVERAL '(Z ON TRANSMIT AND ALMOST TWICE THAT BANDWIDTH ON RECEIVE PHASE AND AMPLITUDE CALIBRATION AND CONTROL ADEQUATE TO PROVIDE AT LEAST n D" RMS SIDELOBES AMPLITUDE CONTROL ADEQUATE TO PROVIDE D" POWER MANAGEMENT NOISE PERFORMANCE ADEQUATE TO SUPPORT THE SUBCLUTTER VISIBILITY REQUIREMENTS AND FINALLY SUF FICIENT STORAGE AND COMPUTING TO ALLOW BEAM REPOINTINGADJUSTMENT IN A FRACTION OF MSEC &AST BEAM ADJUSTMENT REQUIRES HIGH SPEED BUSSES TO EACH 42 CHANNEL /NE OF THE PRINCIPAL ADVANTAGES OF AN !%3! IS THE ABILITY TO MANAGE BOTH POWER AND SPATIAL COVERAGE ON A SHORT TERM BASIS S OF MSEC /FTEN ANOTHER ADVANTAGE IS THAT BOTH THE NOISE FIGURE IS LOWER AND RADIATED POWER IS HIGHER FOR A GIVEN AMOUNT OF PRIME POWER 4HIS IS BECAUSE THE 2& PATH LENGTHS CAN BE MUCH SHORTER WHICH USUALLY LEADS TO LOWER FRONT END LOSSES %ACH RADIATING ELEMENT IS USUALLY DESIGNED TO BE VERY BROADBAND AND IS DRIVEN BY A 42 CHANNEL IN A TYPICAL !%3! ARRAY 4HERE ARE TYPI CALLY A FEW THOUSAND CHANNELS IN AN -&!2 !%3! %ACH CHANNEL CONTAINS FIRST LEVEL POWER REGULATION FILTERING LOGIC CALIBRATION TABLES AS WELL AS THE OBVIOUS 2& FUNC TIONS 3OME CHANNELS IN THE ARRAY ARE DEDICATED TO OTHER FUNCTIONS SUCH AS CALIBRATION JAMMER NULLING SIDELOBE BLANKING CLOSE IN MISSILE DATALINK OUT OF BAND DIRECTION FINDING ETC !LSO THERE ARE USUALLY SOME CHANNELS AT THE EDGE OF THE ARRAY THAT ARE PASSIVE AND IMPROVE THE SIDELOBES AND 2#3 PATTERN &IGURE SHOWS THE COMPARISON BETWEEN A CONVENTIONAL MECHANICALLY SCANNED RADAR WITH THE LOW NOISE AMPLIFIER AND A HIGH POWER TRAVELING WAVE TUBE TRANSMIT TER MOUNTED OFF THE GIMBAL VERSUS A REAL TIME ADAPTED !%3! WITH TWO DIFFERENT SCAN REGIMES FOR THE SAME AMOUNT OF INPUT PRIME POWER !%3! PERFORMANCE FALLS OFF FOR LARGE SCAN COVERAGE BECAUSE OF THE LOWER PROJECTED APERTURE AREA FOR A FIXED MOUNTING AS SHOWN IN &IGURE ! MECHANICAL SCAN HAS THE SAME PROJECTED AREA IN ALL DIRECTIONS AND LARGE SCAN ANGLES MARGINALLY REDUCE RADOME LOSSES WHICH RESULTS IN SLIGHTLY IMPROVED LARGE ANGLE PERFORMANCE .ONETHELESS !%3! PERFORMANCE IS USUALLY SUPERIOR INSIDE
&)'52% %XAMPLE !%3! MANAGEMENT COMPARISON ADAPTED
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A on AZIMUTH SCAN 5SUALLY A FIGHTER CANT ENGAGE AT LONG RANGE OUTSIDE THIS AZIMUTH FOR KINEMATIC REASONS 4HE PERFORMANCE DIFFERENCES DEPICTED IN &IGURE ARE THE RESULT OF THREE FACTORS THE INSTALLED APERTURE CAN BE LARGER IN NET PROJECTED AREA AT THE AIRCRAFT IN FLIGHT HORIZONTAL DUE TO ELIMINATION OF GIMBAL SWING SPACE HIGHER RADIATED POWER DUE TO LOWER LOSSES AND BETTER EFFICIENCY AND LOWER LOSSES BEFORE THE LOW NOISE AMPLI FIER 4HE OTHER MAJOR ADVANTAGE IS THAT SEARCH VOLUME CAN BE CHANGED DYNAMICALLY TO FIT THE INSTANT TACTICAL SITUATION AS SUGGESTED IN &IGURE 4HE FEED NETWORK IS MUNDANE BUT CRITICALLY IMPORTANT )N SINGLE TUBE TRANSMIT TERS THE FEED IS HEAVY BECAUSE IT MUST CARRY HIGH POWER AT LOW LOSS !%3! FEEDS USE SMALLER COAX STRIPLINE MICROSTRIP OR 2& MODULATED LIGHT IN FIBER OPTICS FOR TRANSMIT AND RECEIVE 2& SINCE LESS THAN WATTS 2& OR OPTICAL IS USUALLY REQUIRED (OWEVER SIGNIFICANT $# POWER IS STILL REQUIRED FOR 2& FEED DISTRIBUTION AMPLIFIERS BECAUSE THOU SANDS MUST BE DRIVEN #OST WEIGHT AND COMPLEXITY IS STILL AN ISSUE BECAUSE MULTIPLE PHASE CENTERS NECESSARY FOR ADAPTIVE ARRAY PERFORMANCE REQUIRE MULTIPLE MANIFOLDS 5SUALLY ONCE A SUBARRAY IS FORMED IN THE MANIFOLDS IT IS DIGITIZED AND MULTIPLEXED FOR ADAPTIVE SIGNAL PROCESSING !NOTHER IMPORTANT FUNCTION IS BEAM STEERING CONTROL "3# 4HE "3# DOES ARRAY CALIBRATION FAILED ELEMENT COMPENSATION PHASE AND AMPLITUDE SETTING FOR BEAM STEERING AS WELL AS SPACE TIME ADAPTIVE OPERATIONn 4HE "3# IS USUALLY REALIZED WITH A COMBINATION OF GENERAL PURPOSE PROCESSING OF THE TYPE FOUND IN A PERSONAL COMPUTER WITH VERY HIGH SPEED INCREMENTAL PHASE AND AMPLITUDE CALCULATION AND 42 MODULE INTERFACE HARDWARE "OTH SCANNING AND ADAPTIVE OPERATION REQUIRE VERY LOW LATENCY IE THE TIME BETWEEN THE SENSED NEED AND THE FIRST PULSE AT THE TARGET IS USUALLY MSEC BEAM CONTROL IN A HIGH SPEED AIRCRAFT PLATFORM ,ASTLY THE !%3! REQUIRES A VERY SIGNIFICANT POWER SUPPLY 0OWER SUPPLIES HAVE A HISTORY OF BEING HEAVY HOT AND UNRELIABLE %VEN THE BEST SYSTEMS STILL HAVE OVERALL POWER EFFICIENCIES PRIME POWER IN TO 2& OUT IN SPACE IN THE n REGION IN SPITE OF YEARS OF DEVELOPMENT 4HE TYPICAL !%3! REQUIRES LOW VOLTAGE AND HIGH CURRENT AT THE 42 CHANNEL 4HIS FORCES LARGE CONDUCTORS IN THE ABSENCE OF HIGH POWER LIGHT WEIGHT SUPERCONDUCTORS NOT AVAILABLE AT THIS WRITING )T ALSO REQUIRES VERY LOW VOLTAGE DROP RECTIFIERS AND REGULATORS #OOLING IS GENERALLY A SIGNIFICANT PERFORMANCE BURDEN 5SUALLY THE POWER SUPPLIES ARE DISTRIBUTED TO IMPROVE RELIABILITY AND FAULT TOLERANCE /FTEN POWER CONVERTERS ARE OPERATED AT SWITCHING FREQUENCIES UP TO SEVERAL HUNDRED MEGAHERTZ TO REDUCE THE SIZE OF MAGNETICS AND FILTER COMPONENTS AND SOMETIMES THE SWITCHING FREQUENCIES ARE SYNCHRONIZED TO THE RADAR MASTER CLOCK
x°ÓÊ /9* Ê --" -Ê Ê " !IR TO 3URFACE -ISSION 0ROFILE 4HE MODE STRUCTURE OF ANY MODERN FIGHTER AIR CRAFT ARISES FROM MISSION PROFILES /NE TYPICAL MISSION PROFILE FOR AN AIR TO SURFACE ! 3 STRIKE IS SHOWN IN &IGURE 4HE MISSION PROFILE BEGINS WITH A TAKEOFF CON TINUES THROUGH FLIGHT TO A TARGET AND ULTIMATELY RETURNS TO THE STARTING POINT !LONG THE WAY THE AIRCRAFT USES A VARIETY OF MODES TO NAVIGATE SEARCH AND ACQUIRE TARGETS TRACK TARGETS DELIVER WEAPONS ASSESS BATTLE DAMAGE ENGAGE IN COUNTERMEASURES AND MONI TOR AND CALIBRATE ITS PERFORMANCE !%3!S HAVE DEMONSTRATED SIMULTANEOUS MULTIPLE WEAPON DELIVERIES
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&)'52% 4YPICAL AIR TO SURFACE MISSION PROFILE
!IR TO 3URFACE -ODE 3UITE 4HE MISSION NATURALLY CREATES THE NEED FOR AN AIR TO SURFACE MODE SUITE FOR FIGHTER RADAR AS SHOWN IN &IGURE %ACH GENERAL CAT EGORY OF OPERATION CONTAINS MODES PRIMARILY FOR THAT FUNCTION BUT MODES WILL OFTEN BE INVOKED DURING OTHER PARTS OF THE MISSION 7ITHIN EACH MODE SHOWN IN &IGURE THERE IS OPTIMIZATION FOR THE PARTICULAR COMBINATION OF ALTITUDE RANGE TO THE TARGET ANTENNA FOOTPRINT ON THE %ARTHS SURFACE RELATIVE TARGET AND CLUTTER DOPPLER DWELL TIME AVAILABLE PREDICTED TARGET STATISTICAL BEHAVIOR TRANSMITTED FREQUENCY AND DESIRED RESO LUTION /BVIOUSLY EACH MODE MUST NOT COMPROMISE SOME REQUIRED LEVEL OF MISSION STEALTHn ! MODERN FIGHTER IS NET CENTRIC AND EXCHANGES SUBSTANTIAL INFORMATION WITH OTHER SYSTEMS "OTH THE FIGHTERS WINGMAN SUPPORT AIRCRAFT AND SURFACE NODES MAY EXCHANGE COMPLETE DATA AND TASKING IN REAL TIME TO FACILITATE A MISSION 4HE FIGHTER AND ITS WINGMAN WILL COORDINATE MODE TASKING SO THAT DURING A HIGH RESOLUTION GROUND MAP WHICH COULD TAKE A MINUTE TO FORM THE WINGMAN MIGHT BE PERFORMING AN AIR TO AIR SEARCH AND TRACK TO PROTECT BOTH OF THEM
&)'52% &IGHTER AIRCRAFT AIR TO SURFACE RADAR MODE SUITE
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3OME MODES ARE USED FOR SEVERAL OPERATIONAL CATEGORIES SUCH AS REAL BEAM MAP 2"- FIXED TARGET TRACK &44 DOPPLER BEAM SHARPENING $"3 AND SYNTHETIC APER TURE RADAR 3!2 USED NOT ONLY FOR NAVIGATION BUT ALSO FOR ACQUISITION AND WEAPON DELIVERY TO FIXED TARGETSn 3!2 MAY ALSO BE USED TO DETECT TARGETS IN EARTHWORKS OR TRENCHES COVERED WITH CANVAS AND A SMALL AMOUNT OF DIRT WHICH ARE INVISIBLE TO %/ OR )2 SENSORS 3IMILARLY AIR TO SURFACE RANGING ! 3 2ANGE AND PRECISION VELOCITY UPDATE 065 MAY BE USED FOR WEAPON SUPPORT TO IMPROVE DELIVERY ACCURACY AS WELL AS NAVIGATION 4ERRAIN FOLLOWING AND TERRAIN AVOIDANCE 4&4! IS USED FOR NAVIGATION AT VERY LOW ALTITUDES OR IN MOUNTAINOUS TERRAIN 3EA SURFACE SEARCH 333 SEA SURFACE TRACK 334 AND INVERSE SYNTHETIC APERTURE RADAR )3!2 WHICH WILL BE DESCRIBED LATER IN THE CHAPTER ARE USED PRIMARILY FOR THE ACQUISITION AND RECOGNITION OF SHIP TARGETS 'ROUND MOVING TARGET INDICATION '-4) AND GROUND MOVING TARGET TRACKING '-44 ARE USED PRIMARILY FOR THE ACQUISITION AND RECOGNITION OF SURFACE VEHICLE TARGETS BUT ALSO FOR RECOGNIZING LARGE MOVEMENTS OF SOLDIERS AND MATERIALS IN A BATTLE SPACE (IGH POWER JAMMING (I0WR*AM IS A COUNTERMEASURE AVAILABLE FROM !%3!S DUE TO THEIR NATURAL BROADBAND BEAM AGILE HIGH GAIN AND HIGH POWER ATTRIBUTES !%3!S ALSO ALLOW LONG RANGE AIR TO SURFACE DATA LINKS ! 3 $ATA ,INK THROUGH THE RADAR PRIMARILY FOR MAP IMAGERY "ECAUSE THERE MAY BE THOUSANDS OF WAVELENGTHS AND A GAIN OF MILLIONS THROUGH A RADAR AUTOMATIC GAIN CONTROL AND CALIBRATION !'##!, IS USUALLY REQUIRED FAIRLY OFTEN -ODES OPTIMIZED FOR THIS FUNCTION ARE INVOKED THROUGHOUT A MISSION 7AVEFORM 6ARIATIONS BY -ODE !LTHOUGH THE SPECIFIC WAVEFORM IS HARD TO PRE DICT TYPICAL WAVEFORM VARIATIONS CAN BE TABULATED BASED ON OBSERVED BEHAVIOR OF A NUMBER OF EXISTING ! 3 RADAR SYSTEMS 4ABLE SHOWS THE RANGE OF PARAMETERS THAT CAN BE OBSERVED AS A FUNCTION OF RADAR MODE 4HE PARAMETER RANGES LISTED ARE 02& PULSE WIDTH DUTY CYCLE PULSE COMPRESSION RATIO INDEPENDENT FREQUENCY LOOKS PULSES PER COHERENT PROCESSING INTERVAL #0) TRANSMITTED BANDWIDTH AND TOTAL PULSES IN A 4IME /N 4ARGET 4/4 /BVIOUSLY MOST RADARS DO NOT CONTAIN ALL OF THIS VARIATION BUT MODES EXIST IN MANY FIGHTER AIRCRAFT WHICH REPRESENT A GOOD FRACTION OF THE PARAMETER RANGE -OST FIGHTER RADARS ARE FREQUENCY AGILE SINCE THEY WILL BE OPERATED IN CLOSE PROXIMITY TO SIMILAR OR IDENTICAL SYSTEMS 4HE FREQUENCY USUALLY CHANGES IN A CAREFULLY CONTROLLED COMPLETELY COHERENT MANNER DURING A #0) 4HIS CAN BE A WEAKNESS FOR CERTAIN KINDS OF JAMMING SINCE THE PHASE AND FREQUENCY OF THE NEXT PULSE IS PREDICTABLE 3OMETIMES TO COUNTER ACT THIS WEAKNESS THE FREQUENCY SEQUENCE IS PSEUDORANDOM FROM A PREDETERMINED SET WITH KNOWN AUTOCORRELATION PROPERTIES FOR EXAMPLE &RANK #OSTAS 6ITERBI 0 CODES ! MAJOR DIFFICULTY WITH COMPLEX WIDEBAND FREQUENCY CODING IS THAT THE PHASE SHIFT ERS IN A PHASE SCANNED ARRAY MUST BE CHANGED ON AN INTRA OR INTER PULSE BASIS GREATLY COMPLICATING BEAM STEERING CONTROL AND ABSOLUTE 42 CHANNEL PHASE DELAY !NOTHER CHALLENGE IS MINIMIZING POWER SUPPLY PHASE PULLING WHEN 02&S AND PULSEWIDTHS VARY OVER MORE THAN RANGE -&!2 SYSTEMS NOT ONLY HAVE A WIDE VARIATION IN 02& AND PULSEWIDTH BUT ALSO USUALLY EXHIBIT LARGE INSTANT AND TOTAL BANDWIDTH #OUPLED WITH THE LARGE BANDWIDTH IS THE REQUIREMENT FOR LONG COHERENT INTEGRATION TIMES 4HIS REQUIREMENT NATURALLY LEADS TO EXTREME STABILITY MASTER OSCILLATORS AND ULTRA LOW NOISE SYNTHESIZERS !IR TO !IR -ISSION 0ROFILE *UST AS WITH AN AIR TO SURFACE MISSION THE MODE STRUCTURE OF A MODERN FIGHTER AIRCRAFT AIR TO AIR MISSION ARISES FROM ITS PROFILE ! TYPI CAL MISSION PROFILE FOR AIR TO AIR ! ! IS SHOWN IN &IGURE 4HE MISSION PROFILE
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BEGINS WITH AN AIRFIELD OR CARRIER TAKEOFF CONTINUES THROUGH FLIGHT PENETRATING INTO AN ENEMY BATTLE SPACE SEARCHES FOR AIR TARGETS TO ATTACK AND ULTIMATELY RETURNS TO THE STARTING POINT !LONG THE WAY THE AIRCRAFT USES A VARIETY OF MODES TO NAVIGATE EXCHANGE DATA WITH COMMAND CONTROL COMMUNICATIONS INTELLIGENCE SURVEILLANCE
&)'52% 4YPICAL ! ! MISSION PROFILE
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2!$!2 (!.$"//+
RECONNAISSANCE #)32 ASSETS SEARCH AND ACQUIRE AIRBORNE TARGETS TRACK AND SEPARATE BENIGN TARGETS FROM THREATS DELIVER WEAPONS ESCAPE AND ENGAGE IN COUNTERMEASURES MONITOR AND CALIBRATE ITS PERFORMANCE AND RETURN TO BASE !IR TO !IR -ODE 3UITE 3IMILARLY THE ! ! MISSION NATURALLY CREATES THE NEED FOR A CORRESPONDING MODE SUITE FOR THE RADAR AS SHOWN IN &IGURE !T THE RADAR SEN SOR AND AIR TO AIR MODE SOFTWARE LEVEL THERE IS ADAPTIVE TASK PRIORITIZATION TO INSURE THAT THE HIGHEST PROCESSOR PRIORITIZED PILOT SELECTED THREAT IS SERVICED FIRST 0ASSIVE MODES ARE INTERLEAVED WITH ACTIVE OPERATION TO IMPROVE SURVIVABILITY AND PASSIVE TRACKING AND )$ %ACH MODE SHOWN IN &IGURE IS OPTIMIZED IN REAL TIME FOR THE PARTICULAR COMBI NATION OF ALTITUDE RANGE TO THE TARGET DENSITY OF TARGET THREATS ANTENNA FOOTPRINT ON THE %ARTHS SURFACE RELATIVE TARGET AND CLUTTER DOPPLER DWELL TIME AVAILABLE PREDICTED TARGET STATISTICAL BEHAVIOR TRANSMITTED FREQUENCY AND DESIRED RESOLUTION 4HE MODE CATEGORY hAUTONOMOUS AND CUED SEARCHv CONTAINS THE MODES MOST COM MONLY ASSOCIATED WITH FIGHTER RADARS 4HERE ARE USUALLY TWO RANGE GATED HIGH PULSE REP ETITION FREQUENCY (02& MODES VELOCITY SEARCH 63 PRIMARILY DEDICATED TO LONGEST RANGE DETECTION AND RANGE WHILE SEARCH 273 WHICH USES SOME FORM OF &- RANGING TO ESTIMATE TARGET RANGE 4HERE IS A MEDIUM 02& -02& MODE WHICH PROVIDES ALL ASPECT VELOCITY RANGE SEARCH 623 AT THE EXPENSE OF POORER LONG RANGE PERFORMANCE )N ADDITION THERE ARE TWO PASSIVE MODES PASSIVE SEARCH AND RANGING IN WHICH THE RADAR DETECTS AND ESTIMATES RANGE AND ANGLE TO AN EMITTER OR BISTATICALLY WINGMAN OR SUPPORT AIRCRAFT ILLUMINATED TARGET AND %3- SHARED APERTURE IN WHICH THE 2& AND PRO CESSOR COMPLEX DETECTS ESTIMATES WAVEFORM PARAMETERS AND RECORDS THEM FOR FUTURE USE 0ASSIVE SEARCH MAY BE COMBINED WITH CUED BURST RANGING TO BETTER ESTIMATE EMIT TER LOCATION %XTENDED VOLUME SEARCH IS A MODE USED WITH CUEING FROM ANOTHER ON OR OFF BOARD SENSOR IN WHAT NORMALLY WOULD BE AN UNFAVORABLE GEOMETRY -ANY MODES AND FUNCTIONS ARE SHARED IN COMMON WITH ! 3 ESPECIALLY COUNTERMEA SURES AND PERFORMANCE MONITORING %XTREMELY IMPORTANT IN BOTH MODES IS IMPLEMENTA TION OF EMISSIONS CONTROL TO MINIMIZE THE ABILITY OF THE ADVERSARY TO DETECT TRACK AND ATTACK USING THE RADAR EMISSION 7ITHOUT CARE THESE EMISSIONS CAN EASILY SERVE AS A STRONG GUIDANCE SIGNAL FOR A HOSTILE ANTIRADIATION MISSILE !2- !NTENNA APERTURES THAT HAVE MULTIPLE INDEPENDENT PHASE CENTERS CAN PERFORM BOTH ADAPTIVE CLUTTER CANCEL LATION AS WELL AS JAMMER CANCELLATION WITH SUITABLE HARDWARE AND SOFTWARE n
&)'52% ! ! MODE SUITE
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4HE SUBSUITE OF MULTI TARGET TRACK -44 CONTAINS CONVENTIONAL TRACK WHILE SCAN 473 PASSIVE TRACKING OF EMITTERS OR ECHOES FROM BISTATIC ILLUMINATION MISSILE TRACK ING WITH OR WITHOUT A MISSILE DATALINK OR BEACON AND SEVERAL MODES TO RECOGNIZE TARGET NUMBER AND TYPE RAID ASSESSMENT AND NONCOOPERATIVE TARGET RECOGNITION USU ALLY INCORRECTLY CALLED TARGET IDENTIFICATION 4HE FIGHTER AND WINGMAN WILL COORDINATE MODES THROUGH THE NET SO THAT BOTH HAVE SITUATIONAL AWARENESS DURING THE LONG TIME SPAN REQUIRED TO PROVIDE TARGET RECOGNITION !NOTHER IMPORTANT FIGHTER CATEGORY IS WEAPON SUPPORT -ISSILE UPDATE IS THE MEA SUREMENT OF MISSILE AND TARGET POSITION VELOCITY AND ACCELERATION TO ALLOW STATISTICALLY INDEPENDENT MEASUREMENTS FOR TRANSFER ALIGNMENT AS WELL AS MISSILE STATE OF HEALTH -ISSILE UPDATE PROVIDES THE LATEST TARGET INFORMATION AND FUTURE DYNAMICS PREDICTION BY DATA LINK )2 MISSILE SLAVING CO ALIGNS RADAR AND SEEKER 3INCE GUN EFFECTIVE RANGES ARE VERY SHORT GUN RANGING CAUSES THE RADAR TO SENSE THE GUN FIELD OF FIRE PREDICTS ANGLE RATE AND MEASURES RANGE TO A TARGET FOR TENTATIVE GUNFIRE )T MAY ALSO TRACK GUN ROUNDS DURING FIRE 4HERE ARE THOUSANDS OF ELECTRICAL DEGREES OF PHASE BETWEEN FREE SPACE AND THE !$ CONVERTERS 4HE COMBINATION OF TEMPERATURE TIME AND MANUFACTURING TOLERANCES GIVES RISE TO THE NEED FOR SELF CALIBRATION TEST FAULT DETECTION FAILURE DIAGNOSIS AND NEEDED CORRECTIONS WHICH ARE PERFORMED BY A SUBSUITE OF PERFORMANCE MONITOR SOFTWARE 4IMING 3TRUCTURE 4HE SIGNIFICANCE OF THE REMAINING PARAMETERS IN 4ABLES AND CAN BEST BE ILLUSTRATED WITH A TIMING STRUCTURE TYPICAL OF FIGHTER RADARS &IGURE SHOWS A MODERN RADAR TIMING STRUCTURE IN A SEQUENCE OF PROGRESSIVELY EXPANDED TIMELINES 4HE FIRST ROW OF &IGURE SHOWS A TYPICAL SCAN CYCLE COVERING THE REQUIRED VOLUME OF INTEREST FOR A SPECIFIC MODE 4HE TIME SPAN FOR A FULL SCAN CYCLE MIGHT BE TO SECONDS )NSIDE THE TOTAL SCAN CYCLE TIME THERE MAY BE SEVERAL BARS OF A SCANNED REGION OF SPACE WITH A TIME SPAN OF A FEW TENTHS OF A SECOND ! BAR IS A SCAN SEGMENT ALONG A SINGLE ANGULAR TRAJECTORY AS SHOWN IN &IGURE LATER IN THE CHAPTER
4!",% 4YPICAL 7AVEFORM 0ARAMETERS ! ! -ODES 0ULSE 7IDTH MSEC
2ADAR -ODES
02& K(Z
2ANGE 'ATED (IGH 02&
n
n
-EDIUM 02&
n
"URST 2ANGING
n
!CTIVE 4RACK
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2AID !SSESSMENT .ON #OOP 4ARGET 2EC (I0WR *AM
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n
#AL!'#
n
n
!IR $ATA ,INK
n
n
'UN 2ANGING 7EATHER !VOIDANCE
n n
n n
$UTY 2ATIO
0ULSE #OMP 2ATIO
&REQ ,OOKS
0ULSES 0ER #0)
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n
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n
n
n
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n
n
n
n
n n
n
n
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n
n
n n
n n
n n
)NSTANT "AND 7IDTH -(Z
4OTAL 0ULSES IN 4/4
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n
n
n
n
n
n
n
n
n
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n
n
n
n
n
n
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n
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n
nK
n
n
n
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n n
n n
n n
x°£È
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&)'52% 4YPICAL -&!2 TIMING SEQUENCES #OURTESY 3CI4ECH 0UBLISHING
%ACH BAR CONSISTS OF MULTIPLE BEAM POSITIONS OF A FEW TENS OF MILLISECONDS EACH WHICH ARE COMPUTED ON THE FLY TO OPTIMALLY COVER THE SELECTED VOLUME %ACH BEAM CYCLE IN TURN MAY CONTAIN ONE OR MORE RADAR MODES OR SUBMODES SUCH AS THOSE CONTAINED IN 4ABLES OR AND DEPICTED IN THE LOWEST LINE OF &IGURE 4HE MODES MAY NOT BE INVOKED EACH TIME DEPENDING ON THE GEOMETRY BETWEEN THE AIRCRAFT AND THE INTENDED TARGET SET 4HE MODE TIME IS BROKEN UP INTO COHERENT PROCESSING INTERVALS #0)S ! COHER ENT PROCESSING INTERVAL IS SEGMENTED AS SHOWN IN THE BOTTOM ROW OF &IGURE 4HE PARTICULAR EXAMPLE SHOWN IS TRACKING THAT MIGHT BE USED IN &44 '-44 065 OR ! ' 2ANGING AS SHOWN PREVIOUSLY IN &IGURE AND LATER IN &IGURES AND )T CONSISTS OF A FREQUENCY CHANGE SETTLING TIME PASSIVE RECEIVING TO BE SURE THE BAND ISNT JAMMED CALIBRATE THAT DOESNT INTENTIONALLY RADIATE BUT OFTEN THERE IS SOME 2& LEAKAGE RADIATED AN AUTOMATIC GAIN CONTROL !'# INTERVAL IN WHICH A NUMBER OF PULSES ARE TRANSMITTED TO SET THE RECEIVER GAIN AND FINALLY TWO INTERVALS IN WHICH RANGE DOPPLER AND ANGLE DISCRIMINANTS ARE FORMED 4HESE #0)S OFTEN BUT NOT ALWAYS HAVE CONSTANT POWER FREQUENCY SEQUENCE 02& SEQUENCE PULSEWIDTH PULSE COMPRESSION AND BANDWIDTH
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MAIN BEAM CLUTTER AND GROUND MOVING TARGET FILTER REJECTION NOTCH 4ARGET DETEC TION REQUIRES DETECTIONS IN AT LEAST OF THE 02&S WITH ALL 02&S CLEAR AT MAXIMUM RANGE 4HE 02& SELECTION CRITERIA USUALLY REQUIRES THAT THE 02& SET IS CLEARIN OTHER WORDS AT LEAST A SPECIFIED NUMBER TYPICALLY OF 02&S MUST HAVE AN ABOVE THRESHOLD RETURN ECHO FOR THE MINIMUM SPECIFIED TARGET FOR THE FULL SPECIFIED RANGE DOPPLER COVERAGE ! TYPICAL PROCESSING BLOCK DIAGRAM IS GIVEN IN &IGURE %ACH 02& PROCESSING INTERVAL IS DIFFERENT BUT THEY AVERAGE OUT TO AN OPTIMUM AS SHOWN LATER IN &IGURE "OTH MAIN AND GUARD CHANNEL PROCESSING IS REQUIRED TO REJECT FALSE TARGETS 3OME 34!0 PROCESSING MAY HAVE BEEN PERFORMED BEFORE THIS PROCESS BUT TRADITIONAL SIDE LOBE AND MAIN BEAM CLUTTER IS LESS OF A LIMIT THAN GROUND MOVING TARGETS WHICH HAVE VERY LARGE CROSS SECTIONS AND EXO DOPPLERS IE DOPPLER FAR ENOUGH OUT OF MAIN BEAM CLUTTER THAT DETECTION IS NOT LIMITED BY THE CLUTTER RETURN -02& USUALLY HAS A SMALL AMOUNT OF PULSE COMPRESSION TO WHICH STILL MAY REQUIRE DOPPLER COMPEN SATION -AIN AND GUARD CHANNELS ARE PROCESSED IN THE SAME WAY /BVIOUSLY THE TWO SPECTRA ARE QUITE DIFFERENT AND SEPARATE FALSE ALARM AND NOISE ENSEMBLE ESTIMATES ARE MADE 4HIS LEADS TO SEPARATE THRESHOLD SETTINGS -ULTIPLE CHANNELS ARE USED TO ESTIMATE INTERFERENCE AND SELECT %##- STRATEGY -AIN CHANNEL DETECTIONS ARE EXAMINED FOR '-4S AND CENTROIDED IN RANGE AND DOPPLER BECAUSE A RETURN IN RANGE OR DOPPLER MAY STRADDLE MULTIPLE BINS THE CENTROID OF THOSE RETURNS IN MULTIPLE BINS MUST BE ESTIMATED FROM THE AMPLITUDE IN EACH BIN AND THE NUMBER OF BINS STRADDLED 4HE GUARD CHANNEL IS DETECTED AND THE THRESHOLDED RESULTS ARE USED TO GATE THE MAIN CHANNEL RESULTS FOR THE FINAL HIT MISS COUNT 'ENUINE TARGETS ARE RESOLVED IN RANGE AND DOPPLER PRESENTED TO A DISPLAY AND USED FOR 473 CORRELATION AND TRACKING &ALSE ALARMS ARE A CRITICAL ISSUE IN MOST RADAR MODES 4HESE ARE USUALLY SUPPRESSED FOR THERMAL NOISE BY CONSTANT FALSE ALARM RATE THRESHOLDING COINCIDENCE DETECTION AND POST DETECTION INTEGRATION WITH FREQUENCY AGILITY #LUTTER FALSE ALARMS ARE SUP PRESSED BY ADAPTIVE APERTURE TAPERING LOW NOISE FRONT END HARDWARE WIDE DYNAMIC RANGE !$S CLUTTER REJECTION FILTERING INCLUDING 34!0 PULSE COMPRESSION SIDELOBE SUPPRESSION DOPPLER FILTER SIDELOBE CONTROL GUARD CHANNEL PROCESSING RADOME REFLEC TION LOBE COMPENSATION ANGLE RATIO TESTS SEE &IGURE AND THE hFRINGE REGIONv FOR AN EXAMPLE ANGLE RATIO TEST AND ADAPTIVE 02& SELECTION
&)'52% 4YPICAL -02& PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
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2!$!2 (!.$"//+
&)'52% -EDIUM 02& RANGE VELOCITY BLIND ZONES
-02& 4YPICAL 2ANGE $OPPLER "LIND -AP &OR EXAMPLE A TYPICAL -02& SET FOR 8 BAND WITH RANGE DOPPLER COVERAGE OF KMn K(Z IS SHOWN IN &IGURE 4HIS SET IS FOR A n ANTENNA BEAMWIDTH OWNSHIP IE THE RADAR CARRYING FIGHTER VELOCITY OF MS AND AN ANGLE OFF THE VELOCITY VECTOR OF n 4HE 02& SET IS AND K(Z (ISTORICALLY A 02& SET WAS CALCULATED DURING DESIGN AND REMAINED FIXED DURING DEPLOYMENT -ODERN MULTIFUNC TIONAL RADAR COMPUTING IS SO ROBUST THAT 02& SETS CAN BE SELECTED IN REAL TIME BASED ON SITUATION GEOMETRY AND LOOK ANGLE 4HE SET WHICH GENERATED &IGURE ON THE AVERAGE IS CLEAR ON OUT OF 02&S FOR A SINGLE TARGET %XCEPT FOR TWO SMALL DOPPLER REGIONS ALL THE 02&S ARE CLEAR AT MAXIMUM RANGE WHICH PROVIDES MAXIMUM DETEC TION AND MINIMUM LOSS AT THE DESIGN RANGE &OR SOME PULSE COMPRESSION WAVEFORMS THE ECLIPSING LOSS IS ALMOST LINEAR AND PARTIAL OVERLAP STILL ALLOWS SHORTER RANGE DETEC TION %CLIPSING LOSS IS THAT DIMINISHMENT OF RECEIVED POWER WHEN THE RECEIVER IS OFF DURING THE TRANSMITTED PULSE )T IS OFTEN THE LARGEST SINGLE LOSS IN HIGH DUTY RATIO WAVEFORMS 4HE BAD NEWS IS THAT THE AVERAGE DETECTION POWER LOSS IS SLIGHTLY OVER D" SEE &IGURE -02& 3ELECTION !LGORITHMS /BVIOUSLY SELECTING 02&S IN REAL TIME REQUIRES SEVERAL RULES TO GET CLOSE TO A FINAL SET 4HIS IS FOLLOWED BY SMALL ITERATIONS TO PICK THE OPTIMUM SET &OR MEDIUM 02& BOTH RANGE AND VELOCITY BLIND ZONES ARE IMPORTANT &IRST THE SOFTWARE MUST PICK A CENTRAL 02& ABOUT WHICH ALL THE OTHER 02&S ARE DEVIA TIONS TO FILL OUT THE DESIRED VISIBILITY CRITERIA 3ECOND THE 02& SET SHOULD ALL BE CLEAR AT THE MAXIMUM DESIGN RANGE SO THAT DETECTION LOSSES ARE AT A MINIMUM &IGURE SHOWS ONE EXAMPLE CRITERIA FOR SELECTING THE CENTRAL 02& IE THE HIGH EST PROBABILITY OF VISIBILITY 06 )N THE EXAMPLE THE PRODUCT 06 OF THE RANGE 02 AND DOPPLER 0$ TARGET VISIBILITY PROBABILITIES FOR A SINGLE 02& PEAKS AT APPROXIMATELY AND THUS THE OTHER 02&S MUST FILL IN TO REACH CLEAR OR HIGHER 4HERE ARE SEVERAL
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&)'52% -EDIUM 02& CENTRAL 02& SELECTION EXAMPLE
OTHER FACTORS TO BE CONSIDERED DOPPLER AND RANGE BLIND ZONES AND ECLIPSING AND SIDE LOBE CLUTTER %VEN WITH 34!0 SIDELOBE CLUTTER IS A MAJOR LIMITATION "OTH SIDELOBE AND MAIN BEAM CLUTTER CAN BE MINIMIZED BY NARROW DOPPLER ANDOR RANGE BINS IE RESOLUTION CELLS WHICH IMPLY LONGER DWELL TIMES AND HIGHER TRANSMIT BANDWIDTH /NE EXAMPLE METHOD FOR SELECTING A SET OF 02&S FOR -02& IS GIVEN IN %Q 4HE BASIC IDEA IS TO FIND A TIME INTERVAL 4! REPRESENTING THE DESIRED MAXIMUM CLEAR RANGE AND THEN TO CHOOSE A SET OF 02)S IN WHICH ALL WILL BE CLEAR AT MAXIMUM RANGE 4HIS CAN BE ACHIEVED BY DIVIDING 4! BY AN INTEGER TYPICALLY TO 4HIS SET WILL GENERALLY NOT PROVIDE CLEAR OVER THE RANGE DOPPLER SPACE 4HE EVEN DIVISOR 02)S CAN BE PERTURBED ITERATIVELY BY A SMALL AMOUNT TO ACHIEVE THE DESIRED VISIBILITY 4HE NORMALIZED TARGET SIG NAL TO NOISE RATIO 40 VARIES DRAMATICALLY WITH STRADDLE AND ECLIPSING LOSSES FOR EXAMPLE SEE &IGURE 4HE FUNCTION TO BE OPTIMIZED IS A THRESHOLDED VERSION OF 40K OR J
&)'52% %XAMPLE 2'(02& ECLIPSING AND STRADDLE NEAR MAXIMUM RANGE
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&OR EXAMPLE THE THRESHOLD SCHEME MIGHT BE D" 3.2 PER 02) AND OUT OF FOR ALL 02)S /FTEN MULTIPLE AND DIFFERENT THRESHOLDS ARE USED FOR EACH #0) AND 02) ,OWER THRESHOLDS ARE ALLOWABLE FOR HIGHER NUMBERS OF TOTAL HITS )T SHOULD BE NOTED THAT ECLIPSING AND STRADDLING AND SO ON HAVE MUCH LESS EFFECT AT CLOSER RANGES WHERE THERE IS USUALLY MORE THAN ENOUGH 3.2 !NOTHER SERENDIPITOUS EFFECT OF THIS SELECTION TECHNIQUE IS THAT AS AN INDIVIDUAL 02) RANGE CLEAR REGION GETS SMALLER THE DOPPLER CLEAR REGION GETS LARGER FILLING IN THE BLIND ZONES IN BOTH DIMENSIONS 4! 4! ¤2 ³ 4! r ¥ C T P´ 02) K 02) J # r K # r J D J ¦ C µ 40K OR J F R
# ;MOD = r 2 ;MOD R 02) = 6 F 02) K BLIND OR J BLIND K OR J R
WHERE 2C IS MAXIMUM DESIGN CLEAR RANGE C IS THE VELOCITY OF LIGHT MS S P IS TRANSMITTED PULSE WIDTH K AND J ARE INDICES EG x # IS AN ODD INTEGER EG # IS AN EVEN INTEGER EG CJ IS A SMALL PERTURBATION EG z YIELDING VISIBILITY 6BLIND IS A FUNCTION OF F DESCRIBING ECLIPSING AND STRADDLING 2BLIND IS A FUNCTION OF R DESCRIBING ECLIPSING AND STRADDLING # IS A CONSTANT REPRESENTING THE REMAINDER OF THE RANGE EQUATION F IS FREQUENCY R IS RANGE MOD IS MODULO THE FIRST VARIABLE BY THE SECOND 2ANGE 'ATED (IGH 02& 2ANGE GATED HIGH 02& 2'(02& PERFORMANCE IS DRAMATICALLY BETTER FOR DETECTION OF HIGHER SPEED CLOSING TARGETS 2ANGE GATES ARE OFTEN SMALLER THAN RANGE RESOLUTION CELLS OR BINS 2'(02& PRODUCES THE LONGEST DETECTION RANGE AGAINST CLOSING LOW CROSS SECTION TARGETS 5LTRA LOW NOISE FREQUENCY REFERENCES ARE REQUIRED TO IMPROVE SUBCLUTTER VISIBILITY ON LOW 2#3 TARGETS EVEN USING 34!0 2ANGE GATING DRAMATICALLY IMPROVES SIDELOBE CLUTTER REJECTION WHICH ALLOWS OPERATION AT LOWER OWNSHIP ALTITUDES 0RINCIPAL LIMITATIONS OF 2'(02& CLOSING TARGET DETECTION PERFORMANCE ARE ECLIPSING A RADAR RETURN WHEN THE RECEIVER IS OFF DURING THE TRANSMITTED PULSE AND RANGE GATE STRADDLE LOSSES THE RANGE GATE SAMPLING TIME MISSES THE PEAK OF THE RADAR RETURN &IGURE SHOWS 40I WITH ECLIPSING AND STRADDLE LOSSES NEAR MAXIMUM RANGE FOR A HIGH PERFORMANCE 2'(02& 4HIS MODE IS OPTIMIZED FOR LOW CROSS SECTION TARGETS OUT TO JUST BEYOND KM MAXIMUM RANGE 4HE PARTICULAR EXAMPLE HAS OVERLAPPING RANGE GATES TO MINIMIZE STRADDLE LOSS AND TWO 02&S TO ALLOW AT LEAST ONE CLEAR 02& NEAR MAXIMUM RANGE 4HE 02&S ARE K(Z AND K(Z $UTY RATIO IS WITH D" REQUIRED DETECTION 3.2 !VERAGED OVER ALL POSSIBLE TARGET POSI TIONS AND CLOSING DOPPLERS THE LOSSES FOR THIS MODE ARE A SURPRISINGLY SMALL D" 4HE RANGE DOPPLER BLIND ZONES PLOT IS SHOWN IN &IGURE CORRESPONDING TO THE &IGURE WAVEFORM #OMPARED TO THE MEDIUM 02& PLOT SHOWN IN &IGURE THE CLEAR REGION AND CORRESPONDING LOSSES IS DRAMATICALLY BETTER 5NFORTUNATELY RANGE IS VERY AMBIGUOUS .ORMALLY A 2'(02& RANGE WHILE SEARCH 273 MODE IS INTER LEAVED WITH THE HIGHEST PERFORMANCE VELOCITY SEARCH 63 MODE TO RANGE ON PREVI OUSLY DETECTED TARGETS /FTEN 273 IS 2'(02& WITH THREE PHASES IN WHICH A CONSTANT FREQUENCY AND TWO CHIRP LINEAR &- FREQUENCIES TRIANGULAR UP DOWN OR UP STEEPER UP ARE USED TO RESOLVE RANGE AND DOPPLER IN A SPARSE TARGET SPACE !T LOW ALTITUDES SIDELOBE CLUTTER EVEN WITH 34!0 PROCESSING LIMITS PERFORMANCE FOR ALL TARGETS BUT ESPECIALLY OPENING TARGETS
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&)'52% 2'(02& RANGE VELOCITY BLIND ZONES CORRESPONDING TO &IGURE WAVEFORMS
4HIS LIMITATION LEADS TO THE NEED FOR ANOTHER MODE INTERLEAVED WITH 2'(02& &ORTUNATELY THE TIMELINE FOR OPENING TARGETS IS MUCH LONGER NET SPEED IS LESS AND THE ENGAGEMENT RANGE IS MUCH SHORTER WEAPON CLOSURE RATES ARE TOO SLOW /FTEN IN GENERAL SEARCH -02& 623 MEDIUM 02& VELOCITY RANGE SEARCH IS INTERLEAVED WITH (02& 63 AND 273 AS SHOWN IN &IGURE TO PROVIDE ALL ASPECT DETECTION 5NFORTUNATELY BOTH 273 AND 623 HAVE POORER MAXIMUM DETECTION RANGE 2'(02& CAN PROVIDE ALL ASPECT DETECTION BUT TAIL PERFORMANCE IS DRAMATICALLY POORER DUE TO SIDELOBE CLUTTER %VEN WITH 34!0 WHICH SIGNIFICANTLY IMPROVES SIDELOBE CLUTTER REJECTION LOW ALTITUDE TAIL ASPECT DETECTION FOR 2'(02& IS POORER
&)'52% (IGH AND MEDIUM 02& INTERLEAVE FOR ALL ASPECT DETECTION
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2!$!2 (!.$"//+
&)'52% #OMPARISON OF HIGH AND MEDIUM 02&
!N EXAMPLE COMPARISON OF (02& AND -02& AS A FUNCTION OF ALTITUDE FOR A GIVEN MAXIMUM TRANSMITTER POWER POWER APERTURE PRODUCT AND TYPICAL ANTENNA AND RADOME INTEGRATED SIDELOBE RATIO IS SHOWN IN &IGURE !T HIGH ALTITUDE AND NOSE ON THERE IS MORE THAN AN D" DIFFERENCE CAUSED BY BLIND ZONES STRADDLE FOLDED CLUTTER PROCESS ING AND THRESHOLDING LOSSES 2'(02& 3ELECTION !LGORITHMS &IRST AS IN THE -02& CASE ALL 02&S SHOULD BE CLEAR AT THE MAXIMUM DESIGN RANGE 3ECOND ALL 02&S SHOULD BE CLEAR TO THE MAXIMUM DOPPLER OF INTEREST /NE POSSIBLE SELECTION CRITERIA IS GIVEN IN %Q !LTHOUGH THE DETAILS ARE QUITE DIFFERENT THE BASIC PHILOSOPHY IN 02& SELECTION IS TO OPTIMIZE LONG RANGE CLEAR REGIONS 4!
r 2C r L § 4 ¶ T P AND 02) ! AND ) CEIL ¨ ! · C 6A 6T © 02) ! ¸
THEN 02)
¶ §C r T P 4! AND 02) 02) r ¨ · ) © 2C ¸
WHERE 2C IS MAXIMUM DESIGN CLEAR RANGE C IS THE VELOCITY OF LIGHT r MS SP IS TRANSMITTED PULSE WIDTH K IS TRANSMITTED WAVELENGTH CEIL IS THE NEXT INTEGER ABOVE THE VALUE OF THE VARIABLE 6A AND 6T ARE THE MAXIMUM VELOCITIES OF INTEREST FOR AIRCRAFT AND TARGET RESPECTIVELY .ONCOOPERATIVE !IR 4ARGET 2ECOGNITION -&!2 TARGET RECOGNITION 4)$ RECOGNIZES TARGET TYPE BUT NOT UNIQUE IDENTIFICATION 4HERE ARE COOPERATIVE TARGET
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IDENTIFICATION METHODS SUCH AS *4)$3 )&& AND 2& TAGGING THAT CAN BE UNIQUE 4)$ DEPENDS ON DETECTING FEATURES OF THE RADAR SIGNATURE IN FUSION WITH EMISSIONS AND OTHER SENSORS 4HE FIVE MOST COMMON 4)$ SIGNATURES ARE MONOPULSE EXTENT SIMILAR TO THE EXAMPLE SHOWN IN &IGURE RESONANCES HIGH RESOLUTION RANGE (22 PROFILES DOPPLER SPREAD STEPPED FREQUENCY WAVEFORM MODULATION OR MULTIFRE QUENCY 3&7--&2 WHICH CAN BE TRANSFORMED INTO A RANGE PROFILE AND INVERSE SYNTHETIC APERTURE RADAR )3!2 -ONOPULSE EXTENT ALLOWS ESTIMATION OF LENGTH AND WIDTH AS WELL AS SEPARATION OF CLOSELY SPACED AIRCRAFT ! HIGH RANGE RESOLUTION PROFILE ALSO ALLOWS THE SEPARATION OF TARGETS FLYING IN CLOSE FORMATION AS WELL AS THE SEPARATION OF A MISSILE FROM A TARGET ! HIGH RANGE RESOLUTION PROFILE ON A SINGLE TARGET CAN ALLOW RECOGNITION ASSUMING THE TARGET ATTITUDE IS KNOWN OR HAS BEEN GUESSED ,ENGTH WIDTH AND LOCATION OF MAJOR SCATTERING FEATURES CAN BE PROJECTED INTO A RANGE PROFILE IF THE ATTITUDE IS KNOWN 4HE NUMBER OF TYPES OF MAJOR CIVILIAN AND MILITARY AIRCRAFT AND SHIPS IS AT MOST A FEW THOUSAND EASILY STORABLE IN MEMORY 5NFORTUNATELY RECOGNITION IS LIMITED TO BROAD CATEGORIES RATHER THAN -)' - VERSUS -)' 3 EVEN THOUGH THERE ARE SIGNIFICANT DIFFERENCES THAT AIR SHOW VISI TORS CAN EASILY SEE 4HE BASIC NOTION OF DOPPLER RESONANCES STEPPED 3&7- AND MULTIFREQUENCY -&2 SIGNATURES IS MODULATION EITHER BY REFLECTIONS FROM MOVING PARTS EG ENGINE COMPRESSOR TURBINE ROTOR OR PROPELLER BLADES OR BY INTERACTIONS FROM SCATTERERS ALONG THE AIRCRAFT OR VEHICLE EG FUSELAGE WING ANTENNAS OR STORES 3&7--&2 SIGNA TURES ARE CLOSELY RELATED TO HIGH RANGE RESOLUTION SIGNATURES A &OURIER TRANSFORM EASILY CONVERTS ONE TO THE OTHER AND THEY SUFFER THE SAME ATTITUDE ESTIMATION LIMITATIONS 4HE PRINCIPAL ADVANTAGE TO -&2 IS THAT MANY DEPLOYED RADARS HAVE MULTIPLE CHANNELS AND SWITCHING BETWEEN THEM ON A SINGLE TARGET IS RELATIVELY EASY ! SIMPLIFIED VERSION OF THE RECOGNITION PROCESS IS SUMMARIZED IN &IGURE $OPPLER SIGNATURES REQUIRE HIGH DOPPLER RESOLUTION WHICH IS USUALLY EASILY ACHIEVED AND LIMITED ONLY BY DWELL TIME 4HE INDIVIDUAL SCATTERERS WHICH GIVE RISE TO DOPPLER SPREAD ARE SMALL AND SO RECOGNITION IS USUALLY LIMITED TO A FRACTION TYPICAL OF MAXIMUM RANGE *ET ENGINE MODULATION *%- A SUBSET OF DOPPLER SIGNATURES IS AN EXCELLENT TARGET RECOGNITION METHOD %VEN AIRCRAFT WHICH USE THE SAME ENGINE TYPE OFTEN HAVE VARIATIONS IN THE ENGINE APPLICATION SUCH AS THE NUMBER OF COMPRESSOR BLADES OR NUMBER OF ENGINES WHICH ALLOWS UNIQUE TYPE RECOGNITION 4HE REAL PICTURE OF *%- IS NOT SO CLEAN BECAUSE OF MULTIPLE ON AIRCRAFT BOUNCES STRADDLING AND SPEED VARIATIONS BUT CENTROIDING OF EACH LINE IMPROVES THE SIGNATURE ESTIMATE 4HE LAST METHOD OF 4)$ )3!2 WILL BE DEALT WITH IN ANOTHER SECTION )3!2 WORKS WELL ON BOTH AIRCRAFT AND SHIPS ! TYPICAL TAIL HEMISPHERE AIR TO AIR )3!2 IS SHOWN IN &IGURE
&)'52% .ONCOOPERATIVE TARGET RECOGNITION SUBMODES
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&)'52% ! ! )3!2 EXAMPLE 4! "
4HE FUSION OF THE RECOGNITION OF EACH OF THE SIGNATURES ABOVE PROVIDES EXCELLENT NONCOOPERATIVE RECOGNITION 7EATHER !VOIDANCE -ANY AIRCRAFT HAVE SEPARATE WEATHER RADARS 7EATHER AVOIDANCE IS NORMALLY INCORPORATED INTO MODERN FIGHTER RADARS 4HE NORMAL OPERATING FREQUENCY FOR A FIGHTER RADAR HAS NOT BEEN CONSIDERED OPTIMUM FOR WEATHER DETECTION AND AVOIDANCEPRIMARILY DUE TO LACK OF PENETRATION DEPTH INTO A STORM AND REDUCED OPERATING RANGE (OWEVER WITH COMPLEX ATMOSPHERIC ATTENUATION COMPENSATION AND DOPPLER METHODS WEATHER CAN BE DETECTED WELL ENOUGH TO ALLOW WARNING AND AVOID ANCE OF STORMS 4HE PRINCIPAL CHALLENGE IS COMPENSATING FOR BACKSCATTER FROM THE LEADING EDGE OF A STORM AND ADJUSTING FOR ATTENUATION TO SEE FAR ENOUGH INTO A STORM TO EVALUATE ITS SEVERITY 4HE BACKSCATTER FROM EACH CELL IS MEASURED THE POWER REMAINING IS CALCULATED THE ATTENUATION IN THE NEXT CELL IS ESTIMATED AND THEN THE BACKSCATTER IN THE NEXT CELL IS MEASURED AND SO ON 7HEN THE POWER IN THE CELLS DROPS TO THE NOISE LEVEL THOSE CELLS BEHIND IT ARE DECLARED BLIND 3INCE PENETRATION RANGE INTO A STORM IS NOT GREAT THE -&!2 WEATHER MODE USUALLY HAS PROVISIONS TO MARK THE LAST VISIBLE OR RELIABLE RANGE ON THE WEATHER DISPLAY 4HIS IS SO THE PILOT DOES NOT FLY INTO A DARK AREA BELIEVING THERE IS NO WEATHER !IR $ATA ,INKS 4HE -&!2 IS PART OF A NETWORK OF SENSORS AND INFORMA TION SOURCES #)32 NET SOMETIMES CALLED THE 'LOBAL )NFORMATION 'RID ')' ! MAJOR USE OF RADAR AND AIRCRAFT DATA LINKS IS TO PROVIDE TOTAL SITUATIONAL AWARENESS "Y USING ON BOARD AND OFF BOARD SENSOR FUSION A TOTAL AIR AND GROUND PICTURE CAN BE PRESENTED IN THE COCKPIT 4HIS PICTURE CAN BE A COMBINATION OF DATA FROM
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OTHER RADAR SENSORS WINGMAN OR SUPPORT AIRCRAFT ON SIMILAR PLATFORMS TO REPORTS BY OBSERVERS WITH BINOCULARS "ECAUSE THE MODERN FIGHTER IS NET CENTRIC USING EVERYTHING AVAILABLE ON AND OFF BOARD THE AIRCRAFT NET CENTRIC OPERATION REQUIRES DRAMATICALLY HIGHER LEVELS OF DATA EXCHANGE AND FUSION OF DATA FOR PRESENTATION TO THE OPERATOR 2ADAR MODES CAN BE SCHEDULED BETWEEN MULTIPLE AIRCRAFT IN REAL TIME THROUGH THE DATA LINKS 4HE TWO MAIN USES FOR DATA LINKS ASSOCIATED WITH HIGH PERFORMANCE AIRCRAFT ARE HIGH BANDWIDTH IMAGERY TRANSMISSION FROM A WEAPON OR SENSOR PLATFORM TO A SECOND PLATFORM OR GROUND STATION AND LOW BANDWIDTH TRANSMISSION OF CONTEXT TARGETING DATA GUIDANCE AND HOUSEKEEPING COMMANDSn 4HE LARGEST QUANTITY OF DATA LINKS ARE ASSOCIATED WITH WEAPONS 4HE WAVEFORM SELECTED TO TRANSMIT THIS AND OTHER DATA MUST NOT COMPROMISE THE SIGNATURE OF THE PLATFORM AT EITHER END OF THE LINK n 4HERE ARE NUMEROUS DATA LINKS ON FIGHTERS 4ABLE SHOWS AIR DATA LINKS THAT MIGHT BE ON A FIGHTER PLATFORM )N SPITE OF THIS FACT THE RADAR OR PART OF ITS APERTURE IS OFTEN USED FOR A DATA LINK ESPECIALLY TO MISSILES ON THE FLY AND IN RESPONSE TO PEACETIME AIR TRAFFIC CONTROL INTERROGATIONS 0ULSE AMPLITUDE INCLUDING ON OFF PULSE POSITION PHASE SHIFT AND FREQUENCY SHIFT MODULATION ARE COMMONLY USED ,INKS MAY BE UNIDI RECTIONAL OR BIDIRECTIONAL 3OME MISSILES REQUIRE SEMI ACTIVE ILLUMINATION AS WELL AS REFERENCE SIGNALS AND MIDCOURSE COMMAND DATA DERIVED FROM MISSILE AND TARGET TRACK ING 4HE DATA TO AND FROM THE MISSILE IS OFTEN AN ENCRYPTED PHASE CODE IN OR NEAR THE RADAR OPERATING BAND )N SOME CASES THE FREQUENCY CHANNEL IS RANDOMLY SELECTED AT THE FACTORY AND HARDWIRED INTO THE MISSILE &REQUENCY CHANNELS ARE TYPICALLY SELECTED OR COMMUNICATED TO THE RADAR IMMEDIATELY BEFORE LAUNCH )F THE DATA LINK FREQUENCY IS WELL BELOW THE RADAR BAND USUALLY A SMALL NUMBER OF RADIATORS AT THAT LOWER FREQUENCY ARE IMBEDDED IN THE RADAR APERTURE )F THE FREQUENCY IS CLOSE ENOUGH TO THE RADAR BAND THE RADAR APERTURE OR A SEGMENT OF THE APERTURE IS USED 2ADAR !PERTURE $ATALINKING (ISTORICALLY DATALINK FUNCTIONS EMBEDDED IN -&!2S HAVE BEEN USED FOR THE MIDCOURSE GUIDANCE OF MISSILES !N EMERGING APPLICA TION IS THE USE OF THE RADAR APERTURE AS A HIGH POWER HIGH GAIN PRIMARY DATALINK ANTENNA
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WHERE DATALINK TRANSMISSION AND RECEPTION ARE INTERLEAVED WITH OTHER MODES 4HE PRIN CIPAL LIMITATION OF MOST GENERAL PURPOSE DATALINK EQUIPMENT IS THE LOW POWER APERTURE PERFORMANCE ASSOCIATED WITH OMNIDIRECTIONAL OFTEN SHARED ANTENNA APERTURES AND LIM ITED POWER LEVELS 4HIS CONSTRAINS ACHIEVABLE DATA TRANSFER RATES REGARDLESS OF CHANNEL BANDWIDTH !N ASSOCIATED PROBLEM IS VULNERABILITY TO INTERCEPT AND JAMMING INHERENT IN WIDEBEAM APERTURES !N 8 OR +U BAND -&!2 CAN EMIT POWER LEVELS IN THE MULTI KILO WATT RANGE WITH MAIN BEAM BEAMWIDTHS OF A FEW DEGREES AFFORDING HIGH DATA RATES AND SIGNIFICANT RESISTANCE TO JAMMING AND INTERCEPT 4RANSMIT DATA RATES OF OVER -BPS AND RECEIVE DATA RATES OF UP TO 'BPS HAVE BEEN DEMONSTRATED USING A PRODUCTION !%3! AND A MODIFIED #OMMON $ATA ,INK #$, WAVEFORM -ODELING USING REPRESENTATIVE -&!2 PARAMETERS INDICATES THAT PERFORMANCE BOUNDS ARE AT SEVERAL 'BPS THROUGHPUT OVER DISTANCES IN EXCESS OF NAUTICAL MILES SUBJECT TO -&!2 PERFORMANCE PLATFORM ALTITUDE TROPOSPHERIC CONDITIONS AND FORWARD SCATTERING EFFECTS )MPLEMENTATION REQUIRES ACCURATE ANTENNA POINTING SINCE THERE IS RELATIVE MOTION WITH RESPECT TO THE OTHER END OF THE LINK /NE TECHNIQUE INVOLVES THE USE OF AN OUT OF BAND DATALINK CHANNEL EG *4)$3 TO CARRY '03 POSITION UPDATES $OPPLER SHIFTING DUE TO LINK GEOMETRY DYNAMICS MUST BE ACTIVELY COMPENSATED ! RELATED ISSUE IS SYN CHRONIZATION IN TIME TO ALLOCATE TRANSMISSION AND RECEPTION WINDOWS AND TO SYNCHRONIZE TIMEBASES 7HEN EXISTING WAVEFORMS MUST BE USED THIS CAN PRESENT CHALLENGES %XISTING APERTURE SCHEDULING ALGORITHMS CAN THEN ALLOCATE TIME FOR TRANSMISSION OR RECEPTION 4O ACHIEVE VERY HIGH THROUGHPUTS PHASE LINEARITY IN TRANSMIT AND RECEIVE PATHS IS CRITICAL SINCE DATA TRANSMISSION WAVEFORMS RELY ON MODULATION THAT IS EVERY BIT AS COMPLEX AS MANY RADAR MODES 4HIS CAN ALSO IMPACT CHOICE OF TAPER FUNCTION BECAUSE ANGULAR VARIATIONS IN PHASE ACROSS THE MAIN BEAM WAVEFRONT MAY INCUR PERFORMANCE PENALTIES 7HERE THE -&!2 IS PHASE STEERED APERTURE FILL AND SIDELOBE STEERING EFFECTS CONSTRAIN USABLE APERTURE BANDWIDTH SIMILAR TO 3!2 LIMITATIONS 4HE LATTER IS BECAUSE THE ELEMENT PHASE ANGLES REQUIRED TO POINT THE MAIN BEAM ARE NOT THE SAME AS THOSE FOR THE OUTER SIDELOBES OF THE MODULATION USED ,OW BANDWIDTH DATA LINKS CAN USE ALL THE RADAR BANDWIDTH TO IMPROVE ENCRYPTION AND SIGNAL TO JAM RATIOS (OWEVER THE DATA LINK ON A WEAPON IS TRAVELING TO THE TARGET WHICH WILL INEVITABLY ATTEMPT TO PROTECT ITSELF 7HEN THE WEAPON IS NEAR THE TARGET THE SIGNAL TO JAM RATIO CAN BE VERY UNFAVORABLE !NTENNA JAMMER NULLING IS USUALLY REQUIRED SINCE TRANSMITTING MORE POWER TO BURN THROUGH MAY NOT BE POSSIBLE #LEARLY THE DATA FROM AND TO A WEAPON MUST ALSO BE SUFFICIENTLY ENCRYPTED TO PREVENT TAKE OVER OF THE WEAPON IN FLIGHT 4IME SYNCHRONIZED WITH A RADAR TRANSMISSION ON A DIFFERENT SET OF BEAMS ANDOR FRE QUENCIES MESSAGES ARE SENT TO ONE OR MORE MISSILES ON THE FLY TO THE TARGETS /BVIOUSLY ALL THE RANDOM FREQUENCY DIVERSITY SPREAD SPECTRUM AND ENCRYPTION NECESSARY FOR ROBUST COMMUNICATION SHOULD BE INCORPORATED INTO THE MESSAGE %ACH MISSILE MAY ANSWER BACK AT A KNOWN BUT RANDOMIZED OFFSET FREQUENCY AND TIME WITH IMAGE OR HOUSEKEEPING DATA !GAIN A WAVEFORM AS ROBUST AS POSSIBLE IS USED BUT SINCE THE BASE BAND DATA AND LINK GEOMETRY MAY BE QUITE DIFFERENT THE DATA COMPRESSION DIVERSITY AND ENCRYPTION MAY BE DIFFERENT 4HE MISSILE DATALINK WAVEFORM USUALLY MUST BE STEALTHY AND GREATLY ATTENUATED IN THE DIRECTION OF THE TARGET SINCE ONE COUNTERMEASURES STRATEGY IS A DECEPTION REPEATER JAMMER AT THE TARGET (IGH ACCURACY TIME AND FREQUENCY SYNCHRONIZATION INCLUDING RANGE OPENING AND DOPPLER EFFECTS BETWEEN BOTH ENDS OF THE LINK CAN DRAMATICALLY REDUCE THE EFFECTIVENESS OF JAMMING BY NARROWING THE SUSCEPTIBILITY WINDOW 4IME AND FREQUENCY SYNCHRONIZATION ALSO MINIMIZES ACQUISITION OR REACQUISITION TIME
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!N AIRCRAFT USING A DATA LINK IS MOVING WITH RESPECT TO THE OTHER END OF THE LINK SO THE LINK GEOMETRY IS CONTINUALLY CHANGING IN TIME FREQUENCY ASPECT AND ATTITUDE 4HE SIGNAL PROCESSOR WILL GENERATE WAVEFORMS FOR TRANSMISSION BY THE SEEKER OR DATA LINK )T WILL ALSO MEASURE TARGET RANGE ANGLE DOPPLER AND SO ON AND PROVIDE THOSE TO THE OTHER PLATFORM 4HE -&!2 SIGNAL PROCESSOR SENDS MOTION SENSING AND NAVIGATION ESTIMATES TO CORRECT MEASUREMENTS TO TRACK ENCODE AND DECODE DATALINK MESSAGES AND TO PERFORM JAMMER NULLING "EACON 2ENDEZVOUS AND 3TATION +EEPING -OST MODERN MILITARY AIRCRAFT DEPEND ON IN FLIGHT REFUELING FOR MANY MISSIONS 4HIS REQUIRES RENDEZVOUS WITH TANKER AIRCRAFT DURING ALL WEATHER CONDITIONS AS WELL AS STATION KEEPING UNTIL AIRCRAFT CURRENTLY IN LINE FOR REFUELING DEPART 4HIS MAY INVOLVE DETECTING A CODED BEACON ON THE TANKER SKIN TRACKING TANKERS AND OTHER AIRCRAFT AT CLOSE RANGE 3TATION KEEPING RANGES CAN BE BETWEEN AND S OF METERS 3PECIAL SHORT RANGE RADAR MODES ARE USUALLY USED FOR THIS PURPOSE ,OW POWER SHORT PULSE OR &- #7 WAVEFORMS ARE OFTEN USED /NE METER ACCURACY AND METER MINIMUM RANGE IS USUALLY REQUIRED FOR BLIND TANKING (IGH 0OWER !PERTURE *AMMING 4HE BASIC NOTION BEHIND -&!2 HIGH POWER APERTURE JAMMING IS SUGGESTED IN &IGURE ! THREAT EMITTER WHETHER SURFACE OR AIRBORNE IS FIRST DETECTED AND RECOGNIZED BY THE SPHERICAL COVERAGE RADAR WARNING RECEIVER 272 FUNCTION POSSIBLY JUST AN APPLICATION OVERLAY ON THE 2& AND PROCESSING INFRASTRUCTURE SHOWN IN &IGURE )F THE INTERCEPT IS INSIDE THE RADAR FIELD OF VIEW &/6 FINE ANGLE OF ARRIVAL !/! AND POSSIBLY BURST RANGING ARE PERFORMED WITH THE PRIMARY RADAR APERTURE AS SHOWN IN THE TOP PORTION OF &IGURE (IGH GAIN ELECTRONIC SUPPORT MEASURES %3- ARE THEN PERFORMED AND RECORDED ON THE EMITTER MAIN BEAM OR SIDELOBES USING THE NOSE APERTURE )F IT IS DETERMINED FROM AN ON BOARD THREAT TABLE CURRENT RULES OF ENGAGE MENT OR MISSION PLAN HIGH POWER DENSITY JAMMING BASED ON THE CORRESPONDING ON BOARD TECHNIQUES TABLE MAY BE INITIATED USING THE HIGH GAIN NOSE APERTURE
&)'52% -&!2 %#- EXAMPLE
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"ECAUSE THE ADVERSARY RADAR MAY ALSO BE A -&!2 THREAT TABLES WILL BE REQUIRED TO CATEGORIZE THEM BY THEIR APPARENT STATISTICAL NATURE /LD STYLE MATCHING BY 02& PULSE WIDTH AND PULSE TRAIN ENVELOPE WONT WORK VERY WELL BECAUSE WAVEFORMS VARY SO MUCH 4HE TYPICAL NOSE APERTURE RADARnBASED EFFECTIVE RADIATED PEAK POWER %200 CAN EASILY EXCEED D"7 WHICH IS NORMALLY MORE THAN ENOUGH TO PLAY HOB WITH THREAT RADARS &OR EXAMPLE ASSUMING A '(Z IN BAND SIGNAL n D"I THREAT SIDELOBE AND n D"7 THREAT SENSITIVITY A JAMMING PULSE D" ABOVE MINIMUM SENSITIVITY CAN BE GENERATED AT KM /BVIOUSLY IN THE NEAR SIDELOBES OR MAIN BEAM THE RANGE FOR A D" PULSE WILL BE MUCH GREATER
x°{Ê -Ê " Ê - ,*/" -ÊEÊ76 ", 4ERRAIN &OLLOWING 4ERRAIN !VOIDANCE 4HE NEXT EXAMPLE IS TERRAIN FOLLOWING TERRAIN AVOIDANCE 4&4! SHOWN IN &IGURE )N TERRAIN FOLLOWING 4& THE ANTENNA SCANS SEVERAL VERTICAL BARS ORIENTED ALONG THE AIRCRAFT VELOCITY VECTOR AND GENERATES AN ALTITUDE RANGE PROFILE THAT IS SOMETIMES DISPLAYED TO THE PILOT ON AN % SCAN DISPLAY $EPENDING ON THE AIRCRAFTS MANEUVERING CAPABILITIES THERE IS A CONTROL PROFILE G ACCELERATION MANEUVER CONTROL LINE SHOWN AS AN UPWARD CURVING LINE IN THE UPPER RIGHT OF &IGURE n )F THIS CONCEPTUAL LINE INTERCEPTS THE TERRAIN ANYWHERE IN RANGE AN AUTOMATIC UP MANEUVER IS PERFORMED 4HERE IS ALSO A CONCEPTUAL PUSHOVER LINE NOT SHOWN IN THE FIGURE WHICH CAUSES A CORRESPONDING DOWN MANEUVER 4HE CONTROL PRO FILE IN MODERN AIRCRAFT IS AUTOMATIC BECAUSE A HUMAN PILOT DOES NOT HAVE THE REFLEXES TO AVOID ALL POSSIBLE DETECTED OBSTACLES )N TERRAIN AVOIDANCE 4! THE ANTENNA SCAN IS IN A HORIZONTAL PLANE SHOWN IN THE UPPER LEFT OF &IGURE 3EVERAL ALTITUDE PLANE CUTS ARE ESTIMATED AND PRESENTED TO
&)'52% 4&4! MODE EXAMPLE ADAPTED COURTESY 3CI4ECH 0UBLISHING
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THE PILOT ON AN AZIMUTH RANGE DISPLAY SHOWN IN THE LOWER RIGHT OF &IGURE 4HE TERRAIN AVOIDANCE SCAN PATTERN SHOWS ALL THE TERRAIN THAT IS NEAR OR ABOVE THE FLIGHT ALTITUDE AND ONE CUT BELOW AT A SET CLEARANCE ALTITUDE FT TYPICALLY &IGURE LOWER LEFT AND LOWER RIGHT SHOWS THE SITUATION GEOMETRY OF AN AIRCRAFT FLYING TOWARD TWO HILLS AND THE CORRESPONDING ALTITUDE CUTS DISPLAYED TO THE PILOT 4HIS ALLOWS EITHER MANUAL OR AUTOMATIC TURNING FLIGHT TO MAINTAIN A LOWER ALTITUDE 4&4! ALLOWS AN AIRCRAFT TO PENETRATE AT LOW ALTITUDE USING THE TERRAIN AS MASKING THUS PREVENTING EARLY DETECTION 4&4! IS AN IMPORTANT ASPECT OF STEALTH EVEN WHEN THE ALTITUDE IS NOT ALL THAT LOW BECAUSE LOWER ALTITUDES PROVIDE SOME TERRAIN OBSCURATION AND MANY OTHER COMPETING TARGETS WITH SIMILAR CROSS SECTIONS 4ERRAIN (EIGHT %STIMATION 3OME OF THE FEATURES OF 4&4! ARE THE REQUIRED SCAN PATTERN THE NUMBER OF INDEPENDENT FREQUENCY LOOKS REQUIRED TO OBTAIN A VALID ESTIMATE OF THE HEIGHT OF A POSSIBLY SCINTILLATING OBJECT ALONG THE FLIGHT PATH AND THE RANGE COV ERAGE "ECAUSE TERRAIN HEIGHT IS ESTIMATED THROUGH AN ELEVATION MEASUREMENT ANGLE ACCURACY IS CRITICAL 4HE RANGE COVERAGE ALTHOUGH SHORT REQUIRES MULTIPLE OVERLAPPING BEAMS AND MULTIPLE WAVEFORMS /NE METHOD FOR CALCULATING TERRAIN HEIGHT IS SHOWN IN &IGURE )T CONSISTS OF MEASURING THE CENTROID AND EXTENT OF EACH INDIVIDUAL BEAM POSITION OVER MANY PULSES AND ESTIMATING THE TOP OF THE TERRAIN IN EACH BEAM AS SHOWN IN THE FIGURE 4HE CALCULATION IS SUMMARIZED IN %Q ª£ 3I r $I ¹ 0R £ \ 3I \ POWER RECEIVED #R 2E « I º CENTROID 0R I » ¬ £ \ $I \ %R I
#R EXTENT SQUARED 4 #R r %R TERRAIN TOP ESTIMATE 0R
WHERE 3I IS A SINGLE SUM MONOPULSE MEASUREMENT $I IS THE CORRESPONDING ELEVATION DIFFERENCE MONOPULSE MEASUREMENT 5SUALLY THE RANGE ELEVATION PROFILE IS MEASURED IN MULTIPLE SEGMENTS WITH SEPARATE 02&S AND PULSEWIDTHS 4HE LOWEST 02& IS USED TO MEASURE THE LONGEST RANGE PORTION OF THE PROFILE AT THE TOP OF THE ELEVATION SCAN )T USES THE LARGEST PULSE COMPRESSION RATIO n %ACH BEAM POSITION OVERLAPS BY AS MUCH AS AND MULTIPLE FREQUENCY
&)'52% 4ERRAIN HEIGHT ESTIMATION #OURTESY 3CI4ECH 0UBLISHING
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LOOKS IN EACH BEAM CREATE AS MANY AS INDEPENDENT LOOKS 4HE SHORTEST RANGE AT THE BOTTOM OF THE ELEVATION SCAN USES A SHORT PULSE WITH NO PULSE COMPRESSION AND A MUCH HIGHER 02& BUT THE SAME NUMBER OF LOOKS 4HE PULSES IN A 4/4 ARE ALL THE PULSES THAT ILLUMINATE A SINGLE SPOT FROM THE OVERLAPPING BEAMS %ACH OVERLAPPING BEAM MUST BE COMPENSATED FOR THE ANTENNA LOOK ANGLE BEFORE THE BEAMS CAN BE SUMMED FOR A TERRAIN HEIGHT ESTIMATE FROM ALL THE BEAMS 4HE RADAR CROSS SECTION OF THE TERRAIN COULD BE QUITE LOW EG SNOW COVERED LEVEL TREELESS TERRAIN SO SOME PULSES MAY BE INTEGRATED COHERENTLY TO IMPROVE SIGNAL TO NOISE RATIO FOR A #0) OF UP TO PULSES AS SHOWN IN THE 4&4! ENTRY IN 4ABLE 4ERRAIN $ATABASE -ERGING &OR THE PURPOSES OF SAFETY AS WELL AS STEALTH ACTIVE RADAR MEASUREMENTS ARE MERGED WITH A PRESTORED TERRAIN DATABASE &IGURE SHOWS THE GENERAL CONCEPT OF MERGED 4&4! MEASUREMENTS WITH STORED DATA !CTIVE RADAR MEASUREMENTS ARE MADE OUT TO A FEW MILES 4HE INSTANT USE TERRAIN DATA BASE EXTENDS OUT TO PERHAPS TEN MILES 4HE TERRAIN DATABASE CANNOT BE COMPLETELY CURRENT AND MAY CONTAIN CERTAIN SYSTEMATIC ERRORS &OR EXAMPLE THE DATABASE CANNOT CONTAIN THE HEIGHT OF WIRES STRUNG BETWEEN TOWERS OR STRUCTURES ERECTED SINCE THE DATABASE WAS PREPARED &OR THE LOWEST POSSIBLE FLIGHT PROFILES WITH LESS THAN n PROBABILITY OF CRASH PER MISSION THE PRESTORED DATA IS MERGED AND VERIFIED WITH ACTIVE RADAR MEASUREMENTS ,OW CRASH PROBABILITIES MAY ALSO REQUIRE SOME HARDWARE AND SOFTWARE REDUNDANCY )N ADDITION AS THE AIRCRAFT FLIES DIRECTLY OVER A PIECE OF TERRAIN COMBINED TERRAIN PROFILE IS VERIFIED BY A RADAR ALTIMETER FUNCTION 4%2#/-4%202/- IN THE 2& AND PROCESSOR COMPLEX 5SUALLY THE PRESTORED DATA IS GENERATED AT THE REQUIRED RESOLUTION BEFORE A MISSION FROM THE WORLDWIDE DIGITAL TERRAIN ELEVATION DATABASE $4%$ 3EA 3URFACE 3EARCH !CQUISITION AND 4RACK 3EA SURFACE SEARCH ACQUISITION AND TRACK ARE ORIENTED TOWARD THREE TYPES OF TARGETS SURFACE SHIPS SUBMARINES SNORKEL ING OR NEAR THE SURFACE AND SEARCH AND RESCUE 4RACKING MAY BE PRELIMINARY TO ATTACK WITH ANTISHIP WEAPONS !LTHOUGH MOST SHIPS ARE LARGE RADAR TARGETS THEY MOVE RELA TIVELY SLOWLY COMPARED TO LAND VEHICLES AND AIRCRAFT )N ADDITION SEA CLUTTER EXHIBITS BOTH CURRENT AND WIND DRIVEN MOTION AS WELL AS hSPIKYv BEHAVIOR 4HESE FACTS OFTEN REQUIRE HIGH RESOLUTION AND MULTIPLE LOOKS IN FREQUENCY OR TIME TO ALLOW SMOOTHING OF SEA CLUTTER FOR STABLE DETECTION AND TRACK )F THE TARGET IS A SIGNIFICANT SURFACE VES SEL THEN 2#3 MIGHT BE M AND A M RANGE RESOLUTION MIGHT BE USED FOR SEARCH
&)'52% 4&4! TERRAIN MERGING #OURTESY 3CI4ECH 0UBLISHING
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&)'52% 2ANGE PROFILE SHIP RECOGNITION
AND ACQUISITION )F THE TARGET IS A PERISCOPE OR PERSON IN A LIFE RAFT THEN M RESOLU TION MIGHT BE USED SINCE THE 2#3 MIGHT BE LESS THAN M AND SMOOTHING IS ESPECIALLY IMPORTANT $0#! AND DOPPLER PROCESSING IS OFTEN INTERLEAVED WITH TRADITIONAL BRIGHT D" OR GREATER ABOVE BACKGROUND TARGET DETECTION ,OWER 02&S ARE USUALLY USED WHICH IMPLY RELATIVELY HIGH PULSE COMPRESSION RATIOS AS SHOWN IN 4ABLE 3CAN RATES ARE OFTEN SLOW WITH ONE BAR TAKING SECONDS ! HIGH RANGE RESOLUTION PROFILE CAN BE USED TO RECOGNIZE A SHIP JUST AS WITH AN AIRCRAFT )T NATURALLY HAS THE SAME WEAKNESS PREVIOUSLY MENTIONED AND THE ASPECT OR ATTITUDE MUST BE KNOWN )F THE ATTITUDE IS KNOWN THEN THE MAJOR SCATTERERS CAN BE MAPPED INTO A RANGE PROFILE AND CORRELATED WITH THE SHIP POWER RETURN IN EACH CELL !N EXAMPLE OF A SHIP RANGE PROFILE IS SHOWN IN &IGURE 4HESE PROFILES ARE USUALLY GENERATED IN TRACK WHEN THE PROFILE IS STABILIZED IN RANGE 4HE WAKE OF A SURFACE SHIP OR SUBMARINE NEAR THE SURFACE PROVIDES A SUBSTANTIAL CROSS SECTION OVER TIME BUT REQUIRES SURFACE STABILIZED INTEGRATION OVER nS OF SECONDS %ARTHS SURFACE STABILIZED INTEGRATION CAN BE DONE USING A MOTION COM PENSATED DOPPLER BEAM SHARPENING $"3 MODE )NVERSE 3!2 ! FAR MORE RELIABLE METHOD OF SHIP RECOGNITION IS INVERSE SYNTHETIC APERTURE RADAR )3!2 4HE BASIC NOTION IS THAT THE MOTION OF A RIGID OBJECT CAN BE RESOLVED INTO A TRANSLATION AND ROTATION WITH RESPECT TO THE LINE OF SIGHT TO THE TARGET 4HE ROTATION GIVES RISE TO A DIFFERENTIAL RATE OF PHASE CHANGE ACROSS THE OBJECT 4HE PHASE HISTORY DIFFERENCES CAN BE MATCH FILTERED TO RESOLVE INDIVIDUAL SCATTERERS IN A RANGE CELL #ONCEPTUALLY SUCH A MATCHED FILTER IS NO DIFFERENT THAN A FILTER USED TO MATCH A PHASE CODED PULSE COMPRESSION WAVEFORM 4HIS IS THE BASIS OF ALL 3!2 2#3 RANGE IMAGING OBSERVED GEOMETRIC TARGET ACCELERATION TURNTABLE IMAGING AND )3!2 ! SHIP IN OPEN WATER EXHIBITS ROLL PITCH AND YAW MOTIONS ABOUT ITS CENTER OF GRAV ITY CG &OR EXAMPLE &IGURE SHOWS A ROLLING MOTION OF o n THAT MIGHT BE EXHIBITED BY A SHIP IN CALM SEAS 4HE ROLL MOTION MIGHT HAVE A PERIOD OF SECONDS 4HE MOTION OF ALMOST ALL THE SCATTERERS ON A LARGE COMBATANT ARE MOVING IN ARCS OF CIRCLES PROJECTED AS SEGMENTS OF ELLIPSES TO A RADAR OBSERVER &OR A RADAR OBSERVER THE CHANGE IN RANGE D2 ASSOCIATED WITH A ROLL MOVEMENT IS A FUNCTION OF THE HEIGHT H
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&)'52% )NVERSE 3!2 NOTION
OF THE SCATTERER ABOVE THE CENTER OF GRAVITY 4HE APPROXIMATE RANGE RATE FOR EACH SCAT TERER IN ROLLING PITCH YAW MOTION AT A HEIGHT H IS THE TIME DERIVATIVE OF 2 SHOWN IN &IGURE &OR A GIVEN DESIRED CROSS RANGE RESOLUTION WITH REASONABLE SIDELOBES $RC A MUST BE EQUAL TO $RC K &OR THE EXAMPLE FT CROSS RANGE RESOLUTION IS OBTAINABLE WITH A SECOND OBSERVATION TIME 4HE CORRESPONDING DOPPLER AND DOPPLER RATES ARE ALSO GIVEN IN &IGURE &OR A SHIP WHOSE PRINCIPAL SCATTERERS ARE LESS THAN FT ABOVE THE CENTER OF GRAVITY THE DOPPLERS WILL BE IN THE RANGE OF o (Z AT 8 BAND WITH A RATE OF CHANGE OF UP TO o (ZS !S LONG AS THE IMAGE RESOLUTION IS NOT TOO GREAT EACH RANGE DOPPLER BIN CAN BE MATCH FILTERED USING THE HYPOTHESIZED MOTION FOR EACH SCATTERER AND AN IMAGE CAN BE FORMED ON THE SHIP %ACH RANGE BIN MAY CONTAIN MULTIPLE SCATTERERS FROM THE SHIP IN A GIVEN ROLL PLANE AND THEY MAY BE DISTINGUISHED BY THEIR DIFFERING PHASE HISTORY (OWEVER SCATTERERS IN THE PITCH AXIS AT THE SAME RANGE AND ROLL HEIGHT CANNOT BE SEPA RATED !LTHOUGH PITCH AND YAW MOTIONS ARE SLOWER THEY ALSO EXIST AND ALLOW SEPARATION IN OTHER SIMILAR PLANES 2EASONABLY GOOD IMAGES COUPLED WITH EXPERIENCED RADAR OPERATORS ALLOW RECOGNI TION OF MOST SURFACE COMBATANTS 2ECOGNITION AIDS USING PRESTORED SHIP PROFILES ALLOW IDENTIFICATION TO HULL NUMBER IN MANY CASES !N EXAMPLE OF A SINGLE )3!2 IMAGE OF A LANDING ASSAULT SHIP IS GIVEN IN &IGURE 4HE RADAR IN THIS CASE IS ILLUMINATING
&)'52% 3INGLE )3!2 SHIP IMAGE
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THE SHIP FROM THE BOW AT KM AND n GRAZING 4HE BRIGHT SCATTERERS EXHIBIT CROSS RANGE SIDELOBES WHICH CAN BE PARTIALLY REDUCED BY SENSING LARGE RETURNS THEN APPLY ING AMPLITUDE WEIGHTING AND DISPLAY COMPRESSION AS HAS BEEN DONE IN THIS IMAGE )NTEGRATION OF MULTIPLE )3!2 IMAGES DRAMATICALLY IMPROVES QUALITY !IR TO 'ROUND 2ANGING !IR TO GROUND RANGING IS USED MOST OFTEN FOR TARGET ING OF GUNS DUMB BOMBS AND MISSILES WITH SHORT RANGE SEEKERS AGAINST FIXED OR SLOW MOVING TARGETS 4HE TARGET IS DETECTED AND DESIGNATED IN SOME OTHER MODE SUCH AS '-4) $"3 3!2 OR 333 4HE DESIGNATED TARGET IS TRACKED IN RANGE AND ANGLE TO PROVIDE A MORE ACCURATE DISTANCE AND ANGLE TO THE TARGET 4HE TRACKING MAY BE OPEN OR CLOSED LOOP 4HE ESTIMATES ARE THEN PROVIDED TO THE WEAPON BEFORE AND AFTER LAUNCH $EPENDING ON DISTANCE ANOTHER DESIGNATOR SUCH AS A LASER AND THE RADAR MAY BE ALTERNATELY SLAVED TO ONE ANOTHER "OTH THE RADAR AND THE OTHER DESIGNATOR MAY BE SUBJECT TO ATMOSPHERIC REFRACTION ESPECIALLY AT LOW ALTITUDES WHICH IS SOMETIMES ESTIMATED AND COMPENSATED 0RECISION 6ELOCITY 5PDATE 0RECISION VELOCITY UPDATE 065 IS USED FOR NAVIGA TION CORRECTION TO AN INERTIAL PLATFORM !LTHOUGH '03 UPDATES ARE COMMONLY USED TO PROVIDE NAVIGATION IN MANY SITUATIONS A MILITARY AIRCRAFT CANNOT DEPEND SOLELY ON ITS AVAILABILITY &URTHERMORE INERTIAL SENSORS ARE USED TO FILL IN BETWEEN '03 MEASURE MENTS EVEN UNDER THE BEST CIRCUMSTANCES )NERTIAL SENSORS ARE EXTREMELY GOOD OVER SHORT SPAN TIMES BUT VELOCITY DRIFT IS A MAJOR LONG TIME ERROR SOURCE EG KMH ACCUMULATES M ERROR PER MINUTE ! RADAR MODE MAY REQUIRE POSITION TO KM FOR PROPER OPERATION 065 GENERALLY USES THREE OR MORE ANTENNA BEAM POSITIONS IN WHICH IT MAKES A VELOCITY MEASUREMENT AS SHOWN IN &IGURE 4HIS MODE DIRECTLY EMULATES DEDI CATED RADAR DOPPLER NAVIGATORS 4HERE IS A THREE STAGE VELOCITY MEASUREMENT PROCESS &IRST THE SURFACE IS AUTOMATICALLY ACQUIRED IN RANGE 3ECOND A FINE RANGE MEASUREMENT IS MADE OFTEN USING MONOPULSE DISCRIMINANTS AND RANGE CENTROIDING SIMILAR TO THAT SHOWN IN %Q 4HIRD A LINE OF SIGHT VELOCITY MEASUREMENT 6,/3 USING DOPPLER ANDOR RANGE RATE IS MADE ALSO USING CENTROIDING "ECAUSE TERRAIN MAY BE RISING OR FALL ING AT THE ILLUMINATED PATCHES GIVING RISE TO VELOCITY ERRORS TERRAIN SLOPE IS ESTIMATED AND USED TO CORRECT THE ESTIMATED VELOCITY
&)'52% 0RECISION VELOCITY UPDATE CONCEPT
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2!$!2 (!.$"//+
! +ALMAN FILTER A RECURSIVE FILTER THAT ADAPTIVELY COMBINES MODELS OF TARGET MEA SUREMENTS AND OF ERRORS IS EMPLOYED TO PROVIDE A BETTER ESTIMATE OF AIRCRAFT VELOCITY !LTHOUGH THIS PROCEDURE CAN BE PERFORMED OVER LAND OR WATER SEA CURRENTS MAKE OVER WATER MEASUREMENTS FAR LESS ACCURATE 4HIS VELOCITY MEASUREMENT PROVIDES IN FLIGHT TRANSFER ALIGNMENT OF THE VARIOUS INERTIAL PLATFORMS AIRCRAFT WEAPONS AND RADAR ! SET OF OUTPUTS IS PROVIDED TO THE MISSION MANAGEMENT COMPUTER FUNCTION INCLUDING .ORTH %AST $OWN .%$ VELOCITY ERRORS AND ESTIMATES OF STATISTICAL ACCURACIES 3NIFF OR 0ASSIVE ,ISTENING -OST MODES HAVE A PRECURSOR SUBPROGRAM CALLED SNIFF WHICH LOOKS FOR PASSIVE DETECTIONS IN A TENTATIVE OPERATING CHANNEL BEFORE ANY RADAR EMISSIONS IN THAT CHANNEL 4HE DETECTIONS COULD BE A FRIENDLY INTERFEROR A JAMMER OR AN INADVERTENT INTERFEROR SUCH AS A FAULTY CIVILIAN COMMUNICATIONS TRANSPONDER 4HIS LAST EXAMPLE IS THE MOST COMMON IN THE AUTHORS EXPERIENCE )T IS NOT UNCOMMON FOR A FAULTY TRANSPONDER TO APPEAR AS A MILLION SQUARE METER TARGET $OPPLER "EAM 3HARPENING $"3 $"3 IS VERY SIMILAR TO SYNTHETIC APER TURE RADAR 3!2 SINCE BOTH USE THE DOPPLER SPREAD ACROSS THE ANTENNA MAIN BEAM TO CREATE HIGHER RESOLUTION IN THE CROSS BEAM DIRECTION 4HE PRINCIPAL DIFFERENCE IS THE AMOUNT OF ANGULAR COVERAGE BEAM SCANNING RESOLUTION DATA GATHERING TIME AND ACCURACY OF MATCHED FILTERING IN EACH RANGE DOPPLER CELL ! $"3 MAP MAY TAKE A SEC OND TO GATHER OVER AN ANGLE OF n $EPENDING ON THE ANGLE FROM THE AIRCRAFT VELOCITY VECTOR A 3!2 MAP OF A FEW FEET RESOLUTION MAY TAKE TENS OF SECONDS TO GATHER AT 8 BAND $"3 AND 3!2 ARE COMPARED IN A QUALITATIVE WAY IN &IGURE !S THE BEAM IS POSITIONED CLOSER TO THE VELOCITY VECTOR THE DOPPLER SPREAD IS SMALLER AND SO COHERENT DWELL TIMES MUST INCREASE FOR THE SAME RESOLUTION 5SUALLY THERE IS A TRANSITION FROM SHORTER COHERENT PROCESSING INTERVALS #0)S AND LONGER POST DETECTION INTEGRATIONS 0$)S TO LONGER #0)S AND SHORTER 0$)S AS THE BEAM APPROACHES THE AIR CRAFT VELOCITY VECTOR .EAR NOSE ON DWELL TIMES BECOME PROHIBITIVE AND THE SCAN CENTER IS FILLED WITH REAL BEAM MAPPING 4HE REAL BEAM USES THE SAME RANGE RESOLUTION BUT BECAUSE RETURNS FROM THE ENTIRE BEAM ARE USED SOME AMPLITUDE EQUALIZATION IS REQUIRED TO PROVIDE UNIFORM CONTRAST AND BRIGHTNESS ACROSS THE WHOLE MAP 3OME EFFORT IS MADE
&)'52% $OPPLER BEAM SHARPENING $"3 COMPARISON TO 3!2
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&)'52% $"3 PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
TO MATCH FILTER BOTH IN RANGE CLOSURE AND PHASE HISTORY THE DOPPLER SPREAD SINCE ISO RANGE AND ISO DOPPLERS ARE NOT CLOSE TO ORTHOGONAL NEAR THE AIRCRAFT VELOCITY VECTOR SEE &IGURE 3!2 ON THE OTHER HAND IS USUALLY FULLY MATCHED RELATIVE TO THE DESIRED RESOLUTION AND PHASE HISTORY IN EVERY RANGE DOPPLER CELL &IGURE SHOWS THE SIGNAL PROCESSING THAT MIGHT BE FOUND IN $"3 MODE )T CONSISTS OF MULTIPLE TIME AROUND ECHO -4!% SUPPRESSION AMPLITUDE WEIGHTING TO IMPROVE SIDELOBES PRESUMMATION AN &&4 FILTER BANK MAGNITUDE DETECTION IN EACH USABLE FILTER OUTPUT PLACEMENT OF EACH FILTER OUTPUT IN THE CORRECT GROUND STABILIZED LOCATION FOLLOWED BY POST DETECTION INTEGRATION AND SCALING FOR THE DISPLAY FOR CON STANT BRIGHTNESS AND DYNAMIC RANGE $EPENDING ON GRAZING ANGLE AMBIGUOUS RETURNS MAY COMPETE WITH THE REGION TO BE IMAGED /FTEN A COMBINATION OF SENSITIVITY TIME CONTROL 34# AND PULSE TO PULSE PHASE CODING IS USED TO REJECT MULTIPLE TIME AROUND ECHOES -4!% 4HE AMOUNT OF PRESUMMATION 02%35- AND POST DETECTION INTEGRATION 0$) AS A FUNCTION OF BEAM POSITION OFF THE VELOCITY VECTOR IS SHOWN IN THE LOWER RIGHT OF &IGURE &OR EACH DIFFERENT ANGLE THERE IS A DIFFERENT DOPPLER SPREAD ACROSS THE BEAM 4HEREFORE IN ORDER TO MAINTAIN A CONSTANT BEAM SHARPENING RATIO DIFFERENT AMOUNTS OF PRESUMMING MUST BE USED FOR EACH BEAM POSITION 0RESUMMING IS THE FORMATION OF AN UNFOCUSSED SYNTHETIC BEAM IE THERE IS LITTLE OR NO ATTEMPT TO MATCH THE EXACT PHASE HISTORY OF SURFACE POINTS INSIDE THE REAL ANTENNA BEAM BY WHAT IS ESSENTIALLY A LOWPASS FILTER 4HIS WOULD RESULT IN DIFFERENT TARGET BRIGHTNESS AND CON TRAST IF IT WERE NOT COMPENSATED BY APPLYING A CORRESPONDING POST DETECTION INTEGRATION 0$) FOR EACH ANGLE AS SHOWN IN &IGURE -ULTIPLE FREQUENCY LOOKS ARE USED TO REDUCE SPECKLE IN THE IMAGE AND SO SEVERAL DIFFERENT FREQUENCIES ARE 0$)ED 4HE #0) IS THE PRESUM RATIO TIMES THE NUMBER OF FILTER SAMPLES n IS TYPICAL %ACH #0) MAY HAVE MINOR CHANGES IN THE 02& TO SIM PLIFY PROCESSING AND COMPENSATE FOR AIRCRAFT MANEUVERS 4HE AIRCRAFT MAY TRAVEL FT DURING THE GATHERING TIME 4HERE IS CONSIDERABLE TRANSPORT DELAY IN MOST 3!2 AND $"3 PROCESSING AS A RESULT PROCESSED RETURNS MUST BE RECTIFIED IE COMPENSATED FOR GEOMETRIC DISTORTION MOTION COMPENSATED AND MAPPED INTO THE PROPER SPACE ANGLE AND RANGE POSITION 3INCE $"3 USUALLY MAPS A LARGE AREA TO PROVIDE OVERALL GROUND SITUATIONAL AWARENESS THE TOTAL RANGE COVERAGE IS OFTEN COVERED IN MULTIPLE ELEVATION BEAMS AND RANGE SWATHS 4HIS IS TRANSPARENT TO THE OPERATOR BUT REQUIRES DIFFERENT 02&S PULSEWIDTHS FILTER SHAPES AND DWELL TIMES
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2!$!2 (!.$"//+
!LTHOUGH AN -&!2 CONTAINS A VERY STABLE TIME REFERENCE UNCERTAINTIES IN THE RATE OF CHANGE OF TERRAIN HEIGHT REFRACTION WINDS ALOFT AND VERY LONG COHERENT INTEGRATION TIMES FORCE THE MEASUREMENT OF THE CLUTTER DOPPLER ERROR VERSUS PREDICTED FREQUENCY TO MAINTAIN PROPER FOCUS AND BIN REGISTRATION AS SHOWN IN THE UPPER RIGHT IN &IGURE ! SIMILAR FUNCTION IS PERFORMED IN 3!2 AS WELL 3YNTHETIC !PERTURE 2ADAR !S IS THE CASE FOR $"3 3!2 IS A MULTIRATE FILTERING PROBLEM IE A CASCADE OF FILTERS IN WHICH THE INPUT SAMPLING RATE IS HIGHER THAN THE OUTPUT SAMPLING RATE AS SHOWN IN &IGURE WHICH REQUIRES VERY CAREFUL ATTENTION TO RANGE AND AZIMUTH FILTER SIDELOBES 4YPICALLY THE SPACING OF INDIVIDUAL PULSES ON THE GROUND IS CHOSEN TO BE MUCH CLOSER THAN THE DESIRED ULTIMATE RESOLUTION 4HIS ALLOWS LINEAR RANGE CLOSURE AND PHASE CORRECTION SINCE EACH POINT ON THE SURFACE MOVES A SIGNIFICANT FRACTION OF A RANGE CELL PULSE TO PULSE n 4HE INPUT SIGNAL POINT ! IN &IGURE IS SHOWN AS A SPECTRUM AT ! FOLDED ABOUT THE 02& ON THE LEFT IN &IGURE 3UBSEQUENTLY PRESUMMATION IS APPLIED WHICH FORMS AN UNFOCUSSED SYNTHETIC BEAM OR FILTER INSIDE THE MAIN BEAM GROUND RETURN POINT " IN &IGURE WHICH IMPROVES AZIMUTH SIDELOBES AND NARROWS THE SPECTRUM AS SUGGESTED IN THE CENTER GRAPH SHOWN IN &IGURE 4HE PRESUMMER OUTPUT IS RESAMPLED AT A LOWER RATE F3 CONSISTENT WITH ACCEPTABLE FILTER ALIASING 4HEN RANGE PULSE COMPRESSION IS PERFORMED ASSUMING THE TRANSMITTED PULSE IS VERY LONG COMPARED TO THE RANGE SWATH )F CHIRP LINEAR &- IS USED PART OF THE hSTRETCHv PULSE COMPRESSION PROCESSING IS PERFORMED IN THE RANGE COMPRES SION FUNCTION WITH THE REMAINDER PERFORMED IN POLAR FORMAT PROCESSING 4HE DECHIRPED AND PARTIALLY FILTERED OR COMPRESSED OUTPUT SHOWN AT POINT # IN &IGURE MAY BE RESAMPLED AGAIN AT A NEW F3 AS INDICATED IN THE RIGHT GRAPH SHOWN IN &IGURE POINT # )N ANY CASE AZIMUTH VARIABLE PHASE ADJUSTMENT AND BIN MAPPING WHICH COMPEN SATES FOR CHANGES IN MEASUREMENT SPACE ANGLES AND RANGE CLOSURE SINCE SIGNIFICANT MOTION OCCURS DURING THE DATA GATHERING TIME MUST BE PERFORMED BEFORE AZIMUTH FILTER ING SOMETIMES CALLED COMPRESSION BECAUSE IT IS SIMILAR TO PHASE MATCHED PULSE COM PRESSION 4HE OUTPUT OF AZIMUTH COMPRESSION IS SHOWN AT POINT # 4HE COMPLEX 3!2 OUTPUT MAP MUST BE CHECKED FOR DEPTH OF FOCUS AND USUALLY REQUIRES AUTOFOCUS SINCE BOTH ATMOSPHERIC EFFECTS AND LOCALLY RISING OR FALLING TERRAIN MAY CAUSE DEFOCUSING 3UBSEQUENT TO REFOCUSING THE MAP IS MAGNITUDE DETECTED AND HISTOGRAM AVERAGED TO MAINTAIN UNIFORM BRIGHTNESS 4HE MAP IS INTEGRATED WITH OTHER LOOKS WHICH REQUIRES
&)'52% 3!2 PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
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&)'52% 3!2 -ULTIRATE &ILTERING ADAPTED COURTESY 3CI4ECH 0UBLISHING
GEOMETRICAL CORRECTION AND MOTION COMPENSATION 4HE TOTAL MAP DYNAMIC RANGE CAN EASILY BE GREATER THAN D" 4HE TYPICAL COCKPIT DISPLAY IS LIMITED TO n D" AND DYNAMIC RANGE COMPRESSION SUCH AS CONVERTING MAP AMPLITUDES INTO THEIR LOGARITHMS IS OFTEN PERFORMED $"3 OR 3!2 02& 0ULSE ,ENGTH AND #OMPRESSION 3ELECTION &OR EACH 3!2 OR $"3 GEOMETRY THE TRANSMITTED PULSE WIDTH PULSE REPETITION INTERVAL AND PULSE COMPRESSION RATIO MUST BE CALCULATED /NE POSSIBLE SET OF SELECTION CRITERIA IS GIVEN IN %Q 5SUALLY THE LAST RANGE AMBIGUITY BEFORE THE RANGE SWATH IS CHOSEN TO BE OUTSIDE THE MAIN BEAM FAR ENOUGH TO BE AT LEAST D" DOWN INCLUDING 2 EFFECTS /FTEN IN 3!2 THE TRANSMITTED PULSE IS MUCH LARGER THAN THE RANGE SWATH 2SWATH #LEARLY IN EACH OF THE CASES THE NEAREST INTEGRAL CLOCK INTERVAL AND NEAREST CONVENIENT PULSE COMPRESSION RATIO IS SELECTED BECAUSE THE VALUES IN %Q WILL BE CLOCK INTEGERS ONLY BY COINCIDENCE 0ULSE 2EPETITION )NTERVAL 02)
r 2 2MIN 2SWATH 2P L q 02) q r 6A r 5 r "AZ r SINQ C 0ULSE 7IDTH 2P a $UTYMAX r 02) r C -INIMUM !LLOWABLE !MBIGUOUS 2ANGE 2MIN y H r CSC D 5 r "EL 2ANGE 3WATH IS 'EOMETRY AND )NSTRUMENTATION $EPENDENT 2SWATH a H r ;CSC D "EL CSCD "EL = AND 2SWATH a 2MAXSWATH
WHERE K IS TRANSMITTED WAVELENGTH H IS THE AIRCRAFT ALTITUDE "AZ "EL ARE THE AZIMUTH ELEVATION HALF POWER BEAMWIDTHS P D ARE THE ANGLES BETWEEN THE VELOCITY VECTOR AND ANTENNA BEAM CENTER 2 IS THE DISTANCE TO THE FIRST RANGE BIN 6A IS THE AIRCRAFT VELOCITY 2SWATH IS THE RANGE SWATH LENGTH 2MAXSWATH IS MAXIMUM INSTRUMENTED RANGE SWATH 2MIN IS THE RANGE TO THE CLOSEST ALLOWABLE AMBIGUITY $UTYMAX IS ALLOWABLE DUTY RATIO 2P IS THE TRANSMITTED PULSE LENGTH IN DISTANCE UNITS C IS THE VELOCITY OF LIGHT 5 5 ARE BEAMWIDTH MULTIPLIERS AT PREDEFINED POWER ROLLOFF
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2!$!2 (!.$"//+
&OR EXAMPLE ASSUME 6A MS K M H M P D "AZ "EL 5 5 2SWATH KM 2MIN KM DESIRED MAPPING RANGE 2 KM $UTYMAX SELECTING A FIRST GUESS FOR 2P M THEN 02) MSEC 2MIN IS THE EQUIVALENT OF MSEC AND THE NEXT ALLOWABLE AMBIGUITY WOULD BE PAST THE SWATH AT MSEC THEREFORE A 02) OF OR MSEC COULD BE USED WITH A TRANSMITTED PULSE OF APPROXIMATELY OR MSEC RESPECTIVELY 'ROUND -OVING 4ARGET )NDICATION '-4) AND 4RACK '-44 '-4) IS THE DETECTION AND ACQUISITION OF GROUND MOVING TARGETS '-4) AND '-44 RADAR MODES HAVE A DIFFERENT SET OF CHALLENGES &IRST TARGET DETECTION IS USUALLY THE EASY PART THE 2#3 OF MOST ANTHROPOGENIC OBJECTS AND MANY NATURAL MOVING TARGETS IS LARGE n M 5NFORTUNATELY THERE ARE MANY STATIONARY OBJECTS WITH MOVING PARTS SUCH AS VENTILATORS FANS WATER COURSES AND POWER LINES THAT LEAD TO APPARENT FALSE ALARMS /FTEN SLOW MOVING VEHICLES HAVE FAST MOVING PARTS EG HELICOP TERS AND AGRICULTURAL IRRIGATORS -OST AREAS HAVE LARGE NUMBERS OF VEHICLES AND SCATTERERS THAT COULD BE VEHICLES )T IS TYPICAL TO HAVE UP TO BONA FIDE '-4S IN THE FIELD OF VIEW 0ROCESSING CAPACITY MUST BE ADEQUATE TO HANDLE AND DISCRIMINATE THOUSANDS OF HIGH 3.2 THRESHOLD CROSSINGS AND HUNDREDS OF MOVING TARGETS OF INTEREST 5SUALLY MULTI HYPOTHESIS TRACKING FILTERS WILL BE FOLLOWING SEVERAL HUNDRED '-4S OF INTEREST SIMULTANEOUSLY )N MOST CASES ALL TARGETS MUST BE TRACKED AND THEN RECOGNIZED ON THE BASIS OF DOPPLER SPECTRUM HELICOPTERS VS WHEELED VEHICLES VS TRACKED VEHICLES VS SCANNING ANTENNAS RATE OF MEASURED LOCA TION CHANGE VENTILATOR LOCATIONS DONT CHANGE AND CONSISTENT TRAJECTORY EG MPH WHERE THERE ARE NO ROADS IS IMPROBABLE FOR A SURFACE VEHICLE )N ADDITION VEHICLES OF INTEREST MAY HAVE RELATIVELY LOW RADIAL VELOCITIES REQUIRING ENDOCLUTTER PROCESSING IE FAR ENOUGH INSIDE MAIN BEAM CLUTTER THAT DETECTION IS LIMITED FOR DOPPLER ONLY FILTERING ! PROCESSING BLOCK DIAGRAM FOR '-4) IS SHOWN IN &IGURE !LTHOUGH THERE ARE ALTERNATE WAYS TO PERFORM ENDOCLUTTER PROCESSING A MULTIPLE PHASE CENTERnBASED
&)'52% 'ROUND MOVING TARGET DETECTION PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
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PROCESSING SCHEME IS GIVEN IN &IGURE -ULTIPLE CHANNELS OR PHASE CENTERS ARE DIGITIZED AND PULSE COMPRESSED 0ERIODIC CALIBRATION SIGNALS ARE USED TO CREATE A GAIN PHASE AND BEAM STEERING CORRECTION TABLE FOR ALL FREQUENCIES ANTENNA BEAM STEERING AND CHANNELS WHICH ARE THEN APPLIED TO THE DIGITIZED MEASUREMENTS IN EACH CHANNEL -OTION COMPENSATION TO A FRACTION OF A WAVELENGTH FOR PLATFORM MANEUVERS OR DEVIA TIONS IS APPLIED TO THE DATA ! COARSE TWO DIMENSIONAL &&4 IS PERFORMED FOLLOWED BY SPACE TIME ADAPTIVE CALCULATIONS AND FILTER WEIGHTING IS APPLIED TO REJECT SOME CLUT TER AND JAMMING (IGH RESOLUTION DOPPLER FILTERING IS PERFORMED IN A CONVENTIONAL &&4 PERHAPS WITH $0#! CLUTTER CANCELLATION $OPPLER FILTER OUTPUTS ARE USED TO FORM MAIN BEAM CLUTTER ERROR DISCRIMINANTS FOR PRECISELY MEASURING DOPPLER CENTER FREQUENCY TO PROVIDE FRACTION OF WAVELENGTH MOTION COMPENSATION -AIN BEAM CLUTTER IS NOT IN THE SAME FREQUENCY LOCATION FOR EACH RANGE BIN AND SO FILTER OUTPUT ORDER MUST BE ADJUSTED TO PRESENT A COMMON INPUT TO THE THRESHOLD DETECTOR 4HE DOPPLER FILTER BANK OUTPUTS ALSO ARE APPLIED TO A MULTILEVEL THRESHOLD DETECTOR FOR GROUND MOVING TARGET DETECTION SIMILAR TO THOSE DESCRIBED IN h'ROUND -OVING 4ARGET 4HRESHOLDINGv 3UM AND DIFFERENCE DISCRIMINANT FUNCTIONS ARE FORMED AND STORED IN BUFFER STORAGE FOR EACH DETECTED MOVING TARGET TO IMPROVE TARGET TRACKING AND GEOLOCATION ACCURACY /FTEN 02&S ARE AMBIGUOUS IN BOTH RANGE AND DOPPLER BUT UNAMBIGUOUS INSIDE THE MAIN BEAM AND NEAR SIDELOBES IE THERE IS ONLY ONE RANGE OR DOPPLER AMBIGU ITY INTERVAL IN THE MAIN BEAM AND NEAR SIDELOBES 02& SELECTION IS SIMILAR TO ! ! -02& 5SUALLY FEWER 02&S ARE USED FOUR OR FIVE ARE TYPICAL ! RANGE AMBIGU ITY MAY BE IN THE MAIN BEAM AT LOW GRAZING ANGLES 4WO OUT OF FOUR OR THREE OUT OF FIVE IS USUALLY THE FINAL DETECTION CRITERIA 02&S TYPICALLY ARE n K(Z #ODED WAVEFORMS ARE OFTEN USED TO REJECT AMBIGUOUS RETURNS OUTSIDE THE ANTENNA MAIN BEAM THAT COMPETE WITH THE REGION OF INTEREST ! FT RANGE CELL SIZE IS OFTEN USED TO MATCH THE SMALLEST VEHICLE OF INTEREST AND TO REDUCE BACKGROUND CLUTTER 'ROUND MOVING TARGET RECOGNITION MAY REQUIRE FT RESOLUTION !NTENNA ILLUMINATION MUST BE GROUND STABILIZED SINCE THE AIRCRAFT WILL ENGAGE IN BOTH INTENTIONAL AND UNINTENTIONAL MANEUVERS 'ROUND -OVING 4ARGET 4HRESHOLDING 4HE TYPICAL MULTILEVEL THRESHOLD HAS SEVERAL UNIQUE FEATURES )N ADDITION TO THE OBVIOUS ALERT CONFIRM PROPERTIES A DOUBLE THRESHOLDING METHOD IN WHICH A LOWER FIRST THRESHOLD NOMINATES RADAR RETURNS AS POS SIBLE TARGETS TO BE CONFIRMED BY A RETURN OBSERVATION WITH A HIGHER THRESHOLD IT ALSO USES MULTIPLE PHASE CENTER DISCRIMINANTS AS WELL AS NEAR SIDELOBE THRESHOLD MULTIPLI ERS %VEN WITH 34!0 THE NON GAUSSIAN NATURE OF CLUTTER REQUIRES HIGHER THRESHOLDS IN THE MAIN BEAM AND NEAR SIDELOBES 4HRESHOLD CROSSINGS ARE CORRELATED IN RANGE AND DOPPLER AND BUFFERED ALONG WITH CORRESPONDING PHASE CENTER DISCRIMINANTS WHICH ARE PRESENTED TO TRACKING FILTERS OR ACTIVITY COUNTERS 4HERE ARE THREE REGIONS OF THRESHOLDING MAIN BEAM CLUTTER LIMITED DETECTION NEAR SIDELOBE CLUTTER LIMITED DETECTION AND THERMAL NOISE LIMITED DETECTION .EAR SURFACE TARGETS OF INTEREST WILL OFTEN HAVE RADIAL VELOCITIES OF A FEW MILES PER HOUR FOR LONG PERIODS OF TIME WHICH FORCES THE DETECTION OF GROUND MOVING TARGETS WELL INTO MAIN BEAM CLUTTER 0HASE MONOPULSE $0#! OR 34!0 PROCESSING ALLOWS THE FIRST ORDER CANCELLATION OF CLUTTER FOR MANY SLOW MOVING TARGETS 5NFORTUNATELY CLUTTER DOES NOT ALWAYS HAVE WELL BEHAVED STATISTICAL TAILS AND TO MAINTAIN A CONSTANT FALSE ALARM RATE THE THRESHOLD MUST BE RAISED FOR ENDOCLUTTER TARGETS 4HE OUTPUT OF THE DOPPLER FILTER BANK MIGHT BE THOUGHT OF AS A TWO DIMENSIONAL RANGE DOPPLER IMAGE 4HERE WILL STILL BE PARTS OF MAIN BEAM CLUTTER THAT ARE COMPLETELY DISCARDED EXCEPT FOR MOTION COMPENSA TION BECAUSE CLUTTER CANCELLATION IS INADEQUATE
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2!$!2 (!.$"//+
&)'52% -ULTIREGION '-4 THRESHOLDING #OURTESY 3CI4ECH 0UBLISHING
!N EXAMPLE THRESHOLDING SCHEME BASED ON THESE CONCEPTS IS SHOWN IN &IGURE 4HE RANGE DOPPLER SPACE IS BROKEN UP INTO A GRID OF RANGE BINS AND DOPPLER FILTERS AS SHOWN IN THE FIGURE %ACH CELL IN THE GRID MIGHT BE ¾ RANGE DOPPLER BINS WITH GRID CELLS TOTAL 3OME GRID LOCATIONS CLOSE TO MAIN BEAM CLUTTER -,# IN FIGURE ARE USED FOR FORMING MAIN BEAM CLUTTER DISCRIMINANTS ONLY AND ARE OTHERWISE DISCARDED 4HE BINS IN THE EXAMPLE IN EACH GRID CELL ARE ENSEMBLE AVERAGED %! IN SUM AND DIFFERENCE CHANNELS 4HE POWER IN EACH BIN IN A GRID CELL IN THE CLEAR THERMAL NOISE LIMITED REGION IS COMPARED TO A THRESHOLD 04(%! WHICH IS A FUNCTION OF THE %! IN THAT GRID CELL )N THE ENDOCLUTTER NEAR SIDELOBE REGION A DISCRIMINANT #S IS FORMED AND USED TO PROVIDE ADDITIONAL CLUTTER CANCELLATION PRIOR TO THRESHOLDING !GAIN THE THRESHOLD 04(%! IS A FUNCTION OF THE %! IN THAT GRID CELL AND A PRIORI KNOWLEDGE OF THE CLUTTER STATISTICS !LTHOUGH ONLY ONE THRESHOLD IS DESCRIBED TWO ARE ACTUALLY USED BEFORE HITS AND THEIR CORRESPONDING DISCRIMINANTS ARE PASSED TO THE TRACK FILES !LL LOW THRESHOLD HITS ARE PASSED TO ACTIVITY COUNTERS !S COMPLEX AS THIS THRESHOLDING SCHEME SEEMS TO BE IT IS VERY DETECTION POWER EFFICIENT 4YPICAL '-4 7EAPON $ELIVERY !S MENTIONED PREVIOUSLY MISSILE GUIDANCE REQUIRES TRACKING OF BOTH TARGETS AND MISSILES ALSO BULLETS IN GUN LAYING RADAR GUN LAY ING IS A TERM INVENTED BY THE 5+ DURING 77)) FOR RADAR POINTING OF ANTIAIRCRAFT GUNS 2ANGE ACCURACY IS AT LEAST AN ORDER OF MAGNITUDE BETTER THAN ANGLE ACCURACY 3OME METHOD MUST BE USED TO IMPROVE ANGLE ACCURACY FOR WEAPON DELIVERY !N EXAMPLE PRO CESSING DIAGRAM FOR '-4 WEAPON DELIVERY IS SHOWN IN &IGURE )N THIS CASE THREE DIFFERENT CLASSES OF TARGET OR MISSILE ARE TRACKED ! SINGLE WAVEFORM MAY BE USED TO TRACK STATIONARY ENDO AND EXOCLUTTER MOVING TARGETS AND MISSILES OR BULLETS %ACH CLASS OF RETURN BASED ON ITS RANGE AND DOPPLER LOCATION IS SEPARATELY TRACKED AND GEOLOCATED 4HERE ARE SEVERAL COMMON TYPES OF GEOLOCATION MANY OF THEM ARE BASED ON USING EITHER $4%$ OR CARTOGRAPHIC DATA /NE METHOD USING CARTOGRAPHIC DATA IS SHOWN
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&)'52% 4YPICAL '-4 WEAPON GUIDANCE ADAPTED COURTESY 3CI4ECH 0UBLISHING
IN &IGURE !N ERROR ELLIPSE AND ITS CORRESPONDING ECCENTRICITY ARE CALCULATED FOR EACH TARGET )F THE ECCENTRICITY IS LESS THAN SOME ARBITRARY THRESHOLD EG RELA TIVE THE MINIMUM PERPENDICULAR DISTANCE IS CALCULATED FOR ROAD SEGMENTS INSIDE THE SIGMA ELLIPSE !S SHOWN IN THE FIGURE THE PERPENDICULAR INTERCEPT MAY NOT LIE INSIDE THE ROAD SEGMENT AND WILL BE DISCARDED 4HE MINIMUM DISTANCE FOR VALID ROAD SEGMENT DISTANCES WILL BE SELECTED AS THE '-4 LOCATION )F THE ECCENTRICITY IS GREATER THAN THE THRESHOLD THE ROAD SEGMENTS THAT HAVE A MAJOR ELLIPSE AXIS INTERCEPT INSIDE SIGMA ARE COMPARED AND THE MINIMUM DISTANCE IS SELECTED /BVIOUSLY SOME OTHER SCREENING MUST ALSO BE APPLIED &OR EXAMPLE SOME ROADS CANNOT SUPPORT HIGH SPEEDS AND TANKS DO NOT HAVE TO BE ON ROADS ! COMMON 3!2 -4) DISPLAY MAY BE PRESENTED TO THE OPERATOR )N ADDITION GUID ANCE COMMANDS OR ERRORS ARE DERIVED FROM THE MEASUREMENTS AND PROVIDED TO DOWN LINKS TO EITHER MISSILES ON THE FLY OR GUN DIRECTING COMPUTERS FOR THE NEXT ROUNDS 3HORT TERM COHERENT CHANGE DETECTION MAY BE USED TO SEPARATE STATIONARY TARGETS FROM SLOW MOVING ENDOCLUTTER TARGETS 3HORT TERM COHERENT CHANGE DETECTION IS A METHOD IN WHICH TWO COHERENT 3!2 MAPS TAKEN WITHIN A FEW HOURS OF ONE ANOTHER AT THE SAME FREQUENCY ARE REGISTERED AND CROSS CORRELATED PIXEL BY PIXEL 4HE FAST MOVING TARGET CATEGORY USUALLY INCLUDES BOTH TARGETS AND BULLETS OR MISSILES
&)'52% #ARTOGRAPHIC ASSISTED '-4 GEOLOCATION
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2!$!2 (!.$"//+
-ISSILE 0ERFORMANCE !SSESSMENT 4RACK AND 5PDATE -ISSILE MIDCOURSE GUID ANCE USUALLY CONSISTS OF ASSESSING THE MISSILE PERFORMANCE MEASUREMENT OF THE TARGET AND MISSILE LOCATION PREDICTION OF THE PATH OF EACH AND UPDATING THE RESULTING DATA TO THE MISSILE FOR THE BEST FUTURE INTERCEPT OF THE TARGET )T MAY ALSO INCLUDE THE MOST CURRENT ESTIMATE OF THE TARGET TYPE AND ATTITUDE FOR BEST FUZING 4HE MISSILE USUALLY SENDS DATA ABOUT ITS STATE OF HEALTH OWNSHIP MEASUREMENTS REMAINING FUEL AMOUNTS AND TARGET ACQUISITION IF ANY 7HEN THE MISSILE IS CLOSE TO THE DATA LINK AIRCRAFT WHICH MAY OR MAY NOT BE THE LAUNCHING PLATFORM COMMUNICATION IS OFTEN THROUGH AN APERTURE OTHER THAN IN THE MAIN -&!2 !S THE DISTANCE GETS GREATER THE PRIMARY -&!2 APERTURE IS USED !S THE DATA LINK AIRCRAFT MANEUVERS THE APERTURE THAT HAS THE LARGEST PROJECTED AREA IN THE DIREC TION OF THE MISSILE IS USED 4HE BANDWIDTH TO THE MISSILE IS VERY LOW AND CAN BE REDUNDANT AND HIGHLY ENCRYPTED TO PROVIDE GOOD ANTIJAM !* PROTECTION )F IT CONTAINS IMAGERY THE UPLINK BANDWIDTH FROM THE MISSILE IS RELATIVELY LARGE AND WILL HAVE COMPARATIVELY LOWER !* PERFORMANCE !N ADAPTIVE -&!2 PRIMARY APERTURE CAN IMPROVE A WIDER BAND MISSILE UPLINK !* IF THE JAMMER IS OFFSET FROM THE TARGET !T THE MISSILE END THE MISSILE ANTENNA CAN HAVE JAMMER NULLING TO IMPROVE DOWNLINK !* !'# #ALIBRATE AND 3ELF 4EST 5SUALLY AT THE BEGINNING OF A NEW MODE THE END OF EACH SCAN BAR OR ONCE PER SECOND THE CALIBRATE AND SELF TEST SUBPROGRAM IS INVOKED BY THE OPERATIONAL FLIGHT PROGRAM /&0 EXECUTIVE ! SEQUENCE OF SUBROUTINES IS EXECUTED THAT MEASURES PHASE AND GAIN UNBALANCE BETWEEN CHANNELS USING A SIGNAL INJECTED ON THE ANTENNA 4HIS IS USUALLY DONE OVER A RANGE OF INPUT AMPLITUDES FREQUEN CIES AND !'# SETTINGS BECAUSE OF THE NONLINEAR CHARACTERISTICS OF MOST 2& FRONT ENDS !LSO FOR MODES LIKE 4&4! A FULL SET OF OFF ANGLE DIAGNOSTICS IS PERFORMED WHICH TESTS THE INTEGRITY OF THE ENTIRE MEASUREMENT PROCESSING AND FLIGHT CONTROL CHAIN OFTEN ENOUGH TO KEEP THE PROBABILITY OF A FAILURE INDUCED CRASH PER FLIGHT BELOW n IN THE PRESENCE OF JAMMING OR COMPONENT FAILURES )N ADDITION THERE ARE INITIATED BUILT IN TESTS AT TWO LEVELS AN OPERATIONAL READINESS TEST PERFORMED AS PART OF MISSION INITIATION AND A FAULT ISOLATION TEST PERFORMED BY THE MAINTENANCE CREW IN RESPONSE TO AN OPERATOR DEFICIENCY REPORT "OTH TESTS TAKE LONGER AND ARE MORE EXHAUSTIVE )N THE BEST CASE THE SPECIFIC FLIGHT LINE OR A FIRST LEVEL MAIN TENANCE REPLACEABLE ASSEMBLY IS IDENTIFIED WITH HIGH PROBABILITY 3UCH ASSEMBLIES ARE THEN SENT TO A DEPOT FOR REPLACEMENT REPAIR FAILURE TRACKING ANDOR RECLAMATION &OR ASSEMBLIES THAT HAVE A VERY LOW FAILURE RATE IT IS USUALLY CHEAPER TO REPLACE AND RECLAIM RATHER THAN REPAIR EVEN WHEN THE ASSEMBLY IS VERY EXPENSIVE
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4HIS CHAPTER INCORPORATES MATERIAL WRITTEN BY *OHN 7 4AYLOR *R FOR THE FIRST AND SECOND EDITIONS AND UPDATED BY -ICHAEL 9EOMANS FOR THIS EDITION
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4HE BLOCK DIAGRAM SHOWN IN &IGURE INCLUDES SENSITIVITY TIME CONTROL 34# ATTENUATION AT THE 2& INPUT !LTERNATIVELY ADJUSTABLE 2& ATTENUATION MAY BE USED %ITHER FORM PROVIDES INCREASED DYNAMIC RANGE ABOVE THAT PROVIDED BY THE ANALOG TO DIGITAL !$ CONVERTERS 2& ATTENUATION IS DESCRIBED IN MORE DETAIL IN 3ECTION 4HE 34# ATTENUATOR IS FOLLOWED BY AN 2& AMPLIFIER OFTEN REFERRED TO AS A LOW NOISE AMPLIFIER ,.! 4HIS AMPLIFIER PROVIDES SUFFICIENT GAIN WITH A LOW NOISE FIGURE TO MINIMIZE THE SUBSEQUENT DEGRADATION OF THE OVERALL RADAR NOISE FIGURE BY SUBSEQUENT COMPONENTS )F SUFFICIENT GAIN IS PROVIDED IN THE ANTENNA PRIOR TO THE RECEIVER IT MAY BE POSSIBLE TO ELIMINATE THIS GAIN STAGE 4HE 2& FILTER PROVIDES REJECTION OF OUT OF BAND INTERFERENCE INCLUDING REJECTION AT THE 2& IMAGE FREQUENCY !FTER DOWNCONVERSION TO )& A BANDPASS FILTER PROVIDES REJECTION OF UNWANTED SIGNALS AND SETS THE RECEIVER ANA LOG PROCESSING BANDWIDTH !DDITIONAL GAIN IS PROVIDED AT )& TO OVERCOME LOSSES AND RAISE THE SIGNAL LEVEL REQUIRED FOR SUBSEQUENT PROCESSING AND TO SET THE CORRECT SIGNAL LEVEL INTO THE !$ CONVERTERS !N )& LIMITER PROVIDES GRACEFUL LIMITING OF LARGE SIGNALS THAT WOULD OTHERWISE OVERLOAD THE !$ CONVERTERS 4HE TWO DOMINANT METHODS OF DIGITIZATION )& SAMPLING AND ANALOG )1 DEMODULA TION WITH BASEBAND !$ CONVERSION ARE INCLUDED FOR ILLUSTRATION IN &IGURE THOUGH IN GENERAL RECEIVERS WILL NOT INCLUDE BOTH TECHNIQUES 0RIOR TO THE AVAILABILITY OF AFFORD ABLE DIGITAL SIGNAL PROCESSING A NUMBER OF FUNCTIONS SUCH AS MONOPULSE COMPARISON CURRENTLY PERFORMED IN THE DIGITAL DOMAIN WERE PERFORMED USING ANALOG PROCESSING WITHIN THE RECEIVER 2EADERS INTERESTED IN THE DETAILS OF THESE ANALOG PROCESSING TECH NIQUES WILL FIND DETAILS IN THE FIRST AND SECOND EDITIONS OF THIS HANDBOOK !LL BUT THE SIMPLEST OF RADARS REQUIRE MORE THAN ONE RECEIVER CHANNEL &IGURE SHOWS A SINGLE RECEIVER CHANNEL THAT MAY BE REPLICATED ANY NUMBER OF TIMES DEPENDING ON THE RADAR SYSTEM REQUIREMENTS -ONOPULSE RADARS TYPICALLY INCLUDE THREE RECEIVER CHANNELS SUM DELTA AZIMUTH AND DELTA ELEVATION CHANNELS USED TO PROVIDE IMPROVED ANGLE ACCURACY !DDITIONALLY MANY MILITARY RADAR SYSTEMS INCLUDE A SIDELOBE BLANKER OR SEVERAL SIDELOBE CANCELER CHANNELS TO COMBAT JAMMING 3INCE THE ADVENT OF DIGITAL BEAMFORMING RADAR SYSTEMS THE NUMBER OF RECEIVER CHANNELS REQUIRED HAS INCREASED DRAMATICALLY WITH SOME SYSTEMS NOW REQUIRING HUNDREDS OF RECEIVER CHANNELS )N THESE MULTICHANNEL RECEIVER SYSTEMS CLOSE MATCHING AND TRACKING OF GAIN AND PHASE IS REQUIRED 2ECEIVER CHANNEL TRACKING AND EQUALIZATION ARE DISCUSSED IN 3ECTION 4HE STABLE LOCAL OSCILLATOR 34!,/ BLOCK PROVIDES THE LOCAL OSCILLATOR FREQUENCIES FOR DOWNCONVERSION IN THE RECEIVER AND UPCONVERSION IN THE EXCITER &OR TRUE COHERENT OPERATION THE 34!,/ IS LOCKED TO A LOW FREQUENCY REFERENCE SHOWN BY THE REFERENCE OSCILLATOR IN &IGURE THAT IS USED AS THE BASIS FOR ALL CLOCKS AND OSCILLATORS SUCH AS THE COHERENT LOCAL OSCILLATOR #/(/ WITHIN THE RECEIVER AND EXCITER 4HE CLOCK GENERATOR PROVIDES CLOCKS TO THE !$ CONVERTERS AND THE DIRECT DIGITAL SYNTHESIZER AND PROVIDES THE BASIS FOR THE SIGNALS THAT DEFINE THE RADAR TRANSMIT AND RECEIVE INTERVALS 4HE DIRECT DIGITAL SYNTHESIZER IN &IGURE IS USED TO GENERATE THE TRANSMIT WAVE FORMS AT AN )& FREQUENCY PRIOR TO UPCONVERSION TO THE 2& OUTPUT FREQUENCY &ILTERING IN THE EXCITER IS REQUIRED TO REJECT ALIASED SIGNALS FROM THE DIRECT DIGITAL SYNTHESIZER AND UNWANTED MIXER PRODUCTS 2& GAIN IS TYPICALLY REQUIRED TO PROVIDE A SUFFICIENT DRIVE LEVEL TO THE TRANSMITTER OR PHASED ARRAY ANTENNA !LMOST ALL MODERN RADAR SYSTEMS USE DIGITAL SIGNAL PROCESSING TO PERFORM A VARIETY OF FUNCTIONS INCLUDING PULSE COMPRESSION AND THE DISCRIMINATION OF DESIRED TARGETS FROM INTERFERENCE ON THE BASIS OF VELOCITY OR THE CHANGE IN PHASE FROM ONE PULSE TO THE NEXT 0REVIOUSLY PULSE COMPRESSION WAS PERFORMED USING ANALOG PROCESSING WITH DISPERSIVE DELAY LINES TYPICALLY SURFACE ACOUSTIC WAVE 3!7 DEVICES !NALOG PULSE COMPRES SION HAS LARGELY BEEN REPLACED BY PULSE COMPRESSION USING DIGITAL SIGNAL PROCESSING
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)N THE CASE OF VERY WIDEBAND WAVEFORMS ANALOG STRETCH PROCESSING SEE 3ECTION MAY BE USED TO REDUCE THE SIGNAL BANDWIDTH BEFORE SUBSEQUENT DIGITAL SIGNAL PROCESSING 4HE RECEIVER DISCUSSED HEREIN FOCUSES ON THOSE FUNCTIONS THAT PROVIDE ANALOG PRO CESSING AND DIGITIZATION OF THE INDIVIDUAL PULSE SIGNALS WITH THE MINIMUM OF DISTORTION ENABLING SUBSEQUENT DIGITAL SIGNAL PROCESSING TO MAXIMIZE THE PERFORMANCE OF THE RADAR 4HE DIGITAL SIGNAL PROCESSING FUNCTION IS NOT NORMALLY CONSIDERED TO BE PART OF THE RECEIVER
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" - ,/" 2ECEIVERS GENERATE INTERNAL NOISE THAT MASKS WEAK SIGNALS BEING RECEIVED FROM THE RADAR TRANSMISSIONS 4HIS NOISE CONTRIBUTION WHICH CAN BE EXPRESSED AS EITHER A NOISE TEM PERATURE OR A NOISE FIGURE IS ONE OF THE FUNDAMENTAL LIMITATIONS ON THE RADAR RANGE 4HE NOISE TEMPERATURE OR NOISE FIGURE OF THE RADAR RECEIVER HAS BEEN REDUCED TO THE POINT THAT IT NO LONGER REPRESENTS A DOMINANT INFLUENCE IN CHOOSING BETWEEN AVAILABLE ALTERNATIVES )T IS A PARADOX THAT A NOISE PARAMETER IS USUALLY THE FIRST CHAR ACTERISTIC SPECIFIED FOR A RADAR RECEIVER YET FEW RADARS EMPLOY THE LOWEST NOISE RECEIVER AVAILABLE BECAUSE SUCH A CHOICE REPRESENTS TOO GREAT A SACRIFICE IN OTHER PERFORMANCE PARAMETERS #OST IS RARELY A CONSIDERATION IN REJECTING A LOWER NOISE ALTERNATIVE ! REDUCTION IN REQUIREMENTS FOR ANTENNA GAIN OR TRANSMITTER POWER INVARIABLY PRODUCES COST SAVINGS FAR IN EXCESS OF ANY ADDED COST OF A LOWER NOISE RECEIVER /THER VITAL PERFORMANCE CHARACTERISTICS THAT GENERALLY DICTATE THE CHOICE OF RECEIVER FRONT END INCLUDE L
L
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$YNAMIC RANGE AND SUSCEPTIBILITY TO OVERLOAD )NSTANTANEOUS BANDWIDTH AND TUNING RANGE 0HASE AND AMPLITUDE STABILITY
! DIRECT COMPROMISE MUST BE MADE BETWEEN THE NOISE FIGURE AND THE DYNAMIC RANGE OF A RECEIVER 4HE INTRODUCTION OF AN 2& AMPLIFIER IN FRONT OF THE MIXER NECESSARILY INVOLVES RAISING THE SYSTEM NOISE LEVEL AT THE MIXER TO MAKE THE NOISE CONTRIBUTION OF THE MIXER ITSELF INSIGNIFICANT %VEN IF THE 2& AMPLIFIER ITSELF HAS MORE THAN ADEQUATE DYNAMIC RANGE THE MIXER DYNAMIC RANGE HAS BEEN COMPROMISED AS INDICATED BELOW
2ATIO OF FRONT END NOISE TO MIXER NOISE 3ACRIFICE IN MIXER DYNAMIC RANGE $EGRADATION OF SYSTEM NOISE TEMPERATURE DUE TO MIXER NOISE
%XAMPLE
%XAMPLE
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D" D" D"
D" D" D"
D" D" D"
4HE SAME CONSIDERATIONS APPLY TO THE SETTING OF THE NOISE LEVEL AT THE INPUT TO THE !$ CONVERTERS 4RADITIONALLY THE NOISE CONTRIBUTION OF THE !$ CONVERTER WAS CON SIDERED BY THE SYSTEM ENGINEERS AS A SEPARATE CONTRIBUTION TO THE OVERALL RADAR SYSTEM NOISE DISTINCT FROM RECEIVER NOISE AND WAS ACCOUNTED FOR AT THE SYSTEM LEVEL 4ODAY IT HAS BECOME COMMON TO INCLUDE THE !$ CONVERTER NOISE AS PART OF THE OVERALL RECEIVER NOISE #ONSEQUENTLY IT IS IMPORTANT TO UNDERSTAND WHETHER OR NOT THE CONTRIBUTION OF THE !$ CONVERTER IS INCLUDED IN THE SPECIFICATION FOR THE NOISE FIGURE OF A RECEIVER
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)N ACTIVE ARRAY ANTENNAS AND MANY CONVENTIONAL ANTENNAS LOW NOISE AMPLIFIERS ,.!S ESTABLISH THE SYSTEM NOISE FLOOR PRIOR TO THE RECEIVER INPUT 4HE NOISE FROM THE ANTENNA IS USUALLY SET WELL ABOVE THE RECEIVER NOISE FLOOR SUCH THAT THE RECEIVER HAS ONLY A SMALL IMPACT ON OVERALL SYSTEM NOISE !GAIN THE TRADE OFF MUST BE PERFORMED BETWEEN SYSTEM DYNAMIC RANGE AND NOISE FIGURE $EFINITIONS $YNAMIC 2ANGE REPRESENTS THE RANGE OF SIGNAL STRENGTH OVER WHICH THE RECEIVER WILL PERFORM AS EXPECTED )T REQUIRES THE SPECIFICATION OF A MINIMUM LEVEL TYPICALLY THE NOISE FLOOR THE MAXIMUM LEVEL THAT CAN BE HANDLED WITH SOME ALLOWABLE DEVIATION FROM THE IDEAL RESPONSE AND THE TYPE OF SIGNAL TO BE HANDLED 4HESE PARAMETERS ARE DEFINED THROUGH A VARIETY OF CHARACTERISTICS AS DESCRIBED BELOW -ODERN RADARS SYSTEMS INCREASINGLY RELY SOLELY ON LINEAR RECEIVER CHANNELS FOL LOWED BY DIGITAL SIGNAL PROCESSING PROVIDING BOTH INCREASED FLEXIBILITY AND NEAR IDEAL SIGNAL DETECTION CHARACTERISTICS 0REVIOUSLY A VARIETY OF LIMITING OR LOGARITHMIC RECEIVER APPROACHES WERE USED TO PERFORM VARIOUS SIGNAL PROCESSING FUNCTIONS 4HESE RECEIVERS MUST DEFINE AN ALLOWABLE ERROR IN THEIR OUTPUTS RELATIVE TO THEIR IDEAL NONLIN EAR RESPONSE 2ECEIVERS THAT INCLUDE SOME FORM OF GAIN CONTROL MUST DISTINGUISH BETWEEN INSTAN TANEOUS DYNAMIC RANGE AND THE TOTAL DYNAMIC RANGE THAT IS ACHIEVED AS A RESULT OF PROGRAMMED GAIN VARIATION 2ECEIVER )NPUT .OISE ,EVEL "ECAUSE MANY RADAR SYSTEMS INCLUDE LOW NOISE AMPLIFIERS PRIOR TO THE INPUT OF THE RECEIVER IT IS IMPORTANT TO UNDERSTAND AND SPECIFY THE NOISE LEVEL AT THE RECEIVER INPUT 4HIS NOISE LEVEL IS SET BY THE ANTENNA NOISE TEM PERATURE AND ITS TOTAL EFFECTIVE NOISE GAIN OR LOSS 4HE NOISE LEVEL CAN BE SPECIFIED EITHER AS AN RMS POWER IN A SPECIFIED BANDWIDTH OR AS A NOISE POWER SPECTRAL DENSITY 3YSTEM .OISE 4HE SYSTEM NOISE LEVEL IS THE COMBINED ANTENNA AND RECEIVER NOISE 4YPICALLY THE RECEIVER INPUT NOISE WILL EXCEED THAT OF THE NOISE DUE TO THE RECEIVER ITSELF SO THAT THE RECEIVER HAS ONLY A SMALL IMPACT ON THE SYSTEM NOISE TEMPERATURE OR NOISE FIGURE 4HUS WHEN DEFINING DYNAMIC RANGE PARAMETERS SUCH AS SIGNAL TO NOISE RATIO IT IS IMPORTANT TO SPECIFY WHETHER THE NOISE LEVEL BEING REFERENCED IS THE RECEIVER NOISE OR TOTAL SYSTEM NOISE -INIMUM 3IGNAL OF )NTEREST -INIMUM SIGNAL DEFINITIONS SUCH AS MINIMUM DETECTABLE SIGNAL OR MINIMUM DISCERNABLE SIGNAL HAVE BEEN USED IN THE PAST HOW EVER THESE DEFINITIONS HAVE BECOME LESS COMMON DUE TO THE EXTENSIVE USE OF DIGITAL SIGNAL PROCESSING TECHNIQUES $IGITAL SIGNAL PROCESSING OF THE RECEIVER OUTPUT ALLOWS THE DETECTION OF SIGNALS WELL BELOW THE RECEIVER NOISE FLOOR AND THE MINIMUM DETECT ABLE LEVEL DEPENDS ON THE NATURE OF THE PROCESSING PERFORMED 3IGNAL TO .OISE 2ATIO 3.2 3.2 IS THE RATIO OF THE SIGNAL LEVEL TO THAT OF THE NOISE 3.2 IS TYPICALLY EXPRESSED IN DECIBELS D" 4HE MAXIMUM RECEIVER 3.2 IS SET BY THE NOISE CONTRIBUTION AND MAXIMUM SIGNAL CAPABILITY OF EVERY COMPONENT IN THE CHAIN HOWEVER SINCE THE LIMITING TECHNOLOGY IS OFTEN THE !NALOG TO $IGITAL !$ CONVERTER THE PRECEDING COMPONENTS AND GAIN STRUCTURE ARE OFTEN CHOSEN SUCH THAT THE MAXIMUM 3.2 IS DRIVEN BY THE PERFORMANCE OF THE !$ CONVERTER -ORE DETAILS OF THE RELATIONSHIP BETWEEN !$ CONVERTER AND RECEIVER 3.2 ARE INCLUDED IN 3ECTIONS AND
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3PURIOUS &REE $YNAMIC 2ANGE 3&$2 3&$2 IS THE RATIO OF THE MAXIMUM SIG NAL LEVEL TO THAT OF LARGEST SPURIOUS SIGNAL CREATED WITHIN THE RECEIVER 3&$2 IS TYPI CALLY EXPRESSED IN DECIBELS D" 4HIS PARAMETER IS DETERMINED BY A VARIETY OF FACTORS INCLUDING THE MIXER INTERMODULATION SPURIOUS DESCRIBED IN MORE DETAIL IN 3ECTION THE SPURIOUS CONTENT OF THE RECEIVER LOCAL OSCILLATORS THE PERFORMANCE OF THE !$ CONVERTER AND THE MANY SNEAK PATHS THAT MAY RESULT IN UNWANTED SIGNALS COUPLING ONTO THE RECEIVER SIGNAL PATH )NTERMODULATION $ISTORTION )-$ )NTERMODULATION DISTORTION IS A NONLINEAR PRO CESS THAT RESULTS IN GENERATION OF FREQUENCIES THAT ARE LINEAR COMBINATIONS OF THE FUN DAMENTAL FREQUENCIES OF THE INPUT SIGNALS 3ECOND AND THIRD ORDER INTERMODULATION ARE THE MOST COMMONLY SPECIFIED AND THE PERFORMANCE OF THE RECEIVER IS USUALLY SPECIFIED IN TERMS OF TWO TONE SECOND AND THIRD ORDER INPUT INTERCEPT POINTS 4HE INTERCEPT POINT IS THE EXTRAPOLATED LEVEL AT WHICH THE POWER IN THE INTERMODULATION PRODUCT EQUALS THAT OF THE TWO FUNDAMENTAL SIGNALS &OR INPUT SIGNALS AT FREQUENCIES F AND F SECOND ORDER INTERMODULATION DISTORTION PRODUCES SIGNALS AT FREQUENCIES F n F F F F AND F 4HIRD ORDER INTERMODU LATION DISTORTION PRODUCES SIGNALS AT FREQUENCIES F n F F n F F F F F F AND F &OR NARROW BAND SIGNALS ONLY THE THIRD ORDER PRODUCTS F n F AND F n F FALL IN BAND AND CONSEQUENTLY THIRD ORDER DISTORTION IS TYPICALLY THE PRIMARY CONCERN 4HE POWER LEVELS OF THESE THIRD ORDER INTERMODULATION PRODUCTS ARE GIVEN BY
0 F F D"M 0F D"M 0F D"M 0)0 D"M
0 F F D"M 0F D"M 0F D"M 0)0 D"M
WHERE 0F D"M POWER OF INPUT SIGNAL AT FREQUENCY F IN D"M 0F D"M POWER OF INPUT SIGNAL AT FREQUENCY F IN D"M 0)0D"M THIRD ORDER INTERCEPT POINT IN D"M )NTERMODULATION CAN RESULT IN A VARIETY OF UNDESIRABLE EFFECTS SUCH AS L
L
L
)NTERMODULATION OF CLUTTER RETURNS CAUSING BROADENING OF CLUTTER DOPPLER WIDTH RESULTING IN THE MASKING OF TARGETS 5NWANTED IN BAND SIGNALS DUE TO OUT OF BAND INTERFERING SIGNALS RESULTING IN FALSE TARGETS )NTERMODULATION PRODUCTS FROM IN BAND SIGNALS THAT CANNOT BE READILY CANCELLED THROUGH LINEAR CANCELLATION TECHNIQUES RESULTING IN SUSCEPTIBILITY TO JAMMERS
)NTERMODULATION DISTORTION OCCURS THROUGHOUT THE RECEIVER CHAIN #ONSEQUENTLY THE RECEIVER WILL HAVE A SIGNIFICANTLY DIFFERENT INPUT INTERCEPT POINT DEPENDING ON THE SIGNAL FREQUENCY RELATIVE TO THE RADIO FREQUENCY 2& )& AND VIDEO FILTER BANDWIDTHS )T IS THEREFORE IMPORTANT TO DISTINGUISH BETWEEN THE REQUIREMENTS FOR IN BAND AND OUT OF BAND INTERMODULATION DISTORTION AS DIFFERENT SIGNALS HAVE DIFFERENT EFFECTS ON THE RECEIVER #ROSS -ODULATION $ISTORTION #ROSS MODULATION OCCURS AS A RESULT OF THIRD ORDER INTERMODULATION WHEREBY THE AMPLITUDE MODULATION !- OF ONE SIGNAL TYPICALLY AN UNWANTED INTERFERENCE SIGNAL IN THE OPERATING 2& BAND BUT USUALLY OUTSIDE THE TUNED SIGNAL BANDWIDTH IS TRANSFERRED ONTO THE DESIRED SIGNAL
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4HE RESULTANT PERCENT !- MODULATION D ON THE DESIRED SIGNAL IS GIVEN BY
D U
05 0)0 05
WHERE U PERCENT !- MODULATION OF THE UNWANTED SIGNAL 05 POWER OF UNWANTED SIGNAL 0)0 THIRD ORDER INTERCEPT POINT #ROSS MODULATION CAN RESULT IN THE MODULATION OF CLUTTER AND TARGET RETURNS DUE TO LARGE AMPLITUDE MODULATED OUT OF BAND INTERFERENCES RESULTING IN POOR CLUTTER CANCEL LATION AND POOR RANGE SIDELOBE PERFORMANCE D" #OMPRESSION 0OINT 4HE INPUT D" COMPRESSION POINT OF A RECEIVER IS A MEASURE OF THE MAXIMUM LINEAR SIGNAL CAPABILITY AND IS DEFINED AS THE INPUT POWER LEVEL AT WHICH THE RECEIVER GAIN IS D" LESS THAN THE SMALL SIGNAL LINEAR GAIN 2ECEIVER GAIN COMPRESSION CAN RESULT FROM COMPRESSION IN AMPLIFIERS MIXERS AND OTHER COMPONENTS THROUGHOUT THE RECEIVER CHAIN 4YPICALLY THE RECEIVER IS DESIGNED TO PROVIDE CONTROLLED GAIN COMPRESSION THROUGH A LIMITING STAGE AT THE FINAL )& AS DESCRIBED IN 3ECTION !NALOG TO $IGITAL #ONVERTER &ULL 3CALE 4HE !$ CONVERTER FULL SCALE LEVEL DETER MINES THE MAXIMUM LEVEL THAT CAN BE DIGITIZED 2ECEIVERS TYPICALLY PROVIDE CONTROLLED LIMITING 3ECTION TO PREVENT THE SIGNAL LEVEL FROM EXCEEDING THE FULL SCALE LEVEL OF THE !$ CONVERTER 0RACTICAL CONSIDERATIONS MEAN THAT THE HARD LIMIT LEVEL IS TYPI CALLY SET D" BELOW FULL SCALE TO PREVENT OVERLOAD AS A RESULT OF COMPONENT TOLERANCE VARIATIONS 4YPES OF 3IGNALS 6ARIOUS TYPES OF SIGNALS ARE OF INTEREST IN DETERMINING DYNAMIC RANGE REQUIREMENTS DISTRIBUTED TARGETS POINT TARGETS WIDEBAND NOISE JAM MING AND NARROW BAND INTERFERENCE )F THE RADAR EMPLOYS A PHASE CODED SIGNAL THE ELEMENTS OF THE RECEIVER PRECEDING THE DECODER WILL NOT RESTRICT THE DYNAMIC RANGE OF A POINT TARGET AS SEVERELY AS THEY WILL FOR DISTRIBUTED CLUTTER THE TIME BANDWIDTH PRODUCT OF THE CODED PULSE INDICATES THE ADDED DYNAMIC RANGE THAT THE DECODER WILL EXTRACT FROM THE POINT TARGETS #ONVERSELY IF THE RADAR INCORPORATES AN EXCESSIVELY WIDE BANDWIDTH 2& AMPLIFIER ITS DYNAMIC RANGE MAY BE SEVERELY RESTRICTED DUE TO WIDEBAND NOISE INTERFERENCE 7HEN LOW NOISE AMPLIFIERS ,.!S ARE INCLUDED IN THE ANTENNA PRIOR TO FORMING THE RECEIVE BEAMS THE ANTENNA SIDELOBE LEVELS ACHIEVED ARE DEPENDENT UPON THE DEGREE TO WHICH GAIN AND PHASE CHARACTERISTICS ARE SIMILAR IN ALL ,.!S $YNAMIC RANGE HAS AN EXAGGERATED IMPORTANCE IN SUCH CONFIGURATIONS BECAUSE MATCHING NONLINEAR CHAR ACTERISTICS IS IMPRACTICAL 4HE EFFECT OF STRONG INTERFERENCEMOUNTAIN CLUTTER OTHER RADAR PULSES OR ELECTRONIC COUNTERMEASURES %#- ENTERING THROUGH THE SIDELOBES WILL BE EXAGGERATED IF IT EXCEEDS THE DYNAMIC RANGE OF THE ,.!S BECAUSE SIDELOBES WILL BE DEGRADED 4HE ,.!S ARE WIDEBAND DEVICES VULNERABLE TO INTERFERENCE OVER THE ENTIRE RADAR OPERATING BAND AND OFTEN OUTSIDE THIS BAND ALTHOUGH OFF FREQUENCY INTERFERENCE IS FILTERED IN SUBSEQUENT STAGES OF THE RECEIVER STRONG INTERFERENCE SIGNALS CAN CAUSE CLUTTER RETURNS IN THE ,.! TO BE DISTORTED DEGRADING THE EFFECTIVENESS OF DOPPLER FILTERING AND CREATING FALSE ALARMS 4HIS PHENOMENON IS DIFFICULT TO ISOLATE AS THE CAUSE OF FALSE ALARMS IN SUCH RADARS OWING TO THE NONREPETITIVE CHARACTER OF MANY
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SOURCES OF INTERFERENCE )N MODERN RADAR ARCHITECTURES THAT EMPLOY DIGITAL BEAMFORM ING NONLINEARITY AT ANY STAGE OF THE RECEIVER CHANNEL WILL CREATE SIMILAR PROBLEMS 3YSTEM CALIBRATION TECHNIQUES AND ADAPTIVE BEAMFORMING TECHNIQUES CAN COM PENSATE FOR LINEAR GAIN AND PHASE DEVIATIONS HOWEVER AS FOR THE CASE OF THE ,.! NONLINEARITIES DESCRIBED ABOVE COMPENSATION FOR NONLINEAR CHARACTERISTICS IS EITHER IMPRACTICAL OR IMPOSSIBLE WHEN THE CAUSE OF THE NONLINEAR DISTORTION IS OUTSIDE THE DIGITIZED BANDWIDTH %VALUATION ! THOROUGH EVALUATION OF ALL ELEMENTS OF THE RECEIVER IS NEC ESSARY TO PREVENT UNANTICIPATED DEGRADATION OF NOISE FIGURE OR DYNAMIC RANGE )NADEQUATE DYNAMIC RANGE MAKES THE RADAR RECEIVER VULNERABLE TO INTERFERENCE WHICH CAN CAUSE SATURATION OR OVERLOAD MASKING OR HIDING THE DESIRED SIGNALS ! TABULAR FORMAT FOR SUCH A COMPUTATION A TYPICAL EXAMPLE OF WHICH IS SHOWN IN 4ABLE WILL PERMIT THOSE COMPONENTS THAT CONTRIBUTE SIGNIFICANT NOISE OR RESTRICT THE DYNAMIC RANGE TO BE QUICKLY IDENTIFIED h4YPICALv VALUES ARE INCLUDED IN THE TABLE FOR PURPOSES OF ILLUSTRATION
#OMPONENT .OISE &IGURE #OMPONENT 'AIN #OMPONENT /UTPUT RD /RDER )NTERCEPT #OMPONENT /UTPUT D" #OMPRESSION 0OINT #UMULATIVE 'AIN #UMULATIVE .OISE &IGURE #UMULATIVE /UTPUT RD /RDER )NTERCEPT #UMULATIVE /UTPUT D" #OMPRESSION 0OINT 2ECEIVER .OISE ,EVEL 3YSTEM .OISE ,EVEL "ANDWIDTH !$ 3.2 IN .YQUIST "7 !$ #ONVERTER 3AMPLE 2ATE !$ &ULL 3CALE ,EVEL !$ .OISE ,EVEL 3YSTEM .OISE 2ELATIVE TO !$ .OISE -AXIMUM 0OINT #LUTTER OR 4ARGET ,EVEL
D"
D" D"M
D"M
D" D"
D"M
D"M
D"M(Z
D"M(Z -(Z D" -(Z
D"M
D"M(Z D" D"M
!$ #ONVERTER
,IMITER
!'# !TTENUATOR
!MPLIFIER
"ANDPASS &ILTER
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"ANDPASS &ILTER
)NPUT
!MPLIFIER
5NITS
34# !TTENUATOR
4!",% .OISE AND $YNAMIC 2ANGE #HARACTERISTICS
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È°ÎÊ 7 /Ê " - ,/" $EFINITIONS 4HE INSTANTANEOUS BANDWIDTH OF A COMPONENT IS THE FREQUENCY BAND OVER WHICH THE COMPONENT CAN SIMULTANEOUSLY PROCESS TWO OR MORE SIGNALS TO WITHIN A SPECIFIED ACCURACY 7HEN THE TERM INSTANTANEOUS BANDWIDTH IS USED AS A RADAR RECEIVER PARAMETER IT REFERS TO THE RESULTING BANDWIDTH SET BY THE COMBINATION OF 2& )& VIDEO AND DIGITAL FILTERING THAT OCCURS WITHIN THE RECEIVER 7HEN THE RADAR RECEIVER EMPLOYS STRETCH PROCESSING DEFINED LATER IN THIS SEC TION THE 2& PROCESSING BANDWIDTH IS SIGNIFICANTLY LARGER THAN THE )& BANDWIDTH #ONSEQUENTLY THE TERM INSTANTANEOUS BANDWIDTH CAN BE CONFUSING #ONFUSION CAN BE AVOIDED BY USING THE TERMS 2& WAVEFORM BANDWIDTH ,/ LINEAR &- CHIRP BANDWIDTH AND )& PROCESSING BANDWIDTH 4HE RELATIONSHIP BETWEEN 2& ,/ AND )& BANDWIDTHS USED IN STRETCH PROCESSING IS EXPLAINED IN MORE DETAIL LATER 4HE TUNING RANGE IS THE FREQUENCY BAND OVER WHICH THE COMPONENT MAY OPERATE WITHOUT DEGRADING THE SPECIFIED PERFORMANCE 4UNING IS TYPICALLY ACCOMPLISHED BY ADJUSTING THE LOCAL OSCILLATOR FREQUENCY AND ADJUSTING THE 2& FILTERING CHARACTERIS TICS 4HE FREQUENCY RANGE OVER WHICH THE RADAR OPERATES IS OFTEN REFERRED TO AS THE OPERATING BANDWIDTH )MPORTANT #HARACTERISTICS 4HE ENVIRONMENT IN WHICH A RADAR MUST OPERATE INCLUDES MANY SOURCES OF ELECTROMAGNETIC RADIATION WHICH CAN MASK THE RELATIVELY WEAK RETURNS FROM ITS OWN TRANSMISSION 4HE SUSCEPTIBILITY TO SUCH INTERFERENCE IS DETERMINED BY THE ABILITY OF THE RECEIVER TO SUPPRESS THE INTERFERING FREQUENCIES IF THE SOURCES HAVE NARROW BANDWIDTH OR TO RECOVER QUICKLY IF THEY ARE MORE LIKE IMPULSES IN CHARACTER /NE MUST BE CONCERNED WITH THE RESPONSE OF THE RECEIVER IN BOTH FREQUENCY AND TIME DOMAINS 'ENERALLY THE CRITICAL RESPONSE IS DETERMINED IN THE )& PORTION OF THE RECEIVER THIS WILL BE DISCUSSED IN 3ECTION (OWEVER ONE CANNOT IGNORE THE 2& PORTION OF THE RECEIVER MERELY BY MAKING IT HAVE WIDE BANDWIDTH 3ECTION DISCUSSED HOW EXCES SIVELY WIDE BANDWIDTH CAN PENALIZE DYNAMIC RANGE IF THE INTERFERENCE IS WIDEBAND NOISE %VEN MORE LIKELY IS AN OUT OF BAND SOURCE OF STRONG INTERFERENCE EG OTHER RADARS 46 STATIONS OR MICROWAVE COMMUNICATION LINKS THAT IF ALLOWED TO REACH THIS POINT CAN EITHER OVERLOAD THE MIXER OR BE CONVERTED TO )& BY ONE OF THE SPURIOUS RESPONSES OF THE MIXER )DEAL MIXERS IN A SUPERHETERODYNE RECEIVER ACT AS MULTIPLIERS PRODUCING AN OUTPUT PROPORTIONAL TO THE PRODUCT OF THE TWO INPUT SIGNALS %XCEPT FOR THE EFFECT OF NONLINEARI TIES AND UNBALANCE THESE MIXERS PRODUCE ONLY TWO OUTPUT FREQUENCIES EQUAL TO THE SUM AND THE DIFFERENCE OF THE TWO INPUT FREQUENCIES 4HE NONLINEARITIES AND IMBALANCE OF MIXERS IS DESCRIBED IN MORE DETAIL IN 3ECTION 4HE BEST RADAR RECEIVER IS ONE WITH THE NARROWEST 2& INSTANTANEOUS BANDWIDTH COM MENSURATE WITH THE RADIATED SPECTRUM AND HARDWARE LIMITATIONS AND WITH GOOD FREQUENCY AND IMPULSE RESPONSES ! WIDE TUNING RANGE PROVIDES FLEXIBILITY TO ESCAPE INTERFERENCE BUT IF THE INTERFERENCE IS INTENTIONAL AS IN THE CASE OF JAMMING A CHANGE IN 2& FRE QUENCY ON A PULSE TO PULSE BASIS MAY BE REQUIRED USING SWITCHABLE OR ELECTRONICALLY TUNED FILTERS )F THE 2& FILTERING IS LOCATED PRIOR TO 2& AMPLIFICATION THE FILTER INSERTION LOSS WILL HAVE A D" FOR D" IMPACT ON THE RECEIVER NOISE FIGURE ANOTHER SACRIFICE IN NOISE TEMPERATURE TO ACHIEVE MORE VITAL OBJECTIVES 9TTRIUM IRON GARNET 9)' FILTERS AND PIN DIODE SWITCHED FILTERS HAVE BEEN USED TO PROVIDE THE NECESSARY FREQUENCY AGILITY
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3TRETCH 0ROCESSING 3TRETCH PROCESSING IS A TECHNIQUE FREQUENTLY USED TO PRO CESS WIDE BANDWIDTH LINEAR &- WAVEFORMS 4HE ADVANTAGE OF THIS TECHNIQUE IS THAT IT ALLOWS THE EFFECTIVE )& SIGNAL BANDWIDTH TO BE SUBSTANTIALLY REDUCED ALLOWING DIGITIZA TION AND SUBSEQUENT DIGITAL SIGNAL PROCESSING AT MORE READILY ACHIEVABLE SAMPLE RATES "Y APPLYING A SUITABLY MATCHED CHIRP WAVEFORM TO THE RECEIVER FIRST ,/ COINCIDENT WITH THE EXPECTED TIME OF ARRIVAL OF THE RADAR RETURN THE RESULTANT )& WAVEFORM HAS A SIGNIFICANTLY REDUCED BANDWIDTH FOR TARGETS OVER A LIMITED RANGE WINDOW OF INTER EST 0ROVIDED THAT THE LIMITED RANGE WINDOW CAN BE TOLERATED A SUBSTANTIALLY REDUCED PROCESSING BANDWIDTH ALLOWS MORE ECONOMICAL !$ CONVERSION AND SUBSEQUENT DIGITAL SIGNAL PROCESSING )T ALSO ALLOWS A GREATER DYNAMIC RANGE TO BE ACHIEVED WITH LOWER RATE !$ CONVERTERS THAN WOULD BE ACHIEVABLE IF DIGITIZATION OF THE ENTIRE 2& SIGNAL BANDWIDTH WERE PERFORMED )F THE ,/ CHIRP RATE IS SET EQUAL TO THE RECEIVED SIGNAL CHIRP RATE OF A POINT TARGET THE RESULTANT OUTPUT IS A CONSTANT FREQUENCY TONE AT THE OUTPUT OF THE STRETCH PROCESSOR RECEIVER WITH FREQUENCY $T"4 WHERE $T IS THE DIFFERENCE IN TIME BETWEEN THE RECEIVED SIGNAL AND THE ,/ CHIRP SIGNAL AND "4 IS THE WAVEFORM CHIRP SLOPE CHIRP BANDWIDTH PULSE WIDTH 4ARGET DOPPLER IS MAINTAINED THROUGH THE STRETCH PROCESSING PRODUCING AN OUTPUT FREQUENCY OFFSET EQUAL TO THE DOPPLER FREQUENCY THOUGH THE WIDE PERCENTAGE BANDWIDTH OFTEN USED MEANS THAT THE DOPPLER FREQUENCY CAN CHANGE SIGNIFICANTLY OVER THE DURATION OF THE PULSE )GNORING THE EFFECT OF TARGET DOPPLER THE REQUIRED 2& SIGNAL BANDWIDTH IS EQUAL TO THE TRANSMITTED WAVEFORM BANDWIDTH 'IVEN THE 2& SIGNAL BANDWIDTH "2 THE RECEIVED PULSE WIDTH 42 AND THE RANGE INTERVAL $4 THE REQUIRED ,/ REFERENCE WAVEFORM DURA TION IS GIVEN BY
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6 ,Ê," /Ê #ONFIGURATION 4HE RADAR FRONT END CONSISTS OF A LOW NOISE AMPLIFIER ,.! AND BANDPASS FILTER FOLLOWED BY A DOWNCONVERTER 4HE RADAR FREQUENCY IS DOWNCONVERTED TO AN )& WHERE FILTERS WITH SUITABLE BANDPASS CHARACTERISTICS ARE PHYSICALLY REALIZ ABLE 4HE MIXER ITSELF AND THE PRECEDING CIRCUITS ARE GENERALLY RELATIVELY BROADBAND 4UNING OF THE RECEIVER BETWEEN THE LIMITS SET BY THE PRESELECTOR OR MIXER BANDWIDTH IS ACCOMPLISHED BY CHANGING THE ,/ FREQUENCY /CCASIONALLY RECEIVERS WILL INCLUDE FILTERING BEFORE THE ,.! IN ORDER TO LIMIT THE EFFECTS OF INTERMODULATION DISTORTION THAT CAN OCCUR IN THE ,.! %VEN WHEN FILTERING IS INCLUDED BEFORE THE ,.! A SECOND FILTER IS OFTEN STILL REQUIRED BETWEEN THE ,.! AND THE MIXER IN ORDER TO REJECT THE AMPLIFIER NOISE AT THE IMAGE FREQUENCY 7ITHOUT THIS FILTER THE NOISE CONTRIBUTION OF A BROADBAND ,.! WOULD BE DOUBLED
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4HE RECEIVER FRONT END MAY ALSO INCLUDE A LIMITER USED TO PROTECT THE RECEIVER CIR CUITRY FROM DAMAGE DUE TO HIGH POWER THAT MAY OCCUR EITHER FROM LEAKAGE DURING TRANSMIT MODE OR AS A RESULT OF INTERFERENCE FROM ANOTHER SYSTEM SUCH AS A RADAR AT CLOSE RANGE &RONT END LIMITERS ARE DISCUSSED IN MORE DETAIL IN 3ECTION 4HE RADAR OR RECEIVER FRONT END OFTEN INCLUDES SOME FORM OF GAIN OR ATTENUATION CON TROL AS SHOWN IN &IGURE 'AIN CONTROL IS DESCRIBED IN MORE DETAIL IN 3ECTION %FFECT OF #HARACTERISTICS ON 0ERFORMANCE .ONCOHERENT PULSE RADAR PERFOR MANCE IS AFFECTED BY FRONT END CHARACTERISTICS IN THREE WAYS .OISE INTRODUCED BY THE FRONT END INCREASES THE RADAR NOISE TEMPERATURE DEGRADING SENSITIVITY AND LIMITS THE MAXIMUM RANGE AT WHICH TARGETS ARE DETECTABLE &RONT END SATURATION ON STRONG SIGNALS MAY LIMIT THE MINIMUM RANGE OF THE SYSTEM OR ITS ABILITY TO HANDLE STRONG INTERFERENCE &INALLY THE FRONT END SPURIOUS PERFORMANCE AFFECTS THE SUSCEPTIBILITY TO OFF FREQUENCY INTERFERENCE #OHERENT RADAR PERFORMANCE IS EVEN MORE AFFECTED BY SPURIOUS MIXER CHARACTERIS TICS 2ANGE AND VELOCITY ACCURACY IS DEGRADED IN PULSE DOPPLER RADARS STATIONARY TARGET CANCELLATION IS IMPAIRED IN -4) MOVING TARGET INDICATION RADARS AND RANGE SIDELOBES ARE RAISED IN HIGH RESOLUTION PULSE COMPRESSION SYSTEMS 3PURIOUS $ISTORTION OF 2ADIATED 3PECTRUM )T IS A SURPRISE TO MANY RADAR ENGI NEERS THAT COMPONENTS OF THE RADAR RECEIVER CAN CAUSE DEGRADATION OF THE RADIATED TRANSMITTER SPECTRUM GENERATING HARMONICS OF THE CARRIER FREQUENCY OR SPURIOUS DOP PLER SPECTRA BOTH OF WHICH ARE OFTEN REQUIRED TO BE D" OR MORE BELOW THE CARRIER (ARMONICS CAN CREATE INTERFERENCE IN OTHER ELECTRONIC EQUIPMENT 3PURIOUS DOPPLER SPECTRA LEVELS ARE DICTATED BY REQUIREMENTS TO SUPPRESS CLUTTER INTERFERENCE THROUGH DOPPLER FILTERING (ARMONICS ARE GENERATED BY ANY COMPONENT THAT BECOMES NONLINEAR WHEN SUB JECTED TO THE POWER LEVEL CREATED BY THE TRANSMITTER AND THAT PASSES THOSE HARMONICS TO THE ANTENNA 'ASEOUS OR DIODE RECEIVER PROTECTORS ARE DESIGNED TO BE NONLINEAR DURING THE TRANSMITTED PULSE AND REFLECT THE INCIDENT ENERGY BACK TOWARD THE ANTENNA )SOLATORS OR CIRCULATORS ARE OFTEN EMPLOYED TO ABSORB MOST OF THE REFLECTED FUNDAMENTAL BUT THEY ARE GENERALLY MUCH LESS EFFECTIVE AT THE HARMONICS -OREOVER THESE FERRITE DEVICES ARE NONLINEAR DEVICES AND CAN GENERATE HARMONICS 3PURIOUS DOPPLER SPECTRA ARE CREATED BY ANY PROCESS THAT DOES NOT REOCCUR IDENTI CALLY ON EACH TRANSMITTED PULSE 'ASEOUS RECEIVER PROTECTORS IONIZE UNDER TRANSMITTER POWER LEVELS BUT THERE IS SOME SMALL STATISTICAL VARIATION IN THE INITIATION OF IONIZA TION ON THE LEADING EDGE OF THE PULSE AND IN ITS SUBSEQUENT DEVELOPMENT )N RADARS DEMANDING HIGH CLUTTER SUPPRESSION IN EXCESS OF D" IT HAS SOMETIMES BEEN FOUND NECESSARY TO PREVENT THIS VARIABLE REFLECTED POWER FROM BEING RADIATED BY USE OF BOTH A CIRCULATOR AND AN ISOLATOR IN THE RECEIVE PATH 3PURIOUS 2ESPONSE OF -IXERS 4HE IDEAL MIXER ACTS AS A MULTIPLIER PRODUCING AN OUTPUT PROPORTIONAL TO THE PRODUCT OF THE TWO INPUT SIGNALS 4HE INPUT 2& SIGNAL AT FRE QUENCY F2 IS FREQUENCY SHIFTED OR MODULATED BY THE ,/ SIGNAL AT FREQUENCY F, "ALANCED MIXERS ARE USED TO MINIMIZE CONVERSION LOSS AND UNWANTED SPURIOUS RESPONSES )N ACTIVE MIXERS MODULATION IS PERFORMED USING TRANSISTORS AND IN PASSIVE MIXERS THE MODULATION IS PERFORMED USING 3CHOTTKY BARRIER DIODES OR OTHER SOLID STATE DEVICES EG -%3&%4 WHERE INCREASED DYNAMIC RANGE IS REQUIRED 4HE RESULTING OUTPUT SIGNAL FREQUENCIES F, F2 AND F, n F2 ARE THE SUM AND DIFFERENCE OF THE TWO INPUT FREQUENCIES )N PRACTICE ALL MIXERS PRODUCE UNWANTED INTERMODULATION
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SPURIOUS RESPONSES WITH FREQUENCIES NF, MF2 WHERE M AND N ARE INTEGERS AND THE DEGREE TO WHICH THESE SPURIOUS PRODUCTS IMPACT THE RADAR PERFORMANCE DEPENDS UPON THE TYPE OF MIXER AND THE OVERALL RADAR PERFORMANCE REQUIREMENTS !NALYSIS OF MIXER SPURI OUS LEVELS IS NONTRIVIAL AND THE RECEIVER DESIGNER TYPICALLY REQUIRES TABULATED DATA GENER ATED THROUGH MIXER CHARACTERIZATION MEASUREMENTS TO PREDICT MIXER SPURIOUS LEVELS !DVANCES IN MIXER TECHNOLOGY HAVE RESULTED IN A WIDE VARIETY OF COMMERCIALLY AVAILABLE DEVICES EMPLOYING BALANCED DOUBLE BALANCED AND DOUBLE DOUBLE BALANCED TOPOLOGIES COVERING A WIDE RANGE OF 2& ,/ AND )& FREQUENCIES AND A RANGE OF PER FORMANCE CHARACTERISTICS -IXER 3PURIOUS %FFECTS #HART ! GRAPHICAL DISPLAY OF MIXER SPURIOUS COMPO NENTS UP TO THE SIXTH ORDER IS SHOWN IN &IGURE 4HIS CHART ALLOWS IDENTIFICATION OF THOSE COMBINATIONS OF INPUT FREQUENCIES AND BANDWIDTHS THAT ARE FREE OF STRONG LOW ORDER SPURIOUS COMPONENTS 3UCH CHARTS ARE MOST USEFUL IN DETERMINING OPTIMUM )& AND ,/ FREQUENCIES DURING THE INITIAL DESIGN PHASE /NCE THE FREQUENCY PLAN HAS BEEN DETER MINED COMPUTER ANALYSIS OF SPURIOUS RESPONSES IS TYPICALLY USED TO ENSURE SPURIOUS FREE PERFORMANCE OVER THE ENTIRE RANGE OF ,/ FREQUENCIES AND 2& AND )& BANDWIDTHS 4HE HEAVY LINE IN &IGURE REPRESENTS THE DESIRED SIGNAL AND SHOWS THE VARIATION OF NORMALIZED OUTPUT FREQUENCY ( n , ( WITH NORMALIZED INPUT FREQUENCY ,( !LL OTHER LINES ON THE CHART REPRESENT THE UNWANTED SPURIOUS SIGNALS 4O SIMPLIFY USE OF THE CHART THE HIGHER INPUT FREQUENCY IS DESIGNATED BY ( AND THE LOWER INPUT FREQUENCY BY ,
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3EVEN PARTICULARLY USEFUL REGIONS HAVE BEEN OUTLINED ON THE CHART 5SE OF THE CHART IS ILLUSTRATED BY MEANS OF THE REGION MARKED ! WHICH REPRESENTS THE WIDEST AVAILABLE SPURIOUS FREE BANDWIDTH CENTERED AT ,( 4HE AVAILABLE 2& PASSBAND IS FROM TO AND THE CORRESPONDING )& PASSBAND IS FROM TO (OWEVER SPURI OUS )& FREQUENCIES OF ( n , AND ( n , ARE GENERATED AT THE EXTREMES OF THE 2& PASSBAND !NY EXTENSION OF THE INSTANTANEOUS 2& BANDWIDTH WILL PRODUCE OVERLAPPING )& FREQUENCIES A CONDITION THAT CANNOT BE CORRECTED BY )& FILTERING 4HE ( n , AND ( n , SPURIOUS FREQUENCIES LIKE ALL SPURIOUS )& FREQUENCIES ARISE FROM CUBIC OR HIGHER ORDER INTERMODULATION 4HE AVAILABLE SPURIOUS FREE BANDWIDTH IN ANY OF THE DESIGNATED REGIONS IS ROUGHLY OF THE CENTER FREQUENCY OR ( n , ( 4HUS RECEIVERS REQUIRING A WIDE BAND WIDTH SHOULD USE A HIGH )& FREQUENCY CENTERED IN ONE OF THESE REGIONS &OR )& FREQUEN CIES BELOW ( n , ( THE SPURIOUS FREQUENCIES ORIGINATE FROM HIGH ORDER TERMS IN THE POWER SERIES MODEL AND ARE CONSEQUENTLY LOW ENOUGH IN AMPLITUDE THAT THEY CAN OFTEN BE IGNORED &OR THIS REASON A LOW )& GENERALLY PROVIDES BETTER SUPPRESSION OF SPURIOUS RESPONSES 4HE SPURIOUS EFFECTS CHART ALSO DEMONSTRATES SPURIOUS INPUT RESPONSES /NE OF THE STRONGER OF THESE OCCURS AT POINT " WHERE THE ( n , PRODUCT CAUSES A MIXER OUTPUT IN THE )& PASSBAND WITH AN INPUT FREQUENCY AT !LL THE PRODUCTS OF THE FORM .( n , PRODUCE POTENTIALLY TROUBLESOME SPURIOUS RESPONSES 4HESE FREQUENCIES MUST BE FIL TERED AT 2& TO PREVENT THEIR REACHING THE MIXER )F SUFFICIENT FILTERING CANNOT BE APPLIED PRIOR TO THE MIXING PROCESS SPURIOUS PRODUCTS THAT FALL WITHIN THE OPERATING BAND WILL NO LONGER BE FILTERABLE WHICH WILL SERIOUSLY DEGRADE SYSTEM PERFORMANCE 3PURIOUS RESPONSES NOT PREDICTED BY THE CHART OCCUR WHEN TWO OR MORE 2& INPUT SIG NALS PRODUCE OTHER FREQUENCIES BY INTERMODULATION THAT LIE WITHIN THE 2& PASSBAND )MAGE 2EJECT -IXER ! CONVENTIONAL MIXER HAS TWO INPUT RESPONSES AT POINTS ABOVE AND BELOW THE ,/ FREQUENCY WHERE THE FREQUENCY SEPARATION EQUALS THE )& 4HE UNUSED RESPONSE KNOWN AS THE IMAGE IS SUPPRESSED BY THE IMAGE REJECT OR SINGLE SIDEBAND MIXER SHOWN IN &IGURE 4HE 2& HYBRID PRODUCES A n PHASE DIFFERENTIAL BETWEEN THE ,/ INPUTS TO THE TWO MIXERS 4HE EFFECT OF THIS PHASE DIFFERENTIAL ON THE )& OUTPUTS OF THE MIXERS IS A n SHIFT IN ONE SIDEBAND AND A n SHIFT IN THE OTHER 4HE )& HYBRID ADDING OR SUBTRACTING ANOTHER n DIFFERENTIAL CAUSES THE HIGH SIDEBAND SIGNALS TO ADD AT ONE OUTPUT PORT AND TO SUBTRACT AT THE OTHER 7HERE WIDE BANDWIDTHS ARE INVOLVED THE )& HYBRID IS OF THE ALL PASS TYPE )N PRACTICE IMAGE REJECT MIXERS OFTEN DO NOT PROVIDE SUFFICIENT REJECTION OF THE IMAGE RESPONSE ALONE WITHOUT FILTERING )N THIS CASE THEY CAN BE USED IN CONJUNCTION WITH AN IMAGE REJECTION FILTER REDUCING THE MAGNITUDE OF REJECTION REQUIRED BY THE FILTER
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#HARACTERISTICS OF !MPLIFIERS AND -IXERS .OISE FIGURE AMPLIFIER GAIN MIXER CONVERSION LOSS D" COMPRESSION POINT AND THIRD ORDER INTERCEPT POINT ARE THE MOST COMMON PERFORMANCE PARAMETERS SPECIFIED FOR AMPLIFIERS AND MIXERS /CCASIONALLY A SECOND ORDER INTERCEPT POINT SPECIFICATION IS ALSO REQUIRED FOR VERY WIDE BANDWIDTH SIG NALS )T SHOULD BE NOTED THAT FOR AMPLIFIERS COMPRESSION POINT AND THIRD ORDER INTERCEPT ARE USUALLY SPECIFIED AT THEIR OUTPUT WHEREAS FOR MIXERS THESE PARAMETERS ARE USUALLY SPECIFIED AT THEIR INPUT !DDITIONAL SPECIFICATIONS FOR MIXERS INCLUDE ,/ DRIVE POWER PORT TO PORT ISOLATION AND SINGLE TONE INTERMODULATION LEVELS 4HE ,/ DRIVE POWER SPECIFICATION DEFINES HOW MUCH ,/ POWER IS REQUIRED BY THE MIXER TO MEET ITS SPECIFIED PERFORMANCE LEVELS 4YPICALLY THE HIGHER THE ,/ POWER THE HIGHER THE D" COMPRESSION POINT AND THIRD ORDER INTERCEPT POINT 2ADAR RECEIVERS OFTEN REQUIRE HIGH ,/ DRIVE LEVEL MIXERS IN ORDER TO MEET THE CHALLENGING DYNAMIC RANGE REQUIREMENTS 4HE PORT TO PORT ISOLATION IS USED TO DETERMINE THE POWER LEVEL COUPLED DIRECTLY BETWEEN THE MIXER PORTS WITHOUT FREQUENCY TRANSLATION 4HE SINGLE TONE INTERMODULATION LEVELS SPECIFY THE LEVELS OF THE NF, MF2 SPURIOUS SIGNALS AS DISCUSSED PREVIOUSLY
È°xÊ " Ê"- /",&UNCTIONS OF THE ,OCAL /SCILLATOR 4HE SUPERHETERODYNE RECEIVER UTILIZES ONE OR MORE LOCAL OSCILLATORS AND MIXERS TO CONVERT THE SIGNAL TO AN INTERMEDIATE FRE QUENCY THAT IS CONVENIENT FOR FILTERING AND PROCESSING OPERATIONS 4HE RECEIVER CAN BE TUNED BY CHANGING THE FIRST ,/ FREQUENCY WITHOUT DISTURBING THE )& SECTION OF THE RECEIVER 3UBSEQUENT SHIFTS IN INTERMEDIATE FREQUENCY ARE OFTEN ACCOMPLISHED WITHIN THE RECEIVER BY ADDITIONAL ,/S GENERALLY OF FIXED FREQUENCY 4HESE ,/S ARE GENER ALLY ALSO USED IN THE EXCITER TO UPCONVERT MODULATED WAVEFORMS TO 2& FOR OUTPUT TO THE TRANSMITTER )N MANY EARLY RADARS THE ONLY FUNCTION OF THE LOCAL OSCILLATORS WAS CONVERSION OF THE INPUT SIGNAL FREQUENCY TO THE CORRECT INTERMEDIATE FREQUENCY -ANY MODERN RADAR SYSTEMS HOWEVER COHERENTLY PROCESS A SERIES OF RETURNS FROM A TARGET 4HE LOCAL OSCIL LATORS ACT ESSENTIALLY AS A TIMING STANDARD BY WHICH THE SIGNAL DELAY IS MEASURED TO EXTRACT RANGE INFORMATION ACCURATE TO WITHIN A SMALL FRACTION OF A WAVELENGTH 4HE PROCESSING DEMANDS A HIGH DEGREE OF PHASE STABILITY THROUGHOUT THE RADAR 34!,/ )NSTABILITY 4HE FIRST LOCAL OSCILLATOR GENERALLY REFERRED TO AS A STABLE LOCAL OSCILLATOR 34!,/ TYPICALLY HAS THE GREATEST EFFECT ON RECEIVER EXCITER STABILITY HOWEVER WHEN EVALUATING THE OVERALL PERFORMANCE OTHER CONTRIBUTIONS SHOULD NOT BE NEGLECTED !DVANCES IN STATE OF THE ART 34!,/ OSCILLATOR PERFORMANCE AND THE STRIN GENT CLUTTER CANCELLATION REQUIREMENTS OF MODERN RADARS MEANS THAT THE PHASE NOISE OF ALL OSCILLATORS AND TIMING JITTER OF !$ CONVERTER AND $! CONVERTER CLOCKS AND 42 STROBES MAY BE SIGNIFICANT 4HE SHORT TERM STABILITY REQUIREMENTS OF THE 34!,/ ARE GENERALLY CHARACTERIZED BY DEVICE NOISE RELATIVE TO CARRIER D"C SPECIFIED IN TERMS OF A PHASE NOISE SPECTRUM AND MEASURED IN THE FREQUENCY DOMAIN ,ONG TERM STABILITY IS TYPICALLY CHARACTER IZED BY AGING AND ENVIRONMENTAL EFFECTS SPECIFIED IN TERMS OF FREQUENCY DRIFT AND MEASURED USING AN !LLAN 6ARIANCE TECHNIQUE 2EQUIREMENTS ARE TYPICALLY SPECIFIED IN TERMS OF AN ABSOLUTE FREQUENCY TOLERANCE OR A MAXIMUM FREQUENCY DEVIATION OVER SOME TIME INTERVAL
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)T SHOULD BE NOTED THAT MEASUREMENTS OF PHASE NOISE ARE TYPICALLY PERFORMED BY MEASUREMENT OF DOUBLE SIDEBAND NOISE THE SUM OF THE POWER IN BOTH THE UPPER AND LOWER SIDEBANDS BUT MORE TYPICALLY REPORTED AND SPECIFIED AS SINGLE SIDEBAND 33" VALUES $OUBLE SIDEBAND NOISE CAN BE TRANSLATED TO A SINGLE SIDEBAND VALUE BY SUB TRACTING D" 5NEQUAL SIDEBAND POWER CAN ONLY RESULT FROM ADDITIVE SIGNALS OR NOISE OR CORRELATED AMPLITUDE AND PHASE NOISE COMPONENTS !MPLITUDE MODULATION !- OF THE 34!,/ IS TYPICALLY NOT A SIGNIFICANT FACTOR AS IT IS USUALLY AT A LOWER LEVEL THAN THE PHASE NOISE AT SMALL OFFSET FREQUENCIES FROM CAR RIER AND CAN BE FURTHER REDUCED THROUGH LIMITING -ODERN MIXERS TYPICALLY PROVIDE A SIGNIFICANT REDUCTION IN THE EFFECT OF 34!,/ AMPLITUDE MODULATION AS THEIR CONVERSION GAIN IS RELATIVELY INSENSITIVE TO ,/ POWER VARIATION WHEN OPERATED AT THEIR SPECIFIED DRIVE LEVEL &OR SYSTEMS REQUIRING HIGH SENSITIVITY !- NOISE CAN BECOME DISRUPTIVE IF UNIN TENTIONAL CONVERSION OF !- TO 0- NOISE OCCURS IN THE RECEIVER CHAIN 4HIS PROCESS CAN OCCUR VIA SUBOPTIMUM COMPONENT BIAS TECHNIQUES WHERE HIGH AMPLITUDE SIGNALS OR NOISE CREATE A PHASE SHIFT RESULTING IN ANOTHER PHASE NOISE CONTRIBUTION TO THE RECEIVER CHAIN 6IBRATION 3ENSITIVITY )N ADDITION TO THE PHASE NOISE GENERATED BY THE 34!,/ IN A BENIGN ENVIRONMENT SOURCES OF UNWANTED PHASE MODULATION INCLUDE THE EFFECTS OF POWER SUPPLY RIPPLE AND SPURIOUS SIGNALS AS WELL AS MECHANICAL OR ACOUSTIC VIBRATION FROM FANS MOTORS AND OTHER SOURCES 4HE EFFECTS OF VIBRATION CAN BE SEVERE ESPE CIALLY IN AIRBORNE ENVIRONMENTS WHERE HIGH VIBRATION LEVELS ARE PRESENT 4HE VIBRATION SENSITIVITY OF AN OSCILLATOR IS SPECIFIED BY THE FACTIONAL FREQUENCY VIBRATION SENSITIVITY COMMONLY KNOW AS THE G SENSITIVITY 4YPICALLY A SINGLE CONSTANT VALUE IS SPECIFIED )N PRACTICE THE SENSITIVITY VARIES SIGNIFICANTLY WITH VIBRATION FREQUENCY AND IS DIFFERENT FOR EACH AXIS %QUATION CAN BE USED TO DETERMINE THE EFFECT ON OSCILLATOR PHASE NOISE DUE TO RANDOM VIBRATION IN EACH AXIS
§' F G F ¶ , FV LOG ¨ I I V · D"C 33" IN A (Z BANDWIDTH FV ¨© ·¸
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VIBRATION FREQUENCY (Z OSCILLATOR FREQUENCY (Z OSCILLATOR FRACTIONAL FREQUENCY VIBRATION SENSITIVITY G IN AXIS I VIBRATION POWER SPECTRAL DENSITY G(Z IN AXIS I AT THE VIBRATION FREQUENCY FV
4HE COMPOSITE 34!,/ VIBRATION SENSITIVITY ' IS DEFINED BY THE ROOT SUM SQUARE OF THE SENSITIVITY IN EACH OF THE THREE PRIME AXES AS SHOWN IN %Q
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2ANGE $EPENDENCE -OST MODERN RADARS USE THE 34!,/ IN BOTH THE RECEIVER FOR DOWNCONVERSION AND THE EXCITER FOR UPCONVERSION 4HIS DOUBLE USE OF THE 34!,/ INTRODUCES A DEPENDENCE ON RANGE OF THE CLUTTER AND EXAGGERATES THE EFFECT OF CERTAIN UNINTENTIONAL PHASE MODULATION COMPONENTS BY D" THE CRITICAL FREQUENCIES BEING THOSE WHICH CHANGE PHASE BY ODD MULTIPLES OF DURING THE TIME PERIOD BETWEEN TRANSMISSION AND RECEPTION OF THE CLUTTER RETURN FROM A SPECIFIED RANGE
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4HIS RANGE DEPENDENT FILTER CHARACTERISTIC IS GIVEN BY
\ &2 FM \ SIN P FM 2 C SIN P FM4
WHERE FM MODULATION FREQUENCY (Z 2 RANGE M C PROPAGATION VELOCITY r MS 4 TIME DELAY 2C S ! SHORT TIME DELAY CAN TOLERATE MUCH HIGHER DISTURBANCES AT LOW MODULATION FRE QUENCIES AS ILLUSTRATED BY THE TWO CASES IN &IGURE #ONSEQUENTLY THE EFFECTS OF 34!,/ STABILITY NEED TO BE COMPUTED FOR SEVERAL TIME DELAYS OR RANGES TO ENSURE SUF FICIENT STABILITY EXISTS FOR THE INTENDED APPLICATION #LOSE TO CARRIER PHASE MODULATION IS TYPICALLY DOMINATED BY THAT OF THE OSCILLATORS DUE TO THE INHERENT FEEDBACK PROCESS WITHIN THE OSCILLATOR CIRCUITRY .OISE CONTRIBU TORS WITHIN THE OSCILLATOR LOOP THAT EXHIBIT A F CHARACTERISTIC D"DECADE NOISE SLOPE ARE ENHANCED BY D" VIA THE FEEDBACK MECHANISM WITH A RESULTING NET F CHARACTERISTIC D"DECADE NOISE SIGNATURE CLOSE TO CARRIER WITHIN THE OSCILLATOR LOOP BANDWIDTH /UTSIDE THIS LOOP BANDWIDTH THE OSCILLATOR NOISE SIGNATURE RESUMES A F SLOPE UNTIL REACHING A FLAT THERMAL NOISE FLOOR !T LARGER FREQUENCY OFFSETS SIGNIFICANT NOISE CONTRIBUTIONS CAN RESULT FROM OTHER COMPONENTS SUCH AS AMPLIFIERS IN THE 34!,/ SIGNAL PATH $EPENDING ON THE LOCATION OF THESE AMPLIFIERS THEY MAY EITHER CREATE PHASE MODULATION THAT IS COMMON TO BOTH THE RECEIVER AND EXCITER CORRELATED NOISE OR ADD PHASE NOISE TO ONLY THE RECEIVER OR EXCITER UNCORRELATED NOISE 5NCORRELATED OR UNCOMMON NOISE IS NOT SUBJECT TO THE RANGE DEPENDENT FACTOR DESCRIBED ABOVE SO IT MUST BE ACCOUNTED FOR SEPARATELY /THER SIGNIFICANT CONTRIBUTORS OF UNCOMMON NOISE ARE THE NOISE ON THE EXCITER WAVEFORM BEFORE UPCONVERSION ALONG WITH AMPLIFIERS IN THE RECEIVER AND EXCITER SIGNAL PATHS 4HE UNDESIRED 33" PHASE NOISE AFTER DOWNCONVERSION BY THE 34!,/ IS THE SUM OF THE UNCOMMON PHASE NOISE AND THE COMMON PHASE NOISE REDUCED BY THE RANGE FACTOR
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)F THE RADAR UTILIZES MORE THAN ONE DOPPLER FILTER THE EFFECT OF 34!,/ INSTABILITY SHOULD BE CALCULATED FOR EACH INDIVIDUALLY 0ULSE $OPPLER 0ROCESSING )N PULSE DOPPLER SYSTEMS A SERIES OF PULSES ARE TRANS MITTED AT A FIXED PULSE REPETITION FREQUENCY 02& AND DOPPLER PROCESSING IS PER FORMED WITHIN THE DIGITAL SIGNAL PROCESSOR USING SAMPLES SEPARATED AT THE 02& RATE 4HE RESULTING SAMPLING OF THE RECEIVER OUTPUT AT THE 02& PRODUCES ALIASING OF THE PHASE NOISE SPECTRUM PERIODICALLY AT THE 02& INTERVAL AS SHOWN IN &IGURE WHERE EACH CURVE REPRESENTS THE PHASE NOISE AT THE OUTPUT OF THE RECEIVER INCLUDING THE EFFECTS OF RECEIVER FILTERING AND OFFSET BY A MULTIPLE OF THE 02& FREQUENCY 4HE COMBINED PHASE NOISE DUE TO EACH ALIASED COMPONENT IS CALCULATED USING %Q WITH THE RESULT ILLUSTRATED IN &IGURE 4HIS SAMPLED PHASE NOISE SPECTRUM PROVIDES A METHOD FOR COMPARING DIFFERENT ,/ PHASE NOISE PROFILES AND THEIR RELATIVE IMPACT ON THE OVERALL PERFORMANCE OF THE SYSTEM
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3INUSOIDAL -ODULATIONS 2ADAR PERFORMANCE IS AFFECTED BY BOTH RANDOM AND SINU SOIDAL MODULATIONS 3INUSOIDAL MODULATIONS CAN HAVE A SIGNIFICANT IMPACT ON RADAR PERFORMANCE THOUGH THE DEGREE TO WHICH THEY CAUSE DEGRADATION OFTEN DEPENDS ON THEIR RELATIONSHIP TO THE RADAR 02& AND THEIR MAGNITUDE RELATIVE TO THE RANDOM MODU LATIONS %XAMPLES OF SUCH UNDESIRED SINUSOIDAL MODULATIONS ARE IN BAND UNFILTERABLE MIXER PRODUCTS OR LEAKAGE DUE TO INSUFFICIENT ISOLATION BETWEEN SIGNAL SOURCES WITHIN A RECEIVER OR EXCITER )N ADDITION TO EXTERNAL SOURCES OF INTERFERENCE THE RADAR DESIGNER
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&)'52% 3AMPLED PHASE NOISE SPECTRUM DUE TO PHASE NOISE ALIASING
MUST BE CONCERNED WITH INTERNAL SIGNAL SOURCES -4) AND PULSE DOPPLER RADARS ARE PARTICULARLY SUSCEPTIBLE TO ANY SUCH INTERNAL OSCILLATORS THAT ARE NOT COHERENT IE THAT DO NOT HAVE THE SAME PHASE FOR EACH PULSE TRANSMISSION 4HE EFFECT OF THE SPURIOUS SIGNAL IS THEN DIFFERENT FOR EACH RETURN AND THE ABILITY TO REJECT CLUTTER IS DEGRADED
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! TRULY COHERENT RADAR GENERATES ALL FREQUENCIES INCLUDING ITS INTER PULSE PERIODS FROM A SINGLE FREQUENCY REFERENCE 4HIS FULLY COHERENT ARCHITECTURE INSURES THAT BOTH THE DESIRED FREQUENCIES AND ALL THE INTERNALLY GENERATED SPURIOUS SIGNALS ARE COHERENT ELIMINATING THE DEGRADATION OF CLUTTER REJECTION -ANY RADAR SYSTEMS ARE PSEUDO COHERENT 4HE SAME OSCILLATORS ARE USED IN BOTH TRANSMIT AND RECEIVE BUT NOT NECESSARILY COHERENT WITH EACH OTHER 4HE RESULT IS THAT THE PHASE OF THE TARGET REMAINS CONSTANT BUT THE PHASE OF MANY OF THE SPURIOUS SIGNALS VARIES FROM PULSE TO PULSE )N THIS TYPE OF CONFIGURATION SIGNAL ISOLATION AND FREQUENCY ARCHITECTURE IS CRITICAL TO MINIMIZE THE OCCURRENCE OF SPURIOUS SIGNALS THAT COULD ERRO NEOUSLY BE INTERPRETED AS FALSE TARGETS #/(/ AND 4IMING )NSTABILITY 4HE MAJORITY OF THIS DISCUSSION HAS FOCUSED ON THE 34!,/ AS THE MAJOR CONTRIBUTOR TO RECEIVER STABILITY /THER CONTRIBUTORS SUCH AS THE SECOND ,/ THE COHERENT OSCILLATOR #/(/ IF USED !$ AND $! CONVERTER CLOCKS CAN ALL BECOME SIGNIFICANT !$ AND $! CONVERTER CLOCK JITTER BECOMES INCREASINGLY SIGNIFICANT AS SAMPLE RATES AND )& FREQUENCIES ARE INCREASED 4HE EFFECTS OF !$ AND $! CONVERTER CLOCK PHASE NOISE AND JITTER IS DESCRIBED IN 3ECTIONS AND 4HE JITTER ON TIMING STROBES USED TO PERFORM TRANSMITRECEIVE 42 SWITCHING IS TYPICALLY LESS STRINGENT THAN THAT OF !$ CLOCKS AS IT DOES NOT HAVE A DIRECT IMPACT ON THE SIGNAL PHASE (OWEVER IF COMPONENTS SUCH AS TRANSMITRECEIVE SWITCHES OR POWER AMPLIFIERS HAVE A TRANSIENT PHASE RESPONSE OF SIGNIFICANT DURATION TIME JITTER ON THE SWITCHING TIME CAN BE TRANSLATED INTO A PHASE MODULATION OF THE TRANSMITTER OR RECEIVER SIGNAL 4OTAL 2ADAR )NSTABILITY 4HE PRIMARY SOURCES OF RADAR INSTABILITY ARE USUALLY THE RECEIVER EXCITER COMMON PHASE NOISE RECEIVER AND EXCITER UNCOMMON PHASE NOISE AND THE TRANSMITTER PHASE NOISE )F THE SPECTRA OF THESE COMPONENTS ARE AVAILABLE EITHER THROUGH MEASUREMENTS OR THROUGH PREDICTIONS BASED ON SIMILAR DEVICES THE CONVOLU TION OF RECEIVER EXCITER COMMON PHASE NOISE MODIFIED BY THE RANGE DEPENDENT EFFECT WITH THE OTHER COMPONENTS PROVIDES AN ESTIMATE OF THE SPECTRUM OF RETURNS FROM STABLE CLUTTER WHICH IS THEN MODIFIED BY THE RECEIVER FILTERS AND INTEGRATED TO OBTAIN THE RESI DUE POWER CAUSED BY THESE CONTRIBUTORS 4HESE PROCEDURES ARE EMPLOYED TO DIAGNOSE THE SOURCE OF RADAR INSTABILITY IN AN EXISTING RADAR OR TO PREDICT THE PERFORMANCE OF A RADAR IN THE DESIGN STAGE AND TO ALLOW THE ALLOCATION OF STABILITY REQUIREMENTS TO CRITICAL COMPONENTS OR SUBSYSTEMS WITHIN THE RADAR -EASUREMENT OF TOTAL RADAR INSTABILITY CAN BE CONDUCTED WITH THE RADAR ANTENNA SEARCH LIGHTING A STABLE POINT CLUTTER REFLECTOR THAT PRODUCES A SIGNAL RETURN CLOSE TO BUT BELOW THE DYNAMIC RANGE LIMIT OF THE RECEIVER 3UITABLE CLUTTER SOURCES ARE DIF FICULT TO FIND AT MANY RADAR SITES AND INTERRUPTION OF ROTATION OF THE ANTENNA TO CON DUCT SUCH A TEST MAY BE UNACCEPTABLE AT OTHERS IN THIS CASE A MICROWAVE DELAY LINE CAN BE EMPLOYED TO FEED A DELAYED SAMPLE OF THE TRANSMITTER PULSE INTO THE RECEIVER !LL SOURCES OF INSTABILITY ARE INCLUDED IN THIS SINGLE MEASUREMENT EXCEPT FOR ANY CONTRIBUTORS OUTSIDE THE DELAY LINE LOOP )T IS IMPORTANT TO RECOGNIZE THAT TIMING JIT TER DOES NOT PRODUCE EQUAL IMPACT ON ALL PARTS OF THE RETURN PULSE AND GENERALLY HAS MINIMAL EFFECT ON THE CENTER OF THE PULSE SO IT IS ESSENTIAL TO COLLECT DATA SAMPLES AT A MULTIPLICITY OF POINTS ACROSS THE RETURN INCLUDING LEADING AND TRAILING EDGES 4HE TOTAL RADAR INSTABILITY IS THE RATIO OF THE SUM OF THE MULTIPLICITY OF RESIDUE POWERS AT THE OUTPUT OF THE DOPPLER FILTER TO THE SUM OF THE POWERS AT ITS INPUT DIVIDED BY THE RATIO OF RECEIVER NOISE AT THESE LOCATIONS 3TABILITY IS THE INVERSE OF THIS RATIO BOTH ARE GENERALLY EXPRESSED IN DECIBELS
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)N RADARS WITH PHASE CODED TRANSMISSION AND PULSE COMPRESSION RECEIVERS RESIDUE MAY BE SIGNIFICANT IN THE RANGE SIDELOBE REGION AS WELL AS IN THE COMPRESSED PULSE CAUSED BY PHASE MODULATION DURING THE LONG TRANSMITTED PULSE RATHER THAN SOLELY FROM PULSE TO PULSE -EASUREMENT OF STABILITY OF SUCH RADARS MUST EMPLOY A VERY LARGE NUM BER OF DATA POINTS TO OBTAIN AN ANSWER VALID FOR CLUTTER DISTRIBUTED IN RANGE )N ADDITION TO THE AMPLITUDE AND PHASE NOISE OF THE RECEIVER EXCITER AND THE TRANS MITTER MECHANICALLY SCANNING ANTENNAS PRODUCE A MODULATION THAT IS PREDOMINANTLY !- 4HE COMBINED EFFECT IS THE SUM OF THE RESIDUE POWERS PRODUCED BY EACH COMPO NENT INDIVIDUALLY ,OW .OISE &REQUENCY 3OURCES -ANY RADAR SYSTEMS OPERATE OVER A RANGE OF 2& FREQUENCIES REQUIRING A NUMBER OF ,/ FREQUENCIES THAT ARE TYPICALLY GENERATED USING FREQUENCY SYNTHESIS &REQUENCY SYNTHESIS IS THE PROCESS OF CREATING ONE OR MORE FREQUENCIES FROM A SINGLE REFERENCE FREQUENCY USING FREQUENCY MULTIPLICATION DIVI SION ADDITION AND SUBTRACTION TO SYNTHESIZE THE REQUIRED FREQUENCIES 4HE FUNDAMENTAL BUILDING BLOCK OF ANY FREQUENCY SYNTHESIS APPROACH IS THE OSCILLATOR #RYSTAL OSCILLATORS HAVE HISTORICALLY BEEN THE MOST COMMON SOURCE TECHNOLOGY 6(& CRYSTAL OSCILLATORS EMPLOYING DOUBLY ROTATED 3# )4 ETC CRYSTAL RESONATORS ARE ABLE TO SUPPORT HIGHER POWER LEVELS THAN SINGLE AXIS CRYSTALS 4HIS ENABLES THEM TO ACHIEVE LOWER PHASE NOISE AND IMPROVED VIBRATION IMMUNITY DUE TO PROPERTIES UNIQUE TO THE PARTICULAR AXIS OF ROTATION &REQUENCY MULTIPLICATION OF THESE 6(& SOURCES IS OFTEN USED TO GENERATE THE RADAR 2& FREQUENCIES REQUIRED HOWEVER THIS MULTIPLICATION PROCESS RESULTS IN INCREASE IN PHASE NOISE PERFORMANCE BY LOG- D" WHERE - IS THE MULTIPLICATION FACTOR ! VARIETY OF OTHER SOURCE TECHNOLOGIES SUCH AS 3URFACE !COUSTIC 7AVE 3!7 OSCILLA TORS HAVE BEEN EXPLOITED TO ACHIEVE IMPROVED PHASE NOISE PERFORMANCE 3!7 OSCIL LATORS ENABLE LOWER FAR FROM CARRIER PHASE NOISE LARGELY DUE TO THEIR HIGHER FREQUENCY OPERATION AND THE RESULTING LOWER FREQUENCY MULTIPLICATION FACTOR REQUIRED TO GENERATE THE EQUIVALENT RADAR 2& OUTPUT FREQUENCIES 6ERY ACCURATE FREQUENCY TIMING IS OFTEN REQUIRED IN RADARS WHERE COORDINATION OR HAND OFF FROM ONE RADAR TO ANOTHER OR COMMUNICATION TO A MISSILE IN FLIGHT IS REQUIRED 4HIS IS TYPICALLY THE CASE WHERE A SEARCH RADAR ACQUIRES A TARGET AND QUEUES A PRECI SION TRACKING RADAR !CCURATE TIMING FOR THESE APPLICATIONS MAY BE ACHIEVED BY PHASE LOCKING THE LOW PHASE NOISE RADAR OSCILLATORS TO A LOW FREQUENCY REFERENCE GENERATED FROM EITHER A RUBIDIUM OSCILLATOR OR A '03 RECEIVER )N THIS CONFIGURATION THE LONG TERM STABILITY OF THE REFERENCE OSCILLATOR IS SUPERIOR TO THAT OF THE RADAR OSCILLATOR AND THE SHORT TERM STABILITY OF THE RADAR OSCILLATOR IS SUPERIOR TO THAT OF THE REFERENCE OSCILLATOR 4HE PHASE LOCK LOOP 0,, ARCHITECTURE IS ESTABLISHED TO EXPLOIT THE STRENGTHS OF BOTH TECHNOLOGIES BY SELECTING A 0,, BANDWIDTH AT THE OFFSET FREQUENCY WHERE THE SOURCE STABILITIES CROSS OVER &OR TYPICAL RADAR AND REFERENCE OSCILLATOR TECHNOLOGIES THIS USU ALLY OCCURS IN THE (Z TO K(Z OFFSET REGION &REQUENCY 3YNTHESIS 4ECHNIQUES 4HE MOST COMMON TECHNIQUES ARE DIRECT SYNTHESIS DIRECT DIGITAL SYNTHESIS AND FREQUENCY MULTIPLICATION $IRECT SYNTHESIS IS THE PROCESS OF GENERATING FREQUENCIES THROUGH THE MULTIPLICATION AND MIXING OF A NUMBER OF SIGNALS AT DIFFERENT FREQUENCIES TO PRODUCE THE REQUIRED OUTPUT FREQUENCY &REQUENCY MULTIPLICATION AND DIRECT DIGITAL SYNTHESIS ARE DESCRIBED IN 3ECTION #ONVENTIONAL PHASE LOCKED LOOP SYNTHESIZERS ARE OCCASIONALLY USED BUT THEIR FRE QUENCY SWITCHING TIMES AND PHASE SETTLING RESPONSES ARE GENERALLY INADEQUATE TO MEET THE STRINGENT RADAR RECEIVER EXCITER REQUIREMENTS 0HASE LOCKED LOOPS ARE MORE LIKELY USED TO LOCK FIXED HIGH FREQUENCY OSCILLATORS TO STABLE LOW FREQUENCY REFERENCES TO
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ENSURE COHERENCE OF ALL OSCILLATORS WITHIN THE RECEIVER EXCITER AND OBTAIN AN OPTIMUM BALANCE OF LONG AND SHORT TERM STABILITY #OHERENCE !FTER &REQUENCY 3WITCHING ,ONG RANGE RADARS OFTEN TRANSMIT A SERIES OF PULSES BEFORE RECEIVING RETURNS FROM THE FIRST IN THE SEQUENCE 0ULSES MAY BE TRANSMITTED AT A NUMBER OF DIFFERENT OPERATING FREQUENCIES REQUIRING SWITCHING OF THE ,/ FREQUENCY BETWEEN PULSES )F TARGET RETURNS ARE PROCESSED COHERENTLY THE PHASE OF THE ,/ SIGNAL MUST BE CONTROLLED SUCH THAT EACH TIME IT SWITCHES TO A PARTICULAR FREQUENCY THE PHASE OF THE ,/ IS THE SAME PHASE THAT IT WOULD HAVE BEEN HAD NO FREQUENCY SWITCHING OCCURRED 4HIS REQUIREMENT DRIVES THE ARCHITECTURE USED TO GENERATE ,/ FREQUENCIES 'ENERATING ALL THE FREQUENCIES FROM A SINGLE REFERENCE FREQUENCY DOES NOT GUARANTEE PHASE COHER ENCE WHEN FREQUENCY SWITCHING OCCURS 4HREE SOURCES OF PHASE AMBIGUITY ARE COMMON FREQUENCY DIVIDERS DIRECT DIGITAL SYNTHESIZERS AND VOLTAGE CONTROLLED OSCILLATORS 6#/ &REQUENCY DIVIDERS PRODUCE AN OUTPUT SIGNAL THAT CAN HAVE ANY ONE OF . PHASES WHERE . IS THE DIVIDE RATIO SWITCHING DIVIDERS CAN RESULT IN PHASE AMBIGUITY OF O . )F FREQUENCY DIVIDERS ARE USED IN THE FREQUENCY SYNTHESIS PROCESS THEY MUST BE OPERATED CONSTANTLY WITHOUT SWITCHING THE INPUT FREQUENCY OR DIVIDE RATIO TO AVOID THIS PHASE AMBIGUITY $IRECT DIGITAL SYNTHESIZERS $$3S CAN BE USED EITHER TO GENERATE ,/ FREQUENCIES DIRECTLY OR TO GENERATE MODULATED WAVEFORMS PRIOR TO UPCONVERSION 7HEN PULSE TO PULSE PHASE COHERENCE IS REQUIRED THE STARTING PHASE IS RESET TO ZERO AT THE START OF EACH PULSE )F ALL THE ,/ FREQUENCIES USED ARE MULTIPLES OF THE PULSE REPLETION FREQUENCY THE RESULTING PHASE WILL BE THE SAME FOR EACH PULSE 6#/S CAN BE USED TO CREATE A TUNABLE ,/ BUT ARE USUALLY PHASE LOCKED TO ANOTHER STABLE SOURCE FOR IMPROVED STABILITY 4HE TUNING VOLTAGE DESIGN AND FILTER CAPACITOR TECHNOLOGY USED TO ACHIEVE PHASE LOCK MUST BE CAREFULLY DESIGNED TO ENSURE RAPID VOLTAGE AND STORED CHARGE TRANSITIONS /THERWISE THE 6#/ MAY PROPERLY ACQUIRE AND ACHIEVE PHASE LOCK BUT THE RESIDUAL VOLTAGE DECAY FROM THE TRANSITION WILL MANIFEST ITSELF IN AN INSIDIOUS PHASE AMBIGUITY CALLED POST TUNING DRIFT 3TRETCH 0ROCESSING )N STRETCH PROCESSING THE ,/ SIGNAL FREQUENCY IS MODULATED WITH A CHIRP WAVEFORM SIMILAR TO THAT OF THE RECEIVED SIGNAL TO REDUCE THE BANDWIDTH OF THE )& SIGNAL AS DESCRIBED IN 3ECTION 4HE WIDEBAND CHIRP WAVEFORM IS TYPICALLY GENERATED BY PASSING A NARROWER BANDWIDTH LINEAR FREQUENCY MODULATION ,&- WAVE FORM THROUGH A FREQUENCY MULTIPLIER THAT INCREASES BOTH THE OPERATING FREQUENCY AND BANDWIDTH OF THE CHIRP WAVEFORM &REQUENCY MULTIPLIERS MULTIPLY THE PHASE DISTORTION OF THE INPUT SIGNAL AND OFTEN HAVE SIGNIFICANT PHASE DISTORTION THEMSELVES $ISTORTION OF THE ,/ CHIRP SIGNAL PHASE CAN HAVE A SIGNIFICANT EFFECT ON THE COMPRESSED PULSE PERFOR MANCE EITHER DISTORTING THE COMPRESSED PULSE SHAPE OR DEGRADING SIDELOBE PERFORMANCE 3ECTION 0HASE ERRORS CAN BE MEASURED USING A TEST TARGET INJECTED INTO THE RECEIVER AND MEASURING THE PHASE RIPPLE AT THE RECEIVER OUTPUT "Y PERFORMING THIS MEASUREMENT WITH TARGETS INJECTED AT DIFFERENT SIMULATED RANGES THE ERRORS ASSOCIATED WITH THE RECEIVER ,/ AND TEST SIGNAL CAN BE SEPARATED #ORRECTION OF RECEIVER ,/ PHASE DISTORTION CAN BE READILY CORRECTED WHEN USING A DIRECT DIGITAL SYNTHESIZER AS DESCRIBED IN 3ECTION
È°ÈÊ Ê " /," 3ENSITIVITY 4IME #ONTROL 34# 4HE SEARCH RADAR DETECTS RETURNS OF WIDELY DIF FERING AMPLITUDES OFTEN SO GREAT THAT THE DYNAMIC RANGE OF A FIXED GAIN RECEIVER WILL BE EXCEEDED $IFFERENCES IN RETURN STRENGTH ARE CAUSED BY DIFFERENCES IN RADAR CROSS
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SECTIONS IN METEOROLOGICAL CONDITIONS AND IN RANGE 4HE EFFECT OF RANGE ON RADAR RETURN STRENGTH OVERSHADOWS THE OTHER CAUSES AND CAN BE MITIGATED BY A TECHNIQUE KNOWN AS SENSITIVITY TIME CONTROL WHICH CAUSES THE RADAR RECEIVER SENSITIVITY TO VARY WITH TIME IN SUCH A WAY THAT THE AMPLIFIED RADAR RETURN STRENGTH IS INDEPENDENT OF RANGE 4IME SIDELOBES OF COMPRESSED PULSES IN RADARS THAT TRANSMIT CODED WAVEFORMS CAN BE DEGRADED BY 34# 'RADUAL CHANGES CAN USUALLY BE TOLERATED BUT AT CLOSE RANGE THE RATE OF CHANGE OF ATTENUATION CAN BE VERY LARGE -OST MODERN RADARS THAT INCLUDE 34# USE DIGITAL 34# CONTROL WHICH CAN LEAD TO LARGE STEP SIZES AT CLOSE RANGE UNLESS HIGH DIGITIZATION RATES ARE USED 4HE PHASE STABILITY OF THE 34# ATTENUATOR IS ALSO AN IMPOR TANT CONSIDERATION AS EXCESSIVE PHASE VARIATION AS A FUNCTION OF ATTENUATION CAN HAVE A DRAMATIC IMPACT ON RANGE SIDELOBES #LUTTER -AP !UTOMATIC 'AIN #ONTROL )N SOME RADARS MOUNTAIN OR URBAN CLUT TER CAN CREATE RETURNS THAT WOULD EXCEED THE DYNAMIC RANGE OF THE RECEIVER 4HE SPATIAL AREA OCCUPIED BY SUCH CLUTTER IS TYPICALLY A VERY SMALL FRACTION OF THE RADAR COVERAGE SO CLUTTER MAP !'# HAS BEEN USED AS AN ALTERNATIVE TO BOOSTING THE 34# CURVE 4HIS TECHNIQUE USES A DIGITAL MAP TO RECORD THE MEAN AMPLITUDE OF THE CLUTTER IN EACH MAP CELL OVER MANY SCANS AND ADDS RECEIVER ATTENUATION WHERE NECESSARY TO KEEP THE CLUTTER RETURNS BELOW THE SATURATION LEVEL OF THE RECEIVER 0ROGRAMMABLE 'AIN #ONTROL 2EDUCED GAIN MAY BE DESIRABLE IN A VARIETY OF SITUATIONS SUCH AS HIGH CLUTTER OR HIGH INTERFERENCE ENVIRONMENTS OR IN SHORT RANGE MODES &IXED ATTENUATION IS OFTEN PREFERABLE TO 34# OR CLUTTER MAP CONTROL (IGH 02& PULSE DOPPLER RADARS FOR EXAMPLE CANNOT TOLERATE 34# DUE TO THE RANGE AMBIGUITY OF TARGETS !DDITIONAL ATTENUATION MAY BE PROGRAMMED EITHER MANUALLY VIA OPERATOR CONTROL OR AUTOMATICALLY TO INCREASE THE RECEIVERS LARGE SIGNAL HANDLING CAPABILITY OR TO REDUCE ITS SENSITIVITY 'AIN .ORMALIZATION 2ECEIVER GAIN CAN VARY DUE TO COMPONENT TOLERANCES FRE QUENCY RESPONSE VARIATION WITH TEMPERATURE AND AGING !CCURATE RECEIVER GAIN CONTROL IS REQUIRED FOR A VARIETY OF REASONS THAT INCLUDE TARGET RADAR CROSS SECTION MEASURE MENT MONOPULSE ANGLE ACCURACY MAXIMIZING THE RECEIVER DYNAMIC RANGE AND NOISE LEVEL CONTROL $IGITAL GAIN CONTROL PERMITS THE CALIBRATION OF RECEIVER GAIN BY INJECT ING TEST SIGNALS DURING RADAR DEAD TIME OR DURING SOME SCHEDULED CALIBRATION INTERVAL #ALIBRATION COEFFICIENTS CAN BE STORED AS A FUNCTION OF COMMANDED ATTENUATION OPERAT ING FREQUENCY AND TEMPERATURE AS NEEDED -EASUREMENTS OVER TIME CAN ALSO BE USED TO ASSESS COMPONENT AGING AND POTENTIALLY PREDICT RECEIVER FAILURE PRIOR TO DEGRADATION BEYOND ACCEPTABLE LIMITS !CCURATE GAIN CONTROL IS ESSENTIAL FOR RECEIVER CHANNELS USED TO PERFORM MONOPULSE ANGLE MEASUREMENTS WHERE AMPLITUDES RECEIVED IN TWO OR MORE BEAMS SIMULTANEOUSLY ARE COMPARED TO ACCURATELY DETERMINE THE TARGETS POSITION IN AZIMUTH OR ELEVATION 2ECEIVER DYNAMIC RANGE IS MAXIMIZED WITH ACCURATE GAIN CONTROL AS TOO LITTLE GAIN CAN RESULT IN NOISE FIGURE DEGRADATION AND TOO MUCH GAIN RESULTS IN LARGE SIGNALS EXCEEDING THE !$ CONVERTER FULL SCALE OR CREATING UNWANTED GAIN COM PRESSION INTERMODULATION OR CROSS MODULATION DISTORTION !UTOMATIC .OISE ,EVEL #ONTROL !NOTHER WIDELY EMPLOYED USE FOR !'# IS TO MAINTAIN A DESIRED LEVEL OF RECEIVER NOISE AT THE !$ CONVERTER !S WILL BE DESCRIBED IN 3ECTION TOO LITTLE NOISE RELATIVE TO THE QUANTIZATION INCREMENT OF THE !$ CON VERTER CAUSES A LOSS IN SENSITIVITY 3AMPLES OF NOISE ARE TAKEN AT LONG RANGE OFTEN BEYOND THE INSTRUMENTED RANGE OF THE RADAR OR DURING SOME SCHEDULED PERIOD )F THE RADAR HAS
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2& 34# PRIOR TO ANY AMPLIFICATION IT CAN BE SET TO FULL ATTENUATION TO MINIMIZE EXTER NAL INTERFERENCE WITH MINIMAL AND PREDICTABLE EFFECT ON SYSTEM NOISE TEMPERATURE -OST RADARS EMPLOY AMPLIFIERS PRIOR TO 34# SO THEY CANNOT ATTENUATE EXTERNAL INTERFERENCE WITH OUT AFFECTING THE NOISE LEVEL 4HE NOISE LEVEL CALIBRATION ALGORITHM MUST BE DESIGNED TO TOLERATE EXTERNAL INTERFERENCE AND RETURNS FROM RAINSTORMS OR MOUNTAINS AT EXTREME RANGE !NOTHER CONCERN WITH AMPLIFICATION PRIOR TO 34# IS THAT THE NOISE LEVEL AT THE OUTPUT OF THE 34# ATTENUATOR VARIES WITH RANGE !T CLOSE RANGE THE NOISE LEVEL INTO THE !$ CONVERTER MAY FALL BELOW THE QUANTIZATION INTERVAL !LSO A CONSTANT NOISE LEVEL AS A FUNCTION OF RANGE AT THE RECEIVER OUTPUT IS DESIRABLE IN ORDER TO MAINTAIN A CONSTANT FALSE ALARM RATE .OISE INJECTION AFTER THE 34# ATTENUATOR IS USED TO OVERCOME THIS PROBLEM ! NOISE SOURCE AND ATTENUATOR ARE OFTEN EMPLOYED AT )& TO INJECT ADDITIONAL NOISE TO COMPENSATE FOR THE REDUCED NOISE AFTER THE 34# ATTENUATOR $IGITAL CONTROL OF THE NOISE INJECTION IS SYNCHRONIZED WITH THE 34# ATTENUATION TO PROVIDE AN EFFECTIVE CONSTANT NOISE LEVEL AT THE !$ CONVERTER INPUT 'AIN #ONTROL #OMPONENTS -OST MODERN RADARS PERFORM GAIN CONTROL DIGITALLY $IGITAL CONTROL PERMITS CALIBRATION OF EACH ATTENUATION VALUE TO DETERMINE THE DIFFER ENCE BETWEEN THE ACTUAL ATTENUATION AND THAT COMMANDED BY INJECTING TEST SIGNALS DURING DEAD TIME )N THE PAST GAIN CONTROLLED AMPLIFIERS WERE USED EXTENSIVELY TO CONTROL AND ADJUST RECEIVER GAIN 2ECENTLY THIS APPROACH HAS LARGELY BEEN REPLACED USING DIGITAL SWITCHED OR ANALOG VOLTAGE OR CURRENT CONTROLLED ATTENUATORS DISTRIBUTED THROUGHOUT THE RECEIVER CHAIN 6ARIABLE ATTENUATORS HAVE A NUMBER OF ADVANTAGES OVER VARIABLE GAIN AMPLIFI ERS THEY TYPICALLY PROVIDE BROADER BANDWIDTHS GREATER GAIN CONTROL ACCURACY GREATER PHASE STABILITY IMPROVED DYNAMIC RANGE AND FASTER SWITCHING SPEED 4HE CHOICE BETWEEN VOLTAGE CONTROLLED AND SWITCHED ATTENUATION DEPENDS ON TRADE OFFS BETWEEN PERFORMANCE OF A VARIETY OF PARAMETERS 3WITCHED ATTENUATORS GENERALLY PROVIDE MAXIMUM ATTENUATION ACCURACY FASTER SWITCHING SPEED IMPROVED AMPLITUDE AND PHASE STABILITY GREATER BANDWIDTH HIGHER DYNAMIC RANGE AND HIGHER POWER HAN DLING CAPABILITY 6OLTAGE OR CURRENT CONTROLLED ATTENUATORS CONTROLLED VIA A $! CON VERTER TYPICALLY PROVIDE IMPROVED RESOLUTION AND LOWER INSERTION LOSS 'AIN CONTROL ATTENUATORS ARE OFTEN INCORPORATED WITHIN THE RECEIVER AT BOTH 2& AND )& 2& ATTENUATION IS USED TO PROVIDE INCREASED DYNAMIC RANGE IN THE PRESENCE OF LARGE TARGET RETURNS "Y PLACING THE ATTENUATION AS CLOSE TO THE FRONT END AS POSSIBLE LARGE SIGNALS CAN BE HANDLED BY MINIMIZING GAIN COMPRESSION INTERMODULATION OR CROSS MODULATION DISTORTION IN THE MAJORITY OF RECEIVER COMPONENTS 4HE DISADVANTAGE OF USING FRONT END ATTENUATION IS THAT IT WILL TYPICALLY HAVE A LARGER IMPACT ON RECEIVER NOISE FIGURE THAN ATTENUATION PLACED LATER IN THE RECEIVER 4HIS IS NOT USUALLY AN ISSUE WHEN THE INTENT OF ADDING ATTENUATION IS TO DESENSITIZE THE RECEIVER AS IS THE CASE FOR 34# "ACK END OR )& ATTENUATION IS OFTEN USED TO ADJUST THE GAIN OF THE RECEIVER TO COMPENSATE FOR RECEIVER GAIN VARIATIONS DUE TO COMPONENT VARIATIONS WHERE RECEIVER NOISE FIGURE DEGRADATION CANNOT BE TOLERATED
È°ÇÊ / , &ILTERING OF THE %NTIRE 2ADAR 3YSTEM &ILTERING PROVIDES THE PRINCIPAL MEANS BY WHICH THE RADAR DISCRIMINATES BETWEEN TARGET RETURNS AND INTERFERENCE OF MANY TYPES 4HE FILTERING IS PERFORMED BY A VARIETY OF FILTERS THROUGHOUT THE RECEIVER AND
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IN THE SUBSEQUENT DIGITAL SIGNAL PROCESSING -OST RADARS TRANSMIT MULTIPLE PULSES AT A TARGET BEFORE THE ANTENNA BEAM IS MOVED TO A DIFFERENT DIRECTION AND THE MULTIPLE RETURNS ARE COMBINED IN SOME FASHION 4HE RETURNS MAY BE COMBINED USING COHERENT INTEGRATION OR VARIOUS DOPPLER PROCESSING TECHNIQUES INCLUDING -4) TO SEPARATE DESIRED TARGETS FROM CLUTTER &ROM THE RADAR SYSTEM STANDPOINT THESE ARE ALL FILTER ING FUNCTIONS AND IN MODERN RADAR SYSTEMS THESE FUNCTIONS ARE PERFORMED USING DIGITAL SIGNAL PROCESSING ON THE RECEIVER OUTPUT ) AND 1 DATA 4HESE FUNCTIONS ARE DISCUSSED IN OTHER CHAPTERS OF THIS HANDBOOK 4HE PURPOSE OF THE FILTERING WITHIN THE RECEIVER IS TO REJECT OUT OF BAND INTERFERENCE AND DIGITIZE THE RECEIVED SIGNAL WITH THE MINIMUM OF ERROR SO THAT OPTIMUM FILTERING CAN BE PERFORMED USING DIGITAL SIGNAL PROCESSING -ATCHED &ILTERING !LTHOUGH MATCHED FILTERING IS TYPICALLY NOW PERFORMED WITHIN THE DIGITAL SIGNAL PROCESSING FUNCTION THE CONCEPT IS EXPLAINED HERE FOR COM PLETENESS 4HE OVERALL FILTER RESPONSE OF THE SYSTEM IS CHOSEN TO MAXIMIZE THE RADAR PERFORMANCE )F THE SIGNAL SPECTRUM 8V IN THE PRESENCE OF WHITE NOISE WITH POWER SPECTRAL DENSITY . IS PROCESSED WITH A FILTER WITH FREQUENCY RESPONSE (V THE RESULTING SIGNAL TO NOISE RATIO 3.2 AT TIME 4 IS GIVEN BY
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$EVIATIONS FROM THE IDEAL MATCHED FILTER RESPONSE (-V PRODUCE A REDUCTION IN 3.2 TERMED MISMATCH LOSS 4HIS LOSS CAN OCCUR FOR A NUMBER OF REASONS SUCH AS TARGET DOPPLER OR BECAUSE A FILTER RESPONSE IS CHOSEN THAT IS DIFFERENT FROM THE MATCHED FILTER RESPONSE IN ORDER TO MINIMIZE ANOTHER PARAMETER SUCH AS RANGE SIDELOBES 2ECEIVER FILTERING IS OFTEN MODIFIED FOR DIFFERENT WAVEFORMS USED 7HEN RADAR SYS TEMS USE WAVEFORMS OF WIDELY VARYING BANDWIDTHS DIFFERENT )1 DATA RATES MAY BE USED TO MINIMIZE THE DIGITAL SIGNAL PROCESSING THROUGHPUT REQUIREMENTS 7ITH DIFFER ENT DATA RATES COMES THE NEED TO ADJUST THE RECEIVER FILTERING IN ORDER TO AVOID ALIASING SIGNALS BEYOND THE .YQUIST RATE !LTHOUGH THESE RADARS ADJUST THEIR FILTERING TO THE WAVEFORM BANDWIDTH THEY DO NOT TYPICALLY IMPLEMENT THE MATCHED FILTERING WITHIN THE RECEIVER 4HIS FUNCTION IS USUALLY IMPLEMENTED IN DIGITAL SIGNAL PROCESSING 2ECEIVER &ILTERING &ILTERING IS REQUIRED AT VARIOUS POINTS THROUGHOUT THE RECEIVER CHAIN INCLUDING 2& )& BASEBAND IF USED DIGITAL FILTERING PRIOR TO DECIMATION REDUC TION OF THE SAMPLE RATE AND AS AN INTEGRAL PART OF )1 GENERATION 3ECTION DESCRIBED HOW SPURIOUS RESPONSES ARE GENERATED IN THE MIXING PROCESS 5NWANTED INTERFERENCE SIGNALS CAN BE TRANSLATED TO THE DESIRED INTERMEDIATE FREQUENCY EVEN THOUGH THEY ARE WELL SEPARATED FROM THE SIGNAL FREQUENCY AT THE INPUT TO THE MIXER 4HE ABILITY OF THE RADAR TO SUPPRESS SUCH UNWANTED INTERFERENCE IS DEPENDENT UPON THE FILTERING PRECEDING THE MIXER AS WELL AS ON THE QUALITY OF THE MIXER ITSELF
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4HE PRIMARY FUNCTION OF 2& FILTERING IS THE REJECTION OF THE IMAGE RESPONSE DUE TO THE FIRST DOWNCONVERSION )MAGE REJECTION FILTERING CAN BE ALLEVIATED USING AN IMAGE REJECT MIXER HOWEVER THE MAXIMUM REJECTION ACHIEVABLE BY IMAGE REJECT MIXERS IS TYPICALLY INADEQUATE WITHOUT THE USE OF ADDITIONAL REJECTION THROUGH FILTERING 4HIS IMAGE SUPPRESSION PROBLEM IS THE REASON WHY SOME RECEIVERS DO NOT TRANSLATE FROM THE RECEIVED SIGNAL FREQUENCY DIRECTLY TO THE FINAL INTERMEDIATE FREQUENCY IN A SINGLE STEP 4HE OTHER SPURIOUS PRODUCTS OF A MIXER GENERALLY BECOME MORE SERIOUS IF THE RATIO OF INPUT TO OUTPUT FREQUENCIES OF THE DOWNCONVERTER IS LESS THAN 4HE SPURIOUS EFFECTS CHART &IGURE SHOWS THAT THERE ARE CERTAIN CHOICES OF FREQUENCY RATIO THAT PROVIDE SPURIOUS FREE FREQUENCY BANDS APPROXIMATELY OF THE INTERMEDIATE FRE QUENCY IN WIDTH "Y THE USE OF A HIGH FIRST )& ONE CAN ELIMINATE THE IMAGE PROBLEM AND PROVIDE A WIDE TUNING BAND FREE OF SPURIOUS EFFECTS &ILTERING PRIOR TO THE MIXER REMAINS IMPORTANT HOWEVER BECAUSE THE NEIGHBORING SPURIOUS RESPONSES ARE OF RELA TIVELY LOW ORDER AND MAY PRODUCE STRONG OUTPUTS FROM THE MIXER 2& FILTERING IS ALSO IMPORTANT AS IT REDUCES OUT OF BAND INTERFERENCE BEFORE IT CAN CAUSE INTERMODULATION OR CROSS MODULATION DISTORTION WITHIN THE RECEIVER )F THE RECEIVER OPERATING BANDWIDTH IS A LARGE PERCENTAGE OF THE 2& FREQUENCY SOME FORM OF SWITCHED OR TUNABLE 2& FILTERING MAY BE REQUIRED SO THAT THE IMAGE RESPONSE IS REJECTED AS IT MOVES THROUGH THE OPERATING BANDWIDTH 4HE CHOICE BETWEEN USING SWITCHED OR TUNABLE FILTERING DEPENDS ON THE SWITCHING SPEED LINEARITY AND STABILITY REQUIREMENTS OF THE RECEIVER 3WITCHED FILTERS PROVIDE THE FASTEST RESPONSE TIME WITH EXCELLENT LINEARITY AND STABILITY BUT CAN BE BULKY AND SUFFER FROM THE ADDITIONAL LOSS OF THE SWITCH COMPONENTS !N ALTERNATE APPROACH THAT IS SOMETIMES USED WITH LARGE OPERATING BANDWIDTHS IS TO FIRST UPCONVERT THE INPUT 2& SIGNAL TO AN )& FREQUENCY HIGHER THAN THE 2& OPERATING BAND 4HIS PROCESS VIRTUALLY ELIMINATES THE IMAGE RESPONSE PROBLEM ALLOWING THE USE OF A SINGLE 2& FILTER SPANNING THE ENTIRE OPERATING BANDWIDTH .ARROW BANDWIDTH FILTER ING CAN BE USED ON THE HIGH )& AS DEFINED BY THE SIGNAL BANDWIDTH BEFORE DOWNCONVER SION TO A LOWER )& FOR DIGITIZATION OR BASEBAND CONVERSION )& FILTERING IS THE PRIMARY FILTERING USED TO DEFINE THE RECEIVER BANDWIDTH PRIOR TO !$ CONVERSION IN RECEIVERS USING EITHER )& SAMPLING OR BASEBAND CONVERSION )N )& SAMPLING RECEIVERS THE )& FILTER ACTS AS THE ANTI ALIASING FILTER AND LIMITS THE BANDWIDTH OF SIGNALS ENTERING THE !$ CONVERTER )N RECEIVERS USING BASEBAND CONVERSION THE )& FILTER SETS THE RECEIVER BANDWIDTH 3UBSEQUENT VIDEO FILTERING SHOULD BE OF GREATER BANDWIDTH TO PREVENT THE INTRODUCTION OF )1 IMBALANCE DUE TO FILTER DIFFERENCES BETWEEN ) AND 1 CHANNELS )N )& SAMPLING RECEIVERS DIGITAL FILTERING IS USUALLY THE PRIMARY MEANS OF SETTING THE FINAL RECEIVER BANDWIDTH AND PROVIDES ANTI ALIAS REJECTION REQUIRED TO PREVENT ALIASING IN THE DECIMATION OF THE )1 DATA RATE $IGITAL FILTERING CAN BE PRECISELY CONTROLLED TAILORED TO ALMOST ANY DESIRED PASSBAND AND STOP BAND REJECTION REQUIREMENTS 4HE DIGITAL FILTERS USED ARE TYPICALLY LINEAR PHASE &)2 FILTERS BUT THEY CAN ALSO BE TAILORED TO COMPENSATE FOR VARIATIONS IN THE PASSBAND PHASE AND AMPLITUDE RESPONSES OF 2& AND )& ANALOG FILTERS &ILTER #HARACTERISTICS &ILTER RESPONSES ARE CHARACTERIZED FULLY BY EITHER THEIR FREQUENCY RESPONSE (V OR THEIR IMPULSE RESPONSE HT HOWEVER THEY ARE USUALLY SPECIFIED BY A VARIETY OF PARAMETERS AS DESCRIBED BELOW $IGITAL FILTERS MAY BE SPECI FIED USING THE SAME MEASURES OR BECAUSE THEY CAN BE SPECIFIED EXACTLY THEY ARE FRE QUENTLY SPECIFIED BY THEIR TRANSFER FUNCTION (Z OR IMPULSE RESPONSE HN +EY PASSBAND CHARACTERISTICS ARE INSERTION LOSS BANDWIDTH PASSBAND AMPLITUDE AND PHASE RIPPLE AND GROUP DELAY "ANDWIDTHS ARE FREQUENTLY SPECIFIED IN TERMS OF A D" BANDWIDTH HOWEVER IF A LOW PASSBAND VARIATION IS REQUIRED THE SPECIFIED
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BANDWIDTH MAY BE FOR EXAMPLE SPECIFIED AS A D" OR D" BANDWIDTH 0ASSBAND AMPLITUDE VARIATION RELATIVE TO THE INSERTION LOSS IS A KEY PARAMETER THAT HAS POTENTIAL IMPACT ON RANGE SIDELOBES AND CHANNEL TO CHANNEL TRACKING 0HASE RIPPLE IF SPECIFIED IS RELATIVE TO A BEST FIT LINEAR PHASE AND HAS SIMILAR EFFECTS AS AMPLITUDE RIPPLE 'ROUP DELAY THE RATE OF CHANGE OF PHASE VS FREQUENCY IS IDEALLY CONSTANT FOR LINEAR PHASE FILTERS 4HE ABSOLUTE VALUE OF GROUP DELAY DOES NOT IMPACT THE RANGE SIDELOBE PERFOR MANCE HOWEVER THE RELATIVE GROUP DELAY BETWEEN CHANNELS MUST BE TIGHTLY CONTROLLED OR COMPENSATED IN MONOPULSE SIDELOBE CANCELER AND DIGITAL BEAMFORMING SYSTEMS !LTHOUGH STOPBAND REJECTION IS CLEARLY A KEY PARAMETER FILTERS WITH FAST ROLL OFF MAY NOT PROVIDE THE REQUIRED PHASE AND IMPULSE RESPONSE CHARACTERISTICS &IGURE SHOWS THE MAGNITUDE RESPONSE OF SIX DIFFERENT FIFTH ORDER LOW PASS FILTERS WITH EQUAL D" BANDWIDTH 4HE #HEBSHEV FILTERS AND D" RIPPLE HAVE FLAT PASSBAND RESPONSE AND IMPROVED STOPBAND REJECTION RELATIVE TO THE REMAINING FILTERS HOWEVER AS SHOWN IN &IGURE AND &IGURE THEY HAVE INFERIOR PHASE GROUP DELAY AND IMPULSE RESPONSE CHARACTERISTICS $IGITAL FILTERS CAN BE EITHER &INITE )MPULSE 2ESPONSE &)2 OR )NFINITE )MPULSE 2ESPONSE ))2 &)2 FILTERS ARE TYPICALLY PREFERRED AS THEIR FINITE RESPONSE IS DESIRABLE ALONG WITH THEIR LINEAR PHASE CHARACTERISTIC 0HASE LINEARITY IS ACHIEVED WITH THE SYM METRIC IMPULSE RESPONSE CONDITION DEFINED BY %Q OR THE ANTI SYMMETRIC IMPULSE RESPONSE CONDITIONS DEFINED BY %Q
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2ANGE 3IDELOBES %RRORS IN FILTER RESPONSES CAN PRODUCE DEGRADATION IN PULSE COMPRESSION RANGE SIDELOBES 4HE EFFECT OF A FILTER RESPONSE ON RANGE OR TIME SIDELOBES CAN BE SEEN BY TAKING THE FILTER IMPULSE RESPONSE HT AND ADDING TO THIS A DELAYED IMPULSE RESPONSE LOG@ D" BELOW THE MAIN RESPONSE TO PRODUCE THE MODIFIED RESPONSE HgT WHICH IS GIVEN BY
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4HEREFORE IF THERE ARE N RIPPLES ACROSS THE FILTER BANDWIDTH " THE RANGE SIDELOBE OCCURS AT TIME 4 GIVEN BY
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!SSUMING A COMPRESSED PULSE WIDTH OF " VALUES OF N WILL PUT THE RANGE SIDELOBE WITHIN THE MAIN LOBE OF THE TARGET RETURN RESULTING IN A DISTORTION OF THE MAINLOBE RESPONSE #HANNEL -ATCHING 2EQUIREMENTS 2ADAR RECEIVERS WITH MORE THAN ONE RECEIVER CHANNEL TYPICALLY REQUIRE SOME DEGREE OF PHASE AND AMPLITUDE MATCHING OR TRACKING BETWEEN CHANNELS )N ORDER TO OPERATE EFFECTIVELY SIDELOBE CANCELER CHANNELS MUST TRACK VERY CLOSELY #ONSTANT OFFSETS IN GAIN OR PHASE DO NOT DEGRADE SIDELOBE CANCELER PERFORMANCE BUT SMALL VARIATIONS IN PHASE AND AMPLITUDE ACROSS THE BANDWIDTH CAUSE SIGNIFICANT DEGRADATION &OR EXAMPLE ACHIEVING A CANCELLATION RATIO OF D" REQUIRES A GAIN TRACKING OF LESS THAN D" ACROSS THE RECEIVER BAND WIDTH &ILTERS ARE THE MAIN SOURCE OF AMPLITUDE AND PHASE RIPPLE ACROSS THE SIGNAL BANDWIDTH AS OTHER COMPONENTS SUCH AS AMPLIFIERS AND MIXERS ARE TYPICALLY RELA TIVELY BROADBAND 4HE DEGREE OF TRACKING REQUIRED FOR SIDELOBE CANCELER OPERATION WAS PREVIOUSLY ACHIEVED BY PROVIDING MATCHED SETS OF FILTERS WITH TIGHTLY TRACKING AMPLITUDE AND PHASE RESPONSES -ODERN DIGITAL SIGNAL PROCESSING ALLOWS THE CORREC TION OF THESE CHANNEL TO CHANNEL VARIATIONS USING &)2 EQUALIZATION 3ECTION OR CORRECTION IN THE FREQUENCY DOMAIN IN THE DIGITAL SIGNAL PROCESSOR ALLOWING THE USE OF LESS TIGHTLY CONTROLLED FILTERS
È°nÊ / ,!PPLICATIONS ,IMITERS ARE USED TO PROTECT THE RECEIVER FROM DAMAGE AND TO CON TROL SATURATION THAT MAY OCCUR WITHIN THE RECEIVER 7HEN RECEIVED SIGNALS SATURATE SOME STAGE OF THE RADAR RECEIVER THAT IS NOT EXPRESSLY DESIGNED TO COPE WITH SUCH A
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SITUATION THE DISTORTIONS CAN RESULT IN SEVERELY DEGRADED RADAR PERFORMANCE AND THE DISTORTION OF OPERATING CONDITIONS CAN PERSIST FOR SOME TIME AFTER THE SIGNAL DISAP PEARS 6IDEO STAGES ARE MOST VULNERABLE AND TAKE LONGER TO RECOVER THAN )& STAGES SO IT IS CUSTOMARY TO INCLUDE A LIMITER IN THE LAST )& STAGE DESIGNED TO QUICKLY REGAIN NORMAL OPERATING CONDITIONS IMMEDIATELY FOLLOWING THE DISAPPEARANCE OF A LIMITING SIGNAL ,IMITING PRIOR TO THE !$ CONVERTER ALSO PREVENTS THE DISTORTION THAT OCCURS WHEN SIGNALS EXCEED FULL SCALE !LTHOUGH !$ CONVERTERS CAN OFTEN HANDLE MODEST OVERLOAD WITH FAST RECOVERY THE DISTORTION THAT OCCURS DEGRADES SIGNAL PROCESSING SUCH AS DIGITAL PULSE COMPRESSION AND CLUTTER REJECTION 7ITH )& LIMITING THESE HARMONICS ARE FILTERED OUT USING BANDPASS FILTERING AFTER LIMITING PRIOR TO !$ CONVERSION MINI MIZING THE DEGRADATION DUE TO LIMITING !LL RADAR SYSTEMS CONTAIN SOME FORM OF 4RANSMIT2ECEIVE 42 DEVICE TO PROTECT THE RECEIVE ELECTRONICS FROM THE HIGH POWER TRANSMIT SIGNAL )N MANY SYSTEMS AN 2& FRONT END LIMITER IS ALSO REQUIRED IN ORDER TO PREVENT THE RECEIVER FROM BEING DAMAGED BY HIGH INPUT POWER LEVELS FROM THE ANTENNA THAT MAY OCCUR AS A RESULT OF LEAKAGE FROM THE 42 DEVICE DURING TRANSMIT MODE OR FROM INTERFERENCE DUE TO JAMMERS OR OTHER RADAR SYSTEMS 4HESE LIMITERS ARE TYPICALLY DESIGNED TO LIMIT WELL ABOVE THE MAXIMUM SIGNALS TO BE PROCESSED BY THE RECEIVER )N THE PAST LIMITERS WERE USED TO PERFORM A VARIETY OF ANALOG SIGNAL PROCESSING FUNCTIONS (ARD LIMITERS WITH AS MUCH AS D" OF LIMITING RANGE WERE USED WITH SOME DESIGNED TO LIMIT ON RECEIVER NOISE !PPLICATIONS THAT UTILIZE HARD LIMITING INCLUDING PHASE DETECTORS AND PHASE MONOPULSE RECEIVERS ARE DESCRIBED IN 3ECTION OF THE SECOND EDITION OF THIS HANDBOOK -ODERN RADAR SYSTEMS ARE MOSTLY DESIGNED TO MAXI MIZE THE LINEAR OPERATING REGION WITH LIMITERS USED ONLY TO HANDLE EXCESSIVELY LARGE SIGNALS THAT INEVITABLY EXIST UNDER WORST CASE CONDITIONS #HARACTERISTICS 4HE IDEAL LIMITER IS PERFECTLY LINEAR UP TO THE POWER LEVEL AT WHICH LIMITING BEGINS FOLLOWED BY A TRANSITION REGION BEYOND WHICH THE OUTPUT POWER REMAINS CONSTANT )N ADDITION THE INSERTION PHASE IS CONSTANT FOR ALL INPUT POWER LEV ELS AND RECOVERY FROM LIMITING IS INSTANTANEOUS 4HE OUTPUT WAVEFORM FROM A BAND PASS LIMITER IS SINUSOIDAL WHEREAS THE OUTPUT WAVEFORM FROM A BROADBAND LIMITER APPROACHES A SQUARE WAVE $EVIATIONS FROM THE IDEAL CHARACTERISTICS CAN DEGRADE RADAR PERFORMANCE IN A VARIETY OF WAYS ,INEARITY "ELOW ,IMITING /NE MAJOR DRAWBACK OF ADDING A LIMITER STAGE TO A RECEIVER CHANNEL IS THAT IT IS INHERENTLY NONLINEAR 3INCE ANY PRACTICAL LIMITER HAS A GRADUAL TRANSITION INTO LIMITING THE LIMITER IS OFTEN THE LARGEST CONTRIBUTOR TO RECEIVER CHANNEL NONLINEARITY IN THE LINEAR OPERATING REGION AND CAN CAUSE SIGNIFICANT INTER MODULATION DISTORTION OF IN BAND SIGNALS &OR THIS REASON THE PRIMARY LIMITING STAGE IS USUALLY LOCATED AT THE FINAL )& STAGE WHERE MAXIMUM FILTERING OF OUT OF BAND INTERFER ENCE HAS BEEN ACHIEVED 4HE LOWER OPERATING FREQUENCY ALSO ALLOWS IMPLEMENTATION OF A LIMITER THAT MORE CLOSELY MATCHES THE IDEAL CHARACTERISTICS ,IMITING !MPLITUDE 5NIFORMITY .O SINGLE STAGE LIMITER WILL EXHIBIT A CONSTANT OUTPUT OVER A WIDE RANGE OF INPUT SIGNAL AMPLITUDES /NE CAUSE IS APPARENT IF ONE CONSIDERS THE EFFECT OF A SINGLE STAGE LIMITER HAVING A PERFECTLY SYMMETRICAL CLIPPING AT VOLTAGES o% &OR A SINUSOIDAL INPUT THE OUTPUT SIGNAL AT THE THRESHOLD OF LIMITING IS
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WHICH IS AN INCREASE OF LOG O D" IN THE POWER OF THE FUNDAMENTAL )N PRACTICE THE AMPLITUDE PERFORMANCE IS ALSO DEGRADED BY CAPACITIVE COUPLING BETWEEN INPUT AND OUTPUT OF EACH LIMITING STAGE CHARGE STORAGE IN TRANSISTORS AND DIODES AND 2# TIME CONSTANTS THAT PERMIT CHANGES IN BIAS WITH SIGNAL LEVEL &OR THESE REASONS TWO OR MORE LIMITER STAGES MAY BE CASCADED WHEN GOOD AMPLITUDE UNIFORMITY IS REQUIRED OVER A WIDE DYNAMIC RANGE 0HASE 5NIFORMITY 4HE CHANGE OF INSERTION PHASE OF THE LIMITER WITH AMPLITUDE IS LESS OF A CONCERN FOR MODERN RADAR SYSTEMS THAT OPERATE PRIMARILY IN THE LINEAR OPERAT ING REGION (OWEVER MAINTAINING CONSTANT INSERTION PHASE DURING LIMITING PRESERVES THE PHASE OF TARGET RETURNS IN THE PRESENCE OF LIMITING CLUTTER OR INTERFERENCE 4HE CHANGE OF INSERTION PHASE WITH SIGNAL AMPLITUDE IS GENERALLY DIRECTLY PROPORTIONAL TO THE FREQUENCY AT WHICH IT IS OPERATED 2ECOVERY 4IME 4HE RECOVERY TIME OF A LIMITER IS A MEASURE OF HOW QUICKLY THE LIMITER RETURNS TO LINEAR OPERATION AFTER THE LIMITING SIGNAL IS REMOVED &AST RECOVERY IS PARTICULARLY IMPORTANT WHEN THE RADAR IS EXPOSED TO IMPULSIVE INTERFERENCE
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IN COMPLEX FORM IN %Q )GNORING ANY MIXER INSERTION LOSS OR LOSS ASSOCIATED WITH THE )& SPLIT THE COMPLEX REPRESENTATION OF THE MIXER OUTPUT IS GIVEN BY %Q )DEAL LOW PASS FILTERING REJECTS THE SECOND SUM FREQUENCY TERM OF %Q PRODUCING THE )1 DEMODULATOR OUTPUT AS REPRESENTED BY %Q !3 J V T P E
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)N IMPLEMENTING AN )1 DEMODULATOR IT IS IMPORTANT TO PROVIDE WELL BALANCED ) AND 1 CHANNELS IN ORDER TO MAXIMIZE IMAGE REJECTION AS EXPLAINED BELOW 4HE MIXERS MUST HAVE $# COUPLED )& OUTPUT PORTS AND BE PRESENTED WITH A GOOD MATCH AT BOTH THE WANTED LOW FREQUENCY OUTPUT AND THE UNWANTED SUM FREQUENCY ! MATCH AT THE SUM FREQUENCY CAN BE PROVIDED USING A DIPLEXER FILTER 6IDEO FILTERING IS REQUIRED TO REJECT THE SUM FREQUENCY MIXER OUTPUTS AND ALSO PROVIDES REJECTION OF WIDEBAND NOISE FROM THE VIDEO AMPLIFIERS WHICH WOULD OTHERWISE ALIAS TO BASEBAND THROUGH THE !$ CON VERTER SAMPLING PROCESS PRODUCING AN UNWANTED DEGRADATION OF RECEIVER NOISE FIGURE 6IDEO AMPLIFICATION IS OFTEN REQUIRED TO INCREASE THE SIGNAL LEVEL TO THE FULL SCALE SIGNAL LEVEL OF THE !$ CONVERTER AND ALSO ALLOWS FOR IMPEDANCE MATCHING OF THE MIXER AND !$ CONVERTER 4HE CONVENTION FOR THE ) AND 1 RELATIONSHIP IS THAT THE ) SIGNAL PHASE LEADS THE 1 SIG NAL PHASE FOR RADAR SIGNALS WITH POSITIVE DOPPLER APPROACHING TARGETS &REQUENCY CON VERSIONS WITHIN THE RECEIVER USING ,/ FREQUENCIES GREATER THAN THE 2& FREQUENCY WILL CAUSE A DOPPLER FREQUENCY INVERSION SO EACH CONVERSION MUST BE CONSIDERED IN ORDER TO ACHIEVE THE CORRECT SENSE OF ) AND 1 AT THE RECEIVER OUTPUT &ORTUNATELY AN INCORRECT ) AND 1 RELATIONSHIP CAN EASILY BE FIXED EITHER IN THE RECEIVER OR THE SIGNAL PROCESSOR BY SWITCHING THE ) AND 1 DIGITAL DATA OR BY CHANGING THE SIGN OF EITHER ) OR 1 'AIN OR 0HASE )MBALANCE )F THE GAINS OF THE ) AND 1 CHANNELS ARE NOT EXACTLY EQUAL OR IF THEIR #/(/ PHASE REFERENCES ARE NOT EXACTLY DEGREES APART AN INPUT SIGNAL AT FREQUENCY V WILL CREATE AN OUTPUT AT BOTH THE DESIRED FREQUENCY V V AND
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$# /FFSET 3MALL SIGNALS AND RECEIVER NOISE CAN BE DISTORTED BY AN OFFSET IN THE MEAN VALUE OF THE !$ CONVERTER OUTPUT UNLESS THE DOPPLER FILTER SUPPRESSES THIS COMPONENT &ALSE ALARM CONTROL IN RECEIVERS WITHOUT DOPPLER FILTERS IS SOMETIMES DEGRADED BY ERRORS OF A SMALL FRACTION OF THE LEAST SIGNIFICANT BIT ,3" SO CORRECTION IS PREFERABLY APPLIED AT THE ANALOG INPUT TO THE !$ $# OFFSETS CAN BE MEASURED USING DIGITAL PRO CESSING OF THE !$ CONVERTER OUTPUTS AND A CORRECTION APPLIED USING $! CONVERTERS AS SHOWN IN &IGURE $# OFFSET CORRECTION CAN ALSO BE PERFORMED EFFECTIVELY IN THE DIGITAL DOMAIN PROVIDED THAT THE $# OFFSET AT THE INPUT OF THE !$ CONVERTER IS NOT SO LARGE THAT IT RESULTS IN A SIGNIFICANT LOSS OF AVAILABLE DYNAMIC RANGE -ANY OF THE )1 DEMODULATOR ERRORS DESCRIBED ABOVE ARE EITHER REDUCED DRAMATI CALLY OR ELIMINATED USING )& SAMPLING 4HIS ALONG WITH THE REDUCTION OF HARDWARE REQUIRED ARE THE REASONS THAT )& SAMPLING DESCRIBED IN 3ECTIONS AND IS BECOMING THE DOMINANT APPROACH
È°£äÊ "/" / Ê " 6 ,/ ,4HE HIGH SPEED !$ CONVERTER IS A KEY COMPONENT IN RECEIVERS OF MODERN RADAR SYS TEMS 4HE EXTENSIVE USE OF DIGITAL SIGNAL PROCESSING OF RADAR DATA HAS RESULTED IN A DEMAND FOR CONVERTERS WITH BOTH STATE OF THE ART SAMPLING RATES AND DYNAMIC RANGE !NALOG TO DIGITAL CONVERTERS TRANSFORM CONTINUOUS TIME ANALOG SIGNALS INTO DISCRETE TIME DIGITAL SIGNALS 4HE PROCESS INCLUDES BOTH SAMPLING IN THE TIME DOMAIN CONVERT ING FROM CONTINUOUS TIME TO DISCRETE TIME SIGNALS AND QUANTIZATION CONVERTING FROM CONTINUOUS ANALOG VOLTAGES TO DISCRETE FIXED LENGTH DIGITAL WORDS "OTH THE SAMPLING AND QUANTIZATION PROCESS PRODUCE ERRORS THAT MUST BE MINIMIZED IN ORDER TO LIMIT THE RADAR PERFORMANCE DEGRADATION )N ADDITION A VARIETY OF OTHER ERRORS SUCH AS ADDITIVE NOISE SAMPLING JITTER AND DEVIATION FROM THE IDEAL QUANTIZATION RESULT IN NON IDEAL !$ CONVERSION !PPLICATIONS 4HE CONVENTIONAL APPROACH OF USING A PAIR OF CONVERTERS TO DIGI TIZE THE ) AND 1 OUTPUTS OF AN )1 DEMODULATOR IS IN MANY CASES BEING REPLACED BY DIGITAL RECEIVER ARCHITECTURES WHERE A SINGLE !$ CONVERTER IS FOLLOWED BY DIGITAL SIGNAL PROCESSING TO GENERATE ) AND 1 DATA $IGITAL RECEIVER TECHNIQUES ARE DESCRIBED IN 3ECTION !LTHOUGH THE DIVIDING LINE IS ARBITRARY AND ADVANCING WITH THE STATE OF THE ART RADAR RECEIVERS ARE OFTEN CLASSIFIED AS EITHER WIDEBAND OR HIGH DYNAMIC RANGE $IFFERENT RADAR FUNCTIONS PUT A GREATER EMPHASIS ON ONE OR THE OTHER OF THESE PARAMETERS &OR EXAMPLE IMAGING RADARS PUT A PREMIUM ON WIDE BANDWIDTH WHEREAS PULSE DOPPLER RADARS REQUIRE HIGH DYNAMIC RANGE "ECAUSE RADARS ARE OFTEN REQUIRED TO OPERATE IN A VARIETY OF MODES WITH DIFFERING BANDWIDTH AND DYNAMIC RANGE REQUIREMENTS IT IS NOT UNCOMMON TO USE DIFFERENT TYPES OF !$ CONVERTER SAMPLING AT DIFFERENT RATES FOR THESE DIFFERENT MODES $ATA &ORMATS 4HE MOST FREQUENTLY USED DIGITAL FORMATS FOR !$ CONVERTERS ARE S COMPLEMENT AND OFFSET BINARY 4HE S COMPLEMENT IS THE MOST POPULAR METHOD OF DIGITAL REPRESENTATION OF SIGNED INTEGERS AND IS CALCULATED BY COMPLEMENTING EVERY BIT OF A GIVEN NUMBER AND ADDING ONE
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4HE MOST SIGNIFICANT BIT IS REFERRED TO AS THE SIGN BIT )F THE SIGN BIT IS THE VALUE IS POSI TIVE IF IT IS THE VALUE IS NEGATIVE 4HE REPRESENTATION OF VOLTAGE IN S COMPLEMENT FORM IS GIVEN BY
% K B.. B. . B. . B
WHERE % ANALOG VOLTAGE . NUMBER OF BINARY DIGITS BI STATE OF ITH BINARY DIGIT K QUANTIZATION VOLTAGE /FFSET BINARY IS AN ALTERNATE CODING SCHEME IN WHICH THE MOST NEGATIVE VALUE IS REPRESENTED BY ALL ZEROS AND THE MOST POSITIVE VALUE IS REPRESENTED BY ALL ONES :ERO IS REPRESENTED BY A MOST SIGNIFICANT BIT -3" OF ONE FOLLOWED BY ALL ZEROS 4HE REPRE SENTATION OF VOLTAGE IN OFFSET BINARY IS GIVEN BY
% K;B. . B. . B. . B=
4HE 'RAY CODE IS ALSO USED IN CERTAIN HIGH SPEED !$ CONVERTERS IN ORDER TO REDUCE THE IMPACT OF DIGITAL OUTPUT TRANSITIONS ON THE PERFORMANCE OF THE !$ CON VERTER 4HE 'RAY CODE ALLOWS ALL ADJACENT TRANSITIONS TO BE ACCOMPLISHED BY THE CHANGE OF A SINGLE DIGIT ONLY $ELTA 3IGMA #ONVERTERS $ELTA SIGMA CONVERTERS DIFFER FROM CONVENTIONAL .YQUIST RATE CONVERTERS BY COMBINING OVERSAMPLING WITH NOISE SHAPING TECHNIQUES TO ACHIEVE IMPROVED 3.2 IN THE BANDWIDTH OF INTEREST .OISE SHAPING MAY BE EITHER LOW PASS OR BANDPASS DEPENDING ON THE APPLICATION $ELTA SIGMA ARCHITECTURES PROVIDE POTEN TIAL IMPROVEMENTS IN SPURIOUS FREE DYNAMIC RANGE 3&$2 AND 3.2 OVER CONVENTIONAL .YQUIST CONVERTERS WHERE TIGHT TOLERANCES ARE REQUIRED TO ACHIEVE VERY LOW SPURIOUS PERFORMANCE $IGITAL FILTERING AND DECIMATION IS REQUIRED TO PRODUCE DATA RATES THAT CAN BE HANDLED BY CONVENTIONAL PROCESSORS 4HIS FUNCTION IS EITHER PERFORMED AS AN INTEGRAL PART OF THE !$ CONVERTER FUNCTION OR CAN BE INTEGRATED INTO THE DIGITAL DOWNCONVERSION FUNCTION USED TO GENERATE DIGITAL ) AND 1 DATA AS DESCRIBED IN 3ECTION 0ERFORMANCE #HARACTERISTICS 4HE PRIMARY PERFORMANCE CHARACTERISTICS OF !$ CONVERTERS ARE THE SAMPLE RATE OR USABLE BANDWIDTH AND RESOLUTION THE RANGE OVER WHICH THE SIGNALS CAN BE ACCURATELY DIGITIZED 4HE RESOLUTION IS LIMITED BY BOTH NOISE AND DISTORTION AND CAN BE DESCRIBED BY A VARIETY OF PARAMETERS 3AMPLE 2ATE 3AMPLING OF BAND LIMITED SIGNALS IS PERFORMED WITHOUT ALIASING DISTORTION PROVIDED THAT THE SAMPLE RATE FS IS GREATER THAN TWICE THE SIGNAL BANDWIDTH AND PROVIDED THE SIG NAL BANDWIDTH DOES NOT STRADDLE THE .YQUIST FRE QUENCY FS OR ANY INTEGER MULTIPLE .FS )N CONVENTIONAL BASEBAND APPROACHES SAM PLING IS USUALLY PERFORMED AT THE MINIMUM RATE TO MEET THE .YQUIST CRITERIA 3INCE THE BASEBAND ) AND 1 SIGNALS HAVE BANDWIDTHS " EQUAL TO HALF THE )& SIGNAL BANDWIDTH A SAMPLE RATE JUST GREATER THAN &)'52% "ASEBAND SAMPLING THE )& BANDWIDTH IS REQUIRED SEE &IGURE
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&)'52% )& SAMPLING IN SECOND .YQUIST REGION
&OR )& SAMPLING A FREQUENCY AT LEAST TWICE THE )& BANDWIDTH IS REQUIRED HOWEVER OVERSAMPLING IS TYPICALLY EMPLOYED TO EASE ALIAS REJECTION FILTERING AND TO REDUCE THE EFFECT OF !$ CONVERTER QUANTIZATION NOISE )& SAMPLING IS OFTEN PERFORMED WITH THE SIGNAL LOCATED IN THE SECOND .YQUIST REGION AS SHOWN IN &IGURE OR IN HIGHER .YQUIST REGIONS 3TATED 2ESOLUTION 4HE STATED RESOLUTION OF AN !$ CONVERTER IS THE NUMBER OF OUTPUT DATA BITS PER SAMPLE 4HE FULL SCALE VOLTAGE RANGE OF A .YQUIST RATE CONVERTER IS GIVEN BY 6&3 .1 WHERE . IS THE STATED RESOLUTION AND 1 IS THE LEAST SIGNIFICANT BIT ,3" SIZE 3IGNAL TO .OISE 2ATIO 3.2 3.2 IS THE RATIO OF RMS SIGNAL AMPLITUDE TO RMS !$ CONVERTER NOISE POWER &OR AN IDEAL !$ CONVERTER THE ONLY ERROR IS DUE TO QUAN TIZATION 0ROVIDED THAT THE INPUT SIGNAL IS SUFFICIENTLY LARGE RELATIVE TO THE QUANTIZATION SIZE AND UNCORRELATED TO THE SAMPLING SIGNAL THE QUANTIZATION ERROR IS ESSENTIALLY RAN DOM AND IS ASSUMED TO BE WHITE 4HE RMS QUANTIZATION NOISE IS 1 AND SIGNAL TO QUANTIZATION NOISE RATIO 31.2 OF AN IDEAL !$ CONVERTER IS GIVEN BY
31.2D" .
0RACTICAL !$ CONVERTERS HAVE ADDITIONAL SAMPLING ERRORS OTHER THAN QUANTIZATION INCLUDING THERMAL NOISE AND APERTURE JITTER 0ROVIDED THAT THESE ADDITIONAL ERRORS CAN BE CHARACTERIZED AS WHITE THEY CAN BE COMBINED WITH THE QUANTIZATION NOISE WITH A RESULTING 3.2 LESS THAN THE THEORETICAL 3.2 OF THE IDEAL CONVERTER "ECAUSE VARIOUS !$ CONVERTER ERROR MECHANISMS ARE DEPENDENT ON INPUT SIGNAL LEVEL AND FREQUENCY IT IS IMPORTANT TO CHARACTERIZE DEVICES OVER THE FULL RANGE OF INPUT CONDITIONS TO BE EXPECTED 4HE AVAILABLE SIGNAL TO NOISE RATIO OF STATE OF THE ART HIGH SPEED !$ CON VERTERS HAS BEEN SHOWN TO FALL OFF BY ONE BIT D" FOR EVERY DOUBLING OF THE SAMPLE RATE /VER SAMPLING OF THE SIGNAL FOLLOWED BY FILTERING AND DECIMATION PROVIDES AN IMPROVEMENT OF ONE HALF BIT D" IN THE ACHIEVABLE SIGNAL TO NOISE RATIO FOR EACH DOUBLING OF THE SAMPLE RATE 4HUS FOR HIGH DYNAMIC RANGE APPLICATIONS THE BEST PER FORMANCE IS ACHIEVED USING A STATE OF THE ART !$ CONVERTER THAT HAS A MAXIMUM SAMPLE RATE JUST SUFFICIENT FOR THE APPLICATION 3PURIOUS &REE $YNAMIC 2ANGE 3&$2 3&$2 IS THE RATIO OF THE SINGLE TONE SIG NAL AMPLITUDE TO THE LARGEST SPURIOUS SIGNAL AMPLITUDE AND IS USUALLY STATED IN D" 3IMILAR TO 3.2 THE SPURIOUS PERFORMANCE OF AN !$ CONVERTER IS DEPENDENT ON THE
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INPUT SIGNAL FREQUENCY AND AMPLITUDE 4HE FREQUENCY OF SPURIOUS SIGNALS IS ALSO DEPEN DENT ON THE INPUT SIGNAL FREQUENCY WITH THE HIGHEST VALUES TYPICALLY DUE TO LOW ORDER HARMONICS OR THEIR ALIASES 7HEN USING )& SAMPLING WITH A SIGNIFICANT OVER SAMPLING RATIO FS " THE WORST SPURIOUS SIGNALS MAY BE AVOIDED BY CHOOSING THE SAMPLE FREQUENCY RELATIVE TO SIGNAL FREQUENCY SUCH THAT THE UNWANTED SPURIOUS SIGNALS FALL OUTSIDE THE SIGNAL BANDWIDTH OF INTEREST )F THE WORST CASE SPURIOUS CAN BE AVOIDED THE SPECIFIED 3&$2 IS LESS IMPORTANT THAN THE LEVELS OF THE SPECIFIC SPURIOUS COMPONENTS THAT FALL WITHIN THE BANDWIDTH OF INTEREST !GAIN IT IS IMPORTANT TO CHARACTERIZE DEVICES OVER THE RANGE OF EXPECTED OPERATING CONDITIONS 4HE IMPACT OF !$ CONVERTER SPURIOUS SIGNALS ON RADAR PERFORMANCE DEPENDS ON THE TYPE OF WAVEFORMS BEING PROCESSED AND THE DIGITAL SIGNAL PROCESSING BEING PERFORMED )N APPLICATIONS USING CHIRP WAVEFORMS WITH LARGE TIME BANDWIDTH PRODUCTS SPURIOUS SIGNALS ARE LESS CRITICAL AS THEY ARE EFFECTIVELY REJECTED IN THE PULSE COMPRESSION PRO CESS BECAUSE THEIR CODING DOES NOT MATCH THAT OF THE WANTED SIGNAL )N PULSE DOPPLER APPLICATIONS SPURIOUS SIGNALS ARE OF MUCH GREATER CONCERN BECAUSE THEY CAN CREATE COMPONENTS WITH DOPPLER AT A VARIETY OF FREQUENCIES THAT MAY NOT BE REJECTED BY THE CLUTTER FILTERING 3IGNAL TO .OISE AND $ISTORTION 2ATIO 3).!$ 3).!$ IS THE RMS SIGNAL AMPLI TUDE TO THE RMS VALUE OF THE !$ CONVERTER NOISE PLUS DISTORTION 4HE NOISE PLUS DIS TORTION INCLUDES ALL SPECTRAL COMPONENTS EXCLUDING $# AND THE FUNDAMENTAL UP TO THE .YQUIST FREQUENCY 3).!$ IS A USEFUL FIGURE OF MERIT FOR !$ CONVERTERS BUT IN DIGITAL RECEIVER APPLICATIONS WHERE THE WORST SPURIOUS COMPONENTS MAY FALL OUTSIDE OF THE BANDWIDTH OF INTEREST IT IS NOT NECESSARILY A KEY DISCRIMINATOR BETWEEN COMPETING CONVERTERS FOR A SPECIFIC APPLICATION %FFECTIVE .UMBER OF "ITS %./" 4HE TERM EFFECTIVE NUMBER OF BITS IS OFTEN USED TO STATE THE TRUE PERFORMANCE OF AN !$ CONVERTER AND HAS BEEN STATED IN THE LITERATURE IN TERMS OF 3).!$ AND 3.2 AS GIVEN BELOW #ONSEQUENTLY IT IS IMPORTANT TO DIFFER ENTIATE BETWEEN DEFINITIONS WHEN USING THIS TERM
.EFF ;3).!$D" =
.EFF ;3.2D" =
4WO 4ONE )NTERMODULATION $ISTORTION )-$ 4WO TONE INTERMODULATION DISTORTION IS ALSO IMPORTANT IN RECEIVER APPLICATIONS 4ESTING IS PERFORMED WITH TWO SINUSOIDAL INPUT SIGNALS OF UNEQUAL FREQUENCY AND LEVELS SET SUCH THAT THE SUM OF THE TWO INPUTS DOES NOT EXCEED THE !$ CONVERTER FULL SCALE LEVEL 3IMILAR TO )-$ FOR AMPLIFIERS THE MOST SIGNIFICANT DISTORTION IS USUALLY SECOND ORDER OR THIRD ORDER )-$ PRODUCTS (OWEVER DUE TO THE COMPLEX NATURE OF THE DISTORTION MECHANISM IN !$ CONVERTERS THE AMPLITUDE OF )-$ PRODUCTS IS NOT EASILY CHARACTERIZED AND PREDICTED BY THE MEASUREMENT OF AN INPUT INTERCEPT POINT )NPUT .OISE ,EVEL AND $YNAMIC 2ANGE !CCURATE SETTING OF THE !$ CON VERTER INPUT NOISE LEVEL RELATIVE TO THE !$ CONVERTER NOISE IS CRITICAL TO ACHIEVING THE OPTIMUM TRADE OFF BETWEEN DYNAMIC RANGE AND SYSTEM NOISE FLOOR 4OO HIGH A LEVEL OF NOISE INTO THE !$ CONVERTER WILL DEGRADE THE AVAILABLE DYNAMIC RANGE TOO LOW A LEVEL WILL DEGRADE THE OVERALL SYSTEM NOISE FLOOR 3UFFICIENT TOTAL NOISE SHOULD BE APPLIED TO THE !$ CONVERTER INPUT TO RANDOMIZE OR hWHITENv THE QUANTIZATION NOISE
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&)'52% )& SAMPLING NOISE SPECTRUMS
4HIS CAN BE ACHIEVED WITH RMS INPUT NOISE R EQUAL TO THE ,3" STEP SIZE 1 )N ADDITION THE INPUT NOISE POWER SPECTRAL DENSITY SHOULD BE SUFFICIENT TO MINIMIZE THE IMPACT ON SYSTEM NOISE DUE TO THE !$ CONVERTER NOISE 4HE IMPACT ON OVERALL NOISE DUE TO QUANTIZATION NOISE IS GIVEN BY R 1 R q1 R R 4YPICAL OPERATING POINTS ARE IN THE RANGE OF R 1 TO R 1 WITH CORRESPONDING NOISE POWER DEGRADATION DUE TO QUANTIZATION OF D" AND D" RESPECTIVELY )N PRACTICE THE 3.2 OF HIGH SPEED CONVERTERS IS OFTEN SUCH THAT THE NOISE OF THE !$ CONVERTER IS SIGNIFICANTLY GREATER THAN THE THEORETICAL QUANTIZATION NOISE )N ADDI TION THE !$ CONVERTER INPUT SIGNAL NOISE BANDWIDTH MAY BE SIGNIFICANTLY LESS THAN THE .YQUIST BANDWIDTH 4HIS IS A SIGNIFICANT FACTOR IN )& SAMPLING APPLICATIONS WHERE THE )& NOISE BANDWIDTH IS OFTEN LESS THAN OF THE .YQUIST BANDWIDTH )N THIS CASE THE TOTAL INPUT AND !$ CONVERTER NOISE MUST BE SUFFICIENT TO WHITEN THE QUANTIZATION NOISE AND THE POWER SPECTRAL DENSITY OF THE INPUT NOISE SHOULD BE SUFFICIENTLY GREATER THAN THAT OF THE !$ CONVERTER AS ILLUSTRATED IN &IGURE )N SOME CASES OUT OF BAND NOISE MAY BE ADDED TO WHITEN THE !$ CONVERTER QUANTIZATION NOISE AND SPURIOUS SIGNALS 4HE OUT OF BAND NOISE IS THEN REJECTED THROUGH SUBSEQUENT DIGITAL SIGNAL PROCESSING 4HE RESULTING 3.2 OF THE SYSTEM AFTER DIGITAL FILTERING WITH RECEIVER BANDWIDTH "2 AND SAMPLE RATE FS IS GIVEN BY
¤ F ³ 3.2393 D" 3.2!$# D" LOG ¥ 3 ´ LOG 3)& 3!$# ¦ "2 µ
WHERE 3)&3!$# IS THE RATIO OF NOISE POWER SPECTRAL DENSITY OF THE !$ CONVERTER INPUT SIGNAL TO THE POWER SPECTRAL DENSITY OF THE !$ CONVERTER 4HE DEGRADATION OF OVERALL SENSITIVITY DUE TO THE !$ CONVERTER NOISE IS GIVEN BY
,D" LOG 3!$#3)&
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!$ #ONVERTER 3AMPLE #LOCK 3TABILITY 4HE STABILITY OF THE SAMPLE CLOCK IS CRITICAL TO ACHIEVING THE FULL CAPABILITY OF AN !$ CONVERTER 3AMPLE TO SAMPLE VARIA TION IN THE SAMPLING INTERVAL CALLED APERTURE UNCERTAINTY OR APERTURE JITTER PRODUCES A SAMPLING ERROR PROPORTIONAL TO THE RATE OF CHANGE OF INPUT VOLTAGE &OR A SINUSOIDAL INPUT SIGNAL THE 3.2 DUE TO APERTURE UNCERTAINTY ALONE IS GIVEN BY
3.2D" LOGO FR J
WHERE F INPUT SIGNAL FREQUENCY RJ RMS APERTURE JITTER 3IMILARLY CLOSE TO CARRIER NOISE SIDEBANDS PRESENT ON THE SAMPLE CLOCK SIGNAL ARE TRANSFERRED TO SIDEBANDS ON THE SAMPLED INPUT SIGNAL REDUCED BY LOG F F3 D" &OR EXAMPLE IN AN )& SAMPLING APPLICATION WITH THE INPUT SIGNAL Ð OF THE SAMPLE FREQUENCY THE CLOSE TO CARRIER PHASE NOISE OF THE SAMPLE CLOCK WILL BE TRANSFERRED TO THE OUTPUT OF THE !$ CONVERTER OUTPUT DATA SIGNAL REDUCED BY D"
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6 ,4HE AVAILABILITY OF HIGH SPEED ANALOG TO DIGITAL CONVERTERS CAPABLE OF DIRECT SAM PLING OF RADAR RECEIVER )& SIGNALS HAS RESULTED IN THE ALMOST UNIVERSAL ADOPTION OF DIGITAL RECEIVER ARCHITECTURES OVER CONVENTIONAL ANALOG )1 DEMODULATION )N A DIGITAL RECEIVER A SINGLE !$ CONVERTER IS USED TO DIGITIZE THE RECEIVED SIGNAL AND DIGITAL SIGNAL PROCESSING IS USED TO PERFORM THE DOWNCONVERSION TO ) AND 1 BASEBAND SIG NALS #ONTINUING ADVANCES IN SAMPLING SPEEDS ARE LEADING TO SAMPLING AT INCREASING FREQUENCIES SOMETIMES ELIMINATING THE NEED FOR A SECOND DOWNCONVERSION WITH THE POSSIBILITY APPROACHING OF SAMPLING DIRECTLY AT THE RADAR 2& FREQUENCY 4HE BENEFITS OF )& SAMPLING OVER CONVENTIONAL ANALOG )1 DEMODULATION ARE L
L
L
L
L
L
L
6IRTUAL ELIMINATION OF ) AND 1 IMBALANCE 6IRTUAL ELIMINATION OF $# OFFSET ERRORS 2EDUCED CHANNEL TO CHANNEL VARIATION )MPROVED LINEARITY &LEXIBILITY OF BANDWIDTH AND SAMPLE RATE 4IGHT FILTER TOLERANCE PHASE LINEARITY AND IMPROVED ANTI ALIAS FILTERING 2EDUCED COMPONENT COST SIZE WEIGHT AND POWER DISSIPATION
4HE USE OF A HIGH )& FREQUENCY IS DESIRABLE AS IT EASES THE DOWNCONVERSION AND FILTERING PROCESS HOWEVER THE USE OF HIGHER FREQUENCIES PLACES GREATER DEMANDS ON THE PERFORMANCE OF THE !$ CONVERTER $IRECT 2& SAMPLING IS CONSIDERED THE ULTI MATE GOAL OF DIGITAL RECEIVERS WITH ALL THE TUNING AND FILTERING PERFORMED THROUGH DIGITAL SIGNAL PROCESSING 4HE ADVANTAGE BEING THE ALMOST COMPLETE ELIMINATION OF ANALOG HARDWARE (OWEVER NOT ONLY DOES THE !$ CONVERTER HAVE TO SAMPLE THE 2& DIRECTLY BUT UNLESS IT IS PRECEDED BY TUNABLE 2& PRESELECTOR FILTERS THE !$ CONVERTER INPUT MUST HAVE THE DYNAMIC RANGE TO HANDLE ALL OF THE SIGNALS PRES ENT IN THE RADAR BAND SIMULTANEOUSLY 'ENERALLY THE INTERFERENCE POWER ENTERING THE !$ CONVERTER IS PROPORTIONAL TO THE BANDWIDTH OF COMPONENTS IN FRONT OF THE
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!$ CONVERTER 4HE REQUIRED !$ CONVERTER 3.2 TO AVOID SATURATION ON THE INTERFER ING SIGNALS IS GIVEN BY
¤ 0 # ³ 3.2!$# D" LOG ¥ ) ´ ¦ . !$# µ
WHERE 0) INTERFERENCE POWER AT !$ CONVERTER INPUT # CREST FACTOR .!$# !$ CONVERTER NOISE 4HE CREST FACTOR IS THE PEAK LEVEL THAT CAN BE HANDLED WITHIN THE FULL SCALE RANGE OF THE !$ CONVERTER RELATIVE TO THE RMS INTERFERENCE LEVEL )T IS SET TO ACHIEVE A SUFFICIENTLY HIGH PROBABILITY THAT FULL SCALE WILL NOT BE EXCEEDED &OR EXAMPLE WITH GAUSSIAN NOISE A CREST FACTOR OF SETS THE PEAK LEVEL AT THE R LEVEL D" ABOVE THE RMS LEVEL WITH A PROBABILITY OF THAT THE FULL SCALE IS NOT EXCEEDED ON EACH !$ CONVERTER SAMPLE 3ETTING THE SYSTEM NOISE LEVEL POWER SPECTRAL DENSITY INTO THE !$ CONVERTER 2D" ABOVE THE !$ CONVERTER NOISE GIVES
¤ F. ³ 2 D" LOG ¥ S 393 ´ " . ¦ )& !$# µ
WHERE .393 SYSTEM NOISE AT !$ CONVERTER INPUT IN BANDWIDTH ")& #OMBINING %Q AND GIVES THE REQUIRED 3.2 AS
¤ 0 # ")& ³ 3.2!$# D" LOG ¥ ) 2 D" ¦ F3 . 393 ´µ
4HE GENERATION OF BASEBAND ) AND 1 SIGNALS FROM THE )& SAMPLED !$ CONVERTER DATA IS PERFORMED USING DIGITAL SIGNAL PROCESSING AND CAN BE IMPLEMENTED THROUGH A VARIETY OF APPROACHES 4WO APPROACHES ARE DESCRIBED NEXT $IGITAL $OWNCONVERSION 4HE DIGITAL DOWNCONVERSION APPROACH IS SHOWN IN &IGURE 4HE SIGNAL IS SAMPLED BY THE !$ CONVERTER FREQUENCY SHIFTED TO BASE BAND LOW PASS FILTERED AND DECIMATED TO PRODUCE )1 DIGITAL DATA 4HE SIGNAL SPECTRUM AT EACH STAGE OF THE PROCESS IS SHOWN IN &IGURE )N CONTINUOUS TIME &IG A FREQUENCY IS IN HERTZ AND IS REPRESENTED BY & )N DISCRETE TIME &IG BnE FRE QUENCY IS IN RADIANS PER SAMPLE AND IS REPRESENTED BY V 4HE SPECTRUM OF THE ANA LOG INPUT SIGNAL XT IS SHOWN IN &IGURE A WITH THE SIGNAL SPECTRUM CENTERED AT & HERTZ 4HE SIGNAL IS SAMPLED BY THE !$ CONVERTER AT FREQUENCY &S PRODUCING THE W CENTERED AT FREQUENCY V WITH THE TIME SEQUENCE X N AND FREQUENCY SPECTRUM 8 IMAGE CENTERED AT V 4HE !$ CONVERTER OUTPUT SIGNAL IS THEN FREQUENCY SHIFTED BY COMPLEX MULTIPLICATION WITH THE REFERENCE SIGNAL E JV N CORRESPONDING TO A REFERENCE SIGNAL ROTATING AT V RADIANS PER SAMPLE CENTERING THE SIGNAL SPECTRUM 8V ABOUT ZERO 4HE UNWANTED IMAGE IS RE CENTERED AT V IF V O OR V O IF V a O 4HE UNWANTED IMAGE IS THEN REJECTED USING THE &)2 FILTER WITH IMPULSE RESPONSE HN PRODUCING OUTPUT X} N WITH SPECTRUM 8} V &INALLY THE SAMPLE RATE IS REDUCED BY
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&)'52% $IGITAL DOWNCONVERSION ARCHITECTURE
SELECTING EVERY $TH SAMPLE 0ROVIDED THE FILTER RESPONSE (V HAS SUFFICIENT REJECTION FOR FREQUENCIES \V \ q P $ THERE WILL BE NEGLIGIBLE ALIASING AND LOSS OF INFORMATION IN THE DECIMATION PROCESS
&)'52% $IGITAL DOWNCONVERSION SPECTRA
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&)'52% (ILBERT TRANSFORMER ARCHITECTURE
(ILBERT 4RANSFORMER !N ALTERNATIVE DIGITAL RECEIVER ARCHITECTURE IS SHOWN IN &IGURE WITH THE RELEVANT SIGNAL SPECTRA SHOWN IN &IGURE 4HE !$ CONVERTER OUTPUT SIGNAL X N IS PROCESSED USING A (ILBERT TRANSFORMER COMPRISING &)2 FILTERS HN AND HN WHERE THE FREQUENCY RESPONSES ARE GIVEN BY
\( V \ y \( V \ y \V V \ a "
( V ª J \ V V \ a " y ' V «¬ J \ V V \ a "
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4HE FILTER OUTPUTS FORM THE DESIRED COMPLEX VALUED SIGNAL X N CENTERED AT FREQUENCY V WHILE REJECTING THE IMAGE CENTERED AT V 4HE FINAL STAGE IS TO PERFORM A FREQUENCY SHIFT AND SAMPLE RATE REDUCTION BY DECIMATING THE SIGNAL BY SELECTING EVERY $TH SAMPLE
&)'52% 3PECTRA OF (ILBERT TRANSFORMER RECEIVER
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)F THE SPECTRUM OF 8V IS CENTERED AT FREQUENCY V O K $ K THE DECIMATION WILL CENTER THE SPECTRUM 9V ABOUT ZERO 0ROVIDED THE FILTER RESPONSES HAVE SUFFICIENT REJECTION FOR FREQUENCIES \V o V \ q O $ THERE WILL BE NEGLIGIBLE ALIASING AND LOSS OF INFORMATION IN THE DECIMATION PROCESS )1 %RRORS $IGITAL ) AND 1 GENERATION DOES NOT PRODUCE SIGNALS WITHOUT ERROR AS IS OFTEN STATED BUT INSTEAD ALLOWS THE GENERATION OF THESE SIGNALS WITH ERRORS THAT ARE SUFFICIENTLY SMALL TO BE CONSIDERED NEGLIGIBLE 4HE PRIMARY CAUSE OF THE IMBALANCE IS THE NON IDEAL FILTER RESPONSES !N INFINITE NUMBER OF TAPS WOULD BE REQUIRED TO SET THE PASSBAND GAIN TO UNITY AND THE STOPBAND GAIN TO ZERO HOWEVER FOR MOST APPLICATIONS SUFFICIENT PROCESSING RESOURCES ARE AVAILABLE TO REDUCE THE ERRORS TO INSIGNIFICANT LEVELS &INITE LENGTH WORDS FOR FILTER COEFFICIENTS PRODUCE NON IDEAL FILTER RESPONSES 4HE EFFECT ON PASSBAND RESPONSE IS TYPICALLY NEGLIGIBLE BUT SIGNIFICANT DISTORTION OF THE FILTER STOPBAND REJECTION CAN OCCUR POTENTIALLY EFFECTING )1 BALANCE $IGITAL $OWNCONVERSION 5SING -ULTIRATE 0ROCESSING AND 0OLYPHASE FILTERS 4HERE ARE MANY VARIATIONS TO THESE BASIC APPROACHES AND SPECIFIC IMPLE MENTATIONS OFTEN UTILIZE EFFICIENT APPROACHES THAT MINIMIZE THE NUMBER OF CALCULA TIONS REQUIRED WITH EMPHASIS ON REDUCING THE NUMBER OF MULTIPLICATIONS AS THESE REQUIRE SIGNIFICANTLY MORE RESOURCES THAN ADDITIONS 4WO TECHNIQUES USED TO REDUCE THE &)2 FILTER PROCESSING BURDEN ARE MULTIRATE PROCESSING AND POLYPHASE FILTERING 4HE DIGITAL DOWNCONVERSION APPROACH IS SHOWN IN &IGURE USING MULTIRATE PRO CESSING 4HE FIRST &)2 FILTER HN PROVIDES SUFFICIENT REDUCTION TO PREVENT ALIASING IN THE FIRST DECIMATION BY FACTOR $ THE SECOND FILTER HN PROVIDES ALIAS REDUCTION FOR THE SECOND DECIMATION AND CAN ALSO BE USED TO CORRECT PASSBAND RIPPLE OR DROOP DUE TO FILTER HN &OR LARGE DECIMATION FACTORS MORE THAN TWO DECIMATION STAGES MAY BE USED ! POPULAR FILTER FOR THE FIRST STAGE IS THE #ASCADED )NTEGRATOR #OMB #)# DECIMA TOR FILTER THAT CAN BE IMPLEMENTED WITHOUT MULTIPLIERS 4HESE FILTERS PROVIDE REJECTION IN THE STOPBAND AT FREQUENCIES THAT ALIAS TO THE PASSBAND AS A RESULT OF DECIMATION 3INCE THEY PROVIDE RELATIVELY LARGE PASSBAND DROOP AND SLOW STOPBAND REJECTION THEY ARE GENERALLY FOLLOWED BY A &)2 FILTER THAT CAN BOTH CORRECT FOR #)# PASSBAND DROOP AND
&)'52% $IGITAL DOWNCONVERSION ARCHITECTURE
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! POLYPHASE FILTER IS A FILTER BANK THAT SPLITS AN INPUT SIGNAL INTO $ SUB BAND FILTERS OPERATING AT A SAMPLE RATE REDUCED BY A FACTOR $ PROVIDING A COMPUTATIONALLY EFFICIENT APPROACH TO PERFORMING THE &)2 FILTERING FOLLOWED BY DECIMATION IN A DIGITAL RECEIVER 2ATHER THAN COMPUTING ALL THE FILTER OUTPUT SAMPLES AND ONLY USING EVERY $TH SAMPLE THE POLYPHASE APPROACH CALCULATES ONLY THOSE THAT ARE ACTUALLY USED &IGURE AND %Q DEFINE HOW THE FILTER WITH IMPULSE RESPONSE HN FOLLOWED WITH DECIMATION BY FACTOR $ IS IMPLEMENTED IN A POLYPHASE STRUCTURE 4HE INPUT SIGNAL XN IS DIVIDED INTO $ PARALLEL PATHS BY THE hCOMMUTATOR v WHICH OUTPUTS SAMPLES IN TURN ROTATING IN A COUNTERCLOCKWISE DIRECTION TO EACH OF THE &)2 FILTERS OPERATING AT THE REDUCED SAMPLE RATE 4HE OUTPUTS OF THE &)2 FILTERS ARE SUMMED TO PRODUCE THE OUTPUT SIGNAL YM 4HIS ARCHITECTURE IS BENEFICIAL AS IT PROVIDES AN APPROACH THAT CAN BE EASILY PARALLELIZED AT RATE &8 $
PKN HK N$ K x $
N x +
-ULTI #HANNEL 2ECEIVER #ONSIDERATIONS -ODERN RADAR SYSTEMS RARELY CON TAIN ONLY ONE RECEIVER CHANNEL -ONOPULSE PROCESSING FOR EXAMPLE REQUIRES TWO OR MORE CHANNELS TO PROCESS SUM AND DELTA SIGNALS !DDITIONALLY THE CHANNELS MUST BE COHERENT SYNCHRONIZED IN TIME AND WELL MATCHED IN PHASE AND AMPLITUDE $IGITAL BEAMFORMING SYSTEMS REQUIRE A LARGE NUMBER OF CHANNELS WITH SIMILAR COHERENCE AND SYNCHRONIZATION REQUIREMENTS AND TIGHT PHASE AND AMPLITUDE TRACK ING 4HE COHERENCE REQUIREMENT DICTATES THE RELATIVE PHASE STABILITY OF ,/ AND !$ CONVERTER CLOCK SIGNALS USED FOR EACH RECEIVE CHANNEL 4HE TIME SYNCHRONIZA TION REQUIREMENT MEANS THAT !$ CONVERTER CLOCK SIGNALS FOR EACH CHANNEL MUST BE ALIGNED IN TIME AND DECIMATION MUST BE PERFORMED IN PHASE FOR EACH CHANNEL 0HASE AND AMPLITUDE IMBALANCE BETWEEN CHANNELS IS A RESULT OF VARIATION IN THE
&)'52% $ECIMATION USING POLYPHASE FILTERS
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ANALOG CIRCUITRY PRIOR TO AND WITHIN THE !$ CONVERTER )F THE )& FILTER BANDWIDTH IS WIDE RELATIVE TO THE DIGITAL RECEIVER BANDWIDTH THE MAJORITY OF THE ERROR BETWEEN CHANNELS WILL BE A CONSTANT GAIN AND PHASE OFFSET ACROSS THE RECEIVER BANDWIDTH ! SINGLE CORRECTION APPLIED AS A COMPLEX MULTIPLICATION OF )1 DATA WILL COR RECT FOR GAIN AND PHASE OFFSETS AND IS USUALLY ADEQUATE TO PROVIDE THE REQUIRED CHANNEL TRACKING FOR MONOPULSE APPLICATIONS 7HEN TIGHTER CHANNEL TRACKING IS REQUIRED SUCH AS FOR SIDELOBE CANCELER OR DIGITAL BEAMFORMING APPLICATIONS &)2 FILTER EQUALIZATION CAN BE USED TO CORRECT FOR FREQUENCY DEPENDENT VARIATIONS ACROSS THE RECEIVER BANDWIDTH &)2 FILTER EQUALIZATION CAN BE PERFORMED EITHER SUBSE QUENT TO THE &)2 FILTERING USED TO GENERATE )1 DATA OR COMBINED WITH THESE FILTERS )T SHOULD BE NOTED THAT TO CORRECT FOR FREQUENCY AND PHASE VARIATION ACROSS THE RECEIVER BANDWIDTH REQUIRES &)2 FILTERS WITH COMPLEX COEFFICIENTS APPLIED EQUALLY TO ) AND 1 DATA 2EAL VALUE COEFFICIENTS TYPICALLY USED IN )1 GENERATION PROVIDE FIL TER RESPONSES SYMMETRICAL ABOUT ZERO FREQUENCY #ORRECTION OF )& FILTER FREQUENCY RESPONSE ERRORS WILL IN GENERAL REQUIRE ASYMMETRIC FREQUENCY CORRECTION THAT CAN ONLY BE PROVIDED AT BASEBAND USING COMPLEX COEFFICIENTS 4HE DEGREE TO WHICH THESE MULTIPLE RECEIVER CHANNELS MUST TRACK DEPENDS ON THE SPECIFIC SYSTEM REQUIREMENTS !LTHOUGH MODERN SYSTEMS TYPICALLY INCLUDE SOME DEGREE OF CHANNEL EQUALIZATION FUNCTION A REASONABLE DEGREE OF TRACKING BETWEEN GAIN PHASE AND TIMING MUST BE MAINTAINED IN ORDER TO ALLOW THE CHANNEL EQUALIZATION TO BE PERFORMED USING DIGITAL SIGNAL PROCESSING WITHOUT CONSUMING EXCESSIVE PROCESSING RESOURCES !LSO THE RELATIVE STABILITY OF THE RADAR CHANNELS AS A FUNCTION OF TIME AND TEMPERATURE MUST BE SUCH THAT THE CORRECTIONS CAN MAINTAIN ADEQUATE TRACKING DURING THE TIME BETWEEN CALIBRATION INTERVALS $IGITAL BEAMFORMING SYSTEMS REQUIRE A LARGE NUMBER OF RECEIVER CHANNELS )N THESE APPLICATIONS SIZE WEIGHT POWER DISSIPATION AND COST ARE CRITICAL CONSIDERATIONS
È°£ÓÊ Ê * 8Ê"* ,/" $IPLEX "ENEFITS $IPLEX OPERATION CONSISTS OF TWO RECEIVERS THAT SIMULTANEOUSLY PROCESS RETURNS FROM TRANSMISSIONS ON DIFFERENT FREQUENCIES 4RANSMISSIONS ARE USU ALLY NON OVERLAPPING IN TIME TO AVOID A D" INCREASE IN PEAK POWER AND BECAUSE MOST RADAR TRANSMITTERS ARE OPERATED IN SATURATION AND SIMULTANEOUS TRANSMISSION AT MULTIPLE FREQUENCIES WOULD PRODUCE SIGNIFICANT TRANSMITTED INTERMODULATION DISTORTION 4HE SENSITIVITY BENEFIT OF DIPLEX OPERATION FOR DETECTING 3WERLING TARGETS IS SHOWN IN &IGURE INCREASING WITH PROBABILITY OF DETECTION 0$ &OR EXAMPLE DIPLEX OPER ATION ACHIEVES 0$ WITH D" LESS TOTAL SIGNAL POWER THAN SIMPLEX !SSUMPTIONS MADE IN DERIVING &IGURE ARE 2ETURNS ON THE TWO FREQUENCIES ARE ADDED IN VOLTAGE OR POWER PRIOR TO THE DETECTION DECISION RATHER THAN BEING SUBJECTED TO INDIVIDUAL DETECTION DECISIONS 3EPARATION OF THE TWO FREQUENCIES IS SUFFICIENT TO MAKE THEIR 3WERLING FLUCTUA TIONS INDEPENDENT 4HIS DEPENDS ON THE PHYSICAL LENGTH OF THE TARGET IN THE RANGE DIMENSION K2 4HE MINIMUM FREQUENCY SEPARATION IS -(ZK2 M -(Z WILL MAINTAIN THE DIPLEX BENEFIT FOR AIRCRAFT LONGER THAN M FT %QUAL ENERGY IS TRANSMITTED IN BOTH PULSES ! IMBALANCE SACRIFICES ONLY D" OF THE BENEFIT AT 0$
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&)'52% $IPLEX OPERATION IMPROVES THE SENSITIVITY OF THE RECEIVER
"OTH LINEAR AND ASYMMETRICAL NONLINEAR &- PRODUCE A RANGE ERROR AS A FUNCTION OF DOPPLER DUE TO RANGE DOPPLER COUPLING 4HESE RANGE DISPLACEMENTS MUST MATCH IN THE TWO RECEIVERS TO WITHIN A SMALL FRACTION OF THE COMPRESSED PULSE WIDTH OTHERWISE THE SENSITIVITY BENEFITS OF DIPLEX OPERATION ARE NOT FULLY ACHIEVED AND RANGE ACCURACY MAY BE DEGRADED )MPLEMENTATION $IPLEX OPERATION CAN BE IMPLEMENTED WITH A VARIETY OF APPROACHES #OMPLETE REPLICATION OF THE RECEIVER CHANNELS IS TYPICALLY THE MOST EXPEN SIVE APPROACH AND MAY BE REQUIRED IF THE FREQUENCY SEPARATION IS VERY LARGE ! MORE COMMON APPROACH IS SEPARATION OF THE FREQUENCIES AT THE FIRST )& AS THIS DOES NOT REQUIRE COMPLETE DUPLICATION OF THE 2& FRONT END OR THE FIRST ,/ SIGNAL 3EPARATE SEC OND LOCAL OSCILLATOR OR )1 DEMODULATOR REFERENCE FREQUENCIES CAN BE USED TO PROCESS THE DIFFERENT FREQUENCIES 7ITH THE USE OF HIGH SPEED )& SAMPLING IT IS ALSO POSSIBLE TO DIGITIZE BOTH SIGNALS SIMULTANEOUSLY USING A SINGLE !$ CONVERTER AND PERFORM THE FREQUENCY SEPARATION USING DIGITAL SIGNAL PROCESSING 7HICHEVER APPROACH IS USED CARE MUST BE TAKEN TO PROVIDE ADEQUATE DYNAMIC RANGE AND LINEARITY TO PREVENT INTERMODULA TION DISTORTION FROM DEGRADING RADAR PERFORMANCE
È°£ÎÊ 76 ", Ê ,/" ÊÊ Ê1* " 6 ,-" 4HE EXCITER FUNCTION OF WAVEFORM GENERATION AND UPCONVERSION IS OFTEN TIGHTLY COUPLED WITH THE RECEIVER FUNCTION 4HE REQUIREMENT FOR COHERENCE BETWEEN THE RECEIVER AND EXCITER IS A MAJOR FACTOR FOR THIS TIGHT COUPLING AND THE USE OF THE SAME ,/ FREQUEN CIES WITHIN THE RECEIVER AND EXCITER USUALLY RESULTS IN HARDWARE SAVINGS 3IMILAR TO THE MIGRATION TO DIGITAL RECEIVER ARCHITECTURES THE EXCITER FUNCTIONALITY IS INCREASINGLY BEING IMPLEMENTED USING DIGITAL APPROACHES
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$IRECT $IGITAL 3YNTHESIZER 4HE $IRECT $IGITAL 3YNTHESIZER $$3 PRODUCES WAVEFORMS USING DIGITAL TECHNIQUES AND PROVIDES SIGNIFICANT IMPROVEMENTS IN STABIL ITY PRECISION AGILITY AND VERSATILITY OVER ANALOG TECHNIQUES 4HE MAIN LIMITATIONS ARE THE NOISE AND SPURIOUS SIGNALS AS DESCRIBED BELOW 4HE GENERAL $$3 ARCHITECTURE IS SHOWN IN &IGURE 4HE DOUBLE ACCUMULATOR ARCHITECTURE COMPRISING THE FREQUENCY AND PHASE ACCUMULATORS ENABLES THE GENERATION OF #7 LINEAR &- CHIRP NONLINEAR PIECE WISE LINEAR &- FREQUENCY MODULATED AND PHASE MODULATED WAVEFORMS #7 WAVEFORMS ARE GENERATED BY APPLYING A CONSTANT FREQUENCY WORD DIGITIZED FREQUENCY REPRESENTATION INPUT TO THE PHASE ACCUMULATOR CREATING A LINEAR PHASE SEQUENCE THAT IS FIRST TRUNCATED THEN INPUT TO A COSINE OR SINE LOOKUP TABLE THAT OUTPUTS THE CORRESPOND ING SINUSOIDAL SIGNAL VALUE TO THE DIGITAL TO ANALOG $! CONVERTER 4HE FREQUENCY RESOLUTION IS DEPENDENT ON THE NUMBER OF BITS AND THE CLOCK FREQUENCY OF THE PHASE ACCUMULATOR 4HE OUTPUT FREQUENCY IS GIVEN BY
FOUT
- F FCLK .F
WHERE -F FREQUENCY WORD INPUT TO THE PHASE ACCUMULATOR FCLK PHASE ACCUMULATOR CLOCK FREQUENCY .E NUMBER OF BITS OF PHASE ACCUMULATOR ,INEAR &- OR CHIRP WAVEFORMS ARE GENERATED BY APPLYING A CONSTANT CHIRP SLOPE WORD DIGITIZED CHIRP SLOPE REPRESENTATION TO THE INPUT OF THE FREQUENCY ACCUMULATOR CREATING A QUADRATIC PHASE SEQUENCE AT THE OUTPUT OF THE PHASE REGISTER 0IECEWISE LINEAR OR NONLINEAR &- WAVEFORMS CAN BE GENERATED BY APPLYING A TIME VARYING SLOPE INPUT TO THE FREQUENCY REGISTER 4HE FREQUENCY ACCUMULATOR MAY BE CLOCKED EITHER AT THE SAME RATE AS THE PHASE ACCUMULATOR OR AT A SUB MULTIPLE TO PROVIDE FINER CHIRP SLOPE RESOLU TION )F BOTH ACCUMULATORS ARE CLOCKED AT THE SAME RATE THE CHIRP SLOPE IS GIVEN BY $FOUT - 3 FCLK .F $T
WHERE -3 CHIRP SLOPE WORD INPUT TO THE FREQUENCY ACCUMULATOR .F NUMBER OF BITS OF FREQUENCY ACCUMULATOR &REQUENCY MODULATED AND PHASE MODULATED WAVEFORMS CAN BE CREATED APPLYING TIME VARYING INPUTS TO THE FREQUENCY MODULATION &- AND PHASE MODULATION 0- PORTS
&)'52% $IRECT $IGITAL 3YNTHESIZER BLOCK DIAGRAM
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%RRORS SUCH AS PHASE TRUNCATION AND $! CONVERTER QUANTIZATION AND NONLINEARITY PRODUCE SPURIOUS SIGNALS DUE TO THEIR DETERMINISTIC NATURE 4HE SPURIOUS SIGNAL FRE QUENCIES GENERATED BY A $$3 CAN BE READILY PREDICTED AS THEY ARE A FUNCTION OF THE DIGITAL ARCHITECTURE AND PROGRAMMED FREQUENCY 4HE SPURIOUS SIGNAL MAGNITUDES ARE LESS PREDICTABLE AS THE MAGNITUDES OF THE DOMINANT SPURIOUS SIGNALS ARE A FUNCTION OF THE $! CONVERTER NONLINEARITY 7HEN GENERATING #7 WAVEFORMS THE $! CONVERTER SEQUENCE REPEATS AFTER + SAMPLES WHERE + EQUALS THE GREATEST COMMON DIVISOR OF .E AND -F 4HUS SPURIOUS SIGNALS OCCUR ONLY AT FREQUENCIES
FSPUR
NFCLK N +
)N THE EXTREME CASE WHERE -F DOES NOT CONTAIN THE FACTOR THIS CREATES A SPURIOUS FRE QUENCY SPACING OF FCLK .E &OR EXAMPLE WITH A '(Z CLOCK AND BIT FREQUENCY ACCU MULATOR THE SPURIOUS FREQUENCY SPACING CAN BE AS CLOSE AS (Z )N MOST CASES SUCH CLOSELY SPACED SPURIOUS SIGNALS CANNOT BE DIFFERENTIATED FROM NOISE #ONVERSELY CHOOS ING VALUES OF -F THAT CONTAIN LARGE FACTORS OF . CREATES RELATIVELY LARGE SPURIOUS SPACING &OR EXAMPLE USING A -(Z CLOCK ALLOWS THE GENERATION OF FREQUENCIES AT MULTIPLES OF -(Z WITH ALL THE SPURIOUS COMPONENTS OCCURRING AT MULTIPLES OF -(Z 4HE IMPACT OF $$3 SPURIOUS SIGNALS ON RADAR PERFORMANCE DEPENDS ON THE NATURE OF THE SPURIOUS SIGNALS AND THE TYPE OF RADAR PROCESSING INVOLVED !PPLICATIONS USING CHIRP WAVEFORMS WITH LARGE TIME BANDWIDTH PRODUCTS ARE TYPICALLY LESS SENSITIVE TO $$3 SPURIOUS SIGNALS SINCE THE $$3 SPURIOUS SIGNALS CHIRP AT A DIFFERENT RATE TO THAT OF THE WANTED SIGNAL 4HE SPURIOUS SIGNALS ARE THUS REJECTED DURING PULSE COMPRESSION )N PULSE DOPPLER APPLICATIONS SPURIOUS SIGNALS ARE OF MUCH GREATER CONCERN HOWEVER THEIR EFFECTS CAN BE MITIGATED BY ENSURING THAT THE $$3 GENERATES EACH WAVEFORM FROM THE SAME INITIAL CONDITIONS 2ESTARTING THE $$3 FOR EVERY PULSE GUARANTEES THAT THE SAME DIGITAL SEQUENCE WILL BE INPUT TO THE $! CONVERTER FOR EACH PULSE 4HE RESULT IS A $$3 OUTPUT THAT ONLY CONTAINS SPECTRAL COMPONENTS AT MULTIPLES OF THE 02& 4ECHNIQUES HAVE BEEN PROPOSED OR INCORPORATED INTO $$3 DEVICES THAT REDUCE SPU RIOUS LEVELS BY ADDING DITHERING TO REDUCE THE EFFECTS OF LIMITED WORD LENGTHS 4HE EFFECT OF THESE TECHNIQUES AND THE SPURIOUS SIGNALS THAT THEY ARE DESIGNED TO MITIGATE SHOULD BE CONSIDERED CAREFULLY AS THEY MAY BE DETRIMENTAL TO RADAR PERFORMANCE 4HE USE OF DITHERING WILL RANDOMIZE THE SPURIOUS SIGNAL RESULTING IN PULSE TO PULSE VARIA TIONS IN THE DIGITAL SEQUENCE OUTPUT TO THE $! CONVERTER A RESULT THAT IS UNDESIRABLE IN PULSE DOPPLER APPLICATIONS 4RULY RANDOM ERRORS ARE NOT GENERATED BY THE DIGITAL PORTION OF THE $$3 4HE ONLY NONDETERMINISTIC ERRORS ARE A RESULT OF THE $! CONVERTER PERFORMANCE IN THE FORM OF INTERNAL CLOCK JITTER OR ADDITIVE THERMAL NOISE AND THE EFFECT OF THE PHASE NOISE ON THE INPUT CLOCK SIGNAL )NTERNAL $! CONVERTER CLOCK JITTER PRODUCES PHASE MODULATION OF THE OUTPUT SIGNAL PROPORTIONAL TO THE OUTPUT FREQUENCY 3IMILARLY PHASE NOISE PRESENT ON THE CLOCK INPUT SIGNAL IS TRANSFERRED TO THE OUTPUT SIGNAL REDUCED BY LOG FOUT FCLK D" $! CON VERTER ADDITIVE THERMAL NOISE IS INDEPENDENT OF OUTPUT SIGNAL FREQUENCY AND PRODUCES BOTH PHASE AND AMPLITUDE NOISE COMPONENTS &REQUENCY -ULTIPLIERS &REQUENCY MULTIPLICATION ALLOWS SIGNALS TO BE INCREASED IN BOTH FREQUENCY AND BANDWIDTH &REQUENCY MULTIPLICATION IS FREQUENTLY USED IN GEN ERATING LOCAL OSCILLATOR #7 FREQUENCIES WHERE ALL FREQUENCIES ARE TYPICALLY BASED ON A
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&)'52% &REQUENCY MULTIPLIER OPERATION
LOW FREQUENCY REFERENCE 4HEY ALSO PROVIDE THE CAPABILITY FOR WIDE BANDWIDTH CHIRP WAVEFORMS THAT CANNOT BE GENERATED DIRECTLY USING AVAILABLE $$3 DEVICES &REQUENCY MULTIPLIERS OPERATE AS SHOWN IN &IGURE BY MULTIPLYING THE PHASE OF THE INPUT SIGNAL BY THE INTEGER MULTIPLICATION FACTOR - 3INCE IN PRACTICE THE PROCESS TYPICALLY INCLUDES SOME FORM OF LIMITING THE OUTPUT AMPLITUDE !T GENERALLY HAS A LOWER AMPLI TUDE VARIATION THAN THE INPUT SIGNAL AMPLITUDE !T "ECAUSE THE MULTIPLICATION PROCESS MULTIPLIES UP THE VARIATIONS IN THE SIGNAL PHASE BY FACTOR - INPUT PHASE NOISE AND SPURIOUS PHASE MODULATIONS ARE INCREASED BY LOG- D" 3IMILARLY VARIATIONS IN THE PHASE OF THE SIGNAL AS A FUNCTION OF FRE QUENCY ARE MULTIPLIED UP 4HESE VARIATIONS ARE PRODUCED DURING SIGNAL FILTERING AND MAY BE PRESENT ON THE INPUT SIGNAL &OR CHIRP WAVEFORMS THIS CAN RESULT IN A SIGNIFICANT DEGRADATION IN THE RANGE SIDELOBE PERFORMANCE !LSO PRACTICAL MULTIPLIERS MAY HAVE A SIGNIFICANT PHASE VARIATION AS A FUNCTION OF FREQUENCY )F THE INPUT SIGNAL PHASE DISTOR TION IS GIVEN BY
¤ P NF ³ E F A SIN ¥ ¦ " ´µ
WHERE A PEAK PHASE RIPPLE " WAVEFORM INPUT BANDWIDTH N NUMBER OF CYCLES OF PHASE RIPPLE THE RESULTING OUTPUT DISTORTION PRODUCES RANGE SIDELOBES AT TIMES oN -" AND MAGNITUDE LOG-A RELATIVE TO THE MAIN BEAM OF THE TARGET RETURN !S AN EXAMPLE GENERAT ING A CHIRP WAVEFORM THAT HAS RANGE SIDELOBES BETTER THAN D" USING AN r MULTIPLIER REQUIRES THAT THE INPUT SIGNAL HAS LESS THAN DEGREES PEAK PEAK PHASE RIPPLE &REQUENCY MULTIPLIERS CAN BE IMPLEMENTED USING A VARIETY OF TECHNIQUES SUCH AS USING STEP RECOVERY DIODE MULTIPLIERS OR USING PHASE LOCKED LOOPS 7HERE WIDE PERCENT AGE BANDWIDTH AND FAST SETTLING IS REQUIRED THE MOST COMMON TECHNIQUE IS TO CASCADE A SERIES OF FREQUENCY DOUBLERS OR LOW ORDER MULTIPLIERS 4HIS TYPE OF MULTIPLIER CAN ALSO PROVIDE NEAR IDEAL PHASE NOISE PERFORMANCE BUT HAS SIGNIFICANT PHASE MODULATION AS A FUNCTION OF FREQUENCY AS IT CONTAINS FILTERS BETWEEN EACH STAGE OF MULTIPLICATION 0REDISTORTION OF THE MULTIPLIER INPUT WAVEFORM IS OFTEN USED IN ORDER TO PRODUCE WIDEBAND CHIRP WAVEFORMS WITH LOW RANGE SIDELOBE PERFORMANCE )F THE MULTIPLIER IS CHARACTERIZED BY AN OUTPUT PHASE DISTORTION AS A FUNCTION OF INPUT FREQUENCY GIVEN BY E V THEN A PREDISTORTION OF THE INPUT SIGNAL BY PHASE E V - WILL EQUALIZE THE MULTIPLIER RESPONSE 0REDISTORTION CAN BE PERFORMED VERY PRECISELY BY ADDING THE PHASE MODULATION VIA THE $$3 THAT IS USED TO GENERATE THE CHIRP WAVEFORM 7AVEFORM 5PCONVERSION 5PCONVERSION OF EXCITER WAVEFORMS IS SIMILAR TO DOWNCONVERSION WITHIN THE RECEIVER !LSO SIMILAR PRACTICAL CONSIDERATIONS OF MIXER SPURIOUS AND IMAGE REJECTION APPLY 4HE ONE SIGNIFICANT ADDITIONAL CHALLENGE IS THE REJECTION OF THE ,/ LEAKAGE ,/ REJECTION TYPICALLY IMPOSES TIGHT FILTER REJECTION REQUIREMENTS ON THE 2& FILTERS AND FOR WIDE TUNABLE RANGES SWITCHED FILTERS ARE OFTEN REQUIRED
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Ç°£Ê /," 1 /" !S DIGITAL PROCESSING HAS INCREASED IN SPEED AND DIGITAL HARDWARE HAS DECREASED IN COST AND SIZE RADARS HAVE BECOME MORE AND MORE AUTOMATED SO THAT AUTOMATIC DETECTION AND TRACKING !$4 SYSTEMS ARE ASSOCIATED WITH ALMOST ALL BUT THE SIMPLEST OF RADARS )N THIS CHAPTER AUTOMATIC DETECTION AUTOMATIC TRACKING AND SENSOR INTEGRATION TECHNIQUES FOR SURVEILLANCE RADARS ARE DISCUSSED )NCLUDED IN THE DISCUSSION ARE VARI OUS NONCOHERENT INTEGRATORS THAT PROVIDE TARGET ENHANCEMENT THRESHOLDING TECHNIQUES FOR FALSE ALARMS AND TARGET SUPPRESSION AND ALGORITHMS FOR ESTIMATING TARGET POSITION AND RESOLVING TARGETS 4HEN AN OVERVIEW OF THE ENTIRE TRACKING SYSTEM IS GIVEN FOL LOWED BY A DISCUSSION OF ITS VARIOUS COMPONENTS SUCH AS TRACK INITIATION CORRELATION LOGIC TRACKING FILTER AND MANEUVER FOLLOWING LOGIC &INALLY THE CHAPTER CONCLUDES WITH A DISCUSSION OF SENSOR INTEGRATION AND RADAR NETTING INCLUDING BOTH COLOCATED AND MULTISITE SYSTEMS
Ç°ÓÊ 1/" / Ê / /" )N THE S -ARCUM APPLIED STATISTICAL DECISION THEORY TO RADAR AND LATER 3WERLING EXTENDED THE WORK TO FLUCTUATING TARGETS 4HEY INVESTIGATED MANY OF THE STATISTICAL PROBLEMS ASSOCIATED WITH THE NONCOHERENT DETECTION OF TARGETS IN GAUSSIAN NOISE .OTE )F THE INPHASE AND QUADRATURE COMPONENTS ARE GAUSSIAN DISTRIBUTED THE ENVE LOPE IS 2AYLEIGH DISTRIBUTED AND THE POWER IS EXPONENTIALLY DISTRIBUTED -ARCUMS MOST IMPORTANT RESULT WAS THE GENERATION OF CURVES OF PROBABILITY OF DETECTION 0$ VER SUS SIGNAL TO NOISE RATIO 3. FOR A DETECTOR THAT SUMS . ENVELOPE DETECTED SAMPLES EITHER LINEAR OR SQUARE LAW UNDER THE ASSUMPTION OF EQUAL SIGNAL AMPLITUDES 7HEREAS FOR A PHASED ARRAY THE EQUAL AMPLITUDE ASSUMPTION IS VALID FOR A ROTATING RADAR THE RETURNED SIGNAL AMPLITUDE IS MODULATED BY THE ANTENNA PATTERN AS THE BEAM SWEEPS OVER
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THE TARGET -ANY AUTHORS HAVE INVESTIGATED VARIOUS DETECTORS COMPARING DETECTION PER FORMANCE AND ANGULAR ESTIMATION RESULTS WITH OPTIMAL VALUES AND MANY OF THESE RESULTS ARE PRESENTED LATER IN THIS SECTION )N THE ORIGINAL WORK ON DETECTORS THE ENVIRONMENT WAS ASSUMED KNOWN AND HOMO GENEOUS SO THAT FIXED THRESHOLDS COULD BE USED (OWEVER A REALISTIC RADAR ENVIRON MENT EG CONTAINING LAND SEA AND RAIN WILL CAUSE AN EXORBITANT NUMBER OF FALSE ALARMS FOR A FIXED THRESHOLD SYSTEM THAT DOES NOT UTILIZE EXCELLENT COHERENT PROCESSING 4HREE MAIN APPROACHESADAPTIVE THRESHOLDING NONPARAMETRIC DETECTORS AND CLUTTER MAPSHAVE BEEN USED TO SOLVE THE NONCOHERENT FALSE ALARM PROBLEM "OTH ADAPTIVE THRESHOLDING AND NONPARAMETRIC DETECTORS ARE BASED ON THE ASSUMPTION THAT HOMO GENEITY EXISTS IN A SMALL REGION ABOUT THE RANGE CELL THAT IS BEING TESTED 4HE ADAP TIVE THRESHOLDING METHOD ASSUMES THAT THE NOISE DENSITY IS KNOWN EXCEPT FOR A FEW UNKNOWN PARAMETERS EG THE MEAN AND THE VARIANCE 4HE SURROUNDING REFERENCE CELLS ARE THEN USED TO ESTIMATE THE UNKNOWN PARAMETERS AND A THRESHOLD BASED ON THE ESTIMATED DENSITY IS OBTAINED .ONPARAMETRIC DETECTORS OBTAIN A CONSTANT FALSE ALARM RATE #&!2 BY RANKING ORDERING THE SAMPLES FROM SMALLEST TO LARGEST THE TEST SAMPLE WITH THE REFERENCE CELLS 5NDER THE HYPOTHESIS THAT ALL THE SAMPLES TEST AND REFER ENCE ARE INDEPENDENT SAMPLES FROM AN UNKNOWN DENSITY FUNCTION THE RANK OF THE TEST SAMPLE IS UNIFORM AND CONSEQUENTLY A THRESHOLD THAT YIELDS #&!2 CAN BE SET #LUTTER MAPS STORE AN AVERAGE BACKGROUND LEVEL FOR EACH RANGE AZIMUTH CELL ! TARGET IS THEN DECLARED IN A RANGE AZIMUTH CELL IF THE NEW VALUE EXCEEDS THE AVERAGE BACKGROUND LEVEL BY A SPECIFIED AMOUNT /PTIMAL $ETECTOR 4HE RADAR DETECTION PROBLEM IS A BINARY HYPOTHESIS TESTING PROBLEM IN WHICH ( DENOTES THE HYPOTHESIS THAT NO TARGET IS PRESENT AND ( IS THE HYPOTHESIS THAT THE TARGET IS PRESENT 7HILE SEVERAL CRITERIA IE DEFINITIONS OF OPTIMALITY CAN BE USED TO SOLVE THIS PROBLEM THE MOST APPROPRIATE FOR RADAR IS THE .EYMAN 0EARSON 4HIS CRITERION MAXIMIZES THE PROBABILITY OF DETECTION 0$ FOR A GIVEN PROBABILITY OF FALSE ALARM 0FA BY COMPARING THE LIKELIHOOD RATIO , DEFINED BY %Q TO AN APPROPRIATE THRESHOLD 4 THAT DETERMINES THE 0FA ! TARGET IS DECLARED PRESENT IF
, X XN
P X XN\ ( q4 P X XN\ (
WHERE PX x XN\( AND PX x XN\( ARE THE JOINT PROBABILITY DENSITY FUNCTIONS OF THE N OBSERVATIONS XI UNDER THE CONDITIONS OF TARGET PRESENCE AND TARGET ABSENCE RESPEC TIVELY &OR A LINEAR ENVELOPE DETECTOR THE SAMPLES HAVE A 2AYLEIGH DENSITY UNDER ( AND A 2ICEAN DENSITY UNDER ( AND THE LIKELIHOOD RATIO DETECTOR REDUCES TO N
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WHERE ) IS THE MODIFIED "ESSEL FUNCTION OF ZERO ORDER R IS THE NOISE POWER AND !I IS THE TARGET AMPLITUDE OF THE ITH PULSE AND IS PROPORTIONAL TO THE ANTENNA POWER PATTERN &OR SMALL SIGNALS !I R THE DETECTOR REDUCES TO THE SQUARE LAW DETECTOR N
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AND FOR LARGE SIGNALS !I R IT REDUCES TO THE LINEAR DETECTOR N
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&OR CONSTANT SIGNAL AMPLITUDE IE !I ! THESE DETECTORS WERE FIRST STUDIED BY -ARCUM AND WERE STUDIED IN SUCCEEDING YEARS BY NUMEROUS OTHER PEOPLE 4HE MOST IMPORTANT FACTS CONCERNING THESE DETECTORS ARE THE FOLLOWING 4HE DETECTION PERFORMANCES OF THE LINEAR AND SQUARE LAW DETECTORS ARE SIMILAR DIF FERING ONLY BY LESS THAN D" OVER WIDE RANGES OF 0$ 0FA AND N "ECAUSE THE SIGNAL RETURN OF A SCANNING RADAR IS MODULATED BY THE ANTENNA PATTERN TO MAXIMIZE THE 3. WHEN INTEGRATING A LARGE NUMBER OF PULSES WITH NO WEIGHTING IE !I ONLY OF THE PULSES BETWEEN THE HALF POWER POINTS SHOULD BE INTEGRATED AND THE ANTENNA BEAM SHAPE FACTOR !"3& IS D" 4HE !"3& IS THE NUMBER BY WHICH THE MIDBEAM 3. MUST BE REDUCED SO THAT THE DETECTION CURVES GENERATED FOR EQUAL SIGNAL AMPLITUDES CAN BE USED FOR THE SCANNING RADAR 4HE COLLAPSING LOSS FOR THE LINEAR DETECTOR CAN BE SEVERAL DECIBELS GREATER THAN THE LOSS FOR A SQUARE LAW DETECTOR SEE &IGURE 4HE COLLAPSING LOSS IS THE ADDITIONAL SIGNAL REQUIRED TO MAINTAIN THE SAME 0$ AND 0FA WHEN UNWANTED NOISE SAMPLES ALONG WITH THE DESIRED SIGNAL PLUS NOISE SAMPLES ARE INTEGRATED 4HE NUMBER OF SIGNAL SAM PLES INTEGRATED IS . THE NUMBER OF EXTRANEOUS NOISE SAMPLES INTEGRATED IS - AND THE COLLAPSING RATIO Q . - . -OST AUTOMATIC DETECTORS ARE REQUIRED NOT ONLY TO DETECT TARGETS BUT ALSO TO MAKE ANGU LAR ESTIMATES OF THE AZIMUTH POSITION OF THE TARGET 3WERLING CALCULATED THE STANDARD DEVIATION OF THE OPTIMAL ESTIMATE BY USING THE #RAMER 2AO LOWER BOUND 4HE RESULTS
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ARE SHOWN IN &IGURE WHERE A NORMALIZED STANDARD DEVIATION IS PLOTTED AGAINST THE MIDBEAM 3. 4HIS RESULT HOLDS FOR A MODERATE OR LARGE NUMBER OF PULSES INTEGRATED AND THE OPTIMAL ESTIMATE INVOLVES FINDING THE LOCATION WHERE THE CORRELATION OF THE RETURNED SIGNAL AND THE DERIVATIVE OF THE ANTENNA PATTERN IS ZERO !LTHOUGH THIS ESTI MATE IS RARELY IMPLEMENTED ITS PERFORMANCE IS APPROACHED BY SIMPLE ESTIMATES 0RACTICAL $ETECTORS -ANY DIFFERENT DETECTORS OFTEN CALLED INTEGRATORS ARE USED TO ACCUMULATE THE RADAR RETURNS AS THE RADAR SWEEPS BY A TARGET ! FEW OF THE MOST COMMON DETECTORS ARE SHOWN IN &IGURE 4HE FEEDBACK INTEGRATOR AND TWO POLE FILTER ARE DETECTORS THAT MINIMIZE THE DATA STORAGE REQUIREMENTS 7HILE THESE DETEC TORS MAY STILL BE FOUND IN OLDER RADARS THEY PROBABLY WOULD NOT BE IMPLEMENTED IN NEW RADARS AND WILL NOT BE DISCUSSED IN THIS EDITION 4HOUGH ALL THE DETECTORS ARE SHOWN IN &IGURE AS BEING CONSTRUCTED WITH SHIFT REGISTERS THEY WOULD NORMALLY BE IMPLEMENTED WITH RANDOM ACCESS MEMORY 4HE INPUT TO THESE DETECTORS CAN BE LINEAR VIDEO SQUARE LAW VIDEO OR LOG VIDEO "ECAUSE LINEAR VIDEO IS PROBABLY THE MOST COM MONLY USED THE ADVANTAGES AND DISADVANTAGES OF THE VARIOUS DETECTORS WILL BE STATED FOR THIS VIDEO -OVING 7INDOW 4HE MOVING WINDOW IN &IGURE A PERFORMS A RUNNING SUM OF N PULSES IN EACH RANGE CELL
3I 3I XI XI N
WHERE 3I IS THE SUM AT THE ITH PULSE OF THE LAST N PULSES AND XI IS THE ITH PULSE 4HE PER FORMANCE OF THIS DETECTOR FOR N y IS ONLY D" WORSE THAN THE OPTIMAL DETECTOR GIVEN BY %Q 4HE DETECTION PERFORMANCE CAN BE OBTAINED BY USING AN !"3& OF D" AND STANDARD DETECTION CURVES FOR EQUAL AMPLITUDE PULSES 4HE ANGULAR ESTIMATE THAT IS OBTAINED BY EITHER TAKING THE MAXIMUM VALUE OF THE RUNNING SUM OR TAKING THE MIDPOINT BETWEEN THE FIRST AND LAST CROSSINGS OF THE DETECTION THRESHOLD HAS A BIAS OF N PULSES WHICH IS EASILY CORRECTED 4HE STANDARD DEVIATION OF THE ESTIMATION ERROR OF BOTH THESE ESTIMATORS IS ABOUT PERCENT HIGHER THAN THE OPTIMAL ESTIMATE SPECIFIED
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&)'52% "LOCK DIAGRAMS OF VARIOUS DETECTORS 4HE LETTER # INDICATES A COMPARISON S IS A DELAY AND LOOPS INDICATE FEEDBACK FROM ' 6 4RUNK
BY THE #RAMER 2AO BOUND ! DISADVANTAGE OF THIS DETECTOR IS THAT IT IS SUSCEPTIBLE TO INTERFERENCE THAT IS ONE LARGE SAMPLE FROM INTERFERENCE CAN CAUSE A DETECTION 4HIS PROBLEM CAN BE MINIMIZED BY USING SOFT LIMITING 4HE DETECTION PERFORMANCE DISCUSSED PREVIOUSLY IS BASED ON THE ASSUMPTION THAT THE TARGET IS CENTERED IN THE MOVING WINDOW )N THE REAL SITUATION THE RADAR SCANS OVER THE TARGET AND DECISIONS THAT ARE HIGHLY CORRELATED ARE MADE AT EVERY PULSE (ANSEN ANA LYZED THIS SITUATION FOR . AND PULSES AND CALCULATED THE DETECTION THRESH OLDS SHOWN IN &IGURE THE DETECTION PERFORMANCE SHOWN IN &IGURE AND THE ANGULAR ACCURACY SHOWN IN &IGURE #OMPARING (ANSENS SCANNING CALCULATION WITH THE SINGLE POINT CALCULATION ONE CONCLUDES THAT ABOUT D" OF IMPROVEMENT IS OBTAINED BY MAKING A DECISION AT EVERY PULSE 4HE ANGULAR ERROR OF THE BEAM SPLITTING PROCEDURE IS ABOUT PERCENT GREATER THAN THE OPTIMAL ESTIMATE &OR LARGE SIGNAL TO NOISE RATIOS THE ACCURACY RMS ERROR OF THE BEAM SPLITTING AND MAXIMUM RETURN PROCEDURES WILL BE LIMITED BY THE PULSE SPACING AND WILL APPROACH
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WHERE $P IS THE ANGULAR ROTATION BETWEEN TRANSMITTED PULSES #ONSEQUENTLY IF THE NUM BER OF PULSES PER BEAMWIDTH IS SMALL THE ANGULAR ACCURACY WILL BE POOR &OR INSTANCE IF PULSES ARE SEPARATED BY BEAMWIDTH S Q} IS BOUNDED BY BEAMWIDTHS (OWEVER IMPROVED ACCURACY CAN BE OBTAINED BY USING THE AMPLITUDES OF THE RADAR RETURNS !N ACCURATE ESTIMATE OF THE TARGET ANGLE IS GIVEN BY
$Q N ! ! Q} Q A$Q
&)'52% $ETECTION PERFORMANCE OF THE ANALOG MOVING WINDOW DETECTOR FOR THE NO FADING CASE AFTER 6 ' (ANSEN Ú )%%%
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&)'52% !NGULAR ACCURACY OBTAINED WITH BEAM SPLITTING ESTIMATION PROCEDURE FOR THE NO FADING CASE "ROKEN LINE CURVES ARE LOWER BOUNDS DERIVED BY 3WERLING AND POINTS SHOWN ARE SIMULATION RESULTS AFTER 6 ' (ANSEN Ú )%%%
WHERE
A BEAMWIDTH
AND ! AND ! ARE THE TWO LARGEST AMPLITUDES OF THE RETURNED SAMPLES AND OCCUR AT ANGLES P AND P P $P RESPECTIVELY "ECAUSE THE ESTIMATE SHOULD LIE BETWEEN P AND P AND %Q WILL NOT ALWAYS YIELD SUCH AN ESTIMATE Q} SHOULD BE SET EQUAL TO P IF Q} P AND Q} SHOULD BE EQUAL TO P IF Q} P 4HE ACCURACY OF THIS ESTIMATOR IS GIVEN IN &IGURE FOR THE CASE OF N PULSES PER BEAMWIDTH 4HIS ESTIMATION PROCEDURE CAN ALSO BE USED TO ESTIMATE THE ELEVATION ANGLE OF A TARGET IN MULTIBEAM SYSTEMS WHERE P AND P ARE THE ELEVATION POINTING ANGLES OF ADJACENT BEAMS AND ! AND ! ARE THE CORRESPONDING AMPLITUDES "INARY )NTEGRATOR 4HE BINARY INTEGRATOR IS ALSO KNOWN AS THE DUAL THRESHOLD DETEC TOR - OUT OF . DETECTOR OR RANK DETECTOR SEE h.ONPARAMETRIC $ETECTORS v LATER IN THIS SECTION AND NUMEROUS INDIVIDUALS HAVE STUDIED ITn !S SHOWN IN &IGURE D THE INPUT SAMPLES ARE QUANTIZED TO OR DEPENDING ON WHETHER OR NOT THEY ARE LESS THAN A THRESHOLD 4 4HE LAST . ZEROS AND ONES ARE SUMMED WITH A MOVING WINDOW AND COMPARED WITH A SECOND THRESHOLD 4 - &OR LARGE . THE DETECTION PERFORMANCE OF THIS DETECTOR IS APPROXIMATELY D" LESS THAN THE MOVING WINDOW INTEGRATOR BECAUSE OF THE HARD LIMITING OF THE DATA AND THE ANGULAR ESTIMATION ERROR IS ABOUT PERCENT GREATER THAN THE #RAMER 2AO LOWER BOUND 3CHWARTZ SHOWED THAT WITHIN D" THE OPTIMAL VALUE OF - FOR MAXIMUM 0$ IS GIVEN BY
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WHEN 0FA AND 0$ 4HE OPTIMAL VALUE OF 0N THE PROBABILITY OF EXCEEDING 4 WHEN ONLY NOISE IS PRESENT WAS CALCULATED BY $ILLARD AND IS SHOWN IN &IGURE 4HE CORRESPONDING THRESHOLD 4 IS
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! COMPARISON OF THE OPTIMAL BEST VALUE OF - BINARY INTEGRATOR WITH VARIOUS OTHER PROCEDURES IS GIVEN IN &IGURES AND FOR 0$ AND RESPECTIVELY 4HE BINARY INTEGRATOR IS USED IN MANY RADARS BECAUSE IT IS EASILY IMPLEMENTED IT IGNORES INTERFERENCE SPIKES THAT CAUSE TROUBLE WITH INTEGRATORS THAT DIRECTLY USE SIGNAL AMPLITUDE AND IT WORKS EXTREMELY WELL WHEN THE NOISE HAS A NON 2AYLEIGH DENSITY &OR . COMPARISON OF THE OPTIMAL BINARY INTEGRATOR OUT OF ANOTHER BINARY INTEGRATOR OUT OF AND THE MOVING WINDOW DETECTOR IN LOG NORMAL INTERFER ENCE AN EXAMPLE OF A NON 2AYLEIGH DENSITY WHERE THE LOG OF THE RETURN HAS A GAUSSIAN DENSITY IS SHOWN IN &IGURE 4HE OPTIMAL BINARY INTEGRATOR IS MUCH BETTER THAN THE MOVING WINDOW INTEGRATOR 4HE OPTIMAL VALUES FOR LOG NORMAL INTERFERENCE WERE CALCULATED BY 3CHLEHER AND ARE - AND FOR . AND RESPECTIVELY "ATCH 0ROCESSOR 4HE BATCH PROCESSOR &IGURE E IS VERY USEFUL WHEN A LARGE NUMBER OF PULSES ARE WITHIN THE D" BEAMWIDTH )F +. PULSES ARE IN THE D" BEAM WIDTH + PULSES ARE SUMMED BATCHED AND EITHER A OR A IS DECLARED DEPENDING ON WHETHER OR NOT THE BATCH IS LESS THAN A THRESHOLD 4 4HE LAST . ZEROS AND ONES ARE
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&)'52% /PTIMUM VALUES OF 0. AS A FUNCTION OF THE SAMPLE SIZE N AND THE PROBABILITY OF FALSE ALARM @ 2ICEAN DISTRIBUTION WITH 3. D" PER PULSE AFTER ' - $ILLARD Ú )%%%
&)'52% #OMPARISON OF BINARY INTEGRATOR - OUT OF . WITH OTHER INTEGRATION METHODS 0FA 0$ AFTER - 3CHWARTZ Ú )%%%
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&)'52% #OMPARISON OF BINARY INTEGRATOR - OUT OF . WITH OTHER INTEGRATION METHODS 0FA 0$ AFTER - 3CHWARTZ Ú )%%%
SUMMED AND COMPARED WITH A SECOND THRESHOLD - !N ALTERNATIVE VERSION OF THIS DETEC TOR IS TO PUT THE BATCH AMPLITUDES THROUGH A MOVING WINDOW DETECTOR 4HE BATCH PROCESSOR LIKE THE BINARY INTEGRATOR IS EASILY IMPLEMENTED IGNORES INTER FERENCE SPIKES AND WORKS EXTREMELY WELL WHEN THE NOISE HAS A NON 2AYLEIGH DENSITY &URTHERMORE THE BATCH PROCESSOR REQUIRES LESS STORAGE DETECTS BETTER AND ESTIMATES
&)'52% #OMPARISON OF VARIOUS DETECTORS IN LOG NORMAL R D" INTERFERENCE . 0FA AFTER $ # 3CHLEHER Ú )%%%
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ANGLES MORE ACCURATELY THAN THE BINARY INTEGRATOR &OR INSTANCE IF THERE WERE PULSES ON TARGET ONE COULD BATCH PULSES QUANTIZE THIS RESULT TO A OR A AND DECLARE A TARGET WITH A OUT OF OR OUT OF BINARY INTEGRATOR 4HE DETECTION PERFORMANCE OF THE BATCH PROCESSOR FOR A LARGE NUMBER OF PULSES INTEGRATED IS APPROXIMATELY D" WORSE THAN THE MOVING WINDOW 4HE BATCH PROCESSOR HAS BEEN SUCCESSFULLY IMPLEMENTED BY THE !PPLIED 0HYSICS ,ABORATORY OF 4HE *OHNS (OPKINS 5NIVERSITY 4O OBTAIN AN ACCU RATE AZIMUTH ESTIMATE Q} APPROXIMATELY PERCENT GREATER THAN THE LOWER BOUND £ "IQI Q} £ "I
IS USED WHERE "I IS THE BATCH AMPLITUDE AND PI IS THE AZIMUTH ANGLE CORRESPONDING TO THE CENTER OF THE BATCH &ALSE !LARM #ONTROL )N THE PRESENCE OF CLUTTER IF FIXED THRESHOLDS ARE USED WITH THE PREVIOUSLY DISCUSSED INTEGRATORS AN ENORMOUS NUMBER OF DETECTIONS WILL OCCUR AND WILL SATURATE AND DISRUPT THE TRACKING COMPUTER ASSOCIATED WITH THE RADAR SYSTEM &OUR IMPORTANT FACTS SHOULD BE NOTED L
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! TRACKING SYSTEM SHOULD BE ASSOCIATED WITH THE AUTOMATIC DETECTION SYSTEM THE ONLY EXCEPTION IS WHEN ONE DISPLAYS MULTIPLE SCANS OF DETECTIONS 4HE 0FA OF THE DETECTOR SHOULD BE MATCHED TO THE TRACKING SYSTEM TO PRODUCE THE OVERALL LOWEST 3. REQUIRED TO FORM A TRACK WITHOUT INITIATING TOO MANY FALSE TRACKS SEE &IGURE LATER IN THIS CHAPTER 2ANDOM FALSE ALARMS AND UNWANTED TARGETS EG STATIONARY TARGETS ARE NOT A PROB LEM IF THEY ARE REMOVED BY THE TRACKING SYSTEM 3CAN TO SCAN PROCESSING CAN BE USED TO REMOVE STATIONARY POINT CLUTTER OR MOVING TARGET INDICATION -4) CLUTTER RESIDUES
/NE CAN LIMIT THE NUMBER OF FALSE ALARMS WITH A FIXED THRESHOLD SYSTEM BY SETTING A VERY HIGH THRESHOLD 5NFORTUNATELY THIS WOULD REDUCE TARGET SENSITIVITY IN REGIONS OF LOW NOISE CLUTTER RETURN 4HREE MAIN APPROACHESADAPTIVE THRESHOLD NONPARAMET RIC DETECTORS AND CLUTTER MAPSHAVE BEEN USED TO REDUCE THE FALSE ALARM PROBLEM !DAPTIVE THRESHOLDING AND NONPARAMETRIC DETECTORS ASSUME THAT THE SAMPLES IN THE RANGE CELLS SURROUNDING THE TEST CELL CALLED REFERENCE CELLS ARE INDEPENDENT AND IDENTI CALLY DISTRIBUTED &URTHERMORE IT IS USUALLY ASSUMED THAT THE TIME SAMPLES ARE INDEPEN DENT "OTH KINDS OF DETECTORS TEST WHETHER THE TEST CELL HAS A RETURN SUFFICIENTLY LARGER THAN THE REFERENCE CELLS #LUTTER MAPS ALLOW VARIATION IN SPACE BUT THE CLUTTER MUST BE STATIONARY OVER SEVERAL TYPICALLY TO SCANS #LUTTER MAPS STORE AN AVERAGE BACK GROUND LEVEL FOR EACH RANGE AZIMUTH CELL ! TARGET IS THEN DECLARED IN A RANGE AZIMUTH CELL IF THE NEW VALUE EXCEEDS THE AVERAGE BACKGROUND LEVEL BY A SPECIFIED AMOUNT !DAPTIVE 4HRESHOLDING 4HE BASIC ASSUMPTION OF THE ADAPTIVE THRESHOLDING TECH NIQUE IS THAT THE PROBABILITY DENSITY OF THE NOISE IS KNOWN EXCEPT FOR A FEW UNKNOWN PARAMETERS 4HE SURROUNDING REFERENCE CELLS ARE THEN USED TO ESTIMATE THE UNKNOWN PARAMETERS AND A THRESHOLD BASED ON THE ESTIMATED PARAMETERS IS OBTAINED 4HE SIM PLEST ADAPTIVE DETECTOR SHOWN IN &IGURE IS THE CELL AVERAGE #&!2 CONSTANT FALSE ALARM RATE INVESTIGATED BY &INN AND *OHNSON )F THE NOISE HAS A 2AYLEIGH DEN SITY PX X EXP XR R ONLY THE PARAMETER R R IS THE NOISE POWER NEEDS TO BE ESTIMATED AND THE THRESHOLD IS OF THE FORM 4 +3XI +N P S} WHERE S} IS THE
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&)'52% #ELL AVERAGING #&!2 4HE LETTER # INDICATES A COMPARISON FROM ' 6 4RUNK
ESTIMATE OF R (OWEVER SINCE 4 IS SET BY AN ESTIMATE S} IT HAS SOME ERROR AND MUST BE SLIGHTLY LARGER THAN THE THRESHOLD THAT ONE WOULD USE IF R WERE KNOWN EXACTLY A PRIORI 4HE RAISED THRESHOLD CAUSES A LOSS IN TARGET SENSITIVITY AND IS REFERRED TO AS A #&!2 LOSS 4HIS LOSS HAS BEEN CALCULATED AND IS SUMMARIZED IN 4ABLE !S CAN BE SEEN FOR A SMALL NUMBER OF REFERENCE CELLS THE LOSS IS LARGE BECAUSE OF THE POOR ESTIMATE OF R #ONSEQUENTLY ONE WOULD PREFER TO USE A LARGE NUMBER OF REFERENCE CELLS (OWEVER IF ONE DOES THIS THE HOMOGENEITY ASSUMPTION IE ALL THE REFERENCE CELLS ARE STATISTI CALLY SIMILAR MIGHT BE VIOLATED ! GOOD RULE OF THUMB IS TO USE ENOUGH REFERENCE CELLS SO THAT THE #&!2 LOSS IS BELOW D" AND AT THE SAME TIME NOT LET THE REFERENCE CELLS EXTEND OVER A RANGE INTERVAL THAT VIOLATES THE HOMOGENOUS BACKGROUND ASSUMPTION 5NFORTUNATELY FOR A SPECIFIC RADAR THIS MIGHT NOT BE FEASIBLE )F THERE IS UNCERTAINTY ABOUT WHETHER OR NOT THE NOISE IS 2AYLEIGH DISTRIBUTED IT IS BETTER TO THRESHOLD INDIVIDUAL PULSES AND USE A BINARY INTEGRATOR AS SHOWN IN &IGURE 4HIS DETECTOR IS TOLERANT OF VARIATIONS IN THE NOISE DENSITY BECAUSE BY SETTING + TO YIELD A WITH PROBABILITY A 0FA y CAN BE OBTAINED BY USING A OUT OF DETECTOR 7HILE NOISE MAY BE NON 2AYLEIGH IT WILL PROBABLY BE VERY 2AYLEIGH LIKE OUT TO THE
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TENTH PERCENTILE &URTHERMORE ONE CAN USE FEEDBACK BASED ON SEVERAL SCANS OF DATA TO CONTROL + IN ORDER TO MAINTAIN A DESIRED 0FA ON EITHER A SCAN OR A SECTOR BASIS 4HIS DEMONSTRATES A GENERAL RULE TO MAINTAIN A LOW 0FA IN VARIOUS ENVIRONMENTS ADAPTIVE THRESHOLDING SHOULD BE PLACED IN FRONT OF THE INTEGRATOR )F THE NOISE POWER VARIES FROM PULSE TO PULSE AS IT WOULD IN JAMMING WHEN FRE QUENCY AGILITY IS EMPLOYED ONE MUST #&!2 EACH PULSE AND THEN INTEGRATE 7HILE THE BINARY INTEGRATOR PERFORMS THIS TYPE OF #&!2 ACTION ANALYSIS HAS VERIFIED THAT THE RATIO DETECTOR SHOWN IN &IGURE IS A BETTER DETECTOR 4HE RATIO DETECTOR SUMS SIGNAL TO NOISE RATIOS AND IS SPECIFIED BY N
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WHERE XIJ IS THE ITH ENVELOPE DETECTED PULSE IN THE JTH RANGE CELL AND M IS THE NUMBER OF REFERENCE CELLS 4HE DENOMINATOR IS THE MAXIMUM LIKELIHOOD ESTIMATE OF S I THE NOISE POWER PER PULSE 4HE RATIO DETECTOR WILL DETECT TARGETS EVEN THOUGH ONLY A FEW RETURNED PULSES HAVE A HIGH SIGNAL TO NOISE RATIO 5NFORTUNATELY THIS WILL ALSO CAUSE THE RATIO DETECTOR TO DECLARE FALSE ALARMS IN THE PRESENCE OF NARROW PULSE INTERFERENCE 4O REDUCE THE NUMBER OF FALSE ALARMS WHEN NARROW PULSE INTERFERENCE IS PRESENT THE INDIVIDUAL POWER RATIOS CAN BE SOFT LIMITED TO A SMALL ENOUGH VALUE SO THAT INTERFER ENCE WILL CAUSE ONLY A FEW FALSE ALARMS ! COMPARISON OF THE RATIO DETECTOR WITH OTHER COMMONLY USED DETECTORS IS SHOWN IN &IGURES AND FOR NONFLUCTUATING AND FLUCTUATING TARGETS ! TYPICAL PERFORMANCE IN SIDELOBE JAMMING WHEN THE JAMMING LEVEL VARIES BY D" PER PULSE IS SHOWN IN &IGURE "Y EMPLOYING A SECOND TEST TO
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IDENTIFY THE PRESENCE OF NARROW PULSE INTERFERENCE A DETECTION PERFORMANCE APPROXI MATELY HALFWAY BETWEEN THE LIMITING AND NONLIMITING RATIO DETECTORS CAN BE OBTAINED )F THE NOISE SAMPLES HAVE A NON 2AYLEIGH DENSITY SUCH AS THE CHI SQUARE DENSITY OR LOG NORMAL DENSITY IT IS NECESSARY TO ESTIMATE MORE THAN ONE PARAMETER AND THE ADAP TIVE DETECTOR IS MORE COMPLICATED 5SUALLY TWO PARAMETERS ARE ESTIMATED THE MEAN AND THE VARIANCE AND A THRESHOLD OF THE FORM 4 M} +S} IS USED 4HE SAMPLED MEAN IS EASILY OBTAINED (OWEVER THE USUAL ESTIMATE OF THE STANDARD DEVIATION
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&)'52% #URVES OF PROBABILITY OF DETECTION VERSUS SIGNAL TO NOISE RATIO PER PULSE FOR THE CELL AVERAGING #&!2 RATIO DETECTORS LOG INTEGRATOR AND BINARY INTEGRATOR NONFLUCTUATING TARGET . M REFERENCE CELLS AND 0FA FROM ' 6 4RUNK AND 0 + (UGHES
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IS SOMEWHAT MORE DIFFICULT TO IMPLEMENT CONSEQUENTLY THE MEAN DEVIATE DEFINED BY
S ! £ \ XI M} \
IS SOMETIMES USED BECAUSE OF ITS EASE OF IMPLEMENTATION AND BECAUSE IT IS MORE ROBUST )T SHOULD BE NOTED THAT THE #&!2 LOSS ASSOCIATED WITH A TWO PARAMETER THRESHOLD IS LARGER THAN THOSE ASSOCIATED WITH A ONE PARAMETER THRESHOLD SEE 4ABLE AND FOR THAT REASON A TWO PARAMETER THRESHOLD IS RARELY USED
&)'52% #URVES OF PROBABILITY OF DETECTION VERSUS SIGNAL TO NOISE RATIO FOR THE CELL AVERAGING #&!2 RATIO DETECTORS LOG INTEGRATOR AND BINARY INTEGRATOR 2AYLEIGH PULSE TO PULSE FLUCTUATIONS M REFERENCE CELLS 0FA AND MAXIMUM JAMMING TO NOISE RATIO D" FROM ' 6 4RUNK AND 0 + (UGHES
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)F THE NOISE SAMPLES ARE CORRELATED NOTHING CAN BE DONE TO THE BINARY INTEGRATOR TO YIELD A LOW 0FA 4HUS IT SHOULD NOT BE USED IN THIS SITUATION (OWEVER IF THE CORRELATION TIME IS LESS THAN A BATCHING INTERVAL THE BATCH PROCESSOR WILL YIELD A LOW 0FA WITHOUT MODIFICATIONS 4ARGET 3UPPRESSION 4ARGET SUPPRESSION IS THE LOSS IN DETECTABILITY CAUSED BY OTHER TARGETS OR CLUTTER RESIDUES IN THE REFERENCE CELLS "ASICALLY THERE ARE TWO APPROACHES TO SOLVING THIS PROBLEM REMOVE LARGE RETURN FROM THE CALCULATION OF THE THRESHOLDn OR DIMINISH THE EFFECTS OF LARGE RETURNS BY EITHER LIMITING OR USING LOG VIDEO 4HE TECHNIQUE THAT SHOULD BE USED IS A FUNCTION OF THE PARTICULAR RADAR SYSTEM AND ITS ENVIRONMENT 2ICKARD AND $ILLARD PROPOSED A CLASS OF DETECTORS $+ WHERE THE + LARGEST SAMPLES ARE CENSORED REMOVED FROM THE REFERENCE CELLS ! COMPARISON OF $ NO CENSORING WITH $ AND $ FOR A 3WERLING TARGET AND A SINGLE SQUARE LAW DETECTED PULSE IS SHOWN IN &IGURE WHERE . IS THE NUMBER OF REFERENCE CELLS A IS THE RATIO OF THE POWER OF THE INTERFERING TARGET TO THE TARGET IN THE TEST CELL AND THE BRACKETED PAIR M N INDICATES THE 3WERLING MODELS OF THE TARGET AND THE INTERFERING TARGET RESPECTIVELY !S SHOWN IN &IGURE WHEN ONE HAS AN INTERFERING TARGET THE 0$ DOES NOT APPROACH AS 3. INCREASES !NOTHER APPROACH THAT CENSORS SAMPLES IN THE REFERENCE CELL IF THEY EXCEED A THRESHOLD IS BRIEFLY DISCUSSED IN THE h.ONPARAMETRIC $ETECTORv SUBSECTION &INN INVESTIGATED THE PROBLEM OF THE REFERENCE CELLS SPANNING TWO CONTINUOUS DIF FERENT hNOISEv FIELDS EG THERMAL NOISE SEA CLUTTER ETC /N THE BASIS OF THE SAMPLES HE ESTIMATED THE STATISTICAL PARAMETERS OF THE TWO NOISE FIELDS AND THE SEPARATION POINT BETWEEN THEM 4HEN ONLY THOSE REFERENCE CELLS THAT ARE IN THE NOISE FIELD CONTAINING THE TEST CELL ARE USED TO CALCULATE THE ADAPTIVE THRESHOLD !N ALTERNATIVE APPROACH FOR INTERFERING TARGETS IS TO USE LOG VIDEO "Y TAKING THE LOG LARGE SAMPLES IN THE REFERENCE CELLS WILL HAVE LESS EFFECT THAN LINEAR VIDEO ON THE THRESHOLD 4HE LOSS ASSOCIATED WITH USING LOG VIDEO RATHER THAN LINEAR VIDEO IS D"
&)'52% $ETECTION PROBABILITY VERSUS 3.2 FOR A 3WERLING #ASE PRIMARY TARGET AFTER * 4 2ICKARD AND ' - $ILLARD Ú )%%%
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FOR PULSES INTEGRATED AND D" FOR PULSES INTEGRATED !N IMPLEMENTATION OF THE LOG #&!2 IS SHOWN IN &IGURE )N MANY SYSTEMS THE ANTILOG SHOWN IN &IGURE IS NOT TAKEN 4O MAINTAIN THE SAME #&!2 LOSS AS FOR LINEAR VIDEO THE NUMBER OF REFERENCE CELLS -LOG FOR THE LOG #&!2 SHOULD EQUAL
-LOG -LIN
WHERE -LIN IS THE NUMBER OF REFERENCE CELLS FOR LINEAR VIDEO 4HE EFFECT OF TARGET SUPPRES SION WITH LOG VIDEO IS DISCUSSED LATER IN THIS SECTION SEE 4ABLE LATER IN THE CHAPTER .ONPARAMETRIC $ETECTORS 5SUALLY NONPARAMETRIC DETECTORS OBTAIN #&!2 BY RANK ING THE TEST SAMPLE WITH THE REFERENCE CELLS 2ANKING MEANS THAT ONE ORDERS THE SAMPLES FROM THE SMALLEST TO THE LARGEST AND REPLACES THE SMALLEST WITH RANK THE NEXT SMALLEST WITH RANK AND THE LARGEST WITH RANK N 5NDER THE HYPOTHESIS THAT ALL THE SAMPLES ARE INDEPENDENT SAMPLES FROM AN UNKNOWN DENSITY FUNCTION THE TEST SAMPLE HAS EQUAL PROBABILITY OF TAKING ON ANY OF THE N VALUES &OR INSTANCE REFERRING TO THE RANKER IN &IGURE THE TEST CELL IS COMPARED WITH OF ITS NEIGHBORS 3INCE IN THE SET OF SAMPLES THE TEST SAMPLE HAS EQUAL PROBABILITY OF BEING THE SMALLEST SAMPLE OR EQUIVALENTLY ANY OTHER RANK THE PROBABILITY THAT THE TEST SAMPLE TAKES ON VALUES IS ! SIMPLE RANK DETECTOR IS CONSTRUCTED BY COMPARING THE RANK WITH A THRESHOLD + AND GENERATING A IF THE RANK IS LARGER A OTHERWISE 4HE S AND S ARE SUMMED IN A MOVING WINDOW 4HIS DETECTOR INCURS A #&!2 LOSS OF ABOUT D" BUT ACHIEVES A FIXED 0FA FOR ANY UNKNOWN NOISE DENSITY AS LONG AS THE TIME SAMPLES ARE INDEPENDENT 4HIS DETECTOR WAS INCORPORATED INTO THE !243 ! POSTPROCESSOR USED IN CONJUNCTION WITH THE &EDERAL !VIATION !DMINISTRATION AIRPORT SURVEILLANCE RADAR !32 4HE MAJOR SHORTCOM ING OF THIS DETECTOR IS THAT IT IS FAIRLY SUSCEPTIBLE TO TARGET SUPPRESSION EG IF A LARGE TARGET IS IN THE REFERENCE CELLS THE TEST CELL CANNOT RECEIVE THE HIGHEST RANKS )F THE TIME SAMPLES ARE CORRELATED THE RANK DETECTOR WILL NOT YIELD #&!2 ! MOD IFIED RANK DETECTOR CALLED THE MODIFIED GENERALIZED SIGN TEST -'34 MAINTAINS A LOW 0FA AND IS SHOWN IN &IGURE 4HIS DETECTOR CAN BE DIVIDED INTO THREE PARTS A RANKER AN INTEGRATOR IN THIS CASE A TWO POLE FILTER AND A THRESHOLD DECISION PROCESS ! TARGET IS DECLARED WHEN THE INTEGRATED OUTPUT EXCEEDS TWO THRESHOLDS
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2!$!2 (!.$"//+
&)'52% 2ANK DETECTOR OUTPUT OF A COMPARATOR # IS EITHER A ZERO OR A ONE FROM ' 6 4RUNK
4HE FIRST THRESHOLD IS FIXED EQUALS L 4+ IN &IGURE AND YIELDS 0FA WHEN THE REFERENCE CELLS ARE INDEPENDENT AND IDENTICALLY DISTRIBUTED 4HE SECOND THRESHOLD IS ADAPTIVE AND MAINTAINS A LOW 0FA WHEN THE REFERENCE SAMPLES ARE COR RELATED 4HE DEVICE ESTIMATES THE STANDARD DEVIATION OF THE CORRELATED SAMPLES WITH THE MEAN DEVIATE ESTIMATOR WHERE EXTRANEOUS TARGETS IN THE REFERENCE CELLS HAVE BEEN EXCLUDED FROM THE ESTIMATE BY USE OF A PRELIMINARY THRESHOLD 4 4HE BASIC DISADVANTAGES OF ALL NONPARAMETRIC DETECTORS ARE THAT THEY HAVE RELATIVELY LARGE #&!2 LOSSES THEY HAVE PROBLEMS WITH CORRELATED SAMPLES AND ONE LOSES AMPLITUDE INFORMATION WHICH CAN BE A VERY IMPORTANT DISCRIMINANT BETWEEN TARGET AND CLUTTER &OR EXAMPLE A LARGE RETURN CROSS SECTION q M IN A CLUTTER AREA IS PROBABLY JUST CLUTTER BREAKTHROUGH 3EE h2ADAR $ETECTION !CCEPTANCEv IN 3ECTION #LUTTER -APPING ! CLUTTER MAP USES ADAPTIVE THRESHOLDING WHERE THE THRESHOLD IS CALCULATED FROM THE RETURN IN THE TEST CELL ON PREVIOUS SCANS RATHER THAN FROM THE SUR ROUNDING REFERENCE CELLS ON THE SAME SCAN 4HIS TECHNIQUE HAS THE ADVANTAGE IN THAT FOR ESSENTIALLY STATIONARY ENVIRONMENTS EG LAND BASED RADAR AGAINST GROUND CLUTTER THE RADAR HAS INTERCLUTTER VISIBILITYIT CAN SEE BETWEEN LARGE CLUTTER RETURNS ,INCOLN ,ABORATORY IN ITS MOVING TARGET DETECTOR -4$ USED A CLUTTER MAP FOR THE ZERO DOP PLER FILTER VERY EFFECTIVELY 4HE DECISION THRESHOLD 4 FOR THE ITH CELL IS
4 ! 3I
WHERE THE CLUTTER IS ESTIMATED USING A SIMPLE FEEDBACK INTEGRATOR
3I + 3I 8I
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&)'52% -ODIFIED GENERALIZED SIGN TEST PROCESSOR AFTER ' 6 4RUNK ET AL
WHERE 3I IS THE AVERAGE BACKGROUND LEVEL 8I IS THE RETURN IN THE ITH CELL + IS THE FEED BACK VALUE THAT DETERMINES THE MAP TIME CONSTANT AND ! IS THE CONSTANT THAT DETERMINES THE 0FA )N THE -4$ USED FOR THE !32 APPLICATION + IS WHICH EFFECTIVELY AVERAGES THE LAST EIGHT SCANS 4HE PURPOSE OF THE CLUTTER MAP IS TO DETECT IN CLUTTER FREE AREAS CROSSING TARGETS THAT WOULD HAVE BEEN REMOVED BY THE DOPPLER PROCESSING 4HE MAIN UTILITY OF CLUTTER MAPS IS WITH FIXED FREQUENCY LAND BASED RADARS 7HILE CLUTTER MAPS CAN BE USED WITH FREQUENCY AGILE RADARS AND ON MOVING PLATFORMS EG RADARS ON SHIPS THEY ARE NOT NEARLY AS EFFECTIVE IN THESE ENVIRONMENTS 4ARGET 2ESOLUTION )N AUTOMATIC DETECTION SYSTEMS A SINGLE LARGE TARGET WILL PROB ABLY BE DETECTED IE CROSS A DETECTION THRESHOLD MANY TIMES EG IN ADJACENT RANGE CELLS AZIMUTH BEAMS AND ELEVATION BEAMS 4HEREFORE AUTOMATIC DETECTION SYSTEMS HAVE ALGORITHMS FOR MERGING THE INDIVIDUAL DETECTIONS INTO A SINGLE CENTROIDED DETEC TION -OST ALGORITHMS HAVE BEEN DESIGNED SO THAT THEY WILL RARELY SPLIT A SINGLE TARGET INTO TWO TARGETS 4HIS PROCEDURE RESULTS IN POOR RANGE RESOLUTION CAPABILITY ! MERG ING ALGORITHM OFTEN USED IS THE ADJACENT DETECTION MERGING ALGORITHM WHICH DECIDES WHETHER A NEW DETECTION IS ADJACENT TO ANY OF THE PREVIOUSLY DETERMINED SETS OF ADJACENT DETECTIONS )F THE NEW DETECTION IS ADJACENT TO ANY DETECTION IN THE SET OF ADJACENT DETEC TIONS IT IS ADDED TO THE SET 4WO DETECTIONS ARE ADJACENT IF TWO OF THEIR THREE PARAMETERS RANGE AZIMUTH AND ELEVATION ARE THE SAME AND THE OTHER PARAMETER DIFFERS BY THE RESOLUTION ELEMENT RANGE CELL $2 AZIMUTH BEAMWIDTH P OR ELEVATION BEAMWIDTH F ! STUDY COMPARED THE RESOLVING CAPABILITY OF THREE COMMON DETECTION PROCE DURES LINEAR DETECTOR WITH 4 M} !S} LINEAR DETECTOR WITH 4 "M} AND LOG DETECTOR WITH 4 # M} WHERE THE CONSTANTS ! " AND # ARE USED TO OBTAIN THE SAME 0FA FOR ALL DETECTORS 4HE ESTIMATES M} AND S} OF L AND R WERE OBTAINED FROM EITHER ALL THE REFERENCE CELLS OR THE LEADING OR LAGGING HALF OF THE REFERENCE CELLS CHOOSING THE
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2!$!2 (!.$"//+
4!",% 0ROBABILITY OF $ETECTING "OTH 4ARGETS WITH ,OG 6IDEO 7HEN THE 4WO 4ARGETS !RE 3EPARATED BY OR 2ANGE #ELLS 3. OF TARGET IS D" AND 3. OF TARGET IS OR D"
4HRESHOLDING 4ECHNIQUE !LL REFERENCE CELLS 2EFERENCE CELLS WITH MINIMUM MEAN VALUE
4ARGET 3EPARATION
3. OF 4ARGET NO
AFTER ' 6 4RUNK Ú )%%%
HALF WITH THE LOWER MEAN VALUE 4HE FIRST SIMULATION INVOLVED TWO TARGETS SEPARATED BY OR RANGE CELLS AND A THIRD TARGET RANGE CELLS FROM THE FIRST TARGET 7HEN THE TWO CLOSELY SPACED TARGETS WERE WELL SEPARATED EITHER OR RANGE CELLS APART THE PROBABILITY OF DETECTING BOTH TARGETS 0$ WAS FOR THE LINEAR DETECTOR WITH 4 M} !S} 0$ FOR THE LINEAR DETECTOR WITH 4 "M} AND 0$ FOR THE LOG DETECTOR ! SECOND SIMULATION INVOLVING ONLY TWO TARGETS INVESTIGATED THE EFFECT OF TARGET SUPPRESSION ON LOG VIDEO AND THE RESULTS ARE SUMMARIZED IN 4ABLE 4HE MAXIMUM VALUE OF 0$ IS OBTAINED WHEN BOTH TARGETS HAVE AN 3. OF D" )F ONE OF THE TARGETS HAS A LARGER 3. THAN THE OTHER TARGET SUPPRESSION OCCURSEITHER TARGET SUPPRESSES TARGET OR VICE VERSA !LSO ONE NOTES AN IMPROVED PERFORMANCE FOR A SMALL 3. TO D" WHEN CALCULATING THE THRESHOLD USING ONLY THE HALF OF THE REFERENCE CELLS WITH THE LOWER MEAN VALUE 4HE RESOLUTION CAPABILITY OF THE LOG DETECTOR THAT USES ONLY THE HALF OF THE REFERENCE CELLS WITH THE LOWER MEAN IS SHOWN IN &IGURE 4HE PROBABILITY OF RESOLVING TWO EQUAL AMPLITUDE TARGETS DOES NOT RISE ABOVE UNTIL THEY ARE SEPARATED IN RANGE BY PULSE WIDTHS "Y ASSUMING THAT THE TARGET IS SMALL WITH RESPECT TO THE PULSE WIDTH AND THAT THE PULSE SHAPE IS KNOWN THE RESOLUTION CAPABILITY CAN BE IMPROVED BY FITTING THE KNOWN PULSE SHAPE TO THE RECEIVED DATA AND COMPARING THE RESIDUE SQUARE ERROR WITH A THRESHOLD )F ONLY ONE TARGET IS PRESENT THE RESIDUE SHOULD BE ONLY NOISE AND HENCE SHOULD BE SMALL )F TWO OR MORE TARGETS ARE PRESENT THE RESIDUE WILL CONTAIN SIGNAL FROM THE REMAINING TARGETS AND SHOULD BE LARGE 4HE RESULTS OF RESOLVING TWO TARGETS WITH 3. D" ARE SHOWN IN &IGURE 4HESE TARGETS CAN BE RESOLVED AT A RESOLU TION PROBABILITY OF WITH A FALSE ALARM PROBABILITY OF AT SEPARATIONS VARYING BETWEEN ONE FOURTH AND THREE FOURTHS OF A PULSE WIDTH DEPENDING ON THE RELATIVE PHASE DIFFERENCE BETWEEN THE TWO TARGETS -OREOVER THIS RESULT CAN BE IMPROVED FURTHER BY PROCESSING MULTIPLE PULSES !UTOMATIC $ETECTION 3UMMARY 7HEN ONLY TO SAMPLES PULSES ARE AVAIL ABLE A BINARY INTEGRATOR SHOULD BE USED TO AVOID FALSE ALARMS DUE TO INTERFERENCE 7HEN A MODERATE NUMBER OF PULSES TO ARE AVAILABLE A BINARY INTEGRATOR OR A MOV ING WINDOW INTEGRATOR SHOULD BE USED )F THE NUMBER OF PULSES IS LARGE GREATER THAN A BATCH PROCESSOR SHOULD BE USED )F THE SAMPLES ARE INDEPENDENT A ONE PARAM ETER MEAN THRESHOLD CAN BE USED )F THE SAMPLES ARE DEPENDENT ONE CAN EITHER USE
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&)'52% 2ESOLUTION CAPABILITY OF A LOG DETECTOR THAT USED HALF OF THE REFERENCES CELLS WITH LOWER MEAN AFTER ' 6 4RUNK Ú )%%%
A TWO PARAMETER MEAN AND VARIANCE THRESHOLD OR ADAPT A ONE PARAMETER THRESHOLD ON A SECTOR BASIS (OWEVER THESE RULES SHOULD SERVE ONLY AS A GENERAL GUIDELINE )T IS HIGHLY RECOMMENDED THAT BEFORE A DETECTOR IS CHOSEN THE RADAR VIDEO FROM THE ENVI RONMENT OF INTEREST BE COLLECTED AND ANALYZED AND THAT VARIOUS DETECTION PROCESSES BE SIMULATED ON A COMPUTER AND TESTED AGAINST THE RECORDED DATA
&)'52% 0ROBABILITY OF RESOLUTION AS A FUNCTION OF RANGE SEPARATION PROBABILITY OF FALSE ALARM IS SAMPLING RATE $2 SAMPLES PER PULSE WIDTH TARGET STRENGTHS NONFLUCTUATING ! ! D" PHASE DIFFERENCES AND AFTER ' 6 4RUNK Ú )%%%
Ç°ÓÓ
2!$!2 (!.$"//+
-ANY MODERN RADARS USE COHERENT PROCESSING TO REMOVE CLUTTER &OR THE PURPOSE OF APPLYING THE PREVIOUS DISCUSSIONS ON NONCOHERENT PROCESSING TO COHERENT PROCESSING THE INTEGRATED OUTPUT IN A RANGE DOPPLER CELL OF THE DOPPLER PROCESSOR FOR A SINGLE COHER ENT PROCESSING INTERVAL #0) CAN BE TREATED AS A SINGLE NONCOHERENT PULSE "ECAUSE THREE AMBIGUOUS MEASUREMENTS IE DETECTIONS ARE USUALLY REQUIRED TO REMOVE THE RANGE AND DOPPLER AMBIGUITIES TO #0)S MAY BE TRANSMITTED AND HENCE THERE ARE USUALLY TO NONCOHERENT PULSES AVAILABLE FOR PROCESSING
Ç°ÎÊ 1/" / Ê/, ! TRACK REPRESENTS THE BELIEF THAT A PHYSICAL OBJECT OR hTARGETv IS PRESENT AND HAS ACTU ALLY BEEN DETECTED BY THE RADAR !N AUTOMATIC RADAR TRACKING SYSTEM FORMS A TRACK WHEN ENOUGH RADAR DETECTIONS ARE MADE IN A BELIEVABLE ENOUGH PATTERN TO INDICATE A TARGET IS ACTUALLY PRESENT AS OPPOSED TO A SUCCESSION OF FALSE ALARMS AND WHEN ENOUGH TIME HAS PASSED TO ALLOW ACCURATE CALCULATION OF THE TARGETS KINEMATIC STATEUSUALLY POSITION AND VELOCITY 4HUS THE GOAL OF TRACKING IS TO TRANSFORM A TIME LAPSE DETECTION PICTURE SHOWN IN &IGURE A CONSISTING OF TARGET DETECTIONS FALSE ALARMS AND CLUTTER INTO A TRACK PICTURE SHOWN IN &IGURE B CONSISTING OF TRACKS ON REAL TARGETS OCCASIONAL FALSE TRACKS AND OCCASIONAL DEVIATIONS OF TRACK POSITION FROM TRUE TARGET POSITIONS &IGURES A AND B ALSO ILLUSTRATE SOME OF THE CHALLENGES OF AUTOMATIC TRACK ING $ETECTIONS ARE MADE ON TARGETS BUT SOME DETECTIONS ARE MISSING BECAUSE OF TARGET FADES OR MULTIPLE TARGETS IN THE SAME RESOLUTION CELL WHEREAS ADDITIONAL DETECTIONS ARE PRESENT DUE TO CLUTTER OR NOISE
&)'52% A 4HIRTY MINUTE TIME LAPSE OF !.&0. , BAND AIR TRAFFIC CONTROL RADAR DETECTIONS OVER A Ò KM SQUARE AREA AFTER ( ,EUNG ET AL Ú )%%%
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&)'52% B 4HIRTY MINUTE TIME LAPSE OF TRACKS FORMED FROM DATA IN &IGURE A USING 'LOBAL .EAREST .EIGHBOR '.. 4ECHNIQUE AFTER ( ,EUNG ET AL Ú )%%%
!UTOMATIC TRACKING CAN GENERALLY BE DIVIDED INTO THE FIVE STEPS SHOWN IN &IGURE AND DETAILED HERE 2ADAR DETECTION ACCEPTANCE ACCEPTING OR REJECTING DETECTIONS FOR INSERTION INTO THE TRACKING PROCESS 4HE PURPOSE OF THIS STEP IS TO CONTROL FALSE TRACK RATES !SSOCIATION OF ACCEPTED DETECTIONS WITH EXISTING TRACKS 5PDATING EXISTING TRACKS WITH ASSOCIATED DETECTIONS .EW TRACK FORMATION USING UNASSOCIATED DETECTIONS 2ADAR SCHEDULING AND CONTROL 4HE RESULT OF THE AUTOMATIC TRACKING PROCESS IS A TRACK FILE THAT CONTAINS A TRACK STATE FOR EACH TARGET DETECTED BY THE RADAR !S SHOWN IN &IGURE THERE IS A FEEDBACK LOOP BETWEEN ALL THESE FUNCTIONS SO THE ABILITY TO UPDATE EXISTING TRACKS ACCURATELY NATURALLY AFFECTS THE ABILITY TO ASSOCIATE DETEC TIONS WITH EXISTING TRACKS !LSO THE ABILITY TO CORRECTLY ASSOCIATE DETECTIONS WITH EXISTING TRACKS AFFECTS THE TRACKS ACCURACY AND THE ABILITY TO CORRECTLY DISTINGUISH BETWEEN AN EXIST ING TRACK AND A NEW ONE 4HE DETECTION ACCEPTREJECT STEP MAKES USE OF FEEDBACK FROM THE ASSOCIATION FUNCTION THAT MEASURES THE DETECTION ACTIVITY IN DIFFERENT REGIONS OF THE RADAR COVERAGE -ORE STRINGENT ACCEPTANCE CRITERIA ARE APPLIED IN MORE ACTIVE REGIONS 4RACK &ILE 7HEN A TRACK IS ESTABLISHED IN THE COMPUTER IT IS ASSIGNED A TRACK NUM BER !LL PARAMETERS ASSOCIATED WITH A GIVEN TRACK ARE REFERRED TO BY THIS TRACK NUMBER 4YPICAL TRACK PARAMETERS ARE THE FILTERED AND PREDICTED POSITION VELOCITY ACCELERATION WHEN APPLICABLE TIME OF LAST UPDATE TRACK QUALITY SIGNAL TO NOISE RATIO COVARIANCE MATRICES THE COVARIANCE CONTAINS THE ACCURACY OF ALL THE TRACK COORDINATES AND ALL THE STATISTICAL CROSS CORRELATIONS BETWEEN THEM IF A +ALMAN TYPE FILTER IS BEING USED AND
&)'52% 3TRUCTURE OF AUTOMATIC TRACKING PROCESS
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TRACK HISTORY IE THE LAST N DETECTIONS 4RACKS AND DETECTIONS CAN BE ACCESSED IN VARI OUS SECTORED LINKED LIST AND OTHER DATA STRUCTURES SO THAT THE ASSOCIATION PROCESS CAN BE PERFORMED EFFICIENTLY )N ADDITION TO THE TRACK FILE A CLUTTER FILE IS MAINTAINED ! CLUTTER NUMBER IS ASSIGNED TO EACH STATIONARY OR VERY SLOWLY MOVING ECHO !LL PARAM ETERS ASSOCIATED WITH A CLUTTER POINT ARE REFERRED TO BY THIS CLUTTER NUMBER !GAIN EACH CLUTTER NUMBER IS ASSIGNED TO A SECTOR IN AZIMUTH FOR EFFICIENT ASSOCIATION 2ADAR $ETECTION !CCEPTANCE 7HEN THE RADAR SYSTEM HAS EITHER NO OR LIMITED COHERENT PROCESSING NOT ALL THE DETECTIONS DECLARED BY THE AUTOMATIC DETECTOR ARE USED IN THE TRACKING PROCESS 2ATHER MANY OF THE DETECTIONS CONTACTS ARE FILTERED OUT IN SOFTWARE USING A PROCESS CALLED ACTIVITY CONTROL 4HE BASIC IDEA IS TO USE DETECTION SIGNAL CHARACTERISTICS IN CONNECTION WITH A MAP OF THE DETECTION ACTIVITY TO REDUCE THE RATE OF DETECTIONS TO ONE THAT IS ACCEPTABLE FOR FORMING TRACKS 4HE MAP IS CONSTRUCTED BY COUNTING THE UNASSOCIATED DETECTIONS THOSE THAT DO NOT ASSOCIATE WITH EXISTING TRACKS AT THE POINT IN THE TRACK PROCESSING SHOWN IN &IGURE #OUNTS ARE AVERAGED OVER MANY REVISITS OF THE RADAR TO ACHIEVE STATISTICAL SIGNIFI CANCE 4HE DETECTION SIGNAL CHARACTERISTICS SUCH AS AMPLITUDE OR SIGNAL TO NOISE ARE THEN RE THRESHOLDED TO REDUCE SENSITIVITY IN REGIONS OF UNACCEPTABLY HIGH ACTIVITY )N NO CIRCUMSTANCES ARE DETECTIONS ELIMINATED IF THEY FALL WITHIN A TRACK GATE IE A GATE CENTERED ON THE PREDICTED POSITION OF A FIRM TRACK &IGURE ILLUSTRATES AN EXAMPLE
&)'52% (ISTOGRAM OF DETECTION SIGNAL TO NOISE RATIO DETECTION ILLUSTRATING THE EFFECTIVENESS OF THE ACTIVITY CONTROL USING THE SIGNAL TO NOISE TEST IN RAIN CLUTTER 5NGATED CONTACTS GENERALLY REPRESENT CLUTTER 'ATED CON TACTS GENERALLY REPRESENT TARGETS 2E THRESHOLDING IN THIS CASE SUCCESSFULLY ELIMINATES LARGE NUMBERS OF CLUTTER DETECTIONS WHILE PRESERVING MOST TARGET DETECTIONS AFTER 7 ' "ATH ET AL
Ç°ÓÈ
2!$!2 (!.$"//+
OF THIS PROCESS WHEN LARGE NUMBERS OF RAIN CLUTTER DETECTIONS ARE POTENTIALLY OVERLOAD ING THE TRACKING PROCESS )N THIS CASE ACTIVITY CONTROL EFFECTIVELY ELIMINATES MOST OF THE CLUTTER DETECTIONS WITHOUT ELIMINATING MANY OF THE ACTUAL TARGET DETECTIONS (OWEVER BECAUSE THIS PROCESS ESSENTIALLY CONSTITUTES CONTROLLED DESENSITIZATION OF THE RADAR IT MUST BE USED WITH CARE 4HE MAPPING OF THE DETECTION ACTIVITY MUST BE PRECISE SO THAT DESENSITIZATION OCCURS ONLY IN THOSE REGIONS REQUIRING IT 5PDATING %XISTING 4RACKS WITH !SSOCIATED $ETECTIONS 4HE SIMPLEST METHOD OF UPDATING A TRACK STATE IS THE @ A FILTER DESCRIBED BY
XSK XP K @ ;XMK XPK =
VSK VSK A ;XMK XPK =4
XPK XSK VSK 4
WHERE XSK IS THE FILTERED POSITION VSK IS THE FILTERED VELOCITY XPK IS THE PREDICTED POSITION XMK IS THE MEASURED POSITION 4 IS THE TIME BETWEEN DETECTIONS AND @ A ARE THE POSITION AND VELOCITY GAINS RESPECTIVELY 4HE SELECTION OF @ A IS A DESIGN TRADEOFF 3MALL GAINS MAKE A SMALL CORRECTION IN THE DIRECTION OF EACH DETECTION !S A RESULT THE TRACKING FILTER IS LESS SENSITIVE TO NOISE BUT IS MORE SLUGGISH TO RESPOND TO MANEUVERSDEVIATION FROM THE ASSUMED TARGET MODEL #ONVERSELY LARGE GAINS PRO DUCE MORE TRACKING NOISE BUT QUICKER RESPONSE TO MANEUVERS 4HESE ERRORS ARE READILY CALCULATED AS A FUNCTION OF @ AND A USING THE FORMULAS SHOWN IN 4ABLE 4O TUNE THE @ A FILTER FOR RADAR TRACKING ONE USES THE RADAR PARAMETERS TO CALCULATE THE TRACKING ERRORS LISTED IN 4ABLE AS A FUNCTION OF THE TRACKING GAINS @ AND A 4HEN ONE SELECTS THE GAINS THAT BEST MEET THE NEEDS OF THE APPLICATION &OR EXAMPLE CONSIDER A RADAR THAT HAS METER RANGE MEASUREMENT ACCURACY AND A TWO SECOND CONSTANT UPDATE INTERVAL 4HE APPLICATION OF THIS RADAR SYSTEM IS TO TRACK A TARGET THAT MOVES LINEARLY BUT WITH OCCASIONAL UNPREDICTABLE MANEUVERS OF UP TO G MS
4!",% #HARACTERIZATION OF 4RACKING %RRORS AS A &UNCTION OF 4RACKING 'AINS @ AND A
3TEADY STATE 4RACK %RROR 3TANDARD DEVIATION OF FILTERED TRACKING STATE 2ADAR DETECTION 3TANDARD NOISE STANDARD DEVIATION OF PREDICTED DEVIATION R TRACKING STATE ,AG BIAS IN #ONSTANT FILTERED TRACK MANEUVERA STATE UNITS OF GS ,AG BIAS IN #ONSTANT PREDICTED TRACK MANEUVERA STATE UNITS OF GS %RROR 3OURCE 2ADAR DETECTION NOISE STANDARD DEVIATION R
)N 0OSITION
)N 6ELOCITY
§ A B A ¶ S¨ · © A ; A B = ¸ § A AB B ¶ S¨ · ©A ; A B = ¸ A4 A4 B
A B
¶ B S § r¨ 4 ©A ; A B =·¸ ¶ B S § r 4 ¨©A ; A B =·¸ ¤ A ³ A4 ¥ ´ ¦ B µ ¤ A ³ A4 ¥ ´ ¦ B µ
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&OR SIMPLICITY ASSUME THE "ENEDICT "ORDNER CONSTANT RELATIONSHIP ;A @ @ = BETWEEN @ AND A 4HE POSITION ACCURACY OF THE FILTER CAN THEN BE CALCULATED USING THE FORMULAS IN 4ABLE AND IS SHOWN IN &IGURE 7HEN THE TARGET IS NONMANEUVERING ACCURACY AS MEASURED BY THE STANDARD DEVIATION OF THE PREDICTED TRACKING STATE IMPROVES MONO TONICALLY AS THE TRACKING GAIN @ DECREASES TO #ONVERSELY WHEN THE TARGET IS PER FORMING THE G MANEUVER ACCURACY AS MEASURED BY THE LAG OR BIAS IN THE PREDICTED TRACKING STATE IMPROVES MONOTONICALLY AS THE TRACKING GAIN INCREASES TO 4HE TOTAL TRACKING ERROR CAN BE DEFINED AS THE ERROR THAT IS EXCEEDED ONLY OF THE TIME DUE TO THE SUM OF RANDOM ERRORS AND BIAS 4HE TOTAL RANGE TRACKING ERROR IS BEST IN THE REGION @ WITH A MINIMUM AROUND )F ACCURACY FOR MANEUVERS IS THE DOMINANT CONCERN THEN ONE WOULD PROBABLY TUNE THIS FILTER TO TO ACHIEVE THE LOWEST TOTAL ERROR FOR A G ACCELERATION 4HIS SAME TECHNIQUE CAN BE APPLIED TO MANY DIFFERENT RADAR TRACKING PROBLEMS USING THE EQUATIONS IN 4ABLE TO CALCULATE A GRAPH SUCH AS THE ONE SHOWN IN &IGURE &OR SIMPLE TRACKING PROBLEMS THE @ A FILTER WITH CONSTANT GAINS SELECTED FOR THE APPLI CATION WILL OFTEN BE ADEQUATE (OWEVER MORE COMPLEX TRACKING PROBLEMS REQUIRE VARI ABLE TRACKING GAINS EG LARGER GAINS AT THE BEGINNING OF THE TRACK AND LARGER GAINS AFTER MISSED DETECTIONS OR WHEN THE RANGE TO THE TRACK DECREASES MAKING ANGLE NOISE LESS OF AN ISSUE ! SYSTEMATIC METHOD FOR CALCULATING THE GAINS DEPENDING ON THE SITUATION IS THE
&)'52% %XAMPLE OF THE TUNING OF AN @ A RADAR RANGE TRACKING FILTER BY SELECTING THE GAIN THAT MINI MIZES TOTAL ERROR RADAR PARAMETERS RANGE ACCURACY METERS UPDATE INTERVAL SECONDS TARGET PARAMETER G UNKNOWN ACCELERATION GAIN RELATION ;A @ @ =
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2!$!2 (!.$"//+
+ALMAN FILTER 4HE +ALMAN FILTER MINIMIZES THE MEAN SQUARE PREDICTION ERROR WHEN THE RANDOM PROCESSES ARE GAUSSIAN 4HE +ALMAN FILTER CAN BE FORMULATED FOR TARGET MOTION IN ONE TWO OR THREE DIMENSIONS IN POLAR #ARTESIAN OR %ARTH CENTERED COORDINATES AND FOR THREE DIMENSIONAL TWO DIMENSIONAL OR ONE DIMENSIONAL RADAR MEASUREMENTS &OR SIMPLICITY A THREE DIMENSIONAL TRACKING PROBLEM IN #ARTESIAN SPACE WITH THREE MEASURED RADAR DIMENSIONS IS CONSIDERED HERE 4ARGET MOTION IS DESCRIBED BY
8TK ETK 8TK !TK !PTK
WHERE 8TK IS THE TARGET STATE AT TIME TK CONSISTING OF POSITION AND VELOCITY COMPONENTS ETK IS A TRANSITION MATRIX THAT MOVES THE TARGET LINEARLY OVER AN ELAPSED TIME 4K TK TK FROM TIME TK TO TIME TK !TK IS THE TARGET STATE CHANGE DUE TO AN UNKNOWN ACCELERATION CAUSED BY A MANEUVER OR ATMOSPHERIC DRAG AND !PTK IS TARGET STATE CHANGE DUE TO A KNOWN ACCELERATION THAT CAN BE CORRECTED SUCH AS GRAVITY FOR A FALLING OBJECT OR #ORIOLLIS ACCELERA TION 4HE COMPONENTS OF THE STATE VECTOR AND TRANSITION MATRIX FOR THIS PROBLEM ARE X T K u
8 T K
X T K Y T K u
Y T K Z T K u
Z T K
F T K
4K
4K
4K
4HE UNKNOWN ACCELERATION !TK IS ZERO MEAN AND IS CHARACTERIZED BY ITS COVARIANCE MATRIX 1TK )F ONE VIEWS THE UNKNOWN MANEUVER AS A WHITE NOISE PROCESS WITH SPEC TRAL DENSITY Q G(Z THEN THE ACCELERATION IS SAMPLED BY EACH RADAR DETECTION PRODUCING A DISCRETE COVARIANCE MATRIX
4K 4K 4K 4K 4K 4K 1 T K Q 4K 4K 4K 4K 4K 4K
4HE OBSERVATION EQUATION RELATES THE ACTUAL RADAR MEASUREMENTS 9K AT TIME TK TO THE TARGET STATE
9K H8TK NK
WHERE NK IS THE RADAR MEASUREMENT NOISE HAVING A COVARIANCE MATRIX
S R S Q K S J S $
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COMPOSED OF THE RADAR MEASUREMENT ACCURACIES IN RANGE AZIMUTH ELEVATION AND DOP PLER 4HE FUNCTION H IS THE COORDINATE TRANSFORM THAT RELATES THE MEASUREMENTS TO THE STATE AT TIME TK ACCORDING TO THE COORDINATE FRAME DESIGN CHOICES SEE 4ABLE LATER IN THE CHAPTER )N ORDER TO USE THE +ALMAN FILTER H IS APPROXIMATED AS A LINEAR FUNCTION IN THE VICINITY OF THE PREDICTED TRACK STATE
H 8 H 8 TK \ TK ( ; 8 8 TK \ TK = r 8 8 TK \ TK
WHERE ( IS THE GRADIENT OF H %ACH COORDINATE FRAME HAS ITS OWN APPROXIMATION FOR ( &OR EXAMPLE IF THE STATE COORDINATE SYSTEM IS COMPOSED OF THREE DIMENSIONAL #ARTESIAN COOR DINATES CENTERED AT THE RADAR THEN MULTIPLICATION BY ( TRANSFORMS #ARTESIAN COORDINATES X Y Z INTO POLAR MEASUREMENT COORDINATES RANGE AZIMUTH ELEVATION DOPPLER AND
X § ¨ R ¨ Y ¨ X Y ¨ ( ¨
XZ ¨ ¨R X Y ¨ XR XR ¨ R ©
Y R
X X Y
YZ R X Y YR YR R
Z R
X R
Y R
X Y R ZR ZR R
¶ · · · · · · · Z· · R¸
WHERE R X Y Z IS RANGE 4HE +ALMAN FILTER EQUATIONS FOR RADAR TRACKING ARE THEN SIMPLY GENERALIZATIONS OF THE @ A FILTER EQUATIONS WHERE @ AND A VARY WITH TIME 4HE +ALMAN FILTER UPDATE PROCEDURE CONTINUES AS FOLLOWS &IRST PREDICT A NEW TARGET STATE ESTIMATE 8 TK \ TK OF THE STATE 8TK AT TIME TK GIVEN ALL MEASUREMENTS UP TO TIME TK
8 TK \ TK F TK 8 TK !P TK
ALONG WITH ITS COVARIANCE 0K \ K E¼ TK 0K \ K E¼ TK 4 1TK
4HEN UPDATE THE TARGET STATE USING THE K ST RADAR MEASUREMENT
8 TK \ TK 8 TK \ TK + K ;9K ( TK 8 TK \ TK =
AND ITS COVARIANCE
0K \ K ;( *K (TK =0K \ K
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USING THE +ALMAN GAINS
*K 0K \ K (4TK ;(TK 0K \ K (4TK K=
"ECAUSE THE GAINS ARE CALCULATED USING THE HISTORY OF ALL PAST UPDATE TIMES AND ACCURACIES THE GAINS AUTOMATICALLY INCREASE AFTER MISSED DETECTIONS AND AUTOMATICALLY INCREASE TO GIVE GREATER WEIGHT TO A DETECTION WHEN IT IS KNOWN TO BE MORE ACCURATE AND THEY AUTOMATICALLY DECREASE AS THE TRACK AGES REFLECTING THE VALUE OF THE DETECTIONS ALREADY FILTERED &OR EXAMPLE FOR A ZERO RANDOM ACCELERATION 1K AND A CONSTANT DETECTION COVARIANCE MATRIX K THE @ n A FILTER CAN BE MADE EQUIVALENT TO THE +ALMAN FILTER BY SETTING
A
K K K
K K
AND
B
ON THE KTH SCAN 4HUS AS TIME PASSES @ AND A APPROACH ZERO APPLYING HEAVY FILTERING TO THE NEW SAMPLES )N PRACTICAL RADAR APPLICATIONS 1K AND SO THE TRACKING GAINS EVENTUALLY SETTLE TO A NON ZERO VALUE TERMED THE STEADY STATE TRACKING GAINS 4HE TRADEOFFS FOR EMPLOYING A +ALMAN FILTER FOR RADAR TRACKING GENERALLY ARE TUNING THE FILTER FOR THE DESIRED DEGREE OF FILTERING SELECTING THE TRACKING COORDINATES AND ADAPTING THE FILTER TO DEAL WITH CHANGES IN THE TARGET MOTION EG MANEUVERS DIFFERENT PHASES OF BALLISTIC FLIGHT AND SO ON 4UNING THE +ALMAN &ILTER 4HE GREATEST ADVANTAGE OF THE +ALMAN FILTER FOR RADAR TRACKING IS THAT IT PROVIDES A SYSTEMATIC WAY OF CALCULATING GAINS (OWEVER A DISADVAN TAGE IS THAT THIS GAIN CALCULATION ASSUMES LINEAR TARGET MOTION WITH RANDOM PERTURBA TIONS %Q -OST PRACTICAL RADAR TRACKING PROBLEMS INVOLVE TARGETS THAT DEVIATE FROM LINEAR MOTION IN MORE COMPLEX WAYS EG COURSE CORRECTIONS TERRAIN FOLLOWING EVASIVE MANEUVERS AND ATMOSPHERIC DRAG 4HE +ALMAN FILTER IS TUNED TO A PRACTICAL RADAR TRACKING PROBLEM THROUGH THE SELECTION OF THE COVARIANCE MATRIX 1TK OF THE UNKNOWN RANDOM MANEUVER 4HE GOAL OF THIS SELECTION IS TO OBTAIN THE BEST POSSIBLE TRACKING PERFORMANCE FOR THE MORE COMPLEX CASES OF INTEREST WHILE STILL USING THE SIM PLE +ALMAN RANDOM PERTURBATION MODEL &OR EXAMPLE IN THE SIMPLIFIED CASE OF A SINGLE DIMENSION AND CONSTANT TRACKING CONDITIONS THE MEASUREMENT COVARIANCE MATRIX IS SIMPLY A SINGLE CONSTANT MEASUREMENT VARIANCE K R¼ M AND THE TIME BETWEEN DETEC TIONS IS A CONSTANT 2K 4 )N THIS CASE THE +ALMAN FILTER DESCRIBED IN %QS TO HAS GAINS THAT ARE A FUNCTION OF THE DIMENSIONLESS TRACK FILTERING PARAMETER FTRACK
G TRACK
Q4 S M
"ECAUSE THE RADAR MEASUREMENT ACCURACY AS REPRESENTED BY THE COVARIANCE MATRIX AND THE TIME BETWEEN DETECTION OPPORTUNITIES 4 ARE PARAMETERS OF THE RADAR DESIGN ITSELF THE SELECTION OF 1TK IS THE DEGREE OF FREEDOM AVAILABLE TO THE TRACKING FILTER DESIGN 4ABLE SUMMARIZES THE METHODS FOR TUNING THE +ALMAN FILTER
-ODEL NO 2ANDOM CHANGE IN VELOCITY AT EACH MEASUREMENT INTERVAL
-ODEL NO 2ANDOM CHANGE IN ACCELERATION AT EACH MEASUREMENT INTERVAL 3TANDARD DEVIATION OF ACCELERATION CHANGE IS RA
-ODEL NO 7HITE NOISE SPECTRAL DENSITY Q G(Z ACCELERATION SAMPLED BY RADAR MEASUREMENT
-ANEUVER -ODEL
S V
4K 4K 4K 4K
4K 4K 4K 4K
S A
Q
1 SUBMATRIX
Q4 S M
S A4 S M
S V4 S M
A A
G TRACK
AND
B
G TRACK
B A A
G TRACK AND
A A A AND
B
3TEADY STATE 'AIN 2ELATION AND 4RACKING )NDEX
4!",% #OMPARISON OF -ETHODS OF 4UNING +ALMAN &ILTER FOR 0RACTICAL 2ADAR 4RACKING 0ROBLEMS
6ARY RV TO INCREASE DECREASE GAINS AND OBTAIN DESIRED PERFORMANCE USING EQUATIONS IN 4ABLE
6ARY RA TO INCREASE DECREASE GAINS AND OBTAIN DESIRED PERFORMANCE USING EQUATIONS IN 4ABLE
6ARY Q TO INCREASE DECREASE GAINS AND OBTAIN DESIRED PERFORMANCE USING EQUATIONS IN 4ABLE
4UNING -ETHOD
2ESPONDS VERY WELL TO MANEUVERS BUT OPERATES AT THE EDGE OF FILTER STABILITY (IGHER RADAR MEASUREMENT RATE CAN ACTUALLY RESULT IN LESS ACCURATE TRACK 6ERY CONSERVATIVE WITH RESPECT TO FILTER STABILITY
!CCOMMODATES VARIABLE MEASUREMENT RATES WELL 2ESPONDS TO MANEUVERS BUT NOT AT THE EDGE OF FILTER STABILITY
#HARACTERISTICS
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-ODEL NO #ONSTANT DETERMINISTIC ACCELERATION A G &ILTER OBJECTIVE IS TO MINIMIZE LAG PLUS C STANDARD DEVIATIONS
-ODEL NO #ONSTANTLY ACCELERATING TARGET WITH A WHITE NOISE JERK J ;GS (Z= SAMPLED BY RADAR MEASUREMENT *ERK IS THE RATE OF CHANGE OF ACCELERATION
-ANEUVER -ODEL
4K 4K 4K 4K
4K 4K
1 SUBMATRIX NOT APPLICABLE )NSTEAD ASSUME CONSTANT PARABOLIC MOTION AT
4K 4K J 4K
1 SUBMATRIX
J4 S M
G TRACK
AND
A 4 C S M
B A A
G TRACK
AND
3TEADY STATE GAIN CALCULATIONS DESCRIBED IN &ITZGERALD
3TEADY STATE 'AIN 2ELATION AND 4RACKING )NDEX
6ARY A TO INCREASE DECREASE GAINS AND OBTAIN DESIRED PERFORMANCE USING EQUATIONS IN 4ABLE
3ELECT THIS MODEL WHEN TARGET IS KNOWN EXPECTED TO BE ACCELERATING
4UNING -ETHOD
4!",% #OMPARISON OF -ETHODS OF 4UNING +ALMAN &ILTER FOR 0RACTICAL 2ADAR 4RACKING 0ROBLEMS #ONTINUED
&ILTER MINIMIZES ERROR FOR A WORST CASE DETERMINISTIC MANEUVER VICE A RANDOM ONE
:ERO LAGS TO CONSTANT ACCELERATION HOWEVER NOISE ERRORS ARE MUCH GREATER
#HARACTERISTICS
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!S SEEN IN &IGURE THE SELECTION OF 1TK AND THUS FTRACK ALLOWS ONE TO UNIQUELY DETERMINE THE STEADY STATE TRACKING GAINS AS A FUNCTION OF FTRACK /NE CAN SEE THAT LARGE ASSUMED MANEUVERS LARGE Q @A OR A LARGER TIME BETWEEN UPDATES 4 OR VERY ACCURATE RADAR MEASUREMENTS SMALL WILL RESULT IN LARGE TRACKING GAINS 4HE POSI TION GAIN @ IS NEARLY IDENTICAL FOR THE 1TK MODELS NO AND IN 4ABLE (OWEVER THE VELOCITY GAIN A DIFFERS CONSIDERABLY &OR RANDOM CHANGES IN ACCEL ERATION AT EACH MEASUREMENT INTERVAL MODEL NO THE GAINS INCREASE TO @ A ¼ ¼ WHICH IS THE LIMIT OF FILTER STABILITY 4HUS THIS MODEL PRODUCES FILTER GAINS THAT ARE THE MOST AGGRESSIVE AT MINIMIZING LAGS TO MANEUVERSAT THE EXPENSE OF LARGER % "(%
'! $ $(
% "%
% "(%
% "%
'! $ $ -
$*') ' (*' # $) *') ' (*' # $)
%,$ *+ '' )
$ *+ '' )
%')& ) $) '+"
%$ & ) $) '+"
&)'52% 4HE RELATIONSHIP BETWEEN THE STEADY STATE TRACKING GAINS @ AND A IS SHOWN FOR DIFFERENT 1TK S CORRESPONDING TO DIFFERENT ASSUMPTIONS ABOUT THE UNKNOWN TARGET MANEUVER -ODEL NO WHITE NOISE ACCELERATION SAMPLED AT EACH MEASUREMENT INTERVAL MODEL NO RANDOM CHANGE IN ACCELERATION AT EACH MEASUREMENT INTERVAL MODEL NO RANDOM CHANGE IN VELOCITY AT EACH MEASUREMENT INTERVAL AND MODEL NO CONSTANT DETERMINISTIC ACCELERATION -ODEL NO NOT SHOWN AS IT IS A GAIN MODEL
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TRACKING ERRORS DUE TO RADAR MEASUREMENT NOISE &OR RANDOM CHANGES IN VELOCITY AT EACH MEASUREMENT INTERVAL MODEL NO THE GAINS INCREASE TO @ A WHICH IS VERY CONSERVATIVE FROM A FILTER STABILITY POINT OF VIEW &OR WHITE NOISE ACCELERATION SAMPLED BY RADAR MEASUREMENTS MODEL NO THE GAINS ARE A COMPROMISE INCREASING TO A B "ECAUSE THIS MODEL IS A SAMPLED CONTINUOUS TIME ACCELERATION IT IS PREFERRED WHEN UPDATE TIMES ARE VARIABLE BECAUSE THE TARGET DOES NOT MANEUVER MORE OR LESS WHEN THE UPDATE INTERVAL CHANGES 4HE EQUATIONS IN 4ABLE CAN THEN BE USED TO CALCULATE THE FILTER PERFORMANCE IN TERMS OF VARIANCE REDUCTION RATIOS AND TRACKING LAGS !DJUSTMENTS TO PARAMETERS OF FTRACK CAN BE MADE TO OBTAIN THE DESIRED NOISE AND LAG TRADEOFF 3ELECTION OF 4RACKING #OORDINATES 4HE +ALMAN FILTER ASSUMES LINEAR TARGET MOTION AND A LINEAR RELATION BETWEEN THE RADAR DETECTIONS AND THE TARGET COORDINATES (OWEVER RADARS MAKE DETECTIONS IN POLAR COORDINATES RANGE ANGLE DOPPLER WHILE TARGET MOTION IS MOST LIKELY LINEAR IN #ARTESIAN COORDINATES X Y Z 4HEREFORE SOME COMPROMISES MUST GENERALLY BE MADE IN SELECTING A COORDINATE SYSTEM FOR FILTERING 4ABLE DESCRIBES THE DESIGN TRADEOFFS FOR DIFFERENT SELECTIONS 4HE POLAR +ALMAN FILTER IS RARELY USED BECAUSE OF THE PSEUDO ACCELERATIONS INTRO DUCED BY PROPAGATING THE STATE IN POLAR COORDINATES 4HE #ARTESIAN%ARTH CENTERED +ALMAN FILTER CAN WORK WELL BUT MAY HAVE DIFFICULTY ACCOMMODATING RADAR MEASURE MENTS OF LESS THAN THREE DIMENSIONS 4HE EXTENDEDDUAL COORDINATE SYSTEM +ALMAN FILTER PREVENTS PSEUDO ACCELERATIONS AND ACCOMMODATES MEASUREMENTS OF ANY DIMEN SIONALITY "OTH THE #ARTESIAN%ARTH CENTERED +ALMAN FILTERS INVOLVE NONLINEAR TRANSFOR MATIONS RESULTING IN AN IMPERFECT CALCULATION OF THE TRACKING ACCURACY 7HEN PREDICTION TIMES ARE LONG ANDOR WHEN VERY ACCURATE RESULTS ARE NEEDED THESE IMPERFECTIONS IN THE +ALMAN FILTER COVARIANCE CALCULATION CAN BE SIGNIFICANT AND THE TRACKING ERRORS CAN BE QUITE NON GAUSSIAN 0ARTICLE FILTERS TYPICALLY PROPAGATE A LARGE NUMBER OF RANDOM SAMPLES PARTICLES FROM A STATE TRANSITION PRIOR DISTRIBUTION TO ESTIMATE POSTERIOR DIS TRIBUTIONS THAT ARE NOT REQUIRED TO BE GAUSSIAN IN FORM 4HUS IN A PARTICLE FILTER EVEN MULTI MODAL DISTRIBUTIONS CAN BE USED AS PRIOR AND REALIZED AS POSTERIOR DISTRIBUTIONS (OWEVER PARTICLE FILTERS REQUIRE QUITE A BIT OF COMPUTATION 4HE UNSCENTED +ALMAN FILTER MORE EFFICIENTLY CALCULATES THE TRACKING ACCURACY BY PROPAGATING SELECTED CARDINAL POINTS THROUGH THE FILTER 4HE UNSCENTED +ALMAN &ILTER APPROXIMATES THE COVARIANCE MATRIX WITH A SET OF , SAMPLE POINTS WHERE , IS THE NUMBER OF STATE DIMENSIONS 4HE SAMPLE POINTS ARE PROPAGATED THROUGH AN ARBITRARY TRANSFORM FUNCTION AND THEN USED TO RECONSTRUCT A GAUSSIAN COVARIANCE MATRIX 4HIS TECHNIQUE HAS THE ADVANTAGE OF REPRESENTING THE COVARIANCE ACCURATELY TO THE THIRD ORDER OF A 4AYLOR SERIES EXPANSION !S A RESULT THE CALCULATED TRACKING ACCURACY IS AT LEAST TO THIRD ORDER UNCONTAMINATED OR hUNSCENTEDv BY THE NONLINEARITY !DAPTING &ILTER TO $EAL WITH #HANGES IN 4ARGET -OTION 4HE +ALMAN FILTER ASSUMES LINEAR TARGET MOTION PERTURBED BY A RANDOM MANEUVER MODEL AS A MATHEMATI CAL CONVENIENCE IN CALCULATING TRACKING GAINS (OWEVER MOST RADAR TARGETS DO NOT MOVE IN A RANDOM MANEUVER BUT INSTEAD MOVE LINEARLY AT TIMES AND THEN MANEUVER UNPREDICTABLY AT TIMES 4HE CHALLENGE IN ADAPTING THE FILTER TO DEAL WITH CHANGES IN THE TARGET MOTION EG MANEUVERS BALLISTIC RE ENTRY IS TO ADAPT THE TARGET MOTION MODEL FOR THE +ALMAN FILTER OVER TIME SO THAT MORE ACCURATE TRACKING OCCURS THAN WITH A SINGLE MODEL 4HE SIMPLEST FORM OF ADAPTATION IS A MANEUVER DETECTOR TO MONITOR THE TRACKING FILTER RESIDUALS DIFFERENCES BETWEEN MEASURED AND PREDICTED POSITION ,ARGE CORRELATED
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4!",% !DVANTAGES AND $ISADVANTAGES OF %MPLOYING THE +ALMAN &ILTER IN $IFFERENT #OORDINATE &RAMES #OORDINATES FOR 3TATE 0REDICTION %QS
-ETHOD OF #OVARIANCE 0ROPAGATION
!DVANTAGES
$ISADVANTAGES
0OLAR +ALMAN 0OLAR FILTER
0OLAR
%QS TO IN POLAR COORDINATES
&ILTER COVARIANCES ARE CALCULATED EXACTLY AND STATE ERRORS GAUSSIAN DISTRIBUTED 2ADAR DETECTIONS OF LESS THAN THREE DIMENSIONS CAN BE USED
0SEUDO ACCELERATIONS INTRODUCED IN STATE PROPAGATION
#ARTESIAN %ARTH #ENTERED +ALMAN FILTER
#ARTESIAN %ARTH CENTERED
#ARTESIAN %ARTH CENTERED
%QS TO IN #ARTESIAN %ARTH CENTERED COORDINATES
3TATE PROPAGATION IS LINEAR NO PSEUDO ACCELERATIONS
&ILTER COVARIANCES ARE NOT EXACT DUE TO NONLINEAR TRANSFORMATION
%XTENDED DUAL COORDINATE +ALMAN FILTER
0OLAR
#ARTESIAN %ARTH CENTERED
%QS TO IN POLAR COORDINATES
2EQUIRES FREQUENT COORDINATE TRANSFORMS
5NSCENTED +ALMAN FILTER
0OLAR OR #ARTESIAN %ARTH CENTERED
#ARTESIAN %ARTH CENTERED
#OVARIANCE INFERRED BY PROPAGATING MULTIPLE STATES
3TATE PROPAGATION IS LINEAR NO PSEUDO ACCELERATIONS 2ADAR DETECTIONS OF LESS THAN THREE DIMENSIONS CAN BE EASILY ACCOMMODATED 3TATE PROPAGATION IS LINEAR NO PSEUDO ACCELERATIONS &ILTER COVARIANCE MORE EXACT THAN TRADITIONAL METHODS PARTICULARLY FOR LONG EXTRAPOLATION TIMES
+ALMAN &ILTER #OORDINATE &RAME 6ARIANTS
#OORDINATES FOR 'AIN #ALCULATION %QS AND STATE UPDATE %Q
-ORE COMPLEX BUT NOT NECESSARILY MORE COMPUTATION
RESIDUALS GENERALLY INDICATE A MANEUVER A DEVIATION FROM THE FILTER MODEL 5PON MANEUVER DETECTION THE MANEUVER SPECTRAL DENSITY Q IS INCREASED IN THE +ALMAN FILTER MODEL RESULTING IN HIGHER TRACKING GAINS AND BETTER FOLLOWING OF THE MANEUVER ! MORE COMPLEX APPROACH IS TO USE MULTIPLE +ALMAN FILTERS RUNNING SIMULTANEOUSLY WITH DIFFERENT TARGET MOTION MODELSGENERALLY DIFFERENT Q VALUES OR DIFFERENT EQUA TIONS FOR TARGET MOTION EG CONSTANT ACCELERATION OR CONSTANT VELOCITY &IGURE SHOWS A BANK OF MULTIPLE PARALLEL FILTERS ALL FED BY THE SAME STREAM OF ASSOCIATED MEA SUREMENTS !T EACH DETECTION TIME TK ONE OF THE SEVERAL FILTER OUTPUTS MUST BE SELECTED TO BE THE TRACK STATE USED FOR DETECTION TO TRACK ASSOCIATION ! SYSTEMATIC WAY OF EMPLOYING MULTIPLE TARGET MOTION MODELS IS THE )NTERACTING -ULTIPLE -ODEL )-- APPROACH DIAGRAMMED IN &IGURE -ULTIPLE MODELS RUN SIMULTANEOUSLY HOWEVER THEY DO NOT RUN INDEPENDENTLY )NSTEAD THERE IS MIXING OF
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&)'52% "ANK OF PARALLEL RADAR TRACKING FILTERS EACH EMPLOYING A DIFFERENT TARGET MOTION MODEL AFTER 3 "LACKMAN AND 2 0OPOLI Ú !RTECH (OUSE
&)'52% &LOWCHART OF INTERACTING MULTIPLE MODELS AFTER 3 "LACKMAN AND 2 0OPOLI Ú !RTECH (OUSE
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THE MODEL STATES 4HE UPDATE EQUATION FOR THE ITH MODEL DEPENDS NOT ONLY ON THE ITH MODEL STATE BUT ALSO ON THE STATES OF ALL OTHER MODELS 4HESE STATES ARE MIXED USING INFERRED PROBABILITIES OF THE TARGET TRANSITIONING FROM ONE MOTION MODEL TO ANOTHER !S AN EXAMPLE CONSIDER RADAR TRACKING OF A BALLISTIC MISSILE THAT UNDERGOES DISTINCT PHASES OF FLIGHT BOOST EXO ATMOSPHERIC FLIGHT AND ENDO ATMOSPHERIC RE ENTRY %ACH OF THESE PHASES OF FLIGHT HAS A DISTINCT TARGET MODEL $URING BOOST THE TARGET IS CONTINUALLY ACCELERATING AND INCREASING SPEED 4HIS ACCELERATION IS UNKNOWN AND MUST BE ESTIMATED $URING EXO ATMOSPHERIC FLIGHT THE OBJECT IS FALLING WITH THE KNOWN ACCELERATION OF GRAVITY $URING ENDO ATMOSPHERIC RE ENTRY THE TARGET CONTINUES TO FALL BUT EXPERIENCES A DRAG ACCELERATION DUE TO ITS BALLISTIC COEFFICIENT AN UNKNOWN TARGET PARAMETER RELATED TO THE SHAPE AND MASS OF THE TARGET !N )-- FILTER CAN BE USED TO SYSTEMATICALLY TRANSITION BETWEEN THESE DIFFERENT PHASES OF FLIGHT PROVIDING A SINGLE FILTER OUTPUT &IGURE SHOWS THE MODEL PROBABILITIES FOR SUCH AN )-- FILTER APPLICATION
"$ # "
"$ " $
" " !
! &)'52% -ODEL PROBABILITIES RESULTING FROM THE APPLICATION OF AN )-- FILTER TO A BALLISTIC MISSILE TRACKING PROBLEM A PROBABILITY THAT TARGET MOTION IS hBOOST PHASE v B PROBABILITY THAT TARGET MOTION IS hEXO ATMOSPHERICv FLIGHT C PROBABILITY THAT TARGET MOTION IS hENDO ATMOSPHERICv RE ENTRY AFTER 2 #OOPERMANR Ú &IFTH )NTERNATIONAL #ONFERENCE ON )NFORMATION &USION VOL
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!SSOCIATION OF !CCEPTED $ETECTION WITH %XISTING 4RACKS 4HE GOAL OF DETECTION TO TRACK ASSOCIATION IS TO CORRECTLY ASSIGN RADAR DETECTIONS TO EXISTING TRACKS SO THE TRACK STATES IN THE TRACK FILE CAN BE CORRECTLY UPDATED 4HE BASIS FOR ASSIGNMENT IS A MEASURE OF HOW CLOSE TOGETHER THE DETECTION AND TRACK ARE IN TERMS OF MEASURABLE PARAMETERS SUCH AS RANGE ANGLE DOPPLER AND WHEN AVAILABLE TARGET SIGNATURE 4HE STATISTICAL DISTANCE IS CALCULATED AS A WEIGHTED COMBINATION OF THE AVAILABLE DETECTION TO TRACK COORDINATE DIFFERENCES )N THE MOST GENERAL CASE THIS IS A COMPLEX QUADRATIC FORM
$ 9K H 8 TK \ TK ; ( TK 0 K \ K ( 4 TK 2K = 9K H 8 TK \ TK 4
&OR MOST SINGLE RADAR TRACKING PROBLEMS IT REDUCES TO A SIMPLE WEIGHTED SUM $
RM RP Q M Q P J M J P $M $ P S R S PR S Q S PQ S J S PJ S $ S P$
WHERE RM PM IM $M ARE THE MEASURED RANGE AZIMUTH ELEVATION AND DOPPLER WITH ACCURACIES RR RP RI R$ RP PP IP $P ARE THE RANGE AZIMUTH ELEVATION AND DOP PLER PREDICTED BY THE AUTOMATIC TRACKER WITH ACCURACIES RPR RPP RPI RP$ 4HE PRE DICTED ACCURACIES ARE A BYPRODUCT OF THE RADAR TRACKING FILTER 3TATISTICAL DISTANCE RATHER THAN %UCLIDEAN DISTANCE MUST BE USED BECAUSE THE RANGE ACCURACY IS USUALLY MUCH BETTER THAN THE AZIMUTH ACCURACY 7HEN TARGETS ARE WIDELY SPACED AND IN A CLEAR ENVIRONMENT ONLY ONE TARGET DETECTION PAIR HAS A SMALL $ MAKING THESE ASSIGNMENTS OBVIOUS 4HUS THE DESIGN OF DETECTION TO TRACK ASSOCIATION IS USUALLY DOMINATED BY THE MORE DIFFICULT CONDITIONS OF CLOSELY SPACED TARGETS OR CLOSELY SPACED TARGETS AND CLUTTER &IGURE SHOWS A COMMON SITUATION FOR CLOSELY SPACED TARGETS ANDOR CLUTTER 4HREE ASSOCIATION GATES ARE CONSTRUCTED AROUND THE PREDICTED POSITIONS OF THREE EXISTING TRACKS 4HREE DETECTIONS ARE MADE BUT ASSIGNMENT OF THE DETECTIONS TO THE TRACKS IS NOT OBVIOUS TWO DETECTIONS ARE WITHIN GATE THREE DETEC TIONS ARE WITHIN GATE AND ONE DETECTION IS WITHIN GATE 4ABLE LISTS ALL DETECTIONS
&)'52% %XAMPLES OF THE PROBLEMS CAUSED BY MULTIPLE DETECTIONS AND TRACKS IN CLOSE VICINITY FROM ' 6 4RUNK
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4!",% !SSOCIATION 4ABLE FOR %XAMPLE 3HOWN IN &IGURE
4RACK .O
$ETECTION .O
$ETECTION .O c
$ETECTION .O c c
FROM ' 6 4RUNK
WITHIN THE TRACKING GATES AND THE STATISTICAL DISTANCE BETWEEN THE DETECTION AND TRACK )F THE DETECTION IS OUTSIDE THE TRACK GATE THE STATISTICAL DISTANCE IS SET TO INFINITY .EAREST NEIGHBOR ASSIGNMENT IS THE MOST COMMON SOLUTION TO THIS PROBLEM 4HE SIMPLEST FORM OF NEAREST NEIGHBOR WORKS SEQUENTIALLY ON INCOMING DATA !S EACH NEW DETECTION IS MADE IT IS ASSIGNED TO THE TRACK WITH WHICH IT HAS THE SMALLEST STATISTICAL DISTANCE (ENCE IF DETECTION NO WAS RECEIVED FIRST IT WOULD BE ASSIGNED TO TRACK NO (OWEVER IT IS BETTER TO DELAY THE ASSOCIATION PROCESS SLIGHTLY SO THAT ALL DETECTIONS IN A LOCAL NEIGHBORHOOD ARE RECEIVED AND STORED AND AN ASSOCIATION TABLE SUCH AS 4ABLE GENERATED 4HIS HAS IMPLICATIONS ABOUT HOW SECTORS ARE SCANNED WITH A PHASED ARRAY .EAREST NEIGHBOR ASSIGNMENT CAN NOW BE APPLIED TO THE ASSOCIATION TABLE BY FINDING THE SMALLEST STATISTICAL DISTANCE BETWEEN A DETECTION AND A TRACK MAKING THAT ASSOCIA TION AND ELIMINATING THAT DETECTION AND TRACK ROW AND COLUMN FROM THE TABLE 4HIS PROCESS IS REPEATED UNTIL THERE ARE EITHER NO TRACKS OR NO DETECTIONS LEFT !PPLYING THIS ALGORITHM TO 4ABLE RESULTS IN DETECTION NO UPDATING TRACK NO DETECTION NO UPDATING TRACK NO AND TRACK NO NOT BEING UPDATED "ETTER ASSIGNMENTS ARE POSSIBLE WITH MORE SOPHISTICATED PROCESSING ALGORITHMS 4HE THREE TYPES OF MORE SOPHISTICATED ALGORITHMS MOST FREQUENTLY USED ARE 'LOBAL .EAREST .EIGHBOR '.. #ONSIDER THE WHOLE MATRIX OF STATISTICAL DIS TANCES SIMULTANEOUSLY AND MINIMIZE A METRIC SUCH AS THE SUM OF ALL STATISTICAL DISTANCES FOR A COMPLETE ASSIGNMENT SOLUTION 0ERFORMING THIS OPTIMIZATION CAN BE DONE USING -UNKRES ALGORITHM -UNKRES ALGORITHM IS AN EXACT SOLUTION OF THE MINIMIZATION PROBLEM BUT IS RARELY USED BECAUSE IT IS COMPUTATIONALLY SLOW ! MORE COMPUTATIONALLY EFFICIENT EXACT SOLUTION IS THE *ONKER 6OLGENANT #ASTANON *6# ALGORITHM 4HE *6# IS MUCH MORE EFFICIENT FOR SPARSE ASSIGNMENT MATRICES WHICH ARE LIKELY FOR PRACTICAL RADAR TRACKING PROBLEMS 3PEED IMPROVEMENTS OF TO TIMES HAVE BEEN REPORTED !N EFFECTIVE SUBOPTIMAL SOLUTION IS THE !UCTION ALGORITHM WHICH VIEWS THE TRACKS AS BEING hAUCTIONED OFFv TO THE DETECTIONS ITERATIVELY ASSIGNING HIGHER COSTS TO TRACKS COMPETED FOR BY MORE DETECTIONS &IGURE PROVIDES A COMPARISON OF THE -UNKRES *6# AND !UCTION ALGORITHMS OPTIMIZED FOR SPARSE DATA 4HE *6# AND !UCTION ALGORITHMS PROVIDE A SIGNIFICANT INCREASE IN COMPUTATIONAL SPEED !LTHOUGH THE !UCTION ALGORITHM IS SIMPLER REQUIR ING LESS LINES OF CODE THE *6# ALGORITHM GENERALLY REQUIRES LESS COMPUTATION TIME 0ROBABILISTIC $ATA !SSOCIATION 0$! !NOTHER ALTERNATIVE IS THE PROBABILISTIC DATA ASSOCIATION 0$! ALGORITHM WHERE NO ATTEMPT IS MADE TO ASSIGN TRACKS TO DETECTIONS BUT INSTEAD TRACKS ARE UPDATED WITH ALL THE NEARBY DETECTIONS WEIGHTED BY THE PERCEIVED PROBABILITY OF THE TRACK BEING THE CORRECT ASSOCIATION "ECAUSE 0$! RELIES ON ERRONEOUS ASSOCIATIONS ESSENTIALLY hAVERAGING OUT v IT IS MOST EFFECTIVE WHEN TRACKS ARE FAR ENOUGH APART THAT NEARBY DETECTIONS ORIGINATE FROM SPATIALLY RANDOM NOISE OR CLUTTER EXCLUSIVELY AND WHEN THE TRACKING GAINS ARE SMALL IE WHEN THE TRACKING INDEX FTRACK IS SMALL 4HE *OINT 0ROBABILISTIC $ATA
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&)'52% ! COMPARISON OF THE EXECUTION TIME FOR THE -UNKRES OPTIMUM *6# OPTIMUM AND !UCTION SUBOPTIMUM ALGORITHMS SHOWS THE RAPID INCREASE IN COMPUTATION REQUIRED FOR -UNKRES AS THE NUMBER OF ROWS IN THE ASSIGNMENT MATRIX INCREASES 4HE *6# AND AUCTION ALGORITHMS SHOW MUCH MORE GRADUAL GROWTH AFTER ) +ADAR ET AL Ú 30)%
!SSOCIATION *0$! IS AN EXTENSION OF 0$! THAT HANDLES MORE CLOSELY SPACED TARGETS )N *0$! DETECTIONS ARE WEIGHTED LESS WHEN THEY ARE NEAR ANOTHER TRACK -ULTIPLE (YPOTHESIS !LGORITHMS 4HE MOST SOPHISTICATED ALGORITHMS ARE MULTIPLE HYPOTHESIS ALGORITHMS IN WHICH ALL OR MANY POSSIBLE TRACKS ARE FORMED AND UPDATED WITH EACH POSSIBLE DETECTION )N 4ABLE TRACK NO WOULD BECOME THREE TRACKS OR HYPOTHESES CORRESPONDING TO UPDATING WITH DETECTION NO DETECTION NO AND NO DETECTION %ACH OF THESE TRACKS WOULD UNDERGO A +ALMAN FILTER UPDATE AND BE ELIGIBLE FOR ASSOCIATION WITH THE NEXT SET OF DETECTIONS 4RACKS ARE PRUNED AWAY IN A SYSTEMATIC MANNER LEAVING ONLY THE MOST PROBABLE &IGURE ILLUS TRATES THE TRACKING OF A SINGLE TARGET USING MULTIPLE HYPOTHESIS TECHNIQUES )N THIS EXAMPLE MANY HYPOTHESES ARE FORMED AND OVER SUCCESSIVE MEASUREMENT INTERVALS SUCCESSFULLY PRUNED AWAY LEAVING ONLY ONE CORRECT TRACK 4HE REGION OF APPLICABILITY FOR THE MORE SOPHISTICATED ALGORITHMS IS DETERMINED BY TWO PARAMETERS THE DENSITY OF EXTRANEOUS DETECTIONS K DETECTIONS PER UNIT AREA OR VOLUME
&)'52% %XAMPLE OF THE USE OF MULTIPLE HYPOTHESIS TRACKING ON SCANS OF SIMULATED RADAR DATA CONTAINING A SINGLE TARGET AND MANY FALSE ALARMS A SHOWS ALL HYPOTHESES FORMS AND B SHOWS THE SINGLE HYPOTHESIS SELECTED 0RUNED HYPOTHESES ARE GRAYED OUT AFTER 7 +OCH Ú )%%%
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&)'52% 4HE APPLICABILITY OF DIFFERENT DETECTION TO TRACK ASSOCIATION ALGORITHMS IS DETERMINED BY THE DENSITY OF FALSE ALARMS AND THE DIMENSIONLESS TRACKING PARAMETER FTRACK AFTER $ * 3ALMOND Ú 30)%
AND THE DIMENSIONLESS TRACK FILTERING PARAMETER FTRACK &IGURE BOUNDS THIS REGION OF APPLICABILITY 7HEN K AND FTRACK ARE SMALL THEN THERE IS NO NEED FOR ANY MORE THAN SIMPLE NEAREST NEIGHBOR TRACKING AND INDEED MOST TRACKING SYSTEMS STILL USE THIS APPROACH !S K INCREASES THERE IS GREATER RISK OF FALSE ASSOCIATION DECISIONS HOWEVER THE EFFECT OF THIS IS REDUCED IF FTRACK IS SMALL !T THE OTHER EXTREME WHEN K AND FTRACK ARE LARGE THE TRACKING PROBLEM IS ESSENTIALLY UNSOLVABLE WITHOUT BASIC CHANGES TO THE RADAR DESIGN PARAMETERS TO REDUCE THEM 4HERE IS AN INTERMEDIATE REGION WHERE SOPHISTICATED ASSOCIATION HAS VALUE 4HE WIDTH OF THIS REGION IS VERY SPECIFIC TO THE PARTICULAR PROB LEM 7HEN FTRACK IS LARGE AND VERY LITTLE DELAY IN THE OUTPUT CAN BE TOLERATED THEN THE REGION OF APPLICABILITY IS FAIRLY SMALL AND VERY SIMPLE MULTIPLE HYPOTHESIS APPROACHES SPLITTING TRACKS INTO AT MOST ONE OR TWO HYPOTHESES ARE THEN THE BEST ANSWER 7HEN FTRACK IS SMALL THEN 0$!*0$! CAN BE USED TO OPERATE AT SIGNIFICANTLY HIGHER FALSE ALARM DENSITIES 7HEN SIGNIFICANT DELAY CAN BE TOLERATED IN THE OUTPUT THEN MANY HYPOTHESES CAN BE FORMED AS IN &IGURE AND ORDERS OF MAGNITUDE MORE DETECTIONS HANDLED "LACKMAN AND 0OPOLI PROVIDE A GOOD SURVEY OF COMPARATIVE STUDIES IN THIS AREA /NE STUDY USING DATA RECORDED FROM FLIGHTS OF CLOSELY SPACED AIRCRAFT SHOWED VERY LITTLE DIFFERENCE BETWEEN '.. *0$! AND -(4 (OWEVER THEORETICAL PREDIC TIONS CAN SHOW DIFFERENCES OF ORDERS OF MAGNITUDE IN THE DENSITY OF CLUTTER DETECTIONS THAT CAN BE HANDLED .EW 4RACK &ORMATION 4HERE ARE TWO CLASSES OF TRACK FORMATION ALGORITHMS &ORWARD TRACKING ALGORITHMS BASICALLY PROPAGATE ONE HYPOTHESIS FORWARD IN TIME RECURSIVELY CHECKING FOR hTARGET LIKEv MOTION $ETECTIONS THAT DO NOT CORRELATE WITH CLUTTER POINTS OR TRACKS ARE USED TO INITIATE NEW TRACKS )F THE DETECTION DOES NOT CONTAIN DOPPLER INFORMATION THE NEW DETECTION IS USUALLY USED AS THE PREDICTED POSITION IN SOME MILITARY SYSTEMS ONE ASSUMES A RADIALLY INBOUND VELOCITY AND A LARGE CORRELATION REGION MUST BE USED FOR THE NEXT OBSERVATION 4HE CORRELATION REGION MUST BE LARGE ENOUGH TO CAPTURE THE NEXT DETECTION OF THE TARGET ASSUMING THAT IT COULD HAVE THE MAXIMUM VELOCITY OF INTEREST ! COMMON TRACK INITIATION
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2!$!2 (!.$"//+
CRITERION IS FOUR OUT OF FIVE ALTHOUGH ONE MAY REQUIRE ONLY THREE DETECTIONS OUT OF FIVE OPPORTUNITIES IN REGIONS WITH A LOW FALSE ALARM RATE AND A LOW TARGET DENSITY (OWEVER ONE MAY REQUIRE A MUCH LARGER NUMBER OF DETECTIONS WHEN THE RADAR HAS THE FLEXIBILITY OF AN ELECTRONIC SCAN THAT CAN PLACE MANY DETECTION OPPORTUNITIES IN A SHORT TIME INTERVAL "ACKWARD TRACKING OR hBATCHv ALGORITHMS CONSIDER ALL THE DETECTIONS SIMULTANE OUSLY ATTEMPTING TO MATCH THE DETECTIONS TO A hTARGET LIKEv PATTERN 4HIS CAN BE DONE BY ACTUALLY CONSTRUCTING A LARGE NUMBER OF MATCHED FILTERS AS IN RETROSPECTIVE PRO CESSING SEE &IGURE OR BY USING A FORWARD TRACKING PROCESS WITH MULTIPLE HYPOTHESIS FORMED AND PROPAGATED *UST AS AUTOMATIC RADAR DETECTION IS A TRADEOFF BETWEEN PROBABILITY OF DETECTION AND PROBABILITY OF FALSE ALARM NEW TRACK FORMATION IS A TRADEOFF BETWEEN THE SPEED AT WHICH A TRACK IS FORMED AND THE PROBABILITY OF ERRONEOUSLY FORMING A FALSE TRACK THAT DOES NOT REPRESENT A PHYSICAL OBJECT OF INTEREST 4HERE ARE TWO TYPES OF FALSE TRACKS 4RACKS ON REAL OBJECTS THAT ARE SIMPLY NOT OF INTEREST &OR EXAMPLE IF THE TARGETS OF INTEREST ARE AIRPLANES THEN A FALSE TRACK COULD BE A TRACK ON A BIRD 4RACKS COMPOSED OF UNRELATED DETECTIONS FROM DIFFERENT OBJECTS THAT THE AUTOMATIC TRACKING PROCESS HAS MISTAKENLY ASSOCIATED TOGETHER &OR EXAMPLE A FALSE TRACK COULD BE COMPOSED OF DETEC TIONS FROM SEVERAL DIFFERENT STATIONARY CLUTTER POINTS THAT HAVE BEEN ASSOCIATED TOGETHER OVER TIME TO CREATE A FALSE MOVING TRACK 4HE APPROACH FOR PREVENTING FALSE TRACKS ON OBJECTS NOT OF INTEREST IS TO ACTUALLY DEVELOP TRACKS ON ALL OF THEM BUT THEN OBSERVE THEM LONG ENOUGH TO CLASSIFY THEM AS UNWANTED )N THE CASE OF THE BIRD ONE WOULD GATHER ENOUGH DETECTIONS TO IMPROVE THE VELOCITY ACCURACY OF THE TRACK SO THAT IT IS CLEAR WHETHER THE TRACK IS OF INTEREST OR NOT 4HUS ONE DESIRES TO DELAY THE DISCLOSURE OF A TRACK UNTIL ENOUGH TIME HAS PASSED TO CLASSIFY IT ACCURATELY 4HIS ACCURACY CAN BE DETERMINED BY 4OBS THE AMOUNT OF TIME OVER WHICH THE OBJECT IS OBSERVED AND BY BASIC PARAMETERS OF THE RADAR 4 THE TIME BETWEEN SUCCESSIVE DETECTIONS R THE ACCURACY IN A PARTICULAR DIMENSION OF INTEREST - THE NUMBER OF DETECTIONS USED IN FORMING THE TRACK . 4OBS 4 WHICH IS THE NUMBER OF DETECTION OPPORTUNITIES 4HE VELOCITY ACCURACY IS GIVEN BY THE FOLLOWING EQUATION
SV
S § . ¶ r 4OBS ¨© . . ·¸
4HE DOMINANT DESIGN PARAMETERS IN THE EQUATION ARE THE ACCURACY OF THE RADAR AND THE OBSERVATION TIME "ETTER ACCURACY OR LONGER OBSERVATION TIME ALLOWS MORE ACCURATE MEASUREMENT OF VELOCITY -AKING MORE DETECTIONS IN THE OBSERVATION TIME IMPROVES THE ACCURACY BUT ONLY IN A SQUARE ROOT SENSE 4HE APPROACH TO PREVENTING FALSELY COMPOSED TRACKS FROM DIFFERENT OBJECTS IN A CLUTTER REGION ' IS TO REQUIRE ENOUGH DETECTIONS IN A TIGHT ENOUGH PATTERN TO MAKE %;.&4= THE EXPECTED NUMBER OF FALSE TRACKS SMALL 7HEN THERE IS AN AVERAGE OF .# DETECTIONS IN A $ DIMENSIONAL REGION ' THEN
- %;.&4= K& r K¼ $ . - P r . # r F¼
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&)'52% 4HE RETROSPECTIVE PROCESS A A SINGLE SCAN OF DATA B EIGHT SCANS OF DATA AND C EIGHT SCANS OF DATA WITH TRAJECTORY FILTERS APPLIED AFTER 0RENGAMAN ET AL Ú )%%%
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2!$!2 (!.$"//+
WHERE K& IS THE RATIO OF THE SIZE OF THE POSSIBLE SPACE A TARGET CAN TRAVEL IN ONE DETECTION INTERVAL TO THE SIZE OF ENTIRE CLUTTER REGION '
L&
6-!8 $ '
AND K0 IS THE RATIO OF THE SIZE OF A RADAR RESOLUTION CELL TO THE SIZE OF THE ENTIRE CLUTTER REGION '
L0
T T $ '
$ . - BEING THE COM SI BEING THE RESOLUTION hDISTANCEv IN THE ITH DIMENSION AND F¼ BINATORIAL TERM
¤ . ³ $ - G $ . - . $ ¥ ¦ - ´µ
&IGURE GIVES AN EXAMPLE OF THE APPLICATION OF %QS TO TO A RADAR WITH K0 AND K0 )NCREASING THE NUMBER OF DETECTIONS REQUIRED TO FORM
&)'52% 6ARIATION OF THE EXPECTED NUMBER OF FALSE TRACKS WITH THE TRACK FORMATION - OUT OF . CRITE RION AFTER 7 ' "ATH ET AL
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A TRACK FROM THREE OUT OF FIVE TO FIVE OUT OF EIGHT INCREASES THE DENSITY OF FALSE ALARMS THAT CAN BE TOLERATED BY MORE THAN AN ORDER OF MAGNITUDE &ORWARD AND BACKWARD TRACKING ALGORITHMS PRODUCE SIMILAR NUMBERS OF FALSE TRACKS (OWEVER THE BACKWARD TRACKING ALGORITHMS CAN OPERATE IN MORE AMBIGUOUS SITUATIONS WHERE THE DENSITY OF FALSE ALARMS K IS COMPARABLE TO OR GREATER THAN K& OR K0 5NDER THESE AMBIGUOUS CIRCUMSTANCES THE FORWARD TRACKER WILL HAVE MULTIPLE DETECTIONS IN A TRACK FORMATION OR PROMOTION GATE AND WILL REQUIRE MULTIPLE HYPOTHESIS TO RELIABLY FORM TRACKS 4HE DESIGN OF THE TRACK FORMATION PROCESS AND THE AUTOMATIC DETECTION PROCESS SHOULD BE CONSIDERED TOGETHER ! LONGER TIME ALLOWED FOR TRACK FORMATION HIGHER -. ALLOWS THE RADAR DETECTION PROCESS TO USE LOWER DETECTION THRESHOLDS RESULT ING IN BETTER RADAR SENSITIVITY &OR ANY GIVEN SET OF RADAR PARAMETERS -. TRACK FORMATION CRITERION AND PROBABILITY DISTRIBUTION OF CLUTTER AMPLITUDES THERE EXISTS AN OPTIMUM FALSE ALARM RATE THAT MINIMIZES THE SIGNAL TO NOISE RATIO REQUIRED TO DETECT TARGETS &IGURE ILLUSTRATES THIS OPTIMIZATION FOR AN EIGHT SCAN TRACK FOR MATION PROCESS
&)'52% /VERALL SENSITIVITY OF AN AUTOMATIC DETECTION AND AUTOMATIC TRACKING PROCESS WORKING TOGETHER 4HE SINGLE SCAN FALSE ALARM PROBABILITY CAN BE OPTIMIZED TO PROVIDE THE LOWEST REQUIRED SIGNAL TO NOISE RATIO FOR VARI OUS PROBABILITY DISTRIBUTIONS OF CLUTTER AMPLITUDE AFTER 0RENGAMAN ET AL Ú )%%%
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2!$!2 (!.$"//+
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)DEALLY A SINGLE RADAR CAN RELIABLY DETECT AND TRACK ALL TARGETS OF INTEREST (OWEVER THE ENVIRONMENT AND THE LAWS OF PHYSICS OFTEN WILL NOT PERMIT THIS )N GENERAL NO SINGLE RADAR CAN PROVIDE A COMPLETE SURVEILLANCE AND TRACKING PICTURE 2ADAR NETWORKING CAN BE A GOOD SOLUTION TO THIS PROBLEM AND IN SOME CASES MAY BE MORE COST EFFECTIVE THAN SOLVING THE PROBLEM THROUGH ONE VERY HIGH PERFORMANCE RADAR 2ADAR NETWORKING SYSTEMS ARE GENERALLY CHARACTERIZED BY WHAT RADAR DATA ARE SHARED AND HOW THEY ARE CORRELATED AND FUSED 4HE TWO MOST COMMON WAYS OF COMBINING RADAR DATA ARE AS FOLLOWS
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$ETECTION TO TRACK FUSION SEE &IGURE UPPER HALF ASSOCIATES EACH DETECTION TO THE NETWORKED TRACK CALCULATED POTENTIALLY USING DETECTIONS FROM ALL RADARS 4HUS THE ENTIRE STREAM OF DETECTIONS UP TO THE PRESENT IS POTENTIALLY AVAILABLE TO CALCU LATE THE TRACK STATE USED FOR THE ASSOCIATION DECISION ON THE MOST RECENT DETECTION 4RACK TO TRACK FUSION SEE &IGURE LOWER HALF ASSOCIATES EACH DETECTION TO A SINGLE RADAR TRACK STATE CALCULATED USING ONLY DETECTIONS FROM THAT RADAR 4HE SINGLE RADAR TRACK STATES ARE THEN GROUPED WITH EACH OTHER TO PRODUCE A NETTED TRACK STATE 4HE DESIGN DECISION AS TO WHICH APPROACH IS BETTER FOR GROUPING DATA DEPENDS ON THE RADARS AND TARGETS INVOLVED /NE CASE WHERE DETECTION TO TRACK ASSOCIATION IS CLEARLY BET TER IS WHEN THE RADARS HAVE A REDUCED PROBABILITY OF DETECTION SO THERE ARE POTENTIAL GAPS IN THE DATA STREAM OR PERIODS WHERE THE DATA STREAM IS SPARSE )N THESE CASES A MUCH MORE ACCURATE TRACK STATE CAN BE CALCULATED USING MULTIPLE DATA STREAMS THAN USING ONLY ONE BECAUSE MULTIPLE STREAMS WILL TEND TO FILL IN THE GAPS IN DETECTION AND RESTORE A HIGH CON SISTENT DATA RATE DURING PERIODS OF REDUCED PROBABILITY OF DETECTION &IGURE ILLUSTRATES THE SENSITIVITY TO TARGET FADES BY PLOTTING THE TRACK REGION OF UNCERTAINTY 2/5 VERSUS THE PROBABILITY OF DETECTION FOR SINGLE RADAR TRACKING AND MULTIPLE RADAR TRACKING 4HE 2/5 IS DEFINED AS THE DISTANCE THAT CONTAINS THE ERROR WITH PERCENT PROBABILITY AND IS 2/5 TRACKING ERROR DUE TO DETECTION NOISE TRACKING ERROR DUE TO MANEUVER 4HIS CAN BE CALCULATED FOR ANY CASE OF INTEREST USING THE FORMULAS IN 4ABLE
&)'52% 4HERE ARE TWO COMMON METHODS OF FUSION DATA IN RADAR NETWORKING DETECTION TO TRACK AND TRACK TO TRACK AFTER 7 "ATH Ú )%%
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&)'52% #OMPARISON OF DETECTION TO TRACK AND TRACK TO TRACK ASSOCIATION &OR FAD ING TARGETS 0D DETECTION TO TRACK IS PREFERRED &OR LARGE SENSOR BIASES AND NON FADING TARGETS TRACK TO TRACK IS PREFERRED AFTER 7"ATH Ú )%%
7HEN THE PROBABILITY OF DETECTION IS MUCH LESS THAN UNITY THE MEASUREMENT TO TRACK FUSION IS CONSIDERABLY MORE ACCURATE 4HIS IS EASILY EXPLAINED BY THE FACT THAT THE PROB ABILITY OF A SIGNIFICANT OUTAGE OF DATA IS MUCH REDUCED IF TWO SOURCES ARE AVAILABLE 7ITH A MORE ACCURATE TRACK TIGHTER ASSOCIATION CRITERIA CAN BE USED FOR DETECTIONS )F THE BIASES CANNOT BE EFFECTIVELY REMOVED THEN THERE MAY BE AN ADVANTAGE TO ASSO CIATING TO A SINGLE RADAR TRACKWHICH BY DEFINITION IS UNBIASED WITH RESPECT TO ITSELF )F BIASES CANNOT BE KEPT SMALLER THAN THE 2/5 THEN AT HIGH PROBABILITIES OF DETECTION ONE PREFERS SINGLE RADAR ASSOCIATION FOLLOWED BY TRACK TO TRACK ASSOCIATION )T IS POSSIBLE TO MAKE SIMPLE COMPARISONS BETWEEN THE ACCURACY OF DETECTION FUSION AS OPPOSED TO TRACK FUSION FOR EQUIVALENT USE OF DATA BANDWIDTH TO EXCHANGE RADAR DATA 7HEN 2/5 IS PLOTTED AS A FUNCTION OF THE POSITION GAIN @ IT HAS THE hBATHTUBv SHAPE SHOWN BY THE SINGLE RADAR CURVE IN &IGURE 4HE LEFT HAND SIDE OF THE hBATHTUBv IS DOMINATED BY THE LAG COMPONENT WHILE THE RIGHT HAND SIDE IS DOMINATED BY THE RADAR MEASUREMENT NOISE COMPONENT "ECAUSE THE GAINS HORIZONTAL AXIS ARE THE DESIGNERS CHOICE THE SINGLE RADAR 2/5 IS THE MINIMUM OF THE hBATHTUBv CURVE .OW CONSIDER THE FUSION OF TWO RADARS IN A PARTICULAR DIMENSION )F ONE RADAR HAS ONE TENTH THE 2/5 OF THE OTHER IN THIS DIMENSION THEN THE MORE ACCURATE RADAR IN THIS DIMENSION WILL DOMINATE AND ESSENTIALLY DETERMINE THE RESULT !T LEAST IN STEADY STATE IT IS RELATIVELY EASY TO PRODUCE THIS DOMINANCE BY ANY OF THE FUSION METHODS /F MORE INTEREST IS THE CASE WHERE THE RADARS ARE COMPARABLE IN TERMS OF ACCURACY AND UPDATE RATE PRODUCING COMPA RABLE 2/5S 4HIS CASE MORE CLEARLY SHOWS THE DIFFERENCE IN THE FUSION METHODS &OR EXAMPLE WHEN TWO IDENTICAL RADARS ARE COMBINED BY DETECTION FUSION THEN THE UPDATE RATE IS ESSENTIALLY DOUBLED 4HIS REDUCES THE LAG BY A FACTOR OF ALLOWING A SMALLER GAIN TO BE SELECTED OPTIMIZATION MORE TO THE LEFT OF THE hBATHTUBv REDUCING THE TRACKING ERRORS DUE TO MEASUREMENT NOISE 4HE NET RESULT IS THE MOVEMENT FROM THE SINGLE RADAR CURVE TO THE DETECTION FUSION CURVE IN &IGURE
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&)'52% #OMPARISON OF DETECTION FUSION AND TRACK FUSION APPROACHES &OR AIR BREATHING TARGETS DETECTION FUSION PRODUCES THE MOST ACCURATE TRACK SMALLEST 2/5 AFTER 7"ATH Ú )%%
7HEN TWO IDENTICAL RADARS ARE COMBINED BY TRACK FUSION THE UPDATE RATE FOR EACH TRACKING PROCESS DOES NOT CHANGE AND SO THE LAG DOES NOT CHANGE (OWEVER THE STAN DARD DEVIATION OF THE TRACKING ERRORS DUE TO MEASUREMENT NOISE IS REDUCED BY THE SQUARE ROOT OF ALLOWING A LARGER GAIN TO BE SELECTED OPTIMIZATION MORE TO THE RIGHT OF THE BATHTUB REDUCING THE LAG 4HE NET RESULT IS THE MOVEMENT FROM THE SINGLE RADAR CURVE TO THE TRACK FUSION CURVE IN &IGURE )F THERE IS ANY SIGNIFICANT MANEUVER POSSIBLE THE FACTOR OF IN LAG WILL HAVE A MORE SIGNIFICANT EFFECT THAN THE FACTOR OF THE SQUARE ROOT OF IN THE SQUARE ROOT OF THE TRACKING ERRORS DUE TO MEASUREMENT NOISE 4HUS ONE CAN SEE THE DETECTION FUSION CURVE ACHIEVES A SIGNIFICANTLY LOWER MINIMUM THAN THE TRACK FUSION CURVE 4O COMBINE DATA FROM MULTIPLE RADARS THE DATA MUST BE PLACED IN A COMMON COOR DINATE SYSTEM 4HIS PROCESS IS CALLED GRID LOCKING AND INVOLVES SPECIFYING THE LOCATION OF THE RADARS AND ESTIMATING RADAR BIASES IN RANGE AND ANGLE 4HE PREVIOUS DIFFICULT PROBLEM OF RADAR LOCATION IS SOLVED TRIVIALLY BY THE GLOBAL POSITIONING SYSTEM !N ESTI MATE OF RADAR BIASES BETWEEN TWO RADARS CAN BE OBTAINED FROM A LONG TERM AVERAGE OF THE DIFFERENCE BETWEEN PREDICTED AND MEASURED COORDINATES ON ALL TRACKS THAT HAVE A SUBSTANTIAL NUMBER OF DETECTIONS FROM BOTH RADARS
Ç°xÊ 1 - -",Ê / ,/" ! NUMBER OF SENSORS CAN BE INTEGRATED RADAR IDENTIFICATION FRIEND OR FOE )&& THE AIR TRAFFIC CONTROL RADAR BEACON SYSTEM !4#2"3 INFRARED OPTICAL AND ACOUSTIC 4HE SENSORS THAT ARE MOST EASILY INTEGRATED ARE THE ELECTROMAGNETIC SENSORS IE RADAR )&& AND STROBE EXTRACTORS OF NOISE SOURCES OR EMITTERS
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2!$!2 (!.$"//+
)&& )NTEGRATION 4HE PROBLEM OF INTEGRATING RADAR AND MILITARY )&& DATA IS LESS DIFFICULT THAN THAT OF INTEGRATING TWO RADARS 4HE QUESTION OF WHETHER DETECTIONS OR TRACKS SHOULD BE INTEGRATED IS A FUNCTION OF THE APPLICATION )N A MILITARY SITUATION BY INTEGRATING DETECTIONS ONE COULD INTERROGATE THE TARGET ONLY A FEW TIMES IDENTIFY IT AND THEN ASSOCIATE IT WITH A RADAR TRACK &ROM THEN ON THERE WOULD BE LITTLE NEED FOR RE INTERROGATING THE TARGET (OWEVER IN AN AIR TRAFFIC CONTROL SITUATION USING !4#2"3 TARGETS WOULD BE INTERROGATED AT EVERY SCAN AND CONSEQUENTLY EITHER DETECTIONS OR TRACKS COULD BE INTEGRATED 2ADARn$& "EARING 3TROBE )NTEGRATION #ORRELATING RADAR TRACKS WITH $& DIRECTION FINDING BEARING STROBES ON EMITTERS HAS BEEN CONSIDERED BY #OLEMAN AND LATER BY 4RUNK AND 7ILSON 4RUNK AND 7ILSON CONSIDERED THE PROBLEM OF ASSOCI ATING EACH $& TRACK WITH EITHER NO RADAR TRACK OR ONE OF M RADAR TRACKS )N THEIR FOR MULATION THERE WERE + $& ANGLE TRACKS EACH SPECIFIED BY A DIFFERENT NUMBER OF $& DETECTIONS AND SIMILARLY M RADAR TRACKS EACH SPECIFIED BY A DIFFERENT NUMBER OF RADAR DETECTIONS "ECAUSE EACH TARGET CAN CARRY MULTIPLE EMITTERS IE MULTIPLE $& TRACKS CAN BE ASSOCIATED WITH EACH RADAR TRACK EACH $& TRACK ASSOCIATION CAN BE CONSIDERED BY ITSELF RESULTING IN + DISJOINT ASSOCIATION PROBLEMS #ONSEQUENTLY AN EQUIVALENT PROBLEM IS GIVEN A $& TRACK SPECIFIED BY N $& BEARING DETECTIONS ONE CAN ASSOCIATE THE $& TRACK WITH NO RADAR TRACK OR WITH ONE OF M RADAR TRACKS THE JTH RADAR TRACK BEING SPECIFIED BY MJ RADAR DETECTIONS 5SING A COMBINATION OF "AYES AND .EYMAN 0EARSON PROCEDURES AND ASSUMING THAT THE $& DETECTION ERRORS ARE USUALLY INDEPENDENT AND GAUSSIAN DISTRIBUTED WITH ZERO MEAN AND CONSTANT VARIANCE R BUT WITH OCCASIONAL OUT LIERS IE LARGE ERRORS NOT DESCRIBED BY THE GAUSSIAN DENSITY 4RUNK AND 7ILSON ARGUED THAT THE DECISION SHOULD BE BASED ON THE PROBABILITY
0J PROBABILITY : q DJ
WHERE : HAS A CHI SQUARE DENSITY WITH NJ DEGREES OF FREEDOM AND DJ IS GIVEN BY NJ
D J £ MIN[ ;Q E TI Q J TI = S ] I
J M
WHERE NJ IS THE NUMBER OF $& DETECTIONS OVERLAPPING THE TIME INTERVAL FOR WHICH THE JTH RADAR TRACK EXISTS PETI IS THE $& DETECTION AT TIME TI PJTI IS THE PREDICTED AZIMUTH OF RADAR TRACK J FOR TIME TI AND THE FACTOR LIMITS THE SQUARE ERROR TO R TO ACCOUNT FOR $& OUTLIERS "Y USING THE TWO LARGEST 0JS DESIGNATED 0MAX AND 0NEXT AND THRESHOLDS 4, 4( 4- AND 2 THE FOLLOWING DECISIONS AND DECISION RULES WERE GENERATED &IRM CORRELATION $& SIGNAL GOES WITH RADAR TRACK HAVING LARGEST 0J IE 0MAX WHEN 0MAX q 4( AND 0MAX q 0NEXT 2 4ENTATIVE CORRELATION $& SIGNAL PROBABLY GOES WITH RADAR TRACK HAVING LARGEST 0J IE 0MAX WHEN 4( 0MAX q 4- AND 0MAX q 0NEXT 2 4ENTATIVE CORRELATION WITH SOME TRACK $& SIGNAL PROBABLY GOES WITH SOME RADAR TRACK BUT CANNOT DETERMINE WHICH WHEN 0MAX q 4- BUT 0MAX 0NEXT 2 4ENTATIVELY UNCORRELATED $& SIGNAL PROBABLY DOES NOT GO WITH ANY RADAR TRACK WHEN 4- 0MAX 4, &IRMLY UNCORRELATED $& SIGNAL DOES NOT GO WITH ANY RADAR TRACK WHEN 4, q 0MAX
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4HE LOWER THRESHOLD 4, DETERMINES THE PROBABILITY THAT THE CORRECT RADAR TRACK IE THE ONE ASSOCIATED WITH THE $& SIGNAL WILL BE INCORRECTLY REJECTED FROM FURTHER CONSID ERATION )F THE DESIRED REJECTION RATE FOR THE CORRECT TRACK IS 02 ONE CAN OBTAIN THIS BY SETTING 4, 02 4HE THRESHOLD 4( IS SET EQUAL TO 0FA DEFINED AS THE PROBABILITY OF FALSELY ASSOCIATING A RADAR TRACK WITH A $& SIGNAL WHEN THE $& SIGNAL DOES NOT BELONG WITH THE RADAR TRACK 4HE THRESHOLD 4( IS A FUNCTION OF THE AZIMUTH DIFFERENCE L BETWEEN THE TRUE $& POSITION AND THE RADAR TRACK UNDER CONSIDERATION 4HE THRESHOLD 4( WAS FOUND FOR L R AND L R BY SIMULATION TECHNIQUES AND THE RESULTS FOR 0FA ARE SHOWN IN &IGURE "ETWEEN THE HIGH AND LOW THRESHOLDS THERE IS A TENTATIVE REGION 4HE MIDDLE THRESHOLD DIVIDES THE hTENTATIVEv REGION INTO A TENTATIVELY CORRELATED REGION AND A TENTATIVELY UNCORRELATED REGION 4HE RATIONALE IN SETTING THE THRESHOLD IS TO SET THE TWO ASSOCIATED ERROR PROBABILITIES EQUAL FOR A PARTICULAR SEPARATION 4HE THRESHOLD 4- WAS FOUND BY USING SIMULATION TECHNIQUES AND IS ALSO SHOWN IN &IGURE 4HE PROBABILITY MARGIN 2 ENSURES THE SELECTION OF THE PROPER $& RADAR ASSOCIATION AVOIDING RAPIDLY CHANGING DECISIONS WHEN THERE ARE TWO OR MORE RADAR TRACKS CLOSE TO ONE ANOTHER 4HE CORRECT SELECTION IS REACHED BY POSTPONING A DECISION UNTIL THE TWO HIGHEST ASSOCIATION PROBABILITIES DIFFER BY 2 4HE VALUE FOR 2 IS FOUND BY SPECIFYING A PROBABILITY OF AN ASSOCIATION ERROR 0E ACCORDING TO 0E 0 0MAX q 0NEXT 2 WHERE 0MAX CORRESPONDS TO AN INCORRECT ASSOCIATION AND 0NEXT CORRESPONDS TO THE CORRECT ASSOCIATION 4HE PROBABILITY MARGIN 2 IS A FUNCTION OF 0E AND THE SEPARATION L OF THE RADAR TRACKS 4HE PROBABILITY MARGIN 2 WAS FOUND FOR L R R AND R BY USING SIMULATION TECHNIQUES AND THE RESULTS FOR 0E ARE SHOWN IN &IGURE
&)'52% (IGH THRESHOLD SOLID LINES AND MIDDLE THRESHOLD DASHED LINES VERSUS NUMBER OF SAMPLES FOR TWO DIFFERENT SEPARATIONS AFTER '6 4RUNK AND *$ 7ILSON Ú )%%%
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"ECAUSE THE CURVES CROSS ONE ANOTHER ONE CAN ENSURE THAT 0E a FOR ANY L BY SETTING 2 EQUAL TO THE MAXIMUM VALUE OF ANY CURVE FOR EACH VALUE OF N 4HE ALGORITHM WAS EVALUATED BY USING SIMULATIONS AND RECORDED DATA 7HEN THE RADAR TRACKS ARE SEPARATED BY SEVERAL STANDARD DEVIATIONS OF THE DETECTION ERROR COR RECT DECISIONS ARE MADE RAPIDLY (OWEVER IF THE RADAR TRACKS ARE CLOSE TO ONE ANOTHER ERRORS ARE AVOIDED BY POSTPONING THE DECISION UNTIL SUFFICIENT DATA ARE ACCUMULATED !N INTERESTING EXAMPLE WITH RECORDED DATA IS SHOWN IN &IGURES AND &IGURE SHOWS THE RADAR AZIMUTH DETECTIONS OF THE CONTROL AIRCRAFT THE RADAR DETECTIONS OF FOUR AIRCRAFT OF OPPORTUNITY IN THE VICINITY OF THE CONTROL AIRCRAFT AND THE $& DETECTIONS ON THE RADAR ON THE CONTROL AIRCRAFT 4HE ASSOCIATION PROBABILITIES WITH AND WITHOUT LIMIT ING IN %Q ARE SHOWN IN &IGURE )NITIALLY AN AIRCRAFT OF OPPORTUNITY HAS THE HIGHEST ASSOCIATION PROBABILITY HOWEVER A FIRM DECISION IS NOT MADE BECAUSE 0MAX DOES NOT EXCEED 0NEXT BY THE PROBABILITY MARGIN !FTER THE TH $& DETECTION THE EMITTER IS FIRMLY CORRELATED WITH THE CONTROL AIRCRAFT (OWEVER AT THE TH $& DETEC TION A VERY BAD DETECTION OUTLIER IS MADE AND THE FIRM CORRELATION IS DOWNGRADED TO A TENTATIVE CORRELATION IF LIMITING IS NOT USED )F LIMITING IS EMPLOYED HOWEVER THE CORRECT DECISION REMAINS FIRM )N A COMPLEX ENVIRONMENT WHERE THERE ARE MANY RADAR TRACKS AND $& SIGNAL SOURCES IT IS QUITE POSSIBLE THAT MANY $& SIGNALS WILL BE ASSIGNED THE CATEGORY THAT THE $& SIGNAL PROBABLY GOES WITH SOME RADAR TRACK 4O REMOVE MANY OF THESE AMBIGUITIES MULTISITE $& OPERATION CAN BE CONSIDERED 4HE EXTENSION OF THE PREVIOUS PROCEDURES
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&)'52% 2ADAR DETECTIONS O AND $& DETECTIONS COLLECTED ON THE CONTROL AIRCRAFT 4HE OS $S S AND XS ARE RADAR DETECTIONS ON FOUR AIRCRAFT OF OPPORTUNITY IN THE VICINITY OF THE CONTROL AIRCRAFT AFTER '6 4RUNK AND *$ 7ILSON Ú )%%%
&)'52% !SSOCIATION PROBABILITIES FOR EXPERIMENTAL DATA 4HE BOLD LINES ARE PROBABILITIES FOR THE CONTROL AIRCRAFT THE SOLID LINE FOR LIMITING THE DASHED LINE FOR NO LIMITING THE THIN LINE THE ASSO CIATION PROBABILITY FOR THE AIRCRAFT OF OPPORTUNITY AND THE THIN DASHED LINES THE THRESHOLDS 4- AND 4( AFTER '6 4RUNK AND *$ 7ILSON Ú )%%%
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3 "LACKMAN AND 2 0OPOLI $ESIGN AND !NALYSIS OF -ODERN 4RACKING 3YSTEMS "OSTON !RTECH 2 ! 3INGER h%STIMATING OPTIMAL TRACKING FILTER PERFORMANCE FOR MANNED MANEUVERING TARGETS v )%%% 4RANS VOL !%3 PP n " &RIEDLAND h/PTIMUM STEADY STATE POSITION AND VELOCITY ESTIMATION USING NOISY SAMPLED POSI TION DATA v )%%% 4RANS VOL !%3 P 0 +ALATA h4HE TRACKING INDEX ! GENERALIZED PARAMETER FOR @ A AND @ A F TARGET TRACKERS v )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS !%3 PP n 7 $ "LAIR AND 9 "AR 3HALOM h4RACKING MANEUVERING TARGETS WITH MULTIPLE SENSORS $OES MORE DATA ALWAYS MEAN BETTER ESTIMATES v )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL PP & 2#ASTELLA h!NALYTICAL RESULTS FOR THE X Y +ALMAN TRACKING FILTER v )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS .OVEMBER VOL PP 2 & &ITZGERALD h3IMPLE TRACKING FILTERS 3TEADY STATE FILTERING AND SMOOTHING PERFORMANCE v )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 PP n ' * 0ORTMANN * -OORE AND 7 ' "ATH h3EPARATED COVARIANCE FILTERING v IN 2EC )%%% )NTERNATIONAL 2ADAR #ONFERENCE PP n 0 -OOKERJEE AND & 2EIFLER h2EDUCED STATE ESTIMATOR FOR SYSTEMS WITH PARAMETRIC INPUTS v )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL NO PP n ! 3 'ELB !PPLIED /PTIMAL %STIMATION #AMBRIDGE -! -)4 0RESS & 2 #ASTELLA h-ULTISENSOR MULTISITE TRACKING FILTER v )%% 0ROC 2ADAR 3ONAR .AVIGATION VOL ISSUE PP n % ! 7AN 2 VAN DER -ERWE AND ! 4 .ELSON h$UAL ESTIMATION AND THE UNSCENTED TRANSFORMA TION v IN !DVANCES IN .EURAL )NFORMATION 0ROCESSING 3YSTEMS #AMBRIDGE -)4 0RESS PP n ' ! 7ATSON AND 7 $ "LAIR h)-- ALGORITHM FOR TRACKING TARGETS THAT MANEUVER THROUGH COORDI NATED TURNS v 30)% 3IGNAL AND $ATA 0ROCESSING OF 3MALL 4ARGETS VOL PP n 2 #OOPERMAN h4ACTICAL BALLISTIC MISSILE TRACKING USING THE INTERACTING MULTIPLE MODEL ALGORITHM v IN 0ROC &IFTH )NTERNATIONAL #ONFERENCE ON )NFORMATION &USION VOL PP n # , -OREFIELD h!PPLICATION OF n INTEGER PROGRAMMING TO MULTI TARGET TRACKING PROBLEMS v )%%% 4RANS VOL !# PP n 2 *ONKER AND ! 6OLGENANT h! SHORTEST AUGMENTING PATH ALGORITHM FOR DENSE AND SPARSE LINEAR ASSIGNMENT PROBLEMS v #OMPUTING VOL NO PP n $ "ERTSEKAS h4HE AUCTION ALGORITHM FOR ASSIGNMENT AND OTHER NETWORK FLOW PROBLEMS ! TUTO RIAL v )NTERFACES VOL PP n ) +ADAR % %ADAN AND 2 'ASSNER h#OMPARISON OF ROBUSTIZED ASSIGNMENT ALGORITHMS v 30)% VOL PP n 9 "AR 3HALOM AND % 4SE h4RACKING IN A CLUTTERED ENVIRONMENT WITH PROBABILISTIC DATA ASSOCIA TION v !UTOMATICA VOL PP n 3 " #OLEGROVE AND * + !YLIFFE h!N EXTENSION OF PROBABILISTIC DATA ASSOCIATION TO INCLUDE TRACK INITIATION AND TERMINATION v IN TH )2%% )NT #ONV $IG -ELBOURNE !USTRAILIA PP n 3 " #OLEGROVE ! 7 $AVIS AND * + !YLIFFE h4RACK INITIATION AND NEAREST NEIGHBORS INCORPO RATED INTO PROBABILISTIC DATA ASSOCIATION v * %LEC %LECTRON %NG !USTRALIA )% !UST AND )2%% !UST VOL PP n 9 "AR 3HALOM AND 4 &ORTMANN 4RACKING AND $ATA !SSOCIATION /RLANDO &, !CADEMIC 0RESS 2 7 3ITTLER h!N OPTIMAL ASSOCIATION PROBLEM IN SURVEILLANCE THEORY v )%%% 4RANS VOL -), PP n * * 3TEIN AND 3 3 "LACKMAN h'ENERALIZED CORRELATION OF MULTI TARGET TRACK DATA v )%%% 4RANS VOL !%3 PP n
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! PULSE COMPRESSION RADAR TRANSMITS A LONG PULSE WITH PULSEWIDTH 4 AND PEAK POWER 0T WHICH IS CODED USING FREQUENCY OR PHASE MODULATION TO ACHIEVE A BANDWIDTH " THAT IS LARGE COMPARED TO THAT OF AN UNCODED PULSE WITH THE SAME DURATION 4HE TRANSMIT PULSEWIDTH IS CHOSEN TO ACHIEVE THE SINGLE PULSE TRANSMIT ENERGY GIVEN BY %T 0T4 THAT IS REQUIRED FOR TARGET DETECTION OR TRACKING 4HE RECEIVED ECHO IS PROCESSED USING A PULSE COMPRESSION FILTER TO YIELD A NARROW COMPRESSED PULSE RESPONSE WITH A MAINLOBE WIDTH OF APPROXIMATELY " THAT DOES NOT DEPEND ON THE DURATION OF THE TRANSMITTED PULSE &IGURE SHOWS A BLOCK DIAGRAM OF A BASIC PULSE COMPRESSION RADAR 4HE CODED PULSE IS GENERATED AT A LOW POWER LEVEL IN THE WAVEFORM GENERATOR AND AMPLIFIED TO THE REQUIRED PEAK TRANSMIT POWER USING A POWER AMPLIFIER TRANSMITTER 4HE RECEIVED SIGNAL IS MIXED TO AN INTERMEDIATE FREQUENCY )& AND AMPLIFIED BY THE )& AMPLIFIER 4HE SIG NAL IS THEN PROCESSED USING A PULSE COMPRESSION FILTER THAT CONSISTS OF A MATCHED FILTER TO ACHIEVE MAXIMUM SIGNAL TO NOISE RATIO 3.2 !S DISCUSSED BELOW THE MATCHED FILTER IS FOLLOWED BY A WEIGHTING FILTER IF REQUIRED FOR REDUCTION OF TIME SIDELOBES 4HE OUTPUT OF THE PULSE COMPRESSION FILTER IS APPLIED TO AN ENVELOPE DETECTOR AMPLIFIED BY THE VIDEO AMPLIFIER AND DISPLAYED TO AN OPERATOR 4HE RATIO OF THE TRANSMIT PULSEWIDTH TO THE COMPRESSED PULSE MAINLOBE WIDTH IS DEFINED AS THE PULSE COMPRESSION RATIO 4HE PULSE COMPRESSION RATIO IS APPROXIMATELY 4" OR 4" WHERE 4" IS DEFINED AS THE TIME BANDWIDTH PRODUCT OF THE WAVEFORM 4YPICALLY THE PULSE COMPRESSION RATIO AND TIME BANDWIDTH PRODUCT ARE LARGE COMPARED TO UNITY 4HE USE OF PULSE COMPRESSION PROVIDES SEVERAL PERFORMANCE ADVANTAGES 4HE INCREASED DETECTION RANGE CAPABILITY OF A LONG PULSE RADAR SYSTEM IS ACHIEVED WITH PULSE COMPRESSION WHILE RETAINING THE RANGE RESOLUTION CAPABILITY OF A RADAR THAT USES A NARROW UNCODED PULSE 4HE REQUIRED TRANSMITTED ENERGY CAN BE ESTABLISHED BY
4HE AUTHORS WOULD LIKE TO ACKNOWLEDGE THE USE OF MATERIAL PREVIOUSLY PREPARED BY %DWARD # &ARNETT AND 'EORGE ( 3TEVENS FOR THE h0ULSE #OMPRESSION 2ADARv CHAPTER IN THE SECOND EDITION OF THE 2ADAR (ANDBOOK EDITED BY -ERRILL ) 3KOLNIK
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&)'52% "LOCK DIAGRAM OF A BASIC PULSE COMPRESSION RADAR
INCREASING THE WAVEFORM PULSEWIDTH WITHOUT EXCEEDING CONSTRAINTS ON TRANSMITTER PEAK POWER 4HE AVERAGE POWER OF THE RADAR MAY BE INCREASED WITHOUT INCREASING THE PULSE REPETITION FREQUENCY 02& AND HENCE DECREASING THE RADARS UNAMBIGUOUS RANGE )N ADDITION THE RADAR IS LESS VULNERABLE TO INTERFERING SIGNALS THAT DIFFER FROM THE CODED TRANSMITTED SIGNAL 4HE MAINLOBE OF THE COMPRESSED PULSE AT THE OUTPUT OF THE MATCHED FILTER HAS TIME OR RANGE SIDELOBES THAT OCCUR WITHIN TIME INTERVALS OF DURATION 4 BEFORE AND AFTER THE PEAK OF THE PEAK OF THE COMPRESSED PULSE 4HE TIME SIDELOBES CAN CONCEAL TARGETS WHICH WOULD OTHERWISE BE RESOLVED USING A NARROW UNCODED PULSE )N SOME CASES SUCH AS PHASE CODED WAVEFORMS OR NONLINEAR FREQUENCY MODULATION WAVEFORMS MATCHED FILTER PROCESSING ALONE ACHIEVES ACCEPTABLE TIME SIDELOBE LEVELS (OWEVER FOR THE CASE OF A LINEAR FREQUENCY MODULATION WAVEFORM THE MATCHED FILTER IS GENERALLY FOLLOWED BY A WEIGHTING FILTER TO PROVIDE A REDUCTION IN TIME SIDELOBE LEVELS )N THIS CASE THE WEIGHTING FILTER RESULTS IN A SIGNAL TO NOISE RATIO LOSS COMPARED TO THAT OF MATCHED FILTER PROCESSING ALONE
n°ÓÊ *1 - Ê " *, --" Ê76 ", Ê/9* 4HE FOLLOWING SECTIONS DESCRIBE THE CHARACTERISTICS OF THE LINEAR AND NONLINEAR FRE QUENCY MODULATION WAVEFORMS PHASE CODED WAVEFORMS AND TIME FREQUENCY CODED WAVEFORMS 4HE APPLICATION OF SURFACE ACOUSTIC WAVE 3!7 DEVICES FOR LINEAR FRE QUENCY MODULATION ,&- WAVEFORM PULSE COMPRESSION IS DISCUSSED 7AVEFORM SIGNAL ANALYSIS TECHNIQUES MATCHED FILTER PROPERTIES AND THE WAVEFORM AUTOCOR RELATION AND AMBIGUITY FUNCTION DEFINITIONS USED ARE SUMMARIZED IN THE !PPENDIX AT THE END OF THIS CHAPTER
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,INEAR &REQUENCY -ODULATION 4HE LINEAR FREQUENCY MODULATION OR CHIRP WAVEFORM HAS A RECTANGULAR AMPLITUDE MODULATION WITH PULSEWIDTH 4 AND A LINEAR FREQUENCY MODULATION WITH A SWEPT BANDWIDTH " APPLIED OVER THE PULSE 4HE TIME BANDWIDTH PRODUCT OF THE ,&- WAVEFORM IS EQUAL TO 4" WHERE 4" IS THE PRODUCT OF PULSEWIDTH AND SWEPT BANDWIDTH 4HE D" WIDTH OF THE COMPRESSED PULSE AT THE OUT PUT OF THE MATCHED FILTER IS S " FOR LARGE VALUES OF TIME BANDWIDTH PRODUCT 4HE PEAK TIME SIDELOBE LEVEL OF THE COMPRESSED PULSE IS n D" !S DISCUSSED IN 3ECTION A FREQUENCY DOMAIN WEIGHTING FILTER IS GENERALLY REQUIRED FOLLOWING THE MATCHED FILTER TO PROVIDE REDUCED TIME SIDELOBE LEVELS AT THE COST OF REDUCED 3.2 AND AN INCREASE IN THE WIDTH OF THE COMPRESSED PULSE !S AN EXAMPLE THE USE OF D" 4AYLOR WEIGHTING REDUCES THE PEAK TIME SIDELOBE LEVEL FROM n D" TO n D" AND INTRODUCES A D" LOSS IN 3.2 4HE D" WIDTH OF THE COM PRESSED PULSE WITH WEIGHTING INCREASES FROM S " TO S " 4HE ,&- WAVEFORM HAS A KNIFE EDGE AMBIGUITY FUNCTION WITH CONTOURS THAT ARE APPROXIMATELY ELLIPTICAL WITH A MAJOR AXIS DEFINED BY THE LINE V @S WHERE @ o "4 IS THE ,&- SLOPE 4HIS PROPERTY INTRODUCES RANGE DOPPLER COUPLING AT THE MATCHED FILTER OUTPUT CAUSING THE MATCHED FILTER OUTPUT PEAK TO OCCUR EARLIER IN TIME FOR A TARGET WITH A POSITIVE DOPPLER FREQUENCY COMPARED TO A STATIONARY TARGET AT THE SAME RANGE ASSUMING A POSITIVE LINEAR FREQUENCY MODULATION SLOPE AND LATER IN TIME FOR A NEGATIVE SLOPE 4HE COMPRESSED PULSE SHAPE AND 3.2 ARE TOLERANT TO DOPPLER SHIFT FOR THE ,&- WAVEFORM !S A RESULT IT IS NOT NECESSARY TO IMPLEMENT MULTIPLE MATCHED FILTERS TO COVER THE RANGE OF EXPECTED TARGET DOPPLER SHIFTS ,&- 7AVEFORM $EFINITION 4HE ,&- WAVEFORM IS A SINGLE PULSE BANDPASS SIGNAL DEFINED AS
XT ! RECT T4 COS ;O F T O@ T=
WHERE 4 IS THE PULSEWIDTH F IS THE CARRIER FREQUENCY @ IS THE ,&- SLOPE AND THE RECT FUNCTION IS DEFINED AS
ª \ X \ RECTX « ¬ \ X \
4HE ,&- SLOPE IS GIVEN BY @ o "4 WHERE THE PLUS SIGN APPLIES FOR A POSITIVE ,&- SLOPE TERMED AN UP CHIRP AND THE MINUS SIGN FOR A NEGATIVE ,&- SLOPE A DOWN CHIRP 4HE AMPLITUDE MODULATION IS AT ! RECT T4 AND THE PHASE MODULATION IS A QUADRATIC FUNCTION OF TIME
E T O@ T
4HE FREQUENCY MODULATION DEFINED AS THE INSTANTANEOUS FREQUENCY DEVIATION FROM THE CARRIER FREQUENCY F IS EXPRESSED IN TERMS OF THE PHASE MODULATION BY
FI T
DF P DT
4HE FREQUENCY MODULATION FOR AN ,&- WAVEFORM IS LINEAR WITH SLOPE EQUAL TO @
FI T A T o " 4 T \ T \ a 4
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WHERE THE PLUS SIGN APPLIES FOR A POSITIVE ,&- SLOPE AND THE MINUS SIGN FOR A NEGATIVE SLOPE 4HE COMPLEX ENVELOPE OF THE ,&- WAVEFORM IS EXPRESSED IN TERMS OF THE AMPLITUDE AND PHASE MODULATION FUNCTIONS AS
UT ! RECTT4 EJO @ T
&IGURE SHOWS AN EXAMPLE OF AN ,&- BANDPASS SIGNAL WITH A PULSEWIDTH 4 §S SWEPT BANDWIDTH " -(Z AND TIME BANDWIDTH PRODUCT EQUAL TO 4" 4HE ,&- SLOPE IS "4 -(Z§S 4HE INSTANTANEOUS FREQUENCY OF THE ,&- WAVEFORM VARIES BETWEEN AND -(Z OVER THE PULSE DURATION AS INDICATED BY THE REDUCTION IN THE SPACING OF SUCCESSIVE POSITIVE GOING ZERO CROSSINGS OF THE SIGNALo ,&- 7AVEFORM 3PECTRUM 4HE SPECTRUM OF THE ,&- WAVEFORM HAS A SIGNIFI CANT AMPLITUDE VARIATION VERSUS FREQUENCY FOR SMALL TIME BANDWIDTH PRODUCTS &OR LARGE VALUES OF TIME BANDWIDTH PRODUCT THE MAGNITUDE OF THE SPECTRUM APPROACHES RECT F" UT
RECTT 4 E JPA T 4
\ 5 F \ y RECT F " FOR 4" 4HE ,&- SPECTRUM IS EXPRESSED IN TERMS OF THE COMPLEX &RESNEL INTEGRAL AND THE AMPLITUDE VARIATION PRESENT FOR LOW VALUES OF 4" IS TERMED THE &RESNEL RIPPLE ,&- 7AVEFORM !MBIGUITY &UNCTION 4HE WAVEFORM AUTOCORRELATION FUNCTION AND AMBIGUITY FUNCTION FOR AN ,&- WAVEFORM ARE GIVEN BY
C U T FD ; \ T 4 \= SINC; FD AT 4 \ T 4 \ = REECT T 4 E JP FDT
9U T FD ; \ T 4 \= SINC ; FD AT 4 \ T 4 \ = RECTT 4
WHERE THE SINC FUNCTION IS DEFINED AS
SINCX SINOX OX
4HE MATCHED FILTER TIME RESPONSE FOR A TARGET WITH DOPPLER SHIFT FD IS OBTAINED BY THE SUBSTITUTION T nT IN THE AUTOCORRELATION FUNCTION
YT C U T FD ; \ T 4 \= SINC; FD A T 4 \ T 4 \ = RECTT 4 E JP FD T
,&- 2ANGE DOPPLER #OUPLING 4HE ,&- WAVEFORM EXHIBITS RANGE DOPPLER COU PLING WHICH CAUSES THE PEAK OF THE COMPRESSED PULSE TO SHIFT IN TIME BY AN AMOUNT PROPORTIONAL TO THE DOPPLER FREQUENCY 4HE PEAK OCCURS EARLIER IN TIME AT T nFD4" FOR A POSITIVE ,&- SLOPE COMPARED TO PEAK RESPONSE FOR A STATIONARY TARGET 4HE PEAK OF THE AMBIGUITY FUNCTION IS SHIFTED TO S FD4" FOR A POSITIVE ,&- SLOPE 4IME $ELAY AND 2ANGE 2ESOLUTION 7IDTHS 4HE TIME DELAY RESOLUTION WIDTH IS EQUAL TO THE WIDTH OF THE AMBIGUITY FUNCTION AT A SPECIFIED LEVEL RELATIVE TO THE PEAK VALUE o ,OW VALUES OF CARRIER FREQUENCY AND TIME BANDWIDTH PRODUCT HAVE BEEN USED TO ILLUSTRATE THE VARIATION OF INSTANTA NEOUS FREQUENCY OVER THE PULSE IN &IGURE
05,3% #/-02%33)/. 2!$!2
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&)'52% ,&- BANDPASS SIGNAL EXAMPLE SHOWN FOR 4 §S " -(Z F -(Z
&OR THE CASE OF A LARGE TIME BANDWIDTH THE MAGNITUDE OF THE AUTOCORRELATION FUNCTION MEASURED ALONG THE RELATIVE TIME DELAY AXIS IS GIVEN BY
\ C U T \ y \SINC"T \ \T \ 4
4HE X D" TIME DELAY RESOLUTION IS MEASURED BETWEEN THE VALUES OF T FOR WHICH
LOG \ SINC"S \ X D"
4HE RANGE RESOLUTION IS EQUAL TO C TIMES THE CORRESPONDING TIME DELAY RESOLUTION WHERE C IS THE SPEED OF LIGHT 4ABLE CONTAINS A SUMMARY OF THE RESOLUTION WIDTHS FOR THE ,&- WAVEFORM ,&- 7AVEFORM %XAMPLES &IGURE SHOWS THE MAGNITUDE OF THE AUTOCORRELA TION FUNCTION AS A FUNCTION OF RELATIVE TIME DELAY T FOR DOPPLER SHIFTSp OF n -(Z AND -(Z PULSEWIDTH 4 §S SWEPT BANDWIDTH " -(Z AND ,&- SLOPE @ "4 -(Z§S ! DOPPLER SHIFT OF FD " -(Z CAUSES THE PEAK OF THE CORRELATION FUNCTION TO MOVE TO S FD4" §S &IGURE SHOWS THE RESULT WHEN THE PULSEWIDTH IS INCREASED TO §S TO YIELD A WAVEFORM WITH AN ,&- SLOPE EQUAL 4!",% ,&- 7AVEFORM 4IME $ELAY AND 2ANGE 2ESOLUTION 7IDTHS
-AINLOBE 7IDTH D" D" D" D"
4IME $ELAY 2ESOLUTION S S " S " S " S "
2ANGE 2ESOLUTION M $2 C" $2 C" $2 C" $2 C"
p 4HESE VALUES OF DOPPLER SHIFT ARE LARGE FOR MICROWAVE RADARS AND WERE SELECTED TO SHOW THE EFFECT OF RANGE DOPPLER COUPLING
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&)'52% ,&- WAVEFORM AUTOCORRELATION FUNCTION 4 §S " -(Z 4"
TO -(Z§S )N THIS CASE A DOPPLER SHIFT OF -(Z SHIFTS THE PEAK OF AUTOCOR RELATION FUNCTION TO S §S AN INCREASE OF A FACTOR OF TEN COMPARED TO THE RESULT FOR A §S PULSEWIDTH
&)'52% ,&- WAVEFORM AUTOCORRELATION FUNCTION 4 §S " -(Z 4"
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&REQUENCY $OMAIN 7EIGHTING FOR ,&- 4IME 3IDELOBE 2EDUCTION ! FREQUENCY DOMAIN WEIGHTING FILTER IS USED FOLLOWING THE MATCHED FILTER FOR TIME SIDELOBE REDUCTION 4AYLOR WEIGHTING PROVIDES A REALIZABLE APPROXIMATION TO THE IDEAL $OLPH #HEBYSHEV WEIGHTING WHICH ACHIEVES THE MINIMUM MAINLOBE WIDTH FOR A GIVEN VALUE OF PEAK TIME SIDELOBE LEVEL 4HE FREQUENCY RESPONSE OF THE EQUIVALENT LOW PASS FILTER FOR THE 4AYLOR WEIGHING FILTER IS
N ¤ MF ³ 7 F £ &M COS ¥ P ´ "µ ¦ M
WHERE &M IS THE 4AYLOR COEFFICIENT AND N IS THE NUMBER OF TERMS IN THE WEIGHTING FUNC TION 4HE COMPRESSED PULSE RESPONSE AT THE OUTPUT OF THE WEIGHTING FILTER IS GIVEN BY N
YO T SINC"T £ &M ;SINC"T M SINC"T M =
M
!S DISCUSSED BELOW THE COMPRESSED PULSE RESPONSE %Q IS BASED ON THE ASSUMP TION THAT THE TIME BANDWIDTH PRODUCT OF THE ,&- WAVEFORM IS MUCH GREATER THAN UNITY 4" 4HE FILTER MATCHING LOSS FOR 4AYLOR WEIGHTING IS GIVEN BY +LAUDER ET AL AS N
,M £ &M
M
&IGURE SHOWS A COMPARISON OF THE COMPRESSED PULSE RESPONSE FOR THREE FRE QUENCY DOMAIN WEIGHTING TYPES #URVE ! IS FOR UNIFORM WEIGHTING WHERE 7 F
&)'52% #OMPARISON OF COMPRESSED PULSE SHAPES FOR THREE FREQUENCY DOMAIN WEIGHTING FUNCTIONS
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MATCHED FILTER PROCESSING #URVE # IS FOR 4AYLOR WEIGHTING WITH n D" PEAK TIME SIDELOBE LEVEL N AND #URVE " IS FOR (AMMING WEIGHTING WHERE ¤ MF ³ 7 F & COS ¥ P ´ "µ ¦
&
4HE 4AYLOR COEFFICIENTS FOR n D" 4AYLOR WEIGHTING N ARE LISTED HERE
& & & & &
4ABLE SHOWS THE PEAK TIME SIDELOBE LEVEL D" AND D" COMPRESSED PULSE WIDTHS AND FILTER MATCHING LOSS FOR THE THREE WEIGHTING FUNCTION TYPES 4HE APPLICATION OF n D" 4AYLOR WEIGHTING REDUCES THE PEAK TIME SIDELOBE LEVEL FROM n D" TO n D" AND INCREASES THE FILTER MATCHING LOSS FROM D" TO D" 4HE D" COM PRESSED PULSE MAINLOBE WIDTH INCREASES FROM " TO " WHEN n D" 4AYLOR WEIGHTING IS USED 4HE D" AND D" MAINLOBE WIDTHS AND FILTER MATCHING LOSS FOR (AMMING WEIGHTING ARE APPROXIMATELY THE SAME AS FOR n D" 4AYLOR WEIGHTING 4HESE RESULTS ASSUME THAT THE TIME BANDWIDTH PRODUCT OF THE ,&- WAVEFORM IS MUCH GREATER THAN UNITY SO THAT THE TIME SIDELOBE PERFORMANCE IS NOT LIMITED BY THE &RESNEL AMPLITUDE RIPPLE IN THE SPECTRUM OF THE ,&- WAVEFORM #OOK AND 0AOLILLO AND #OOK AND "ERNFELD HAVE ANALYZED THE EFFECT OF THE &RESNEL AMPLITUDE RIPPLE AND PULSE RISE TIME AND FALL TIME ON TIME SIDELOBE LEVELS ! PHASE PREDISTORTION TECHNIQUE IS DESCRIBED BY #OOK AND 0AOLILLO WHICH REDUCES THE &RESNEL AMPLITUDE RIPPLE TO ALLOW LOW TIME SIDELOBES TO BE ACHIEVED FOR ,&- WAVEFORMS WITH RELATIVELY SMALL TIME BANDWIDTH PRODUCTS 2ADAR EQUIPMENT DISTORTION SOURCES ALSO ESTABLISH LIMITATIONS ON ACHIEVABLE TIME SIDELOBE LEVELS AND ARE DISCUSSED BY +LAUDER ET AL AND #OOK AND "ERNFELD 4HE METHOD OF PAIRED ECHO ANALYSIS IS USED TO EVALUATE THE EFFECT OF AMPLITUDE AND PHASE DISTORTION ON THE TIME SIDELOBE LEVELS &REQUENCY DOMAIN AMPLITUDE AND PHASE DIS TORTION IS TYPICALLY CAUSED BY FILTERS AND TRANSMISSION LINE REFLECTIONS 4IME DOMAIN AMPLITUDE AND PHASE DISTORTION TERMED MODULATION DISTORTION BY #OOK AND "ERNFELD CAN RESULT FROM POWER SUPPLY RIPPLE IN HIGH POWER TRANSMITTER AMPLIFIERS
4!",% #OMPARISON OF ,&- 7EIGHTING &ILTERS
7EIGHTING &UNCTION
0EAK 4IME 3IDELOBE ,EVEL D"
D" -AINLOBE 7IDTH S
D" -AINLOBE 7IDTH S
&ILTER -ATCHING ,OSS D"
5NIFORM 4AYLOR D" N (AMMING
" "
" "
"
"
05,3% #/-02%33)/. 2!$!2
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4AYLOR 6ERSUS #OSINE 3QUARED 0LUS 0EDESTAL 7EIGHTING &IGURE A PLOTS THE TAPER COEFFICIENT & AND PEDESTAL HEIGHT ( VERSUS THE PEAK TIME SIDELOBE LEVEL FOR COSINE SQUARED PLUS PEDESTAL WEIGHTING &OR A GIVEN PEAK TIME SIDELOBE LEVEL 4AYLOR WEIGHTING OFFERS THEORETICAL ADVANTAGES IN RANGE RESOLUTION AND 3.2 PERFORMANCE AS ILLUSTRATED IN &IGURE B AND &IGURE C
&)'52% A 4APER COEFFICIENT AND PEDESTAL HEIGHT VERSUS PEAK TIME SIDELOBE LEVEL B #OMPRESSED PULSE WIDTH VERSUS PEAK TIME SIDELOBE LEVEL C 3.2 LOSS VERSUS PEAK TIME SIDELOBE LEVEL
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3!7 $EVICES FOR ,&- 0ULSE #OMPRESSION ! 3URFACE !COUSTIC 7AVE 3!7 DEVICE CONSISTS OF AN INPUT TRANSDUCER AND AN OUTPUT TRANSDUCER MOUNTED ON A PIEZO ELECTRIC SUBSTRATE 4HESE TRANSDUCERS ARE USUALLY IMPLEMENTED AS INTERDIGITAL DEVICES THAT CONSIST OF A METAL FILM DEPOSITED ON THE SURFACE OF THE ACOUSTIC MEDIUM 4HIS METAL FILM IS MADE OF FINGERS SEE &IGURE THAT DICTATE THE FREQUENCY CHARACTERISTIC OF THE UNIT 4HE INPUT TRANSDUCER CONVERTS AN ELECTRICAL SIGNAL INTO A SOUND WAVE WITH OVER OF THE ENERGY TRAVELING ALONG THE SURFACE OF THE MEDIUM 4HE OUTPUT TRANSDUCER TAPS A PORTION OF THIS SURFACE SOUND WAVE AND CONVERTS IT BACK INTO AN ELECTRIC SIGNAL 4HE 3!7 DEVICE HAS UNIQUE FEATURES THAT DICTATE ITS USEFULNESS FOR A GIVEN RADAR APPLICATION )T REPRESENTS ONE OF THE FEW ANALOG PROCESSING DEVICES USED IN MODERN RADAR 4HE ADVANTAGES OF THE 3!7 DEVICE ARE ITS COMPACT SIZE THE WIDE BANDWIDTHS THAT CAN BE ATTAINED THE ABILITY TO TAILOR THE TRANSDUCERS TO A PARTICULAR WAVEFORM THE ALL RANGE COVERAGE OF THE DEVICE AND THE LOW COST OF REPRODUCING A GIVEN DESIGN 4HE MAJOR SHORTCOMINGS OF THE 3!7 APPROACH ARE THAT THE WAVEFORM LENGTH IS RESTRICTED 3INCE SOUND TRAVELS ABOUT TO MM§S ON THE SURFACE OF A 3!7 DEVICE A MM QUARTZ DEVICE ABOUT THE LARGEST AVAILABLE HAS A USABLE DELAY OF ABOUT §S FOR A SINGLE PASS !LSO BECAUSE EACH 3!7 DEVICE IS WAVEFORM SPECIFIC EACH WAVEFORM REQUIRES A DIFFERENT DESIGN 3!7 PULSE COMPRESSION DEVICES DEPEND ON THE INTERDIGITAL TRANSDUCER FINGER LOCA TIONS OR THE SURFACE ETCHED GRATING TO DETERMINE ITS BANDPASS CHARACTERISTICS &IGURE SHOWS THREE TYPES OF FILTER DETERMINATION APPROACHES ! WIDEBAND INPUT TRANSDUCER AND A FREQUENCY SELECTIVE DISPERSIVE OUTPUT TRANSDUCER ARE USED IN &IGURE A 7HEN AN IMPULSE IS APPLIED TO THE INPUT THE OUTPUT SIGNAL IS INITIALLY A LOW FREQUENCY THAT INCREASES BASED ON THE OUTPUT TRANSDUCER FINGER SPACINGS AT LATER PORTIONS OF THE PULSE 4HIS RESULTS
&)'52% 3!7 TRANSDUCER TYPES A DISPERSIVE OUTPUT B BOTH INPUT AND OUTPUT DISPERSIVE AND C DISPERSIVE REFLECTIONS
05,3% #/-02%33)/. 2!$!2
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IN AN UP CHIRP WAVEFORM THAT WOULD BE A MATCHED FILTER FOR A DOWN CHIRP TRANSMITTED WAVEFORM )N &IGURE B BOTH THE INPUT TRANSDUCER AND THE OUTPUT TRANSDUCER ARE DIS PERSIVE WHICH WOULD RESULT IN THE SAME IMPULSE RESPONSE AS THAT SHOWN IN &IGURE A &OR A GIVEN CRYSTAL LENGTH AND MATERIAL THE WAVEFORM DURATION FOR THE APPROACHES IN &IGURE A AND &IGURE B WOULD BE THE SAME AND IS LIMITED TO THE TIME THAT IT TAKES AN ACOUSTIC WAVE TO TRAVERSE THE CRYSTAL LENGTH &IGURE C SHOWS A REFLECTION ARRAY COMPRESSION 2!# APPROACH THAT ESSENTIALLY DOUBLES THE ACHIEVABLE PULSE LENGTH FOR THE SAME CRYSTAL LENGTH )N AN 2!# THE INPUT AND OUTPUT TRANSDUCERS HAVE A BROAD BAND WIDTH ! FREQUENCY SENSITIVE GRATING IS ETCHED ON THE CRYSTAL SURFACE TO REFLECT A PORTION OF THE SURFACE WAVE SIGNAL TO THE OUTPUT TRANSDUCER 4HIS GRATING COUPLING DOES NOT HAVE A SIGNIFICANT IMPACT ON THE SURFACE WAVE ENERGY %XCEPT FOR A INCREASE IN THE WAVEFORM DURATION THE IMPULSE RESPONSE OF THE 2!# IS THE SAME AS FOR THE APPROACHES SHOWN IN &IGURE A AND B 4HUS THESE THREE APPROACHES YIELD A SIMILAR IMPULSE RESPONSE &IGURE SHOWS A SKETCH OF A 3!7 PULSE COMPRESSION DEVICE WITH DISPERSIVE INPUT AND OUTPUT TRANSDUCERS !S THE ENERGY IN A 3!7 DEVICE IS CONCENTRATED IN ITS SUR FACE WAVE THE 3!7 APPROACH IS MUCH MORE EFFICIENT THAN BULK WAVE DEVICES WHERE THE WAVE TRAVELS THROUGH THE CRYSTAL 4HE PROPAGATION VELOCITY OF THE SURFACE WAVE IS IN THE RANGE OF TO MS DEPENDING ON THE CRYSTAL MATERIAL AND ALLOWS A LARGE DELAY IN A COMPACT DEVICE !COUSTIC ABSORBER MATERIAL IS REQUIRED AT THE CRYSTAL EDGES TO REDUCE THE REFLECTIONS AND HENCE THE SPURIOUS RESPONSES 4HE UPPER FREQUENCY LIMIT DEPENDS ON THE ACCURACY THAT CAN BE ACHIEVED IN THE FABRICATION OF THE INTERDIGITAL TRANSDUCER 4HE 3!7 DEVICE MUST PROVIDE A RESPONSE THAT IS CENTERED ON A CARRIER AS THE LOWEST FREQUENCY OF OPERATION IS ABOUT -(Z AND IS LIMITED BY THE CRYSTAL ! MATCHED FILTER 3!7 PULSE COMPRESSION DEVICE CAN USE VARIABLE FINGER LENGTHS TO ACHIEVE FREQUENCY WEIGHTING AND THIS INTERNAL WEIGHTING CAN CORRECT FOR THE &RESNEL AMPLITUDE RIPPLES IN THE &- SPECTRUM 7ITH THIS CORRECTION n D" TIME SIDELOBE LEVELS CAN BE ACHIEVED FOR A LINEAR &- WAVEFORM WITH 4" AS LOW AS 4HE LEVEL OF SIDELOBE SUPPRESSION DEPENDS UPON THE TIME BANDWIDTH PRODUCT THE WEIGHTING FUNC TION APPLIED AND FABRICATION ERRORS IN THE 3!7 DEVICE 4IME SIDELOBE LEVELS OF n D" HAVE BEEN ACHIEVED FOR 4" BETWEEN AND 4" PRODUCTS OF UP TO HAVE BEEN ACHIEVED WITH TIME SIDELOBES BETTER THAN n D" $YNAMIC RANGE IS LIMITED BY NON LINEARITIES IN THE CRYSTAL MATERIAL BUT DYNAMIC RANGES OVER D" HAVE BEEN ACHIEVED 4HE MOST COMMON 3!7 MATERIALS ARE QUARTZ LITHIUM NIOBATE AND LITHIUM TANTALITE
&)'52% 3URFACE WAVE DELAY LINE
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.ONLINEAR &REQUENCY -ODULATION 7AVEFORMS 4HE NONLINEAR &- WAVE FORM HAS SEVERAL DISTINCT ADVANTAGES OVER ,&- )T REQUIRES NO FREQUENCY DOMAIN WEIGHTING FOR TIME SIDELOBE REDUCTION BECAUSE THE &- MODULATION OF THE WAVEFORM IS DESIGNED TO PROVIDE THE DESIRED SPECTRUM SHAPE THAT YIELDS THE REQUIRED TIME SIDELOBE LEVEL 4HIS SHAPING IS ACCOMPLISHED BY INCREASING THE RATE OF CHANGE OF FREQUENCY MODULATION NEAR THE ENDS OF THE PULSE AND DECREASING IT NEAR THE CENTER 4HIS SERVES TO TAPER THE WAVEFORM SPECTRUM SO THAT THE MATCHED FILTER RESPONSE HAS REDUCED TIME SIDELOBES 4HUS THE LOSS IN SIGNAL TO NOISE RATIO ASSOCIATED WITH FREQUENCY DOMAIN WEIGHTING AS FOR THE ,&- WAVEFORM IS ELIMINATED )F A SYMMETRICAL &- MODULATION IS USED &IGURE A WITH TIME DOMAIN AMPLITUDE WEIGHTING TO REDUCE THE FREQUENCY SIDELOBES THE NONLINEAR &- WAVEFORM WILL HAVE A THUMBTACK LIKE AMBIGUITY FUNCTION &IGURE ! SYMMETRICAL WAVEFORM TYPICALLY HAS A FREQUENCY THAT INCREASES OR DECREASES WITH TIME DURING THE FIRST HALF OF THE PULSE AND DECREASES OR INCREASES DURING THE LAST HALF OF THE PULSE ! NONSYMMETRICAL WAVEFORM IS OBTAINED BY USING ONE HALF OF A SYMMETRICAL WAVEFORM &IGURE B (OWEVER THE NONSYMMETRICAL WAVEFORM RETAINS SOME OF THE RANGE DOPPLER COUPLING OF THE LINEAR &- WAVEFORM /NE OF THE PRIMARY DISADVANTAGES OF THE NONLINEAR &- WAVEFORM IS THAT IT IS LESS DOPPLER TOLERANT THAN THE ,&- )N THE PRESENCE OF DOPPLER SHIFT THE TIME SIDELOBES OF THE PULSE COMPRESSED .,&- TEND TO INCREASE COMPARED TO THOSE OF THE ,&- &IGURE SHOWN LATER IN THIS SECTION AND 4ABLE ILLUSTRATE THIS BEHAVIOR FOR A TYPICAL .,&- PULSE 4HIS CHARACTERISTIC OF THE .,&- WAVEFORM SOMETIMES NECESSITATES PROCESSING USING MULTIPLE MATCHED FILTERS OFFSET IN DOPPLER SHIFT TO ACHIEVE THE REQUIRED TIME SIDELOBE LEVEL "ECAUSE OF THE DOPPLER SENSITIVITY OF THE AMBIGUITY FUNCTION THE NONLINEAR FRE QUENCY MODULATION WAVEFORM IS USEFUL IN A TRACKING SYSTEM WHERE RANGE AND DOPPLER FREQUENCY ARE APPROXIMATELY KNOWN AND THE TARGET DOPPLER SHIFT CAN BE COMPENSATED IN THE MATCHED FILTER 4HE NONSYMMETRICAL .,&- WAVEFORM IS USED IN THE --2 SYSTEM FOR EXAMPLE WHICH DETECTS AND TRACKS ORDNANCE SUCH AS MORTARS ARTILLERY AND ROCKETS 4O ACHIEVE A n D" 4AYLOR COMPRESSED PULSE RESPONSE FOR EXAMPLE THE FRE QUENCY VERSUS TIME FREQUENCY MODULATION FUNCTION OF A NONSYMMETRICAL .,&- WAVEFORM OF BANDWIDTH " IS
¤T P NT ³ F T " ¥ £ + N SIN 4 4 ´µ ¦ N
&)'52% 3YMMETRICAL AND NONSYMMETRICAL NONLINEAR &- WAVEFORMS
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&)'52% !MBIGUITY FUNCTION OF AN ,&- WAVEFORM COMPARED TO A SYMMETRICAL .,&- WAVEFORM
WHERE THE COEFFICIENTS ARE
+ + + + + + +
/THER .,&- WAVEFORMS THAT HAVE BEEN UTILIZED IN RADAR INCLUDE THE NONSYM METRICAL SINE BASED AND TANGENT BASED WAVEFORMSe &OR THE SINE BASED WAVEFORM THE RELATIONSHIP BETWEEN TIME AND FREQUENCY MODULATION IS GIVEN AS
T F K SIN P F " 4 " P
FOR " a F a "
WHERE 4 IS THE PULSEWIDTH " IS THE SWEPT BANDWIDTH AND K IS A TIME SIDELOBE LEVEL CONTROL FACTOR 4YPICAL K VALUES ARE AND WHICH YIELD TIME SIDELOBE LEVELS OF n D" AND n D" RESPECTIVELY &IGURE IS A PLOT OF PEAK TIME SIDELOBE LEVEL AS A FUNCTION OF THE TIME SIDELOBE CONTROL FACTOR K FOR VARIOUS 4" PRODUCTS FOR THIS .,&- WAVEFORM e #OURTESY OF %DWIN - 7ATERSCHOOT ,OCKHEED -ARTIN -ARITIME AND 3ENSOR 3YSTEMS 3YRACUSE .9
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&)'52% 0EAK TIME SIDELOBE LEVEL FOR A SINE BASED .,&- WAVEFORM AS A FUNCTION OF K FACTOR #OURTESY OF $R 0ETER ( 3TOCKMANN ,OCKHEED -ARTIN -ARITIME AND 3ENSOR 3YSTEMS 3YRACUSE .9
4HE FREQUENCY MODULATION VERSUS TIME FUNCTION FOR A TANGENT BASED WAVEFORM IS GIVEN AS
F T " TAN B T 4 TAN B FOR 4 a T a 4
WHERE 4 IS THE PULSEWIDTH " IS THE SWEPT BANDWIDTH AND A IS DEFINED AS
B TAN A a A c
WHERE @ IS A TIME SIDELOBE LEVEL CONTROL FACTOR 7HEN @ IS ZERO THE TANGENT BASED .,&- WAVEFORM REDUCES TO AN ,&- WAVE FORM (OWEVER @ CANNOT BE MADE ARBITRARILY LARGE BECAUSE THE COMPRESSED PULSE TENDS TO DISTORT #OLLINS AND !TKINS DISCUSS AN EXTENSION OF THE TANGENT BASED .,&- FOR WHICH THE FREQUENCY MODULATION FUNCTION IS A WEIGHTED SUM OF TANGENT BASED AND LINEAR FREQUENCY MODULATION TERMS &IGURE SHOWS THE FREQUENCY MODULATION VERSUS TIME FUNCTIONS FOR A SINE BASED .,&- WAVEFORM WITH K A TANGENT BASED .,&- WAVEFORM WITH @ AND AN ,&- WAVEFORM 4HE SENSITIVITY OF A .,&- WAVEFORM TO DOPPLER SHIFT CAN BE SEEN IN &IGURE WHICH SHOWS THE MATCHED FILTER OUTPUT FOR A SINE BASED .,&- WAVEFORM IN THE PRES ENCE OF DOPPLER SHIFT 4HE AMBIGUITY FUNCTION OF A .,&- SINE BASED WAVEFORM IS SHOWN IN &IGURE )T CAN BE NOTED THAT THIS AMBIGUITY FUNCTION IS MORE THUMBTACK LIKE IN NATURE THAN FOR AN ,&- WAVEFORM INDICATING THAT THIS WAVEFORM IS MORE DOPPLER SENSITIVE THAN THE ,&- WAVEFORM 4ABLE PROVIDES A COMPARISON OF .,&- WAVEFORMS WITH WEIGHTED AND UNWEIGHTED ,&- FOR DIFFERENT VALUES OF THE TARGET RADIAL VELOCITY IN TERMS OF PEAK AND AVERAGE TIME SIDELOBE LEVELS AND 3.2 LOSS 4HE .,&- WAVEFORM SHOWS BETTER
05,3% #/-02%33)/. 2!$!2
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&)'52% &REQUENCY MODULATION VERSUS TIME FOR SINE BASED .,&- TANGENT BASED .,&- AND ,&- WAVEFORMS
PERFORMANCE IN TERMS OF 3.2 LOSS AND PEAK TIME SIDELOBE LEVEL 43, THAN THE ,&- WAVEFORM 4HE 43, LEVEL DOES NOT DEGRADE APPRECIABLY FOR THE ,&- WAVEFORM FOR HIGHER RADIAL VELOCITIES DEMONSTRATING THE HIGHER DOPPLER TOLERANCE OF ,&-
&)'52% -ATCHED FILTER OUTPUT OF 3 BAND §S PULSEWIDTH -(Z BAND WIDTH .,&- SINE BASED WAVEFORM WITH MS RADIAL VELOCITY #OURTESY OF %DWIN - 7ATERSCHOOT ,OCKHEED -ARTIN -ARITIME AND 3ENSOR 3YSTEMS 3YRACUSE .9
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&)'52% !MBIGUITY FUNCTION OF A SINE BASED SYMMETRICAL .,&- WAVEFORM
0HASE #ODED 7AVEFORMS )N PHASE CODED WAVEFORMS THE PULSE IS SUBDIVIDED INTO A NUMBER OF SUBPULSES EACH OF DURATION C 4. WHERE 4 IS THE PULSEWIDTH AND . IS THE NUMBER OF SUBPULSES 0HASE CODED WAVEFORMS ARE CHARACTERIZED BY THE PHASE MODULATION APPLIED TO EACH SUBPULSE "INARY 0HASE #ODES ! PHASE CODED WAVEFORM THAT EMPLOYS TWO PHASES IS CALLED BINARY OR BIPHASE CODING ! BINARY PHASE CODED WAVEFORM IS CONSTANT IN MAGNITUDE WITH TWO PHASE VALUES n OR n 4HE BINARY CODE CONSISTS OF A SEQUENCE OF EITHER S AND S OR S AND S 4HE PHASE OF THE SIGNAL ALTERNATES
4!",% #OMPARISON OF ,INEAR &- AND .ONLINEAR &- 7AVEFORM 0ERFORMANCE
7EIGHTING ,&- UNWEIGHTED ,&- UNWEIGHTED ,&- WITH n D" 4AYLOR WEIGHTING ,&- WITH n D" 4AYLOR WEIGHTING 3INE BASED .,&- WITH K 3INE BASED .,&- WITH K
4ARGET 2ADIAL 6ELOCITY MS
0EAK 43, D"
!VERAGE 43, D"
&ILTER -ATCHING ,OSS D"
o
o
o
!N 3 BAND RADAR WITH §S TRANSMIT PULSEWIDTH AND -(Z BANDWIDTH WAS USED IN THIS COMPARISON 4HE DOPPLER SHIFT EXPRESSED IN (Z IS FD K 6R 6R WHERE 6R IS THE RADIAL VELOCITY EXPRESSED IN MS 6R FOR AN OUT BOUND TARGET
!VERAGE OF 43, POWER RATIO
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BETWEEN n AND n IN ACCORDANCE WITH THE SEQUENCE OF ELEMENTS S AND S OR S AND S IN THE PHASE CODE AS SHOWN IN &IGURE "ECAUSE THE FREQUENCY IS NOT USUALLY A MULTIPLE OF THE RECIPROCAL OF THE SUBPULSE WIDTH THE CODED SIGNAL IS GENERALLY DISCON TINUOUS AT THE PHASE REVERSAL POINTS 4HIS DOES NOT IMPACT ITS TIME SIDE LOBES BUT DOES CAUSE SOME INCREASE &)'52% "INARY PHASE CODED SIGNAL IN THE SPECTRUM SIDELOBE LEVELS 5PON RECEPTION THE COMPRESSED PULSE IS OBTAINED BY MATCHED FILTER PROCESSING 4HE WIDTH OF THE COMPRESSED PULSE AT THE HALF AMPLITUDE POINT IS NOMINALLY EQUAL TO THE SUBPULSE WIDTH 4HE RANGE RESOLUTION IS HENCE PROPORTIONAL TO THE TIME DURATION OF ONE ELEMENT OF THE CODE ONE SUBPULSE 4HE TIME BANDWIDTH PRODUCT AND PULSE COM PRESSION RATIO ARE EQUAL TO THE NUMBER OF SUBPULSES IN THE WAVEFORM IE THE NUMBER OF ELEMENTS IN THE CODE /PTIMAL "INARY #ODES /PTIMAL BINARY CODES ARE BINARY SEQUENCES WHOSE PEAK SIDELOBE OF THE APERIODIC AUTOCORRELATION FUNCTION IS THE MINIMUM POSSIBLE FOR A GIVEN CODE LENGTH #ODES WHOSE AUTOCORRELATION FUNCTION OR ZERO DOPPLER RESPONSE EXHIBIT LOW SIDELOBES ARE DESIRABLE FOR PULSE COMPRESSION RADARS 2ESPONSES DUE TO MOVING TARGETS WILL DIFFER FROM THE ZERO DOPPLER RESPONSE )F THE MATCHED FILTER IS BASED ONLY ON THE ZERO DOPPLER RESPONSE AN INCREASE IN THE TIME SIDELOBES WILL RESULT 5LTIMATELY IF THE DOPPLER SHIFT BECOMES VERY LARGE THE MATCHED FILTER RESPONSE WILL DEGRADE 4HIS CAN BE ALLEVIATED BY UTILIZING A BANK OF MATCHED FILTERS COVERING THE EXPECTED RANGE OF DOPPLER SHIFTS "ECAUSE THIS IS MORE COMPUTATIONALLY INTENSIVE THAN A SINGLE MATCHED FILTER OLDER RADAR SYSTEMS TEND NOT TO EMPLOY BANKS OF FILTERS 4HE INCREASE IN COMPU TATIONAL CAPACITY OF MODERN RADAR SYSTEMS HOWEVER CAN MAKE THIS MORE ATTRACTIVE "ARKER #ODES ! SPECIAL CLASS OF BINARY CODES IS THE "ARKER CODES "ARKER CODES ARE BINARY CODES WITH PEAK TIME SIDELOBE LEVELS EQUAL TO nLOG. WHERE . IS THE LENGTH OF THE CODE 4HE ENERGY IN THE SIDELOBE REGION IS MINIMUM AND UNIFORMLY DIS TRIBUTED 4HE "ARKER CODE IS THE ONLY UNIFORM PHASE CODE THAT REACHES THIS LEVEL !LL THE KNOWN BINARY "ARKER CODES ARE LISTED IN 4ABLE /NLY BINARY "ARKER CODES OF LENGTHS AND HAVE BEEN FOUNDn ! PULSE COMPRESSION RADAR USING "ARKER CODES WOULD BE LIMITED TO A MAXIMUM TIME BANDWIDTH PRODUCT OF &IGURE SHOWS THE AUTOCORRELATION FUNCTION OF
4!",% +NOWN "INARY "ARKER #ODES
,ENGTH
#ODE
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&)'52% 3UPERPOSITION OF THE AUTOCORRELATION FUNCTIONS FOR ALL POSSIBLE BIT CODE SEQUENCES WITH THE "ARKER #ODE HIGHLIGHTED DARK SHOWN FOR ZERO DOPPLER SHIFT
A LENGTH "ARKER CODE FOR ZERO DOPPLER SHIFT SUPERIMPOSED UPON ALL POSSIBLE AUTO CORRELATION FUNCTIONS OF BIT BINARY SEQUENCES )T CAN BE SEEN THAT THE "ARKER CODE PROVIDES THE LOWEST TIME SIDELOBE LEVELS OF ALL POSSIBLE CODES
!LLOMORPHIC &ORMS ! BINARY CODE MAY BE REPRESENTED IN ANY ONE OF FOUR ALLO MORPHIC FORMS ALL OF WHICH HAVE THE SAME CORRELATION CHARACTERISTICS 4HESE FORMS ARE THE CODE ITSELF THE INVERTED CODE THE CODE WRITTEN IN REVERSE ORDER THE COMPLEMENTED CODE S CHANGED TO S AND S TO S AND THE INVERTED COMPLEMENTED CODE &OR SYM METRICAL CODES THE CODE AND ITS INVERSE ARE IDENTICAL -AXIMAL ,ENGTH 3EQUENCES -AXIMAL LENGTH SEQUENCES HAVE A STRUCTURE SIMI LAR TO RANDOM SEQUENCES AND THEREFORE POSSESS DESIRABLE AUTOCORRELATION FUNCTIONS 4HEY ARE OFTEN CALLED PSEUDORANDOM NOISE 02. SEQUENCES (ISTORICALLY THESE SEQUENCES WERE GENERATED USING N STAGES OF SHIFT REGISTERS WITH SELECTED OUTPUT TAPS USED FOR FEEDBACK SEE &IGURE 7HEN THE FEEDBACK CONNECTIONS ARE PROPERLY CHOSEN THE OUTPUT IS A SEQUENCE OF MAXIMAL LENGTH WHICH IS THE MAXIMUM LENGTH OF A SEQUENCE OF S AND S THAT CAN BE FORMED BEFORE THE SEQUENCE IS REPEATED 4HE LENGTH OF THE MAXIMAL SEQUENCE IS . N WHERE N IS THE NUMBER OF STAGES IN THE SHIFT REGISTER GENERATOR 4HE FEEDBACK CONNECTIONS THAT PROVIDE THE MAXIMAL LENGTH SEQUENCES MAY BE DETERMINED FROM A STUDY OF PRIMITIVE AND IRREDUCIBLE POLYNOMIALS !N EXTENSIVE LIST OF THESE POLYNOMIALS IS GIVEN BY 0ETERSON AND 7ELDON !LTHOUGH MAXIMAL LENGTH SEQUENCES HAVE SOME DESIRABLE AUTOCORRELATION CHAR ACTERISTICS A MAXIMUM LENGTH SEQUENCE DOES NOT GUARANTEE LOWEST TIME SIDELOBES WHEN COMPARED TO OTHER BINARY CODES !N EXAMPLE OF THIS IS PROVIDED FOR A BIT SEQUENCE &IGURE A IS A HISTOGRAM OF THE PEAK TIME SIDELOBE LEVEL FOR THE AUTO CORRELATION OF EVERY POSSIBLE COMBINATION OF A BIT CODE &IGURE B IS THE SAME BUT FOR ONLY MAXIMAL LENGTH SEQUENCES OF LENGTH CODE A SUBSET OF &IGURE A &IGURE A SHOWS A LOWEST TIME SIDELOBE LEVEL OF n D" 4HE LOWEST SIDELOBE FOR THE MAXIMAL LENGTH SEQUENCE IS SEEN FROM &IGURE B TO BE ONLY n D" &)'52% 3HIFT REGISTER GENERATOR
05,3% #/-02%33)/. 2!$!2
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#+!- ) (, %/
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"!$ ! #& - #*
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!+.!$# % + (, % *
&)'52% (ISTOGRAM OF PEAK TIME SIDELOBE LEVELS FOR BIT SEQUENCES A ALL POSSIBLE BIT SEQUENCES AND B BIT MAXIMAL LENGTH SEQUENCES
-INIMUM 0EAK 3IDELOBE #ODES "INARY CODES THAT PROVIDE MINIMUM PEAK TIME SIDE LOBE LEVELS BUT EXCEED THE TIME SIDELOBE LEVELS ACHIEVED BY "ARKER CODES n LOG . ARE TERMED MINIMUM PEAK SIDELOBE CODES 4HESE CODES ARE USUALLY FOUND USING COMPUTER SEARCH TECHNIQUES 3KOLNIK AND ,EVANON AND -OZESON PROVIDE THESE CODES FOR VARIOUS SEQUENCE LENGTHS ALONG WITH THE RESULTING TIME SIDELOBE LEVELS #OMPLEMENTARY 3EQUENCES #OMPLEMENTARY SEQUENCES CONSIST OF TWO SEQUENCES OF THE SAME LENGTH . WHOSE APERIODIC AUTOCORRELATION FUNCTIONS HAVE SIDELOBES EQUAL IN MAGNITUDE BUT OPPOSITE IN SIGN 4HE SUM OF THE TWO AUTOCORRELATION FUNCTIONS HAS A PEAK OF . AND A SIDELOBE LEVEL OF )N A PRACTICAL APPLICATION THE TWO SEQUENCES MUST BE SEPARATED IN TIME FREQUENCY OR POLARIZATION WHICH RESULTS IN DECORRELATION OF RADAR RETURNS SO THAT COMPLETE SIDELOBE CANCELLATION MAY NOT OCCUR (ENCE THEY HAVE NOT BEEN WIDELY USED IN PULSE COMPRESSION RADARS 0OLYPHASE #ODES 7AVEFORMS CONSISTING OF MORE THAN TWO PHASES MAY ALSO BE USED 0OLYPHASE CODES CAN BE CONSIDERED AS COMPLEX SEQUENCES WHOSE ELEMENTS HAVE A MAGNITUDE OF ONE BUT WITH VARIABLE PHASE 4HE PHASES OF THE SUBPULSES ALTERNATE AMONG MULTIPLE VALUES RATHER THAN JUST THE n AND n OF BINARY PHASE CODES 4HESE CODES TEND TO BE DISCRETE APPROXIMATIONS TO ,&- WAVEFORMS AND HENCE POSSESS SIMI LAR AMBIGUITY FUNCTIONS AND DOPPLER SHIFT CHARACTERISTICS 4HE AUTOCORRELATION FUNCTIONS ARE SIMILAR WITH A PEAK TO SIDELOBE RATIO OF ABOUT . &RANK #ODES 4HE &RANK CODE CORRESPONDS TO A STEPPED PHASE APPROXIMATION OF AN ,&- WAVEFORM (ERE THE PULSE IS BROKEN UP INTO - GROUPS EACH OF WHICH IS FURTHER BROKEN UP INTO - SUBPULSES (ENCE THE TOTAL LENGTH OF THE &RANK CODE IS - WITH A CORRESPONDING COMPRESSION RATIO OF - 4HE &RANK POLYPHASE CODES DERIVE THE SEQUENCE OF PHASES FOR THE SUBPULSES BY USING A MATRIX TECHNIQUE AS FOLLOWS
§ ¨ ¨ ¨ " " ¨" ¨ - - ©
! ¶ ! - · · ! - · " " · ! - ·¸
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4HE MATRIX ELEMENTS REPRESENT THE MULTIPLYING COEFFICIENTS OF A BASIC PHASE SHIFT O - WHERE - IS AN INTEGER 4HE PHASE SHIFT CORRESPONDING TO THE ELEMENT M N OF THE MATRIX CAN BE WRITTEN AS
FM N
P M N M - N - -
!N EXAMPLE OF A &RANK #ODE MATRIX FOR - IS GIVEN HERE
§ P ¨ ¨ ¨ ©¨
¶ § · P ¨ · ¨ · ¨ ·¸ ¨©
¶ ¶ § C C ¨ · C· · · ¨ · ¨ C C · ¸· ¨© C C C ·¸
#ONCATENATING THE ROWS OF THIS MATRIX YIELDS THE PHASE FOR EACH OF THE SUBPULSES &IGURE SHOWS THE PHASE MODULATION CHARACTERISTIC OF THE &RANK #ODE FOR THE ABOVE EXAMPLE .OTE HOW THE PHASE STEP BETWEEN SUBPULSES INCREASES BETWEEN SUBPULSE GROUPS WITH A LENGTH EQUAL TO FOUR 4HIS CHARACTERISTIC CAN BE REGARDED AS A STEPPED PHASE APPROXIMATION TO QUADRATIC PHASE MODULATION !S - INCREASES THE PEAK SIDELOBEnVOLTAGE RATIO APPROACHES O - 4HIS COR RESPONDS TO APPROXIMATELY A D" IMPROVEMENT OVER PSEUDORANDOM SEQUENCES OF SIMILAR LENGTH 4HE AMBIGUITY FUNCTION GROSSLY RESEMBLES THE KNIFE EDGE RIDGE CHARACTERISTIC ASSOCIATED WITH ,&- WAVEFORMS AS CONTRASTED WITH THE THUMBTACK CHARACTERISTIC OF PSEUDORANDOM SEQUENCES &IGURE (OWEVER FOR SMALL RATIOS OF DOPPLER SHIFT TO WAVEFORM BANDWIDTH A GOOD DOPPLER RESPONSE CAN BE OBTAINED FOR REASONABLE TARGET VELOCITIES ,EWIS AND +RETSCHMER #ODES 0 0 0 0 ,EWIS AND +RETSCHMER HAVE STUD IED THE 0 0 0 AND 0 POLYPHASE CODES 4HESE CODES ARE STEP APPROXIMATIONS TO THE ,&- PULSE COMPRESSION WAVEFORMS HAVE LOW RANGE SIDELOBES AND HAVE THE
&)'52% 0HASE VERSUS TIME RELATIONSHIP FOR &RANK CODE OF LENGTH -
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&)'52% !MBIGUITY FUNCTION OF A &RANK CODE OF LENGTH -
DOPPLER TOLERANCE OF THE ,&- CODES 4HE 0 AND 0 CODES ARE MODIFIED VERSIONS OF THE &RANK CODE WITH THE $# FREQUENCY TERM AT THE CENTER OF THE PULSE INSTEAD OF AT THE BEGINNING 4HEY ARE MORE TOLERANT OF RECEIVER BAND LIMITING PRIOR TO PULSE COMPRESSION ENCOUNTERED IN DIGITAL RADAR SYSTEMS 4HE 0 CODES CONTAINS - ELEMENTS AS DOES THE &RANK CODE BUT THE RELATIONSHIP OF THE ITH ELEMENT TO THE JTH GROUP IS EXPRESSED AS
FI J P - ; - J =; J - I =
WHERE I AND J ARE INTEGERS RANGING FROM TO - 0 CODES ARE SIMILAR BUT THE PHASE IS SYMMETRIC WITH THE FOLLOWING CHARACTERISTIC
FI J [P ; - - = P - I J ]; - J=
4HE 0 AND 0 CODES ARE DERIVED BY ESSENTIALLY CONVERTING AN ,&- WAVEFORM TO BASEBAND 4HESE TEND TO BE MORE DOPPLER TOLERANT THAN THE &RANK 0 OR 0 CODES AND ARE ALSO MORE TOLERANT OF PRECOMPRESSION BANDWIDTH LIMITATIONS THAT APPEAR IN RADAR SYSTEMS 4HE PHASE OF THE 0 CODE IS GIVEN AS
JN
P N x . n N .
4HE 0 CODE PHASE RELATIONSHIP IS SIMILAR
FN
P N
P K a N a . .
4ABLE SUMMARIZES THE PHASE AND AUTOCORRELATION CHARACTERISTICS OF THE &RANK CODE AND THE ,EWIS AND +RETSCHMER 0 THROUGH 0 POLYPHASE CODES
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4!",% 3UMMARY OF 0HASE AND !UTOCORRELATION #HARACTERISTICS OF &RANK AND ,EWIS AND +RETSCHMER 0OLYPHASE #ODES
0OLYPHASE #ODE 0HASE
&RANK
P I J . I x. J x.
P 0
0
0
0HASE VS 4IME #HARACTERISTIC !UTOCORRELATION D" . %XAMPLE . %XAMPLE
; - J =
s ;J - I = FOR ITH ELEMENT IN THE JTH GROUP
[P ; - - =
P - I J ] ; ; - J= FOR ITH ELEMENT IN THE JTH GROUP
P N . N x . n
0
P N
PK . a N a .
0N K 0OLYPHASE #ODES 7HEREAS THE PREVIOUSLY DISCUSSED POLYPHASE CODES ARE DERIVED FROM ,&- WAVEFORMS 0N K CODES ARE DERIVED FROM STEP APPROXIMATIONS OF THE PHASE CHARACTERISTIC OF THE WEIGHTING FUNCTION OF .,&- WAVEFORMS 4HE WEIGHT ING FUNCTION IS GIVEN BY
¤P F ³ 7 F K K COSN ¥ ´ ¦ "µ
WHERE K AND N ARE PARAMETERS OF THE WEIGHTING FUNCTION " IS THE SWEPT BANDWIDTH OF THE WAVEFORM AND n" a F a " 4HIS IS A COSN WEIGHTING ON A PEDESTAL OF HEIGHT K &IGURE (AMMING WEIGHTING IS ACHIEVED FOR N AND K
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N
&)'52% COS ON PEDESTAL WEIGHTING FUNCTION SHOWN FOR N
&OR THE CASE WHERE N THE WEIGHTING FUNCTION CAN BE INTEGRATED TO OBTAIN THE FOLLOWING RELATIONSHIP BETWEEN TIME AND FREQUENCY
T F A SIN P F " WHERE A n K K 4 "
WHICH IS SIMILAR TO THE SINE BASED .,&- DISCUSSED EARLIER 4HIS PARTICULAR CODE IS CALLED 0HASE FROM .ONLINEAR &REQUENCY 0., AND ITS AUTOCORRELATION FUNCTION IS SHOWN IN &IGURE FOR A §S PULSEWIDTH -(Z BANDWIDTH WAVEFORM WITH A AND FD 4HE TIME SIDELOBE LEVELS ARE SEEN TO BE BELOW n D" 4HE AMBIGUITY FUNCTION IS SIMILAR TO THAT PROVIDED IN THE DISCUSSION OF .,&- WHICH IS EXPANDED IN &IGURE TO SHOW IN MORE DETAIL THE IMPACT OF DOPPLER SHIFT ON THE PULSE COMPRESSED WAVEFORM FOR PRACTICAL VALUES OF DOPPLER SHIFTS
&)'52% §S 0., PULSE AUTOCORRELATION FUNCTION FOR 4" A AND FD
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&)'52% %XPANDED VIEW OF 0., AMBIGUITY DIAGRAM FOR §S PULSE A AND " -(Z
!S THE DOPPLER SHIFT MOVES AWAY FROM ZERO THE PEAK DECREASES AND THE CLOSE IN TIME SIDELOBE LEVELS ON ONE SIDE OR THE OTHER BEGIN TO INCREASE .OTE THAT AN F" RATIO OF CORRESPONDS TO A DOPPLER SHIFT ASSOCIATED WITH APPROXIMATELY A -ACH TARGET AT A 3 BAND CARRIER FREQUENCY )N GENERAL FOR 0N K WAVEFORMS THE INTEGRAL OF THE WEIGHTING FUNCTION PROVIDES THE RELATIONSHIP BETWEEN TIME AND FREQUENCY MODULATION AS SHOWN IN %Q PF
T " ;K K COSN X = DX 4 P ¯ P
3INCE FREQUENCY MODULATION IS PROPORTIONAL TO THE TIME DERIVATIVE OF PHASE PHASE IS OBTAINED BY INTEGRATING THE FREQUENCY WITH RESPECT TO TIME 4HE EXPRESSION FOR FRE QUENCY HOWEVER IS NOT STRAIGHTFORWARD AND IS USUALLY OBTAINED THROUGH NUMERICAL EVALUATION 1UADRIPHASE #ODES 1UADRIPHASE CODES ARE AN EXAMPLE OF A PHASE CODED WAVE FORM WITHOUT PHASE DISCONTINUITIES 1UADRIPHASE CODES ARE BASED ON THE USE OF SUBPULSES WITH A HALF COSINE SHAPE AND PHASE CHANGES BETWEEN ADJACENT SUBPULSES OF MULTIPLES OF on 4HE COSINE WEIGHTING PROVIDES FASTER SPECTRUM ROLL OFF LOWER FILTER MATCHING LOSS AND SMALLER RANGE SAMPLING LOSS WHEN COMPARED TO RECTANGULAR SUBPULSE PHASE CODED WAVEFORMS 4ABLE
4!",% 1UADRIPHASE 7AVEFORM 0ERFORMANCE 3UMMARY
2ADIATED 3PECTRUM D" 7IDTH &ALLOFF C SUBPULSE DURATION 2ANGE 3AMPLING ,OSS &ILTER -ATCHING ,OSS
1UADRIPHASE #ODE
2ECTANGULAR 3UBPULSE #ODE
C D" /CTAVE D" D"
C D" /CTAVE D" D"
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&)'52% 4IME FREQUENCY CODED WAVEFORM
4IME &REQUENCY #ODED 7AVEFORMS ! TIME FREQUENCY CODED WAVEFORM &IGURE CONSISTS OF A TRAIN OF . PULSES WITH EACH PULSE AT A DIFFERENT FREQUENCY 'ENERALLY THE FREQUENCIES ARE EQUALLY SPACED AND THE PULSES ARE OF THE SAME AMPLI TUDE 4HE AMBIGUITY FUNCTION FOR A PERIODIC WAVEFORM OF THIS TYPE CONSISTS OF A CENTRAL SPIKE PLUS MULTIPLE SPIKES OR RIDGES DISPLACED IN TIME AND FREQUENCY !LTHOUGH IT IS UNACHIEVABLE IN PRACTICE THE OBJECTIVE IS TO CREATE A HIGH RESOLUTION THUMBTACK LIKE CENTRAL SPIKE WITH A CLEAR AREA AROUND IT -EASUREMENT IS THEN PERFORMED ON THE HIGH RESOLUTION CENTRAL SPIKE 4HE RANGE RESOLUTION OR COMPRESSED PULSE WIDTH IS DETERMINED BY THE TOTAL BANDWIDTH OF ALL THE PULSES AND THE DOPPLER RESOLUTION IS DETERMINED BY THE RECIPROCAL OF THE WAVEFORM DURATION 4 &OR EXAMPLE A TYPICAL WAVEFORM IN THIS CLASS HAS . CONTIGUOUS PULSES OF WIDTH T WHOSE SPECTRA OF WIDTH S ARE PLACED SIDE BY SIDE IN FREQUENCY TO ELIMINATE GAPS IN THE COMPOSITE SPECTRUM 3INCE THE WAVEFORM BAND WIDTH IS NOW .S THE NOMINAL COMPRESSED PULSE WIDTH IS S . 4HESE RELATIONSHIPS ARE SUMMARIZED IN 4ABLE 3HAPING OF THE HIGH RESOLUTION CENTRAL SPIKE AREA AS WELL AS THE GROSS STRUCTURE OF THE AMBIGUITY SURFACE CAN BE ACCOMPLISHED BY VARIATIONS OF THE BASIC WAVEFORM PARAM ETERS SUCH AS AMPLITUDE WEIGHTING OF THE PULSE TRAIN STAGGERING OF THE PULSE REPETITION INTERVAL AND FREQUENCY OR PHASE CODING OF THE INDIVIDUAL PULSES #OSTAS #ODES #OSTAS CODES ARE A CLASS OF FREQUENCY CODED WAVEFORMS THAT HAVE NEAR IDEAL RANGE AND DOPPLER SIDELOBE BEHAVIOR )N OTHER WORDS THEIR AMBI GUITY FUNCTION APPROACHES THE IDEAL THUMBTACK PROVIDING BOTH DOPPLER AND RANGE INFORMATION &IGURE !LL SIDELOBES EXCEPT FOR A FEW NEAR THE ORIGIN HAVE AN AMPLITUDE OF - ! FEW SIDELOBES CLOSE TO THE ORIGIN ARE ABOUT TWICE AS LARGE OR ABOUT - WHICH IS CHARACTERISTIC OF #OSTAS CODES 4HE COMPRESSION RATIO OF A #OSTAS CODE IS ABOUT - 4HE #OSTAS CODE IS A BURST OF - CONTIGUOUS UNCODED PULSE WAVEFORMS EACH WITH A DIFFERENT FREQUENCY SELECTED FROM A FINITE SET OF - EQUALLY SPACED FREQUENCIES THAT ARE 4!",% . 0ULSES #ONTIGUOUS IN 4IME AND &REQUENCY
7AVEFORM DURATION 4 7AVEFORM BANDWIDTH " 4IME BANDWIDTH PRODUCT 4" #OMPRESSED PULSE WIDTH " $OPPLER RESOLUTION 4
.S .S . S . S . .S
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&)'52% #OMPARISON OF AMBIGUITY FUNCTIONS FOR . STEPPED LINEAR AND #OSTAS SEQUENCE SHOWING THE IMPACT OF FREQUENCY ORDER
PROCESSED COHERENTLY 4HE ORDER IN WHICH THE FREQUENCIES ARE GENERATED GREATLY INFLU ENCES THE NATURE OF THE AMBIGUITY FUNCTION OF THE BURST )F THE FREQUENCIES ARE MONOTONI CALLY INCREASING OR DECREASING THE WAVEFORM IS SIMPLY A STEPPED APPROXIMATION TO AN ,&- WHICH HAS A RIDGE IN ITS AMBIGUITY FUNCTION &IGURE )N ORDER TO APPROACH A THUMBTACK LIKE AMBIGUITY FUNCTION THE ORDER OF THE FREQUENCIES NEEDS TO BE MORE RAN DOM IN NATURE 4HE ORDER OF FREQUENCIES IS THE CODE AND IT IS GENERATED VIA A SPECIAL CLASS OF - ¾ - #OSTAS ARRAYS #OSTAS SUGGESTED A TECHNIQUE FOR SELECTING THE ORDER OF THESE FREQUENCIES TO PROVIDE MORE CONTROLLED RANGE AND DOPPLER SIDELOBES !N EXAMPLE OF A #OSTAS CODE OF LENGTH IS SHOWN IN &IGURE AS IT COMPARES TO THE STEPPED ,&- 4ABLES SHOWING THE SEQUENCE ORDER FOR EACH WAVEFORM ARE ALSO PROVIDED
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Ê"ÊÊ *1 - Ê " *, --" Ê-9-/ 4HE CHOICE OF A PULSE COMPRESSION SYSTEM INVOLVES THE SELECTION OF THE TYPE OF WAVE FORM AND THE METHOD OF GENERATION AND PROCESSING -ETHODS OF GENERATING AND PROCESS ING PULSE COMPRESSION WAVEFORMS ARE DISCUSSED IN THE SECTION ON PULSE COMPRESSION IMPLEMENTATION IN THIS CHAPTER $ISCUSSIONS HERE WILL CONCENTRATE ON THE WAVEFORM ITSELF 4HE PRIMARY FACTORS INFLUENCING THE SELECTION OF A PARTICULAR WAVEFORM ARE USU ALLY THE RADAR REQUIREMENTS OF DOPPLER TOLERANCE AND TIME SIDELOBE LEVELS 4ABLE SUMMARIZES THESE FACTORS FOR THREE &- TYPES ,&- .,&- AND PHASE CODED WAVEFORMS 4HE SYSTEMS ARE COMPARED ON THE ASSUMPTION THAT INFORMATION IS EXTRACTED BY PROCESSING A SINGLE WAVEFORM AS OPPOSED TO MULTIPLE PULSE PROCESSING 4HE SYMBOLS " AND 4 DENOTE THE BANDWIDTH AND THE PULSEWIDTH OF THE WAVEFORM RESPECTIVELY )N CASES WHERE AN INSUFFICIENT DOPPLER SHIFT OCCURS SUCH AS WITH A STATIONARY OR TANGENTIAL TARGET RANGE RESOLUTION IS THE CHIEF MEANS FOR SEEING A TARGET IN CLUTTER
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4!",% #OMPARISONS OF 0ERFORMANCE #HARACTERISTICS FOR ,&- .,&- AND 0HASE #ODED
7AVEFORMS &ACTOR
,INEAR &-
$OPPLER TOLERANCE
3UPPORTS DOPPLER !DEQUATE INSENSITIVITY (IGHER SENSITIVITY TO (IGHEST SENSITIVITY SHIFTS UP TO o " TO DOPPLER TO ALLOW USE DOPPLER SHIFT 4IME TO DOPPLER SHIFT 4IME SHIFT OF FD4" GENERALLY UP TO -ACH SIDELOBES INCREASE 4IME SIDELOBES INCREASE WHILE IS INTRODUCED BY 4IME SHIFT OF FD4" IS WHILE MAINLOBE RESPONSE DECREASES MAINLOBE RESPONSE RANGE DOPPLER INTRODUCED BY RANGE COUPLING DOPPLER COUPLING FOR A FOR HIGHER DOPPLER DECREASES FOR HIGHER DOPPLER 4IME SIDELOBE NONSYMMETRICAL .,&- CHARACTERISTIC CHARACTERISTIC OF PERFORMANCE WAVEFORM #OMMON OF A THUMBTACK A THUMBTACK LIKE LIKE AMBIGUITY REMAINS EXCELLENT THEREFORE IN !4# AMBIGUITY FUNCTION FOR LARGE DOPPLER RADARS -ULTIPLE TUNED FUNCTION 5SED 5SED THEREFORE FOR THEREFORE FOR SHIFTS PULSE COMPRESSORS LOW SPEED TARGET REQUIRED FOR HIGH SPEED LOW SPEED TARGET APPLICATIONS AND APPLICATIONS AND TARGETS WITH SMALL 4" WITH SMALL 4" PRODUCTS ,ONGER PRODUCTS PHASE CODED WAVEFORMS ARE MORE SENSITIVE TO DOPPLER SHIFTS THAN THE SHORTER ONES "ETTER TIME SIDELOBES 'OOD TIME &OR NONSYMMETRICAL !DEQUATE SIDELOBES THAT ARE THAN BINARY PHASE .,&- EXCELLENT WEIGHTING HIGH CODED WAVEFORMS DETERMINED BY 4" PRODUCT AND TIME SIDELOBES IF CODING THERE IS ADEQUATE LOW AMPLITUDE AND PHASE ERRORS .,&- PHASE CODING ARE NECESSARY TO A HIGH 4" PRODUCT ACHIEVE GOOD TIME AND SUFFICIENTLY LOW AMPLITUDE AND PHASE SIDELOBES ERRORS )NCREASING .,&- PHASE CODE WEIGHTING INTRODUCES INCREASED RADIAL VELOCITY SENSITIVITY
4IME SIDELOBE LEVEL
'ENERAL
/FTEN USED FOR HIGH SPEED TARGET CAPABILITY -ACH %XTREMELY WIDE BANDWIDTHS ACHIEVABLE
.ONLINEAR &-
"INARY 0HASE #ODED 0OLYPHASE #ODED
'ENERALLY FOUND IN 'ENERALLY FOUND IN 5SE IS GENERALLY RESTRICTED TO APPLICATIONS LOW DOPPLER SHIFT LOW DOPPLER SHIFT APPLICATIONS APPLICATIONS WHERE PRIMARY TARGET RADIAL VELOCITIES -ACH -ULTIPLE TUNED MATCHED FILTERS ARE GENERALLY NOT COMPUTATIONALLY PRACTICAL
#LUTTER REJECTION WITH PULSE COMPRESSION WAVEFORMS IS DUE TO THE GREATER RANGE RESO LUTION ACHIEVABLE OVER UNCODED WAVEFORMS "ECAUSE THE RANGE RESOLUTION IS PRO PORTIONAL TO THE RECIPROCAL OF THE BANDWIDTH WIDER BANDWIDTH PULSE COMPRESSION WAVEFORMS CAN OFFER GREATER CLUTTER REJECTION
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n°{Ê *1 - Ê " *, --" Ê * //" Ê Ê, ,Ê-9-/ Ê 8 * 4HIS SECTION DESCRIBES THE GENERATION AND PROCESSING OF PULSE COMPRESSION WAVEFORMS AND PROVIDES EXAMPLES OF RADAR SYSTEMS THAT UTILIZE THESE PROCESSING TECHNIQUES -AJOR ADVANCES ARE CONTINUALLY BEING MADE IN THE DEVICES AND TECHNIQUES USED IN PULSE COM PRESSION RADARS 3IGNIFICANT ADVANCES ARE EVIDENT IN THE DIGITAL AND 3!7 TECHNIQUES THAT ALLOW THE IMPLEMENTATION OF A VARIETY OF PULSE COMPRESSION WAVEFORM TYPES 4HE DIGITAL APPROACH HAS BLOSSOMED BECAUSE OF THE MANIFOLD INCREASE IN COMPUTATIONAL SPEED AND ALSO BECAUSE OF THE SIZE REDUCTION AND THE SPEED INCREASE OF THE MEMORY UNITS 3!7 TECHNOLOGY HAS EXPANDED BECAUSE OF THE INVENTION OF THE INTERDIGITAL TRANS DUCER WHICH PROVIDES EFFICIENT TRANSFORMATION OF AN ELECTRICAL SIGNAL INTO ACOUSTIC ENERGY AND VICE VERSA $IGITAL 7AVEFORM 'ENERATION &IGURE SHOWS A DIGITAL APPROACH FOR GEN ERATING THE RADAR WAVEFORM 4HE PHASE CONTROL ELEMENT SUPPLIES DIGITAL SAMPLES OF THE IN PHASE COMPONENT ) AND THE QUADRATURE COMPONENT 1 WHICH ARE CONVERTED TO THEIR ANALOG EQUIVALENTS 4HESE PHASE SAMPLES MAY DEFINE THE BASEBAND COMPONENTS OF THE DESIRED WAVEFORM OR THEY MAY DEFINE THE WAVEFORM COMPONENTS ON A LOW FREQUENCY CARRIER )F THE WAVEFORM IS ON A CARRIER THE BALANCED MODULATOR IS NOT REQUIRED AND THE FILTERED COMPONENTS WOULD BE ADDED DIRECTLY 4HE SAMPLE AND HOLD CIRCUIT REMOVES THE TRANSIENTS DUE TO THE NONZERO TRANSITION TIME OF THE DIGITAL TO ANALOG $! CON VERTER 4HE LOW PASS FILTER SMOOTHES OR INTERPOLATES THE ANALOG SIGNAL COMPONENTS BETWEEN WAVEFORM SAMPLES TO PROVIDE THE EQUIVALENT OF A MUCH HIGHER WAVEFORM SAMPLING RATE 4HE )T COMPONENT MODULATES A n CARRIER SIGNAL AND THE 1T COMPO NENT MODULATES A n PHASE SHIFTED CARRIER SIGNAL 4HE DESIRED WAVEFORM IS THE SUM OF THE n MODULATED CARRIER AND THE n MODULATED CARRIER !S MENTIONED EARLIER WHEN THE DIGITAL PHASE SAMPLES INCLUDE THE CARRIER COMPONENTS THE ) AND 1 COMPONENTS ARE CENTERED ON THIS CARRIER FREQUENCY AND THE LOW PASS FILTER CAN BE REPLACED WITH A BAND PASS FILTER CENTERED ON THE )& CARRIER 7HEN A LINEAR &- WAVEFORM IS DESIRED THE PHASE SAMPLES FOLLOW A QUADRATIC PAT TERN AND CAN BE GENERATED BY TWO CASCADED DIGITAL INTEGRATORS 4HE INPUT DIGITAL COM MAND TO THE FIRST INTEGRATOR DEFINES THIS QUADRATIC PHASE FUNCTION 4HE DIGITAL COMMAND TO THE SECOND INTEGRATOR IS THE OUTPUT OF THE FIRST INTEGRATOR PLUS THE DESIRED CARRIER FREQUENCY 4HIS CARRIER MAY BE DEFINED BY THE INITIAL VALUE OF THE FIRST INTEGRATOR 4HE DESIRED INITIAL PHASE OF THE WAVEFORM IS THE INITIAL VALUE OF THE SECOND INTEGRATOR OR ELSE MAY BE ADDED TO THE SECOND INTEGRATOR OUTPUT 7ITH ADVANCES IN DIGITAL TECHNOLOGY IT HAS BECOME POSSIBLE AND PRACTICAL TO GENERATE WAVEFORMS DIRECTLY AT )& OR 2& CARRIER FREQUENCIES ON A SINGLE INTEGRATED CIRCUIT CHIP 4HIS TECHNIQUE IS CALLED $IRECT $IGITAL 3YNTHESIS OR $$3 AND INVOLVES GENERATING WAVEFORMS AT
&)'52% $IGITAL WAVEFORM GENERATION BLOCK DIAGRAM
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HIGH SAMPLING RATES AND FILTERING THE OUTPUT 4HESE DEVICES GENERATE THE WAVEFORM BY ACCU MULATING PHASE INFORMATION WHICH IS THEN USED TO LOOK UP VALUES OF THE WAVEFORM USUALLY A SINE WAVE 4HIS IS CONVERTED TO AN ANALOG SIGNAL WITH A DIGITAL TO ANALOG CONVERTER $!# OR $! CONVERTER AND FILTERED ! VARIETY OF WAVEFORM TYPES EG ,&- .,&- AND #7 WAVEFORMS CAN BE GENERATED IN THIS WAY BY USING THE APPROPRIATE PHASE MODULATION CHAR ACTERISTIC !S AN EXAMPLE THE !NALOG $EVICES !$ $IRECT $IGITAL 3YNTHESIZER USES A BIT $!# OPERATING AT UP TO A '(Z INTERNAL CLOCK SPEED $!# UPDATE RATE $IGITAL 0ULSE #OMPRESSION n $IGITAL PULSE COMPRESSION TECHNIQUES ARE ROUTINELY USED FOR MATCHED FILTERING OF RADAR WAVEFORMS 4HE MATCHED FILTER MAY BE IMPLEMENTED BY USING A DIGITAL CONVOLUTION FOR ANY WAVEFORM OR ELSE BY USE OF STRETCH PROCESSING FOR A LINEAR &- WAVEFORM $IGITAL PULSE COMPRESSION HAS DISTINCT FEATURES THAT DETERMINE ITS ACCEPTABILITY FOR A PARTICULAR RADAR APPLICATION $IGITAL MATCHED FILTERING USUALLY REQUIRES MULTIPLE OVERLAPPED PROCESSING UNITS FOR EXTENDED RANGE COVERAGE 4HE ADVANTAGES OF THE DIGI TAL APPROACH ARE THAT LONG DURATION WAVEFORMS PRESENT NO PROBLEM THE RESULTS ARE EXTREMELY STABLE UNDER A WIDE VARIETY OF OPERATING CONDITIONS AND THE SAME IMPLEMEN TATION COULD BE USED TO HANDLE MULTIPLE WAVEFORM TYPES !NALOG PRODUCT DETECTORS USED TO EXTRACT ) AND 1 BASEBAND COMPONENTS HAVE BEEN REPLACED IN MANY SYSTEMS BY DIGITAL DOWN CONVERSION TECHNIQUES )N THIS APPROACH THE COMPLEX ENVELOPE SEQUENCE IS EVALUATED BY DIGITAL SIGNAL PROCESSING OF !$ CONVERTER SAMPLES AT THE FINAL )& OUTPUT OF THE RECEIVER RATHER THAN BY SEPARATE !$ CONVERSION OF BASEBAND ANALOG ) AND 1 COMPONENTSn $IGITAL DOWN CONVERSION IS ADVANTAGEOUS BECAUSE PERFORMANCE IS NOT LIMITED BY AMPLITUDE AND PHASE IMBALANCES THAT EXIST IN ANALOG PRODUCT DETECTION HARDWARE &IGURE ILLUSTRATES TWO DIGITAL SIGNAL PROCESSING APPROACHES TO PROVIDING THE MATCHED FILTER FOR A PULSE COMPRESSION WAVEFORM )N BOTH CASES THE INPUT SIGNAL IS THE COMPLEX ENVELOPE SEQUENCE AS FORMED USING EITHER DIGITAL DOWN CONVERSION OR ANALOG #!
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&)'52% A 4IME DOMAIN DIGITAL PULSE COMPRESSION PROCESSOR AND B FREQUENCY DOMAIN DIGITAL PULSE COMPRESSION PROCESSOR
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PRODUCT DETECTION FOLLOWED BY !$ CONVERSION IN EACH BASEBAND CHANNEL &IGURE A SHOWS A DIGITAL IMPLEMENTATION OF A TIME DOMAIN CONVOLUTION PROCESSOR THAT WILL PRO VIDE MATCHED FILTER PERFORMANCE FOR ANY RADAR WAVEFORM )N THIS CASE DISCRETE TIME CONVOLUTION IS DONE IN THE TIME DOMAIN BY CONVOLUTION OF THE COMPLEX ENVELOPE INPUT SEQUENCE FOLLOWING DIGITAL DOWN CONVERSION WITH THE MATCHED FILTER IMPULSE RESPONSE SEQUENCE "ECAUSE TIME DOMAIN CONVOLUTION CAN BE COMPUTATIONALLY INTENSIVE A MORE ECONOMICAL APPROACH FROM A COMPUTATIONAL STANDPOINT IS SHOWN IN &IGURE B IN WHICH FREQUENCY DOMAIN PROCESSING IS USED TO IMPLEMENT THE CONVOLUTION 4HE FREQUENCY DOMAIN DIGITAL PULSE COMPRESSION PROCESSOR OPERATES ON THE PRINCI PLE THAT THE DISCRETE &OURIER TRANSFORM $&4 OF THE TIME CONVOLUTION OF TWO SEQUENCES IS EQUAL TO THE PRODUCT OF THE DISCRETE &OURIER TRANSFORMS OF EACH OF THE SEQUENCES )F - RANGE SAMPLES ARE TO BE PROVIDED BY ONE PROCESSOR THE LENGTH OF THE $&4 MUST EXCEED - PLUS THE NUMBER OF SAMPLES IN THE REFERENCE WAVEFORM MINUS ONE TO ACHIEVE AN APERIODIC CONVOLUTION 4HESE ADDED - SAMPLES ARE FILLED WITH ZEROS IN THE REFER ENCE WAVEFORM $&4 &OR EXTENDED RANGE COVERAGE REPEATED PROCESSING OPERATIONS ARE REQUIRED WITH RANGE DELAYS OF - SAMPLES BETWEEN ADJACENT OPERATIONS USING THE OVER LAP SAVE CONVOLUTION TECHNIQUE 4HIS PROCESSOR CAN BE USED WITH ANY WAVEFORM AND THE REFERENCE WAVEFORM CAN BE OFFSET IN DOPPLER FREQUENCY TO ACHIEVE A MATCHED FILTER AT THIS DOPPLER FREQUENCY 0ULSE #OMPRESSION 2ADAR %XAMPLES 4HERE ARE MANY RADARS UNDER DEVELOP MENT OR DEPLOYED THAT UTILIZE SOME OF THE PULSE COMPRESSION WAVEFORMS PREVIOUSLY DIS CUSSED !DVANCES IN DIGITAL SIGNAL PROCESSING TECHNOLOGY HAVE ENABLED A WIDER VARIETY OF WAVEFORM IMPLEMENTATIONS &OR EXAMPLE RADAR SYSTEMS ARE NO LONGER LIMITED TO THE ,&- WAVEFORM INSTEAD RADAR SYSTEM CAPABILITIES CAN BE EXTENDED TO TAKE ADVANTAGE OF THE MORE COMPLEX PROCESSING ASSOCIATED WITH THE NONLINEAR &- WAVEFORM !.403 AND !.&03 3URVEILLANCE 2ADARS 4HE !.403 AND !. &03 ARE A FAMILY OF , BAND LONG RANGE SURVEILLANCE RADARS THAT EMPLOY ,&- WAVEFORMS 4HE ANTENNA IS MECHANICALLY ROTATED IN AZIMUTH AND ELECTRONIC PENCIL BEAM SCANNING IS PERFORMED IN ELEVATION 4HE TRANSMISSION UTILIZES TWO TIME SEQUENCED ,&- PULSES OF DIFFERENT FREQUENCIES IN ORDER TO CREATE 3WERLING #ASE TARGET STATISTICS "OTH RADARS EMPLOY FREQUENCY DOMAIN DIGITAL PULSE COMPRESSION PROCESSING !IR 3URVEILLANCE AND 0RECISION !PPROACH 2ADAR 3YSTEM 4HE !IR 3URVEILLANCE AND 0RECISION !PPROACH 2ADAR 3YSTEM !30!2#3 IS INTENDED TO PROVIDE THE NEXT GENERATION AIR TRAFFIC CONTROL !4# RADAR AS PART OF THE -ULTI -ISSION 3URVEILLANCE 2ADAR --32 FAMILY OF !4# RADARS BUILT BY ,OCKHEED -ARTIN #O .ONLINEAR &- WAVEFORMS ARE USED BECAUSE THE TARGETS OF INTEREST HAVE RELATIVELY LOW DOPPLER SHIFTS LESS THAN -ACH ,IKE THE !.&03 RADAR THIS SYSTEM IMPLEMENTS FREQUENCY DOMAIN DIGITAL PULSE COMPRESSION PROCESSING -ULTI -ISSION 2ADAR 4HE -ULTI -ISSION 2ADAR --2 IS DESIGNED TO DETECT AND TRACK MORTARS ARTILLERY AND ROCKETS 4HIS RADAR USES A NONLINEAR &- SINE BASED WAVE FORM $IGITAL FREQUENCY DOMAIN PULSE COMPRESSION PROCESSING IS PERFORMED !32 .EXT 'ENERATION 3OLID 3TATE !IR 4RAFFIC #ONTROL 2ADAR 4HE !32 TER MINAL AIRPORT SURVEILLANCE RADAR TRANSMITS A §S PULSE WITH PEAK POWER OF K7 TO PROVIDE A SINGLE PULSE TRANSMIT ENERGY OF * .ONLINEAR FREQUENCY MODULATION IS USED WITH A PULSE COMPRESSION RATIO OF TO ACHIEVE RANGE RESOLUTION EQUIVALENT TO AN UNCODED §S PULSE 4HE FILTER MATCHING LOSS IS LESS THAN D" AND TYPICAL TIME
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SIDELOBE LEVELS MEASURED ON PRODUCTION HARDWARE ARE n D" $IGITAL PULSE COMPRES SION IS USED !N UNCODED §S PULSE IS USED TO PROVIDE COVERAGE FOR TARGETS WITHIN THE RANGE INTERVAL FROM TO NMI 3TRETCH 0ULSE #OMPRESSIONn 3TRETCH PULSE COMPRESSION IS A TECHNIQUE FOR PERFORMING ,&- PULSE COMPRESSION OF WIDEBAND WAVEFORMS USING A SIGNAL PROCESSOR WITH BANDWIDTH THAT IS MUCH SMALLER THAN THE WAVEFORM BANDWIDTH WITHOUT LOSS OF SIGNAL TO NOISE RATIO OR RANGE RESOLUTION 3TRETCH PULSE COMPRESSION IS USED FOR A SINGLE TARGET OR FOR MULTIPLE TARGETS THAT ARE LOCATED WITHIN A RELATIVELY SMALL RANGE WINDOW CENTERED AT A SELECTED RANGE &IGURE SHOWS A BLOCK DIAGRAM OF A STRETCH PULSE COMPRESSION SYSTEM 4HE ,&- WAVEFORM HAS A SWEPT BANDWIDTH " PULSEWIDTH 4 AND ,&- SLOPE A 4HE REFER ENCE WAVEFORM IS GENERATED WITH TIME DELAY S2 SWEPT BANDWIDTH "2 PULSEWIDTH 42 AND ,&- SLOPE @2 4HE REFERENCE WAVEFORM TIME DELAY IS TYPICALLY DERIVED BY RANGE TRACKING OF A SELECTED TARGET WITHIN THE RANGE WINDOW 4HE CORRELATION MIXER #- IN &IGURE PERFORMS A BANDPASS MULTIPLICATION OF THE RECEIVED SIGNAL BY THE OUTPUT OF THE REFERENCE WAVEFORM GENERATOR 4HE LOWER SIDEBAND AT THE #- OUTPUT IS SELECTED BY A BANDPASS FILTER "0& 3PECTRUM ANALYSIS IS PERFORMED WHEN THE ,&- SLOPES OF THE TRANSMIT AND REFERENCE WAVEFORMS ARE EQUAL @ @2 2EDUCED BANDWIDTH PULSE COMPRESSION PROCESSING IS PERFORMED IF THE REFERENCE WAVEFORM ,&- SLOPE IS LESS THAN THE TRANSMIT WAVEFORM ,&- SLOPE @2 @ )N BOTH CASES THE REQUIRED PROCESSING BANDWIDTH "P IS MUCH SMALLER THAN THE WAVEFORM BANDWIDTH &IGURE SHOWS THE PRINCIPLE OF STRETCH PULSE COMPRESSION FOR THE CASE WHERE THE ,&- SLOPES OF THE TRANSMIT AND REFERENCE WAVEFORMS ARE EQUAL 4HE INSTANTANEOUS FRE QUENCY IS PLOTTED AS A FUNCTION OF TIME AT THREE POINTS IN THE STRETCH PULSE COMPRESSION SYSTEM BLOCK DIAGRAM CORRELATION MIXER INPUT CORRELATION MIXER ,/ REFERENCE WAVEFORM GENERATOR OUTPUT AND CORRELATION MIXER OUTPUT OUTPUT OF BANDPASS FILTER 4HREE ,&- TARGET SIGNALS ARE SHOWN AT THE CORRELATION MIXER INPUT TARGET IS AT ZERO TIME OFFSET RELATIVE TO THE REFERENCE WAVEFORM TARGET IS EARLIER IN TIME THAN THE REFERENCE WAVEFORM AND TARGET IS LATER IN TIME )N EACH CASE THE ,&- SLOPE FOR THE TARGET SIGNALS IS "4 4HE REFERENCE WAVEFORM APPLIED TO THE ,/ PORT OF THE #- HAS ,&- SLOPE EQUAL TO "242 "4 4HE INSTANTANEOUS FREQUENCY AT THE CORRELATION MIXER OUTPUT IS THE DIFFERENCE BETWEEN THE INSTANTANEOUS FREQUENCIES AT THE #- INPUT AND ,/ PORTS !S A RESULT THE #- OUTPUT SIGNALS FOR THE THREE TARGET SIGNALS ARE UNCODED PULSES PULSED #7 SIGNALS WITH FREQUENCY OFFSET FROM THE MIXER )& OUTPUT F)& GIVEN BY ¤ "³ D F ¥ ´ TD ¦4µ
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&)'52% 3TRETCH PULSE COMPRESSION SYSTEM BLOCK DIAGRAM
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"# $# ! % !
! $ &
#
#
"# $# $#
&)'52% #ORRELATION MIXER SIGNALS IN STRETCH PULSE COMPRESSION AFTER 2OTH ET AL
WHERE TD IS THE TIME DELAY OF THE MIDPOINT OF THE SIGNAL MEASURED RELATIVE TO THE MID POINT OF THE REFERENCE WAVEFORM &OR THE CASE SHOWN WHERE THE 2& CARRIER FREQUENCY IS ABOVE THE CARRIER FREQUENCY OF THE REFERENCE WAVEFORM A POSITIVE TIME DELAY RESULTS IN A NEGATIVE FREQUENCY OFFSET 4HE SIGNALS AT THE CORRELATION MIXER OUTPUT ARE THEN RESOLVED IN THE FREQUENCY DOMAIN BY SPECTRAL ANALYSIS PROCESSING ! TYPICAL IMPLEMENTATION FOR THE SPECTRAL ANALYSIS PROCESSING INCLUDES A SECOND FREQUENCY CONVERSION FOLLOWING THE #- TO A FINAL INTERMEDIATE FREQUENCY )& ANTI ALIASING FILTERING DIRECT SAMPLING AT THE FINAL )& USING AN ANALOG TO DIGITAL CONVERTER !$# DIGITAL DOWN CONVERSION $$# TO A COMPLEX ENVELOPE SEQUENCE TIME DOMAIN WEIGHTING AND SPECTRAL ANALYSIS USING AN &&4 PADDED WITH ZEROS 0REVIOUS IMPLE MENTATIONS USED ANALOG PRODUCT DETECTORS TO EXTRACT ) AND 1 BASEBAND SIGNALS WITH SEPARATE !$#S IN THE ) AND 1 BASEBAND CHANNELS #ORRELATION -IXER /UTPUT 3IGNAL !NALYSIS 4HE RECEIVED SIGNAL AT THE #- INPUT PORT FROM A POINT TARGET IS
¤T T³ XIN T ! RECT ¥ COS;P F FD T T PA T T = ¦ 4 ´µ
WHERE ! IS THE AMPLITUDE 4 IS THE TRANSMIT PULSEWIDTH F IS THE CARRIER FREQUENCY FD IS THE DOPPLER FREQUENCY S IS THE SIGNAL TIME DELAY AND @ IS THE ,&- SLOPE FOR THE TRANSMIT WAVEFORM 4HE REFERENCE WAVEFORM APPLIED TO THE ,/ PORT IS
¤T T2³ X 2 T RECT ¥ COS;P F2 T T 2 PA 2 T T 2 = ¦ 42 ´µ
WHERE 42 IS THE PULSEWIDTH F2 IS THE CARRIER FREQUENCY S2 IS THE REFERENCE WAVEFORM TIME DELAY AND @2 IS THE ,&- SLOPE FOR THE REFERENCE WAVEFORM @2 a @
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4HE CORRELATION MIXER ACTS AS A BANDPASS MULTIPLIER WITH OUTPUT XINT X2T 4HE )& OUTPUT OF THE CORRELATION MIXER IS EVALUATED USING THE IDENTITY
COS X COS Y COSX Y COS X Y
WHERE THE FIRST TERM ON THE RIGHT HAND SIDE OF THE EQUATION CORRESPONDS TO THE UPPER SIDEBAND AND THE SECOND TO THE LOWER SIDEBAND AT THE MIXER OUTPUT 4HE UPPER SIDEBAND IS REJECTED BY THE BANDPASS FILTER TO YIELD ¤T T2³ ¤T T³ X)& T ! RECT ¥ RECT ¥ ¦ 4 ´µ ¦ 42 ´µ COS;P F)& T T P FD T T PA 2 T 2 T T T P A A 2 T T F =
WHERE F)& F F2 IS THE )& CARRIER FREQUENCY F F2 IS ASSUMED AND THE CARRIER PHASE SHIFT IS
F P F2 T T 2 PA 2 T T 2
4HE )& SIGNAL IS AN ,&- WAVEFORM WITH REDUCED SLOPE @ @2 THE FACTOR THAT MULTI PLIES THE QUADRATIC TERM IN THE ARGUMENT OF THE COSINE AND A FREQUENCY OFFSET RELATIVE TO THE )& CARRIER FREQUENCY F)& GIVEN BY
D F FD A 2 T 2 T
4HE DURATION OF THE REFERENCE WAVEFORM IS REQUIRED TO EXCEED THE TRANSMIT PULSE WIDTH TO AVOID A LOSS IN 3.2 CAUSED BY TARGET ECHOES THAT ARE NOT CONTAINED WITHIN THE REFERENCE WAVEFORM %QUAL 4RANSMIT AND 2EFERENCE 7AVEFORM ,&- 3LOPES &OR THE CASE WHERE THE TRANSMIT AND REFERENCE WAVEFORM ,&- SLOPES ARE EQUAL @ @ 2 THE )& SIGNAL IS AN UNCODED PULSE WITH FREQUENCY OFFSET GIVEN BY
D F FD A T 2 T
4HE FREQUENCY OFFSET IS MEASURED USING SPECTRUM ANALYSIS AND CONVERTED TO TARGET TIME DELAY AND RANGE RELATIVE TO THE REFERENCE WAVEFORM BY $T T T 2
DF A
$R 2 2
C $T
WHERE 2 CS2 IS THE RANGE CORRESPONDING TO THE TIME DELAY OF THE REFERENCE WAVEFORM +ELLOG DESCRIBES ADDITIONAL CONSIDERATIONS FOR APPLICATION OF TIME DOMAIN WEIGHTING IN STRETCH PROCESSING AND PROVIDES DETAILS ON COMPENSATION TECHNIQUES FOR HARDWARE ERRORS 4HE EFFECT OF TIME MISMATCH BETWEEN THE SIGNAL AND THE WEIGHTING FUNCTION IS ANALYZED BY 4EMES
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5NEQUAL 4RANSMIT AND 2EFERENCE 7AVEFORM 3LOPES ! STRETCH PROCESSOR WITH UNEQUAL FREQUENCY SLOPE WAVEFORMS REQUIRES PULSE COMPRESSION OF THE RESIDUAL LINEAR &- AT THE OUTPUT OF THE CORRELATION MIXER ! LINEAR &- SIGNAL WITH A SLOPE OF @ IN @ 2 OCCURS AT THE TARGET RANGE WHICH IS OFFSET IN FREQUENCY FROM THE )& CARRIER FREQUENCY BY @ 2S2 S 7ITH THE RANGE DOPPLER COUPLING OF THE ,&- WAVEFORM THE APPARENT TIME DELAY OF THIS TARGET WILL BE
SAPP @2 S2 S @ @2
4HIS RESULT CAN BE INTERPRETED AS YIELDING A TIME EXPANSION FACTOR OF @ 2@ @ 2 FOR THE COMPRESSED PULSE !S FOR THE CASE OF EQUAL ,&- SLOPES THE RANGE WINDOW WIDTH DEPENDS ON THE ACHIEVABLE PROCESSING BANDWIDTH 3TRETCH 0ROCESSING 2ANGE 2ESOLUTION 7IDTH 4HE D" FREQUENCY RESOLUTION WIDTH FOR SPECTRAL ANALYSIS USING A RECTANGULAR WINDOW OF TIME DURATION EQUAL TO THE TRANSMIT PULSEWIDTH IS
$F
4
4HE D" TIME DELAY RESOLUTION WIDTH OBTAINED BY STRETCH PROCESSING IS OBTAINED BY DIVIDING $F BY \@ \ TO CONVERT TO UNITS OF TIME DELAY
T
$F " 4 "
#ONSEQUENTLY THE D" RESOLUTION WIDTH ACHIEVED BY STRETCH PROCESSING IS THE SAME AS THAT ACHIEVED BY THE MATCHED FILTER FOR THE ,&- WAVEFORM 4HE D" RANGE RESOLU TION WIDTH IS
$2
C "
4IME DOMAIN WEIGHTING IS UTILIZED IN THE SPECTRAL ANALYSIS PROCESSING TO REDUCE THE TIME SIDELOBES OF THE COMPRESSED PULSE AND IMPROVE THE RESOLUTION PERFORMANCE WHEN MULTIPLE TARGETS ARE PRESENT WITHIN THE RANGE WINDOW !S AN EXAMPLE THE USE OF (AMMING TIME DOMAIN WEIGHTING REDUCES THE PEAK TIME SIDELOBE LEVEL FROM n D" TO n D" WITH AN INCREASE IN THE D" FREQUENCY RESOLUTION WIDTH TO $F 4 4HE D" RANGE RESOLUTION WIDTH FOR (AMMING WEIGHTING IS
$2
C (AMMING 7EIGHTING "
2ANGE 7INDOW 7IDTH 4HE WIDTH OF THE RANGE WINDOW IS ESTABLISHED BY THE BAND WIDTH OF THE SPECTRAL ANALYSIS AND THE ,&- SLOPE OF THE TRANSMIT WAVEFORM !SSUME A TIME WINDOW OF WIDTH $T AND A STRETCH PROCESSING BANDWIDTH "P ! TARGET AT THE EDGE OF THE TIME WINDOW YIELDS A FREQUENCY OFFSET EQUAL TO ONE HALF OF THE PROCESSING BANDWIDTH OR
" $T " P 4 $T 4
"P "P " " 4
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4HE RANGE WINDOW WIDTH IS
$R
C4 " P C "P " " 4
3TRETCH 0ULSE #OMPRESSION 2ADAR %XAMPLES 4HIS SECTION DESCRIBES THREE EXAMPLES OF RADARS THAT EMPLOY STRETCH PULSE COMPRESSION SYSTEMS ,ONG 2ANGE )MAGING 2ADAR 4HE ,ONG 2ANGE )MAGING 2ADAR ,2)2 IS AN 8 BAND RADAR WITH STRETCH PROCESSING BANDWIDTHS OF -(Z AND -(Z 4HE WIDEBAND WAVEFORM HAS A SWEPT BANDWIDTH OF -(Z TO A PULSEWIDTH OF APPROXI MATELY §S AND A ,&- SLOPE "4 y -(Z §S -(Z§S 4HE RANGE WINDOW WIDTH FOR THE -(Z PROCESSING BANDWIDTH IS
$R
M MS r -(Z C "P M " 4 -(Z MS
-ILLIMETER 7AVE 2ADAR 4HE STRETCH PROCESSING IMPLEMENTATION FOR THE -ILLIMETER 7AVE RADAR --7 LOCATED AT +WAJALEIN !TOLL IS DESCRIBED BY !BOUZAHARA AND !VENT 4HE --7 RADAR OPERATES AT A CARRIER FREQUENCY OF '(Z USING WAVEFORMS WITH A MAXIMUM SWEPT BANDWIDTH OF -(Z AND PULSEWIDTH OF §S 4HE ,&- SLOPE FOR THE TRANSMIT WAVEFORM IS
A
" -(Z -(ZMS 4 MS
4HE STRETCH PROCESSING BANDWIDTH IS "P -(Z 4HE WIDTH OF THE STRETCH PROCESSING TIME WINDOW IS
$T
-(Z MS -(Z MS
4HE REFERENCE WAVEFORM PULSEWIDTH IS 42 §S TO AVOID A LOSS IN 3.2 FOR TARGETS AT THE EDGES OF THE RANGE WINDOW 4HE SWEPT BANDWIDTH OF THE REFERENCE WAVEFORM AND THE RANGE WINDOW WIDTH ARE
"2 -(ZMS r MS -(Z C $R $T M MS r MS M
4HE D" RANGE RESOLUTION WIDTH WITH (AMMING WEIGHTING APPLIED OVER THE §S PULSEWIDTH IN THE SPECTRAL ANALYSIS PROCESSING IS
$2
C M MS M " -(Z
#OBRA $ANE 7IDEBAND 0ULSE #OMPRESSION 3YSTEM 4HE CHARACTERISTICS OF THE WIDEBAND PULSE COMPRESSION SYSTEM DEVELOPED FOR THE #OBRA $ANE RADAR ARE SUM MARIZED IN 4ABLE
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4!",% #OBRA $ANE 7IDEBAND 0ULSE #OMPRESSION 3YSTEM #HARACTERISTICS ADAPTED FROM &ILER AND (ARTT Ú )%%%
#HARACTERISTIC
6ALUE
4RANSMIT ,&- BANDWIDTH 2EFERENCE ,&- BANDWIDTH 4RANSMIT WAVEFORM SWEPT BANDWIDTH " 2EFERENCE WAVEFORM SWEPT BANDWIDTH "REF 4RANSMIT PULSEWIDTH 4 2EFERENCE PULSEWIDTH 4REF 4RANSMIT WAVEFORM ,&- SLOPE #OMPRESSED PULSEWIDTH n D" S 4IME BANDWIDTH PRODUCT 4" 4IME SIDELOBE LEVEL 4ARGET RANGE WINDOW .UMBER OF RANGE SAMPLES 2ANGE SAMPLE SPACING &IRST )& AT OUTPUT OF CORRELATION MIXER 3ECOND )& 3TRETCH PROCESSING BANDWIDTH "P !$ CONVERTER SAMPLING FREQUENCY
TO -(Z TO -(Z
-(Z -(Z §S §S
-(Z§S UP CHIRP FT n D" FT FT -(Z -(Z K(Z -(Z IN ) AND 1 BASEBAND CHANNELS
%XCLUDES PULSEWIDTH AND SWEPT BANDWIDTH EXTENSION DUE TO FT RANGE WINDOW
** 8 3IGNAL !NALYSIS 3UMMARYn 4ABLE IS A SUMMARY OF SIGNAL ANALYSIS DEFI NITIONS AND RELATIONSHIPS 4ABLE SHOWS 7OODWARDS &OURIER TRANSFORM RULES AND PAIRS 4HESE RELATIONSHIPS SIMPLIFY THE APPLICATION OF SIGNAL ANALYSIS TECHNIQUES )N MOST CASES IT WILL NOT BE NECESSARY TO EXPLICITLY PERFORM AN INTEGRATION TO EVALUATE THE &OURIER TRANSFORM OR INVERSE &OURIER TRANSFORM
4!",% 3IGNAL !NALYSIS $EFINITIONS AND 2ELATIONSHIPS
&OURIER TRANSFORM SPECTRUM OF SIGNAL XT
c
8 F
¯ XT E J P FT DT
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)NVERSE &OURIER TRANSFORM OF SPECTRUM 8 F
c
X T
¯ 8 F E J P FT DF
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#ONVOLUTION OF SIGNALS XT AND YT
Y T X T H T c
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&ILTER FREQUENCY RESPONSE %ULERS IDENTITY
( F 9 F 8 F
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¯ XT HT T DT ¯ XT T HT DT
E JQ COS Q J SIN Q
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4!",% 3IGNAL !NALYSIS $EFINITIONS AND 2ELATIONSHIPS #ONTINUED
#OSINE AND SINE FUNCTIONS EXPRESSED IN TERMS OF COMPLEX EXPONENTIALS
COS Q E JQ E JQ SIN Q E JQ E JQ J
0ARSEVALS THEOREM SUPERSCRIPT ASTERISK INDICATES COMPLEX CONJUGATE
c
c
¯ XT Y T DT
¯ 8 F 9 F DF
c c
c
c
¯ \ XT \ DT ¯ \ 8 F \ DF
c
c
RECT FUNCTION
ª \ T \ RECTT « ¬ \ T \
SINC FUNCTION
SINC F SINP F P F
2EPETITION OPERATOR
c
REP4 ; XT =
£ XT N4
N c
#OMB OPERATOR
c
COMB & ; 8 F =
£ 8 N& D F N&
N c
3AMPLING PROPERTY OF DELTA FUNCTION
c
¯ XT D T T DT XT
c
#AUCHY 3CHWARZ INEQUALITY
c
¯ F X G X DX
c
c
c
a ¯ \ F X \ DX ¯ \ G X \ DX
c
c
WITH EQUALITY IF AND ONLY IF F X KG X
2ADAR 4RANSMIT 7AVEFORMS n 4HE TRANSMITTED WAVEFORMS USED IN RADAR ARE BANDPASS SIGNALS THAT CAN BE EXPRESSED IN THE FORM
XT AT COS;P FT F T =
WHERE AT IS THE AMPLITUDE MODULATION 6 ET IS THE PHASE MODULATION RAD AND F IS THE CARRIER FREQUENCY (Z 4HE AMPLITUDE AND PHASE MODULATION FUNCTIONS VARY SLOWLY COMPARED TO THE PERIOD OF THE CARRIER F #ONSEQUENTLY XT IS A NARROWBAND WAVEFORM WITH A BANDWIDTH THAT IS SMALL COMPARED TO THE CARRIER FREQUENCY #OMPLEX %NVELOPE 4HE COMPLEX ENVELOPE OF XT IS GIVEN BY
UT AT E JF T
A
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4!",% &OURIER 4RANSFORM 2ULES AND 0AIRS
XT YT
REP4 ; XT =
#OMMENTS &OURIER TRANSFORM PAIR ,INEARITY 3IGNAL TIME REVERSAL #ONJUGATE OF SIGNAL 4IME DOMAIN DIFFERENTIATION &REQUENCY DOMAIN DIFFERENTIATION 3IGNAL TIME SHIFT 3IGNAL FREQUENCY SHIFT 4IME SCALING 4IME DOMAIN CONVOLUTION 4IME DOMAIN MULTIPLICATION 8 F 9 F \ 4 \ COMB 4 ; 8 F = 7OODWARDS REPETITION OPERATOR
COMB4 ; XT =
\ 4 \ REP 4 ; 8 F =
7OODWARDS COMB OPERATOR
8T C T RECTT SINCT EXPnPT
XnF C F SINC F RECT F EXPnP F
4IME FREQUENCY INTERCHANGE DUALITY $ELTA FUNCTION IN TIME $ELTA FUNCTION IN FREQUENCY RECT FUNCTION IN TIME RECT FUNCTION IN FREQUENCY 'AUSSIAN TIME FUNCTION
3IGNAL XT !XT "UT X T X T DXDT
JPTXT XT S XT EXPJPFT XT4
X T Y T
3PECTRUM 8 F !8 F "5 F 8 F 8 F JPF8 F D8DF 8 F EXP JPFS 8 F F \4\8 F4 8 F 9 F
4HE BANDPASS SIGNAL IS EXPRESSED IN TERMS OF THE COMPLEX ENVELOPE BY
UT 2E; XT E J P FT =
B
#OMPLEX %NVELOPE 2EPRESENTATION OF 2ADAR %CHOES 4HE RADAR ECHO SIGNAL FROM A POINT TARGET IS
SR T !R AT TD COS;P F FD T TD F T TD =
WHERE !R IS A DIMENSIONLESS AMPLITUDE SCALE FACTOR TD IS THE TARGET TIME DELAY S FD IS THE TARGET DOPPLER SHIFT (Z AT IS THE AMPLITUDE MODULATION 6 E T IS THE PHASE MODULATION RAD AND F IS THE TRANSMIT CARRIER FREQUENCY (Z 4HE COMPLEX ENVELOPE OF SRT IS
UR T !R E J P FTD UT TD E J P FD T TD
4HE TERM UT n TD IS THE COMPLEX ENVELOPE OF THE TRANSMIT WAVEFORM DELAYED IN TIME BY TD 4HE COMPLEX EXPONENTIAL EXP;JO FDT n TD = REPRESENTS A LINEAR PHASE MODULATION VERSUS TIME THAT IS IMPRESSED ON THE RECEIVED ECHO SIGNAL BY THE DOPPLER SHIFT FD 4HE CARRIER PHASE SHIFT IS PC nO FTD 4HE TIME DELAY AND DOPPLER SHIFT ARE EXPRESSED IN TERMS OF TARGET RANGE AND RANGE RATE BY TD 2C S AND FD nK 6R (Z WHERE 2 IS THE TARGET RANGE M 6R D2DT
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IS THE RANGE RATE NEGATIVE FOR AN INCOMING TARGET C IS THE SPEED OF LIGHT AND K CF M IS THE CARRIER WAVELENGTH -ATCHED &ILTERS ! MATCHED FILTER ACHIEVES MAXIMUM OUTPUT SIGNAL TO NOISE RATIO FOR A SIGNAL RECEIVED IN WHITE NOISE 4HE MATCHED FILTER FREQUENCY RESPONSE FOR A SIGNAL UT IS
( MF F K5 F E J P FT
WHERE K IS AN ARBITRARY COMPLEX CONSTANT AND 5 F IS THE SPECTRUM OF UT 4HE TIME DELAY T IS REQUIRED TO EXCEED THE DURATION OF UT TO ACHIEVE A CAUSAL IMPULSE RESPONSE THAT IS ZERO FOR NEGATIVE TIME 4HE MATCHED FILTER IMPULSE RESPONSE IS
HMF T KU T T
4HE PEAK SIGNAL TO NOISE TO MEAN NOISE POWER RATIO AT THE OUTPUT OF A FILTER WITH FREQUENCY RESPONSE ( F IS DEFINED AS
3 . O
! S NO
WHERE !O IS THE MATCHED FILTER OUTPUT SIGNAL AMPLITUDE AT THE PEAK OF THE SIGNAL AND R NO IS THE MATCHED FILTER OUTPUT NOISE POWER 4HE MATCHED FILTER OUTPUT 3.2 IS GIVEN BY
3 . MF
% .
WHERE % IS THE ENERGY OF THE RECEIVED BANDPASS SIGNAL AT THE MATCHED FILTER INPUT * AND . IS THE ONE SIDED NOISE POWER SPECTRUM AT THE MATCHED FILTER INPUT 7(Z &ILTER -ATCHING ,OSS &ILTER MATCHING LOSS ,M IS THE LOSS IN 3.2 THAT RESULTS WHEN A SIGNAL IS NOT PROCESSED USING A MATCHED FILTER 4HE FILTER MATCHING LOSS IS DEFINED AS
,M
3 . MF 3 . O
WHERE 3. O IS THE 3.2 AT THE OUTPUT OF A FILTER WITH FREQUENCY RESPONSE ( F AND 3. MF IS THE MATCHED FILTER 3.2 4HE FILTER MATCHING LOSS CAN ALSO BE EXPRESSED AS
,M
% . 3 . O
WHERE THE MATCHED FILTER 3.2 IS GIVEN BY 3. MF %. 4HE FILTER MATCHING LOSS IS q WHERE ,M FOR THE MATCHED FILTER 4HE FILTER MATCHING LOSS EXPRESSED IN DECIBELS IS ,MD" LOG,M AND EQUALS D" FOR THE MATCHED FILTER
!N ALTERNATE DEFINITION OF SIGNAL TO NOISE RATIO IS ALSO USED IN THE LITERATURE IN WHICH THE SIGNAL POWER AT THE PEAK OF THE WAVEFORM IS AVERAGED OVER ONE CYCLE OF THE CARRIER )N THIS CASE THE AVERAGE SIGNAL POWER IS ONE HALF OF THE PEAK SIGNAL POWER AND THE MATCHED FILTER OUTPUT 3.2 IS %.
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!MBIGUITY &UNCTIONS n 4HE AUTOCORRELATIONo FUNCTION FOR A TRANSMIT WAVEFORM WITH COMPLEX ENVELOPE UT IS DEFINED AS
c
C U T FD ¯ UT U T T E J P FD T DT
c
WHERE S IS THE RELATIVE TIME DELAY AND FD IS DOPPLER SHIFT 4HE RELATIVE TIME DELAY IS POSITIVE FOR A TARGET FURTHER IN RANGE THAN A REFERENCE TARGET AND DOPPLER FREQUENCY IS POSITIVE FOR AN INCOMING TARGET NEGATIVE RANGE RATE 4HE COMPLEX ENVELOPE UT IS NORMALIZED TO UNIT ENERGY c
¯ \ UT \ DT
c
4HE AMBIGUITY FUNCTION OF UT IS DEFINED AS THE SQUARE MAGNITUDE OF THE AUTOCORRELATION FUNCTION
9U T FD \ C U T FD \
4HE AMBIGUITY FUNCTION IS INTERPRETED AS A SURFACE ABOVE THE DELAY DOPPLER S n FD PLANE 4HE MAXIMUM VALUE OF THE AMBIGUITY FUNCTION IS UNITY AT THE ORIGIN S FD
9 U T FD a 9 U
4HE VOLUME UNDER THE AMBIGUITY SURFACE IS UNITY FOR ANY WAVEFORM UT c
c
¯ ¯ 9 U T FD DT DFD
c c
)N THE GENERAL CASE WHERE THE ENERGY OF THE COMPLEX ENVELOPE IS NOT NORMALIZED TO UNITY THE VALUE OF THE AMBIGUITY FUNCTION AT THE ORIGIN IS EQUAL TO % WHERE % IS THE ENERGY OF THE BANDPASS SIGNAL CORRESPONDING TO UT AND THE VOLUME UNDER THE AMBIGUITY FUNCTION IS ALSO EQUAL TO % 4HE NORMALIZATION CONDITION IS EQUIVALENT TO THE ASSUMPTION THAT THE ENERGY OF THE BANDPASS TRANSMIT WAVEFORM EQUALS * -ATCHED &ILTER 4IME 2ESPONSE 4HE MATCHED FILTER TIME RESPONSE TO A TARGET WITH DOPPLER SHIFT FD CAN BE EXPRESSED IN TERMS OF THE AUTOCORRELATION FUNCTION 4HE MATCHED FILTER IMPULSE RESPONSE WITH K AND T IS
HMF T U T
4HE MATCHED FILTER INPUT SIGNAL IS ASSUMED TO HAVE ZERO TIME DELAY AND A DOPPLER SHIFT FD
ST UT E J P FD T
o 4HE TERMINOLOGY FOR THIS FUNCTION IS NOT STANDARDIZED IN THE LITERATURE 7OODWARD USES THE TERM CORRELATION FUNC TION 4HE TERM TIME FREQUENCY AUTOCORRELATION FUNCTION IS USED BY 3PAFFORD 4HE SIGNS ASSOCIATED WITH S AND FD WITHIN THE INTEGRAND ALSO DIFFER IN THE LITERATURE 4HE STANDARDIZED DEFINITION PROPOSED BY 3INSKY AND 7ANG IS USED IN THIS CHAPTER
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4HE MATCHED FILTER OUTPUT SIGNAL YT IS FOUND BY CONVOLUTION OF ST WITH THE MATCHED FILTER IMPULSE RESPONSE HMFT c
YT
¯ UT ` U T ` T E J P F T ` DT ` D
c
#OMPARISON OF THIS RESULT WITH THE DEFINITION OF THE AUTOCORRELATION FUNCTION SHOWS THAT THE MATCHED FILTER RESPONSE CAN BE EXPRESSED AS
YT 8U T FD
!S A RESULT THE MATCHED FILTER TIME RESPONSE FOR A TARGET WITH DOPPLER FREQUENCY FD IS A TIME REVERSED VERSION OF THE AUTOCORRELATION FUNCTION #ONDITIONS FOR 4ARGET 2ESOLUTION IN 4IME $ELAY AND $OPPLER &REQUENCY !SSUME THAT TWO TARGETS WITH EQUAL RADAR CROSS SECTIONS ARE PRESENT AT THE SAME ANGULAR POSITION 4HE FIRST TARGET TERMED THE REFERENCE TARGET IS LOCATED AT THE ORIGIN OF THE DELAY DOPPLER PLANE WITH ZERO RELATIVE TIME DELAY AND ZERO DOPPLER FREQUENCY AND THE SECOND TARGET IS AT RELATIVE TIME DELAY S AND DOPPLER FREQUENCY FD 4HE RELATIVE TIME DELAY IS POSITIVE WHEN THE SECOND TARGET IS FARTHER IN RANGE THAN THE REFERENCE TARGET AND THE DOPPLER FREQUENCY IS POSITIVE FOR AN INCOMING TARGET 4HE MATCHED FILTER OUTPUT POWER FOR THE REFERENCE TARGET IS PROPORTIONAL TO THE AMBIGUITY FUNCTION AND IS GIVEN BY
0REF 9U
4HE MATCHED FILTER OUTPUT POWER FOR THE SECOND TARGET EVALUATED AT THE PEAK OF THE REFERENCE TARGET IS
0 9U S FD
4HE SECOND TARGET IS UNRESOLVED FROM THE REFERENCE TARGET AT LOCATIONS IN THE DELAY DOPPLER PLANE WHERE 9US FD y
, ,
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°£Ê /," 1 /" 4YPICAL TRACKING RADARS HAVE A PENCIL BEAM TO RECEIVE ECHOES FROM A SINGLE TARGET AND TRACK THE TARGET IN ANGLE RANGE ANDOR DOPPLER )TS RESOLUTION CELLDEFINED BY ITS ANTENNA BEAMWIDTH TRANSMITTER PULSE LENGTH EFFECTIVE PULSE LENGTH MAY BE SHORTER WITH PULSE COMPRESSION ANDOR DOPPLER BANDWIDTHIS USUALLY SMALL COMPARED WITH THAT OF A SEARCH RADAR AND IS USED TO EXCLUDE UNDESIRED ECHOES OR SIGNALS FROM OTHER TARGETS CLUTTER AND COUNTERMEASURES %LECTRONIC BEAM SCANNING PHASED ARRAY RADARS MAY TRACK MULTIPLE TARGETS BY SEQUENTIALLY DWELLING UPON AND MEASURING EACH TARGET WHILE EXCLUDING OTHER ECHO OR SIGNAL SOURCES "ECAUSE OF ITS NARROW BEAMWIDTH TYPICALLY FROM A FRACTION OF n TO OR n TRACKING RADARS USUALLY DEPEND UPON INFORMATION FROM A SURVEILLANCE RADAR OR OTHER SOURCE OF TARGET LOCATION TO ACQUIRE THE TARGET IE TO PLACE ITS BEAM ON OR IN THE VICINITY OF THE TARGET BEFORE INITIATING A TRACK 3CANNING OF THE BEAM WITHIN A LIMITED ANGLE SECTOR MAY BE NEEDED TO ACQUIRE THE TARGET WITHIN ITS BEAM AND CENTER THE RANGE TRACKING GATES ON THE ECHO PULSE PRIOR TO LOCKING ON THE TARGET OR CLOSING THE TRACKING LOOPS 4HE GATE ACTS LIKE A FAST ACTING ON OFF SWITCH THAT TURNS THE RECEIVER hONv AT THE LEADING EDGE OF THE TARGET ECHO PULSE AND hOFFv AT THE END OF THE TARGET ECHO PULSE TO ELIMINATE UNDESIRED ECHOES 4HE RANGE TRACKING SYSTEM PERFORMS THE TASK OF KEEPING THE GATE CENTERED ON THE TARGET ECHO AS DESCRIBED IN 3ECTION 4HE PRIMARY OUTPUT OF TRACKING RADAR IS THE TARGET LOCATION DETERMINED FROM THE POINTING ANGLES OF THE BEAM AND POSITION OF ITS RANGE TRACKING GATES 4HE ANGLE LOCA TION IS THE DATA OBTAINED FROM SYNCHROS AND ENCODERS ON THE ANTENNA TRACKING AXES OR DATA FROM A BEAM POSITIONING COMPUTER ON AN ELECTRONIC SCAN PHASED ARRAY RADAR )N SOME CASES TRACKING LAG IS MEASURED BY CONVERTING TRACKING LAG ERROR VOLTAGES FROM THE TRACKING LOOPS TO UNITS OF ANGLE 4HIS DATA IS USED TO ADD TO OR SUBTRACT FROM THE ANGLE SHAFT POSITION DATA FOR REAL TIME CORRECTION OF TRACKING LAG 4HERE ARE A LARGE VARIETY OF TRACKING RADAR SYSTEMS INCLUDING SOME THAT ACHIEVE SIMULTANEOUSLY BOTH SURVEILLANCE AND TRACKING FUNCTIONS ! WIDELY USED TYPE OF TRACKING RADAR AND THE ONE DISCUSSED IN DETAIL IN THIS CHAPTER IS A GROUND BASED SYS TEM CONSISTING OF A PENCIL BEAM ANTENNA MOUNTED ON A ROTATABLE PLATFORM WITH SERVO MOTOR DRIVE OF ITS AZIMUTH AND ELEVATION POSITION TO FOLLOW A TARGET &IGURE A %RRORS IN POINTING DIRECTION ARE DETERMINED BY SENSING THE ANGLE OF ARRIVAL OF THE ECHO WAVEFRONT AND CORRECTED BY POSITIONING THE ANTENNA TO KEEP THE TARGET CENTERED °£
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IN THE BEAM -ODERN REQUIREMENTS FOR SIMULTANEOUS PRECISION TRACKING OF MULTIPLE TARGETS HAS DRIVEN THE DEVELOPMENT OF THE ELECTRONIC SCAN ARRAY MONOPULSE RADAR WITH THE CAPABILITY TO SWITCH ITS BEAM PULSE TO PULSE AMONG MULTIPLE TARGETS 4HE !.-03 SHOWN IN &IGURE B IS AN EXAMPLE OF A HIGHLY VERSATILE ELECTRONIC SCAN MONOPULSE MISSILE RANGE INSTRUMENTATION RADAR 4HE PRINCIPAL APPLICATIONS OF PRECISION TRACKING RADAR ARE WEAPON CONTROL AND MISSILE RANGE INSTRUMENTATION )N BOTH APPLICATIONS A HIGH DEGREE OF PRECISION AND AN ACCURATE PREDICTION OF FUTURE POSITION OF THE TARGET ARE GENERALLY REQUIRED 4HE EARLIEST USE OF TRACKING RADAR WAS GUNFIRE CONTROL 4HE AZIMUTH ANGLE ELEVATION ANGLE AND THE RANGE TO THE TARGET WERE MEASURED AND FROM THE RATE OF CHANGE OF THESE PARAMETERS THE VELOCITY VECTOR OF THE TARGET SPEED AND DIRECTION WAS COMPUTED AND ITS FUTURE POSITION PREDICTED 4HIS INFORMATION WAS USED TO MOVE THE GUN TO LEAD THE TARGET AND SET THE FUZE DELAY 4HE TRACKING RADAR PERFORMS A SIMILAR ROLE IN PROVIDING GUIDANCE INFORMATION AND STEERING COMMANDS FOR MISSILE CONTROL )N MISSILE RANGE INSTRUMENTATION THE TRACKING RADAR OUTPUT IS USED TO MEASURE THE TRAJECTORY OF THE MISSILE AND TO PREDICT FUTURE POSITION 4RACKING RADARS ARE USED TO COM PUTE THE IMPACT POINT OF A LAUNCHED MISSILE CONTINUOUSLY DURING THE LAUNCH PHASE IN CASE OF MISSILE FAILURE FOR RANGE SAFETY )F THE IMPACT POINT APPROACHES A POPULATED OR OTHER CRITICAL AREA THE MISSILE IS DESTROYED -ISSILE RANGE INSTRUMENTATION RADARS ARE NORMALLY USED WITH A BEACON PULSE REPEATER TO PROVIDE A POINT SOURCE ECHOUSUALLY ITS PULSE IS DELAYED TO SEPARATE IT FROM THE TARGET ECHOAND WITH HIGH SIGNAL TO NOISE RATIO TO ACHIEVE PRECISION TRACKING ON THE ORDER OF MIL IN ANGLE AND M IN RANGE
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&)'52% A !.&01 # BAND MONOPULSE PRECISION TRACKING RADAR INSTALLATION AT THE .!3! 7ALLOPS )SLAND 3TATION 6! )T HAS A FT DIAMETER DISH AND A SPECIFIED TRACKING PRECISION OF MRAD RMS B !.-03 # BAND ELECTRONIC SCAN PHASED ARRAY -ULTI /BJECT 4RACKING 2ADAR -/42 INSTALLED AT THE 7HITE 3ANDS -ISSILE 2ANGE 0HOTO OF THE !.-03 COURTESY OF THE 7HITE 3ANDS -ISSILE 2ANGE AND ,OCKHEED -ARTIN
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4HIS CHAPTER DESCRIBES THE MONOPULSE SIMULTANEOUS LOBING WITH EITHER PHASE COM PARISON OR AMPLITUDE COMPARISON CONICAL SCAN AND SEQUENTIAL LOBING TRACKING RADAR TECHNIQUES WITH THE MAIN EMPHASIS ON THE AMPLITUDE COMPARISON MONOPULSE SIMUL TANEOUS LOBING RADAR
°ÓÊ " "*1 - Ê- 1 / "1-Ê " ® 4HE SUSCEPTIBILITY OF CONICAL SCANNING AND SEQUENTIAL LOBING TRACKING TECHNIQUES TO ECHO AMPLITUDE FLUCTUATIONS AND AMPLITUDE JAMMING AS DESCRIBED IN 3ECTION WAS THE MAJOR REASON FOR THE DEVELOPMENT OF TRACKING RADAR THAT PROVIDES SIMULTANE OUSLY ALL THE NECESSARY LOBES FOR ANGLE ERROR SENSING 4HIS REQUIRED THAT THE OUTPUT FROM THE LOBES BE COMPARED SIMULTANEOUSLY ON A SINGLE PULSE ELIMINATING THE EFFECTS OF ECHO AMPLITUDE CHANGE WITH TIME 4HE TECHNIQUE TO ACCOMPLISH THIS WAS INITIALLY CALLED SIMULTANEOUS LOBING WHICH WAS DESCRIPTIVE OF THE TECHNIQUE ,ATER THE TERM MONOPULSE WAS COINED REFERRING TO THE ABILITY TO OBTAIN ANGLE ERROR INFORMATION ON A SINGLE PULSE )T HAS BECOME THE COMMONLY USED NAME FOR THIS TRACKING TECHNIQUE EVEN THOUGH THE LOBES ARE GENERATED SIMULTANEOUSLY AND MONOPULSE TRACKING CAN BE PERFORMED WITH #7 RADAR 4HE ORIGINAL MONOPULSE TRACKING RADARS SUFFERED IN ANTENNA EFFICIENCY AND COM PLEXITY OF MICROWAVE CIRCUITRY BECAUSE WAVEGUIDE SIGNAL COMBINING CIRCUITRY WAS A RELATIVELY NEW ART 4HESE PROBLEMS WERE OVERCOME AND MONOPULSE RADAR WITH MOD ERN COMPACT OFF THE SHELF PROCESSING CIRCUITRY CAN READILY OUTPERFORM SCANNING AND LOBING SYSTEMS 4HE MONOPULSE TECHNIQUE ALSO HAS AN INHERENT CAPABILITY FOR HIGH PRECISION ANGLE MEASUREMENT BECAUSE ITS FEED STRUCTURE IS COMPACT WITH SHORT SIGNAL PATHS AND RIGIDLY MOUNTED WITH NO MOVING PARTS 4HIS HAS MADE POSSIBLE THE DEVEL OPMENT OF PENCIL BEAM TRACKING RADARS THAT MEET MISSILE RANGE INSTRUMENTATION RADAR REQUIREMENTS OF n ANGLE TRACKING PRECISION 4HIS CHAPTER IS DEVOTED TO TRACKING RADAR BUT MONOPULSE TECHNIQUES ARE USED IN OTHER SYSTEMS INCLUDING HOMING DEVICES DIRECTION FINDERS AND SOME SEARCH RADARS (OWEVER MOST OF THE BASIC PRINCIPLES AND LIMITATIONS OF MONOPULSE APPLY FOR ALL APPLI CATIONS -ORE GENERAL COVERAGE IS FOUND IN 3HERMAN AND ,EONOV AND &ORMICHEV !MPLITUDE #OMPARISON -ONOPULSE ! METHOD FOR VISUALIZING THE OPERATION OF AN AMPLITUDE COMPARISON RECEIVER IS TO CONSIDER THE ECHO SIGNAL AT THE FOCAL PLANE OF AN ANTENNA 4HE ECHO IS FOCUSED TO A FINITE SIZE hSPOTv 4HE hSPOTv IS CENTERED ON THE FOCAL PLANE WHEN THE TARGET IS ON THE ANTENNA AXIS AND MOVES OFF CENTER WHEN THE TAR GET MOVES OFF AXIS 4HE ANTENNA FEED IS LOCATED AT THE FOCAL POINT TO RECEIVE MAXIMUM ENERGY FROM A TARGET ON AXIS 4HE AMPLITUDE COMPARISON FEED IS DESIGNED TO SENSE ANY FEED PLANE DISPLACEMENT OF THE SPOT FROM THE CENTER OF THE FOCAL PLANE ! MONOPULSE FEED USING THE FOUR HORN SQUARE FOR EXAMPLE WOULD BE CENTERED AT THE FOCAL PLANE )T PROVIDES SYMMETRY SO THAT WHEN THE SPOT IS CENTERED EQUAL ENERGY FALLS ON EACH OF THE FOUR HORNS 4HE RADAR SENSES TARGET DISPLACEMENT FROM THE ANTENNA AXIS THAT SHIFTS THE SPOT OFF OF THE CENTER OF THE FOCAL PLANE BY MEASURING THE RESULTANT UNBALANCE OF ENERGY RECEIVED IN THE FOUR HORNS 4HIS IS ACCOMPLISHED BY USE OF MICROWAVE WAVEGUIDE HYBRIDS TO SUBTRACT OUTPUTS OF PAIRS OF HORNS PROVIDING A SENSITIVE DEVICE THAT GIVES SIGNAL OUT PUT WHEN THERE IS AN UNBALANCE CAUSED BY THE TARGET BEING OFF AXIS 4HE 2& CIRCUITRY FOR A CONVENTIONAL FOUR HORN SQUARE FEED SEE &IGURE SUBTRACTS THE OUTPUT OF
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&)'52% -ICROWAVE COMPARATOR CIRCUITRY USED WITH A FOUR HORN MONOPULSE FEED
THE LEFT PAIR FROM THE OUTPUT OF THE RIGHT PAIR TO SENSE ANY UNBALANCE IN THE AZIMUTH DIRECTION )T ALSO SUBTRACTS THE OUTPUT OF THE TOP PAIR FROM THE OUTPUT OF THE BOTTOM PAIR TO SENSE ANY UNBALANCE IN THE ELEVATION DIRECTION )N ADDITION THE CIRCUITRY ADDS THE OUTPUT OF ALL FOUR HORNS FOR A SUM SIGNAL FOR DETECTION MONOPULSE PROCESSING AND RANGE TRACKING 4HE COMPARATOR SHOWN IN &IGURE IS THE CIRCUITRY THAT PERFORMS THE ADDITION AND SUBTRACTION OF THE FEED HORN OUTPUTS TO OBTAIN MONOPULSE SUM AND DIFFERENCE SIGNALS )T IS ILLUSTRATED WITH HYBRID 4 OR MAGIC 4 WAVEGUIDE COMPONENTS 4HESE ARE FOUR PORT DEVICES THAT IN BASIC FORM HAVE THE INPUTS AND OUTPUTS LOCATED AT RIGHT ANGLES TO EACH OTHER (OWEVER THE MAGIC 4S HAVE BEEN DEVELOPED IN CONVENIENT hFOLDEDv CONFIGU RATIONS FOR A VERY COMPACT COMPARATOR 4HE PERFORMANCE OF THESE AND OTHER SIMILAR FOUR PORT DEVICES IS DESCRIBED IN #HAPTER OF 3HERMAN 4HE SUBTRACTOR OUTPUTS ARE CALLED DIFFERENCE SIGNALS WHICH ARE ZERO WHEN THE TARGET IS ON AXIS INCREASING IN AMPLITUDE WITH INCREASING DISPLACEMENT OF THE TARGET FROM THE ANTENNA AXIS 4HE DIFFERENCE SIGNALS ALSO CHANGE n IN PHASE FROM ONE SIDE OF CENTER TO THE OTHER 4HE SUM OF ALL FOUR HORN OUTPUTS PROVIDES A REFERENCE SIGNAL TO CONTROL ANGLE TRACKING SENSITIVITY VOLTS PER DEGREE OF ERROR TO REMAIN CONSTANT EVEN THOUGH THE TARGET ECHO SIGNAL MAY VARY OVER A LARGE DYNAMIC RANGE 4HIS IS ACCOMPLISHED BY AUTOMATIC GAIN CONTROL !'# TO KEEP THE SUM SIGNAL OUTPUT AND ANGLE TRACKING LOOP GAINS CONSTANT FOR STABLE AUTOMATIC ANGLE TRACKING &IGURE IS A BLOCK DIAGRAM OF TYPICAL MONOPULSE RADARS 4HE SUM SIGNAL ELEVA TION DIFFERENCE SIGNAL AND AZIMUTH DIFFERENCE SIGNAL ARE EACH CONVERTED TO INTERMEDI ATE FREQUENCY )& USING A COMMON LOCAL OSCILLATOR TO MAINTAIN RELATIVE PHASE AT )& 4HE )& SUM SIGNAL OUTPUT IS DETECTED AND PROVIDES THE VIDEO INPUT TO THE RANGE TRACKER 4HE RANGE TRACKER MEASURES AND TRACKS THE TIME OF ARRIVAL OF THE DESIRED TARGET ECHO AND PROVIDES GATE PULSES THAT TURN ON THE RADAR RECEIVER CHANNELS ONLY DURING THE BRIEF PERIOD WHEN THE DESIRED ECHO IS EXPECTED 4HE GATED VIDEO IS USED TO GENERATE THE DC
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&)'52% "LOCK DIAGRAM OF A CONVENTIONAL MONOPULSE TRACKING RADAR
VOLTAGE PROPORTIONAL TO THE MAGNITUDE OF THE 3 SIGNAL OR ¨3 ¨FOR THE !'# OF ALL THREE )& AMPLIFIER CHANNELS 4HE !'# MAINTAINS CONSTANT ANGLE TRACKING SENSITIVITY VOLTS PER DEGREE ERROR EVEN THOUGH THE TARGET ECHO SIGNAL VARIES OVER A LARGE DYNAMIC RANGE BY CONTROLLING GAIN OR DIVIDING BY ¨3 ¨ !'# IS NECESSARY TO KEEP THE GAIN OF THE ANGLE TRACKING LOOPS CONSTANT FOR STABLE AUTOMATIC ANGLE TRACKING 3OME MONOPULSE SYSTEMS SUCH AS THE TWO CHANNEL MONOPULSE CAN PROVIDE INSTANTANEOUS !'# OR NORMALIZING BY USE OF LOG DETECTORS AS DESCRIBED LATER IN THIS SECTION 4HE SUM SIGNAL AT THE )& OUTPUT ALSO PROVIDES A REFERENCE SIGNAL TO PHASE DETECTORS THAT DERIVE ANGLE TRACKING ERROR VOLTAGES FROM THE DIFFERENCE SIGNALS 4HE PHASE DETEC TORS ARE ESSENTIALLY DOT PRODUCT DEVICES PRODUCING THE OUTPUT VOLTAGE
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WHERE E ANGLE ERROR DETECTOR OUTPUT VOLTAGE ¨3 ¨ MAGNITUDE OF SUM SIGNAL ¨$ ¨ MAGNITUDE OF DIFFERENCE SIGNAL P PHASE ANGLE BETWEEN SUM AND DIFFERENCE SIGNALS 4HE DOT PRODUCT ERROR DETECTOR IS ONLY ONE OF A WIDE VARIETY OF MONOPULSE ANGLE ERROR DETECTORS DESCRIBED IN #HAPTER OF 3HERMAN .ORMALLY P IS EITHER n OR n WHEN THE RADAR IS PROPERLY ADJUSTED AND THE ONLY PURPOSE OF THE PHASE SENSITIVE CHARACTERISTIC IS TO PROVIDE A PLUS OR MINUS POLARITY COR RESPONDING TO P n AND P n RESPECTIVELY GIVING A OR n POLARITY TO THE ANGLE ERROR DETECTOR OUTPUT TO INDICATE TO THE SERVO WHICH DIRECTION TO DRIVE THE PEDESTAL )N A PULSED TRACKING RADAR THE ANGLE ERROR DETECTOR OUTPUT IS BIPOLAR VIDEO THAT IS IT IS A VIDEO PULSE WITH AN AMPLITUDE PROPORTIONAL TO THE ANGLE ERROR AND WHOSE POLARITY POSITIVE OR NEGATIVE CORRESPONDS TO THE DIRECTION OF THE ERROR 4HIS VIDEO IS TYPICALLY PROCESSED BY A SAMPLE AND HOLD CIRCUIT THAT CHARGES A CAPACITOR TO THE PEAK VIDEO PULSE VOLTAGE AND HOLDS THE CHARGE UNTIL THE NEXT PULSE AT WHICH TIME THE CAPACITOR IS DISCHARGED AND RECHARGED TO THE NEW PULSE LEVEL 7ITH MODERATE LOW PASS FILTERING THIS GIVES THE DC ERROR VOLTAGE OUTPUT TO THE SERVO AMPLIFIER TO CORRECT THE ANTENNA POSITION
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4HE THREE CHANNEL AMPLITUDE COMPARISON MONOPULSE TRACKING RADAR IS THE MOST COMMONLY USED MONOPULSE SYSTEM (OWEVER THE THREE SIGNALS MAY SOMETIMES BE COMBINED IN OTHER WAYS TO PERFORM WITH A TWO CHANNEL RECEIVER SYSTEM AS DESCRIBED LATER IN THIS SECTION USED IN SOME CURRENT SURFACE TO AIR MISSILE 3!- SYSTEMS -ONOPULSE !NTENNA &EED 4ECHNIQUES -ONOPULSE RADAR FEEDS MAY HAVE ANY OF A VARIETY OF CONFIGURATIONS 3INGLE APERTURES ARE ALSO EMPLOYED BY USE OF HIGHER ORDER WAVEGUIDE MODES TO EXTRACT ANGLE ERROR SENSING DIFFERENCE SIGNALS 4HERE ARE MANY TRADEOFFS IN FEED DESIGN BECAUSE OPTIMUM SUM AND DIFFERENCE SIGNALS LOW SIDELOBE LEVELS SELECTABLE POLARIZATION CAPABILITY AND SIMPLICITY CANNOT ALL BE FULLY SATISFIED SIMULTANEOUSLY 4HE TERM SIMPLICITY REFERS NOT ONLY TO COST SAVINGS BUT ALSO TO THE USE OF NONCOMPLEX CIRCUITRY WHICH IS NECESSARY TO PROVIDE A BROADBAND SYSTEM WITH GOOD BORESIGHT STABILITY TO MEET PRECISION TRACKING REQUIREMENTS "ORESIGHT IS THE ELECTRICAL AXIS OF THE ANTENNA OR THE ANGULAR LOCATION OF A SIGNAL SOURCE WITHIN THE ANTENNA BEAM AT WHICH THE ANGLE ERROR DETECTOR OUTPUTS GO TO ZERO 3OME OF THE TYPICAL MONOPULSE FEEDS ARE DESCRIBED TO SHOW THE BASIC RELATIONS AND TRADEOFFS INVOLVED IN THE VARIOUS PERFORMANCE FACTORS AND HOW THE MORE IMPORTANT FACTORS CAN BE OPTIMIZED BY A FEED CONFIGURATION BUT AT THE PRICE OF LOWER PERFORMANCE IN OTHER AREAS -ANY NEW TECHNIQUES HAVE BEEN ADDED SINCE THE ORIGINAL FOUR HORN SQUARE FEED IN ORDER TO PROVIDE GOOD OR EXCELLENT PERFORMANCE IN ALL DESIRED FEED CHAR ACTERISTICS IN A WELL DESIGNED MONOPULSE RADAR 4HE ORIGINAL FOUR HORN SQUARE MONOPULSE FEED IS INEFFICIENT BECAUSE THE OPTIMUM FEED SIZE APERTURE FOR THE DIFFERENCE SIGNALS IS APPROXIMATELY TWICE THE OPTIMUM SIZE FOR THE SUM SIGNAL #ONSEQUENTLY AN INTERMEDIATE SIZE IS TYPICALLY USED WITH A SIGNIFI CANT COMPROMISE FOR BOTH SUM AND DIFFERENCE SIGNALS 4HE OPTIMUM FOUR HORN SQUARE FEED WHICH IS SUBJECT TO THIS COMPROMISE DESCRIBED IN 3HERMAN IS BASED ON MINI MIZING THE ANGLE ERROR CAUSED BY RECEIVER THERMAL NOISE (OWEVER IF SIDELOBES ARE A PRIME CONSIDERATION A SOMEWHAT DIFFERENT FEED SIZE MAY BE DESIRED 4HE LIMITATION OF THE FOUR HORN SQUARED FEED IS THAT THE SUM AND DIFFERENCE SIGNAL % FIELDS CANNOT BE CONTROLLED INDEPENDENTLY )F INDEPENDENT CONTROL COULD BE PROVIDED THE IDEAL WOULD BE APPROXIMATELY AS DESCRIBED IN &IGURE WITH TWICE THE DIMENSION FOR THE DIFFERENCE SIGNALS IN THE PLANE OF ERROR SENSING THAN FOR THE SUM SIGNAL ! TECHNIQUE USED BY THE -)4 ,INCOLN ,ABORATORY TO APPROACH THE IDEAL IS A HORN FEED &IGURE 4HE OVERALL FEED AS ILLUSTRATED IS DIVIDED INTO SMALL PARTS AND THE MICROWAVE CIRCUITRY SELECTS THE PORTIONS NECESSARY FOR THE SUM AND DIFFERENCE SIGNALS TO APPROACH THE IDEAL /NE DISADVANTAGE IS THAT THIS FEED REQUIRES A VERY COMPLEX MICROWAVE CIRCUIT !LSO THE DIVIDED FOUR HORN PORTIONS OF THE FEED ARE EACH FOUR ELEMENT ARRAYS THAT GENERATE LARGE FEED SIDELOBES IN THE ( PLANE BECAUSE OF THE DOUBLE PEAK % FIELD !NOTHER CONSIDERATION IS THAT THE HORN FEED IS NOT PRACTICAL FOR FOCAL POINT FED PARABOLAS OR REFLECTARRAYS BECAUSE OF ITS SIZE ! FOCAL POINT FEED IS USUALLY SMALL TO PRODUCE A BROAD PATTERN AND MUST BE COMPACT TO AVOID BLOCKAGE OF THE ANTENNA APERTURE )N SOME CASES THE SMALL OPTIMUM SIZE REQUIRED IS BELOW WAVEGUIDE CUTOFF AND DIELECTRIC LOADING OF THE HORN APERTURES BECOMES NEC &)'52% !PPROXIMATELY IDEAL FEED APERTURE ESSARY TO AVOID CUTOFF % FIELD DISTRIBUTION FOR SUM AND DIFFERENCE SIGNALS
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&)'52% 4WELVE HORN FEED
! PRACTICAL APPROACH TO MONOPULSE FEED DESIGN USES HIGHER ORDER WAVEGUIDE MODES RATHER THAN MULTIPLE HORNS FOR INDEPENDENT CONTROL OF SUM AND DIFFERENCE SIGNAL % FIELDS 4HIS ALLOWS MUCH GREATER SIMPLICITY AND FLEXIBILITY ! TRIPLE MODE TWO HORN FEED USED BY 2#! RETRACTS THE % PLANE SEPTA TO ALLOW BOTH THE 4% AND 4% MODES TO BE EXCITED AND PROPAGATE IN THE DOUBLE WIDTH SEPTUMLESS REGION AS ILLUSTRATED IN &IGURE !T THE SEPTUM THE DOUBLE HUMPED % FIELD IS REPRESENTED BY THE COMBINED 4% AND 4% MODES SUBTRACTING AT THE CENTER AND ADDING AT THE 4% MODE OUTER PEAKS (OWEVER BECAUSE THE TWO MODES PROPAGATE AT DIFFERENT VELOCITIES A POINT IS REACHED FARTHER DOWN THE DOUBLE WIDTH GUIDE WHERE THE TWO MODES ADD IN THE CENTER AND SUBTRACT AT THE OUTER HUMPS OF THE 4% MODE 4HE RESULT IS A SUM SIGNAL % FIELD CONCENTRATED AS DESIRED TOWARD THE CENTER OF THE FEED APERTURE 4HIS SHAPING OF THE SUM SIGNAL % FIELD IS ACCOMPLISHED INDEPENDENTLY OF THE DIFFERENCE SIGNAL % FIELD 4HE DIFFERENCE SIGNAL IS TWO 4% MODE SIGNALS SIDE BY SIDE ARRIVING AT THE SEPTUM OF &IGURE OUT OF PHASE !T THE SEPTUM IT BECOMES THE 4% MODE WHICH PROPAGATES TO THE HORN APERTURE AND USES THE FULL WIDTH OF THE HORN AS DESIRED 4HE 4% MODE HAS ZERO % FIELD IN THE CENTER OF THE WAVEGUIDE WHERE THE SEPTUM IS LOCATED AND IS UNAFFECTED BY THE SEPTUM ! FURTHER STEP IN FEED DEVELOPMENT IS THE FOUR HORN TRIPLE MODE FEED ILLUSTRATED IN &IGURE 4HIS FEED USES THE SAME APPROACH AS DESCRIBED ABOVE BUT WITH THE ADDI TION OF A TOP AND BOTTOM HORN 4HIS ALLOWS THE % PLANE DIFFERENCE SIGNAL TO COUPLE TO ALL FOUR HORNS AND USES THE FULL HEIGHT OF THE FEED 4HE SUM SIGNAL USES ONLY THE CENTER TWO HORNS TO LIMIT ITS % FIELD IN THE % PLANE AS DESIRED FOR THE IDEAL FIELD SHAPING
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&)'52% 5SE OF RETRACTED SEPTUM TO SHAPE THE SUM SIGNAL % FIELD
4HE USE OF SMALLER TOP AND BOTTOM HORNS IS A SIMPLER METHOD OF CONCENTRATING THE % FIELD TOWARD THE CENTER OF THE FEED WHERE THE FULL HORN WIDTH IS NOT NEEDED 4HE FEEDS DESCRIBED THUS FAR ARE FOR LINEAR POLARIZATION OPERATION 7HEN CIRCULAR POLARIZATION IS NEEDED IN A PARABOLOID TYPE ANTENNA SQUARE OR CIRCULAR CROSS SECTION HORN THROATS ARE USED 4HE VERTICAL AND HORIZONTAL COMPONENTS FROM EACH HORN ARE
&)'52% &OUR HORN TRIPLE MODE FEED AFTER 0 7 (ANNAN Ú )%%%
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SEPARATED AND COMPARATORS PROVIDED FOR EACH POLARIZATION 4HE SUM AND DIFFERENCE SIGNALS FROM THE COMPARATORS ARE COMBINED WITH RELATIVE PHASE TO OBTAIN CIRCULAR POLARIZATION 5SE OF THE PREVIOUSLY DESCRIBED FEEDS FOR CIRCULAR POLARIZATION WOULD REQUIRE THE WAVEGUIDE CIRCUITRY TO BE PROHIBITIVELY COMPLEX #ONSEQUENTLY A FIVE HORN FEED HAS BEEN USED AS ILLUSTRATED IN &IGURE 4HE FIVE HORN FEED IS SELECTED BECAUSE OF THE SIMPLICITY OF THE COMPARATOR THAT REQUIRES ONLY TWO MAGIC OR HYBRID 4S FOR EACH POLARIZATION 4HE SUM AND DIFFER ENCE SIGNALS ARE PROVIDED FOR THE TWO LINEAR POLARIZATION COMPONENTS AND IN AN !.&01 RADAR ARE COMBINED IN A WAVEGUIDE SWITCH FOR SELECTING POLARIZATION 4HE SWITCH SELECTS EITHER THE VERTICAL OR THE HORIZONTAL INPUT COMPONENT OR COMBINES THEM WITH A RELATIVE PHASE FOR CIRCULAR POLARIZATION 4HIS FEED DOES NOT PROVIDE OPTIMUM SUM AND DIFFERENCE SIGNAL % FIELDS BECAUSE THE SUM HORN OCCUPIES SPACE DESIRED FOR THE DIFFERENCE SIGNALS 'ENERALLY AN UNDERSIZED SUM SIGNAL HORN IS USED AS A COMPROMISE (OWEVER THE FIVE HORN FEED IS A PRACTICAL CHOICE BETWEEN COM PLEXITY AND EFFICIENCY )T HAS BEEN USED IN SEVERAL INSTRUMENTATION RADARS INCLUDING THE !.&01 !.&01 !.401 AND!.-03 AND IN THE !.401 TACTICAL PRECISION TRACKING RADAR 4HE MULTIMODE FEED TECHNIQUE CAN BE EXPANDED TO OTHER HIGHER ORDER MODES FOR ERROR SENSING AND % FIELD SHAPING 4HE DIFFERENCE SIGNALS ARE CONTAINED IN UNSYM METRICAL MODES SUCH AS THE 4% MODE FOR ( PLANE ERROR SENSING AND COMBINED 4% AND 4- MODES FOR % PLANE ERROR SENSING 4HESE MODES PROVIDE THE DIFFERENCE SIG NALS AND NO COMPARATORS ARE USED 'ENERALLY MODE COUPLING DEVICES CAN GIVE GOOD PERFORMANCE IN SEPARATING THE SYMMETRICAL AND UNSYMMETRICAL MODES WITHOUT SIGNIFI CANT CROSS COUPLING PROBLEMS
&)'52% &IVE HORN FEED WITH COUPLING TO BOTH LINEAR POLARIZATION COMPONENTS WHICH ARE COMBINED BY THE SWITCH MATRIX TO SELECT HORIZONTAL VERTICAL OR CIRCULAR POLARIZATION
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-ULTIBAND MONOPULSE FEED CONFIGURATIONS ARE PRACTICAL AND IN USE IN SEVERAL SYS TEMS ! SIMPLE EXAMPLE IS A COMBINED 8 BAND AND +A BAND MONOPULSE PARABOLOID ANTENNA RADAR 3EPARATE CONVENTIONAL FEEDS ARE USED FOR EACH BAND WITH THE +A BAND FEED AS A #ASSEGRAIN FEED AND THE 8 BAND FEED AT THE FOCAL POINT 4HE #ASSEGRAIN SUB DISH IS A HYPERBOLIC SHAPED HIGHLY EFFICIENT GRID OF WIRES REFLECTIVE TO PARALLEL POLARIZA TION AND TRANSPARENT TO ORTHOGONAL POLARIZATION )T IS ORIENTED TO BE TRANSPARENT TO THE 8 BAND FOCAL POINT FEED BEHIND IT AND REFLECTIVE TO THE ORTHOGONALLY POLARIZED +A BAND FEED EXTENDING FROM THE VERTEX OF THE PARABOLOID -ONOPULSE FEED HORNS AT DIFFERENT MICROWAVE FREQUENCIES CAN ALSO BE COMBINED WITH CONCENTRIC FEED HORNS 4HE MULTIBAND FEED CLUSTERS WILL SACRIFICE EFFICIENCY BUT CAN SATISFY MULTIBAND REQUIREMENTS IN A SINGLE ANTENNA !'# !UTOMATIC 'AIN #ONTROL 4O MAINTAIN A STABLE CLOSED LOOP SERVOSYSTEM FOR ANGLE TRACKING THE RADAR MUST MAINTAIN ESSENTIALLY CONSTANT LOOP GAIN INDEPENDENT OF TARGET ECHO SIZE AND RANGE 4HE PROBLEM IS THAT MONOPULSE DIFFERENCE SIGNALS FROM THE ANTENNA ARE PROPORTIONAL TO BOTH THE ANGLE DISPLACEMENT OF THE TARGET FROM THE ANTENNA AXIS AND THE ECHO SIGNAL AMPLITUDE &OR A GIVEN TRACKING ERROR THE ERROR VOLTAGE WOULD CHANGE WITH ECHO AMPLITUDE AND TARGET RANGE CAUSING A CORRESPONDING CHANGE IN LOOP GAIN !'# IS USED TO REMOVE THE ANGLE ERROR DETECTOR OUTPUT DEPENDENCE ON ECHO AMPLI TUDE AND RETAIN CONSTANT TRACKING LOOP GAIN ! TYPICAL !'# TECHNIQUE IS ILLUSTRATED IN &IGURE FOR A ONE ANGLE COORDINATE TRACKING SYSTEM 4HE !'# SYSTEM DETECTS THE PEAK VOLTAGE OF THE SUM SIGNAL AND PROVIDES A NEGATIVE DC VOLTAGE PROPORTIONAL TO THE PEAK SIGNAL VOLTAGE 4HE NEGATIVE VOLTAGE IS FED TO THE )& AMPLIFIER STAGE WHERE IT IS USED TO DECREASE GAIN AS THE SIGNAL INCREASES ! HIGH GAIN IN THE !'# LOOP IS EQUIVALENT TO DIVIDING THE )& OUTPUT BY A FACTOR PROPORTIONAL TO ITS AMPLITUDE )N A THREE CHANNEL MONOPULSE RADAR ALL THREE CHANNELS ARE CONTROLLED BY THE !'# VOLTAGE WHICH EFFECTIVELY PERFORMS A DIVISION BY THE MAGNITUDE OF THE SUM SIGNAL OR ECHO AMPLITUDE #ONVENTIONAL !'# ESSENTIALLY HOLDS CONSTANT GAIN DURING THE PULSE REPETITION INTERVAL !LSO THE !'# OF THE SUM CHANNEL NORMALIZES THE SUM ECHO PULSE AMPLITUDE TO SIMILARLY MAINTAIN A STABLE RANGE TRACKING SERVO LOOP 4HE ANGLE ERROR DETECTOR ASSUMED TO BE A PRODUCE DETECTOR HAS AN OUTPUT \E\ K
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WHERE \ E \ IS THE MAGNITUDE OF THE ANGLE ERROR VOLTAGE 0HASES ARE ADJUSTED TO PROVIDE OR ON A POINT SOURCE TARGET 4HE RESULTANT IS \E\ o K
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&)'52% !'# IN MONOPULSE TRACKING
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#OMPLEX TARGETS CAN CAUSE OTHER PHASE RELATIONS AS A PART OF THE ANGLE SCINTILLATION PHENOMENON 4HE ABOVE ERROR VOLTAGE PROPORTIONAL TO THE RATIO OF THE DIFFERENCE SIGNAL DIVIDED BY THE SUM SIGNAL IS THE DESIRED ANGLE ERROR DETECTOR OUTPUT GIVING A CONSTANT ANGLE ERROR SENSITIVITY 7ITH LIMITED !'# BANDWIDTH SOME RAPID SIGNAL FLUCTUATIONS MODULATE ¨E ¨BUT THE LONG TIME AVERAGE ANGLE SENSITIVITY IS CONSTANT 4HESE FLUCTUATIONS ARE LARGELY FROM RAPID CHANGES IN TARGET REFLECTIVITY R T THAT ARE FROM TARGET AMPLITUDE SCINTILLATION 4HE RANDOM MODULATION OF ¨E ¨CAUSES AN ADDITIONAL ANGLE NOISE COMPONENT THAT AFFECTS THE CHOICE OF !'# BANDWIDTH 4HE !'# PERFORMANCE IN CONICAL SCAN RADARS PROVIDES SIMILAR CONSTANT ANGLE ERROR SENSITIVITY /NE MAJOR LIMITATION IN CONICAL SCAN RADARS IS THAT THE !'# BANDWIDTH MUST BE SUFFICIENTLY LOWER THAN THE SCAN FREQUENCY TO PREVENT THE !'# FROM REMOVING THE MODULATION CONTAINING THE ANGLE ERROR INFORMATION 0HASE #OMPARISON -ONOPULSE ! SECOND MONOPULSE TECHNIQUE IS THE USE OF MUL TIPLE ANTENNAS WITH OVERLAPPING NONSQUINTED BEAMS POINTED AT THE TARGET )NTERPOLATING TARGET ANGLES WITHIN THE BEAM IS ACCOMPLISHED AS SHOWN IN &IGURE BY COMPARING THE PHASE OF THE SIGNALS FROM THE ANTENNAS FOR SIMPLICITY A SINGLE COORDINATE TRACKER IS DESCRIBED )F THE TARGET WERE ON THE ANTENNA BORESIGHT AXIS THE OUTPUTS OF EACH
&)'52% A 7AVEFRONT PHASE RELATIONSHIPS IN A PHASE COMPARISON MONOPULSE RADAR AND B BLOCK DIAGRAM OF A PHASE COMPARISON MONOPULSE RADAR ONE ANGLE COORDINATE
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INDIVIDUAL APERTURE WOULD BE IN PHASE !S THE TARGET MOVES OFF AXIS IN EITHER DIREC TION THERE IS A CHANGE IN RELATIVE PHASE 4HE AMPLITUDES OF THE SIGNALS IN EACH APER TURE ARE THE SAME SO THAT THE OUTPUT OF THE ANGLE ERROR PHASE DETECTOR IS DETERMINED BY THE RELATIVE PHASE SEE &IGURE 4HE PHASE DETECTOR CIRCUIT IS ADJUSTED WITH A PHASE SHIFT ON ONE CHANNEL TO GIVE ZERO OUTPUT WHEN THE TARGET IS ON AXIS AND AN OUTPUT INCREASING WITH INCREASING ANGULAR DISPLACEMENT OF THE TARGET WITH A POLARITY CORRESPONDING TO THE DIRECTION OF ERROR 4YPICAL FLAT FACE CORPORATE FED PHASED ARRAYS COMPARE THE OUTPUT OF HALVES OF THE APERTURE AND FALL INTO THE CLASS OF PHASE &)'52% A 2& PHASE COMPARISON MONO COMPARISON MONOPULSE (OWEVER THE PULSE SYSTEM WITH SUM AND DIFFERENCE OUTPUTS AND BASIC SIGNAL PROCESSING OF AMPLITUDE AND B VECTOR DIAGRAM OF THE SUM AND DIFFERENCE SIGNALS PHASE COMPARISON MONOPULSE IS SIMILAR BUT THE CONTROL OF AMPLITUDE DISTRIBUTION ACROSS AN ARRAY APERTURE FOR THE SUM AND DIFFERENCE SIGNALS MAINTAINS EFFICIENCY AND LOWER SIDELOBES &IGURE SHOWS THE ANTENNA AND RECEIVER FOR ONE ANGULAR COORDINATE TRACKING BY PHASE COMPARISON MONOPULSE !NY PHASE SHIFTS OCCURRING IN THE MIXER AND )& AMPLI FIER STAGES CAUSES A SHIFT IN THE BORESIGHT OF THE SYSTEM 4HE DISADVANTAGES OF PHASE COMPARISON MONOPULSE WITH SEPARATE APERTURES COMPARED WITH AMPLITUDE COMPARISON MONOPULSE ARE THE RELATIVE DIFFICULTY IN MAINTAINING A HIGHLY STABLE BORESIGHT AND THE DIFFICULTY IN PROVIDING THE DESIRED ANTENNA ILLUMINATION TAPER FOR BOTH SUM AND DIF FERENCE SIGNALS 4HE LONGER PATHS FROM THE ANTENNA OUTPUTS TO THE COMPARATOR CIR CUITRY MAKE THE PHASE COMPARISON SYSTEM MORE SUSCEPTIBLE TO BORESIGHT CHANGE DUE TO MECHANICAL LOADING SAG DIFFERENTIAL HEATING ETC ! TECHNIQUE GIVING GREATER BORESIGHT STABILITY COMBINES THE TWO ANTENNA OUT PUTS AT 2& WITH PASSIVE CIRCUITRY TO YIELD SUM AND DIFFERENCE SIGNALS AS SHOWN IN &IGURE 4HESE SIGNALS MAY THEN BE PROCESSED LIKE A CONVENTIONAL AMPLITUDE COMPARISON MONOPULSE RECEIVER 4HE SYSTEM SHOWN IN &IGURE WOULD PROVIDE A RELATIVELY GOOD DIFFERENCE CHANNEL TAPER HAVING SMOOTHLY TAPERED % FIELDS ON EACH ANTENNA (OWEVER A SUM SIGNAL EXCITATION WITH THE TWO ANTENNAS PROVIDES A TWO HUMPED IN PHASE % FIELD DISTRIBUTION THAT CAUSES HIGH SIDELOBES SINCE IT LOOKS LIKE A TWO ELEMENT ARRAY 4HIS PROBLEM MAY BE REDUCED BY ALLOWING SOME APERTURE OVERLAP BUT AT THE PRICE OF LOSS OF ANGLE SENSITIVITY AND ANTENNA GAIN %LECTRONIC 3CAN 0HASED !RRAY -ONOPULSE 4RACKING RADARS DEDICATED TO SINGLE TARGET TRACKING CAN PROVIDE VERY HIGH PRECISION LONG RANGE PERFORMANCE SUCH AS THE !.&01 &IGURE A WITH A SPECIFIED PRECISION OF MILLIRADIAN 7ITH HIGH POWER AND A HIGH GAIN ANTENNA D" AND SPECIAL TRACKING TECHNIQUES THEY ARE THE WORKHORSE FOR PRECISION TRACKING OF SATELLITES AND SIMILAR TASKS (OWEVER MOST MODERN TASKS REQUIRE PRECISION SIMULTANEOUS TRACKING OF MULTIPLE SIMULTANEOUS TARGETS WHERE USE OF MULTIPLE SINGLE TARGET TRACKING RADARS ARE NOT COST EFFECTIVE 4HE DEVELOP MENT OF ELECTRONIC SCAN PHASED ARRAY TECHNOLOGY HAS RESULTED IN VERSATILE HIGH PRECI SION MONOPULSE TRACKING WITH THE CAPABILITY OF SIMULTANEOUS MULTITARGET TRACKING BY SWITCHING ITS BEAM TO EACH OF SEVERAL TARGETS ON A PULSE TO PULSE BASIS OR BY GROUPS
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OF PULSES -ONOPULSE TRACKING IS NECESSARY TO OBTAIN ANGLE DATA ON EACH PULSE TO MAINTAIN ADEQUATE DATA RATES WHEN SHARING PULSES AND POWER AMONG SEVERAL TARGETS ! DETAILED DISCUSSION OF ELECTRONIC SCAN PHASED ARRAYS IS GIVEN IN #HAPTER HOWEVER SOME CHARACTERISTICS OF THE ARRAYS REQUIRE SPECIAL CONSIDERATION FOR THE ANGLE TRACKING PERFORMANCE OF TRACKING RADARS USING MONOPULSE PHASED ARRAY ANTENNAS /PTICAL FEED -ONOPULSE %LECTRONIC 3CAN !RRAYS /PTICAL FEED MONOPULSE ARRAYS INCLUDE THE LENS ARRAY AND REFLECTARRAY #HAPTER THAT ARE OPTICALLY FED BY A CONVEN TIONAL MONOPULSE FEED 4HE !.-01 &IGURE B IS AN EXAMPLE OF AN OPTICALLY FED ARRAY LENS WITH THE ANTENNA MOUNTED ON A TWO AXIS PEDESTAL 4YPICAL INSTANTANEOUS ELECTRONIC ANGLE COVERAGE IS o TO AN ALMOST o CONE FIELD OF VIEW THAT MAY BE MOVED BY PEDESTAL DRIVE TO CENTER ON A MULTITARGET EVENT OR FOLLOW AN EVENT PROGRESS ING TO A DIFFERENT AREA 3OME MILITARY SYSTEMS SUCH AS THE 0ATRIOT WITH THE o CONE OF INSTANTANEOUS VIEW IS FIXED ON ITS VEHICLE WITHOUT A PEDESTAL AND IS DEPENDENT ON MOVEMENT OF ITS VEHICLE TO CHANGE THE REGION OF ANGULAR COVERAGE AS NEEDED 4HE ADVANTAGES OF SPACE FED ARRAYS ARE #ONVENTIONAL MONOPULSE MICROWAVE HORN FEEDS ARE USED !RRAY ELEMENTS ARE AVAILABLE WITH SELECTABLE POLARIZATION OF THE RADIATED ENERGY WHEN FED BY AN OPTIMIZED LINEAR POLARIZED MONOPULSE FEED SUCH AS IN &IGURE AND SELECT ABLE RECEIVE POLARIZATION AS WELL 4HIS AVOIDS THE TYPICAL COMPROMISE AND GREATER COM PLEXITY OF A POLARIZATION CONTROLLED MONOPULSE FEED AS DESCRIBED IN &IGURE %LECTRONIC SCAN ARRAY LENSES CAN ALSO REFOCUS FROM A TRANSMIT FEED HORN TO AN ADJACENT RECEIVE FEED HORN ON RECEPTION TO ALLOW HIGH POWER TRANSMISSION THROUGH A SIMPLE SINGLE HORN FEED TO SIMPLIFY ISOLATION OF THE RECEIVER FROM THE TRANSMIT POWER !RRAYS ALLOW GREATER FLEXIBILITY TO OPTIMIZE AMPLITUDE DISTRIBUTION OF THE RADIATED ENERGY ACROSS THE ARRAY TO REDUCE SIDELOBES
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-OST OF THE ELECTRONIC SCAN PHASED ARRAY DISADVANTAGES ARE DESCRIBED IN #HAPTER AND INCLUDE LOSSES IN THE ARRAY PHASE SHIFTING ELEMENTS LIMITATION OF INSTANTANEOUS BANDWIDTH WITH CONVENTIONAL PHASE CONTROL ELEMENTS IMPROVED WITH SPECIAL TRUE TIME DELAY PHASE SHIFTING PHASE QUANTIZATION ERRORS #HAPTER RESULTING FROM PHASE SHIFTING IN STEPS RESTRICTION TO A SINGLE RF BAND MULTIBAND ARRAYS REQUIRE SPECIAL TECHNIQUES WITH MAJOR COMPROMISES AND GRADUAL DEGRADATION OF PERFORMANCE AS THE BEAM IS SCANNED FROM THE NORMAL TO THE ARRAY 4HE QUANTIZATION ERRORS FROM PHASE SHIFTING IN STEPS ARE OF CONCERN TO MONOPULSE RADAR BECAUSE IT RESULTS IN CORRESPONDING RANDOM ERROR STEPS IN THE ELECTRONIC AXIS OF THE ARRAY !S DESCRIBED IN #HAPTER THE QUANTIZATION ERRORS ARE INVERSELY PROPORTIONAL TO THE NUMBER OF PHASE SHIFTING ELEMENTS AND 0 WHERE 0 IS THE NUMBER OF BITS OF PHASE CONTROL IN EACH ELEMENT #ONSEQUENTLY THE HIGH PRECISION TRACKING RADARS WITH TYPICALLY TO PHASE SHIFTERS AND FOUR OR MORE PHASE SHIFT BITS HAVE SMALL RESULTANT ELECTRICAL AXIS ERROR STEPS ON THE ORDER OF MILLIRADIANS OR LESS 4HE ELECTRICAL AXIS ERRORS ARE ESSENTIALLY RANDOM AND CAN BE FURTHER REDUCED BY AVERAGING )NTENTIONAL DITHER OF PHASE STEPS MAY BE INTRODUCED TO AID IN AVERAGING 4HE OPTICALLY FED TECHNIQUE RESULTS IN FEED ENERGY SPILLOVER AROUND THE APERTURE HOWEVER THESE RESULTANT SPILLOVER SIDELOBES CAN BE ELIMINATED BY AN ABSORBING CONE BETWEEN THE FEED AND THE ARRAY APERTURE 4HE ABSORBING CONE IS OBSERVED IN THE !. -01 &IGURE B (OWEVER COOLING IS ALSO NECESSARY AND PROVIDED AS OBSERVED BY THE COOLING COILS AROUND THE ABSORBING CONE
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/F FURTHER CONCERN TO HIGH PRECISION MONOPULSE APPLICATIONS IS DRIFT OF THE ELEC TRONIC AXIS THAT CAUSES VARIATIONS IN PHASE AND TEMPERATURE VARIATION ACROSS THE ARRAY SURFACE THAT CAUSES DISTORTION OF THE LENS 3IGNIFICANT VARIATION OF HEAT DISTRIBUTION ACROSS THE ARRAY FACE CAN RESULT FROM HIGH POWER TRANSMITTED THROUGH THE PHASE SHIFTING ELEMENTS AS WELL AS THE ELECTRONIC PHASE CONTROL #ONSEQUENTLY WHERE HIGH PRECISION TRACKING IS REQUIRED SPECIAL COOLING TECHNIQUES MAY BE NECESSARY TO MAINTAIN CONSTANT TEMPERATURE ACROSS THE APERTURE #ORPORATE &EED -ONOPULSE %LECTRONIC 3CAN 0HASED !RRAY 4HE CORPORATE FEED ARRAY IS FED BY DIVIDING AND SUBDIVIDING THE TRANSMIT SIGNAL THROUGH TRANSMISSION LINES TYPICALLY TO SUBARRAYS OF MULTIPLE ARRAY RADIATING ELEMENTS 4HIS TECHNIQUE ALTHOUGH TYPICALLY RESULTING IN HEAVIER AND HIGHER COST IMPLEMENTATION OFFERS THE ADVANTAGE OF FLEXIBILITY OF CONTROL OF THE SIGNAL PATHS THROUGH THE ARRAY STRUCTURE AS DESCRIBED IN #HAPTER !NOTHER ADVANTAGE IS THE CAPABILITY TO TRANSMIT VERY HIGH PEAK POWER WITHOUT THE LIMITATIONS OF FULL PEAK POWER PROPAGATING THROUGH A SINGLE TRANSMISSION LINE 4HIS IS ACCOMPLISHED IN THE CORPORATE FEED ARRAY BY PLACING HIGH POWER AMPLIFIERS WHERE THE POWER DIVIDES TO THE SUBARRAYS ALLOWING THE SUM OF THE HIGH PEAK POWER AMPLIFIER OUTPUTS TO ADD IN SPACE TO MEET REQUIREMENTS FOR LONG RANGE TRACKING AND POWER SHARING BETWEEN MULTIPLE SIMULTANEOUS TARGETS 4HE PARALLEL POWER AMPLIFIER CONFIGURATION ALSO PROVIDES A PRACTICAL MEANS FOR OVERCOMING THE NARROW INSTANTANEOUS BANDWIDTH OF TYPICAL PHASED ARRAYS AT WIDE SCAN ANGLES &ULL ARRAY INSTANTANEOUS BANDWIDTH REQUIRES EQUAL PATH LENGTHS BETWEEN EACH ARRAY ELEMENT AND THE TARGET REQUIRING MANY WAVELENGTHS OF PHASE CONTROL OR THE EQUIVALENT TIME DELAY IN ARRAY ELEMENTS AT WIDE ANGLE SCANS (OWEVER THIS CONTROL HAS PROHIBITIVELY HIGH LOSS FOR TYPICAL PHASED ARRAY RADIATING ELEMENTS CONSEQUENTLY TYPI CAL PHASED ARRAY ELEMENTS PROVIDE ONLY SUFFICIENT PHASE CONTROL OF UP TO OR TO ONE WAVELENGTH LIMITED TO TOLERABLE LOSS TO CAUSE THE SIGNAL FROM EACH ELEMENT TO ARRIVE APPROXIMATELY IN PHASE AT THE TARGET 5NFORTUNATELY THIS SHORTCUT IS ADEQUATE FOR ONLY A NARROW INSTANTANEOUS BANDWIDTH 4HE PARALLEL POWER AMPLIFIERS AS DESCRIBED ABOVE PROVIDE A LOW POWER AMPLIFIER DRIVE STAGE WHERE THE HIGH LOSS OF THE DESIRED TIME DELAY CONTROL CAN BE TOLERATED TO GAIN WIDE INSTANTANEOUS BANDWIDTH AS DESCRIBED IN #HAPTER 4HE TIME DELAY MAY BE CONTROLLED SIMILAR TO THE DIODE PHASE SHIFTERS USED IN RADIATING ELEMENTS THAT SWITCH BETWEEN DIFFERENT LINE LENGTHS TO ADJUST PHASE ,ONGER TIME DELAY TRANSMISSION LINE COULD BE SIMILARLY CONTROLLED BY DIODE SWITCHING TO PRO VIDE THE WIDE INSTANTANEOUS BANDWIDTH TO ALLOW FOR EXAMPLE USE OF WIDEBAND NARROW PULSES TO PROVIDE THE RANGE RESOLUTION REQUIREMENTS FOR TRACKING RADAR APPLICATIONS 4WO #HANNEL -ONOPULSE -ONOPULSE RADARS MAY BE DESIGNED WITH FEWER THAN THE CONVENTIONAL THREE )& CHANNELS 4HIS IS ACCOMPLISHED FOR EXAMPLE BY COMBINING THE SUM AND DIFFERENCE SIGNALS IN TWO )& CHANNELS AND THE SUM AND TWO DIFFERENCE SIGNAL OUTPUTS ARE THEN INDIVIDUALLY RETRIEVED AT THE OUTPUT 4HESE TECHNIQUES PROVIDE SOME ADVANTAGES IN !'# OR OTHER PROCESSING TECHNIQUES BUT AT THE COST OF REDUCED 3.2 REDUCED ANGLE DATA RATE AND POTENTIAL FOR CROSS COUPLING BETWEEN AZIMUTH AND ELEVATION INFORMATION ! TWO CHANNEL MONOPULSE RECEIVER COMBINES THE SUM AND DIFFERENCE SIGNALS AT 2& AS SHOWN IN &IGURE 4HE MICROWAVE RESOLVER IS A MECHANICALLY ROTATED 2& COUPLING LOOP IN CYLINDRICAL WAVEGUIDE 4HE AZIMUTH AND ELEVATION DIFFERENCE SIGNALS ARE EXCITED IN THIS GUIDE WITH % FIELD POLARIZATION ORIENTED AT O 4HE ENERGY IN THE COUPLER CONTAINS BOTH DIFFERENCE SIGNALS COUPLED AS THE COSINE AND SINE OF THE ANGULAR POSITION OF THE COUPLER VST WHERE VS IS THE ANGULAR RATE OF ROTATION 4HE HYBRID ADDS THE COMBINED DIFFERENCE SIGNALS $ AT THE ANGULAR
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&)'52% "LOCK DIAGRAM OF A TWO CHANNEL MONOPULSE RADAR SYSTEM FROM 2 3 .OBLIT
RATE OF ROTATION 4HE 3 $ AND 3 n $ OUTPUTS EACH LOOK LIKE THE OUTPUT OF A CONICAL SCAN TRACKER EXCEPT THAT THEIR MODULATION FUNCTION DIFFERS BY )N CASE ONE CHANNEL FAILS THE RADAR CAN BE OPERATED AS A SCAN ON RECEIVE ONLY CONICAL SCAN RADAR WITH ESSENTIALLY THE SAME PERFORMANCE AS A CONICAL SCAN RADAR 4HE ADVANTAGE OF TWO CHANNELS WITH OPPOSITE SENSE ANGLE ERROR INFORMATION ON ONE CHANNEL WITH RESPECT TO THE OTHER IS THAT SIGNAL AMPLITUDE FLUCTUATIONS IN THE RECEIVED SIGNAL ARE CANCELED IN THE POST DETECTION SUBTRACTION AT THE )& OUTPUT THAT RETRIEVES THE ANGLE ERROR INFORMATION 4HE LOG )& PERFORMS ESSENTIALLY AS AN INSTANTANEOUS !'# GIVING THE DESIRED CONSTANT ANGLE ERROR SENSITIVITY OF THE DIFFERENCE SIGNALS NORMALIZED BY THE SUM SIGNAL 4HE DETECTED $ INFORMATION IS A BIPOLAR VIDEO WHERE THE ERROR INFORMATION IS CONTAINED IN THE SINUSOIDAL ENVELOPE 4HIS SIGNAL IS SEPARATED INTO ITS TWO COMPONENTS AZIMUTH AND ELEVATION ERROR INFORMATION BY AN ANGLE DEMODULATION 4HE DEMODULATOR USING A REFERENCE FROM THE DRIVE ON THE ROTATING COUPLER EXTRACTS THE SINE AND COSINE COMPONENTS FROM $ TO GIVE THE AZIMUTH AND ELEVATION ERROR SIGNALS 4HE MODULATION CAUSED BY THE MICROWAVE RESOLVER IS OF CONCERN IN INSTRUMENTATION RADAR APPLICATIONS BECAUSE IT ADDS SPECTRAL COMPONENTS IN THE SIGNAL COMPLICATING THE POSSIBLE ADDITION OF PULSE DOPPLER TRACKING CAPABILITY TO THE RADAR 4HIS SYSTEM PROVIDES INSTANTANEOUS !'# OPERATION WITH ONLY TWO )& CHANNELS AND OPERATION WITH REDUCED PERFORMANCE IN CASE OF FAILURE OF EITHER CHANNEL (OWEVER THERE IS A LOSS OF D" 3.2 AT THE RECEIVER INPUTS ALTHOUGH THIS LOSS IS PARTLY REGAINED BY COHERENT ADDITION OF THE 3 SIGNAL INFORMATION 4HE DESIGN OF THE MICROWAVE RESOLVER MUST MINIMIZE LOSS THROUGH THE DEVICE AND PRECISELY MATCHED )& CHANNELS ARE REQUIRED TO MINIMIZE CROSS COUPLING BETWEEN THE AZIMUTH AND ELEVATION CHANNELS )N SOME MOD ERN SYSTEMS THE RESOLVER PERFORMANCE IS IMPROVED BY USE OF FERRITE SWITCHING DEVICES TO REPLACE THE MECHANICAL ROTATING COUPLER #ONOPULSE #ONOPULSE ALSO CALLED SCAN WITH COMPENSATION IS A RADAR TRACKING TECHNIQUE THAT IS A COMBINATION OF MONOPULSE AND CONICAL SCAN ! PAIR OF ANTENNA
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BEAMS IS SQUINTED IN OPPOSITE DIRECTIONS FROM THE ANTENNA AXIS AND ROTATED LIKE A PAIR OF CONICAL SCAN RADAR BEAMS 3INCE THEY EXIST SIMULTANEOUSLY MONOPULSE INFORMATION CAN BE OBTAINED FROM THE PAIR OF BEAMS 4HE PLANE IN WHICH MONOPULSE INFORMATION IS MEASURED ROTATES #ONSEQUENTLY ELEVATION AND AZIMUTH INFORMATION IS SEQUENTIAL AND MUST BE SEPARATED FOR USE IN EACH TRACKING COORDINATE #ONOPULSE PROVIDES THE MONOPULSE ADVANTAGE OF AVOIDING ERRORS CAUSED BY AMPLITUDE SCINTILLATION AND IT REQUIRES ONLY TWO RECEIVERS (OWEVER IT HAS THE DISADVANTAGE OF LOWER ANGLE DATA RATES AND THE MECHANICAL COMPLEXITY OF PROVIDING AND COUPLING TO A PAIR OF ROTATING ANTENNA FEEDHORNS
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4HE FIRST TECHNIQUE USED FOR RADAR ANGLE TRACKING WAS TO DISPLACE THE ANTENNA BEAM ABOVE AND BELOW THE TARGET IN ELEVATION AND SIDE TO SIDE OF THE TARGET IN AZIMUTH TO COMPARE BEAM AMPLITUDES SIMILAR TO MONOPULSE RADAR SIMULTANEOUS LOBING BUT DIFFER ING BY BEING IN A TIME SEQUENCE 4HIS WAS PERFORMED BY A CONTINUOUS CONICAL BEAM SCAN AS ILLUSTRATED IN &IGURE OR BY SEQUENTIALLY LOBING UPDOWN AND RIGHTLEFT AND OBSERVING THE DIFFERENCE BETWEEN AMPLITUDES AS A MEASURE OF DISPLACEMENT OF THE ANTENNA AXIS FROM THE TARGET 4HE SIGNAL OUTPUT FOR A CONICAL SCAN RADAR ILLUSTRATED IN &IGURE IS TYPICALLY A SINUSOID AMPLITUDE MODULATION OF THE RECEIVED TARGET ECHO PULSES 4HE AMPLITUDE OF THE MODULATION IS A MEASURE OF THE MAGNITUDE OF THE ANGLE ERROR AND THE PHASE RELATIVE TO THE SCANNING BEAM ROTATION ANGLE INDICATES THE PORTION OF THE ERROR CAUSED BY EACH TRACKING AXIS 4HE PERFORMANCE OF SCANNING AND LOBING RADAR RELATIVE TO THE BEAM OFFSET ANGLE IS DESCRIBED IN "ARTON !N OPTIMUM BEAM OFFSET IS DESCRIBED AS A COMPROMISE BETWEEN THE LOSS OF ANTENNA GAIN AND THE INCREASE IN SENSITIVITY TO TARGET ANGLE DISPLACEMENT FROM THE ANTENNA AXIS AS BEAM OFFSET IS INCREASED 4HE OPTIMUM OFFSET IS TYPICALLY CHOSEN TO PROVIDE THE MINIMUM RMS ANGLE TRACKING ERROR AS AFFECTED BY THE SIGNAL TO NOISE RATIO AND TRACKING SENSITIVITY 3PECIAL TRACKING RADAR APPLICATIONS WITH NONTYPICAL REQUIREMENTS COULD ARRIVE AT A DIFFERENT OPTIMUM BEAM OFFSET ! MAJOR LIMITATION OF SCANNING AND LOBING RADAR IS THE SUSCEPTIBILITY TO TARGET AMPLI TUDE FLUCTUATIONS THAT OCCUR DURING THE TIME THE BEAM IS MOVED FROM SIDE TO SIDE OR UP AND DOWN )T IS ALSO SUSCEPTIBLE TO FALSE MODULATION ON SIGNALS FROM COUNTERMEASURES 4HE ECHO FLUCTUATIONS NOT RELATED TO ANTENNA BEAM POSITION CAUSE FALSE TARGET ANGLE TRACKING ERRORS
&)'52% #ONICAL SCAN TRACKING
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&)'52% A !NGLE ERROR INFORMATION CONTAINED IN THE ENVELOPE OF THE RECEIVED PULSES IN A CONICAL SCAN RADAR AND B REFERENCE SIGNAL DERIVED FROM THE DRIVE OF THE CONICAL SCAN FEED
-ONOPULSE RADAR WAS DEVELOPED TO PROVIDE SIMULTANEOUS OFFSET ANTENNA BEAMS FOR COMPARISON OF TARGET ECHO AMPLITUDES ON A SINGLE PULSE INDEPENDENT OF ECHO SIGNAL AMPLITUDE FLUCTUATIONS (OWEVER FEW MICROWAVE DEVICES AND COMPONENTS WERE INI TIALLY AVAILABLE AND THE FIRST MONOPULSE SYSTEMS WERE COMPLEX AND RESULTED IN CUM BERSOME AND INEFFICIENT ANTENNAS !T PRESENT MODERN MONOPULSE RADARS AS DESCRIBED IN 3ECTION PROVIDE HIGHLY STABLE AND EFFICIENT ANTENNAS WITH HIGH PRECISION PERFOR MANCE AND HAVE GENERALLY DISPLACED SCANNING AND LOBING TRACKING RADARS FOR MEETING THE INCREASING DEMANDS FOR HIGH PRECISION AND HIGH DATA RATE OF ANGLE INFORMATION ON EACH PULSE (OWEVER SPECIAL RADAR TRACKING REQUIREMENTS MAY EXIST WHERE A PRACTICAL IMPLEMENTATION OF CONICAL SCAN OR LOBING TRACKING RADAR MAY MORE EFFECTIVELY PROVIDE ADEQUATE PERFORMANCE
°{Ê - ,6"-9-/ -Ê",Ê/, Ê, , 4HE SERVOSYSTEM OF A TRACKING RADAR IS THE SUBSYSTEM OF THE RADAR THAT RECEIVES AS ITS INPUT THE TRACKING ERROR VOLTAGE AND PERFORMS THE TASK OF MOVING THE ANTENNA BEAM IN A DIRECTION THAT WILL REDUCE TO ZERO THE ALIGNMENT ERROR BETWEEN THE ANTENNA AXIS AND THE TARGET &OR TWO AXIS TRACKING WITH A MECHANICAL TYPE ANTENNA PEDESTAL THERE ARE TYPI CALLY SEPARATE AXES OF ROTATION FOR AZIMUTH AND ELEVATION AND SEPARATE SERVOSYSTEMS TO MOVE THE ANTENNA ABOUT EACH AXIS ! CONVENTIONAL SERVOSYSTEM IS COMPOSED OF AMPLI FIERS FILTERS AND A MOTOR THAT MOVES THE ANTENNA IN A DIRECTION TO MAINTAIN THE ANTENNA AXIS ON THE TARGET 2ANGE TRACKING IS ACCOMPLISHED BY A SIMILAR SYSTEM TO MAINTAIN RANGE GATES CENTERED ON THE RECEIVED ECHO PULSES 4HIS MAY BE ACCOMPLISHED BY ANALOG TECHNIQUES OR BY DIGITAL COUNTER REGISTERS THAT RETAIN NUMBERS CORRESPONDING TO TARGET RANGE TO PROVIDE A CLOSED RANGE TRACKING LOOP DIGITALLY 3ERVOSYSTEMS MAY USE HYDRAULIC DRIVE MOTORS CONVENTIONAL ELECTRIC MOTORS GEARED DOWN TO DRIVE THE ANTENNA OR DIRECT DRIVE ELECTRIC MOTORS WHERE THE ANTENNA MECHANICAL AXIS SHAFT IS PART OF THE ARMATURE AND THE MOTOR FIELD IS BUILT INTO THE SUPPORT CASE 4HE DIRECT DRIVE IS HEAVIER FOR A GIVEN HORSEPOWER BUT ELIMINATES
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GEAR BACKLASH "ACKLASH MAY ALSO BE REDUCED WITH CONVENTIONAL MOTORS BY DUPLICATE PARALLEL DRIVES WITH A SMALL RESIDUAL OPPOSING TORQUE WHEN NEAR ZERO ANGLE RATE !MPLIFIER GAIN AND FILTER CHARACTERISTICS AS WELL AS MOTOR TORQUE AND INERTIA DETER MINE THE VELOCITY AND ACCELERATION CAPABILITY OR THE ABILITY TO FOLLOW THE HIGHER ORDER MOTION OF THE TARGET )T IS DESIRED THAT THE ANTENNA BEAM FOLLOW THE CENTER OF THE TARGET AS CLOSELY AS POS SIBLE WHICH IMPLIES THAT THE SERVOSYSTEM SHOULD BE CAPABLE OF MOVING THE ANTENNA QUICKLY 4HE COMBINED VELOCITY AND ACCELERATION CHARACTERISTICS OF A SERVOSYSTEM CAN BE DESCRIBED BY THE FREQUENCY RESPONSE OF THE TRACKING LOOP WHICH ACTS ESSENTIALLY LIKE A LOW PASS FILTER )NCREASING THE BANDWIDTH INCREASES THE QUICKNESS OF THE SERVOSYS TEM AND ITS ABILITY TO FOLLOW A STRONG STEADY SIGNAL CLOSELY (OWEVER A TYPICAL TARGET CAUSES SCINTILLATION OF THE ECHO SIGNAL GIVING ERRONEOUS ERROR DETECTOR OUTPUTS AND AT LONG RANGE THE ECHO IS WEAK ALLOWING RECEIVER NOISE TO CAUSE ADDITIONAL RANDOM FLUC TUATIONS ON THE ERROR DETECTOR OUTPUT #ONSEQUENTLY A WIDE SERVO BANDWIDTH WHICH REDUCES LAG ERRORS ALLOWS THE NOISE TO CAUSE GREATER ERRONEOUS MOTIONS OF THE TRACKING SYSTEM 4HEREFORE FOR BEST OVERALL PERFORMANCE IT IS NECESSARY TO LIMIT THE SERVO BAND WIDTH TO THE MINIMUM NECESSARY TO MAINTAIN A REASONABLY SMALL TRACKING LAG ERROR 4HERE IS AN OPTIMUM BANDWIDTH THAT MAY BE CHOSEN TO MINIMIZE THE AMPLITUDE OF THE TOTAL ERRONEOUS OUTPUTS INCLUDING BOTH TRACKING LAG AND RANDOM NOISE DEPENDING UPON THE TARGET ITS TRAJECTORY AND OTHER RADAR PARAMETERS 4HE OPTIMUM BANDWIDTH FOR ANGLE TRACKING IS RANGE DEPENDENT ! TARGET WITH TYPICAL VELOCITY AT LONG RANGE HAS LOW ANGLE RATES AND A LOW 3.2 AND A NARROWER SERVO PASSBAND WILL FOLLOW THE TARGET WITH REASONABLY SMALL TRACKING LAG WHILE MINIMIZING THE RESPONSE TO RECEIVER THERMAL NOISE !T CLOSE RANGE THE SIGNAL IS STRONG OVERRIDING RECEIVER NOISE BUT TARGET ANGLE SCINTILLATION ERRORS PROPORTIONAL TO THE ANGULAR SPAN OF THE TARGET ARE LARGE ! WIDER SERVO BANDWIDTH IS NEEDED AT CLOSE RANGE TO KEEP TRACKING LAG WITHIN REASONABLE VALUES BUT IT MUST NOT BE WIDER THAN NECESSARY OR THE TARGET ANGLE SCINTILLATION ERRORS WHICH INCREASE INVERSELY PROPORTIONAL TO TARGET RANGE MAY BECOME EXCESSIVE 4HE LOW PASS CLOSED LOOP CHARACTERISTIC OF A SERVOSYSTEM IS UNITY AT ZERO FREQUENCY TYPICALLY REMAINING NEAR THIS VALUE UP TO A FREQUENCY NEAR THE LOW PASS CUTOFF WHERE IT MAY PEAK UP TO HIGHER GAIN AS SHOWN IN &IGURE A 4HE PEAKING IS AN INDICATION OF SYSTEM INSTABILITY BUT IS ALLOWED TO BE AS HIGH AS TOLERABLE TYPICALLY TO ABOUT D" ABOVE UNITY GAIN TO OBTAIN MAXIMUM BANDWIDTH FOR A GIVEN SERVOMOTOR DRIVE SYSTEM 3YSTEM ! IN &IGURE A IS A CASE OF EXCESSIVE PEAKING OF ABOUT D" 4HE EFFECT OF THE PEAKING IS OBSERVED BY APPLYING A STEP ERROR INPUT TO THE SERVOSYSTEM 4HE PEAKING OF THE LOW PASS CHARACTERISTIC RESULTS IN AN OVERSHOOT WHEN THE ANTENNA AXIS MOVES TO ALIGN WITH THE TARGET (IGH PEAKING CAUSES A LARGE OVERSHOOT AND A RETURN TO THE TARGET WITH ADDITIONAL OVERSHOOT )N THE EXTREME AS IN SYSTEM ! SHOWN IN &IGURE B THE ANTENNA ZEROS IN ON THE TARGET WITH A DAMPED OSCILLATION !N OPTIMUM SYSTEM COMPROMISE BETWEEN SPEED OF RESPONSE AND OVERSHOOT AS IN SYSTEM " ALLOWS THE ANTENNA TO MAKE A SMALL OVERSHOOT WITH REASONABLY RAPID EXPONENTIAL MOVEMENT BACK TO THE TARGET 4HIS CORRESPONDS TO ABOUT D" PEAKING OF THE CLOSED LOOP LOW PASS CHARACTERISTIC 4HE RESONANT FREQUENCY OF THE ANTENNA AND SERVOSYSTEM STRUCTURE INCLUDING THE STRUCTURE FOUNDATION WHICH IS A CRITICAL ITEM MUST BE KEPT WELL ABOVE THE BANDWIDTH OF THE SERVOSYSTEM OTHERWISE THE SYSTEM CAN OSCILLATE AT THE RESONANT FREQUENCY ! FACTOR OF AT LEAST IS DESIRABLE FOR THE RATIO OF SYSTEM RESONANCE FREQUENCY TO SERVO BANDWIDTH (IGH RESONANT FREQUENCY IS DIFFICULT TO OBTAIN WITH A LARGE ANTENNA SUCH AS THE !.&01 RADAR WITH A FT DISH BECAUSE OF THE LARGE MASS OF THE SYSTEM
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&)'52% A #LOSED LOOP FREQUENCY RESPONSE CHARACTERISTICS OF TWO SERVOSYSTEMS AND B THEIR CORRESPONDING TIME RESPONSE TO A STEP INPUT
4HE RATIO WAS PUSHED TO A VERY MINIMUM OF ABOUT TO OBTAIN SERVOSYSTEM BANDWIDTH OF THE SPECIFIED (Z ! SMALLER RADAR WITH A FT DISH FOR EXAMPLE CAN PROVIDE A SERVOSYSTEM BANDWIDTH UP TO OR (Z WITH CONVENTIONAL DESIGN ,OCKE DESCRIBES METHODS FOR CALCULATING ANGLE TRACKING LAG FOR A GIVEN TARGET TRAJECTORY VERSUS TIME AND SET OF SERVOSYSTEM CHARACTERISTICS 2ANGE TRACKING LAGS MAY BE SIMILARLY CALCULATED BUT WITH TYPICAL INERTIALESS ELECTRONIC TRACKING SYSTEMS TRACKING LAGS ARE USUALLY NEGLIGIBLE %LECTRONICALLY STEERABLE ARRAYS PROVIDE A MEANS FOR INERTIALESS ANGLE TRACKING (OWEVER BECAUSE OF THIS CAPABILITY THE SYSTEM CAN TRACK MULTIPLE TARGETS BY RAPIDLY SWITCHING FROM ONE TO ANOTHER RATHER THAN CONTINUOUSLY TRACKING A SINGLE TARGET 4HE TRACKER SIMPLY PLACES ITS BEAM AT THE LOCATION WHERE THE TARGET IS EXPECTED CORRECTS FOR THE POINTING ERROR BY CONVERTING ERROR VOLTAGES WITH KNOWN ANGLE ERROR SENSITIVITY TO UNITS OF ANGLE AND MOVES TO THE NEXT TARGET 4HE SYSTEM DETERMINES WHERE THE TARGET WAS AND FROM CALCULATIONS OF TARGET VELOCITY AND ACCELERATION PRE DICTS WHERE IT SHOULD BE THE NEXT TIME THE BEAM LOOKS AT THE TARGET 4HE LAG ERROR IN THIS CASE IS DEPENDENT ON MANY FACTORS INCLUDING THE ACCURACY OF THE VALUE OF ANGLE SENSITIVITY USED TO CONVERT ERROR VOLTAGES TO ANGULAR ERROR THE SIZE OF THE PREVIOUS TRACKING ERROR AND THE TIME INTERVAL BETWEEN LOOKS
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°xÊ /, /Ê +1-/" Ê Ê, Ê/, 2ANGE TRACKING IS ACCOMPLISHED BY CONTINUOUSLY MEASURING THE TIME DELAY BETWEEN THE TRANSMISSION OF AN 2& PULSE AND THE ECHO SIGNAL RETURNED FROM THE TARGET AND CON VERTING THE ROUNDTRIP DELAY TO UNITS OF DISTANCE 4HE RANGE MEASUREMENT IS THE MOST PRECISE POSITION COORDINATE MEASUREMENT OF THE RADAR TYPICALLY WITH HIGH 3.2 IT CAN BE WITHIN A FEW METERS AT HUNDREDS OF MILES RANGE 2ANGE TRACKING USUALLY PROVIDES THE MAJOR MEANS FOR DISCRIMINATING THE DESIRED TARGET FROM OTHER TARGETS ALTHOUGH DOPPLER FREQUENCY AND ANGLE DISCRIMINATION ARE ALSO USED BY PERFORMING RANGE GAT ING TIME GATING TO ELIMINATE THE ECHO OF OTHER TARGETS AT DIFFERENT RANGES FROM THE ERROR DETECTOR OUTPUTS 4HE RANGE TRACKING CIRCUITRY IS ALSO USED FOR ACQUIRING A DESIRED TARGET 2ANGE TRACKING REQUIRES NOT ONLY THAT THE TIME OF TRAVEL OF THE PULSE TO AND FROM THE TARGET BE MEASURED BUT ALSO THAT THE RETURN IS IDENTIFIED AS A TARGET RATHER THAN NOISE AND A RANGE TIME HISTORY OF THE TARGET BE MAINTAINED !LTHOUGH THIS DISCUSSION IS FOR TYPICAL PULSE TYPE TRACKING RADARS RANGE MEASURE MENT MAY ALSO BE PERFORMED WITH #7 RADARS USING &- #7 A FREQUENCY MODULATED #7 THAT IS TYPICALLY A LINEAR RAMP &- 4HE TARGET RANGE IS DETERMINED BY THE RANGE RELATED FREQUENCY DIFFERENCE BETWEEN THE ECHO FREQUENCY RAMP AND THE FREQUENCY OF THE RAMP BEING TRANSMITTED 4HE PERFORMANCE OF &- #7 SYSTEMS WITH CONSIDERATION OF THE DOPPLER EFFECT IS DESCRIBED IN 3HERMAN !CQUISITION 4HE FIRST FUNCTION OF THE RANGE TRACKER IS ACQUISITION OF A DESIRED TARGET !LTHOUGH THIS IS NOT A TRACKING OPERATION IT IS A NECESSARY FIRST STEP BEFORE RANGE TRACKING OR ANGLE TRACKING MAY TAKE PLACE IN A TYPICAL RADAR 3OME KNOWLEDGE OF TARGET ANGULAR LOCATION IS NECESSARY FOR PENCIL BEAM TRACKING RADARS TO POINT THEIR TYPICALLY NARROW ANTENNA BEAMS IN THE DIRECTION OF THE TARGET 4HIS INFORMATION CALLED DESIGNA TION DATA MAY BE PROVIDED BY SURVEILLANCE RADAR OR SOME OTHER SOURCE )T MAY BE SUF FICIENTLY ACCURATE TO PLACE THE PENCIL BEAM ON THE TARGET OR IT MAY REQUIRE THE TRACKER TO SCAN A LARGER REGION OF UNCERTAINTY 4HE RANGE TRACKING PORTION OF THE RADAR HAS THE ADVANTAGE OF SEEING ALL TARGETS WITHIN THE BEAM FROM CLOSE RANGE OUT TO THE MAXIMUM RANGE OF THE RADAR )T TYPICALLY BREAKS THIS RANGE INTO SMALL INCREMENTS EACH OF WHICH MAY BE SIMULTANEOUSLY EXAMINED FOR THE PRESENCE OF A TARGET 7HEN BEAM SCANNING IS NECESSARY THE RANGE TRACKER EXAMINES THE INCREMENTS SIMULTANEOUSLY FOR SHORT PERIODS SUCH AS S MAKES ITS DECISION ABOUT THE PRESENCE OF A TARGET AND ALLOWS THE BEAM TO MOVE TO A NEW LOCATION IF NO TARGET IS PRESENT 4HIS PROCESS IS TYPICALLY CONTINUOUS FOR MECHANICAL TYPE TRACKERS THAT MOVE THE BEAM SLOWLY ENOUGH THAT A TARGET WILL REMAIN WELL WITHIN THE BEAM FOR THE SHORT EXAMINATION PERIOD OF THE RANGE INCREMENTS 4ARGET ACQUISITION INVOLVES CONSIDERATION OF THE 3. THRESHOLD AND INTEGRATION TIME NEEDED TO ACCOMPLISH A GIVEN PROBABILITY OF DETECTION WITH A GIVEN FALSE ALARM RATE SIMILAR TO SURVEILLANCE RADAR (OWEVER HIGH FALSE ALARM RATES AS COMPARED WITH VALUES USED FOR SURVEILLANCE RADARS ARE USED BECAUSE THE OPERATOR KNOWS THAT THE TARGET IS PRES ENT AND OPERATOR FATIGUE FROM FALSE ALARMS WHEN WAITING FOR A TARGET IS NOT INVOLVED /PTIMUM FALSE ALARM RATES ARE SELECTED ON THE BASIS OF PERFORMANCE OF ELECTRONIC CIR CUITS THAT OBSERVE EACH RANGE INTERVAL TO DETERMINE WHICH INTERVAL HAS THE TARGET ECHO ! TYPICAL TECHNIQUE IS TO SET A VOLTAGE THRESHOLD SUFFICIENTLY HIGH TO PREVENT MOST NOISE PEAKS FROM CROSSING THE THRESHOLD BUT SUFFICIENTLY LOW THAT A WEAK SIGNAL MAY CROSS !N OBSERVATION IS MADE AFTER EACH TRANSMITTER PULSE AS TO WHETHER IN THE RANGE INTERVAL BEING EXAMINED THE THRESHOLD HAS BEEN CROSSED 4HE INTEGRATION TIME ALLOWS THE RADAR TO MAKE THIS OBSERVATION SEVERAL TIMES BEFORE DECIDING IF THERE IS A TARGET PRESENT
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4HE MAJOR DIFFERENCE BETWEEN NOISE AND A TARGET ECHO IS THAT NOISE SPIKES EXCEEDING THE THRESHOLD ARE RANDOM BUT IF A TARGET IS PRESENT THE THRESHOLD CROSSINGS ARE MORE REGULAR /NE TYPICAL SYSTEM SIMPLY COUNTS THE NUMBER OF THRESHOLD CROSSINGS OVER THE INTEGRATION PERIOD AND IF CROSSINGS OCCUR FOR MORE THAN HALF THE NUMBER OF TIMES THAT THE RADAR HAS TRANSMITTED A TARGET IS INDICATED AS BEING PRESENT )F THE RADAR PULSE REPETITION FREQUENCY IS (Z AND THE INTEGRATION TIME IS S THE RADAR WILL OBSERVE THRESHOLD CROSSINGS IF THERE IS A STRONG AND STEADY TARGET (OWEVER BECAUSE THE ECHO FROM A WEAK TARGET COMBINED WITH NOISE MAY NOT ALWAYS CROSS THE THRESHOLD A LIMIT MAY BE SET SUCH AS CROSSINGS THAT MUST OCCUR DURING THE INTEGRATION PERIOD FOR A DECISION THAT A TARGET IS PRESENT &OR EXAMPLE PERFORMANCE ON A NON SCINTILLATING TARGET HAS A PROBABILITY OF DETECTION AT A D" PER PULSE 3.2 AND A FALSE ALARM PROBABILITY OF n 4HE !. &03 AND !.&01 INSTRUMENTATION RADARS USE THESE DETECTION PARAMETERS WITH CONTIGUOUS RANGE GATES OF YD EACH FOR ACQUISITION 4HE GATES GIVE COVERAGE OF A NMI RANGE INTERVAL AT THE RANGE WHERE THE TARGET IS EXPECTED POSSIBLY FROM COARSE RANGE DESIGNATION FROM SEARCH RADAR 2ANGE 4RACKING /NCE A TARGET IS ACQUIRED IN RANGE IT IS DESIRABLE TO FOLLOW THE TARGET IN THE RANGE COORDINATE TO PROVIDE DISTANCE INFORMATION OR SLANT RANGE TO THE TAR GET !PPROPRIATE TIMING PULSES PROVIDE RANGE GATING SO THE ANGLE TRACKING CIRCUITS AND !'# CIRCUITS LOOK AT ONLY THE SHORT RANGE INTERVAL OR TIME INTERVAL WHEN THE DESIRED ECHO PULSE IS EXPECTED 4HE RANGE TRACKING OPERATION IS PERFORMED BY CLOSED LOOP TRACKING SIMILAR TO THE ANGLE TRACKER %RROR IN CENTERING THE RANGE GATE ON THE TARGET ECHO PULSE IS SENSED ERROR VOLTAGES ARE GENERATED AND CIRCUITRY IS PROVIDED TO RESPOND TO THE ERROR VOLTAGE BY CAUSING THE GATE TO MOVE IN A DIRECTION TO RECENTER ON THE TARGET ECHO PULSE 4HE RANGE TRACKING ERROR MAY BE SENSED IN MANY WAYS 4HE MOST COMMONLY USED METHOD IS THE EARLY AND LATE GATE TECHNIQUE SEE &IGURE 4HESE GATES ARE TIMED SO THAT THE EARLY GATE OPENS AT THE BEGINNING OF THE MAIN RANGE GATE AND CLOSES AT THE CENTER OF THE MAIN GATE 4HE LATE GATE OPENS AT THE CENTER AND CLOSES AT THE END OF THE MAIN RANGE GATE 4HE EARLY AND LATE GATES EACH ALLOW THE TARGET VIDEO TO CHARGE CAPACITORS DURING THE TIME WHEN THE GATES ARE OPEN 4HE CAPACITORS ACT AS INTEGRATORS 4HE EARLY GATE CAPACITOR CHARGES TO A VOLTAGE PROPORTIONAL TO THE AREA OF THE FIRST HALF OF THE TARGET VIDEO PULSE AND THE LATE GATE CAPACITOR CHARGES NEGATIVELY PROPORTION ALLY TO THE LATE HALF OF THE TARGET VIDEO 7HEN THE GATES ARE PROPERLY CENTERED ABOUT A SYMMETRICAL VIDEO PULSE THE CAPACITORS ARE EQUALLY CHARGED 3UMMING THEIR CHARGE VOLTAGES YIELDS A ZERO OUTPUT 7HEN THE GATES ARE NOT CENTERED ABOUT THE TARGET VIDEO SO THAT THE EARLY GATE EXTENDS PAST THE CENTER OF THE TARGET VIDEO THE EARLY GATE CAPACITOR CHARGED POSI TIVELY RECEIVES A GREATER CHARGE 4HE LATE GATE SEES ONLY A SMALL PORTION OF THE PULSE RESULTING IN A SMALLER NEGATIVE CHARGE 3UMMING THE CAPACITOR VOLTAGES RESULTS IN A NEGATIVE OUTPUT /VER A RANGE OF ERRORS OF APPROXIMATELY o OF THE TARGET VIDEO PULSE WIDTH THE VOLTAGE OUTPUT IS ESSENTIALLY A LINEAR FUNCTION OF TIMING ERROR AND OF A POLARITY CORRESPONDING TO THE DIRECTION OF ERROR $URING ACQUISITION THE TARGET IS CENTERED IN THE YD ACQUISITION GATE BY RANGE TRACKING TECHNIQUES DESCRIBED AS FOLLOWS AND THE GATE IS REDUCED TO APPROXIMATELY THE WIDTH OF THE RADAR TRANSMIT PULSE FOR NORMAL TRACKING -ANY RADAR RANGE TRACKING SYSTEMS USE HIGH SPEED SAMPLING CIRCUITRY TO TAKE THREE TO FIVE SAMPLES IN THE VICINITY OF THE ECHO VIDEO PULSE 4HE AMPLITUDES OF THE SAMPLES ON THE LEADING AND LAGGING HALVES OF THE PULSE ARE COMPARED FOR RANGE ERROR SENSING SIMILAR TO THE COMPARISON OF AMPLITUDES IN THE EARLY LATE GATES RANGE TRACKER
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&)'52% %ARLY AND LATE GATE RANGE ERROR SENSING CIRCUIT
)N SOME CASES LEADING OR LAGGING EDGE RANGE TRACKING IS DESIRED 4HIS HAS BEEN ACCOMPLISHED IN SOME APPLICATIONS BY SIMPLY ADDING A BIAS TO MOVE THE ERROR SENSING GATES EITHER TO LEAD OR LAG THE CENTER OF THE TARGET 4HIS PROVIDES SOME REJECTION BY THE GATES OF UNDESIRED RETURNS THAT MIGHT OCCUR NEAR THE TARGET SUCH AS THE ECHOES FROM OTHER NEARBY TARGETS 4HRESHOLD DEVICES ARE ALSO USED AS LEADING OR LAGGING EDGE TRACKERS BY OBSERVING WHEN THE TARGET VIDEO EXCEEDS A GIVEN THRESHOLD LEVEL 4HE POINT OF CROSSING THE THRESHOLD IS USED TO TRIGGER GATING CIRCUITS TO READ OUT A TARGET RANGE FROM TIMING DEVICES OR TO GENERATE A SYNTHETIC TARGET PULSE 4HE RANGE TRACKING LOOP IS CLOSED BY USING THE RANGE ERROR DETECTOR OUTPUT TO REPO SITION RANGE GATES AND CORRECT RANGE READOUT /NE TECHNIQUE USES A HIGH SPEED DIGITAL COUNTER DRIVEN BY A STABLE OSCILLATOR 4HE COUNTER IS RESET TO ZERO AT THE TIME OF THE TRANSMIT PULSE 4ARGET RANGE IS REPRESENTED BY A NUMBER STORED IN A DIGITAL REGISTER AS SHOWN IN &IGURE ! COINCIDENCE CIRCUIT SENSES WHEN THE DIGITAL COUNTER REACHES THE NUMBER IN THE RANGE REGISTER AND GENERATES THE RANGE GATE AS INDICATED IN THE BLOCK DIA GRAM SHOWN IN &IGURE ! RANGE ERROR SENSED BY THE RANGE ERROR DETECTOR RESULTS IN AN ERROR VOLTAGE THAT DRIVES A VOLTAGE CONTROLLED VARIABLE FREQUENCY OSCILLATOR TO INCREASE OR DECREASE THE COUNT IN THE RANGE REGISTER DEPENDING ON THE POLARITY OF THE ERROR VOLT AGE 4HIS CHANGES THE NUMBER IN THE RANGE REGISTER TOWARD THE VALUE CORRESPONDING TO THE RANGE OF THE TARGET 2ANGE READOUT IS ACCOMPLISHED BY READING THE NUMBER IN THE REGISTER WHERE FOR EXAMPLE EACH BIT MAY CORRESPOND TO A YD RANGE STEP
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&)'52% $IGITAL RANGE TRACKER OPERATION
!NOTHER TECHNIQUE IS TO USE A PAIR OF OSCILLATORSONE CONTROLLING THE TRANSMITTER TRIGGER AND THE OTHER CONTROLLING THE RANGE GATE 4HE RANGE RATE IS CONTROLLED BY THE BEAT FREQUENCY BETWEEN THE OSCILLATORS WHERE ONE IS FREQUENCY CONTROLLED BY THE RANGE
&)'52% "LOCK DIAGRAM OF A DIGITAL RANGE TRACKER
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ERROR DETECTOR OUTPUT VOLTAGE 4HE BEAT FREQUENCY IS A SMALL FRACTION OF ONE (Z AND IS BETTER VISUALIZED AS A PHASE RATE BETWEEN THE TRANSMIT PULSE CYCLE AND CYCLE OF THE RANGE GATE 4HE CHANGING PHASE CAUSES THE RANGE GATE TO FOLLOW A MOVING TARGET 4HE ELECTRONIC RANGE TRACKER IS INERTIALESS ALLOWING ANY DESIRED SLEW SPEED AND PRO VIDES FLEXIBILITY FOR CONVENIENTLY GENERATING ACQUISITION GATES FOR AUTOMATIC DETECTION CIRCUITRY AS WELL AS TRANSMITTER TRIGGER AND PRE TRIGGER PULSES 4RACKING BANDWIDTH IS USU ALLY LIMITED TO THAT NECESSARY FOR TRACKING TO MINIMIZE LOSS OF TRACK TO FALSE TARGETS AND COUNTERMEASURES -ANY OTHER ELECTRONIC RANGE TRACKING TECHNIQUES ALSO OFFERING MOST OF THESE ADVANTAGES ARE USED NTH 4IME !ROUND 4RACKING 4O EXTEND UNAMBIGUOUS RANGE BY REDUCING THE 02& INCREASES THE ACQUISITION TIME AND REDUCES THE DATA RATE ! SOLUTION TO THIS PROB LEM IS CALLED NTH TIME AROUND TRACKING WHICH AVOIDS TRANSMITTING AT THE TIME THAT AN ECHO IS EXPECTED TO ARRIVE AND CAN RESOLVE THE RANGE AMBIGUITY 4HIS ALLOWS THE RADAR TO OPERATE AT HIGH 02& AND TRACK UNAMBIGUOUSLY TO LONG RANGES WHERE SEVERAL PULSES MAY BE PROPAGATING IN SPACE TO AND FROM THE TARGET 4HE TECHNIQUE IS USEFUL ONLY WHEN A TARGET IS BEING TRACKED $URING ACQUISITION THE RADAR MUST LOOK AT THE REGION BETWEEN TRANSMITTER PULSES AND UPON INITIAL ACQUISITION IT CLOSES THE RANGE AND ANGLE TRACK ING LOOPS WITHOUT RESOLVING THE RANGE AMBIGUITY 4HE NEXT STEP IS TO FIND WHICH RANGE INTERVAL OR BETWEEN WHICH PAIR OF TRANSMIT PULSES THE TARGET IS LOCATED 4HE ZONE N IS DETERMINED BY CODING A TRANSMIT PULSE AND COUNTING HOW MANY PULSES RETURN BEFORE THE CODED PULSE RETURNS )NSTRUMENTATION RADARS PROVIDE NTH TIME AROUND TRACKING CAPABILITY BECAUSE BEA CONS ARE USED ON ROCKETS AND SPACE VEHICLES TO PROVIDE SUFFICIENT SIGNAL LEVEL AT VERY LONG RANGES 4O PREVENT THE TARGET ECHO FROM BEING BLANKED BY A TRANSMIT PULSE IT IS NECESSARY TO SENSE WHEN THE TARGET IS APPROACHING AN INTERFERENCE REGION AND SHIFT THE REGION 4HIS IS ACCOMPLISHED BY CHANGING THE 02& OR ALTERNATELY DELAYING GROUPS OF PULSES EQUAL TO THE NUMBER OF PULSES IN PROPAGATION 4HIS CAN BE PERFORMED AUTOMATICALLY TO PROVIDE AN OPTIMUM 02& SHIFT OR TO ALTERNATELY DELAY PULSE GROUPS OF THE CORRECT NUMBER OF PULSES
°ÈÊ -* Ê " "*1 - Ê/ +1 $UAL "AND -ONOPULSE $UAL BAND MONOPULSE CAN BE EFFICIENTLY ACCOMMO DATED ON A SINGLE ANTENNA TO COMBINE THE COMPLEMENTARY FEATURES OF TWO 2& BANDS ! USEFUL COMBINATION OF BANDS IS 8 BAND '(Z AND +A BAND '(Z 4HE 8 BAND OPERATION PROVIDES THE EXPECTED MICROWAVE PERFORMANCE OF GOOD RADAR RANGE AND PRECISE TRACKING )TS WEAKNESS IS THE LOW ANGLE MULTIPATH REGION AND THE AVAILABIL ITY OF ELECTRONIC COUNTERMEASURES IN THE BAND 4HE +A BAND ALTHOUGH ATMOSPHERIC AND RAIN ATTENUATION LIMITED PROVIDES MUCH GREATER TRACKING PRECISION IN THE LOW ANGLE MULTIPATH REGION AND A SECOND AND MORE DIFFICULT BAND THAT THE ELECTRONIC COUNTERMEA SURES TECHNIQUES MUST COVER ! .AVAL 2ESEARCH ,ABORATORY SYSTEM CALLED 42!+8 4RACKING 2ADAR !T +A AND 8 BANDS WAS DESIGNED FOR INSTRUMENTATION RADAR APPLICATIONS FOR MISSILE AND TRAINING RANGES )TS PURPOSE WAS TO ADD PRECISION TRACKING ON TARGETS ESSENTIALLY TO hSPLASHv AND PROVIDE PRECISION TRACKING AT +A BAND IN AN ENVIRONMENT OF 8 BAND COUNTERMEA SURE EXPERIMENTS
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! SIMILAR 8 AND +A BAND SYSTEM WAS DEVELOPED BY (OLLANDSE 3IGNAALAPPARATEN OF THE .ETHERLANDS FOR TACTICAL APPLICATION 4HE LAND BASED VERSION CALLED &,9 #!4#(%2 IS PART OF A MOBILE ANTI AIR WARFARE SYSTEM !NOTHER VERSION '/!, +%%0%2 IS FOR A SHIPBOARD ANTI AIR WARFARE APPLICATION FOR THE FIRE CONTROL OF 'ATLING GUNS "OTH SYSTEMS TAKE FULL ADVANTAGE OF THE TWO BANDS TO PROVIDE PRECISION TRACKING IN MULTIPATH AND ELECTRONIC COUNTERMEASURES ENVIRONMENTS -IRROR 3CANNED !NTENNA )NVERSE #ASSEGRAIN !N ANTENNA TECHNIQUE THAT USES A MOVABLE 2& MIRROR FOR SCANNING THE BEAM CALLED A MIRROR SCANNED ANTENNA OR INVERSE #ASSEGRAIN PROVIDES USEFUL APPLICATIONS TO MONOPULSE RADAR 4HE TECHNIQUE USES A RADOME SUPPORTED WIRE GRID PARABOLOID THAT REFLECTS PARALLEL POLARIZED FEED ENERGY 4HE BEAM POLARIZED PARALLEL TO THE GRID IS COLLIMATED BY THE PARABOLOID AND IS REFLECTED BY A FLAT MOVEABLE POLARIZATION ROTATING MIRROR 4HE BASIC POLARIZATION ROTATING MIRROR IS A FLAT METAL SURFACE WITH A GRID OF WIRES LOCATED A QUARTER WAVE LENGTH ABOVE THE METAL SURFACE AND ORIENTED AT RELATIVE TO THE 2& ENERGY REFLECTED FROM THE PARABOLOID 4HE 2& ENERGY MAY BE VISUALIZED AS BEING COMPOSED OF A COMPONENT PARALLEL TO AND REFLECTING FROM THE GRID AND A COMPONENT PERPENDICULAR TO AND PASSING THROUGH THE GRID TO REFLECT FROM THE METAL MIRROR SURFACE BELOW "Y TRAVELING THE QUARTER WAVESPACE TWICE THIS COMPONENT IS SHIFTED BY IN PHASE 7HEN ADDED TO THE REFLECTION FROM THE GRID IT RESULTS IN A CHANGE IN POLARIZA TION 4HE TOTAL REFLECTED ENERGY FROM THE MIRROR ROTATED BY WILL EFFICIENTLY PASS THROUGH THE WIRE GRID PARABOLOID 4HE ADVANTAGES ARE AS FOLLOWS 4HE MIRROR AND ITS DRIVE MECHANISM ARE THE ONLY MOVING PARTS FOR BEAM MOVEMENT 4HE FEED AND RADOME SUPPORTED PARABOLOID REMAIN FIXED 4HE BEAM MOVEMENT IS BY SPECULAR REFLECTION TWICE THE ANGLE OF THE MIRROR TILT 4HIS PROVIDES A COMPACT STRUCTURE FOR A GIVEN ANGLE COVERAGE REQUIREMENT 4HE NORMALLY LIGHTWEIGHT MIRROR AND THE BEAM DISPLACEMENT VERSUS MIRROR TILT ALLOW REDUCED SIZE AND VERY RAPID BEAM SCAN WITH LOW SERVO DRIVE POWER 4HE COMPACTNESS AND LIGHTNESS ARE PARTICULARLY ATTRACTIVE FOR AIRBORNE APPLICATIONS SUCH AS THE 4HOMPSON #3& !GAVE RADAR IN THE 3UPER %NTENDARDS WHICH DETERMINES TARGET RANGE AND DESIGNATION DATA FOR THE %XOCET MISSILE )T IS A COMPACT MONOPULSE ROLL AND PITCH STABILIZED RADAR WITH AZIMUTH AND ELEVATION SCAN 4HE )SRAELI %LTA SUBSIDIARY OF )SRAELI !IRCRAFT )NDUSTRIES ALSO DEVELOPED AN AIRBORNE TRACKING RADAR USING THIS ANTENNA TECHNOLOGY FOR AIR TO AIR COMBAT AND GROUND WEAPON DELIVERY ! GROUND OR SHIPBOARD BASED EXPERIMENTAL MIRROR ANTENNA SYSTEM CONCEPT WAS DEVELOPED WITH DUAL BAND MONOPULSE CAPABILITY '(Z AND '(Z BANDS 4HE OBJECTIVE INCLUDED HIGH SPEED BEAM MOVEMENT FOR HIGH DATA RATE $ SURVEILLANCE AND MULTITARGET PRECISION TRACKING $UAL BAND POLARIZATION TWIST MIRROR DESIGN WAS ACCOMPLISHED WITH A TWO LAYER MIRROR GRID CONFIGURATION /N !XIS 4RACKING 4HE BEST RADAR TRACKING PERFORMANCE IS USUALLY ACCOMPLISHED WHEN THE TARGET IS ESSENTIALLY ON THE RADAR ANTENNA AXIS 4HEREFORE FOR MAXIMUM PRECISION TRACKING IT IS DESIRABLE TO MINIMIZE LAG AND OTHER ERROR SOURCES AFFECTING THE BEAM POINTING ! TECHNIQUE CALLED ON AXIS TRACKING WAS DEVELOPED TO MINIMIZE RADAR AXIS DEVIATION FROM THE TARGET BY PREDICTION AND OPTIMUM FILTERING WITHIN THE TRACKING LOOP 4HE TECHNIQUE IS PARTICULARLY EFFECTIVE WHEN THE TARGET TRAJECTORY IS KNOWN APPROXIMATELY SUCH AS WHEN TRACKING SATELLITES IN ORBIT OR A BALLISTIC TARGET ! COMPUTER IN THE TRACKING LOOP CAN CAUSE THE RADAR TO FOLLOW AN ESTIMATED SET OF ORBITAL PARAMETERS FOR EXAMPLE )T ALSO PERFORMS OPTIMUM FILTERING OF RADAR ANGLE ERROR DETECTOR OUTPUT TO GENERATE AN ERROR TREND FROM WHICH IT CAN UPDATE THE ASSUMED SET
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OF ORBITAL PARAMETERS TO CORRECT THE RADAR BEAM MOVEMENT TO UPDATE THE ORIGINAL SET OF ORBITAL PARAMETERS AND BY THIS MEANS THE RADAR ANTENNA AXIS CAN BE HELD ON TARGET WITH MINIMUM ERROR )MPROVED TRACKING CAN ALSO BE PROVIDED ON OTHER TARGETS WHERE THE APPROXIMATE TRAJECTORY CAN BE ANTICIPATED (OWEVER PERFORMANCE OF ON AXIS TRACKING IS LIMITED WHEN TRACKING TARGETS WITH UNANTICIPATED MANEUVERS
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-Ê"Ê ,,", 4HERE ARE MANY SOURCES OF ERROR IN RADAR TRACKING PERFORMANCE &ORTUNATELY MOST ARE INSIGNIFICANT EXCEPT FOR VERY HIGH PRECISION TRACKING RADAR APPLICATIONS SUCH AS RANGE INSTRUMENTATION WHERE THE ANGLE PRECISION REQUIRED MAY BE OF THE ORDER OF MRAD MRAD OR MILLIRADIAN IS ONE THOUSANDTH OF A RADIAL OR THE ANGLE SUBTENDED BY M CROSS RANGE AT M RANGE -ANY SOURCES OF ERROR CAN BE AVOIDED OR REDUCED BY RADAR DESIGN OR MODIFICATION OF THE TRACKING GEOMETRY #OST IS A MAJOR FACTOR IN PROVID ING HIGH PRECISION TRACKING CAPABILITY 4HEREFORE IT IS IMPORTANT TO KNOW HOW MUCH ERROR CAN BE TOLERATED WHICH SOURCES OF ERROR AFFECT THE APPLICATION AND WHAT IS THE MOST COST EFFECTIVE MEANS TO SATISFY THE ACCURACY REQUIREMENTS "ECAUSE TRACKING RADARS TRACK TARGETS NOT ONLY IN ANGLE BUT ALSO IN RANGE AND SOME TIMES IN DOPPLER THE ERRORS IN EACH OF THESE TARGET PARAMETERS MUST BE CONSIDERED ON MOST ERROR BUDGETS 4HE REST OF THIS CHAPTER WILL PROVIDE A GUIDE FOR DETERMINING THE SIGNIFICANT ERROR SOURCES AND THEIR MAGNITUDES )T IS IMPORTANT TO RECOGNIZE WHAT THE ACTUAL RADAR INFORMATION OUTPUT IS &OR A MECHANICALLY MOVED ANTENNA THE ANGLE TRACKING OUTPUT IS USUALLY OBTAINED FROM THE SHAFT POSITION OF THE ELEVATION AND AZIMUTH ANTENNA AXES !BSOLUTE TARGET LOCATION RELATIVE TO EARTH COORDINATES WILL INCLUDE THE ACCURACY OF THE SURVEY OF THE ANTENNA PEDESTAL SITE 0HASED ARRAY INSTRUMENTATION RADAR SUCH AS THE -ULTI OBJECT 4RACKING 2ADAR -/42 PROVIDE ELECTRONIC BEAM MOVEMENT OVER A LIMITED SECTOR OF ABOUT o O TO APPROXIMATELY o O PLUS MECHANICAL MOVEMENT OF THE ANTENNA TO MOVE THE COVERAGE SECTORn 4HE OUTPUT WILL BE MECHANICAL SHAFT POSITIONS LOCATING THE NORMAL TO THE ARRAY PLUS DIGITAL ANGLE INFORMATION FROM THE ELECTRONIC BEAM SCAN FOR EACH TARGET
°nÊ /, / 1- Ê ,,",-Ê/, /Ê "- ® 2ADAR TRACKING OF TARGETS IS PERFORMED BY USE OF THE ECHO SIGNAL REFLECTED FROM A TARGET ILLUMINATED BY THE RADAR TRANSMIT PULSE 4HIS IS CALLED SKIN TRACKING TO DIFFERENTIATE IT FROM BEACON TRACKING WHERE A BEACON OR A TRANSPONDER TRANSMITS ITS SIGNAL TO THE RADAR AND USUALLY PROVIDES A STRONGER POINT SOURCE SIGNAL "ECAUSE MOST TARGETS SUCH AS AIRCRAFT ARE COMPLEX IN SHAPE THE TOTAL ECHO SIGNAL IS COMPOSED OF THE VECTOR SUM OF A GROUP OF SUPERIMPOSED ECHO SIGNALS FROM THE INDIVIDUAL PARTS OF THE TARGET SUCH AS THE ENGINES PROPELLERS FUSELAGE AND WING EDGES 4HE MOTIONS OF A TARGET WITH RESPECT TO THE RADAR CAUSES THE TOTAL ECHO SIGNAL TO CHANGE WITH TIME RESULTING IN RANDOM FLUCTUATIONS IN THE RADAR MEASUREMENTS OF THE PARAMETERS OF THE TARGET 4HESE FLUCTUA TIONS CAUSED BY THE TARGET ONLY EXCLUDING ATMOSPHERIC EFFECTS AND RADAR RECEIVER NOISE CONTRIBUTIONS ARE CALLED TARGET NOISE
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4HIS DISCUSSION OF TARGET NOISE IS BASED LARGELY ON AIRCRAFT BUT IT IS GENERALLY APPLI CABLE TO ANY TARGET INCLUDING LAND TARGETS OF COMPLEX SHAPE THAT ARE LARGE WITH RESPECT TO A WAVELENGTH 4HE MAJOR DIFFERENCE IS IN THE TARGET MOTION BUT THE DISCUSSIONS ARE SUFFICIENTLY GENERAL TO APPLY TO ANY TARGET SITUATION 4HE ECHO RETURN FROM A COMPLEX TARGET DIFFERS FROM THAT OF A POINT SOURCE BY THE MODULATIONS THAT ARE PRODUCED BY THE CHANGE IN AMPLITUDE AND RELATIVE PHASE OF THE RETURNS FROM THE INDIVIDUAL ELEMENTS 4HE WORD MODULATIONS IS USED IN PLURAL FORM BECAUSE FIVE TYPES OF MODULATION OF THE ECHO SIGNAL THAT ARE CAUSED BY A COMPLEX TARGET AFFECT RADARS 4HESE ARE AMPLITUDE MODULATION PHASE FRONT MODULATION GLINT POLAR IZATION MODULATION DOPPLER MODULATION AND PULSE TIME MODULATION RANGE GLINT 4HE BASIC MECHANISM BY WHICH THE MODULATIONS ARE PRODUCED IS THE MOTION OF THE TARGET INCLUDING YAW PITCH AND ROLL WHICH CAUSES THE CHANGE IN RELATIVE RANGE OF THE VARIOUS INDIVIDUAL ELEMENTS WITH RESPECT TO THE RADAR !LTHOUGH THE TARGET MOTIONS MAY APPEAR SMALL A CHANGE IN RELATIVE RANGE OF THE PARTS OF A TARGET OF ONLY ONE HALF WAVELENGTH BECAUSE OF THE TWO WAY RADAR SIGNAL PATH CAUSES A FULL CHANGE IN RELATIVE PHASE !T 8 BAND THIS IS ABOUT CM WHICH IS SMALL EVEN COMPARED WITH THE FLEXURE BETWEEN PARTS OF AN AIRCRAFT 4HE FIVE TYPES OF MODULATION CAUSED BY A COMPLEX TARGET ARE DISCUSSED NEXT !MPLITUDE .OISE !MPLITUDE NOISE IS THE CHANGE IN ECHO SIGNAL AMPLITUDE CAUSED BY A COMPLEX SHAPED TARGET EXCLUDING THE EFFECTS OF CHANGING TARGET RANGE )T IS THE MOST OBVIOUS OF THE VARIOUS TYPES OF ECHO SIGNAL MODULATION BY A COMPLEX SHAPED TARGET AND IS READILY VISUALIZED AS THE FLUCTUATING SUM OF MANY SMALL VECTORS CHANGING RANDOMLY IN RELATIVE PHASE !LTHOUGH IT IS CALLED NOISE IT MAY INCLUDE PERIODIC COMPO NENTS !MPLITUDE NOISE TYPICALLY FALLS INTO A LOW FREQUENCY AND HIGH FREQUENCY REGION OF INTEREST 4HESE CATEGORIES OVERLAP IN SOME RESPECTS BUT IT IS CONVENIENT TO SEPARATE THE NOISE IN THESE TWO FREQUENCY RANGES BECAUSE THEY ARE GENERATED BY DIFFERENT PHE NOMENA AND THEY ARE EACH SIGNIFICANT TO DIFFERENT FUNCTIONS OF THE RADAR ,OW &REQUENCY !MPLITUDE .OISE 4HE LOW FREQUENCY AMPLITUDE NOISE IS THE TIME VARIATION OF THE VECTOR SUM OF THE ECHOES FROM ALL THE REFLECTING SURFACES OF THE TARGET 4HE TIME VARIATION IS VISUALIZED BY CONSIDERING THE TARGET AS A RELATIVELY RIGID BODY WITH NORMAL YAW PITCH AND ROLL MOTIONS 4HE SMALL CHANGES IN RELATIVE RANGE OF THE REFLECTORS CAUSED BY THIS MOTION RESULT IN CORRESPONDING hRANDOMv CHANGE IN THE RELA TIVE PHASES #ONSEQUENTLY THE VECTOR SUM FLUCTUATES RANDOMLY 4YPICALLY TARGET RAN DOM MOTION IS LIMITED TO SMALL ASPECT CHANGES SUCH THAT THE AMPLITUDES OF THE ECHOES FROM THE INDIVIDUAL REFLECTORS VARY LITTLE OVER A PERIOD OF A FEW SECONDS AND CHANGE IN RELATIVE PHASE IS THE MAJOR CONTRIBUTOR %XCEPTIONS ARE LARGE FLAT SURFACES WITH NARROW REFLECTION PATTERNS !N EXAMPLE OF A TARGET CONFIGURATION IS A DISTRIBUTION OF REFLECTING SURFACES THAT CHANGE IN RELATIVE RANGE WITH TARGET MOTION ! TYPICAL PULSE AMPLITUDE TIME FUNCTION IS A SLOWLY VARYING ECHO AMPLITUDE 4HE LOW FREQUENCY AMPLITUDE NOISE CONTRIBUTES THE LARGEST PORTION OF THE NOISE MODULATION DENSITY AND IS CONCENTRATED MAINLY BELOW ABOUT (Z AT 8 BAND 4HE AMPLITUDE NOISE SPECTRUM IS SIMILAR FOR BOTH LARGE AND SMALL TARGETS 4HIS IS BECAUSE THE RATE OF RELATIVE RANGE CHANGE IS A FUNCTION OF BOTH ANGULAR YAW AND DISTANCE FROM THE CENTER OF GRAVITY OF THE AIRCRAFT 4HUS A LARGER AIRCRAFT WITH SLOW YAW RATES BUT GREATER WINGSPAN GENERATES A LOW FREQUENCY NOISE SPECTRUM SIMI LAR TO THAT OF A SMALL AIRCRAFT WITH HIGH YAW RATES BUT SMALLER WINGSPAN (OWEVER THE LARGER AIRCRAFT TYPICALLY HAS THE BROADER NOISE SPECTRUM BECAUSE OF THE DIFFERENCE IN DISTRIBUTION OF DOMINANT REFLECTORS
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4HE RADAR FREQUENCY AFFECTS THE LOW FREQUENCY AMPLITUDE NOISE SPECTRUM SHAPE WHERE THE SPECTRUM WIDTH IS CLOSELY PROPORTIONAL TO THE RADAR FREQUENCY IF THE TARGET SPAN IS ASSUMED TO BE AT LEAST SEVERAL WAVELENGTHS 4HE REASON FOR THIS DEPENDENCE IS THAT THE RELATIVE PHASE OF THE INDIVIDUAL ECHO SIGNALS IS A FUNCTION OF THE NUMBER OF WAVELENGTHS OF CHANGE IN RELATIVE RANGE CAUSED BY THE TARGETS RANDOM MOTION 4HUS WITH SHORTER WAVELENGTHS A GIVEN RELATIVE RANGE CHANGE WILL SUBTEND MORE WAVE LENGTHS CAUSING HIGHER PHASE RATE RESULTING IN HIGHER FREQUENCY NOISE COMPONENTS 4HE RATE OF AMPLITUDE FLUCTUATIONS OF THE ENVELOPE OF THE ECHO PULSES IS APPROXIMATELY PROPORTIONAL TO THE RADAR FREQUENCY ! MATHEMATICAL MODEL OF LOW FREQUENCY AMPLITUDE NOISE OF A TYPICAL AIRCRAFT IS GIVEN BY
! F
" " F
WHERE ! F FRACTIONAL MODULATION (Z " HALF POWER BANDWIDTH (Z F FREQUENCY (Z 4HE VALUE OF " FALLS TYPICALLY BETWEEN (Z AND (Z AT 8 BAND WITH THE LARGER AIRCRAFT AT THE HIGHER VALUES BECAUSE OF THE LARGER REFLECTORS SUCH AS ENGINES SPREAD OUT ALONG THE WINGS 4HESE REFLECTORS WITH THE GREATER SEPARATION CONTRIBUTE TO THE HIGHER FREQUENCIES BECAUSE THEIR RELATIVE RANGE CHANGE IS LARGE FOR A GIVEN ANGULAR MOVEMENT OF THE TARGET ! F IS THE MODULATION POWER DENSITY SUCH THAT THE SPECTRUM MAY BE INTEGRATED OVER ANY FREQUENCY RANGE TO FIND THE TOTAL NOISE POWER WITHIN A FREQUENCY BAND OF INTEREST 4AKING THE SQUARE ROOT OF THE VALUE OF THE INTEGRAL GIVES THE RMS MODULATION (IGH &REQUENCY !MPLITUDE .OISE (IGH FREQUENCY AMPLITUDE NOISE CONSISTS OF BOTH RANDOM NOISE AND PERIODIC MODULATION 4HE RANDOM NOISE IS LARGELY A RESULT OF THE VIBRATION AND MOVING PARTS OF THE AIRCRAFT PRODUCING A RELATIVELY FLAT NOISE SPEC TRUM SPREAD OUT TO A FEW HUNDRED (Z DEPENDING ON THE TYPE OF AIRCRAFT 4HE RMS NOISE DENSITY IS TYPICALLY A FEW PERCENT OF MODULATION PER (Z 4HE PERIODIC MODULATION APPEARING AS SPIKES IN THE &IGURE SPECTRUM ARE CAUSED BY RAPIDLY ROTATING PARTS OF AN AIRCRAFT SUCH AS THE PROPELLERS !S THE ECHO FROM A PROPELLER BLADE CHANGES WITH ASPECT WHEN IT ROTATES A PERIODIC MODULATION
&)'52% 4YPICAL AMPLITUDE SPECTRAL VOLTAGE DISTRIBUTION SHOWING THE PROPELLER MODULATION MEASURED ON A PROPELLER DRIVEN AIRCRAFT IN FLIGHT &IGURE FROM $UNN (OWARD AND +ING ¡ )2%
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IS PRODUCED 4HE BACKGROUND NOISE FROM THE AIRFRAME IS ALSO OBSERVED 4HE SPIKES IN THE SPECTRUM RESULT FROM A FUNDAMENTAL MODULATION FREQUENCY RELATED TO THE PRO PELLER REVMIN AND NUMBER OF BLADES 3INCE IT IS NOT USUALLY SINUSOIDAL THERE ARE HARMONIC FREQUENCIES SPREAD THROUGHOUT THE SPECTRUM AS SHOWN IN &IGURE FOR THE 3." A SMALL AIRCRAFT WITH TWO PROPELLER ENGINES 4HE LOCATION OF THESE SPIKES IS NOT DEPENDENT ON 2& FREQUENCY AS IN THE CASE OF LOW FREQUENCY AMPLITUDE NOISE BECAUSE THE TARGET CONTROLS THE PERIODICITY OF THE MODULATION WHICH IS DEPENDENT ONLY ON THE AIRCRAFT PROPELLER ROTATION RATE AND NUMBER OF BLADES *ET AIRCRAFT MAY ALSO CAUSE ECHO AMPLITUDE MODULATION OF RADAR SIGNALS REFLECTED FROM ROTATING FAN BLADES FROM WITHIN THE JET ENGINES 4HE JET ENGINE CAUSED MODULATION IS CALLED *ET %NGINE -ODULATION *%- SPECTRAL MODULATION LINES 4HE HIGH FREQUENCY NOISE MODULATION AFFECTS SCAN TYPE TRACKING RADARS AS DESCRIBED LATER AND GIVES SOME INFORMATION AS TO THE TYPE OF AIRCRAFT %FFECTS OF !MPLITUDE 3CINTILLATION ON 2ADAR 0ERFORMANCE !MPLITUDE NOISE TO SOME EXTENT AFFECTS ALL TYPES OF RADARS IN PROBABILITY OF DETECTION AND TRACKING RADAR ACCURACYn /NE EFFECT ON ALL TYPES OF TRACKING RADARS IS THE INTERRELATION BETWEEN THE LOW FREQUENCY SPECTRUM OF AMPLITUDE NOISE THE !'# CHARACTERISTICS WHICH DETERMINE TO WHAT EXTENT THE SLOW FLUCTUATIONS ARE SMOOTHED AND THE ANGLE NOISE 4HE EFFECTS ON ANGLE NOISE ARE DESCRIBED LATER IN THIS SECTION WHERE IT IS DESCRIBED WHY A FAST ACTING !'# IS GENERALLY THE PREFERRED CHOICE FOR MAXIMIZING OVERALL TRACKING ACCURACY (IGH FREQUENCY AMPLITUDE NOISE CAUSES ERRORS ONLY IN CONICAL SCAN OR SEQUENTIAL LOB ING TRACKING RADARS BECAUSE THE EFFECTS ARE ELIMINATED BY THE MONOPULSE TECHNIQUES #ONICAL SCAN OR SEQUENTIAL LOBING TO SENSE TARGET DIRECTION DEPEND UPON MEASURING THE AMPLITUDE OF THE SIGNAL FOR AT LEAST TWO DIFFERENT ANTENNA BEAM POSITIONS FOR EACH TRACKING AXIS )N AZIMUTH TRACKING FOR EXAMPLE THE ANTENNA BEAM IS DISPLACED TO THE LEFT OF THE TARGET AND THEN TO THE RIGHT )F THE TARGET WERE ON THE ANTENNA AXIS THE SIGNAL WOULD DROP THE SAME AMOUNT WHEN THE BEAM ASSUMED TO BE SYMMETRICAL IS MOVED AN EQUAL AMOUNT IN EITHER DIRECTION 4HE AMPLITUDES FOR EACH BEAM POSITION ARE SUBTRACTED IN AN ANGLE ERROR DETECTOR HENCE THE OUTPUT IS ZERO IF THE TARGET IS ON THE ANTENNA AXIS AND BECOMES FINITE INCREASING POSITIVELY OR NEGATIVELY AS THE TARGET MOVES OFF AXIS TO THE RIGHT OR LEFT (IGH FREQUENCY NOISE CAN CAUSE THE AMPLITUDE TO CHANGE DURING THE TIME TAKEN TO MOVE THE ANTENNA BEAM FROM ONE POSITION TO THE NEXT %VEN IF THE TARGET IS ON AXIS HIGH FREQUENCY NOISE CAN CAUSE THE AMPLITUDE AT THE TWO BEAM POSITIONS TO DIFFER THUS CAUSING AN ERRONEOUS INDICATION THAT THE TARGET IS OFF AXIS 4HIS EFFECT IS AVERAGED OUT EXCEPT FOR THE NOISE SPECTRAL ENERGY NEAR THE SCAN RATE &OR EXAMPLE A PERIODIC MODULATION SPIKE NEAR THE SCAN RATE WILL CAUSE THE TRACKING RADAR TO DRIVE ITS ANTENNA IN A CIRCULAR MOTION AROUND THE TARGET AT A RATE EQUAL TO THE DIFFERENCE IN FREQUENCY BETWEEN THE SCAN RATE AND THE FREQUENCY OF THE SPECTRAL LINE 4HE DIRECTION CLOCKWISE OR COUNTERCLOCKWISE DEPENDS UPON WHETHER THE SPECTRAL LINE IS ABOVE OR BELOW THE SCAN RATE AND WHETHER THE SCAN IS CLOCKWISE OR COUNTERCLOCKWISE 4HE SERVOSYSTEM FILTERS OUT ALL FREQUENCIES OUTSIDE THE FREQUENCY RANGE BETWEEN THE SCAN RATE PLUS THE SERVO BANDWIDTH AND THE SCAN RATE MINUS THE SERVO BANDWIDTH AND AN ANGLE SENSITIVITY CONSTANT THAT CONVERTS RMS MODULATION TO RMS ANGLE ERROR !N EQUATION USING THIS RELATION TO CALCULATE RMS NOISE IN SCANNING AND LOBING TYPE TRACKING RADARS CAUSED BY HIGH FREQUENCY AMPLITUDE NOISE IS
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WHERE RS RMS ANGLE ERROR IN SAME ANGULAR UNITS AS P" ! FS RMS FRACTIONAL MODULATION NOISE DENSITY IN VICINITY OF SCAN RATE KS CONICAL SCAN ERROR SLOPE KS FOR SYSTEM OPTIMUM P" ONE WAY ANTENNA BEAMWIDTH A SERVO BANDWIDTH (Z ! SAMPLE CALCULATION FOR AN FS OF (Z WHERE !FS FROM MEASURED DATA TAKEN ON A LARGE JET AIRCRAFT IS APPROXIMATELY (Z P" IS MILS AND A IS (Z GIVES A RS OF MIL RMS )N THE CASE OF A PERIODIC MODULATION WHERE A SPECTRAL LINE FALLS WITHIN THE BAND FS o A THE RMS NOISE IS RS P" ! FS WHERE ! FS IS THE RMS FRACTIONAL MODULATION CAUSED BY THE SPECTRAL LINE 4HE RESULTANT RMS TRACKING ERROR RS WILL BE PERIODIC AT THE FREQUENCY FS FT WHERE FT IS THE FREQUENCY OF THE SPECTRAL LINE 4HE EFFECTS OF AMPLITUDE NOISE ON TARGET DETECTION AND ACQUISITION ARE OF CONCERN IN ALL TYPES OF RADARS PARTICULARLY AT LONG RANGES WHERE THE SIGNAL IS WEAK 4HE AMPLITUDE FLUCTUATIONS CAN CAUSE THE SIGNAL TO DROP BELOW THE NOISE LEVEL FOR SHORT PERIODS OF TIME THUS AFFECTING THE CHOICE OF THRESHOLDS ACQUISITION SCAN RATE AND DETECTION LOGICn !NGLE .OISE 'LINT !NGLE NOISE CAUSES A CHANGE WITH TIME IN THE APPARENT LOCATION OF THE TARGET WITH RESPECT TO A REFERENCE POINT ON THE TARGET 4HIS REFERENCE POINT IS USUALLY CHOSEN AS THE CENTER OF hGRAVITYv OF THE REFLECTIVITY DISTRIBUTION ALONG THE TARGET COORDINATE OF INTEREST 4HE CENTER OF GRAVITY IS THE LONG TIME AVERAGED TRACK ING ANGLE ON A TARGET 4HE TERM GLINT IS SOMETIMES USED FOR ANGLE NOISE BUT IT GIVES THE FALSE IMPRESSION THAT THE WANDER IN THE APPARENT POSITION OF A TARGET ALWAYS FALLS WITHIN THE TARGET SPAN )T WAS ORIGINALLY EXPECTED THAT ANGLE FLUCTUATIONS CAUSED IN A MONOPULSE RADAR BY A TARGET WOULD BE SIMPLE VARIATIONS IN THE CENTER OF GRAVITY OF THE REFLECTING AREAS HOWEVER MUCH LARGER ANGLE ERRORS WERE OBSERVED 4HE APPARENT ANGULAR LOCATION OF A TARGET CAN FALL AT A POINT COMPLETELY OUTSIDE THE EXTREMITIES OF THE TARGET 4HIS CAN BE DEMONSTRATED BOTH EXPERIMENTALLY AND THEORETICALLY ! PAIR OF SCATTERERS CAN BE APPROPRIATELY SPACED TO CAUSE A TRACKING RADAR WITH CLOSED LOOP TRACKING TO ALIGN ITS ANTENNA AXIS AT A POINT MANY TIMES THE SCATTERER SPACING AWAY FROM THE SCATTERERS )F THE SCATTERERS ARE STATIONARY THE RADAR ANTENNA WILL STAY POINTING IN THE ERRONEOUS DIRECTION &IGURE SHOWS EXPERIMENTAL DATA DEMONSTRATING THIS PHENOMENON WITH A TWO REFLECTOR TARGET 4HE ANGLE NOISE PHENOMENON AFFECTS ALL TYPES OF TRACKING RADARS BUT IS MAINLY OF CONCERN FOR TRACKING RADARS WHERE PRECISION TARGET LOCATION IS NEEDED 4O AID IN VISU ALIZING WHY ANGLE NOISE AFFECTS ANY RADAR TYPE ANGULAR DIRECTION SENSING DEVICE THE ECHO SIGNAL PROPAGATING IN SPACE WAS ANALYZED SHOWING THAT THE ANGLE NOISE IS PRES ENT IN THIS PROPAGATING ENERGY AS A DISTORTION OF THE PHASE FRONT 4HEORETICAL PLOTS OF A DISTORTED PHASE FRONT FROM DUAL SOURCES COMPARE VERY CLOSELY WITH PHOTOGRAPHS OF THE PHASE FRONT OF THE RADIATING SURFACE RIPPLES IN THE RIPPLE TANK EXPERIMENT WITH DUAL VIBRATING PROBES !LL RADAR ANGLE SENSING DEVICES SENSE BY ONE MEANS OR ANOTHER THE PHASE FRONT OF THE SIGNAL AND INDICATE THE TARGET TO BE IN A DIRECTION NORMAL TO THE PHASE FRONT 4HUS THE PHASE FRONT DISTORTIONS AFFECT ALL TYPES OF ANGLE SENSING RADARS -ANY MEASUREMENTS OF ANGLE NOISE HAVE BEEN MADE ON A VARIETY OF AIRCRAFT AND THE RESULTS OF THEORETICAL STUDIES HAVE BEEN VERIFIED 4HE THEORY AND MEASUREMENTS SHOW THAT ANGLE NOISE EXPRESSED IN LINEAR UNITS OF DISPLACEMENT SUCH AS METERS OF THE APPARENT POSITION OF THE TARGET FROM THE CENTER OF GRAVITY OF THE TARGET IS INDEPENDENT OF RANGE EXCEPT FOR VERY SHORT RANGES 4HEREFORE RMS ANGLE NOISE RANG IS EXPRESSED IN
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&)'52% !PPARENT LOCATION OF A DUAL SOURCE TARGET AS A FUNCTION OF RELATIVE PHASE E FOR DIFFERENT VALUES OF RELATIVE AMPLITUDE A MEASURED WITH A TRACKING RADAR &IGURE FROM (OWARD
UNITS OF METERS OF ERROR MEASURED AT THE TARGET LOCATION 4HE RESULTS SHOW THAT THE RMS VALUE OF ANGLE NOISE RANG IS EQUAL TO 2O WHERE 2O IS THE RADIUS OF GYRATION TAKEN ALONG THE ANGULAR COORDINATE OF INTEREST OF THE DISTRIBUTION OF THE REFLECTING AREAS OF THE TARGET &OR EXAMPLE IF A TARGETS REFLECTING AREAS HAVE A COS O@, SHAPED DISTRIBU TION WHERE @ IS A VARIABLE AND THE TARGET SPAN IS FROM , TO n, CALCULATION OF THE RADIUS OF GYRATION DIVIDED BY GIVES A VALUE OF RANG OF , 4YPICAL VALUES OF RANG ON ACTUAL AIRCRAFT FALL BETWEEN , AND , DEPENDING UPON THE DISTRIBUTION OF THE MAJOR REFLECTING AREAS SUCH AS ENGINES WING TANKS AND SO ON ! SMALL AIRCRAFT NOSE ON VIEW WITH A SINGLE ENGINE AND NO SIGNIFICANT REFLECTORS ATTACHED TO THE WINGS WILL HAVE A RANG OF APPROXIMATELY , WHEREAS LARGER AIRCRAFT WITH AN OUTBOARD ENGINE AND POSSIBLY WING TANKS WILL HAVE A RANG APPROACHING THE VALUE OF , 4HE AIRCRAFT SIDE VIEW ALSO TENDS TOWARD THE VALUE OF , BECAUSE OF A MORE CONTINUOUS DISTRIBUTION OF REFLECTING AREAS %STIMATION OF ANGLE SCINTILLATION RMS ERROR IN UNITS OF TARGET SPAN CAN BE MADE BY RELATING THE APPROXIMATE TARGET DISTRIBUTION IN &IGURE WITH ACTUAL AIRCRAFT CONFIGURATIONS 4HE VALUE OF RANG FOR A COMPLEX TARGET IS ESSENTIALLY A FIXED VALUE REGARDLESS OF 2& FREQUENCY IF A TARGET SPAN OF AT LEAST SEVERAL WAVELENGTHS IS ASSUMED AND IS INDEPENDENT OF THE RATE OF RANDOM MOTION OF THE TARGET (OWEVER AS DESCRIBED LATER THE SPECTRAL DISTRIBUTION OF ANGLE NOISE POWER IS DIRECTLY AFFECTED BY RADAR FREQUENCY ATMOSPHERIC TURBULENCE AND OTHER PARAMETERS
2ADIUS OF GYRATION IS CALCULATED ASSUMING THE hWEIGHTv OF THE SCATTERERS IS THEIR EFFECTIVE RADAR SCATTERING CROSS SECTION
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&)'52% 2-3 ANGLE SCINTILLATION BASED ON THE THEORETICAL RELATION TO THE RADIUS OF GYRATION OF THE DISTRIBUTION OF REFLECTING AREAS OF THE TARGET
4ARGET ANGLE NOISE IS TYPICALLY GAUSSIAN DISTRIBUTED !N EXAMPLE OF THE MEASURED DISTRIBUTION OF THE APPARENT TARGET ANGLE OF A SMALL TWO ENGINE AIRCRAFT IS SHOWN IN &IGURE ! RELATIVELY LONG TIME SAMPLE IS NEEDED SINCE SHORT TIME SAMPLES OF DATA CAN DEPART FROM THE GAUSSIAN SHAPE 5NUSUAL TARGETS MAY ALSO DEPART FROM GAUSSIAN DISTRIBUTED ANGLE NOISE $ELANO GIVES DATA FROM TWO AIRCRAFT IN FORMATION THAT ARE GAUSSIAN DISTRIBUTED WHEN COMPLETELY UNRESOLVED BUT CHANGE SHAPE AT CLOSE RANGE WHERE THE ANTENNA BEGINS TO RESOLVE THE TWO AIRCRAFT AS DESCRIBED IN 3ECTION
&)'52% !MPLITUDE PROBABILITY DISTRIBUTION OF ANGLE SCINTILLATION MEASURED ON A SMALL TWO ENGINE AIRCRAFT
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!LTHOUGH THE RMS VALUE OF ANGLE NOISE IS ESSENTIALLY A CONSTANT FOR A GIVEN TARGET AND ASPECT THE SPECTRAL DISTRIBUTION OF THIS ENERGY IS DEPENDENT ON RADAR FREQUENCY AND THE RANDOM TARGET MOTION ! TYPICAL SPECTRUM SHAPE IS
. F S ANG
" P " F
WHERE . F SPECTRAL NOISE POWER DENSITY POWER(Z " NOISE BANDWIDTH (Z F FREQUENCY (Z 4HE VALUES OF " ARE PROPORTIONAL TO RADAR FREQUENCY AND DEPENDENT UPON AIR TUR BULENCE EFFECTS ON TARGET MOTION AND TARGET ASPECT !N EXAMPLE OF A MEASURED ANGLE SCINTILLATION SPECTRUM IS SHOWN IN &IGURE 4YPICAL VALUES OF " AT 8 BAND IN RELA TIVELY TURBULENT AIR RANGE FROM ABOUT (Z FOR SMALL AIRCRAFT TO ABOUT (Z FOR LARGER AIRCRAFT " CHANGES IN PROPORTION TO RADAR FREQUENCY PROVIDED THAT THE TARGET SPAN IS AT LEAST A FEW WAVELENGTHS !GAIN LONG TIME SAMPLES ARE NECESSARY TO OBTAIN A RELATIVELY SMOOTH SPECTRUM FROM MEASURED DATA &OR THE ABOVE VALUES OF " ABOUT MINUTES OF DATA WAS NECESSARY TO REACH ESSENTIALLY THE LONG TIME AVERAGED CHARACTERISTIC 4HIS IS A REFERENCE POINT ABOUT WHICH THERE WILL BE CONSIDERABLE VARIATION FOR A TYPICAL TIME PERIOD OF INTEREST &OR EXAMPLE WITH ONLY MINUTE OF DATA THE NOISE POWER RANG WOULD VARY OVER TO TIMES THE LONG TIME AVERAGED RANG !T LOWER RADAR FREQUENCIES AND IN LESS TURBULENT ATMOSPHERE " MAY BE SMALLER AND PROPORTIONATELY LONGER TIME SAMPLES ARE NECESSARY THUS FOR SHORT TIME SAMPLES OF RADAR PERFORMANCE SIGNIFICANT STATISTICAL VARIATIONS MUST BE EXPECTED 4O CONVERT RANG EXPRESSED IN LINEAR UNITS MEASURED AT THE TARGET TO ANGULAR UNITS FOR A RADAR AT RANGE R THE FOLLOWING RELATION MAY BE USED RANG ANGULAR MILS RANG M RKM "ECAUSE THE ANGULAR ERRORS CAUSED BY ANGLE NOISE ARE INVERSELY PROPORTIONAL TO RANGE ANGLE NOISE IS OF CONCERN MAINLY AT MEDIUM AND CLOSE RANGES 4HE RESULTANT TRACKING NOISE CAN BE REDUCED BY LOWERING THE SERVO BANDWIDTH TO REDUCE THE RADARS ABILITY TO FOLLOW THE HIGHER FREQUENCY COMPONENTS OF THE NOISE 4HE AMOUNT OF NOISE REDUCTION MAY BE ESTIMATED BY COMPARING THE AREA UNDER A SPECTRAL POWER DENSITY PLOT OF ANGLE NOISE BELOW THE FREQUENCY CORRESPONDING TO THE RADAR SERVO BANDWIDTH WITH THE TOTAL AREA UNDER THE POWER DENSITY PLOT 4HE SPECTRAL POWER DENSITY PLOT MAY BE OBTAINED BY SQUARING THE ORDINATE VALUES OF A SPECTRAL DISTRIBUTION PLOT SUCH AS SHOWN IN &IGURE 4HE CHOICE OF !'# CHARACTERISTICS ALSO AFFECTS THE AMOUNT OF ANGLE NOISE FOLLOWED BY A TRACKING ANTENNA 4HE !'# VOLTAGE IS GENERATED FROM THE SUM SIGNAL AND FOL LOWS THE ECHO SIGNAL AMPLITUDE FLUCTUATION 4HERE IS A DEGREE OF CORRELATION BETWEEN THE ANGLE NOISE MAGNITUDE AND ECHO SIGNAL MAGNITUDE SUCH THAT ANGLE NOISE PEAKS ARE GENERALLY ACCOMPANIED BY A DIP OR FADE IN AMPLITUDE ! SLOW !'# SYSTEM THAT DOES NOT MAINTAIN CONSTANT SIGNAL LEVEL DURING RAPID CHANGES ALLOWS THE SIGNAL LEVEL TO DROP DURING A RAPID FADE REDUCING SENSITIVITY VOLTS PER DEGREE ANGLE ERROR DURING THE LARGE ANGLE NOISE PEAKS 4HIS RESULTS IN A SMALLER RMS TRACKING NOISE WITH A SLOW !'# SYSTEM (OWEVER THIS REASONING NEGLECTS AN ADDITIONAL NOISE TERM CAUSED BY THE LACK OF FULL !'# ACTION WHICH IS PROPORTIONAL TO TRACKING LAG ! TRACKING LAG CAUSES A DC ERROR
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&)'52% 3PECTRAL ENERGY DISTRIBUTION OF ANGLE SCINTILLATION MEASURED ON THE NOSE ASPECT OF A SMALL TWO ENGINE AIRCRAFT
VOLTAGE IN THE ANGLE ERROR DETECTOR OUTPUT EQUAL TO ANGLE ERROR TIMES THE ANGLE SEN SITIVITY ! SLOW !'# ALLOWS THE AMPLITUDE NOISE TO MODULATE THE TRUE TRACKING ERROR VOLTAGE CAUSING ADDITIONAL NOISE IN ANGLE TRACKING 4HUS THERE WILL BE AN ADDITIONAL RMS ANGLE ERROR PROPORTIONAL TO TRACKING LAG AND DEPENDENT ON THE !'# TIME CON STANT AS ILLUSTRATED IN &IGURE )N GENERAL A FAST !'# IS RECOMMENDED BECAUSE IT REDUCES THE ADDITIONAL NOISE TERM ALLOWED BY SLOW !'# AND THE POSSIBILITY OF LARGER RMS TRACKING ERRORS WHICH CAN BE CONSIDERABLY GREATER THAN THE ANGLE NOISE WITH A FAST !'# !S PREVIOUSLY DISCUSSED ANGLE NOISE IS SIGNIFICANT MAINLY AT MEDIUM AND CLOSE RANGE WHERE TARGET ANGLE RATES ARE GREATEST !S SEEN IN &IGURE A TRACKING LAG OF ONLY ONE HALF THE
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&)'52% !NGLE SCINTILLATION NOISE POWER AS A FUNCTION OF TRACKING ERROR FOR THREE DIFFERENT !'# BANDWIDTHS FROM $UNN (OWARD AND +ING ¡ )2%
TARGET SPAN WILL RESULT IN GREATER TRACKING NOISE IN A SLOW !'# SYSTEM WITH THE DANGER OF MUCH HIGHER NOISE WITH GREATER LAG 4HEREFORE FOR OVERALL PERFORMANCE A FAST !'# IS RECOMMENDED 2ANGE .OISE 2ANGE 'LINT 2ANGE NOISE OR RANDOM TRACKING ERRORS IN THE RANGE COORDINATE CAUSED BY COMPLEX TARGETS IS A SIGNIFICANT BASIC LIMITATION IN RANGE TRACKING !CQUISITION OF A DESIRED SPECTRAL LINE BY A DOPPLER FREQUENCY TRACKING SYSTEM IS ALSO LIMITED BY RANGE NOISE #OARSE VELOCITY INFORMATION IS OBTAINED BY DIFFERENTIATION OF RANGE TO DETERMINE THE DESIRED SPECTRAL LINE 2ANGE NOISE IS A MAJOR LIMITATION TO THE ACCURACY OF VELOCITY OBTAINED FROM RANGE RATE AND CAN PREVENT SELECTION OF THE DESIRED SPECTRAL LINE 4HE RANGE TRACKING ERRORS CAUSED BY A FINITE SIZE TARGET AND BY MULTIPATH ALSO CAUSE SIGNIFICANT ANGLE TRACKING ERRORS IN MULTILATERATION TRACKING SYSTEMS THAT TRIANGULATE USING HIGH PRECISION RANGE MEASUREMENTS FROM MULTIPLE LOCATIONS TO CALCULATE TARGET ANGLE LOCATION -ULTILATERATION SYSTEMS SUCH AS THE 0ACIFIC -ISSILE 2ANGE %XTENDED !REA 4RACKING 3YSTEM %!43 DEPEND UPON VERY PRECISE RANGE MEASUREMENTS 3MALL RANGE TRACKING ERRORS CAUSE SIGNIFICANT ERRORS IN CALCULATED TARGET ANGLE BASED ON THE RANGE MEASUREMENTS 4HESE ERRORS MUST BE FULLY UNDERSTOOD TO ASSESS THE PERFORMANCE OF MULTILATERATION SYSTEMS 4ARGET CAUSED RANGE TRACKING ERRORS SIMILAR TO TARGET CAUSED ANGLE ERRORS ARE GREATER THAN THE WANDER OF THE TARGET CENTER OF GRAVITY AND CAN FALL OUTSIDE THE TARGET SPAN &IGURE SHOWS TYPICAL SAMPLES OF SPECTRAL ENERGY DISTRIBUTIONS AND PROB ABILITY DENSITY FUNCTIONS FOR DIFFERENT TARGET CONFIGURATIONS 4HE RANGE NOISE MEASURE MENTS WERE MADE ON SMALL AND LARGE AIRCRAFT AND MULTIPLE AIRCRAFT USING THE SPLIT VIDEO RANGE ERROR DETECTOR 4HE CHARACTERISTICS FOLLOW VERY CLOSELY TO THE RELATIONS OF TARGET ANGLE NOISE TO THE TARGET CONFIGURATION RADIUS OF GYRATION ALONG THE ANGLE COORDINATE
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&)'52% 4YPICAL SPECTRAL ENERGY DISTRIBUTIONS FOR THE THREE VIEWS OF THE 3." AIRCRAFT A NOSE VIEW B SIDE VIEW C TAIL VIEW AND D SIDE VIEW OF TWO SMALL TWO ENGINE AIRCRAFT FLYING IN FORMATION
&OR RANGE TRACKING IT IS NECESSARY TO RELATE RANGE NOISE TO THE TARGET REFLECTIVITY DISTRI BUTION ALONG THE RANGE COORDINATE )N GENERAL THE LONG TIME AVERAGE VALUE OF THE RMS RANGE ERROR MAY BE CLOSELY ESTIMATED BY TAKING TIMES THE RADIUS OF GYRATION OF THE DISTRIBUTION OF THE REFLECTING AREAS IN THE RANGE DIMENSION BASED ON MANY MEASURE MENTS OF SMALL LARGE AND MULTIPLE AIRCRAFT 4YPICALLY IN TERMS OF TARGET SPAN ALONG THE RANGE COORDINATE THE RMS VALUE WILL FALL BETWEEN AND TIMES THE TARGET SPANBEING CLOSE TO THE MULTIPLIER FOR THE TAIL VIEW AND NOSE VIEW AND FOR THE SIDE VIEW 4HE SPECTRAL SHAPE MAY BE CLOSELY ESTIMATED BY USING THE SAME FUNCTION OF FREQUENCY AS DESCRIBED FOR ANGLE NOISE AND THE SAME VALUE OF BANDWIDTH 4HE ERROR AS A FUNCTION OF RELATIVE PHASE AND AMPLITUDE OF THE TARGET REFLECTORS IS SIMILAR TO THE ANGLE NOISE PHENOMENON ! BEACON ON A COOPERATIVE TARGET CAN PROVIDE A POINT SOURCE SINGLE PULSE RESPONSE TO ELIMINATE RANGE ERROR CAUSED BY THE TARGET (OWEVER VERY STABLE CIRCUITRY IS REQUIRED TO AVOID PULSE JITTER AND DRIFT $OPPLER 3CINTILLATION AND 3PECTRAL ,INES $OPPLER SCINTILLATION AND SPECTRAL LINES CAUSED BY A COMPLEX TARGET MAY BE DIVIDED INTO TWO PHENOMENA SPECTRAL LINES CAUSED BY PARTS OF THE AIRCRAFT SUCH AS PROPELLERS AND JET TURBINE BLADES AND A CONTINUOUS DOPPLER SPECTRUM SPREAD BY THE MOTION OF AN AIRCRAFT IN FLIGHT SYMMETRICALLY
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ABOVE AND BELOW THE AVERAGE DOPPLER OF THE TARGET ! TARGET TYPICALLY HAS A SIGNIFICANT RANDOM YAW PITCH AND ROLL MOTION EVEN ON A hFIXEDv HEADING 4IME PLOTS OF TYPICAL AIRCRAFT HEADING FOR AN AIRCRAFT FLYING A hSTRAIGHT COURSEv ARE OBSERVED TO HAVE TYPICAL RANDOM YAW MOTION THAT CAUSES SMALL CHANGES IN THE DOPPLER FROM EACH OF THE SCATTERING SURFACES OF THE AIRCRAFTS RIGID STRUCTURE 2ELATIVE TO THE AVERAGE DOPPLER OF THE AIRCRAFT THE SCATTERING SURFACES LOCATED AWAY FROM THE AIRCRAFT CENTER WILL HAVE A SMALL INCREASING AND DECREASING RELATIVE DOPPLER FREQUENCY AS THE AIRCRAFT YAWS RIGHT AND LEFT 4HIS CAUSES A SPECTRAL SPREAD OF THE DOPPLER OF THE ECHO FROM THE RIGID BODY OF THE AIRCRAFT AND IS ACCOMPANIED BY SPECTRAL LINES CAUSED BY MOVING PARTS ON THE AIRCRAFT #OMPONENTS OF THE TARGET ECHO FROM ROTATING OR MOVING PARTS OF THE TARGET CAUSE DOPPLER LINES AT FREQUENCIES DISPLACED FROM THE AIRFRAME DOPPLER SPECTRUM 4HE PERIODIC AMPLITUDE MODULATION CAUSES PAIRS OF DOPPLER LINES SYMMETRICAL ABOUT THE DOPPLER OF THE AIRFRAME VELOCITY -OVING PARTS CAN ALSO CAUSE PURE FREQUENCY MODULATION THAT WILL RESULT IN A SINGLE SET OF DOPPLER LINES ON ONE SIDE OF THE AIRFRAME DOPPLER SPECTRUM ! MAJOR SIGNIFICANCE OF THE DOPPLER MODULATION IS ITS EFFECT ON DOPPLER MEASURING RADARS ! DOPPLER TRACKING SYSTEM THAT AUTOMATICALLY TRACKS THE FREQUENCY OF A SPECTRAL LINE OF THE ECHO IS SUBJECTED TO TWO PROBLEMS THERE IS THE POSSIBILITY OF LOCKING ON A FALSE LINE CAUSED BY MOVING PARTS OF THE TARGET AND WHEN PROPERLY LOCKED ONTO THE AIRFRAME DOPPLER SPECTRUM THE DOPPLER READING WILL BE NOISY AS DEFINED BY THE RANDOM FLUCTUATION IN INSTANTANEOUS FREQUENCY AS OBSERVED BY THE SPREAD OF THE DOP PLER SPECTRUM #OHERENT BEACONS WHICH RECEIVE AMPLIFY AND TRANSMIT RECEIVED RADAR PULSES CAN PROVIDE A DOPPLER SHIFTED RESPONSE FREE OF TARGET CAUSED SPECTRAL SPREAD AND PERIODIC MODULATIONS ! DELAY TIME IS PROVIDED TO SEPARATE THE BEACON RESPONSE FROM THE TARGET ECHO 4ARGET DOPPLER SCINTILLATION ALSO OFFERS USEFUL INFORMATION ABOUT THE TARGET CONFIGURA TION .ORMAL TARGET MOTION WILL RESULT IN DIFFERENT DOPPLER SHIFTS FOR EACH MAJOR SCAT TERER OF A RIGID BODY TARGET AND THE SHIFTS WILL BE A FUNCTION OF THE DISPLACEMENT OF THE SCATTERER FROM A REFERENCE POINT SUCH AS THE CENTER OF ROTATION OF THE TARGETS RANDOM MOTIONS 4HEREFORE A HIGH RESOLUTION DOPPLER SYSTEM CAN RESOLVE MAJOR REFLECTORS AND LOCATE THEM IN CROSS RANGE AS A FUNCTION OF THE DOPPLER DIFFERENCE FROM THE REFERENCE REFLECTOR 4HIS TECHNIQUE CALLED INVERSE SYNTHETIC APERTURE RADAR )3!2 USES THE TARGET MOTION FOR THE NEEDED ASPECT CHANGE INSTEAD OF RADAR MOTION AS USED IN CONVENTIONAL SYNTHETIC APERTURE RADAR TO OBTAIN DETAILED CROSS RANGE TARGET IMAGE INFORMATION
°Ê "/ ,Ê 8/ , Ê 1- -Ê"Ê ,,", -ULTIPATH -ULTIPATH ANGLE ERRORS RESULT FROM REFLECTIONS OF THE TARGET ECHO FROM OBJECTS OR SURFACES CAUSING ECHO PULSES TO ARRIVE BY OTHER THAN THE DIRECT PATH TO THE RADAR BEAM IN ADDITION TO THE DIRECT PATH 4HESE ERRORS ARE SOMETIMES CALLED LOW ANGLE TRACKING ERRORS WHEN APPLIED TO TRACKING OF TARGETS AT SMALL ELEVATION ANGLES OVER THE %ARTH OR OCEAN SURFACEn -ULTIPATH ERRORS ARE TYPICALLY A SPECIAL DUAL SOURCE CASE OF 'EOMETRY OF THE RADAR MULTIPATH ANGLE NOISE RESULTING FROM THE GEOMETRY &)'52% TRACKING CONDITION WHERE THE REFLECTION FROM A AS DESCRIBED IN &IGURE WHERE THE SURFACE APPEARS TO THE RADAR AS AN IMAGE BELOW TARGET AND ITS IMAGE REFLECTED FROM A THE SURFACE
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SURFACE TO THE RADAR BEAM ARE THE TWO SOURCES /VER A SMOOTH OCEAN SURFACE THEY ARE SEPARATED ONLY IN THE ELEVATION COORDINATE SO THAT MOST OF THE ERROR APPEARS IN THE ELEVATION TRACKING CHANNEL 3EVERE ELEVATION ERRORS MAY CAUSE SOME CROSS COUPLING OF THE ERROR TO THE AZIMUTH CHANNEL 2OUGH SURFACES CAUSE DIFFUSE SCATTERING WHICH CAN CONTRIBUTE ERRORS TO BOTH AZIMUTH AND ELEVATION TRACKING $IFFERENT PATH GEOMETRIES SUCH AS NON FLAT LAND OR A BUILDING MAY ALSO CAUSE A SIGNIFICANT ERROR TO APPEAR IN THE AZIMUTH TRACKING CHANNEL 4HE MAJOR DIFFICULTY WITH LOW ANGLE TRACKING IS THAT THE TARGET AND ITS IMAGE ARE ESSENTIALLY COHERENT AND THEIR RELATIVE PHASE CHANGES SLOWLY AND THE ANGULAR ERROR IT CAUSES IS READILY FOLLOWED BY AN ANGLE TRACKING SYSTEM &URTHERMORE THE PATHS ARE ALMOST EQUAL AND IN MOST CASES THEY CANNOT BE RESOLVED BY HIGH RANGE RESOLUTION TECHNIQUES ,ONG TIME AVERAGES OF THE DATA DO NOT IN PRACTICE GIVE TARGET ELEVATION THUS THE MULTIPATH ANGLE ERROR HAS NO SIMPLE SOLUTION AND IS GENERALLY MINIMIZED BY USING NARROW BEAM ANTENNAS 7HEN THE TARGET IS AT LOW ALTITUDE THE MULTIPATH ERRORS ARE SEVERE AS OBSERVED IN THE MEASURED DATA SHOWN IN &IGURE 4HIS DATA IS THE MULTIPATH ERROR OF A BEAMWIDTH 3 BAND '(Z TRACKING RADAR THAT IS TRACKING AN AIRCRAFT TARGET WITH A BEACON AT FT ALTITUDE !N !.&03 TRACKING RADAR WITH A BEAMWIDTH AT # BAND '(Z WAS USED TO SIMULTANEOUSLY TRACK WITH ITS NARROW BEAM WHICH REMAINED ABOVE THE SEA SURFACE WITHOUT SIGNIFICANT MULTIPATH ERROR TO PROVIDE A TRUE TARGET ALTITUDE REFERENCE FOR THE DATA IN &IGURE 4HERE IS A MEASUREMENT BIAS ERROR OBSERVED IN &IGURE OF ABOUT 4HE TRACKING DATA FROM A RADAR TRACKING A TARGET WITH A BEACON IS PLOTTED IN &IGURE SHOWING A TYPICAL MULTIPATH ERROR ILLUSTRATING THE PHENOMENON FROM THE REGION WHERE THE IMAGE ENTERS THE SIDELOBES TO THE REGION WHERE IT ENTERS THE MAIN BEAM 4HERE ARE THREE METHODS USED FOR PREDICTING MULTIPATH ERRORS DEPENDING UPON WHERE THE REFLECTED TARGET IMAGE ENTERS THE ANTENNA PATTERN !T THE FAR RANGE
&)'52% -EASURED ELEVATION TRACKING ERROR OF AN 3 BAND RADAR USING AN !.&03 RADAR FOR A TARGET ELEVATION REFERENCE
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THE IMAGE ENTERS THE ANTENNA MAIN BEAM AND THE ERROR IS ESSENTIALLY THAT OF A TWO REFLECTOR TARGET GLINT ERROR FOLLOWING APPROXIMATELY THE EQUATION WHERE E Q H E
E H
R R COS F R R COS F
ERROR SAME UNITS AS H MEASURED AT THE TARGET RANGE RELATIVE TO THE TARGET MAGNITUDE OF SURFACE REFLECTION COEFFICIENT HEIGHT OF TARGET RELATIVE PHASE DETERMINED BY GEOMETRY OF DIRECT AND SURFACE REFLECTED SIGNAL PATHS AS SHOWN IN &IGURE
!LTHOUGH THE FLUCTUATIONS IN Q AND E ALTER THE ACTUAL TRACKING FROM THE THEORETICAL THE EQUATION GIVES A GOOD INDICATION OF THE ERRORS TO BE EXPECTED WHEN TRACKING A POINT SOURCE SUCH AS A BEACON (OWEVER SKIN TRACKING OF AN AIRCRAFT AT LOW ELEVATION MAY RESULT IN A DEPARTURE FROM THE CLASSIC PERIODIC ERROR VERSUS ELEVATION AS ILLUSTRATED IN &IGURE BECAUSE OF AN INTERACTION BETWEEN TARGET ANGLE SCINTILLATION AND MULTIPATH ERROR THAT CAN CHANGE THE CHARACTERISTICS OF THE MULTIPATH ERROR 7HEN TRACKING A POINT SOURCE TARGET AT CLOSE RANGE THE RADAR MAIN BEAM IS ABOVE THE IMAGE BUT THE IMAGE IS SEEN BY THE DIFFERENCE PATTERN SIDELOBES 4HE MULTIPATH ERRORS THAT RESULT ARE CYCLIC ALMOST SINUSOIDAL WITH AN RMS VALUE PRE DICTED BY THE EQUATION
S%
RQ " 'SE PEAK
WHERE R% RMS ELEVATION ANGLE MULTIPATH ERROR SAME UNITS AS P" P" ONE WAY ANTENNA BEAMWIDTH Q REFLECTION COEFFICIENT AND 'SE PEAK IS THE POWER RATIO OF THE TRACKING ANTENNA SUM PATTERN PEAK TO THE ERROR PATTERN PEAK SIDELOBE LEVEL AT THE ANGLE OF ARRIVAL OF THE IMAGE SIGNAL 4HE CYCLIC RATE MAY BE APPROXIMATED BY THE EQUATION WHERE FM H K %
FM
H% L
FREQUENCY OF CYCLIC MULTIPATH ERROR RADS HEIGHT OF RADAR ANTENNA WAVELENGTH SAME UNITS AS H RATE OF TARGET ELEVATION CHANGE AS SEEN BY RADAR RADS
4HE INTERMEDIATE RANGE IS BETWEEN THE SHORT RANGE REGION WHERE THE IMAGE APPEARS IN THE SIDELOBES AND THE LONG RANGE REGION WHERE THE IMAGE APPEARS WITHIN THE HALF POWER BEAMWIDTH 4HE ERROR IS DIFFICULT TO CALCULATE IN THIS REGION BECAUSE IT FALLS IN THE NONLINEAR ERROR SENSING PORTION OF THE ANTENNA PATTERNS AND THE RADAR RESPONSE IS STRONGLY DEPENDENT UPON THE SPECIFIC FEED DESIGN AND ERROR PROCESSING TECHNIQUE (OWEVER &IGURE PROVIDES A PRACTICAL MEANS FOR APPROXIMATING MULTIPATH ERROR VALUES IN THIS REGION 4HE CURVES ARE CALCULATED MULTIPATH ERRORS BASED ON AN ASSUMED GAUSSIAN SHAPED SUM PATTERN AND DERIVATIVE OF THE SUM PATTERN
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&)'52% #ALCULATED RMS MULTIPATH ERROR R% VERSUS TARGET ELEVATION %T BOTH NORMALIZED TO RADAR BEAMWIDTH P"
AS THE MONOPULSE DIFFERENCE PATTERN &IGURE SHOWS TYPICAL SIDELOBE MULTIPATH ERRORS FOR HIGHER ELEVATION TARGETS AND THE LINEARLY DECREASING ERROR VERSUS TARGET ELEVATION PREDICTED BY THE ABOVE EQUATION FOR VERY LOW ELEVATION TARGETS 4HE GRAPH IS NORMALIZED TO RADAR BEAMWIDTH ON BOTH AXES FOR CONVENIENT USE WITH A WIDE VARI ETY OF RADARS 4HE DASHED PORTIONS OF THE CURVES ARE REGIONS OF UNCERTAINTY BECAUSE OF SIGNIFICANT VARIATIONS OF REFLECTION FOR A GIVEN SEA STATE )N THE INTERMEDIATE REGION THE ERROR INCREASES TO A PEAK AT TARGET ELEVATIONS OF ABOUT BEAMWIDTH 4HE PEAK VALUE IS DEPENDENT ON SEVERAL FACTORS INCLUDING SURFACE ROUGHNESS WHICH IN PART DETERMINES THE VALUE OF Q SERVO BANDWIDTH AND ANTENNA CHARACTERISTICS IN THE REGION 4HE ERRORS ARE SEVERE AND WITH UN SMOOTHED TRACK WIDE SERVO BANDWIDTH THE RADAR CAN BREAK LOCK AND LOSE TRACK OF THE TARGET 7HEN THE SURFACE IS ROUGH CORRESPONDING TO A REFLECTION COEFFICIENT OF ABOUT THE CHARACTERISTIC OF THE ERROR VERSUS ELEVATION CHANGES IS OBSERVED IN &IGURE 4HE ROUGH SURFACE CAUSES SIGNIFICANT DIFFUSE SCATTERING RATHER THAN A MIRROR REFLECTION 4HIS CHANGES THE SHAPE OF THE ERROR CURVE AND RESULTS IN SOME RESIDUAL ELEVATION ANGLE ERROR WHEN THE TARGET ELEVATION GOES TO ZERO )T ALSO CAUSES SOME SIGNIFICANT AZIMUTH ERROR #ROSSTALK #AUSED BY #ROSS 0OLARIZED %NERGY 4ARGET ECHO ENERGY CROSS POLAR IZED TO THE RADAR ANTENNA CAUSES CROSSTALK CROSS COUPLING IN RADARS IE THE AZIMUTH ERROR CAUSES OUTPUT FROM THE ELEVATION ERROR DETECTOR AND THE ELEVATION ERROR CAUSES OUTPUT FROM THE AZIMUTH ERROR DETECTOR 'ENERALLY THIS EFFECT IS NEGLIGIBLE BECAUSE THE CROSS POLARIZED ENERGY IS USUALLY A SMALL FRACTION OF THE RECEIVED POLARIZATION FROM TYPICAL TARGETS AND IT IS NORMALLY REDUCED BY ABOUT D" BY THE ANTENNA DESIGN (OWEVER IN SPECIAL CASES THE RESULTANT CROSSTALK CAN BE VERY HIGH AND MAY CAUSE A LARGE TRACKING ERROR AND POSSIBLE LOSS OF TRACK &OR EXAMPLE POLARIZATION OF A LINEARLY POLARIZED BEACON ON A TARGET COULD ROTATE WITH TARGET ASPECT CHANGE AND IN THE WORST CASE APPROACH A CROSS POLARIZED CONDITION
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4HEORETICALLY THE COUPLING TO CROSS POLARIZED ENERGY IS ZERO WHEN THE SOURCE IS PRE CISELY ON AXIS AND INCREASES WITH DISPLACEMENT FROM THE AXIS 4HE CROSS POLARIZATION ERROR IN A TRACKING RADAR SYSTEM IS PURE CROSSTALK SO THAT A SMALL TRUE TRACKING ERROR IN ONE TRACKING COORDINATE CAUSES THE ANTENNA TO MOVE IN THE OTHER COORDINATE 4HE ERROR IN THE SECOND COORDINATE THEN CAUSES THE ANTENNA TO MOVE FARTHER FROM THE SOURCE IN THE FIRST COORDINATE 7HEN THERE IS NO RETARDING EFFECT THE CROSS POLARIZED ENERGY CAUSES THE ANTENNA TO DRIVE OFF TARGET IN ONE OF THE QUADRANTS OF THE TWO AXIS ANGLE TRACKING COORDINATE SYSTEM DEPENDING UPON THE DIRECTION OF THE INITIAL ERROR THAT MOVED THE SOURCE OFF THE PRECISE ON AXIS POSITION ! SOLUTION USED WITH MISSILE RANGE INSTRUMENTATION RADAR WHERE TARGET ASPECT CHANGES CAN CAUSE A LINEARLY POLARIZED BEACON TO ROTATE TO A CROSS POLARIZED ASPECT IS TO PROVIDE A CIRCULAR POLARIZATION TRACKING CAPABILITY #OUPLING A LINEARLY POLARIZED SIGNAL TO A CIRCULARLY POLARIZED ANTENNA RESULTS IN A D" SIGNAL LOSS BUT IT IS INDEPEN DENT OF THE DIRECTION OF THE LINEAR POLARIZATION WHEN ROTATED ABOUT A LINE IN THE DIRECTION TOWARD THE RADAR 4ROPOSPHERE 0ROPAGATION 4HE TROPOSPHERE IS TYPICALLY A NONHOMOGENEOUS MEDIUM FOR PROPAGATION AND WILL CAUSE RANDOM BEAM BENDING &IGURE ILLUSTRATES THE APPROXIMATE RELATION OF RMS ANGLE ERROR TO VARIOUS ATMOSPHERIC CONDITIONS 4HE WORST CASE IS HEAVY CUMULUS CLOUDS WHICH CAUSE COLUMNS OF AIR SHADED FROM THE SUN BY THE CLOUDS THAT ARE COOLER THAN THE SURROUNDING AIR AND CONSEQUENTLY OF A DIFFERENT DIELECTRIC CONSTANT 4HE RESULT IS TYPICALLY A RANDOM BEAM BENDING AS THE RADIATED ENERGY PASSES THROUGH THESE COLUMNS &IGURE APPLIES ONLY FOR THE PORTION
&)'52% !NGLE FLUCTUATION VERSUS PATH LENGTH FOR DIFFERENT TROPOSPHERES FROM &INAL 2EPORT )NSTRUMENTATION 2ADAR !.&03 8. BY 2#! UNDER CONTRACT "U !ER ./AS C
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OF THE BEAM THAT IS WITHIN THE TROPOSPHERE /NCE THE BEAM GOES ABOVE THE TROPOSPHERE TYPICALLY ABOUT TO KM THERE IS NO FURTHER BEAM BENDING 4HE TROPOSPHERE ALSO AFFECTS TARGET RANGE MEASUREMENT BUT THE ERRORS ARE SMALL IN THE ORDER OF TO M MAXIMUM (OWEVER EVEN SMALL ERRORS OF THIS MAGNITUDE WILL CAUSE SIGNIFICANT ERRORS IN MULTILATERATION SYSTEMS THAT DETERMINE TARGET ANGLE BY CALCULATIONS USING PRECISE RANGE MEASUREMENTS FROM SEPARATE LOCATIONS
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-Ê"Ê ,,", 2ECEIVER 4HERMAL .OISE 4HE ANGLE ERROR CAUSED BY RECEIVER THERMAL NOISE IN A MONOPULSE TRACKING SYSTEM IS
ST
KM
Q" "T 3 . FR BN
WHERE KM IS THE ANGLE ERROR DETECTOR SLOPE 4HE VALUE OF KM IS DETERMINED BY THE STEEPNESS OF THE ANTENNA DIFFERENCE PATTERNS AND A VARIETY OF VALUES CAN BE OBTAINED DEPENDING ON THE TYPE OF FEED USED 4HE VALUES VARY FROM FOR THE ORIGINAL FOUR HORN SQUARE FEED TO A MAXIMUM OF FOR THE -)4 HORN FEED (OWEVER AS DESCRIBED IN THE DISCUSSION ON FEEDS THE HORN FEED GIVES A LOWER ANTENNA EFFICIENCY THAN AN OPTIMUM MULTIMODE MONOPULSE FEED WHICH CAN APPROACH AN EFFICIENCY OF ALTHOUGH ITS ANGLE SENSITIVITY IS LESS TYPICALLY HAVING A VALUE OF 4HEREFORE THERE IS A TRADEOFF BETWEEN SLOPE AND EFFICIENCY ! SLOPE FOR MONO PULSE RADARS IS DEPENDENT UPON FEED DESIGN AND IS TYPICALLY FOR A GOOD MODERN FOUR HORN MULTIMODE FEED DESIGN 7HEN THERE IS A SIGNIFICANT TRACKING LAG OR DELIBERATE BEAM OFFSET FROM THE TARGET THE ERROR RTO DUE TO RECEIVER NOISE FOR A GIVEN 3.2 IS GIVEN BY THE EQUATION
S T S T ,; K Q , Q " =
WHERE P, LAG ANGLE SAME UNITS AS P" , ANTENNA SUM PATTERN LOSS AT ANGLE P, ! SIMILAR RANGE TRACKING ERROR RRT RESULTS FROM RECEIVER NOISE 4HE EQUATION RELATING THE ERROR TO THE 3.2 AND SYSTEM PARAMETERS IS
S RT
T KR 3 . FR BN
FT RMS
WHERE S PULSE LENGTH IN FT KR R ANGE ERROR DETECTOR SENSITIVITY MAXIMUM VALUE OF FOR A RECEIVER WHERE " 3. SIGNAL TO NOISE RATIO AN SERVO BANDWIDTH /THER )NTERNAL 3OURCES OF %RROR 4HERE ARE MANY OTHER SOURCES OF INTERNAL ERRORS THAT ARE SMALL IN WELL DESIGNED TRACKING RADARS 4HESE INCLUDE CHANGES IN RELATIVE PHASE AND AMPLITUDE BETWEEN MONOPULSE RECEIVER CHANNELS AS A FUNCTION OF SIGNAL STRENGTH
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4!",% )NVENTORY OF 2ANGE %RROR #OMPONENTS
#OMPONENT
"IAS
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2ADAR DEPENDENT TRACKING ERRORS
:ERO RANGE SETTING 2ANGE DISCRIMINATOR SHIFT SERVO UNBALANCE 2ECEIVER DELAY
2ECEIVER THERMAL NOISE -ULTIPATH 3ERVO ELECTRICAL NOISE 3ERVO MECHANICAL NOISE 6ARIATION IN RECEIVER DELAY 2ANGE RESOLVER ERROR )NTERNAL JITTER $ATA GEAR NONLINEARITY AND BACKLASH $ATA TAKEOFF NONLINEARITY AND GRANULARITY 2ANGE OSCILLATOR INSTABILITY $YNAMIC LAG 'LINT 3CINTILLATION "EACON JITTER )RREGULARITIES IN TROPOSPHERIC REFRACTION )RREGULARITIES IN IONOSPHERIC REFRACTION
2ADAR DEPENDENT 2ANGE OSCILLATOR FREQUENCY TRANSLATION ERRORS $ATA TAKEOFF ZERO SETTING
4ARGET DEPENDENT TRACKING ERRORS
$YNAMIC LAG "EACON DELAY
0ROPAGATION ERROR
!VERAGE TROPOSPHERIC REFRACTION !VERAGE IONOSPHERIC REFRACTION
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2& FREQUENCY DETUNING AND TEMPERATURE !LSO PEDESTAL BENDING FROM SOLAR HEATING NONORTHOGONALITY OF PEDESTAL AXES GEARING BACKLASH BEARING WOBBLE GRANULARITY OF DATA READOUT AND MANY OTHER FACTORS CONTRIBUTE TO ERRORS 4ABLE LISTS THE MAGNITUDE OF THESE ERRORS FOR THE PRECISION INSTRUMENTATION RADAR !.&03 #ALIBRATION IS IMPORTANT TO MINIMIZE ERRORS 7HEN MAXIMUM PERFORMANCE IS REQUIRED TIMELY ACCURATE CALIBRATION MUST BE PERFORMED 4HE PROCEDURE MAY REQUIRE UP TO FOUR HOURS TO FULLY STABILIZE THE RADAR SYSTEM &OR INSTRUMENTATION RADAR WHERE THE TIME OF A TRACKING EVENT IS KNOWN FINAL CALIBRATION IS PERFORMED JUST PRECEDING THE EVENT TO MINIMIZE DRIFT ERRORS
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-Ê"Ê ,,", !NGLE -EASUREMENT %RRORS !N INVENTORY OF ANGLE MEASUREMENT ERRORS IS GIVEN IN 4ABLE 4HIS INCLUDES SEVERAL SOURCES OF ERROR THAT SHOULD BE CONSIDERED IN ADDITION TO THE RADAR RELATED SOURCES &IGURE IS AN EXAMPLE OF THE MEASURED TRACKING PERFORMANCE OF AN !.&03 RADAR TRACKING A IN METAL SPHERE THAT PROVIDES A POINT SOURCE TARGET TO ELIMINATE TARGET CAUSED ERRORS 4HE DATA ILLUSTRATES WHICH ERROR SOURCES DOMINATE AT DIFFERENT REGIONS OF THE RADAR RANGE AND THEIR CHARACTERISTICS VERSUS RANGE 4HE TARGET CAUSED ERRORS DISCUSSED IN 3ECTION INCLUDE THE USUAL TRACKING EVENTS WHERE THE TARGET EXTENT IS WITHIN THE D" BEAMWIDTH OF THE RADAR (OWEVER A LARGE TARGET SUCH AS AN AIRCRAFT FORMATION MAY EXTEND BEYOND THE LINEAR ANGLE ERROR REGION OF THE ANTENNA PATTERNS AND EVENTUALLY REACH THE POINT OF RESOLUTION OF ONE OF THE AIRCRAFT 4HE RESULTANT ANGLE TRACKING ERROR FOR LARGE TARGETS IS ILLUSTRATED BY THE EXAMPLE IN &IGURE )N &IGURE A THE TYPICAL GAUSSIAN LIKE GLINT ERROR DISTRIBUTION IS OBSERVED 7ITH THE WIDER SEPARATION OF THE AIRCRAFT THE TRACKING ERROR
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4!",% )NVENTORY OF !NGLE %RROR #OMPONENTS
#OMPONENT
"IAS
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2ADAR DEPENDENT TRACKING ERRORS DEVIATION OF ANTENNA FROM TARGET
"ORESIGHT AXIS COLLIMATION !XIS SHIFT WITH 2& AND )& TUNING 2ECEIVER PHASE SHIFT 4ARGET AMPLITUDE 4EMPERATURE 7IND FORCE !NTENNA UNBALANCE 3ERVO UNBALANCE ,EVELING OF PEDESTAL .ORTH ALIGNMENT 3TATIC FLEXURE OF PEDESTAL AND ANTENNA /RTHOGONALITY OF AXES SOLAR HEATING
2ECEIVER THERMAL NOISE -ULTIPATH ELEVATION ONLY 7IND GUSTS 3ERVO ELECTRICAL NOISE 3ERVO MECHANICAL NOISE
2ADAR DEPENDENT TRANSLATION ERRORS ERRORS IN CONVERTING ANTENNA POSITION TO ANGULAR COORDINATES
4ARGET DEPENDENT TRACKING ERRORS
0ROPAGATION ERRORS
$YNAMIC LAG
!VERAGE REFRACTION OF TROPOSPHERE !VERAGE REFRACTION OF IONOSPHERE 4ELESCOPE OR REFERENCE !PPARENT OR INSTRUMENTATION ERRORS INSTRUMENT STABILITY FOR OPTICAL REFERENCE &ILM EMULSION AND BASE STABILITY /PTICAL PARALLAX
$YNAMIC DEFLECTION OF PEDESTAL AND ANTENNA "EARING WOBBLE $ATA GEAR NONLINEARITY AND BACKLASH $ATA TAKEOFF NONLINEARITY AND GRANULARITY 'LINT $YNAMIC LAG VARIATION 3CINTILLATION "EACON MODULATION )RREGULARITIES IN TROPOSPHERIC REFRACTION )RREGULARITIES IN IONOSPHERIC REFRACTION 4ELESCOPE CAMERA OR REFERENCE INSTRUMENT VIBRATION &ILM TRANSPORT JITTER 2EADING ERROR 'RANULARITY ERROR 6ARIATION IN OPTICAL PARALLAX
&ROM $ + "ARTON IN h-ODERN 2ADAR v 2 3 "ERKOWITZ ED .EW 9ORK *OHN 7ILEY 3ONS CHAP P
DISTRIBUTION CHANGES SHAPE BECOMING SOMEWHAT RECTANGULAR WITH A SEPARATION OF AIRCRAFT AS IN &IGURE B !T THE WIDEST SEPARATION WHERE THE AIRCRAFT ARE ALMOST RESOLVED AS IN &IGURE C THE RADAR WILL TRACK ONE AIRCRAFT UNTIL IT FADES AND THE OTHER AIRCRAFT BLOSSOMS IN AMPLITUDE 4HEN THE RADAR TRACKING POINT WILL MOVE TO THE OTHER AIRCRAFT 4HE DWELL ON EACH TARGET WITH RANDOM SWITCHING BETWEEN THE TWO AIRCRAFT CAUSES THE DOUBLE HUMPED DISTRIBUTION OF ERROR 2ANGE -EASUREMENT %RRORS 4HE MAJOR SOURCES OF TARGET RANGE ERROR MEASUREMENT ERRORS ARE GIVEN IN 4ABLE 4YPICAL BIAS AND NOISE OF TARGET RANGE MEASUREMENT ERRORS IN A PRECISION RANGING RADAR ARE EQUAL TO A TOTAL RMS VALUE OF M RMS &URTHER DETAILS OF RANGE ERROR SOURCES AND THEIR MAGNITUDE ARE GIVE IN 3ECTION OF "ARTON ,IMITATIONS OF 0ERFORMANCE -ITCHELL ET AL DESCRIBE BASIC PERFORMANCE LIMITATIONS OF THE !.&01 HIGH PRECISION TRACKING RADAR MEASURED UNDER IDEAL
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&)'52% !ZIMUTH TRACKING NOISE VERSUS RANGE USING A IN METAL SPHERE TARGET SUPPORTED INSIDE A BALLOON TO MINIMIZE TARGET MOTION ESTIMATED AT IN RMS AN SERVO BANDWIDTH
CONDITIONS WITH A CAREFULLY DESIGNED BORESIGHTING FACILITY 4HIS TASK PROVIDED MEA SURED DATA VERIFYING THE ANTICIPATED PERFORMANCE OF THE HIGHEST PRECISION TRACKING RADAR AT THAT TIME 4!",% )NVENTORY OF 2ANGE %RROR #OMPONENTS
#OMPONENT
"IAS
.OISE
2ADAR DEPENDENT TRACKING ERRORS
:ERO RANGE SETTING 2ANGE DISCRIMINATOR SHIFT SERVO UNBALANCE 2ECEIVER DELAY
2ADAR DEPENDENT TRANSLATION ERRORS
2ANGE OSCILLATOR FREQUENCY $ATA TAKEOFF ZERO SETTING
4ARGET DEPENDENT TRACKING ERRORS
$YNAMIC LAG "EACON DELAY
0ROPAGATION ERROR
!VERAGE TROPOSPHERIC REFRACTION !VERAGE IONOSPHERIC REFRACTION
2ECEIVER THERMAL NOISE -ULTIPATH 3ERVO ELECTRICAL NOISE 3ERVO MECHANICAL NOISE 6ARIATION IN RECEIVER DELAY 2ANGE RESOLVER ERROR )NTERNAL JITTER $ATA GEAR NONLINEARITY AND BACKLASH $ATA TAKEOFF NONLINEARITY AND GRANULARITY 2ANGE OSCILLATOR INSTABILITY $YNAMIC LAG 'LINT 3CINTILLATION "EACON JITTER )RREGULARITIES IN TROPOSPHERIC REFRACTION )RREGULARITIES IN IONOSPHERIC REFRACTION
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&)'52% 0ROBABILITY DISTRIBUTION OF RADAR POINTING WHEN TRACKING TWO TARGETS WHERE THE LEFT TARGET IS APPROXIMATELY D" LARGER THAN THE RIGHT TARGET 4HREE DIFFERENT ANGULAR SEPARATIONS OF THE TARGETS ARE A ANTENNA BEAMWIDTH B ANTENNA BEAMWIDTH AND C ANTENNA BEAMWIDTH
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4HIS APPROACH CAN REDUCE ERRORS BY TWO EFFECTS &IRST AS OBSERVED IN &IGURE THE MAGNITUDE OF THE ELEVATION MULTIPATH ERROR REDUCES IN DIRECT PROPORTION TO THE BEAM WIDTH 4HE SECOND ADVANTAGE OF SHORTER WAVELENGTHS IS THAT EVEN A RELATIVELY SMOOTH SEA SUCH AS SEA STATE HAS WAVE HEIGHTS OF MANY WAVELENGTHS AND APPEARS ROUGH RESULTING IN A SMALLER REFLECTION COEFFICIENT 4HIS IS OBSERVED IN &IGURE TO GIVE SMALL MULTIPATH ERRORS 4HE MM WAVELENGTH MONOPULSE CAPABILITY MAY BE EFFEC TIVELY COMBINED WITH A LOWER MICROWAVE BAND AS DESCRIBED IN 3ECTION TO TAKE ADVANTAGE OF THE COMPLEMENTARY FEATURES OF BOTH BANDS 4ARGET !NGLE AND 2ANGE 3CINTILLATION 'LINT 2EDUCTION 4ARGET CAUSED ERRORS IN ANGLE AND RANGE TRACKING MAY BE REDUCED BY FILTERING SUCH AS REDUCING TRACKING SERVO BANDWIDTH (OWEVER SUFFICIENT SERVO BANDWIDTH MUST BE RETAINED TO FOLLOW TARGET TRAJECTORIES 5NFORTUNATELY TARGET ANGLE AND RANGE SCINTILLATION POWER DENSITY IS NORMALLY CONCENTRATED BELOW ABOUT TO (Z WHEN OPERATING AT MICROWAVE BANDS AND FALLS WITHIN NORMALLY REQUIRED BANDWIDTHS 4ARGET SCINTILLATION TOTAL NOISE POWER IS RELATIVELY INDEPENDENT OF FREQUENCY BUT THE SPECTRAL ENERGY TENDS TO SPREAD UPWARD IN FREQUENCY AS WAVELENGTH IS REDUCED RESULTING IN LOWER NOISE POWER DENSITY IN THE SERVO PASSBAND 4HEREFORE OPERATING AT A SHORTER WAVELENGTH WILL RESULT IN LOWER TARGET NOISE EFFECTS ON CLOSED LOOP TRACKING $IVERSITY TECHNIQUES WHICH CAN PROVIDE STATISTICALLY INDEPENDENT SAMPLES OF TARGET SCINTILLATION OFFER A MEANS FOR REDUCING TARGET SCINTILLATION EFFECTS 4HE MOST PRACTICAL TECHNIQUE IS FREQUENCY DIVERSITY USING PULSE TO PULSE RADAR FREQUENCY CHANGE WHICH WILL ALTER THE PHASE RELATIONS BETWEEN THE ECHOES FROM DOMINANT REFLECTING SURFACES OF THE TARGETn 4HE FREQUENCY CHANGE MUST BE SUFFICIENT TO CAUSE ENOUGH CHANGE IN RELATIVE PHASES OF THE REFLECTORS TO RESULT IN STATISTICALLY INDEPENDENT SAMPLES OF TARGET SCINTILLATION AT EACH NEW FREQUENCY !N APPROXIMATE RULE IS A MINIMUM FREQUENCY CHANGE OF S WHERE S IS THE RADAR RANGE DELAY TIME BETWEEN THE LEADING AND LAGGING EXTREMITIES OF THE TARGET 4HE REDUCTION IN RMS ANGLE AND RANGE TARGET SCINTILLATION MAY BE APPROXIMATED BY DIVIDING BY THE SQUARE ROOT OF N WHERE N IS THE NUMBER OF FREQUENCY STEPS PROVIDED 2EDUCTION OF )NTERNALLY #AUSED %RRORS !NGLE ERRORS CAUSED BY RECEIVER THER MAL NOISE AS WELL AS TARGET SCINTILLATION ARE MINIMIZED BY MAINTAINING THE TARGET AS CLOSELY AS POSSIBLE TO THE TRACKING AXES 4HE TECHNIQUE CALLED ON AXIS TRACKING DESCRIBED IN 3ECTION IS A MEANS OF PLACING A COMPUTER IN THE TRACKING LOOP TO MINIMIZE LAG AND PROVIDE OPTIMUM ANGLE ERROR FILTERING !CCURATE SYSTEM CALIBRATION ALSO GREATLY REDUCES INTERNAL SOURCES OF ERROR &REQUENT CALIBRATION CORRECTS FOR DRIFT IN COMPONENT GAIN AND PHASE AND PEDESTAL FLEXURE /THER INTERNAL SOURCES OF ERROR WITH KNOWN CHARACTERISTICS CAN BE AUTOMATICALLY CORRECTED TO MINIMIZE THEIR CONTAMINATION OF THE OUTPUT DATA
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£ä°£Ê /," 1 /" 2OLE OF THE 4RANSMITTER IN 2ADAR )F A RADAR SYSTEMS DESIGNER COULD ASK FOR ANYTHING HE OR SHE WANTED IN A RADAR TRANSMITTER THAT WISH MIGHT BE SOMETHING LIKE THE FOLLOWING 0ROVIDE THE NECESSARY TRANSMITTED ENERGY WITH THE NEEDED AVERAGE AND PEAK POWER AS WELL AS THE REQUIRED STABILITY AND LOW NOISE FOR GOOD DOPPLER PROCESS ING OPERATE WITH HIGH EFFICIENCY HAVE WIDE BANDWIDTH AND BE EASILY TUNABLE BE READILY MODULATED IN AMPLITUDE FREQUENCY OR PHASE AS NECESSARY HAVE HIGH RELIABILITY AND LONG LIFE REQUIRE MINIMUM MAINTENANCE HAVE NO DANGEROUS 8 RAY EMISSIONS REQUIRE NO PERSONNEL TO OPERATE BE OF AN AFFORDABLE PRICE AND BE OF REASONABLE SIZE AND WEIGHT FOR THE DESIRED APPLICATION /F COURSE NOT ALL OF THESE DESIRABLE ATTRIBUTES CAN BE ACHIEVED IN ANY GIVEN RADAR TRANS MITTER APPLICATION #OMPROMISES NEED TO BE MADE DEPENDING ON THE APPLICATION 4HE RADAR EQUATION FOR A SURVEILLANCE RADAR ONE THAT HAS TO COVER A FIXED VOLUME OF SPACE ON A REGULAR BASIS INDICATES THAT THE MAXIMUM RANGE OF SUCH A RADAR IS PRO PORTIONAL TO 0AV ! WHERE 0AV IS THE AVERAGE POWER OF THE TRANSMITTER AND ! IS THE AREA OF THE ANTENNA APERTURE ! FUNDAMENTAL MEASURE OF THE RADAR RANGE PERFORMANCE IS THEREFORE THE POWER APERTURE PRODUCT /NE CAN OBTAIN A LONG RANGE BY HAVING A LARGE ANTENNA A LARGE TRANSMITTER OR A COMBINATION OF BOTH )T IS NOT USUAL UNDER MOST CIRCUMSTANCES FOR A RADAR TO HAVE A HUGE COSTLY ANTENNA AND A SMALL INEXPENSIVE TRANSMITTER OR VICE VERSA 4HERE HAS TO BE A REASONABLE BALANCE BETWEEN THESE TWO MAJOR SUBSYSTEMS OF A RADAR )N A SURVEILLANCE RADAR STRAIGHTFORWARD CALCULUS WILL SHOW THAT UNDER SIMPLE ASSUMPTIONS THE MINIMUM TOTAL COST OF A RADAR OCCURS WHEN THE COST OF THE TRANSMITTER EQUALS THE COST OF THE ANTENNA BUT THIS IS TRUE ONLY WHEN THERE ARE NO CRITERIA OTHER THAN MINIMUM COST THAT HAVE TO BE SATISFIEDAND THERE ARE USUALLY OTHER CRITERIA THAT NEED TO BE CONSIDERED !S IS WELL KNOWN IN RADAR THE DOPPLER EFFECT IS EXTENSIVELY USED TO DETECT MOVING TARGETS IN THE PRESENCE OF LARGE CLUTTER ECHOES )T IS THE BASIS FOR SEVERAL OF THE CHAPTERS IN THIS (ANDBOOK 3OME TRANSMITTER TYPES HOWEVER ARE FAR BETTER THAN OTHERS WHEN THE RADAR HAS TO EMPLOY THE DOPPLER SHIFTED SIGNAL TO DETECT MOVING TARGETS IN THE MIDST OF HEAVY CLUTTER ECHOES %XAMINATION OF THE BASIC RADAR EQUATION FOR DETECTION OF TARGETS AT LONG RANGE INDI CATES THAT THE AVERAGE POWER IS FAR MORE IMPORTANT THAN THE PEAK POWER AS A MEASURE
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OF THE RADARS CAPABILITY ! VACUUM TUBE WITH A GIVEN AVERAGE POWER CAN USUALLY BE DESIGNED TO HANDLE THE HIGH VOLTAGES ASSOCIATED WITH A LARGE PEAK POWER WITHOUT BREAK DOWN ! SOLID STATE TRANSMITTER CANNOT )N THE PAST AVERAGE POWERS OF RADAR TRANSMIT TERS HAVE BEEN FROM A SMALL FRACTION OF A WATT TO THE ORDER OF A MEGAWATT 4YPES OF 2ADAR 4RANSMITTERS 4HE VERY FIRST hRADARS v SUCH AS THOSE USED BY (EINRICH (ERTZ THE FIRST RADAR SCIENTIST IN THE LATE S AND THE SHIPBOARD RADAR INVENTED BY #HRISTIAN (ULSMEYER THE FIRST RADAR ENGINEER IN THE EARLY S USED THE SPARK GAP AS THE TRANSMITTER )T WAS A VERY POOR TRANSMITTER BUT THAT IS NOT UNUSUAL IN THE EARLY DAYS OF A NEW AND DIFFERENT DEVELOPMENT 4HE $E&OREST GRID CONTROLLED VACUUM TUBE TRIODE WAS INVENTED SHORTLY THEREAFTER AND BY THE EARLY S IT HAD BEEN WELL DEVELOPED TO WHERE IT WAS SUCCESSFULLY AND EXTENSIVELY USED IN THOSE COUNTRIES THAT BUILT THE FIRST 6(& AND 5(& RADARS USED FOR AIR DEFENSE EARLY IN 7ORLD 7AR )) 3OME 5(& RADARS EFFECTIVELY USED THE GRID CONTROLLED VACUUM TUBE WELL INTO THE EARLY PART OF THE CURRENT CENTURY )T HAS BEEN A VERY COMPETITIVE POWER SOURCE FOR 5(& RADAR APPLI CATIONS 4HE DRAWBACK OF THE GRID CONTROLLED VACUUM TUBE IS THAT TRANSIT TIME EFFECTS LIMIT ITS APPLICATION AT MICROWAVE FREQUENCIES BUT VARIANTS OF GRID CONTROLLED VACUUM TUBES HAVE BEEN SUCCESSFULLY USED UP TO ABOUT -(Z 4HE BARRIER OF TRANSIT TIME EFFECTS WAS OVERCOME WITH THE INVENTION OF THE MICRO WAVE CAVITY MAGNETRON EARLY IN 7ORLD 7AR )) IN BY THE 5NITED +INGDOM 5+ 4HE INTRODUCTION OF THE MAGNETRON ALLOWED HIGH POWER RADAR TO BE SUCCESSFULLY DEVELOPED FOR USE AT THE HIGHER FREQUENCIES WHERE SMALLER SIZE ANTENNAS COULD BE USED )T IS OF INTEREST TO NOTE THAT THE *APANESE INVENTED THE MAGNETRON BEFORE THE 5+ DID AND 3OVIET 5NION ENGINEERS PUBLISHED A PAPER DESCRIBING THEIR MAGNETRON IN THE -ARCH ISSUE OF 0ROCEEDINGS OF THE )NSTITUTE OF 2ADIO %NGINEERS NOW THE 0ROCEEDINGS OF THE )%%% BUT THE WARTIME CHAOS IN THE MILITARY DEVELOPMENTS OF BOTH THE 3OVIET 5NION AND *APAN WAS SUCH THAT THESE INVENTIONS WERE NOT FULLY EXPLOITED BY THESE TWO COUNTRIES DURING 77)) 4HE INVENTION OF THE MAGNETRON WAS IMPORTANT BECAUSE IT ALLOWED RADAR TO BE DEVELOPED FOR USE AT MICROWAVE FREQUENCIES RATHER THAN BE LIMITED TO 6(& AND 5(& FREQUENCIES )T CAUGHT THE 'ERMAN ELECTRONIC COUNTER MEASURES EFFORT OFF GUARD BECAUSE THEY HAD NO IDEA THAT THE 5NITED +INGDOM AND THE 5NITED 3TATES COULD PRODUCE MICROWAVE RADAR 4HE SUCCESS OF THE MAGNETRON WAS A LARGE FACTOR IN THE EFFECTIVE APPLICATION OF MILITARY RADAR BY THE 5NITED 3TATES AND THE 5NITED +INGDOM DURING 7ORLD 7AR )) 4HE MAGNETRON IS AN EXAMPLE OF WHAT IS CALLED A CROSSED FIELD TUBE IN THAT IT EMPLOYS A MAGNETIC FIELD AND AN ELECTRIC FIELD THAT ARE ORTHOGONAL TO ONE ANOTHER 4HE MAGNETRON IS AN OSCILLATOR BUT THE GRID CONTROLLED VACUUM TUBE COULD BE OPERATED AS EITHER AN OSCIL LATOR OR AN AMPLIFIER 4HE OTHER ELECTRONIC TUBES MENTIONED IN THIS CHAPTER ARE USUALLY OPERATED AS AMPLIFIERS !MPLIFIERS AT MICROWAVE FREQUENCIES HAVE GENERALLY PRODUCED HIGHER POWERS THAN OSCILLATORS BUT PROBABLY MORE IMPORTANT THEY ALLOW THE USE OF STABLE MODULATED WAVEFORMS NEEDED FOR WAVEFORMS IN RADARS THAT DEPEND ON THE USE OF PULSE COMPRESSION AND FOR THE DOPPLER EFFECT TO DETECT MOVING TARGETS IN CLUTTER 4HE MICROWAVE KLYSTRON AMPLIFIER WAS INVENTED BEFORE THE MAGNETRON AND WAS DESCRIBED IN A PAPER IN THE -AY ISSUE OF THE *OURNAL OF !PPLIED 0HYSICS &OR THE MOST PART THE KLYSTRON AMPLIFIER WAS IGNORED DURING 77)) AND DIDNT ATTRACT
)N THE 5NITED 3TATES THE DEVICE THAT GENERATES THE 2& POWER IS CALLED A TUBE BUT IN THE 5NITED +INGDOM IT IS CALLED A VALVE ! BOOK ON MICROWAVE POWER SOURCES SUGGESTS THAT THESE DEVICES BE CALLED MICROWAVE VACUUM ELECTRONIC DEVICES -6%$ )N THIS CHAPTER HOWEVER THE NAME TUBE WILL BE RETAINED
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THE ATTENTION OF RADAR ENGINEERS UNTIL THE ANNOUNCEMENT IN A PAPER IN THE .OVEMBER 0ROCEEDINGS OF THE )%%% BY 3TANFORD 5NIVERSITY ENGINEERS OF THE DEVELOPMENT OF AN 3 BAND MULTICAVITY KLYSTRON CAPABLE OF -7 PEAK POWER AND K7 AVERAGE POWER FOR USE IN A LINEAR ACCELERATOR 4HIS WAS A GREAT ACCOMPLISHMENT IN ITS TIME 4HE HIGH POWER HIGH EFFICIENCY GOOD STABILITY AND WIDE BANDWIDTH AT HIGH POWER OF THE MICROWAVE KLYSTRON AMPLIFIER HAVE CAUSED SOME RADAR DESIGN ENGINEERS TO SAY THAT THE KLYSTRON SHOULD BE THE FIRST MICROWAVE POWER SOURCE TO CONSIDER WHEN DESIGNING A NEW HIGH PERFORMANCE RADAR 4HERE WAS AT ONE TIME A SINGLE CAVITY KLYSTRON OSCILLATOR CALLED THE REFLEX KLYSTRON THAT WAS OF LOW POWER AND MAINLY USED AS A RECEIVER LOCAL OSCILLATOR BUT IT HAS GENERALLY BEEN REPLACED BY SOLID STATE DEVICES AND IS NOT DISCUSSED FURTHER IN THIS CHAPTER 4HE KLYSTRON IS AN EXAMPLE OF A LINEAR BEAM TUBE BECAUSE THE DIRECTION OF THE DC ELECTRIC FIELD THAT ACCELERATES THE ELECTRON BEAM COINCIDES WITH THE AXIS OF THE MAGNETIC FIELD THAT FOCUSES AND CONFINES THE BEAM )T GENERATES A HIGHLY CONCENTRATED HIGH ENERGY LINEAR BEAM OF ELECTRONS THAT INTERACTS WITH THE MICROWAVE STRUCTURE TWO OR MORE MICRO WAVE CAVITIES TO ACHIEVE AMPLIFICATION !NOTHER EXAMPLE OF THE LINEAR BEAM TUBE IS THE TRAVELING WAVE TUBE 474 AMPLIFIER )T GENERALLY CAN DO ALMOST WHAT A KLYSTRON CAN DO BUT IT IS CAPABLE OF VERY WIDE BANDWIDTH AT LOW POWERS WHICH THE KLYSTRON IS NOT 4HE 474 USUALLY HAS SLIGHTLY LESS GAIN THAN A KLYSTRON AND LESS STABILITY )T SHOULD BE NOTED HOWEVER THAT AS THE POWER OF A 474 INCREASES ITS BANDWIDTH DECREASES AND AS THE POWER OF A KLYSTRON AMPLIFIER INCREASES ITS BANDWIDTH INCREASES 4HUS AT THE HIGH POWERS NEEDED FOR MANY RADAR APPLICATIONS THE BANDWIDTHS OF THESE TWO TYPES OF LINEAR BEAM TUBES ARE APPROXIMATELY COMPARABLE 4HERE ALSO HAVE BEEN HYBRIDS OF THE KLYSTRON AND THE 474 THAT HAVE BEEN OF INTEREST FOR RADAR APPLICATIONS AND WHICH HAVE INTERESTING CHARACTERISTICS 4HE CROSSED FIELD AMPLIFIER LIKE THE MAGNETRON IS A CROSSED FIELD TUBE THAT EMPLOYS A MAGNETIC FIELD ORTHOGONAL TO THE ELECTRIC FIELD )T IS CAPABLE OF WIDE BANDWIDTH AND GENERALLY IS OF SMALLER SIZE AND DOES NOT REQUIRE THE VERY HIGH VOLTAGES OF THE LINEAR BEAM TUBE !LTHOUGH IT HAS SOME ADVANTAGES NOT FOUND IN OTHER TUBES IT HAS LOWER GAIN THAN LINEAR BEAM AMPLIFIERS SO MULTIPLE STAGES OF AMPLIFICATION ARE REQUIRED AND ITS NOISE LEVEL IS HIGHER THAN THE LINEAR BEAM TUBE WHICH MAKES IT LESS CAPABLE FOR DETECTING MOVING TARGETS IN CLUTTER 4HE GYROTRON WHICH CAN BE EITHER AN OSCILLATOR OR AN AMPLIFIER IS AN 2& POWER SOURCE THAT CAN PRODUCE VERY HIGH POWER AT MILLIMETER WAVELENGTHS #ONVENTIONAL MICROWAVE POWER SOURCES UTILIZE RESONANT STRUCTURES IN WHICH THE PHASE VELOCITY OF THE ELECTROMAGNETIC FIELD PROPAGATING ALONG THE 2& STRUCTURE IS SLOWED SO AS TO BE CLOSE TO THE ELECTRON BEAM VELOCITY 4HUS THEY ARE KNOWN AS SLOW WAVE TUBES 4HE CHARACTERISTIC SIZE OF THE INCREMENTS OF THE 2& STRUCTURE OF SLOW WAVE TUBES IS TYPICALLY A FRACTION OF A WAVELENGTH 4HEY BECOME SMALLER AS THE FREQUENCY IS INCREASED WAVELENGTH IS DECREASED 3MALLER SIZE MEANS THAT A TUBE CANNOT DISSIPATE HEAT AS WELL AS A LARGER TUBE SO THAT THE POWER CAPABILITY OF MICROWAVE POWER TUBES DECREASES APPROXIMATELY INVERSELY AS THE SQUARE OF THE FREQUENCY 4HE GYROTRON ON THE OTHER HAND DOES NOT HAVE THIS TYPE OF FREQUENCY DEPENDENCE SINCE IT USES WHAT IS CALLED A FAST WAVE STRUCTURE 4HIS IS USUALLY A SMOOTH WAVEGUIDE OR A LARGE RESONATOR .O ATTEMPT IS MADE TO REDUCE THE PROPAGATION VELOCITY OF THE ELECTROMAGNETIC WAVE WITHIN THIS STRUCTURE 4HE ELECTRON BEAM IS NOT CLOSE TO THE 2& STRUCTURE SO IT IS NOT AS LIMITED IN SIZE AS ARE THE STRUCTURES OF
)N ELECTRICAL ENGINEERING 2& STANDS FOR RADIO FREQUENCY BUT IN RADAR IT IS OFTEN USED TO MEAN THE RADAR FREQUENCY
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SLOW WAVE TUBES 4HE LARGER SIZE OF THE FAST WAVE TUBE MEANS THAT IT CAN HANDLE LARGER POWER AT THE HIGHER FREQUENCIES 4HE GYROTRON HAS MAINLY BEEN OF SIGNIFICANCE FOR HIGH POWER APPLICATIONS AT MILLIMETER WAVE FREQUENCIES 4HE SOLID STATE TRANSISTOR AMPLIFIER HAS BEEN OF INTEREST FOR RADAR APPLICATIONS 3UCH INTEREST IN SOLID STATE HAS ALSO BEEN DUE IN PART TO ITS COMPLETELY REPLACING VACUUM TUBES IN RECEIVER AND COMPUTER APPLICATIONS 4HE SOLID STATE TRANSMITTER IS DISCUSSED IN #HAPTER AND A BRIEF COMPARISON OF IT WITH THE VACUUM TUBE TRANSMITTER IS GIVEN AT THE END OF THIS CHAPTER 4HE CHIEF ADVANTAGES OF A SOLID STATE RADAR TRANSMITTER ARE THAT IT CAN OPERATE WITH WIDE BANDWIDTHS IT HAS THE POTENTIAL FOR LONG LIFE AND IT IS FAVORED BY SOME BUYERS OF RADAR )T CANNOT HOWEVER EMPLOY HIGH PEAK POWER WAVEFORMS 4HE LIMITATION ON PEAK POWER IN A SOLID STATE TRANSMITTER RESULTS IN COMPROMISES THAT HAVE TO BE MADE IN THE DESIGN OF THE OVERALL RADAR SYSTEM /SCILLATOR 6ERSUS !MPLIFIER 4HE POWER AMPLIFIER IS OFTEN PREFERRED OVER THE POWER OSCILLATOR AS THE TRANSMITTER POWER SOURCE IN HIGH POWER HIGH PERFORMANCE RADAR SYSTEMS )N AN AMPLIFIER THE SIGNAL TO BE TRANSMITTED IS PRECISELY GENERATED AT A LOW POWER LEVEL AND IS THEN AMPLIFIED TO ACHIEVE THE REQUIRED POWER TO BE RADI ATED FROM THE ANTENNA !MPLIFIERS HAVE THE ADVANTAGE OF BEING ABLE TO PROVIDE STABLE WAVEFORMS CODED OR FREQUENCY MODULATED PULSE COMPRESSION WAVEFORMS FREQUENCY AGILITY AS WELL AS COMBINING AND ARRAYING 4HE MAGNETRON IS AN OSCILLATOR THAT HAS LESS FLEXIBILITY AND IS USUALLY NOISIER THAN A LINEAR BEAM AMPLIFIER %ACH TIME A PULSE IS TRANSMITTED ITS PHASE IS DIFFERENT FROM THE PHASE OF PREVIOUS PULSES 4HAT IS ITS PHASE IS RANDOM FROM PULSE TO PULSE 4O DETECT THE DOPPLER FREQUENCY SHIFT FOR -4) PROCESSING THE PHASE CANNOT CHANGE IN A RANDOM MANNER AT THE RECEIVER FROM PULSE TO PULSE 4HIS LIMITATION IS OVERCOME BY TAKING A SAMPLE OF THE RANDOM PHASE OF EACH TRANSMITTED PULSE AND USING IT TO RESET THE PHASE OF THE LOCAL OSCILLATOR IN THE RECEIVER TO MATCH THE PHASE OF THE TRANSMITTED SIGNAL 4HIS IS SOMETIMES CALLED COHERENT ON RECEIVE 'ENERALLY THE -4) IMPROVE MENT FACTOR THAT CAN BE OBTAINED WITH A MAGNETRON IS NOT AS GOOD AS CAN BE OBTAINED WITH A LINEAR BEAM AMPLIFIER )N THE PAST THERE MIGHT HAVE BEEN DEBATE AS TO WHETHER TO USE AN OSCILLATOR OR AN AMPLIFIER FOR A HIGH PERFORMANCE RADAR TRANSMITTER 4HERE IS USUALLY NO QUESTION THAT THE AMPLIFIER IS USUALLY THE PREFERRED CHOICE EXCEPT IN SITUATIONS WHERE THE LOW COST OF A MAGNETRON TRANSMITTER IS MORE IMPORTANT THAN THE LOWER -4) IMPROVEMENT FACTOR IT PROVIDES COMPARED TO A LINEAR BEAM TRANSMITTER 4HE MAGNETRON OSCILLATOR HOWEVER HAS BEEN USED IN SOME SHORT OR MEDIUM RANGE RADARS AND IN THE WIDELY POPULAR CIVIL MARINE RADAR #HAPTER WHICH REQUIRES ONLY A SMALL POWER TRANSMITTER AND HAS NO NEED FOR -4) CAPABILITY
£ä°ÓÊ , Ê * ,- Ó 4HE KLYSTRON 474 AND HYBRIDS OF THE TWO HAVE BEEN IMPORTANT SOURCES OF 2& POWER FOR MANY SUCCESSFUL RADAR SYSTEMS 4HE ELECTRONS EMITTED FROM THE CATHODE ARE FORMED INTO A LONG CYLINDRICAL BEAM THAT RECEIVES THE FULL POTENTIAL ENERGY OF THE ELECTRIC FIELD BEFORE THE BEAM ENTERS THE MICROWAVE INTERACTION REGION 4HE ELECTRON BEAM GENERATED BY AN hELECTRON GUN v ESSENTIALLY FLOWS IN A STRAIGHT LINE IN LINEAR BEAM TUBES TO INTERACT WITH A MICROWAVE CIRCUIT TO PRODUCE AMPLIFICATION OF AN INPUT SIGNAL 4HE MAJOR DIFFERENCE AMONG THE SEVERAL TYPES OF LINEAR BEAM TUBES IS THE TYPE OF MICROWAVE CIRCUIT EMPLOYED
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AND THE NATURE OF THE INTERACTION THAT PRODUCES AMPLIFICATION 4RANSIT TIME EFFECTS WHICH LIMIT THE HIGH FREQUENCY PERFORMANCE OF GRID CONTROLLED TUBES ARE TAKEN ADVANTAGE OF IN LINEAR BEAM TUBES TO VELOCITY MODULATE THE UNIFORM ELECTRON BEAM TO CREATE BUNCHES OF ELECTRONS FROM WHICH 2& ENERGY CAN BE EXTRACTED AT THE OUTPUT OF THE TUBE ,INEAR BEAM TUBES AS AMPLIFIERS CAN PRODUCE HIGH POWER WITH GOOD EFFICIENCY AND HIGH GAIN AND WITH WIDE BANDWIDTH 4HEY HAVE BEEN CAPABLE OF PRODUCING AVERAGE POWERS OF A MEGAWATT AS WELL AS AVERAGE POWERS OF MANY KILOWATTS IN A SIZE SUITABLE FOR USE IN A MILITARY FIGHTERATTACK AIRCRAFT +LYSTRON 4HE KLYSTRON AMPLIFIER HAS BEEN AN IMPORTANT 2& POWER SOURCE FOR MANY RADAR APPLICATIONS !S MENTIONED IT IS CAPABLE OF HIGH AVERAGE AND HIGH PEAK POWER HIGH GAIN GOOD EFFICIENCY STABLE OPERATION LOW INTERPULSE NOISE LARGE BAND WIDTH AT HIGH POWER AND BEING AN AMPLIFIER IT CAN WORK WELL WITH THE FREQUENCY AND PHASE MODULATED WAVEFORMS NEEDED FOR PULSE COMPRESSION +LYSTRONS HAVE OPER ATED AT FREQUENCIES FROM 5(& TO MILLIMETER WAVELENGTHS AND HAVE FOUND USE IN SUCH DIVERSE APPLICATIONS AS AIRPORT SURVEILLANCE RADARS WHERE THE AVERAGE POWERS MIGHT BE MORE THAN ONE KILOWATT IN AIRBORNE MILITARY AIRCRAFT WHERE THE AVERAGE POWER MIGHT BE OF THE ORDER OF K7 OR MORE AND IN LONG RANGE DETECTION OF INTERCONTINENTAL BALLISTIC MISSILES WHERE THE AVERAGE POWER PER TUBE CAN BE GREATER THAN K7 &IGURE DEPICTS THE PRINCIPAL PARTS OF A THREE CAVITY KLYSTRON !T THE LEFT IS THE HEATER THAT HEATS THE CATHODE AND THE CATHODE THAT EMITS A STREAM OF ELECTRONS THAT ARE COLLIMATED INTO A NARROW CYLINDRICAL BEAM OF HIGH ELECTRON DENSITY 4HE ELECTRON GUN THAT GENERATES THE BEAM CONSISTS OF THE CATHODE THE MODULATING ANODE ALSO CALLED THE BEAM CONTROL GRID AND THE ANODE 4HE MODULATING ANODE PROVIDES THE MEANS TO PULSE THE ELECTRON BEAM ON AND OFF 4HE 2& CAVITIES ARE THE MICROWAVE EQUIVALENT OF A RESONANT CIRCUIT %LECTRONS ARE NOT INTENTIONALLY COLLECTED AT THE ANODE AS THEY ARE IN GRID CONTROLLED TUBES AND CROSSED FIELD TUBES BUT IN THE COLLECTOR SHOWN AT THE RIGHT HAND SIDE OF THE ILLUSTRATION AFTER THE ELECTRON BEAM HAS GIVEN UP ITS 2& ENERGY AT THE OUTPUT CAVITY ! LOW POWER SIGNAL IS APPLIED TO THE INPUT OF THE FIRST CAVITY AND APPEARS AT THE INTERACTION GAP 4HOSE ELECTRONS IN THE BEAM THAT ARRIVE AT THE FIRST INTERACTION GAP WHEN THE INPUT SIGNAL VOLTAGE IS AT A MAXIMUM THE POSITIVE PEAK OF THE SINE WAVE ARE SPEEDED UP COMPARED TO THOSE ELECTRONS THAT ARRIVE AT THE GAP WHEN THE INPUT SIGNAL VOLTAGE IS A MINIMUM THE NEGATIVE TROUGH OF THE SINE WAVE
&)'52% 2EPRESENTATION OF THE PRINCIPAL PARTS OF A THREE CAVITY KLYSTRON AMPLIFIER
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)N THE FIRST DRIFT SPACE THOSE ELECTRONS SPEEDED UP DURING THE PEAK OF ONE CYCLE CATCH UP TO THOSE THAT WERE SLOWED DOWN DURING THE MINIMUM OF THE PREVIOUS 2& CYCLE 4HE RESULT IS THAT THE ELECTRONS BECOME hBUNCHEDv PERIODICALLY 4HIS BUNCHING CAN BE THOUGHT OF AS PRODUCING A MODULATION OF THE DENSITY OF ELECTRONS 4HE BUNCHES PASS THROUGH THE INTERACTION SPACE OF THE SECOND CAVITY WHICH REINFORCES THE DENSITY MODULATION TO ENHANCE THE BUNCHING 4HIS PROCESS OF IMPRESSING A TIME VARIATION IN VELOCITY THAT RESULTS IN BUNCHING OF THE ELECTRONS OF AN INITIALLY UNIFORM ELECTRON BEAM IS CALLED VELOCITY MODULATION 4HREE OR MORE 2& CAVITIES MIGHT BE USED 4HE INTERACTION GAP OF THE OUTPUT CAVITY IS PLACED AT THE POINT OF MAXIMUM BUNCHING SO THAT THE 2& POWER CAN BE EXTRACTED FROM THE DENSITY MODULATED ELECTRON BEAM BY A COUPLING LOOP IN A LOWER POWER TUBE OR BY A WAVEGUIDE NOT SHOWN IN A HIGH POWER TUBE )N ESSENCE THE DC ENERGY OF THE ELECTRON BEAM AT THE FIRST CAVITY IS CONVERTED TO 2& ENERGY AT THE OUTPUT CAVITY BY THE VELOCITY MODULATION PROCESS 4HE LARGER THE NUMBER OF CAVITIES THE GREATER CAN BE THE GAIN OF THE KLYSTRON 4HE GAIN OF A FOUR CAV ITY KLYSTRON CAN BE MORE THAN D" DEPENDING ON THE BANDWIDTH !FTER THE BUNCHED ELECTRONS DELIVER THEIR 2& POWER TO THE OUTPUT THE SPENT ELECTRONS ARE REMOVED BY THE COLLECTOR ELECTRODE !N AXIAL MAGNETIC FIELD IS EMPLOYED TO COUNTERACT THE MUTUAL REPULSION OF THE ELECTRONS THAT FORM THE ELECTRON BEAM 4HE MAGNETIC FIELD CONFINES THE ELECTRONS TO A RELATIVELY LONG THIN BEAM AND PREVENTS THEM FROM DISPERSING )T CAN BE GENER ATED BY A LONG SOLENOID THAT HAS IRON SHIELDING AROUND ITS OUTSIDE DIAMETER OR BY A LIGHTER WEIGHT PERIODIC PERMANENT MAGNETIC 00- SYSTEM THAT CONSISTS OF A SERIES OF MAGNETIC LENSES ! MULTICAVITY KLYSTRON CAN HAVE ITS BANDWIDTH INCREASED BY STAGGER TUNING THE CAVITIES SIMILAR TO THE MANNER IN WHICH STAGGER TUNING IS DONE IN AN )& AMPLIFIER OF A SUPERHETERODYNE RECEIVER TO OBTAIN BROADER BANDWIDTH )T IS MORE COMPLICATED HOWEVER TO DO THIS IN THE KLYSTRON SINCE THE VELOCITY MODULATION THAT APPEARS AT EACH INTERACTION GAP CONTRIBUTES A COMPONENT TO THE EXCITING CURRENT AT THE SUCCEEDING GAPS SOMETHING THAT DOES NOT OCCUR IN AN )& AMPLIFIER 4HE EARLY 6! FOUR CAVITY 3 BAND KLYSTRON HAD A -(Z BANDWIDTH AND A GAIN OF D" WHEN ITS FOUR CAVITIES WERE SYNCHRONOUSLY TUNED BUT WHEN STAGGER TUNED ITS BANDWIDTH WAS -(Z AND A GAIN OF D" 4HEORY SHOWS THAT THE BANDWIDTH OF A KLYSTRON CAN BE SIGNIFICANTLY INCREASED BY INCREASING ITS CURRENT AND THUS ITS POWER ! -7 PEAK POWER KLYSTRON FOR EXAMPLE CAN HAVE AN BANDWIDTH AS COMPARED TO A K7 TUBE WHICH MIGHT HAVE A BANDWIDTH AND A K7 TUBE HAVING ONLY A BANDWIDTH (IGH POWER MULTICAV ITY KLYSTRONS CAN BE DESIGNED WITH BANDWIDTHS AS LARGE AS TO 4HE KLYSTRON IS SOMETIMES THOUGHT OF AS HAVING A NARROW BANDWIDTH AND THE TRAVELING WAVE TUBE IS THOUGHT OF AS HAVING WIDE BANDWIDTH BUT AT THE HIGH POWER LEVELS NEEDED FOR LONG RANGE RADARS THEIR BANDWIDTHS ARE COMPARABLE )T IS SOMETIMES UNFORTUNATE THAT THIS FACT IS NOT ALWAYS UNDERSTOOD 4HE KLYSTRON AS AN EXAMPLE OF A LINEAR BEAM TUBE IS CAPABLE OF HIGH POWER BECAUSE THE GENERATION OF THE ELECTRON BEAM ITS INTERACTION WITH THE ELECTROMAGNETIC FIELD AND THE COLLECTION OF THE SPENT ELECTRONS ARE PERFORMED IN SEPARATE PARTS OF THE TUBE WHERE THE GENERATED HEAT CAN BE DISSIPATED EFFECTIVELY 4HE KLYSTRON AND OTHER LINEAR BEAM TUBES CAN HAVE LONG LIFE 'ILMOUR REPORTS THAT THE MEAN TIME BETWEEN FAILURES -4"& OF DIFFERENT APPLICATIONS OF KLYS TRONS IN RADAR SYSTEMS VARIED FROM HOURS TO HOURS WITH AN AVERAGE OF HOURS FOR ALL APPLICATIONS 4HERE ARE HOURS IN A YEAR 4HE 6!
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HIGH POWER KLYSTRON TUBE USED IN THE ORIGINAL "ALLISTIC -ISSILE %ARLY 7ARNING 3YSTEM HAD A DEMONSTRATED LIFE IN EXCESS OF HOURS 3YMONS REPORTS THAT ONE OF THE "-%73 TUBES THAT HE DESIGNED WAS STILL OPERATING AFTER HOURS WHEN THE RADAR IN 'REENLAND WAS REPLACED BY THE SOLID STATE 0AVE 0AWS RADAR 4HE 6! % WAS ALSO A HIGH POWER 5(& KLYSTRON THAT HAD A -7 PEAK POWER -(Z D" BANDWIDTH D" GAIN AND AN AVERAGE POWER OF K7 AT A DUTY CYCLE OF AND A §S PULSE WIDTH 4HE 6! % ORIGINALLY DEVELOPED BY 6ARIAN !SSOCIATES )NC IS A CAVITY 3 BAND PULSE KLYSTRON THAT OPERATES FROM TO '(Z PRODUCES A PEAK POWER OF FROM TO -7 AN AVERAGE POWER UP TO K7 HAS A GAIN OF ABOUT D" AN EFFICIENCY BETWEEN AND AND A D" BANDWIDTH OF -(Z )T HAS DEMONSTRATED A MEAN TIME BETWEEN FAILURES OF HOURS )T WAS USED IN THE !32 AIRPORT SURVEILLANCE RADAR AND IN THE 732 $ .EXRAD DOPPLER WEATHER RADAR WHERE ITS OPERATING BAND IS FROM TO '(Z AS WELL AS IN OTHER RADARS 6ERY HIGH POWER KLYSTRONS ARE EMPLOYED IN LINEAR ACCELERATORS SUCH AS FOUND AT THE 3TANFORD ,INEAR !CCELERATOR #ENTER +LYSTRONS FOR THIS APPLICATION FOR EXAMPLE MIGHT HAVE -7 PEAK POWER WITH EFFICIENCY USING SOLENOID MAGNETS OR n -7 PEAK POWER WITH EFFICIENCY USING PERIODIC PERMANENT MAGNETS )MPROVEMENTS TO THE KLYSTRON AS A RADAR POWER SOURCE ARE DISCUSSED LATER IN THE SUBSECTION ON HYBRIDS OF WHICH THE CLUSTERED CAVITY KLYSTRON IS A GOOD EXAMPLE OF WHAT CAN BE PROVIDED IN THE WAY OF HIGH POWER AND WIDE BANDWIDTH -ULTIPLE "EAM +LYSTRON -"+ 4HE KLYSTRON AMPLIFIER IS AN IMPORTANT TUBE FOR HIGH POWER HIGH PERFORMANCE RADAR APPLICATIONS (OWEVER IT REQUIRES A LARGE VOLTAGE WHEN HIGH POWER IS NEEDED (IGH VOLTAGE RESULTS IN GREATER SIZE AND THE NEED FOR SHIELDING FROM THE 8 RAYS THAT ARE GENERATED )N A KLYSTRON THE POWER AVAILABLE FOR CONVERSION OF THE DC POWER OF THE ELECTRON BEAM TO 2& POWER OF AN ELECTROMAGNETIC WAVE IS GIVEN BY THE PRODUCT OF THE BEAM CURRENT AND THE BEAM VOLTAGE !LTHOUGH KLYSTRONS HAVE BEEN OPERATED AT VERY HIGH VOLTAGES IT IS USUALLY PREFERRED TO OPERATE IT AT A LOWER VOLTAGE IF POSSIBLE BECAUSE LOWER VOLTAGES GENERALLY MAKE THE POWER SUP PLIES SIMPLER LIGHTER AND MORE RELIABLE ! REDUCTION OF BEAM VOLTAGE IN A CONVENTIONAL KLYSTRON MEANS AN INCREASE OF THE BEAM CURRENT IN ORDER TO MAINTAIN THE SAME POWER !N INCREASE IN BEAM CURRENT HOWEVER RESULTS IN AN INCREASE IN THE CURRENT DENSITY WHERE SPACE CHARGE EFFECTS MAY NOT BE NEGLIGIBLE AND THE REPULSIVE FORCES THAT OCCUR AMONG THE ELECTRONS ARE INCREASED AND CAN CAUSE THE ELECTRON DENSITY BUNCHES TO LOSE COHERENCE 4HE RESULT IS A DECREASE IN EFFICIENCY (IGHER CURRENT DENSITIES ALSO REQUIRE STRONGER MAGNETS TO KEEP THE ELECTRON BEAM CONFINED LEADING TO LARGER VOLUME AND WEIGHT 4HUS SIMPLY LOWERING THE BEAM VOLTAGE AND INCREASING THE CURRENT DENSITY DOES NOT USUALLY PROVIDE A NET ADVANTAGE 4HE LIMITATIONS OF LOWER BEAM VOLTAGE HOWEVER CAN BE OVERCOME BY SEPARATING THE SINGLE ELECTRON BEAM INTO A NUMBER OF SMALLER BEAMS CALLED BEAMLETS SO THAT EACH OF THE BEAMLETS HAS A LOW ENOUGH CURRENT DENSITY TO AVOID THE UNDESIRABLE REPULSIVE EFFECTS OF A HIGH CURRENT DENSITY BEAM !CCORDING TO .USINOVICH ET AL EACH BEAMLET IS TRANSPORTED DOWN ITS OWN INDIVIDUAL DRIFT CHANNEL A METALLIC WALLED TUBE PARALLEL TO BUT ISOLATED FROM THE OTHER BEAMLETS 4HEY ARE ALLOWED TO INTERACT ONLY OVER THE SMALL AXIAL EXTENT OF THE CAVITY GAP !FTER PASSING BY THE CAVITY GAP THE BEAMLETS REENTER THEIR INDIVIDUAL DRIFT CHANNELS AND PROPAGATE IN ISOLATION FROM ONE ANOTHER 3UCH KLYSTRONS ARE CALLED MULTIPLE BEAM KLYSTRONS OR -"+ )T HAS BEEN SAID THAT THE NUMBER OF BEAMLETS IN AN -"+ MIGHT BE FROM TO
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4HE CHIEF MOTIVATION FOR THE MULTIPLE BEAM KLYSTRON IS THE EFFICIENT GENERATION OF HIGH 2& POWER AT A LOWER VOLTAGE THAN IN A CONVENTIONAL KLYSTRON "ECAUSE OF ITS LOWER VOLTAGE TWO OR THREE TIMES LOWER AN -"+ CAN BE MORE COMPACT HAVE A LOWER MAGNET WEIGHT UP TO TEN TIMES LESS BE OF LOWER WEIGHT AND VOLUME GENERATE LESS 8 RAYS HAVE HIGH ELECTRONIC EFFICIENCY UP TO PERCENT AND HAVE THE POTENTIAL FOR A HIGHER INSTAN TANEOUS BANDWIDTH THAN DOES A CONVENTIONAL KLYSTRON 4HE LOWER VOLTAGES AT WHICH THEY OPERATE RESULT IN POWER SUPPLIES THAT CAN BE SIMPLER LIGHTER CHEAPER AND MORE RELIABLE 4HE -"+ CAN HAVE A HIGH OUTPUT POWER TO WEIGHT RATIO THAT MIGHT BE TWO TO THREE TIMES GREATER THAN THAT OF AN EQUIVALENT SINGLE BEAM KLYSTRON 4HEY CAN ALSO HAVE REDUCED NOISE AND LESS PHASE SENSITIVITY TO DEVIATIONS IN VOLTAGE WHICH AIDS IN THE DETECTION OF LOW CROSS SECTION MOVING TARGETS IN CLUTTER #OMPARED TO A CROSSED FIELD AMPLIFIER THEY HAVE A LARGER DYNAMIC RANGE #OMPARED TO A 474 THEY ARE CAPABLE OF HIGHER PEAK AND AVERAGE POWERS AND THEY ARE LESS SENSITIVE TO VIBRATIONS 4HE 2USSIAN COMPANY KNOWN AS &EDERAL 3TATE 5NITARY %NTERPRISE 20# )STOK USUALLY SHORTENED TO )STOK HAS BEEN PRODUCTIVE IN THE DEVELOPMENT OF -"+S FOR RADAR !T 8 BAND THEY REPORT AN -"+ WITH BEAMLETS PRODUCING K7 PEAK POWER K7 AVERAGE POWER BANDWIDTH AN ANODE VOLTAGE OF K6 WITH A MAG NET WEIGHING KG !T 3 BAND ONE OF THEIR TUBES WITH BEAMS HAD A PEAK POWER OF K7 K7 AVERAGE POWER OPERATED WITH K6 ANODE VOLTAGE HAD A BANDWIDTH AND A WEIGHT WITHOUT MAGNET OF KG !N APPARENT EXTENSION OF THE MULTIPLE BEAM CONCEPT IS TO EMPLOY A SHEET ELECTRON BEAM WHICH IS AS THIN AND AS WIDE AND HAS AS MUCH CURRENT AS CAN BE ACHIEVED CON SISTENT WITH OTHER CONSTRAINTS )T HAS BEEN CONSIDERED FOR VERY HIGH POWER KLYSTRONS -7 PEAK POWER AND PERIODIC PERMANENT MAGNETIC OR 00- FOCUSING DESIGNED FOR A VERY LARGE LINEAR ACCELERATOR )T IS CLAIMED THAT THE BEAM CURRENT DENSITY AND THE FOCUSING MAGNETIC FIELD CAN BE REDUCED BE MADE WITH FEWER PARTS MIGHT BE MORE RELI ABLE AND CAN HAVE LOWER ACQUISITION AND OPERATING COSTS /NE POSSIBLE DISADVANTAGE IS THAT SHEET BEAM KLYSTRONS MIGHT NOT BE WIDEBAND 4HE PRINCIPLE OF THE MULTIPLE BEAM LINEAR BEAM TUBE HAS ALSO BEEN CONSIDERED FOR THE TRAVELING WAVE TUBE BUT IT IS NOT OBVIOUS WHETHER IT HAS ANY SIGNIFICANT ADVANTAGES OVER THE -"+ 4RAVELING 7AVE 4UBE 474 4HE 474 LINEAR BEAM TUBE IS SIMILAR TO THE KLYSTRON IN THAT THE CATHODE 2& CIRCUIT AND COLLECTOR ARE ALL SEPARATE FROM ONE ANOTHER 4HERE IS HOWEVER CONTINUOUS INTERACTION OF THE ELECTRON BEAM AND THE 2& FIELD OVER THE ENTIRE LENGTH OF THE MICROWAVE PROPAGATING STRUCTURE OF THE 474 AS COMPARED TO THE KLYSTRON WHERE THE INTERACTION OCCURS ONLY AT THE GAPS OF A RELATIVELY FEW RESO NANT CAVITIES 4HE 474 WAS ORIGINALLY CONCEIVED WITH A HELIX AS THE SLOW WAVE 2& STRUCTURE AS IN THE ILLUSTRATION SHOWN IN &IGURE 4HE ELECTRON BEAM IS SIMILAR TO
&)'52% 2EPRESENTATION OF THE PRINCIPLE PARTS OF A TRAVELING WAVE TUBE SHOWING A HELIX SLOW WAVE CIRCUIT SHOWN FOR SIMPLICITY
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THAT OF THE KLYSTRON AND THEY BOTH USE THE PROCESS OF VELOCITY MODULATION TO CAUSE THE ELECTRON BEAM TO BE PERIODICALLY BUNCHED DENSITY MODULATION 4HE ELECTRON BEAM PASSES THROUGH THE 2& INTERACTION CIRCUIT )N THE EXAMPLE SHOWN IN &IGURE WHERE A HELIX IS SHOWN AS THE SLOW WAVE STRUCTURE THE 2& SIGNAL IS SLOWED DOWN BY THE HELIX SO THAT ITS FORWARD VELOCITY IS VERY NEARLY EQUAL TO THAT OF THE VELOCITY OF THE ELECTRON BEAM 4HIS NEAR MATCH OF VELOCITIES IS WHAT CAUSES THE CUMULATIVE INTERAC TION THAT TRANSFERS DC ENERGY FROM THE ELECTRON BEAM TO AMPLIFY THE ELECTROMAGNETIC WAVE PROPAGATING ON THE HELIX !FTER DELIVERING ITS ENERGY TO THE 2& FIELD THE SPENT ELECTRONS ARE REMOVED BY THE COLLECTOR USUALLY A MULTISTAGE DEPRESSED COLLECTOR !N AXIAL MAGNETIC FIELD KEEPS THE ELECTRON BEAM FROM DISPERSING AS IT TRAVELS DOWN THE TUBE JUST AS IN THE KLYSTRON 4HE HELIX 474 IS CAPABLE OF BANDWIDTH IN EXCESS OF AN OCTAVE TO WHICH IS MUCH HIGHER THAN OTHER RADAR TUBES 4HE 474 IS OFTEN THOUGHT OF AS A VERY BROADBAND TUBE BUT THE BROAD BANDWIDTH OF A HELIX 474 IS NOT OF GREAT SIGNIFICANCE IN RADAR APPLICATIONS SINCE THE HELIX 474 IS LIMITED IN ITS PEAK POWER TO A FEW K7 4HIS MEANS THAT THE HELIX 474 IS BEST USED IN #7 OR HIGH DUTY CYCLE RADAR APPLICATIONS IF AT ALL !LSO SUCH BROAD BANDWIDTHS ARE SELDOM AVAILABLE FOR RADAR APPLICATIONS BECAUSE OF REGULATORY RESTRICTIONS IN THE USE OF THE ELECTROMAGNETIC SPECTRUM 4O ACHIEVE HIGH POWER IN A 474 OTHER TYPES OF SLOW WAVE STRUCTURES HAVE TO BE EMPLOYED AND THESE USUALLY PROVIDE LESS BANDWIDTH THAN THE HELIX 3UCH STRUCTURES ARE THE COUPLED CAVITY OF WHICH THE CLOVERLEAF IS AN EXAMPLE RING BAR AND THE SO CALLED LADDER NETWORK 4HE BANDWIDTH OF A COUPLED CAVITY 474 CAN BE TO 4HE RING BAR HAS BROADER BANDWIDTH AND HIGHER EFFICIENCY THAN THE COUPLED CAVITY CIRCUIT BUT IT IS NOT CAPABLE OF AS HIGH A POWER AS THE COUPLED CAVITY 4HUS THE BANDWIDTH OF A 474 DECREASES AS ITS POWER INCREASES /N THE OTHER HAND AS MENTIONED PREVIOUSLY THE BANDWIDTH OF A KLYSTRON INCREASES WITH INCREASING POWER SO THAT THE BANDWIDTHS OF THE 474 AND THE KLYSTRON ARE GENERALLY COMPARABLE FOR MANY HIGH POWER RADAR APPLICATIONS "OTH FORWARD AND BACKWARD WAVES MAY PROPAGATE ALONG THE MICROWAVE STRUCTURE OF A 474 LEADING TO A POSSIBILITY OF BACKWARD WAVE OSCILLATIONS )N &IGURE ATTENUATION IS SHOWN ALONG THE HELIX SO AS TO PREVENT OSCILLATION DUE TO REFLECTIONS AT THE OUTPUT AND THE INPUT OF THE STRUCTURE 4HE ATTENUATION MAY BE DISTRIBUTED OR LUMPED BUT IT IS USUALLY FOUND IN THE MIDDLE THIRD OF THE TUBE !LTHOUGH OSCILLATION CAN BE PREVENTED BY DISTRIBUTING LOSS ALONG THE STRUCTURE IT RESULTS IN LOWER EFFI CIENCYSOMETHING UNATTRACTIVE IN HIGH POWER TUBES )NSTEAD OSCILLATIONS MAY BE PREVENTED BY THE USE OF DISCONTINUITIES CALLED SEVERS WITH ONE SEVER FOR EVERY TO D" OF TUBE GAIN !T EACH SEVER THE POWER TRAVELING IN THE REVERSE DIRECTION IS DISSIPATED IN THE SEVER LOADS WITHOUT SERIOUSLY AFFECTING THE POWER TRAVELING IN THE FORWARD DIRECTION 4HE SEVER LOADS MAY BE PLACED EXTERNAL TO THE TUBE TO REDUCE DIS SIPATION WITHIN THE 2& STRUCTURE ITSELF 4HE EFFICIENCY OF A 474 IS USUALLY LESS THAN THAT OF A KLYSTRON BECAUSE OF THE LOSS DUE TO THE ATTENUATION OF THE SEVERS AS WELL AS BY THE PRESENCE OF RELATIVELY HIGH 2& POWER OVER AN APPRECIABLE PART OF THE ENTIRE STRUCTURE ! TECHNIQUE FOR IMPROVING THE EFFICIENCY OF HIGH POWER 474S IS CALLED VELOCITY TAPERING 4HIS TECHNIQUE CONSISTS OF TAPERING THE LENGTH OF THE LAST FEW SEC TIONS OF THE SLOW WAVE CIRCUIT TO TAKE INTO ACCOUNT THE SLOWING DOWN OF THE BEAM AS THE ENERGY IS EXTRACTED FROM IT 6ELOCITY TAPERING PERMITS EXTRACTING MORE OF THE ENERGY FROM THE BEAM AND SIGNIFICANTLY IMPROVES THE POWER BANDWIDTH PERFORMANCE OF THE TUBE .EVERTHELESS HIGH POWER 474S GENERALLY SHOW AN APPRECIABLE FALLOFF OF POWER OUTPUT TOWARD THE BAND EDGES SO THAT THE RATED BANDWIDTH DEPENDS VERY MUCH ON HOW MUCH POWER FALLOFF CAN BE TOLERATED BY THE SYSTEM
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)F A 474 USING A COUPLED CAVITY CIRCUIT IS CATHODE PULSED 3ECTION THERE IS AN INSTANT DURING THE RISE AND FALL OF VOLTAGE WHEN THE BEAM VELOCITY BECOMES SYNCHRO NOUS WITH THE CUTOFF FREQUENCY THE SO CALLED O MODE OF THE MICROWAVE CIRCUIT AND THE TUBE CAN GENERATE OSCILLATIONS 4HESE OSCILLATIONS AT THE LEADING AND TRAILING EDGES OF THE 2& OUTPUT PULSE HAVE A CHARACTERISTIC APPEARANCE ON A POWER TIME PRESENTATION THAT HAS GIVEN THEM THE NAME RABBIT EARS /NLY IN RARE CASES HAS IT BEEN POSSIBLE TO SUP PRESS THESE OSCILLATIONS COMPLETELY (OWEVER SINCE THIS PARTICULAR OSCILLATION DEPENDS ON ELECTRON VELOCITY WHICH IN TURN DEPENDS ON BEAM VOLTAGE THE PROBLEM IS AVOIDED BY THE USE OF MOD ANODE OR GRID PULSING 3ECTION )N THIS CASE IT IS ONLY NECESSARY TO BE SURE NOT TO LET THE MODULATOR BEGIN PULSING THE BEAM CURRENT DURING TURN ON OF THE HIGH VOLTAGE POWER SUPPLY UNTIL THE VOLTAGE IS SAFELY ABOVE THE OSCILLATION RANGE WHICH IS TYPICALLY SOMEWHERE BETWEEN AND OF FULL OPERATING VOLTAGE ! MODIFICATION OF THE HELIX SLOW WAVE STRUCTURE IS THE RING BAR CIRCUIT WHICH CAN BE USED IF THE PEAK POWER IS LESS THAN TO K7 4HE 2AYTHEON 1+7 ! IS AN EXAMPLE WITH A PEAK POWER OF K7 DUTY CYCLE AND D" GAIN )T OPERATES AT , BAND FROM TO -(Z 4HE 53 !IR &ORCE #OBRA $ANE OPERATING FROM TO -(Z IS A LONG RANGE RADAR LOCATED IN THE !LEUTIAN )SLANDS THAT USES RING BAR 474S 1+7 EACH WITH A PEAK POWER OF K7 AND AVERAGE POWER OF K7 4HE 3 BAND 6! ! 474 AMPLIFIER EMPLOYS A CLOVERLEAF COUPLED CAVITY MICRO WAVE SLOW WAVE STRUCTURE 7ITH THE USE OF LIQUID COOLING IT IS CAPABLE OF -7 PEAK POWER OVER A -(Z BANDWIDTH )TS DUTY CYCLE IS WITH A GAIN OF D" AND A §S PULSE WIDTH 4HIS 474 WAS ORIGINALLY DESIGNED TO BE USED INTERCHANGEABLY WITH THE POPULAR 6! KLYSTRON EXCEPT THAT THE 6! ! 474 HAS A WIDER BANDWIDTH THAN THE 6! KLYSTRON )T ALSO REQUIRES A GREATER POWER INPUT SIGNAL BECAUSE OF ITS LOWER GAIN THAN THE KLYSTRON 7HEN HIGH POWER IS REQUIRED THE KLYSTRON TENDS TO BE PREFERRED OVER THE 474 SINCE IT DOESNT EXPERIENCE THE STABILITY PROBLEMS OF THE 474 'ILMOUR GIVES THE MEAN TIME BETWEEN FAILURES -4"& FOR NINE DIFFERENT TYPES OF COUPLED CAVITY 474S AS VARYING FROM HOURS TO HOURS WITH AN AVER AGE OF HOURS FOR ALL NINE CLASSES OF TUBES (E ALSO SAYS THAT 474S FOR SPACE APPLICATION WHICH ARE OF LOWER POWER THAN RADAR 474S HAVE -4"&S OF THE ORDER OF ONE MILLION HOURS $EPRESSED #OLLECTOR 4HE EFFICIENCY OF A 474 OR A KLYSTRON CAN BE IMPROVED BY THE USE OF A SO CALLED DEPRESSED COLLECTOR 7ITH A SINGLE COLLECTOR A SIGNIFICANT FRACTION OF THE POWER INPUT TO THE TUBE IS DISSIPATED AS HEAT IN THE COLLECTOR )F THE VOLT AGE ON THE COLLECTOR IS REDUCED DEPRESSED BELOW THE BODY VOLTAGE THE VELOCITY OF THE ELECTRONS STRIKING THE COLLECTOR IS REDUCED AND SO IS THE HEAT GENERATED IN THE COLLECTOR 4HUS THE COLLECTOR RECOVERS SOME OF THE POWER IN THE SPENT ELECTRON BEAM 4HE USE OF MULTIPLE DEPRESSED COLLECTORS AT INTERMEDIATE VOLTAGES RATHER THAN A SINGLE COLLECTOR ALLOWS CATCHING EACH SPENT ELECTRON AT A VOLTAGE NEAR OPTIMUM 5P TO TEN COLLECTOR SEC TIONS HAVE BEEN USED IN SOME COMMUNICATION TUBES BUT THREE SECTIONS ARE MORE TYPICAL FOR HIGH POWER 474S FOR RADAR SYSTEMS 4HE SEVERAL DIFFERENT VOLTAGES NEEDED FOR THE DEPRESSED COLLECTORS ADD COMPLEXITY TO THE HIGH POWER VOLTAGE SUPPLY BUT THESE VOLTAGES NEED NOT BE AS WELL REGULATED AS THE MAIN BEAM VOLTAGE )T IS USUALLY EASIER TO DESIGN A DEPRESSED COLLECTOR FOR A 474 THAN FOR A KLYSTRON SINCE THE SPENT ELECTRON BEAM OF A 474 MIGHT HAVE A SPREAD IN VELOCITY BUT THE KLYSTRON MIGHT HAVE A VELOCITY SPREAD OF ALMOST "ECAUSE THE EFFICIENCY IN A CONVENTIONAL 474 IS USUALLY LOWER THAN THAT OF A KLYSTRON THE INCREASE IN EFFICIENCY IN THE 474 PROVIDED BY A DEPRESSED COLLECTOR HAS A GREATER RELATIVE EFFECT THAN WITH A KLYSTRON
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6ARIANTS OF THE +LYSTRON AND THE 474 )T WAS MENTIONED THAT THE BANDWIDTH OF A KLYSTRON INCREASES AS ITS POWER IS INCREASED 4HE BANDWIDTH CAN ALSO BE INCREASED BY COMBINING THE BEST FEATURES OF THE KLYSTRON AND THE TRAVELING WAVE TUBE TO OBTAIN BETTER BANDWIDTH EFFICIENCY AND GAIN FLATNESS THAN EITHER THE CONVENTIONAL KLYSTRON OR THE 474 )N THESE TUBES THE BASIC STRUCTURE IS THAT OF A KLYSTRON BUT INSTEAD OF A NUMBER OF SINGLE CAVITIES BEING USED THE SINGLE CAVITY IS REPLACED BY A MORE COMPLEX MULTIPLE CAVITY 4HREE SUCH VARIANTS ARE THE 4WYSTRON EXTENDED INTERACTION KLYSTRON AND THE CLUSTERED CAVITY KLYSTRON -OST HIGH PERFORMANCE RADAR KLYSTRONS TEND TO EMPLOY THE MORE INTRICATE CAVITY STRUCTURE BECAUSE OF THE BETTER PERFORMANCE IT PROVIDES #OMPARISON OF 6ARIOUS ,INEAR "EAM 4UBE 3TRUCTURES &IGURE ILLUSTRATES THE BASIC STRUCTURE OF THE 2& CIRCUITS THAT CHARACTERIZE THE VARIOUS TYPES OF LINEAR BEAM TUBES 4WYSTRON 4HE BANDWIDTH OF A CONVENTIONAL KLYSTRON IS LIMITED PRIMARILY BY THE BANDWIDTH OF THE OUTPUT RESONANT CAVITY )F A COUPLED CAVITY SLOW WAVE CIRCUIT AS IS USED IN THE 474 IS SUBSTITUTED FOR THE OUTPUT RESONANT CAVITY OF A KLYSTRON &IGURE D THE BANDWIDTH OF THE KLYSTRON CAN BE INCREASED SIGNIFICANTLY AND THERE IS A SLIGHT INCREASE IN EFFICIENCY 4HIS REQUIRES THAT THE INTERMEDIATE CAVITIES AND THE INPUT CAVITY OF SUCH A TUBE BE STAGGER TUNED TO ACCOMMODATE THE INCREASED BANDWIDTH OFFERED BY THE OUTPUT CIRCUIT "ECAUSE THIS TYPE OF TUBE IS PART KLYSTRON AND PART 474 IT WAS NAMED 4WYSTRON 4HE 6! 3 BAND 4WYSTRON HAS A BANDWIDTH OF WITH A EFFICIENCY D" GAIN AT MIDBAND PEAK POWER OF -7 AND AVERAGE POWER OF K7 %XTENDED )NTERACTION +LYSTRON %)+ )N THE %)+ THE SINGLE GAP RESONANT CAVITIES OF THE KLYSTRON ARE REPLACED BY A RESONATED SLOW WAVE 474 LIKE CIRCUIT THAT CONTAINS TWO OR MORE INTERACTION GAPS &IGURE C 3UCH CAVITIES CAN BE USED FOR THE PRIOR CAVITIES AS WELL AS THE OUTPUT CAVITY 4HIS ALLOWS WIDER BANDWIDTH AND GREATER POWER THAN THE CONVENTIONAL KLYSTRON AMPLIFIER 3TAPRANS ET AL STATE THAT THE HIGH POWER 6! # %)+ OPERATED OVER A FREQUENCY RANGE FROM TO -(Z BANDWIDTH WITH A PEAK POWER OF -7 AND AN AVERAGE POWER OF K7 AND AN EFFICIENCY OF %)+ DEVICES HAVE BEEN OF INTEREST FOR MILLIMETER WAVE APPLICATIONS !CCORDING TO THE #OMMUNICATIONS 0OWER )NDUSTRIES #0) BROCHURE ITS 6+" MILLIMETER WAVE %)+ WHEN OPERATING AT A CENTER FREQUENCY OF '(Z WITH A '(Z BANDWIDTH HAS A PEAK POWER OF K7 AVERAGE POWER OF 7 ABOUT DUTY CYCLE GAIN OF D" PULSE WIDTH OF §S AND IS LIQUID COOLED )T HAS MUCH LOWER POWER THAN A GYROKLYSTRON DISCUSSED LATER AT THIS FREQUENCY BUT ITS CM BY CM DIAMETER SIZE IS CONSIDERABLY SMALLER AND IT COSTS CONSIDERABLY LESS THAN A GYROKLYSTRON ! SIMILAR %)+ ALSO BUILT BY #0) HAS BEEN USED IN THE .!3! #LOUD3AT SPACEBORNE RADAR THAT PROVIDES THE VERTICAL PROFILE OF CLOUDS FOR UNDERSTANDING CLOUD EFFECTS ON BOTH THE WEATHER AND CLIMATE )T OPERATES AT A CENTER FREQUENCY OF '(Z WITH A -(Z BANDWIDTH K7 PEAK POWER §S PULSE DURATION (Z PRF AND AN EFFICIENCY OF )T IS CONDUCTION COOLED %ACH CAVITY IS A SHORT PIECE OF RESONANT SLOW WAVE STRUCTURE BASED ON LADDER GEOMETRY 4HE TUBE WEIGHS KG AND CAN OPER ATE OVER A TEMPERATURE RANGE FROM TO O# )T WAS PREDICTED THAT THIS %)+ WOULD BE CAPABLE OF TWO YEARS OF CONTINUOUS OPERATION WITH A CONFIDENCE LEVEL 4WO %)+S WERE EMPLOYED IN #LOUD3AT ONE PRIME ONE REDUNDANT SO AS TO ACHIEVE A CONFIDENCE OF MEETING THE TWO YEAR LIFE REQUIREMENT
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)NTERACTION STRUCTURE
0 /UT #OLLECTOR
)NTERACTION )MPEDANCE $ISTANCE A
:
)MPEDANCE B
)MPEDANCE C )NPUT
/UTPUT LOAD
)MPEDANCE D &)'52% "ASIC STRUCTURE OF SEVERAL TYPES OF LINEAR BEAM TUBES A KLYSTRON B COUPLED CAVITY 474 C EXTENDED INTERACTION KLYSTRON AND D 4WYSTRON AFTER ! 3TAPRANS ET AL Ú )%%%
#LUSTERED #AVITY +LYSTRONS 4HIS IS A GOOD EXAMPLE OF THE TECHNIQUE OF GROUPING CAVITIES TO IMPROVE THE OPERATION OF A KLYSTRON 4HE INDIVIDUAL INTERMEDIATE CAVITIES OF A MULTICAVITY KLYSTRON ARE EACH REPLACED BY A CLUSTER OF TWO OR THREE ARTIFICIALLY LOADED LOW 1 CAVITIES WITH 1S OF ONE HALF TO ONE THIRD OF THE SINGLE CAVITY THEY REPLACE &IGURE COMPARES SCHEMATICALLY THE BASIC DIFFERENCE BETWEEN THE CONVENTIONAL STAGGER TUNED KLYSTRON AND THE CLUSTERED CAVITY KLYSTRON )T HAS BEEN SAID FOR A GIVEN
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&)'52% #OMPARISON OF THE STRUCTURES OF A CONVENTIONAL STAGGER TUNED KLYSTRON TOP AND CLUSTERED CAVITY KLYSTRON BOTTOM #OURTESY OF THE )%%%
GAIN BANDWIDTH PRODUCT THIS FORM OF STRUCTURE CAN PRODUCE A TUBE OF MUCH SHORTER LENGTH SO THAT THERE CAN BE SUBSTANTIAL SAVINGS IN MAGNET WEIGHT AND POWER 3YMONS THE INVENTOR OF THE CLUSTERED CAVITY KLYSTRON STATES THAT ONE OF THESE WIDE BANDWIDTH TUBES CAN BE USED TO REPLACE THE TWO NARROWER BAND KLYSTRONS IN THE !7!#3 RADAR 7HEN EACH OF THE TWO NARROW BAND TUBES IS REPLACED BY A WIDEBAND CLUSTERED CAVITY TUBE REDUNDANT OPERATION CAN BE PROVIDED WITH HIGHER RELIABILITY AND WITHOUT A LARGE WEIGHT PENALTY BECAUSE EITHER OF THESE CLUSTERED CAVITY KLYSTRONS PROVIDE FULL OPERA TIONAL CAPABILITY SIMILAR TO THE REDUNDANCY COMMONLY EMPLOYED IN &!! AIR TRAFFIC CONTROL RADARS -ICROWAVE 0OWER -ODULE -0- ! NOVEL VARIANT OF THE LINEAR BEAM TUBE IS THE MICROWAVE POWER MODULE WHICH IS AN AMPLIFIER THAT EMPLOYS A SOLID STATE MICRO WAVE INTEGRATED CIRCUIT AMPLIFIER TO DRIVE A MODERATE POWER HELIX TRAVELING WAVE TUBE ALONG WITH AN INTEGRATED CIRCUIT POWER CONDITIONER ALL IN A LIGHTWEIGHT PACKAGE )T CAN PROVIDE HIGH EFFICIENCY WIDE INSTANTANEOUS BANDWIDTH LOW NOISE AND AVERAGE POWER LEVELS FROM SEVERAL TENS TO SEVERAL HUNDREDS OF WATTS )T IS SAID TO BE SMALLER AND LIGHTER THAN COMPARABLE 474 AND SOLID STATE POWER SOURCES AND IS CAPABLE OF OPERATING AT HIGH AMBIENT TEMPERATURES 4HE GAIN OF AN -0- MIGHT BE NOMINALLY D" AND IS DIVIDED BETWEEN THE SOLID STATE DRIVER AND THE 474 POWER BOOSTER IN THE RATIOS FROM TO 4HE -0- SEEMS BEST SUITED FOR THE HIGHER MICROWAVE FREQUENCIES PERHAPS FROM TO '(Z ! SERIOUS CONSTRAINT OF THE -0- FOR RADAR APPLICATIONS IS THAT THE HELIX 474 LIMITS ITS USE TO #7 OR HIGH DUTY CYCLE TRANSMISSIONS PREFERABLY GREATER THAN )T ALSO IS OF RELATIVELY MODEST POWER FOR MANY RADAR APPLICATIONS
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£ä°ÎÊ /," 5NLIKE LINEAR BEAM TUBES THAT ARE NORMALLY OPERATED AS AMPLIFIERS THE MAGNETRON IS AN OSCILLATOR !S EXAMPLE OF A COMMONLY USED EARLY MAGNETRON WAS THE * AN , BAND TUBE THAT WAS MECHANICALLY TUNABLE FROM TO -(Z )T COULD OPERATE WITH A PEAK POWER OF K7 A §S PULSE WIDTH AND A PULSE REPETITION FREQUENCY OF (Z THAT PROVIDED AN AVERAGE POWER OF 7 )TS EFFICIENCY WAS TYPICAL FOR MAGNETRONS AT THAT TIME 4HE COMPACT SIZE AND EFFICIENT OPERATION OF THE MAGNETRON AT MICROWAVE FREQUENCIES ALLOWED RADARS IN 7ORLD 7AR )) TO BE SMALL ENOUGH TO FLY IN MILITARY AIRCRAFT AND TO BE MOBILE FOR GROUND WARFARE -AGNETRONS HOWEVER SEEM TO BE LIMITED TO ABOUT A FEW KILOWATTS OF AVERAGE POWER WHICH CAN RESTRICT THEIR UTILITY 4HEY ALSO HAVE LIMITATIONS IN STABILITY AND THEREFORE IN THE -4) IMPROVEMENT FACTOR THEY CAN ACHIEVE AND THEY OFTEN HAVE A SHORTER LIFE THAN LINEAR BEAM TUBES "ECAUSE THE MAGNETRON IS AN OSCILLATOR RATHER THAN AN AMPLIFIER THE STARTING PHASE OF EACH PULSE IS RANDOM FROM PULSE TO PULSE 4HIS RANDOM CHANGE OF PHASE CAN BE ACCOMMODATED IN A -4) RADAR RECEIVER BY USE OF A COHERENT OSCILLATOR COHO AS THE REFERENCE SIGNAL IN THE PHASE DETECTOR STAGE OF THE RECEIVER /N EACH PULSE THE PHASE OF THE MAGNETRON PULSE SETS THE PHASE OF THE COHO )N THIS MANNER THE RECEIVED SIGNAL APPEARS TO BE COHERENT PULSE TO PULSE 4HIS IS SOMETIMES CALLED COHERENT ON RECEIVE 4HE -4) IMPROVEMENT FACTOR OBTAINED WITH A MAGNETRON AND A COHERENT ON RECEIVE OPERATION USUALLY IS NOT AS GOOD AS CAN BE OBTAINED WITH AN -4) SYSTEM THAT USES A POWER AMPLIFIER AS THE TRANSMITTER !UTOMATIC FREQUENCY CONTROL !&# IS OFTEN EMPLOYED TO KEEP THE RECEIVER TUNED TO THE FREQUENCY OF THE TRANSMITTER SINCE THE MAGNETRON FREQUENCY CAN SLOWLY DRIFT WITH CHANGES IN AMBIENT TEMPERATURE AND SELF HEATING 4HE !&# CAN BE APPLIED TO THE MAGNETRON ITSELF TO KEEP IT OPERATING ON ITS ASSIGNED FREQUENCY WITHIN THE LIMITS OF THE ACCURACY OF THE TUNING MECHANISM ! MAGNETRON CAN BE MECHANICALLY CHANGED IN FREQUENCY OVER A TO FREQUENCY RANGE AND IN SOME CASES AS MUCH AS 2APID MECHANICAL TUNING CAN BE ACHIEVED WITH A SLOTTED DISK SUSPENDED ABOVE THE ANODE CAVITIES 7HEN ROTATED IT ALTERNATELY PROVIDES INDUCTIVE AND CAPACITIVE LOADING OF THE CAVITIES TO RAISE AND LOWER THE FRE QUENCY 3UCH A ROTARY TUNED MAGNETRON CAN PROVIDE VERY FAST TUNING RATES &OR EXAM PLE AT A ROTATION RATE OF RPM A MAGNETRON WITH CAVITIES CAN TUNE ACROSS A BAND TIMES PER SECOND #OAXIAL -AGNETRON ! SIGNIFICANT IMPROVEMENT IN THE POWER EFFICIENCY STA BILITY AND LIFE OF THE ORIGINAL FORM OF THE MAGNETRON OCCURRED WITH THE INTRODUCTION OF THE COAXIAL MAGNETRON 4HE KEY DIFFERENCE IS THE INCORPORATION OF A STABILIZING CAVITY SURROUNDING THE CONVENTIONAL MAGNETRON CAVITIES WITH THE STABILIZING CAVITY COUPLED TO THE MAGNETRON CAVITIES SO AS TO PROVIDE BETTER STABILIZATION 4HE FREQUENCY OF A COAXIAL MAGNETRON CAN BE CHANGED BY MECHANICALLY MOVING ONE OF THE END PLATES CALLED A TUNING PISTON OF THE STABILIZING CAVITY 4HE TUNING PISTON CAN BE POSITIONED MECHANICALLY FROM THE OUTSIDE OF THE VACUUM BY MEANS OF A VACUUM BELLOWS )N THE COAXIAL MAGNETRON THE OUTPUT OF EVERY OTHER RESONANT CAVITY IS COUPLED TO THE STABILIZING CAVITY THAT SURROUNDS THE ANODE STRUCTURE 4HE OUTPUT POWER IS THEN COUPLED FROM THE STABILIZING CAVITY O -ODE OF /PERATION ! MAGNETRON WHETHER CONVENTIONAL OR COAXIAL CAN OSCIL LATE AT A NUMBER OF DIFFERENT CLOSELY SPACED FREQUENCIES DUE TO VARIOUS POSSIBLE CON FIGURATIONS OF THE 2& FIELD THAT CAN EXIST BETWEEN THE CATHODE AND THE RESONANT CAVITIES
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4HESE DIFFERENT 2& FIELD CONFIGURATIONS ALONG WITH COUPLING AMONG THE CAVITY RESO NATORS OF THE MAGNETRON RESULT IN DIFFERENT MODES OF OSCILLATION 4HE MAGNETRON CAN SHIFT ALMOST UNPREDICTABLY FROM ONE MODE TO ANOTHER WHICH MEANS THE FREQUENCY SHIFTS UNPREDICTABLY AS THE VOLTAGE CHANGES OR AS THE INPUT IMPEDANCE THAT THE MAG NETRON EXPERIENCES CHANGES 4HE SHIFT FROM ONE MODE TO ANOTHER OFTEN CALLED MODING IS ESPECIALLY BAD SINCE IT CAN OCCUR WHEN THE RADAR ANTENNA SCANS AND VIEWS DIFFERENT ENVIRONMENTS )T IS IMPORTANT TO AVOID MODING 4HE PREFERRED MAGNETRON MODE OF OPERATION IS THE SO CALLED O MODE THAT OCCURS WHEN THE 2& FIELD CONFIGURATION IS SUCH THAT THE 2& PHASE ALTERNATES O O RADIANS BETWEEN ADJACENT CAVITIES 4HE ADVANTAGE OF THE O MODE IS THAT ITS FREQUENCY CAN BE MORE READILY SEPARATED FROM THE FREQUENCIES OF THE OTHER POSSIBLE MODES !N . CAVITY MAGNETRON CAN HAVE . POSSIBLE MODES 4HE O MODE OSCILLATES AT A SINGLE FREQUENCY BUT THE OTHER MODES CAN OSCILLATE AT TWO DIFFERENT FREQUENCIES SO THAT THE MAGNETRON CAN OSCILLATE AT . DIFFERENT FREQUENCIES #OAXIAL -AGNETRON ,IFE 4HE POWER THAT CAN BE PRODUCED BY A MAGNETRON DEPENDS ON ITS SIZE ! LARGER SIZE MEANS MORE RESONATORS WHICH MAKES IT MORE DIFFICULT TO SEPARATE THE VARIOUS MODES OF OSCILLATION IN A CONVENTIONAL MAGNETRON 4HE COAXIAL MAGNETRON HOWEVER WITH STABILIZATION CONTROLLED BY THE OUTER CAVITY PERMITS STABLE OPERATION WITH A LARGER NUMBER OF CAVITIES AND THUS WITH GREATER POWER 4HE ANODE AND CATHODE STRUCTURES OF A COAXIAL MAGNETRON CAN ALSO BE BIGGER WHICH FURTHER ALLOWS OPERATION AT HIGHER POWER 4HE LARGER STRUCTURES PERMIT MORE CONSERVATIVE DESIGN WITH THE RESULT THAT IT HAS LONGER LIFE AND BETTER RELIABILITY THAN CONVENTIONAL MAGNETRONS AS WELL AS MORE STABLE OPERATION 4HE OPERATING LIFE OF A COAXIAL MAGNETRON HAS BEEN SAID TO BE BETWEEN AND HOURS WHICH IS A FIVE TO TWENTYFOLD INCREASE COMPARED TO CONVENTIONAL HIGH POWER MAGNETRONS ,IMITATIONS OF -AGNETRONS 7HEN THE MAGNETRON WAS FIRST INTRODUCED IT PRO VIDED A CAPABILITY NOT AVAILABLE WITH THE GRID CONTROLLED TUBES USED FOR EARLY RADARS !S TIME PASSED THE DEMANDS FOR IMPROVED RADAR PERFORMANCE OUTRAN THE CAPABILITIES AVAILABLE FROM THE MAGNETRON &ORTUNATELY OTHER TUBE TYPES WERE INVENTED THAT OVER CAME THE LIMITATIONS OF THE MAGNETRON !LTHOUGH THE MAGNETRON HAS HAD IMPORTANT APPLICATIONS IN THE PAST IT HAS ALSO HAD SERIOUS LIMITATIONS THAT CONSTRAIN ITS USEFULNESS FOR RADAR )TS MAJOR LIMITATIONS ARE ITS POOR STABILITY WHICH LIMITS THE ABILITY TO DETECT MOVING TARGETS IN CLUTTER ITS RELATIVELY MODEST AVERAGE POWER AND ITS SIGNAL CANNOT BE READILY MODULATED FOR PULSE COMPRES SION 4HESE AND OTHERS ARE DISCUSSED NEXT 4HE USE OF THE DOPPLER FREQUENCY SHIFT TO DETECT MOVING TARGETS IN THE MIDST OF LARGE CLUTTER ECHOES REQUIRES THAT THE TRANSMITTER PRODUCE A STABLE SIGNAL WITH LITTLE EXTRANEOUS NOISE "ECAUSE OF THEIR POOR STABILITY AND NOISY TRANSMISSIONS MAGNETRONS ARE LIMITED IN THE AMOUNT OF -4) )MPROVEMENT &ACTOR THEY CAN ACHIEVE TO ABOUT OR PERHAPS D" -ANY RADAR APPLICATIONS REQUIRE GREATER -4) )MPROVEMENT &ACTORS 3OME RADARS ALSO REQUIRE THE USE OF PULSE COMPRESSION WAVEFORMS TO OBTAIN THE RESO LUTION OF A SHORT PULSE WITH THE ENERGY OF A LONG PULSE )T IS DIFFICULT TO PHASE OR FRE QUENCY MODULATE THE WAVEFORM OF A MAGNETRON AS IS NEEDED FOR PULSE COMPRESSION 4HUS POWER AMPLIFIERS ARE ALMOST ALWAYS USED FOR PULSE COMPRESSION APPLICATIONS -AGNETRONS ARE NOT STABLE ENOUGH TO BE SUITABLE FOR VERY LONG PULSES EG §S AND STARTING JITTER LIMITS THEIR USE AT VERY SHORT PULSE WIDTHS EG §S ESPECIALLY AT HIGH POWER AND AT THE LOWER FREQUENCY BANDS )TS MAXIMUM AVERAGE POWER IS OF THE ORDER OF SEVERAL KILOWATTS WHICH IS LESS THAN THAT REQUIRED FOR SOME MILITARY APPLICATIONS
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3INCE THE MAGNETRON IS AN OSCILLATOR WITH A RANDOM STARTING PHASE ON EACH PULSE IT CAN NOT BE USED TO ELIMINATE SECOND TIME AROUND CLUTTER ECHOESAS CAN AN AMPLIFIER TRANS MITTER 3IMILARLY COMBINING THE POWER OUTPUTS OF MULTIPLE MAGNETRONS HAS NOT BEEN ATTRACTIVE -AGNETRONS CAN PRODUCE CONSIDERABLE ELECTROMAGNETIC INTERFERENCE ACROSS A BANDWIDTH MUCH WIDER THAN THE SIGNAL BANDWIDTH COAXIAL MAGNETRONS ARE SOMEWHAT BETTER IN THIS RESPECT !LSO MAGNETRONS DO NOT HAVE PRECISE FREQUENCY CONTROL NOR ARE THEY ABLE TO PERFORM PRECISE FREQUENCY JUMPING )N SPITE OF ITS MANY UNFAVORABLE CHARACTERISTICS THE MAGNETRON IS A TUBE THAT CAN BE CONSIDERED FOR LESS DEMANDING RADAR TASKS &OR A LONG TIME IT WAS THE TRANSMITTER OF CHOICE FOR USE IN THE CIVIL MARINE RADAR ONE OF THE MOST WIDELY USED RADARS AS BRIEFLY DISCUSSED NEXT #IVIL -ARINE 2ADAR -AGNETRONS 4HE MAGNETRON HAS BEEN WELL SUITED FOR APPLICATION IN CIVIL MARINE RADARS USED ON SMALL PLEASURE BOATS OR LARGE COMMERCIAL SHIPS )TS SUCCESS HAS BEEN DUE IN PART TO THE RADAR NEEDING ONLY SMALL TRANSMITTER POWER AND THE RADAR DOES NOT REQUIRE DOPPLER PROCESSING TO SEPARATE MOVING TARGETS FROM LARGE FIXED CLUTTER ECHOES 4HUS MANY OF THE PROBLEMS THAT OCCUR WITH MAGNE TRONS WHEN USED IN OTHER APPLICATIONS ARE NOT FOUND IS THIS APPLICATION !LSO IMPORTANT IS THAT THE CIVIL MARINE RADAR BUSINESS IS VERY COMPETITIVE BECAUSE OF THE LARGE WORLD WIDE NEED FOR SUCH RADARS 4HIS HAS RESULTED IN THE DEVELOPMENT OF LOW COST HIGHLY RELIABLE MAGNETRONS FOR THIS IMPORTANT RADAR APPLICATION 4HESE MAGNETRONS GENERATE PEAK POWERS FROM TO K7 AND HAVE RELATIVELY LOW AVERAGE POWERS OF A FEW WATTS TO A FEW TENS OF WATTS !N EXAMPLE OF A MAGNETRON FOR A CIVIL MARINE RADAR IS THE -' MANUFACTURED BY %%9 OF #HELMSFORD %NGLAND )T IS AN CAVITY 8 BAND MAGNETRON THAT OPERATES AT A FIXED FREQUENCY WITHIN THE BAND FROM TO -(Z WITH A PEAK POWER OF K7 AND AN EFFICIENCY OF )T OPERATES WITH AN ANODE VOLTAGE OF K6 AND AN ANODE CURRENT OF AMPS 4YPICALLY ITS PULSE WIDTH MIGHT BE §S WITH A DUTY CYCLE OF 4HE MANUFAC TURER CLAIMS AN EXPECTED TYPICAL LIFE OF OVER HOURS AND GUARANTEES A MINIMUM LIFE OF HOURS )T MIGHT ALSO BE MENTIONED THAT THE MAGNETRON HAS HAD OUTSTANDING SUCCESS AS THE POWER SOURCE FOR THE MICROWAVE OVEN /VER THE YEARS IT HAS DEVELOPED INTO A VERY LOW COST AND HIGHLY RELIABLE GENERATOR OF MICROWAVE POWER THAT IS WELL SUITED FOR THIS APPLICATION
£ä°{Ê ,"-- Ê * ,- Ón 4HE CROSSED FIELD AMPLIFIER OR #&! LIKE THE MAGNETRON HAS A MAGNETIC FIELD THAT IS ORTHOGONAL TO THE ELECTRIC FIELD BUT IT IS AN AMPLIFIER RATHER THAN AN OSCILLATOR )T IS SIMILAR IN APPEARANCE TO A MAGNETRON EXCEPT THAT THE 2& CIRCUIT IS INTERRUPTED TO PRO VIDE THE INPUT AND OUTPUT CONNECTIONS AS NEEDED FOR AN AMPLIFIER #&!S MIGHT HAVE AN EFFICIENCY FROM TO USE A LOWER VOLTAGE THAN LINEAR BEAM TUBES ARE LIGHTER IN WEIGHT AND SMALLER IN SIZE AND HAVE BEEN FOUND FROM 5(& TO + BAND (OWEVER THEY HAVE RELATIVELY LOW GAIN AND THEIR STABILITY AND NOISE ARE NOT AS GOOD AS FOUND IN LINEAR BEAM TUBES SO THEIR APPLICATION FOR -4) RADAR HAS BEEN LIMITED "ECAUSE OF THE #&!S LOW GAIN THE CROSSED FIELD AMPLIFIER TRANSMITTER NEEDS MORE THAN ONE STAGE OF 2& AMPLIFICATION EACH WITH ITS OWN POWER SUPPLY MODULATOR AND CONTROLS !LL THESE STAGES MUST BE STABLE TO ACHIEVE GOOD -4) PERFORMANCE
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"ECAUSE THE #&! HAS RELATIVELY LOW GAIN IT IS SOMETIMES USED ONLY IN ONE OR TWO OF THE HIGHEST POWER STAGES OF AN AMPLIFIER CHAIN WHERE IT MAY OFFER AN ADVANTAGE IN EFFICIENCY OPERATING VOLTAGE SIZE ANDOR WEIGHT COMPARED TO OTHER TUBES 4HE OUTPUT STAGE #&! MIGHT BE PRECEDED BY A MEDIUM POWER 474 THAT PROVIDES MOST OF THE GAIN OF THE TOTAL AMPLIFIER CHAIN 7HEN COMPARING THE #&! WITH THE LINEAR BEAM TUBE THE ENTIRE TRANSMITTER SYSTEM NEEDS TO BE COMPARED AND NOT JUST THE TUBE ITSELF 4HE #&! HAS ALSO BEEN CONSIDERED AS A MEANS TO BOOST THE POWER OUTPUT OF PREVIOUSLY EXISTING RADAR SYSTEMS THAT EMPLOYED MAGNETRONS 4HERE HAVE BEEN BOTH BACKWARD WAVE AND FORWARD WAVE #&!S 4HE BACKWARD WAVE #&! IS ALSO KNOWN AS THE !MPLITRON )T IS POSSIBLE TO PULSE SOME #&!S WHICH HAVE COLD CATHODES TO EMPLOY WHAT IS CALLED $# OPERATION WHERE THE TRANSMITTER IS TURNED ON AND OFF TO GENERATE A PULSE WAVEFORM WITHOUT THE NEED FOR A HIGH POWER MODULATOR )N DC OPERATION THE HIGH VOLT AGE IS CONTINUOUSLY PRESENT BETWEEN ANODE AND CATHODE AND THE CURRENT IS TURNED ON BY APPLYING THE 2& DRIVE AND TURNED OFF BY PULSING THE CONTROL ELECTRODE 4HE CONTROL ELECTRODE CONSISTS OF A SEGMENT OF THE CATHODE STRUCTURE IN THE DRIFT REGION 4O PREVENT THE TUBE FROM STARTING WITHOUT 2& DRIVE THE CATHODE MUST BE KEPT COOL ENOUGH TO PRE VENT THERMIONIC EMISSION 4HE CONTROL ELECTRODE NEEDS ONLY A SHORT MEDIUM POWER PULSE TYPICALLY ONE THIRD OF THE ANODE VOLTAGE AND ONE THIRD OF THE ANODE PEAK CURRENT 3INCE THE CONTROL ELECTRODE IS INSULATED AND SINCE SOME ENERGY IS DISSIPATED ON THE CONTROL ELECTRODE IT CAN BE DIFFICULT TO COOL 4HIS CAN LIMIT THE MAXIMUM PULSE REPETI TION FREQUENCY THAT CAN BE USED )N SPITE OF IT REQUIRING NO MODULATOR DC OPERATION HAS SELDOM BEEN USED BECAUSE OF ITS MANY LIMITATIONS #ROSSED FIELD AMPLIFIERS HAVE BEEN USED IN RADARS IN THE PAST BUT THEY HAVE SIGNIFI CANT DISADVANTAGES AS WAS DESCRIBED IN THE SECOND EDITION OF THIS 2ADAR (ANDBOOK THAT MAKE IT LESS LIKELY THEY WILL BE WIDELY USED IN THE FUTURE
£ä°xÊ 9,"/," - Σ]ÎÓ]ÎÎ )T HAS BEEN NOTED PREVIOUSLY THAT THE POWER HANDLING CAPABILITY OF THE MICROWAVE POWER TUBES DISCUSSED THUS FAR IN THIS CHAPTER DECREASES AS THE FREQUENCY IS INCREASED 4HIS RESULTS BECAUSE THE RESONANT STRUCTURES OF THE SLOW WAVE MICROWAVE CIRCUITRY OF THESE TUBES BECOME SMALLER WITH INCREASING FREQUENCY 4HE SMALLER THE DEVICE THE MORE DIFFICULT IT IS TO DISSIPATE THE HEAT THAT IS GENERATED 4HUS THE POWER OUTPUT DECREASES APPROXIMATELY INVERSELY AS THE SQUARE OF THE RADAR FREQUENCY 4HE GYROTRON 2& POWER GENERATOR HOWEVER DOES NOT HAVE THIS LIMITATION BECAUSE IT DOES NOT EMPLOY SLOW WAVE RESONANT MICROWAVE STRUCTURES 4HESE DEVICES EMPLOY A FAST WAVE STRUCTURE SUCH AS A SMOOTH CIRCULAR TUBE ONE WHERE THE PHASE VELOCITY OF THE ELECTROMAGNETIC WAVE IS GREATER THAN THE VELOCITY OF LIGHT 7ITH A SLOW WAVE DEVICE THE PHASE VELOCITY IS LESS THAN THE VELOCITY OF LIGHT 4HE DIAMETER OF THE GYROTRON CIRCUIT CAN BE MANY WAVELENGTHS AND THE ELECTRON BEAM NEED NOT BE PLACED CLOSE TO DELICATE 2& STRUCTURES "ECAUSE A FAST WAVE STRUCTURE RATHER THAN A SLOW WAVE STRUCTURE IS USED THEY DO NOT HAVE THE SIZE LIMITATIONS OF OTHER MICROWAVE POWER SOURCES AS THE FREQUENCY IS INCREASED 4HUS THEY CAN GENERATE GREATER POWER AT THE HIGHER FREQUENCIES THAN CAN OTHER 2& POWER SOURCES SOMETHING ESPECIALLY ATTRACTIVE AT MILLIMETER WAVELENGTHS
4UBE IS USED HERE AS BEING A hHOLLOW ELONGATED CYLINDERv
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4HE MAGNETIC FIELD IN A GYROTRON SERVES A DIFFERENT FUNCTION FROM THE MAGNETIC FIELD IN A SLOW WAVE DEVICE )N THE SLOW WAVE DEVICE THE MAGNETIC FIELD KEEPS THE ELECTRONIC BEAM COLLIMATED )N THE FAST WAVE DEVICE HOWEVER THE MAGNETIC FIELD DETERMINES THE FREQUENCY BUT THE FREQUENCY OF A CONVENTIONAL SLOW WAVE DEVICE IS DETERMINED BY THE CIRCUIT DIMENSIONS !N ELECTRON IN AN APPLIED AXIAL MAGNETIC FIELD "O WILL ROTATE AT WHAT IS CALLED THE ELECTRON CYCLOTRON FREQUENCY WHICH IS GIVEN BY VC E"OMG WHERE E ELECTRON CHARGE M ELECTRON REST MASS AND G IS THE RELATIVISTIC FACTOR WHICH IS ; EMC 6O= WHERE C VELOCITY OF LIGHT AND 6O BEAM VOLTAGE 4HE BEAM VOLTAGE AND THE CORRESPONDING ELECTRON VELOCITY IN A GYROTRON ARE HIGH ENOUGH TO CAUSE RELATIV ISTIC EFFECTS 4HE ELECTRONS FOLLOW HELICAL PATHS AROUND THE MAGNETIC FIELD LINES WHEN IN THE PRESENCE OF AN ELECTROMAGNETIC WAVE WITH A TRANSVERSE COMPONENT OF ELECTRIC FIELD %LECTRONS THAT LOSE ENERGY TO THE ELECTROMAGNETIC WAVE BECOME LIGHTER AND ACCUMULATE PHASE LEAD AND THEN CATCH UP WITH THE ELECTRONS THAT GAIN ENERGY AND BECOME HEAVIER AND ACCUMULATE PHASE LAG 4HUS ELECTRONS BECOME PHASE BUNCHED IN THEIR CYCLOTRON ORBITS AS A RESULT OF THE RELATIVISTIC MASS CHANGE OF THE ELECTRONS 4HE GYROTRON BUNCHING OPERATION ALSO CAN BE OBTAINED AT HARMONICS OF THE CYCLOTRON FREQUENCY BUT THERE CAN BE PROBLEMS WITH HIGHER CIRCUIT LOSSES AND COMPETITION WITH MODES OPERATING AT LOWER HARMONICS SO THAT MOST HIGH POWER GYROTRONS OPERATE AT THE FUNDAMENTAL FREQUENCY OR ITS SECOND HARMONIC "ECAUSE THE FREQUENCY OF A GYROTRON IS DETERMINED BY THE MAGNETIC FIELD AND NOT BY THE SIZE OF THE FAST WAVE STRUCTURE THE STRUCTURE CAN BE LARGE AND IT IS THEN POSSIBLE TO GENERATE QUITE HIGH POWER AT MILLIMETER WAVE FREQUENCIES 4HE LARGE MAGNETIC FIELDS NEEDED FOR MILLIMETER WAVE GYROTRONS OFTEN HAVE TO BE GENERATED BY SUPERCONDUCTING MAGNETS 4HE GYROTRON WITH A SINGLE CAVITY OPERATES AS AN OSCILLATOR )T IS SOMETIMES CALLED A GYRO OSCILLATOR TO DIFFERENTIATE IT FROM A GYRO AMPLIFIER THAT UTILIZES SEVERAL RESONANT CAVITIES OR A TRAVELING WAVE CIRCUIT TO OPERATE AS AN AMPLIFIER 4HE GYRO AMPLIFIER THAT EMPLOYS SEVERAL RESONANT CAVITIES IS CALLED A GYROKLYSTRON AND WHEN A TRAVELING WAVE CIRCUIT IS USED IT IS CALLED A GYRO TRAVELING WAVE TUBE OR MORE COMMONLY GYRO 474 4HERE IS ALSO A GYROTWYSTRON WITH THE RESONANT OUTPUT CAVITY REPLACED BY A 474 CIR CUIT SO AS TO ACHIEVE GREATER BANDWIDTH THAN CAN BE OBTAINED WITH A RESONANT CAVITY !LTHOUGH GYRO OSCILLATORS HAVE BEEN CAPABLE OF GREATER POWER THAN GYRO AMPLIFIERS THE GYRO AMPLIFIER HAS USUALLY BEEN PREFERRED FOR RADAR APPLICATIONS FOR THE SAME REA SON THE AMPLIFIER HAS BEEN PREFERRED AT MICROWAVE FREQUENCIES ESPECIALLY WHEN DOP PLER PROCESSING IS IMPORTANT !N EXAMPLE OF A HIGH POWER GYROKLYSTRON FOR RADAR APPLICATIONS IS THE 6'" THAT WAS USED IN THE EXPERIMENTAL 7 BAND RADAR KNOWN AS 7ARLOC AT THE 53 .AVAL 2ESEARCH ,ABORATORY )T HAD FIVE CAVITIES OPERATED OVER A -(Z BANDWIDTH CENTERED AT '(Z WITH AN AVERAGE POWER OF K7 A PEAK POWER OF K7 DUTY CYCLE AND EFFICIENCY WITH A K6 ! ELECTRON BEAM )T USED A SUPER CONDUCTING MAGNET WITH A CLOSED CYCLE COOLING SYSTEM SO THAT NO LIQUID CRYOGENS WERE REQUIRED )T PROVIDED A MAGNETIC FIELD OF K' 4HE FIVE CAVITY GYROKLYSTRON COULD ACHIEVE A BANDWIDTH OF -(Z AT AN AVERAGE POWER OF K7 4HE RADAR USED A FT DIAMETER ANTENNA THAT PROVIDED A BEAMWIDTH OF 4HIS 7 BAND 7ARLOC WAS INSTALLED IN A VAN AND WAS USED FOR VARIOUS EXPERIMENTS 4HE 7ARLOC RADAR WAS ABOUT THREE ORDERS OF MAGNITUDE MORE CAPABLE THAN MOST PREVIOUS RADARS USED FOR MILLIME TER WAVE RADAR 4HIS EXPERIMENTAL 7ARLOC RADAR WAS EMPLOYED TO DEMONSTRATE AT 7 BAND THE )3!2 IMAGING OF MOVING TARGETS CLOUD STRUCTURE LOW ANGLE OPERATION AND UNUSUAL ATMOSPHERIC RESEARCH INCLUDING WHAT HAVE BEEN CALLED hAIR SPIKESv
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4HE ABOVE DISCUSSION WAS MAINLY ABOUT THE GYROTRON AMPLIFIER 4HE GYROTRON HAS ALSO BEEN OPERATED AS AN OSCILLATOR TO PRODUCE VERY HIGH POWER BUT THE OSCILLATOR VER SION HAS NOT BEEN AS POPULAR AS THE AMPLIFIER FOR RADAR APPLICATIONS 4HIS MIGHT BE DUE TO THE AMPLIFIER BEING BETTER ABLE TO PRODUCE THE DESIRED RADAR WAVEFORMS
£ä°ÈÊ /, - // ,Ê-* /,1 Ê " /," 4HE INCREASING DEMAND FOR ELECTROMAGNETIC SPECTRUM FOR BOTH CIVILIAN AND MILITARY APPLICATIONS HAS ACCENTUATED THE NEED TO CONTROL THE SPECTRUM OF RADAR TRANSMITTERS TO AVOID INTERFERENCE WITH USERS OF THE ELECTROMAGNETIC SPECTRUM OPERATING AT OTHER FREQUENCIES 4HE ASPECTS OF CONCERN HERE ARE THOSE THAT AFFECT 2& TUBE SELECTION AND ACHIEVEMENT OF MINIMUM SPECTRUM OCCUPANCY BY THE TRANSMITTERS DISCUSSED PREVIOUSLY IN THIS CHAPTER 2EDUCTION OF 3PURIOUS /UTPUTS 2& TUBE SPURIOUS OUTPUTS MAY BE GROUPED INTO THREE KINDS HARMONICS ADJACENT BAND AND IN BAND !LL 2& TUBES PRODUCE SOME HARMONIC OUTPUT )N GENERAL LITTLE CAN BE DONE IN TUBE DESIGN TO REDUCE HARMONIC OUTPUTS BUT IT IS FEASIBLE TO FILTER OUT HARMONICS TO D" REDUCTION WITH HIGH POWER FILTERS !DJACENT BAND SPURIOUS OUTPUT CAN ALSO OCCUR IN SOME CATHODE PULSED 474S AND #&!S !DJACENT BAND SPURIOUS OUTPUT IS AFFECTED BY TUBE AND MODULATOR SELECTION BUT IT CAN BE FILTERED BY A HIGH POWER MICROWAVE FILTER IF NECESSARY !LL 2& TUBES PRODUCE SOME IN BAND BACKGROUND NOISE LEVEL )N A -(Z BANDWIDTH THIS NOISE MIGHT BE TO D" DOWN IN CONVENTIONAL #&!S TO D" DOWN IN THE LOW NOISE HIGH GAIN #&! AND D" DOWN OR BETTER IN LINEAR BEAM TUBES )N BAND SPURIOUS CANNOT NORMALLY BE IMPROVED WITH FILTERS BECAUSE IT OCCURS WITHIN THE SAME FREQUENCY RANGE AS THE DESIRED SIGNAL SPECTRUM !TTEMPTS TO USE NOISE DEGENERATION TO REDUCE THE INHERENT 2& TUBE NOISE LEVELS ARE SUBJECT TO LIMITATIONS )N BAND SPURIOUS SIGNALS CAN ALSO RESULT FROM POWER SUPPLY AND MODULATOR INSTABILITIES 2EDUCTION OF 3PECTRUM !MPLITUDE %XCEEDING SIN X X 4HE SPECTRUM OF A PERFECTLY RECTANGULAR PULSE HAS THE FAMILIAR SIN X X FORM WHERE X IS O FO F S FO IS THE RADAR CARRIER FREQUENCY AND S IS THE PULSE WIDTH )F S IS CALLED THE NOMINAL BAND WIDTH OF THE SIGNAL THE ENVELOPE OF THE SPECTRUM PEAKS FALLS OFF AT THE RATE OF D" PER OCTAVE OF BANDWIDTH AND THIS REDUCTION WILL CONTINUE UNTIL THE ENVELOPE REACHES THE INHERENT NOISE OUTPUT LEVEL OF THE TRANSMITTER 4HIS RATE OF SPECTRUM FALLOFF IS TOO SLOW TO MEET MOST SYSTEM REQUIREMENTS .EVERTHELESS WITHOUT SPECIAL CARE THE ACTUAL SPECTRUM ENVELOPE MIGHT BE EVEN WORSE THAN THIS DEPENDING ON TUBE CHARACTERISTICS AS A RESULT OF PHASE MODULATION DURING THE FINITE RISE AND FALL OF PRACTICAL MODULATOR AND 2& DRIVE PULSE SHAPES )N THESE CASES EITHER THE LEADING AND TRAILING EDGES MUST BE APPROPRIATELY TAILORED OR ELSE IN LINEAR BEAM TUBES THE 2& DRIVE MAY BE WITHHELD DURING THE RISE AND FALL TIME !LTHOUGH THIS MAY SLIGHTLY REDUCE APPARENT EFFICIENCY IT SHOULD BE NOTED THAT ENERGY OUTSIDE THE APPROXIMATELY S GENERATED DURING RISE AND FALL WITH THE 2& DRIVE PRESENT IS NOT UTILIZED BY THE RECEIVER ANYWAY )MPROVEMENT BY -EANS OF 3HAPED 0ULSES 3INCE THE ENERGY IN THE SPECTRUM BEYOND PLUS OR MINUS S FROM FO IS NOT USED BY THE RECEIVER IT IS DESIRABLE FOR
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ELECTROMAGNETIC COMPATIBILITY PURPOSES TO AVOID TRANSMITTING ENERGY BEYOND THOSE LIMITS 4HIS OBJECTIVE MAY BE APPROACHED BY USING A PULSE SHAPE DIFFERENT FROM THE CONVENIENT AND CONVENTIONAL RECTANGULAR PULSE (IGHLY SHAPED PULSES HAVE NOT BEEN USED OFTEN IN RADAR SYSTEMS BECAUSE OF THE LOSS OF EFFICIENCY THAT RESULTS 4HESE LIMITATIONS HOWEVER DO NOT APPLY WHEN USING THE GRID CONTROLLED TUBES KNOWN AS THE #ONSTANT %FFICIENCY !MPLIFIER OR THE )NDUCTIVE /UTPUT 4UBE AS DISCUSSED LATER IN 3ECTION !NOTHER APPROACH TO SPECTRUM IMPROVEMENT IS TO SHAPE THE RISE AND FALL OF A RECT ANGULAR PULSE 4HIS ATTENUATES THE SPECTRUM OF FREQUENCIES FAR FROM FO WHILE THE FLAT TOPPED PORTION OF THE PULSE RETAINS THE HIGH TRANSMITTER EFFICIENCY FOR MOST OF THE PULSE DURATION 3INCE A RECTANGULAR PULSE HAS THE BEST TRANSMITTER EFFICIENCY BUT HAS HIGH SPECTRAL ENERGY AT FREQUENCIES FAR FROM THE CENTER FREQUENCY WHEREAS A HIGHLY SHAPED PULSE HAS LESS FAR OUT SPECTRAL ENERGY BUT POOR TRANSMITTER EFFICIENCY THE FRACTION OF THE PULSE LENGTH TO BE USED FOR THE SHAPED RISE AND FALL IS A CRUCIAL DECISION !LTHOUGH THE IMPROVEMENT ATTAINABLE IN PRACTICE IS LIMITED BY PHASE MODULATION IN THE TRANSMITTER DURING THE RISE AND FALL SIGNIFICANT IMPROVEMENTS CAN BE OBTAINED )N A LINEAR BEAM TUBE TRANSMITTER WITH PROPERLY SHAPED 2& DRIVE FOR EXAMPLE THE SPECTRUM WIDTH AT D" DOWN CAN USUALLY BE NARROWED BY ABOUT AN ORDER OF MAGNI TUDE AT A COST OF ABOUT D" IN TRANSMITTER EFFICIENCY !MPLIFIER CHAIN RADAR SYSTEMS WHETHER TUBE OR SOLID STATE OFTEN USE SOME SHAPING OF THE EDGES OF THE TRANSMITTED 2& PULSE TO REDUCE THE 2& SPECTRUM WIDTH 4HIS CAN BE DONE BY SIMPLY SLOWING THE RISE AND FALL TIMES OF THE EXCITER SIGNAL TO THE TRANSMITTER AND THIS APPROACH GENERALLY HAS BEEN ADEQUATE TO SATISFY -ILITARY 3TANDARDS AND RELATED SYSTEM REQUIREMENTS 3PECTRAL .OISE IN $OPPLER 2ADARS 4HE DOPPLER FREQUENCY SHIFT IS WIDELY USED TO DETECT MOVING TARGET ECHO SIGNALS IN THE PRESENCE OF LARGE CLUTTER ECHOES (OWEVER IF THE RADAR TRANSMITTER GENERATES NOISE OR ITS PULSE WAVEFORM HAS SIGNIFICANT SPEC TRAL ENERGY AT THE DOPPLER FREQUENCIES EXPECTED FROM MOVING TARGETS THIS UNWANTED NOISE OR SPECTRA WILL DEGRADE THE DETECTION OF DESIRED TARGETS 4HE TRANSMITTER NOISE IS REFLECTED BACK FROM THE CLUTTER AND ENTERS THE RECEIVER AND IS SOMETIMES CALLED hTRANSMITTED CLUTTERv 3OME TYPES OF MICROWAVE TUBES ARE MORE OF A PROBLEM THAN OTHERS %XTRANEOUS NOISE IN A MICROWAVE AMPLIFIER TUBE AT THE FREQUENCIES EXPECTED FROM DOPPLER SHIFTED TARGET ECHOES CAN BE PRODUCED BY ION OSCILLATIONS !CCORDING TO ! ! !CKER hTHESE ARE PERIODIC INSTABILITIES THAT CAN OCCUR IN THE ELECTRON BEAM AT VIDEO FREQUENCIES RESULTING IN SIGNALS OTHER THAN THE CARRIER FREQUENCY CAUSING SEVERE PROBLEMS TO DOPPLER RADAR PERFORMANCEv !CKER ALSO STATES THAT ION OSCILLATIONS REQUIRE A FINITE TIME TO DEVELOP SO THAT IF A TUBE IS OPERATED WITH LESS THAN A §S PULSE WIDTH ION NOISE IS USUALLY NOT OF CONCERN !DVANCES IN DIGITAL TECHNOLOGY HAVE ALLOWED A METHOD TO REDUCE INTRA PULSE TRANS MITTER NOISE AND POWER SUPPLY INSTABILITIES THAT AFFECT RADAR PERFORMANCE BY THE PRESENCE OF STRONG CLUTTER ECHOES 4HE TECHNIQUE KNOWN AS 4RANSMITTER .OISE #OMPENSATION 4.# CAPTURES AND PROCESSES AN ACCURATE REPLICA OF EACH TRANSMITTED PULSE "Y MEANS OF PULSE TO PULSE COMPARISONS THE MEASURED TRANSMITTER ERRORS ARE USED TO DERIVE A DIGITAL FILTER THAT COMPENSATES FOR THE TRANSMITTER NOISE THAT ARRIVES IN THE RECEIVER DIGITAL SIGNAL PROCESSOR 4.# COMPENSATES FOR INTRA PULSE TRANSMITTER NOISE AS WELL AS POWER SUPPLY INSTABILITIES !LTHOUGH 4.# WORKS ONLY IN A SINGLE UNAMBIGUOUS RANGE INTERVAL IT IS SAID THAT IT SHOULD BE ABLE TO OPERATE WITH SOME MEDIUM 02& RADARS IF SIGNIFICANT CLUTTER IS NOT LIKELY TO EXTEND OVER MORE THAN ONE 02& INTERVAL
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!N EXPERIMENTAL IMPLEMENTATION USING DATA COLLECTED ON AN OPERATIONAL RADAR WITH A #&! TRANSMITTER SHOWED THAT hTHE 4.# TECHNIQUE CAN IMPROVE RADAR DETECTION OF TARGETS IN CLUTTER BY D" OR MOREv
£ä°ÇÊ , " /," Ê/1 4HE GRID CONTROLLED TUBE IS A MODERN VERSION OF THE CLASSICAL TRIODE OR TETRODE VACUUM TUBE THAT DATES BACK TO THE EARLY YEARS OF THE TH CENTURY 4HESE DEVICES EMPLOY A CATHODE TO GENERATE ELECTRONS ONE FOR A TRIODE OR TWO FOR A TETRODE CONTROL GRIDS AND AN ANODE TO COLLECT THE ELECTRONS ! SMALL VOLTAGE APPLIED TO THE CONTROL GRID ACTS TO CONTROL THE NUMBER OF ELECTRONS TRAVELING FROM CATHODE TO ANODE 4HE PROCESS BY WHICH THE ELECTRON DENSITY OF THE ELECTRON STREAM IS MODULATED BY THE SIGNAL ON THE CONTROL GRID TO PRODUCE AMPLIFICATION IS CALLED DENSITY MODULATION )N THE LATTER HALF OF THE TH CENTURY GRID CONTROLLED TUBES WERE SUCCESSFULLY EMPLOYED IN SUCH IMPORTANT RADAR APPLICATIONS AS (& OVER THE HORIZON RADAR 6(& AND 5(& AIRCRAFT SURVEILLANCE RADARS AND SATELLITE SURVEILLANCE RADARS 'RID CONTROLLED TUBES ARE CAPABLE OF HIGH POWER WIDE BANDWIDTH GOOD EFFICIENCY AND INHERENT LONG LIFE BUT THEY ARE OF LOW OR MODERATE GAIN 4HEIR CHIEF LIMITATION IS THAT THEY ARE NOT CAPABLE OF OPERATING AT HIGHER FREQUEN CIES BUT THEY ARE CAPABLE UP TO FREQUENCIES APPROACHING '(Z 'RID CONTROLLED TUBES HAVE BEEN OPERATED AT 5(& AND HIGHER FREQUENCIES BY USING MICROWAVE TECHNIQUES IN THEIR CONSTRUCTION AS WAS DONE IN THE #OAXITRON 4HEY CAN ALSO BE MADE TO OPERATE WITH CONSTANT EFFICIENCY WHEN SHAPING OF THE PULSE AMPLITUDE IS USED TO REDUCE INTERFERENCE CAUSED BY ITS FAR OUT SPECTRUM SOMETHING NOT AS PRACTICAL TO DO WITH OTHER TYPES OF MICROWAVE TUBES #OAXITRON 4HE PERFORMANCE OF CONVENTIONAL GRID CONTROL TUBES AT THE HIGHER FRE QUENCIES IS LIMITED BY THE TIME IT TAKES FOR THE ELECTRONS TO TRANSIT FROM THE CATHODE TO THE ANODE OF THE TUBE 4HIS TRANSIT TIME MUST BE SMALL COMPARED TO THE PERIOD OF THE 2& SIGNAL TO BE AMPLIFIED 4O MINIMIZE THE UNDESIRED TRANSIT TIME EFFECTS THE COMPLETE 2& INPUT AND OUTPUT CIRCUIT AND THE ELECTRICAL INTERACTION SYSTEM CAN BE PLACED WITHIN THE VACUUM ENVELOPE 3UCH A GRID CONTROLLED TUBE IS CALLED A #OAXITRON )N ONE EMBODI MENT OF THE #OAXITRON THE ELECTRON INTERACTION STRUCTURE CONSISTED OF A CYLINDRICAL ARRAY OF ESSENTIALLY INDEPENDENT GROUNDED GRID UNIT TRIODES 4HE SO CALLED !& #OAXITRON DESCRIBED IN 6INGST ET AL OPERATED OVER A FREQUENCY RANGE FROM TO -(Z WITH A PEAK POWER OF -7 A PULSE WIDTH OF §S A DUTY CYCLE OF AN AVERAGE POWER OF JUST UNDER K7 AND A PLATE EFFICIENCY OF 4HE #OAXITRON HAS BEEN SUCCESSFULLY EMPLOYED FOR 5(& RADARS INCLUDING AIRBORNE #ONSTANT %FFICIENCY !MPLIFIER #%! )T HAS BEEN SAID THAT hA CONSTANT EFFICIENCY AMPLIFIER HAS BEEN A GOAL FOR TRANSMITTER ENGINEERS EVER SINCE ,EE $E&OREST AND !MBROSE &LEMING INVENTED THE FIRST ELECTRONIC AMPLIFIERSv 4HIS GOAL SEEMS TO HAVE BEEN ACHIEVED BY THE #%! GRID CONTROLLED TUBE )T IS CUSTOMARY TO THINK OF THE SHAPE OF A CONVENTIONAL RADAR PULSE AS BEING RECTANGULAR )T IS SELDOM HOWEVER PERFECTLY RECTANGULAR WITH VERY SHORT RISE AND FALL TIMES BECAUSE SUCH A WAVEFORM HAS A VERY LARGE BANDWIDTH AS ONE CAN OBSERVE FROM ITS &OURIER TRANSFORM %VEN IF A LARGE BANDWIDTH WERE AVAILABLE TO SUPPORT A
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RECTANGULAR PULSE A LARGE BANDWIDTH WOULD LIKELY CAUSE INTERFERENCE TO OTHER RADARS AND OTHER ELECTROMAGNETIC SYSTEMS &OR THIS REASON GOVERNMENT FREQUENCY ALLOCATION AGENCIES USUALLY REQUIRE THAT THE FREQUENCY SPECTRUM FROM A RADAR NOT CONTAIN LARGE ENERGY AT OTHER FREQUENCIES 4HIS IS BECOMING MORE IMPORTANT AS THE OCCUPANCY OF THE ELECTROMAGNETIC SPECTRUM IS INCREASINGLY CROWDED WITH TRANSMITTERS 4HE CLASSICAL WAY TO REDUCE THE FAR OUT SPECTRUM FROM A RADAR TRANSMITTER IS TO SHAPE OR TAPER ITS WAVEFORM SUCH AS BY USING A TRAPEZOIDAL SHAPE A GAUSSIAN LIKE PULSE SHAPE A TRUNCATED GAUSSIAN PERHAPS A COSINE ON A PEDESTAL OR OTHER TYPE OF NONRECTANGULAR SHAPE 4HE PROBLEM WITH USING CONVENTIONAL TRANSMITTERS SUCH AS DISCUSSED IN THIS CHAPTER IS THAT WHEN USING A SHAPED WAVEFORM SOME LOSS IN EFFICIENCY RESULTS 4HUS IT IS SELDOM THAT A RADAR DESIGNER WOULD WANT TO USE A HIGHLY SHAPED PULSE WAVEFORM IN ORDER TO REDUCE THE SPECTRUM RADIATED OUTSIDE OF THE RADARS NORMAL OPERATING SIGNAL BANDWIDTH 4HE #%! HOWEVER IS AN 2& POWER SOURCE THAT DOES NOT HAVE ITS EFFICIENCY DECREASED WHEN A NONRECTANGULAR OR SHAPED WAVEFORM IS USED 4HE #%! HAS BEEN WIDELY USED FOR COMMERCIAL 46 TRANSMITTERS THAT HAVE HIGHLY MODULATED NONCONSTANT AMPLITUDE WAVEFORMS 4HE #%! IS BASED ON A GRID CONTROLLED TUBE KNOWN AS AN )NDUCTIVE /UTPUT 4UBE OR )/4 4HE #%! IS SIMILAR TO SOMETHING CALLED A +LYSTRODE EXCEPT THAT THE #%! EMPLOYS THE )/4 WITH A MULTISTAGE DEPRESSED COLLECTOR SIMILAR TO THAT USED IN KLYS TRONS AND 474S )N THE )/4 THE WIRE GRID OF A GRID CONTROLLED TUBE IS REPLACED WITH AN APERTURE THAT DOES NOT INTERCEPT THE ELECTRONS AND IT HAS A COAXIAL MAGNETIC FIELD THAT CONFINES THE ELECTRON STREAM AS IN A KLYSTRON OR A 474 !LTHOUGH AN 2& CAVITY IS USED IN AN )/4 THE BEAM IS DENSITY MODULATED OR BUNCHED WITH A GRID SIMILAR TO HOW IT IS MODULATED IN A TRIODE OR TETRODE GRID CONTROLLED TUBE 4HIS MAKES IT SMALLER AND LIGHTER THAN A COMPARABLE KLYSTRON 4HE DENSITY MODULATED ELECTRONS THUS FORM BUNCHES AND 2& ENERGY IS EXTRACTED BY PASSING THE BEAM THROUGH THE RESONANT CAVITY 4HE #%! HAS BEEN WIDELY USED FOR 5(& 46 TRANSMITTERS A HIGHLY COMPETITIVE INDUSTRY CONCERNED WITH COST )T HAS BEEN SAID THAT IN 5(& 46 THE USE OF A #%! REDUCES THE REQUIRED PRIME POWER BY ONE HALF COMPARED TO A CONVENTIONAL TUBE TRANSMITTER AND BY ONE THIRD OF THE PRIME POWER OF A SILICON CARBIDE SOLID STATE TRANSMITTER 4HE #%! ACHIEVES THESE EFFICIENCIES SINCE THERE IS NO LOSS OF EFFI CIENCY WHEN USING SHAPED PULSE WAVEFORMS AS THERE IS WITH OTHER MICROWAVE TUBES 4HIS IS AN IMPORTANT REASON FOR ITS USE FOR 5(& 46 WITH ITS TIME VARYING AMPLITUDE WAVEFORM )T ALSO SHOULD BE AN ADVANTAGE FOR RADAR APPLICATIONS THAT REQUIRE SHAPED WAVEFORMS AT FREQUENCIES UP TO -(Z WHEN IT IS REQUIRED TO REDUCE THE FAR OUT SPECTRAL ENERGY ! #%! SUCH AS MANUFACTURED BY , #OMMUNICATIONS CAN OPERATE WITHIN THE 5(& 46 BAND FROM TO -(Z WITH AN -(Z BANDWIDTH THE SPECTRAL WIDTH OF A 46 CHANNEL K7 PEAK POWER AT EFFICIENCY AND AN AVERAGE POWER OF K7 OR GREATER 4HE SINGLE INPUT CAVITY CAN BE MADE TO TUNE OVER THE ENTIRE BAND WITH LOW 6372 4HUS THE CONSTANT EFFICIENCY AMPLIFIER IS A GRID CONTROLLED TUBE OPERATING AS CLASS !" THAT CONSISTS OF AN INDUCTIVE OUTPUT TUBE WITH A MULTISTAGE DEPRESSED COLLECTOR )T IS A LINEAR AMPLIFIER WHOSE PRIME POWER CAN BE PROPORTIONAL TO THE OUTPUT POWER PRO VIDING CONSTANT EFFICIENCY OVER A WIDE RANGE OF OUTPUT POWERS 4HE #%! SEEMS TO BE THE PREFERRED TUBE FOR 5(& 46 TRANSMITTERS RATHER THAN OTHER TYPES OF GRID CONTROLLED TUBES SOLID STATE OR KLYSTRONS )T WOULD SEEM THAT THE #%! OUGHT TO BE OF INTEREST FOR RADAR APPLICATIONS AT FREQUENCIES AS HIGH AS -(Z WHEN HIGHLY SHAPED PULSES NEED TO BE USED
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!PPLICATION OF 'RID #ONTROLLED 4UBES 4HERE HAS BEEN IMPORTANT APPLICATION OF THE GRID CONTROLLED TUBE FOR RADARS IN THE PAST AT (& 6(& AND 5(& )T IS STILL OF VALUE FOR APPLICATIONS IN THESE FREQUENCY REGIONS AND SHOULD BE CONSIDERED AS A CANDIDATE WHEN DESIGNING A RADAR TO OPERATE AT THE LOWER FREQUENCIES 4HE CONSTANT EFFICIENCY AMPLI FIER SHOULD BE OF INTEREST BECAUSE OF ITS HIGHER EFFICIENCY WHEN SHAPED WAVEFORMS ARE NEEDED FOR CONTROL OF THE RADIATED SPECTRUM
£ä°nÊ " 1 /",4HIS SECTION BRIEFLY REVIEWS THE MODULATOR SOMETIMES CALLED THE PULSER WHICH IS THE DEVICE THAT TURNS THE TRANSMITTER TUBE ON AND OFF TO GENERATE THE DESIRED PULSE WAVE FORM 4HOSE DESIRING MORE INFORMATION MIGHT EXAMINE #HAPTER IN , 3IVANS BOOK ON TRANSMITTERS THE CHAPTER BY 4 ! 7EIL IN THE SECOND EDITION OF 2ADAR (ANDBOOK THE #ONFERENCE 2ECORDS OF THE )NTERNATIONAL 0OWER -ODULATOR 3YMPOSIA AND THE #ONFERENCE 0ROCEEDINGS OF THE )%%% 0ULSE 0OWER #ONFERENCES 4HE TYPE OF TUBE DETERMINES TO SOME EXTENT THE TYPE OF MODULATOR ! MODULA TOR BASICALLY CONSISTS OF AN ENERGY STORAGE DEVICE WHICH MAY BE A CAPACITANCE OR A PULSE FORMING NETWORK AND A SWITCH FOR TRIGGERING THE DC PULSE 4HE SWITCH IN THE PAST MIGHT HAVE BEEN A VACUUM TUBE THYRATRON IGNITRON SILICON CONTROLLED RECTIFIER 3#2 REVERSE SWITCHING RECTIFIER SPARK GAP OR MAGNETIC (OWEVER THE SOLID STATE SWITCH SEEMS TO BE THE SWITCHING MECHANISM THAT SHOULD BE CONSIDERED INITIALLY WHEN DESIGNING A TRANSMITTER MODULATOR -ODULATORS CAN BE CLASSED AS EITHER LOW POWER OR HIGH POWER DEPENDING ON HOW THE TUBE IS MODULATED )F THE TUBE HAS A GRID A SMALL AND RELATIVELY INEXPENSIVE TYPE OF MODULATOR CAN BE USED BUT GRIDS USUALLY ARE NOT FEASIBLE WITH HIGH POWER TUBES ! WIDELY USED SWITCHING ELEMENT FOR LOW POWER MODULATORS IS THE -/3&%4 TRANSISTOR ,OW POWER MODULATORS CAN BE USED WITH TUBES THAT EMPLOY A MODULATING ANODE AS DOES THE LINEAR BEAM AMPLIFIER 4HE MODULATING ANODE IN A LINEAR BEAM TUBE IS PART OF THE ELECTRON GUN AND IS SEPARATED FROM THE BODY OF THE TUBE 4HE VOLTAGE OF THE MODULATING ANODE IS VARIED OVER A LARGE RANGE IN ORDER TO VARY THE ELECTRON BEAM CUR RENT BUT THE POWER NEEDED TO DRIVE THE MODULATING ANODE IS SMALL BECAUSE THE CURRENT INTERCEPTED BY THE MODULATING ANODE IS VERY SMALL 6ERY HIGH POWER TUBES CANNOT USE A MODULATING ANODE BECAUSE THE CONTROL ELECTRODE MIGHT NOT BE ABLE TO HANDLE THE POWER 7HEN THIS OCCURS A HIGH POWER MODULATOR CALLED A CATHODE PULSER MIGHT HAVE TO BE USED TO SWITCH THE TUBE ON AND OFF #ATHODE PULSERS MUST SWITCH THE FULL BEAM VOLTAGE AND CURRENT SIMULTANEOUSLY WHICH INVOLVES HIGH INSTANTANEOUS POWERS 4HEY MUST CONTROL THE FULL BEAM POWER OF THE 2& TUBE EITHER DIRECTLY OR THROUGH A COUPLING CIRCUIT 4HE ENERGY STORAGE DEVICE MIGHT BE MADE UP OF CAPACITORS INDUCTORS OR SOME COMBINATION OF THE TWO AS IN PULSE FORMING NETWORKS 4HE ENERGY IN THE ENERGY STORAGE DEVICE IS DISCHARGED BY A VERY CAPABLE SWITCH 4HE LINE TYPE MODULATOR USES A DELAY LINE OR A PULSE FORMING NETWORK 0&. AS THE ENERGY STORAGE ELEMENT ! SWITCH INITIATES THE DISCHARGE OF THE ENERGY STORED IN THE 0&. 4HE SHAPE AND DURATION OF THE PULSE ARE DETERMINED BY THE PASSIVE ELEMENTS OF THE 0&. 4HE SWITCH HAS NO CONTROL OVER THE PULSE SHAPE OTHER THAN TO INITIATE IT 4HE PULSE ENDS WHEN THE 0&. HAS DISCHARGED SUFFICIENTLY ! DISADVANTAGE OF THIS ACTION IS THAT THE TRAILING EDGE OF THE PULSE IS USUALLY NOT SHARP SINCE IT DEPENDS ON THE DISCHARGE CHARACTERISTICS OF THE 0&. )T HAS BEEN WIDELY USED IN THE PAST FOR MAGNETRON PULSING
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)N AN ACTIVE SWITCH MODULATOR THE SWITCH HAS TO BE TURNED OFF AS WELL AS TURNED ON /RIGINALLY THE SWITCH WAS A VACUUM TUBE AND THE MODULATOR WAS CALLED A HARD TUBE MODULATOR TO DISTINGUISH IT FROM THE GAS TUBE SWITCH OFTEN USED IN A LINE TYPE MODULATOR 3INCE OTHER THAN VACUUM TUBES CAN BE USED AS THE SWITCH IN AN ACTIVE SWITCH MODULATOR THE hHARD TUBEv DESIGNATION MEANING A VACUUM TUBE MIGHT NOT ALWAYS APPLY 5NLIKE THE LINE TYPE MODULATOR THE SWITCH IN THE ACTIVE SWITCH MODULATOR CONTROLS BOTH THE BEGINNING AND END OF THE PULSE 3INCE THE ENERGY STORAGE DEVICE IS A CAPACITOR THE PULSE CAN DROOP SOMETHING THAT CAN BE PREVENTED BY EXTRACTING ONLY A SMALL FRACTION OF THE STORED ENERGY FROM THE CAPACITOR 4HIS REQUIRES A LARGE CAPACITANCE WHICH MAY BE OBTAINED WITH A COLLECTION OF CAPACITORS CALLED A CAPACITOR BANK 4HE ACTIVE SWITCH MODULATOR PERMITS GREATER FLEXIBILITY AND PRECISION THAN THE LINE TYPE MODULATOR )T CAN PROVIDE EXCELLENT PULSE SHAPE VARYING PULSE DURATIONS AND PULSE REPETITION FREQUEN CIES INCLUDING MIXED PULSE LENGTHS AND BURSTS OF PULSES WITH CLOSE PULSE SPACINGS -ICROWAVE TUBES AND THEIR HIGH VOLTAGE SWITCHES CAN SOMETIMES PRODUCE AN UNWANTED ARC DISCHARGE THAT EFFECTIVELY PLACES A SHORT CIRCUIT ACROSS THE POWER SUP PLY ANDOR MODULATOR DELIVERING POWER TO THE TUBE 3INCE * OF ENERGY CAN USUALLY CAUSE DAMAGE TO AN 2& TUBE OR THE SWITCHING DEVICE AND SINCE THE CAPACITOR BANK FOR AN ACTIVE SWITCH MODULATOR MUST OFTEN STORE FAR MORE THAN * TO PREVENT EXCES SIVE DROOP SOME MEANS MUST BE PROVIDED TO DIVERT THE STORED ENERGY WHEN AN ARC DISCHARGE OCCURS 3UCH A DEVICE IS THE CROWBAR SO CALLED BECAUSE IT IS EQUIVALENT TO PLACING A HEAVY CONDUCTOR LIKE A CROWBAR DIRECTLY ACROSS THE POWER SUPPLY TO DIVERT THE ENERGY AND THUS PREVENT THE ENERGY FROM DISCHARGING THROUGH THE TUBE AND CAUS ING SERIOUS DAMAGE ! CROWBAR IS THEREFORE NEEDED FOR A HIGH POWER ACTIVE SWITCH MODULATOR BECAUSE OF THE LARGE AMOUNT OF ENERGY STORED IN ITS CAPACITOR BANK /N THE OTHER HAND CROWBARS ARE NOT USUALLY NEEDED WITH LINE TYPE MODULATORS WHICH STORE LESS ENERGY IN THEIR PULSE FORMING NETWORK #ERTAIN CROSSED FIELD AMPLIFIERS CAN BE PULSED BY MEANS OF A CONTROL ELECTRODE LOCATED IN THE TUBES DRIFT REGION WITHOUT A SEPARATE FULL POWER PULSE MODULATOR 4HIS IS CALLED DC OPERATION %VEN THOUGH DC OPERATION AVOIDS A HIGH POWER MODULA TOR IT HAS SELDOM BEEN USED BECAUSE IT REQUIRES A MUCH LARGER CAPACITOR BANK TO LIMIT DROOP AN ARC IN THE TUBE REQUIRES A CROWBAR THAT INTERRUPTS OPERATION FOR A FEW SECONDS INSTEAD OF ONLY FOR A SINGLE PULSE AND THE ADJACENT RADARS MIGHT INJECT ENOUGH 2& POWER INTO THE RADAR ANTENNA AND BACK TO THE TRANSMITTER TO TURN ON A DC OPERATED #&! AT THE WRONG TIMES 4HERE HAS BEEN AT LEAST ONE EXAMPLE IN THE PAST WHERE A MAJOR RADAR SYSTEM ORIGINALLY DESIGNED WITH #&!S BASED ON DC OPERATION HAD TO HAVE ITS DC OPERATED #&!S REPLACED DURING THE MIDDLE OF ITS DEVELOPMENT WITH #&!S THAT USED CONVENTIONAL PULSE MODULATORS !T THE BEGINNING OF THE TH CENTURY THE SOLID STATE MODULATOR WAS DEVELOPED AND BEGAN TO BE USED FOR RADAR TRANSMITTERS AS EITHER CATHODE PULSED OR MODULATING ANODE PULSED MODULATORS AS WELL AS GRID PULSED 3OLID STATE MODULATORS OFFER IMPROVED TRANS MITTER PERFORMANCE BY ALLOWING A WIDE VARIATION IN PARAMETERS PULSE WIDTH PULSE REPETITION FREQUENCY PULSE AGILITY AND PULSE TO PULSE CONSISTENCY 4HEY ALSO PROVIDE COST SAVINGS THAT RESULT FROM THE INHERENT RELIABILITY OF THESE SWITCH MODULES COMPARED TO CONVENTIONAL SWITCH TUBES AND THE ELIMINATION OF NUMEROUS AUXILIARY COMPONENTS NEEDED FOR THE OPERATION OF SWITCH TUBES ,OWER OPERATING COSTS AND SMALLER COOL ING REQUIREMENTS OCCUR BECAUSE OF THEIR HIGHER CONVERSION EFFICIENCY 4HEY ARE ALSO SAID TO HAVE HIGHER RELIABILITY WITH LONGER COMPONENT LIFE 4HE ABILITY OF THE SOLID STATE SWITCH TO OPEN QUICKLY LESS THAN ONE MICROSECOND WHEN A FAULT IS DETECTED ELIMINATES THE NEED FOR A CROWBAR 4HE ENERGY STORAGE DEVICE DOES NOT DISCHARGE DURING AN ARC SO WHEN THE FAULT HAS CLEARED THE TRANSMITTER CAN RESUME OPERATION IN MICROSECONDS
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! SOLID STATE CATHODE MODULATOR CAN PROVIDE PULSE WIDTHS VARYING FROM NS TO hDCv ON A PULSE TO PULSE BASIS AND CAN SUPPORT PULSE REPETITION FREQUENCIES UP TO K(Z 4HE HIGH VOLTAGE SOLID STATE SWITCHES ARE BUILT FROM MODULES THAT MIGHT CONTAIN FROM TO INDIVIDUAL TRANSISTORS CONNECTED IN SERIES TO PROVIDE THE REQUIRED TRANSMITTER CATHODE VOLTAGE 2ISE TIMES CAN BE AS LOW AS NS
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Ê/"Ê1- ¶ 4HERE IS NO GOOD SIMPLE ANSWER TO THIS QUESTION BUT IN THIS SECTION WE SHALL ATTEMPT TO DISCUSS SOME OF THE VARIOUS ISSUES THAT MIGHT BE INVOLVED 4HIS CHAPTER HAS BRIEFLY DESCRIBED THE VARIOUS VACUUM TUBES THAT HAVE BEEN USED OR CONSIDERED FOR RADAR APPLICATIONS AND THE NEXT CHAPTER DISCUSSES THE SOLID STATE TRANSMIT TER WHICH HAS ALSO BEEN WIDELY USED IN RADAR ! QUESTION THAT NATURALLY ARISES IS WHICH 2& POWER SOURCE SHOULD BE USED FOR SOME PARTICULAR RADAR APPLICATION 2ADAR SYSTEM DESIGN USUALLY INVOLVES MAKING CHOICES AMONG THE VARIOUS POSSIBILITIES AVAILABLE 7HEN TRYING TO DETERMINE WHICH 2& POWER SOURCE TO USE A CHOICE CAN BE MADE BY DOING A SEPARATE SYSTEM DESIGN WITH EACH 2& POWER SOURCE THAT SEEMS PROMISING 4HE DECISION AS TO WHICH TO USE CAN BE BASED ON HOW WELL EACH SYSTEM DESIGN PERFORMS THE DESIRED TASK ACCORDING TO SOME PRE ESTABLISHED CRITERIA 4HIS UNFORTUNATELY IS SELDOM DONE )T IS SUSPECTED THAT SOMETIMES THE DECISION AS TO WHICH 2& POWER SOURCE TO USE IS DETER MINED BY WHAT THE RADAR SYSTEM DESIGNER THINKS THE BUYER OR CUSTOMER OF THE RADAR DESIRES 3OMETIMES THE BUYER WILL ACTUALLY SPECIFY THE TYPE OF TRANSMITTER TO BE DELIVERED -ANUFACTURING A PRODUCT BASED ON WHAT THE BUYER THINKS HE OR SHE WANTS MAY BE A GOOD MARKETING STRATEGY FOR MANY PRODUCTS BUT IN SOMETHING LIKE A RADAR IT MIGHT BE BETTER FOR A CUSTOMER TO CLEARLY SPECIFY WHAT PERFORMANCE IS WANTED AND THEN LEAVE THE DECISION AS TO WHAT 2& POWER SOURCE SHOULD BE USED TO THE RADAR SYSTEM DESIGNER )T IS USUALLY BETTER IF THE RADAR DESIGN CAN BE DETERMINED BY THE RADAR SYSTEM DESIGNER AND NOT BY THE MANUFACTURERS MARKETING DEPARTMENT 4HE GOALS OF THE RADAR DESIGNER AND THE MARKET ING DEPARTMENT ARE NOT ALWAYS THE SAME )T IS APPRECIATED HOWEVER THAT SOMETIMES THE MARKETING MANAGERS OPINION HAS TO PREVAIL IF THE COMPANY IS TO REMAIN IN BUSINESS ! NUMBER OF DIFFERENT 2& POWER SOURCES HAVE BEEN CONSIDERED THAT AT ONE TIME OR OTHER HAVE BEEN EMPLOYED IN RADAR .OT ALL MIGHT BE POPULAR OR DESIRED AT SOME PARTIC ULAR TIME BUT MOST SHOULD BE CONSIDERED EVEN IF BRIEFLY BY THE RADAR SYSTEM DESIGNER WHEN TRYING TO DETERMINE A NEW RADAR SYSTEM DESIGN OR AN UPGRADE OF SOME EXISTING SYSTEM /PINIONS ABOUT THE UTILITY OF THE VARIOUS VACUUM TUBE TRANSMITTERS MENTIONED HERE WILL BE BRIEFLY GIVEN NEXT WITH THE SUGGESTION TO THE READER TO KEEP IN MIND THAT CIRCUMSTANCES CAN CHANGE AND THESE OPINIONS CAN CHANGE AS WELL 4HESE OPINIONS ARE NOT hWRITTEN IN STONE v AND ARE NOT LIKELY TO BE UNIVERSALLY AGREED TO BY ALL THOSE WHO WORK IN RADAR "UT THAT IS THE NATURE OF ANY ENGINEERING ENDEAVOR "RIEF /PINIONS !BOUT THE 5TILITY OF 6ARIOUS 2ADAR 6ACUUM 4UBES 4HE TYPES OF 2& POWER SOURCES ARE MENTIONED BELOW IN NO PARTICULAR ORDER 'RID #ONTROLLED 4UBE !LTHOUGH SOME MIGHT THINK THESE SHOULD HAVE DISAPPEARED ALONG WITH THE OLD RADIO VACUUM TUBE THERE HAVE BEEN MANY (& 6(& AND 5(& RADARS THAT SUCCESSFULLY OPERATED WITH GRID CONTROL TUBES /FTEN WITH SUCH RADARS IT WOULD COST MORE TO REPLACE THEM WITH SOLID STATE TRANSMITTERS AND THERE MIGHT BE LITTLE GAINED BY DOING SO 4HE GRID CONTROLLED TUBE KNOWN AS THE CONSTANT EFFICIENCY AMPLIFIER #%!
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AND ITS PREDECESSORS THE )/4 AND THE +LYSTRODE ARE THE ONLY 2& POWER SOURCES THAT CAN OPERATE EFFICIENTLY WHEN AMPLITUDE SHAPED WAVEFORMS ARE DESIRED FOR MINIMIZING OUT OF BAND INTERFERENCE TO OTHER RADARS 4HUS THE #%! PROBABLY SHOULD BE A CANDIDATE WHEN CONSIDERING ANY NEW 5(& RADAR SYSTEM AS WELL AS RADARS AT LOWER FREQUENCIES ESPECIALLY IF MUTUAL INTERFERENCE IS A POTENTIAL PROBLEM -AGNETRON )T WAS MENTIONED THAT THE MAGNETRON WAS WHAT MADE MICROWAVE RADAR POSSIBLE IN THE S 4HE MAGNETRON IS STILL A VALID CANDIDATE FOR SMALL NON DOPPLER RADARS SUCH AS CIVIL MARINE RADARS ALTHOUGH SUCH RADARS ALSO HAVE BEEN MANU FACTURED WITH SOLID STATE TRANSMITTERS )T IS NOT LIKELY THAT MAGNETRONS WILL BE USED IN HIGH PERFORMANCE RADARS ESPECIALLY THOSE THAT REQUIRE AVERAGE POWERS MORE THAN ONE OR TWO KILOWATTS OR WHERE -4) IMPROVEMENT FACTORS HAVE TO BE GREATER THAN TO D" &OR EXAMPLE DURING THE PROCUREMENT OF THE .EXRAD DOPPLER WEATHER RADAR IN THE MID S THE MAGNETRON WAS CONSIDERED BUT IT COULD NOT MEET THE CLUTTER CAN CELLATION SPECIFICATIONS WHICH IS WHY .EXRAD EMPLOYS A KLYSTRON )N THE PAST SOME LONG RANGE !IR 4RAFFIC #ONTROL !IR 2OUTE 3URVEILLANCE 2ADARS USED A MAGNETRON BUT THE KLYSTRON SEEMS TO BE THE PREFERRED CHOICE FOR THIS APPLICATION #ROSSED &IELD !MPLIFIER !LTHOUGH THESE TUBES WERE EMPLOYED FOR SOME MAJOR RADAR APPLICATIONS BECAUSE THEY HAVE GOOD EFFICIENCY REQUIRE RELATIVELY LOW VOLTAGE AND HAVE WIDE BANDWIDTH ABOUT THEY ARE LESS LIKELY TO BE USED BECAUSE THEY ARE NOISY WHICH AFFECTS THEIR DOPPLER PROCESSING PERFORMANCE THEY ARE OF RELATIVELY LOW GAIN WHICH REQUIRES THE TRANSMITTER TO HAVE MULTIPLE STAGES AND BECAUSE THE KLYSTRON IS USUALLY A BETTER OVERALL CHOICE +LYSTRON 4HE ORIGINAL KLYSTRONS EMPLOYED RESONANT CAVITIES THAT RESTRICTED THEIR BANDWIDTH 4HE BANDWIDTH OF A KLYSTRON HOWEVER INCREASES AS ITS POWER INCREASES 2ESONANT CAVITIES WERE LATER REPLACED BY WIDER BAND CIRCUITS WHICH WERE RELATED TO THE TYPE OF CIRCUITS USED IN 474S 3UCH KLYSTRONS ARE KNOWN AS THE #LUSTERED #AVITY +LYSTRON %XTENDED )NTERACTION +LYSTRON AND THE 4WYSTRON 7HEN CONSIDERING A TRANS MITTER FOR HIGH PERFORMANCE RADAR THESE VARIANTS OF THE KLYSTRON ARE LIKELY TO BE HIGHLY FAVORED FOR MANY APPLICATIONS 4HE KLYSTRON HAS GOOD STABILITY AND LOW NOISE SO AS TO ENABLE LARGER -4) IMPROVEMENT FACTORS TO BE OBTAINED WHEN USING THE DOPPLER SHIFT TO DETECT MOVING TARGETS IN CLUTTER !T HIGH POWER HIGH VOLTAGES HAVE TO BE USED AND PROTECTION FROM 8 RAYS GENERATED BY THE HIGH VOLTAGE MUST BE EMPLOYED (OWEVER THE -"+ MULTIPLE BEAM KLYSTRON VERSION OF THE KLYSTRON CAN BE USED TO ACHIEVE HIGH POWER WITH LOWER VOLTAGE 4RAVELING 7AVE 4UBE !S MENTIONED THE 474 AND THE KLYSTRON CAN HAVE COMPA RABLE BANDWIDTHS WHEN THE TUBE PRODUCES HIGH POWER 4HE PERFORMANCE OF A 474 IS SIMILAR TO THAT OF A WIDEBAND KLYSTRON EXCEPT THAT IT MIGHT NOT BE AS STABLE AS THE KLYSTRON AND HAVE SLIGHTLY LESS GAIN 4HE MICROWAVE POWER MODULE -0- WHICH IS A COMBINA TION OF HELICAL 474 AND SOLID STATE DEVICE HAS NOT HAD SIGNIFICANT APPLICATION IN RADAR 'YROTRONS )F VERY HIGH POWER IS NEEDED AT MILLIMETER WAVE FREQUENCIES THE GYROTRON AMPLIFIER OR OSCILLATOR IS THE ONLY 2& POWER SOURCE AVAILABLE &OR LOW POWER RADAR APPLICATIONS AT MILLIMETER WAVES THE %)+ CAN BE USED 3OLID 3TATE !MPLIFIERS FOR 2ADAR 4RANSMITTERS 3OLID STATE TRANSMITTERS AND VACUUM TUBE TRANSMITTERS HAVE SIGNIFICANT DIFFERENCES YET THEY ARE BOTH EMPLOYED
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IN RADAR 3OME OF THESE DIFFERENCES ARE MENTIONED IN 3ECTION OF #HAPTER h3OLID 3TATE 4RANSMITTERSv "RIEFLY PROPONENTS OF SOLID STATE MIGHT SAY THAT THEY DO NOT NEED A HOT CATHODE AS DOES A VACUUM TUBE DO NOT REQUIRE HIGH VOLTAGES OR MAGNETS DO NOT PRODUCE 8 RAY RADIATIONS AS SOME VACUUM TUBES DO HAVE hGRACEFUL DEGRADATION v AND THAT MAINTAINABILITY IS ITS KEY ASSET /N THE OTHER HAND PROPONENTS OF VACUUM TUBES MIGHT SAY THAT RADARS USING SOLID STATE TRANSMITTERS HAVE LIMITED PEAK POWER AND THUS NEED TO OPERATE WITH A LONG PULSE AND A HIGH DUTY CYCLE WHICH REQUIRE THE USE OF PULSE COMPRESSION 4HE LONG PULSE CAN MASK OR ECLIPSE TARGET ECHOES AT SHORT RANGE SO THAT AN ADDITIONAL SHORT PULSE TRANSMISSION IS NEEDED TO UNMASK THE ECLIPSED ECHOES AT SHORT RANGES 7HEN 3ENSITIVITY 4IME #ONTROL WHICH HAS A VARYING RECEIVER GAIN WITH RANGE IS USED WITH A LONG PULSE AND PULSE COMPRESSION DISTORTION CAN RESULT IN THE COMPRESSED PULSE )T HAS ALSO BEEN SAID THAT SOLID STATE TRANSMITTERS ARE OFTEN LESS EFFICIENT THEY MIGHT BE HEAVIER AND THEIR COST MIGHT BE GREATER THAN AN EQUIVALENT VACUUM TUBE RADAR SYSTEM 4HE ABOVE HAVE ALL BEEN SAID AT ONE TIME OR ANOTHER BUT THERE IS NOT UNIVERSAL AGREEMENT ABOUT THE IMPORTANCE OF THESE CHARACTERISTICS FOR ALL RADAR APPLICATIONS 4HE RADAR ENGINEER SHOULD NOT SIMPLY COMPARE THE PARTICULAR DIFFERENCES BETWEEN A SOLID STATE TRANSMITTER AND A VACUUM TUBE TRANSMITTER WHEN DETERMINING WHAT TYPE OF 2& POWER SOURCE TO USE IN ANY PARTICULAR APPLICATION 4HE CHOICE BETWEEN THE TWO SHOULD BE MADE BY COMPARING A RADAR SYSTEM DESIGNED TO EFFECTIVELY USE SOLID STATE AND A RADAR SYSTEM DESIGNED TO EFFECTIVELY USE VACUUM TUBES !SSUMING THE SOLID STATE AND VACUUM TUBE RADARS ARE DESIGNED TO PROVIDE IDENTICAL PERFORMANCE FOR THE DESIRED APPLICATION THEN THE CHOICE SHOULD BE BASED ON COMPARING COST SIZE WEIGHT RELIABIL ITY MAINTAINABILITY AND ANY OTHER SYSTEM REQUIREMENT THAT IS IMPORTANT FOR DECISION MAKING 5NFORTUNATELY THIS IS NOT ALWAYS DONE "UYERS OF RADARS SHOULD BE ENCOUR AGED NOT TO INSIST THAT THE RADAR DESIGNER USE SOME PARTICULAR TECHNOLOGY BECAUSE IT IS CONSIDERED THE FASHIONABLE THING TO DO AT THE TIME 4HEY MIGHT NOT ALWAYS BE GETTING THE BEST RADAR FOR THE PARTICULAR APPLICATION 4HERE HAVE BEEN AT LEAST THREE WAYS TO APPLY SOLID STATE TRANSMITTERS TO HIGH PERFOR MANCE RADARS AS A REPLACEMENT FOR A VACUUM TUBE TRANSMITTER IN AN ALREADY EXIST ING RADAR AS THE TRANSMITTER FOR A NEW RADAR DESIGN AND AS AN ACTIVE APERTURE PHASED ARRAY RADAR !N EXAMPLE OF REPLACING AN EXISTING VACUUM TUBE TRANSMITTER WITH A SOLID STATE TRANSMITTER IS THE 53 .AVYS !.303 A RELATIVELY MODEST CAPABILITY 5(& RADAR FOR AIR SURVEILLANCE 4HIS RADAR WAS CHOSEN FOR HAVING ITS VACUUM TUBE TRANSMITTER REPLACED WITH A SOLID STATE TRANSMITTER USING TRANSISTOR AMPLIFIERS BECAUSE IT ALREADY USED A LONG PULSE WAVEFORM WITH A HIGH DUTY CYCLE AND PULSE COMPRESSION WHICH IS WHAT SOLID STATE RADARS USUALLY REQUIRE 4HE SOLID STATE TRANSMITTER WAS PUT INTO PRODUC TION AND INSTALLED IN EXISTING RADARS )T DID THE JOB IT WAS SUPPOSED TO DO BUT IT IS NOT OBVIOUS THAT THE SOLID STATE TRANSMITTER HAD A NET ADVANTAGE OVER THE TUBE TRANSMITTER 4HE SOLID STATE TRANSMITTER WAS SUPPOSED TO OCCUPY THE SAME FLOOR SPACE AS THE VACUUM TUBE TRANSMITTER BUT IT OCCUPIED ABOUT THE SAME FLOOR SPACE AS THE ENTIRE !.303 RADAR WHICH USED A VACUUM TUBE !LSO THE SOLID STATE TRANSMITTER COST MORE THAN THE TUBE VERSION /NE HIGHLY SIGNIFICANT ADVANTAGE OF THE SOLID STATE VERSION OF THE 303 HOWEVER WAS THAT IT COULD INCLUDE SPARE SOLID STATE MODULES AS PART OF THE TRANSMITTER ITSELF SO THAT TIME TO REPAIR WAS REDUCED !N EXAMPLE OF THE SECOND APPROACH TO ACHIEVING A SOLID STATE RADAR TRANSMITTER IS THE !32 AIRPORT SURVEILLANCE RADAR )N THE MID S THE !32 AIR SURVEILLANCE RADAR AT 3 BAND WAS DEVELOPED BY .ORTHROP 'RUMMAN THEN 7ESTINGHOUSE FOR USE AT MAJOR AIRPORTS TO CONTROL LOCAL AIR TRAFFIC )T WAS AN EXCELLENT RADAR THAT USED A
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WELL TESTED KLYSTRON AMPLIFIER VACUUM TUBE AND IT WAS INSTALLED THROUGHOUT THE 5NITED 3TATES 4HE SAME TUBE IS USED IN THE .EXRAD DOPPLER WEATHER RADAR (OWEVER IN THE LATE S SOLID STATE TECHNOLOGY HAD ADVANCED SUFFICIENTLY SO THAT .ORTHROP 'RUMMAN DEVELOPED THE !32 ALSO AT 3 BAND USING A SOLID STATE TRANSMITTER )TS OVERALL RADAR PERFORMANCE WAS SIMILAR TO THE !32 BUT IT WAS NOT JUST A REPLACEMENT OF THE TRANSMIT TER BUT A NEW DESIGN TO USE SOLID STATE TRANSMITTERS EFFECTIVELY )T ALSO TOOK IMPORTANT ADVANTAGE OF ADVANCES IN DIGITAL RECEIVERS AND DIGITAL PROCESSING THAT OCCURRED SINCE THE DEVELOPMENT OF THE !32 TO SIGNIFICANTLY IMPROVE WHAT COULD BE ACCOMPLISHED WITH THIS RADAR !S MENTIONED SOLID STATE TRANSMITTERS REQUIRE THE USE OF LONG PULSES 4HE !32 EMPLOYED A §S PULSE DURATION AT A PEAK POWER OF K7 4HIS MEANS THAT TARGETS OUT TO A RANGE OF ABOUT NMI WOULD BE MASKED OR ECLIPSED BY THE LONG PULSE AND MIGHT NOT BE DETECTED 4O DETECT TARGETS AT RANGES MASKED BY THE LONG PULSE A SEC OND SHORT PULSE §S IN DURATION AND AT A DIFFERENT FREQUENCY FROM THE LONG PULSE WAS TRANSMITTED ALMOST IMMEDIATELY AFTER THE LONG PULSE )T DETECTS TARGETS WITHIN THE RANGE FROM NMI OR LESS TO A RANGE OF ABOUT NMI 4HE LONG PULSE EMPLOYS NONLINEAR &- PULSE COMPRESSION WITH A PULSE COMPRESSION RATIO TO ACHIEVE A RANGE RESOLUTION OF LESS THAN NMI AS REQUIRED FOR AN AIR TRAFFIC CONTROL RADAR 4YPICAL TIME SIDELOBES WITH THE NONLINEAR &- WAVEFORM WERE D" BELOW THE PEAK RESPONSE )T MIGHT BE NOTED THAT #OLE ET AL STATE THAT IN ORDER hTO ENSURE CONTINUED AVAILABILITY OF THE POWER TRANSISTORS REQUIRED TO PRODUCE THE POWER AMPLIFIER PANELS .ORTHROP 'RUMMAN HAS DEVELOPED AN IN HOUSE MANUFACTURING CAPABILITY FOR HIGH POWER 3 BAND TRANSISTORSv 4HE THIRD APPROACH TO EMPLOYING SOLID STATE TRANSMITTERS IS THE ACTIVE APERTURE PHASED ARRAY RADAR !T EACH ELEMENT OF A PHASED ARRAY RADAR ANTENNA IS A SOLID STATE MODULE KNOWN AS A 42 MODULE THAT CONTAINS A TRANSMITTER RECEIVER AND DUPLEXER 4HE VACUUM TUBE IS NOT USUALLY COMPETITIVE FOR THIS APPLICATION )N #HAPTER h-ULTIFUNCTIONAL 2ADAR 3YSTEMS FOR &IGHTER !IRCRAFT v THE ACTIVE APERTURE RADAR IS CALLED AN !CTIVE %LECTRONICALLY 3CANNED !NTENNA !%3! 4HE SUBSECTION ENTITLED h!CTIVE %LECTRONIC 3CANNED !RRAY !%3! v IN 3ECTION DESCRIBES QUITE WELL THE MILITARY AIRBORNE APPLICATION OF SOLID STATE RADAR AND ENUMERATES ITS ADVANTAGES AND WHY IT IS IMPORTANT 4HERE IT IS STATED THAT hONE OF THE PRINCIPAL ADVANTAGES OF AN !%3! IS THE ABILITY TO MANAGE BOTH POWER AND SPATIAL COVERAGE ON A SHORT TERM BASIS S OF MS v )T IS ALSO SAID THAT hBANDWIDTH OF SEVERAL '(Z ON TRANSMITv IS REQUIRED AND THIS IS WITHIN THE CAPABILITY OF SOLID STATE TRANSMITTERS 4HE READER IS REFERRED TO 3ECTION #HAPTER AND 3ECTION FOR FURTHER INFORMATION ABOUT THIS IMPORTANT APPLICATION OF SOLID STATE !LTHOUGH ANY OF THE 2& POWER SOURCES MENTIONED HERE COULD BE USED IN FUTURE RADAR SYSTEMS IT SEEMS LIKELY THAT THE LINEAR BEAM AMPLIFIER PARTICULARLY ONE OF THE VARIANTS OF THE KLYSTRON MIGHT BE THE FIRST 2& POWER SOURCE TO CONSIDER FOR A HIGH PERFORMANCE MICROWAVE RADAR THAT EMPLOYS A MECHANICALLY STEERED ANTENNA OR A CON VENTIONAL PHASED ARRAY RADAR THAT DOES NOT EMPLOY THE ACTIVE APERTURE &OR ACTIVE APERTURE PHASED ARRAY RADARS IT IS LIKELY THAT THE SOLID STATE TRANSISTOR AMPLIFIER WILL BE THE CHOICE
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#HAPTER
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££°£Ê /," 1 /" &OR COMMERCIAL APPLICATIONS THE TRANSISTOR HAS ALL BUT REPLACED VACUUM TUBE TECHNOL OGY IN TRANSMITTERS OPERATING AT 6(& AND BELOW 3INCE THE S THE POWER OUTPUT CAPABILITY AMONG VARIOUS SOLID STATE TECHNOLOGIES HAS INCREASED TO THE POINT WHERE THEY ARE ACTIVELY PURSUED AS REPLACEMENTS FOR SOME VACUUM ELECTRONICS IN RADAR TRANSMITTERS THIS IS NOT HOWEVER A UNIVERSALLY ATTRACTIVE SOLUTION 4HE TRANSITION FROM HIGH POWER KLYSTRONS TRAVELING WAVE TUBES 474S CROSSED FIELD AMPLIFIERS #&!S AND MAGNE TRONS TO SOLID STATE ELECTRONICS HAS ACTUALLY BEEN VERY GRADUAL BECAUSE THE POWER OUTPUT OF INDIVIDUAL SOLID STATE DEVICES IS QUITE LIMITED COMPARED TO TYPICAL RADAR REQUIREMENTS .EVERTHELESS TRANSMITTER DESIGNERS HAVE LEARNED THAT THE REQUIRED HIGHER POWER LEVELS FOR RADAR TRANSMITTERS CAN BE ACHIEVED WITH A SOLID STATE TECHNOLOGY BECAUSE TRANSIS TORS AND TRANSISTOR AMPLIFIER MODULES CAN BE READILY COMBINED IN PARALLEL TO ACHIEVE A COMPOSITE HIGHER EQUIVALENT POWER OUTPUT !S DEPICTED IN &IGURE THIS DESIGN ATTRIBUTE HELPS TO EXTEND THE SOLID STATE PERFORMANCE ENVELOPE WELL INTO THE REGION THAT HAD PREVIOUSLY BEEN DOMINATED BY ONLY VACUUM ELECTRONICS )T IS NOT THE INTENT OF THIS CHAPTER TO DELINEATE THE RELATIVE MERITS OF THESE SOMETIMES COMPETING TECHNOLOGIES BUT RATHER TO DESCRIBE THE LIMITS DESIGN PRACTICES AND CHARACTERISTICS OF THE SOLID STATE TECHNOLOGY FOR USE IN THE COMMON RADAR FREQUENCY RANGES 4HE ADVANTAGES OF SOLID STATE TECHNOLOGIES WILL BE DESCRIBED SOME OF THE KEY SEMICONDUCTOR TECHNOLOGIES AND DEVICES WILL BE DISCUSSED AND SOME EXAMPLES OF SOLID STATE COMPONENT AND TRANSMITTER DESIGN WILL BE PRESENTED
££°ÓÊ 6 / -Ê"Ê-" Ê-// !LTHOUGH THE GAP IN PERFORMANCE CAPABILITIES BETWEEN THE SOLID STATE AND VACUUM ELECTRONICS TECHNOLOGIES CAN BE WIDE THERE STILL EXIST RELEVANT TRADES INVOLVING COST MAINTAINABILITY AND RELIABILITY AND THIS DESIGN TRADESPACE CAN BE VERY COMPLICATED 3OME POINT TO THE CONTINUED MATURATION OF VACUUM ELECTRONICS AND SUGGEST THAT BOTH VACUUM TUBES AND SOLID STATE DEVICES WILL BE APPEALING IN HIGH PERFORMANCE RADARS FOR MANY YEARS TO COME /THERS NOTE STILL THAT THE BEST VALUE IN ELECTRONIC EQUIPMENT IS PRO VIDED WHEN THE hAPPROPRIATE TECHNOLOGYv IS APPLIED TO AFFORDABLE MILITARY ELECTRONICS RECOGNIZING THAT TUBES AND SOLID STATE MAY REMAIN AS COMPLEMENTARY DESIGN SOLUTIONS ££°£
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&)'52% "Y COMBINING THE OUTPUTS OF THOUSANDS OF TRANSISTOR AMPLIFIERS THE CUMULATIVE AVERAGE POWER OUTPUT OF SOLID STATE TECHNOLOGIES CAN EFFECTIVELY COMPETE WITH THE PERFORMANCE CAPABILITIES OF VACUUM TUBE TECHNOLOGY AS SHOWN IN THE CENTER OVERLAP REGION WHERE COMPETING AMPLIFIER SOLUTIONS COEXIST
FOR FUTURE SYSTEM REQUIREMENTS &OR EXAMPLE MICROWAVE POWER TUBES CONTINUE TO PRO VIDE SIGNIFICANTLY HIGHER POWER OUTPUT AND EFFICIENCIES THAN SOLID STATE POWER AMPLI FIERS FOR HIGH PERFORMANCE MILLIMETER WAVE RADARS #OMPARED WITH TUBES SOLID STATE DEVICES OFFER THE FOLLOWING ADVANTAGES .O HOT CATHODES ARE REQUIRED THEREFORE THERE IS NO WARMUP DELAY NO WASTED HEATER POWER AND VIRTUALLY NO LIMIT ON TRANSISTOR OPERATING LIFE 5NDER CERTAIN OPERATING CONDITIONS THE PREDICTION OF THE MEDIAN TIME TO FAILURE -44& FOR SOME 2& TRANSIS TORS CAN EXCEED YEARS 4RANSISTOR AMPLIFIERS OPERATE AT MUCH LOWER VOLTAGES THEREFORE POWER SUPPLY VOLT AGES ARE ON THE ORDER OF VOLTS RATHER THAN KILOVOLTS TO AVOID THE NEED FOR LARGE SPAC INGS OIL FILLING OR ENCAPSULATION #OMPARED WITH A HIGH VOLTAGE POWER SUPPLY A LOW VOLTAGE SUPPLY USES FEWER NONSTANDARD PARTS AND IS GENERALLY LESS EXPENSIVE 4RANSMITTERS DESIGNED WITH SOLID STATE DEVICES EXHIBIT IMPROVED MEANTIME BETWEEN FAILURES -4"& IN COMPARISON WITH TUBE TYPE TRANSMITTERS !MPLIFIER MODULE -4"&S GREATER THAN HOURS HAVE BEEN EXTRAPOLATED FROM ACCELERATED LIFE TESTING ! FACTOR OF IMPROVEMENT IN TRANSMITTER SYSTEM -4"& HAS BEEN REPORTED FOR AN 3 BAND SOLID STATE TRANSMITTER REPLACING A KLYSTRON TRANSMITTER 'RACEFUL DEGRADATION OF SYSTEM PERFORMANCE OCCURS WHEN INDIVIDUAL MODULES FAIL 0OWER OUTPUT DEGRADES BY LOG nA AS DEVICES FAIL WHERE A IS THE FRACTION OF FAILED DEVICES 4HIS RESULTS BECAUSE A LARGE NUMBER OF SOLID STATE DEVICES MUST BE COMBINED TO PROVIDE THE POWER FOR A RADAR TRANSMITTER AND THEY ARE EASILY COMBINED IN WAYS THAT DEGRADE GRACEFULLY WHEN INDIVIDUAL UNITS FAIL 4HE ABILITY TO DEMONSTRATE WIDE BANDWIDTH IS A SIGNIFICANT CHARACTERISTIC OF SOLID STATE DEVICES 7HILE HIGH POWER MICROWAVE RADAR TUBES CAN ACHIEVE TO BAND WIDTH SOLID STATE TRANSMITTER MODULES CAN ACHIEVE UP TO BANDWIDTH OR MORE WITH ACCEPTABLE EFFICIENCY
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&LEXIBILITY CAN BE REALIZED ! MODULE WITH BOTH TRANSMIT AND RECEIVE PATH AMPLIFIERS 42 MODULE CAN BE ASSOCIATED WITH EVERY ANTENNA ELEMENT IN PHASED ARRAY SYS TEMS 2& DISTRIBUTION LOSSES THAT NORMALLY OCCUR IN A TUBE POWERED SYSTEM BETWEEN A POINT SOURCE TUBE AMPLIFIER AND THE FACE OF THE ARRAY ARE THUS ELIMINATED )N ADDI TION PHASE SHIFTING FOR BEAM STEERING CAN BE IMPLEMENTED AT LOW POWER LEVELS ON THE INPUT FEED SIDE OF AN ACTIVE ARRAY MODULE THIS AVOIDS THE HIGH POWER LOSSES OF THE PHASE SHIFTERS AT THE RADIATING ELEMENTS AND RAISES OVERALL EFFICIENCY !LSO PEAK 2& POWER LEVELS AT ANY POINT ARE RELATIVELY LOW BECAUSE THE OUTPUTS ARE COMBINED ONLY IN SPACE &URTHERMORE AMPLITUDE TAPERING CAN BE ACCOMPLISHED BY TURNING OFF OR ATTENUATING INDIVIDUAL ACTIVE ARRAY AMPLIFIERS &OR PHASED ARRAY SYSTEMS WITH MODEST POWER LEVELS THE SOLID STATE SOLUTION OFFERS ADVANTAGES THAT MAKE IT ATTRACTIVE AS THE BASIS FOR A RADAR TRANSMITTER
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4HE GENERAL REPLACEMENT OF HIGH POWER MICROWAVE TUBES BY SOLID STATE DEVICES HAS NOT BEEN STRAIGHTFORWARD !TTEMPTS TO REPLACE EXISTING TUBE TYPE TRANSMITTERS WITH A SOLID STATE RETROFIT HAVE BEEN HINDERED BY THE REQUIREMENT TO BE A FORM FIT FUNCTIONAL REPLACE MENT FOR THE INCUMBENT HARDWARE 2ADAR TRANSMIT WAVEFORMS THAT PREVIOUSLY HAD BEEN ARCHITECTED TO MAKE OPTIMUM USE OF THE HIGH PEAK POWER AND LOW DUTY CYCLE CAPABILITY OF THE TUBE NO LONGER FAVOR THE SOLID STATE TRANSMITTER ! LOW DUTY CYCLE ENVIRONMENT IS NOT THE MOST COST EFFECTIVE SOLUTION FOR SOLID STATE DEVICES BECAUSE TRANSISTORS EXHIBIT MUCH SHORTER THERMAL TIME CONSTANTS THAN THE REPLACEMENT TUBE AND ARE MORE EFFICIENTLY OPERATED USING A LOWER COMPOSITE PEAK POWER AT A HIGHER DUTY CYCLE !S AN EXAMPLE OF THE DILEMMA AN , BAND MICROWAVE TRANSISTOR THAT IS CAPABLE OF PERHAPS WATTS 7 AVERAGE POWER CANNOT PROVIDE MUCH MORE THAN WATTS OF PEAK POWER WITHOUT OVER HEATING DURING THE PULSE 4HE SHORT PULSE LENGTHS AND LOW DUTY CYCLES TYPICAL OF OLDER TUBE TYPE RADARS THUS MAKE VERY INEFFICIENT USE OF THE AVERAGE POWER CAPABILITIES OF MICROWAVE TRANSISTORS 4O REPLACE THE OLD WELL PROVEN * , BAND MAGNETRON THAT DEVELOPS 7 OF AVERAGE 2& POWER AT TYPICAL DUTY CYCLE WOULD REQUIRE TO OF THE WATT TRANSISTORS JUST DESCRIBED (OWEVER WITH A DUTY CYCLE THE WATT AVERAGE POWER REQUIREMENT COULD BE PROVIDED BY ONLY TO OF THE WATT TRANSISTORS )N OTHER WORDS MICROWAVE TRANSISTORS ARE MUCH MORE COST EFFECTIVE WHEN THE REQUIRED RADAR SYSTEM AVERAGE POWER CAN BE PROVIDED BY A LOWER PEAK POWER AT A HIGHER DUTY CYCLE !S A RESULT THERE HAVE BEEN RELATIVELY FEW DIRECT REPLACEMENTS OF OLDER LOW DUTY CYCLE TRANSMITTERS BY SOLID STATE TRANSMITTERS 3OME INITIATIVES SUCH AS THE SOLID STATE !.303 REPLACEMENT THAT WAS MOTIVATED BY THE ATTRACTIVE RELIABILITY MAINTAINABILITY AND AVAILABILITY CHARACTERISTICS OF A MODULAR SOLID STATE SYSTEM HAVE NOT SEEN THE SUCCESS ONCE ENVISIONED DUE TO THE ACQUISITION COST OF SOLID STATE REPLACE MENT TRANSMITTERS &OR NEW RADAR SYSTEMS SYSTEM DESIGNERS HAVE BEEN MOTIVATED BY THESE CONSIDERATIONS TO CHOOSE AS HIGH A DUTY CYCLE AS POSSIBLE BOTH TO REDUCE THE PEAK POWER REQUIRED AND TO PERMIT USING SOLID STATE DEVICES AT A REASONABLE COST 4HE DECISION TO USE A HIGH TRANSMITTER DUTY CYCLE HOWEVER HAS SIGNIFICANT IMPACT ON THE REST OF THE RADAR SYSTEM /PERATION AT A HIGH DUTY CYCLE GENERALLY REQUIRES THE USE OF PULSE COMPRESSION TO PROVIDE THE DESIRED UNAMBIGUOUS RANGE COVERAGE TOGETHER WITH REASONABLY SMALL RANGE RESOLUTION /THER CONSEQUENCES FOLLOW IN TURN THE WIDE TRANSMITTED PULSE USED WITH PULSE COMPRESSION BLINDS THE RADAR AT SHORT RANGES SO A hFILL INv PULSE MUST ALSO BE TRANSMITTED AND PROCESSED 4O PREVENT POINTS OF STRONG CLUT TER FROM MASKING SMALL MOVING TARGETS THE SIGNAL PROCESSOR MUST ACHIEVE LOW PULSE COMPRESSION TIME SIDELOBES AND HIGH CLUTTER CANCELLATION RATIO !S A RESULT IT IS MUCH EASIER TO DESIGN A SOLID STATE TRANSMITTER AS PART OF A NEW SYSTEM THAN IT IS TO RETROFIT ONE INTO AN OLD SYSTEM THAT USUALLY DOES NOT HAVE ALL THESE FEATURES
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4HE USE OF SOLID STATE DOES NOT ELIMINATE ALL THE PROBLEMS OF TRANSMITTER DESIGN 4HE 2& COMBINING NETWORKS MUST BE DESIGNED WITH GREAT CARE AND SKILL TO MINIMIZE COMBINING LOSSES IN ORDER TO KEEP TRANSMITTER EFFICIENCY HIGH 3UITABLE ISOLATION FROM EXCESSIVE VOLTAGE STANDING WAVE RATIO 6372 MUST BE PROVIDED TO PROTECT THE MICRO WAVE TRANSISTORS FROM UNDESIRED OPERATIONAL STRESSES AND THEIR HARMONIC POWER OUTPUT MUST BE PROPERLY FILTERED TO MEET -), 34$ AND OTHER SPECIFICATIONS ON 2& SPEC TRUM QUALITY !LSO JUST AS IN TUBE TYPE TRANSMITTERS ENERGY MANAGEMENT IS STILL CRUCIAL %ACH DC POWER SUPPLY MUST HAVE A CAPACITOR BANK LARGE ENOUGH TO SUPPLY THE ENERGY DRAWN BY ITS SOLID STATE MODULES DURING AN ENTIRE PULSE AND EACH POWER SUPPLY MUST RECHARGE ITS CAPACITOR BANK SMOOTHLY BETWEEN PULSES WITHOUT DRAWING AN EXCESSIVE CURRENT SURGE FROM THE POWER LINE !S A RESULT OF UNAVOIDABLE LOSSES IN COMBINING THE OUTPUTS OF MANY SOLID STATE DEVICES IT IS ESPECIALLY TEMPTING TO AVOID COMBINING BEFORE RADIATING SINCE COMBINING IN SPACE IS ESSENTIALLY LOSSLESS &OR THIS REASON MANY SOLID STATE TRANSMITTERS CONSIST OF AMPLIFIER MODULES THAT FEED EITHER ROWS COLUMNS OR SINGLE ELEMENTS OF AN ARRAY ANTENNA %SPECIALLY IN THE LAST NAMED CASE IT IS NECESSARY TO BUILD THE MODULES AND USUALLY THEIR POWER SUPPLIES INTO THE ARRAY STRUCTURE 'ENERALLY SOLID STATE DEVICES OR MODULES ARE COMBINED IN ONE OF THREE FUNDAMENTAL CONFIGURATIONS TO GENERATE THE REQUIRED TRANSMITTER POWER LEVELS &IGURE SHOWS THAT THIS MAY INVOLVE EITHER THE COMBINATION OF AMPLIFIER OUTPUTS TO A SINGLE PORT TO FEED A MECHANICALLY ROTATING ANTENNA OR SOME COMBINATION OF ELECTRONIC PHASE STEERING AND AMPLIFICATION DISTRIB UTED AMONG MANY FIXED ELEMENTS OF A PLANAR TWO DIMENSIONAL ARRAY "ECAUSE OF THE LARGE NUMBER OF INDIVIDUAL MODULES IN A TYPICAL SOLID STATE TRANS MITTER FAILURE OF AN INDIVIDUAL OR A FEW MODULES HAS LITTLE EFFECT ON OVERALL TRANSMITTER PERFORMANCE 4HE MODULE OUTPUTS ADD AS VOLTAGE VECTORS SO THE LOSS OF OF THE MODULES FOR EXAMPLE RESULTS IN A REDUCTION TO OF VOLTAGE OUTPUT WHICH IS OF POWER OUTPUT %VEN THIS IS ONLY A D" REDUCTION THE DIFFERENCE BETWEEN AND OF THE POWER ENDS UP IN THE COMBINER LOADS OR IN SIDELOBES IF THE COMBINING IS IN SPACE !S A RESULT OF THIS hGRACEFUL DEGRADATION v OVERALL RELIABILITY OF SOLID STATE TRANSMITTERS IS VERY HIGH EVEN IF MAINTENANCE IS DELAYED UNTIL CONVENIENT SCHEDULED PERIODS HOWEVER THIS ADVANTAGE SHOULD NOT BE ABUSED #ONSIDER A CASE WHERE OF MODULES ARE ALLOWED TO FAIL BEFORE OUTPUT POWER FALLS BELOW REQUIREMENTS AND ASSUME THAT MAINTENANCE OCCURS AT SCHEDULED THREE MONTH INTERVALS )N THIS CASE MODULE -4"& NEED ONLY BE H TO PROVIDE CONFIDENCE THAT THE TRANSMITTER
&)'52% #OMMON SOLID STATE TRANSMITTER CONFIGURATIONS MAY COMBINE MANY AMPLIFIERS IN PARALLEL TO A SINGLE ANTENNA PORT A OR MAY USE PHASE SHIFT ELEMENTS TO ELECTRONICALLY STEER A BEAM B OR MAY UTILIZE TRANSMITRECEIVE MODULES WITH PHASE SHIFT CAPABILITY AT EVERY ELEMENT TO STEER A BEAM C
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WILL NOT hFAILv IN LESS THAN THREE MONTHS HOWEVER THE COST OF REPLACEMENT MODULES AND LABOR WOULD BE VERY UNATTRACTIVE BECAUSE NEARLY OF THE TRANSMITTER WOULD HAVE TO BE REPLACED EVERY YEAR (IGHER -4"&S ARE THUS ESSENTIAL TO ENSURE THAT THE TRANSMITTER IS NOT ONLY AVAILABLE BUT ALSO AFFORDABLE &ORTUNATELY SOLID STATE MODULE RELIABILITY HAS PROVEN TO BE EVEN BETTER THAN THE -), ($"+ PREDICTIONS !.&03 0!6% 0!73 FOR EXAMPLE HAS GROWN TO HOURS WHICH IS TIMES THE PREDICTED VALUE 4HIS INCLUDES THE ACTUAL 42 MODULE -4"& ALONG WITH THE RECEIVER TRANSMIT RECEIVER 42 SWITCHES AND PHASE SHIFTERS AS WELL AS THE POWER AMPLIFIERS )N FACT -4"& FOR THE OUTPUT POWER TRANSISTORS MEASURES BETTER THAN MILLION HOURS
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!LTHOUGH THE 2& POWER GENERATING CAPABILITY OF SINGLE TRANSISTORS IS SMALL WITH RESPECT TO THE OVERALL PEAK AND AVERAGE POWER REQUIREMENTS OF A RADAR TRANSMITTER TRANSISTORS ARE USED QUITE EFFECTIVELY BY COMBINING THE OUTPUTS OF MANY IDENTICAL SOLID STATE AMPLIFIERS 4HE POWER OUTPUT LEVEL FROM A PARTICULAR DEVICE IS A FUNCTION OF NOT ONLY THE CHOSEN TECHNOLOGY BUT ALSO THE FREQUENCY AND OTHER CONDITIONS SUCH AS PULSE WIDTH DUTY CYCLE AMBIENT TEMPERATURE OPERATING VOLTAGE AND THE PRESENTED LOAD IMPEDANCE 4ECHNOLOGIES AND #ONSTRUCTION 3EMICONDUCTING MATERIALS USED IN THE FABRI CATION OF TRANSISTORS ARE CONSIDERED TO BE THOSE MATERIALS THAT ARE TYPICALLY NEITHER CONDUCTORS NOR INSULATORS 4HE CHARGE CARRYING PROPERTIES OF THESE SEMICONDUCTING MATERIALS CAN BE MODIFIED DRAMATICALLY THROUGH THE SUBSTITUTION OF MINUTE AMOUNTS OF IMPURITY IONS OR THROUGH CRYSTAL LATTICE DEFECTS EITHER OF WHICH ACT TO MODULATE THE FLOW OF ELECTRONS 3EMICONDUCTOR MATERIALS FROM WHICH TRANSISTORS ARE FABRICATED FOR USE IN SOLID STATE RADAR TRANSMITTERS HAVE GENERALLY BEEN EITHER SILICON OR ONE OF THE SO CALLED COMPOUND SEMICONDUCTORS SUCH AS GALLIUM ARSENIDE 'A!S INDIUM PHOS PHIDE )N0 SILICON CARBIDE 3I# GALLIUM NITRIDE 'A. OR SILICON GERMANIUM 3I'E 3EMICONDUCTORS LIKE SILICON OR GALLIUM ARSENIDE HAVE FOUND EARLY WIDE ACCEPTANCE BECAUSE IT HAS PROVEN PRACTICAL TO CONTROL THEIR CRYSTAL LATTICE DEFECTS ACCURATELY AND REPEATABLY DURING TRANSISTOR MANUFACTURING 3OME SEMICONDUCTORS SUCH AS GALLIUM NITRIDE 'A. OR SILICON CARBIDE 3I# ARE REFERRED TO AS WIDE BANDGAP SEMICONDUC TORS 3EMICONDUCTORS THAT EXHIBIT LARGE BANDGAP VALUES ARE ESPECIALLY CAPABLE OF PRO DUCING VERY HIGH OUTPUT POWER LEVELS WITH ACCEPTABLE GAIN AT THE FREQUENCIES USED IN MOST RADAR APPLICATIONS 4RANSISTORS ARE THREE TERMINAL DEVICES AND ARE CLASSIFIED AS EITHER BIPOLAR OR UNIPOLAR &IGURE HELPS TO PORTRAY THE CONSTRUCTION DIFFERENCES AMONG COMMON MICROWAVE THREE TERMINAL DEVICES AND THIS FIGURE IS REFERENCED MULTIPLE TIMES IN SUCCEEDING SEC TIONS 4HE BIPOLAR JUNCTION TRANSISTOR "*4 IS SO NAMED BECAUSE THE CONDUCTION PATH THROUGH THE TRANSISTOR MAKES USE OF BOTH MAJORITY AND MINORITY CHARGE CARRIERS TO ESTAB LISH CURRENT FLOW IN THE SEMICONDUCTOR )T IS A CURRENT CONTROLLED DEVICE WITH THE COLLEC TOR CURRENT MODULATED BY THE CURRENT FLOWING BETWEEN THE BASE EMITTER JUNCTION 4HIS COMPARES TO THE OPERATION OF A FIELD EFFECT TRANSISTOR &%4 OR A UNIPOLAR DEVICE WHERE CHARGE IS CARRIED WITH ONLY ONE TYPE OF CHARGE CARRIER 4HE REMAINING TRANSISTOR CONSTRUC TIONS IN &IGURE ARE ALL VARIANTS OF A &%4 !N EXTERNAL VOLTAGE APPLIED TO THE GATE TERMINAL OF A &%4 CONTROLS THE WIDTH OF THE DEPLETION REGION BELOW THE GATE TERMINAL !S THE WIDTH OF THE DEPLETION REGION IS VARIED SO TOO IS THE EQUIVALENT RESISTANCE BETWEEN
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&)'52% 4RANSISTORS ARE THREE TERMINAL SEMICONDUCTOR DEVICES THAT ALLOW A SMALL VOLTAGE OR CURRENT TO CONTROL A LARGER VOLTAGE OR CURRENT 3OME CROSS SECTIONS OF COMMON TRANSISTOR TYPES USED IN THE DESIGN OF RADAR TRANSMITTERS ARE THE A 'A!S -%3&%4 B 'A!S 0(%-4 C 3ILICON -/3&%4 D 3ILICON ,$-/3 &%4 E 3ILICON "*4 AND F 'A. (%-4 ON 3I# 3UBSTRATE
THE DRAIN AND SOURCE CONTACTS ALLOWING THE CURRENT FLOWING BETWEEN THE DRAIN AND SOURCE TO BE MODULATED ACCORDINGLY HENCE &%4S ARE REFERRED TO AS VOLTAGE CONTROLLED DEVICES 4HERE EXIST NUMEROUS &%4 VARIANTS DUE TO SOMETIMES SUBTLE CONSTRUCTION OR MATE RIAL DIFFERENCES !MONG THESE ARE THE -/3&%4 -ETAL /XIDE 3EMICONDUCTOR &%4 -%3&%4 -ETAL 3EMICONDUCTOR &%4 AND (&%4 (ETEROSTRUCTURE &%4 4HE COMMON (&%4 DEVICES ARE REFERRED TO AS THE (%-4 (IGH %LECTRON -OBILITY 4RANSISTOR AND 0(%-4 0SEUDOMORPHIC (IGH %LECTRON -OBILITY 4RANSISTOR 4O BE USEFUL IN A RADAR TRANSMITTER AMPLIFIER THE TRANSISTOR MUST BE CAPABLE OF OPER ATING AT THE APPROPRIATE HIGH FREQUENCY WITH GOOD EFFICIENCY WHILE DEMONSTRATING USEFUL POWER GAIN WITH ADEQUATE THERMAL MANAGEMENT PROPERTIES TO ENSURE HIGH RELI ABILITY 4HERE IS NOT ONE TRANSISTOR TYPE OR ONE SEMICONDUCTOR MATERIAL THAT IS UNIVER SALLY USEFUL ACROSS ALL THE COMMON RADAR BANDS FROM 5(& THROUGH 7 BAND )N FACT AMONG THE RADAR BANDS THERE IS OFTEN A DIFFERENT DOMINANT DEVICE TYPE ALONG WITH ITS ATTENDANT DESIGN AND FABRICATION METHODOLOGIES THAT OFFERS THE OPTIMUM PERFORMANCE FOR THAT BAND ! FIRST ORDER APPROXIMATION OF THE POWER OUTPUT FROM A SINGLE STAGE SOLID STATE AMPLIFIER USING A &%4 AS THE SEMICONDUCTOR DEVICE IS GIVEN BY THE RELATIONSHIP
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)N THIS RELATIONSHIP )-!8 IS THE MAXIMUM OPEN CHANNEL CURRENT 6$'" IS THE GATE DRAIN BREAKDOWN VOLTAGE 60 IS THE PINCHOFF VOLTAGE AND 6+ IS THE KNEE VOLTAGE 4HESE TRANSISTOR PARAMETERS DEFINE THE TRANSFER CHARACTERISTICS IN THE ) 6 CURRENT VOLTAGE PLANE AND THE BOUNDARIES OF THE ) 6 PLANE DEFINE THE PEAK POWER PERFORMANCE ENVE LOPE OF THE TRANSISTOR !LSO THERE IS AN OPTIMUM LOAD IMPEDANCE THAT WILL MAXIMIZE THE POWER OUTPUT THAT CAN BE DELIVERED FROM AN AMPLIFIER AND TO A FIRST ORDER ESTIMATE THAT LOAD IMPEDANCE IS REPRESENTED BY THE LINE THAT TRANSVERSELY CUTS ACROSS THE ) 6 PLANE FROM THE REGION OF THE BREAKDOWN VOLTAGE TO THE REGION OF THE KNEE VOLTAGE AS SHOWN IN &IGURE 4HE ABILITY OF A TRANSISTOR TO DEMONSTRATE GAIN AT HIGH FREQUENCIES IS IMPACTED BY THE MOBILITY AND SATURATED VELOCITY OF CHARGE CARRIERS IN THE SEMICONDUC TOR 4HE ABILITY OF A TRANSISTOR TO DEMONSTRATE HIGH POWER OUTPUT IS IMPACTED BY THE BREAKDOWN VOLTAGE THE CURRENT CAPABILITY AND THE KNEE VOLTAGE OF THE TRANSISTOR 3ILICON DEVICE TYPES COST EFFECTIVELY SATISFY THE REQUIREMENTS OF RELIABILITY ELEC TRICAL PERFORMANCE PACKAGING COOLING AVAILABILITY AND MAINTAINABILITY AT LOWER RADAR BAND FREQUENCIES TYPICALLY 5(& , BAND AND INTO 3 BAND 4HESE DEVICES ARE USUALLY MANUFACTURED AS DISCRETELY PACKAGED TRANSISTORS AND REQUIRE EXTERNAL IMPEDANCE MATCHING CIRCUITRY IN ORDER TO FUNCTION APPROPRIATELY IN AN AMPLIFIER (IGH PERFORMANCE TRANSISTORS AT HIGHER FREQUENCIES THAN 3 BAND ARE USUALLY BUILT USING COMPOUND SEMICONDCTORS 3UCH TRANSISTORS CAN RESULT IN HIGH CUTOFF FREQUENCIES AND DEMONSTRATE GAIN AT FREQUENCIES MUCH HIGHER THAN SILICON &OR EXAMPLE ELECTRONS IN GALLIUM ARSENIDE 'A!S TRAVEL APPROXIMATELY TWICE AS FAST AS THEY DO IN SILICON )T HAS A HIGHER SATURATED ELECTRON VELOCITY AND HIGHER ELECTRON MOBILITY ALLOWING IT TO FUNC TION AT FREQUENCIES INTO THE 7 BAND 'A!S TRANSISTORS GENERATE LESS NOISE THAN SILICON DEVICES WHEN OPERATED AT HIGH FREQUENCY SO THEY ALSO MAKE SUPERIOR LOW NOISE AMPLI FIERS ! KEY ATTRIBUTE THAT MAKES 'A!S AN ATTRACTIVE TECHNOLOGY IS THAT THE 'A!S &%4 CAN BE FULLY INTEGRATED WITH THE PASSIVE CIRCUITRY THAT IS NECESSARY TO PROVIDE THE BIAS ING LOADING FILTERING AND SWITCHING FUNCTIONS THAT ARE NECESSARY FOR MULTISTAGE 42 MODULE DESIGNS 5NLIKE THE SILICON POWER TRANSISTORS THE 'A!S &%4 AND ITS ASSOCIATED
&)'52% 4YPICAL TRANSISTOR CURRENT VOLTAGE CONTINUUM ) 6 PLANE SHOWING KEY &%4 DC PERFORMANCE LIMITS WITH OPTIMUM LOAD LINE FOR POWER OUTPUT SHOWN (IGHER POWER OUTPUT IS ACHIEVED WHEN THE MAXI MUM CHANNEL CURRENT )-!8 AND THE BREAKDOWN VOLTAGE 6$'" ARE BOTH INCREASED /PTIMUM AMPLIFIER DESIGN PLACES THE LOAD LINE AS INDICATED
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BATCH PROCESSED MONOLITHIC MICROWAVE INTEGRATED CIRCUITRY --)# FABRICATION TECH NOLOGY ALLOW FOR CIRCUIT FUNCTIONS TO BE PROCESSED INTO VERY VERY SMALL CONVENIENTLY PACKAGED CHIPS 4HE WIDE BANDGAP SEMICONDUCTORS SUCH AS 3I# AND 'A. ARE ALSO COMPATIBLE WITH --)# PROCESSING BUT ARE ALSO CAPABLE OF VERY HIGH POWER OUTPUT LEVELS 4HESE SEMICONDUCTORS HAVE MATERIAL PROPERTIES THAT LEAD TO HIGH BREAKDOWN VOLTAGE WITH COMMENSURATELY HIGH CHANNEL CURRENTSAN ORDER OF MAGNITUDE HIGHER POWER OUTPUT THAN 'A!S 4ABLE &OR THE UPPER END OF THE SOLID STATE MICROWAVE SPECTRUM IE THE MILLIMETER WAVE RANGE THE SINGLE PORT MICROWAVE DIODE CAN BE USED AS A LOW POWER OSCILLATOR 5NFORTUNATELY THE POWER OUTPUT AND EFFICIENCY OF THESE DEVICES ARE IN GENERAL VERY LOW IN FACT THE EFFICIENCY IS SIGNIFICANTLY LOWER THAN THAT OF THEIR TUBE COUNTERPARTS (OWEVER #7 AND PULSED POWER OUTPUT ARE ATTAINABLE UP TO '(Z 0EAK AND !VERAGE 0OWER ,IMITATIONS ! FIRST ORDER LIMIT ON THE 2& POWER OUT PUT CAPABILITY OF A TRANSISTOR IS ITS BREAKDOWN VOLTAGE AND MAXIMUM CURRENT HANDLING CAPABILITY 7ITHIN THAT LIMIT THE MAXIMUM PRACTICAL LEVEL OF POWER OUTPUT THAT CAN BE OBTAINED FROM A SINGLE TRANSISTOR OVER A GIVEN BANDWIDTH IS GOVERNED BY THE THERMAL DISSIPATION LIMIT OF THE DEVICE !S DEVICES BECOME LARGER AND THE DISSIPATIVE HEAT FLUX FROM THE TOP SURFACE OF THE TRANSISTOR CHIP TO THE BOTTOM LAYER OF THE TRANSISTOR CHIP INCREASES THE JUNCTION TEMPERATURE INCREASES TO THE POINT WHERE THE TRANSISTOR BECOMES THERMALLY LIMITED 2EGARDLESS OF THE SEMICONDUCTOR USED THE ELECTRICAL PERFORMANCE AND OPERATING LIFETIME DEGRADE AT INCREASINGLY HIGHER TEMPERATURES 4HERE IS A COMPOSITE THERMAL TIME CONSTANT ASSOCIATED WITH THE NUMEROUS THERMALLY RESISTIVE LAYERS BETWEEN THE TRANSISTOR JUNCTION AND THE HEAT SINK OR COLD PLATE TO WHICH THE DEVICE IS ATTACHED 4HIS OCCURS BECAUSE EACH LAYER SEMICONDUCTOR CERAMIC SUB STRATE METAL BASE ETC EXHIBITS BOTH A THERMAL RESISTANCE AND A THERMAL CAPACITANCE 4HEN THERE EXISTS AN EQUIVALENT THERMAL TIME CONSTANT S FOR EACH PACKAGING MATERIAL LAYER 4HIS THERMAL TIME CONSTANT HAS BEEN APPROXIMATEDED AS
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WHERE & IS THICKNESS CM Q IS DENSITY GMCC # IS SPECIFIC HEAT 7SECGMn# AND +4( IS THERMAL CONDUCTIVITY 7CMn# &OR EXAMPLE &IGURE SHOWS THAT WHEN THE PULSE WIDTH AND DUTY CYCLE FOR A GIVEN 'A!S TRANSISTOR IS INCREASED FROM §S AND TO §S AND RESPECTIVELY THERE IS A n# INCREASE IN THE OVERALL JUNCTION TEM PERATURE !LTHOUGH THE TRANSISTOR MAY OPERATE RELIABLY AT A DESIRED OUTPUT POWER LEVEL FOR THE SHORTER PULSE WIDTH IT WOULD SUFFER FROM A DECREASE IN LONG TERM RELIABILITY IF OPERATED AT THE SAME POWER LEVEL FOR THE LONGER PULSE WIDTH 4HUS IF REQUIRED TO
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&)'52% /NE LIMIT OF TRANSISTOR CAPABILITY IS DETERMINED BY THE MAXIMUM JUNCTION TEMPERATURE WHICH IN TURN IS DETERMINED BY THE THERMAL TIME CONSTANT AND THIS RESULTS IN VERY DIFFERENT CAPABILITIES AS A FUNCTION OF OPERATING PULSE WIDTH AND DUTY CYCLE
MAINTAIN LONG TERM RELIABILITY AT THE LONGER PULSE WIDTH THE DISSIPATION IN THE TRANSIS TOR WOULD HAVE TO BE REDUCED TO BRING THE JUNCTION TEMPERATURE DOWN TO AN ACCEPTABLE LEVEL $E RATING THE INHERENT SHORT PULSE CAPABILITY BY LOWERING THE DISSIPATED POWER IN THE TRANSISTOR PERHAPS BY REDUCING THE OPERATING VOLTAGE AND POWER OUTPUT IS ONE METHOD OF ACHIEVING THE DESIRED RELIABILITY !NOTHER METHOD MAY INVOLVE THE REDUCTION IN AMBIENT TEMPERATURE WITH THE USE OF CHILLED FLUID IN THE AMPLIFIER HEAT SINK 4HESE ARE NOT ALWAYS PRACTICAL SOLUTIONS AND ONE FINDS THAT THE LAYOUT OF THE TRANSISTOR ITSELF IS OFTEN OPTIMIZED FOR A PARTICULAR PULSE WIDTH AND DUTY CYCLE IN ORDER TO ACHIEVE THE OPTIMUM PERFORMANCE AND RELIABILITY AT THE LOWEST OPERATING TEMPERATURE 4HE ACTIVE TRANSISTOR AREA ON THE SURFACE OF THE CHIP THE CHIP IS SOMETIMES CALLED THE DIE IS TYPICALLY DIVIDED INTO MANAGEABLE UNITS CELLS WHERE THE CELL SIZE IS OFTEN OPTIMIZED FOR A PARTICULAR APPLICATION OR RANGE OF APPLICATIONS )N ADDITION TO FREQUENCY CONSIDERATIONS PULSE WIDTH AND DUTY CYCLE OR AS A RESULT THE PEAK AND AVERAGE DIS SIPATED POWER ARE THE PARAMETERS THAT DETERMINE THE CELL SIZE AND ARRANGEMENT OF CELLS ON A CHIP 4HE ULTIMATE OPERATING JUNCTION TEMPERATURE OF THE TRANSISTOR IS LARGELY DEPENDENT ON THE TRANSIENT HEATING THAT WILL BE ENCOUNTERED AND THE LAYOUT AND AREA OF THE INDIVIDUAL CELLS &OR DEVICES THAT ARE DESIGNED TO OPERATE FOR LONG PULSES OR #7 AN INCREASE IN THE AVERAGE POWER CAPABILITY OF THE TRANSISTOR CAN BE ACHIEVED BY DIVIDING THE ACTIVE AREA OF A TRANSISTOR INTO SMALL THERMALLY ISOLATED CELL AREAS 3INCE THE OVERALL THERMAL TIME CONSTANT FOR A TYPICAL POWER TRANSISTOR DIE ITSELF MAY BE ON THE ORDER OF n §S THE TRADEOFF BETWEEN PEAK AND AVERAGE POWER VERSUS DEVICE SIZE CAN BE SIGNIFICANT FOR SOLID STATE RADARS USING PULSE COMPRESSION WITH PULSE WIDTHS IN THE TO §S RANGE !S AN EXAMPLE THE THERMAL TIME CONSTANT OF A SILICON DIE WITH A THICKNESS OF MILS IS APPROXIMATELY §S WHEREAS A GALLIUM ARSENIDE DIE WITH A THICKNESS OF MILS IS APPROXIMATELY §S 4HUS FOR AN OPERATING PULSE WIDTH
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REPRESENTATIVE OF A SOLID STATE RADAR WITH PULSE COMPRESSION ^ §S THE TEMPERA TURE RISE ACROSS THE SILICON DIE HAS REACHED OF ITS STEADY STATE VALUE BUT FOR AN OPERATING PULSE WIDTH REPRESENTATIVE OF A SHORTER RANGE FIRE CONTROL RADAR ^ §S THE TEMPERATURE RISE ACROSS THE SILICON DIE HAS ONLY REACHED OF ITS STEADY STATE VALUE )F THE VOLTAGE AND CURRENT THRESHOLD OF THE TRANSISTOR HAS NOT BEEN REACHED THE SHORTER PULSE WIDTH OPERATION COULD ALLOW FOR SIGNIFICANTLY LARGER POWER CAPABILITY TO BE DEM ONSTRATED 5SUALLY A VERY DETAILED THERMAL ANALYSIS USING THE FINITE ELEMENT METHOD IS REQUIRED TO QUANTIFY THESE RELATIONSHIPS DURING TRANSISTOR AND AMPLIFIER DESIGN "ACKGROUND AND DESCRIPTIONS OF THE COMMON THREE TERMINAL DEVICE TYPES AND THEIR ASSOCIATED TECHNOLOGIES AS UTILIZED FOR THE COMMON RADAR BANDS ARE DESCRIBED IN THE FOLLOWING SECTIONS 3ILICON "IPOLAR *UNCTION 4RANSISTOR 4HE SILICON BIPOLAR JUNCTION TRANSISTOR "*4 WAS THE EARLIEST OF THE MICROWAVE POWER DEVICES AND FOUND ITS WAY INTO TUBE REPLACEMENT TRANSMITTERS AND PHASED ARRAY APPLICATIONS STARTING IN THE LATE S !T LOWER FREQUENCIES ESPECIALLY BELOW '(Z THE 3I "*4 HAS BEEN SHOWN TO BE CAPABLE OF VERY HIGH POWER LEVELS FOR TRANSISTORS !MPLIFIER DESIGN IS REALIZABLE FOR FREQUENCIES UP THROUGH 3 BAND WHERE THE TRADEOFF BETWEEN DEVICE PERFORMANCE AND OVERALL SYS TEM COST BEGINS TO REACH A POINT OF DIMINISHING RETURNS 4HE SILICON BIPOLAR TRANSISTOR TECHNOLOGY IS NOW VERY MATURE BUT THE DEMAND FOR THESE HIGH PERFORMANCE DEVICES IS LOW BECAUSE THE PRODUCTION QUANTITIES REQUIRED FOR RADAR SYSTEMS IS SMALL RELATIVE TO COMMERCIAL SILICON ELECTRONIC PRODUCTS 4HUS THERE TENDS TO BE A SMALL NUMBER OF MANUFACTURERS WHO PROVIDE QUALITY DEVICES FOR USE IN AMPLIFIER DESIGNS 3ILICON BASED MICROWAVE POWER TRANSISTORS CAN ACTUALLY BE CONSIDERED HYBRID MICROELECTRONIC CIRCUITS AND ARE GENERALLY SINGLE CHIP OR MULTICHIP TRANSISTORS COM BINED IN PARALLEL WITHIN A FLANGED HERMETIC PACKAGE 3OME FORM OF INTERNAL IMPEDANCE PREMATCHING CIRCUITRY IS OFTEN INCLUDED IN ORDER TO PRESERVE THE INTRINSIC BANDWIDTH OF THE SEMICONDUCTOR CHIP AND TO MAKE THE TASK OF EXTERNAL IMPEDANCE MATCHING EASIER 4HE INTERNAL MATCHING ALSO INCREASES THE TERMINAL IMPEDANCES OF THE PACKAGED DEVICE TO A LEVEL WHERE THE COMPONENT LOSSES OF THE CIRCUITRY EXTERNAL TO THE TRANSISTOR BECOME LESS CRITICAL &IGURE IS AN EXAMPLE OF A WATT INTERNALLY MATCHED POWER TRAN SISTOR HYBRID USING THE 3I "*4 SEMICONDUCTOR TECHNOLOGY )T SHOWS THE TRANSISTOR DIE ALONG WITH THE CAPACITORS AND WIRES THAT ARE USED AS LOW PASS AND HIGH PASS IMPEDANCE MATCHING COMPONENTS TO ACHIEVE AN ACCEPTABLE LEVEL OF IMPEDANCE PREMATCHING 4HE MICROWAVE POWER 3I "*4 IS INVARIABLY AN .0. STRUCTURE &IGURE E WITH A VERTICAL DIFFUSION PROFILE IE THE COLLECTOR CONTACT FORMS THE BOTTOM LAYER OF THE CHIP 4HE 0 TYPE BASE REGION HAS BEEN DIFFUSED OR IMPLANTED INTO THE COLLECTOR THE . TYPE EMITTER HAS BEEN DIFFUSED OR IMPLANTED INTO THE BASE AND BOTH BASE AND EMITTER REGIONS ARE ACCESSIBLE FROM THE TOP SURFACE OF THE CHIP 4HE COLLECTOR REGION CONSISTS OF AN . DOPED LOW RESISTIVITY EPITAXIAL LAYER THAT IS GROWN ON A VERY LOW RESISTIVITY SILICON SUBSTRATE 4HE CHARACTERISTICS OF THE EPITAXIAL LAYER IE THICKNESS AND RESISTIV ITY CAN DETERMINE THE UPPER LIMIT OF PERFORMANCE OF THE DEVICE IN TERMS OF RUGGEDNESS EFFICIENCY AND SATURATED POWER OUTPUT 4HE FUNDAMENTAL LIMITATION ON HIGH FREQUENCY 3I "*4 PERFORMANCE IS THE OVERALL COLLECTOR TO EMITTER DELAY TIME )F A SIGNAL IS INTRODUCED TO EITHER THE BASE OR THE EMIT TER FOUR SEPARATE REGIONS OF ATTENUATION OR TIME DELAY ARE ENCOUNTERED THE EMITTER BASE JUNCTION CAPACITY CHARGING TIME THE BASE TRANSIT TIME THE COLLECTOR DEPLETION LAYER TRANSMIT TIME AND THE COLLECTOR CAPACITANCE RESISTANCE CHARGING TIME (IGH FREQUENCY TRANSISTOR DESIGN IS CONCERNED WITH OPTIMIZING THE PHYSICAL PARAMETERS THAT CONTRIBUTE TO THE TIME DELAY COMPONENTS
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&)'52% ! WATT , BAND LONG PULSE AND HIGH DUTY CYCLE SILICON BIPOLAR POWER TRANSISTOR IN A CUSTOM HERMETIC DUAL LEADED LOW INDUCTANCE PACKAGE HAS AN OVERALL FOOTPRINT OF r 0HOTOGRAPH COURTESY OF 2AYTHEON #OMPANY
4HE DESIGN CHALLENGE FOR HIGH POWER 3I "*4S IS TO MAINTAIN A UNIFORM HIGH CURRENT DENSITY OVER A LARGE EMITTER AREA WITH A MINIMUM TEMPERATURE RISE (IGH FREQUENCY DEVICES REQUIRE SHALLOW NARROW HIGH RESISTANCE BASE REGIONS UNDER THE EMITTER REGION CAUSING MOST OF THE CURRENT CARRIED IN THE DEVICE TO BE CROWDED ALONG THE PERIPHERY OF THE EMITTER 4HUS IN ORDER TO MAXIMIZE THE CURRENT HANDLING CAPABILITY OF THE DEVICE AND HENCE THE POWER OUTPUT CAPABILITY OF THE DEVICE THE EMITTER PERIPHERY IS MAXIMIZED "ECAUSE THE CAPACITANCE OF THE COLLECTOR BASE JUNCTION APPEARS AS A DELETERIOUS PARASITIC ELECTRICAL COMPONENT THE EMITTER PERIPHERY TO BASE AREA RATIO OR %P"A IS MAXIMIZED WHERE POSSIBLE 'ENERALLY HIGHER FREQUENCY DEVICES EXHIBIT HIGHER %P"A RATIOS AND TO OBTAIN A HIGH %P"A RATIO VERY FINE LINE GEOMETRIES ARE REQUIRED WHERE THE TERM GEOMETRY REFERS TO THE SURFACE CONSTRUCTION DETAILS OF THE TRANSISTOR DICE 3ILICON ,$-/3 &%4 4HE SILICON ,ATERALLY $IFFUSED -ETAL /XIDE 3EMI CONDUCTOR ,$-/3 TRANSISTOR IS BEGINNING TO SUPERSEDE THE SILICON POWER "*4 AS A REPLACEMENT DEVICE ESPECIALLY AT THE 6(& 5(& AND , BAND FREQUENCIES )N PAR TICULAR THE COMMERCIAL COMMUNICATIONS INDUSTRY HAS FOUND THAT THE 3I ,$-/3 &%4 DOMINATES AS A CELL PHONE BASE STATION POWER AMPLIFIER BECAUSE OF THE HIGHER GAIN LINEARITY AND EFFICIENCY THAT IT DEMONSTRATES COMPARED TO THE SILICON "*4 !LTHOUGH IT IS A &%4 ITS CONSTRUCTION CHARACTERISTICS PACKAGING AND DESIGN CHALLENGES ARE VERY SIMILAR TO THE DESIGN CHALLENGES OF THE 3I "*4
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4HE SILICON ,$-/3 &%4 &IGURE D IS PROCESSED ON P MATERIAL WITH A LIGHTLY DOPED P TYPE EPITAXIAL LAYER AND JUST LIKE THE SILICON "*4 MULTIPLE IMPURITY IMPLANTS FORM THE VARIOUS JUNCTIONS )T IS STILL CONSIDERED A SLOWER DEVICE THAN OTHER SEMICONDUC TORS SUCH AS 'A!S BECAUSE THE MOBILITY IN SILICON -/3&%4 CHANNELS IS RELATIVELY LOW !LTHOUGH THE BULK MOBILITY OF SILICON IS LOWER THAN 'A!S IT DOES NOT PRECLUDE THE SILI CON ,$-/3 &%4 AS A HIGH FREQUENCY POWER TRANSISTOR 4HE CONTINUOUS PROCESS FABRICA TION IMPROVEMENT IN THE SILICON #-/3 INDUSTRY HAS RESULTED IN SUB MICRON PRODUCTION TRANSISTOR FEATURE SIZES AND THE SMALLER FEATURE SIZES ALLOW FOR A COMPENSATED INCREASE IN HIGHER FREQUENCY OPERATION THAT IS IT CAN EXHIBIT USABLE GAIN INTO 3 BAND )N PARTICU LAR THE ,$-/3 STRUCTURE ENABLES A SHORT CHANNEL AS A RESULT OF THE LATERAL DIFFUSION OF THE P TYPE IMPLANT 4HE RESULTING SHORT CHANNEL CONTRIBUTES TO IMPROVED HIGH FREQUENCY RESPONSE IN SPITE OF THE LOWER MOBILITY OF SILICON 4HE MEASURED BREAKDOWN VOLTAGES CAN BE IN EXCESS OF 6 SO OPERATION AT HIGHER VOLTAGES IS POSSIBLE OR CONVERSELY A HIGHER LEVEL OF MARGIN IN RUGGEDNESS CAN BE ACHIEVED FOR A GIVEN OPERATING VOLTAGE THE LATTER IS A KEY ADVANTAGE FOR HIGH RELIABILITY POWER AMPLIFIER APPLICATIONS 4HE UNDERSIDE OF THE ,$-/3 TRANSISTOR DICE IS THE SOURCE CONNECTION THUS THE CHIP CAN BE MOUNTED DIRECTLY TO A METAL PACKAGE BASE 4HIS IS UNLIKE THE 3I "*4 WHERE THE HIGH VOLTAGE COLLECTOR CONTACT IS THE UNDERSIDE OF THE CHIP !S A RESULT OF NOT HAVING TO ELECTRICALLY ISOLATE THE UNDERSIDE OF THE ,$-/3 CHIP THERE IS NO NEED TO USE THE POTEN TIALLY TOXIC BERYLLIUM OXIDE BASED PACKAGES THAT PERMEATE THE 3I "*4 PRODUCT LINES 4HE LOWER SOURCE INDUCTANCE ACHIEVED WITH DIRECT ATTACHMENT TO THE METAL FLANGE OF A PACKAGE BASE ENABLES HIGHER GAINS TO BE DEMONSTRATED FOR COMPARABLE 3I "*4 POWER LEVELS AT FREQUENCIES BELOW '(Z BUT THESE DEVICES ARE PRESENTLY NOT ATTRACTIVE AT FREQUENCIES ABOVE 3 BAND ! PRIMARY ADVANTAGE OF THE ,$-/3 DEVICE IS THERMAL STABILITY 4HE DRAIN CURRENT HAS A NEGATIVE TEMPERATURE COEFFICIENT THEREFORE THE ,$-/3 &%4 IS NOT SUSCEP TIBLE TO THERMAL RUNAWAY AND DOES NOT REQUIRE THE AMOUNT OF GAIN DEGRADING RESISTIVE EMITTER BALLASTING THAT IS COMMONLY REQUIRED IN A 3I "*4 TO HELP NORMALIZE JUNCTION TEMPERATURES ! MORE THERMALLY STABLE DEVICE ALLOWS FOR THE MORE EFFICIENT POWER COM BINING OF TRANSISTOR CELLS WITHIN A PACKAGE 4HIS CONTRIBUTES TO A LOWER PERFORMANCE SENSITIVITY TO LOAD MISMATCHA PROBLEM THAT HAS COMPLICATED THE DESIGN PROCESS FOR THE 3I "*4 &IGURE AND &IGURE SUMMARIZE THE PERFORMANCE ENVELOPE FOR COM MERCIALLY AVAILABLE SILICON BIPOLAR JUNCTION TRANSISTORS AND SILICON ,$-/3 &%4S FOR GIVEN TRANSMIT WAVEFORMSn 'A!S 0(%-4 4HE 'A!S 0SEUDOMORPHIC (IGH %LECTRON -OBILITY 4RANSISTOR 0(%-4 IS ACTUALLY A HETEROSTRUCTURE MATERIAL &IGURE B CONSISTING OF SLIGHTLY STRAIN MISMATCHED CRYSTAL LAYERS ! VERY SIMPLIFIED DESCRIPTION PORTRAYS AN !L'A!S LAYER OVER AN )N'A!S CHANNEL ON A 'A!S SUBSTRATE FORMING A HIGH QUALITY TWO DIMENSIONAL ELECTRON GAS LAYER OFTEN REFERRED TO AS THE $%' 4HIS $%' EXHIBITS SUPERIOR ELECTRON TRANSPORT PROPERTIES RESULTING IN A VERY CONFINED CHANNEL WITH FEWER OPPORTUNITIES FOR CHARGE CARRIER COLLISIONS 4HIS ALLOWS FOR A VERY HIGH QUALITY TRANSISTOR THAT CAN BE MADE WITH USEFUL GAIN BEYOND 7 BAND (IGHER MOBILITY AND ELECTRON VELOCITY CAN BE ENGINEERED BY INCREASING THE PERCENTAGE CONTENT OF INDIUM IN THE CHANNEL OF THE &%4 4HIS CAN BE ACCOMPLISHED UP TO A POINT WHERE BEYOND APPROXIMATELY INDIUM CONTENT THE LATTICE STRAIN DIFFERENTIAL RESULTS IN DEGRADING PERFORMANCE AND RELIABILITY 4HESE TECHNIQUES CAN RESULT IN TRANSISTORS WITH BIGGER BANDGAP DIFFERENCES THAN OTHERWISE POSSIBLE FOR THE CHOSEN MATERIALS 4HE FABRICATION OF THESE TRANSISTORS EMPLOYS THE USE OF ADVANCED SEMICONDUCTOR PROCESSING SUCH AS -OLECULAR "EAM %PITAXY -"% OR -OLECULAR /RGANIC #HEMICAL 6APOR $EPOSITION
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-/#6$ FABRICATION TECHNIQUES TO ACHIEVE THE HIGH PERFORMANCE CHARACTERISTICS 4HESE ARE CAPITAL INTENSIVE SEMICONDUCTOR PROCESSING STEPS THAT ARE REQUIRED IN ORDER TO ACHIEVE THE HIGH QUALITY CHANNEL CHARACTERISTICS THAT DEFINE A MICROWAVE OR MILLIMETER WAVE POWER TRANSISTOR /PTIMIZING THE MOLECULAR CONTENT OF THE &%4 CHANNEL FOR BEST PERFORMANCE IS SOMETIMES REFERRED TO AS BANDGAP ENGINEERING 4HE CHALLENGE FOR THE DEVICE ENGINEER IS TO DEVELOP A TRANSISTOR THAT SUPPORTS THE HIGHEST VOLTAGECURRENT OPERATION WHILE DEMONSTRATING THE BEST HIGH FREQUENCY GAIN
&)'52% 0ERFORMANCE SPACE OF COMMERCIALLY AVAILABLE SILICON POWER TRANSISTORS
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4HE COMPLICATION IN POWER TRANSISTOR DESIGN EXTENDS BEYOND THE EXOTIC MATERIAL FABRICATION TECHNOLOGIES THAT ARE USED TO DEFINE THE BASIC &%4 4AILORED CONSTRUCTION TECHNIQUES ARE USED TO CONTROL THE ELECTRIC FIELD INTENSITY AND IMPROVE THE BREAKDOWN VOLTAGE ENHANCEMENTS SUCH AS THE FIELD PLATE DOUBLE GATE RECESS OR AUTOMATIC ETCH STOP LAYERS ARE FABRICATION AND DESIGN TECHNIQUES THAT ARE USED TO OPTIMIZE THE 0(%-4 PERFORMANCE FOR A GIVEN OPERATING FREQUENCY RANGE TO BRING HIGHER VALUE PERFORMANCE OR RELIABILITY TO THE SEMICONDUCTOR FABRICATION PROCESS 4HE FUNDAMENTAL THREE FINGERED &%4 STRUCTURE DRAIN GATE SOURCE SHOWN AS A 'A!S 0(%-4 &%4 IN CROSS SECTION IN &IGURE HAS POWER PERFORMANCE LIMITATIONS THAT ARE MITIGATED BY EMPLOYING A STRUCTURED DESIGN APPROACH FOR ACHIEVING HIGH POWER OUTPUT LEVELS !S SHOWN IN &IGURE THE SMALLEST PHYSICAL CONSTRUCTION DIMENSION OF THE GATE ELECTRODE IS CALLED THE GATE LENGTH THE LONGER OF THE DIMENSIONS IS CALLED THE GATE WIDTH 4HE CURRENT CARRYING CAPABILITY AND HENCE THE POWER CAPABILITY OF THE &%4 IS INCREASED AS THE GATE WIDTH IS INCREASED 4HERE IS A LIMIT AS TO HOW LONG THE GATE WIDTH CAN BE INCREASED BEFORE PHASE DIFFERENTIAL AND SIGNAL ATTENUATION ALONG THE LONGER DIMENSION OF THE GATE WIDTH BEGIN TO HAVE A DELETERIOUS IMPACT ON AMPLIFIER PERFOR MANCE )N PRACTICE THE MAXIMUM GATE WIDTH CAN BE FOUND TO APPROACH APPROXIMATELY §M §M OR §M FOR 3 BAND 8 BAND OR +A BAND FREQUENCIES RESPECTIVELY 7ITH A LIMITATION ON MAXIMUM GATE WIDTH ADDITIONAL CURRENT AND HENCE POWER CAPABILITY CAN ONLY BE ACHIEVED BY COMBINING MULTIPLE GATE ELECTRODES IN PARALLEL 'ATE ELECTRODES OR FINGERS AS THEY ARE OFTEN REFERRED TO ARE GENERALLY GROUPED IN LOGICALLY CONVENIENT SUBSTRUCTURES CELLS THAT ARE STEPPED AND REPEATED TO FORM A SYMMETRIC COR PORATE HIERARCHY OF COMBINED TRANSISTORS 4HE OUTPUTS OF ALL FINGERS ARE REQUIRED TO BE COMBINED IN PHASE AND THEN IMPEDANCE MATCHED TO THE APPROPRIATE LEVEL !N INDUSTRY WIDE FIGURE OF MERIT FOR CAPABILITY OF THE SEMICONDUCTOR AND THE UNIT &%4 IS THE POWER OUTPUT DENSITY AND THIS IS GIVEN IN UNITS OF WATTSMM OF TOTAL &%4 GATE WIDTH OR GATE PERIPHERY &OR OPERATING VOLTAGES OF n VOLTS A NORMALIZED POWER OUTPUT DENSITY OF n 7MM SHOULD BE EXPECTED FOR MORE ADVANCED 'A!S 0(%-4 STRUCTURES OPER ATING AT n VOLTS ONE CAN EXPECT TO DELIVER n 7MM OF NORMALIZED POWER OUTPUT DENSITY 4HUS TO ACHIEVE A POWER LEVEL OF WATTS AT '(Z WHEN OPERATING FROM VOLTS APPROXIMATELY GATE FINGERS MUST SOMEHOW BE COMBINED IN PARALLEL TO
&)'52% #ROSS SECTION OF A §M DOUBLE GATEnRECESSED 'A!S 0(%-4 TRANSISTOR SHOWING GATE DRAIN AND SOURCE METALS 0HOTOGRAPH COURTESY OF 2AYTHEON #OMPANY
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&)'52% 4YPICAL TWO STAGE 'A!S --)# POWER AMPLIFIER WITH INSERT SHOWING MULTIPLE PARALLELED GATE FINGERS IN FINAL STAGE UNIT CELL 0HOTOGRAPH COURTESY OF 2AYTHEON #OMPANY
DELIVER THE POWER (IGHER NUMBERS OF PARALLELED FINGERS NECESSARILY LEAD TO DECREASING INPUT AND OUTPUT IMPEDANCES FURTHER COMPLICATING THE ABILITY TO PROVIDE THE DESIRED IMPEDANCE MATCH OVER THE DESIRED BANDWIDTH (IGHER IMPEDANCE TRANSFORMATION RATIOS AND WIDER BANDWIDTHS INVARIABLY CONTRIBUTE TO ADDITIONAL LOSS IN THE MATCH ING NETWORKS WHETHER THESE NETWORKS ARE HYBRID CONSTRUCTION OR --)# CONSTRUCTION !DDITIONAL LOSSES DEGRADE THE INHERENT POWER GAIN AND EFFICIENCY CHARACTERISTICS OF THE INTRINSIC &%4 4HE MOST APPROPRIATE AMPLIFIER DESIGN FOR A GIVEN APPLICATION REQUIRES OPTIMIZATION OF THE TRANSISTOR AND THE VARIABLES THAT AFFECT THAT OPTIMIZATION SUCH AS UNIT GATE LENGTH GATE WIDTH NUMBER OF GATE FINGERS CELL CONSTRUCTION IMPEDANCE MATCHING CIRCUITS AND BIAS NETWORKS ALL REQUIRE DETAILED ATTENTION DURING THE DESIGN OF THE AMPLIFIER %XCELLENT COMPILATIONS OF INDUSTRY PERFORMANCE HAVE BEEN PUBLISHED FOR FURTHER INSIGHT 4HESE REFERENCES OUTLINE STATE OF THE ART POWER OUTPUT DENSITY AND EFFICIENCIES OF COMPOUND SEMICONDUCTORS FROM THROUGH '(Z 7IDE "ANDGAP 3EMICONDUCTORS 3INCE THE INCEPTION OF SOLID STATE :OLPER DRAWS HISTORICAL REFERENCE TO THE FIRST SECOND AND THIRD GENERATION OF SEMICONDUC TOR MATERIALS AS SILICON GALLIUM ARSENIDE OR INDIUM PHOSPHIDE AND THE SO CALLED WIDE BANDGAP SEMICONDUCTORS 7"'3 4HE LATTER ARE DOMINATED BY THE SILICON CARBIDE 3I# -%3&%4 AND THE GALLIUM NITRIDE !L'A.'A. HETEROJUNCTION FIELD EFFECT TRANSISTOR (&%4 4HE ADVENT OF THE THIRD SEMICONDUCTOR GENERATION OPENS ENORMOUS NEW POSSIBILITIES IN THE AREA OF HIGH POWER AMPLIFIERS FOR USE IN SOLID STATE 4HE 7"'3 MATERIALS ARE ABLE TO PRODUCE VERY HIGH POWER OUTPUT LEVELS n WMM
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FROM HIGH BUS VOLTAGES n VOLTS WHILE MAINTAINING TRANSISTOR LIKE PROPERTIES AT HIGHER OPERATING TEMPERATURES THAN 3I OR 'A!S 4HEY ARE FINDING APPLICATION IN THE 3 BAND # BAND OR 8 BAND FREQUENCY RANGES 4HE INTEREST IN DEVELOPMENT IS BEING FUELED BY BOTH THE MILITARY FOR HIGH PERFORMANCE SENSORS AND ALSO BY COMMERCIAL INTERESTS FOR HIGH POWER WIRELESS BASE STATION AMPLIFIERS )N PARTICULAR THE 'A. (&%4 DEVICE DEMONSTRATES PHYSICAL PROPERTIES THAT MAKE IT USEFUL AS A HIGH GAIN DEVICE WITH VERY HIGH POWER OUTPUT CAPABILITY INTO THE 7 BAND 4HE 3I# -%3&%4 WILL LIKELY BE COMPETITIVE AT THE LOWER FREQUENCY RANGES OF , BAND THROUGH # BAND 4HE THERMAL CONDUCTIVITY OF THE 3I# SUBSTRATE IS SUPERIOR TO 'A!S BY NEARLY AN ORDER OF MAGNITUDE AND THE NORMALIZED POWER OUTPUTS ARE MUCH MUCH HIGHER IN THE WIDE BANDGAP SEMICONDUCTORS THAN CURRENTLY BEING ACHIEVED USING 'A!S AT ANY VOLT AGE 4HE HIGHER THERMAL CONDUCTIVITY OF 3I# ENABLES MORE EFFICIENT THERMAL MANAGE MENT #OUPLED WITH THE HIGH BREAKDOWN VOLTAGE AND CHANNEL CURRENT CAPABILITY OF THE 3I# -%3&%4 MEASURED RESULTS OF WATTS OF #7 POWER OUTPUT WITH AN D" ASSOCI ATED LEVEL OF LARGE SIGNAL GAIN AT '(Z FROM A 6 DRAIN SUPPLY VOLTAGE HAVE BEEN REPORTED FROM A SINGLE TRANSISTOR CELL %LECTRON MOBILITY IN THE 'A. (%-4 AT SATURATED DRIFT VELOCITIES IS HIGH ENOUGH THAT HIGH GAIN WITH SIMULTANEOUS HIGH POWER OUTPUT AND HIGH EFFICIENCIES CAN BE ACHIEVED WITH VOLTAGES AS LOW AS TO VOLTS 7ITH A 'A. EPITAXIAL LAYER PROCESSED ON A 3I# SUBSTRATE THE CURRENT STATE OF THE ART FOR TRANSISTOR PERFORMANCE IS DEFINED ON SEVERAL FRONTS IN THE SEMICONDUCTOR INDUSTRY BY THE FOLLOWING PERFORMANCES PULSED POWER ADDED EFFICIENCY 0!% OF AT 6 AND '(Z ON A MM &%4 AND #7 POWER OF 7 AT 6 AND '(Z ON A SINGLE MM TRANSISTOR POWER DENSITY OF 7MM AT '(Z LESS THAN D" POWER DEGRADATION AFTER HOURS 2& OPERATION AT 6 WITH CHANNEL TEMPERATURES OF n# 0OWER ADDED EFFICIENCY IS A CIRCUIT DESIGNERS TERM AND IS DEFINED BY 0!% 0/ 0) 0$#
WHERE 0/ IS THE 2& POWER OUTPUT 0) IS THE 2& POWER INPUT AND 0$# IS THE TOTAL DC POWER INPUT &IGURE AND &IGURE ILLUSTRATE THE ADVANTAGES OF 'A. AT '(Z WHEN COMPARED WITH THE PHYSICAL GEOMETRY OF AN IDENTICALLY SIZED 'A!S 0(%-4 TRANSISTOR
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&)'52% 4YPICAL '(Z PERFORMANCE CURVES FOR A MM PERIPHERY 'A. (%-4 &%4 OPERATING AT 6 USING A #7 DUTY WAVEFORM
)N THIS EXAMPLE A 'A!S 0(%-4 WITH MM OF TOTAL GATE PERIPHERY &IGURE IS COMPARED WITH AN IDENTICAL MM 'A. (%-4 &IGURE 4HESE FIGURES PORTRAY THE POWER OUTPUT 0O POWER ADDED EFFICIENCY 0!% AND GAIN 'N 0ERFORMANCE FOR EACH IS REFERENCED TO '(Z FOR #7 OPERATION 4HE 'A!S 0(%-4 OPERATES AT 6 THE 'A. (%-4 OPERATES AT 6 &ROM THESE PERFORMANCE CURVES ONE SEES THAT THE SMALL SIGNAL GAINS ARE NEARLY IDENTICAL IN THE n D" RANGE AS ARE THE LARGE SIGNAL EFFICIENCIES BUT THE POWER OUTPUT CAPABILITY OF THE 'A. (%-4 IS D" GREATER THAN FOR THE 'A!S 0(%-4 OF THE SAME SIZE
££°{Ê - Ê",Ê/ Ê-" -// ÊÊ "// Ê/, - // , 2ADAR TRANSMITTER DESIGN INVARIABLY REQUIRES SIGNIFICANT RADIATED POWER FROM THE ANTENNA IN ORDER TO PROJECT TO THE MINIMUM RANGE REQUIREMENT WHILE MAINTAINING SOME MINIMUM SIGNAL TO NOISE RATIO ON RECEIVE 4HE IMPACT OF THE REQUIREMENT FOR HIGH RADI ATED POWER IS FUNDAMENTAL TO THE DESIGN OF SOLID STATE TRANSMITTERSHIGH POWER MUST BE ACHIEVED BY COMBINING THE OUTPUTS OF LOWER POWER AMPLIFIERS IN ORDER TO DEVELOP THE REQUIRED RADIATED LEVELS 4RANSISTOR FINGERS ARE COMBINED INTO --)# AMPLIFI ERS AMPLIFIERS ARE COMBINED INTO MODULES AND MODULES ARE COMBINED INTO SYSTEMS 'ENERALLY THE COMBINING TAKES ON ONE OF TWO DIFFERENT CONFIGURATIONS USING EITHER SPACE COMBINED OR CORPORATE COMBINED ARCHITECTURES 4HE PHASED ARRAY IS A COMMON EXAMPLE OF THE SPACE COMBINED CONFIGURATION WHEREIN EACH RADIATING ANTENNA ELE MENT IS FED BY AN AMPLIFIER MODULE AND THE WAVEFRONT IS FORMED IN SPACE 4HE COM MON EXAMPLE OF THE CORPORATE COMBINED DESIGN IS THE hSOLID STATE BOTTLE v WHEREIN A MECHANICALLY ROTATING ANTENNA IS FED FROM A SINGLE PORT AND THE POWER AT THE PORT IS THE SUMMATION OF THE OUTPUTS OF MANY AMPLIFIER MODULES 4HOSE MODULES MIGHT BE PHYSICALLY LOCATED FOR EXAMPLE BELOW DECK ON A SHIP AWAY FROM THE ANTENNA 3OLID STATE TRANSMITTER DESIGNS HAVE BEEN BUILT AROUND EACH OF THESE GENERIC FORMS AND THE COMPONENTS THAT ARE REQUIRED IN THE IMPLEMENTATION OF EACH SHARE SIMILAR CHARACTER ISTICS AND DEVICES
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)N THE CORPORATE COMBINED SOLID STATE BOTTLE HIGH POWER LEVELS ARE GENERATED AT A SINGLE POINT BY COMBINING THE OUTPUTS OF MANY POWER AMPLIFIER MODULES )N GENERAL A POWER AMPLIFIER MODULE AS SHOWN IN &IGURE CONSISTS OF A NUMBER OF IDENTICAL AMPLIFIERS THAT ARE PARALLEL COMBINED AND ISOLATED FROM ONE ANOTHER THROUGH THE USE OF MICROWAVE COMBINING AND ISOLATING TECHNIQUES $RIVE POWER FOR THIS PARALLEL GROUP IS OBTAINED FROM DRIVER OR PREDRIVER STAGES USING PHASE AND AMPLITUDE MATCHED MIR ROR IMAGED MICROWAVE POWER DIVIDERS ! CIRCULATOR AT THE MODULE OUTPUT PORT IS COM MONLY USED TO PROTECT THE AMPLIFIER FROM THE DAMAGING EFFECTS OF HIGH LOAD 6372 MOST NOTABLY FROM THE ANTENNA !LSO ANCILLARY CIRCUITRY SUCH AS ENERGY STORAGE CAPACI TANCE FOR PULSED OPERATION BUILT IN TEST ")4 SENSORS OR ADAPTIVE CONTROL COMPONENTS MAY BE INCLUDED !MPLIFIER -ODULE $ESIGN 3OLID STATE AMPLIFIERS FOR USE IN TRANSMITTER DESIGN ARE OFTEN REFERENCED BY THEIR CLASS OF OPERATION !MPLIFIERS ARE DESIGNATED AS OPERATING EITHER #LASS ! " !" # $ % & OR ' #LASS ! !" " AND
# GENERALLY REFER TO ANALOG AMPLIFIERS WHEREAS #LASS $ % & AND ' GENERALLY REFER TO SWITCHING MODE AMPLIFIERS %ACH CLASS OF OPERATION FOR THE ANALOG MODES IS DEFINED BY THE MANNER IN WHICH THE TRANSISTOR IS BIASED EACH CLASS OF OPERATION
&)'52% 3OLID STATE POWER AMPLIFIER MODULE COMBINES MANY SINGLE STAGE AMPLIFIERS TOGETHER WITH MATCHED PHASE AND AMPLITUDE USING RESISTIVELY ISOLATING COMBINING TECHNIQUES
3/,)$ 34!4% 42!.3-)44%23
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FOR THE SWITCHING MODES IS DEFINED BY THE MANNER IN WHICH THE TRANSISTOR IS BIASED AND HOW THE WAVESHAPE OF CURRENT AND VOLTAGE IS MANIPULATED &OR EXAMPLE CURRENT SWING IN AN AMPLIFIER THAT IS BIASED #LASS ! REPLICATES EXACTLY THE INPUT SIGNAL UP TO THE POINT WHERE THE TRANSISTOR VOLTAGE AND CURRENT LIMITS ARE REACHED )N PRACTICE #LASS ! AMPLIFIERS ARE THE MOST LINEAR AS WELL AS THE LEAST EFFICIENT (IGH DYNAMIC RANGE LINEAR RECEIVE AMPLIFIERS ARE BIASED #LASS ! AND AUDIO AMPLIFIERS MAY BE ALSO BE BIASED #LASS ! TO PRESERVE THE LINEARITY OF THE INPUT SIGNAL #LASS " AMPLIFIERS ARE BIASED SUCH THAT CONDUCTING CURRENT IN THE TRANSISTOR FLOWS FOR EXACTLY ONE HALF OF THE INPUT SIGNAL VOLTAGE SWING 0USH PULL AMPLIFIERS MAY BE BIASED IN THIS FASHION SUCH THAT ONE TRANSISTOR OPERATES OVER THE POSITIVE INPUT SIGNAL SWING AND THE SEC OND TRANSISTOR OPERATES OVER THE NEGATIVE INPUT SIGNAL SWING (IGHER EFFICIENCY BUT HIGHER DISTORTION IS EXPERIENCED WHEN COMPARED WITH A #LASS ! DESIGN 4HE #LASS !" OPERATED AMPLIFIER IS BIASED JUST ABOVE CONDUCTION USING A TRICKLE QUIESCENT CURRENT AND IS ALSO COMMONLY USED AS A PUSH PULL AMPLIFIER #LASS # AMPLIFIERS ARE BIASED SUCH THAT CONDUCTING CURRENT IN THE TRANSISTOR FLOWS FOR LESS THAN OF THE INCIDENT INPUT VOLTAGE SIGNAL 4HIS ALLOWS FOR THE HIGHEST EFFICIENCY AT THE EXPENSE OF POWER GAIN AND WITH THE HIGHEST LEVEL OF NONLINEAR OPERATION #LASS # BIASED TRANSISTORS ARE ACTUALLY hOFFv WITHOUT THE PRESENCE OF AN 2& SIGNAL ON THE INPUT &OR USE IN RADAR TRANSMITTER AMPLIFIERS THE #LASS # AMPLIFIER OFFERS HIGHER EFFICIENCY OVER #LASS ! " OR !" )N PRACTICE THEY CAN BE MADE TO BE hSELF BIASINGv AND HAVE BEEN THE PREFERRED CLASS OF OPERATION FOR THE SILICON BIPOLAR TRANSISTORS USED AT 5(& , BAND AND 3 BAND "ECAUSE THIS CLASS OF OPERATION IS INHERENTLY NONLINEAR AS THE TRANSISTOR MODULATES BETWEEN BEING OFF AND SATURATED THROUGH EACH 2& CYCLE THE HARMONIC CONTENT IS HIGH AND APPROPRIATE FILTERING OF UNDESIRED HIGHER ORDER SPEC TRAL CONTENT MUST BE APPLIED AT THE OUTPUT OF THE TRANSMITTER 4HE AMPLIFIER #LASS $
% & AND ' ARE HIGH EFFICIENCY SWITCHING AMPLIFIER CONFIGURATIONS THAT REQUIRE SPECIALIZED TERMINATION OF THE SIGNAL HARMONICS FILTERING IN ORDER TO MAXIMIZE THE AMPLIFIER EFFICIENCY 4HESE CAN BE COMPLICATED HARDWARE IMPLEMENTATIONS BUT MAY BE WARRANTED WHERE INCREMENTAL IMPROVEMENT IN EFFICIENCY BRINGS BENEFIT TO THE TRANSMITTER SYSTEM 3ILICON "*4S THAT OPERATE IN THE (& THROUGH 3 BAND FREQUENCY RANGES ARE COMMONLY BIASED EITHER #LASS " OR #LASS # #LASS # OPERATION IS THE PREFERRED MODE BECAUSE THE 2& OUTPUT POWER OF THE AMPLIFIER IS MAXIMIZED FOR A GIVEN PRIME POWER INPUT )N GENERAL THE BASE EMITTER JUNCTION IS REVERSE BIASED AND COLLECTOR CURRENT IS DRAWN FOR LESS THAN HALF OF AN 2& CYCLE #OLLECTOR CURRENT IS DRAWN ONLY WHEN THE INPUT VOLTAGE EXCEEDS THE REVERSE BIAS ACROSS THE INPUT AND THE OUTPUT VOLTAGE IS DEVELOPED ACROSS A RESONANT TUNED LOAD 4HE NET RESULT IS HIGH AMPLIFIER EFFICIENCY 4HE PRACTICAL IMPLICA TIONS OF A #LASS # BIASED AMPLIFIER STAGE ARE AS FOLLOWS .O QUIESCENT DC CURRENT IS DRAWN WHILE THE DEVICE IS NOT BEING DRIVEN SUCH AS IN THE RADAR RECEIVE MODE (ENCE THERE IS NO POWER DISSIPATION IN THE AMPLIFIER WHILE THE TRANSMITTER IS OPERATING IN THIS MODE /NLY ONE POWER SUPPLY VOLTAGE IS NECESSARY FOR THE COLLECTOR TERMINAL OF THE TRANSIS TOR 4HE #LASS # OPERATION IS A SELF BIAS WHEREIN THE TRANSISTOR DRAWS COLLECTOR CUR RENT ONLY WHEN THE 2& VOLTAGE SWING ON THE INPUT EXCEEDS THE BUILT IN POTENTIAL OF THE EMITTER BASE JUNCTION !DDITIONAL REVERSE BIASING MAY BE INTRODUCED AS A RESULT OF THE VOLTAGE DROP INDUCED BY CURRENT FLOW ACROSS PARASITIC RESISTANCE OF THE BASE OR EMITTER BIAS RETURN AND IN COMMON BASE OPERATION THIS WILL RESULT IN DEGRADED POWER GAIN
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#LASS # BIASED AMPLIFIERS ARE VERY SENSITIVE TO ANY DEVIATIONS FROM THE NOMINAL OPERATING POINT #LASS # BIASED AMPLIFIERS EXHIBIT SENSITIVITY TO 2& DRIVE LEVEL AND LOAD IMPEDANCE THAT MAY DEGRADE THE OUTPUT PULSE CHARACTERISTICS ! SINGLE STAGE #LASS # BIASED "*4 AMPLIFIER WILL TYPICALLY EXHIBIT A VERY NARROW hLINEARv TRANSFER CHARACTERISTIC THE LINEAR REGION MAY EXIST OVER ONLY A NARROW TO D" WINDOW OF 2& INPUT DRIVE 4HIS BECOMES STRIKINGLY CRITICAL WHEN SEVERAL #LASS # BIASED STAGES ARE CASCADED IN SERIES AS IS COMMON IN MOST AMPLIFIER CONFIGURATIONS 4HE FINAL TIER OF OUTPUT TRANSISTORS IN A SERIAL AMPLIFIER CHAIN MUST BE DRIVEN INTO SATURATION BY THE PRECEDING STAGES AND THE DRIVE LEVEL MUST BE HELD RELATIVELY CONSTANT AS A FUNCTION OF TIME AND TEMPERATURE 3INCE THESE DEVICES EXHIBIT THIS NARROW OPERATING RANGE SMALL DECREASES IN THE INPUT 2& DRIVE LEVEL TO A MULTISTAGE AMPLIFIER MAY BRING THE FINAL TIER OF DEVICES OUT OF SATURATION &AILURE TO CONTROL THESE CONDITIONS ACCURATELY CAN RESULT IN UNACCEPTABLY DEGRADED OUTPUT PULSE FIDELITY
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)N A VERY SIMPLE SENSE THE DESIGN OF AN AMPLIFIER MODULE CONSISTS OF MATCHING THE POWER TRANSISTORS TO THE PROPER IMPEDANCE LEVEL AND THEN COMBINING THE POWER LEVELS AT THESE IMPEDANCES ! TYPICAL PACKAGED POWER TRANSISTOR HAS LOW INPUT AND OUTPUT IMPEDANCES THAT MUST BE TRANSFORMED UP TO HIGHER LEVEL USUALLY OHMS 4HUS THE TYPICAL AMPLIFIER DESIGN TASK MUST ADDRESS BOTH LOW LOSS AND INEXPENSIVE REACTIVE IMPEDANCE TRANSFORMING NETWORKS THAT CAN PROVIDE THE PROPER SOURCE AND LOAD IMPED ANCES TO THE TRANSISTOR 4HE COMMON MEDIUM FOR PROVIDING THIS FUNCTION IS A MICROSTRIP TRANSMISSION LINE -ICROSTRIP IS A QUASI 4%- MODE TRANSMISSION LINE MEDIUM THAT REQUIRES PHOTOLITHOGRAPHICALLY DEFINED LINES ON A LOW LOSS HIGH QUALITY DIELECTRIC SUB STRATE 2EACTIVE COMPONENTS THAT ARE NECESSARY AS IMPEDANCE MATCHING ELEMENTS CAN BE APPROXIMATED IN THE MICROSTRIP FORMAT !N INEXPENSIVE REACTIVE MATCHING NETWORK CAN BE FORMED BY USING AN INTERCONNECTED PATTERN OF MICROSTRIP ELEMENTS 3HUNT AND SERIES CONNECTED INDUCTIVE REACTANCES AS WELL AS SHUNT CAPACITIVE REACTANCES ARE THE MOST EASILY FABRICATED AND MOST FREQUENTLY USED MATCHING ELEMENTS 0OWER #OMBINING ! POWER COMBINER COHERENTLY ADDS TOGETHER THE 2& OUTPUT VOLTAGES OF INDIVIDUAL AMPLIFIERS AND DELIVERS THE SUM TOTAL OF THE MODULES OUTPUT POWER MINUS THE LOSSES OF THE COMBINER TO A SINGLE PORT 4HE OUTPUTS OF IDENTICAL SINGLE STAGE POWER AMPLIFIERS ARE COMMONLY SUMMED BY USING WELL DOCUMENTED SPLITTING AND COMBINING TECHNIQUES &IGURE 4HESE TECHNIQUES ALSO ADDRESS ISOLATION BETWEEN PARALLELED AMPLIFIERS (AVING ISOLATION BETWEEN ADJACENT PORTS MEANS THAT IF ONE DEVICE FAILS THE POWER COMBINER PROVIDES A FIXED LOAD IMPEDANCE TO THE REMAINING DEVICE HOWEVER HALF THE POWER OF THE REMAINING ACTIVE DEVICE WILL BE DISSIPATED IN THE ISOLATION RESISTOR OF THE COMBINER )N ORDER TO ACHIEVE THE MOST EFFICIENT COMBINING OF PARALLEL AMPLIFIER STAGES THE PHASE AND AMPLITUDE BALANCE OF INDIVIDUAL STAGES SHOULD BE AS SIMILAR AS POSSIBLE !NY DEVIATIONS FROM IDENTICAL PHASE AND AMPLITUDE BALANCE RESULT IN POWER OUTPUT LOST TO THE RESISTIVE TERMINATING PORT OF THE COMBINER 4HE POWER LOST TO SIMILARITY DIFFERENCES FROM EITHER PHASE OR AMPLITUDE IS DICTATED BY VECTOR ADDITION AND IS GIVEN BY
0,/34 LOG 31240 0 0 0 #/3P 0 0
WHERE P IS THE PHASE DIFFERENCE IN DEGREES BETWEEN TWO AMPLIFIERS THAT ARE SUMMED TOGETHER 3124 INDICATES THE hSQUARE ROOT OF v AND 0 AND 0 ARE THE POWER LEVELS OF EACH AMPLIFIER IN WATTS &IGURE QUANTIFIES THE IMPACT OF LOST PERFORMANCE DUE TO PHASE OR AMPLITUDE IMBALANCE
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&)'52% #OMMON MICROWAVE POWER COMBINING CIRCUIT TOPOLOGIES THAT ARE USED TO PROVIDE ISOLATION AMONG ADJACENT PARALLEL AMPLIFIERS IN A CORPORATE COMBINING STRUCTURE
#ONTOURS OF 6ECTORAL 0OWER ,OST
0HASE )MBALANCE DEG
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!MPLITUDE )MBALANCE D" &)'52% #ONTOURS OF POWER LOST TO THE ISOLATION LOAD RESISTOR OF AN ISOLATED POWER COM BINER FOR A RANGE OF AMPLITUDE AND PHASE IMBALANCES BETWEEN TWO COMBINED AMPLIFIERS 7ITH AN AMPLITUDE IMBALANCE OF D" AND A PHASE IMBALANCE OF n APPROXIMATELY D" OF POWER WILL BE LOST TO THE ISOLATING TERMINATION OF THE POWER COMBINER
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)N GENERAL THE REQUIREMENTS FOR A POWER COMBINER ARE 4HE COMBINER SHOULD HAVE LOW INSERTION LOSS TO MAXIMIZE TRANSMITTER EFFICIENCY 4HE COMBINER SHOULD HAVE 2& ISOLATION AMONG PORTS SUCH THAT FAILED MODULES DO NOT AFFECT THE LOAD IMPEDANCES OR COMBINING EFFICIENCY FOR THE REMAINING FUNCTIONING MODULES 4HE COMBINER SHOULD PROVIDE A CONTROLLED 2& IMPEDANCE TO THE AMPLIFIER MODULES SUCH THAT THE AMPLIFIER CHARACTERISTICS ARE NOT DEGRADED 4HE DISSIPATED POWER CAPABILITY OF THE POWER COMBINER TERMINATIONS SHOULD BE SUF FICIENT TO ACCOMMODATE ANY COMBINATION OF POWER AMPLIFIER FAILURES 4HE MECHANICAL PACKAGING OF THE POWER COMBINER SHOULD ALLOW MODULES TO BE REPAIRED EASILY 4HE PACKAGING SHOULD ALSO PROVIDE SHORT EQUAL PHASE AND LOW LOSS INTERCONNECTIONS BETWEEN THE AMPLIFIER MODULES AND THE COMBINER
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0OWER COMBINERS MAY BE EITHER ISOLATIVE OR REACTIVE DESIGNS )N ISOLATIVE DESIGNS ANY IMBALANCE OR DIFFERENCE BETWEEN THE PHASE AND AMPLITUDE OF THE VOLTAGES THAT ARE BEING COMBINED IS DIRECTED TO A RESISTIVE TERMINATION 4HE NET RESULT IS THAT A CON STANT LOAD IMPEDANCE IS PRESENTED TO THE AMPLIFIER UNDER ALL CONDITIONS EVEN WHEN AN ADJACENT AMPLIFIER IN A COMBINING TIER HAS FAILED )N A REACTIVE COMBINER DESIGN ANY IMBALANCE IN POWER OR PHASE BETWEEN TWO INPUT SIGNALS RESULTS IN REFLECTED POWER AND INCREASED 6372 TO THE MODULE DRIVING IT (IGHER THAN DESIRED FREQUENCY DEPENDENT PHASE AND AMPLITUDE RIPPLE MAY RESULT FROM IMPROPER USE OF THIS CONFIGURATION ! SPLITTER AND COMBINER NETWORK MAY ALSO PROVIDE SERIAL ISOLATION AMONG CAS CADED AMPLIFIER STAGES AS WELL AS PARALLEL ISOLATION &OR EXAMPLE WHEN A #LASS # BIASED TRANSISTOR IS PULSED IT PASSES THROUGH ITS CUTOFF LINEAR AND SATURATION REGIONS #ONSEQUENTLY THE INPUT AND OUTPUT IMPEDANCES ARE DYNAMICALLY VARYING AND THE INPUT IMPEDANCE CHANGES VERY DRAMATICALLY 4HE DRAMATICALLY CHANGING INPUT IMPED ANCE WILL PRESENT AN UNDESIRABLE LOAD TO THE PRECEDING AMPLIFIER STAGE SUPPLYING THE 2& DRIVE POWER 4HIS MAY VERY WELL SEND THE PREVIOUS STAGE INTO UNWANTED OSCIL LATION (OWEVER A QUADRATURE SPLITTER NETWORK IE A POWER DIVIDER THAT PROVIDES A D" SPLIT AS WELL AS A n PHASE OFFSET CAN BE USED TO PROVIDE A CONSTANT IMPEDANCE AT THE INPUT TO THE SPLITTER REGARDLESS OF THE INDIVIDUAL AMPLIFIER INPUT IMPEDANCES &IGURE 4HIS ENSURES THAT A DRIVER AMPLIFIER STAGE IS PRESENTED WITH A WELL MATCHED LOAD 4YPICAL 2& TRANSMISSION MEDIA THAT ARE USED IN THE CONSTRUCTION OF HIGH POWER COMBINERS INCLUDE COAXIAL TRANSMISSION LINES MICROSTRIP OR STRIPLINE TRANSMISSION LINES OR WAVEGUIDE 4HE CHOICE OF TRANSMISSION MEDIUM IS GENERALLY A FUNCTION OF MANY PARAMETERS INCLUDING PEAK AND AVERAGE POWER HANDLING CAPABILITY OPERAT ING FREQUENCY AND BANDWIDTH MECHANICAL PACKAGING CONSTRAINTS AND OF COURSE THE OVERALL LOSS THAT CAN BE TOLERATED -ORE OFTEN THAN NOT A COMBINER DESIGN UTILIZES A HIERARCHY OF CASCADED DESIGNS TO SUM THE OUTPUTS OF MANY MODULES HOWEVER UNIQUE CONFIGURATIONS THAT SUM MANY PORTS TO A SINGLE PORT HAVE BEEN BUILT !MPLITUDE AND 0HASE 3ENSITIVITIES 4HE PHASE AND AMPLITUDE SENSITIVITY OF TRANSISTOR AMPLIFIERS TO POWER SUPPLY RIPPLE MAY IMPACT THE -4) IMPROVEMENT FACTOR THAT CAN BE ATTAINED )N A MULTISTAGE AMPLIFIER THE PHASE ERRORS DUE TO POWER SUPPLY SENSITIVITY OF SERIALLY CASCADED STAGES WILL ADD )N ADDITION CAREFUL DESIGN MUST TAKE INTO ACCOUNT INTERACTIONS THAT CAN OCCUR AS A RESULT OF THE MANY CASCADED STAGES OF SOLID STATE AMPLIFICATION 4HESE INCLUDE THE FOLLOWING
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&)'52% 0OWER AMPLIFIER COMBINING CONFIGURATIONS THAT PROVIDE MINIMUM INPUT PORT REFLECTED POWER A QUADRATURE COUPLED AMPLIFIER PAIR AND B SPLIT 4 AMPLIFIER PAIR WITH A n OFFSET 4HE AMPLIFIER INPUT VOLTAGE REFLECTION COEFFICIENT IS GIVEN AS ' AND THE AMPLIFIER VOLTAGE GAIN AS ! 2EPRINTED WITH PERMISSION FROM % $ /STROFF ET AL 3OLID 3TATE 4RANSMITTERS .ORWOOD -! !RTECH (OUSE
0HASE ERRORS IN CASCADED STAGES SIMPLY ADD (OWEVER IT MAY ALSO BE POSSIBLE TO ARRANGE THEM TO CANCEL BY PROPER PHASING OF POWER SUPPLY RIPPLES FOR DIFFERENT STAGES 3IMILARLY IN A STAGE WITH . MODULES IN PARALLEL EACH WITH ITS OWN HIGH FREQUENCY POWER CONDITIONED POWER SUPPLY THE OVERALL PHASE RIPPLE CAN USUALLY BE ASSUMED TO BE REDUCED BY A FACTOR EQUAL TO THE SQUARE ROOT OF . IF THE POWER SUPPLY CLOCKS ARE PURPOSELY NOT SYNCHRONIZED "ECAUSE OF SATURATION EFFECTS AMPLITUDE ERRORS IN CASCADED STAGES DO NOT SIMPLY ADD (OWEVER AMPLITUDE ERRORS IN DRIVING STAGES WILL CAUSE DRIVE INDUCED PHASE VARIA TIONS IN THE FOLLOWING STAGES AS NOTED ABOVE ALL OF WHICH MUST BE COUNTED 4IME JITTER IN CASCADED STAGES SIMPLY ADDS UNLESS THE STAGES ARE ARRANGED TO CANCEL OR TO BE ROOT SUM SQUARED )N ADDITION AMPLITUDE FLUCTUATIONS IN THE 2& DRIVE WILL ALSO CAUSE DRIVE INDUCED JITTER WHICH MAY EVEN EXCEED POWER SUPPLY RIPPLE INDUCED JITTER SO THIS FACTOR MUST BE CAREFULLY MEASURED
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3PECTRAL %MISSIONS 7HEN A RECTANGULAR 2& DRIVE PULSE IS APPLIED TO A SINGLE MODULE THE AMPLIFIER WILL TYPICALLY SHOW RISE AND FALL TIMES THAT ARE ON THE ORDER OF NANOSECONDS 4HE OUTPUT SIGNAL SPECTRUM OF THIS PULSE SHAPE MAY NOT MEET SPEC TRAL EMISSIONS REQUIREMENTS AND IT MAY BE NECESSARY TO SLOW THE RISE AND FALL TIMES (OWEVER THE AMPLIFIER OPERATING REGION OF OPTIMUM EFFICIENCY OCCURS AS THE TRAN SISTOR IS DRIVEN INTO SATURATION AND FOR A LARGE TRANSMITTER THERE MAY BE NUMEROUS TIERS OF CASCADED SATURATED AMPLIFIERS 7ITH SO MANY CASCADED SATURATING AMPLIFIERS IT BECOMES VERY DIFFICULT TO CONTROL THE RISE AND FALL TIMES AS A RESULT OF THE NONLINEARITY THAT IS INTRODUCED INTO THE POWER TRANSFER FUNCTION FOR THE TRANSMITTER #ONSEQUENTLY AN INPUT PULSE SHAPE WITH VERY EXAGGERATED SLOW RISE AND FALL TIMES MAY BE NECESSARY TO ACHIEVE THE DESIRED OUTPUT PULSE SPECTRAL COMPOSITION
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2!$!2 (!.$"//+
££°xÊ - Ê",Ê/ Ê-" -// Ê *- Ê,,9Ê/, - // , )N CONTRAST TO THE DESIGN OF THE SOLID STATE BOTTLE TRANSMITTER WHERE SIGNIFICANT LOSSES CAN ACCRUE IN THE COMBINING CIRCUITRY THE SOLID STATE PHASED ARRAY ANTENNA USES INDIVIDUAL TRANSMITRECEIVE 42 MODULES WITH INTERNAL PHASE SHIFT CAPABILITY %ACH 42 MODULE IS LOCATED BEHIND AN ASSOCIATED RADIATING ELEMENT IN A TWO DIMENSIONAL ARRAY )N THIS FASHION THE BEAM IS MORE EFFICIENTLY FORMED IN SPACE AND ONE AVOIDS THE LOSSES THAN CAN ACCUMULATE IN CORPORATE COMBINING 4HE TRANSMITRECEIVE 42 MODULE REGARD LESS OF COMPLEXITY HAS FIVE FUNDAMENTAL FUNCTIONS TO PROVIDE GAIN AND POWER OUTPUT IN THE TRANSMIT MODE TO PROVIDE GAIN AND LOW NOISE FIGURE IN THE RECEIVE MODE TO SWITCH BETWEEN TRANSMIT AND RECEIVE STATES TO PROVIDE PHASE SHIFT FOR BEAM STEERING FOR BOTH TRANSMIT AND RECEIVE PATHS AND TO PROVIDE SELF PROTECTION FOR THE LOW NOISE AMPLIFIER 4HE FIRST 42 MODULE WAS DEVELOPED BY 4EXAS )NSTRUMENTS IN THE MID S AS PART OF THE -OLECULAR %LECTRONICS FOR 2ADAR !PPLICATIONS -%2! PROGRAM INITI ATED BY THE 53 !IR &ORCE TO DETERMINE THE FEASIBILITY OF USING 8 BAND 42 MODULES IN A SOLID STATE PHASED ARRAY RADAR !S A RESULT OF CONTINUOUS DEVELOPMENT PHASED ARRAYS ARE USED IN MULTIPLE MILITARY AND COMMUNICATIONS SYSTEMS 4HE ADVANTAGES OF A PHASED ARRAY TRANSMITTER INCLUDE THE ABILITY TO HAVE MULTIPLE INDEPENDENTLY STEERED BEAMS FROM A SINGLE APERTURE THE SPEED OF ELECTRONIC VERSUS MECHANI CAL BEAM LOCATIONS AND THE EFFICIENCY OF UTILIZING SPACE COMBINING INSTEAD OF PERFORMING THE POWER COMBINING BEFORE THE ANTENNA "LOCK DIAGRAMS OF REPRESEN TATIVE 42 MODULE FUNCTIONS ARE SHOWN IN &IGURE &UNCTIONALLY THESE ARE ALL EQUIVALENT BUT THE PARTITIONING OF CIRCUIT FUNCTIONS IS DEPENDENT ON THE CAPABILITY OF THE --)#S USED AND DIFFERENT IMPLEMENTATIONS MAY BE REQUIRED TO ADDRESS A KEY RELIABILITY REQUIREMENT OR A KEY PERFORMANCE PARAMETER &OR EXAMPLE THE USE OF A SINGLE HIGH PERFORMANCE POWER AMPLIFIER MAY OBVIATE THE NEED FOR COMBIN ING TWO LESSER POWER AMPLIFIERS TOGETHER TO ACHIEVE THE SAME PERFORMANCE 4HESE REPRESENT COST CAPABILITY AND AVAILABILITY TRADES THAT MIGHT BE EXERCISED BY THE 42 MODULE ARCHITECT -ICROWAVE -ONOLITHIC )NTEGRATED #IRCUITS --)#S $URING THE S IT WAS THE REDUCTION TO PRACTICE OF THE MICROWAVE MONOLITHIC INTEGRATED CIRCUIT --)# THAT ENABLED MOST HIGH FREQUENCY PHASED ARRAYS TO BE REALIZED --)# USE IN 42 MODULE DESIGN HAS ENABLED BOLD NEW MODULE CONFIGURATIONS AND HENCE PHASED ARRAY SYSTEMS TO BE ENVISIONED "ECAUSE SOME OF THE MORE COMPLEX FUNCTIONS IN THE GENERIC 42 MODULE BLOCK DIAGRAM CAN BE FABRICATED BY USING --)# TECHNOLOGY THE COM PONENTS THAT CAN BE REALIZED THROUGH THE USE OF THIS TECHNOLOGY CAN BE EMPLOYED TO CREATE SYSTEM ARCHITECTURES THAT ARE DIFFICULT IF NOT IMPRACTICAL TO DESIGN WITH OTHER LESS INTEGRATED TECHNOLOGIES 4HE --)# DESIGN APPROACH UTILIZES ACTIVE AND PASSIVE DEVICES THAT HAVE BEEN MANUFACTURED BY USING A SINGLE PROCESS !CTIVE AND PASSIVE CIR CUIT ELEMENTS ARE FORMED ON A SEMI INSULATING SEMICONDUCTOR SUBSTRATE THROUGH VARI OUS DEPOSITION SCHEMES 4HE MONOLITHIC APPROACH TO CIRCUIT DESIGN INHERENTLY OFFERS SEVERAL ADVANTAGES ,OW COST CIRCUITRY #OMPONENT ASSEMBLY IS ELIMINATED BECAUSE COMPLEX CIRCUIT CONFIGURATIONS USING BOTH ACTIVE AND PASSIVE COMPONENTS ARE BATCH PROCESSED ON THE SAME SUBSTRATE
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3/,)$ 34!4% 42!.3-)44%23
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&)'52% #OMMON 42 MODULE CONFIGURATIONS MAKE USE OF POWER AMPLIFIERS LOW NOISE AMPLIFIERS DUPLEXERS SWITCHES AND CONTROLS TO ENABLE ON FACE BEAM STEERING IN A PHASED ARRAY ANTENNA !RCHITECTURE VARIATIONS MAY RESULT FROM COMPONENT CAPABILITY DIFFERENCES AS WELL AS PERFORMANCE AND PACKAGING CONSTRAINTS
)NCREASED RELIABILITY "ATCH PROCESSED COMPONENTS LEAD TO A REDUCED NUMBER OF PARTS FROM THE RELIABILITY STANDPOINT AND HENCE TO INCREASED OPERATING LIFETIMES )NCREASED REPRODUCIBILITY #IRCUITRY THAT IS BATCH PROCESSED OR CIRCUITS THAT ORIGI NATE FROM THE SAME WAFER EXHIBIT CONSISTENT ELECTRICAL CHARACTERISTICS FROM COMPONENT TO COMPONENT 3MALL SIZE AND WEIGHT )NTEGRATION OF ACTIVE AND PASSIVE COMPONENTS ONTO A SINGLE CHIP RESULTS IN HIGH DENSITY CIRCUITRY WITH MULTIPLE FUNCTIONS ON A SINGLE CHIP /VERALL THE 42 MODULE CAN BE MADE MUCH SMALLER THAN WITH DISCRETE COMPONENTS
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4HE PARTITIONING OF 42 MODULE CIRCUIT FUNCTIONS ONTO MONOLITHIC CHIPS USUALLY REP RESENTS A TRADEOFF AMONG SEVERAL DESIGN ISSUES AND THE RESULTANT CIRCUIT CONFIGURATIONS REPRESENT A COMPROMISE AMONG THE GOALS OF OPTIMUM 2& PERFORMANCE HIGH LEVELS OF INTEGRATION AND FABRICATION YIELDS THAT ARE CONSISTENT WITH PROCESSING CAPABILITIES OF 'A!S --)#S !MONG THE SINGLE CHIP CIRCUIT DESIGNS THAT HAVE BEEN REPORTED FROM 5(& THROUGH MILLIMETER WAVE FREQUENCIES ARE POWER AMPLIFIERS LOW NOISE AMPLIFI ERS WIDEBAND AMPLIFIERS PHASE SHIFTERS ATTENUATORS 42 SWITCHES AND OTHER SPECIAL FUNCTION DESIGNS .OTEWORTHY DESIGN CONSIDERATIONS FOR THESE --)# FUNCTIONS ARE DESCRIBED NEXT
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2!$!2 (!.$"//+
0OWER !MPLIFIERS 4HE AREA CONSUMED BY COMBINING IN PARALLEL THE TOTAL NUM BER OF GATE FINGERS IE TOTAL GATE PERIPHERY IS USUALLY AT A PREMIUM &OR HIGH POWER DESIGN THE LOAD IMPEDANCE PRESENTED TO THE FINAL DEVICE MUST BE CAREFULLY CHOSEN SUCH THAT POWER OUTPUT AND EFFICIENCY ARE MAXIMIZED !LSO TOO MUCH GATE PERIPHERY MAY INCREASE THE CHIP AREA SUCH THAT COST OF THE COMPONENT BECOMES UNATTRACTIVE ,OSSES IN THE OUTPUT CIRCUIT OF THE FINAL STAGE CAN SIGNIFICANTLY REDUCE POWER OUTPUT AND EFFICIENCY /FF CHIP MATCHING MAY BE NECESSARY TO MAXIMIZE POWER OUTPUT FOR A GIVEN DESIGN 'A!S IS A POOR THERMAL CONDUCTOR 0OWER &%4 DESIGN THAT ADDRESSES THERMAL MANAGEMENT IS REQUIRED !DEQUATE HEAT SINKING OF THE CHIP IS MANDATORY AND MAY BECOME A LIMITING FACTOR IN HIGH PERFORMANCE DESIGNS #AREFUL ATTENTION MUST BE PAID TO UNPLANNED VOLTAGE STRESSES ON THE POWER AMPLIFIER EITHER FROM TRANSIENT INDUCED EFFECTS OR LOAD IMPEDANCE VARIATIONS IN ORDER TO MAINTAIN THE DESIRED RELI ABILITY &OR EFFICIENT MULTIPLE STAGE DESIGNS IT IS NECESSARY THAT THE FINAL STAGE OF THE AMPLIFIER REACH SATURATION BEFORE THE PRECEDING STAGES 4HIS MUST BE ADDRESSED IN THE CIRCUIT DESIGN ,OW .OISE !MPLFIIERS -ULTIPLE STAGE LINEAR DESIGNS REQUIRE PROPER DEVICE SIZING OF SUCCESSIVE STAGES IN ORDER TO MAINTAIN LOW INTERMODULATION DISTORTION PRODUCTS #IRCUIT LOSSES ON THE INPUT BEFORE THE FIRST STAGE DEGRADE THE NOISE FIGURE OF THE DESIGN THEREFORE SOME DESIGNS UTILIZE OFF CHIP MATCHING 4HE BEST NOISE FIGURE USUALLY REQUIRES A BIAS CONDITION THAT IS CLOSER TO THE PINCH OFF VOLTAGE OF THE &%4 THAN FOR A POWER AMPLIFIER 4HE PINCH OFF VOLTAGE IS THE VOLTAGE THAT WHEN APPLIED TO THE GATE TERMINAL CAUSES THE CURRENT IN THE TRAN SISTOR CHANNEL TO STOP FLOWING 4HUS THE TRANSISTOR IS hPINCHED OFFv AND VARIABILITY AROUND THIS OPERATING POINT CAN CAUSE LARGE CIRCUIT PERFORMANCE VARIABILITY IF DESIGNED POORLY "OTH GAIN AND NOISE FIGURES ARE HIGHLY DEPEN DENT ON THE PINCH OFF VOLTAGE WHEN THE &%4 IS BIASED CLOSE TO PINCH OFF "ECAUSE THE PINCH OFF VOLTAGE CAN VARY AMONG DEVICES FROM THE SAME WAFER THE BIAS CONDITION MUST BE CHOSEN CARE FULLY 'AIN AND NOISE FIGURES ARE USUALLY TRADED OFF AGAINST REPEAT ABLE PERFORMANCE %XAMPLES OF AN , BAND TWO STAGE LOW NOISE AMPLIFIER 'A!S --)# AND AN , BAND LOW NOISE AMPLIFIER --)# 3HOWN 8 BAND POWER AMPLIFIER 'A!S &)'52% HERE ARE THE SPIRAL INDUCTORS METAL NITRIDE METAL CAPACITORS --)# ARE SHOWN IN &IGURE AND VIA HOLE CONNECTIONS TO GROUND 0HOTOGRAPH COURTESY OF AND &IGURE RESPECTIVELY 2AYTHEON #OMPANY
3/,)$ 34!4% 42!.3-)44%23
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&)'52% 8 BAND TWO STAGE POWER AMPLIFIER --)# SHOWING PARAL LEL COMBINATION OF &%4 CELLS IN THE OUTPUT STAGE 4HIS EXAMPLE WAS FABRI CATED ON §M THICK 'A!S SUBSTRATE 4HE 2& LINES ARE MICROSTRIP FORMAT 4%- MODE TRANSMISSION LINES 0HOTOGRAPH COURTESY OF 2AYTHEON #OMPANY
4RANSMIT2ECEIVE 3WITCHING &OR SWITCHING APPLICATIONS THE &%4 DESIGN SHOULD BE CHOSEN SUCH THAT THE RATIO OF /&& /. RESISTANCE OF THE &%4 IS KEPT AS HIGH AS POSSIBLE 4HE CHANNEL LENGTH LARGELY DETERMINES THE /. RESISTANCE AND HENCE THE INSER TION LOSS OF THE DEVICE 4HE TRADEOFF BETWEEN SHORT GATE LENGTH THUS LOWER PROCESSING YIELD AND INSERTION LOSS MUST BE EXAMINED 4HE VALUE OF THE PARASITIC DRAIN SOURCE CAPACITANCE WILL AFFECT THE /&& STATE ISOLATION OF THE DEVICE 4HIS CAPACITANCE DEPENDS LARGELY ON THE SOURCE DRAIN SPACING OF THE &%4 GEOMETRY #RITICAL APPLICATIONS ARE USUALLY ONLY THE FRONT END SWITCHING CONFIGURATIONS IN A 42 MODULE IE BEFORE THE RECEIVE LOW NOISE AMPLIFIER OR AFTER THE TRANSMIT AMPLIFIER 0HASE 3HIFTERS $IGITALLY CONTROLLED PHASE SHIFTER DESIGNS GENERALLY UTI LIZE EITHER A SWITCHED LINE OR A LOADED LINE CIRCUIT CONFIGURATION USING EITHER DISTRIBUTED TRANSMISSION LINE COMPONENTS OR LUMPED ELEMENT EQUIVALENT CIRCUITS TO ACHIEVE MULTIPLE BIT PHASE SHIFTING 3WITCHED LINE CONFIGURATIONS RELY ON &%4 SWITCHES TO SWITCH LENGTHS OF TRANSMISSION LINE IN AND OUT OF THE CIRCUIT AND ARE TYPICALLY USED FOR HIGHER FREQUENCIES WHERE LESS CHIP AREA IS NEEDED ,OADED LINE CONFIGURATIONS USE THE SWITCHED &%4 PARASITICS AS CIRCUIT ELEMENTS TO INTRODUCE THE NECESSARY PHASE CHANGES 4HE TYPICAL PROCESSING AND CONSTRUCTION SEQUENCE FOR A --)# CHIP IS FAIRLY SIMILAR AMONG THE 'A!S FOUNDRIES &IGURE )N THIS FIGURE THE ACTIVE CHANNEL REGION
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&)'52% 'A!S --)# PROCESSING MAKES USE OF DEPOSITION AND ETCHING TECHNIQUES TO FIRST DEFINE THE ACTIVE CHANNEL REGION OF THE TRANSISTOR n FOLLOWED BY THE DEPOSITION OF METALS DIELECTRIC LAYERS AND RESISTIVE LAYERS FORMING THE PASSIVE COMPONENTS n 4HEN THICK METAL INTERCONNECTS ARE INTRODUCED FOLLOWED BY BACKSIDE PROCESSING TO CONNECT 2& GROUND TO THE TOPSIDE COMPONENTS n
3/,)$ 34!4% 42!.3-)44%23
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OF A &%4 IS DELINEATED BY ANY OF SEVERAL PATTERNING TECHNIQUES ON A SEMI INSULATING 'A!S SUBSTRATE SUCH AS ION IMPLANTATION OR MOLECULAR BEAM EPITAXY /NCE THE &%4 HAS BEEN DEFINED A COMBINATION OF DEPOSITED DIELECTRIC FILMS AND METAL LAYERS IS USED TO FORM THE PASSIVE COMPONENTS SUCH AS METAL INSULATOR METAL CAPACITORS AND ALSO TO INTERCONNECT ALL THE ELEMENTS OF THE CIRCUIT 3TANDARD LIBRARIES OF CIRCUIT ELEMENTS MAY INCLUDE &%4S USED AS LINEAR AMPLIFIERS LOW NOISE AMPLIFIERS SATURATING POWER AMPLIFIERS OR SWITCHES RESISTORS CAPACITORS INDUCTORS DIODES TRANSMISSION LINES INTERCONNECTS AND PLATED GROUND VIAS 4RANSMIT2ECEIVE -ODULE #HARACTERISTICS 4HE IMPACT OF ANTENNA ARRAY ELEC TRICAL REQUIREMENTS ON THE PACKAGING OF --)# COMPONENTS INTO A 42 MODULE IS FUN DAMENTAL 4HE PERIODIC NATURE OF DIGITAL PHASE SHIFTING AT EACH RADIATING ELEMENT CAN CREATE MULTIPLE DISTINCT LOCATIONS IN SPACE WHERE PARASITIC BEAMS GRATING LOBES CAN OCCUR )N ARRAY DESIGN THIS IS AVOIDED IF THE RADIATING ELEMENT SPACING D IS LESS THAN THAT DESCRIBED BY D K SINP
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7HERE D IS THE SPACING BETWEEN ADJACENT RADIATING ELEMENTS K IS THE WAVELENGTH OF THE HIGHEST OPERATING FREQUENCY AND P IS THE MAXIMUM SCAN ANGLE OF THE ARRAY &OR HEMISPHERICAL PHASED ARRAY COVERAGE THE MAXIMUM SCAN ANGLE CAN BE UPWARDS OF o n DEPENDING ON THE NUMBER OF ARRAY FACES USED IN THE SYSTEM CONFIGURATION 4HUS FOR AN 8 BAND ARRAY THAT REQUIRES SCANNING TO LARGE ANGLES THE SPACING BETWEEN RADIAT ING ELEMENTS AND BY IMPLICATION THE MAXIMUM SPACING AVAILABLE FOR 42 MODULES WHEN THEY ARE ALIGNED BEHIND THE RADIATING ELEMENTS MUST BE ON THE ORDER OF INCHES OR LESS !LLEVIATIONS IN PACKAGING MAY BE ALLOWABLE IF THE SCAN VOLUME IS NOT REQUIRED TO EXTEND TO A FULL FIELD OF VIEW 6ALUES OF ELEMENT SPACING THAT SATISFY %Q ARE SHOWN AS A FUNCTION OF SCAN ANGLE FOR SOME OF THE COMMON RADAR FREQUENCY BANDS THROUGH MM WAVE FREQUENCIES IN &IGURE 4HE IMPLICATION OF THIS GRAPH IS THAT FULL 42 MODULE FUNCTIONALITY MUST BE PACKAGED INTO THE SPACE AND VOLUME BEHIND THE PLANAR ARRAY AND THIS REQUIREMENT CAN POSE VERY DIFFICULT CHALLENGES TO THE 42 MODULE
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&)'52% -AXIMUM OPERATING FREQUENCY AND WORST CASE SCAN ANGLE DEFINE THE MAXIMUM ALLOWABLE DISTANCE AMONG ADJACENT RADIAT ING ELEMENTS 42 MODULES FITTING BEHIND EACH ELEMENT ARE CONSTRAINED BY THESE SPACINGS
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2!$!2 (!.$"//+
DESIGNER IN ORDER TO SATISFY THE 2& ELECTRICAL DC ELECTRICAL THERMAL AND RELIABILITY REQUIREMENTS 0ACKAGING OF --)# COMPONENTS INTO THE 42 MODULE MUST TAKE INTO CONSIDERATION MULTIPLE ELEMENTS AS THEY IMPACT THE ELECTRICAL PERFORMANCE 0OWER #ONDITIONING #ONSIDERATIONS 0ULSED TRANSMIT AMPLIFIERS CAN CONSUME VERY HIGH DC CURRENTS AND SPECIAL DESIGN ATTENTION MUST BE PAID TO PARASITIC INDUC TANCE THAT CAN GENERATE VERY HIGH VOLTAGE SPIKES AND CAUSE DAMAGE TO --)# POWER AMPLIFIERS )N ADDITION THE DC POWER SOURCE MUST INCLUDE APPROPRIATE ENERGY STORAGE SOMETIMES LOCALLY IN THE MODULE IN ORDER TO SUPPORT THE MINIMUM VOLTAGE PULSE DROOP AS A FUNCTION OF TIME %NVIRONMENTAL 0ROTECTION #ONSIDERATIONS --)# COMPONENTS UTILIZE THIN FILM METAL DEPOSITION TECHNIQUES TO DELINEATE THE VERY FINE FEATURES THAT MAKE UP THE MICRO WAVE CIRCUITRY 4HESE FEATURES ARE SUSCEPTIBLE TO POTENTIAL SHORT TERM FAILURE DUE TO CORROSION METAL MIGRATION AND DENDRITIC GROWTH IF THERE ARE VOLTAGES ON THE CIRCUITRY WHEN EXPOSED TO AN ATMOSPHERE THAT CAUSES MOISTURE TO CONDENSE ON THE CIRCUITRY 4HUS A HERMETIC PACKAGE WITH A DRY NITROGEN FILLED INTERIOR IS USUALLY EMPLOYED TO ENSURE LONG TERM RELIABILITY (ERMETIC PACKAGING ALSO BRINGS WITH IT THE UNDESIRABLE EFFECT OF TRAPPING INSIDE THE HOUSING ANY MOLECULAR CONTENT THAT OUTGASES INTO THE INTERIOR CAVITY )N PARTICULAR HYDROGEN CAN BE PRESENT IN THE INTERIOR METAL PLATING AND HAS BEEN KNOWN TO CAUSE LONG TERM RELIABILITY CONCERNS IN SOME 'A!S AMPLIFIERS /NE SOLUTION INVOLVES THE USE OF AN INTERNAL HYDROGEN GETTER TO COUNTERBALANCE THE RELIABILITY IMPACT ! GETTER IS A MATERIAL INCLUDED IN THE MODULE HOUSING TO ABSORB RESIDUAL HYDROGEN -ECHANICAL 0ACKAGING #ONSIDERATIONS 4HE 42 MODULE HOUSING MUST BE MADE OF MATERIALS THAT PROVIDE FOR ADEQUATE THERMAL MANAGEMENT AND LONG TERM RELIABIL ITY -ATERIALS THAT SIMULTANEOUSLY SUPPORT EXPOSURE TO SHOCK VIBRATION TEMPERATURE CYCLING AND ADEQUATE THERMAL MANAGEMENT MUST BE USED -ATERIALS THAT MATCH VERY CLOSELY THE COEFFICIENT OF THERMAL EXPANSION #4% OF THE SEMICONDUCTOR MATERIAL MUST BE USED IN THE DESIGN OF THE HOUSING SUCH THAT CRACKING OF THE SEMICONDUCTOR DEVICES DOES NOT OCCUR DURING THERMAL CYCLING THAT HAPPENS DURING NORMAL OPERATION OR DURING TEMPERATURE CHANGES DURING ASSEMBLY AND TEST %LECTRICAL )NTERCONNECTION #ONSIDERATIONS 4HE INTERCONNECTION OF --)# CHIPS WITHIN THE 42 MODULE MUST UTILIZE CONTROLLED IMPEDANCE TRANSMISSION LINES WITH LOW INSERTION LOSS 4HUS SOME COMBINATION OF HIGH QUALITY MICROWAVE DIELECTRIC MATERIAL MUST BE INTEGRAL TO THE MICROWAVE ELECTRICAL AND MECHANICAL DESIGN OF THE MODULE !TTENTION TO THE COEFFICIENT OF THERMAL EXPANSION AND MANUFACTURABILITY ISSUES WILL IMPACT THE CHOICE OF USABLE MATERIALS 42 MODULES ALSO GENERALLY REQUIRE AS MANY AS n CONTROL OR BIAS CONNECTIONS IN ORDER TO INTERFACE WITH AMPLIFIERS CONTROL CIRCUITRY AND PHASE SHIFTERS 4HE INTERCONNECTION DENSITY ESPECIALLY AT HIGHER FREQUENCIES CAN BECOME A PACKAGING DESIGN CHALLENGE !T FREQUENCIES ABOVE '(Z THE USE OF CON VENTIONAL CONNECTORS IS USUALLY PROHIBITIVE DUE TO THE SMALL WIDTH AVAILABLE IN FULL FIELD OF VIEW ARRAYS -ANUFACTURABILITY #ONSIDERATIONS "Y DEFINITION THE USE OF --)# COMPONENTS INVOKES A MICROELECTRONIC ASSEMBLY TEST AND HANDLING MANUFACTURING INFRASTRUCTURE 4HE MANUFACTURING OF LOW COST 42 MODULES IS PARAMOUNT TO BEING ABLE TO EFFECTIVELY PRODUCE AFFORDABLE ARRAYS $ESIGN METHODOLOGIES SUCH AS STATISTICAL PERFORMANCE
3/,)$ 34!4% 42!.3-)44%23
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REPRESENTATION ARE OFTEN EXPLOITED TO MAXIMIZE FUNCTIONAL YIELD 4HE INTEGRATION OF DESIGN AND MANUFACTURING PROCESSES IS A KEY COMPONENT TO SUCCESSFUL EXECUTION OF PRODUCT MANUFACTURING
££°ÈÊ -" -// Ê-9-/ Ê 8 * 0!6% 0!73 5(& %ARLY 7ARNING 2ADAR 4HE 0!6% 0!73 !.&03 SYSTEM IS A 5(& SOLID STATE ACTIVE APERTURE PHASED ARRAY RADAR THAT WAS BUILT FOR THE %LECTRONIC 3YSTEMS $IVISION OF THE 53 !IR &ORCE BY THE %QUIPMENT $IVISION OF THE 2AYTHEON #OMPANY DURING THE LATE S 4HE RADAR IS A LONG RANGE SYSTEM WITH A PRIMARY MISSION TO DETECT AND TRACK SEA LAUNCHED BALLISTIC MISSILES 4HE TWO FACED RADAR USES ACTIVE 42 MODULES PER FACE AND EACH MODULE INTERFACES WITH A DIPOLE ANTENNA ELEMENT %XTRA ELEMENTS AND A NARROW BEAM ARE USED ON RECEIVE AND UPGRADE CAPABILITY HAS BEEN INCLUDED FOR THE FUTURE INSTALLATION OF UP TO 42 MODULES PER ARRAY FACE 4HE PEAK POWER OUTPUT FROM EACH FACE WHEN POPULATED WITH MODULES IS K7 AND THE AVERAGE POWER OUTPUT IS K7 !MONG THE MODULES PER FACE GROUPS OF 42 MODULES ARE OPERATED AS A SUBARRAY )N TRANSMIT A HIGH POWER ARRAY PREDRIVER IS USED TO DRIVE SUBARRAY DRIVER AMPLIFIERS %ACH OF THESE POWER AMPLIFIERS PROVIDES ENOUGH 2& DRIVE FOR ALL MOD ULES IN ONE SUBARRAY )N RECEIVE THE SIGNAL FROM EACH OF THE SUBARRAYS IS FED INTO A RECEIVE BEAMFORMING NETWORK 4HE 42 MODULE CONTAINS PREDRIVER DRIVER AND FINAL TRANSMIT AMPLIFIERS TRANSMIT RECEIVE SWITCHING LOW NOISE AMPLIFIERS LIMITER PHASE SHIFTERS AND LOGIC CONTROL 4HE 42 MODULE BLOCK DIAGRAM IS SHOWN IN &IGURE AND A PHOTOGRAPH IS SHOWN IN
&)'52% "LOCK DIAGRAM OF THE 0!6% 0!73 TRANSMITRECEIVE MODULE SHOWS A TRANSISTOR DRIVING CONFIGURATION FOR THE TRANSMIT AMPLIFIER AND A QUADRATURE SPLITTER ON THE OUTPUT TO GENERATE A POLAR IZED FEED TO THE RADIATING ELEMENT
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&)'52% 0!6% 0!735(& 42 MODULE CONSISTS OF TRANSMIT MODULE AND RECEIVE MODULE IN A NESTED CONFIGURATION OF CAST ALUMINUM HOUSINGS 0HOTOGRAPH COURTESY OF 2AYTHEON #OMPANY
&IGURE 4HE TRANSMITTER PORTION OF THE 42 MODULE CONTAINS SEVEN SILICON BIPO LAR POWER TRANSISTORS OPERATED #LASS # FROM A 6 DC POWER SUPPLY 4HE TRANSMIT AMPLIFIER CHAIN CONSISTS OF A PREDRIVER TRANSISTOR FEEDING TWO DRIVER TRANSISTORS IN TURN FEEDING FOUR FINAL TRANSISTORS IE A CONFIGURATION %ACH OF THE FOUR FINAL STAGES DELIVERS 7 PEAK FOR MS PULSE WIDTHS AT DUTY CYCLES UP TO -ORE THAN TRANSISTORS HAVE BEEN BUILT INTO MORE THAN MODULES &UTURE UPGRADES OF THIS DESIGN IN THE "-%73 ARRAYS WILL USE THE MORE POWERFUL AND EFFICIENT 3I ,$-/3 &%4 TECHNOLOGY FOR ENHANCED PERFORMANCE CAPABILITIES !.303 3HIPBOARD 3EARCH 2ADAR 4HE !.303 WAS AN EXISTING 5(& TUBE TYPE LONG RANGE $ SHIPBOARD SEARCH RADAR SYSTEM FOR WHICH A NEW SOLID STATE TRANSMITTER WAS BUILT DURING THE S TO REPLACE THE TUBE 4HE SOLID STATE TRANSMITTER WAS BUILT FOR THE .AVAL 3EA 3YSTEMS #OMMAND BY THE THEN 7ESTINGHOUSE %LECTRIC #ORPORATION 4HE EXISTING WAVEFORM FROM THE ORIGINAL TRANSMITTER WAS NOT CHANGED AND THE SOLID STATE UNIT WAS INSTALLED AS A DIRECT RETROFIT 4HIS WAS NOT QUITE AS DIFFICULT AS USUAL BECAUSE THE TUBE TYPE SYSTEM ALREADY USED LONG PULSES AND PULSE COMPRES SION WITH A DUTY CYCLE OF NEARLY WHICH IS MUCH HIGHER THAN OLDER DUTY CYCLE SYSTEMS !LTHOUGH IT MAY HAVE BEEN DESIRABLE TO GO TO A HIGHER DUTY CYCLE AND LOWER PEAK POWER TO MAKE THE SOLID STATE RETROFIT EASIER THE .AVY PREFERRED NOT TO HAVE TO MODIFY THE REST OF THE SYSTEM 4HE K7 PEAK POWER TRANSMITTER USED A TOTAL OF HIGH POWER AMPLIFIER MOD ULES WHICH ALONG WITH POWER COMBINING PREDRIVERS DRIVERS AND CONTROL CIRCUITRY WERE HOUSED IN THREE SEPARATE CABINETS 4HERE WERE FINAL POWER OUTPUT MODULES ARRANGED IN TWO GROUPS OF %ACH MODULE &IGURE PRODUCED 7 PEAK AND 7 AVERAGE FOR A §S PULSE WIDTH AT A DUTY CYCLE $RIVE POWER FOR THE TWO
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&)'52% !.303 TRANSMITTER AMPLIFIER MODULE 0HOTOGRAPH COURTESY OF 7ESTINGHOUSE %LECTRIC #ORPORATION
BANKS OF FINAL OUTPUT MODULES K7 WAS PROVIDED FROM THE COMBINED OUTPUTS OF MORE IDENTICAL MODULES IN THE DRIVER GROUP 0REDRIVERS AND A REDUNDANT PREAMPLIFIER WERE USED AS PRECEDING DRIVE STAGES 4HE POWER AMPLIFIER MODULE CONSISTED OF TEN IDENTICAL SILICON BIPOLAR POWER TRAN SISTORS ARRANGED IN A DRIVING AMPLIFIER CONFIGURATION TO DEVELOP MORE THAN 7 PEAK POWER OUTPUT OVER THE TO -(Z FREQUENCY BANDWIDTH %ACH TRANSISTOR WAS A 7 PEAK POWER DEVICE THAT WAS OPERATED IN A BALANCED PUSH PULL CIRCUIT DESIGN "Y USING A PUSH PULL CONFIGURATION THE CIRCUIT DESIGNERS ALLEVIATED SOME OF THE LOW IMPEDANCE MATCHING PROBLEMS NORMALLY ASSOCIATED WITH VERY HIGH POWER TRANSISTORS 4HE 2& INPUT DRIVE TO THE MODULE WAS 7 PEAK AND WAS USED TO DRIVE TWO DEVICES ! COMBINED POWER LEVEL OF GREATER THAN 7 WAS SPLIT EIGHT WAYS TO DRIVE THE EIGHT IDENTICAL OUTPUT STAGES ,OSSES IN THE OUTPUT CIRCULATOR FINAL POWER COMBINING AND THE FAULT DETECTION CIRCUITRY REDUCED THE COMBINED POWER LEVEL TO 7 /UTPUT MODULES WERE LIQUID COOLED FOR NORMAL OPERATION BUT AN EMERGENCY BACKUP FORCED AIR COOLING WAS PROVIDED IN THE EVENT OF A PRIMARY COOLING SYSTEM FAILURE 4HE DISSIPATED HEAT COULD BE TOLERATED BECAUSE THE SYSTEM OPERATED AT A LOW DUTY CYCLE 4HE POWER COMBINING FOR EACH OUTPUT CABINET CONSISTED OF COMBINERS 4HE REACTIVE POWER COMBINER CONSISTED OF SEVEN GROUPS OF COMBINERS FABRICATED IN AIR STRIPLINE USING IN GROUND PLANE SPACING 4HE SEVEN OUTPUTS WERE COMBINED BY USING A SINGLE AIR STRIPLINE COMBINER WITH IN GROUND PLANE SPACING 4HE K7 OUTPUTS OF THE TWO COMBINERS WERE COMBINED IN A SINGLE ISOLATED HYBRID THAT WAS MANUFACTURED BY USING A COAXIAL TRANSMISSION LINE 4HE ADVERTISED LOSSES OF THE AND COMBINERS WERE D" AND D" RESPECTIVELY 2!-0 , "AND !IR 4RAFFIC #ONTROL 4RANSMITTER 4HE 2ADAR -ODERNIZATION 0ROJECT 2!-0 RADAR SYSTEM IS AN , BAND SYSTEM BUILT BY THE 2AYTHEON #OMPANY DUR ING THE LATE S TO REPLACE THE EARLIER PRIMARY AND SECONDARY SURVEILLANCE RADARS USED FOR AIR TRAFFIC CONTROL BY #ANADAS -INISTRY OF 4RANSPORT 4HE PRIMARY SURVEILLANCE RADAR CONSISTS OF A ROTATING REFLECTOR HORN FED BY A SOLID STATE TRANSMITTER AND INTERFAC ING WITH REDUNDANT RECEIVE CHANNELS WITH RECEIVER EXCITERS AND SIGNAL PROCESSORS 4HE PRIMARY SURVEILLANCE RADAR OPERATES BETWEEN AND -(Z WITH A K7 PEAK
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POWER OUTPUT AND PROVIDES RADAR COVERAGE TO NMI AND TO AN ALTITUDE OF FT WITH AN PROBABILITY OF DETECTION FOR A M TARGET WITH AZIMUTH AND RANGE RESOLUTION TO n AND NMI RESPECTIVELY 4HE RECEIVER EXCITER EFFICIENTLY UTILIZES THE TRANSMIT TER SOLID STATE DEVICES WITH A HIGH DUTY CYCLE WAVEFORM ! PAIR OF PULSES IS USED IN THE FREQUENCY AGILE SYSTEM AND TARGET RETURNS ARE PROCESSED BY A MOVING TARGET DETECTOR 4HE PULSE PAIR CONSISTS OF A §S SINGLE TONE PULSE THAT PROVIDES COVERAGE TO NMI AND A §S NONLINEAR CHIRP PULSE THAT PROVIDES COVERAGE TO NMI 4HE §S PULSE IS COMPRESSED TO §S SUCH THAT HIGH DUTY CYCLE IS ACHIEVED WITHOUT COMPROMISING RANGE RESOLUTION 4HE TRANSMITTER CONSISTS OF MODULES EACH CAPABLE OF 7 POWER OUT PUT &IGURE THAT ARE COMBINED TO PRODUCE THE GREATER THAN K7 PEAK POWER LEVEL 4WO MODULES AND A 6 DC POWER SUPPLY MAKE UP A SINGLE TRANSMITTING GROUP 4HE MODULE CONSISTS OF A DRIVING DRIVING TRANSISTOR AMPLIFIER CONFIGURA TION OF SILICON BIPOLAR POWER DEVICES 4HE TWO FINAL OUTPUT DEVICES AND THE EIGHT DRIVER DEVICES ARE 7 TRANSISTORS CAPABLE OF OPERATING UP TO A DUTY CYCLE OVER THE -(Z BANDWIDTH AT COLLECTOR EFFICIENCIES GREATER THAN %ACH MODULE IS AIR COOLED AND THE MEASURED EFFICIENCY IS GREATER THAN WHEN THE MODULE IS OPERATING AT AN AVERAGE DUTY CYCLE -ODULE POWER GAIN IS GREATER THAN D" ! CIRCULATOR IS USED ON THE OUTPUT PORT TO PROTECT THE 7 DEVICES FROM ANTENNA GENERATED REFLECTIONS AND CONTROL CIRCUITRY HAS BEEN INCLUDED TO SWITCH OFF MODULES IN THE EVENT OF COOLING SYSTEM FAILURE ! HIGH POWER REPLICATED COMBINER BUILT BY USING A COMBINATION OF REACTIVE AND RESISTIVE POWER COMBINING TECHNIQUES IN AIR DIELECTRIC STRIPLINE IS EMPLOYED TO SUM THE MODULE OUTPUTS TO THE K7 LEVEL
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- -ETH h)NDUSTRIAL ASSESSMENT OF THE MICROWAVE POWER TUBE INDUSTRY v $EPARTMENT OF $EFENSE 2EPORT !PRIL P 6 'RANATSTEIN 2 0ARKER AND # !RMSTRON h3CANNING THE TECHNOLOGY 6ACUUM ELECTRONICS AT THE DAWN OF THE ST CENTURY v 0ROCEEDINGS OF THE )%%% VOL NO PP n -AY
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6 'REGERS (ANSEN h2ADAR SYSTEMS TRADE OFFS VACUUM ELECTRONICS VS SOLID STATE v IN TH )NTERNATIONAL 6ACUUM %LECTRONICS #ONFERENCE !PRIL n PP n 2 3YMONS h-ODERN MICROWAVE POWER SOURCES v )%%% !%33 3YSTEMS -AGAZINE PP n *ANUARY 4 3ERTIC h)DIOSYNCRASIES OF 474 AMPLIFIERS v PRESENTED AT 4HE &UTURE OF %LECTRONIC $EVICES #ONFERENCE )NSTITUTE OF 0HYSICS -ARCH - (ANCZOR AND - +UMAR h K7 3 BAND SOLID STATE TRANSMITTER FOR MODERN RADAR 3934%-3 v )%%% 4RANSACTIONS ON -ICROWAVE 4HEORY AND 4ECHNIQUES VOL NO PP n $ECEMBER $ 2UTLEDGE . #HENG 2 9ORK 2 7EIKLE AND - $E,ISIO h&AILURES IN POWER COMBINING ARRAYS v )%%% 4RANSACTIONS ON -ICROWAVE 4HEORY AND 4ECHNIQUES VOL NO PP n *ULY , " 7ALKER (IGH 0OWER 'A!S &%4 !MPLIFIERS .ORWOOD -! !RTECH (OUSE P (EWLETT 0ACKARD !PPLICATION .OTES (IGH &REQUENCY 4RANSISTOR 0RIMER 0ART 4HERMAL 0ROPERTIES P ( #OOKE h-ICROWAVE TRANSISTORS THEORY AND DESIGN v 0ROCEEDINGS OF THE )%%% VOL PP n !UGUST 6ENDOR TRANSISTOR DATASHEET )NTEGRA 4ECHNOLOGIES )NC WWWINTEGRATECHCOM 6ENDOR TRANSISTOR DATASHEET 4YCO %LECTRONICS -! #/- WWWMACOMCOM 6ENDOR TRANSISTOR DATASHEET 34-ICROELECTRONIC WWWSTCOM 6ENDOR TRANSISTOR DATASHEET 0HILIPS WWWDATASHEETCATALOGCOM . 3AKURA + -ATSUNAGE + )SHIKURA ) 4AKENAKE + !SANO . )WATA - +ANAMORI AND - +UZUHARA h7 , BAND 'A!S POWER &0 (&%4 OPERATED AT 6 v IN )%%% -ICROWAVE 4HEORY AND 4ECHNIQUES 3YMPOSIUM $IGEST PP n 4 7INSLOW h0OWER DEPENDENT INPUT IMPEDANCE OF FIELD PLATE -%3&%4S v #OMPOUND 3EMICONDUCTOR )NTEGRATED #IRCUIT $IGEST PP n * (UANG ' *ACKSON 3 3HANFIELD ! 0LATZKER 0 3ALEDAS AND # 7EICHERT h!N !L'A!S )N'A!S PSEUDOMORPHIC HIGH ELECTRON MOBILITY TRANSISTOR WITH IMPROVED BREAKDOWN VOLTAGE FOR 8 AND +U BAND POWER APPLICATIONS v )%%% 4RANSACTIONS ON -ICROWAVE 4HEORY AND 4ECHNIQUES VOL NO PP n -AY + !LAVI 3 /GUT 0 ,YMNA AND - "ORKOWSKI h! HIGHLY UNIFORM AND HIGH THROUGHPUT DOUBLE SELECTIVE 0(%-4 PROCESS USING AN ALL WET ETCH CHEMISTRY v PRESENTED AT 'A!S -A4ECH #ONFERENCE # 3NOWDEN h2ECENT DEVELOPMENT IN COMPOUND SEMICONDUCTOR MICROWAVE POWER TRANSISTOR TECHNOLOGY v )%% 0ROC #IRCUITS $EVICES 3YST VOL NO PP n *UNE $ -ILLER AND - $RINKWINE h(IGH VOLTAGE MICROWAVE DEVICES !N OVERVIEW v PRESENTED AT )NTERNATIONAL #ONFERENCE ON #OMPOUND 3EMICONDUCTOR -FG * :OLPER h3CANNING THE SPECIAL ISSUE SPECIAL ISSUE ON WIDE BANDGAP SEMICONDUCTOR DEVICES v 0ROCEEDINGS OF THE )%%% VOL NO PP n *UNE 5 -ISHRA 0 0ARIKH AND 9 7U h!L'A.'A. (%-4S!N OVERVIEW OF DEVICE OPERATION AND APPLICATIONS v 0ROCEEDINGS OF THE )%%% VOL NO PP n *UNE 2 4REW h3I# AND 'A. TRANSISTORS)S THERE ONE WINNER FOR MICROWAVE POWER APPLICATIONS v 0ROCEEDINGS OF THE )%%% VOL NO PP n *UNE 3 !LLEN 2 3ADLER 4 !LCORN * 0ALMOUR AND # #ARTER h3ILICON CARBIDE -%3&%4S FOR HIGH POWER 3 BAND APPLICATIONS v IN )%%% -44 3 )NTERNATIONAL -ICROWAVE 3YMPOSIUM *UNE PP n 4HOMAS +AZIOR PERSONAL COMMUNICATION 2AYTHEON 2& #OMPONENTS !UGUST 9 7U AND 0 0ARIKH h(IGH POWER 'A. (%-4S BATTLE FOR VACUUM TUBE TERRITORY v #OMPOUND 3EMICONDUCTOR -AGAZINE *ANUARY&EBRUARY #OLIN 7HELAN PERSONAL COMMUNICATION 2AYTHEON 2& #OMPONENTS !UGUST ( (OWE 3TRIPLINE #IRCUIT $ESIGN .ORWOOD -! !RTECH (OUSE PP n $ -C1UIDDY 2 'ASSNER 0 (ULL 0 * -ASON AND * "EDINGER h4RANSMITRECEIVE MODULE TECHNOLOGY FOR 8 BAND ACTIVE ARRAY RADAR v 0ROCEEDINGS OF THE )%%% VOL NO PP n -ARCH
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' *ERINIC AND - "ORKOWSKI h-ICROWAVE MODULE PACKAGING v IN )%%% -ICROWAVE 4HEORY AND 4ECHNIQUES 3YMPOSIUM $IGEST PP n " +OPP - "ORKOWSKI AND ' *ERINIC h4RANSMITRECEIVE MODULES v )%%% 4RANSACTIONS ON -ICROWAVE 4HEORY AND 4ECHNIQUES VOL NO PP n -ARCH " +OPP # -OORE AND 2 #OFFMAN h4RANSMITRECEIVE MODULE PACKAGING %LECTRICAL DESIGN ISSUES v *OHNS (OPKINS !0, 4ECHNICAL $IGEST VOL NO PP n $ (OFT h3OLID STATE TRANSMITRECEIVE MODULE FOR THE 0!6% 0!73 PHASED ARRAY RADAR v -ICROWAVE *OURNAL PP n /CTOBER + ,EE # #ORSON AND ' -OLS h! K7 SOLID STATE !.303 RADAR TRANSMITTER v -ICROWAVE *OURNAL VOL PP n *ULY * $YCK AND ( 7ARD h2!-0S NEW PRIMARY SURVEILLANCE RADAR v -ICROWAVE *OURNAL P $ECEMBER ( 7ARD h4HE 2!-0 032 A SOLID STATE SURVEILLANCE RADAR v PRESENTED AT )%% )NTERNATIONAL 2ADAR #ONFERENCE ,ONDON /CTOBER
#HAPTER
,iviVÌÀÊÌi>Ã V
>iÊ °Ê iÞÊ>`Ê >iÊ >ÛÃ %LECTRONIC 3YSTEMS .ORTHROP 'RUMMAN #ORPORATION
£Ó°£Ê /," 1 /" 2OLE OF THE 2ADAR 2EFLECTOR !NTENNA 2ADAR REFLECTOR ANTENNAS PROVIDE THE MEANS BY WHICH THE TRANSMIT RECEIVE ENERGY AND ITS ASSOCIATED WAVEFORM IS RADIATED INTO COUPLED FROM FREE SPACE )N TRANSMIT MODE THE ANTENNA LAUNCHES A GUIDED WAVE FROM THE TRANSMITTER INTO FREE SPACE AND TYPICALLY FOCUSES THIS RADIATED ENERGY OVER A LIMITED ANGULAR RANGE OR BEAMWIDTH )N RECEIVE MODE THE REFLECTOR ANTENNA OPERATES IN A RECIPROCAL MANNER RECEIVING REFLECTED RADAR TARGET ENERGY IE ECHOES FROM A LIMITED ANGULAR RANGE 4HESE RECEIVED ECHOES ARE THEN CONVERTED INTO GUIDED WAVES THAT ARE AMPLIFIED AND SUBSEQUENTLY PROCESSED IN THE RADAR RECEIVER 4YPICALLY THE RADAR REFLECTOR ANTENNA MUST BE DESIGNED TO ENABLE BEAM SCANNING OVER THE FIELD OF VIEW &/6 VIA EITHER MECHANICAL OR ELECTRONIC MEANS OR SOME COM BINATION OF BOTH )N 3ECTION METHODS OF ELECTRONIC BEAM SCANNING LIMITED &/6 USING ARRAY FEEDS ARE DISCUSSED 4HUS THE RADAR REFLECTOR ANTENNA PERFORMS SEVERAL IMPORTANT FUNCTIONS )T CONVERTS THE GUIDED WAVE FROM THE TRANSMITTER TO A RADIATED WAVE OR VICE VERSA ON RECEIVE )T CONCENTRATES OR COLLIMATES THE RADIATED ENERGY INTO A DIRECTIVE BEAM OF SPECIFIED GAIN AND BEAMWIDTH )T COLLECTS THE REFLECTED ENERGY SCATTERED FROM THE RADAR TARGET AND )T SUPPORTS BEAM SCANNING VIA EITHER ELECTRONIC OR MECHANICAL MEANS OR BOTH !NTENNA "EAM 3CANNING &OR MOST RADAR APPLICATIONS THE TRADE OR CHOICE BETWEEN A REFLECTOR ANTENNA AND A DIRECT RADIATING PHASED ARRAY IS TYPICALLY DRIVEN BY FACTORS RELATING TO SCAN RATE SCAN VOLUME AND COST 2EFLECTOR ANTENNAS ARE TYPICALLY EMPLOYED IN A RADAR WHEN SLOWER SCAN RATES ARE SUFFICIENT AND MECHANICAL SCAN NING SUFFICES ANDOR A VERY HIGH GAIN ELECTRICALLY LARGE APERTURE IS REQUIRED AND A PHASED ARRAY IE AN ELECTRONIC SCANNING ARRAY %3! IS COST PROHIBITIVE ANDOR THE REQUIRED SCAN VOLUME IS LIMITED AND CAN BE SATISFIED VIA USE OF AN ARRAY FED REFLECTOR $URING THE S AND S PHASE SHIFTER AND 42 MODULE TECHNOLOGY GREATLY MATURED AND %3! COSTS DROPPED DRAMATICALLY 4HESE ADVANCES HAVE RESULTED IN INCREASED INTER EST AND UTILIZATION OF %3!S FOR WIDE SCAN RADAR APPLICATIONS AND ARRAY FED REFLECTORS WHERE LIMITED ELECTRONIC SCAN SUFFICES !DVANTAGES AND !PPLICATIONS OF THE 2ADAR 2EFLECTOR !NTENNA )N THE PREVIOUS PARAGRAPH THE PROLIFERATION OF %3! ANTENNAS IN MODERN RADAR SYSTEMS IS LINKED TO THE £Ó°£
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DRAMATIC 42 MODULE COST REDUCTIONS AND TECHNOLOGY IMPROVEMENTS 4HE IMPROVED PER FORMANCE OF %3! RADARS IS CITED AS A REASON FOR DECREASED UTILIZATION OF REFLECTOR ANTENNAS IN MANY OF TODAYS RADAR SYSTEM DESIGNS (OWEVER THERE ARE STILL APPLICATIONS WHERE THE REFLECTOR ANTENNA IS WELL SUITED TO RADAR APPLICATIONS AND WILL CONTINUE TO FIND APPLICATIONS IN THE FUTURE 4HREE RELEVANT EXAMPLES OF RADAR APPLICATIONS WELL SUITED TO THE USE OF REFLECTOR ANTENNAS ARE BRIEFLY DESCRIBED BELOW ,OW #OST 2ADAR &OR VERY COST CONSTRAINED APPLICATIONS WHERE MECHANICAL SCAN RATES SUFFICE REFLECTOR ANTENNAS ARE STILL THE DOMINANT CHOICE /NE SUCH NICHE IS COM MERCIAL WEATHER RADAR EG .%82!$ AND 4$72 6ERY (IGH 'AIN ,ONG 2ANGE 2ADAR &OR VERY HIGH GAIN RADAR APPLICATIONS THE COST OF AN %3! IS TYPICALLY STILL PROHIBITIVE AND THE REFLECTOR PROVIDES AN ECONOMICAL MEANS OF REALIZING SUCH HIGH GAINS 4WO EXAMPLES OF LONG RANGE RADAR APPLICATIONS GENERALLY REQUIR ING VERY HIGH ANTENNA GAINS ARE MISSILE DEFENSE RADAR AND SPACE BASED RADAR ,IMITED 3CAN 2ADARS 3OME RADARS OPERATE OVER A LIMITED FIELD OF VIEW ANDOR THE REQUIREMENTS DICTATE FAST ELECTRONIC SCANNING OVER A SMALL &/6 AND SLOWER MECHANICAL SCANNING OVER A LARGER FIELD OF VIEW %3! FED REFLECTOR ARCHITECTURES ARE WELL SUITED FOR SUCH APPLICATIONS AND ARE DESCRIBED IN GREATER DETAIL IN 3ECTION 4HREE RELEVANT EXAM PLES ARE MISSILE DEFENSE RADAR SPACE BASED RADAR AND GROUND BASED SEARCH AND TRACK RADAR $ AZIMUTH ELECTRONIC SCANNING SUFFICES FOR SOME OF THESE APPLICATIONS #LASSIFICATION OF 2EFLECTOR !NTENNAS 2ADAR REFLECTOR ANTENNAS CAN BE CLASSIFIED IN VARIOUS WAYS /NE USEFUL CLASSIFICATION CRITERIA IS ELECTRICAL DESIGN IE THE REFLECTOR OPTICS CONFIGURATION 4ABLE PROVIDES A SUMMARY LEVEL COMPARISON OF SOME COMMON RADAR
4!",% #OMPARISON OF +EY &EATURES OF 2EFLECTOR !RCHITECTURES
3INGLE 2EFLECTOR 0ARABOLIC
%LECTRONIC s ,IMITED IN BOTH !ZIMUTH AND 3CANNING %LEVATION %SCAN s !CHIEVED VIA &EED SWITCHING
#YLINDRICAL 2EFLECTOR
$UAL 2EFLECTOR #ASSEGRAIN OR 'REGORIAN
#ONFOCAL 0ARABOLOIDS
3PHERICAL AND 4ORUS
s ,IMITED IN BOTH s 5SES PLANAR s 0OTENTIAL FOR s 7IDE $ VERY WIDE $ %3! SOURCE !ZIMUTH AND SCANNING SCANNING TORUS s 4YPICALLY %LEVATION s 5SES %3! OR $ 3CANNING LIMITED BUT LINE SOURCE s !CHIEVED VIA SPHERICAL TRADABLE FEED SWITCHING FOR WIDE $ s !CHIEVED VIA BY VARYING SCANNING MAGNIFICATION FEED SWITCHING
s -ODEST TO LOW s (IGH !PERTURE s -EDIUM TO HIGH s -EDIUM TO s (IGH s 3 WITCHED s $ %3! s . O ESCAN O ESCAN 3INGLE HIGH %FFICIENCY s . BEAM ARRAY ON PLANAR SOURCE s $ %3! LINE 3INGLE HORN HORN &EED CIRCULAR ARC s %SCAN !RRAY SOURCE s %SCAN !RRAY 4YPES TORUS REFLECTOR SWITCHED FEEDS SWITCHED FEEDS OR SPHERICAL ARC SPHERICAL REFLECTOR "LOCKAGE #ONCERNS
s -ITIGATE FEED BLOCKAGE VIA OFFSET GEOMETRY
s -ITIGATE FEED s -ITIGATE FEED s -ITIGATE FEED s 3ERIOUS CONCERN FOR BLOCKAGE BLOCKAGE VIA BLOCKAGE VERY WIDE SCAN VIA OFFSET OFFSET GEOMETRY VIA OFFSET CONFIGURATIONS GEOMETRY s #AN MOVE FEED GEOMETRY BEHIND REFLECTOR
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REFLECTOR ARCHITECTURES FROM THIS PERSPECTIVE -ORE DETAILED DISCUSSIONS OF THE CHARACTERIS TICS OF THESE ARCHITECTURES ARE INCLUDED IN 3ECTION WHEREIN EACH OF THESE ARCHITECTURES IS AFFORDED A DEDICATED SUBSECTION !NOTHER MEANS OF CLASSIFICATION IS VIA PLATFORM VEHI CLE OR SITE GROUND BASED SHIP BASED AIRBORNE OR SPACE BORNE 4HE PLATFORM FREQUENTLY DRIVES MECHANICAL AND ENVIRONMENTAL REQUIREMENTS AND OFTEN EITHER ENABLES OR CONSTRAINS THE REFLECTOR SIZE )N 3ECTION REFLECTOR ARCHITECTURES ARE DISCUSSED AND COMPARED AND IN 3ECTION MECHANICAL AND ENVIRONMENTAL DESIGN CONSIDERATIONS ARE ADDRESSED #HAPTER 3YNOPSIS 4HE BALANCE OF THIS CHAPTER IS DIVIDED INTO FIVE SECTIONS 3ECTION SUMMARIZES THE BASIC DESIGN PRINCIPLES AND PARAMETERS GOVERNING REFLEC TOR ANTENNA DESIGN 3ECTION PROVIDES A BRIEF OVERVIEW OF CONIC SECTIONS AND CLASSES OF REFLECTOR SYSTEMS AND ASSOCIATED OPTICS 3ECTION DISCUSSES VARIOUS TYPES OF REFLECTOR FEEDS AND RELATED DESIGN PRINCIPLES 3ECTION DESCRIBES REFLECTOR ANALYSIS AND SYNTHESIS METHODS AND ASSOCIATED DESIGN SOFTWARE PACKAGES &INALLY 3ECTION BRIEFLY REVIEWS MECHANICAL DESIGN ISSUES AND CONSIDERATIONS
£Ó°ÓÊ - Ê*, * -Ê Ê*, / ,&UNDAMENTALLY REFLECTORS ARE ANTENNAS THAT WORK ON OPTICAL PRINCIPLES ON RECEIVE FOCUSING ENERGY TO A FOCAL POINT AS A LENS DOES FOR LIGHT /N TRANSMIT POWER EMANAT ING SPHERICALLY FROM A LOW GAIN BROAD PATTERNED FEED IS REFLECTED AND ENERGY IS COL LIMATED TO FORM A PLANE WAVE THEREBY PROVIDING INCREASED ANTENNA GAIN AND A NARROWER BEAMWIDTH )N DISCUSSING ANTENNAS ONE CAN USE EITHER TRANSMIT OR RECEIVE ARGUMENTS BECAUSE ANTENNAS ARE RECIPROCAL DEVICES 4HIS MEANS THAT BOTH THE TRANSMIT AND RECEIVE PERFORMANCE OF A PASSIVE ANTENNA EG PATTERNS GAIN LOSSES ETC CAN BE PREDICTED USING BASIC APERTURE ANTENNA PRINCIPLES )N THIS SECTION THESE BASIC REFLECTOR DESIGN PRINCIPLES ARE REVIEWED VIA USE OF A CANONICAL EXAMPLE #ONSIDER A PARABOLIC SHAPED REFLECTOR FORMING A CIRCULAR APERTURE FED BY A HORN AT A CENTRAL FOCAL POINT 4HIS SIMPLE REFLECTOR CONFIGURATION HAS A SURFACE SHAPE DEFINED BY THE EQUATION Z
X Y
F F
WHERE F IS THE FOCAL LENGTH AND THE VERTEX IS LOCATED AT Z F 4HE RESULTANT ANTENNA BEAM PATTERN POINTS IN THE POSITIVE Z DIRECTION &OR A ROUND REFLECTOR OF DIAMETER $ THE EDGE OR RIM IS A CIRCLE AND THE EDGE DIMENSIONS ARE ON THIS CIRCLE DEFINED BY
XEDGE YEDGE
$
4HIS REFLECTOR IS SHOWN IN &IGURE /NE FREQUENTLY IS INTERESTED IN THE ANGLE @ FROM THE Z AXIS TO POINTS ON THE REFLECTOR SURFACE
¤ X Y ³ A ARCTAN ¥ ´ ¦ F µ
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4HUS THE EDGE ANGLE FOR A ROUND REFLECTOR IS
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!NOTHER USEFUL PARAMETER IS THE DISTANCE R FROM THE FOCAL POINT TO A POINT ON THE REFLECTOR R F
X Y F
!PERTURE 'AIN AND ,OSSES 4HE GAIN OF THE REFLECTOR ANTENNA IS ONE OF ITS MOST IMPORTANT PARAMETERS )T IS CONVENIENT TO DESCRIBE THE REFLECTOR ANTENNA GAIN WITH REF ERENCE TO THE FUNDAMENTAL GAIN LIMIT AN APERTURE OF AREA ! 4HIS LIMIT APPLICABLE TO APERTURE ANTENNAS OF SUFFICIENT ELECTRICAL SIZE APPROXIMATELY SQUARE WAVELENGTHS OR GREATER IS THE SO CALLED APERTURE GAIN 'AP
'AP
P ! L
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WHERE K IS THE WAVELENGTH &OR A ROUND REFLECTOR OF DIAMETER $ THIS APERTURE GAIN LIMIT IS ¤ P $³ 'AP ¥ ¦ L ´µ
)N PRACTICE IT IS SOMETIMES USEFUL TO DESCRIBE REFLECTOR GAIN BY DECREMENTING THE APERTURE GAIN BY SUBTRACTING VARIOUS APERTURE RADIATION LOSSES SUCH AS SPILLOVER TAPER EFFICIENCY FEED BLOCKAGE REFLECTOR LEAKAGE SURFACE DISTORTION STRUT BLOCKAGE FEED ALIGN MENT ETC FROM 'AP 4HESE LOSS FACTORS ARE DESCRIBED IN DETAIL LATER WITHIN THIS SECTION $IRECTIVE 'AIN AND &EED ,OSSES $IRECTIVE GAIN OR DIRECTIVITY IS A MEASURE OF THE PEAK POWER RELATIVE TO THE AVERAGE POWER RADIATED BY AN ISOTROPIC RADIATOR IE A RADIATOR THAT RADIATES ENERGY EQUALLY IN ALL DIRECTIONS $IRECTIVE GAIN CONSIDERS ONLY THE RADIATED POWER THUS ANTENNA LOSSES SUCH AS FEED MISMATCH FEED LOSS AND WAVEGUIDE ANDOR CABLE LOSSES MUST ALSO BE CONSIDERED (OWEVER THE RADAR ENGINEER TYPICALLY TABULATES THESE LOSSES SEPARATELY FOR USE IN OTHER RADAR CALCULATIONS !NTENNA DIRECTIV ITY IS AN IMPOSING CALCULATION REQUIRING VOLUME INTEGRALS BUT TYPICAL REFLECTOR PATTERN COMPUTATION CODES EXPRESS THE PATTERN IN TERMS OF DIRECTIVITY AND THE ANTENNA LOSSES ARE GENERALLY ACCOUNTED FOR SEPARATELY )N THE TEXT THAT FOLLOWS REFLECTOR DIRECTIVITY IS DESCRIBED BASED UPON AVAILABLE hAPERTURE GAINv AND ASSOCIATED RADIATION LOSSES 4HIS APPROACH SHOULD BE INTUITIVE TO THE RADAR ENGINEER !PERTURE &IELD -ETHOD OF !NALYSIS 4HE APERTURE FIELD REFLECTOR ANALYSIS METHOD IS BASED UPON RAY TRACING PRINCIPLES AND WORKS WELL FOR SYMMETRIC CENTER FED PARABOLIC REFLECTORS 7ITH THIS METHOD THE APERTURE FIELD DISTRIBUTION IS CALCULATED IN AN X Y PLANE AT Z &IGURE BY ASSUMING COHERENT REFLECTION OF SPHERICAL RADIATION FROM A FEED AT THE FOCAL POINT 4HE FIELD DISTRIBUTION IS THEN USED TO COMPUTE THE FAR FIELD RADIATION PATTERN &OR MORE COMPLEX GEOMETRIES EG OFFSET FED REFLECTORS THIS METHOD DOES NOT WORK AS WELL AS THE MORE RIGOROUS PHYSICAL OPTICS 0/ METHOD THAT IS DESCRIBED IN 3ECTION &OR THE SIMPLE CENTER FED FOCAL FEED EXAMPLE SHOWN IN &IGURE THE SIMPLER APERTURE FIELD METHOD OF ANALYSIS IS ACCURATE AND ITS APPLICATION IS SIMPLE AND STRAIGHT FORWARD AND MAKES THE DISCUSSION OF THE RADIATION LOSSES EASIER TO FOLLOW 5SING THIS METHOD OF ANALYSIS THE FIELD AMPLITUDE ON AN X Y GRID &GRID IN THE APERTURE PLANE IS EASILY DETERMINED FROM THE FEED AND SPACE TAPERING &GRID X Y &FEED X Y Z
F &FEED X Y Z R X Y F
WHERE &FEED IS THE FEED RADIATION PATTERN &OR THIS CASE WITH THE FEED AT THE FOCAL POINT THE TOTAL DISTANCE TRAVELED FROM THE FEED TO THE REFLECTOR AND BACK TO THE APERTURE PLANE IS EQUAL 4HIS EXPRESSION IS DECEPTIVELY SIMPLE AND ACCURATELY ACCOUNTS FOR THE FEED REFLECTOR TRANSFORMATIONS AND AREA PROJECTIONS 4HE RESULTANT APERTURE FIELD & V} IS THEN TRANSFORMED TO THE FAR FIELD USING THE SPATIAL TRANSFORMATION & V} £ &GRID X Y E
X Y
J
P L
X I} Y I} X
Y
u V}
£Ó°È
2!$!2 (!.$"//+
WHERE V} IS A UNIT VECTOR IN THE DIRECTION OF INTEREST .OTE THAT %Q IS A SIMPLE $ SPATIAL SUMMATION ANALOGOUS TO THAT USED FOR ARRAY ANTENNA PATTERN CALCULATIONS 4APER %FFICIENCY )N ANTENNA DESIGN APERTURE TAPER IS USED TO LOWER SIDELOBES 4HE MODEST RESULTANT LOSS AND INCREASED BEAMWIDTH IS THE PRICE AND ONE IS USUALLY WILLING TO PAY TO OBTAIN THE DESIRED SIDELOBE LEVEL 4HE LOSS ASSOCIATED WITH APERTURE TAPER IS ACCOUNTED FOR IN THE TAPER EFFICIENCY (OWEVER THE TAPER EFFICIENCY IS NOT AN OHMIC LOSS WHERE ENERGY IS DISSIPATED BUT IS A REDISTRIBUTION OF ENERGY )N THE CASE OF A REFLECTOR FED BY A HORN THE TAPER DISTRIBUTION IS DETERMINED BY THE FEED HORN PATTERN THE DISTANCE TO THE REFLECTOR AND THE PROJECTED AREA IN THE DIRECTION OF PEAK RADIATION &OR A RADIALLY SYMMETRIC FEED AND REFLECTOR WHERE THE FIELD IS RADIALLY SYMMETRIC AND &GRIDX Y GR THE EFFICIENCY G IS COMPUTED AS
¯ GR P R DR H ¯ G R P R DR ¯ P R DR
3PILLOVER ,OSS 3PILLOVER LOSS REFERS TO FEED POWER THAT MISSES OR SPILLS OVER THE EDGES OF THE REFLECTOR )N THE RADAR REFLECTOR DESIGN PROCESS ONE TYPICALLY ADJUSTS THE EDGE ILLUMINATION TO ACHIEVE A DESIRED TAPER AND SIDELOBE LEVEL RESULTING IN MODEST SPILLOVER LOSS 3PILLOVER LOSS IS THE FEED POWER THAT IS LOST VIA RADIATION BEYOND THE EDGES OF THE REFLECTOR 4HIS LOSS CAN BE COMPUTED AS ¤ &EED 0OWER )NCIDENT ON 2EFLECTOR ³ 3PILLOVER ,OSS 4OTAL &EED 0OWER ¥ ´µ 4OTAL &EED 0OWER ¦ &OR A RADIALLY SYMMETRIC FEED AND REFLECTOR THIS CALCULATION IS STRAIGHTFORWARD %DGE DIFFRACTION AND RESULTANT ANTENNA BACKLOBES ARE A RELATED CONSEQUENCE OF FEED SPILLOVER AND EDGE TAPER &OR ANY GIVEN REFLECTOR DESIGN EDGE ILLUMINATION OF THE REFLECTOR WILL PRODUCE RADIATION BEHIND THE REFLECTOR DUE TO DIFFRACTION 4HIS DIFFRACTION MAY BE THOUGHT OF AS RE RADIATION FROM THE EDGE OF THE REFLECTOR THAT CAUSES RADIATION LOBES BEHIND THE REFLECTOR &OR A CENTER FED REFLECTOR SUCH AS THAT SHOWN IN &IGURE A PRIMARY BACKLOBE WILL ARISE DIRECTLY BEHIND THE REFLECTOR DUE TO COHERENT ADDITION OF THE EDGE DIFFRACTION CURRENTS /NE COMMON MEANS OF SPECIFYING THIS BACKLOBE LEVEL IS VIA THE FRONT TO BACK &" RATIO IE THE RATIO OF THE MAIN BEAM AND BACKLOBE GAINS 4HE ANALYSIS OF THESE REFLECTOR EDGE DIFFRACTION EFFECTS AND ASSOCIATED &" RATIOS FOR SOME COMMON REFLECTOR GEOMETRIES ARE DESCRIBED BY +NOP &EED "LOCKAGE -ANY REFLECTOR SYSTEMS SUFFER FEED ANDOR FEED SUPPORT BLOCKAGE TO SOME DEGREE &OR CENTER FED GEOMETRIES THERE WILL DEFINITELY BE BLOCK AGE BECAUSE THE FEED IS WITHIN THE &/6 OF THE REFLECTOR ! CONSEQUENCE OF BLOCKAGE IS HIGHER SIDELOBES THE LEVELS OF WHICH DEPEND UPON THE BLOCKAGE AREA !NOTHER CON SEQUENCE IS LOSS DUE TO BLOCKAGE AND DEPENDS UPON THE BLOCKED ELECTRIC FIELD TO MAIN ELECTRIC FIELD RATIO %B%M WHICH IN TURN IS DETERMINED FROM THE RATIO OF BLOCKED POWER TO TOTAL POWER ON THE MAIN REFLECTOR 0B0M AND RATIO OF THE GAIN OF THE BLOCKING OBJECT TO THE GAIN OF THE MAIN REFLECTOR 'B'M
0B ¤ %B ³ ¥¦ % ´µ 0 M M
'B 'M
2%&,%#4/2 !.4%..!3
£Ó°Ç
&)'52% 'RAPHICAL REPRESENTATION OF SPILL OVER LOSS
2EFLECTOR TAPER IS OFTEN APPROXIMATED BY A RADIAL AMPLITUDE DISTRIBUTION
GR R
WHERE R IS THE RADIAL DISTANCE NORMALIZED TO THE REFLECTOR RADIUS AND GR DROPS TO ZERO AT THE EDGE 4HE USE OF THIS TAPER FUNCTION LEADS TO A SIMPLE BLOCKAGE LOSS EQUATION
0B G ¯ P R DR $B 0M $ ¯ G R P R DR M
$B 'B 'M H $M
WHERE G IS THE EFFICIENCY AS GIVEN IN %Q 5SING %Q AND %Q LEADS TO THE SIMPLE EXPRESSION FOR BLOCKAGE LOSS TYPICALLY FOUND IN THE LITERATURE %B $ B %M $M
¤ % ³ $ ³ ¤ "LOCKAGE ,OSS ¥ B ´ ¥ B ´ $M µ ¦ %M µ ¦
WHERE $B AND $M ARE THE DIAMETER OF THE BLOCKAGE AND REFLECTOR RESPECTIVELY 4HE EFFECTIVE FEED HORN DIMENSIONS CAUSING BLOCKAGE MAY BE DIFFERENT FROM THE PHYSICAL DIMENSIONS )F THE WALLS ARE NOT TAPERED SUCH AS SHOWN IN &IGURE THE EFFECTIVE SIZE OF THE BLOCKAGE HOLE CAN BE LARGER THAN THE PROJECTED OBSTACLE AREA
£Ó°n
2!$!2 (!.$"//+
&)'52% #APACITIVE LOADING TO REDUCE FEED HORN BLOCKAGE
&OR FEEDS WITH CONDUCTING WALLS THE EFFECTIVE ( PLANE WIDTH Wg IS AT LEAST K AND INCREASES WITH DEPTH $
[
W ` W MAX L L $
]
WHERE MAX INDICATES TAKING THE LARGER OF THE TWO VALUES 4HE INCREASE IN EFFECTIVE WIDTH CAN SOMETIMES BE REDUCED BY ADDING CAPACITIVE LOADING WHICH CAN CONSTRAIN THE EFFEC TIVE WIDTH TO ABOUT A QUARTER WAVELENGTH WIDER THAN THE PHYSICAL WIDTH 4HE EFFECTIVE % PLANE DIMENSION IS THE SAME AS THE ACTUAL DIMENSION 'AIN /PTIMIZATION 4HREE OF THE PRINCIPAL REFLECTOR ANTENNA LOSSES TAPER EFFI CIENCY LOSS SPILLOVER AND BLOCKAGE HAVE BEEN EXPLAINED IN DETAIL ABOVE 4HESE DESIGN PARAMETERS LOSS FACTORS AFFECT ONE ANOTHER AND ARE OFTEN TRADED TO OPTIMIZE ANTENNA PERFORMANCE EG GAIN SIDELOBES ETC /THER TYPICAL REFLECTOR LOSSES DESCRIBED LATER IN THIS SECTION ARE RESISTIVE LOSS FACTORS THAT SIMPLY REDUCE THE ANTENNA GAIN 4HE DESIGN TRADES ASSOCIATED WITH TAPER EFFICIENCY SPILLOVER AND BLOCKAGE ARE ILLUSTRATED BY USE OF AN EXAMPLE #OMPUTED LOSSES ARE SHOWN IN &IGURE FOR A WAVELENGTH DIAMETER CENTER FED CIRCULAR REFLECTOR WITH A WAVELENGTH FOCAL LENGTH AND A GAUSSIAN FEED HORN A HORN WITH A RADIATION PATTERN DESCRIBED BY A GAUSS IAN FUNCTION 4HE GAUSSIAN FEED USED IN THIS SAMPLE ANALYSIS IS A HYPOTHETICAL FEED WITH A RADIALLY SYMMETRIC PATTERN AND VERY LOW SPILLOVER AND MOST TYPICAL FEED HORN PATTERNS ARE WELL APPROXIMATED BY A GAUSSIAN FEED MODEL 4HE FEED SIZE DETERMINES THE EDGE TAPER IE THE LARGER THE FEED THE GREATER THE EDGE TAPER 4HE PLOT IN &IGURE SHOWS HOW THE THREE LOSS TERMS AND THE TOTAL LOSS VARY AS A FUNCTION OF FEED PATTERN EDGE TAPER THAT IS THE FEED POWER DIRECTED AT THE EDGE OF THE REFLECTOR RELATIVE TO THE FEED PATTERN PEAK 4HIS IS USED HERE BECAUSE THE FEED PATTERN IS MEASURED INDEPENDENT OF THE REFLECTOR 7HEN THE EDGE TAPER IS LOW VIRTUALLY ALL THE POWER STRIKES THE REFLECTOR AND THE LOSS IS INSIGNIFICANT !S TAPER DECREASES THERE IS MORE SPILLOVER AND FEED POWER MISSES THE REFLECTOR INCREASING THE LOSS /N THE OTHER HAND WITH TOO MUCH TAPER THE TAPER EFFICIENCY IS POOR BECAUSE THE REFLECTOR IS UNDER ILLUMINATED
2%&,%#4/2 !.4%..!3
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"
&)'52% 4APER EFFICIENCY SPILLOVER BLOCKAGE AND TOTAL LOSS VS FEED PATTERN EDGE TAPER
&IGURE DEMONSTRATES THE GAIN OPTIMIZATION PROCESS WITH A HYPOTHETICAL FEED PATTERN BLOCKAGE ETC AND THE TOTAL LOSS IS D" EFFICIENCY WHEN A D" EDGE TAPER IS IMPLEMENTED !LTHOUGH THE PLOT OF &IGURE INCLUDES TAPER BLOCKAGE AND SPILLOVER LOSSES THERE ARE ADDITIONAL LOSSES THAT MUST BE INCLUDED WHEN ASSESSING THE OVERALL APERTURE EFFICIENCY 4HESE LOSSES EG FEED BLOCKAGE SURFACE REFLECTION FEED MISMATCH AND RESISTIVE LOSSES ETC VARY FROM SYSTEM TO SYSTEM BUT D" IS TYPICAL 7ITH THESE ADDITIONAL LOSSES THE OVERALL LOSS BECOMES D" OR APERTURE EFFICIENCY TYPICAL FOR A SINGLE REFLECTOR SYSTEM 3IDELOBE REQUIREMENTS MUST ALSO BE CONSIDERED !S SHOWN IN &IGURE FOR THE SAME CENTER FED REFLECTOR SYSTEM THE SIDELOBE LEVEL CAN BE REDUCED BY INCREASING THE FEED PATTERN EDGE TAPER
! !
&)'52% 3IDELOBE LEVELS WITH AND WITHOUT BLOCKAGE VS FEED PATTERN EDGE TAPER
£Ó°£ä
2!$!2 (!.$"//+
&)'52% 5NPERTURBED FIELD AND FIELD INCLUDING FEED BLOCKAGE
&IGURE ALSO SHOWS THAT FEED BLOCKAGE INCREASES THE SIDELOBE LEVEL FOR EXAMPLE WITH A n D" EDGE TAPER ONE OBTAINS n D" SIDELOBES RATHER THAN D" SIDE LOBES &IGURES AND FURTHER ILLUSTRATE THIS IMPACT 4HIS BLOCKAGE EFFECT CAN BE MODELED AS A hHOLEv IN THE APERTURE THAT CAN BE REPRESENTED BY A BROAD PATTERN WITH LESS GAIN 4HIS BLOCKAGE PATTERN IS SUBTRACTED FROM UNPERTURBED UNBLOCKED APERTURE FIELDS AS SHOWN IN &IGURE 4HE ASSOCIATED PATTERNS WITH AND WITHOUT BLOCKAGE ARE SHOWN IN &IGURE 4HE ALTERNATING LARGE SMALL LARGE AND SO ON SIDELOBE PROGRESSION IS CHARACTERISTIC OF A BLOCKED APERTURE 3URFACE ,EAKAGE ,OSS -ANY REFLECTOR SURFACES ARE DESIGNED WITH A GRID A WIRE MESH OR METALIZED FABRIC SURFACE IN ORDER TO MINIMIZE WIND RESISTANCE REDUCE WEIGHT ANDOR ENABLE STOWAGEDEPLOYMENT 3OME COMMON REFLECTOR MESH SURFACE PATTERNS ARE
&)'52% 5NPERTURBED PATTERN AND PATTERN INCLUDING BLOCKAGE
2%&,%#4/2 !.4%..!3
£Ó°££
&)'52% #OMMON REFLECTOR SURFACE MATERIALS FOR REDUCED WIND RESISTANCE A TUBING B EXPANDED METAL C RECTANGULAR D DOUBLE LAYER AND E SCREEN
SHOWN IN &IGURE 4HE MESH OPENING SIZE IS GENERALLY CHOSEN TO BE AS LARGE AS POS SIBLE BUT THE GAP S BETWEEN CONDUCTORS MUST BE SUBSTANTIALLY LESS THAN K TO CUTOFF AND PREVENT SIGNIFICANT TRANSMISSION OF ELECTROMAGNETIC ENERGY THROUGH THE SURFACE 4HE ATTENUATION IN DECIBELS THROUGH THE PASSAGE DEPTH T IS APPROXIMATELY TS PLUS FRINGING LOSSES WHICH ARE APPROXIMATELY K S 4HE POWER PASSING THROUGH THE REFLECTOR OR TRANSMISSION LOSS CAN BE DETERMINED USING A HANDY NOMOGRAPH /NE SELECTS THE GRID SPACING AND THREAD RADIUS TO ACHIEVE THE TRANSMISSION LOSS REQUIRED 4HE RESULTING LOSS IN ANTENNA GAIN IS TERMED LEAKAGE LOSS AND THE RELATIONSHIP BETWEEN LEAKAGE LOSS AND TRANSMISSION LOSS IS PLOTTED IN &IGURE FOR A CONDUCTIVE REFLECTOR NO OHMIC LOSSES 4HE LEAKAGE LOSS VS SPACING RELATIONSHIP FOR &IGURE A CAN ALSO BE COMPUTED USING AN EQUIVALENT CIRCUIT WITH SHUNT SUSCEPTANCE B DEVELOPED BY -UMFORD THE SOURCE OF THE NOMOGRAPH B
L ¤ ³ S LN ¥ ¦ E P D S ´µ
,EAKAGE ,OSS
B
£Ó°£Ó
2!$!2 (!.$"//+
&)'52% 2EFLECTOR LEAKAGE LOSS VS TRANSMISSION LOSS
4HIS NOMOGRAPH IS FREQUENTLY USED FOR THE SIMPLE CONFIGURATIONS IN &IGURE A &OR OTHER CONFIGURATIONS AND THREAD FORMS THE SAME EQUATION CAN BE USED BY COMPUTING AN EQUIVALENT RADIUS BY MATCHING THE CROSS SECTIONAL AREAS /NE SIGNIFICANT SOURCE OF RADIATION IN THE BACK HEMISPHERE IS LEAKAGE THROUGH THE REFLECTOR 4HIS RADIATION LEVEL IS DETERMINED FROM THE DIFFERENCE BETWEEN PRIMARY FEED HORN AND SECONDARY REFLECTOR GAINS AND THE LEAKAGE LOSS RADIATION THROUGH THE MESH 4HERE ARE TWO CONSIDERATIONS REGARDING THE REFLECTOR SURFACE LEAKAGE 4HE LEAKAGE LOSS AFFECTS THE REFLECTOR GAIN DIRECTLY 4HE RADIATION LEVEL IN THE BACK HEMISPHERE IS A FUNCTION OF THE FEED GAIN REDUCED BY THE TRANSMISSION LOSS THROUGH THE REFLECTOR 4HUS THE REFLECTOR DESIGNER MUST CONSIDER BOTH THE LEAKAGE LOSS AND THE TRANSMISSION LOSS &IGURE 4HERE ARE HOWEVER ADDITIONAL BACKLOBES THAT ARE DISTINCT FROM THE BACK RADIATION DUE TO SURFACE LEAKAGE 4HESE ADDITIONAL LOBES ARE DUE TO REFLECTOR EDGE DIFFRACTION THAT ADDS COHERENTLY AND TYPICALLY CAUSES A RELATIVELY STRONG MAIN BACKLOBE BEHIND THE REFLECTOR #ENTER FED GEOMETRIES IE THOSE WITH REFLECTOR EDGES EQUIDISTANT FROM THE FEED ENABLE COHERENT ADDITION OF THE DIFFRACTED ENERGY DIRECTLY TO THE REAR OF THE REFLECTOR &OR THESE GEOMETRIES THE BACKLOBE LEVEL IS DIRECTLY RELATED TO THE EDGE ILLUMINATION LEVEL 3URFACE 2OUGHNESS ,OSS !LL RADAR REFLECTOR ANTENNAS ESPECIALLY THOSE THAT ARE MECHANICALLY SCANNED OR DEPLOYED REQUIRE CAREFUL CONSIDERATION OF MECHANICAL DESIGN DETAILS &IRST THE REFLECTING SURFACE MUST BE DESIGNED AND BUILT SO THAT IT REMAINS WITHIN CLOSE TOLERANCES TYPICALLY o K EVEN UNDER DYNAMIC OPERATING AND ENVIRONMENTAL CONDITIONS !LSO THE FEED MUST BE ACCURATELY ALIGNED WITH RESPECT TO THE REFLECTOR 4HE FEED SUPPORT STRUCTURE AND THE REFLECTOR STIFFENING STRUCTURE MUST MAINTAIN THE FEED LOCATION AND SURFACE DIMENSIONS WHILE THE ANTENNA IS BEING ROTATED 4HIS DIMENSIONAL STABILITY MUST BE MAINTAINED THROUGH WIND LOADING TEMPERATURE VARIATIONS OR OTHER ENVIRONMENTAL FACTORS TO ENSURE THAT PATTERN PERFORMANCE IS MAINTAINED
2%&,%#4/2 !.4%..!3
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&)'52% 3URFACE ROUGHNESS DK VS LOSS
2EFLECTOR ANTENNA GAIN LOSS DUE TO SURFACE ROUGHNESS HAS BEEN DISCUSSED BY *OHN 2UZE USING A STATISTICAL POINT OF VIEW 4HE LOSS OF GAIN DUE TO SMALL ROUGHNESS ERRORS IS APPROXIMATELY
' ¤ P E ³ y D ¥ ' ¦ L ´µ
WHERE D IS THE MEAN SQUARE PHASE ERROR D IS THE EFFECTIVE RMS SURFACE ERROR K IS THE WAVELENGTH ' IS THE GAIN WITHOUT PHASE ERROR AND ' IS THE GAIN WITH PHASE ERROR 4HE ROUGHNESS LOSS EFFECTS EMBODIED IN %Q ARE CAPTURED IN &IGURE WHERE GAIN LOSS VS SURFACE ROUGHNESS IN LIEU OF PHASE ERROR IS PLOTTED 4HE PLOT SHOWS THAT FOR D" GAIN LOSS THE RMS SURFACE ERROR MUST BE LESS THAN K 4O MAINTAIN MODEST LOSSES SURFACE ERRORS MUST BE TIGHTLY CONTROLLED !NOTHER CONSIDERATION IN MESH REFLECTORS IS SYSTEM ATIC SURFACE DEFORMATION &OR MANY REFLECTORS A MESH IS ATTACHED TO A METAL OR COMPOSITE BACKING STRUCTURE &OR SPACEBORNE DEPLOYABLE REFLECTORS THE MESH IS TYPI CALLY A VERY SHEER FABRIC LIKE MEMBRANE THAT IS STRETCHED ACROSS THE SURFACE AND ATTACHED AT A FINITE NUMBER OF POINTS TO FORM THE REFLECTING SURFACE )N EITHER CASE THERE ARE SURFACE DISTORTIONS BETWEEN THE PRECISELY CON TROLLED MOUNTING POINTS 4HIS SETS UP A SYSTEMATIC ERROR IN THE FORM OF PERIODIC CUSPS SEE &IGURE 4HESE ERRORS TYPICALLY CAUSE PATTERN GRATING LOBES BECAUSE THESE &)'52% 3YSTEMATIC DIS ERROR CUSPS ARE NORMALLY SEVERAL WAVELENGTHS APART PLACEMENT BETWEEN SUPPORTS WITH 4HE GRATING LOBES ARE EASILY RECOGNIZABLE BASED ON THEIR A CUSP BETWEEN SUPPORTS
£Ó°£{
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WELL DEFINED ANGULAR SPACING &OR A GRID WITH SUPPORTS AND ASSOCIATED ERRORS A DISTANCE S APART THE GRATING LOBE APPEARS AT
P ARCSINSK
4HE GRATING LOBE AMPLITUDE DEPENDS ON THE DEPTH OF THE DISTORTION &IGURE AND IS TYPICALLY
¤ P E ³ 'RATING ,OBE ¥ ¦ L ´µ
WHERE D IS THE DEPTH OF THE CUSP &EED $ISPLACEMENT 4HE PERMISSIBLE TOTAL ERROR IN THE OVERALL FEED REFLECTOR SYSTEM ALIGNMENTn IS GENERALLY RESTRICTED TO K OR oK /N THE BASIS OF THIS CRITERION THE RESULTANT MAXIMUM DEVIATION FROM THE PARABOLIC CONDITION FEED AT FOCUS WOULD BE oK $ISPLACEMENT OF THE FEED ALONG THE FOCAL AXIS THE Z AXIS IN &IGURE PRODUCES AN EVEN ORDER PHASE ERROR ON THE APERTURE ILLUMINATION 4HIS RESULTS IN MODEST BEAM BROADENING AND SOME FILLING OF THE FIRST NULL BUT IS NORMALLY NOT TOO DETRIMENTAL $ISPLACEMENT OF THE FEED NORMAL TO THE Z AXIS PRODUCES AN ODD ORDER PHASE ERROR IN THE APERTURE AND CAUSES HIGHER SIDELOBES ON ONE SIDE OF THE BEAM &URTHERMORE SUCH DISPLACEMENT WILL CAUSE THE BEAM TO MISPOINT )F THE DISPLACEMENT IS SMALL FIXED AND KNOWN ONE CAN TYPICALLY CALIBRATE OUT THE FIXED MISPOINTING BIAS (OWEVER IF THE DISPLACEMENT IS RANDOM SAY CAUSED BY VIBRATION THE BEAM POINTING ERROR CAN BE A PROBLEM 4HE REFLECTOR BEAM WILL BE STEERED BY P RADIANS IF THE FEED IS DISPLACED OFF AXIS BY AN AMOUNT D
P ARCTANDF RADIANS
WHERE F IS THE FOCAL LENGTH 3O IF THE LATERAL FEED DISPLACEMENT ERROR IS D THE BEAM POINTING ERROR $P IS $Q
E F RADIANS E F
3TRUT "LOCKAGE 3TRUTS ARE USED TO SUPPORT THE FEED AND FOR CENTER FED REFLEC TORS TYPICALLY FORM A TRIPOD AS SHOWN IN &IGURE 3TRUT SCATTERING IS A COMPLEX PHENOMENA THAT DEPENDS ON STRUT SIZE STRUT GEOMETRY FIELD POLARIZATION AND OTHER FAC TORS (OWEVER IN GENERAL STRUT INTERFERENCE SCATTERING WILL LIE WITHIN A CONICAL REGION ABOUT THE STRUT AXIS 4HE STRUT IS ILLUMINATED BY A PLANAR WAVEFRONT AND ONE EDGE OF THE SCATTERING CONE LIES ON THE REFLECTOR AXIS SEE &IGURE )F THE STRUT TILTS AT TO THE AXIS THE SCATTERING CONE MAXIMUM ANGLE IS TWICE THE TILT ANGLE OR 4HUS THE SCATTERING FROM THREE STRUTS FORMS INTERSECTING RINGS AS SHOWN IN &IGURE 4HIS CAUSES THE MOST BLOCKAGE AT THE PATTERN PEAK WHERE THE THREE RINGS INTERSECT 0OLARIZATION PLAYS A SIGNIFICANT ROLE IN STRUT SCATTERING &OR THE EXAMPLE SHOWN IN &IGURE STRUT IS PARALLEL TO THE % FIELD AND ITS BLOCKAGE AREA IS LARGER THAN ITS ACTUAL PHYSICAL CROSS SECTION (OWEVER THE LOWER STRUTS AND ARE TILTED WITH RESPECT TO THE % FIELD AND THEREFORE APPEAR SMALLER THAN THEIR PHYSICAL CROSS SECTION
2%&,%#4/2 !.4%..!3
£Ó°£x
&)'52% #ENTER FED REFLECTOR WITH TRIPOD STRUTS SIDE VIEW AND AXIAL VIEW
&)'52% 3TRUT AND MAXIMUM SCATTERING CONE
&)'52% !XIAL VIEW OF TRIPOD STRUT BLOCKAGE INTERFERENCE PATTERNS
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2!$!2 (!.$"//+
Ê, / /1, -
2EFLECTOR ANTENNAS ARE BUILT IN A WIDE VARIETY OF SHAPES AND SIZES WITH A CORRESPONDING VARIETY OF FEED SYSTEMS TO ILLUMINATE THE SURFACES EACH SUITED TO ITS PARTICULAR APPLI CATION &IGURE ILLUSTRATES THE MOST COMMON OF THESE REFLECTORS EACH OF WHICH IS DESCRIBED IN SOME DETAIL IN THE FOLLOWING SUBSECTIONS 4HE PARABOLOID IN &IGURE A COLLIMATES RADIATION FROM A FEED AT THE FOCUS INTO A PENCIL BEAM PROVIDING HIGH GAIN AND MINIMUM BEAMWIDTH 4HE PARABOLIC CYLINDER IN &IGURE B PERFORMS THIS COLLIMA TION IN ONE PLANE BUT ALLOWS THE USE OF A LINEAR ARRAY IN THE OTHER PLANE THEREBY ALLOWING FLEXIBILITY IN EITHER STEERING OR SHAPING OF THE BEAM IN THAT PLANE )F BEAM SHAPING NOT SCANNING IS THE GOAL AN ALTERNATIVE METHOD USING A SINGLE FEED IN LIEU OF A LINEAR ARRAY IS SHOWN IN &IGURE C 3HAPING OF THE SURFACE ALONG THE VERTICAL AXIS IS USED TO SPOIL THE BEAM SHAPE IN THIS PLANE BUT BECAUSE ONLY THE PHASE OF THE WAVE ACROSS THE APERTURE IS CHANGED THERE IS LESS CONTROL OVER THE BEAM SHAPE THAN IN THE PARABOLIC ANDOR PHASE CYLINDER SHOWN IN &IGURE B WHEREIN THE LINEAR ARRAY MAY BE ADJUSTED IN AMPLITUDE 6ERY OFTEN THE RADAR DESIGNER NEEDS MULTIPLE BEAMS TO PROVIDE INCREASED COVERAGE OR TO DETERMINE ANGLE &IGURE D SHOWS HOW MULTIPLE DISCRETE FEED LOCATIONS PRO DUCE A SET OF SECONDARY BEAMS AT DISTINCT ANGLES 4HE ADDITIONAL FEEDS MUST BE OFFSET FROM THE FOCUS AND THE RESULTANT SECONDARY BEAMS WILL SUFFER SOME GAIN LOSS AND DIS TORTION COMMENSURATE WITH THE ASSOCIATED FEED DISPLACEMENT )F AN %3! FEED IS USED THE REFLECTOR SYSTEM CAN BE DESIGNED TO ENABLE ELECTRONIC BEAM SCANNING ALBEIT OVER A LIMITED &/6 4HE USE OF MODERN %3! AND %3! LIKE REFLECTOR FEEDS TO ACHIEVE ELEC TRONIC SCANNING IS DISCUSSED FURTHER IN 3ECTION !N ESPECIALLY COMMON MULTIPLE BEAM DESIGN IS THE MONOPULSE ANTENNA IN &IGURE E USED FOR ANGLE DETERMINATION ON A SINGLE PULSE AS THE NAME IMPLIES )N THIS INSTANCE THE SECOND BEAM IS NORMALLY A DIFFERENCE BEAM WITH ITS NULL AT THE PEAK OF THE FIRST BEAM
&)'52% #OMMON REFLECTOR ANTENNA TYPES A PARABOLOID B PARABOLIC CYLINDER C SHAPED D STACKED BEAM E MONOPULSE AND F #ASSEGRAIN
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-ULTIPLE REFLECTOR SYSTEMS TYPIFIED BY THE #ASSEGRAIN ANTENNA SHOWN IN &IGURE F OFFER ONE MORE DEGREE OF FLEXIBILITY BY SHAPING THE PRIMARY BEAM AND OR ALLOWING THE FEED SYSTEM TO BE CONVENIENTLY LOCATED BEHIND THE MAIN REFLECTOR 4HE SYMMETRICAL ARRANGEMENT SHOWN HAS SIGNIFICANT BLOCKAGE BUT OFFSET GEOMETRIES MITIGATE FEED BLOCKAGE )N MODERN REFLECTOR ANTENNA DESIGN COMBINATIONS AND VARIATIONS OF THESE BASIC TYPES ARE WIDESPREAD HOWEVER DESIGN GOALS GENERALLY STRESS BEAM GAINS SHAPES LOCATIONS ETC WHILE STIPULATING MINIMAL LOSSES AND LOW SIDELOBE LEVELS 0ARABOLOIDAL 2EFLECTOR !NTENNAS 4HE THEORY AND DESIGN OF PARABOLOIDAL REFLEC TOR ANTENNAS ARE EXTENSIVELY DISCUSSED IN THE LITERATUREn ! BASIC GEOMETRY IS SHOWN IN &IGURE A WHICH ASSUMES A PARABOLIC REFLECTOR SURFACE OF FOCAL LENGTH F WITH A FEED AT THE FOCAL POINT )T CAN BE SHOWN FROM GEOMETRICAL OPTICS CONSIDERATIONS THAT A SPHERICAL WAVE EMERGING FROM THE FOCAL POINT & AND INCIDENT ON THE REFLECTOR IS TRANSFORMED AFTER REFLECTION INTO A PLANE WAVE TRAVELING IN THE POSITIVE Z DIRECTION &IGURE B !LTHOUGH REFLECTORS ARE COMMONLY ILLUSTRATED WITH A ROUND OUTLINE OR RIM AND A CEN TRAL FEED POINT A VARIETY OF REFLECTOR APERTURE SHAPES ARE USED IN PRACTICE AS SHOWN IN &IGURE /FTEN THE AZIMUTH AND ELEVATION BEAMWIDTH REQUIREMENTS DIFFER REQUIR ING AN OBLONG APERTURE AS SHOWN IN &IGURE B E )F LOW SIDELOBE LEVELS ARE REQUIRED FEED BLOCKAGE MAY BECOME INTOLERABLE REQUIR ING THE USE OF AN OFFSET FEED &IGURE C 4HE FEED IS STILL GENERALLY LOCATED AT THE FOCAL POINT BUT THE REFLECTOR IS REALIZED VIA USE OF A DIFFERENT PORTION OF THE PARABOLA &OR OFFSET FED REFLECTOR CONFIGURATIONS THE FOCAL AXIS GENERALLY DOES NOT INTERSECT THE REFLECTOR SURFACE &EEDS FOR OFFSET FED REFLECTORS ARE GENERALLY AIMED CLOSE TO BUT SLIGHTLY BEYOND THE CENTER OF THE REFLECTOR AREA TO ACCOUNT FOR THE LARGER SPACE TAPER SPREADING LOSS ON THE FAR SIDE OF THE REFLECTOR 4HIS GENERALLY RESULTS IN A SLIGHTLY UNSYMMETRICAL APERTURE ILLUMINATION 4HE CORNERS OF MOST PARABOLOIDAL REFLECTORS ARE FREQUENTLY ROUNDED NOT SHOWN OR MITERED &IGURE D TO REDUCE EXTRANEOUS SURFACE AREA ANDOR MINIMIZE THE TORQUE REQUIRED TO TURN THE ANTENNA "ECAUSE THESE CORNER REGIONS ARE GENERALLY WEAKLY
&)'52% 'EOMETRICAL REPRESENTATION OF A PARABOLOIDAL REFLECTOR A GEOMETRY AND B OPERATION
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&)'52% 0ARABOLOIDAL REFLECTOR APERTURE SHAPES OR RIMS A ROUND OUTLINERIM B OBLONG C OFFSET FEED D MITERED CORNER E SQUARE CORNER AND F STEPPED CORNER
ILLUMINATED BY THE FEED THEIR REMOVAL GENERALLY HAS LITTLE IMPACT ON THE GAIN (OWEVER CIRCULAR AND ELLIPTICAL OUTLINESRIMS WILL PRODUCE MODEST SIDELOBES IN BOTH PRINCIPAL AND NONPRINCIPAL PLANES )F VERY LOW SIDELOBES ARE SPECIFIED IN NONPRINCIPAL PLANES IT MAY BE NECESSARY TO MAINTAIN SQUARE CORNERS AS SHOWN IN THE UPPER PART OF &IGURE E 0ARABOLIC #YLINDER !NTENNA )T IS QUITE COMMON THAT EITHER THE BEAM MUST BE STEERABLE OR SHAPED IN ONLY ONE PLANE EITHER AZIMUTH OR ELEVATION ! PARABOLIC CYLINDRICAL REFLECTOR FED BY A LINEAR ARRAY FEED CAN ACCOMPLISH THIS AT MODERATELY HIGHER COST 4HE PARABOLIC CYLINDER ANTENNA CAN BE APPLIED TO ACHIEVE A PRECISELY SHAPED BEAM FROM A COMMON APERTURE 4HE !.403 &IGURE USES A VERTICAL ARRAY TO PRO VIDE FINE CONTROL OF THE ELEVATION PATTERN WITH A SINGLE ELEVATION COLUMN FEED ARRAY AND SO IS VERY COST EFFECTIVE 4HE ELEVA TION BEAM SHAPING INCORPORATES A STEEP BEAM SLOPE AT THE HORIZON TO ALLOW RADAR OPERATION AT LOW ELEVATION ANGLES WITHOUT DEGRADATION FROM GROUND REFLECTIONS 4HE 403 PRODUCES A MUCH SHARPER SLOPE AT THE HORIZON THAN A SHAPED REFLECTOR OF EQUAL HEIGHT 4HE ARRAY FEED ENABLES SUPERPOSI TION OF BEAMS CLOSE TO THE APERTURE NORMAL THEREBY ENABLING VERY HIGH TAPER EFFICIENCY NEAR FULL APERTURE GAIN
&)'52% !.403 PARABOLIC CYLINDER ANTENNA #OURTESY .ORTHROP 'RUMMAN #ORPORATION
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4HE BASIC PARABOLIC CYLINDER GEOMETRY IS SHOWN IN &IGURE 4HE REFLECTOR SURFACE IS DEFINED AS Z
Y
F F
WHERE Z IS THE DISTANCE FROM THE FOCAL PLANE F IS THE FOCAL LENGTH OF THE CYLINDRICAL REFLECTOR AND Y IS THE HORIZONTAL DIMENSION &OR THE PARABOLIC CYLINDER THE SURFACE DOES NOT VARY WITH X THE HEIGHT 4HE FEED IS GENERALLY ON THE FOCAL LINE AND IN MANY WAYS THE DESIGN OF PARABOLIC CYLINDER REFLECTORS IS SIMILAR TO THAT OF PARABOLOIDAL REFLECTORS /NE SIGNIFICANT DIFFERENCE IS THAT THE FEED ENERGY DIVERGES CYLINDRICALLY RATHER THAN SPHERICALLY AND SO THE FEED POWER DENSITY FALLS OFF AS Q RATHER THAN Q 4HE HEIGHT OF THE PARABOLIC CYLINDER &IGURE A MUST ALLOW FOR BEAMWIDTH SHAPING AND STEERING OF THE LINEAR FEED ARRAY 7HEN THE LINE SOURCE STEERS AT ANGLE P FROM BROADSIDE THE PRIMARY BEAM FROM THE SOURCE LIES ON A CONIC AND THE INTERCEPTS AT THE UPPER RIGHT AND LEFT CORNERS OF THE REFLECTOR ARE FARTHER UP THAN IN THE CENTER AS SHOWN IN &IGURE B 4HEREFORE THE CORNERS OF PARABOLIC CYLINDER REFLECTORS ARE SELDOM ROUNDED IN PRACTICE 3HAPED 2EFLECTORS &AN BEAMS WITH A SPECIFIED SHAPE ARE REQUIRED FOR A VARIETY OF REASONS ! COMMON ELEVATION SHAPED BEAM REQUIREMENT IS TO PROVIDE EQUAL ECHO SIGNAL POWER ON TARGETS AT CONSTANT ALTITUDE )F THE TRANSMIT AND RECEIVE BEAMS ARE IDENTICAL AND IF SECONDARY EFFECTS ARE IGNORED THIS CAN BE ACHIEVED WITH A POWER RADIATION PAT TERN PROPORTIONAL TO CSCP WHERE P IS THE ELEVATION ANGLE )N PRACTICE THE WELL KNOWN COSECANT SQUARED PATTERN IS TYPICALLY MODIFIED TO ACCOUNT FOR THE CURVATURE OF THE EARTH AND THE CHARACTERISTICS OF SENSITIVITY TIME CONTROL 34#
&)'52% 0ARABOLIC CYLINDER A GEOMETRY AND B SURFACE EXTENSION ENABLES LINE SOURCE STEERING
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&)'52% 2EFLECTOR SHAPING
! RELATIVELY SIMPLE WAY TO SHAPE THE BEAM IS TO SHAPE THE REFLECTOR AS &IGURE ILLUSTRATES %ACH PORTION OF THE REFLECTOR IS DESIGNED TO REFLECT A PORTION OF THE INCI DENT ENERGY IN A DIFFERENT DIRECTION AND TO THE EXTENT THAT GEOMETRIC OPTICS IS VALID THE POWER DENSITY AT THAT ANGLE IS THE INTEGRATED SUM OF THE POWER DENSITY FROM THE FEED ACROSS THAT PORTION OF THE REFLECTOR 3ILVER GRAPHICALLY DESCRIBES A PROCEDURE FOR DETERMINING THE REFLECTOR CONTOUR FOR A COSECANT SQUARED BEAM (OWEVER COMPUTER SOFTWARE PACKAGES NOW EXIST THAT ENABLE SYNTHESIS OF ARBITRARY BEAM SHAPES VIA APPLI CATION OF ITERATIVE OPTIMIZATION TECHNIQUES IN CONJUNCTION WITH PHYSICAL OPTICSnBASED PATTERN COMPUTATIONS 4HESE ANALYSIS METHODS AND SOFTWARE PACKAGES ARE SUMMARIZED IN 3ECTION /FFSET FED PARABOLIC REFLECTORS ARE OFTEN USED TO MITIGATE FEED BLOCKAGE (OWEVER REFLECTOR SHAPING CAN ALSO BE USED TO MITIGATE BLOCKAGE AND IS SOMETIMES APPLIED TO REDIRECT THE REFLECTED ENERGY AWAY FROM THE FEED AS SHOWN IN &IGURE &IGURE ILLUSTRATES HOW SHAPING CAN BE APPLIED TO VIRTUALLY ELIMINATE BLOCKAGE EVEN THOUGH THE FEED APPEARS TO BE WITHIN THE &/6 OF THE REFLECTOR 4HE !32 ANTENNA &IGURE FOUND AT MAJOR AIRPORTS TYPIFIES SHAPED REFLEC TOR ANTENNA DESIGN 4HE ELEVATION BEAM SHAPE IS TAILORED USING A COMPUTER AIDED DESIGN PROCESS AND AZIMUTH SIDELOBES ARE LOWERED BY OFFSETTING THE FEED SO THERE IS NO BLOCKAGE 4WO LINEAR OR CIRCULARLY POLARIZED ELEVATION BEAMS ARE PRODUCED BY USING TWO FEEDHORNS /NE BEAM IS CLOSE TO THE HORIZON FOR CLOSE IN TARGETS AND THE SECOND IS HIGHER IN ELEVATION SO IT RECEIVES LESS GROUND CLUTTER FOR LONG RANGE TARGETS /NE TYPICAL CHARACTERISTIC OF SHAPED REFLECTORS IS LOWER APERTURE EFFICIENCY 'ENERALLY THE SURFACE SHAPING PROCESS SPOILS THE APERTURE PHASE AND BROADENS THE BEAM THEREBY INHERENTLY REDUCING THE APER TURE EFFICIENCY (OWEVER THIS SACRIFICE IN APERTURE EFFICIENCY IS GENERALLY ACCEPTED BY THE RADAR DESIGNER WHEN BEAM SHAPING IS DESIRED OR REQUIRED 4HE SECOND ANTENNA ATOP THE !32 REFLECTOR &IGURE PROVIDES AN INDE PENDENT TRACKING SYSTEM )T IS AN !IR 4RAFFIC #ONTROL 2ADAR "EACON 3YSTEM ARRAY ANTENNA THAT TRANSMITS AND RECEIVES NARROW AZIMUTH SUM DIFFERENCE AND GUARD BEAMS ALL SHAPED IN ELEVATION )T REQUIRES A TRANSPONDER ABOARD &)'52% %LIMINATION OF BLOCKAGE THE AIRCRAFTS TARGETED AS IT HAS LOW GAIN
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&)'52% !32 SHAPED REFLECTOR WITH OFFSET FEED !IR 4RAFFIC #ONTROL 2ADAR "EACON 3YSTEM !4#2"3 ARRAY IS MOUNTED ON TOP #OURTESY .ORTHROP 'RUMMAN #ORPORATION
-ULTIPLE 2EFLECTOR !NTENNASn 4HERE ARE BOTH DIFFICULTIES AND ADVANTAGES ASSOCIATED WITH ADDING A SECONDARY OR SUBREFLECTOR TO A PARABOLOIDAL REFLECTOR SYSTEM 4HE SHAPE OF THE SUBREFLECTOR DETERMINES HOW THE POWER WILL BE DISTRIBUTED ACROSS THE PRIMARY REFLECTOR AND THEREBY PROVIDES SOME CONTROL OVER AMPLITUDE IN ADDITION TO PHASE IN THE APERTURE MAKING IT POSSIBLE TO PRODUCE VERY LOW SPILLOVER OR TO PRODUCE A SPECIFIC LOW SIDELOBE DISTRIBUTION "Y SUITABLE CHOICE OF SHAPE THE APPARENT FOCAL LENGTH CAN BE ENLARGED SO THAT THE FEED SIZE IS PRACTICAL OR EVEN FEASIBLE 4HIS IS SOME TIMES NECESSARY FOR MONOPULSE OPERATION 4HE #ASSEGRAIN DUAL REFLECTOR ANTENNA &IGURE DERIVED FROM OPTICAL TELE SCOPE DESIGNS IS THE MOST PREVALENT DUAL REFLECTOR CONFIGURATION &IGURE A SHOWS A SMALL SUBREFLECTOR BETWEEN THE FEED AND PARABOLIC MAIN REFLECTOR 4HE FEED ILLUMI NATES THE HYPERBOLOIDAL SUBREFLECTOR WHICH IN TURN ILLUMINATES THE PARABOLOIDAL MAIN REFLECTOR 4HE FEED IS PLACED AT ONE FOCUS OF THE HYPERBOLOID AND THE PARABOLOID FOCUS IS COINCIDENT WITH THE SECOND FOCUS OF THE HYPERBOLOID 4HE USE OF A SUBREFLECTOR ALSO ALLOWS THE FEED TO BE LOCATED BEHIND THE MAIN REFLECTOR AND CLOSER TO THE TRANSMITTER AND RECEIVER IN ORDER TO MINIMIZE TRANSMISSION LINE LOSSES &URTHERMORE IF THE FEED IS LOCATED BEHIND THE MAIN REFLECTOR THE CENTER OF GRAVITY WILL BE BIASED CLOSER TO THE MAIN REFLECTOR VERTEX THEREBY SIMPLIFYING THE DESIGN OF BOTH THE STRUCTURE AND THE GIMBAL PRECISION MECHANICAL POSITIONING SYSTEM 4HE 'REGORIAN DUAL REFLECTOR ANTENNA SYSTEM NOT SHOWN IN &IGURE IS SIMILAR TO THE #ASSEGRAIN BUT IT USES AN ELLIPSOIDAL SUBREFLECTOR IN LIEU OF A HYPERBOLOID RESULT ING IN A LENGTHENING OF THE REFLECTOR SYSTEM ALONG THE FOCAL AXIS 4HE PARAMETERS OF THE #ASSEGRAIN REFLECTOR ARE RELATED BY THE FOLLOWING EXPRESSIONS
TAN XV $M FM
TAN XV TAN XR FC $S
E ,V FC
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&)'52% #ASSEGRAIN DUAL REFLECTOR ANTENNA SYSTEMS THE LARGER SURFACE IS THE MAIN REFLECTOR AND THE SMALLER SURFACE IS THE SUBREFLECTOR A RAY OPTICS B TYPICAL AXIAL CONFIGURATION AND C OFFSET CONFIGURATION
WHERE THE ECCENTRICITY E OF THE HYPERBOLOID IS GIVEN BY
E SIN;XV XR = SIN;XV XR =
4HE EQUIVALENT PARABOLOID CONCEPT IS A CONVENIENT METHOD OF ANALYZING THE RADIA TION CHARACTERISTICS USING A SINGLE REFLECTOR hEQUIVALENTv MODEL 4HIS METHOD UTILIZES A PARABOLOID OF EQUAL DIAMETER BUT A LARGER FOCAL LENGTH TO MODEL THE DUAL REFLECTOR #ASSEGRAIN SYSTEM 4HE EQUATION
FC $M TANXR
DEFINES THE EQUIVALENT FOCAL LENGTH AND THE FOCAL LENGTH RATIO OR MAGNIFICATION M IS GIVEN BY
M FC FM E E
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4HE MAGNIFICATION M IS A USEFUL METRIC IN THAT IT PROVIDES A MEASURE OF THE REDUCTION IN SIZELENGTH ALONG THE FOCAL AXIS THAT IS ENABLED BY USE OF THE #ASSEGRAIN REFLECTOR SYSTEM IN LIEU OF A SINGLE PARABOLIC REFLECTOR SYSTEM 4HE FEED IS DESIGNED TO PRODUCE SUITABLE ILLUMINATION WITHIN SUBTENDED ANGLES oXR ASSOCIATED WITH THE LONGER FOCAL LENGTH FC !PERTURE BLOCKING CAN BE LARGE FOR CENTER FED #ASSEGRAIN ANTENNAS 4HE BLOCKAGE CAN BE MINIMIZED BY CHOOSING THE DIAMETER OF THE SUBREFLECTOR TO BE EQUAL TO THAT OF THE FEED 4HIS OCCURS WHEN
$3 FM L K
WHERE K IS THE RATIO OF THE FEED APERTURE DIAMETER TO ITS EFFECTIVE BLOCKING DIAMETER /RDINARILY K IS SLIGHTLY LESS THAN &OR LINEARLY POLARIZED RADAR APPLICATIONS APERTURE BLOCKING CAN BE SIGNIFICANTLY REDUCED BY USING A POLARIZATION TWIST REFLECTOR AND A SUBREFLECTOR MADE OF PARALLEL WIRES 4HIS TWIST REFLECTOR DESIGN ENABLES A ROTATION OF THE POLARIZATION SUCH THAT THE POLARIZATION OF THE BEAM UPON REFLECTION FROM THE MAIN REFLECTOR IS ORTHOGONAL AND TRANSPARENT TO THE GRIDDED SUBREFLECTOR "LOCKAGE CAN ALSO BE ELIMINATED BY OFFSETTING BOTH THE FEED AND THE SUBREFLECTOR &IGURE C 7ITH BLOCKAGE AND SUPPORTING STRUTS AND SPILLOVER VIRTUALLY ELIMI NATED THIS GEOMETRY IS USEFUL FOR VERY LOW SIDELOBE APPLICATIONS !S DESCRIBED EARLIER THE APERTURE EFFICIENCY OF SINGLE REFLECTOR SYSTEMS IS MAXI MIZED BY BALANCING THE FEED TAPER AND THE FEED SPILLOVER AND MINIMIZING OTHER LOSSES BUT IS TYPICALLY n (OWEVER DUAL REFLECTOR SYSTEMS EG #ASSEGRAIN HAVE AN ADDITIONAL DEGREE OF FREEDOM AND SURFACE SHAPING CAN BE APPLIED TO DECREASE THE TAPER LOSS AND ENABLE APERTURE EFFICIENCIES IN EXCESS OF ! DIFFERENT TYPE OF DUAL REFLECTOR SYSTEM THAT IS PARTICULARLY WELL SUITED TO APPLICA TIONS WHERE LIMITED ELECTRONIC SCANNING IS REQUIRED IS THE SO CALLED CONFOCAL REFLECTOR SYSTEMn SHOWN IN &IGURE 4HIS SYSTEM EMPLOYS TWO PARABOLIC REFLECTORS A MAIN AND A SUB THAT SHARE A COMMON FOCAL POINT 4HE OPTICS OF THIS SYSTEM IS DESIGNED SUCH THAT A PLANE WAVE SOURCE SAY FROM AN ARRAY IS FIRST CONVERTED TO A SPHERICAL WAVE AT THE SUBREFLECTOR 4HEN UPON REFLECTION FROM THE SUBREFLECTOR THE FEED ENERGY CONVERGES AT THE COMMON FOCUS AND DIVERGES AGAIN AS A SPHERICAL WAVE BEFORE FINALLY REFLECTING FROM THE MAIN REFLECTOR 4HE CONFOCAL SYSTEM HAS SEVERAL INTERESTING PROPERTIES TIED TO THE MAGNIFICATION FACTOR -
- F- F3
WHERE F- AND F3 ARE THE FOCAL LENGTHS OF MAIN AND SUBREFLECTORS RESPECTIVELY 4HE FIRST PROPERTY SHOWS THAT THE SYSTEM IS ESSENTIALLY A FEED SOURCE MAGNIFIER 4HE REFLECTOR GAIN 'R IS DESCRIBED BY
'R y 'F r - r COSPR
WHERE 'F IS THE GAIN OF THE FEED ARRAY AND PR IS THE SCAN ANGLE OF THE REFLECTOR SECOND ARY BEAM 4HE SECOND PROPERTY DEFINES THE SCANNING 4HE REFLECTOR SCAN ANGLE PR IS DEFINED BY THE FOLLOWING EQUATION
PR y PF -
WHERE PF IS THE FEED SCAN ANGLE &OR EXAMPLE IF THE MAGNIFICATION FACTOR IS AND THE %3! FEED ARRAY IS SCANNED THE REFLECTOR BEAM WILL SCAN APPROXIMATELY
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0ARABOLIC -AIN 2EFLECTOR A2EF A!%3! -AG
$MAIN
#OMMON &OCUS
FMAIN
FSUB
0HASED !RRAY &EED
-AG
$SUB
FMAIN FSUB
A!%3!
0ARABOLIC 3UBREFLECTOR
&)'52% #ONFOCAL DUAL REFLECTOR ANTENNA
3CAN ABERRATIONS LEAD TO MODERATELY HIGHER SCAN LOSSES AND SLIGHT BEAM SCAN ANGLE DEVIATIONS FROM THOSE PREDICTED BY %QS AND WHEN IDEAL %3! PLANE WAVE EXCITATIONS IE LINEAR PHASE SLOPE ARE APPLIED (OWEVER THE AMPLITUDE AND PHASE CONTROLS IN THE %3! ALLOW FOR SCAN ABERRATION COMPENSATION VIA CONJUGATE MATCHING OF THE APERTURE FIELDS 4HUS THE USE OF AN %3! FEED ENABLES RECOVERY OF SCAN LOSSES RESULTING FROM ABERRATIONS IN THE SYSTEM #ONFOCAL REFLECTOR ARCHITECTURES HAVE BEEN THE SUBJECT OF STUDY AND ANALYSIS FOR MANY YEARS AND NUMEROUS DEMONSTRATION SYSTEMS HAVE ALSO BEEN DEVELOPEDn !LTHOUGH CONFOCAL REFLECTORS HAVE NOT BEEN ADOPTED FOR SIGNIFICANT USAGE IN OPERA TIONAL SYSTEMS THESE REFLECTOR SYSTEMS ARE LIKELY TO BE PART OF SOME NEXT GENERATION RADARS DUE TO THE RELATIVELY RECENT MATURATION OF ENABLING %3! TECHNOLOGY 3PHERICAL 2EFLECTORS n 4HE SPHERICAL REFLECTOR IS SOMETIMES USED FOR APPLI CATIONS REQUIRING SCANNING OR MULTIPLE BEAMS OVER VERY WIDE ANGLES )TS DESIGN IS BASED UPON THE FACT THAT OVER LIMITED ANGULAR REGIONS A SPHERICAL SURFACE VIEWED FROM ANY POINT HALFWAY BETWEEN THE CENTER OF A SPHERE AND ITS SURFACE IS NEARLY PARABOLIC 4HIS MEANS THAT IF A FEED IS MOVED ALONG AN INNER SPHERICAL SURFACE OF CONSTANT RADIUS 2 WHERE 2 IS THE RADIUS OF THE SPHERICAL REFLECTOR THE SECONDARY BEAM CAN BE STEERED 4HE RANGE OF BEAM STEERING IS LIMITED BY THE SIZE OF THE SPHERICAL REFLECTOR IE THE PORTION OF A FULL SPHERE REALIZED BY THE REFLECTOR 4HE SCANNING CAPABILITY CAN BE IMPLEMENTED VIA USE OF EITHER A SINGLE MOVABLE FEED OR AN ARRAY WITH SWITCHABLE FEEDS 3ELF BLOCKAGE REFLECTOR BLOCKING ITSELF IS ANOTHER POTENTIAL LIMITING FACTOR IN SPHER ICAL REFLECTOR SYSTEMS (OWEVER OF AZIMUTH STEERING CAN BE ACCOMPLISHED VIA A POLARIZATION DESIGN SCHEME SIMILAR TO THE POLARIZATION TWIST SUBREFLECTOR DESCRIBED
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ABOVE FOR THE #ASSEGRAIN SYSTEM )N THIS DESIGN THE FEED POLARIZATION IS TILTED AND THE REFLECTOR IS FORMED OF CONDUCTING STRIPS PARALLEL TO THE POLARIZATION (OWEVER THE CONDUCTING STRIPS ON OPPOSING SIDES OF THE REFLECTOR ARE TWISTED THEREBY ENABLING TRANSMISSION OF THE REFLECTED ENERGY 4HIS TYPE OF ANTENNA IS KNOWN AS A HELISPHERE )F WIDE ANGLE SCANNING IN ONLY ONE PLANE IE AZIMUTH OR ELEVATION IS REQUIRED A SIM ILAR DESIGN CALLED THE PARABOLIC TORUS IS MORE APPLICABLE 4HE PARABOLIC TORUS REFLECTOR IS A SURFACE THAT IS SPHERICAL IN ONE PLANE AZIMUTH OR ELEVATION AND PARABOLIC IN THE OTHER PLANE 4HIS DESIGN TAKES ADVANTAGE OF BOTH THE WIDE SCANNING ENABLED BY THE SPHERICAL SHAPING AND THE HIGH APERTURE EFFICIENCY ENABLED BY THE PARABOLIC SHAPING 4HE HEIGHT ELEVATION DIMENSION OF THE REFLECTOR IS SET BY THE REQUIRED ELEVATION BEAMWIDTH 4HE PARABOLIC TORUS HAS SEEN APPLICATION IN VARIOUS RADARS INCLUDING THE ORIGINAL "-%73 SYSTEM AND THE 303 AND 301 " SYSTEMS
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7HEREAS PHASED ARRAY ANTENNAS ARE FREQUENTLY CHOSEN FOR RADAR SYSTEM DESIGNS REFLEC TOR ANTENNAS WERE ONCE THE DOMINANT ANTENNA DESIGN CHOICE FOR MEDIUM TO HIGH GAIN RADAR APERTURES /BVIOUSLY THE COST OF A SINGLE FEED HORN AND METAL REFLECTOR IS MUCH LESS THAN THE SAME SIZE ARRAY WITH MANY INDIVIDUAL ELEMENTS AND ASSOCIATED PHASE SHIFTERS AMPLIFIERS RECEIVERS ETC #ONSEQUENTLY MANY RADARS CURRENTLY IN THE FIELD USE REFLEC TOR ANTENNAS &URTHERMORE REFLECTOR ANTENNA DESIGNS ARE USED IN MODERN RADAR DESIGNS WHERE MODERATE SCAN RATES AND SCAN VOLUMES ARE REQUIRED OR LOW COST IS ESSENTIAL -ANY LEGACY RADARS EMPLOY REFLECTOR ANTENNAS WITH SINGLE FEED ELEMENTS OR A CLUSTER OF FEEDS IE AN ARRAY WITH A FIXED BEAM 2& COMBINER OR DIVIDER NETWORK &IGURE SHOWS SOME TYPICAL SINGLE FEED REFLECTOR CONFIGURATIONS UTILIZING HORN WAVEGUIDE AND DIPOLE FEEDS &IGURE SHOWS A FEW COMMON TYPES OF FLARED HORN FEEDS
&)'52% 3OME TYPICAL REFLECTOR ANTENNA CONFIGURATIONS
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&)'52% 6ARIOUS TYPES OF HORN FEEDS FOR REFLECTOR ANTENNAS
/THER TYPES OF FEEDS SUCH AS DIPOLES MICROSTRIP PATCHES NOTCHES ETC ARE SOMETIMES USED BUT FOR SINGLE FEED REFLECTOR IMPLEMENTATIONS FLARED WAVEGUIDE HORNS ARE THE MOST COMMON 4HE FEED IN CONJUNCTION WITH THE REFLECTOR MUST ALSO SATISFY THE ANTENNA POLARIZATION REQUIREMENTS AND HANDLE REQUIRED PEAK AND AVERAGE POWER LEVELS UNDER ALL OPERATIONAL ENVIRONMENTS /THER FEED DESIGN CONSIDERATIONS INCLUDE THE OPERATING BANDWIDTH AND THE POTENTIAL IMPLEMENTATION OF ANY ADDITIONAL MODESPATTERNS EG DIFFERENCE OR SQUINTED BEAMS &OR SINGLE FEED RADAR REFLECTOR ANTENNAS SUCH AS THOSE DEPICTED IN &IGURES MECHANICAL SCANNING IS GENERALLY ACHIEVED VIA A GIMBAL A PRECISION MECHANICAL POINT ING SYSTEM 2ADAR ANTENNA GIMBAL DESIGNS VARY GREATLY DEPENDING UPON SCAN RATE &/6 TRACKING REQUIREMENTS ANTENNA SIZE MASS ETC "ASIC &EEDS &OR RADARS REQUIRING A SIMPLE PENCIL BEAM BASIC SINGLE MODE WAVEGUIDE HORN FEEDS SUCH AS PYRAMIDAL 4% MODE AND CONICAL 4% MODE HORNS ARE WIDELY USED 3INGLE MODE FLARED HORNS WILL PROVIDE LINEARLY POLARIZED PENCIL BEAMS AND WILL GENERALLY HANDLE HIGH POWER &OR MORE DEMAND ING APPLICATIONS REQUIRING TRACKING MODES POLARIZATION DIVERSITY HIGH BEAM EFFICIENCY OR ULTRA LOW SIDELOBES FEED DESIGNS BECOME CORRESPONDINGLY MORE COMPLEX &OR SUCH APPLICATIONS SEGMENTED FINNED MULTIMODE ANDOR CORRUGATED HORNS AS ILLUSTRATED IN &IGURE ARE OFTEN USED -ULTIMODE FEEDS ENABLE REALIZATION OF DIFFERENCE MODE PATTERNS WITH A COMPACT SINGLE FEED HORN AND AS SUCH ARE ESPECIALLY USEFUL FOR TRACKING APPLICATIONS -ONOPULSE &EEDS n -ONOPULSE IS FREQUENTLY USED IN RADAR TRACKING AND SURVEILLANCE SYSTEMS TO EITHER KEEP THE BEAM POINTED ON THE TARGET TRACKING OR TO ACCURATELY MEASURE THE ANGLE TO THE TARGET SUR VEILLANCE n !MPLITUDE COMPARISON MONOPULSE SYSTEMS ILLUS TRATED IN &IGURE USE THE SUM OF THE TWO FEED
&)'52% !MPLITUDE COM PARISON MONOPULSE ANTENNA SHOWING SUM AND DIFFERENCE BEAMS
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OUTPUTS TO FORM A HIGH GAIN LOW SIDELOBE BEAM AND THE DIFFERENCE OF THE TWO SQUINTED BEAMS TO FORM A PRECISE DEEP NULL AT BORESIGHT 4HE SUM BEAM IS USED ON BOTH TRANS MIT AND RECEIVE TO DETECT THE TARGET 4HE DIFFERENCE BEAM IS RECEIVE ONLY AND PROVIDES ANGLE DETERMINATION )N MOST APPLICATIONS BOTH AZIMUTH AND ELEVATION DIFFERENCE BEAM PORTS ARE IMPLEMENTED &IGURE ILLUSTRATES THE CONCEPT OF AMPLITUDE COMPARI SON MONOPULSE ! FEEDBACK LOOP MINIMIZES THE RECEIVED DIFFERENCE BEAM SIGNAL BY MECHANICALLY STEERING THE ANTENNA TO KEEP THE NULL AND THE CORRESPONDING SUM BEAM PEAK ON TARGET 4HERE ARE NUMEROUS WAYS TO REALIZE AMPLITUDE MONOPULSE BEAMS IN A REFLECTOR ANTENNA DESIGN BUT MOST DESIGNS GENERALLY FALL INTO TWO CLASSES MULTIFEED AND MULTIMODE -ULTIFEED DESIGNS USE COMBINING NETWORKS TO GENERATE DIFFERENTIAL FEED DISTRIBUTIONS )N ITS SIMPLEST FORM AN AZEL MULTIFEED MONOPULSE FEED ARRAY CAN BE REALIZED AS A FOUR ELEMENT FEED AS SHOWN IN &IGURE (OWEVER SOME APPLICATIONS USE MORE FEED ELEMENTS TO FURTHER TAILOR THE DISTRIBUTION TO IMPROVE EFFICIENCY ANDOR DIFFERENCE BEAM SLOPE )F THE REFLECTOR IS ILLUMINATED WITH A SIMPLE FOUR ELEMENT FEED A CONFLICT GENERALLY ARISES BETWEEN THE GOALS OF HIGH SUM BEAM EFFICIENCY AND HIGH DIFFERENCE BEAM SLOPE FROM THE MONOPULSE COMPARATOR 4HE FORMER REQUIRES A SMALL OVERALL FEED SIZE WHEREAS THE LATTER REQUIRES LARGE INDIVIDUAL FEEDS &IGURE .UMEROUS DESIGN METHODS HAVE BEEN DEVISED TO OVERCOME THIS PROBLEM AS WELL AS THE ASSOCIATED HIGH DIFFERENCE PATTERN SIDELOBES 4HESE METHODS EITHER USE DIFFERENT SETS OF FEED ELEMENTS FOR THE SUM AND DIFFERENCE BEAMS OR APPLY DIFFERENT ARRAY AMPLITUDEPHASE WEIGHTINGS FOR EACH OF THE BEAMS )F HORN FEED ELEMENTS ARE USED ONE APPROACH IS TO OVERSIZE THE FEEDS TO ENABLE MULTIMODE EXCITATION FOR THE SUM BEAM AS DESCRIBED BY (ANNAN ! COMPARISON OF SOME COMMON MONOPULSE FEED CONFIGURATIONS IS INCLUDED IN 4ABLE
, "))"&%( &' $& (*$ #)# % #) .#*( (% "%*( ( %&) #)"+ !( (% /" '- ' (
&)'52% &OUR ELEMENT MONOPULSE FEED WITH DUM DELTA AZ AND DELTA EL PORTS
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&)'52% 0LOTS OF SUM BEAM EFFICIENCY AND DIFFERENCE BEAM SLOPE AS A FUNCTION OF ASSOCIATED EDGE TAPERS ( PLANE SHOWN
!RRAY &EEDS ! SINGLE FEED AT THE FOCAL POINT OF A PARABOLA FORMS A BEAM PARALLEL TO THE FOCAL AXIS !DDITIONAL FEEDS DISPLACED FROM THE FOCAL POINT FORM ADDITIONAL BEAMS AT ANGLES FROM THE AXIS SEE %Q 4HUS ONE CAN EMPLOY A MULTIPLE FEED ARRAY WITH APPROPRIATE ELECTRONICS TO FEED A REFLECTOR AND PROVIDE EITHER MULTIPLE DISPLACED BEAMS OR ELECTRONIC BEAM SWITCHING IE BEAM SCANNING TO DISCRETE ANGLES ! REFLECTOR SYSTEM SUCH AS THIS CAN EFFECTIVELY PROVIDE ELECTRONIC SCANNING OVER A NARROW &/6 (OWEVER THIS TYPE OF ARRAY FED REFLECTOR ARCHITECTURE DOES SUFFER FROM ONE DRAWBACK ! PARABOLA CONVERTS A SPHERICAL WAVE INTO A PURE PLANE WAVE ONLY WHEN THE SOURCE FEED IS AT THE FOCUS )F THE SOURCE FEED IS DISPLACED FROM THE FOCUS THE REFLECTED WAVE IS SOMEWHAT DISTORTED AND THIS RESULTS IN GAIN LOSS AND BEAM SHAPE DISTORTION &IGURE SHOWS THE EFFECT OF THIS DISTORTION ON THE PATTERN OF A TYPICAL CENTER FED REFLECTOR AS THE FEED IS MOVED OFF AXIS 4!",% -ONOPULSE &EEDHORN 0ERFORMANCE
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! PHASED ARRAY %3! TYPE FEED COVERING THE FOCAL REGION PLANAR OR CURVED IN SHAPE SUCH AS THAT SHOWN IN &IGURE B CAN PROVIDE IMPROVED CAPABILITY )T OFFERS TWO ENHANCEMENTS THAT EXTEND THE CAPABILITY ABOVE AND BEYOND THAT OF A MULTIPLE FEED ARRAY WITH SWITCHED BEAMS 4HE PHASED ARRAY FED REFLECTOR CAN TRANSMIT OR RECEIVE BEAMS OVER CONTINUOUS ANGLES WITHIN THE &/6 WHEREAS THE MULTIPLE FEED ARRAY IS LIMITED TO DISCRETE BEAM POSITIONS )T ALSO PROVIDES GREATER APERTURE EFFICIENCY BECAUSE IT ALLOWS FOR ADJUSTMENT OF THE ELEMENT AMPLITUDES AND PHASES TO REDUCE SCAN LOSSES DUE TO ABERRATIONS )F WE VIEW THE REFLECTOR AS A COLLECTOR OF PARALLEL RAYS FROM A RANGE OF ANGLES COVERING THE &/6 AND EXAMINE THE CONVERGING RAY PATHS &IGURE A IT IS EVIDENT THAT AN APPROPRIATELY SIZED FEED REGION CAN BE FOUND THAT INTERCEPTS MOST OF THE ENERGY )F THE PHASED ARRAY FEED ARRAY IS APPROPRIATELY DESIGNED BEAM DISTORTION AND SCAN LOSSES SUCH AS THOSE SHOWN IN &IGURE CAN BE EFFECTIVELY ELIMINATED 4HIS SORT OF DESIGN APPROACH WHEREIN THE FEED ARRAY AMPLITUDEPHASE DISTRIBUTION IS hMATCHEDv TO THE FOCAL PLANE FIELDS IS OFTEN REFERRED TO AS CONJUGATE FIELD MATCHING
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2EFLECTOR ANTENNA ANALYSIS METHODS CAN GENERALLY BE LUMPED INTO THREE CLASSES OR CATEGO RIES 0HYSICAL /PTICS 0/ OR INDUCED CURRENT METHODS 'EOMETRICAL /PTICS '/ METHODS WITH AND WITHOUT DIFFRACTION TERMS AND RIGOROUS OR FULL WAVE METHODS 0HYSICAL /PTICS 0/ 2EFLECTOR !NALYSIS 4HE 0HYSICAL /PTICS 0/ METHOD IS COMMONLY EMPLOYED FOR THE MOST RIGOROUS REFLECTOR ANALYSIS DUE TO ITS ACCURACY )T INCORPORATES THE FIELD PROPERTIES OF THE FEED AND MODELS THE RESULTANT FIELDS FROM THE REFLECTOR THUS ENABLING THE COMPUTATION OF THE CROSS POLARIZATION PROPERTIES &URTHERMORE THE METHOD IS MORE ACCURATE FOR FEEDS THAT ARE NOT AT THE FOCAL POINT AND REFLECTORS THAT ARE NOT PARABOLIC 4HERE ARE MANY GOOD REFERENCES THAT DESCRIBE THE THE ORY BEHIND THE METHOD AND HOW IT IS APPLIED TO THE ANALYSIS OF REFLECTOR ANTENNASn 0/ IS A VERY GENERAL hHIGH FREQUENCYv ANALYSIS METHOD THAT GENERALLY PROVIDES HIGH FIDELITY PATTERN PREDICTIONS FOR MOST REFLECTOR SYSTEMS AS LONG AS THE REFLECTOR DIMEN SIONS ARE LARGE SAY GREATER THAN ABOUT FIVE WAVELENGTHS IN BOTH DIMENSIONS !N OVER VIEW OF 0/ IS PROVIDED HERE TO ENABLE AN UNDERSTANDING OF THE FUNDAMENTALS OF THE METHOD 4HE 0/ METHOD CAN BE BROKEN INTO TWO STEPS THE CALCULATION OF INDUCED REFLECTOR SURFACE CURRENTS AND THE INTEGRATION OF THESE CURRENTS WITH AN APPROPRIATE FREE SPACE VECTOR 'REENS FUNCTION KERNEL TO DETERMINE THE FAR FIELD PATTERNS &IRST CONSIDER THE CALCULATION OF THE REFLECTOR SURFACE CURRENTS )T IS ASSUMED THAT THE FIELD FROM THE FEED THAT IS INCIDENT ON THE REFLECTOR HAS A SPHERICAL WAVEFRONT WITH AMPLITUDE TAPERING DEFINED BY THE FEED PATTERN 3O AS A FIRST STEP THE FEED IS MATHEMATICALLY MODELED TO DETERMINE THE INCIDENT FIELD AMPLITUDE AND PHASE AT THE REFLECTOR SURFACE $IFFERENT MODELS ARE APPLIED DEPENDING ON THE CHOICE OF FEED USED IN THE DESIGN EXAMPLES INCLUDE WAVEGUIDE FEED HORNS MICROSTRIP PATCHES DIPOLES ETC 3OMETIMES THE FEED MODEL WILL INSTEAD EMPLOY MEASURED FEED PATTERNS IF SUCH DATA IS AVAILABLE !LL MODELS MUST BE NORMALIZED TO SOME PRESCRIBED RADIATED POWER LEVEL EG WATT &IGURE SHOWS A TYPICAL WAVEGUIDE FEED HORN MODEL AND ITS ASSOCIATED LOCAL COORDINATE SYSTEM "ASED ON AN APPROPRIATE APPLICATION OF EQUIVALENCE PRINCIPLE AND THE INDUCTION THEOREM n THE CURRENTS INDUCED ON THE REFLECTOR CAN BE DETERMINED FROM THE FEED
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( FIELD INCIDENT AT THE SURFACE OF THE REFLECTOR 4HE KEY PREMISE OF THE EQUIVALENCE PRINCIPLE IS THAT FIELDS FROM A SCATTERER EG A REFLECTOR CAN BE REPRESENTED BY AN hEQUIVALENTv ELECTRIC CURRENT * AND MAGNETIC CURRENT - THAT ARE DIRECTLY RELATED TO THE INCIDENT % AND ( FIELDS VIA
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4HE FINAL STEP IN THE 0/ BASED PATTERN SOLUTION IS TO CALCULATE THE REFLECTOR FAR FIELDS VIA A VECTOR INTEGRATION OF THE PRODUCT OF THE SURFACE CURRENT AND THE FREE SPACE 'REENS FUNCTION 4HE MAGNETIC VECTOR POTENTIAL ! IS DEFINED BY THE EQUATION
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4HE VECTOR % AND ( FIELDS ARE RELATED TO ! VIA SIMPLE DERIVATIVES ANDOR VECTOR MULTIPLICATIONS )N PRACTICE %Q IS COMPUTED AS A SUMMATION OF NUMERICAL INTE GRATIONS 0ROPER CONVERGENCE OF THE FIELD SOLUTION AND RESULTING PATTERNS IS A FUNCTION OF THE GRID SIZE AND THIS IS GENERALLY ACHIEVED AND VERIFIED BY INCREMENTALLY DECREASING THE GRID SIZE UNTIL THE SOLUTION STABILIZES !CHIEVING SUFFICIENT CONVERGENCE IN REFLECTOR 0/ COMPUTATIONS WITHIN REASONABLE COMPUTER RUN TIMES A FEW MINUTES OR LESS IS RARELY A PROBLEM WITH MODERN COMPUTERS 'EOMETRICAL /PTICS '/ 2EFLECTOR !NALYSIS )NCLUDING '4$54$ 4HERE ARE A VARIETY OF '/ BASED PATTERN REFLECTOR ANALYSIS METHODS ALL OF WHICH ARE ROOTED IN RAY TRACING AND SOME OF WHICH ARE AUGMENTED WITH DIFFRACTION TERMS FOR IMPROVED ACCURACY !LTHOUGH THE SIMPLE '/ METHOD NO DIFFRACTION TERMS WORKS REASONABLY WELL IT IS NOT GENERALLY AS ACCURATE AS 0/ (OWEVER TWO OF THE MORE COMMON ENHANCED METHODS 'EOMETRICAL 4HEORY OF $IFFRACTION '4$ AND 5NIFORM 4HEORY OF $IFFRACTION 54$ INCLUDE EDGE DIFFRACTION AND ARE MUCH MORE ACCURATE 54$ IS ESSENTIALLY AN ENHANCE MENT OF '4$ WHEREIN LOCALIZED '4$ SINGULARITIES ARE CORRECTED 4HE DIFFRACTION TERMS IN 54$ INCREASE THE ACCURACY OF THE BASIC '/ SOLUTION AND WILL PROPERLY PREDICT THE PATTERN ASYMMETRIES OF MORE GENERALIZED REFLECTOR GEOMETRIES ,IKE 0/ '4$54$ METHODS WILL GENERALLY PROVIDE HIGH FIDELITY PATTERN PREDICTIONS FOR MOST REFLECTOR SYSTEMS CENTER FED OFFSET SINGLE DUAL ETC AS LONG AS THE REFLECTOR SIZE IS APPROXIMATELY K OR LARGER -ORE DETAILED DESCRIPTIONS OF '4$54$ CAN BE FOUND IN VARIOUS REFERENCES &ULL 7AVE 2EFLECTOR !NALYSIS -ETHODS 2IGOROUS OR FULL WAVE METHODS INCLUDE FOR EXAMPLE THE METHOD OF MOMENTS -/- THE FINITE ELEMENT METHOD &%- AND THE FINITE DIFFERENCE TIME DOMAIN &$4$ METHOD !LTHOUGH THESE METHODS ARE VERY RIGOROUS AND HIGHLY ACCURATE THEY ARE NOT GENERALLY EMPLOYED FOR REFLECTOR DESIGN ANALYSIS BECAUSE THEY TEND TO BE TOO COMPUTATIONALLY INTENSIVE 4HESE METHODS ARE MORE TYPICALLY APPLIED FOR PRECISION ANALYSIS OF MICROWAVE DEVICES OR ELECTRICALLY hSMALLERv ANTENNAS EG RADIATORS AND FEEDS THAT ARE NO MORE THAN A FEW WAVELENGTHS IN SIZE )N RECENT YEARS HYBRID METHODS INCORPORATING 0/ OR '/'4$ ALONG WITH -/- &%- OR &$4$ HAVE BEEN DEVELOPED 4HESE METHODS ENABLE ENHANCED REFLEC TOR FEED MODELING IE INTEGRATED WITH REFLECTOR ANALYSIS AND RIGOROUS MODELING OF ELECTRICALLY SMALL SCATTERERS EG SMALL SUBREFLECTORS OR FEED SUPPORT STRUTS #OMPUTER #ODES FOR 2EFLECTOR $ESIGN AND !NALYSIS ! NUMBER OF COMMER CIAL AND UNIVERSITY CODES HAVE BEEN DEVELOPED FOR THE ANALYSIS AND DESIGN OF REFLEC TOR SYSTEMS 4WO OF THE MORE WELL KNOWN AND COMMONLY USED CODES ARE '2!30 AND THE 3!4#/- 7ORKBENCH WITH ITS .%# 2%& MODULE '2!30 IS A COMMERCIALLY AVAILABLE 0/ BASED REFLECTOR DESIGN AND SCATTERING ANALYSIS CODE DEVELOPED BY 4)#2! #OPENHAGEN $ENMARK 4HE 3!4#/- 7ORKBENCH WAS DEVELOPED BY 4HE /HIO 3TATE 5NIVERSITY %LECTRO3CIENCE ,ABORATORY /35 %3, AND IS A USER FRIENDLY CODE THAT INCORPORATES A WIDE VARIETY OF SOFTWARE MODULES SOME OF WHICH ARE BASED UPON LEGACY
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/35 CODES SUCH AS .%# 2%& /35 2EFLECTOR #ODE 4HE 3!4#/- 7ORKBENCH IS AVAILABLE TO MEMBERS OF THE 53! 3ATELLITE )NDUSTRY #ODE #ONSORTIUM 4)#2! '2!30 IS A GENERALIZED 0/ BASED CODE INTENDED FOR BOTH REFLECTOR SYSTEM DESIGNANALYSIS AND SCATTERING ANALYSES '2!30 HAS POPULAR '5) VERSIONS THAT RUN ON -ICROSOFT 0# BASED 7INDOWS OPERATING SYSTEMS .4 80 AS WELL AS ,).58 !LTHOUGH THE '2!30 CODE IS 0/ BASED IT ALSO INCLUDES A 0HYSICAL 4HEORY OF $IFFRACTION 04$ OPTION AS WELL AS A 'EOMETRICAL /PTICS '/ 5NIFORM 'EOMETRICAL 4HEORY OF $IFFRACTION 5'4$ OPTION THAT CAN BE TURNED ON WHEN NEEDED 4HE CODE IS VERY GENERAL IN THAT IT CAN MODEL STANDARD CONIC SECTION BASED REFLECTORS AS WELL AS ARBITRARILY SHAPED SURFACES OR SCATTERERS IF DESIRED )T ALSO HAS A SUITE OF FEED MODELS TO DRAW UPON AND HAS TOOLS TO ENABLE FEED ARRAY MODELING &IGURE SHOWS A SNAPSHOT OF THE '2!30 '5) WINDOW INCLUDING A RENDERING OF AN ARRAY FED REFLECTOR AND ITS ASSOCIATED BEAM ROSETTA IE AN OVERLAY OF BEAMS ASSOCIATED WITH EACH OF THE INDI VIDUAL ARRAY FEEDS 3OME OTHER NOTABLE FEATURES OF THE '2!30 CODE INCLUDE SCATTERING MODELS FOR MESH FREQUENCY SELECTIVE OR LOSSY REFLECTOR SURFACES AND A SPHERICAL WAVE EXPANSION 37% FEATURE FOR MODELING OF SYSTEMS WHEREIN THE REFLECTOR OR SCATTERER IS IN THE NEAR FIELD OF THE FEED SOURCE &INALLY THERE ARE VARIOUS OTHER ANTENNA SOFTWARE MODULES AVAILABLE FROM 4)#2! THAT CAN BE USED IN CONJUNCTION WITH '2!30 /NE NOTABLE EXAMPLE IS 0HYSICAL /PTICS 3HAPER 0/3 AN OPTIMIZER MODULE FOR SHAPED REFLECTOR SYNTHESIS ANDOR FEED ARRAY AMPLITUDEPHASE WEIGHT SYNTHESIS -ORE INFORMA TION IS AVAILABLE AT WWWTICRACOM 4HE /35 %3, 3!4#/- 7ORKBENCH IS A -ICROSOFT 7INDOWSnBASED MODULAR SOFTWARE PACKAGE FOR 0# PLATFORMS RUNNING 7INDOWS 80 )T CONTAINS A VARIETY OF MODULES OR SO CALLED WIZARDS IN ADDITION TO THE GENERALIZED '/'4$ BASED REFLECTORSCATTERING CODE BACKBONE 4HE CORE '/'4$ REFLECTORSCATTERING
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£Ó°ÈÊ Ê - Ê " - ,/" 2EFLECTOR MECHANICAL DESIGN IS A DETAILED DISCIPLINE UNTO ITSELF WITH A MULTITUDE OF FACTORS TO CONSIDER &URTHERMORE DESIGNS VARY SIGNIFICANTLY DEPENDING UPON MANY FACTORS INCLUDING PLATFORM REFLECTOR SIZE ENVIRONMENT FREQUENCY OF OPERATION SCAN &/6 AND COST CONSTRAINTS !LTHOUGH IT IS NOT WITHIN THE SCOPE OF THIS CHAPTER TO ADDRESS MECHANICAL DESIGN IN DETAIL A BRIEF SURVEY OF DESIGN FACTORS AND CONSIDERATIONS PRO VIDES SOME USEFUL INSIGHTS 4HE PLATFORM IE VEHICLE OR INSTALLATION SITE IS A SIGNIFICANT DRIVER FOR RADAR SEN SORS IN GENERAL INCLUDING THE ANTENNA 0LATFORM IS A GENERIC TERM REFERRING TO THE VEHICLE WHERE THE RADAR AND ANTENNA ARE INSTALLED 4YPICAL RADAR PLATFORMS INCLUDE PEDESTAL FIXED SITE GROUND VEHICLES SHIPS AIRPLANES 5!6S AND SPACECRAFTSATELLITES 4HE FOLLOWING SHORT SECTION IS DEVOTED TO PLATFORM IMPACTS AND SOME KEY ASSOCIATED DESIGN DRIVERS 4HESE INCLUDE MASS VOLUME STOWAGEDEPLOYMENT GIMBALS PRECISION MECHANICAL POSITIONING SYSTEMS MATERIALS AND MECHANICAL TOLERANCES &INALLY THERE IS A BRIEF DISCUSSION OF ENVIRONMENTAL DESIGN CONSIDERATIONS AND RADOMES
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)NSTALLATION )S A 3IGNIFICANT -ECHANICAL $ESIGN $RIVER 4HE PLATFORM IS GEN ERALLY A DOMINANT MECHANICAL DESIGN DRIVER BECAUSE IT DETERMINES THE ENVIRONMENT THERMAL VIBRATION ETC AND IT TYPICALLY DRIVES THE AVAILABLE SIZE WEIGHT AND POWER 37!0 FOR THE RADAR AND THE REFLECTOR ANTENNA 4ABLE PROVIDES A QUALITATIVE COM PARISON OF TYPICAL DESIGN REQUIREMENTS AND FEATURES FOR RADAR REFLECTOR ANTENNAS ON GROUND BASED SHIP BASED AIRBORNE AND SPACEBORNE PLATFORMS -ASS 6OLUME 3TOWAGE $EPLOYMENT AND 'IMBALING 4HE DEGREE TO WHICH THESE FIVE FACTORS MASS VOLUME STOWAGE DEPLOYMENT AND GIMBALING DRIVE THE REFLEC TOR DESIGN VARY IN ACCORDANCE WITH THE REFLECTOR SYSTEM AND THE PLATFORM (OWEVER 4!",% -ECHANICAL $ESIGN $RIVERS FOR 2EFLECTOR !NTENNA 3YSTEMS AS A &UNCTION OF 0LATFORM 0,!4&/2- $2)6%3 2%&,%#4/2 !.4%..! -%#(!.)#!, $%3)'. 'ROUND BASED -ASS
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s 4YPICALLY REQUIRED GENERALLY A MAJOR DESIGN DRIVER s 2ELIABILITY OF DEPLOYMENT IS A MAJOR CONCERN MISSION DEPENDS ON IT s 7HERE ON THE s 6OLUME IS A MAJOR s 3PECIALIZED ENVIRONMENTS SHIP IS THE RADAR CONSTRAINT NOT s ,AUNCH DRIVES MUCH ROOM FOR ANTENNA )S IT VIBRATION AND COVERED WITH A ANTENNA APERTURES ACOUSTIC LOADS RADOME 7ILL IT s 2ADIATION A DRIVER AT BE EXPOSED TO SOME ORBITS WATER OR WAVE s 4HERMAL EXTREMES SLAP INCLUDING GRADIENTS ARE A CONCERN s 4YPICALLY NOT A s 4YPICALLY NOT REQUIREMENT A REQUIREMENT BUT THERE ARE EXCEPTIONS
MASS AND VOLUME CONSTRAINTS GENERALLY HAVE A SIGNIFICANT IMPACT ON THE REFLECTOR SYSTEM DESIGN &URTHERMORE SOME SORT OF STOWAGE AND DEPLOYMENT OF THE REFLECTOR IS SOME TIMES REQUIRED ESPECIALLY FOR LARGER REFLECTORS 4HESE CONSIDERATIONS AND CONSTRAINTS DRIVE THE CHOICES OF MATERIALS STRUCTURAL DESIGNS PASSIVE AND ACTIVE MECHANISMS ETC )T IS BEYOND THE SCOPE OF THIS CHAPTER TO ADDRESS THIS TOPIC IN DETAIL (OWEVER ITS USEFUL TO SHOW A COUPLE EXAMPLES FOR ILLUSTRATION #ONSIDER FIRST A GROUND BASED DUAL REFLECTOR DESIGN WITH A METER MAIN REFLECTOR APERTURE 4HIS REFLECTOR SHOWN IN &IGURE IS USED FOR AN 3 BAND METEOROLOGICAL RADAR APPLICATION 4HE PANELIZED ALUMINUM REFLECTOR IS MECHANICALLY SCANNED VIA USE OF A GIMBAL NOT SHOWN 4HE FEED A DUAL POLARIZED WAVEGUIDE HORN IS ALSO SHOWN IN &IGURE 4HE STRUCTURAL DESIGN OF THIS LARGE REFLECTOR WAS A SIGNIFICANT TASK DRIVEN BY THE NEED TO MAINTAIN LOW REFLECTOR SURFACE DISTORTION LESS THAN MILS WITH SEVERE WIND AND GRAVITY LOADING FORCES AND THERMAL GRADIENTS 4HE SECOND EXAMPLE IS A SPACE BASED DEPLOYABLE REFLECTOR 4HE MESH REFLECTOR SHOWN IN BOTH STOWED AND DEPLOYED CONFIGURATIONS IN &IGURE IS AN OFFSET REFLEC TOR WITH A METER CIRCULAR PROJECTED APERTURE 4HIS , BAND DESIGN DEVELOPED BY .ORTHROP 'RUMMAN 3PACE 4ECHNOLOGIES !STRO !EROSPACE GROUP HAS BEEN SUCCESSFULLY LAUNCHED AND DEPLOYED AND IS CURRENTLY IN USE ON SEVERAL COMMUNICATION SATELLITES ! TOTAL OF FIVE REFLECTORS OF APERTURE DIAMETERS METERS METERS AND METERS HAVE BEEN FLOWN 3TUDIES HAVE ADDRESSED THE POTENTIAL USAGE OF THIS REFLECTOR TECHNOL OGY FOR VARIOUS SPACE BASED RADAR APPLICATIONS INCLUDING WEATHER SENSINGMONITORING .%82!$ AND PLANETARY 3!2 MAPPING MISSIONS LUNAR AND -ARS 3IGNIFICANT FEA TURES OF THIS REFLECTOR INCLUDE ITS PRECISE SURFACE ACCURACY HIGH STIFFNESS AND STABILITY LOW MASS AND RELIABLE DEPLOYMENT &OR EXAMPLE FOR THE REFLECTOR SHOWN IN &IGURE AN 2-3 SURFACE ACCURACY OF LESS THAN MILS FROM ALL ERROR SOURCES INCLUDING IN ORBIT THER MAL GRADIENTS WAS ACHIEVED VIA PRUDENT MATERIAL CHOICES AND MATCHING OF THE ASSOCIATED MATERIAL COEFFICIENTS OF THERMAL EXPANSION #4%S 0OINTING PRECISION DUE TO ECLIPSE THERMAL SNAP HAS BEEN MEASURED IN ORBIT AT LESS THAN DEGREES
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$EPLOYABLE SPACE BASED REFLECTORS HAVE ALSO BEEN DEVELOPED BY THE (ARRIS #ORPO RATION FOR VARIOUS SPACE BASED COMMUNICATIONS APPLICATIONS 3EE WWWHARRISCOM FOR MORE DETAILS "ECAUSE MOST REFLECTOR DESIGNS HAVE AT BEST LIMITED ELECTRONIC SCAN CAPABILITY A GIMBAL IS TYPICALLY NEEDED TO EXTEND THE MECHANICAL &/6 FOR THE RADAR 4HE KEY FACTORS OR SPECIFICATIONS THAT TYPICALLY DRIVE THE DESIGN OR PROCUREMENT OF THE GIMBAL ARE SCAN RATE SLEW REQUIREMENTS ACCELERATIONDECELERATION REQUIREMENTS TORQUE AND LOAD REFLECTOR MASS REQUIREMENTS POWER REQUIREMENTS ETC )T IS IMPORTANT FOR THE RADAR SYSTEM ENGINEER TO UNDERSTAND THESE FACTORS AND ASSOCIATED PRACTICAL GIMBAL DESIGN LIMITS %NVIRONMENTAL &ACTORS AND #ONSIDERATIONS 4HE IMPACT OF ENVIRONMENTAL FAC TORS VARIES WIDELY BUT SOME OF THE FACTORS THAT ARE TYPICALLY SIGNIFICANT INCLUDE THERMAL VIBRATION AND EXPOSURE EG SALT SAND WATER RADIATION ETC 4HERMAL EFFECTS IE SPATIAL OR TEMPORAL TEMPERATURE VARIATIONS ARE OF PARTICULAR CONCERN FOR SPACEBORNE SENSORS THAT OFTEN SEE VERY SIGNIFICANT TEMPERATURE CHANGES GREATER THAN # TEM PORAL OR SPATIAL VARIATION IS NOT UNCOMMON 6IBRATION IS ANOTHER CONCERN ESPECIALLY FOR AIRBORNE AND SPACEBORNE REFLECTORS 2EFLECTORS ON THESE PLATFORMS GENERALLY SEE PARTICULARLY STRESSING VIBRATION LEVELS DRIVEN BY AIRPLANE OR LAUNCH VEHICLE ROCKET ENVIRONMENTS 0OTENTIAL EXPOSURE TO SALT SAND WATER ETC IS HIGHLY DEPENDENT UPON PLATFORM USE OF RADOME OR NOT ETC BUT MUST BE CONSIDERED IN THE DESIGN 2ADOMES 2ADOMES ARE USED WHEN IT IS NECESSARY TO PROTECT ANTENNAS FROM ADVERSE ENVIRONMENTAL EFFECTS )DEALLY A RADOME SHOULD BE PERFECTLY TRANSPARENT TO THE 2& RADIATION FROM OR TO THE ANTENNA AND YET BE ABLE TO WITHSTAND SUCH ENVIRONMENTAL EFFECTS AS WIND RAIN HAIL SNOW ICE SAND SALT SPRAY LIGHTNING AND IN THE CASE OF HIGH SPEED AIRBORNE APPLICATIONS THERMAL EROSION AND OTHER AERODYNAMIC EFFECTS )N PRACTICE THESE ENVIRONMENTAL FACTORS DETERMINE THE MECHANICAL DESIGN OF THE RADOME AND THE DESIRE FOR IDEAL 2& TRANSPARENCY MUST BE COMPROMISED BECAUSE MECHANICAL AND ELECTRICAL REQUIREMENTS ARE OFTEN IN CONFLICT 2ADOMES CAUSE FOUR MAJOR ELECTRICAL EFFECTS ON ANTENNA PERFORMANCE "EAM DEFLEC TION IS THE SHIFT OF THE ELECTRICAL AXIS WHICH IS CRITICAL FOR TRACKING RADAR 4RANSMISSION LOSS IS THE MEASURE OF ENERGY LOST BY REFLECTION AND ABSORPTION 4HE REFLECTED POWER CAUSES ANTENNA MISMATCH IN SMALL RADOMES AND SIDELOBES IN LARGER RADOMES 2ADOME DESIGN IS A SPECIALIZED ART AND MANY BOOKS ARE DEVOTED TO ITS INTRICATE DETAILS 4HIS SECTION MAKES NO ATTEMPT TO PROVIDE RADOME DESIGN INFORMATION AS SUCH BUT INSTEAD IS AIMED AT MAKING THE RADAR SYSTEM DESIGNER AWARE OF THE BASIC CONCEPTS BEHIND THE TYPES OF RADOMES AVAILABLE FOR VARIOUS APPLICATIONS 4HREE GENERAL CLASSES OF RADOME ARE OF INTEREST FOR REFLECTOR ANTENNA APPLICA TIONS FEED COVERS WHICH OFTEN HAVE TO ENDURE PRESSURE HIGH VOLTAGE AND HEATING COVERS ATTACHED TO THE REFLECTOR WHICH ALTER THE PATTERN IN A FIXED MANNER AND EXTERNAL RADOMES WITHIN WHICH THE ANTENNA MOVES %XTERNAL RADOMES ARE THE MOST COMMON AND WILL THEREFORE BE EMPHASIZED 7ITHIN EACH CLASS A VARIETY OF SKIN AND SKIN SUPPORTING DESIGNS IS AVAILABLE TO MINIMIZE THE ELECTRICAL EFFECTS UNDER THE CONSTRAINTS OF THE ENVIRONMENT 4HE RADOME SKIN MAY BE RIGID SUPPORTED BY A FRAMEWORK OR AIR SUPPORTED 4HE MOST COMMON RIGID RADOME WALL STRUCTURES ARE SHOWN IN &IGURE AND ARE KNOWN AS HOMOGENEOUS SINGLE LAYER ! SANDWICH " SANDWICH # SANDWICH MULTIPLE LAYER SANDWICH AND DIELECTRICS WITH METAL INCLUSIONS
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&)'52% #OMMON RADOME WALL CROSS SECTIONS A SINGLE LAYER B ! SANDWICH C " SANDWICH D # SANDWICH E MULTIPLE LAYER SAND WICH AND F DIELECTRICS WITH METAL INCLUSIONS
3INGLE ,AYER 4HE HOMOGENEOUS SINGLE LAYER RADOME HAS BEEN USED IN MANY RADOME APPLICATIONS -ATERIALS FOR THIS TYPE HAVE INCLUDED FIBERGLASS REINFORCED PLAS TICS CERAMICS ELASTOMERS AND MONOLITHIC FOAM 4HE OPTIMUM THICKNESS FOR A SINGLE LAYER IS A MULTIPLE OF A HALF WAVELENGTH IN THE DIELECTRIC MATERIAL AT THE APPROPRIATE INCIDENCE ANGLE BUT MANY SINGLE LAYER RADOMES ARE SIMPLY THIN WALL APPROXIMATIONS TO THE ZERO THICKNESS CASE ! 3ANDWICH ! COMMONLY USED RADOME WALL CROSS SECTION IS THE ! SANDWICH WHICH CONSISTS OF TWO RELATIVELY DENSE THIN SKINS AND A THICKER LOW DENSITY CORE 4HIS CONFIGURATION EXHIBITS HIGH STRENGTH TO WEIGHT RATIOS 4HE SKINS ARE GENERALLY FIBERGLASS REINFORCED PLASTICS AND THE CORE IS A FOAM OR HONEYCOMB )NORGANIC SKIN AND CORE SAND WICHES ALSO HAVE BEEN DEVELOPED FOR HIGH TEMPERATURE APPLICATIONS !S A RULE THE SKINS OF THE SANDWICH ARE MADE SYMMETRICAL OR OF EQUAL THICKNESS TO ALLOW MIDBAND CANCEL LATION OF REFLECTIONS " 3ANDWICH )N CONTRAST TO THE ! SANDWICH THE " SANDWICH IS A THREE LAYER CON FIGURATION WHOSE SKINS HAVE A DIELECTRIC CONSTANT LOWER THAN THAT OF THE CORE MATERIAL 4HIS WALL CROSS SECTION IS HEAVIER THAN THAT OF THE ! SANDWICH BECAUSE OF THE RELATIVELY DENSE CORE 4HE " SANDWICH IS NOT COMMONLY USED BECAUSE THE CORE DIELECTRIC CONSTANT IS QUITE HIGH FOR A PROPER MATCH # 3ANDWICH 4HE # SANDWICH IS A FIVE LAYER DESIGN CONSISTING OF OUTER SKINS A CENTER SKIN AND TWO INTERMEDIATE CORES 4HE SYMMETRICAL # SANDWICH CAN BE THOUGHT OF AS TWO BACK TO BACK ! SANDWICHES 4HIS CONFIGURATION IS USED WHEN THE ORDINARY ! SANDWICH WILL NOT PROVIDE SUFFICIENT STRENGTH OR FOR CERTAIN ELECTRICAL PERFORMANCE CHARACTERISTICS OR WHEN ONE LAYER IS TO SERVE AS A WARM AIR DUCT FOR DEICING -ULTIPLE ,AYER 3ANDWICH -ULTIPLE LAYER SANDWICHES OF OR MORE LAYERS ARE SOMETIMES CONSIDERED WHEN GREAT STRENGTH GOOD ELECTRICAL PERFORMANCE AND LIGHTWEIGHT ARE REQUIRED 3OME OF THESE DESIGNS HAVE USED THIN LAYERS OF FIBERGLASS
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LAMINATES AND LOW DENSITY CORES TO ATTAIN HIGH TRANSMISSION PERFORMANCE OVER LARGE FREQUENCY BANDS $IELECTRIC ,AYERS WITH -ETAL )NCLUSIONS -ETAL INCLUSIONS HAVE BEEN CONSIDERED FOR USE WITH DIELECTRIC LAYERS TO ACHIEVE FREQUENCY FILTERING BROAD FREQUENCY BAND PERFORMANCE OR REDUCED THICKNESS RADOMES 4HIN LAYERS OF METAL INCLUSIONS EXHIBIT THE CHARACTERISTICS OF LUMPED CIRCUIT ELEMENTS SHUNTED ACROSS A TRANSMISSION LINE &OR EXAMPLE A GRID OF PARALLEL METAL WIRES EXHIBITS THE PROPERTIES OF A SHUNT INDUCTIVE SUSCEPTANCE 4HERE ARE MANY ADDITIONAL RADOME DESIGN ISSUES AND APPLICATION SPECIFIC CONSIDER ATIONS AND DESIGN DRIVERS BUT THESE ARE BEYOND THE SCOPE OF THIS CHAPTER
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0HASED !RRAY 2ADARS %ARLY RADAR SYSTEMS USED ANTENNA ARRAYS FORMED BY THE COMBINATION OF INDIVIDUAL RADIATORS 3UCH ANTENNAS DATE BACK TO THE TURN OF THE TWEN TIETH CENTURY !NTENNA CHARACTERISTICS ARE DETERMINED BY THE GEOMETRIC POSITION OF THE RADIATORS AND THE AMPLITUDE AND PHASE OF THEIR EXCITATION !S RADARS PROGRESSED TO SHORTER WAVELENGTHS ARRAYS WERE DISPLACED BY SIMPLER ANTENNAS SUCH AS PARABOLIC REFLECTORS &OR MODERN RADAR APPLICATIONS THE ADVENT OF ELECTRONICALLY CONTROLLED PHASE SHIFTERS SWITCHES AND TRANSMITRECEIVE MODULES HAS ONCE MORE DIRECTED ATTENTION TO ARRAY ANTENNAS 4HE APERTURE EXCITATION MAY NOW BE MODULATED BY CONTROLLING THE PHASE OF THE INDIVIDUAL ELEMENTS TO GIVE BEAMS THAT ARE SCANNED ELECTRONICALLY 4HE DRAMATIC ADVANTAGE OF ELECTRONICALLY STEERED PHASED ARRAYS AS COMPARED TO REFLECTORS IS PROVIDED BY THE TIME REQUIRED TO STEER BEAMS AND THE FLEXIBILITY IN STEERING 7HILE PRIOR RADARS TOOK SECONDS TO STEER TO A NEW LOCATION PHASED ARRAYS TAKE MICROSECONDS )N ADDITION THE NEW LOCATION CAN BE ANYWHERE IN A HEMISPHERE 4HIS CHAPTER WILL BE DEVOTED TO ARRAYS OF THIS TYPE -ULTIFUNCTION 2ADAR 4HE CAPABILITY OF RAPIDLY AND ACCURATELY SWITCHING BEAMS PERMITS MULTIPLE RADAR FUNCTIONS TO BE PERFORMED INTERLACED IN TIME !N ELECTRONICALLY STEERED ARRAY RADAR MAY TRACK A GREAT MULTIPLICITY OF TARGETS ILLUMINATE A NUMBER OF TARGETS WITH 2& ENERGY AND GUIDE MISSILES TOWARD THEM AND PERFORM COMPLETE HEMI SPHERICAL SEARCH WITH AUTOMATIC TARGET SELECTION AND HANDOVER TO TRACKING )T MAY EVEN ACT AS A COMMUNICATION SYSTEM DIRECTING HIGH GAIN BEAMS TOWARD DISTANT RECEIVERS AND TRANSMITTERS #OMPLETE FLEXIBILITY IS POSSIBLE SEARCH AND TRACK RATES MAY BE ADJUSTED TO BEST MEET PARTICULAR SITUATIONS ALL WITHIN THE LIMITATIONS SET BY THE TOTAL USE OF TIME
0ORTIONS OF THIS CHAPTER THAT APPEARED IN EARLIER EDITIONS OF THE 2ADAR (ANDBOOK WERE WRITTEN BY THE LATE 4HEODORE # #HESTON A PIONEER IN PHASED ARRAY ANTENNAS
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4HE ANTENNA BEAMWIDTH MAY BE CHANGED TO SEARCH SOME AREAS MORE RAPIDLY WITH LESS GAIN &REQUENCY AGILITY IS POSSIBLE WITH THE FREQUENCY OF TRANSMISSION CHANGING AT WILL FROM PULSE TO PULSE OR WITH CODING WITHIN A PULSE 6ERY HIGH POWERS MAY BE GENER ATED FROM A MULTIPLICITY OF AMPLIFIERS DISTRIBUTED ACROSS THE APERTURE %LECTRONICALLY CONTROLLED ARRAY ANTENNAS CAN GIVE RADARS THE FLEXIBILITY NEEDED TO PERFORM ALL THE VARI OUS FUNCTIONS IN A WAY BEST SUITED FOR THE SPECIFIC TASK AT HAND 4HE FUNCTIONS MAY BE PROGRAMMED ADAPTIVELY TO THE LIMIT OF ONES CAPABILITY TO EXERCISE EFFECTIVE AUTOMATIC MANAGEMENT AND CONTROL 0HASED ARRAY THEORY WAS STUDIED INTENSIVELY IN THE S 4ECHNOLOGY ADVANCED AND LED TO A SERIES OF OPERATIONAL SYSTEMS IN THE S MANY PUBLICATIONS BECAME AVAILABLEn )N TERMS OF PERFORMANCE IMPROVEMENT ULTRALOW SIDELOBES LESS THAN
D" WERE DEMONSTRATED FIRST IN THE S BY 7ESTINGHOUSE %LECTRIC #ORPORATIONS !7!#3 !IRBORNE 7ARNING AND #ONTROL 3YSTEM AND BROUGHT ABOUT TIGHT TOLERANCES IN CONSTRUCTION AND PHASE SETTINGS 4HE ADVENT OF MORE AND BETTER COMPUTER MODELING AND SOPHISTICATED TEST EQUIPMENT SUCH AS NETWORK ANALYZERS HAS LED TO IMPROVED METHODS OF DESIGNING WELL MATCHED APERTURES "ETTER COMPONENTS SUCH AS RADIATING ELEMENTS PHASE SHIFTERS AND POWER DIVIDERS ARE NOW AVAILABLE -ORE ECONOMICAL SOLID STATE DEVICES AND MEMORY CHIPS HAVE LED TO PRECISION APERTURE PHASE CONTROL WITH CORREC TIONS FOR FREQUENCY AND TEMPERATURE VARIATIONS 3OLID STATE MICROWAVE DEVICES HOLD GREAT PROMISE FOR FUTURE SYSTEMS WHERE A SOLID STATE MODULE IS ASSOCIATED WITH EACH RADIATING ELEMENT IMPROVEMENTS IN TERMS OF APERTURE CONTROL RELIABILITY AND EFFI CIENCY CONTINUE 0HASED ARRAYS CAN BE CONTROLLED ADAPTIVELY PARTICULARLY FOR SIDELOBE CANCELLATION 4HIS IS AN AREA WHERE THEORY AND UNDERSTANDING HAVE ADVANCED MUCH !LSO GREAT PROGRESS HAS BEEN MADE WITH INDOOR NEAR FIELD ANTENNA RANGES WHERE COMPUTER CONTROLLED PRECISION TWO DIMENSIONAL RADIATION PATTERNS ARE DERIVED AT MUL TIPLE FREQUENCIES AND WITH SCANNING 0HASED ARRAYS ARE VERY EXPENSIVE !S TECHNOLOGY ADVANCES COSTS ARE EXPECTED TO BE REDUCED !T THE SAME TIME THE QUEST FOR BETTER PERFORMANCE WITH LOWER SIDELOBES AND WIDER BANDWIDTH KEEPS THE COSTS HIGH 0HASED !RRAY !NTENNAS 4HE PHASED ARRAY ANTENNA HAS AN APERTURE THAT IS ASSEM BLED FROM A GREAT MANY SIMILAR RADIATING ELEMENTS SUCH AS SLOTS DIPOLES OR PATCHES EACH ELEMENT BEING INDIVIDUALLY CONTROLLED IN PHASE AND AMPLITUDE !CCURATELY PRE DICTABLE RADIATION PATTERNS AND BEAM POINTING DIRECTIONS CAN BE ACHIEVED 4HE GENERAL PLANAR ARRAY CHARACTERISTICS ARE READILY OBTAINED FROM A FEW SIMPLE EQUATIONS THAT ARE GIVEN HERE BUT DISCUSSED LATER IN GREATER DETAIL 7ITH THE ELEMENTS SPACED BY K K WAVELENGTH TO AVOID THE GENERATION OF MULTIPLE BEAMS GRATING LOBES THE NUMBER OF RADIATING ELEMENTS . FOR A PENCIL BEAM IS APPROXIMATELY RELATED TO THE BEAMWIDTH BY
.y
P "
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'P y O .G COS P
3IMILARLY THE SCANNED BEAMWIDTH IS INCREASED FROM THE BROADSIDE BEAMWIDTH EXCEPT IN THE VICINITY OF ENDFIRE P n
P " SCANNED y
P " BROADSIDE COS P
4HE TOTAL NUMBER OF BEAMS - WITH BROADSIDE BEAMWIDTH AND SQUARE STACKING THAT FIT INTO A SPHERE IS APPROXIMATELY EQUAL TO THE GAIN AND WITH G y IS THUS SIMPLY RELATED TO . BY
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0ULSE LENGTH r APERTURE SIZE
7ITH THESE CRITERIA THE SCANNED RADIATION PATTERN AT n IS STEERED BY o ONE FOURTH OF THE BEAMWIDTH AT THE ANGLE OF SCAN AS THE FREQUENCY IS CHANGED OVER THE BAND )F ALL THE FREQUENCIES IN THE BAND ARE USED WITH EQUAL WEIGHTING THEN TWICE THE BANDWIDTH HALF THE PULSE LENGTH BECOMES ACCEPTABLE !T A SCAN ANGLE P THE BEAM STEERS WITH FREQUENCY THROUGH AN ANGLE CP SO THAT
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DF TAN P F
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&OR WIDER BANDWIDTHS TIME DELAY NETWORKS HAVE TO BE INTRODUCED TO SUPPLEMENT THE PHASE SHIFTERS #ONFORMAL !RRAYS 0HASED ARRAYS MAY CONFORM TO CURVED SURFACES AS REQUIRED FOR EXAMPLE FOR FLUSH MOUNTING ON AIRCRAFT OR MISSILES )F THE SURFACE HAS A LARGE RADIUS OF CURVATURE SO THAT ALL THE RADIATING ELEMENTS POINT IN SUBSTANTIALLY THE SAME DIRECTION THEN THE CHARACTERISTICS ARE SIMILAR TO THOSE OF A PLANAR ARRAY EVEN THOUGH THE EXACT $ POSITION OF THE ELEMENT HAS TO BE TAKEN INTO ACCOUNT TO CALCULATE THE REQUIRED PHASE ! SMALL RADIUS OF CURVATURE IS FOUND WITH CYLINDRICAL OR SPHERICAL ARRAYS USED FOR n COVERAGE %LEMENTS ARE SWITCHED TO AVOID SECTIONS OF THE ANTENNA WHERE THEY POINT AWAY FROM THE DESIRED BEAM DIRECTION $IFFICULTIES MAY BE ENCOUN TERED IN MATCHING THE RADIATING ELEMENTS AND IN MAINTAINING POLARIZATION PURITY 4HE DISCUSSION IN THIS CHAPTER WILL CONCENTRATE ON PLANAR PHASED ARRAYS RATHER THAN CON FORMAL ARRAYS
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$ 6OLUMETRIC 3EARCH 4HREE DIMENSIONAL $ VOLUMETRIC RADAR SEARCH IS POS SIBLE WITH ELECTRONIC SCANNING IN BOTH AZIMUTH AND ELEVATION IMPORTANT REGIONS EG THE HORIZON MAY BE EMPHASIZED AT WILL AND SEARCHED MORE FREQUENTLY 4HE RADAR MAY OPERATE WITH A HIGHER THAN NORMAL FALSE ALARM RATE SINCE TARGETS CAN EASILY BE CON FIRMED BY ADDITIONAL DWELLS 0HASE CONTROL ALLOWS BEAMS TO BE WIDENED FOR EXAMPLE TO REDUCE SEARCH TIME FOR THE MORE ELEVATED REGIONS WHERE REDUCED RANGES NEED LESS ANTENNA GAIN ! SEPARATE ROTATING SURVEILLANCE RADAR SYSTEM MAY BE ADDED FOR EXTRA COVERAGE AT A SECOND FREQUENCY AND TO ALLOW THE $ RADAR MORE TIME FOR TRACKING -ONOPULSE 4RACK 0HASED ARRAY RADARS ARE WELL SUITED FOR MONOPULSE TRACKING 4HE RADIATING ELEMENTS OF THE ARRAY CAN BE COMBINED IN THREE DIFFERENT WAYS TO GIVE THE SUM PATTERN AND THE AZIMUTH AND ELEVATION DIFFERENCE PATTERNS #ONTRADICTORY REQUIRE MENTS IN OPTIMUM AMPLITUDE DISTRIBUTION FOR SUM AND DIFFERENCE PATTERNS EXIST BUT AS WITH OTHER ANTENNA SYSTEMS THEY MAY BE INDEPENDENTLY SATISFIED 4HE SUM AND DIF FERENCE PATTERNS ARE SCANNED SIMULTANEOUSLY 4HE DIFFERENCE PATTERN NULL IN A PHASED ARRAY SYSTEM GIVES GOOD BEAM POINTING ACCURACY !BSOLUTE BEAM POINTING ACCURACIES TO WITHIN LESS THAN ONE FIFTIETH OF A SCANNED BEAMWIDTH HAVE BEEN MEASURED WITH SCANS UP TO n 4HE ACCURACY IS LIMITED BY PHASE AND AMPLITUDE ERRORS 3INCE PHASE SHIFT RATHER THAN TIME DELAY IS USED AS THE FREQUENCY IS CHANGED THE DIRECTION OF THE NULL OF THE SCANNED BEAM IS ALSO CHANGED AND THE BEAM MOVES TOWARD BROADSIDE WITH AN INCREASE IN FREQUENCY 3HAPED "EAMS 4HE RADIATION PATTERN OF AN ARRAY MAY BE SHAPED BY MODIFYING THE APERTURE DISTRIBUTION 'OOD PATTERN APPROXIMATIONS CAN BE OBTAINED BY USING PHASE ONLY )N PARTICULAR THE BEAM MAY BE BROADENED BY APPLYING A SPHERICAL PHASE DISTRIBU TION TO THE APERTURE OR BY APPROXIMATING IT WITH A GABLE TRIANGULAR PHASE DISTRIBUTION "EAMS OF THIS TYPE ARE OF PARTICULAR INTEREST BECAUSE THEY ARE EASILY GENERATED 4HEY MAY BE USED FOR TRANSMISSION IN A SYSTEM WHERE THE RECEIVING ANTENNA HAS A CLUSTER OF SIMULTANEOUS BEAMS OR AS PREVIOUSLY DISCUSSED THEY MAY BE USED IN A SEARCH SYSTEM TO REDUCE THE NUMBER OF ANGULAR CELLS IN REGIONS OF SHORTER RANGE -ONITORING %LECTRONICALLY SCANNED ARRAYS ARE COMPOSED OF VERY MANY PARTS AND INCLUDE ELECTRONIC CIRCUITRY TO DRIVE THE PHASE SHIFTERS OR SWITCHES THAT STEER THE BEAM 4HE OVERALL RELIABILITY OF SUCH ARRAYS CAN BE GREAT GRACEFUL DEGRADATION HAS BEEN CLAIMED BECAUSE THE FAILURE OF AS MUCH AS OF THE COMPONENTS LEADS TO A LOSS IN GAIN OF ONLY D" 4HERE IS HOWEVER A DEGRADATION OF LOW SIDELOBES .EVERTHELESS THE FUNCTIONING OF THE ANTENNA IS COMPLEX AND THERE IS NEED FOR PROVIDING TEST OR MON ITORING CIRCUITRY 4HE DECISION TO POINT A BEAM IN A CERTAIN DIRECTION IS MADE SOME WHERE IN THE RADAR CONTROL SYSTEM AND IS NORMALLY DEFINED BY TWO DIRECTION COSINES ! TEST OR MONITORING CIRCUIT SHOULD ESTABLISH THE CORRECT FUNCTIONING OF ALL COMPO NENTS INCLUDING ALL BEAM POINTING COMPUTATIONS ELECTRONIC DRIVERS AND PHASE SHIFTERS OR SWITCHES AND ALL THEIR INTERCONNECTIONS &REQUENT INDICATIONS THAT THE ANTENNA SYS TEM IS FUNCTIONING OR IS CAPABLE OF FUNCTIONING SHOULD BE AVAILABLE )N ONE POSSIBLE METHOD THE PHASE SHIFTERS ARE PROGRAMMED TO FOCUS ON A NEARBY MONITOR PROBE AND SCAN PAST IT 4HIS WILL YIELD A CLOSE APPROXIMATION OF THE COMPLETE RADIATION PATTERN WHERE GAIN AND SIDELOBES CAN BE MEASURED AND COMPARED WITH PREVIOUS RESULTS 4HE COMBINATION OF INDIVIDUAL ELEMENTS AND THEIR PHASE SHIFTERS AND DRIVERS CAN ALSO BE CHECKED WITH THIS CONFIGURATION 4HE PHASE AT EACH ELEMENT IS SEQUENTIALLY ROTATED AT SOME LOW FREQUENCY THE AMPLITUDE AND PHASE OF THIS MODULATION AS RECEIVED BY THE PROBE RELATE DIRECTLY TO BOTH THE RELATIVE AMPLITUDE EXCITATION OF THE ELEMENT AND ITS
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RELATIVE PHASE SETTING /THER METHODS HAVE BEEN PROPOSED WHERE MEASUREMENTS ARE COMPARED WITH PREVIOUSLY RECORDED ONES $EPLOYMENT OF !PERTURES 7ITH PLANAR ARRAYS SCANNING IS LIMITED BY THE LOSS IN GAIN AND THE INCREASE IN BEAMWIDTH CORRESPONDING TO THE REDUCTION OF THE APERTURE TO ITS PROJECTED AREA 0RACTICAL EXTREME VALUES OF SCANNING ARE THEREFORE IN THE REGION OF TO n ! MINIMUM OF THREE PLANAR ARRAY APERTURES IS THEN NECESSARY FOR HEMISPHERICAL COVERAGE 4HE ANTENNAS MAY BE POSITIONED AS SHOWN IN &IGURE PERMITTING A VIEW THAT IS UNIMPEDED BY THE CENTRAL SUPERSTRUCTURE 4HE APERTURES WOULD NORMALLY BE TILTED BACK FROM THE VERTICAL TO BALANCE THE SCAN ANGLES 2ADIATING %LEMENTS 4HE MOST COMMONLY USED RADIATORS FOR PHASED ARRAYS ARE DIPOLES SLOTS OPEN ENDED WAVEGUIDES OR SMALL HORNS AND PRINTED CIRCUIT hPATCHESv ORIGINALLY CALLED #OLLINGS RADIATOR AFTER THEIR INVENTOR 4HE ELEMENT HAS TO BE SMALL ENOUGH TO FIT IN THE ARRAY GEOMETRY THEREBY LIMITING THE ELEMENT TO AN AREA OF A LITTLE MORE THAN K )N ADDITION MANY RADIATORS ARE REQUIRED AND THE RADIATING ELEMENT SHOULD BE INEXPENSIVE AND RELIABLE AND HAVE IDENTICAL CHARACTERISTICS FROM UNIT TO UNIT "ECAUSE THE IMPEDANCE AND PATTERN OF A RADIATOR IN AN ARRAY ARE DETERMINED PRE DOMINANTLY BY THE ARRAY GEOMETRY 3ECTION THE RADIATING ELEMENT MAY BE CHOSEN TO SUIT THE FEED SYSTEM AND THE PHYSICAL REQUIREMENTS OF THE ANTENNA &OR EXAMPLE IF THE RADIATOR IS FED FROM A STRIPLINE PHASE SHIFTER A STRIPLINE DIPOLE WOULD BE A LOGICAL CHOICE )F A WAVEGUIDE PHASE SHIFTER IS USED AN OPEN ENDED WAVEGUIDE OR A SLOT MIGHT BE CONVENIENT !T THE LOWER FREQUENCIES WHERE COAXIAL COMPONENTS ARE PREVALENT DIPOLES HAVE BEEN FAVORED ! GROUND PLANE IS USUALLY PLACED ABOUT K BEHIND AN ARRAY OF PARALLEL DIPOLES SO THAT THE ANTENNA FORMS A BEAM IN ONLY ONE HEMISPHERE &OR LIMITED SCANNING SAY LESS THAN n IT IS POSSIBLE TO USE DIRECTIVE RADIATORS HAVING DIMENSIONS OF HEIGHT AND WIDTH OF SEVERAL WAVELENGTHS 7ITH SUCH SEPARATION THE MUTUAL COUPLING EFFECTS SEE 3ECTION CAN BE SMALL AND THE PATTERN AND IMPED ANCE OF AN ELEMENT IN THE ARRAY APPROACH THOSE OF THE ISOLATED ELEMENT
&)'52% 'UIDED MISSILE CRUISER SHOWING TWO OUT OF FOUR PHASED ARRAY ANTENNAS #OURTESY OF )NGALLS 3HIPBUILDING $IVISION OF ,ITTON
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4HE ELEMENT MUST BE CHOSEN TO GIVE THE DESIRED POLARIZATION USUALLY VERTICAL OR HORIZONTAL 4HE SPECIAL CASE OF CIRCULAR POLARIZATION IS DISCUSSED BELOW )F POLARIZATION DIVERSITY IS REQUIRED OR IF AN ARRAY IS REQUIRED TO TRANSMIT ONE POLAR IZATION AND RECEIVE THE ORTHOGONAL OR BOTH POLARIZATIONS EITHER CROSSED DIPOLES OR CIRCULAR OR SQUARE RADIATORS SEEM SUITABLE 7ITH APPROPRIATE FEED SYSTEMS BOTH ARE CAPABLE OF PROVIDING VERTICAL AND HORIZONTAL POLARIZATION INDEPENDENTLY AND MAY BE COMBINED TO PROVIDE ANY DESIRED POLARIZATION INCLUDING CIRCULAR 3UCH POLARIZATION DIVERSITY ADDS CONSIDERABLE COMPLEXITY REQUIRING TWO FEED SYSTEMS OR SWITCHES AT THE RADIATING ELEMENT LEVEL #IRCULAR 0OLARIZATION &ROM THE POINT OF VIEW OF THE ANTENNA DESIGNER CIRCULAR POLARIZATION IS POSSIBLE THOUGH DIFFICULTIES MAY BE ENCOUNTERED IN MATCHING FOR LARGE SCAN ANGLES /N SCANNING A COMPONENT OF THE UNDESIRED ORTHOGONAL POLARIZATION WILL BE GENERATED AND SOME PROVISION SHOULD BE MADE TO ABSORB THAT ENERGY 7ITH A CONVENTIONAL CIRCULARLY POLARIZED ANTENNA SUCH AS A PARABOLIC DISH WITH A CIRCULARLY POLARIZED FEED GOOD CIRCULARITY MAY BE OBTAINED OVER PART OF THE MAIN BEAM WITH RAPID DETERIORATION OVER THE REST OF THE PATTERN 7ITH A PLANAR ARRAY THE RELEVANT BEAM WIDTH IS THE BEAMWIDTH OF THE ELEMENT IN THE ARRAY RATHER THAN THE ARRAY BEAMWIDTH 7ITH CIRCULAR POLARIZATION THE SIGNAL RETURNED FROM A SINGLE BOUNCE TARGET IE A SPHERE OR FLAT PLATE WILL REQUIRE AN ANTENNA MATCHED TO THE OPPOSITE SENSE OF CIRCULAR POLARIZATION FROM THAT TRANSMITTED )F THE SAME ANTENNA IS USED THEN SINGLE BOUNCE TARGETS ARE REJECTED 3UCH A SYSTEM CAN THEREFORE GIVE A MEASURE OF SUPPRESSION OF RAIN ECHOES IDEALLY AMOUNTING TO
LOG E E D"
WHERE E IS THE VOLTAGE ELLIPTICITY RATIO !N EARLY MODEL OF A 2AYTHEON REFLECTARRAY GAVE AN ELLIPTICITY RATIO OF LESS THAN D" WITH SCANS UP TO n CORRESPONDING TO A THEORETICAL RAIN REJECTION OF AT LEAST D" !T THE SAME TIME AN AIRCRAFT TARGET WOULD TYPICALLY LOSE APPROXIMATELY D" LEAVING A RELATIVE NET IMPROVEMENT OF D" OF RAIN REJECTION 0HASED !RRAYS WITH 6ERY 7IDE "ANDWIDTH ! RADAR SYSTEM THAT HAS THE CAPABIL ITY OF CHANGING FREQUENCY OVER A VERY WIDE BANDWIDTH CAN WITH ADVANTAGE ADAPT ITS TRANSMISSION TO TAKE INTO ACCOUNT FREQUENCY DEPENDENT MULTIPATH CHARACTERISTICS TAR GET RESPONSE ENVIRONMENTAL CONDITIONS INTERFERENCE AND JAMMING &URTHER WIDEBAND PROCESSING CAN GIVE FINE RANGE RESOLUTION 0HASED ARRAYS HAVE THE POTENTIAL OF OPERATING OVER VERY WIDE BANDWIDTHS 4HE HIGH END OF THE FREQUENCY BAND IS LIMITED BY THE PHYSICAL SIZE OF THE ELEMENTS WHICH MUST BE SPACED CLOSE ENOUGH IN THE ARRAY TO AVOID THE GENERATION OF GRATING LOBES SEE 3ECTION &OR WIDE INSTANTANEOUS BANDWIDTH RATHER THAN TUNABLE BANDWIDTH TIME DELAYS HAVE TO BE ADDED TO PREVENT THE BEAM FROM BEING SCANNED AS THE FREQUENCY IS CHANGED 4HE IMPEDANCE OF THE RADIATING ELEMENT AT THE APERTURE WITH CLOSELY SPACED ELEMENTS IS APPROXIMATELY INDEPENDENT OF FREQUENCY BUT THE ELEMENT MUST BE MATCHED OVER THE WIDE BANDWIDTH 4HIS IS DIFFICULT TO ACHIEVE WITHOUT EXCITING HARMFUL SURFACE WAVES WHEN SCANNING .EVERTHELESS MATCHING WITH OCTAVE BAND WIDTH FOR SCANNING TO on HAS BEEN ACHIEVED ,IMITED 3CANNING )F SCANNING IS LIMITED TO A SMALL ANGULAR VOLUME CONSIDERABLE SIMPLIFICATIONS BECOME POSSIBLE 4HE TOTAL NUMBER OF ACTIVE CONTROLS CAN BE REDUCED TO
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ABOUT EQUAL THE TOTAL NUMBER OF BEAMS 3UBARRAYS SEE 3ECTION MAY BE FORMED EACH WITH ONLY ONE PHASE CONTROL OF A SIZE SUCH THAT THE SUBARRAY BEAMWIDTH INCLUDES ALL THE SCAN ANGLES !LTERNATIVELY A SMALL PHASED ARRAY COULD BE PLACED IN THE FOCAL REGION OF A LARGE REFLECTOR TO SCAN THE NARROW BEAMWIDTH OF THE REFLECTOR OVER A LIMITED SCAN ANGLE 3CANNING OF !RRAYS 0HASE 3CANNING 4HE BEAM OF AN ANTENNA POINTS IN A DIRECTION THAT IS NORMAL TO THE RADIATED PHASE FRONT )N PHASED ARRAYS THIS PHASE FRONT IS ADJUSTED TO STEER THE BEAM BY INDIVIDUAL CONTROL OF THE PHASE OF EXCITATION OF EACH RADIATING ELEMENT 4HIS IS INDICATED IN &IGURE A 4HE PHASE SHIFTERS ARE ELECTRONICALLY ACTUATED TO PERMIT RAPID SCANNING AND ARE ADJUSTED IN PHASE TO A VALUE BETWEEN AND O RAD 7ITH AN INTERELEMENT SPACING S THE INCREMENTAL PHASE SHIFT X BETWEEN ADJACENT ELEMENTS FOR A SCAN ANGLE P IS X O K S SIN P )F THE PHASE X IS CONSTANT WITH FREQUENCY THE SCAN ANGLE P IS FREQUENCY DEPENDENT 4IME $ELAY 3CANNING 0HASE SCANNING WAS SEEN TO BE FREQUENCY SENSITIVE HOW EVER TIME DELAY SCANNING IS INDEPENDENT OF FREQUENCY $ELAY LINES ARE USED INSTEAD OF PHASE SHIFTERS AS SHOWN IN &IGURE B PROVIDING AN INCREMENTAL DELAY FROM ELEMENT TO ELEMENT OF S SC SIN P WHERE C VELOCITY OF PROPAGATION )NDIVIDUAL TIME DELAY CIRCUITS 3ECTION ARE NORMALLY TOO CUMBERSOME TO BE ADDED TO EACH RADIATING ELE MENT ! REASONABLE COMPROMISE MAY BE REACHED BY ADDING ONE TIME DELAY NETWORK TO A GROUP OF ELEMENTS SUBARRAY WHERE EACH ELEMENT HAS ITS OWN PHASE SHIFTER &REQUENCY 3CANNING &REQUENCY RATHER THAN PHASE MAY BE USED AS THE ACTIVE PARAMETER TO EXPLOIT THE FREQUENCY SENSITIVE CHARACTERISTICS OF PHASE SCANNING &IGURE C SHOWS THE ARRANGEMENT !T ONE PARTICULAR FREQUENCY ALL RADIATORS ARE IN PHASE !S THE FREQUENCY IS CHANGED THE PHASE ACROSS THE APERTURE TILTS LINEARLY AND THE BEAM IS SCANNED &REQUENCY SCANNING ARRAYS ARE RELATIVELY SIMPLE AND INEXPENSIVE
&)'52% 'ENERATION OF SCANNED BEAMS A PHASED ARRAY B TIME DELAY ARRAY C FREQUENCY SCANNED ARRAY AND D "LASS TYPE ARRAY
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TO IMPLEMENT 4HEY HAVE BEEN DEVELOPED AND DEPLOYED IN THE PAST TO PROVIDE ELEVATION ANGLE SCANNING IN COMBINATION WITH MECHANICAL HORIZONTAL ROTATION FOR $ RADARS ! CHAPTER IN THE FIRST EDITION OF THIS HANDBOOK WAS DEVOTED TO THIS APPROACH WHICH SINCE THEN HAS RECEIVED MUCH LESS ATTENTION FREQUENCY IS TOO IMPORTANT A PARAMETER FOR ACHIEVING HIGH RANGE RESOLUTION ELECTRONIC COUNTER COUNTERMEASURES AND MULTIPLE RADAR OCCUPANCY TO GIVE IT UP FOR ANTENNA SCANNING &REQUENCY SCANNING IS SELDOM USED ANYMORE )& 3CANNING &OR RECEIVING THE OUTPUT FROM EACH RADIATING ELEMENT MAY BE HET ERODYNED MIXED TO AN INTERMEDIATE FREQUENCY )& !LL THE VARIOUS METHODS OF SCAN NING ARE THEN POSSIBLE INCLUDING THE BEAM SWITCHING SYSTEM DESCRIBED BELOW AND CAN BE CARRIED OUT AT )& WHERE AMPLIFICATION IS READILY AVAILABLE AND LUMPED CONSTANT CIRCUITS MAY BE USED $IGITAL "EAMFORMINGn &OR RECEIVING THE OUTPUT FROM EACH RADIATING ELEMENT MAY BE AMPLIFIED AND DIGITIZED 4HE SIGNAL IS THEN TRANSFERRED TO A COMPUTER FOR PRO CESSING WHICH CAN INCLUDE THE FORMATION OF MULTIPLE SIMULTANEOUS BEAMS FORMED WITH APPROPRIATE APERTURE ILLUMINATION WEIGHTING AND ADAPTIVELY DERIVED NULLS IN THE BEAM PATTERNS TO AVOID SPATIAL INTERFERENCE OR JAMMING ,IMITATIONS ARE DUE TO THE AVAILABILITY AND COST OF ANALOG TO DIGITAL !$ CONVERTERS AND TO THEIR FREQUENCY AND DYNAMIC RANGE CHARACTERISTICS 0ARTIAL IMPLEMENTATION IS POSSIBLE BY DIGITIZING AT SUB ARRAY LEVELS ONLY "EAM 3WITCHING 7ITH PROPERLY DESIGNED LENSES OR REFLECTORS A NUMBER OF INDE PENDENT BEAMS MAY BE FORMED BY FEEDS AT THE FOCAL SURFACE %ACH BEAM HAS SUBSTAN TIALLY THE GAIN AND BEAMWIDTH OF THE WHOLE ANTENNA !LLEN HAS SHOWN THAT THERE ARE EFFICIENT EQUIVALENT TRANSMISSION NETWORKS THAT USE DIRECTIONAL COUPLERS AND HAVE THE SAME COLLIMATING PROPERTY ! TYPICAL FORM AFTER "LASS IS SHOWN IN &IGURE D 4HE GEOMETRY CAN BE ADJUSTED TO PROVIDE EQUAL PATH LENGTHS THUS PROVIDING FRE QUENCY INDEPENDENT TIME DELAY SCANNING !NOTHER POSSIBLE CONFIGURATION PROVIDING MULTIPLE BROADBAND BEAMS USES PARALLEL PLATES CONTAINING A WIDE ANGLE MICROWAVE LENS %ACH PORT CORRESPONDS TO A SEPARATE BEAM 4HE LENS PROVIDES APPROPRIATE TIME DELAYS TO THE APERTURE GIVING FREQUENCY INVARIANT SCANNING 4HE BEAMS MAY BE SELECTED THROUGH A SWITCHING MATRIX REQUIRING - SINGLE POLEnDOUBLE THROW 30$4 SWITCHES TO SELECT ONE OUT OF - BEAMS 4HE BEAMS ARE STATIONARY IN SPACE AND OVERLAP AT APPROXIMATELY THE D" POINTS 4HIS IS IN CONTRAST TO THE PREVIOUSLY DISCUSSED METHODS OF SCANNING WHERE THE BEAM CAN BE STEERED ACCURATELY TO ANY POSI TION 4HE BEAMS ALL LIE IN ONE PLANE 4HE SYSTEM MAY BE COMBINED WITH MECHANICAL ROTATION OF THE ANTENNA GIVING VERTICAL SWITCHED SCANNING FOR $ COVERAGE -UCH GREATER COMPLEXITY IS REQUIRED FOR A SYSTEM SWITCHING BEAMS IN BOTH PLANES -ULTIPLE 3IMULTANEOUS "EAMS )NSTEAD OF SWITCHING THE BEAMS AS DESCRIBED IN THE PRECEDING PARAGRAPH ALL THE BEAMS MAY BE CONNECTED TO SEPARATE RECEIVERS GIVING MULTIPLE SIMULTANEOUS RECEIVE BEAMS 4HE TRANSMITTER RADIATION PATTERN WOULD NEED TO BE WIDE TO COVER ALL THE RECEIVE BEAMS 3UCH MULTIBEAM SYSTEMS HAVE FOUND APPLICA TION IN COMBINATION WITH MECHANICAL ROTATION FOR $ COVERAGE -ULTIPLE )NDEPENDENTLY 3TEERED "EAMS )NDEPENDENT MULTIPLE BEAMS MAY BE GENERATED WITH A SINGLE BEAMFORMER BY MODIFYING BOTH AMPLITUDE AND PHASE AT THE APERTURE 4HIS CAN BE SEEN FROM &IGURE WHERE FOR EXAMPLE TWO INDEPENDENT
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&)'52% !PERTURE DISTRIBUTION GIVING TWO BEAMS
BEAMS ARE GENERATED "OTH BEAMS HAVE THE SAME AMPLITUDE VOLTAGE DISTRIBUTION &X BUT DIFFERENTLY INCLINED LINEAR PHASED FRONTS 4HE TOTAL APERTURE EXCITATION WITH BOTH BEAMS IS
X¶ § & X Y & X E J Y X A & X E J Y X A & X COS ¨Y Y · E J Y Y X A A¸ ©
4HAT IS THE APERTURE AMPLITUDE DISTRIBUTION REQUIRED FOR TWO SEPARATE BEAMS VARIES COSINUSOIDALLY AND THE PHASE DISTRIBUTION IS LINEAR AND HAS THE AVERAGE INCLINATION )N MOST PHASED ARRAY SYSTEMS ONLY THE PHASE CAN BE CONTROLLED )GNORING THE REQUIRED AMPLITUDE VARIATIONS STILL LEADS TO GOOD APPROXIMATIONS FOR FORMING MULTIPLE BEAMS BY SUPERIMPOSING THE VARIOUS REQUIRED PHASE SHIFTER SETTINGS MODULO O )N THE CASE OF TWO BEAMS THE APERTURE PHASE SLOPE HAS THE AVERAGE INCLINATION AND VARIES PERIODICALLY FROM TO O 6ERTICAL 3CAN /NLY ! GREATLY SIMPLIFIED PHASED ARRAY SYSTEM BECOMES POSSIBLE IF THERE IS NO NEED FOR MULTIFUNCTION CAPABILITIES INCLUDING FIRE CONTROL WHERE A BEAM MAY HAVE TO BE POINTED IN ANY GIVEN DIRECTION AT ANY TIME 4HE ARRAY IS SCANNED IN THE VERTICAL PLANE ONLY AND MECHANICALLY ROTATED TO GIVE AZIMUTH COVERAGE 4HE NUMBER OF PHASE CONTROL POINTS IS THEN REDUCED TO THE NUMBER OF HORIZONTAL ROWS )N THE CASE OF A SHIPS SURVEILLANCE RADAR THE ANTENNA SHOULD BE POSITIONED AS HIGH AS POSSIBLE TO AVOID SHADOWING BY THE SUPERSTRUCTURE BUT THE PEDESTAL NEED NOT BE STABILIZED SINCE STABILIZATION CAN BE ACHIEVED BY ELECTRONIC BEAM STEERING 3CANNING CAN BE IN THE FORM OF PHASE SCANNING OR MULTIPLE SIMULTANEOUS BEAMS MAY BE USED ON RECEIVE WITH A WIDE ANTENNA PATTERN ON TRANSMIT
£Î°ÓÊ ,,9Ê/ ",9 !RRAY WITH 4WO %LEMENTS &IGURE SHOWS TWO ISOTROPIC RADIATORS THAT ARE SPACED BY A DISTANCE S AND EXCITED WITH EQUAL AMPLITUDE AND PHASE 7ITH UNITY INPUT
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&)'52% 2ADIATION PATTERN OF TWO ISOTROPIC RADIATORS
POWER THE VECTOR SUM OF THEIR CONTRIBUTIONS ADDED AT A GREAT DISTANCE AS A FUNCTION OF P IS THE RADIATION PATTERN
%A P
J P L S SINP ;E E J P L S SINP =
WHERE P IS MEASURED FROM THE BROADSIDE DIRECTION .ORMALIZING TO GET UNITY AMPLI TUDE WHEN P AND SIMPLIFYING GIVE § S ¶ %A P COS ¨P SIN P · © L ¸ 4HE ABSOLUTE VALUE OF %A P IS PLOTTED IN &IGURE AS A FUNCTION OF O SK SIN P )F THE PLOT HAD BEEN IN TERMS OF THE ANGLE P THE LOBES WOULD HAVE BEEN FOUND TO INCREASE IN WIDTH AS \P \ INCREASED 4HE MAIN BEAM OCCURS WHEN SIN P 4HE OTHER LOBES HAVE THE SAME AMPLITUDE AS THE MAIN BEAM AND ARE REFERRED TO AS GRATING LOBES
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4HEY OCCUR AT ANGLES GIVEN BY SIN P o ;MSK = WHERE M IS AN INTEGER &OR THE HALF SPACE GIVEN BY n P n THERE ARE M` GRATING LOBES WHERE M` IS THE LARGEST INTEGER SMALLER THAN SK )F S K GRATING LOBE MAXIMA DO NOT OCCUR AND THE VALUE AT on IS COS O SK 4HIS VALUE IS FOR ISOTROPIC RADIATORS AND IS REDUCED IF THE RADIATORS HAVE DIRECTIVITY ,INEAR !RRAY 7ITH A LINEAR ARRAY OF . ISOTROPIC RADIATORS EXCITED WITH EQUAL AMPLITUDES AND PHASE AND SEPARATED BY DISTANCES S AS SHOWN IN &IGURE THE CON DITION FOR THE OCCURRENCE OF GRATING LOBES IS UNCHANGED FROM THE SIMPLER CASE JUST CONSIDERED 4HEY OCCUR FOR THE SAME VALUES OF O SK SIN P BUT THE WIDTH OF THE LOBES IS REDUCED AND THEY ARE SEPARATED BY MINOR LOBES 3UMMING THE VECTOR CONTRIBUTIONS FROM ALL ELEMENTS WITH ELEMENT AS PHASE REFERENCE GIVES N . J P L NS SIN P £ E . N 4HE FACTOR . SHOWS THAT EACH ELEMENT IS ENERGIZED WITH . OF THE UNITY INPUT POWER .ORMALIZING THE GAIN TO UNITY AT BROADSIDE P GIVES THE PATTERN
%A P
%A P
SIN; .P S L SIN P = . SIN ;P S L SIN P =
%AP GIVES THE RADIATION PATTERN FOR ISOTROPIC RADIATORS AND IS KNOWN AS THE ARRAY FACTOR )T IS SHOWN IN &IGURE FOR . 4HIS PATTERN IS REPETITIVE AND THE LOCATIONS OF THE ADJACENT GRATING LOBES AT ANGLES P AND P ARE SEPARATED BY O SK SIN P SIN P O
&)'52% ,INEAR ARRAY WITH . RADIATORS UNIFORMLY SPACED BY A DISTANCE S
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&)'52% !RRAY FACTOR WITH . ELEMENTS
4HE RADIATING ELEMENTS ARE NOT ISOTROPIC BUT HAVE A RADIATION PATTERN %EP KNOWN AS THE ELEMENT FACTOR OR ELEMENT PATTERN THEN THE COMPLETE RADIATION PATTERN %P IS THE PRODUCT OF THE ARRAY FACTOR AND THE ELEMENT PATTERN
% P %E Q %A P %E P
SIN ; .P S L SINP = . SIN;P S L SINP =
!N APPROXIMATION TO THE PATTERN OF %Q IS IN THE FORM
% P
SIN ;P A L SIN P = P A L SIN P
WHERE THE EFFECTIVE APERTURE IS A .S WHICH EXTENDS BY S BEYOND THE CENTERS OF THE END ELEMENTS )N CONTRAST TO THE ARRAY FACTOR THIS PATTERN HAS ONLY ONE MAXIMUM AND IS NONREPETITIVE )T IS THE WELL KNOWN &OURIER TRANSFORM OF A CONTINUOUS CONSTANT AMPLITUDE DISTRIBUTION &OR UNIFORM ILLUMINATION THE BEAMWIDTH IS
P"
RAD n AL AL
4HE FIRST SIDELOBE IS D" DOWN FROM THE PEAK OF THE MAIN BEAM &OR LARGER VALUES OF P THE PATTERN OF A CONTINUOUS APERTURE IS MODIFIED FROM %Q BY THE OBLIQUITY FACTOR COS P 4HIS GIVES
% P
COSP
SIN;P A L SIN P = P A L SINP
&OR CLOSELY SPACED ELEMENTS THE OBLIQUITY FACTOR IS VERY SIMILAR TO THE AMPLITUDE PATTERN OF A WELL DESIGNED MATCHED RADIATING ELEMENT COSP FOR VALUES UP TO SOME OR n !T GREATER ANGLES THE ELEMENT PATTERN HAS VALUES THAT ARE GREATER THAN THOSE GIVEN BY COSP AND THAT ARE A FUNCTION OF THE TOTAL NUMBER OF ELEMENTS 3CANNED ,INEAR !RRAYS 4HE PATTERN OF THE ARRAY MAY BE STEERED TO AN ANGLE P BY APPLYING LINEARLY PROGRESSIVE PHASE INCREMENTS FROM ELEMENT TO ELEMENT SO THAT THE PHASE BETWEEN ADJACENT ELEMENTS DIFFERS BY O SK SIN P %QUATION IS THEN MODIFIED GIVING THE NORMALIZED ARRAY FACTOR OF A UNIFORMLY ILLUMINATED ARRAYS AS
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SIN .P S L SINP SINP . SIN P S L SINP SINP
%A P
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AND THE PATTERN IS
% P %E P
SIN .P S L SINP SINP . SIN;P S L SINP SINP =
%QUATION DESCRIBES THE FUNDAMENTAL RESPONSE OF A SCANNED ARRAY SYSTEM 4HE ARRAY WILL HAVE ONLY ONE SINGLE MAJOR LOBE AND GRATING LOBE MAXIMA WILL NOT OCCUR FOR n P n AS LONG AS
S \ SIN P SIN P \ P L
P
OR S L \ SINP \
WHICH IS ALWAYS TRUE IF SK 7HEN SCANNING IS LIMITED THE VALUE OF SK MAY BE INCREASED FOR EXAMPLE TO SK FOR SCANNING TO A MAXIMUM OF n OR SK FOR SCANNING TO A MAXIMUM OF on &OR LARGER VALUES OF SK GRATING LOBES OCCUR AT ANGLES P GIVEN BY
SIN Q SIN Q o
N SL
WHEN N IS AN INTEGER )N THE LIMIT THE INEQUALITY %Q DOES ALLOW A GRATING LOBE PEAK TO OCCUR AT n WHEN SCANNING TO P %VEN THOUGH THE GRATING LOBE IS REDUCED WHEN MULTIPLIED BY THE ELEMENT PATTERN IT MAY BE PRUDENT TO SPACE THE ELEMENTS SUCH THAT THE FIRST NULL OF THE GRATING LOBE RATHER THAN THE PEAK OCCURS AT n 7ITH . ELEMENTS THIS MORE RESTRICTIVE CONDITION IS GIVEN BY S . r L . \ SIN P \
%QUATION MAY AGAIN BE APPROXIMATED BY THE &OURIER TRANSFORM OF THE ILLUMINA TION ACROSS THE CONTINUOUS APERTURE
% P
COS P
SIN P A L SIN P SINP P A L SIN P SIN P
4HE &OURIER TRANSFORM SOLUTIONS FOR CONTINUOUS APERTURES MAY BE USED TO APPROXIMATE PATTERNS FOR PRACTICAL AMPLITUDE AND PHASE DISTRIBUTIONS AS LONG AS THE ELEMENT TO ELEMENT SPACING IS SMALL ENOUGH TO SUPPRESS GRATING LOBES -ONOPULSE DIFFERENCE PATTERNS MAY BE APPROXIMATED IN THE SAME WAY FROM THE &OURIER TRANSFORMS OF THE CORRESPONDING CONTINUOUS ODD APERTURE DISTRIBUTIONS %LEMENT &ACTOR AND 'AIN OF 0LANAR !RRAYS 4HE MAXIMUM GAIN OF A UNIFORMLY ILLUMINATED AND LOSSLESS APERTURE OF AREA ! WITH A BROADSIDE BEAM IS 'MAX P ! L
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7ITH A NONUNIFORM APERTURE DISTRIBUTION AND WITH LOSSES PRESENT THE GAIN IS REDUCED BY THE EFFICIENCY TERM G TO ! H L )F THE APERTURE IS CONSIDERED AS A MATCHED RECEIVER THEN THE AMOUNT OF ENERGY ARRIV ING FROM A DIRECTION P IS PROPORTIONAL TO ITS PROJECTED AREA 4HE GAIN WITH SCANNING THEREFORE IS
'MAX P
' P P
! COS P H L
)F THE APERTURE IS MADE UP OF . EQUAL RADIATING ELEMENTS AND IS MATCHED TO ACCEPT THE INCIDENT POWER THEN THE CONTRIBUTION TO THE OVERALL GAIN IS THE SAME FROM ALL ELEMENTS HENCE
'P .'EP G
WHERE 'E IS THE GAIN PER ELEMENT )T FOLLOWS FROM %Q THAT THE MATCHED ELEMENT POWER PATTERN IS ! COS P .L AND THE NORMALIZED RADIATION AMPLITUDE PATTERN OF THE MATCHED ELEMENT OR MATCHED ELEMENT PATTERN IS
'E P P
%E P COS P
&OR A GIVEN ELEMENT SPACING S THE TOTAL NUMBER OF RADIATORS . IN THE AREA ! IS . !S AND %Q GIVES
§S¶ 'E P P ¨ · COS P ©L ¸
7HEN THE ELEMENT SPACING IS S K THEN THE POWER PATTERN OF AN ELEMENT THAT IS PERFECTLY MATCHED AT ALL SCAN ANGLES IS
'EP O COS P
!ND THE PEAK ANTENNA GAIN IN THE DIRECTION OF SCAN P IS
'P O .G COS P
WHERE THE EFFICIENCY TERM G ACCOUNTS FOR LOSSES AND FOR A NONUNIFORM APERTURE DISTRI BUTION &OR A BROADSIDE BEAM P AND
' O .G
AND THE ELEMENT GAIN IS 'E O &IGURE SHOWS A THEORETICAL EXAMPLE OF THE ARRAY AND ELEMENT FACTORS AND THE RESULTING PATTERN FOR A ELEMENT ARRAY WITH ELEMENT SPACING S K SCANNED TO n
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&)'52% 4EN ELEMENT LINEAR ARRAY SCANNED TO n ELEMENT SPACING S K
4HE PATTERN MAXIMUM IS NOTED TO OCCUR AT LESS THAN n BECAUSE THE GAIN OF THE ELEMENT PATTERN INCREASES TOWARD BROADSIDE 4HE ELEMENT PATTERN VALUE AT n IS COS n IN POWER OR IN AMPLITUDE RELATIVE TO THE MAXIMUM AT BROADSIDE AS EXPECTED 4HE SIDELOBES IN THE GENERAL REGION OF BROADSIDE ARE NOT REDUCED BECAUSE IN THAT REGION THE ELEMENT PATTERN IS APPROXIMATELY UNITY 2ELATIVE TO THE BEAM MAXIMUM THEREFORE THE SIDELOBES NEAR BROADSIDE ARE INCREASED BY APPROXIMATELY D"
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, 0LANAR !RRAYS ! PLANAR ARRAY IS CAPABLE OF STEERING THE BEAM IN TWO DIMEN SIONS )N A SPHERICAL COORDINATE SYSTEM THE TWO COORDINATES P AND E DEFINE POINTS ON THE SURFACE OF A UNIT HEMISPHERE !S SHOWN IN &IGURE P IS THE ANGLE OF SCAN MEASURED FROM BROADSIDE AND E IS THE PLANE OF SCAN MEASURED FROM THE X AXIS 6ON !ULOCK HAS PRESENTED A SIMPLIFIED METHOD FOR VISUALIZING THE PATTERNS AND THE EFFECT OF SCANNING (E CONSIDERS THE PROJECTION OF THE POINTS ON A HEMISPHERE ONTO A PLANE &IGURE THE AXES OF THE PLANE ARE THE DIRECTION COSINES COS @X COS @Y &OR ANY DIRECTION ON THE HEMISPHERE THE DIRECTION COSINES ARE
COS A X SIN P COS F COS A Y SIN P SIN F
4HE DIRECTION OF SCAN IS INDICATED BY THE DIRECTION COSINES COS @XS COS @YS (ERE THE PLANE OF SCAN IS DEFINED BY THE ANGLE E MEASURED COUNTERCLOCKWISE FROM THE COS @X AXIS AND IS GIVEN BY
F TAN
COS A YS COS A XS
4HE ANGLE OF SCAN P IS DETERMINED BY THE DISTANCE OF THE POINT COS @XS COS @YS FROM THE ORIGIN 4HIS DISTANCE IS EQUAL TO SIN P &OR THIS REASON A REPRESENTATION OF THIS SORT IS CALLED SIN P SPACE ! FEATURE OF SIN P SPACE IS THAT THE ANTENNA PATTERN SHAPE IS INVARIANT
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&)'52% 0LANAR ARRAY ELEMENT GEOMETRY AND PHASING
TO THE DIRECTION OF SCAN !S THE BEAM IS SCANNED EVERY POINT ON THE PLOT IS TRANSLATED IN THE SAME DIRECTION AND BY THE SAME DISTANCE AS IS THE BEAM MAXIMUM 4HE REGION INSIDE THE UNIT CIRCLE WHERE
COS A X COS A Y a
&)'52% 0ROJECTION OF POINTS ON A HEMISPHERE ONTO THE PLANE OF THE ARRAY
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IS DEFINED AS REAL SPACE THE HEMISPHERE INTO WHICH ENERGY IS RADIATED 4HE INFINITE REGION OUTSIDE THE UNIT CIRCLE IS REFERRED TO AS IMAGINARY SPACE !LTHOUGH NO POWER IS RADIATED INTO IMAGINARY SPACE THE CONCEPT IS USEFUL FOR OBSERVING THE MOTION OF GRAT ING LOBES AS THE ARRAY IS SCANNED )N ADDITION THE PATTERN IN IMAGINARY SPACE REPRESENTS STORED ENERGY AND CONTRIBUTES TO THE ELEMENT IMPEDANCE IN THE ARRAY 4HE MOST COMMON ELEMENT LATTICES HAVE EITHER A RECTANGULAR OR A TRIANGULAR GRID !S SHOWN IN &IGURE THE MNTH ELEMENT IS LOCATED AT MDX NDY 4HE TRIANGULAR GRID MAY BE THOUGHT OF AS A RECTANGULAR GRID WHERE EVERY OTHER ELEMENT HAS BEEN OMITTED 4HE ELEMENT LOCATIONS CAN BE DEFINED BY REQUIRING THAT M N BE EVEN #ALCULATIONS FOR THE ELEMENT STEERING PHASES ARE GREATLY SIMPLIFIED BY THE ADOP TION OF THE DIRECTION COSINE COORDINATE SYSTEM )N THIS SYSTEM THE LINEAR PHASE TAPERS DEFINED BY THE BEAM STEERING DIRECTION COS @XS COS @YS MAY BE SUMMED AT EACH ELE MENT SO THAT THE PHASING AT THE MNTH ELEMENT IS GIVEN BY
Y MN M4XS N4YS
WHERE 4XS O K DX COS @XS ELEMENT TO ELEMENT PHASE SHIFT IN THE X DIRECTION 4YS O K DY COS @YS ELEMENT TO ELEMENT PHASE SHIFT IN THE Y DIRECTION 4HE ARRAY FACTOR OF A TWO DIMENSIONAL ARRAY MAY BE CALCULATED BY SUMMING THE VECTOR CONTRIBUTION OF EACH ELEMENT IN THE ARRAY AT EACH POINT IN SPACE &OR AN ARRAY SCANNED TO A DIRECTION GIVEN BY THE DIRECTION COSINES COS @XS AND COS @YS THE ARRAY FAC TOR OF AN - r . RECTANGULAR ARRAY OF RADIATORS MAY BE WRITTEN - .
%A COS A XS COS A YS
£ £
\ !MN \ E J; M 4X 4XS N4Y 4YS =
M N
WHERE 4X OK DX COS @X 4Y O K DY COS @Y !MN AMPLITUDE OF MNTH ELEMENT !N ARRAY MAY BE VISUALIZED AS HAVING AN INFINITE NUMBER OF GRATING LOBES ONLY ONE OF WHICH NAMELY THE MAIN BEAM IS DESIRED IN REAL SPACE )T IS CONVENIENT TO PLOT THE POSITION OF THE GRATING LOBES WHEN THE BEAM IS PHASED FOR BROADSIDE AND OBSERVE THE MOTION OF THESE LOBES AS THE BEAM IS SCANNED &IGURE SHOWS THE GRATING LOBE LOCATIONS FOR BOTH RECTANGULAR AND TRIANGULAR SPACING &OR A RECTANGULAR ARRAY THE GRAT ING LOBES ARE LOCATED AT COS A XS COS A X o
L P DX
L Q DY P Q
COS A YS COS A Y o
4HE LOBE AT P Q IS THE MAIN BEAM ! TRIANGULAR GRID IS MORE EFFICIENT FOR SUPPRESSING GRATING LOBES THAN A RECTANGULAR GRID SO THAT FOR A GIVEN APERTURE SIZE
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FEWER ELEMENTS ARE REQUIRED )F THE TRIANGULAR LATTICE CONTAINS ELEMENTS AT MDX NDY WHERE M N IS EVEN THE GRATING LOBES ARE LOCATED AT COS A XS COS A X o
L P DX
COS A YS COS A Y o
L Q DY
WHERE P Q IS EVEN
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"ECAUSE ONLY ONE MAIN BEAM IS NORMALLY DESIRED IN REAL SPACE AN APPROPRIATE DESIGN WILL PLACE ALL BUT ONE MAXIMUM IN IMAGINARY SPACE FOR ALL ANGLES OF SCAN 7ITH SCANNING LOBES THAT WERE ORIGINALLY IN IMAGINARY SPACE MAY MOVE INTO REAL SPACE IF THE ELEMENT SPACING IS GREATER THAN K !S THE ARRAY IS SCANNED AWAY FROM BROADSIDE EACH GRATING LOBE IN SIN P SPACE WILL MOVE A DISTANCE EQUAL TO THE SINE OF THE ANGLE OF SCAN AND IN A DIRECTION DETERMINED BY THE PLANE OF SCAN 4O ENSURE THAT NO GRATING LOBES ENTER REAL SPACE THE ELEMENT SPACING MUST BE CHOSEN SO THAT FOR THE MAXIMUM SCAN ANGLE PM THE MOVEMENT OF A GRATING LOBE BY SIN PM DOES NOT BRING THE GRATING LOBE INTO REAL SPACE )F A SCAN ANGLE OF n FROM BROADSIDE IS REQUIRED FOR EVERY PLANE OF SCAN NO GRATING LOBES MAY EXIST WITHIN A CIRCLE OF RADIUS SIN PM 4HE SQUARE GRID THAT MEETS THIS REQUIREMENT HAS
L L OR D X D Y L DX DY
(ERE THE AREA PER ELEMENT IS D X D Y L L
&OR AN EQUILATERAL TRIANGULAR ARRAY THE REQUIREMENT IS SATISFIED BY
L DY
L OR D Y L D X L DX
"ECAUSE ELEMENTS ARE LOCATED ONLY AT EVERY OTHER VALUE OF MN THE AREA PER ELEMENT IS
D X D Y L L L
&OR THE SAME AMOUNT OF GRATING LOBE SUPPRESSION THE SQUARE GEOMETRY REQUIRES APPROXIMATELY MORE ELEMENTS %LEMENT 0HASING #ALCULATIONS ! COMPUTER IS USUALLY REQUIRED TO PERFORM THE STEERING COMPUTATIONS FOR A PHASED ARRAY ANTENNA )T CAN COMPENSATE FOR MANY OF THE KNOWN PHASE ERRORS CAUSED BY THE MICROWAVE COMPONENTS THE OPERATING ENVIRON MENT AND THE PHYSICAL PLACEMENT OF THE ELEMENTS &OR EXAMPLE IF THE INSERTION AND DIFFERENTIAL PHASE VARIATIONS WHICH MAY OCCUR FROM PHASE SHIFTER TO PHASE SHIFTER ARE KNOWN THEY MAY BE TAKEN INTO ACCOUNT IN THE COMPUTATIONS +NOWN TEMPERATURE VARIATIONS ACROSS THE ARRAY THAT WOULD INDUCE PHASE ERRORS MAY BE COMPENSATED FOR &INALLY MANY FEEDS EG OPTICAL AND SERIES FEEDS DO NOT PROVIDE EQUAL PHASE EXCITA TION AT THE INPUT TO EACH PHASE SHIFTER 4HE RELATIVE PHASE EXCITATION CAUSED BY THESE FEEDS IS A KNOWN FUNCTION OF FREQUENCY )N THESE CASES THE COMPUTER MUST PROVIDE A CORRECTION BASED ON THE LOCATION OF THE ELEMENT IN THE ARRAY AND ON THE FREQUENCY OF OPERATION &OR A LARGE ARRAY WITH THOUSANDS OF ELEMENTS MANY CALCULATIONS ARE REQUIRED TO DETERMINE THE PHASING OF THE ELEMENTS 4HESE CALCULATIONS MUST BE PERFORMED IN A SHORT PERIOD OF TIME 4HE USE OF THE ORTHOGONAL PHASE COMMANDS M4XS N4YS HELPS TO MINIMIZE THESE CALCULATIONS /NCE THE ELEMENT TO ELEMENT PHASE INCREMENTS 4XS 4YS HAVE BEEN COMPUTED FOR A GIVEN BEAM POINTING DIRECTION THE INTEGRAL MULTIPLES OF 4YS MAY BE USED TO STEER THE COLUMNS &IGURE
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£Î°{Ê * ,/1, Ê / ÊÊ Ê 1/1 Ê "1* Ê{x 3IGNIFICANCE OF !PERTURE -ATCHING !N ANTENNA IS A DEVICE THAT ACTS AS A TRANS FORMER TO PROVIDE A GOOD MATCH BETWEEN A SOURCE OF POWER AND FREE SPACE )F THE ANTENNA IS NOT MATCHED TO FREE SPACE POWER WILL BE REFLECTED BACK TOWARD THE GENERA TOR RESULTING IN A LOSS IN RADIATED POWER )N ADDITION A MISMATCH PRODUCES STANDING WAVES ON THE FEED LINE TO THE ANTENNA 4HE VOLTAGE AT THE PEAKS OF THESE STANDING WAVES IS \ ' \ TIMES GREATER THAN THE VOLTAGE OF A MATCHED LINE WHERE ' IS THE VOLTAGE REFLECTION COEFFICIENT 4HIS CORRESPONDS TO AN INCREASED POWER LEVEL THAT IS \ ' \ TIMES AS GREAT AS THE ACTUAL INCIDENT POWER 4HEREFORE WHILE THE ANTENNA IS RADIATING LESS POWER INDIVIDUAL COMPONENTS MUST BE DESIGNED TO HANDLE MORE PEAK POWER 7ITH ANTENNAS THAT DO NOT SCAN THE MISMATCH MAY OFTEN BE TUNED OUT BY CONVENTIONAL TECH NIQUES PREFERABLY AT A POINT AS CLOSE TO THE SOURCE OF THE MISMATCH AS POSSIBLE )N A SCANNING ARRAY THE IMPEDANCE OF A RADIATING ELEMENT VARIES AS THE ARRAY IS SCANNED AND THE MATCHING PROBLEM IS CONSIDERABLY MORE COMPLICATED 5NLIKE A CONVEN TIONAL ANTENNA WHERE MISMATCH AFFECTS ONLY THE LEVEL OF THE POWER RADIATED AND NOT THE SHAPE OF THE PATTERN SPURIOUS LOBES IN THE SCANNING ARRAY MAY APPEAR AS A CONSEQUENCE OF THE MISMATCH &URTHER THERE ARE CONDITIONS WHERE AN ANTENNA THAT IS WELL MATCHED AT BROADSIDE MAY HAVE SOME ANGLE OF SCAN AT WHICH MOST OF THE POWER IS REFLECTED 4HE VARIATION IN ELEMENT IMPEDANCE AND ELEMENT PATTERN IS A MANIFESTATION OF THE MUTUAL COUPLING BETWEEN RADIATING ELEMENTS THAT ARE IN CLOSE PROXIMITY TO ONE ANOTHER &OR A PRACTICAL DESIGN TWO EMPIRICAL TECHNIQUES ARE OF GREAT VALUE 7AVEGUIDE SIMULATORS PROVIDE A MEANS FOR DETERMINING THE ELEMENT IMPEDANCE IN AN INFINITE ARRAY WITH THE USE OF ONLY A FEW ELEMENTS 4HE EFFECTIVENESS OF A MATCHING STRUCTURE BASED ON THESE MEASUREMENTS MAY ALSO BE DETERMINED IN THE SIMULATOR ! SMALL ARRAY IS THE BEST TECHNIQUE FOR DETERMINING THE ACTIVE ELEMENT PATTERN 4HE ACTIVE ELEMENT PATTERN OBTAINED BY EXCITING ONE ELEMENT AND TERMINATING ITS NEIGH BORS IS THE BEST OVERALL MEASURE OF ARRAY PERFORMANCE OTHER THAN THE FULL ARRAY ITSELF )F A LARGE REFLECTION OCCURS AT SOME ANGLE OF SCAN IT CAN BE RECOGNIZED BY A NULL IN THE ELEMENT PATTERN 4HE SMALL ARRAY CAN ALSO PROVIDE DATA ON THE COUPLING BETWEEN ELEMENTS 4HIS DATA CAN BE USED TO CALCULATE THE VARIATION IN IMPEDANCE AS THE ARRAY IS SCANNED "OTH THESE TECHNIQUES WILL BE DISCUSSED LATER IN THIS SECTION %FFECTS OF -UTUAL #OUPLING 7HEN TWO ANTENNAS OR ELEMENTS ARE WIDELY SEPA RATED THE ENERGY COUPLED BETWEEN THEM IS SMALL AND THE INFLUENCE OF ONE ANTENNA ON THE CURRENT EXCITATION AND PATTERN OF THE OTHER ANTENNA IS NEGLIGIBLE !S THE ANTENNAS ARE BROUGHT CLOSER TOGETHER THE COUPLING BETWEEN THEM INCREASES )N GENERAL THE MAG NITUDE OF THE COUPLING IS INFLUENCED BY THE DISTANCE BETWEEN THE ELEMENTS THE PATTERN OF THE ELEMENTS AND THE STRUCTURE IN THE VICINITY OF THE ELEMENTS &OR EXAMPLE THE RADIATION PATTERN OF A DIPOLE HAS A NULL IN THE P on DIRECTION AND IS OMNIDIRECTIONAL IN THE P n PLANE 4HEREFORE IT CAN BE EXPECTED THAT DIPOLES IN LINE WILL BE LOOSELY COUPLED AND PARALLEL DIPOLES WILL BE TIGHTLY COUPLED 7HEN AN ELEMENT IS PLACED IN AN ARRAY OF MANY ELEMENTS THE EFFECTS OF COUPLING ARE SUFFICIENTLY STRONG THAT THE PATTERN AND IMPEDANCE OF THE ELEMENTS IN THE ARRAY ARE DRASTICALLY ALTERED
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4HE TERMS ACTIVE ELEMENT PATTERN AND ELEMENT IMPEDANCE REFER TO AN ELEMENT IN ITS OPERATING ENVIRONMENT IE IN AN ARRAY WITH ITS NEIGHBORING ELEMENTS EXCITED )N THE ARRAY EACH EXCITED ELEMENT COUPLES TO EVERY OTHER ELEMENT 4HE COUPLING FROM SEVERAL ELEMENTS TO A TYPICAL CENTRAL ELEMENT ELEMENT IS SHOWN IN &IGURE 4HE #MN PQ ARE MUTUAL COUPLING COEFFICIENTS RELATING THE VOLTAGE AMPLITUDE AND PHASE INDUCED IN THE MNTH ELEMENT TO THE VOLTAGE EXCITATION AT THE PQTH ELEMENT 4HE COUPLED SIGNALS ADD VECTORIALLY TO PRODUCE A WAVE TRAVELING TOWARD THE GENERATOR OF ELEMENT THAT APPEARS TO BE A REFLECTION FROM THE RADIATOR OF ELEMENT !S THE PHASES OF THE NEIGHBORING ELEMENTS ARE VARIED TO SCAN THE BEAM THE VECTOR SUM OF THE COUPLED SIGNALS CHANGES AND CAUSES AN APPARENT CHANGE IN THE IMPEDANCE OF ELEMENT &OR SOME SCAN ANGLES THE COUPLED VOLTAGES TEND TO ADD IN PHASE CAUSING A LARGE REFLECTION AND POSSIBLY THE LOSS OF THE MAIN BEAM ,ARGE REFLECTIONS OFTEN OCCUR AT SCAN ANGLES JUST PRIOR TO THE EMERGENCE OF A GRATING LOBE INTO REAL SPACE BUT IN SOME INSTANCES SUCH REFLECTIONS MAY OCCUR AT SMALLER SCAN ANGLES 4HE DESCRIPTION OF THE IMPEDANCE VARIATION GIVEN ABOVE MADE NO REFERENCE TO THE FEED NETWORK OR THE PHASE SHIFTERS AND ASSUMED THAT THE ONLY COUPLING BETWEEN ELE MENTS IS VIA THE RADIATING APERTURE 4HE COUPLING COEFFICIENTS WOULD BE MEASURED AND BY SUPERPOSITION THE PHASED VOLTAGE CONTRIBUTIONS FROM EVERY ELEMENT IN THE ARRAY OR AT LEAST THOSE IN THE IMMEDIATE VICINITY WOULD BE ADDED VECTORIALLY TO PRODUCE THE VOLTAGE REFLECTED BACK TOWARD THE GENERATOR )N A PRACTICAL ARRAY THE IMPEDANCE VARIATION DEPENDS UPON THE FEED SYSTEM AND THE PHASE SHIFTER )F THESE ARE TAKEN INTO ACCOUNT THE IMPEDANCE VARIATION MAY BE DIFFERENT FROM WHAT THE ABOVE MODEL MIGHT PREDICT )N MOST ANALYSES ONLY THE COUPLING AT THE APERTURE IS CONSIDERED 4HIS DESCRIP TION PROVIDES INSIGHT INTO THE INTRINSIC IMPEDANCE VARIATION OF THE APERTURE WHEN IT IS ISOLATED FROM OTHER EFFECTS AS IN THE CASE WHERE EACH ELEMENT HAS AN INDEPENDENT FEED EG ITS OWN GENERATOR AND ISOLATOR )N THIS CASE IT IS A SIMPLE MATTER TO MEASURE THE VOLTAGE STANDING WAVE RATIO 6372 IN ANY LINE AND DETERMINE EXACTLY THE EXTENT OF THE IMPEDANCE AND MISMATCH VARIATION &OR MANY FEED SYSTEMS THIS IS NOT POSSIBLE AND A MEASUREMENT OF THE REFLECTED ENERGY WILL PROVIDE ERRONEOUS INFORMATION AND A
&)'52% #OUPLED SIGNALS TO A CENTRAL ELEMENT FROM NEIGHBORING ELEMENTS
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FALSE SENSE OF SECURITY 5NLESS ALL THE REFLECTIONS ARE COLLIMATED BACK AT SOME CENTRAL POINT OR INDEPENDENT FEEDS ARE USED SOME OF THE REFLECTED ENERGY WILL GENERALLY BE RE REFLECTED AND CONTRIBUTE TO UNDESIRABLE SIDELOBES &OR LARGE ARRAYS THE IMPEDANCE OF AN ELEMENT LOCATED NEAR THE CENTER OF THE ARRAY IS OFTEN TAKEN AS TYPICAL OF THE IMPEDANCE OF EVERY ELEMENT IN THE ARRAY !S MIGHT BE EXPECTED THIS ELEMENT IS MOST STRONGLY INFLUENCED BY ELEMENTS IN ITS IMMEDIATE VICINITY 7HEN THE ARRAY IS SCANNED THE INFLUENCE OF ELEMENTS SEVERAL WAVELENGTHS DISTANT IS ALSO SIGNIFICANT &OR DIPOLES ABOVE A GROUND PLANE THE MAGNITUDE OF THE COUPLING BETWEEN ELEMENTS DECAYS RAPIDLY WITH DISTANCE &OR A REASONABLE INDICATION OF ARRAY PERFORMANCE AN ELEMENT IN THE CENTER OF A BY ARRAY MAY BE TAKEN AS TYPICAL OF AN ELEMENT IN A LARGE ARRAY &OR DIPOLES WITH NO GROUND PLANE THE COUPLING BETWEEN ELEMENTS DOES NOT DECAY SO RAPIDLY AND A BY ARRAY APPEARS REASONABLE &OR AN ARRAY OF OPEN ENDED WAVEGUIDES A BY ARRAY SHOULD SUFFICE )F ACCURATE PREDICTION OF THE ARRAY PERFORMANCE IS REQUIRED MANY MORE ELEMENTS ARE NEEDED THAN ARE INDICATED ABOVE )T IS OFTEN CONVENIENT TO ASSUME THAT THE ARRAY IS INFINITE IN EXTENT AND HAS A UNIFORM AMPLITUDE DISTRIBUTION AND A LINEAR PHASE TAPER FROM ELEMENT TO ELEMENT )N THIS MAN NER EVERY ELEMENT IN THE ARRAY SEES EXACTLY THE SAME ENVIRONMENT AND THE CALCULATIONS FOR ANY ELEMENT APPLY EQUALLY TO ALL 4HESE ASSUMPTIONS PROVIDE A SIGNIFICANT SIMPLIFI CATION IN THE CALCULATION OF THE ELEMENT IMPEDANCE VARIATIONS )N ADDITION IMPEDANCE MEASUREMENTS MADE IN SIMULATORS CORRESPOND TO THE ELEMENT IMPEDANCE IN AN INFINITE ARRAY )N SPITE OF THE ASSUMPTIONS THE INFINITE ARRAY MODEL HAS PREDICTED WITH GOOD ACCURACY THE ARRAY IMPEDANCE AND THE IMPEDANCE VARIATIONS %VEN ARRAYS OF MOD EST PROPORTIONS LESS THAN ELEMENTS HAVE BEEN IN REASONABLE AGREEMENT WITH THE RESULTS PREDICTED FOR AN INFINITE ARRAY %LEMENT 0ATTERN &ROM ENERGY CONSIDERATIONS THE DIRECTIONAL GAIN OF A PERFECTLY MATCHED ARRAY WITH CONSTANT AMPLITUDE DISTRIBUTION G WILL VARY AS THE PROJECTED APERTURE AREA FROM %Q
' P
P ! COS P L
)F IT IS ASSUMED THAT EACH OF THE . ELEMENTS IN THE ARRAY SHARES THE GAIN EQUALLY THE GAIN OF A SINGLE ELEMENT IS FROM %Q
'E P
P ! COS P .L
)F THE ELEMENT IS MISMATCHED HAVING A REFLECTION COEFFICIENT 'P E THAT VARIES AS A FUNCTION OF SCAN ANGLE THE ELEMENT GAIN PATTERN IS REDUCED TO
'E P
P ! COS P ; \ ' Q F \ = .L
4HE ELEMENT PATTERN IS SEEN TO CONTAIN INFORMATION PERTAINING TO THE ELEMENT IMPEDANCEn 4HE DIFFERENCE BETWEEN THE TOTAL POWER RADIATED IN THE ELEMENT PAT TERN AND THE POWER DELIVERED TO THE ANTENNA TERMINALS MUST EQUAL THE REFLECTED POWER )N TERMS OF THE RADIATION PATTERN OF THE SCANNING ARRAY THIS MEANS THAT SINCE THE SCANNED ANTENNA PATTERNS TRACE OUT THE ELEMENT PATTERN IT FOLLOWS THAT THE AVERAGE POWER LOST FROM THE SCANNED PATTERN IS EQUAL TO THE POWER LOST FROM THE ELEMENT
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PATTERN BECAUSE OF REFLECTIONS )T IS NOT ENOUGH TO MATCH ONE ELEMENT IN THE PRES ENCE OF ALL ITS TERMINATED NEIGHBORS 4HE ELEMENT WILL DELIVER POWER TO ITS NEIGHBORS AND THIS LOSS IN POWER CORRESPONDS TO THE AVERAGE POWER LOST WHEN SCANNING !N IDEAL ALTHOUGH NOT NECESSARILY REALIZABLE ELEMENT PATTERN WOULD PLACE ALL THE RADIATED POWER INTO THE SCAN REGION GIVING A PATTERN LIKE A COSINE ON A PEDESTAL AND THEREBY PROVIDING MAXIMUM ANTENNA GAIN FOR THE NUMBER OF ELEMENTS USED 4HINNED !RRAYS 4HE NUMBER OF RADIATING ELEMENTS IN AN ARRAY MAY BE REDUCED TO A FRACTION OF THOSE NEEDED COMPLETELY TO FILL THE APERTURE WITHOUT SUFFERING SERIOUS DEGRADATION IN THE SHAPE OF THE MAIN BEAM (OWEVER AVERAGE SIDELOBES ARE DEGRADED IN PROPORTION TO THE NUMBER OF ELEMENTS REMOVED 4HE ELEMENT DENSITY MAY BE THINNED SO AS TO TAPER THE AMPLITUDE DISTRIBUTION EFFECTIVELY AND THE SPACING IS SUCH THAT NO COHERENT ADDITION CAN OCCUR TO FORM GRATING LOBES ! THINNED APERTURE WHERE ELEMENTS HAVE BEEN REMOVED RANDOMLY FROM A REGULAR GRID IS SHOWN IN &IGURE 4HE GAIN IS THAT DUE TO THE ACTUAL NUMBER OF ELEMENTS .'EP BUT THE BEAMWIDTH IS THAT
&)'52% A 4HINNED ARRAY WITH A ELEMENT GRID CONTAINING ELEMENTS B 0ATTERN FOR A THINNED ARRAY 3! IS THE AVERAGE SIDELOBE LEVEL AFTER 2 % 7ILLEY Ú )2% #OURTESY OF "ENDIX 2ADIO
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OF THE FULL APERTURE &OR EXAMPLE IF THE ARRAY HAS BEEN THINNED SO THAT ONLY OF THE ELEMENTS ARE USED THE GAIN OF THE ARRAY WILL DROP BY D" (OWEVER BECAUSE THE MAIN BEAM IS VIRTUALLY UNCHANGED ABOUT OF THE POWER IS DELIVERED TO THE SIDELOBE REGION 4HINNED ARRAYS ARE SELDOM USED )F THE REMOVED ELEMENTS IN A REGULAR THINNED ARRAY ARE REPLACED WITH ELEMENTS WITH MATCHED LOADS THE ELEMENT PATTERN IS IDENTICAL TO THAT OF ONE IN THE REGULAR ARRAY WITH ALL ELEMENTS EXCITED 4HE ELEMENT PATTERN IS INDEPENDENT OF THE ARRAY EXCITATION AND THE SAME FRACTIONAL AMOUNT OF POWER WILL BE LOST BECAUSE OF MISMATCH WHETHER THE ARRAY IS THINNED TAPERED OR UNIFORMLY ILLUMINATED )T SHOULD BE NOTED THAT THE CONCEPT OF AN ELEMENT PATTERN THAT APPLIES EQUALLY TO EVERY ELEMENT IS VALID ONLY WHEN ISOLATING FEEDS ARE USED AND EDGE EFFECTS ARE IGNORED ! THINNED ARRAY MAY ALSO BE IMPLEMENTED WITH AN IRREGULAR ELEMENT SPACING ALTHOUGH THIS IS NOT COMMON )N THIS CASE THE ELEMENT GAIN AND IMPEDANCE WILL VARY FROM ELEMENT DEPENDING UPON THE ENVIRONMENT OF A GIVEN ELEMENT 4O OBTAIN THE GAIN OF THE ARRAY IT IS NECESSARY TO SUM ALL THE DIFFERENT ELEMENT GAINS 'ENP 4HUS
' P £ 'EN P N
)MPEDANCE 6ARIATION OF &REE 3PACE )T IS OF INTEREST TO EXAMINE THE CASE OF A LARGE CONTINUOUS APERTURE THAT MAY BE CONSIDERED TO BE THE LIMITING CASE OF AN ARRAY OF MANY VERY SMALL ELEMENTS 4HE FREE SPACE IMPEDANCE %( VARIES AS COS P FOR SCANNING IN THE % PLANE AND AS SEC P FOR SCANNING IN THE ( PLANE 4HE IMPEDANCE OF A MEDIUM IS THUS DEPENDENT UPON THE DIRECTION OF PROPAGATION AND THE IMPEDANCE VARIATION OF A SCANNING APERTURE IS A NATURAL CONSEQUENCE OF THIS DEPENDENCE 4HE CONTINUOUS APERTURE APPEARS TO REPRESENT A LOWER LIMIT TO THE IMPEDANCE VARIATION WITH SCANNING 4HIS IS INDICATED BY !LLENS RESULTS WHERE IMPEDANCE VARIATION WITH SCAN NING WAS CALCULATED FOR DIPOLES ABOVE A GROUND PLANE )N SPITE OF INCREASED MUTUAL COU PLING OR PERHAPS BECAUSE OF IT THE MORE CLOSELY THE DIPOLES WERE SPACED THE SMALLER THE IMPEDANCE VARIATION WITH SCANNING !LTHOUGH THE IMPEDANCE VARIATION DECREASED THE ABSOLUTE IMPEDANCE OF THE DIPOLES ALSO DECREASED MAKING THEM MORE DIFFICULT TO MATCH AT BROADSIDE )T IS EXPECTED THAT TO OBTAIN AN IMPEDANCE VARIATION SMALLER THAN THAT OF FREE SPACE SOME IMPEDANCE COMPENSATION MUST BE EMPLOYED -UTUAL #OUPLING AND 3URFACE 7AVES 4HE MUTUAL COUPLING BETWEEN TWO SMALL ISOLATED DIPOLES SHOULD DECREASE AS R IN THE ( PLANE AND R IN THE % PLANE % AND ( PLANES ARE INTERCHANGED FOR SLOTS #OUPLING MEASUREMENTS HAVE SHOWN THAT IN THE ARRAY ENVIRONMENT THE RATE OF DECAY IS SLIGHTLY GREATER THAN PREDICTED ABOVE INDICATING THAT SOME OF THE ENERGY IS DELIVERED TO OTHER ELEMENTS IN THE ARRAY AND MAY BE DIS SIPATED AND RERADIATED FROM THESE ELEMENTS 4HE SAME MEASUREMENTS HAVE SHOWN THAT THE PHASE DIFFERENCE OF THE ENERGY COUPLED TO ELEMENTS IS DIRECTLY PROPORTIONAL TO THEIR DISTANCE FROM THE EXCITED ELEMENTS INDICATIVE OF A SURFACE WAVE TRAVELING ALONG THE ARRAY LEAKING ENERGY TO EACH OF THE ELEMENTS &OR BEST PERFORMANCE THE VELOCITY OF THE SURFACE WAVE SHOULD BE VERY CLOSE TO THAT OF FREE SPACE )F THE ARRAY CONTAINS WAVE GUIDES OR HORNS LOADED WITH DIELECTRIC THE VELOCITY WILL DECREASE SLIGHTLY &URTHER IF THE DIELECTRIC PROTRUDES FROM THE RADIATORS OR IF A DIELECTRIC SHEET IS USED IN FRONT OF THE ARRAY THE VELOCITY OF THE SURFACE WAVE MAY DECREASE DRAMATICALLY 4HIS SURFACE WAVE IS IMPORTANT BECAUSE IT CAN CAUSE A LARGE REFLECTION AND AN ACCOMPANYING LOSS OF THE BEAM FOR SOME ANGLES OF SCAN 4HIS CAN BEST BE SEEN BY EXAMINING THE CONDITION OF
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PHASING FOR WHICH THE COUPLINGS FROM MANY ELEMENTS WILL ADD IN PHASE TO CAUSE A LARGE REFLECTION IN A TYPICAL ELEMENT #ONSIDER AN ARRAY IN WHICH THE VELOCITY OF THE SURFACE WAVE IS THAT OF FREE SPACE 4HE DIFFERENCE IN THE PHASE OF THE VOLTAGES COUPLED FROM AN ADJACENT PAIR OF ELEMENTS TO ELEMENT E IN &IGURE IS RELATED TO THE SCAN ANGLE BY
P S P S P S SIN P SIN P L L L 4HE COUPLINGS WILL BE IN PHASE WHEN $X O OR WHEN
S L SIN P
4HIS IS SEEN TO BE EXACTLY THE SAME CONDITIONS AS PREVIOUSLY DETERMINED FOR THE EMER GENCE OF A GRATING LOBE INTO REAL SPACE 4HEREFORE IT MAY BE EXPECTED THAT WHEN A GRAT ING LOBE IS ABOUT TO EMERGE INTO REAL SPACE THE COUPLED VOLTAGES TEND TO ADD IN PHASE AND CAUSE A LARGE MISMATCH !RRAY 3IMULATORS ! GOOD DEAL OF EFFORT HAS GONE INTO MATCHING A RADIATOR IN THE PRESENCE OF AN ARRAY OF RADIATORS 4HE USE OF WAVEGUIDE SIMULATORS AS DEVELOPED BY 7HEELER ,ABORATORIES HAS MADE IT POSSIBLE TO DETERMINE THE MATCHING STRUCTURE EXPERIMENTALLY WITHOUT NEEDING TO BUILD AN ARRAY ! WAVEGUIDE OPERATING IN A 4% MODE MAY BE CONSIDERED TO CONTAIN TWO INCLINEDnPLANE WAVES PROPAGATING DOWN THE GUIDE 4HE ANGLE THAT EACH OF THE PLANE WAVES MAKES WITH THE LONGITUDINAL DIRECTION &IGURE IS DETERMINED BY THE ( DIMENSION OF THE WAVEGUIDE AND SIMULATES THE ANGLE OF SCAN OF AN INFINITE ARRAY
SIN Q
L LC
WHERE P SCAN ANGLE K FREE SPACE WAVELENGTH KC CUTOFF WAVELENGTH OF GUIDE
&)'52% 4WO ADJACENT ELEMENTS COUPLING TO ANOTHER ELEMENT IN THE SAME ROW
£Î°ÓÈ
2!$!2 (!.$"//+
&)'52% !RRAY SIMULATOR TERMINATED WITH TWO DUMMY ELEMENTS
!DDITIONAL SCAN ANGLES MAY BE SIMULATED BY EXCITING OTHER MODES 4HE WAVEGUIDE DIMENSIONS ARE CHOSEN SO THAT A RADIATING ELEMENT OR ELEMENT PLACED IN THE WAVEGUIDE SEES MIRROR IMAGES IN THE WALLS OF THE WAVEGUIDE THAT APPEAR TO BE AT THE SAME SPACING AS THE ARRAY TO BE SIMULATED "OTH RECTANGULAR AND TRIANGULAR ARRAYS MAY BE SIMULATED AS SHOWN IN &IGURE 4HE IMPEDANCE MEASUREMENTS ARE MADE BY LOOKING INTO A WAVEGUIDE SIMULATOR THAT IS TERMINATED WITH DUMMY ELEMENTS 4HIS IS EQUIVALENT TO LOOKING AT AN INFINITE ARRAY FROM FREE SPACE AT A SCAN ANGLE GIVEN BY %Q ! MATCHING STRUCTURE DESIGNED FROM THE SIMULATOR IMPEDANCE DATA MAY BE PLACED INTO THE SIMULATOR TO MEASURE ITS EFFECTIVENESS 3EVERAL SIMULATOR DESIGNS RESULTS AND A COMPLETE DISCUSSION OF THE TOPIC HAVE BEEN PRESENTED BY (ANNAN AND "ALFOUR 4HE TECHNIQUE IS LIMITED IN THAT ONLY DISCRETE SCAN ANGLES CAN BE SIMULATED 3EVERAL SCAN ANGLES IN BOTH PLANES OF SCAN GIVE A GENERAL IDEA OF THE ARRAY IMPEDANCE
&)'52% 2ECTANGULAR AND TRIANGULAR ARRAY GEOMETRIES WITH SIMULATOR BOUNDARIES SUPERIMPOSED A SQUARE ARRAY WITH SIMULATOR SUPERIMPOSED AND B TRIANGULAR ARRAY WITH SIMULATOR SUPERIMPOSED
0(!3%$ !22!9 2!$!2 !.4%..!3
£Î°ÓÇ
#OMPENSATION FOR 3CANNED )MPEDANCE 6ARIATION 4HE IMPEDANCE OF AN ELE MENT IN AN ARRAY HAS BEEN DISCUSSED AND HAS BEEN SHOWN TO VARY AS THE ARRAY IS SCANNED !N ARRAY THAT IS MATCHED AT BROADSIDE CAN BE EXPECTED TO HAVE AT LEAST A 6372 AT A n ANGLE OF SCAN 4O COMPENSATE FOR THE IMPEDANCE VARIATION IT IS NECESSARY TO HAVE A COMPENSATION NETWORK THAT IS ALSO DEPENDENT ON SCANNING 3MALL !RRAYS 4HE ELEMENT PATTERN IS THE BEST SINGLE INDICATOR OF IMPEDANCE MATCHING IN A SCANNING ARRAY /NE WAY OF DETERMINING THE ELEMENT PATTERN IS TO BUILD A SMALL ARRAY ! CENTRAL ELEMENT IS EXCITED AND ALL OTHER ELEMENTS ARE TERMINATED 4HE PATTERN OF THIS CENTRAL ELEMENT IS THE ACTIVE ELEMENT PATTERN $IAMOND HAS EXAMINED THE NUMBER OF ELEMENTS REQUIRED IN A SMALL ARRAY TO PROVIDE A REASONABLE APPROXIMA TION TO AN ELEMENT IN AN INFINITE ARRAY (E CONCLUDES THAT TO ELEMENTS ARE REQUIRED TO PROVIDE A GOOD INDICATION &IGURE SHOWS THE CHANGE IN THE MEASURED ACTIVE ELEMENT PATTERN AS THE NUMBER OF ELEMENTS IS INCREASED &OR A ELEMENT ARRAY THE NULL IS VERY PRONOUNCED %VEN FOR THE ELEMENT ARRAY IT IS CLEAR THAT THE GAIN VARIA TION WITH SCANNING IS DRAMATICALLY GREATER THAN COS P 4HE SMALL ARRAY CAN ALSO BE USED TO MEASURE COUPLING COEFFICIENTS AS DEMONSTRATED BY &IGURE 4HESE COUPLING COEFFICIENTS CAN BE USED TO CALCULATE THE IMPEDANCE VARIATION AS THE ARRAY IS SCANNED 'ROVE -ARTIN AND 0EPE HAVE NOTED THAT FOR THE ELE MENT TO BE MATCHED IN ITS OPERATING ENVIRONMENT THE SELF COUPLING MUST EXACTLY CANCEL THE COUPLING FROM ALL OTHER ELEMENTS 4HEY HAVE USED THIS TECHNIQUE TO PROVIDE A GOOD MATCH ON AN ULTRALOW SIDELOBE WIDEBAND PHASED ARRAY 4HE COMBINATION OF WAVEGUIDE SIMULATORS AND SMALL ARRAYS PROVIDES POWERFUL EMPIRICAL TOOLS TO SUPPLEMENT THE ANALYTICAL TECHNIQUES %XPERIENCE HAS DEMONSTRATED THAT A LARGE ANTENNA SHOULD NOT BE BUILT UNTIL THE ELEMENT PATTERN HAS BEEN VERIFIED WITH A SMALL ARRAY
&)'52% %XPERIMENTAL ( PLANE PATTERNS OF THE CENTER ELEMENTS OF WAVEGUIDES ARRAYS AFTER " , $IAMOND Ú !RTECH (OUSE
£Î°Ón
2!$!2 (!.$"//+
£Î°xÊ "7- " Ê*- Ê,,9,OW SIDELOBES HAVE LONG BEEN OF INTEREST TO ANTENNA DESIGNERS 4HIS INTEREST HAS BEEN HEIGHTENED BY THE JAMMING THAT THREATENS MOST MILITARY RADARS 4HE REQUIREMENT FOR LOW SIDELOBES FOR CLUTTER REJECTION IN THE !7!#3 RADAR RESULTED IN TECHNOLOGY THAT NOW SUPPORTS SIDELOBE LEVELS OF MORE THAN D" BELOW THE MAIN BEAM PEAK 4HE PRICE THAT MUST BE PAID TO ACHIEVE THESE LOW SIDELOBES INCLUDES A REDUCTION IN GAIN AN INCREASE IN BEAMWIDTH INCREASED TOLERANCE CONTROL INCREASED COST AND THE NEED TO OPERATE IN AN ENVIRONMENT FREE FROM OBSTRUCTIONS THAT CAN READILY INCREASE THE SIDELOBES )N SPITE OF THESE DRAWBACKS THE TREND TO LOW SIDELOBE ANTENNAS HAS ACCEL ERATED SINCE LOW SIDELOBES PROVIDE A COUNTER TO ELECTRONIC COUNTERMEASURES %#- !NTENNA SIDELOBES CAN BE CONTROLLED BY THE APERTURE AMPLITUDE DISTRIBUTION &OR PHASED ARRAYS THE AMPLITUDE OF EACH ELEMENT MAY BE CONTROLLED INDIVIDUALLY AND THEREFORE GOOD SIDELOBE CONTROL CAN BE ACHIEVED 4HE PROCESS OF DESIGNING A LOW SIDELOBE ANTENNA CAN BE CONSIDERED IN TWO PARTS #HOOSE THE CORRECT ILLUMINATION FUNCTION TO ACHIEVE THE DESIRED DESIGN ERROR FREE SIDELOBES #ONTROL THE PHASE AND AMPLITUDE ERRORS THAT CONTRIBUTE TO THE RANDOM SIDELOBES /F THE TWO CONTROLLING ERRORS FUNDAMENTALLY LIMITS SIDELOBE PERFORMANCE 4HE EFFECTS OF ILLUMINATION FUNCTION AND ERRORS ARE DISCUSSED BELOW )LLUMINATION &UNCTIONS 4HE RELATION BETWEEN APERTURE ILLUMINATION AND THE FAR FIELD PATTERN HAS BEEN STUDIED EXTENSIVELY AND IS WELL DOCUMENTED IN THE LITERA TUREn &OR A CONTINUOUS APERTURE THE FAR FIELD PATTERN IS THE &OURIER TRANSFORM OF THE DISTRIBUTION ACROSS THE APERTURE &OR AN ARRAY SAMPLES ARE TAKEN OF THE CONTINUOUS DISTRIBUTION AT EACH OF THE DISCRETE LOCATIONS 3OME TYPICAL ILLUMINATION FUNCTIONS ARE GIVEN IN 4ABLE )T IS SEEN THAT UNIFORM ILLUMINATION CONSTANT AMPLITUDE RESULTS IN THE HIGHEST GAIN AND THE NARROWEST BEAMWIDTH BUT AT THE COST OF HIGH SIDELOBES !S THE AMPLITUDE IS TAPERED THE GAIN DROPS THE BEAM BROADENS AND THE SIDELOBES MAY BE REDUCED )T IS IMPORTANT FOR THE ANTENNA DESIGNER TO CHOOSE AN EFFICIENT AND REALIZ ABLE ILLUMINATION FUNCTION THAT PROVIDES LOW SIDELOBES AT A MINIMUM LOSS IN GAIN &OR LOW SIDELOBE RADARS THE 4AYLOR ILLUMINATION FOR THE SUM PATTERNS AND THE "AYLISS ILLUMINATION FOR THE DIFFERENCE PATTERNS HAVE ALMOST BECOME AN INDUSTRY STANDARD 4HE 4AYLOR ILLUMINATION IS SOMEWHAT SIMILAR TO A COSINE SQUARED ON A PEDESTAL AND IS READILY IMPLEMENTED 4HE "AYLISS ILLUMINATION IS A DERIVATIVE FORM OF THE 4AYLOR ILLUMINATION AND IS ALSO READILY IMPLEMENTED )T SHOULD BE NOTED THAT IN MANY PHASED ARRAYS THE SIDELOBE PERFORMANCE FOR THE DIFFERENCE PATTERN IS COMPARABLE TO THAT OF THE SUM PATTERN &OR BOTH SUM AND DIFFERENCE PATTERNS THE SIDELOBES ARE REFERENCED TO THE PEAK OF THE SUM PATTERN 4HE BEAMWIDTH FACTOR PROVIDES THE BEAMWIDTH IN DEGREES OF AN APERTURE WITH LENGTH A &IGURE GIVES THE APPROXIMATE LOSS IN GAIN AND THE BEAMWIDTH FACTOR FOR THE 4AYLOR ILLUMINATION AS THE SIDELOBES CHANGE &OR A MORE COMPREHENSIVE TREATMENT SEE "ARTON AND 7ARD 4HE SIDELOBES PREDICTED BY 4ABLE ARE FOR ANTENNAS THAT HAVE PERFECT PHASE AND AMPLITUDE ACROSS THE APERTURE 4O ALLOW FOR ERRORS APERTURE ILLUMINATIONS ARE OFTEN CHOSEN TO PROVIDE PEAK SIDELOBES BELOW THOSE REQUIRED &OR EXAMPLE IF THE ANTENNA SPECIFICATION CALLS FOR D" SIDELOBES A 4AYLOR ILLUMINATION THAT PROVIDES D" DESIGN SIDELOBES MIGHT BE CHOSEN 4HE TERMINOLOGY N INDICATES THAT THE FIRST N SIDELOBES ARE HELD TO THE SPECIFIED LEVEL
0(!3%$ !22!9 2!$!2 !.4%..!3
£Î°Ó
4!",% )LLUMINATION &UNCTIONS
)LLUMINATION &UNCTION
%FFICIENCY G
0EAK 3IDELOBE D"
"EAMWIDTH &ACTOR K
,INEAR ILLUMINATION FUNCTIONS BEAMWIDTH KK A DEGREES A LENGTH OF ANTENNA 5NIFORM #OSINE #OSINE SQUARE (ANNING #OSINE SQUARED ON D" PEDESTAL #OSINE SQUARE ON D" PEDESTAL (AMMING 4AYLOR N 4AYLOR N 4AYLOR N
#IRCULAR ILLUMINATION FUNCTIONS BEAMWIDTH KK $ DEGREES $ DIAMETER OF ANTENNA 5NIFORM 4AYLOR N 4AYLOR N 4AYLOR N
)T SHOULD BE NOTED THAT FOR A RECTANGULAR ARRAY A DIFFERENT ILLUMINATION MAY BE CHOSEN FOR EACH PLANE 4HIS IS APPROPRIATE IF THE SIDELOBE REQUIREMENTS IN EACH OF THE PLANES ARE DIFFERENT 4HE RESULTANT LOSS IN GAIN IS THEN THE SUM IN DECIBELS OF THE LOSSES IN EACH PLANE
&)'52% 4AYLOR ILLUMINATION LOSS AND BEAMWIDTH FACTOR
£Î°Îä
2!$!2 (!.$"//+
%FFECT OF %RRORS 7HEN ERRORS OCCUR IN PHASE OR AMPLITUDE ENERGY IS REMOVED FROM THE MAIN BEAM AND DISTRIBUTED TO THE SIDELOBES )F THE ERRORS ARE PURELY RANDOM THEY CREATE RANDOM SIDELOBES THAT ARE CONSIDERED TO BE RADIATED WITH THE GAIN AND PATTERN OF THE ELEMENT 7HEN THE ERRORS ARE CORRELATED THE SIDELOBE ENERGY WILL BE LUMPED AT DISCRETE LOCATIONS IN THE FAR FIELD 4HE CORRELATED ERRORS WILL THEREFORE PRO VIDE HIGHER SIDELOBES BUT ONLY AT A LIMITED NUMBER OF LOCATIONS "OTH CORRELATED AND RANDOM SIDELOBES ARE OF CONCERN TO ANTENNA DESIGNERS #ORRELATED ERRORS ARE DISCUSSED IN 3ECTION !NALYSES OF THE FAR FIELD EFFECT OF ERRORS ARE BASED ON THE FACT THAT ANTENNAS ARE LINEAR DEVICES 4HAT IS THE FAR FIELD PATTERN IS THE SUM OF THE VOLTAGE AMPLITUDE AND PHASE OF EACH RADIATING ELEMENT IN THE ANTENNA &OR THIS REASON THE FAR FIELD VOLTAGE PATTERN CAN BE CONSIDERED TO BE THE SUM OF THE DESIGN PATTERN PLUS THE PATTERN CREATED SOLELY BY THE ERRORS
%4 P F %DESIGN P F %ERROR P F
)N GENERAL THREE REGIONS WILL BE RECOGNIZED IN THE TOTAL RESULTANT PATTERN A LOW NOISE FLOOR GENERATED BY RANDOM ERRORS THAT FOLLOW THE ELEMENT PATTERN A FEW PEAK SIDELOBES DUE TO CORRELATED ERRORS AND THE MAIN BEAM WITH ITS SIDELOBES DUE TO THE DESIGN DISTRIBUTION 2ANDOM %RRORS !LLEN AND 2UZE HAVE MADE DETAILED ANALYSES OF THE EFFECTS OF RANDOM ERRORS ON ANTENNAS 4HIS DISCUSSION WILL FOLLOW THE ANALYSIS PERFORMED BY !LLEN !S PREVIOUSLY MENTIONED AMPLITUDE AND PHASE ERRORS TAKE A FRACTION OF THE ENERGY FROM THE MAIN BEAM AND DISTRIBUTE THIS ENERGY TO THE SIDELOBES 4HIS FRACTION IS FOR SMALL INDEPENDENT RANDOM ERRORS
S 4 S F S !
WHERE RE RMS PHASE ERROR RAD R! RMS AMPLITUDE ERROR VOLTSVOLT 66 4HIS ENERGY IS RADIATED INTO THE FAR FIELD WITH THE GAIN OF THE ELEMENT PATTERN 4O DETERMINE THE MEAN SQUARED SIDELOBE LEVEL -33, IT IS NECESSARY TO COMPARE THIS ENERGY WITH THE PEAK OF THE PATTERN OF AN ARRAY OF . ELEMENTS SO THAT THE MEAN SQUARED SIDELOBE LEVEL IS
-33,
S 4 HA . S 4
.OTE THAT IN THE DENOMINATOR OF THIS EXPRESSION THE GAIN DUE TO THE ARRAY FACTOR . IS REDUCED BY THE APERTURE EFFICIENCY GA AND BY THE ERROR POWER LOST FROM THE MAIN BEAM S 4 !S AN EXAMPLE CONSIDER AN ARRAY OF ELEMENTS WITH AN APERTURE EFFICIENCY OF RA VV AND RE RAD 4HEN S 4
-33,
S 4 r D" H . S 4
4HE RESULT IS THAT THIS ARRAY HAS A MEAN FLOOR OF RANDOM SIDELOBES THAT ON THE AVERAGE IS D" BELOW THE PEAK OF THE BEAM )T ALSO ILLUSTRATES THAT TO ACHIEVE LOW SIDELOBES
0(!3%$ !22!9 2!$!2 !.4%..!3
£Î°Î£
VERY TIGHT TOLERANCES ARE REQUIRED 4HE AMPLITUDE OF VV IS EQUIVALENT TO A TOTAL AMPLITUDE STANDARD DEVIATION OF D" RMS 4HE TOTAL RMS PHASE ERROR IS n )T SHOULD BE NOTED THAT THERE ARE NUMEROUS SOURCES OF PHASE AND AMPLITUDE ERRORS THAT ARE INDUCED BY THE PHASE SHIFTERS THE FEED NETWORK THE RADIATING ELEMENTS AND THE MECHANICAL STRUCTURE 4HE TASK OF BUILDING A LOW SIDELOBE ANTENNA IS ONE OF REDUCING EACH OF THE AMPLITUDE ERRORS TO A FEW TENTHS OF A DECIBEL AND THE PHASE ERRORS TO A FEW DEGREES 4HE FEWER THE NUMBER OF ELEMENTS USED THE TIGHTER THE TOLERANCE BECOMES 4HE INDIVIDUAL EFFECTS OF PHASE AND AMPLITUDE ERRORS AND FAILED ELEMENTS ARE SUM MARIZED IN &IGURE 4HE RESULTANT RMS SIDELOBES ARE REFERENCED TO THE GAIN OF A SINGLE ELEMENT SO THAT THE CURVE CAN BE USED FOR ANY NUMBER OF ELEMENTS WITH INDEPEN DENT ERRORS &OR EXAMPLE A n RMS PHASE ERROR WILL PRODUCE AN RMS SIDELOBE LEVEL THAT IS APPROXIMATELY D" BELOW THE GAIN OF AN ELEMENT )F ELEMENTS D" ARE USED THE RMS SIDELOBE LEVEL IS D" BELOW THE GAIN OF THE ARRAY 4HIS IS THE EFFECT OF ONLY THE RANDOM PHASE ERRORS 4HE EFFECTS DUE TO AMPLITUDE ERRORS AND FAILED ELEMENTS MUST ALSO BE INCLUDED 4HE PREVIOUS DISCUSSION APPLIES TO THE RMS SIDELOBE LEVEL 4HIS ANALYSIS HAS BEEN EXTENDED BY !LLEN TO APPLY THE PROBABILITY OF KEEPING A SINGLE SIDELOBE BELOW A GIVEN
&)'52% 2ANDOM ERRORS AND RMS SIDELOBES
£Î°ÎÓ
2!$!2 (!.$"//+
LEVEL AND THEN THE PROBABILITY OF KEEPING A NUMBER OF SIDELOBES BELOW A GIVEN LEVEL "Y IGNORING THE ELEMENT PATTERN THE -33, INCLUDING FAILED ELEMENTS IS GIVEN BY
-33,
0 S ! 0S F HA 0.
WHERE 0 PROBABILITY OF A FAILED ELEMENT .OTE THAT IF 0 NO FAILED ELEMENTS THIS EQUATION BECOMES
-33,
S ! S F S 4 HA . HA .
4HIS IS THE SAME AS %Q EXCEPT FOR S 4 IN THE DENOMINATOR WHICH IS NOT SIGNIFICANT FOR LOW SIDELOBE ANTENNAS &OR THE CASE IN WHICH THE DESIGN SIDELOBES ARE WELL BELOW THE SIDELOBES CAUSED BY ERRORS !LLEN HAS DEVELOPED THE SET OF CURVES SHOWN IN &IGURE !N EXAMPLE WILL ILLUSTRATE THE USE OF THESE CURVES )F YOU DESIRE TO HOLD THE SIDELOBE AT A GIVEN POINT IN SPACE TO LESS THAN D" BELOW THE PEAK OF THE BEAM WITH A PROBABILITY OF DRAW A VERTICAL LINE FROM D" ON THE ABSCISSA UNTIL IT INTERSECTS THE CURVE &ROM THIS INTERSECTION DRAW A HORIZONTAL LINE AND READ THE VALUE OF -33, IN THIS CASE D" 4HEN
-33, D"
OR
-33, r
0 S ! 0S F HA 0.
&)'52% 3IDELOBE LEVEL TO BE HELD WITH PROBABILITY 0 AFTER * , !LLEN
0(!3%$ !22!9 2!$!2 !.4%..!3
£Î°ÎÎ
&OR A ELEMENT ARRAY
0 S ! 0S F HA 0
&OR GA THIS ARRAY CAN TOLERATE 0 OR R! D" OR RE n .ATURALLY EACH TYPE OF ERROR MUST BE ANTICIPATED AND ONE MUST ALLOW A BUDGET FOR FAILED ELE MENTS AMPLITUDE ERRORS AND PHASE ERRORS &OR A NUMBER OF INDEPENDENT SIDELOBES THE PROBABILITY THAT N SIDELOBES CAN BE KEPT BELOW A GIVEN LEVEL 24 IS EQUAL TO THE PRODUCT OF THE PROBABILITIES THAT EACH SIDELOBE CAN BE HELD BELOW THIS LEVEL N
0 ;N SIDELOBES 24 = 0 ; 2P I 24 =
2P I SIDELOBE LEVEL AT P I
I
!SSUMING THE SAME SIDELOBE REQUIREMENT AT EACH PI
0 ;N SIDELOBES 24= [ 0 ;ONE SIDELOBE 24=]N
AND FOR 0 ;ONE SIDELOBE 24=
0 ;N SIDELOBES 24= N 0 ;ONE SIDELOBE 24=
! SIMPLE EXAMPLE WILL ILLUSTRATE THE PROCESS )F IT IS NECESSARY TO KEEP ALL SIDELOBES IN A SECTOR BELOW D" WITH A PROBABILITY OF DETERMINE THE REQUIRED PROBABILITY ON ANY ONE GIVEN SIDELOBE
0 ; SIDELOBES D"=
4HEN
0 ;ONE GIVEN SIDELOBE D"=
0 ;ONE GIVEN SIDELOBE D"=
0 ;ONE GIVEN SIDELOBE D"=
4HAT IS TO KEEP ALL SIDELOBES BELOW D" WITH A PROBABILITY OF IT IS NECESSARY TO KEEP ANY GIVEN SIDELOBE BELOW D" WITH A PROBABILITY OF 4HE PROCESS OF CONTROLLING EACH AND EVERY SIDELOBE IS THUS SEEN AS FORMIDABLE SINCE THE TOTAL NUM BER OF SIDELOBES IS APPROXIMATELY EQUAL TO THE NUMBER OF ELEMENTS IN A PHASED ARRAY &OR A ELEMENT ARRAY AND A PROBABILITY OF THAT A SINGLE SIDELOBE WILL NOT EXCEED 24 AT ANY SINGLE LOCATION IT WILL STILL BE EXPECTED THAT SIDELOBES WILL EXCEED 24 WHEN ALL SIDELOBE LOCATIONS ARE TAKEN INTO ACCOUNT &OR VERY LOW SIDELOBE ARRAYS IT IS REASONABLE TO ALLOW A FEW SIDELOBES TO EXCEED THE -33, VALUE BY AS MUCH AS TO D" TO ACCOUNT FOR RANDOM VARIATIONS 4HIS CAN BE SEEN FROM &IGURE AS THE DIFFERENCE BETWEEN 0 AND 0 OR 0 )F THIS ALLOWANCE IS NOT GRANTED THE ANTENNA WILL BE OVERDESIGNED )T IS WORTHWHILE TO DO SOME PROBABILITY CALCULATIONS BEFORE SPECIFYING THE EXACT SIDELOBE REQUIREMENTS
£Î°Î{
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£Î°ÈÊ +1 /</" Ê //F CONCERN HERE ARE ERRORS PECULIAR TO PHASED ARRAYS WHICH ARE DUE TO THE QUANTIZATION OF AMPLITUDE AND PHASE AND TO THE LOBES THAT OCCUR WHEN THESE ERRORS ARE REPEATED PERI ODICALLY 4HE EFFECT ON THE GAIN AND RADIATION PATTERN OF RANDOM ERRORS IN THE ANTENNA EXCITATION FUNCTION IS DISCUSSED IN 3ECTION 0HASE 1UANTIZATION 0HASE SHIFTERS SUITABLE FOR STEERING PHASED ARRAYS ARE DESCRIBED IN 3ECTION -OST OF THESE PHASE SHIFTERS ARE DIGITALLY CONTROLLED AND CAN BE SET WITH AN ACCURACY THAT IS A FUNCTION OF THE NUMBER OF BITS ! SMALL NUMBER OF BITS IS DESIRED FOR SIMPLICITY OF PHASE SHIFT COMPUTATION AND OPERATION FOR MINIMAL INSER TION LOSS IN THE CASE OF DIODE PHASE SHIFTERS AND FOR MINIMAL COST /N THE OTHER HAND A LARGE NUMBER OF BITS IS REQUIRED FOR BEST PERFORMANCE IN TERMS OF GAIN SIDELOBES AND BEAM POINTING ACCURACY 0HASE %RRORS 4HE PHASE OF A PHASE SHIFTER HAVING 0 BITS CAN BE SET TO THE DESIRED VALUE WITH A RESIDUAL ERROR
P 0 P 2-3 PHASE ERROR S F 0 0EAK PHASE ERROR A o
,OSS IN 'AIN !S DISCUSSED IN 3ECTION THE LOSS IN GAIN IS S F WHICH WITH %Q GIVES
$' y S F
P 0
7ITH MANY ARRAY ELEMENTS THIS RESULT IS STATISTICALLY INDEPENDENT OF THE AMPLITUDE DISTRIBUTION !N ENUMERATION OF %Q GIVES
.UMBER OF PHASE SHIFTER BITS 0 ,OSS IN GAIN $' D"
&ROM THE POINT OF VIEW OF GAIN THEREFORE OR BITS WOULD APPEAR AMPLE 2-3 3IDELOBES 0HASE QUANTIZATION DECREASES THE GAIN OF THE MAIN BEAM AS SHOWN ABOVE 4HE ENERGY THAT HAS BEEN LOST IS DISTRIBUTED TO THE SIDELOBES 4HE RESULT ING RMS SIDELOBES ARE THEREFORE S F RELATIVE TO THE GAIN OF A SINGLE ELEMENT AS SHOWN IN &IGURE "EAM 0OINTING !CCURACY 4HE ACCURATE DETERMINATION OF THE DIRECTION OF TARGETS IS MADE WITH THE MONOPULSE DIFFERENCE PATTERN 4HE ACCURACY OF THE NULL POSITION OF THE DIFFERENCE PATTERN IS THEREFORE OF INTEREST 7ITH QUANTIZED PHASE SHIFTERS THE POSITION OF THIS NULL CAN BE MOVED WITH A GRANULARITY THAT IS A FUNCTION OF THE BIT SIZE &OLLOWING THE ANALYSIS OF &RANK AND 2UZE &IGURE SHOWS AN APERTURE WITH AN EVEN NUMBER OF ELEMENTS . SEPARATED BY DISTANCES S !LL ELEMENTS ARE EXCITED WITH
0(!3%$ !22!9 2!$!2 !.4%..!3
£Î°Îx
&)'52% !NTISYMMETRICALLY PHASED ARRAY
EQUAL AMPLITUDE AND ANTISYMMETRIC PHASE TO GIVE A DIFFERENCE PATTERN 4HE STEERING INCREMENT IS SHOWN TO BE
DP
Q SCANNED . 0 "
0ERIODIC %RRORS 0ERIODIC !MPLITUDE AND 0HASE -ODULATION "OTH AMPLITUDE AND PHASE QUANTIZA TION LEAD TO DISCONTINUITIES THAT MAY BE PERIODIC AND GIVE RISE TO QUANTIZATION LOBES THAT ARE SIMILAR TO GRATING LOBES !MPLITUDE OR PHASE ERRORS THAT VARY COSINUSOIDALLY MAY BE ANALYZED SIMPLY AFTER "ROWN &IGURE A SHOWS AN ORIGINAL AMPLITUDE DISTRIBUTION &X DISTURBED BY A COSINUSOIDAL RIPPLE Q COS O XS GIVING A NEW DISTRIBUTION & ` X SUCH THAT & ` X & X Q& X COS & X
P X S
Q §& X E J P X S & X E J P X S ¶¸ ©
7HEN THE BEAM IS SCANNED TO P THE QUANTIZATION LOBES OCCUR AT AN ANGLE P WHERE SL 4HE GAIN OF THE APERTURE VARIES AS COS P AND THE RELATIVE AMPLITUDE OF THE QUANTI ZATION LOBE IS MODIFIED BY THE FACTOR COS P COS P &IGURE BnG SHOWS THE EFFECTS OF VARIOUS OTHER PERIODIC APERTURE MODULATIONS
SIN P SIN P o
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&)'52% %FFECTS OF PERIODIC AMPLITUDE AND PHASE MODULATION SIN P SIN P o K S
0HASE 3HIFTER 1UANTIZATION ,OBES 0EAK QUANTIZATION SIDELOBE VALUES ARE DERIVED BY -ILLER CONSIDERING THE ACTUAL APERTURE PHASE DISTRIBUTION &IGURE SHOWS THIS DISTRIBUTION FOR SOME SCAN ANGLE P AND THE RESULTING ERRORS DUE TO PHASE QUANTIZATION !LTHOUGH A CONTINUOUS CURVE HAS BEEN DRAWN ONLY POINTS CORRESPONDING TO INTEGRAL VALUES OF - ARE MEANINGFUL 4HE GREATEST PHASE QUANTIZATION LOBES SEEM TO OCCUR WITH A PHASE SLOPE SUCH THAT THE ELEMENTS ARE SPACED BY A DISTANCE EXACTLY ONE HALF OF THE PERIOD OR AN EXACT ODD MULTIPLE THEREOF 4HE PHASE ERROR UNDER THIS CONDITION HAS ELEMENT TO ELEMENT PHASE RIPPLES WITH A PEAK TO PEAK VALUE OF A P P 4HE VALUE OF THE PEAK PHASE QUANTIZATION LOBES FOR THE CASE SHOWN IN &IGURES F AND ARE GIVEN IN &IGURE !N EXAMINATION OF &IGURE SHOWS THAT PEAK PHASE QUANTIZATION LOBES ARE SIGNIFICANT AND ATTEMPTS SHOULD BE MADE TO REDUCE THEM 2EDUCTION OF 0EAK 0HASE 1UANTIZATION ,OBES -ILLER POINTS OUT THAT PEAK QUAN TIZATION LOBES CAN BE REDUCED BY DECORRELATING THE PHASE QUANTIZATION ERRORS 4HIS MAY BE DONE BY ADDING A CONSTANT PHASE SHIFT IN THE PATH TO EACH RADIATOR WITH A VALUE THAT DIFFERS FROM RADIATOR TO RADIATOR BY AMOUNTS THAT ARE UNRELATED TO THE BIT SIZE
0(!3%$ !22!9 2!$!2 !.4%..!3
&)'52% !PERTURE PHASE ERROR DUE TO PHASE QUANTIZATION FROM -ILLER
&)'52% 0EAK SIDELOBES DUE TO PHASE QUANTIZATION
£Î°ÎÇ
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4HE VARIABLE PHASE SHIFTER IS THEN PROGRAMMED TO ACCOUNT FOR THIS ADDITIONAL INSER TION PHASE 7ITH A SPHERICAL OR QUADRATIC LAW OF INSERTION PHASE VARIATION AS OBTAINED WITH OPTICAL FEED SYSTEMS 3ECTION THE REDUCTIONS IN PEAK QUANTIZATION LOBES ARE EQUIVALENT TO ADDING BIT TO THE PHASE SHIFTERS IN A ELEMENT ARRAY BITS IN A ELEMENT ARRAY AND BITS IN A ELEMENT ARRAY !MPLITUDE 1UANTIZATION 7HEN THE APERTURE OF A PHASED ARRAY IS DIVIDED INTO EQUAL SUBARRAYS THEN THE AMPLITUDE DISTRIBUTION ACROSS EACH SUBARRAY IS CONSTANT !PERTURE TAPER FOR THE ANTENNA IS APPROXIMATED BY CHANGING THE AMPLITUDE FROM SUBAR RAY TO SUBARRAY AND QUANTIZATION LOBES ARISE FROM THESE DISCONTINUITIES 4HE VALUE OF THESE LOBES MAY BE ESTIMATED FROM THE VARIOUS RESULTS SHOWN IN &IGURE OR ACTU ALLY COMPUTED BY SUMMING ALL CONTRIBUTIONS AT THE KNOWN QUANTIZATION GRATING LOBE ANGLES 4HE DISTRIBUTION BECOMES SMOOTHER AS THE NUMBER OF SUBARRAYS IS INCREASED OR AS THEY ARE INTERLACED
£Î°ÇÊ 7 /Ê"Ê*- Ê,,94HE PHENOMENON OF FOCUSING AN ARRAY IS THE RESULT OF THE ENERGY FROM EACH ELEMENT ADDING IN PHASE AT SOME DESIRED POINT WITHIN THE ANTENNA 7HEN ENERGY IS INCIDENT NORMAL TO THE ARRAY EACH ELEMENT RECEIVES THE SAME PHASE INDEPENDENT OF FREQUENCY 7HEN ENERGY IS INCIDENT FROM SOME ANGLE OTHER THAN NORMAL THE PHASE DIFFERENCE FROM THE PLANAR PHASE FRONT TO EACH ELEMENT IS A FUNCTION OF FREQUENCY AND MOST PHASED ARRAYS WITH PHASE SHIFTERS BECOME FREQUENCY DEPENDENT 4HIS SAME PHENOMENON CAN BE VIEWED IN THE TIME DOMAIN !S SHOWN IN &IGURE WHEN A PULSE OF ENERGY IS INCIDENT AT AN ANGLE OTHER THAN NORMAL THE ENERGY IS RECEIVED EARLIER AT ONE EDGE OF THE ARRAY THAN AT THE OTHER EDGE AND A PERIOD OF TIME MUST ELAPSE BEFORE ENERGY APPEARS IN ALL ELEMENTS 4HE CONCEPT OF APERTURE FILL TIME 4 ,C SIN P IS JUST ANOTHER WAY OF EXPLAINING THE BANDWIDTH OF A PHASED ARRAY 4HE BANDWIDTH OF PHASED ARRAYS IS DESCRIBED BY &RANK AS BEING COMPOSED OF TWO EFFECTS THE APERTURE EFFECT AND THE FEED EFFECT )N BOTH EFFECTS IT IS THE PATH LENGTH DIFFER ENCES THAT CONTRIBUTE TO THE BANDWIDTH SENSITIVITY OF A PHASED ARRAY &OR A PARALLEL FED
&)'52% !PERTURE FILL TIME PARALLEL FED ARRAY AFTER * &RANK Ú !RTECH (OUSE
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ARRAY EQUAL LINE LENGTH THE FEED NETWORK DOES NOT CONTRIBUTE TO A CHANGE IN PHASE WITH FREQUENCY AND SO ONLY THE APERTURE EFFECT REMAINS 4HIS WILL BE DISCUSSED FIRST AND THE EFFECT OF THE FEED WILL FOLLOW !PERTURE %FFECTS 7HEN ENERGY IS INCIDENT ON AN ARRAY AT AN ANGLE OTHER THAN BROADSIDE &IGURE THE PHASE REQUIRED ON THE EDGE ELEMENT IS X O , K SIN P .OTE THE K IN THE DENOMINATOR 4HIS INDICATES THAT THE REQUIRED PHASE IS FREQUENCY DEPENDENT )F FREQUENCY IS CHANGED AND THE PHASE SHIFTERS ARE NOT CHANGED THE BEAM WILL MOVE &OR AN EQUAL LINE LENGTH FEED THE BEAM SHAPE WILL BE UNDISTORTED IN SINE SPACE AND THE BEAM WILL MOVE TOWARD BROADSIDE AS THE FREQUENCY IS INCREASED )F THE PHASE SHIFTERS ARE REPLACED BY TIME DELAY NETWORKS THEN THE PHASE THROUGH THE TIME DELAY NETWORKS WILL CHANGE WITH FREQUENCY AND THE BEAM WILL REMAIN STATIONARY 7HEN PHASE SHIFT INDEPENDENT OF FREQUENCY IS USED TO STEER THE BEAM THE BEAM IS STEERED TO A DIRECTION P WITH A PHASE OF
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P X P X SIN P F SIN P C L
ON THE ELEMENT LOCATED A DISTANCE X FROM THE ARRAY CENTER !T FREQUENCY F THIS SAME PHASE SETTING STEERS THE BEAM TO A NEW DIRECTION P $P WHICH IS SHOWN IN &RANK TO BE
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!S THE FREQUENCY IS INCREASED THE BEAM SCANS TOWARD BROADSIDE BY AN ANGLE THAT IS INDEPENDENT OF THE APERTURE SIZE OR BEAMWIDTH (OWEVER THE PERMISSIBLE AMOUNT THAT THE BEAM MAY SCAN WITH FREQUENCY IS RELATED TO THE BEAMWIDTH BECAUSE PATTERN AND GAIN DETERIORATIONS ARE A FUNCTION OF THE FRACTIONAL BEAMWIDTH SCANNED 4HE ANGLE THAT THE BEAM ACTUALLY SCANS ON THE OTHER HAND IS RELATED TO THE PER CENTAGE BANDWIDTH ! BANDWIDTH FACTOR MAY THEREFORE BE DEFINED IN TERMS OF THE BROADSIDE BEAMWIDTH
"ANDWIDTH FACTOR +
BANDWIDTH BEAMWIDTH n
! REASONABLE CRITERION IS TO LIMIT THE BANDWIDTH SO THAT THE BEAM NEVER SCANS BY MORE THAN o ONE FOURTH OF A LOCAL BEAMWIDTH FREQUENCY IE
#RITERION
$P a P " SCANNED
7ITH A SCAN OF n THIS GIVES + AND IN TERMS OF BROADSIDE BEAMWIDTH THE LIMIT IS
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&OR EXAMPLE IF THE ARRAY HAS A BEAMWIDTH OF n THIS CRITERION PERMITS A CHANGE IN FREQUENCY PRIOR TO RESETTING THE PHASE SHIFTERS 4HIS ALLOWS THE BEAM TO MOVE FROM ONE FOURTH BEAMWIDTH ON ONE SIDE OF THE DESIRED DIRECTION TO ONE FOURTH BEAMWIDTH ON THE OTHER SIDE AS THE FREQUENCY CHANGES BY !T SMALLER SCAN ANGLES THE EFFECT IS REDUCED AS GIVEN BY %Q AND BROADER BAND OPERATION IS POSSIBLE
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4HE EXPLANATION GIVEN ABOVE APPLIES TO AN ANTENNA OPERATING AT A SINGLE #7 FRE QUENCY AND DESCRIBES HOW THE BEAM MOVES AS THIS FREQUENCY IS CHANGED (OWEVER MOST RADARS ARE PULSED AND RADIATE OVER A BAND OF FREQUENCIES &OR A BEAM SCANNED FROM BROADSIDE EACH SPECTRAL COMPONENT IS STEERED TO A SLIGHTLY DIFFERENT DIREC TION 4O DETERMINE THE COMPOSITE EFFECT OF THE COMPONENTS IT IS NECESSARY TO ADD THE FAR FIELD PATTERNS OF ALL SPECTRAL COMPONENTS 4HIS ANALYSIS HAS BEEN PERFORMED AND IT IS APPARENT THAT THE OVERALL ANTENNA GAIN OF THE PULSE WILL BE LESS THAN THAT OF A SINGLE SPECTRAL COMPONENT THAT HAS MAXIMUM GAIN IN THE DESIRED DIRECTION !S WITH THE #7 SITUATION THE GREATEST LOSS OCCURS AT THE MAXIMUM SCAN ANGLE WHICH IS ASSUMED TO BE n &OR THIS SITUATION THE CRITERION CHOSEN IS TO ALLOW A SPECTRUM THAT LOSES D" OF ENERGY ON TARGET DUE TO FREQUENCY SCANNED SPECTRAL COMPONENTS &OR A BEAM SCANNED TO n THIS BECOMES
"ANDWIDTH BEAMWIDTH n PULSE
.OTE THAT THIS IS TWICE THE BANDWIDTH PERMITTED FOR THE #7 SITUATION !NOTHER WAY OF ANALYZING THIS PHENOMENON IS IN TERMS OF APERTURE FILL TIME !S SHOWN IN &IGURE THE TIME IT TAKES TO FILL THE APERTURE WITH ENERGY IS
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7ITH A CHANGE IN FREQUENCY A NONDISPERSIVE TRANSMISSION LINE HAVING FREE SPACE PROPAGATION CHARACTERISTICS AND A LENGTH , EQUAL TO THE SIZE OF THE APERTURE THAT IT FEEDS WILL PRODUCE A LINEAR PHASE VARIATION ACROSS THE APERTURE WITH A MAXIMUM VALUE AT THE EDGES OF
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WHERE $F F IS THE FRACTIONAL CHANGE IN FREQUENCY 4HIS LINEAR PHASE PROGRESSION ACROSS THE APERTURE WILL SCAN THE BEAM BY
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&OR ONE DIRECTION OF SCANNING THIS EFFECT WILL ADD TO THE APERTURE EFFECT FOR THE OPPOSITE DIRECTION IT WILL TEND TO CANCEL THE APERTURE EFFECT )N A WAVEGUIDE WITH THE GUIDE WAVELENGTH DENOTED K G THE EFFECT IS MORE PRONOUNCED AND THE RESULTANT CHANGE IN BEAM POSITION IS
$P
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7HEN ANALYZING AN END FED SERIES FEED IT IS NECESSARY TO CONSIDER BOTH THE FEED EFFECT AND THE APERTURE EFFECT 4HE TOTAL FREQUENCY SCAN OF THIS FEED WILL BE
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#ENTER &ED 3ERIES &EED ! CENTER FED ARRAY &IGURE CAN BE CONSIDERED AS TWO END FEEDS %ACH FEED CONTROLS AN APERTURE THAT IS HALF THE TOTAL AND THEREFORE HAS TWICE THE BEAMWIDTH !S THE FREQUENCY IS CHANGED EACH HALF OF THE APERTURE SCANS IN THE OPPOSITE DIRECTION 4HIS INITIALLY CREATES A BROADER BEAM WITH REDUCED GAIN !S FREQUENCY CONTINUES TO CHANGE THE TWO BEAMS WILL EVENTUALLY SPLIT APART !T BROAD SIDE THE CENTER FED ANTENNA HAS POORER PERFORMANCE THAN A PARALLEL FEED SINCE EACH HALF SCANS (OWEVER AT n SCAN THE COMPENSATION ON ONE HALF OF THE ARRAY ASSISTS IN KEEPING THE GAIN COMPARABLE TO THAT OF A PARALLEL FEED &ROM THE VIEWPOINT OF GAIN REDUCTION THE CRITERION FOR A CENTER FED ARRAY IS
"ANDWIDTH
L BEAMWIDTH n #7 LG
WHERE KG IS THE WAVEGUIDE WAVELENGTH (OWEVER FROM THE VIEWPOINT OF SIDELOBES THIS CRITERION MAY BE UNACCEPTABLE &OR A LOW SIDELOBE DESIGN EITHER #7 OR PULSED THE SIDELOBES FOR THIS FEED SHOULD BE CAL CULATED BECAUSE A CHANGE IN FREQUENCY NO LONGER PRODUCES A TRANSLATED BEAM BUT RATHER A BROADER BEAM COMPOSED OF TWO TRANSLATED BEAMS 3PACE &EED 4HE SPACE OPTICAL FEED CAN BE CONSIDERED TO BE SOMEWHAT BETWEEN A PARALLEL FEED AND A CENTER FED SERIES FEED 7ITH A VERY LONG FOCAL LENGTH THE SPACE FEED APPROXIMATES A PARALLEL FEED 7ITH A VERY SHORT FOCAL LENGTH IT APPROXIMATES A
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"ANDWIDTH BANDWIDTH n #7
4ABLE SUMMARIZES THE BANDWIDTH CRITERIA FOR THE VARIOUS FEED NETWORKS "OTH THE #7 CRITERION AND THE COMPARABLE PULSE CRITERION ARE GIVEN "ROAD )NSTANTANEOUS "ANDWIDTH &OR A STATIONARY BEAM IN SPACE INDEPENDENT OF FREQUENCY IT IS NECESSARY TO USE TIME DELAY RATHER THAN PHASE STEERING )T IS NOT PRACTICAL TO PROVIDE A TIME DELAY NETWORK AT EACH ELEMENT IN A PHASED ARRAY BECAUSE 4!",% "ANDWIDTH #RITERIA FOR 3EVERAL &EED .ETWORKS
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THESE NETWORKS ARE EXPENSIVE AND LOSSY AND CONTAIN ERRORS !N ALTERNATIVE IS TO USE A BROADBAND BEAM SWITCHING TECHNIQUE SUCH AS THE EQUAL LINE LENGTH "LASS MATRIX OR A 2OTMAN LENS &OR $ SCANNING THESE TECHNIQUES BECOME QUITE COMPLEX !NOTHER TECHNIQUE FOR IMPROVING THE BANDWIDTH BY A CONSIDERABLE FACTOR IS TO USE AN ARRAY OF SUBARRAYS 4HE RADIATING ELEMENTS OF A PHASED ARRAY MAY BE GROUPED INTO SUBAR RAYS WHERE TIME DELAY ELEMENTS ARE ADDED 4HIS IS SHOWN IN &IGURE 4HE ANTENNA MAY BE REGARDED AS AN ARRAY OF SUBARRAYS 4HE SUBARRAY PATTERN FORMS THE ELEMENT FAC TOR IT IS STEERED BY PHASE SHIFTERS IN THE DESIRED DIRECTION BUT IT SCANS WITH FREQUENCY AS INDICATED BY %Q 4HE ARRAY FACTOR IS SCANNED BY ADJUSTING THE FREQUENCY INDEPENDENT TIME DELAY ELEMENTS !LL SUBARRAYS ARE STEERED IN THE SAME MANNER 4HE TOTAL RADIATION PATTERN IS THE PRODUCT OF THE ARRAY FACTOR AND THE ELEMENT FACTOR ! CHANGE IN FREQUENCY GIVES RISE TO GRATING LOBES RATHER THAN SHIFTS OF THE BEAM POSITION 4HIS CAN BE SEEN FROM &IGURE 4HE SUBARRAY PATTERN IS SHOWN AT THE DESIGN FREQUENCY F AND IS SEEN TO HAVE A NULL AT THE POSITION OF THE GRATING LOBE !S FREQUENCY IS CHANGED BY C F THE PATTERN IS SCANNED )T IS SHOWN DASHED IN A POSITION WHERE IT HAS BEEN SCANNED BY A LITTLE MORE THAN HALF OF ITS BEAMWIDTH 4HIS IS CLEARLY TOO MUCH FOR THE PRODUCT OF ARRAY AND ELEMENT FACTORS GIVES TWO BEAMS OF EQUAL AMPLITUDE 4HE LOSS IN GAIN AND THE MAGNITUDE OF THE GRATING LOBE ARE FUNCTIONS OF THE FRACTIONAL SUBARRAY BEAMWIDTH THAT HAS BEEN SCANNED AS A RESULT OF THE CHANGE IN FREQUENCY 4HE RESULTS MAY BE EXPRESSED IN TERMS OF THE BANDWIDTH FACTOR + REFERRED TO AS THE SUBARRAY BROADSIDE BEAMWIDTH &IGURE SHOWS THESE VALUES AS FUNCTIONS OF + FOR A SCAN OF n 4HE VALUE PREVIOUSLY USED FOR SCANNING n WAS + AND THIS VALUE APPEARS ACCEPTABLE HERE WHERE THE RELEVANT BEAMWIDTH IS THE BROADSIDE BEAMWIDTH OF THE SUBARRAY 4HUS IF THE APERTURE IS SPLIT INTO . SUBARRAYS IN ONE PLANE WITH TIME DELAY NETWORKS AT EACH SUBARRAY LEVEL THE BANDWIDTH IS INCREASED BY A FACTOR OF . 4HIS SAME BANDWIDTH CRITERION LEADS TO A REDUCTION IN GAIN OF ABOUT D" AND A GRATING LOBE OF ABOUT D" AT THE EDGES OF THE BAND WITH n OF SCAN )NTERLACING OF SUBARRAYS CAN REDUCE THE GRATING LOBES
&)'52% 0HASED ARRAY USING SUBARRAYS WITH TIME DELAY
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4HE MONOPULSE NULL POSITION IS UNAFFECTED BY THE BEHAVIOR OF THE SUBARRAYS AS LONG AS THEY ALL RESPOND IN THE SAME WAY 4HE NULL POSITION IS DETERMINED ONLY BY THE TIME DELAY NETWORKS BEHIND THE SUBARRAY AND CORRESPONDS TO THE ARRAY FACTOR NULL WHICH IS UNAFFECTED WHEN MULTIPLIED BY THE SUBARRAY PATTERN 4IME $ELAY .ETWORKS &IGURE A SHOWS A TIME DELAY NETWORK THAT IS DIGI TALLY CONTROLLED BY SWITCHES 4HE TOTAL DELAY PATH LENGTH THAT HAS TO BE PROVIDED NON DISPERSIVELY AMOUNTS TO , SIN PMAX WHERE PMAX IS THE MAXIMUM SCAN ANGLE FOR THE APERTURE , 4HE SMALLEST BIT SIZE IS ABOUT K OR K WITH THE PRECISE SETTING ADJUSTED BY
&)'52% ,OSS OF GAIN AND GRATING LOBE AMPLITUDE AS FUNCTIONS OF BANDWIDTH PHASED SUBARRAYS WITH TIME DELAY SCANNED n 4HE VALUE OF THE GRATING LOBE WILL BE MODIFIED BY THE ELEMENT PATTERN
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AN ADDITIONAL VARIABLE PHASE SHIFTER ! n BEAM SCANNED n FOR EXAMPLE REQUIRES A TIME DELAY OF BITS THE LARGEST BEING WAVELENGTHS AS WELL AS AN ADDITIONAL PHASE SHIFTER 4HE TOLERANCES ARE TIGHT AMOUNTING IN THIS CASE TO A FEW DEGREES OUT OF ABOUT AND ARE DIFFICULT TO MEET 0ROBLEMS MAY BE DUE TO LEAKAGE PAST THE SWITCH TO A DIFFERENCE IN INSERTION LOSS BETWEEN THE ALTERNATE PATHS TO SMALL MISMATCHES AT THE VARIOUS JUNCTIONS TO VARIATIONS IN TEMPERATURE OR TO THE DISPERSIVE CHARACTERISTICS OF SOME OF THE COMPONENTS 0AINSTAKING DESIGN IS NECESSARY 4HE SWITCHES MAY BE DIODES OR CIRCULATORS ,EAKAGE PAST THE SWITCHES MAY BE REDUCED BY ADDING ANOTHER SWITCH IN SERIES IN EACH LINE 4HE DIFFERENCE IN INSERTION LOSS BETWEEN THE TWO PATHS MAY BE EQUALIZED BY PADDING THE SHORTER ARM 4HE VARIOUS PROBLEMS HAVE BEEN COMPREHEN SIVELY ASSESSED AND ANALYZED BY ,INCOLN ,ABORATORY /N TRANSMITTING THE TOLERANCES ARE LESS SEVERE BECAUSE THE REQUIREMENTS ARE USUALLY FOR POWER ON TARGET RATHER THAN FOR ACCURATE ANGLE DETERMINATION OR LOW SIDELOBES &IGURE B SHOWS ANOTHER CONFIGURATION THAT HAS THE ADVANTAGE OF SIMPLICITY %ACH OF THE SWITCHABLE CIRCULATORS CONNECTS EITHER DIRECTLY ACROSS COUNTERCLOCKWISE OR VIA THE SHORT CIRCUITED LENGTH )SOLATION IN EXCESS OF D" IS REQUIRED )T IS CLEAR THAT THE INSERTION LOSS OF TIME DELAY CIRCUITS IS VERY HIGH FOR MOST PRACTICAL SYSTEMS 4HEY WOULD THEREFORE PRECEDE A FINAL POWER AMPLIFIER FOR TRANSMITTING AND FOLLOW A PREAMPLIFIER FOR RECEIVING ! FURTHER METHOD OF PROVIDING DELAY IS POSSIBLE BY TRANSLATING THE PROBLEM FROM THE MICROWAVE DOMAIN AND DELAYING AT )&
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Ê /7", -Ê ", ,-® /PTICAL &EED 3YSTEMS 0HASED ARRAYS MAY BE IN THE FORM OF LENS ARRAYS OR REFLEC TARRAYS AS SHOWN IN &IGURE WHERE AN OPTICAL FEED SYSTEM PROVIDES THE PROPER APERTURE ILLUMINATION 4HE LENS HAS INPUT AND OUTPUT RADIATORS COUPLED BY PHASE SHIFT ERS "OTH SURFACES OF THE LENS REQUIRE MATCHING 4HE PRIMARY FEED SHOULD BE DESIGNED WITH CARE AND CAN BE COMPLEX TO GIVE THE DESIRED APERTURE AMPLITUDE DISTRIBUTION WITH LOW SPILLOVER LOSSES 4HE TRANSMITTER FEED CAN BE SEPARATED FROM THE RECEIVER FEED BY AN ANGLE @ AS SHOWN IN &IGURE 4HE PHASE SHIFTERS ARE THEN RESET BETWEEN TRANS MITTING AND RECEIVING SO THAT IN BOTH CASES THE BEAM POINTS IN THE SAME DIRECTION 4HIS METHOD ALLOWS FLEXIBILITY IN OPTIMIZING THE TRANSMITTER APERTURE DISTRIBUTION PERHAPS FOR MAXIMUM POWER ON THE TARGET AND SEPARATELY OPTIMIZING THE RECEIVER SUM AND DIFFERENCE PATTERNS FOR LOW SIDELOBES 3INCE A CHANGE IN FEED POSITION CORRESPONDS TO SCANNING WITH TIME DELAY ADDITIONAL FEEDS MAY BE ADDED TO PROVIDE SEVERAL TIME DELAY COMPENSATED DIRECTIONS OF SCAN FOR A CORRESPONDING INCREASE IN BANDWIDTH 4HE PHASING OF THE ANTENNA HAS TO INCLUDE A CORRECTION FOR THE SPHERICAL PHASE FRONT 4HIS CAN BE SEEN &IGURE A TO AMOUNT TO
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7ITH A SUFFICIENTLY LARGE FOCAL LENGTH THE SPHERICAL PHASE FRONT MAY BE APPROXI MATED BY THAT OF TWO CROSSED CYLINDERS PERMITTING THE CORRECTION TO BE APPLIED SIMPLY WITH ROW AND COLUMN STEERING COMMANDS #ORRECTION OF A SPHERICAL PHASE FRONT WITH THE PHASE SHIFTERS REDUCES PEAK PHASE QUANTIZATION LOBES 3ECTION 3PACE PROBLEMS MAY BE ENCOUNTERED IN ASSEMBLING AN ACTUAL SYSTEM ESPECIALLY AT HIGHER FREQUENCIES BECAUSE ALL CONTROL CIRCUITS HAVE TO BE BROUGHT OUT AT THE SIDE OF THE APERTURE OF THE LENS ARRAY -ULTIPLE BEAMS MAY BE GENERATED BY ADDING FURTHER PRIMARY FEEDS !LL THE BEAMS WILL BE SCANNED SIMULTANEOUSLY BY EQUAL AMOUNTS IN SIN P 4HE REFLECTARRAY SHOWN IN &IGURE B HAS GENERAL CHARACTERISTICS SIMILAR TO THOSE OF THE LENS (OWEVER THE SAME RADIATING ELEMENT COLLECTS AND RADIATES AFTER REFLECTION !MPLE SPACE FOR PHASE SHIFTER CONTROL CIRCUITS EXISTS BEHIND THE REFLECTOR 4O AVOID APERTURE BLOCKING THE PRIMARY FEED MAY BE OFFSET AS SHOWN !S BEFORE TRANSMITTING AND RECEIVING FEEDS MAY BE SEPARATED -ULTIPLE BEAMS ARE AGAIN POSSIBLE WITH ADDI TIONAL FEEDS 4HE PHASE SHIFTER MUST BE RECIPROCAL SO THAT THERE IS A NET CONTROLLABLE PHASE SHIFT AFTER PASSING THROUGH THE DEVICE IN BOTH DIRECTIONS 4HIS RULES OUT FREQUENTLY USED NONRECIPROCAL FERRITE OR GARNET PHASE SHIFTERS #ONSTRAINED &EEDS 4HE OPTICAL FEED SYSTEM DIVIDES POWER VERY SIMPLY IN ONE STEP FROM THE FEED TO THE MANY ELEMENTS ON THE APERTURE )N CONTRAST THE CONSTRAINED FEED SYSTEM USES MANY STEPS &OR A HIGH PERFORMANCE LOW SIDELOBE SYSTEM EACH OF THESE POWER DIVIDING STEPS HAS TO BE WELL MATCHED OVER THE BAND )F MISMATCHES ARE PRESENT THEY WILL BE SEPARATED BY MANY WAVELENGTHS AND WILL ADD UP TO GIVE FREQUENCY SENSITIVE PHASE AND AMPLITUDE PERTURBATIONS AT THE APERTURE )N GENERAL THESE PERTURBATIONS WILL BE DIFFERENT FOR THE MONOPULSE SUM AND DIFFERENCE PATTERNS SO THAT ONLY A COMMON AVERAGE CAN BE COMPENSATED BY CALIBRATION
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&)'52% /PTICAL FEED SYSTEMS A LENS ARRAY AND B REFLECTARRAY
3ERIES &EEDS &IGURE SHOWS SEVERAL TYPES OF SERIES FEEDS )N ALL CASES EXCEPT D THE ELECTRICAL PATH LENGTH TO EACH RADIATING ELEMENT HAS TO BE COMPUTED AS A FUNCTION OF FREQUENCY AND TAKEN INTO ACCOUNT WHEN SETTING THE PHASE SHIFTERS 4YPE A IS AN END FED ARRAY )T IS FREQUENCY SENSITIVE AND LEADS TO MORE SEVERE BANDWIDTH RESTRICTIONS THAN MOST OTHER FEEDS 4YPE B IS CENTER FED AND HAS ALMOST THE SAME BANDWIDTHS AS A
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PARALLEL FEED NETWORK 3UM AND DIFFERENCE PATTERN OUTPUTS ARE AVAILABLE BUT THEY HAVE CONTRADICTORY REQUIREMENTS FOR OPTIMUM AMPLITUDE DISTRIBUTIONS THAT CANNOT BOTH BE SATISFIED !S A RESULT EITHER GOOD SUM OR GOOD DIFFERENCE PATTERNS CAN BE OBTAINED !T THE COST OF SOME ADDITIONAL COMPLEXITY THE DIFFICULTLY CAN BE OVERCOME BY THE METHOD SHOWN IN &IGURE C 4WO SEPARATE CENTER FED FEED LINES ARE USED AND COMBINED IN A NETWORK TO GIVE SUM AND DIFFERENCE PATTERN OUTPUTS )NDEPENDENT CONTROL OF THE TWO AMPLITUDE DISTRIBUTIONS IS POSSIBLE &OR EFFICIENT OPERATION THE TWO FEED LINES REQUIRE DISTRIBUTIONS THAT ARE ORTHOGONAL THAT IS THAT GIVE RISE TO PATTERNS WHERE THE PEAK VALUE OF ONE COINCIDES WITH A NULL FROM THE OTHER AND APERTURE DISTRIBUTIONS ARE RESPECTIVELY EVEN AND ODD ! VERY WIDEBAND SERIES FEED WITH EQUAL PATH LENGTHS IS SHOWN IN &IGURE D )F THE BANDWIDTH IS ALREADY RESTRICTED BY PHASE SCANNING THEN VERY LITTLE ADVAN TAGE IS OBTAINED AT THE COST OF A CONSIDERABLE INCREASE IN SIZE AND WEIGHT 4HE NETWORK IN &IGURE E GIVES SIMPLICITY IN PROGRAMMING BECAUSE EACH PHASE SHIFTER REQUIRES THE SAME SETTING 4HE INSERTION LOSS INCREASES FOR SUCCESSIVE RADIA TORS AND THE TOLERANCES REQUIRED FOR SETTING THE PHASES ARE HIGH 4HIS TYPE IS NOT COMMONLY USED 0ARALLEL &EEDS &IGURE SHOWS A NUMBER OF PARALLEL FEED SYSTEMS 4HEY FREQUENTLY COMBINE A NUMBER OF RADIATORS INTO SUBARRAYS AND THE SUBARRAYS ARE THEN COMBINED IN SERIES OR IN PARALLEL TO FORM SUM AND DIFFERENCE PATTERNS &IGURE A SHOWS A MATCHED CORPORATE FEED WHICH IS ASSEMBLED FROM MATCHED HYBRIDS 4HE OUT OF PHASE COMPONENTS OF MISMATCH REFLECTIONS FROM THE APERTURE AND OF OTHER UNBALANCED REFLECTIONS ARE ABSORBED IN THE TERMINATIONS 4HE IN PHASE AND
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&)'52% 0ARALLEL FEED NETWORKS
BALANCED COMPONENTS ARE RETURNED TO THE INPUT 4O BREAK UP PERIODICITY AND REDUCE PEAK QUANTIZATION LOBES 3ECTION SMALL ADDITIONAL FIXED PHASE SHIFTS MAY BE INTRODUCED IN THE INDIVIDUAL LINES AND COMPENSATED BY CORRESPONDING READJUSTMENTS OF THE PHASE SHIFTERS 4HE REACTIVE FEED NETWORK SHOWN IN &IGURE B IS SIMPLER THAN THE MATCHED CONFIGURATION )T HAS THE DISADVANTAGE OF NOT TERMINATING UNBALANCED REFLECTIONS THAT ARE LIKELY TO BE AT LEAST PARTLY RERADIATED AND THUS CONTRIBUTE TO THE SIDELOBES ! STRIPLINE POWER DIVIDER IS SHOWN IN &IGURE C AND A CONSTRAINED OPTICAL POWER DIVIDER USING AN ELECTROMAGNETIC LENS IS SHOWN IN &IGURE D 4HE LENS MAY BE OMITTED AND THE CORRECTION APPLIED AT THE PHASE SHIFTERS 7ITH NONRECIPROCAL PHASE SHIFTERS A FRACTION OF THE POWER REFLECTED FROM THE APERTURE WILL THEN BE RERADIATED AS SIDELOBES RATHER THAN RETURNED TO THE INPUT 4HE AMPLITUDE DISTRIBUTION ACROSS THE HORN IS GIVEN BY THE WAVEGUIDE MODE )T IS CONSTANT WITH AN % PLANE HORN AS SHOWN 3UBARRAYS 4HE PHASED ARRAY APERTURE MAY BE DIVIDED INTO SUBARRAYS ALL SIMILAR TO SIMPLIFY MANUFACTURING AND ASSEMBLY "EAMFORMING NOW REQUIRES COM BINING THE SUBARRAYS FOR SUITABLE SUM AND DIFFERENCE PATTERNS &IGURE A SHOWS A METHOD OF COMBINING OPPOSITE SUBARRAYS INTO THEIR SUMS AND DIFFERENCES !LL SUM CHANNELS ARE THEN ADDED WITH PROPER WEIGHTING TO OBTAIN THE DESIRED AMPLI TUDE DISTRIBUTION 4HE DIFFERENCE CHANNELS ARE TREATED SIMILARLY WITH INDEPENDENT AMPLITUDE WEIGHTING 4HIS METHOD MAY BE EXTENDED TO INCLUDE COMBINATIONS IN THE OTHER PLANE !MPLIFICATION ON RECEIVING OR ON BOTH RECEIVING AND TRANSMITTING MAY BE CON VENIENT AT THE SUBARRAY LEVEL /N RECEIVING THE NOISE FIGURE IS ESTABLISHED BY THE
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&)'52% #OMBINATION OF SUBARRAYS TO FORM SUM AND DIFFERENCE CHANNELS A COMBINING OPPOSITE SUBARRAYS AND B COMBINING SUBARRAYS AFTER AMPLIFICATION
PREAMPLIFIER SO THAT FURTHER PROCESSING MAY INCLUDE LOSSY CIRCUITS 4HE RECEIVING CHANNEL MAY BE SPLIT THREE WAYS AS INDICATED IN &IGURE B INTO THE SUM AND THE ELEVATION AND AZIMUTH DIFFERENCE CHANNELS 4HESE ARE THEN WEIGHTED AND SUMMED WITH CORRESPONDING OUTPUTS FROM THE OTHER SUBARRAYS /N TRANSMITTING ALL SEPARATE POWER AMPLIFIERS MAY BE ENERGIZED EQUALLY TO GIVE MAXIMUM POWER ON THE TARGET 4HE ADDITION OF PHASE SHIFTERS SHOWN AT THE SUBARRAY LEVEL SIMPLIFIES THE BEAM STEERING COMPUTATION PERMITTING ALL SUBARRAYS TO RECEIVE IDENTICAL STEERING COM MANDS 4HEY MAY BE REPLACED BY TIME DELAY CIRCUITS GIVING A WIDE INSTANTANEOUS BANDWIDTH 3ECTION 4HE SIMPLE METHOD OF PROVIDING 42 TRANSMIT RECEIVE SWITCHING CAN BE OBTAINED BY COMBINING TWO HALVES OF A SUBARRAY WITH A FOUR PORT HYBRID JUNCTION 4HE TRANSMIT TER INPUT INTO ONE PORT ENERGIZES BOTH HALVES OF THE APERTURE FOR EXAMPLE IN PHASE 4HE RECEIVER CONNECTED TO THE REMAINING PORT THEN REQUIRES THAT THE PHASE SHIFTERS OF HALF THE APERTURE GIVE AN ADDITIONAL PHASE SHIFT OF O DURING THE RECEIVING PERIOD 4HIS IS EASILY PROGRAMMED -ULTIPLE RECEIVE BEAMS MAY BE FORMED BY COMBINING THE SUBARRAYS AFTER AMPLIFICA TION IN AS MANY DIFFERENT WAYS AS SEPARATE BEAMS ARE REQUIRED 4HE LIMITATION IS THAT THE BEAMS HAVE TO LIE WITHIN THE BEAMWIDTH OF THE SUBARRAY IN ORDER TO AVOID EXCESSIVE GRATING LOBES ! CLUSTER OF SUCH SIMULTANEOUS RECEIVER BEAMS REQUIRES A WIDER TRANS MITTER BEAM 4HIS MAY BE OBTAINED EFFICIENTLY FROM THE SAME ANTENNA WITH A GABLED OR SPHERICAL PHASE DISTRIBUTION 7ITH IDENTICAL SUBARRAYS A DESIRED APERTURE AMPLITUDE TAPER FOR LOW SIDELOBES IS APPLIED WITH A GRANULARITY THAT DEPENDS ON THEIR SIZE AND SHAPE 4HE RESULTING AMPLI TUDE STEPS WILL CAUSE QUANTIZATION LOBES 3ECTION
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£Î°Ê *- Ê-/ ,4HE THREE BASIC TECHNIQUES FOR ELECTRONIC BEAM STEERING ARE FREQUENCY SCANNING BEAM SWITCHING AND PHASE SCANNING WITH PHASE SHIFTERS /F THE THREE TECH NIQUES THE USE OF PHASE SHIFTERS IS BY FAR THE MOST POPULAR AND CONSIDERABLE EFFORT HAS GONE INTO THE DEVELOPMENT OF A VARIETY OF PHASE SHIFTERS 0HASE SHIFTERS CAN BE SEPA RATED INTO TWO CATEGORIES RECIPROCAL AND NONRECIPROCAL 4HE RECIPROCAL PHASE SHIFTER IS NOT DIRECTIONALLY SENSITIVE 4HAT IS THE PHASE SHIFT IN ONE DIRECTION EG TRANSMIT IS THE SAME AS THE PHASE SHIFT IN THE OPPOSITE DIRECTION EG RECEIVE 4HEREFORE IF RECIPROCAL PHASE SHIFTERS ARE USED IT IS NOT NECESSARY TO SWITCH PHASE STATES BETWEEN TRANSMIT AND RECEIVE 7ITH A NONRECIPROCAL PHASE SHIFTER IT IS NECESSARY TO SWITCH THE PHASE SHIFTER IE CHANGE PHASE STATE BETWEEN TRANSMIT AND RECEIVE 4YPICALLY IT TAKES A FEW MICROSECONDS TO SWITCH NONRECIPROCAL FERRITE PHASE SHIFTERS $URING THIS TIME THE RADAR IS UNABLE TO DETECT TARGETS &OR LOW PULSE REPETITION FREQUENCY 02& RADARS ;EG TO PULSES PER SECOND PPS = THIS MAY NOT CAUSE A PROBLEM &OR EXAMPLE IF THE 02& IS PPS OR (Z THE TIME BETWEEN PULSES IS MS )F THE SWITCHING TIME FOR THE PHASE SHIFTER IS MS ONLY OF THE TIME IS WASTED AND LESS THAN NMI OF MINI MUM RANGE IS LOST /N THE OTHER HAND IF THE 02& K(Z THE TIME BETWEEN PULSES IS MS AND IT WOULD NOT BE POSSIBLE TO TOLERATE MS OF DEAD TIME FOR THE SWITCHING OF PHASE SHIFTERS !LL DIODE PHASE SHIFTERS ARE RECIPROCAL ALONG WITH CERTAIN TYPES OF FERRITE PHASE SHIFTERS )T IS WORTH NOTING THAT OWING TO LOSSES ASSOCIATED WITH THEIR MAGNETIC PROPER TIES FERRITE PHASE SHIFTERS ARE ALMOST NEVER USED AT FREQUENCIES BELOW '(Z $IODE PHASE SHIFTERS IN CONTRAST IMPROVE AS THE FREQUENCY GETS LOWER 4HERE ARE THREE BASIC TYPES OF PHASE SHIFTERS THAT TYPICALLY COMPETE FOR USE IN A PHASED ARRAY 4HEY ARE THE DIODE PHASE SHIFTER THE NONRECIPROCAL FERRITE PHASE SHIFTER AND THE RECIPROCAL DUAL MODE FERRITE PHASE SHIFTER %ACH HAS ITS STRENGTHS AND THE CHOICE OF WHICH TO USE IS HIGHLY DEPENDENT ON THE RADAR REQUIREMENTS %ACH WILL BE DISCUSSED IN TURN &OR SOLID STATE SYSTEMS DIODES ARE USED AND CAN BE SWITCHED IN A FRACTION OF A MICROSECOND $IODE 0HASE 3HIFTERS n $IODE PHASE SHIFTERS ARE TYPICALLY DESIGNED BY USING ONE OF THREE TECHNIQUES SWITCHED LINE HYBRID COUPLED AND LOADED LINE 4HESE ARE SHOWN DIAGRAMMATICALLY IN &IGURE 4HE SWITCHED LINE TECHNIQUE SIM PLY SWITCHES IN LENGTHS OF LINE IN BINARY INCREMENTS EG n n AND n AND REQUIRES A SET OF DIODES FOR EACH BIT 4HE DIODES ARE USED AS SWITCHES TO CONTROL WHICH BITS ARE ACTIVATED TO ACHIEVE A PARTICULAR PHASE STATE 4HE HYBRID COUPLED TECHNIQUE USES A MICROWAVE HYBRID AND EFFECTIVELY CHANGES THE DISTANCE AT WHICH THE REFLECTION TAKES PLACE 4HIS TECHNIQUE IS USUALLY USED IN BINARY INCREMENTS AND AN ADDITIONAL SET OF DIODES IS REQUIRED FOR EACH PHASE STATE 4HE DIODE PHASE SHIFTERS DESCRIBED ABOVE ARE LIMITED IN THEIR ABILITY TO HANDLE HIGH PEAK POWER $EPENDING ON THEIR SIZE AND FREQUENCY THEY ARE NORMALLY RESTRICTED TO POWER LEVELS OF LESS THAN K7 &OR HIGHER POWER LEVELS THE LOADED LINE TECHNIQUE IS USED 4HE DIODES ARE USED TO SWITCH IN INCREMENTS OF CAPACITANCE AND INDUCTANCE THAT PROVIDE SMALL CHANGES IN PHASE "ECAUSE THE DIODES ARE DECOUPLED FROM THE MAIN TRANSMISSION LINE THEY NEED TO HANDLE ONLY MODEST AMOUNTS OF POWER IN EACH DIODE 6ERY HIGH POWER IE KILOWATT CONFIGURATIONS ARE POSSIBLE 4HE TECHNIQUE DOES REQUIRE MANY DIODES AND THE PHASE SHIFTERS ARE TYPICALLY LARGE AND BULKY AS COMPARED WITH THE SWITCHED LINE AND HYBRID COUPLED TECHNIQUES
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&)'52% $IODE PHASE SHIFTER CONFIGURATIONS AFTER , 3TARK ET AL A SWITCHED LINE PHASE BIT B HYBRID COUPLED PHASE BIT AND C LOADED LINE PHASE BIT
$IODE PHASE SHIFTERS HAVE THE ADVANTAGE OF BEING SMALL AND LIGHT IN WEIGHT EXCEPT FOR HIGH POWER DEVICES 4HEY ARE SUITABLE FOR STRIPLINE MICROSTRIP AND MONOLITHIC CONFIGURATIONS 4HE MAIN DISADVANTAGE OF THE DIODE PHASE SHIFTER IS THAT AN ADDITIONAL SET OF DIODES IS NORMALLY REQUIRED FOR EACH ADDITIONAL BIT !S LOWER SIDELOBE ANTENNAS ARE REQUIRED THE NUMBER OF BITS INCREASES &OR LOW SIDELOBE ANTENNAS OR BITS MAY BE REQUIRED !S THE NUMBER OF BITS INCREASES BOTH COST AND LOSS OF THE DIODE PHASE SHIFTERS ARE ALSO INCREASED &OR ACTIVE ARRAYS THE PHASE SHIFTER LOSSES ARE NOT OF SIGNIFICANCE BECAUSE THEY OCCUR PRIOR TO THE POWER AMPLIFIER ON TRANSMIT AND AFTER THE LOW NOISE AMPLIFIER ON RECEIVE 4HIS IS NOT THE CASE WITH MOST FERRITE DEVICES &ERRITE 0HASE 3HIFTERS -OST FERRITE PHASE SHIFTERS ARE NONRECIPROCAL n AND THEIR EARLY VERSIONS USED DISCRETE LENGTHS OF FERRITE AS SHOWN IN &IGURE TO IMPLEMENT EACH OF THE BITS n n n ETC )N THIS CONFIGURATION A CUR RENT PULSE IS PASSED THROUGH EACH BIT AND THE FERRITE TOROID IS SATURATED 7HEN THE CURRENT IS REMOVED THE FERRITE TOROID IS SAID TO BE LATCHED AND RETAINS ITS MAGNETIZATION OWING TO ITS HYSTERESIS PROPERTIES )F THE CURRENT IS IN A FORWARD DIRECTION THE FER RITE IS LATCHED WITH A PARTICULAR PHASE EG n 4HE FERRITE MAINTAINS THE PHASE UNTIL A CURRENT PULSE IN THE OPPOSITE DIREC TION IS APPLIED 4HE FERRITE PHASE SHIFTER IS THEN LATCHED TO THE REFERENCE PHASE n 4HIS CHANGE IN PHASE WITH A CHANGE IN CUR RENT DIRECTION IS DUE TO THE NONRECIPROCAL NATURE OF THE DEVICE !S MENTIONED EARLY DEVICES SATURATED EACH BIT SO THAT A FERRITE &)'52% $IGITAL FERRITE PHASE SHIFTER USING TOROID AND ELECTRONIC DRIVER WERE REQUIRED TOROIDS AFTER , 3TARK
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TO CONTROL EACH BIT INDIVIDUALLY /THER PHASE SHIFTERS USE A SINGLE TOROID AND A SINGLE DRIVER )N THIS CONFIGURATION THE PHASE SHIFTER IS LATCHED ON A MINOR HYSTERESIS LOOP BY ONLY PARTIALLY MAGNETIZING THE FERRITE 4HE DISTINCT ADVANTAGE OF THIS TECHNIQUE IS THAT ANY NUMBER OF BITS MAY BE IMPLEMENTED WHILE USING ONLY A SINGLE TOROID 4HEY HAVE THE ADVANTAGE OF LOW LOSS AND RELATIVELY HIGH POWER OPERATION $EVICES THAT HAN DLE UP TO K7 OF PEAK POWER HAVE BEEN BUILT 4HEY ARE AMENABLE TO WAVEGUIDE CONSTRUCTION AND ARE HEAVIER AND BULKIER THAN COMPARABLE DIODE DEVICES )N SUMMARY DIODES AND NONRECIPROCAL FERRITE PHASE SHIFTERS ARE VIABLE COMPETITORS !T , BAND AND LOWER DIODE PHASE SHIFTERS ARE AN OBVIOUS CHOICE !T 3 BAND AND HIGHER FERRITES SHOULD CONTINUE TO HOLD AN EDGE IN HIGHER POWER SYSTEMS AND WHERE ADDITIONAL BITS ARE NEEDED FOR THE LOW PHASE ERRORS REQUIRED FOR LOW SIDELOBE ANTENNAS 4HESE COM MENTS DO NOT APPLY FOR THE SOLID STATE SYSTEMS DESCRIBED BELOW &ERRITE PHASE SHIFTERS ARE MORE TEMPERATURE SENSITIVE THAN DIODES AND THE PHASE WILL CHANGE WITH A CHANGE IN TEMPERATURE 4HIS CAN BE CONTROLLED BY KEEPING THE TEMPERATURE CONSTANT WITHIN A FEW DEGREES ACROSS THE ARRAY ! MORE COMMON TECHNIQUE IS TO SENSE THE TEMPERATURE AT SEV ERAL LOCATIONS IN THE ARRAY AND THEN CORRECT THE PHASE COMMANDS TO THE PHASE SHIFTERS
£Î°£äÊ -" -// Ê " 1 -Èqn ! SOLID STATE MODULE MAY BE CONNECTED TO EVERY RADIATING ELEMENT OR TO EVERY SUBAR RAY OF A PHASED ARRAY ANTENNA FORMING WHAT IS SOMETIMES CALLED AN ACTIVE APERTURE !PPLICATIONS RANGE FROM ULTRAHIGH FREQUENCY 5(& FOR SURVEILLANCE TO 8 BAND AND ABOVE FOR AIRBORNE SYSTEMS ! TYPICAL MODULE IS SHOWN IN SIMPLE SCHE MATIC IN &IGURE )T CONSISTS OF A TRANSMITTER AMPLIFIER CHAIN A PREAMPLIFIER FOR RECEIVING A SHARED PHASE SHIFTER WITH DRIVER AND CIRCULATORS ANDOR SWITCHES TO SEPARATE THE TRANSMIT AND RECEIVE PATHS THE GAIN AROUND THE LOOP MUST BE LESS THAN UNITY TO AVOID OSCILLATIONS 0OWER AMPLIFIERS FOR TRANSMITTING AT THE ELEMENT LEVEL WOULD TYPICALLY HAVE A GAIN OF D" OR MORE TO COMPENSATE FOR THE LOSS OF POWER DIVIDING IN THE BEAMFORMER 4RANSISTORS ARE CAPABLE OF GENERATING HIGH AVERAGE POWER BUT ONLY RELATIVELY LOW PEAK POWER (IGH DUTY CYCLE WAVEFORMS TO ARE THERE FORE REQUIRED TO TRANSMIT ENOUGH ENERGY EFFI CIENTLY 4HIS LACK IN HIGH PEAK POWER IS THE MAIN DISADVANTAGE OF THE SOLID STATE MODULES IN PHASED ARRAY RADARS 4O A GREAT EXTENT IT CAN BE COMPENSATED FOR BY USING MORE PULSE COM PRESSION IN THE RECEIVER AND EXTRA WIDE BAND WIDTH TO COUNTERACT JAMMING BUT AT THE COST OF INCREASED SIGNAL PROCESSING !N IMPORTANT ADVANTAGE OF TRANSISTORS IS THEIR POTENTIAL FOR WIDE BANDWIDTH &)'52% 4YPICAL SOLID STATE MODULE
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4HE RECEIVER REQUIRES AN EARLY GAIN OF TYPICALLY TO D" TO ADEQUATELY ESTABLISH A LOW NOISE FIGURE AND ALLOW FOR PHASE SHIFTING AND BEAMFORMING LOSSES 4HE MODULE ALSO RECEIVES INTERFERING SIGNALS FROM ALL DIRECTIONS WITHIN THE ELEMENT PATTERN NOT SIMPLY THE ANTENNA PATTERN AT ALL FREQUENCIES IN THE BAND 4IGHT TOLERANCES BETWEEN MODULES ARE NEEDED TO PROVIDE AMPLITUDE AND PHASE TRACKING OVER THE BAND FOR LOW SIDELOBE PERFORMANCE !N ELECTRONICALLY PROGRAMMABLE GAIN ADJUSTMENT MAY BE HELP FUL TO CORRECT MODULE TO MODULE VARIATIONS ALLOWING LESS DEMANDING SPECIFICATIONS 4HE TRIMMER WOULD ALSO PROVIDE A DEGREE OF FREEDOM IN APERTURE CONTROL FOR SPECIAL SITUATIONS "ECAUSE THE NOISE FIGURE HAS BEEN ESTABLISHED THE FEED NETWORK MAY BE SPLIT TO GIVE SEPARATE OPTIMUM APERTURE AMPLITUDE DISTRIBUTIONS FOR TRANSMITTING AS WELL AS FOR RECEIVING ON SUM AND DIFFERENCE CHANNELS )N AN ALTERNATIVE CONFIGURATION THE FEED NETWORK COULD BE DESIGNED FOR A CONSTANT AMPLITUDE APERTURE DISTRIBUTION TO GIVE HIGHEST TRANSMIT POWER ON THE TARGET AND THE RECEIVER GAIN CONTROL COULD BE USED TO PROVIDE AN AMPLITUDE TAPER FOR THE SUM CHANNEL 0ERHAPS A SECONDARY FEED SYSTEM COULD BE ADDED FOR THE DIFFERENCE CHANNELS 0OIRIER HAS ANALYZED THIS CASE THE EFFECT ON NOISE AND THE DEGRADATION DUE TO AMPLITUDE QUANTIZATION STEPS 4HE MODULE PHASE SHIFTER OPERATES AT LOW SIGNAL POWER LEVELS )TS INSERTION LOSS MAY BE HIGH BECAUSE IT IS FOLLOWED BY AMPLIFICATION ON TRANSMIT AND PRECEDED BY AMPLI FICATION ON RECEIVE $IODE PHASE SHIFTERS ARE THEREFORE QUITE PERMISSIBLE EVEN WITH MANY BITS EG OR BITS FOR LOW SIDELOBES 6ARIATIONS IN INSERTION LOSS MAY BE COMPENSATED FOR DYNAMICALLY WITH THE GAIN ADJUSTMENT 4HE CIRCULATOR AT THE HIGH POWER SIDE PROVIDES AN IMPEDANCE MATCH TO THE POWER AMPLIFIER AND MAY BE ADEQUATE BY ITSELF FOR PROTECTING THE RECEIVER )N &IGURE THE MODULE IS SHOWN AUGMENTED BY A SWITCH THAT CAUSES ABSORPTION OF POWER REFLECTED FROM ANTENNA MISMATCHES AND ALSO GIVES ADDED PROTECTION TO THE RECEIVER DURING TRANS MISSION )F WEIGHT IS AN IMPORTANT CONSIDERATION AS IT WOULD BE IN A SPACE BASED SYS TEM THEN THE CIRCULATOR COULD BE REPLACED BY DIODE SWITCHES REQUIRING ADDITIONAL LOGIC AND DRIVING CIRCUITRY
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6 Ê 7ITH THE PROLIFERATION OF BALLISTIC MISSILES FUTURE SHIPBOARD RADAR SYSTEMS WILL PROB ABLY NEED MULTI MISSION CAPABILITY WHICH INCLUDES BOTH ANTInAIR WARFARE !!7 AND BALLISTIC MISSILE DEFENSE "-$ 4HE "-$ REQUIREMENT TO DISCRIMINATE SMALL RADAR CROSS SECTION 2#3 RE ENTRY VEHICLES 26S AT LONG RANGES REQUIRES THAT ACTIVE ARRAY RADARS HAVE A LARGE POWER APERTURE GAINLOSS NOISE TEMPERATURE 0!',4 WHICH IS A MEASURE OF THE SENSITIVITY OF THE RADAR )NCREASING THE OUTPUT POWER OF A 42 MODULE ONLY INCREASES THE TRANSMIT POWER COMPONENT OF THE 0!' PRODUCT (OWEVER ADDING AN ADDITIONAL 42 MODULE TO THE ARRAY INCREASES EACH OF THE COMPONENTS OF THE 0!' THE TRANSMIT POWER THE RECEIVE APERTURE AND THE TRANSMIT GAIN 4HEREFORE RADARS WITH A "-$ FUNCTION TYPICALLY HAVE A LARGE NUMBER OF ELEMENTS WHICH RESULTS IN A LARGE APERTURE "ECAUSE A LARGE ANTENNA APERTURE PRODUCES A NARROW ANTENNA BEAMWIDTH THE VOLUME SEARCH FUNCTION WILL REQUIRE SCANNING A LARGE NUMBER OF BEAM POSITIONS .AVAL SHIPS NEED TO OPERATE IN LITTORAL CLOSE TO LAND ENVIRONMENTS AS WELL AS IN THE OPEN OCEAN 4HE DESIRE TO OPERATE CLOSER TO LAND REQUIRES SHIPBOARD RADARS TO HAVE THE CAPABILITY TO REJECT HIGH CLUTTER RETURNS (IGH CLUTTER REJECTION IS USUALLY ACHIEVED THROUGH THE USE OF PULSE DOPPLER WAVEFORMS IN THE FIRST FEW ELEVATION BEAM POSITIONS
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)N ADDITION MANY OF THE RADAR WAVEFORMS MAY BE DESIGNED TO PROPAGATE OUT TO THE INSTRUMENTED RANGE OF THE RADAR !S A RESULT A MAJOR COMPONENT OF THE DWELL TIME AT EACH BEAM POSITION IS THE TIME REQUIRED FOR THE PULSE TO PROPAGATE TO THE INSTRUMENTED RANGE AND BACK 4HIS LONG PROPAGATION TIME COMBINED WITH THE LARGE NUMBER OF BEAM POSITIONS DUE TO A NARROW ANTENNA BEAMWIDTH AND A PULSE DOPPLER WAVEFORM WITH A LARGE NUMBER OF PULSES RESULTS IN UNSATISFACTORY LONG SEARCH FRAME TIMES WHEN USING A SINGLE BEAM RADAR )F THE ACTIVE ARRAY RADAR IS SIZED FOR LONG RANGE DETECTION OF BALLISTIC MISSILES THE RADAR WILL MOST LIKELY HAVE SUFFICIENT POWER TO DETECT OTHER TARGETS ! CLUSTER OF MULTIPLE SIMUL TANEOUS RECEIVE BEAMS CAN BE USED TO TRADE ENERGY FOR A REDUCTION IN THE VOLUME SEARCH FRAME TIME 4HE USE OF MULTIPLE SIMULTANEOUS RECEIVE BEAMS WILL REDUCE THE SEARCH FRAME TIME SINCE MANY BEAM POSITIONS ARE SEARCHED AT THE SAME TIME 7HEN USING MULTIPLE SIMULTANEOUS RECEIVE BEAMS THE TRANSMIT BEAM CAN BE BROADENED BY BEAM SPOILING SO THAT THE D" BEAMWIDTH IS LARGER THAN THAT OF A UNIFORMLY ILLUMINATED ARRAY WITH A LINEAR PHASE FRONT "ROADENING THE BEAM ON TRANSMIT REDUCES THE GAIN OF THE TRANSMIT BEAM BUT THIS LOSS IN GAIN MAY BE NECESSARY TO PRODUCE THE SEARCH FRAME TIME REQUIRED /N RECEIVE MULTIPLE BEAMS ARE SIMULTANEOUSLY FORMED IN A CLUSTER THAT COVERS THE VOLUME ILLUMINATED BY THE TRANSMIT BEAM %ACH RECEIVE BEAM HAS THE FULL GAIN AND BEAMWIDTH OF A SINGLE BEAM ARRAY WITH THE SAME APERTURE DIMENSIONS )N THE CLUSTER OF RECEIVE BEAMS EACH OF THE RECEIVE BEAMS MAY BE OFFSET IN VARIOUS DIRECTIONS FROM THE CENTER OF THE SPOILED TRANSMIT BEAM !N EXAMPLE OF FOUR SIMULTANEOUS RECEIVE BEAMS IN A CLUSTER IS SHOWN IN &IGURE 4O SEARCH THE SAME VOLUME COVERED BY THIS FOUR BEAM CLUSTER WITH A SINGLE BEAM RADAR WOULD TAKE APPROXIMATELY FOUR TIMES AS LONG SINCE THE TRANS MIT AND RECEIVE BEAMS WOULD NEED TO BE SEQUENTIALLY SCANNED TO EACH BEAM POSITION )NCREASING THE NUMBER OF BEAMS IN THE RECEIVE CLUSTER WHILE ALSO INCREASING THE TRANSMIT BEAM SPOILING BY AN EQUIVALENT AMOUNT REDUCES THE SEARCH FRAME TIME 4HERE IS ANOTHER TECHNIQUE FOR GENERATING MULTIPLE SIMULTANEOUS BEAMS THAT DOES NOT USE BEAM BROADENING ON TRANSMIT )N THIS TECHNIQUE EACH PULSE IN THE WAVEFORM IS DIVIDED INTO AS MANY SEGMENTS AS THERE ARE BEAM POSITIONS ! PULSE SEGMENT IS TRANSMIT TED SEQUENTIALLY IN EACH OF THE DESIRED BEAM POSITIONS ONE TRANSMIT PULSE RIGHT AFTER THE OTHER !FTER ALL THE PULSES HAVE BEEN TRANSMITTED MULTIPLE SIMULTANEOUS RECEIVE BEAMS ARE FORMED WITH A RECEIVE BEAM LOCATED IN EACH OF THE TRANSMIT BEAM POSITIONS )N THIS METHOD EACH OF THE TRANSMIT BEAMS HAS THE FULL ARRAY GAIN )N ORDER TO HAVE SIMILAR PER FORMANCE TO THE BEAM BROADENING TECHNIQUE THE TRANSMIT PULSE SEGMENT IN EACH BEAM POSITION WOULD BE . TIMES AS LONG AS THE TRANSMIT PULSE IN THE BEAM BROADENED TECH NIQUE WHERE . IS THE NUMBER OF SIMULTANEOUS RECEIVE BEAMS )N EITHER CASE IT IS NECES SARY TO TRADE ENERGY FOR TIME IN ORDER TO ACHIEVE THE DESIRED SEARCH FRAME TIME
&)'52% ! SPOILED TRANSMIT BEAM AND A CLUSTER OF FOUR SIMULTANEOUS RECEIVE BEAMS
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! MULTIPLE SIMULTANEOUS RECEIVE BEAM CLUSTER CAN BE FORMED IN SEVERAL DIFFERENT WAYS )F ANALOG BEAMFORMING IS USED THE RECEIVE SIGNALS CAN BE SPLIT . WAYS INTO . SEPARATE ANALOG BEAMFORMERS %ACH ANALOG BEAMFORMER IS DESIGNED TO PRODUCE ONE OF THE . OFFSET BEAMS IN A BEAM CLUSTER !NOTHER WAY TO GENERATE MULTIPLE SIMULTANEOUS RECEIVE BEAMS IS TO USE DIGITAL BEAMFORMING $"& WHICH IS DISCUSSED IN MORE DETAIL IN THE NEXT SEC TION $"& IS USUALLY PREFERRED WHEN A LARGE NUMBER OF BEAMS ARE TO BE FORMED
£Î°£ÓÊ / Ê ", -ANY PHASED ARRAY RADARS USE ANALOG BEAMFORMING )N AN ANALOG BEAMFORMER THE RECEIVED SIGNALS FROM EACH ELEMENT ARE COMBINED AT RADIO FREQUENCIES !T THE OUTPUT OF THE ANALOG BEAMFORMER CENTRALIZED RECEIVERS DOWNCONVERT THE SIGNAL FROM RADIO FREQUENCY 2& TO AN INTERMEDIATE FREQUENCY )& AND AN ANALOG TO DIGITAL CONVERTER !$# IS USED TO DIGITIZE THE )& SIGNAL )N DIGITAL BEAMFORMING $"& THE 2& SIGNALS ARE DIGITIZED AT EITHER EACH INDIVIDUAL ELEMENT OR EACH SUBARRAY /NCE THE SIGNALS HAVE BEEN DIGITIZED VARIOUS WEIGHTED COMBINATIONS OF THE DIGITIZED SIGNALS CAN BE USED TO FORM MULTIPLE SIMULTANEOUS RECEIVE BEAMS &IGURE SHOWS ARRAY ARCHITECTURES FOR ANALOG BEAMFORMING AND $"& AT THE ELEMENT AND SUBARRAY LEVEL
&)'52% !RRAY ARCHITECTURES FOR ANALOG AND DIGITAL BEAMFORMING
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4HE BENEFITS OF $"& INCLUDE IMPROVED DYNAMIC RANGE FASTER SEARCH FRAME TIMES IF MULTIPLE SIMULTANEOUS BEAMS ARE USED AND BETTER CONTROL OF AMPLITUDE AND PHASE FOR ADAPTIVE NULLING AND LOWER SIDELOBE LEVELS 3HIPBOARD RADARS HAD BEEN DESIGNED TO OPERATE PRIMARILY IN OPEN OCEAN ENVIRON MENTS (OWEVER THE CHANGING WORLD WILL REQUIRE SHIPBOARD RADARS TO OPERATE MUCH CLOSER TO LAND !S A RESULT .AVY RADARS MUST HAVE SIGNIFICANTLY HIGHER CLUTTER REJECTION CAPABILITIES AND LARGER DYNAMIC RANGES THAN EXISTING RADAR SYSTEMS 2ECENTLY DIGITAL BEAMFORMING HAS BEEN PROPOSED FOR RADAR SYSTEMS THAT MUST DETECT SMALL 2#3 TARGETS IN SEVERE CLUTTER ENVIRONMENTS 4HE DYNAMIC RANGE DETERMINES THE RANGE OF POWER LEVELS THAT CAN BE PROCESSED IN THE LINEAR OPERATING REGION OF THE RECEIVER 4HE RADAR SYSTEM MUST BE ABLE TO PRO CESS HIGH POWER CLUTTER RETURNS WITHOUT SATURATING THE RECEIVER /NE REASON $"& HAS BEEN PROPOSED FOR FUTURE RADAR IS BECAUSE $"& PROVIDES THE RADAR SYSTEM WITH A SIGNIFICANTLY HIGHER DYNAMIC RANGE THAN CAN BE ACHIEVED WITH ANALOG BEAMFORMING WHICH HAS A CENTRALIZED RECEIVER )N A $"& ARCHITECTURE THERE ARE . DIGITAL RECEIVERS ONE AT EACH OF THE . ELEMENTS OR SUBARRAYS 4HEREFORE THE DYNAMIC RANGE OF A $"& RADAR SYSTEM HAS LOG. HIGHER DYNAMIC RANGE THAN AN ANALOG BEAMFORMING RADAR THAT UTILIZES THE SAME RECEIVER PROVIDED THE NOISE AND DISTORTION IN EACH RECEIVER ARE DECORRELATED AMONG ALL RECEIVERS $"& CAN BE IMPLEMENTED AT EITHER THE ELEMENT LEVEL OR THE SUBARRAY LEVEL %LEMENT LEVEL $"& REQUIRES A DIGITAL RECEIVER WHICH CONSISTS OF A DOWNCONVERTER AND AN !$# AT EACH ELEMENT 3UBARRAY LEVEL $"& REQUIRES A DIGITAL RECEIVER AT EACH SUB ARRAY ! FULLY DIGITAL ARRAY WHICH HAS $"& AT THE ELEMENT LEVEL ALLOWS FOR MULTIPLE SIMULTANEOUS INDEPENDENT BEAMS 4HESE INDEPENDENT BEAMS CAN BE STEERED IN ANY DIRECTION $"& AT THE SUBARRAY LEVEL CAN PRODUCE A MULTIPLE SIMULTANEOUS BEAM CLUS TER LOCATED WITHIN THE SUBARRAY PATTERN $"& AT THE SUBARRAY LEVEL USES PHASE SHIFTERS AT THE ELEMENT AND AN ANALOG SUBARRAY BEAMFORMER WITH A DIGITAL RECEIVER LOCATED AT THE OUTPUT OF EACH SUBARRAY 4IME DELAY STEERING CAN BE ACHIEVED AT THE SUBARRAY LEVEL THROUGH THE USE OF DIGITAL TIME DELAYS 4HE MULTIPLE BEAM CLUSTER IS FORMED BY DIGITALLY COMBINING THE SUBARRAYS TO FORM SIMULTANEOUS BEAMS THAT ARE OFFSET FROM ONE ANOTHER )N PRACTICE $"& IS FREQUENTLY IMPLEMENTED AT THE SUBARRAY LEVEL RATHER THAN THE ELE MENT LEVEL DUE TO THE SIZE WEIGHT AND HIGH COST OF DIGITAL RECEIVERS !NOTHER PRACTICAL ADVANTAGE OF SUBARRAY LEVEL $"& IS THAT LESS DIGITAL DATA WHICH MUST BE PROCESSED TO FORM THE RECEIVE BEAMS IS PRODUCED THAN FOR ELEMENT LEVEL $"& $"& CAN PROVIDE MORE EFFICIENT TIME ENERGY MANAGEMENT THAN A SINGLE BEAM ANA LOG BEAMFORMING ARRAY 3INCE $"& CAN PRODUCE MULTIPLE SIMULTANEOUS BEAMS ENERGY CAN BE TRADED OFF FOR IMPROVED SEARCH FRAME TIMES AS WAS DISCUSSED IN 3ECTION
£Î°£ÎÊ , /" Ê*// , Ê 1 0HASED ARRAY ANTENNAS CAN BE DESIGNED TO HAVE DETERMINISTIC ANTENNA PATTERNS OR ADAP TIVE ANTENNA PATTERNS 7HEN NO INTERFERING SIGNALS ARE PRESENT A PHASED ARRAY ANTENNA WITH A DETERMINISTIC ANTENNA PATTERN WILL TYPICALLY UTILIZE PHASE WEIGHTS THAT PROVIDE A LINEAR PHASE FRONT OVER THE ARRAY FACE AND AMPLITUDE WEIGHTS THAT PRODUCE THE DESIRED SIDELOBE LEVELS 4HE ANTENNA PERFORMANCE CAN BE CHARACTERIZED BY PARAMETERS SUCH AS ANTENNA BEAMWIDTH GAIN AND PEAK AND 2-3 SIDELOBE LEVELS )NTERFERING RADIO FREQUENCY SIGNALS THAT ARE INTENTIONAL SUCH AS THOSE PRODUCED BY JAMMERS OR UNINTEN TIONAL SUCH AS THOSE PRODUCED BY OTHER RADARS OR CLUTTER MAY SIGNIFICANTLY DEGRADE THE
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2!$!2 (!.$"//+
PERFORMANCE OF STATIC PATTERN PHASED ARRAY ANTENNAS !S A RESULT METHODS FOR PLACING NULLS IN THE DIRECTION OF THE INTERFERENCE IN THE PHASED ARRAY RADIATION PATTERNS HAVE BEEN THE SUBJECT OF MUCH RESEARCHn %ITHER DETERMINISTIC RADIO FREQUENCY NULLING OR ADAPTIVE NULLING CAN BE USED TO PLACE NULLS IN THE ANTENNA PATTERN IN THE DIRECTION OF THE INTERFERING SOURCE )F THE LOCATION OF THE INTERFERING SOURCE IS STATIONARY AND THE DIRECTION OF THE INTERFERER IS KNOWN A DETERMINISTIC 2& NULL CAN BE PLACED IN THE ANTENNA PATTERN AT THAT SPECIFIC DIRECTION $ETERMINISTIC ANTENNA PATTERNS WITH NULLS STEERED IN SPECIFIC DIRECTIONS CAN BE ACHIEVED BY MODIFYING THE WEIGHTS AT EACH ELEMENT 4HESE MODIFIED WEIGHTS CAN BE EITHER THE AMPLITUDE AND PHASE OF EACH ELEMENT OR ONLY THE PHASE OF EACH ELEMENT 2EGARDLESS OF WHETHER AMPLITUDE AND PHASE NULLING OR PHASE ONLY NULLING IS USED THE WEIGHTS AT EACH ELEMENT ARE NOT TIME VARYING FOR DETERMINISTIC 2& NULLING !RRAY CON FIGURATIONS FOR PERFORMING DETERMINISTIC 2& NULLING USING AMPLITUDE AND PHASE WEIGHTS AND PHASE ONLY WEIGHTS AT EACH ELEMENT ARE SHOWN IN &IGURE $ETERMINISTIC 2& NULLING USING AMPLITUDE AND PHASE CONTROL AT EACH ELEMENT PRO VIDES BETTER PERFORMANCE THAN PHASE ONLY NULLING $ETERMINISTIC 2& NULLING CAN BE ACCOMPLISHED BY USING PERTURBATION TECHNIQUES TO GENERATE THE WEIGHTS AT EACH ELEMENT THAT WILL PRODUCE THE ANTENNA PATTERN WITH NULLS 7ITH PERTURBATION TECHNIQUES FIRST THE WEIGHTS AT EACH ELEMENT ARE COMPUTED TO GENERATE THE ORIGINAL ANTENNA PATTERN WITH OUT NULLS 4HEN THE ORIGINAL WEIGHTS ARE PERTURBED TO PRODUCE NULLS IN THE DESIRED DIREC TIONS OF THE ANTENNA PATTERN 4HE INTENT OF THE PERTURBATION ALGORITHM IS TO MAXIMIZE THE SIGNAL TO INTERFERENCE PLUS NOISE RATIO WHILE MINIMIZING THE DEVIATION BETWEEN THE ORIGINAL ELEMENT WEIGHTS AND THE PERTURBED ELEMENT WEIGHTS &ULL AMPLITUDE AND PHASE CONTROL AT EACH ELEMENT ENSURES THAT THE PERTURBED ANTENNA PATTERN HAS NULLS IN THE DESIRED DIRECTIONS WITH MINIMALLY PERTURBED WEIGHTS (OWEVER PHASE ONLY CONTROL
&)'52% !RRAY CONFIGURATIONS FOR PERFORM ING DETERMINISTIC 2& NULLING A AMPLITUDE AND PHASE CONTROL AT EACH ELEMENT AND B PHASE ONLY CONTROL AT EACH ELEMENT
0(!3%$ !22!9 2!$!2 !.4%..!3
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AT EACH ELEMENT MAY RESULT IN SITUATIONS WHERE A SOLUTION DOES NOT EXIST !N EXAMPLE OF A DETERMINISTIC ANTENNA PATTERN WITH AND WITHOUT NULLING IS SHOWN IN &IGURE 4HE SOLID LINE IN &IGURE SHOWS A DETERMINISTIC ANTENNA PATTERN AT BROADSIDE FOR A ELEMENT LINEAR ARRAY WITH K ELEMENT SPACING WHEN NO INTERFERENCE IS PRESENT 5NIFORM ILLUMINATION AND NO AMPLITUDE AND PHASE ERRORS WERE ASSUMED 4HE DASHED LINE IN &IGURE SHOWS THE ANTENNA PATTERN FOR THE SAME ARRAY WHEN AN INTERFERING SOURCE IS PRESENT AT n AND AMPLITUDE AND PHASE WEIGHTING IS USED TO STEER A NULL IN THE PATTERN IN THE DIRECTION OF THE INTERFERING SOURCE 2ADAR SYSTEMS CAN UTILIZE DETERMINISTIC 2& NULLING TO PLACE NULLS IN BOTH THE TRANS MIT AND THE RECEIVE ANTENNA PATTERNS /N TRANSMIT NULLS CAN BE PLACED IN THE DIRECTION OF HIGH GROUND CLUTTER TO REDUCE THE CLUTTER POWER REFLECTED BACK TOWARD THE ANTENNA !CTIVE ARRAYS TYPICALLY HAVE BOTH AMPLITUDE AND PHASE CONTROL AT EACH ELEMENT WHICH ALLOWS EITHER FULL AMPLITUDE AND PHASE NULLING OR PHASE ONLY NULLING TO BE USED (OWEVER WHEN TRANSMITTING IT IS DESIRABLE TO HAVE UNIFORM ILLUMINATION ACROSS THE APERTURE TO PRODUCE THE HIGHEST APERTURE EFFICIENCY POSSIBLE !LSO FOR ACTIVE ARRAYS IT IS DESIRABLE TO KEEP THE HIGH POWER TRANSMIT AMPLIFIERS IN SATURATION (ENCE WHEN NULLING ON TRANSMIT IT IS DESIRABLE TO USE PHASE ONLY NULLING TO MAINTAIN THE APERTURE EFFICIENCY /N RECEIVE AMPLITUDE WEIGHTING ACROSS THE ARRAY IS TYPICALLY USED TO PRO DUCE THE DESIRED SIDELOBE LEVELS "ECAUSE THIS AMPLITUDE WEIGHTING PRODUCES A TAPER LOSS ON RECEIVE USING FULL AMPLITUDE AND PHASE CONTROL FOR NULLING THE RADIATION PATTERN IS LESS OF A CONCERN THAN ON TRANSMIT 4HE INCORPORATION OF ADAPTIVE NULLING INTO PHASED ARRAY ANTENNAS ALLOWS PHASED ARRAYS TO HAVE ADAPTIVE ANTENNA PATTERNS ON RECEIVE !DAPTIVE TECHNIQUES ARE USED TO SENSE AND AUTOMATICALLY RESPOND TO A TIME VARYING INTERFERENCE ENVIRONMENT 4HE GOAL IS TO PRESERVE THE DESIRED SIGNAL WHILE SIMULTANEOUSLY REDUCING UNWANTED INTERFERENCE 4HIS REAL TIME ANTENNA PATTERN CONTROL IS ACCOMPLISHED BY ADJUSTING THE WEIGHTS AT EACH RECEIVER TO MAXIMIZE SIGNAL TO INTERFERENCE PLUS NOISE RATIO 4HE AMPLITUDE AND PHASE WEIGHT FOR THE SIGNAL AT EACH RECEIVER IS ADAPTIVELY COMPUTED AND IMPLEMENTED SO THAT THE DESIRED SIGNAL COMBINES COHERENTLY WHEREAS THE INTERFERENCE COMBINES INCOHERENTLY
&)'52% $ETERMINISTIC ANTENNA PATTERN WITH AND WITHOUT NULLING FOR A ELEMENT LINEAR ARRAY )NTERFERING SOURCE IS LOCATED AT DEGREES
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2!$!2 (!.$"//+
!DAPTIVE BEAMFORMING CAN BE IMPLEMENTED BY USING AUXILIARY RECEIVERS IN A SIDE LOBE CANCELLATION SYSTEM OR BY USING DIGITAL BEAMFORMING )N A $"& SYSTEM ADAPTIVE BEAMFORMING IS ACCOMPLISHED EITHER WITH THE USE OF SUBARRAY RECEIVERS OR WITH AUX ILIARY RECEIVERS )F SUBARRAY RECEIVERS ARE USED THE NUMBER OF NULLS THAT CAN BE PLACED IN THE ANTENNA PATTERN DEPENDS UPON THE NUMBER OF DEGREES OF FREEDOM $/& &OR ADAPTIVE BEAMFORMING THE NUMBER OF DEGREES OF FREEDOM IS . WHERE . IS THE NUM BER OF RECEIVERS IN THE $"& ARRAY )F ADAPTIVE BEAMFORMING IS IMPLEMENTED USING DIGITAL BEAMFORMING ELEMENT LEVEL $"& WILL HAVE SIGNIFICANTLY BETTER PERFORMANCE THAN SUBARRAY LEVEL $"& BECAUSE SUBARRAY LEVEL $"& HAS FAR FEWER DEGREES OF FREE DOM (OWEVER ELEMENT LEVEL $"& IS USUALLY COST PROHIBITIVE EXCEPT FOR ARRAYS WITH A SMALL NUMBER OF ELEMENTS (ENCE SUBARRAY LEVEL $"& IS FREQUENTLY PURSUED BECAUSE IT REQUIRES FAR FEWER DIGITAL RECEIVERS (OWEVER SUBARRAYS ARE NOT THE BEST CHOICE OF ARRAY ARCHITECTURES FOR A GIVEN NUMBER OF $/& IN AN ADAPTIVE ARRAY )N SUBARRAY $"& THE MAIN BEAM OF EACH SUBARRAY MUST BE ALIGNED WITH THE MAIN BEAM DIRECTION OF THE ARRAY 7HEN AN INTERFERING SOURCE IS PRESENT IN THE SIDELOBE REGION THE SUBARRAY LEVEL $"& ARCHITECTURE DOES A POOR JOB OF SENSING THIS INTERFERING SIGNAL BECAUSE THE SUBARRAY GAIN IS LOW IN THE SIDELOBE REGION
£Î°£{Ê ,/" Ê"Ê /6 ÊÊ *- Ê,,9Ê / !CTIVE PHASED ARRAY ANTENNAS MUST BE CALIBRATED IN ORDER TO ENSURE THAT THE RADIA TION PATTERN OF THE ANTENNA MEETS THE ANTENNA PERFORMANCE SPECIFICATIONS !NTENNA CHARACTERISTICS SUCH AS SIDELOBE LEVEL AND MAIN BEAM GAIN ARE TYPICALLY SPECIFIED BUT THESE SPECIFICATIONS CAN BE TRANSLATED INTO ALLOWABLE AMPLITUDE AND PHASE ERRORS AT EACH ELEMENT #ALIBRATION CAN BE DIVIDED INTO TWO CATEGORIES FACTORY CALIBRATION AND IN THE FIELD CALIBRATION &ACTORY CALIBRATION IS ONLY PERFORMED ONCE USUALLY AT THE ANTENNA TEST RANGE OF THE PHASED ARRAY MANUFACTURER )N THE FIELD CALIBRATION IS PERFORMED AT REGU LAR INTERVALS THROUGHOUT THE LIFE OF THE ARRAY AFTER IT HAS BEEN DEPLOYED 4HE ANTENNA MEASUREMENTS REQUIRED FOR FACTORY CALIBRATION CAN BE MADE IN THREE DIFFERENT TYPES OF ANTENNA RANGES NEAR FIELD COMPACT OR FAR FIELD &OR LARGE GROUND BASED OR SHIP BOARD PHASED ARRAYS FACTORY CALIBRATION IS USUALLY PERFORMED USING A PLANAR NEAR FIELD ANTENNA MEASUREMENT FACILITY !N ATTRACTIVE FEATURE OF THE NEAR FIELD RANGE IS THAT THE AMPLITUDE AND PHASE OF EACH ELEMENT CAN BE MEASURED AND A FULL HEMISPHERIC ANTENNA PATTERN CAN BE GENERATED .EAR FIELD RANGES ARE SUITABLE FOR MEASURING LOW SIDELOBE HIGH GAIN ANTENNAS 0LANAR NEAR FIELD ANTENNA MEASUREMENTS ARE MADE BY SCANNING A PROBE IN A PLANE PARALLEL TO THE ANTENNA UNDER TEST AND MEASURING THE AMPLITUDE AND PHASE AT EACH PROBE LOCATION )N RECTANGULAR COORDINATES THE PROBE POSITION IS GIVEN BY X Y Z $URING THE SCANNING THE X AND Y COORDINATES OF THE PROBE ARE VARIED AND THE DISTANCE OF THE SCANNING PLANE FROM THE ANTENNA UNDER TEST IS KEPT CONSTANT AT ZO 4HE VALUE OF ZO IS TYPICALLY A LITTLE MORE THAN THREE WAVELENGTHS 4HE PHASE FRONT SHOULD BE SAMPLED WITH PROBE POSITIONS THAT SATISFY THE .YQUIST SAMPLING THEOREM WHICH YIELDS A MAXIMUM SAMPLING DISTANCE BETWEEN POINTS IN THE X Y PLANE OF $X $Y K )N PRACTICE THE ACTIVE ARRAY ELEMENTS ARE TURNED ON ONE AT A TIME IN COORDINATION WITH THE PROBE POSI TION 3OME EXAMPLES OF EXISTING SYSTEMS THAT USE NEAR FIELD RANGES TO PERFORM FACTORY CALIBRATION ARE 4(!!$ AND 3!-03/.
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&OR AN ACTIVE ARRAY BOTH THE PHASE AND AMPLITUDE OF EACH ELEMENT MUST BE MEASURED IN ORDER TO DETERMINE THE CORRECTION CONSTANTS FOR EACH ARRAY ELEMENT IN BOTH TRANSMIT AND RECEIVE MODE &ULL CALIBRATION OF AN ACTIVE ARRAY IS MEASUREMENT INTENSIVE )T IS COM MON FOR PHASE SHIFTERS AND ATTENUATORS TO EACH HAVE AS MANY AS BITS OR DIFFERENT STATES )N ADDITION ACTIVE COMPONENTS SHOULD BE CHARACTERIZED AT SEVERAL FREQUENCIES IN THE OPERATING FREQUENCY BAND AND OVER SEVERAL TEMPERATURES !S A RESULT THOUSANDS OF MEASUREMENTS ARE REQUIRED TO FULLY CHARACTERIZE THE PERFORMANCE OF EACH ELEMENT .OT ALL STATES NEED TO BE MEASURED FOR EACH ELEMENT BUT ELIMINATING MEASUREMENTS AT SOME OF THE STATES WILL CAUSE THE CALIBRATED AMPLITUDE AND PHASE ERRORS TO INCREASE 0HASE SHIFTERS USUALLY EXHIBIT SMALL VARIATIONS IN AMPLITUDE OVER PHASE STATES WHEREAS ATTENUATORS EXHIBIT LARGE VARIATIONS IN PHASE OVER GAIN STATES 4HEREFORE IT IS DESIRABLE TO CALIBRATE THE ATTENUATOR FIRST 4HE PHASE SHIFTER CAN THEN BE CALIBRATED WITH OUT CHANGING THE ATTENUATOR SETTING /NCE THE CHARACTERISTICS OF EACH 42 CHANNEL ARE MEASURED CORRECTION FACTORS ARE CALCULATED AND STORED FOR FUTURE USE 4HE APPROPRIATE CORRECTION FACTORS ARE APPLIED TO BRING THE ANTENNA INTO CALIBRATION FOR A GIVEN MODE OF RADAR OPERATION /NCE THE ACTIVE PHASED ARRAY IS FIELDED IN THE FIELD CALIBRATION MUST BE PERFORMED TO KEEP THE ANTENNA WITHIN SPECIFICATIONS !CTIVE COM PONENTS DRIFT OVER TIME AND THESE AGING EFFECTS REQUIRE CALIBRATION TO BE PERFORMED IN THE FIELD ! NUMBER OF DIFFERENT TECHNIQUES HAVE BEEN PROPOSED FOR IN THE FIELD CALIBRATION INCLUDING MUTUAL COUPLING NEAR FIELD ANTENNAS AND 2& SAMPLING -UTUAL COUPLING TECHNIQUES UTILIZE THE MUTUAL COUPLING PATHS BETWEEN ADJACENT ARRAY ELEMENTS FOR TRANSMISSION OF CALIBRATION SIGNALS SEE &IGURE A )N THIS TECHNIQUE A SIGNAL IS TRANSMITTED FROM AN ARRAY ELEMENT AND THE NEAREST ELEMENTS SURROUNDING THE TRANSMIT ELE MENT ARE USED TO RECEIVE THE TRANSMITTED CALIBRA TION SIGNAL 4HE SIGNAL RECEIVED IS COMPARED TO A STORED REFERENCE OBTAINED DURING FACTORY TESTS /NLY ONE ELEMENT TRANSMITS AT A GIVEN TIME AND THIS PROCEDURE IS REPEATED UNTIL ALL THE ELEMENTS ARE MEASURED #ALIBRATION USING MUTUAL COUPLING CAN BE INTERSPERSED WITH NOR MAL RADAR OPERATING MODES AND REQUIRES ONLY A SMALL FRACTION OF THE AVAILABLE RADAR RESOURCES !NOTHER TECHNIQUE TO PERFORM IN THE FIELD CALIBRATION USES RADIATORS PLACED IN THE NEAR FIELD AROUND THE PERIPHERY OF THE ARRAY SEE &IGURE B 4HESE ADDITIONAL RADIA TORS ARE DEDICATED TO THE CALIBRATION OF THE ACTIVE ARRAY 4O CALIBRATE THE ARRAY IN RECEIVE MODE TEST SIGNALS ARE ROUTED TO EACH OF THE RADIATORS USED FOR CALIBRATION 4HE SIGNAL &)'52% !CTIVE ARRAY CALIBRATION RECEIVED FROM A 42 MODULE IS COMPARED TO A TECHNIQUES A MUTUAL COUPLING B NEAR FIELD STORED REFERENCE OBTAINED DURING FACTORY TEST ANTENNAS AND C 2& SAMPLING
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4HE CALIBRATION CONSTANTS ARE THEN MODIFIED IN ORDER TO RESTORE THE ANTENNA SO ITS CALIBRATION IS AS CLOSE AS POSSIBLE TO THE ORIGINAL FACTORY CALIBRATION 4HIS TECHNIQUE REQUIRES SEVERAL ADDITIONAL TRANSMIT AND RECEIVE HARDWARE CHANNELS TO BE DEDICATED FOR IN THE FIELD CALIBRATION 2& SAMPLING CAN ALSO BE USED TO CALIBRATE AN ACTIVE PHASED ARRAY SEE &IGURE C 4HE 2& SAMPLING TECHNIQUE USES BUILT IN CALIBRATION CIRCUITRY IN THE ARRAY TO INJECT A CALIBRATION SIGNAL BETWEEN THE 42 MODULE AND THE RADIATOR 4HIS TECHNIQUE CAN BE USED TO MEASURE 2& OUTPUT POWER RECEIVE GAIN AND PHASE AND ATTENUATION BIT ACCURACY 4HESE MEASURED VALUES ARE THEN COMPARED WITH REFERENCE VALUES ! MAJOR DISADVANTAGE OF THIS TECHNIQUE IS THAT IT REQUIRES SIGNIFICANT ADDITIONAL HARDWARE INCLUDING A SEPARATE BUILT IN TEST ")4 MANIFOLD !LSO THE CALIBRATION PATH DOES NOT INCLUDE THE RADIATOR
£Î°£xÊ *- Ê,,9Ê-9-/ ! NUMBER OF PHASED ARRAY RADAR SYSTEMS HAVE BEEN BUILT AND A REPRESENTATIVE SELEC TION IS BRIEFLY REVIEWED BELOW ,OCKHEED -ARTIN #ORPORATION 0HASED !RRAY 2ADARS #OURTESY OF ,OCKHEED -ARTIN #ORPORATION !.309 4HIS 3 BAND PHASED ARRAY RADAR IS PART OF THE .AVY !EGIS WEAPON SYSTEM AND WAS DEVELOPED BY 2#! NOW ,OCKHEED -ARTIN )T HAS FOUR PHASED ARRAY APERTURES TO GIVE UNOBSTRUCTED HEMISPHERICAL COVERAGE &IGURE )N ITS EARLY CON FIGURATION IT USED A SIMPLE FEED SYSTEM WITH ON RECEIVE SUBARRAYS EACH CONTAIN ING WAVEGUIDE TYPE RADIATORS FOR A TOTAL OF ELEMENTS /N TRANSMIT SUBARRAYS WERE COMBINED IN PAIRS AND SUCH PAIRS GAVE A TRANSMIT APERTURE OF RADIATORS 4HE PHASE SHIFTERS FED DIRECTLY INTO WAVEGUIDE RADIATORS HAD BITS AND WERE OF THE NONRECIPROCAL LATCHING GARNET CONFIGURATION ! LATER VERSION WAS DESIGNED FOR LOW SIDELOBES 4HE SUBARRAY SIZE HAD TO BE REDUCED TO ELEMENTS TO AVOID QUANTIZATION LOBES AND SIMILARLY THE PHASE SHIFTER HAD TO BE REFINED BY DRIVING IT WITH BIT ACCU RACY 4HE RESULTING PHASED ARRAY HAS AN APERTURE WITH A CONSTRAINED FEED STRUCTURE AND WAVEGUIDE TYPE RADIATORS -ONOPULSE SUM AND DIFFERENCE RECEIVE PATTERNS AND THE TRANSMIT PATTERN ARE SEPARATELY OPTIMIZED #/"2! 4HE #/UNTER "ATTERY 2!DAR #/"2! # "AND SOLID STATE PHASED ARRAY RADAR SEE &IGURE LOCATES ROCKET LAUNCHERS ARTILLERY BATTERIES MORTARS SHELL IMPACT POINTS AND JAMMING DIRECTIONS 4HE ANTENNA WHICH IS MECHANICALLY TRAINED HAS RADIATING ELEMENTS EACH FED BY A SOLID STATE 42 MODULE TO PROVIDE WIDE ELECTRONIC SCAN COVERAGE )T IS PRODUCED BY %URO !RT 'MB( A CONSORTIUM OF ,OCKHEED -ARTIN -3 -OORESTOWN .* %!$3 $EUTSCHLAND 5NTERSCHLEISSHEIM 'ERMANY 4HALES !IR $EFENCE "AGNEUX &RANCE AND 4HALES 5+ ,IMITED #RAWLEY 7EST 3USSEX %NGLAND FOR THE -INISTRIES OF $EFENCE OF &RANCE 'ERMANY AND THE 5NITED +INGDOM 6OLUME 3EARCH 2ADAR 4HE 3 BAND 6OLUME 3EARCH 2ADAR 632 PHASED ARRAY SEE &IGURE PROVIDES SEARCH AND !!7 CAPABILITY TO THE $UAL "AND 2ADAR 3YSTEM FOR $$8 )T HAS RADIATING ELEMENTS WITH A 42 MODULE PER ELEMENT !LTHOUGH THE ACTIVE RADIATING APERTURE IS APPROXIMATELY CIRCULAR THE CORNERS HAVE BEEN FILLED IN
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&)'52% #/"2! PHASED ARRAY MOUNTED ON RADAR SYSTEM VEHICLE #OURTESY OF ,OCKHEED -ARTIN #ORPORATION
WITH TERMINATED ELEMENTS TO FORM A RECTANGULAR APERTURE FOR PURPOSES OF MINIMIZING ANTENNA RADAR CROSS SECTION !LL ACTIVE COMPONENTS ARE ACCESSIBLE FROM THE REAR FOR EASE OF MAINTENANCE ABOARD SHIP 'ROUND "ASED 2ADARS !.403 !.&03 AND !.403 ,OCK HEED -ARTINS LONG RANGE SOLID STATE $ RADAR SYSTEMS SEE &IGURE OPERATE AT , BAND BETWEEN n '(Z 4HESE SYSTEMS PROVIDE POSITION DATA FOR EN ROUTE TRACKING OF COMMERCIAL AIRCRAFT AIR SURVEILLANCEAIR DEFENSE NAVIGATIONAL ASSISTANCE TACTICAL CONTROL AND TACTICAL BALLISTIC MISSILE 4"- DEFENSE 4HE !.403 WAS THE WORLDS FIRST TOTALLY SOLID STATE ANTENNAARRAY 4HE !.&03 WAS DEVELOPED SHORTLY THEREAFTER AND IS TYPICALLY INSTALLED AND OPERATED AT A FIXED SITE BUT IT CAN ALSO BE CON FIGURED ON A TRAILER FOR DEPLOYMENT 4HE !.403 IS A MOBILETRANSPORTABLE SERIES OF SOLID STATE RADAR SYSTEMS %ACH SYSTEM INCORPORATES PRIMARY SURVEILLANCE RADAR SEC ONDARY SURVEILLANCE RADAR )&& COMMAND AND CONTROL DISPLAY CONSOLES COMMUNICA TIONS EQUIPMENT VARIOUS OPTIONS AND TRANSPORT CONFIGURATIONS CUSTOMIZED FOR EACH CUSTOMERS SPECIFIC MISSION
&)'52% &RONT LEFT AND REAR VIEWS OF 6OLUME 3EARCH 2ADAR 3 "AND ENGINEERING DEVELOPMENT MODEL ACTIVE PHASED ARRAY MOUNTED IN NEAR FIELD TEST FACILITY DURING ASSEMBLY 2EAR VIEW SHOWS DETAIL OF EASILY REPLACEABLE LOWEST REPLACEABLE UNITS #OURTESY OF ,OCKHEED -ARTIN #ORPORATION
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&)'52% 'ROUND BASED RADAR SYSTEM CONFIGURATIONS #OURTESY OF ,OCKHEED -ARTIN #ORPORATION
4HE MAIN FEATURE OF THESE SYSTEMS IS THE PLANAR PHASED ARRAY WHICH HAS MODULAR CONSTRUCTION WITH DISTRIBUTED ALL SOLID STATE ELECTRONICS INCLUDING 2& POWER GENERA TION AND ELECTRONIC STEERING IN THE ELEVATION AXIS !NTENNA ROTATION FOR THE SYSTEM IS AT OR REVOLUTIONS PER MINUTE RPM PROVIDING n AZIMUTH COVERAGE WHILE ELECTRONICALLY STEP SCANNING IN ELEVATION )T PROVIDES FULL PERFORMANCE OVER A NOMINAL n IN THE ELEVATION PLANE TO AN ALTITUDE OF FEET AND UP TO n IN ELEVATION DURING 4"- TRACKING 4HE ANTENNAARRAY INCORPORATES MONOPULSE RADAR TECHNIQUES 4HESE TECHNIQUES ALLOW ACCURATE TARGET ANGULAR POSITION USING THREE DATA CHANNELSSUM DELTA AZIMUTH !: AND DELTA ELEVATION %, WITHIN THE ARRAY AND THE DATA PROCESSING GROUP 4HE DATA PROCESSING GROUP APPLIES MOVING TARGET INDICATOR -4) AND DOPPLER PROCESSING TO THE RECEIVE SIGNAL TO PRODUCE SUBCLUTTER VISIBILITY FOR TARGET DETECTION 3ELECTION OF THE OPERATING FREQUENCY IS DEPENDENT UPON THE RADARS MODE OF OPERA TION AND THE FREQUENCY OPTIONS SELECTED BY THE OPERATOR 4HE ANTENNAARRAY SHOWN IN &IGURE IS CONSTRUCTED OF EITHER !.403 !.&03 OR !.403 IDENTICAL HORIZONTAL PASSIVE ROW FEED NETWORKS ONE ABOVE ANOTHER ON INCH CENTERS -OUNTED DIRECTLY BEHIND EACH ROW FEED IS A DEDICATED ROW TRANSMIT TER AND RECEIVER 4HE ROW TRANSMITTERS AND RECEIVERS ARE SIMILAR FOR EACH ROW 4HEY PERFORM ALL THE 2& FUNCTIONS INCLUDING 2& POWER GENERATION PHASE SHIFTING TO STEER THE ANTENNA BEAM IN ELEVATION AND RECEIVE PREAMPLIFICATION TO PROVIDE A LOW NOISE FIGURE 4HE 2& POWER IS GENERATED BY DIRECT AMPLIFICATION THROUGH MODULAR SOLID STATE POWER AMPLIFIERS IN THE ROW TRANSMITTERS 4HE ENERGY FROM THESE POWER MODULES IS COMBINED WITHIN THE ROW TRANSMITTER WHICH DRIVES THE ROW FEED 4HE 2& ENERGY FROM THE ROW FEEDS IS COMBINED IN SPACE TO FORM THE RADIATED BEAM 5NLIKE A TUBE TRANSMITTER WHICH OPERATES AT HIGH PEAK POWER AND LOW DUTY FACTOR THE POWER MOD ULES OPERATE AT LOW PEAK POWER AND HIGH DUTY FACTORS TO ,ONG DURATION PULSES ARE TRANSMITTED AND THEN COMPRESSED DURING RECEIVE TO OBTAIN THE REQUIRED RANGE RESOLUTION ! PERFORMANCE MARGIN IS BUILT IN TO THE RADAR SYSTEM TO ALLOW FOR FIELD DEGRADATION OF THE DISTRIBUTED ARRAY COMPONENTS BETWEEN SCHEDULED MAINTE NANCE PERIODS 3INCE ARRAY COMPONENT FAILURES INDUCE ONLY A GRADUAL DEGRADATION MAINTENANCE CAN BE PERFORMED ON A PLANNED BASIS /NLINE SYSTEM SENSITIVITY AND PERFORMANCE LEVEL IS CHECKED AND DISPLAYED BY THE PERFORMANCE MONITORING AND FAULT ISOLATION -&) FUNCTION
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4HESE LONG RANGE THREE DIMENSIONAL AIR SURVEILLANCE RADARS PROVIDE AN OFF THE SHELF SOLUTION TO PRIMARY AIR SURVEILLANCE NEEDS 4HEY HAVE BEEN DESIGNED FOR REMOTE OPERATION IN HARSH ENVIRONMENTS AND WITH THEIR ESTABLISHED LOGISTICS SUPPORT BUILT IN PERFORMANCE MONITORING AND FAULT ISOLATION HIGH RELIABILITY AND WORLDWIDE INVEST MENT THESE SYSTEMS HAVE AN INHERENT LOW COST OF OWNERSHIP .ORTHROP 'RUMMAN #ORPORATION 0HASED !RRAY 2ADARS #OURTESY OF .ORTHROP 'RUMMAN #ORPORATION !7!#3 !IRBORNE 7ARNING AND #ONTROL 3YSTEM 4HE !IRBORNE 7ARNING AND #ONTROL 3YSTEM !7!#3 PROVIDES ALL WEATHER LONG RANGE SURVEILLANCE COM MAND CONTROL AND COMMUNICATIONS 4HE PHASED ARRAY ANTENNA IS A FT BY FT ELLIPTICALLY SHAPED ULTRA LOW SIDELOBE ARRAY CONSISTING OF SLOTTED WAVEGUIDES WITH OVER SLOTS SEE &IGURE -OUNTED ATOP THE AIRCRAFT FUSELAGE IN A ROTATING DOME THE 3 BAND ANTENNA SCANS MECHANICALLY OVER n IN AZIMUTH AND SCANS ELEC TRONICALLY IN ELEVATION THROUGH RECIPROCAL BEAM STEERING PHASE SHIFTERS )N ADDITION NONRECIPROCAL BEAM OFFSET PHASE SHIFTERS PROVIDE OFFSET OF THE RECEIVE BEAM FROM THE TRANSMIT BEAM DURING ELEVATION SCANNING TO COMPENSATE FOR TIME DELAY BETWEEN TRANSMIT AND RECEIVE OF LONG RANGE AIRCRAFT RETURNS 4HE 2ADAR 3YSTEM )MPROVEMENT 0ROGRAM 23)0 PROVIDES THE MOST SIGNIFICANT UPGRADE TO THE !7!#3 RADAR SINCE ITS DEVELOPMENT IN THE EARLY S 23)0 INTRODUCES NEW WAVEFORMS AND PROCESSING PROVIDING IMPROVEMENTS IN DETECTION RANGE ANGULAR ACCURACY AS WELL AS RANGE AND ANGULAR RESOLUTION !.403 4HE !.403 IS AN UPDATE TO THE !.403 3 BAND THREE DIMENSIONAL TACTICAL RADAR FAMILY DEVELOPED BY THE .ORTHROP 'RUMMAN #ORPORATION &IGURE 4HE !.403 PLANAR ARRAY SHOWN IN &IGURE EXHIBITS VERY LOW
&)'52% !7!#3 ANTENNA #OURTESY OF .ORTHROP 'RUMMAN #ORPORATION
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&)'52% !.403 ANTENNA #OURTESY OF .ORTHROP 'RUMMAN #ORPORATION
AZIMUTH SIDELOBES 4HE ARRAY IS A SLOTTED WAVEGUIDE DESIGN OF STICKS AND HORIZON TALLY POLARIZED SLOTS PER STICK 4HE ARRAY IS FED FROM A SOLID STATE TRANSMITTER AND TRANS MITS A SINGLE FAN BEAM IN ELEVATION OPTIMIZED FOR MAXIMUM GAIN AT LOW ALTITUDES /N RECEIVE THE ARRAY OUTPUT IS COMBINED INTO SIX SIMULTANEOUS NARROW ELEVATION BEAMS THAT COVER FROM TO n %ACH RECEIVE BEAM IS PROCESSED IN A DIGITAL RECEIVER !CCURATE HEIGHT INFORMATION IS EXTRACTED USING AMPLITUDE MONOPULSE TECHNIQUES BY COMPAR ING RECEIVE ENERGY IN ADJACENT BEAMS ! NARROW AZIMUTH BEAMWIDTH ON TRANSMIT AND RECEIVE AND STACKED RECEIVE BEAMS PROVIDE GOOD RADAR ANGLE RESOLUTION !ZIMUTH COV ERAGE OF n IS ACHIEVED BY ROTATING THE ARRAY AT A NOMINAL SURVEILLANCE RATE ! UNIQUE FEATURE OF THE !.403 ARRAY IS THAT THE ARRAY HAS AN INTEGRAL LOW SIDE LOBE )&& ARRAY EMBEDDED IN THE ARRAY FACE 4HIS NOT ONLY PROVIDES EXCELLENT REGISTRA TION BETWEEN RADAR AND )&& RETURNS BUT ALSO SUPPORTS FAST SETUP AND TEARDOWN TIME FOR TRANSPORTING THE RADAR IN ITS MOBILE CONFIGURATION
*OINT 34!23 !NTENNA 4HE *OINT 3URVEILLANCE 4ARGET !TTACK 2ADAR 3YSTEM *OINT 34!23 PROVIDES LONG RANGE AIRBORNE SURVEILLANCE AND TRACKING OF STA TIONARY AND MOVING GROUND TARGETS SEE &IGURE 4HE PHASED ARRAY ANTENNA FOR THIS SYSTEM IS A FT WIDE BY FT HIGH PLANAR 8 BAND SLOTTED ARRAY )T IS MOUNTED INSIDE A RADOME UNDERNEATH THE FUSELAGE OF AN % ! AIRCRAFT AND CAN BE MECHANICALLY ROTATED on IN ELEVATION FOR OPERATION LOOKING OUT EITHER SIDE OF THE AIRCRAFT 4HE SYSTEM OPERATES IN A SYNTHETIC APERTURE RADAR 3!2 MAPPING MODE AS WELL AS IN A THREE PORT AZIMUTH INTERFEROMETER GROUND MOVING TARGET INDICATION '-4) TARGET DETECTION AND TRACKING MODE 5SE OF THE THREE PORT APERTURE ON RECEIVE ENABLES A CLUTTER SUPPRESSION INTERFEROMETRY TECHNIQUE THAT ALLOWS THE OPERATOR TO DETECT ACCURATELY LOCATE AND TRACK SLOW MOVING GROUND TARGETS IN THE PRESENCE OF COMPETING GROUND CLUTTER 2AYTHEON #OMPANY 0HASED !RRAY 2ADARS #OURTESY OF 2AYTHEON #OMPANY 0!42)/4 4HE 0!42)/4 IS A MULTIFUNCTION PHASED ARRAY RADAR SYSTEM DEVEL OPED BY 2AYTHEON FOR THE !RMY IN THE FORM OF A LENS USING AN OPTICAL FEED AS SHOWN PREVIOUSLY IN &IGURE 3UM AND DIFFERENCE PATTERNS ARE SEPARATELY OPTIMIZED WITH A MONOPULSE FEED 4HE APERTURE IS ROUND AND CONTAINS APPROXIMATELY ELEMENTS
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&)'52% *OINT 34!23 ANTENNA AND AIRCRAFT #OURTESY OF .ORTHROP 'RUMMAN #ORPORATION
)T USES BIT FLUX DRIVEN NONRECIPROCAL FERRITE PHASE SHIFTERS AND WAVEGUIDE TYPE RADIA TORS AT BOTH APERTURES 4HE ANTENNA IS SHOWN IN &IGURE )T IS MOUNTED ON A VEHICLE AND FOLDS FLAT FOR TRANSPORTATION
&)'52% 0!42)/4 MULTIFUNCTION PHASED ARRAY #OURTESY OF 2AYTHEON #OMPANY
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4ERMINAL (IGH !LTITUDE !REA $EFENSE 4(!!$ 4(!!$ IS A GROUND BASED SYS TEM DESIGNED TO DESTROY THE THEATER BALLISTIC MISSILE THREATS TO TROOPS MILITARY ASSETS AND ALLIED TERRITORIES 4(!!$ CONSISTS OF A HIT TO KILL MISSILE RADAR LAUNCHER AND "ATTLE -ANAGEMENT#OMMAND #ONTROL AND #OMMUNICATIONS "-# SYSTEM 4HE 4(!!$ RADAR SEE &IGURE IS AN 8 BAND PHASED ARRAY SOLID STATE RADAR CAPABLE OF SEARCH THREAT DETECTION CLASSIFICATION AND PRECISION TRACKING AT LONG RANGES 4HE RADAR DESIGN DELIVERS HIGH POWER OUTPUT AND BEAMWAVEFORM AGILITY IN ORDER TO SUPPORT THE LONG RANGE FUNCTIONAL REQUIREMENTS OF THE 4(!!$ MISSION 4HE 4(!!$ ELEMENT COMPONENTS WORK IN CONCERT TO DETECT ASSIGN AND DESTROY INCOMING SHORT TO MEDIUM RANGE BALLISTIC MISSILES BY PROVIDING THE FIRING BATTERY WITH TARGET ACQUISI TION INTERCEPTOR SUPPORT AND INTERCEPT ASSESSMENT FUNCTIONS 4HESE FUNCTIONS INCLUDE SURVEILLANCE 4(!!$ MISSILE TRACK IN FLIGHT DATA UPLINKDOWNLINK TARGET CLASSIFICA TIONTYPINGIDENTIFICATION AND INTERCEPT ASSESSMENT 4HE SINGLE FACE PHASED ARRAY RADAR IS M LONG MOUNTED ON A (EAVY %XPANDED -OBILE 4ACTICAL 4RUCK AND CAPABLE OF BEING TRANSPORTED IN A # (ERCULES AIRCRAFT 4HE RADAR IS NONROTATING AND HAS A FIELD OF VIEW 4HE RADAR USES ITS M FULL FIELD OF VIEW PHASED ARRAY APERTURE TO ACQUIRE THEATER MISSILE THREATS AT A RANGE OF UP TO KM 4HIS RADAR USES 8 BAND SOLID STATE TRANSMITRECEIVE MODULES IN THE PHASED ARRAY 8 "AND 2ADAR 8"2 4HE NINE STORY HIGH 8"2 IS THE WORLDS LARGEST 8 BAND RADAR WEIGHING FOUR MILLION POUNDS SEE &IGURE 4HE 3"8 PLATFORM THAT IT SITS ON STANDS MORE THAN FT TALL AND DISPLACES MORE THAN TONS )T CONSISTS OF A SEMI SUBMERSIBLE OIL PRODUCTION PLATFORM TOPPED WITH THE 8"2 8"2 IS THE PRIMARY PAYLOAD ON THE SEMI SUBMERSIBLE PLATFORM SUPPORTING THE 'ROUND "ASED -IDCOURSE $EFENSE '-$ PHASE OF THE -ISSILE $EFENSE !GENCY -$! "ALLISTIC -ISSILE $EFENSE 3YSTEM "-$3 3"8S FLOATING PLATFORM A MODIFIED OIL DRILLING VESSEL WAS DESIGNED FOR
&)'52% 4(!!$ RADAR #OURTESY OF 2AYTHEON #OMPANY
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&)'52% 3"8OVER FT TALL AND DISPLACING MORE THAN TONS #OURTESY OF 2AYTHEON #OMPANY
EXCEPTIONAL STABILITY IN HIGH WINDS AND STORMS -EASURING FT WIDE AND FT LONG THE VESSEL INCLUDES A POWER PLANT BRIDGE AND CONTROL ROOMS LIVING QUARTERS STORAGE AREAS AND ENOUGH FLOOR SPACE AND INFRASTRUCTURE TO SUPPORT THE 8 BAND RADAR 4HE 8 BAND RADAR ITSELF WHICH SITS ON TOP OF THE FLOATING PLATFORM IS THE LARG EST MOST SOPHISTICATED PHASED ARRAY ELECTRO MECHANICALLY STEERED 8 BAND RADAR IN THE WORLD )T CONSISTS OF THOUSANDS OF ELEMENTS DRIVEN BY TRANSMITRECEIVE 42 MODULES )N THE 8 BAND RADAR THEY WILL PROVIDE THE FULL FIRE CONTROL SENSOR FUNCTIONS FOR THE 'ROUND "ASED -IDCOURSE $EFENSE SYSTEM INCLUDING SEARCH ACQUISITION TRACKING DISCRIMINATION AND KILL ASSESSMENT 309 4HE !.309 -ULTI &UNCTION 2ADAR -&2 IS THE 53 .AVYS FIRST SHIP BOARD ACTIVE PHASED ARRAY MULTIFUNCTION RADAR )T IS AN 8 BAND ACTIVE PHASED ARRAY RADAR DESIGNED TO MEET ALL HORIZON SEARCH AND FIRE CONTROL REQUIREMENTS FOR THE .AVY -&2 IS DESIGNED TO DETECT LOW OBSERVABLE ANTI SHIP CRUISE MISSILE !3#- THREATS AND SUPPORT FIRE CONTROL ILLUMINATION REQUIREMENTS FOR MULTIPLE MISSILES -&2 COMBINES THE FUNCTIONS PROVIDED BY SEVERAL SEPARATE RADARS ABOARD .AVY COMBATANT SHIPS AND ALSO SUPPORTS NEW SHIP DESIGN REQUIREMENTS FOR REDUCED RADAR CROSS SECTION AND SIG NIFICANTLY REDUCED MANNING NO OPERATORS 4HE RADAR PERFORMS SUCH FUNCTIONS AS HORIZON SEARCH LIMITED ABOVE THE HORIZON SEARCH AND FIRE CONTROL TRACK AND ILLUMINATION /NE OF THE MOST SIGNIFICANT DESIGN FEATURES OF THE RADAR IS TO PROVIDE AUTOMATIC DETECTION TRACKING AND ILLUMINATION OF LOW ALTITUDE THREAT MISSILES IN THE ADVERSE ENVIRONMENTAL CONDITIONS ROUTINELY FOUND IN COASTAL WATERS 309 USES THREE FIXED FACE ARRAYS EACH CONTAINING AROUND TRANSMIT RECEIVE 42 ELEMENTS SEE &IGURE 4HESE ELEMENTS ARE CONNECTED TO 42 INTEGRATED MULTI CHANNEL MODULES EACH OF WHICH DRIVES EIGHT ELEMENTS )NDIVIDUAL MODULES ARE DESIGNED TO SLIDE INTO THE ARRAY STRUCTURE AND PROVIDE A HIGH CONDUCTIVITY THERMAL PATH TO THE COOLING ARRAY MANIFOLD WITHOUT HAVING ANY CONNECTION TO THE 42 MODULE ITSELF
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&)'52% !.309 -ULTI &UNCTION 2ADAR #OURTESY OF 2AYTHEON #OMPANY
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! +SIENSKI h%QUIVALENCE BETWEEN CONTINUOUS AND DISCRETE RADIATING ARRAYS v #AN * 0HYS VOL PP n 7 ( 6ON !ULOCK h0ROPERTIES OF PHASED ARRAY v )2% 4RANS 6OL !0 PP n /CTOBER % $ 3HARP v 4RIANGULAR ARRANGEMENT OF PLANAR ARRAY ELEMENTS THAT REDUCES NUMBER NEEDED v )2% 4RANS VOL !0 PP n -ARCH * , !LLEN ET AL h0HASED ARRAY RADAR STUDIES v -)4 ,INCOLN ,AB 4ECH 2EPT -ARCH * , !LLEN AND " , $IAMOND h-UTUAL COUPLING IN ARRAY ANTENNAS v -)4 ,INCOLN ,AB 4ECH 2EPT /CTOBER 2 7 "ICKMORE h.OTE ON EFFECTIVE APERTURE OF ELECTRICALLY SCANNED ARRAYS v )2% 4RANS VOL !0 PP n !PRIL " , $IAMOND #HAPTER IN -UTUAL #OUPLING IN !RRAY !NTENNAS * , !LLEN AND " , $IAMOND EDS -)4 ,INCOLN ,AB 4ECH 2EPT PT ))) /CTOBER * &RANK h0HASED ARRAY ANTENNA DEVELOPMENT v *OHNS (OPKINS 5NIVERSITY !PPL 0HYS ,AB 2EPT 4' -ARCH 0 7 (ANNAN h%LEMENT GAIN PARADOX FOR A PHASED ARRAY ANTENNA v )%%% 4RANS VOL !0 PP n *ULY 7 7ASYLKIWSKYJ AND 7 + +AHN h%LEMENT PATTERNS AND ACTIVE REFLECTION COEFFICIENT IN UNIFORM PHASED ARRAYS v )%%% 4RANS VOL !0 -ARCH 7 7ASYLKIWSKYJ AND 7 + +AHN h%LEMENT PATTERN BOUNDS IN UNIFORM PHASED ARRAYSv )%%% 4RANS VOL !0 3EPTEMBER 7 + +AHN h)MPEDANCE MATCH AND ELEMENT PATTERN CONSTRAINTS FOR FINITE ARRAYS v )%%% 4RANS VOL !0 .OVEMBER 2 % 7ILLEY h3PACE TAPERING OF LINEAR AND PLANAR ARRAYS v )2% 4RANS VOL !0 PP n *ULY ( ! 7HEELER h3IMPLE RELATIONS DERIVED FROM A PHASED ARRAY ANTENNA MADE OF AN INFINITE CURRENT SHEET v )%%% 4RANS VOL !0 PP n *ULY * , !LLEN h/N ARRAY ELEMENT IMPEDANCE VARIATION WITH SPACING v )%%% 4RANS VOL !0 P -AY 0 7 (ANNAN h4HE ULTIMATE DECAY OF MUTUAL COUPLING IN A PLANAR ARRAY ANTENNA v )%%% 4RANS VOL !0 PP n -ARCH 4 4 $EBSKI AND 0 7 (ANNAN h#OMPLEX MUTUAL COUPLING MEASURED IN A LARGE PHASED ARRAY ANTENNA v -ICROWAVE * PP n *UNE 0 7 (ANNAN AND - ! "ALFOUR h3IMULATION OF A PHASED ARRAY ANTENNA IN A WAVEGUIDE v )%%% 4RANS VOL !0 PP n -AY " , $IAMOND h3MALL !RRAYS4HEIR ANALYSIS AND THEIR USE FOR THE DESIGN OF ARRAY ELEMENTS v IN 0HASED !RRAY !NTENNAS ! ! /LINER AND ' ( +NITTEL EDS .ORWOOD -! !RTECH (OUSE # % 'ROVE $ * -ARTIN AND # 0EPE h!CTIVE IMPEDANCE EFFECTS IN LOW SIDELOBE AND ULTRA WIDEBAND PHASED ARRAYS v 0ROC 0HASED !RRAYS 3YMP PP n ' % %VANS AND ( % 3CHRANK h,OW SIDELOBE RADAR ANTENNAS v -ICROWAVE * PP n *ULY ' % %VANS AND 3 ' 7INCHELL h! WIDE BAND ULTRALOW SIDELOBE ANTENNA v PRESENTED AT !NTENNA !PPLICATIONS 3YMP !LLERTON ), 3EPTEMBER 3 ' 7INCHELL AND $ $AVIS h.EAR FIELD BLOCKAGE OF AN ULTRALOW SIDELOBE ANTENNA v )%%% 4RANS VOL !0 PP n *ULY $ + "ARTON AND ( 2 7ARD (ANDBOOK OF 2ADAR -EASUREMENT %NGLEWOOD #LIFFS .* 0RENTICE (ALL PP n * & 2AMSEY h,AMBDA FUNCTIONS DESCRIBE ANTENNADIFFRACTION PATTERNS v -ICROWAVES P *UNE 7 - 9ARNALL h4WENTY SEVEN DESIGN AIDS FOR ANTENNAS PROPAGATION EFFECTS AND SYSTEMS PLANNING v -ICROWAVES PP n -AY
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£{°£Ê /," 1 /" ! RADAR DETECTS OR TRACKS A TARGET AND SOMETIMES CAN CLASSIFY IT ONLY BECAUSE THERE IS AN ECHO SIGNAL )T IS THEREFORE CRITICAL IN THE DESIGN AND OPERATION OF RADARS TO BE ABLE TO QUANTIFY OR OTHERWISE DESCRIBE THE ECHO ESPECIALLY IN TERMS OF SUCH TARGET CHARACTERISTICS AS SIZE SHAPE AND ORIENTATION &OR THAT PURPOSE THE TARGET IS ASCRIBED AN EFFECTIVE AREA CALLED THE RADAR CROSS SECTION OR 2#3 4HE 2#3 IS THE PROJECTED AREA OF A METAL SPHERE THAT WOULD RETURN THE SAME ECHO SIGNAL AS THE TARGET HAD THE SPHERE BEEN SUBSTITUTED FOR IT 5NLIKE THE ECHO OF THE SPHERE HOWEVER WHICH IS INDEPENDENT OF THE VIEWING ANGLE THE ECHOES OF ALL BUT THE SIMPLEST TARGETS VARY SIGNIFICANTLY WITH ORIENTATION !S WILL BE SHOWN LATER THIS VARIATION CAN BE QUITE RAPID ESPECIALLY FOR TARGETS MANY WAVELENGTHS IN SIZE 4HE ECHO CHARACTERISTICS DEPEND IN STRONG MEASURE ON THE SIZE AND NATURE OF THE TARGET SURFACES EXPOSED TO THE RADAR BEAM 4HE VARIATION IS SMALL FOR ELECTRICALLY SMALL TARGETS TARGETS LESS THAN A WAVELENGTH OR SO IN SIZE BECAUSE THE INCIDENT WAVELENGTH IS TOO LONG TO RESOLVE TARGET DETAILS /N THE OTHER HAND THE FLAT SINGLY CURVED AND DOUBLY CURVED SURFACES OF ELECTRICALLY LARGE TARGETS ALL GIVE RISE TO DIFFERENT ECHO CHARACTERISTICS 2EENTRANT STRUCTURES SUCH AS JET ENGINE INTAKES AND EXHAUSTS GENERALLY HAVE LARGE ECHOES AND EVEN THE TRAILING EDGES OF AIRFOILS CAN BE SIGNIFICANT ECHO SOURCES 4HE RADAR CROSS SECTIONS OF SIMPLE BODIES CAN BE COMPUTED EXACTLY BY A SOLUTION OF THE WAVE EQUATION IN A COORDINATE SYSTEM FOR WHICH A CONSTANT COORDINATE COINCIDES WITH THE SURFACE OF THE BODY 4HE EXACT SOLUTION REQUIRES THAT THE ELECTRIC AND MAGNETIC FIELDS JUST INSIDE AND JUST OUTSIDE THE SURFACE SATISFY CERTAIN CONDITIONS THAT DEPEND ON THE ELECTROMAGNETIC PROPERTIES OF THE MATERIAL OF WHICH THE BODY IS MADE 7HILE THESE SOLUTIONS CONSTITUTE INTERESTING ACADEMIC EXERCISES AND CAN WITH SOME STUDY REVEAL THE NATURE OF THE SCATTERING MECHANISMS THAT COME INTO PLAY THERE ARE NO KNOWN TACTICAL TARGETS THAT FIT THE SOLUTIONS 4HUS EXACT SOLUTIONS OF THE WAVE EQUA TION ARE AT BEST GUIDELINES FOR GAUGING OTHER APPROXIMATE METHODS OF COMPUTING SCATTERED FIELDS !N ALTERNATIVE APPROACH IS THE SOLUTION OF THE INTEGRAL EQUATIONS GOVERNING THE DIS TRIBUTION OF INDUCED FIELDS ON TARGET SURFACES 4HE MOST USEFUL APPROACH TO A SOLUTION IS KNOWN AS THE METHOD OF MOMENTS IN WHICH THE INTEGRAL EQUATIONS ARE REDUCED TO A SYSTEM OF LINEAR HOMOGENEOUS EQUATIONS 4HE ATTRACTION OF THIS METHOD IS THAT THE SURFACE PROFILE OF THE BODY IS UNRESTRICTED ALLOWING THE COMPUTATION OF THE SCATTERING £{°£
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FROM TRULY TACTICAL OBJECTS !NOTHER IS THAT ORDINARY METHODS OF SOLUTION MATRIX INVER SION AND GAUSSIAN ELIMINATION FOR EXAMPLE MAY BE EMPLOYED TO EFFECT A SOLUTION 4HIS METHOD IS LIMITED BY COMPUTER MEMORY AND EXECUTION TIME HOWEVER TO OBJECTS A FEW DOZEN WAVELENGTHS IN SIZE AT BEST !LTERNATIVES TO THESE EXACT SOLUTIONS ARE SEVERAL APPROXIMATE METHODS THAT MAY BE APPLIED WITH REASONABLE ACCURACY TO ELECTRICALLY LARGE TARGET FEATURES 4HEY INCLUDE THE THEORIES OF GEOMETRICAL AND PHYSICAL OPTICS THE GEOMETRICAL AND PHYSICAL THEORIES OF DIFFRACTION AND THE METHOD OF EQUIVALENT CURRENTS 4HESE APPROXIMATIONS ARE DIS CUSSED IN 3ECTION /THER APPROXIMATE METHODS NOT DISCUSSED HERE ARE EXPLORED IN DETAIL IN SOME OF THE REFERENCES LISTED AT THE END OF THIS CHAPTER 4HE PRACTICAL ENGINEER CANNOT RELY ENTIRELY ON PREDICTIONS AND COMPUTATIONS AND MUST EVENTUALLY MEASURE THE ECHO CHARACTERISTICS OF SOME TARGETS 4HIS MAY BE DONE BY USING FULL SCALE TEST OBJECTS OR SCALE MODELS THEREOF 3MALL TARGETS OFTEN MAY BE MEASURED INDOORS BUT LARGE TARGETS MUST USUALLY BE MEASURED ON AN OUTDOOR TEST RANGE 4HE CHAR ACTERISTICS OF TYPICAL INDOOR AND OUTDOOR TEST FACILITIES ARE DESCRIBED IN 3ECTION #ONTROL OF THE ECHO CHARACTERISTICS OF SOME TARGETS IS OF VITAL TACTICAL IMPORTANCE NAMELY STEALTH 4HERE ARE ONLY TWO PRACTICAL WAYS OF REDUCING THE ECHO THROUGH SHAP ING AND RADAR ABSORBERS 3HAPING IS THE SELECTION OR DESIGN OF SURFACE PROFILES SO THAT LITTLE OR NO ENERGY IS REFLECTED BACK TOWARD THE RADAR "ECAUSE TARGET CONTOURS ARE DIF FICULT TO CHANGE ONCE THE TARGET HAS BECOME A PRODUCTION ITEM SHAPING IS BEST IMPLE MENTED IN THE CONCEPT DEFINITION STAGE BEFORE PRODUCTION DECISIONS HAVE BEEN MADE 2ADAR ABSORBING MATERIALS ACTUALLY SOAK UP RADAR ENERGY ALSO REDUCING THE ENERGY REFLECTED BACK TO THE RADAR (OWEVER THE APPLICATION OF ABSORBERS IS ALWAYS EXPENSIVE WHETHER GAUGED IN TERMS OF NONRECURRING ENGINEERING COSTS LIFETIME MAINTENANCE OR REDUCED MISSION CAPABILITIES 4HE TWO METHODS OF ECHO CONTROL ARE DISCUSSED IN 3ECTION AND A COLLECTION OF FOUR STEALTHY PLATFORMS IS SURVEYED THERE 3EVEN "ASIC %CHO -ECHANISMS &IGURE ILLUSTRATES SEVEN BASIC ECHO SOURCES THAT MIGHT BE FOUND ON A TYPICAL AIRBORNE TARGET !LL DEPEND IN VARYING DEGREE ON THE
&)'52% %XAMPLES OF SEVEN BASIC ECHO SOURCE MECHANISMS AFTER % & +NOTT Ú !MERICAN )NSTITUTE OF !ERONAUTICS AND !STRONAUTICS
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TARGET ASPECT ANGLE AS SEEN FROM THE RADAR 3OME ARE DOMINANT SCATTERING MECHANISMS WHEREAS OTHERS ARE WEAK .OT ALL ARE SIGNIFICANT ON OTHER KINDS OF PLATFORMS SUCH AS WARSHIPS OR MILITARY GROUND VEHICLES 7E BRIEFLY DISCUSS THE SEVEN IN DESCENDING ORDER OF SIGNIFICANCE 2EENTRANT 3TRUCTURES 4HE ONLY REENTRANT STRUCTURE APPEARING ON THE HYPOTHETI CAL MISSILE IN &IGURE IS ITS EXHAUST DUCT AT THE REAR BUT JET INTAKE DUCTS BEHAVE MUCH THE SAME WAY 4HE ECHOES FROM CAVITIES SUCH AS INTAKE DUCTS EXHAUST DUCTS AND COCKPITS ARE LARGE AND TEND TO PERSIST OVER ASPECT ANGLES AS WIDE AS n OR n 4HIS IS BECAUSE MOST OF THE INTERNAL DUCT SURFACES IE COMPRESSOR STAGES AND TURBINE FACES ARE METALLIC AND ANY RADAR WAVE THAT FINDS ITS WAY INTO THE STRUCTURE WILL LIKELY FIND ITS WAY BACK OUT TOWARD THE RADAR 4HIS IS ALSO TRUE OF INTERNAL REFLECTIONS FROM WITHIN COCKPIT CANOPIES 3PECULAR 3CATTERERS ! SPECULAR SCATTERER IS ANY TARGET SURFACE THAT IS ORIENTED PER PENDICULAR TO THE LINE OF SIGHT TO THE RADAR &LAT SURFACES OFFER PARTICULARLY LARGE ECHOES IN THE SPECULAR DIRECTION BUT THE ECHOES DROP OFF SHARPLY AWAY FROM THAT DIRECTION 4HE SPECULAR ECHOES FROM SINGLY AND DOUBLY CURVED SURFACES CYLINDRICAL AND SPHEROIDAL SURFACES ARE SOMEWHAT LOWER THAN THOSE FROM FLAT SURFACES BUT ARE MORE PERSISTENT WITH CHANGES IN ASPECT ANGLE 4RAVELING WAVE %CHOES 7HEN THE ANGLE OF INCIDENCE IS A SMALL GRAZING ANGLE OFF THE SURFACE A SURFACE TRAVELING WAVE CAN BE INDUCED 4HE SURFACE WAVE TENDS TO BUILD UP TOWARD THE REAR OF THE BODY AND IS USUALLY REFLECTED BACK TOWARD THE FRONT BY ANY DISCONTINUITY AT THE REAR 4RAVELING WAVE ECHOES AT LOW GRAZING ANGLES ARE NEARLY AS SIGNIFICANT AS SPECULAR ECHOES AT NORMAL INCIDENCE 4IP %DGE AND #ORNER $IFFRACTION 3CATTERING FROM TIPS EDGES AND CORNERS IS LESS SIGNIFICANT THAN SPECULAR ECHOES AND THUS ARE WORRISOME TO THE DESIGNER ONLY WHEN MOST OTHER SOURCES OF ECHO HAVE BEEN SUPPRESSED 4HE ECHOES FROM TIPS AND CORNERS ARE LOCALIZED AND TEND TO INCREASE WITH THE SQUARE OF THE WAVELENGTH NOT THE SIZE OF ANY SURFACE FEATURE 4HUS THEY BECOME PROGRESSIVELY LESS IMPORTANT AS THE RADAR FRE QUENCY RISES 3URFACE $ISCONTINUITIES -OST AIRFRAMES HAVE SLOTS OR GAPS WHERE CONTROL SURFACES MEET THE STATIONARY AIRFRAME 3LOTS GAPS AND EVEN RIVET HEADS CAN REFLECT ENERGY BACK TO THE RADAR "ECAUSE THESE TEND TO BE SMALL EFFECTS IT IS NOT EASY TO ISOLATE AND CHAR ACTERIZE THEM #REEPING 7AVES ! CREEPING WAVE IS ONE THAT GETS BOUND TO A SMOOTH SHADED SUR FACE IS GUIDED AROUND THE REAR OF A SMOOTH BODY AND IS THEN LAUNCHED BACK TO THE RADAR WHEN IT REAPPEARS AT THE SHADOW BOUNDARY ON THE OPPOSITE SIDE !S SHOWN IN THE NEXT SECTION THE CREEPING WAVE CAUSES THE ECHOES FROM SMALL SPHERES TO VARY WITH SPHERE SIZE 4HE MECHANISM CAN ALSO BE PRESENT FOR OTHER SMOOTH BODIES SUCH AS THE GENERIC MISSILE DEPICTED IN &IGURE 4HE CREEPING WAVE MECHANISM IS NEVER A SIGNIFICANT ONE FOR MILITARY AND CIVILIAN TARGETS )NTERACTIONS 2ELATIVELY STRONG ECHOES CAN OCCUR WHEN A PAIR OF TARGET SURFACES ARE ORIENTED FOR A FAVORABLE BOUNCE FROM ONE SURFACE TO ANOTHER AND THEN BACK TO THE RADAR AS IN THE INTERACTION BETWEEN THE FUSELAGE AND THE TRAILING EDGE OF THE RIGHT WING SHOWN
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IN &IGURE 3IMILAR INTERACTIONS OCCUR FOR SHIP TARGETS WHEN BULKHEADS RAILINGS MASTS AND OTHER TOPSIDE FEATURES BECOME MIRRORED IN THE MEAN SEA SURFACE .OT ALL OF THESE MECHANISMS ARE REVEALED IN THE CHARACTERISTICS OF THE SELECTION OF SIMPLE AND COMPLEX TARGETS AS SHOWN IN THE NEXT SECTION
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*/Ê"Ê "Ê*"7 , $EFINITION OF 2#3 !N OBJECT EXPOSED TO AN ELECTROMAGNETIC WAVE DISPERSES INCIDENT ENERGY IN ALL DIRECTIONS 4HIS SPATIAL DISTRIBUTION OF ENERGY IS CALLED SCATTER ING AND THE OBJECT ITSELF IS OFTEN CALLED A SCATTERER 4HE ENERGY SCATTERED BACK TO THE SOURCE OF THE WAVE CALLED BACKSCATTERING CONSTITUTES THE RADAR ECHO OF THE OBJECT 4HE INTENSITY OF THE ECHO IS DESCRIBED EXPLICITLY BY THE RADAR CROSS SECTION OF THE OBJECT FOR WHICH THE ACRONYM 2#3 HAS BEEN GENERALLY RECOGNIZED %ARLY PAPERS ON THE SUBJECT CALLED IT THE ECHO AREA OR THE EFFECTIVE AREA TERMS STILL FOUND OCCASIONALLY IN CONTEM PORARY TECHNICAL LITERATURE 4HE FORMAL DEFINITION OF RADAR CROSS SECTION IS
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WHERE % IS THE ELECTRIC FIELD STRENGTH OF THE INCIDENT WAVE IMPINGING ON THE TARGET AND %S IS THE ELECTRIC FIELD STRENGTH OF THE SCATTERED WAVE AT THE RADAR 4HE DERIVATION OF THE EXPRESSION ASSUMES THAT A TARGET EXTRACTS POWER FROM AN INCIDENT WAVE AND THEN RADI ATES THAT POWER UNIFORMLY IN ALL DIRECTIONS !LTHOUGH THE VAST MAJORITY OF TARGETS DO NOT SCATTER ENERGY UNIFORMLY IN ALL DIRECTIONS THE DEFINITION ASSUMES THAT THEY DO 4HIS PERMITS ONE TO CALCULATE THE SCATTERED POWER DENSITY ON THE SURFACE OF A LARGE SPHERE OF RADIUS 2 CENTERED ON THE SCATTERING OBJECT 2 IS TYPICALLY TAKEN TO BE THE RANGE FROM THE RADAR TO THE TARGET 4HE SYMBOL R HAS BEEN WIDELY ACCEPTED AS THE DESIGNATION FOR THE 2#3 OF AN OBJECT ALTHOUGH THIS WAS NOT SO AT FIRST 4HE 2#3 IS THE PROJECTED AREA OF A METAL SPHERE THAT IS LARGE COMPARED WITH THE WAVELENGTH AND THAT IF SUBSTITUTED FOR THE OBJECT WOULD SCATTER IDENTICALLY THE SAME POWER BACK TO THE RADAR (OWEVER THE 2#3 OF ALL BUT THE SIMPLEST SCATTERERS FLUCTUATES GREATLY WITH THE ORIENTATION OF THE OBJECT SO THE NOTION OF AN EQUIVALENT SPHERE IS NOT VERY USEFUL 4HE LIMITING PROCESS IN %Q IS NOT ALWAYS AN ABSOLUTE REQUIREMENT )N BOTH MEA SUREMENT AND ANALYSIS THE RADAR RECEIVER AND TRANSMITTER ARE USUALLY TAKEN TO BE IN THE FAR FIELD OF THE TARGET DISCUSSED IN 3ECTION AND AT THAT DISTANCE THE SCATTERED FIELD %S DECAYS INVERSELY WITH THE DISTANCE 2 4HUS THE 2 TERM IN THE NUMERATOR OF %Q IS CANCELED BY AN IDENTICAL BUT IMPLICIT 2 TERM IN THE DENOMINATOR #ONSEQUENTLY THE DEPENDENCE OF THE 2#3 ON 2 AND THE NEED TO FORM THE LIMIT USUALLY DISAPPEARS 4HE RADAR CROSS SECTION IS THEREFORE A COMPARISON OF THE SCATTERED POWER DENSITY AT THE RECEIVER WITH THE INCIDENT POWER DENSITY AT THE TARGET !N EQUALLY VALID DEFINITION OF THE 2#3 RESULTS WHEN THE ELECTRIC FIELD STRENGTHS IN %Q ARE REPLACED WITH THE INCI DENT AND SCATTERED MAGNETIC FIELD STRENGTHS )T IS OFTEN NECESSARY TO MEASURE OR CALCU LATE THE POWER SCATTERED IN SOME OTHER DIRECTION THAN BACK TO THE TRANSMITTER A BISTATIC SITUATION ! BISTATIC 2#3 MAY BE DEFINED FOR THIS CASE AS WELL AS FOR BACKSCATTERING PROVIDED IT IS UNDERSTOOD THAT THE DISTANCE 2 IS MEASURED FROM THE TARGET TO THE RECEIVER
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&ORWARD SCATTERING IS A SPECIAL CASE OF BISTATIC SCATTERING IN WHICH THE BISTATIC ANGLE IS n WHENCE THE DIRECTION OF INTEREST IS ALONG THE SHADOW ZONE BEHIND THE TARGET 4HE SHADOW ITSELF CAN BE REGARDED AS THE SUM OF TWO FIELDS OF NEARLY EQUAL STRENGTH BUT n OUT OF PHASE /NE IS THE INCIDENT FIELD AND THE OTHER IS THE SCATTERED FIELD 4HE FORMATION OF THE SHADOW IMPLIES THAT THE FORWARD SCATTERING IS LARGE WHICH IS INDEED THE CASE 4HE FIELDS BEHIND THE TARGET ARE HARDLY EVER PRECISELY ZERO HOWEVER BECAUSE SOME ENERGY USUALLY LEAKS INTO THE SHADOW ZONE VIA DIFFRACTION FROM THE SIDES OF THE TARGET %XAMPLES OF 2#3 #HARACTERISTICS 4HE DISCUSSION OF RADAR CROSS SECTION CHAR ACTERISTICS WILL FIRST CONSIDER SIMPLE TARGETS OF WHICH THE SPHERE IS A CLASSIC EXAMPLE 4HIS WILL BE FOLLOWED BY COMPLEX OBJECTS OF WHICH AN AIRCRAFT IS A GOOD EXAMPLE 3IMPLE /BJECTS "ECAUSE OF ITS PURE RADIAL SYMMETRY THE PERFECTLY CONDUCTING SPHERE IS THE SIMPLEST OF ALL THREE DIMENSIONAL SCATTERERS $ESPITE THE SIMPLICITY OF ITS GEOMETRICAL SURFACE HOWEVER AND THE INVARIANCE OF ITS ECHO WITH ORIENTATION THE 2#3 OF THE SPHERE VARIES CONSIDERABLY WITH ELECTRICAL SIZE 4HE EXACT SOLUTION FOR THE SCATTER ING BY A CONDUCTING SPHERE IS KNOWN AS THE -IE SERIES AND IS SHOWN IN &IGURE .OTE THAT THE CHART IS SPLIT ROUGHLY INTO THREE REGIONS )N THE 2AYLEIGH REGION BELOW KA THE 2#3 RISES WITH THE FOURTH POWER OF THE SPHERE RADIUS AN ECHO DEPENDENCE CHARACTERISTIC OF ELECTRICALLY SMALL BODIES WHETHER SPHERICAL OR NOT )N THIS REGION THE INCIDENT WAVE CANNOT ACCURATELY RESOLVE BODY LENGTH TO WIDTH VARIATIONS )N THE OPTICS REGION ABOVE KA OPTICS FORMULAS FOR PREDICTING THE 2#3 OF THE METAL BODY GENERALLY WORK REASONABLY WELL 3ANDWICHED BETWEEN THE 2ALEIGH REGION BELOW AND THE OPTICS REGION ABOVE IS THE RESONANCE REGION WHERE TWO OR MORE MECHANISMS MAY COMBINE IN AND OUT OF PHASE WITH EACH OTHER TO PRODUCE THE UNDULATIONS IN THE 2#3 )N THE CASE OF THE SPHERE THE UNDULATIONS IN THE RESONANCE REGION ARE DUE TO TWO DISTINCT CONTRIBUTIONS TO THE ECHO ONE A SPECULAR REFLECTION FROM THE FRONT OF THE SPHERE AND THE OTHER A CREEPING WAVE THAT CIRCLES AROUND ITS SHADOWED SIDE 4HE TWO GO IN AND OUT OF PHASE AS THE SPHERE GROWS LARGER BECAUSE THE DIFFERENCE IN THE LENGTHS OF THEIR ELECTRICAL PATH FROM SOURCE TO RECEIVER INCREASES CONTINUOUSLY WITH INCREASING KA 4HE UNDULATIONS BECOME WEAKER WITH INCREASING KA BECAUSE THE CREEPING WAVE LOSES MORE ENERGY THE LONGER THE ELECTRICAL PATH AROUND THE SHADOWED SIDE
&)'52% 2ADAR CROSS SECTION OF A PERFECTLY CONDUCTING SPHERE NORMALIZED TO THE OPTICS VALUE OA 4HE PARAMETER KA OAK IS THE CIRCUMFERENCE OF THE SPHERE EXPRESSED IN WAVELENGTHS
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)F ONLY THE SPECULAR REFLECTION IS SIGNIFICANT THE OPTICS REGION 2#3 OF THE PERFECTLY CONDUCTING SPHERE IS SIMPLY
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WHERE A IS THE RADIUS OF THE SPHERE "UT THE 2#3 OF PERMEABLE DIELECTRIC BODIES IS MORE COMPLICATED THAN THIS BECAUSE ENERGY CAN ENTER THE BODY AND RATTLE AROUND INSIDE BEFORE COMING BACK OUT !N EXAMPLE IS THE DIELECTRIC SPHERE WHOSE 2#3 IS PLOTTED IN &IGURE "ECAUSE THE DIELECTRIC MATERIAL IS SLIGHTLY LOSSY AS INDICATED BY THE NON ZERO IMAGINARY COMPONENT OF THE INDEX OF REFRACTION THE 2#3 OF THE SPHERE DECAYS GRADUALLY WITH INCREASING ELECTRICAL SIZE !TLAS ET AL WENT EVEN FURTHER BY COMPARING THE MEASURED AND THEORETICAL 2#3 OF 0LEXIGLAS SPHERES IN THEIR ATTEMPTS TO UNDERSTAND THE SCATTERING BY HAILSTONES 4HE 2#3 OF VERY SLENDER DIELECTRIC BODIES DOES NOT EXHIBIT THIS COMPLEXITY HOW EVER BECAUSE THE SOURCES OF REFLECTION FRONT AND BACK SIDES OF A DIELECTRIC CYLINDER FOR EXAMPLE ARE TOO CLOSE TO EACH OTHER TO BE RESOLVABLE BY THE INCIDENT WAVE !N EXAMPLE IS THE BROADSIDE 2#3 OF A THIN STRING SHOWN IN &IGURE 4HE STRING WAS ANGLED n ACROSS THE TEST ZONE OF A LARGE INDOOR TEST CHAMBER AND THE 2#3 WAS MEASURED AS A FUNCTION OF FREQUENCY FOR FOUR TRANSMIT RECEIVE POLARIZATION COMBINATIONS /NLY THE COPOLARIZED 66 AND CROSS POLARIZED 6( TRACES ARE SHOWN BECAUSE THE (( AND (6 MEASUREMENTS CLOSELY TRACK THE 66 AND 6( DATA 4HE MEASURED DATA ARE THE RAPIDLY VARYING TRACES AND WERE FITTED STATISTICALLY TO THE SMOOTHLY VARYING TRACES REPRESENTING THE EXACT SOLUTION OF THE TWO DIMENSIONAL WAVE EQUATION FOR DIELECTRIC CYLINDERS 4HE STRING DIAMETER WAS INCH AND ITS ILLUMINATED LENGTH WAS ESTIMATED TO BE ABOUT FT "ASED ON A MEAN SEPARATION BETWEEN THE MEASURED 66 AND 6( DATA OF D" THE EFFECTIVE DIELECTRIC CONSTANT OF THE STRING WAS ESTIMATED TO BE DR 4HIS MAY BE THE FIRST TIME THAT 2#3 MEASUREMENTS WERE EVER USED TO ESTIMATE THE DIELECTRIC CONSTANT OF A STRING 3TRINGS ARE OF INTEREST AT 2#3 TEST FACILITIES BECAUSE THEY SOMETIMES ARE USED AS hINVISIBLEv TARGET SUPPORTS
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&)'52% -EASURED AND PREDICTED BROADSIDE 2#3 OF A STRING STRETCHED ACROSS THE TEST ZONE OF AN INDOOR TEST CHAMBER AT n ANGLE Ú (ORIZON (OUSE 2EPRINTED WITH PERMISSION
4HE BEHAVIOR OF SHORT WIRE DIPOLES IS MARKEDLY DIFFERENT FROM THAT OF LONG DIELECTRIC STRINGS !S SHOWN IN &IGURE THE BROADSIDE ECHO OF A METAL WIRE EXHIBITS RESO NANCES AT ODD MULTIPLES OF A HALF WAVELENGTH WITH PLATEAUS OF NEARLY CONSTANT RETURN BETWEEN THE RESONANT PEAKS 4HESE PLATEAUS RISE WITH INCREASING DIPOLE LENGTH AND BECOME LESS DISTINCT AS THE DIPOLE BECOMES THICKER AND LONGER 4HEY EVENTUALLY DISAP PEAR WHEN THE DIPOLE BECOMES FAT ENOUGH AND LONG ENOUGH 4HE 2#3 CAN RISE TO SIGNIFICANT LEVELS AT END ON ASPECTS AS WELL AS IN THE BROADSIDE REGIONS OF BODIES BOTH FAT AND THIN 4HESE NEAR END ON ECHOES ARE ATTRIBUTABLE TO SUR FACE TRAVELING WAVES THAT RADIATE POWER IN THE BACKWARD DIRECTION !N EXAMPLE IS THE OGIVE A SPINDLE SHAPED OBJECT FORMED BY ROTATING AN ARC OF A CIRCLE ABOUT ITS CHORD
&)'52% -EASURED BROADSIDE RETURNS OF A THIN DIPOLE #OURTESY OF 5NIVERSITY OF -ICHIGAN 2ADIATION ,ABORATORY
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&IGURE IS THE 2#3 PATTERN OF A K LONG n HALF ANGLE OGIVE RECORDED FOR HORI ZONTAL POLARIZATION INCIDENT ELECTRIC FIELD IN THE PLANE OF THE OGIVE AXIS AND THE LINE OF SIGHT 4HE LARGE LOBE AT THE RIGHT SIDE OF THE PATTERN IS A SPECULAR ECHO IN THE BROADSIDE SECTOR AND THE SEQUENCE OF PEAKS AT THE LEFT SIDE IS THE CONTRIBUTION OF THE SURFACE TRAV ELING WAVE NEAR END ON INCIDENCE .OTE THAT THE 2#3 IS EXTREMELY SMALL NOT MEASUR ABLE IN THIS CASE AT PRECISELY END ON INCIDENCE 4HEORETICAL PREDICTIONS IN THE END ON REGION CLOSELY MATCH THE MEASURED PATTERN FOR THIS PARTICULAR BODY ! METAL PLATE IS A MORE ELEMENTARY STRUCTURE THAN THE OGIVE SHOWN IN &IGURE BUT ITS 2#3 PATTERN IS NO LESS COMPLEX 3AMPLE PATTERNS ARE REPRODUCED IN &IGURE FOR FOUR DIFFERENT INCIDENT AND RECEIVED POLARIZATION COMBINATIONS 4HE TRACES FOR (( DOTS AND (6 SHORT DASHES ARE EACH SHIFTED DOWN BY D" FOR CLARITY WHEREAS THOSE FOR THE 66 LONG DASHES AND 6( SOLID ARE hAS ISv NOT SHIFTED 4HE PLATE WAS ROTATED ABOUT A VERTICAL AXIS PARALLEL TO ONE EDGE OF THE PLATE AND THE INCIDENT OR RECEIVED POLARIZATION WAS EITHER PARALLEL TO 6 OR PERPENDICULAR TO ( THAT AXIS RESPECTIVELY
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&)'52% 2#3 OF A SQUARE FLAT PLATE IN ALONG A SIDE MEASURED AT -(Z 4HE (( AND (6 PATTERNS HAVE BEEN ARTIFICIALLY LOWERED D" FOR CLARITY #OURTESY OF 3 0 7EI ET AL THE "OEING #OMPANY /RIGINAL DATA COURTESY OF THE "OEING #OMPANY 3EATTLE 7ASHINGTON
4HE PLATE IS PRESENTED BROADSIDE TO THE INCIDENT WAVE AT THE CENTER OF THE CHART n AND IS SEEN EDGE ON AT THE LEFT AND RIGHT SIDES n 4HE LARGE SPECULAR RETURN FROM THE PLATE AT THE CENTER OF THE CHART IS PREDICTED WITH QUITE GOOD ACCURACY BY THE FLAT PLATE FORMULA GIVEN IN 4ABLE LATER IN THIS SECTION 4HE EDGE ON RETURN FOR 66 POLARIZA TION IS WELL PREDICTED BY THE STRAIGHT EDGE FORMULA ALSO GIVEN IN 4ABLE 4HESE UNDULATING PLATE PATTERNS FOLLOW A SIN XX VARIATION QUITE CLOSELY FOR ASPECT ANGLES OUT TO ABOUT n "EYOND THAT ANGLE THE TWO PATTERNS DIFFER BY PROGRESSIVELY WIDER MARGINS 4HE SIN XX BEHAVIOR IS CHARACTERISTIC OF A UNIFORMLY ILLUMINATED APER TURE BUT UNLIKE THE ONE WAY ILLUMINATION FUNCTION ENCOUNTERED IN ANTENNA WORK THE ARGUMENT X FOR THE FLAT PLATE INCLUDES A TWO WAY ROUND TRIP ILLUMINATION FUNCTION 4HUS THE BEAMWIDTH OF THE ECHO RESPONSE OF A FLAT PLATE IS HALF THE BEAMWIDTH OF AN ANTENNA APERTURE OF THE SAME SIZE 4HE PROMINENT LOBE IN THE HORIZONTAL PATTERN IN THE REGION BETWEEN n AND n IS DUE TO A SURFACE TRAVELING WAVE )N CONTRAST TO THE PATTERN OF A FLAT PLATE THE 2#3 PATTERN OF A CORNER REFLECTOR IS QUITE BROAD 4HIS IS BECAUSE THE CORNER REFLECTOR IS A REENTRANT STRUCTURE AND NO MATTER WHAT ITS ORIENTATION WITHIN LIMITS OF COURSE INTERNALLY REFLECTED WAVES ARE DIRECTED BACK TOWARD THE SOURCE OF THE INCIDENT WAVE ! CORNER REFLECTOR IS FORMED BY TWO OR THREE FLAT PLATES INTERSECTING AT RIGHT ANGLES AND WAVES IMPINGING ON THE FIRST FACE ARE REFLECTED ONTO THE SECOND IF THERE IS A THIRD FACE IT RECEIVES WAVES REFLECTED BY THE FIRST TWO FACES 4HE MUTUAL ORTHOGONALITY OF THE FACES ENSURES THAT THE DIRECTION TAKEN BY WAVES UPON FINAL REFLECTION IS BACK TOWARD THE SOURCE 4HE INDIVIDUAL FACES OF THE CORNER REFLECTOR MAY BE OF ARBITRARY SHAPE BUT THE MOST COMMON IS AN ISOSCELES TRIANGLE FOR THE TRIHEDRAL CORNER DIHEDRAL CORNERS TYPICALLY HAVE RECTANGULAR FACES 4HE 2#3 OF A CORNER REFLECTOR SEEN ALONG ITS AXIS OF SYMMETRY
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4!",% 2#3 !PPROXIMATIONS FOR 3IMPLE 3CATTERING &EATURES
3CATTERING &EATURE #ORNER REFLECTOR &LAT PLATE 3INGLY CURVED SURFACE $OUBLY CURVED SURFACE 3TRAIGHT PLATE EDGE #URVED EDGE #ONE TIP !CUTE FLAT METAL CORNER !CUTE FLAT METAL CORNER
/RIENTATION
!PPROXIMATE 2#3
.OTES
!XIS OF SYMMETRY ALONG ,/3 3URFACE PERPENDICULAR TO ,/3 3URFACE PERPENDICULAR TO ,/3 3URFACE PERPENDICULAR TO ,/3 ,/3 PERPENDICULAR TO FRONT EDGE AND % IN PLANE OF PLATE %DGE ELEMENT PERPENDICULAR TO ,/3 !XIAL INCIDENCE ,/3 PERPENDICULAR TO REAR EDGE AND % IN PLANE OF PLATE ,/3 ALONG CORNER BISECTOR AND % IN PLANE OF PLATE
O !EFF K
O ! K O A,K O AA ,O
AK K SIN@ K
K
./4%3 ,/3 LINE OF SIGHT !EFF EFFECTIVE AREA CONTRIBUTING TO MULTIPLE INTERNAL REFLECTIONS ! ACTUAL AREA OF THE PLATE A MEAN RADIUS OF CURVATURE , LENGTH OF SLANTED SURFACE A A PRINCIPAL RADII OF SURFACE CURVATURE IN ORTHOGONAL PLANES , EDGE LENGTH A RADIUS OF EDGE CONTOUR @ HALF ANGLE OF THE CONE %MPIRICAL VALUES REPORTED BY +NOTT 3HAEFFER AND 4ULEY
IS IDENTICAL TO THAT OF A FLAT PLATE WHOSE PHYSICAL AREA MATCHES THE EFFECTIVE AREA OF THE CORNER REFLECTOR 4HE MAGNITUDE OF THE ECHO MAY BE DETERMINED BY FINDING THE POLYGO NAL AREAS ON EACH FACE OF THE CORNER RECEIVING WAVES REFLECTED BY THE OTHER FACES AND FROM WHICH THE FINAL REFLECTION IS BACK TOWARD THE SOURCE 4HE EFFECTIVE AREA IS DETER MINED BY SUMMING THE PROJECTIONS OF THE AREAS OF THOSE POLYGONS ON THE LINE OF SIGHT THE 2#3 IS THEN FOUND BY SQUARING THAT AREA MULTIPLYING BY O AND DIVIDING BY K &IGURE IS A COLLECTION OF 2#3 PATTERNS OF A TRIHEDRAL CORNER REFLECTOR WITH TRIANGULAR FACES 4HE REFLECTOR WAS FABRICATED OF THREE TRIANGULAR PLYWOOD PANELS METALLIZED TO ENHANCE THEIR SURFACE REFLECTIVITIES 4HE APERTURE EXPOSED TO THE RADAR WAS THEREFORE AN EQUILATERAL TRIANGLE AS SHOWN IN &IGURE 4HE EIGHT PATTERNS IN &IGURE WERE MEASURED WITH THE PLANE OF THE APERTURE TILTED ABOVE OR BELOW THE LINE OF SIGHT BY THE ANGLE E 4HE BROAD CENTRAL PART OF THESE PATTERNS IS DUE TO A TRIPLE BOUNCE MECHANISM BETWEEN THE THREE PARTICIPATING FACES WHILE THE hEARSv AT THE SIDES OF THE PATTERNS ARE DUE TO THE SINGLE BOUNCE FLAT PLATE SCATTERING FROM THE INDIVIDUAL FACES !LONG THE AXIS OF SYMMETRY OF THE TRIHEDRAL REFLECTOR IN &IGURE P n E n THE 2#3 IS O,K WHERE , IS THE LENGTH OF ONE OF THE EDGES OF THE APERTURE .OT SHOWN ARE THE ECHO REDUCTIONS OBTAINED WHEN THE TRIHEDRAL FACES ARE NOT PERPEN DICULAR TO EACH OTHER 4HOSE REDUCTIONS DEPEND ON THE SIZE OF THE FACES EXPRESSED IN WAVELENGTHS 4HE 2#3 OF MOST OF THE SIMPLE SCATTERING FEATURES DISCUSSED IN THIS SECTION MAY BE ESTIMATED BY USING THE SIMPLE FORMULAS LISTED IN 4ABLE 4HE 2#3 OF SOME COM PLICATED TARGETS MAY BE ESTIMATED BY REPRESENTING THE TARGET AS A COLLECTION OF FEATURES LIKE THOSE LISTED IN 4ABLE CALCULATING THE INDIVIDUAL CONTRIBUTIONS AND THEN SUM MING THE CONTRIBUTIONS COHERENTLY OR NONCOHERENTLY AS GOVERNED BY THE OBJECTIVE OF THE CALCULATIONS
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&)'52% 2#3 PATTERNS OF A TRIHEDRAL CORNER REFLECTOR %DGE OF APERTURE IN K CM 3 3 2OBERTSON Ú !44 2EPRINTED WITH PERMISSION FROM !44 4ECHNICAL *OURNAL
#OMPLEX /BJECTS /BJECTS SUCH AS INSECTS BIRDS AIRPLANES SHIPS AND ANTENNAS CAN BE MUCH MORE COMPLEX THAN THOSE JUST DISCUSSED EITHER BECAUSE OF THE MULTIPLIC ITY OF SCATTERERS ON THEM OR BECAUSE OF THE COMPLEXITY OF THEIR SURFACE PROFILES AND DIELECTRIC CONSTANTS )NSECTS ARE EXAMPLES OF THE LATTER -EASURED VALUES FOR A DOZEN SPECIES OF INSECTS ARE LISTED IN 4ABLE 4HE BUGS WERE ALIVE FOR THE MEASUREMENTS BUT HAD TO BE DRUGGED TO IMMOBILIZE THEM &IGURE SHOWS THE RELATIONSHIP BETWEEN THE 2#3 AND THE MASS OF AN INSECT WITH THE VARIATION OF A WATER DROPLET SHOWN FOR COMPARISON 4ABLE LISTS THE 2#3 OF A MAN AS REPORTED BY 3CHULTZ ET AL /THER COMPARISONS HAVE BEEN MADE FOR BOTH BIRDS AND INSECTS
&)'52% #OORDINATE SYSTEM FOR THE 2#3 PATTERNS IN &IGURE 3 3 2OBERTSON Ú !44 2EPRINTED WITH PERMISSION FROM !44 4ECHNICAL *OURNAL
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4!",% -EASURED )NSECT 2#3 AT '(Z
)NSECT
,ENGTH MM
7IDTH MM
"ROADSIDE 2#3 D"SM
%ND ON 2#3 D"SM
"LUE WINGED LOCUST !RMYWORM MOTH !LFALFA CATERPILLAR BUTTERFLY (ONEYBEE WORKER #ALIFORNIA HARVESTER ANT 2ANGE CRANE FLY 'REEN BOTTLE FLY 4WELVE SPOTTED CUCUMBER BEETLE #ONVERGENT LADY BEETLE 3PIDER UNIDENTIFIED
./4% /RIGINAL VALUES REPORTED IN SQUARE CENTIMETERS HAVE BEEN CONVERTED HERE TO D"SM WHICH IS DECIBELS RELATIVE TO A SQUARE METER
4!",% -EASURED 2#3 OF A -AN
&REQUENCY '(Z
2#3 M n n n n n
&)'52% 3AMPLE OF MEASURED 2#3 OF INSECTS AS A FUNCTION OF INSECT MASS AT '(Z BASED ON 2ILEYS SUMMARY 4HE DASHED LINE IS THE CALCULATED 2#3 OF WATER DROPLETS FOR COMPARISON AFTER * 2 2ILEY Ú )%%%
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&)'52% -EASURED 2#3 PATTERN OF A " BOMBER AT A FREQUENCY OF '(Z
%XAMPLES OF 2#3 PATTERNS FOR AIRCRAFT ARE SHOWN IN &IGURES AND 4HE " PATTERN IN &IGURE WAS MEASURED AT A FREQUENCY OF '(Z 4HE POLAR FORMAT IS USEFUL FOR DISPLAY PURPOSES BUT IS NOT AS CONVENIENT FOR DETAILED COMPARISONS AS IS A RECTANGULAR FORMAT LIKE THE ONE USED IN &IGURE 4HAT RECTANGULAR PATTERN IS OF A ONE THIRD SCALE MODEL # AIRCRAFT AND WAS DISPLAYED IN THE EARLY S ON A 53 !IR &ORCE WEB SITE 4HE # IS A MILITARY VERSION OF THE 2AYTHEON (AWKER 80 MID SIZE BUSINESS JET 4HE !IR &ORCE WEB SITE REVEALS VERY LITTLE TECHNICAL DETAIL ABOUT THE TEST CONDITIONS ATTENDING THE DATA COLLECTION SUCH AS THE FREQUENCY AND POLARIZATION OF THE MEASURE MENTS NOT EVEN THE UNITS IN WHICH THE 2#3 DATA ARE DISPLAYED (OWEVER EVEN IF WE DO NOT KNOW THE TEST FREQUENCY OR POLARIZATION WE DO KNOW THAT THE FULL SCALE 2#3 WILL BE LOG r D" HIGHER THAN THOSE CHARTED IN THE FIGURE IE HIGHER BY THE SQUARE OF THE INVERSE SCALE FACTOR 7E SUSPECT THAT NOSE ON INCIDENCE IS AT THE CENTER OF THE PATTERN AND THAT THE CHARTED 2#3 DATA ARE IN DECIBELS ABOVE A SQUARE METER AT THE TEST FREQUENCY &IGURE CHARTS THE 2#3 OF A SHIP MEASURED AT AND '(Z AT HORIZONTAL POLARIZATION 4HE DATA WERE COLLECTED BY A SHORE BASED RADAR INSTRUMENTATION COMPLEX AS THE SHIP STEAMED IN A LARGE CIRCLE ON #HESAPEAKE "AY 4HE THREE TRACES IN THESE CHARTS ARE THE AND PERCENTILE LEVELS OF THE SIGNALS COLLECTED OVER ASPECT ANGLE hWIN DOWSv n WIDE 4HE PATTERNS ARE NOT SYMMETRICAL ESPECIALLY AT THE HIGHER FREQUENCY .OTE THAT THE 2#3 CAN EXCEED MI D"SM
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&)'52% -EASURED 2#3 OF A ONE THIRD SCALE MODEL # MILITARY AIRCRAFT
!N EMPIRICAL FORMULA FOR THE 2#3 OF A NAVAL SHIP IS
R F
$
WHERE d IS THE RADAR FREQUENCY IN MEGAHERTZ AND $ IS THE FULL LOAD DISPLACEMENT OF THE VESSEL IN KILOTONS 4HE RELATIONSHIP IS BASED ON MEASUREMENTS OF SEVERAL SHIPS AT LOW GRAZING ANGLES AND REPRESENTS THE AVERAGE OF THE MEDIAN 2#3 IN THE PORT AND STARBOARD BOW AND QUARTER ASPECTS BUT EXCLUDING THE BROADSIDE PEAKS 4HE STATISTICS INCLUDE DATA COLLECTED AT NOMINAL WAVELENGTHS OF AND CM FOR SHIP DIS PLACEMENTS RANGING FROM TO KILOTONS &IGURE SUMMARIZES THE GENERAL 2#3 LEVELS OF THE WIDE VARIETY OF TARGETS DISCUSSED IN THIS SECTION WITH THE 2#3 OF A METALLIC SPHERE SHOWN AS A FUNCTION OF ITS VOLUME FOR COMPARISON 4HE ORDINATE IS THE 2#3 IN SQUARE METERS AND THE ABSCISSA IS THE VOLUME OF THE TARGET IN CUBIC FEET "ECAUSE THE CHART IS INTENDED ONLY TO DISPLAY THE WIDE RANGE IN 2#3 THAT MAY BE ENCOUNTERED IN PRACTICE THE LOCATIONS OF TARGETS ON THE CHART ARE APPROXIMATE AT BEST 7ITHIN GIVEN TARGET CLASSES THE 2#3 MAY BE EXPECTED TO VARY BY AS MUCH AS OR D" DEPENDING ON FREQUENCY ASPECT ANGLE AND SPECIFIC TARGET CHARACTERISTICS 2EADERS SEEKING MORE EXPLICIT DETAIL THAN THIS SHOULD CONSULT REFERENCED MATERIAL AT THE END OF THIS CHAPTER
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&)'52% -EASURED 2#3 OF A LARGE NAVAL AUXILIARY SHIP FOR HORIZONTAL INCIDENT POLARIZATION 4HE UPPER PATTERN A IS FOR '(Z AND THE LOWER PATTERN B IS FOR '(Z 3HOWN ARE THE AND PERCENTILE LEVELS BASED ON THE STATISTICS OF THE DATA OVER n ASPECT ANGLE WINDOWS
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&)'52% 3UMMARY OF 2#3 LEVELS OF TARGETS DISCUSSED IN THIS SECTION 4HE LOCATIONS OF TARGETS ON THE CHART ARE GENERAL INDICATIONS ONLY
£{°ÎÊ , -Ê*, /" Ê/ +1 !S SHOWN IN &IGURE SCATTERING OBSTACLES ARE GENERALLY SORTED INTO THREE DIFFERENT REGIMES BASED ON THEIR BODY SIZE IN WAVELENGTHS 6ERY LOOSELY THESE THREE REGIONS ARE L
L
L
2AYLEIGH REGION TYPICAL BODY SIZE K 2ESONANCE REGION K TYPICAL BODY SIZE K /PTICS REGION K TYPICAL BODY SIZE
4HE BOUNDARIES SEPARATING THE THREE REGIMES ARE DIFFUSE AT BEST 4HE UTILITY OF OUR 2#3 ESTIMATION AND COMPUTATION METHODS DEPENDS IN LARGE MEASURE ON WHERE IN THIS SIZE SCHEME WE FIND OUR TARGET !LTHOUGH THE COMPLEXITY AND SIZE OF MOST SCATTERING OBJECTS PRECLUDE THE APPLICA TION OF EXACT METHODS OF RADAR CROSS SECTION PREDICTION EXACT SOLUTIONS FOR SIMPLE BODIES PROVIDE VALUABLE CHECKS FOR APPROXIMATE METHODS 4HE EXACT METHODS ARE RESTRICTED TO RELATIVELY SIMPLE OR RELATIVELY SMALL OBJECTS IN THE 2AYLEIGH AND RESONANT REGIONS WHEREAS MOST OF THE APPROXIMATE METHODS HAVE BEEN DEVELOPED FOR THE OPTICS REGION ALSO CALLED THE HIGH FREQUENCY REGION 4HERE ARE EXCEPTIONS TO THESE GENERAL LIMITATIONS OF COURSE 4HE EXACT SOLUTIONS FOR MANY OBJECTS CAN BE USED FOR LARGE BOD IES WELL INTO THE OPTICS REGION IF ONE USES ARITHMETIC OF SUFFICIENT PRECISION AND MANY OPTICS APPROXIMATIONS CAN BE EXTENDED TO BODIES OF MODEST ELECTRICAL SIZE INTO THE RESONANCE REGION ,OW FREQUENCY APPROXIMATIONS DEVELOPED FOR THE 2AYLEIGH REGION CAN EXTEND UPWARD INTO THE RESONANCE REGION %XACT -ETHODS 4HE EXACT METHODS ARE BASED ON EITHER THE INTEGRAL OR DIFFEREN TIAL FORM OF -AXWELLS EQUATIONS
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$IFFERENTIAL %QUATIONS -AXWELLS FOUR DIFFERENTIAL EQUATIONS CONSTITUTE A SUC CINCT STATEMENT OF THE RELATIONSHIP BETWEEN ELECTRIC AND MAGNETIC FIELDS PRODUCED BY CURRENTS AND CHARGES AND BY EACH OTHER 4HE FOUR EQUATIONS MAY BE MANIPULATED FOR ISOTROPIC SOURCE FREE REGIONS TO GENERATE THE WAVE EQUATION
& K &
WHERE & REPRESENTS EITHER THE VECTOR ELECTRIC FIELD OR THE VECTOR MAGNETIC FIELD %QUATION IS A SECOND ORDER DIFFERENTIAL EQUATION THAT MAY BE SOLVED AS A BOUNDARY VALUE PROBLEM WHEN THE FIELDS ON THE SURFACE OF THE SCATTERING OBSTACLE ARE SPECIFIED 4HE FIELDS ARE TYPICALLY REPRESENTED AS THE SUM OF KNOWN AND UNKNOWN COMPONENTS INCIDENT AND SCATTERED FIELDS AND THE BOUNDARY CONDITIONS ARE THE KNOWN RELATION SHIPS THAT MUST BE SATISFIED BETWEEN THE FIELDS BOTH ELECTRIC AND MAGNETIC JUST INSIDE AND JUST OUTSIDE THE SURFACE OF THE OBSTACLE 4HOSE BOUNDARY CONDITIONS ARE PARTICULARLY SIMPLE FOR SOLID CONDUCTING OR DIELECTRIC OBJECTS 4HE BOUNDARY CONDITIONS INVOLVE ALL THREE COMPONENTS OF THE VECTOR FIELDS AND THE SURFACE OF THE BODY MUST COINCIDE WITH A COORDINATE OF THE GEOMETRICAL SYSTEM IN WHICH THE BODY IS DESCRIBED &OR EXAMPLE THE COORDINATE R CONSTANT COULD REPRESENT A SPHERICAL SURFACE 4HE SOLUTION OF THE WAVE EQUATION IS MOST USEFUL FOR THOSE SYSTEMS IN WHICH THE EQUATION IS SEPARABLE INTO ORDINARY DIFFERENTIAL EQUATIONS IN EACH OF THE VARIABLES 4HE SCATTERED FIELDS ARE TYPICALLY EXPRESSED IN TERMS OF INFINITE SERIES THE COEFFICIENTS OF WHICH ARE TO BE DETERMINED IN THE ACTUAL SOLUTION OF THE PROBLEM /NCE OBTAINED THE SOLUTION ALLOWS THE FIELDS TO BE CALCULATED AT ANY POINT IN SPACE WHICH IN 2#3 PROBLEMS IS THE LIMIT AS THE DISTANCE FROM THE OBSTACLE BECOMES INFINITE 4HE SOLUTION OF THE WAVE EQUATION MAY THEN BE USED IN %Q TO DETERMINE THE SCATTERING CROSS SECTION !SIDE FROM A FEW VERY SIMPLE OBJECTS SUCH AS THE SPHERE AND THE INFINITE CIRCULAR CYLINDER THE SOLUTION FOR %Q IS MORE ACADEMIC THAN PRACTICAL 4HE SOLUTION FOR OTHER STRUCTURES SUCH AS INFINITE PARABOLIC AND ELLIPTIC CYLINDERS ARE DIFFICULT AT BEST AND FOR MANY STRUCTURES WHOSE SURFACES MAY COINCIDE WITH A COORDINATE SYSTEM THERE IS NO CONVENIENT METHOD OF SOLUTION 4HE MOST USEFUL AND PRACTICAL OF THE EXACT SOLUTIONS AVAILABLE IS THAT OF THE PER FECTLY CONDUCTING SPHERE SHOWN EARLIER IN &IGURE -ETAL SPHERES ARE USED ROU TINELY AS CALIBRATION TARGETS FOR 2#3 MEASUREMENTS BECAUSE AN EXACT SOLUTION IS AVAILABLE METAL SPHERES ARE NOT VERY HARD TO BUILD AND EFFICIENT COMPUTER CODES ARE AVAILABLE FOR OBTAINING THE EXACT SOLUTION .O OTHER SCATTERING BODY AFFORDS ALL THESE CONVENIENCES )NTEGRAL %QUATIONS -AXWELLS EQUATIONS MAY ALSO BE MANIPULATED TO GENERATE A PAIR OF INTEGRAL EQUATIONS KNOWN AS THE 3TRATTON #HU EQUATIONS
%S u ¯ [IK: N r ( 9 N r % r 9 N ; % 9] D3
(S u ¯ [ IK9 N r % 9 N r ( r 9 N ; % 9] D3
WHERE N IS THE UNIT SURFACE NORMAL ERECTED AT THE SURFACE PATCH D3 AND Y IS THE 'REENS FUNCTION
9 EIKR P R
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4HE DISTANCE R IN %Q IS MEASURED FROM THE SURFACE PATCH D3 TO THE POINT AT WHICH THE SCATTERED FIELDS ARE DESIRED WHICH COULD BE ANOTHER SURFACE PATCH 4HESE EXPRESSIONS STATE THAT IF THE TOTAL ELECTRIC AND MAGNETIC FIELD DISTRIBUTIONS ARE KNOWN OVER A COMPLETELY CLOSED SURFACE 3 AS INDICATED BY THE LITTLE CIRCLE ON THE INTEGRAL SIGN THE FIELDS ANYWHERE IN SPACE MAY BE COMPUTED BY SUMMING INTEGRATING THOSE SURFACE FIELD DISTRIBUTIONS OVER THE ENTIRE SURFACE 4HIS SCATTERING PROBLEM RELIES ON THE SAME TWO EQUATIONS BUT INSTEAD OF MEASURING THE TOTAL FIELDS OVER A CLOSED SURFACE SURROUNDING THE BODY ONE DETERMINES THE FIELDS INDUCED ON THE BODY SURFACES THEM SELVES BY THE INCIDENT WAVE AND THEN SOLVES A SYSTEM OF LINEAR EQUATIONS 4HESE SURFACE FIELDS BECOME UNKNOWNS TO BE DETERMINED 4HE TWO EQUATIONS ARE COUPLED BECAUSE THE UNKNOWNS APPEAR ON BOTH SIDES OF BOTH EQUATIONS 4HE METHOD OF SOLUTION IS KNOWN AS THE METHOD OF MOMENTS -/- WHICH REDUCES THE INTEGRAL EQUATIONS TO A COLLECTION OF HOMOGENEOUS LINEAR EQUATIONS THAT MAY BE SOLVED BY MATRIX TECHNIQUES /NCE THE BOUNDARY CONDITIONS HAVE BEEN SPECIFIED THE SURFACE 3 IS SPLIT INTO A COL LECTION OF DISCRETE PATCHES AS SUGGESTED IN &IGURE 4HE PATCHES MUST BE SMALL ENOUGH TYPICALLY LESS THAN K THAT THE UNKNOWN CURRENTS AND CHARGES OVER EACH PATCH ARE CONSTANT OR AT LEAST CAN BE DESCRIBED BY SIMPLE FUNCTIONS ! WEIGHTING FUNCTION MAY BE ASSIGNED TO EACH PATCH AND THE PROBLEM IS ESSENTIALLY SOLVED WHEN THE AMPLITUDE AND PHASE OF THOSE FUNCTIONS HAVE BEEN DETERMINED )F THE POINT OF OBSERVATION IS FORCED DOWN TO A GENERAL SURFACE PATCH THE FIELDS ON THE LEFT SIDES OF %QS AND ARE THOSE DUE TO THE CONTRIBUTIONS OF THE FIELDS ON ALL OTHER PATCHES PLUS THE INCIDENT FIELDS AND A hSELF FIELDv 4HE SELF FIELD OR SELF CURRENT OR SELF CHARGE IS MOVED TO THE RIGHT SIDE OF THE EQUATIONS LEAVING ONLY THE KNOWN INCIDENT FIELD ON THE LEFT SIDE 7HEN THE PROCESS IS REPEATED FOR EACH PATCH ON THE SURFACE A SYS TEM OF N LINEAR HOMOGENEOUS EQUATIONS IN N UNKNOWNS IS GENERATED )F THE BOUNDARY CONDITIONS PERMIT THE DECOUPLING OF THE EQUATIONS THE NUMBER OF UNKNOWNS MAY BE HALVED TO N EQUATIONS IN N UNKNOWNS 4HE COEFFICIENTS OF THE RESULTING MATRIX INVOLVE ONLY THE ELECTRICAL DISTANCES IN WAVELENGTHS BETWEEN ALL PATCHES TAKEN BY PAIRS AND THE ORIENTATION OF PATCH SURFACE NORMALS 4HE UNKNOWN FIELDS MAY BE FOUND BY INVERTING THE RESULTING MATRIX AND MULTIPLYING THE INVERTED MATRIX BY A COLUMN MATRIX REPRESENTING THE INCIDENT FIELD AT EACH PATCH 4HE SURFACE FIELDS ARE THEN SUMMED IN INTEGRALS SIMILAR TO %QS AND TO OBTAIN THE SCATTERED FIELD WHICH THEN MAY BE INSERTED IN %Q TO COMPUTE THE 2#3
&)'52% 4HE METHOD OF MOMENTS DIVIDES THE BODY SURFACE INTO A COLLECTION OF DISCRETE PATCHES 4HIS PLANFORM OF THE 53 !IR &ORCE " 3PIRIT STEALTH BOMBER USES TRIANGULAR PATCHES
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&)'52% !ZIMUTH PLANE -/- PREDICTED EDGE ON 2#3 OF A FLAT PLATE HAVING THE PLANFORM SHOWN IN &IGURE FOR WING LEADING EDGES K IN LENGTH 4HE INCIDENT ELECTRIC FIELD WAS IN THE PLANE OF THE PLATE
4HE METHOD OF MOMENTS HAS BECOME A POWERFUL TOOL IN THE PREDICTION AND ANALYSIS OF ELECTROMAGNETIC SCATTERING WITH APPLICATIONS FOR ANTENNA DESIGN AS WELL AS 2#3 PREDICTION 4HIS METHOD HAS THREE LIMITATIONS HOWEVER &IRST BECAUSE COMPUTER MEMORY AND PROCESSING TIME BOTH INCREASE RAPIDLY WITH THE ELECTRICAL SIZE OF THE OBJECT THERE MIGHT BE AN ECONOMIC LIMIT FOR THE MAXIMUM TARGET ELECTRICAL SIZE IN WAVELENGTHS FOR WHICH -/- CAN BE USED 3ECOND -/- YIELDS NUMBERS NOT FORMULAS AND IS THEREFORE A NUMERICAL EXPERIMENTAL TOOL (OWEVER TRENDS MAY BE ESTABLISHED BY RUNNING THESE NUMERICAL EXPERIMENTS REPEATEDLY FOR PARA METRIC CHANGES IN THE GEOMETRY OR CONFIGURATION OF AN OBJECT OR IN THE ANGLE OF ARRIVAL OR OF THE FREQUENCY OF THE INCIDENT WAVE 4HIRD THE SOLUTIONS FOR SOME OBJECTS MAY CONTAIN SPURIOUS RESONANCES THAT DO NOT ACTUALLY EXIST THEREBY REDUCING THE CONFIDENCE ONE MAY HAVE IN APPLYING THE METHOD TO ARBITRARY STRUCTURES &IGURE SHOWS A -/- CODE PREDICTION OF THE EDGE ON 2#3 PATTERN OF A LARGE FLAT METAL PLATE OF ZERO THICKNESS HAVING THE PLANFORM OF &IGURE &OR THE PURPOSE OF ILLUSTRATION WE CHOSE A SIMULATION FREQUENCY SUCH THAT THE LEADING EDGES OF THE WINGS WERE K LONG 4HE INCIDENT POLARIZATION AND THE DIRECTION OF THE INCIDENT WAVE WERE BOTH IN THE PLANE OF THE PLATE .OSE ON INCIDENCE LIES AT ZERO DEGREE ASPECT AT THE CENTER OF THE CHART AND THE TAIL ON ASPECT LIES AT n AT BOTH SIDES OF THE CHART !S SHOWN IN 4ABLE THE APPROXIMATE 2#3 OF A STRAIGHT EDGE OF LENGTH , PRE SENTED PERPENDICULAR TO THE INCIDENT WAVE IS R ,O (OWEVER THIS ESTIMATE IS SOME D" LOWER THAN THE PEAK AMPLITUDE ATTAINED IN &IGURE BY THE LEADING EDGE ECHOES EITHER SIDE OF NOSE ON INCIDENCE %VIDENTLY THERE ARE OTHER MORE SUBTLE ECHO SOURCES THAT CONTRIBUTE TO THE 2#3 AT THESE ASPECTS POSSIBLY SURFACE TRAVELING WAVE CONTRIBUTIONS !PPROXIMATE -ETHODS !PPROXIMATE METHODS FOR COMPUTING SCATTERED FIELDS ARE AVAILABLE IN BOTH THE 2AYLEIGH AND THE OPTICS REGIONS 2AYLEIGH REGION APPROXIMA TIONS MAY BE DERIVED BY EXPANDING THE WAVE EQUATION %Q IN A POWER SERIES OF THE WAVENUMBER K (IGHER ORDER TERMS OF THE EXPANSION BECOME PROGRESSIVELY MORE DIFFICULT TO OBTAIN 4HE 2#3 PATTERN OF A 2AYLEIGH SCATTERER IS VERY BROAD ESPECIALLY IF THE OBJECT HAS SIMILAR TRANSVERSE AND LONGITUDINAL DIMENSIONS 4HE MAGNITUDE OF THE ECHO IS PROPORTIONAL TO THE SQUARE OF THE VOLUME OF THE OBJECT AND VARIES AS THE FOURTH
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POWER OF THE FREQUENCY OF THE INCIDENT WAVE "ECAUSE THE METHOD OF MOMENTS IS QUITE WELL SUITED TO THE SOLUTION OF 2AYLEIGH REGION PROBLEMS ANALYTICAL 2AYLEIGH REGION EXPANSIONS FOR PREDICTING THE 2#3 OF ELECTRICALLY SMALL OBJECTS HAVE LAPSED INTO DISUSE 3EVERAL APPROXIMATE METHODS HAVE BEEN DEVISED FOR THE OPTICS REGION EACH WITH ITS PARTICULAR ADVANTAGES AND LIMITATIONS 4HE MOST MATURE OF THE METHODS ARE GEOMETRIC OPTICS AND PHYSICAL OPTICS WITH LATER METHODS ATTACKING THE PROBLEM OF DIFFRACTION FROM EDGES AND FROM SHADOW BOUNDARY FIELD DISCONTINUITIES 7HILE THE GENERAL ACCU RACY OF THE OPTICS REGION APPROXIMATIONS IMPROVES AS THE SCATTERING OBSTACLE BECOMES ELECTRICALLY LARGER SOME OF THEM GIVE REASONABLY ACCURATE RESULTS WITHIN OR D" FOR OBJECTS AS SMALL AS A WAVELENGTH OR SO 'EOMETRIC /PTICS 4HE THEORY OF GEOMETRIC OPTICS '/ IS BASED ON THE CONSERVA TION OF ENERGY WITHIN A SLENDER FICTITIOUS TUBE CALLED A RAY 4HE DIRECTION OF PROPAGATION IS ALONG THE TUBE AND CONTOURS OF EQUAL PHASE ARE PERPENDICULAR TO IT )N A LOSSLESS MEDIUM ALL THE ENERGY ENTERING THE TUBE AT ONE END MUST COME OUT THE OTHER END BUT ENERGY LOSSES WITHIN THE MEDIUM MAY ALSO BE ACCOUNTED FOR !N INCIDENT WAVE MAY BE REPRESENTED AS A COLLECTION OF A LARGE NUMBER OF RAYS AND WHEN A RAY STRIKES A SURFACE PART OF THE ENERGY IS REFLECTED AND PART IS TRANSMITTED ACROSS THE SURFACE 4HE AMPLITUDE AND PHASE OF THE REFLECTED AND TRANSMITTED RAYS DEPEND ON THE PROPERTIES OF THE MEDIA ON EITHER SIDE OF THE SURFACE 4HE REFLECTION IS PERFECT IF THE SURFACE IS PERFECTLY CON DUCTING AND NO ENERGY IS TRANSMITTED ACROSS THE BOUNDARY INTO THE BODY 7HEN ENERGY CAN PASS THROUGH THE SURFACE TRANSMITTED RAYS ARE BENT TOWARD THE SURFACE NORMAL IN CROSSING A SURFACE INTO AN ELECTRICALLY DENSER MEDIUM HIGHER INDEX OF REFRACTION AND AWAY FROM THE SURFACE NORMAL INTO A LESS DENSE MEDIUM 4HIS BENDING OF RAYS IS KNOWN AS REFRACTION $EPENDING ON SURFACE CURVATURE AND BODY MATERIAL REFLECTED AND TRANSMITTED RAYS MAY DIVERGE FROM ONE ANOTHER OR THEY MAY CONVERGE TOWARD EACH OTHER 4HIS DEPENDENCE IS THE BASIS FOR THE DESIGN OF LENSES AND REFLECTORS AT RADAR WAVELENGTHS AS WELL AS AT OPTICAL WAVELENGTHS 4HE REDUCTION IN INTENSITY AS THE RAYS DIVERGE SPREAD AWAY FROM THE POINT OF REFLECTION CAN BE CALCULATED FROM THE CURVATURES OF THE REFLECTING SURFACE AND THE INCIDENT WAVE AT THE SPECULAR POINT WHICH IS THAT POINT ON THE SURFACE WHERE THE ANGLE OF REFLECTION EQUALS THE ANGLE OF INCIDENCE 4HE PRINCIPAL RADII OF CURVATURE OF THE SURFACE ARE MEASURED IN TWO ORTHOGONAL PLANES AT THE SPECULAR POINT AS SHOWN IN &IGURE 7HEN THE INCIDENT WAVE IS PLANAR AND THE DIRECTION OF INTEREST IS BACK TOWARD THE SOURCE THE GEOMETRIC OPTICS 2#3 IS SIMPLY
R P AA
WHERE A AND A ARE THE RADII OF CURVATURE OF THE BODY SURFACE AT THE SPECULAR POINT 4HIS FORMULA BECOMES EXACT IN THE OPTICAL LIMIT OF VANISHING WAVELENGTHS AND IS PROBABLY ACCURATE TO OR PERCENT FOR RADII OF CURVATURE AS SMALL AS K OR K )T ASSUMES THAT THE SPECULAR POINT IS NOT CLOSE TO AN EDGE 7HEN APPLIED TO DIELECTRIC OBJECTS THE EXPRESSION SHOULD BE MULTIPLIED BY THE SQUARE OF THE VOLTAGE REFLECTION COEFFICIENT ASSOCIATED WITH THE MATERIAL PROPERTIES OF THE OBJECT )NTERNAL REFLECTIONS MAY ALSO BE ACCOUNTED FOR AND THE PHASE OF INTERNALLY REFLECTED RAYS SHOULD BE ADJUSTED ACCORDING TO THE ELECTRICAL PATH LENGTHS TRAVERSED WITHIN THE BODY MATERIAL 4HE NET 2#3 SHOULD THEN BE COMPUTED AS THE COHERENT SUM OF THE SURFACE REFLECTION PLUS ALL SIGNIFICANT INTERNAL REFLECTIONS %QUATION FAILS WHEN ONE OR BOTH SURFACE RADII OF
2!$!2 #2/33 3%#4)/.
£{°Ó£
&)'52% 4HE GEOMETRIC OPTICS 2#3 OF A DOUBLY CURVED SURFACE DEPENDS ON THE PRINCIPAL RADII OF CURVATURE AT THE SPECULAR POINT 4HE SPECULAR POINT IS WHERE THE SURFACE NORMAL POINTS TOWARD THE RADAR
CURVATURE AT THE SPECULAR POINT BECOME INFINITE YIELDING INFINITE 2#3 WHICH IS OBVI OUSLY WRONG 4HIS OCCURS FOR FLAT AND SINGLY CURVED SURFACES 0HYSICAL /PTICS 4HE THEORY OF PHYSICAL OPTICS 0/ IS A SUITABLE ALTERNATIVE FOR BODIES WITH FLAT AND SINGLY CURVED SURFACE FEATURES 4HE THEORY IS BASED ON TWO APPROXIMATIONS IN THE APPLICATION OF %QS AND BOTH OF WHICH ARE REASONABLY EFFECTIVE IN A HOST OF PRACTICAL CASES 4HE FIRST IS THE FAR FIELD APPROXIMATION WHICH ASSUMES THAT THE DISTANCE FROM THE SCATTERING OBSTACLE TO THE POINT OF OBSERVATION IS LARGE COMPARED WITH ANY DIMENSION OF THE OBSTACLE ITSELF 4HIS ALLOWS US TO REPLACE THE GRADIENT OF 'REENS FUNCTION WITH
Y IKY OS
Y O E IKR r S E IK2O P 2O
WHERE R IS THE POSITION VECTOR OF INTEGRATION PATCH D3 AND S IS A UNIT VECTOR POINTING FROM AN ORIGIN IN OR NEAR THE OBJECT TO THE FAR FIELD OBSERVATION POINT USUALLY BACK TOWARD THE RADAR 2O IS THE DISTANCE FROM THE ORIGIN OF THE OBJECT TO THE FAR FIELD OBSER VATION POINT 4HE SECOND IS THE TANGENT PLANE APPROXIMATION IN WHICH THE TANGENTIAL FIELD COM PONENTS N r % AND N r ( ARE APPROXIMATED BY THEIR GEOMETRIC OPTICS VALUES 4HAT IS A TANGENT PLANE IS PASSED THROUGH THE SURFACE COORDINATE AT THE PATCH D3 AND THE TOTAL SURFACE FIELDS ARE TAKEN TO BE PRECISELY THOSE THAT WOULD HAVE EXISTED HAD THE SURFACE AT D3 BEEN INFINITE AND PERFECTLY FLAT )N ESSENCE WE DO NOT KNOW THESE FIELDS BUT WE TAKE OUR BEST GUESS AS TO WHAT THEY ARE AND INSERT THAT ESTIMATE INTO EITHER OF THE TWO INTEGRALS 4HAT DONE THE ESTIMATE OF THE UNKNOWN FIELDS IN THE INTEGRALS OF %QS AND MAY BE EXPRESSED ENTIRELY IN TERMS OF THE KNOWN INCIDENT FIELD VALUES 4HE PROBLEM THEN BECOMES ONE OF EVALUATING THE CHOSEN INTEGRAL AND SUBSTITUTING THE RESULT INTO %Q TO OBTAIN THE 2#3
£{°ÓÓ
2!$!2 (!.$"//+
)F THE SURFACE IS A GOOD CONDUCTOR THE TOTAL TANGENTIAL ELECTRIC FIELD IS VIRTUALLY ZERO AND THE TOTAL TANGENTIAL MAGNETIC FIELD IS TWICE THE AMPLITUDE OF THE INCIDENT TANGENTIAL MAGNETIC FIELD N r%
ªN r (I Nr( « ¬N
ILLUMINATED SURFACES SHADED SURFACEES
.OTE THAT THE TANGENTIAL COMPONENTS OF BOTH THE ELECTRIC AND THE MAGNETIC FIELDS ARE SET TO ZERO OVER THOSE PARTS OF THE SURFACE SHADED FROM THE INCIDENT FIELD BY OTHER BODY SURFACES /THER APPROXIMATIONS MAY BE DEVISED FOR NONCONDUCTING SURFACES )F THE INCIDENT WAVELENGTH IS LONG ENOUGH FOR EXAMPLE THE SURFACE OF A SOAP BUBBLE OR THE LEAF OF A TREE MAY BE MODELED AS A THIN MEMBRANE OVER WHICH NEITHER THE ELECTRIC NOR MAGNETIC FIELDS ARE ZERO 4HE PHYSICAL OPTICS INTEGRAL IS EASY TO EVALUATE FOR FLAT METALLIC PLATES BECAUSE THE PHASE IS THE ONLY QUANTITY WITHIN THE INTEGRAL THAT VARIES AND IT VARIES LINEARLY ACROSS THE SURFACE 7HEN APPLIED TO A RECTANGULAR METAL PLATE THE INTEGRAL EVALUATION LEADS TO THE 2#3
R P
! COSP K
;
SIN K@ SINP COSE SIN KW SINP SIN E ; K@ SINP COSE KW SINP SIN E
WHERE ! @W IS THE PHYSICAL AREA OF THE PLATE P IS THE ANGLE BETWEEN THE SURFACE NORMAL OF THE PLATE AND THE DIRECTION TO THE RADAR E IS THE ANGLE BETWEEN THE PLANE CONTAINING THE LINE OF SIGHT AND THE EDGE WHOSE LENGTH IS @ AND W IS THE WIDTH OF THE PLATE ! MORE GENERAL PHYSICAL OPTICS FORMULA IS AVAILABLE FOR THE BISTATIC SCATTERING FROM ANY POLYGONAL PLATE )F WE SET E n OR n WE OBTAIN A PRINCIPAL PLANE 2#3 PATTERN INCIDENCE IN A PLANE PERPENDICULAR TO A PAIR OF EDGES 7HEN E n %Q BECOMES
R P
! COSP K
;
SIN K@ SINP K@ SINP
)F WE SET E n INSTEAD OF E n WE GET NEARLY THE SAME ANSWER EXCEPT THAT K@ IN %Q BECOMES KW 4HE PHYSICAL OPTICS INTEGRAL IS NOT DEPENDENT ON THE POLAR IZATION OF THE INCIDENT WAVE AND IS UNRELIABLE FOR ANGLES MUCH GREATER THAN n FROM BROADSIDE INCIDENCE "Y WAY OF COMPARISON THE PHYSICAL OPTICS FORMULA FOR THE 2#3 OF A CIRCULAR METAL DISK IS
R P
! COSP K
;
* KD SINP KD SINP
WHERE ! IS THE PHYSICAL AREA OF THE DISK D IS ITS DIAMETER AND *X IS THE "ESSEL FUNC TION OF THE FIRST KIND OF ORDER %QUATIONS THROUGH ALL REDUCE TO THE VALUE LISTED IN 4ABLE FOR NORMAL INCIDENCE &OR FURTHER COMPARISON THE 0/ PATTERNS OF TWO SQUARE PLATES AND A CIRCULAR DISK ARE PLOTTED IN &IGURE
2!$!2 #2/33 3%#4)/.
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&)'52% 0/ PATTERNS OF THE 2#3 OF A SQUARE PLATE A DISK AND SECOND SQUARE PLATE
4HE THREE PATTERNS EACH COVER A n SECTOR FROM BROADSIDE TO EDGE ON AND ARE PLACED SIDE BY SIDE FOR CLARITY 4HE AREAS OF ALL THREE PLATES WERE FIXED AT K HENCE ALL THREE PATTERNS RISE TO THE SAME AMPLITUDE AT BROADSIDE INCIDENCE ZERO ASPECT 4HE CENTER PATTERN IS FOR THE DISK WHILE THE FIRST AND THIRD ARE BOTH FOR A SQUARE PLATE (OWEVER THE SQUARE PLATE WAS ORIENTED FOR A PRINCIPAL PLANE PATTERN IN THE LEFTMOST CHART AND LIKE A DIAMOND E n IN THE RIGHTMOST CHART 4HE AMOUNT OF SURFACE DISTRIBUTED TOWARD THE SIDES OF THE PLATES INFLUENCES THE SIDELOBE LEVELS 4HE 0/ INTEGRAL IS SOMEWHAT MORE COMPLICATED TO EVALUATE WHEN THE SURFACE IS SINGLY OR DOUBLY CURVED !N EXACT EVALUATION CAN BE PERFORMED FOR A CIRCULAR CYLINDER AND A SPHERICAL CAP VIEWED ALONG THE AXIS OF SYMMETRY BUT NOT FOR A TRUNCATED CONE OR A SPHERICAL CAP SEEN ALONG OTHER THAN THE AXIS OF SYMMETRY %VEN SO THE EXACT EVALU ATION FOR THE CYLINDER INCLUDES FICTITIOUS CONTRIBUTIONS FROM THE SHADOW BOUNDARIES AT THE SIDES OF THE CYLINDER THAT DO NOT APPEAR IN A STATIONARY PHASE APPROXIMATION 4HE AMPLITUDE OF THE ELEMENTAL SURFACE CONTRIBUTIONS CHANGES SLOWLY OVER THE SURFACE OF INTEGRATION WHEREAS THE PHASE CHANGES MUCH MORE RAPIDLY !S SUCH THE NET CONTRIBU TION IN REGIONS OF RAPID PHASE CHANGE IS ESSENTIALLY ZERO AND MAY BE IGNORED !S THE SPEC ULAR REGIONS ARE APPROACHED ON THE OTHER HAND THE PHASE VARIATION SLOWS DOWN AND THEN REVERSES AS THE SPECULAR POINT IS CROSSED 4HIS RESULTS IN A NONZERO SPECULAR CONTRIBUTION TO THE INTEGRAL 4HE PHASE VARIATION NEAR THE SHADOW BOUNDARIES IS RAPID HENCE SURFACE CONTRIBUTIONS THERE ARE IGNORED IN A STATIONARY PHASE EVALUATION BUT AN EXACT EVALUATION INCLUDES THEM BECAUSE THE SHADOW BOUNDARIES ARE THE LIMITS OF INTEGRATION "ECAUSE THE ACTUAL SURFACE FIELD DISTRIBUTIONS DO NOT SUDDENLY DROP TO ZERO AS THE SHADOW BOUNDARY IS CROSSED AS ASSUMED BY THE THEORY THE SHADOW BOUNDARY CONTRIBUTIONS ARE SPURIOUS 4HUS A STATIONARY PHASE APPROXIMATION OF THE PHYSICAL OPTICS INTEGRAL OVER CLOSED CURVED SURFACES TENDS TO BE MORE RELIABLE THAN AN EXACT EVALUATION OF THE INTEGRAL 7ITH THIS IN MIND THE STATIONARY PHASE RESULT FOR A CIRCULAR CYLINDER IS
R KA@
SIN K@ SINP K@ SINP
WHERE A IS THE RADIUS OF THE CYLINDER @ IS ITS LENGTH AND P IS THE ANGLE OFF BROADSIDE INCIDENCE %QUATION INCLUDES ONLY THE CONTRIBUTION FROM THE CURVED SIDE OF THE
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2!$!2 (!.$"//+
CYLINDER AND NOT ITS FLAT ENDS WHICH MAY BE INCLUDED BY USING THE PRESCRIPTION OF %Q %QUATION MAY ALSO BE USED TO ESTIMATE THE 2#3 OF A TRUNCATED RIGHT CIRCULAR CONE IF THE RADIUS A IS REPLACED BY THE MEAN RADIUS OF THE CONE AND @ IS REPLACED BY THE LENGTH OF THE SLANTED SURFACE !LTHOUGH THE THEORY OF PHYSICAL OPTICS OFFERS A SIGNIFICANT IMPROVEMENT OVER GEO METRIC OPTICS FOR FLAT AND SINGLY CURVED SURFACES IT SUFFERS OTHER DRAWBACKS %VEN THOUGH WE OBTAIN THE PROPER RESULT FOR MOST OF THE ILLUMINATED SURFACE THE PHYSI CAL OPTICS INTEGRAL YIELDS FALSE CONTRIBUTIONS FROM THE SHADOW BOUNDARIES AS ALREADY NOTED -OREOVER PHYSICAL OPTICS SHOWS NO DEPENDENCE ON THE POLARIZATION OF THE INCIDENT WAVE AND YIELDS DIFFERENT RESULTS WHEN THE RECEIVER AND THE TRANSMITTER ARE INTERCHANGED 4HESE EFFECTS CONTRADICT OBSERVED BEHAVIOR &INALLY IT ERRS BY WIDER MAR GINS AS THE DIRECTION OF OBSERVATION MOVES FARTHER AWAY FROM THE SPECULAR DIRECTION +ELLERS GEOMETRICAL THEORY OF DIFFRACTION '4$ OFFERS AN IMPROVEMENT IN BOTH THE POLARIZATION DEPENDENCE AND THE PREDICTED VALUES IN THE WIDE ANGLE REGIONS 'EOMETRIC 4HEORY OF $IFFRACTION '4$ IS A RAY TRACING METHOD THAT ASSIGNS AN AMPLITUDE AND PHASE TO FIELDS DIFFRACTED AT SMOOTH SHADOW BOUNDARIES AND AT SURFACE DISCONTINUITIES "ECAUSE THE LATTER ARE MUCH MORE SIGNIFICANT IN BACKSCATTERING COM PUTATIONS THAN THE FORMER WE FOCUS HERE ON EDGE DIFFRACTION 4HE THEORY ASSUMES THAT A RAY STRIKING AN EDGE EXCITES A CONE OF DIFFRACTED RAYS AS IN &IGURE 4HE HALF ANGLE OF THIS DIFFRACTION CONE IS EQUAL TO THE ANGLE BETWEEN THE INCIDENT RAY AND THE EDGE 5NLESS THE POINT OF OBSERVATION LIES ON THE DIFFRACTION CONE NO VALUE IS ASSIGNED THE DIFFRACTED FIELD 4HE SCATTERING DIRECTION IN BACKSCATTERING PROBLEMS IS THE REVERSE OF THE DIRECTION OF INCIDENCE WHENCE THE DIFFRACTION CONE BECOMES A DISK AND THE SCAT TERING EDGE ELEMENT IS PERPENDICULAR TO THE LINE OF SIGHT 4HE AMPLITUDE OF THE DIFFRACTED FIELD IS GIVEN BY THE PRODUCT OF A DIFFRACTION COEFFI CIENT AND A DIVERGENCE FACTOR AND THE PHASE DEPENDS ON THE PHASE OF THE EDGE EXCITATION AND ON THE DISTANCE BETWEEN THE OBSERVATION POINT AND THE DIFFRACTING EDGE ELEMENT 4WO CASES ARE RECOGNIZED DEPENDING ON WHETHER THE INCIDENT FIELD IS POLARIZED PARALLEL OR PERPENDICULAR TO THE EDGE 4HE DIFFRACTED FIELD IS GIVEN BY THE FORMULA
%D
'E IKS EIP 8 A 9 P KS SIN A
WHERE ' IS A DIVERGENCE FACTOR 8 AND 9 ARE DIFFRACTION COEFFICIENTS A IS THE ANGLE BETWEEN THE INCIDENT RAY AND THE EDGE AND S IS THE DISTANCE TO THE OBSERVATION POINT FROM THE POINT OF DIFFRACTION 4HE DIFFERENCE OF THE TWO DIFFRACTION COEFFICIENTS IS
&)'52% 4HE +ELLER CONE OF DIFFRACTED RAYS
2!$!2 #2/33 3%#4)/.
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USED WHEN THE INCIDENT ELECTRIC FIELD IS PARALLEL TO THE EDGE 4- POLARIZATION AND THE SUM WHEN THE INCIDENT MAGNETIC FIELD IS PARALLEL TO THE EDGE 4% POLARIZATION 4HE DIVERGENCE FACTOR ACCOUNTS FOR THE DECAY IN AMPLITUDE AS THE RAYS SPREAD AWAY FROM THE EDGE ELEMENT AND INCLUDES THE EFFECTS OF THE RADIUS OF THE EDGE IF IT IS CURVED AS AT THE END OF A TRUNCATED CYLINDER AND THE RADIUS OF CURVATURE OF THE INCIDENT PHASE FRONT 4HE DIVERGENCE FACTOR FOR A TWO DIMENSIONAL EDGE OF INFINITE LENGTH ILLUMI NATED BY A PLANE WAVE IS ' S 4HE DIFFRACTION COEFFICIENTS ARE
8
SINP N N COSP N COS;EI ES N=
9
SINP N N COSP N COS;EI ES N=
WHERE EI AND ES ARE THE ANGLES OF THE PLANES OF INCIDENCE AND SCATTERING AS MEASURED FROM ONE FACE OF THE WEDGE SAY THE ILLUMINATED ONE AND N IS THE EXTERIOR WEDGE ANGLE NORMALIZED WITH RESPECT TO O 7HEN THESE EXPRESSIONS ARE EVALUATED FOR THE CASE OF A FLAT METAL EDGE VIEWED EDGE ON WITH THE INCIDENT POLARIZATION IN THE PLANE OF THE PLATE THEY YIELD THE EDGE ON FORMULA R ,O LISTED IN 4ABLE +ELLERS DIFFRACTION COEFFICIENTS ARE BASED ON AN APPROXIMATION OF THE EXACT SOLUTION FOR AN INFINITE TWO DIMENSIONAL METAL WEDGE AS APPLIED TO A THREE DIMENSIONAL PROB LEM !LTHOUGH THIS ADAPTATION OF A TWO DIMENSIONAL SOLUTION TO THE THREE DIMENSIONAL WORLD IS REASONABLY EFFECTIVE MOST OF THE TIME THE DIFFRACTION COEFFICIENTS INCONVE NIENTLY BLOW UP JUST WHEN NEEDED MOST ! CURSORY EXAMINATION OF %QS AND WILL SHOW WHY 4HE DENOMINATORS OF BOTH EXPRESSIONS CONTAIN THE DIFFERENCE OF TWO COSINE TERMS THAT BECOME EQUAL IN TWO DIFFERENT CASES 7HEN THE SCATTERING DIRECTION ES IS ALIGNED ALONG THE SHADOW BOUNDARY WHERE EI ES O THE DIFFRACTION COEFFICIENT 8 IN %Q BECOMES SINGULAR A MEANINGLESS RESULT 7HEN THE SCATTERING DIRECTION ES IS ALIGNED ALONG THE SPECULAR DIRECTION WHERE THE LOCAL ANGLE OF REFLECTION IS EQUAL TO THE LOCAL ANGLE OF INCIDENCE THEN EI ES O )N THIS CASE IT IS THE DIFFRACTION COEFFICIENT 9 IN %Q THAT BECOMES SINGULAR A SIMILARLY MEANINGLESS RESULT .OTE THAT THESE TWO SINGULARITIES DO NOT DEPEND ON BODY GEOMETRY BUT ONLY ON THE RELATIVE DISPOSITIONS OF THE INCIDENCE AND SCATTERING DIRECTIONS 0HYSICAL 4HEORY OF $IFFRACTION 4HE SINGULARITIES IN '4$ ARE OVERCOME IN THE PHYSICAL THEORY OF DIFFRACTION 04$ FORMULATED BY 0 )A 5FIMTSEV !LTHOUGH THESE PUBLICATIONS MAY BE DIFFICULT TO FIND WE CITE THEM HERE FOR COMPLETENESS .OTE FROM THE EDITOR 4HE READER INTERESTED IN THIS SUBJECT MIGHT ALSO SEE THE 5FIMTSEV PAPER h#OMMENTS ON $IFFRACTION 0RINCIPLES AND ,IMITATIONS OF 2#3 2EDUCTION 4ECHNIQUES v 0ROC )%%% VOL PP n $ECEMBER ,IKE +ELLER 5FIMTSEV RELIED ON THE APPROXIMATE WIDE ANGLE SOLUTION OF THE TWO DIMENSIONAL WEDGE PROBLEM BUT HE DISTINGUISHED BETWEEN hUNIFORMv AND hNONUNIFORMv INDUCED SURFACE CURRENTS 4HE UNIFORM CURRENTS WERE NONE OTHER THAN THE SURFACE CURRENTS OF PHYSICAL OPTICS WHEREAS THE NONUNIFORM CURRENTS WERE TAKEN TO BE UNDEFINED FILAMENTARY CURRENTS ALONG THE EDGE ITSELF 5FIMTSEV NEVER ATTEMPTED TO WORK OUT HIS FILAMENTARY FRINGE CURRENTS BUT INSTEAD TRACED THEIR EFFECT DIRECTLY TO THE FAR SCATTERED FIELD 2ECOGNIZING THAT THE FAR FIELD 0/ CONTRIBUTION TO THE FAR FIELD WAS THE PART OF THE '4$ PRESCRIPTION GIVING RISE TO SINGULARITIES IN THE 8 AND 9 OF %QS AND 5FIMTSEV DEVISED A MODIFIED SET OF DIFFRACTION COEFFICIENTS BY SIMPLY SUBTRACTING AWAY
£{°ÓÈ
2!$!2 (!.$"//+
THE OFFENSIVE 0/ DIFFRACTION COEFFICIENTS FROM THE TIME HONORED WIDE ANGLE WEDGE SOLUTION 4HIS GENERATED A NEW SET OF DIFFRACTION COEFFICIENTS THAT RETAINED ONLY THE EDGE TERMS THEREFORE EXCLUDING ANY SURFACE TERMS 5FIMTSEVS 04$ COEFFICIENTS WERE WELL BEHAVED IN ALMOST ALL DIRECTIONS IN SPACE BUT SUFFERED ONE DISADVANTAGE IN ORDER TO CALCULATE THE 2#3 OF AN ARBITRARY EDGED BODY ONE HAD TO SUM ALL THE 04$ EDGE CONTRIBUTIONS PLUS ALL THE 0/ AND '/ SURFACE CONTRIBUTIONS (OWEVER THE PROCEDURE IS VIABLE AND HAS BEEN WELL DOCUMENTED )NCREMENTAL ,ENGTH $IFFRACTION #OEFFICIENT '4$ AND 04$ ARE BOTH BASED ON THE EXACT SOLUTION OF THE TWO DIMENSIONAL WEDGE PROBLEM FOR WHICH THE DIRECTIONS OF INCIDENCE AND SCATTERING ARE PERPENDICULAR TO THE EDGE 7HEN EXTENDED TO THE CASE OF OBLIQUE INCIDENCE THE DIRECTION OF OBSERVATION MUST LIE ALONG A GENERATOR OF THE +ELLER CONE DEPICTED IN &IGURE )F THE EDGE IS STRAIGHT AND OF FINITE LENGTH AS IN THE THREE DIMENSIONAL WORLD %Q OF +NOTT PROVIDES AN APPROXIMATION OF THE 2#3 )F THE EDGE IS CURVED IT MAY BE REGARDED AS A COLLECTION OF INFINITESIMALLY SHORT SEGMENTS BUTTED TOGETHER AND THE SCATTERED FIELDS MAY BE COMPUTED VIA AN INTEGRATION OF INCREMENTAL FIELDS DIFFRACTED BY EACH ELEMENT OF THE EDGE 4HIS IS THE CONCEPT INTRO DUCED BY -ITZNER AND THE SUMMATION OF THE FIELDS DIFFRACTED BY THE EDGE ELEMENTS IMPLIES AN INTEGRAL AROUND THE EDGE CONTOUR -ITZNER HOWEVER SOUGHT THE FIELDS SCATTERED IN ARBITRARY DIRECTIONS NOT JUST THOSE ALONG THE LOCAL +ELLER CONES AND FOR THIS PURPOSE HE DEVELOPED HIS INCREMENTAL LENGTH DIFFRACTION COEFFICIENT ),$# %XTENDING THE EXAMPLE PROVIDED BY 5FIMTSEV HE DEVISED A SET OF DIFFRACTION COEFFICIENTS FOR ARBITRARY DIRECTIONS OF INCIDENCE AND SCAT TERING .OT UNEXPECTEDLY THOSE COEFFICIENTS ARE MORE COMPLICATED THAN THE 8S AND 9S APPEARING IN %QS AND -ITZNER EXPRESSED HIS RESULT AS THE DIFFRACTED ELECTRIC FIELD COMPONENTS PARALLEL AND PERPENDICULAR TO THE PLANE OF SCATTERING IN TERMS OF THE COMPONENTS OF THE INCI DENT ELECTRIC FIELD PARALLEL AND PERPENDICULAR TO THE PLANE OF INCIDENCE !S SUCH THE DIFFRACTION COEFFICIENTS MAY BE EXPRESSED AS THREE SEPARATE PAIRS REPRESENTING PARAL LEL PARALLEL PERPENDICULAR PERPENDICULAR AND PARALLEL PERPENDICULAR OR PERPENDICU LAR PARALLEL COMBINATIONS /NE MEMBER OF EACH PAIR IS DUE TO THE TOTAL SURFACE CURRENT ON THE DIFFRACTING EDGE INCLUDING THE ASSUMED FILAMENTARY EDGE CURRENTS AND THE OTHER IS DUE TO THE UNIFORM PHYSICAL OPTICS CURRENTS -ITZNER SUBTRACTED ONE MEMBER OF EACH PAIR FROM THE OTHER THEREBY RETAINING THE CONTRIBUTIONS FROM THE FILAMENTARY EDGE CURRENTS ALONE 4HE RESULTS HAVE THE IDENTICAL FORM OF 5FIMTSEVS EXPRESSIONS IN WHICH THE 0/ COEFFICIENTS ARE SUBTRACTED FROM THE NON 0/ COEFFICIENTS 4HUS -ITZNERS EXPRES SION FOR THE SCATTERED FIELD CONTAINS ONLY THE CONTRIBUTIONS FROM THE FILAMENTARY EDGE CURRENTS )N APPLYING HIS THEORY TO SCATTERING OBJECTS THEREFORE THE CONTRIBUTIONS OF NONFILAMENTARY INDUCED SURFACE CURRENTS MUST BE ACCOUNTED FOR SEPARATELY JUST AS IN 5FIMTSEVS 04$ 7HEN THE DIRECTIONS OF INCIDENCE AND SCATTERING BECOME PERPENDICU LAR TO AN EDGE THE PERPENDICULAR PARALLEL TERMS DISAPPEAR AND -ITZNERS DIFFRACTION COEFFICIENTS THEN REDUCE IDENTICALLY TO 5FIMTSEVS -ETHOD OF %QUIVALENT #URRENTS 5NDERTAKING WHAT HE CALLED A MORE RIGOROUS EVALUATION OF THE FIELDS INDUCED ON A WEDGE -ICHAELI DUPLICATED -ITZNERS RESULT FOR THE TOTAL SURFACE CURRENTS CONFIRMING -ITZNERS PRIOR DEVELOPMENT BUT HE DID NOT EXPLICITLY REMOVE THE 0/ SURFACE CURRENT CONTRIBUTIONS 4HUS LIKE +ELLERS 8 AND 9 -ICHAELIS DIFFRACTION COEFFICIENTS BECOME SINGULAR IN THE TRANSITION REGIONS ALONG
2!$!2 #2/33 3%#4)/.
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THE REFLECTION AND SHADOW BOUNDARY DIRECTIONS -ICHAELI LATER INVESTIGATED THE REMOVAL OF THE SINGULARITIES THE CLEVEREST OF WHICH WAS THE USE OF A SKEWED COORDINATE SYSTEM ALONG THE WEDGE SURFACES 7HILE THESE METHODS OF EVALUATING THE FIELDS SCATTERED BY EDGE ELEMENTS MAY BE APPLICABLE TO SMOOTH UNBOUNDED EDGES THEY DO NOT ACCOUNT FOR THE DISCONTINUITIES AT CORNERS WHERE THE EDGES TURN ABRUPTLY IN OTHER DIRECTIONS !N ATTACK ON THE CORNER PROBLEM HAS BEEN SUGGESTED BY 3IKTA ET AL
£{°{Ê , -Ê -1, /Ê/ +1 2#3 MEASUREMENTS MAY BE REQUIRED FOR ANY OF SEVERAL REASONS RANGING FROM SCIENTIFIC INQUIRY TO VERIFICATION OF COMPLIANCE WITH PRODUCT SPECIFICATIONS 4HERE ARE NO FORMAL STANDARDS GOVERNING INSTRUMENTATION AND MEASUREMENT METHODS BUT INFORMAL STAN DARDS OF GOOD MEASUREMENT PRACTICE HAVE BEEN RECOGNIZED FOR DECADES $EPENDING ON THE SIZE OF THE TEST OBJECT THE FREQUENCIES TO BE USED AND OTHER TEST REQUIREMENTS MEASUREMENTS MAY BE MADE IN INDOOR TEST FACILITIES OR ON OUTDOOR RANGES "ECAUSE ONE IS SELDOM INTERESTED IN THE 2#3 OF AN OBJECT FOR ONLY ONE ASPECT ANGLE ALL STATIC TEST RANGES USE TURNTABLES OR ROTATORS TO VARY THE TARGET ASPECT ANGLE !LTHOUGH THE PURPOSE OF TESTING OFTEN GOVERNS HOW THE MEASUREMENTS WILL BE MADE -ACK AND $YBDAL PRO VIDE GOOD OVERALL GUIDES FOR ROUTINE 2#3 TESTING 'ENERAL 2EQUIREMENTS 4HE MOST IMPORTANT REQUIREMENT FOR 2#3 MEASURE MENTS IS THAT THE TEST OBJECT BE ILLUMINATED BY A RADAR WAVE OF ACCEPTABLY UNIFORM AMPLITUDE AND PHASE 'OOD PRACTICE DICTATES THAT THE AMPLITUDE OF THE INCIDENT WAVE DEVIATE BY NO MORE THAN D" OVER THE TRANSVERSE AND LONGITUDINAL EXTENT OF THE TAR GET AND THAT THE PHASE DEVIATION BE LESS THAN )T IS STANDARD PRACTICE AT SOME TEST RANGES TO PHYSICALLY PROBE THE INCIDENT FIELD AT THE ONSET OF A TEST PROGRAM TO VERIFY THE AMPLITUDE UNIFORMITY OF THE INCIDENT WAVE 4HE PHASE REQUIREMENT IS THE BASIS OF THE FAR FIELD RANGE CRITERION
2 $K
WHERE 2 IS THE DISTANCE BETWEEN THE INSTRUMENTATION RADAR AND THE TEST OBJECT AND $ IS THE MAXIMUM TARGET DIMENSION TRANSVERSE TO THE LINE OF SIGHT !LL OTHER ERROR SOURCES BEING FIXED COMPLIANCE WITH THE FAR FIELD REQUIREMENT IS GENERALLY FELT TO YIELD DATA WITH AN ACCURACY OF D" OR BETTER &IGURE ILLUSTRATES THE FAR FIELD REQUIREMENT FOR A VARIETY OF FREQUENCIES AND TARGET SIZES %RRORS ATTRIBUTABLE TO RADAR INSTRUMENTATION SHOULD BE HELD TO D" OR LESS WHICH REQUIRES CAREFUL DESIGN AND SELECTION OF COMPONENTS 4HE DRIFT IN SYSTEM SENSITIVITY SHOULD NOT EXCEED THIS VALUE FOR THE TIME IT TAKES TO RECORD A SINGLE 2#3 PATTERN WHICH SOMETIMES MAY APPROACH AN HOUR 4HE DYNAMIC RANGE OF THE SYSTEM SHOULD BE AT LEAST D" WITH D" PREFERRED ,INEARITY OVER THIS RANGE SHOULD BE D" OR BETTER AND IF NOT STEPS SHOULD BE TAKEN TO CORRECT MEASURED DATA VIA CALIBRATION OF THE RECEIVER TRANSFER FUNCTION GAIN CHARACTERISTICS 2#3 MEASUREMENTS SHOULD BE CALIBRATED BY THE SUBSTITUTION METHOD IN WHICH AN OBJECT OF KNOWN SCATTERING CHARACTERISTICS IS SUBSTITUTED FOR THE TARGET UNDER TEST 'IVEN THE KNOWN MEASURED OR CALIBRATED RECEIVER GAIN CHARACTERISTICS THIS ESTABLISHES THE CON STANT BY WHICH A RECEIVER OUTPUT INDICATION MAY BE CONVERTED TO AN ABSOLUTE 2#3 VALUE
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2!$!2 (!.$"//+
&)'52% 4HE FAR FIELD DISTANCE 2EPRINTED WITH PERMISSION OF 3CI4ECH 0UBLISHING )NC
#OMMON CALIBRATION TARGETS INCLUDE METAL SPHERES RIGHT CIRCULAR CYLINDERS FLAT PLATES AND CORNER REFLECTORS 4HE RADAR CROSS SECTIONS OF THESE OBJECTS MAY BE CALCULATED BY USING THE EXPRESSIONS GIVEN IN 3ECTION "ECAUSE RESIDUAL BACKGROUND REFLEC TIONS CONTAMINATE THE DESIRED TARGET ECHO SIGNAL THEY SHOULD BE MINIMIZED BY CAREFUL RANGE DESIGN AND OPERATION )NTERIOR WALLS IN INDOOR TEST CHAMBERS MUST BE COVERED WITH HIGH QUALITY RADAR ABSORBING MATERIAL AND THE SURFACE OF THE GROUND ON OUTDOOR RANGES SHOULD BE SMOOTH AND FREE OF VEGETATION 4ARGET SUPPORT STRUCTURES SHOULD BE DESIGNED SPECIFICALLY FOR LOW ECHO CHARACTERISTICS 4HE EFFECTS OF UNDESIRED BACKGROUND SIG NALS ARE ILLUSTRATED IN &IGURE "ECAUSE THE RELATIVE PHASE BETWEEN THE BACKGROUND SIGNAL AND THE TARGET SIGNAL IS UNKNOWN TWO CURVES ARE SHOWN THEY CORRESPOND TO PERFECT IN PHASE AND OUT OF PHASE CONDITIONS )F THE BACKGROUND SIGNAL IS EQUAL TO THE TARGET SIGNAL RATIO OF D" AND THE TWO ARE IN PHASE THE TOTAL RECEIVED POWER IS FOUR TIMES THE POWER DUE TO EITHER ONE 4HIS IS THE VALUE SHOWN AT THE UPPER LEFT OF THE CHART D" )F THE TWO ARE OUT OF PHASE THEY CANCEL EACH OTHER AND &)'52% -EASUREMENT ERROR AS A FUNC THERE IS NO SIGNAL AT ALL OFF THE LOWER LEFT OF TION OF THE RELATIVE BACKGROUND POWER LEVEL
2!$!2 #2/33 3%#4)/.
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r M PER FT OF EXPOSED COLUMN AT '(Z 3TRING SUSPENSION METHODS ARE BEST IMPLEMENTED INDOORS WHERE AN OVERHEAD SUP PORT POINT IS NORMALLY AVAILABLE ALTHOUGH ONE DOCUMENTED DESIGN WAS SERIOUSLY CON SIDERED FOR OUTDOOR USE /NE OF THREE CONFIGURATIONS MAY BE SELECTED ALL REQUIRING A CUSTOM MADE SLING OR HARNESS TO SUPPORT THE TARGET 4HE FIRST USES A SINGLE OVERHEAD SUPPORT POINT AND GUY LINES TO A FLOOR MOUNTED TURNTABLE TO ROTATE THE TARGET 4HE SEC OND CONFIGURATION SUSPENDS THE TARGET FROM AN OVERHEAD TURNTABLE REDUCING THE GUY LINES AND STRING LOADS AT THE EXPENSE OF A MORE COSTLY INSTALLATION 4HE THIRD CONFIGURA TION IS THE MOST COSTLY USING A PAIR OF TURNTABLES SLAVED TOGETHER ONE IN THE CEILING AND ONE ON THE FLOOR 4HE ECHO SIGNAL FROM A STRING DEPENDS ON THE LENGTH AND DIAMETER OF THE STRING ITS TILT ANGLE WITH RESPECT TO THE INCIDENT WAVE AND ITS DIELECTRIC CONSTANT .O MATTER WHAT THE TILT OF THE STRING IT WILL BE PRESENTED NORMAL TO THE LINE OF SIGHT TWICE IN A COMPLETE ROTATION OF THE TARGET AND MAY CAUSE A SPIKE IN THE 2#3 PATTERN THAT COULD BE ERRONEOUSLY ATTRIBUTED TO THE TARGET UNLESS OTHERWISE ACCOUNTED FOR 4HE 2#3 OF A STRING RISES WITH THE FOURTH POWER OF ITS DIAMETER IN THE 2AYLEIGH REGION SEE &IGURE AND FOR A GIVEN TENSILE STRENGTH THE DIAMETER RISES ONLY AS THE SQUARE ROOT OF THE LOAD TO BE SUPPORTED 4HUS BECAUSE THE ECHO SIGNAL INCREASES WITH THE SQUARE OF THE LOAD CARRYING CAPACITY STRING SUSPENSION TECHNIQUES ARE BEST SUITED FOR MEASUREMENTS OF LIGHT OBJECTS AT LOW FREQUENCIES 4HE METAL TARGET SUPPORT PYLON WAS FIRST SUGGESTED IN BUT A PRACTICAL IMPLE MENTATION OF THE CONCEPT DID NOT APPEAR UNTIL 4HE CONFIGURATION OF THE PYLON IS SHOWN IN &IGURE AND IT OWES ITS ELECTROMAGNETIC PERFORMANCE TO THE SHARPNESS OF ITS LEADING EDGE AND ITS TILT TOWARD THE RADAR TO THE LEFT IN THE DIAGRAM 0YLONS AS TALL AS FT HAVE BEEN BUILT AND IT IS CUSTOMARY TO TREAT THEM WITH RADAR ABSORBING MATERIAL TO SUPPRESS THE ECHOES FROM THE LEADING AND TRAILING EDGES 4HE OBVIOUS ADVANTAGE OF THE METAL PYLON IS ITS SUPERIOR WEIGHT CARRYING CAPABIL ITY COMPARED WITH THAT OF STRINGS AND PLASTIC FOAM COLUMNS (OWEVER BECAUSE THE TOP OF THE PYLON IS SMALL THE ROTATION MECHANISM NEEDED TO VARY THE ASPECT ANGLE OF THE TARGET MUST BE EMBEDDED IN THE TARGET ITSELF 4HIS USUALLY DESTROYS THE OPERATIONAL VALUE OF THE TARGET -OST OF THE ROTATORS FOR THESE PYLONS ARE DUAL AXIS AZIMUTH OVER ELEVATION DESIGNS 7HEN MEASUREMENTS ARE MADE WITH THE AZIMUTH ROTATION ANGLE TILTED BACK AWAY FROM THE RADAR PARTS OF THE TARGET MAY SWEEP THROUGH THE SHADOW CAST BY THE TOP OF THE PYLON POSSIBLY DEGRADING THE MEASUREMENTS /NE WAY TO AVOID THIS IS TO INVERT THE TARGET AND TILT THE ROTATION AXIS TOWARD THE RADAR INSTEAD OF AWAY FROM IT 4HIS REQUIRES THE INSTALLATION OF THE ROTATOR IN THE TOP OF THE TARGET AS WELL AS IN THE BOTTOM 4HE UNUSED INTERNAL CAVITIES CREATED FOR SUCH INSTALLATIONS MUST BE CONCEALED BY COVERS OR SHIELDS
£{°Îä
2!$!2 (!.$"//+
&)'52% 4HE METAL SUPPORT PYLON 4HE DESIGN IS FOR AN INCIDENT WAVE ARRIVING FROM THE LEFT 2EPRINTED WITH PERMISSION OF 3CI4ECH 0UBLISHING )NC
)T IS OFTEN NECESSARY TO MEASURE SCALE MODELS WHICH REQUIRES THE APPLICATION OF SCALING LAWS "ECAUSE NONCONDUCTING MATERIALS MUST BE SCALED DIFFERENTLY THAN GOOD CONDUCTORS IT IS NOT POSSIBLE TO SATISFY ALL THE SCALING REQUIREMENTS FOR ARBITRARY TARGETS COMPOSED OF CONDUCTING AND NONCONDUCTING MATERIALS -OST TARGETS REQUIRING SCALE MODEL TESTING HOWEVER ARE DOMINANTLY METALLIC FOR WHICH THE PERFECTLY CONDUCTING SCALING LAW IS GENERALLY REGARDED AS ADEQUATE 7HEN NORMALIZED WITH RESPECT TO THE SQUARE OF THE WAVELENGTH THE 2#3 PATTERNS OF TWO PERFECTLY CONDUCTING OBJECTS OF IDENTICAL SHAPE BUT DIFFERENT SIZE WILL BE IDENTI CAL IF THE OBJECTS ARE THE SAME NUMBER OF WAVELENGTHS IN SIZE )F A MODEL IS ONE TENTH OF FULL SCALE FOR EXAMPLE IT SHOULD BE MEASURED AT ONE TENTH OF THE FULL SCALE WAVE LENGTH TEN TIMES THE FULL SCALE FREQUENCY 4HE 2#3 OF THE FULL SCALE TARGET MAY BE OBTAINED FROM THE SCALE MODEL MEASUREMENTS BY MULTIPLYING THE SCALE MODEL 2#3 BY THE SQUARE OF THE RATIO OF THE TWO FREQUENCIES )N THIS EXAMPLE THAT FACTOR IS OR D" /UTDOOR 4EST 2ANGES /UTDOOR TEST RANGES ARE REQUIRED WHEN TEST TARGETS ARE TOO LARGE TO BE MEASURED INDOORS 4HE FAR FIELD CRITERION OFTEN REQUIRES THAT THE RANGE TO THE TARGET BE SEVERAL THOUSAND FEET SEE &IGURE "ECAUSE THE TYPICAL TARGET HEIGHT ABOVE THE GROUND IS A FEW DOZEN FEET AT BEST THE ELEVATION ANGLE TO THE TARGET AS SEEN FROM THE RADAR IS AT MOST AND OFTEN LESS !T SUCH LOW GRAZING ANGLES THE GROUND IS STRONGLY ILLUMINATED BY THE ANTENNAS AND UNLESS THE GROUND BOUNCE CAN BE SUPPRESSED THE TARGET WILL BE ILLUMINATED BY A MULTIPATH FIELD )N THE DESIGN OF AN OUTDOOR TEST RANGE THEREFORE A DECISION MUST BE MADE WHETHER TO EXPLOIT THE GROUND BOUNCE OR TO ATTEMPT TO DEFEAT IT )T IS GENERALLY EASIER TO EXPLOIT IT THAN TO ELIMINATE IT
2!$!2 #2/33 3%#4)/.
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4EST RANGES DESIGNED TO EXPLOIT THE MULTIPATH EFFECT MAY BE ASPHALTED TO IMPROVE THE GROUND REFLECTION ALTHOUGH MANY RANGES ARE OPERATED OVER NATURAL SOIL 0AVING THE RANGE ENSURES UNIFORMITY IN THE CHARACTERISTICS OF THE GROUND PLANE FROM DAY TO DAY AND EXTENDS ITS OPERATIONAL USEFULNESS TO HIGHER FREQUENCIES THAN MIGHT OTHERWISE BE POS SIBLE ! CONDUCTING SCREEN EMBEDDED IN THE ASPHALT MAY IMPROVE THE REFLECTION 0AVING ALSO REDUCES MAINTENANCE OF THE GROUND PLANE SUCH AS MIGHT BE REQUIRED BY PERIODI CALLY REMOVING VEGETATION AND SMOOTHING OUT WINDBLOWN RIDGES IN UNSTABLE SOIL 4HE ANGLE OF INCIDENCE AND THE DIELECTRIC PROPERTIES OF ASPHALT AND NATURAL SOIL ARE SUCH THAT THE PHASE OF THE VOLTAGE REFLECTION COEFFICIENT IS WITHIN A FEW DEGREES OF 4HIS BEING THE CASE ONE CAN USUALLY CHOOSE A COMBINATION OF TARGET AND ANTENNA HEIGHTS SUCH THAT THE WAVE REFLECTED BY THE GROUND ARRIVES AT THE TARGET IN PHASE WITH THE WAVE PROPAGATED DIRECTLY FROM THE ANTENNAS 4HE RESULT IS THE FOLLOWING RULE FOR SELECTING THE ANTENNA AND TARGET HEIGHTS
HA HT L 2
WHERE HA AND HT ARE THE ANTENNA AND TARGETS HEIGHTS RESPECTIVELY AND 2 IS THE RANGE TO THE TARGET "ECAUSE MOST TEST RANGES HAVE TURNTABLES OR TARGET PYLONS INSTALLED AT A FEW FIXED LOCATIONS RELATIVE TO A PERMANENT RADAR COMPLEX THE RANGE 2 IS USUALLY RESTRICTED TO A FEW PRESET VALUES 4HE TARGET IS INSTALLED AT A HEIGHT HT HIGH ENOUGH TO MINIMIZE SPURI OUS INTERACTIONS WITH THE GROUND YET LOW ENOUGH TO MINIMIZE THE SIZE AND COMPLEX ITY OF THE TARGET SUPPORT STRUCTURE 4HEREFORE IT IS THE ANTENNA HEIGHT HA THAT IS MOST READILY CONTROLLED AND ADJUSTED TO OPTIMIZE THE LOCATION OF THE FIRST LOBE IN THE VERTI CAL MULTIPATH INTERFERENCE PATTERN 4HIS IS EASILY ACCOMPLISHED BY MOUNTING THE RADAR ANTENNAS ON CARRIAGES THAT CAN BE RAISED OR LOWERED ALONG RAILS INSTALLED ON THE SIDE OF A BUILDING OR A TOWER 4HE IDEAL GROUND PLANE OFFERS A THEORETICAL SENSITIVITY ENHANCEMENT OF D" OVER IDENTICAL MEASUREMENTS MADE IN FREE SPACE 4HE ACTUAL ENHANCEMENT IS USUALLY LESS THAN THIS PRIMARILY BECAUSE OF THE DIRECTIVITY OF THE ANTENNAS AND IMPERFECTIONS IN THE GROUND PLANE !NTENNA DIRECTIVITY PRECLUDES THE TARGET EVER BEING SQUARELY ALIGNED ON THE BORESIGHTS OF BOTH THE REAL ANTENNA AND ITS IMAGE IN THE GROUND PLANE AT THE SAME TIME AND THE REFLECTION COEFFICIENT OF TYPICAL GROUND PLANES VARIES FROM TO AS LOW AS OR LESS &OR ALL EXCEPT VERY HIGH AND VERY LOW FREQUENCIES MILLIMETER WAVE LENGTHS AND 6(& TYPICAL SENSITIVITIES ARE OF THE ORDER OF TO D" ABOVE FREE SPACE INSTEAD OF THE IDEAL D" 7HEN THE RANGE TO THE TARGET IS RELATIVELY SHORT AND TESTS MUST BE PERFORMED OVER A WIDE RANGE OF FREQUENCIES IT IS SOMETIMES ADVANTAGEOUS TO ATTEMPT TO DEFEAT THE GROUND PLANE EFFECT /NE OPTION IS TO INSTALL A BERM SHAPED LIKE AN INVERTED 6 RUNNING BETWEEN THE RADAR AND THE TARGET 4HE PURPOSE OF THE BERMS SLANTED TOP IS TO DEFLECT THE GROUND REFLECTED WAVE OUT OF THE TARGET ZONE !NOTHER OPTION IS TO INSTALL A SERIES OF LOW RADAR FENCES ACROSS THE RANGE 4HE DESIGN OBJECTIVE IS TO BLOCK GROUND REFLECTED RAYS FROM REACHING THE TARGET FROM THE RADAR AND VICE VERSA BY SHIELDING THE SPECULAR ZONE ON THE GROUND FROM BOTH 4HE NEAR SIDES OF THE FENCES SHOULD BE SLANTED TO DEFLECT ENERGY UPWARD OUT OF THE TARGET TEST ZONE AND MAY BE COVERED WITH ABSORBING MATE RIAL )T IS DIFFICULT HOWEVER TO PREVENT DIFFRACTION OF RADAR ENERGY FROM THE TOP OF THE FENCES FROM REACHING THE TARGET OR TO PREVENT TARGET DIFFRACTED SIGNALS FROM REACHING THE RADAR RECEIVER VIA THE SAME KIND OF MECHANISM "ECAUSE OF THE LARGE DISTANCES FROM THE RADAR TO THE TARGET ON OUTDOOR RANGES INSTRU MENTATION RADARS AT ONE TIME DEVELOPED PEAK SIGNAL POWERS RANGING FROM TO K7
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2!$!2 (!.$"//+
4HE HIGH POWER INSTRUMENTATION OF YESTERYEAR HAS BEEN LARGELY REPLACED ON STATIC TEST RANGES WITH COHERENT STEPPED FREQUENCY RADARS THAT ARE FAR MORE VERSATILE BUT HIGH POWER SYSTEMS REMAIN USEFUL FOR DYNAMIC TESTING OF TARGETS FLYING OR SAILING PAST THEM ON DYNAMIC TEST RANGES 3TEPPED AND SWEPT FREQUENCY INSTRUMENTATION SYSTEMS ON STATIC RANGES CAN COLLECT 2#3 PATTERNS AT HUNDREDS OF FREQUENCIES FOR A SINGLE ROTATION OF THE TEST TARGET 4HE SIGNAL TO NOISE RATIO CAN BE IMPROVED WHEN NECESSARY BY MEANS OF MULTISWEEP OR MULTISTEP SIGNAL INTEGRATION SCHEMES 4HE PRICE PAID FOR MUCH OF THIS VERSATILITY IS THE REQUIREMENT FOR MORE ACTIVE TEST TIME PER TARGET ROTATION THEREBY INCREASING MEASUREMENT COSTS )NDOOR 4EST 2ANGES )NDOOR TEST RANGES OFFER PROTECTION FROM WEATHER AND THERE FORE MORE PRODUCTIVE TESTING BUT UNLESS A VERY LARGE FACILITY IS AVAILABLE MAXIMUM TARGET SIZES ARE LIMITED TO ONE OR TWO DOZEN FEET "ECAUSE OF THEIR PROXIMITY THE WALLS FLOOR AND CEILING MUST BE COVERED WITH HIGH QUALITY ABSORBING MATERIAL 4HE LOWER THE INTENDED FREQUENCY OF OPERATION THE MORE EXPENSIVE THE ABSORBER BECOMES !BSORBER REFLECTIVITY RATINGS OF D" ARE COMMON AMONG THE MATERIALS USED 4HIS PERFOR MANCE IS USUALLY ACHIEVABLE ONLY WITH THE PYRAMIDAL DESIGN %ARLY INDOOR CHAMBERS WERE RECTANGULAR IN SHAPE AND DESPITE THE INSTALLATION OF GOOD ABSORBENT MATERIALS ON THE WALLS 2#3 MEASUREMENTS COULD BE CONTAMINATED BY WALL REFLECTIONS 4HE MOST SENSITIVE PART OF THE ANECHOIC CHAMBER IS THE REAR WALL WHICH RECEIVES TO PERCENT OF THE POWER RADIATED BY THE RADAR HENCE THE BEST ABSORBER SHOULD BE RESERVED FOR THE REAR WALL 4HE FLOOR CEILING AND SIDEWALLS ALSO CONTRIBUTE ERRORS VIA A QUADRUPLET OF REFLECTIONS NOT UNLIKE THOSE DUE TO THE GROUND PLANE OF OUTDOOR RANGES ! REMEDY IS THE TAPERED ANECHOIC CHAMBER WHICH ELIMINATES MOST OF THE SIDEWALL REFLECTIONS PURELY BY TILTING PORTIONS OF THE WALLS FLOOR AND CEIL ING AWAY FROM THE CHAMBER CENTERLINE %VEN TARGETS OF MODEST SIZE CANNOT BE MEASURED AT THE FAR FIELD DISTANCE IN INDOOR FACILITIES BECAUSE MOST CHAMBERS ARE NOT MUCH MORE THAN FT OR SO IN LENGTH )T IS POSSIBLE HOWEVER TO PROVIDE THE NECESSARY UNIFORMITY OF ILLUMINATION BY COLLIMATING THE RADIATED BEAM 4HIS CAN BE DONE BY INSERTING A LENS BETWEEN THE RADAR AND THE TAR GET OR BY REFLECTING THE RADAR BEAM OFF A COLLIMATING REFLECTOR 4HIS LATTER CONCEPT IS KNOWN AS THE COMPACT RANGE BECAUSE A BEAM OF PARALLEL RAYS CAN BE GENERATED IN A MUCH SHORTER DISTANCE THAN WOULD BE POSSIBLE WITHOUT THE COLLIMATING DEVICE 4HE REFLECTOR OFFERS A DIFFERENT WAY TO COLLIMATE A BEAM )N CONTRAST TO THE LENS WHICH IS PLACED BETWEEN THE RADAR AND THE TEST OBJECT THE RADAR AND THE TEST OBJECT REMAIN ON THE SAME SIDE OF THE REFLECTOR AS SHOWN IN &IGURE 4HE REFLECTOR IS TYPICALLY AN OFFSET PARABOLOID MEANING THE PARABOLOIDAL SURFACE DOES NOT INCLUDE THE VERTEX OF THE GENERATING PARABOLA 4HIS PERMITS THE FEED THAT EXCITES THE REFLECTOR TO BE PLACED OUT OF THE BEAM REFLECTED TOWARD THE TARGET )F THE TEST OBJECT IS HELD WITHIN ONE OR TWO FOCAL LENGTHS OF THE REFLECTOR AND IF THE REFLECTOR IS EXCITED BY A SUITABLY DESIGNED FEED THE REFLECTED WAVE IS SENSIBLY PLANAR (OWEVER UNLESS THE EDGES OF THE REFLECTOR ARE CAREFULLY DESIGNED THE INCIDENT FIELD IN THE TARGET ZONE WILL BE CONTAMINATED BY UNDESIRED FIELDS DIFFRACTED FROM THE EDGES OF THE REFLECTOR 4HE DIFFRACTION CAUSES RIPPLES IN BOTH THE AMPLITUDE AND THE PHASE OF THE FIELD DISTRIBUTION IN THE TARGET ZONE )N SOME CASES THE EFFECT IS SMALL ENOUGH TO BE IGNORED BUT IN HIGH QUALITY INSTALLATIONS THE RIPPLE MAY BE OBJECTIONABLY LARGE 2OLLED EDGE CONFIGURATIONS SUCH AS THE ONE ON THE UPPER EDGE OF THE MAIN REFLECTOR IN &IGURE CAN BE DESIGNED TO MINIMIZE EDGE DIFFRACTION (OWEVER THE PRICE PAID FOR THIS IMPROVEMENT IN PERFORMANCE IS A MUCH LARGER AND MORE COMPLICATED REFLECTOR STRUCTURE
2!$!2 #2/33 3%#4)/.
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&)'52% ! COMPACT RANGE USING AN OFFSET PARABOLOIDAL REFLECTOR
4HE SINGLE REFLECTOR DESIGN SHOWN IN &IGURE WORKED TOLERABLY WELL FOR SMALL TEST TARGETS BUT IT SOON BECAME APPARENT THAT THE REFLECTOR HAD TO BE CONSIDERABLY LARGER FOR MANY TARGETS OF VITAL MILITARY INTEREST 4HIS COULD BE ACCOMPLISHED BY DOUBLING OR TRIPLING THE SIZE OF THE REFLECTOR BUT THAT BROUGHT ON A ROUND OF OTHER PROBLEMS MAINLY THE INCREASED FOCAL LENGTH OF THE REFLECTOR 7HILE THE FOCAL DISTANCE COULD BE SHORTENED TO COMFORTABLY FIT AXIAL SPACE LIMITATIONS ALONG THE BORESIGHT OF THE REFLECTOR IT WAS THEN HARDER TO CONTROL THE FIELD AMPLITUDE TAPER ACROSS THE REFLECTOR DUE TO THE PROXIM ITY OF THE FEEDHORN 4HE SOLUTION WAS TO ADD A SMALLER SUBREFLECTOR IN A SUBTERRANEAN GALLERY BUILT ESPECIALLY FOR IT AS SUGGESTED IN &IGURE 4HE SUBREFLECTOR HAD THE EFFECT OF GREATLY INCREASING THE FOCAL LENGTH OF THE MAIN REFLECTOR MAKING IT EASIER TO OPTIMIZE ITS ILLUMINATION 4HIS PARTICULAR CONFIGURATION IS KNOWN AS A 'REGORIAN SYSTEM CHARACTERIZED BY A FOCUS BETWEEN THE TWO REFLECTORS
&)'52% 'ENERIC DUAL REFLECTOR COMPACT RANGE CONFIGURATION
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2!$!2 (!.$"//+
WHERE MOST OF THE RAYS BETWEEN THE TWO REFLECTORS CONVERGE )N A SECOND CONFIGURA TION KNOWN AS THE #ASSEGRAIN THE FOCUS IS A VIRTUAL ONE LYING BEHIND THE SUBREFLECTOR 4HE 'REGORIAN CONFIGURATION PERMITS THE CONSTRUCTION OF A SMALLER APERTURE BETWEEN THE MAIN CHAMBER AND THE SUBREFLECTOR GALLERY THAN DOES THE #ASSEGRAIN CONFIGURATION ,ARGE COMPACT RANGES SUCH AS THE ONE SHOWN IN &IGURE ARE VERY COSTLY AND CAN BE AFFORDED BY ONLY THE LARGEST OF COMPANIES OR THE GOVERNMENT THUS RANGE TIME IS PREMIUM 3OME COMPANIES KEEP THEIR COMPACT RANGES BUSY HOURS PER DAY 4ARGETS MEASURED INDOORS ARE PLACED MUCH CLOSER TO THE RADAR THAN THOSE MEASURED OUTDOORS AND USEFUL MEASUREMENTS MAY BE MADE BY USING MUCH LESS RADIATED POWER %ARLY INDOOR INSTRUMENTATION RADARS RELIED ON SIMPLE #7 SOURCES AND UNDESIRED CHAM BER REFLECTIONS WERE SUPPRESSED BY A CANCELLATION PROCESS 4HE PROCEDURE IS TO PREPARE THE CHAMBER FOR A MEASUREMENT IN EVERY RESPECT EXCEPT FOR THE INSTALLATION OF THE TARGET ON ITS SUPPORT FIXTURE ! SMALL SAMPLE OF THE TRANSMITTED SIGNAL IS PASSED THROUGH A VARI ABLE ATTENUATOR AND A VARIABLE PHASE SHIFTER AND COMBINED WITH THE RECEIVED SIGNAL 4HE AMPLITUDE AND PHASE OF THE SIGNAL SAMPLE ARE THEN ADJUSTED SO AS TO CANCEL THE SIGNAL RECEIVED IN THE ABSENCE OF THE TARGET 4HE AVAILABILITY OF LOW COST PHASE LOCKED FREQUENCY SYNTHESIZED SOURCES NOW MAKES IT ATTRACTIVE TO COLLECT WIDEBAND 2#3 DATA WHICH CONTAIN FAR MORE TARGET SCATTERING INFORMATION THAN #7 MEASUREMENTS MADE AT SINGLE FREQUENCIES 7HEN COHERENT 2#3 SCATTERING DATA ARE SUITABLY PROCESSED IT IS POSSIBLE TO GENERATE )3!2 IMAGERY OR TWO DIMENSIONAL MAPS OF THE ECHO SOURCES OF TEST OBJECTS &IGURE IS AN EXAMPLE OF SUCH AN IMAGE )N THIS CASE THE PROCESSING REQUIRED TO GENERATE THIS IMAGE IS A DOUBLE &OURIER TRANSFORMATION ONE FROM THE FREQUENCY DOMAIN TO THE TIME DOMAIN AND THE OTHER FROM THE ANGLE DOMAIN TO THE CROSS RANGE DOMAIN 4HE FREQUENCY TIME DOMAIN PROCESSING MAY BE PERFORMED VIRTUALLY IN REAL TIME A SECOND OR TWO FOR PROCESSING AND DISPLAY ON A VIDEO SCREEN BUT THE CONVERSION
&)'52% 2ADAR IMAGE OF A SMALL DRONE AIRCRAFT 0LANFORM OUTLINE HAS BEEN ADDED FOR CLARITY #OURTESY $ , -ENSA 53 .AVY 0ACIFIC -ISSILE 4EST #ENTER
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FROM THE ANGLE DOMAIN TO THE CROSS RANGE DOMAIN MUST BE PERFORMED OFFLINE IN THIS EXAMPLE 4HE FAST &OURIER TRANSFORM &&4 IS INVARIABLY EXPLOITED TO EXPEDITE THE PROCESSING 4HE IMAGE DATA PRESENTED IN &IGURE WERE COLLECTED FOR A STEPPED FREQUENCY SIGNAL WITH A BANDWIDTH OF '(Z CENTERED AT '(Z 4HE ASPECT ANGLE WAS VARIED OVER A SECTOR n WIDE CENTERED ON THE NOSE ON ASPECT 4HE CHARTED IMAGE CONTOURS ARE D" APART AND THE TOTAL AMPLITUDE VARIATION IS D" 4HE RESOLUTION OF THE PROCESSED IMAGE IN THE TIME RANGE DOMAIN IS INVERSELY PROPORTIONAL TO THE BANDWIDTH OF THE EMITTED WAVEFORM 4HE RESOLUTION IN THE CROSS RANGE DOMAIN IS INVERSELY PROPORTIONAL TO THE ASPECT ANGLE WINDOW OVER WHICH THE DATA ARE COLLECTED 4HUS THE OPERATING CHARACTERISTICS OF THE INSTRUMENTATION SYSTEM AND THE AZIMUTHAL DATA SAMPLING RATE MUST BE DECIDED BEFORE THE DATA ARE COLLECTED "ECAUSE THE CROSS RANGE COORDINATE OF THE RESULTING IMAGE IS PERPENDICULAR TO THE AXIS OF ROTATION OF THE TARGET IT MAY BE NECESSARY TO MULTIPLY THAT COORDINATE BY A SCALE FACTOR THAT EFFECTIVELY REGISTERS THE GENERATED IMAGE WITH SAY A PLAN VIEW OF THE TARGET 4HE RESULTING DATA MAY BE PRESENTED IN THE FORM OF A CONTOUR MAP AS IN &IGURE OR IN A COLOR CODED OR GRAYSCALE PIXEL FORMAT (ERE THE TARGET OUTLINE HAS BEEN SUPER POSED ON THE IMAGE DATA FOR DIAGNOSTIC ANALYSIS AND THE PARTICULAR ATTITUDE SHOWN IS FOR NOSE ON INCIDENCE 3IMILAR IMAGES CAN BE GENERATED FOR OTHER ANGLES OF INCIDENCE PROVIDED THE TARGET IS ROTATED THROUGH A SECTOR WIDE ENOUGH TO YIELD THE DESIRED CROSS RANGE RESOLUTION AND SAMPLED AT A SUFFICIENT NUMBER OF ANGLES OVER THAT SECTOR )N PRACTICE THE TARGET IS ROTATED CONTINUOUSLY WHILE THE SWEPT OR STEPPED FREQUENCY DATA ARE COLLECTED ! RULE OF THUMB IS THAT THE ANGULAR SPEED BE SLOW ENOUGH THAT THE PHASE OF THE RETURN AT THE END OF A FREQUENCY SWEEP DUE TO TARGET MOTION NOT BE MORE THAN FROM WHAT IT WOULD HAVE BEEN HAD THE TARGET NOT MOVED .OTE THAT THE NOSE SECTION OF THE DRONE IS SPECKLED WITH HEAVY CONCENTRATIONS OF SCATTERING CENTERS POSSIBLY DUE TO CONTRIBUTIONS FROM INTERNAL STRUCTURAL FEATURES 4HE REAR EDGES OF THE FORWARD CANARDS SEEM TO BE STRONGER SCATTERERS THAN THE LEADING EDGES !T THE NOSE ON ASPECT ANGLE FOR WHICH THE IMAGE DATA WERE COLLECTED THE LEADING EDGES OF THE WINGS ARE VIRTUALLY INVISIBLE (OWEVER NOTE A FEW ECHO SOURCES ALONG A LINE PARALLEL TO AND SLIGHTLY FORWARD OF THE WING TRAILING EDGES )F THE TARGET ROTATION HAD BEEN CENTERED ON AN ASPECT ANGLE PERPENDICULAR TO ONE OF THE WINGS THE LEADING EDGE OF THAT ONE WING WOULD HAVE hLIT UPv )N THE REGION OF THE MAIN WING ROOTS WE SEE HEAVY CONCENTRATIONS OF ECHO SOURCES 3OME OF THEM LIE FORWARD OF ANY WING SURFACE !LTHOUGH WE MAY CONCEIVE OF APPARENT SOURCES BEING STRUNG OUT BEHIND ANY PHYSICAL SCATTERING OBSTACLE DUE TO TIME DELAYS OF MULTIPLE REFLECTIONS IT IS HARD TO RECONCILE THEM BEING STRUNG OUT IN FRONT OF THE BODY 7E DO SEE SEVERAL CLUSTERS OF APPARENT SCATTERING CENTERS POSITIONED AFT OF THE TAIL OF THE AIRCRAFT BUT LACKING ANY DETAILED DESCRIPTION OF THE TEST OBJECT WE CANNOT INTERPRET THEIR MEANING 4HESE hGHOSTv SCATTERERS OWE THEIR EXISTENCE TO THE WAY IN WHICH THE DATA PROCESSING SYSTEM SORTS THE RANGE AND CROSS RANGE LOCATIONS OF SCATTERERS $OWN RANGE LOCATIONS ARE SORTED ACCORDING TO THEIR PROCESSED TIME DELAYS AND CROSS RANGE LOCATIONS ACCORD ING TO THEIR TIME DELAY RATES WHETHER DUE TO REAL SCATTERERS OR TO INTERACTIONS BETWEEN SCATTERERS %VEN THOUGH THE CONTRIBUTIONS OF SOME SCATTERING CENTERS MAY INVOLVE PROPAGATION IN DIRECTIONS OTHER THAN ALONG THE LINE OF SIGHT FROM THE RADAR THE SYSTEM HAS NO WAY OF DISCERNING THAT FACT 4HEREFORE DESPITE THE POWERFUL DIAGNOSTIC VALUE OF IMAGES LIKE THESE ONE MUST ALWAYS BE AWARE THAT MULTIPLE INTERACTIONS BETWEEN TARGET ELEMENTS CAN CREATE SCATTERING SOURCES THAT ARE NOT WHERE THEY APPEAR TO BE
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£{°xÊ , ,Ê "Ê-1**, --" 4HE PROBABILITY OF BEING DETECTED BY HOSTILE RADARS CAN BE REDUCED BY DECREASING THE TARGETS RADAR CROSS SECTION 4HE MAJOR METHODS TO REDUCE THE 2#3 ARE BY SHAPING OF THE TARGET AND THE USE OF ABSORBERS "Y SHAPING WE MEAN THE INTENTIONAL SELECTION OF TARGET SURFACES AND FEATURES SO AS TO MINIMIZE THE AMOUNT OF ENERGY SCATTERED BACK TO THE RADAR 3HAPING INCLUDES SPECIFIC DESIGN CONFIGURATIONS SUCH AS THE PLACEMENT OF ENGINE INTAKES WHICH CAN HAVE LARGE RADAR ECHOES WHERE THEY MAY BE SHIELDED FROM THE INCIDENT WAVE BY OTHER PARTS OF THE TARGET 4HE PURPOSE OF RADAR ABSORBING MATERIALS 2!- IS TO ABSORB THE INCIDENT RADAR ENERGY SO AS TO MINIMIZE THE ENERGY SCATTERED BACK TO THE RADAR "OTH METHODS HAVE ADVANTAGES AND DISADVANTAGES 2ADAR !BSORBERS 4HE PURPOSE OF THE RADAR ABSORBER IS TO ATTENUATE INCIDENT ENERGY AND THEREBY REDUCE THE ENERGY SCATTERED OR REFLECTED BACK TO THE RADAR -OST ABSORBERS ARE DESIGNED TO REDUCE SPECULAR REFLECTIONS FROM METALLIC SURFACES BUT STEALTH TECHNOLOGY HAS SPAWNED THE DEVELOPMENT OF NONSPECULAR ABSORBERS INTENDED PRIMARILY TO SUPPRESS ECHOES DUE TO SURFACE TRAVELING WAVES 4HE SIMPLEST SPECULAR ABSORBER IS THE 3ALISBURY SCREEN WHICH IS A THIN RESISTIVE SHEET MOUNTED A QUARTER WAVELENGTH ABOVE THE METAL SURFACE TO BE HIDDEN FROM A RADAR 4HE DESIGN WORKS BEST FOR INCIDENCE NORMAL TO THE SHEET AND IF IT CAN BE MANU FACTURED WITH A RESISTIVITY OF OHMS PER SQUARE THE IMPEDANCE OF FREE SPACE ALL THE POWER IN THE INCIDENT WAVE IS TRANSFERRED TO THE SHEET AND NONE IS REFLECTED (OWEVER THE SINGLE SHEET 3ALISBURY SCREEN SUFFERS SEVERAL LIMITATIONS )TS THIN SHEETS AND LOW LOSS SPACERS ARE FRAGILE ITS D" BANDWIDTH IS BARELY AND ITS PERFORMANCE DETE RIORATES PROGRESSIVELY AS THE ANGLE OF INCIDENCE MOVES AWAY FROM NORMAL INCIDENCE )T IS DIFFICULT TO OVERCOME THE FRAGILITY PROBLEM WITH ROBUST MATERIALS BUT THE BAND WIDTH CAN BE IMPROVED BY CASCADING SEVERAL SHEETS AS SHOWN IN &IGURE 4HIS CREATES WHAT IS KNOWN AS A *AUMANN ABSORBER 4HE BANDWIDTH RISES WITH THE NUMBER OF LAYERS AND CAN ATTAIN A RESPECTABLE FOR A FOUR SHEET DESIGN AS SUGGESTED IN &IGURE 4HE PRICE PAID FOR THIS BANDWIDTH EXPANSION IS A MUCH THICKER BULKIER MATERIAL THAT TENDS TO BE IMPRACTICAL FOR TACTICAL MILITARY TARGETS ,IKE THE 3ALISBURY SCREEN THE $ØLLENBACH LAYER IS ALSO A SIMPLE ABSORBER 4HE MATE RIAL IS UNIFORM THROUGHOUT ITS VOLUME AND IS A MIXTURE OF COMPOUNDS DESIGNED TO HAVE A SPECIFIED INDEX OF REFRACTION 4HAT DESIGN MAY INCLUDE MATERIALS WITH MAGNETIC LOSSES AS WELL AS CARBON PARTICLES RESPONSIBLE FOR ELECTRIC LOSSES 4HEREFORE THE ELECTRIC AND MAGNETIC SUSCEPTANCES RELATIVE PERMITTIVITY AND RELATIVE PERMEABILITY HAVE IMAGI NARY COMPONENTS RESULTING IN AN INDEX OF REFRACTION WITH AN IMAGINARY COMPONENT
&)'52% 4HE *AUMANN ABSORBER IS A CASCADED COLLECTION OF THIN RESISTIVE SHEETS STACKED IN FRONT OF A METAL BULKHEAD SPACED K APART WHERE + SPACER DIELECTRIC CONSTANT 4HE CLASSIC 3ALISBURY SCREEN IS THE DEGENERATIVE CASE OF A SINGLE SHEET
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&)'52% 0ERFORMANCE OF *AUMANN ABSORBERS WITH AS MANY AS FOUR SHEETS !LL FOUR OF THESE TRACES WERE OPTIMIZED FOR MAXIMUM BANDWIDTH AT THE n D" LEVEL 4HE SHEET RESISTIVITIES MUST INCREASE FROM A LOW VALUE AT THE INNER SHEET TO A HIGH VALUE AT THE OUTER SHEET
4HE RESULTING IMAGINARY PART OF THE PROPAGATION CONSTANT ATTENUATES WAVES TRAVELING THROUGH THE MATERIAL -OST OF THE COMMERCIAL VERSIONS OF $ØLLENBACH ABSORBERS ARE FLEXIBLE AND CAN BE APPLIED TO MODESTLY CURVED SURFACES 4HE DIELECTRIC ABSORBERS ARE TYPICALLY MADE OF A RUBBERY FOAM SOMETIMES URETHANE IMPREGNATED WITH CARBON PARTICLES )MPREGNATION MAY BE PERFORMED BY DIPPING A COMPRESSED SLAB OF MATERIAL IN A GRAPHITE SUSPENSION BATH THEN WRINGING IT OUT AND DRYING IT -AGNETIC $ØLLENBACH LAYERS CAN BE ROLLED FROM A MIXTURE OF NATURAL OR SYNTHETIC RUBBER LOADED WITH CARBONYL IRON OR FERRITE POWDERS 4HE LOWER THE POWDER CONTENT THE MORE FLEXIBLE THE SHEET BUT THE LESS EFFECTIVE ITS ELEC TROMAGNETIC PERFORMANCE $IELECTRIC AND MAGNETIC $ØLLENBACH LAYERS TYPICALLY RANGE FROM ABOUT MM TO CM IN THICKNESS 4HE MAGNETIC VERSIONS ARE AS HEAVY LBFT MAKING THEM IMPRACTICAL FOR MOST TACTICAL APPLICATIONS 4HE FRONT FACE AND THE METAL BACKING OF THE $ØLLENBACH LAYER ARE ITS ONLY SOURCES OF REFLECTION 4HE USE OF PHYSICALLY REALIZABLE MATERIALS MAKES IT IMPOSSIBLE TO FORCE EITHER REFLECTION TO ZERO 4HE DESIGN OBJECTIVE THEREFORE IS TO CHOOSE THE ELECTRICAL PROPERTIES OF THE LAYER SO THAT THE FRONT FACE AND METAL BACK REFLECTIONS TEND TO CANCEL EACH OTHER )F THE MATERIAL PROPERTIES ARE DOMINATED BY ELECTRIC EFFECTS THE OPTIMUM LAYER THICKNESS IS CLOSE TO K AS MEASURED IN THE MATERIAL )F THEY ARE DOMINANTLY MAGNETIC THE LAYER CAN BE MUCH THINNER !S WITH THE SIMPLE 3ALISBURY SCREEN $ØLLENBACH LAYERS CAN BE CASCADED IN ATTEMPTS TO EXPAND BANDWIDTH PRODUCING WHAT IS KNOWN AS GRADED ABSORBERS &OR OPTIMUM PERFORMANCE THE INTRINSIC IMPEDANCE OF EACH LAYER TYPICALLY GETS SMALLER THE CLOSER THE LAYER IS TO THE METAL BULKHEAD OR BACKING LAYER &IVE OR MORE LAYERS HAVE BEEN USED IN THE COMMERCIAL PRODUCTION OF GRADED DIELECTRIC ABSORBERS BUT COMMERCIAL GRADED MAGNETIC ABSORBERS APPEAR TO HAVE BEEN LIMITED TO THREE LAYERS )T IS IMPORTANT IN THE DESIGN PROCESS TO ACCOUNT FOR THE ACTUAL THICKNESS AND ELECTRICAL PROPERTIES OF THE ADHE SIVE FILMS USED TO BOND THE LAYERS TO EACH OTHER 4HESE MATERIALS ARE TOO FLIMSY OR TOO HEAVY FOR MOST MILITARY APPLICATIONS 4HE PYRAMIDAL ABSORBER USED TO SUPPRESS WALL REFLECTIONS IN INDOOR CHAMBERS REPRESENTS A PARTICULARLY EFFECTIVE METHOD OF VARYING THE EFFECTIVE IMPEDANCE hSEENv
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BY AN INCIDENT WAVE 4HE ABSORBER IS MADE OF FLEXIBLE CARBON IMPREGNATED PLASTIC FOAM CUT IN THE FORM OF PYRAMIDS )T EXHIBITS OPTIMUM PERFORMANCE WHEN THE PYRA MIDS ARE POINTED TOWARD THE DIRECTION OF THE INCIDENT WAVE AND THE PYRAMIDS SHOULD BE OF THE ORDER OF TO WAVELENGTHS DEEP &IRE RETARDANT PAINT IS USUALLY APPLIED TO PYRAMIDAL ABSORBERS TO SATISFY SAFETY REQUIREMENTS BUT AT HIGH FREQUENCIES THE PAINT TENDS TO DEGRADE THE PERFORMANCE OF THE MATERIAL .EVERTHELESS PYRAMIDAL ABSORBERS OF SUFFICIENT DEPTH CONSISTENTLY TURN IN PERFORMANCES BETTER THAN LESS THAN D" "ECAUSE THESE ABSORBERS DO NOT RELY ON THE CANCELLATION OF A FRONT FACE REFLECTION BY A REAR FACE REFLECTION THEY EXHIBIT GREAT BANDWIDTH )N GENERAL A PYRAMIDAL ABSORBER WITH SHARP TIPS AND UNIFORM BULK LOSS CHARACTERISTICS CAN HAVE A BANDWIDTH THAT EXCEEDS .ONSPECULAR ABSORBERS NEED NOT HAVE THE GREAT THICKNESS CHARACTERIZED BY SPECU LAR ABSORBERS )NTENDED PRIMARILY FOR SUPPRESSION OF SURFACE TRAVELING WAVE ECHOES NONSPECULAR MATERIALS HAVE THE OPPORTUNITY TO REDUCE THE BUILDUP OF SURFACE CUR RENTS OVER SEVERAL WAVELENGTHS ALONG THE SURFACE 4HEY ARE ABLE TO REGISTER QUITE RESPECTABLE PERFORMANCES THEREFORE SIMPLY BECAUSE A THIN LAYER ATTACHED TO A METALLIC SURFACE NEED NOT BE VERY HEAVY )N THIS RESPECT THE SURFACE TRAVELING WAVE CONTRIBUTION DUE TO LONG SMOOTH SURFACES IS ONE OF THE EASIEST TO SUPPRESS %VEN SO THE THICKNESS AND GEOMETRIC DISTRIBUTION OF SURFACE WAVE ABSORBERS SHOULD BE VARIED FOR OPTIMUM PERFORMANCE "Y THIS POINT IT SHOULD BE APPARENT THAT THE APPLICATION OF RADAR ABSORBING MATERI ALS TO VULNERABLE TARGETS IS NOT A VERY EFFECTIVE WAY TO ENHANCE THEIR SURVIVABILITY 4HESE MATERIALS ARE HEAVY DEMAND UNDUE SURFACE CARE AND MAINTENANCE SUFFER LIMITED BANDWIDTH AND NOT LEAST ARE COSTLY ! FAR MORE VIABLE OPTION TARGET SHAPING IS USUALLY AVAILABLE IF ONE IS WILLING TO CONSIDER IT AT THE ONSET OF SYSTEM DEVELOPMENT 3HAPING 3HAPING IS THE RESULT OF JUDICIOUSLY ORIENTING TARGET SURFACES AND EDGES IN A WAY THAT MINIMIZES THEIR CONTRIBUTIONS TO THE TOTAL RADAR ECHO 4HIS OFTEN MEANS SELECTING AIRFRAME SHAPES AND NAVAL HULL PROFILES THAT INITIALLY OUTRAGE AIR FRAME DESIGNERS AND NAVAL ARCHITECTS "UT THERE IS NO POINT IN CONSIDERING SHAPE CONTROL UNLESS A SPECIFIC THREAT DIRECTION CAN BE IDENTIFIED IN AZIMUTH OR ELEVATION OR BOTH )F ALL DIRECTIONS ARE EQUALLY LIKELY THEN THE ADVANTAGE OF CHOOSING FAVOR ABLE SURFACE ORIENTATIONS FOR ONE THREAT DIRECTION IS CANCELED BY AN ACCOMPANYING ENHANCEMENT IN ANOTHER )N MANY SITUATIONS HOWEVER THE GENERAL DIRECTION OF THE THREAT CAN BE FORECAST &IGURE ILLUSTRATES THE 2#3 REDUCTION AVAILABLE THROUGH SHAPING 4HE PLOTTED CURVES ARE BASED ON THEORY AND MEASUREMENTS AND SHOW HOW THE NOSE ON AXIAL 2#3 VARIES WITH THE ELECTRICAL SIZE OF EACH OF THE SIX ROTATIONALLY SYMMETRICAL METALLIC BOD IES SHOWN IN &IGURE 4HE DIAMETERS AND PROJECTED AREAS OF THE OBJECTS ARE IDENTI CAL AND THEIR VOLUMES DIFFER AT MOST BY A FACTOR OF %XCEPT FOR THE SPHERE WHOSE GEOMETRIC OPTICS 2#3 IS SHOWN BY THE UPPERMOST TRACE ALL THE OBJECTS HAVE THE SAME NOSE ANGLE AND OF THE SIX SHAPES THE OGIVE EXHIBITS THE LOWEST 2#3 4HUS AT LEAST ALONG THE AXES OF THESE PARTICULAR BODIES THE 2#3 CAN BE MINIMIZED BY SELECTING THE APPROPRIATE SURFACE PROFILE (OWEVER THE ATTAINMENT OF LOW ECHOES OVER A RANGE OF ASPECT ANGLES IS USUALLY ACCOMPANIED BY HIGHER ECHO LEVELS AT OTHER ANGLES 4HUS THE SELECTION OF AN OPTIMUM SHAPE SHOULD ALWAYS INCLUDE AN EVALUATION OF THE VARIATION OF THE 2#3 OVER A RANGE OF ASPECTS WIDE ENOUGH TO COVER THE ANTICIPATED THREAT DIRECTIONS 4HIS IMPLIES THE CAPA BILITY TO MEASURE THE 2#3 PATTERNS OF A COLLECTION OF OBJECTS WITH CANDIDATE SURFACE PROFILES OR THE CAPABILITY TO PREDICT THOSE PATTERNS OR BOTH
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&)'52% 2#3 OF A COLLECTION OF BODIES OF REVOLUTION OF SIMILAR SIZE AND PROJECTED AREA AFTER 7 % "LORE Ú )%%%
4WO APPROACHES MAY BE TAKEN IN THE APPLICATION OF SHAPING /NE IS TO REPLACE FLAT SURFACES WITH CURVED SURFACES AND THEREBY ELIMINATE NARROW BUT INTENSE SPECULAR LOBES 4HIS IS NOT VERY EFFECTIVE BECAUSE IT INCREASES THE GENERAL ECHO LEVELS AT NEARBY ASPECT ANGLES 4HE SECOND APPROACH IS TO EXTEND FLAT AND SINGLY CURVED SURFACES SO AS TO FURTHER NARROW THE SPECULAR LOBE EVEN IF THIS INCREASES ITS INTENSITY 4HE LOGIC OF THIS APPROACH IS THAT THE PROBABILITY OF DETECTION IS PROPORTIONAL TO THE AVERAGE 2#3 OVER A RANGE OF SOLID ANGLES OF OBSERVATION AND IF THE WIDTH OF THE LOBE IS NARROW ENOUGH ITS CONTRIBUTION TO THE AVERAGE 2#3 MAY BE LESS THAN IF IT WERE A WIDER BUT LESS INTENSE LOBE 4HE REQUIRED 2#3 PATTERN LEVELS OF SPECIFIC VEHICLE CONCEPTS SHOULD BE ESTABLISHED BY MEANS OF MISSION ANALYSES BEFORE DECIDING WHICH SHAPING CRITERION IS APPLICABLE 3HAPING IS USUALLY DIFFICULT TO EXPLOIT OR EXPENSIVE TO IMPLEMENT FOR VEHICLES OR OBJECTS ALREADY IN PRODUCTION BECAUSE THE VEHICLE CONFIGURATION AND PROFILE HAVE BEEN SELECTED AND OPTIMIZED FOR SPECIFIC MISSION OBJECTIVES #HANGES IN THE CONFIGURATION AFTER PRODUCTION THEREFORE ARE LIKELY TO IMPAIR THE MISSION CAPABILITIES OF THE VEHICLE )F CONSIDERED AN OPTION IN THE CONTROL OF 2#3 SHAPING MUST BE INCLUDED IN THE CONCEP TUAL DESIGN OF THE VEHICLE WELL BEFORE ANY PRODUCTION DECISIONS ARE MADE &URTHERMORE SHAPING IS NOT VERY EFFECTIVE FOR BODIES THAT ARE NOT ELECTRICALLY LARGE ,OW 2ADAR #ROSS 3ECTION 6EHICLES 4HE FOLLOWING ARE SOME EXAMPLES OF LOW CROSS SECTION VEHICLES FROM THE EARLY DAYS OF LOW CROSS SECTION VEHICLE DEIGN 4HE 32 4HE DESIGN OF LOW CROSS SECTION VEHICLES PROBABLY BEGAN WHEN #LARENCE h+ELLYv *OHNSON ,OCKHEEDS FAMOUS DESIGNER UNDERTOOK DEVELOPMENT
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&)'52% 4HE OBJECTS WHOSE RADAR CROSS SECTIONS ARE PLOTTED IN &IGURE
OF THE ! AN EARLY PROTOTYPE OF THE 32 "LACKBIRD RECONNAISSANCE PLATFORM !T ,OCKHEEDS FABLED 3KUNK 7ORKS HE RECOGNIZED THE IMPORTANCE OF BRINGING THE 2#3 DESIGN ENGINEER INTO THE INNER CIRCLE DESIGN TEAM 4HE ! DEVELOPMENT CONTRACT WAS AWARDED IN AND BY EARLY THE ! WAS FLYING MISSIONS AROUND THE WORLD 4HE INFLUENCE OF *OHNSONS RADAR SIGNATURE SPECIALISTS IS EVIDENT IN &IGURE 4HE MOST REMARKABLE FEATURE OF THE 32 IS THE CHINE THAT RUNS FROM THE NOSE TO THE ROOT OF THE DELTA WING )N THE NOSE ON SECTOR THE RADAR ECHO WILL BE DOMINATED BY RETURNS FROM THE ENGINE INLETS WHERE THE CHINE CONTRIBUTION IS NO DOUBT NEGLIGIBLE 7HEN SEEN FROM THE BROADSIDE ASPECTS THE CHINE REDUCES THE SPECULAR ECHO THAT WOULD HAVE COME FROM THE OTHERWISE ROUNDED SIDES OF THE FORWARD FUSELAGE .OTE THAT THE TAIL FINS ARE CANTED INWARD THEREBY DEFLECTING INCIDENT RADAR WAVES UPWARD AWAY FROM THE RADAR WHEN SEEN FROM THE SIDE 4HIS DESIGN GREATLY REDUCES THE 32 S ECHO IN A NARROW BROADSIDE SECTOR OF ANGLES 4HE & 4HE LARGEST ECHO SOURCE IN THE 32 NOSE ON REGION IS PROBABLY THE ENGINE INTAKES BECAUSE THEY ARE THRUST WELL FORWARD OF THE WING LEADING EDGES 4HE INTAKES OF THE & .IGHTHAWK BY CONTRAST ARE INSTALLED ABOVE THE WING AND WELL AFT OF THE LEADING EDGE THEY ARE THE LITTLE BLACK DIAMONDS SEEN IN THE NOSE ON VIEW OF THE & SHOWN IN &IGURE !S SUCH THE INTAKES ARE SHIELDED FROM GROUND BASED
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&)'52% ,OCKHEEDS 32 "LACKBIRD
RADARS WHEN THE & IS IN LEVEL FLIGHT %VEN SO THE & DEVELOPERS CONTRIVED AN EGG CRATE COVERING FOR THE INTAKES THAT IN THEORY PREVENTS APPROACHING RADAR WAVES FROM ENTERING THE INLET DUCTS WHERE THEY RATTLE AROUND AND EVENTUALLY COME BACK OUT AGAIN HEADING DIRECTLY BACK TO THE RADAR "ECAUSE THE EGG CRATE GRILLWORK REDUCED AIRFLOW THE INTAKE HAD TO BE ENLARGED TO RESTORE NORMAL FLOW !ND THE DESIGNERS LATER DISCOVERED THAT THE GRILLWORK TENDED TO ICE UP WHICH THEY OVERCAME WITH AN ELECTRICAL HEATING SYSTEM 4HE MOST REMARKABLE FEATURES OF THE & ARE ITS FACETTED AERODYNAMICALLY POOR SURFACE PROFILE AND ITS
&)'52% ,OCKHEEDS & .IGHTHAWK FIGHTER
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SHARPLY SWEPT TAIL FINS 4HE TAIL FINS ARE CANTED OUT AS WELL AS BEING SWEPT AFT AND THE WINGS ARE ALSO SHARPLY SWEPT !LTHOUGH ,OCKHEED MANAGED TO PRODUCE A SUPERSONIC 32 AIRFRAME USING EXOTIC MATERIALS THE LOW 2#3 DEMANDED OF THE & REQUIRED A SUBSONIC AIRFRAME 4HE AIRFRAME IS COVERED WITH THIN ABSORBING MATERIAL WHOSE EDGES ARE SERRATED TO REDUCE REFLECTIONS WHERE HATCHES AND COVERS FIT INTO THE FUSELAGE " 3PIRIT "OMBER .ORTHROP THE PRIME CONTRACTOR FOR THE " 3PIRIT FACED THE SAME PROBLEM WITH ENGINE PLACEMENT THAT ,OCKHEED DID WITH THE & .IGHTHAWK 4HE SOLUTION WAS THE SAME EMBED THE ENGINES INTAKES IN THE TOP SIDE OF THE AIRFRAME 0OSSIBLY BECAUSE THE " HAD A DIFFERENT MISSION THAN THE & DID .ORTHROP DID NOT INSTALL EGG CRATE GRILLWORK OVER THE ENGINE INTAKES )NDEED .ORTHROP DESIGNERS DEVISED HINGED COWLINGS THAT OPEN UP AT LANDING AND TAKEOFF SPEEDS TO INCREASE AIR FLOW INTO THE ENGINES 4HE COWLINGS ARE THEN RETRACTED AT CRUISING SPEED FOR OPTIMUM THRUST AND EFFICIENCY )N THE INTEREST OF LOWERING THE AIRFRAMES RADAR ECHO .ORTHROPS DESIGN TEAM DELIB ERATELY BUILT THE " WITHOUT A TAILFIN !SIDE FROM THIS IT IS INTERESTING THAT THE & AND " SHARE SOME COMMON FEATURES /NE IS THE ROUNDED WINGTIPS WHICH TEND TO REDUCE TIP SPAWNED REFLECTIONS OF SURFACE TRAVELING WAVES THAT MIGHT BUILD UP ALONG THE WINGS LEADING EDGES !NOTHER IS THE USE OF THIN ABSORBER COATINGS THAT ARE SERRATED AROUND THE EDGES OF HATCHES COVERS AND CANOPIES TO SUPPRESS REFLECTIONS FROM EDGE DISCONTINUITIES 9ET ANOTHER IS THE FACT THAT THE " LIKE THE & HAS A SUBSONIC AIRFRAME 4HIS SUGGESTS THAT ALTHOUGH THE CHINE CONCEPT MAY HAVE WORKED FOR THE FUSE LAGE OF THE FABLED -ACH 32 IT IS BY NO MEANS A VIABLE APPROACH FOR REDUCING THE ECHOES FROM WING LEADING EDGES )NDEED THE DESIGNERS OF THE " AIRFRAME APPARENTLY RECOGNIZED EARLY IN THE DESIGN WORK THAT IT WOULD BE NEARLY IMPOSSIBLE TO REDUCE THE LEADING EDGE 2#3 OF THEIR SUB SONIC AIRFRAME TO ACCEPTABLE LEVELS 4HAT BEING THE CASE THEY DECIDED TO ANGLE ALL LEADING AND TRAILING EDGES AT A COMMON SWEEP ANGLE n 4HEIR PHILOSOPHY WAS THAT IF THEY COULDNT SUPPRESS THE EDGE RETURNS THE NEXT BEST OPTION WOULD BE TO ANGLE THEM ALL INTO FOUR COMMON DIRECTIONS IN SPACE 4HUS ALL TRAILING EDGES IN THE " ARE PARALLEL TO LEADING EDGES 8 # 5NMANNED #OMBAT 6EHICLE 4HE "OEING #OMPANY UNVEILED A MOCKUP OF THE h#v VERSION OF ITS UNMANNED COMBAT VEHICLE IN THE MID S LESS THAN A DECADE AFTER THE PROJECT WAS FUNDED BY THE $EFENSE !DVANCED 2ESEARCH 0ROJECTS !DMINISTRATION $!20! !N !SSOCIATED 0RESS PHOTO OF THE AIRCRAFT MOCKUP IS SHOWN IN &IGURE 4HE AIRFRAME IS FT WIDE AND FT LONG 4HE NOSE ANGLE OF THE PLANFORM IS NEARLY DOUBLE THAT OF THE & YET BARELY HALF THAT OF THE " SO THE PLANFORM NOSE ANGLE SEEMS TO BE A COMPROMISE BETWEEN THE TWO .OTE THAT THE ABSENCE OF A COCKPIT IMPROVES THE STEALTHINESS OF THE AIRFRAME )NDEED THE ENGINE INLET COWLING REPLACES THE COCKPIT AND EVEN THE LIPS OF THE INLET ARE BROADLY SERRATED TO REDUCE THEIR CONTRIBUTION TO THE RADAR ECHO 4HE LACK OF ANY TAILFIN AND THE CONTOUR OF THE TRAILING EDGES OF THE PLANFORM REVEAL STRONG INFLUENCES FROM THE " DESIGN PHILOSOPHY ,OW #ROSS 3ECTION 3HIPS #ONVENTIONAL SHIPS USUALLY HAVE VERY LARGE STRUCTURES WITH MANY HORIZONTAL AND VERTICAL REFLECTING SURFACES THAT MEET AT RIGHT ANGLES FORM ING CORNER REFLECTORS WITH STRONG ECHOES 4HEY ALSO CAN HAVE MANY INDIVIDUAL SCAT TERERS THAT CAN CONTRIBUTE TO A LARGE RADAR CROSS SECTION 4O ACHIEVE LOW RADAR CROSS SECTION THE HORIZONTALVERTICAL DESIGN PLAN IS CHANGED SO AS TO EMPLOY TILTED SURFACES
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% & +NOTT 2ADAR #ROSS 3ECTION -EASUREMENTS .EW 9ORK 6AN .OSTRAND 2EINHOLD PP n $ , -ENSA (IGH 2ESOLUTION 2ADAR )MAGING .ORWOOD -! !RTECH (OUSE 7 7 3ALISBURY h!BSORBENT "ODY FOR %LECTROMAGNETIC 7AVES v 53 0ATENT *UNE 7 % "LORE h4HE RADAR CROSS SECTION OF OGIVES DOUBLE BACKED CONES DOUBLE ROUNDED CONES AND CONE SPHERES v )%%% 4RANS VOL !0 PP n 3EPTEMBER - $ /,EARY AND %RIC 3CHULZINGER 32 )NSIDE ,OCKHEEDS "LACKBIRD /SEOLA 7) -OTORBOOKS )NTERNATIONAL 0UBLISHERS 7HOLESALERS " 3WEETMAN AND * 'OODALL ,OCKHEED & ! /SEOLA 7) -OTORBOOKS )NTERNATIONAL 0UBLISHERS 7HOLESALERS % & +NOTT h2#32 'UIDELINES (ANDBOOK v &INAL 4ECHNICAL 2EPORT ON %%3')4 0ROJECT ! v %NGINEERING %XPERIMENT 3TATION 'EORGIA )NSTITUTE OF 4ECHNOLOGY !PRIL
#HAPTER
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£x°£Ê /," 1 /" &OR AN OPERATIONAL RADAR BACKSCATTER OF THE TRANSMITTED SIGNAL BY ELEMENTS OF THE SEA SURFACE OFTEN PLACES SEVERE LIMITS ON THE DETECTABILITY OF RETURNS FROM SHIPS AIR CRAFT AND MISSILES NAVIGATION BUOYS AND OTHER TARGETS SHARING THE RADAR RESOLUTION CELL WITH THE SEA SURFACE 4HESE INTERFERING SIGNALS ARE COMMONLY REFERRED TO AS SEA CLUTTER OR SEA ECHO 4HE SEARCH FOR A USEFUL UNDERSTANDING OF THIS IMPORTANT RADAR CONTAMINANT BEGAN WITH THE COLLECTION AND ANALYSIS OF CLUTTER DATA FROM OPERATING RADARS WITH THE GOAL OF ESTABLISHING THE RELATIONSHIP BETWEEN CLUTTER SIGNALS AND THE PARAMETERS OF BOTH THE RADAR AND THE SEA ENVIRONMENT -UCH OF THE EARLIEST WORK TOOK PLACE DURING 77)) AND CAN BE FOUND IN ONE OF THE COMPREHENSIVE SERIES OF 2!$,!" VOLUMES DOCUMENTING THE RADAR RESEARCH THAT WAS DONE AT THAT TIME "UT MOST OF THE CLUTTER DATA FROM THIS PERIOD AND EVEN INTO THE S WAS COLLECTED IN BITS AND PIECES FROM ISOLATED EXPERIMENTS OFTEN WITH POOR INCOMPLETE OR MISLEAD ING DESCRIPTIONS OF THE SEA SURFACE )T WOULD SEEM A SIMPLE MATTER TO REFINE THESE RESULTS BY USING INSTRUMENTATION RADARS OPERATING OVER THE WIDE VARIETY OF RADAR AND ENVIRONMENTAL PARAMETERS ENCOUN TERED IN PRACTICE "UT WHILE THE PARAMETERS RELATING TO THE RADAR SYSTEM AND ITS CONFIGU RATION SUCH AS FREQUENCY CELL SIZE POLARIZATION GRAZING ANGLE AT THE SURFACE ETC CAN BE SPECIFIED SELECTING AND QUANTIFYING THE ENVIRONMENTAL PARAMETERS IS QUITE ANOTHER MATTER &IRST IT HAS NOT ALWAYS BEEN CLEAR WHICH ENVIRONMENTAL PARAMETERS ARE IMPOR TANT &OR EXAMPLE WIND SPEED CERTAINLY SEEMS TO AFFECT CLUTTER LEVELS BUT THE COR RELATION OF CLUTTER WITH SAY A SHIPS ANEMOMETER READINGS IS OFTEN INCONSISTENT !ND ALTHOUGH THE STATE OF AGITATION OF THE SEA SURFACE SEA STATE APPEARS TO HAVE A STRONG EFFECT IT IS A SUBJECTIVE MEASURE AND ITS RELATION TO PREVAILING LOCAL WINDS IS OFTEN UNCERTAIN -OREOVER IT HAS BEEN FOUND THAT THE TEMPERATURES OF THE AIR AND THE SEA SURFACE CAN AFFECT THE WAY IN WHICH MEASURED WIND SPEED IS RELATED TO THE GENERATION OF CLUTTER PRODUCING WAVES YET THE IMPORTANCE OF THESE EFFECTS WERE UNAPPRECIATED OVER MOST OF THE HISTORY OF SEA CLUTTER MEASUREMENTS SO AIR AND SEA TEMPERATURES WERE SELDOM RECORDED &INALLY EVEN IF THE IMPORTANCE OF AN ENVIRONMENTAL PARAMETER HAS BEEN RECOGNIZED IT IS OFTEN DIFFICULT OR TOO EXPENSIVE TO MEASURE IT ACCURATELY IN THE FIELD UNDER REAL SEA CONDITIONS 7HILE MANY ASPECTS OF SEA CLUTTER THUS REMAINED FRUSTRATINGLY ILL DEFINED THE EARLIER WORK DID DISCLOSE SOME GENERAL TRENDS SUCH AS THE TENDENCY OF AVERAGE CLUTTER SIGNAL STRENGTHS AT LOW TO INTERMEDIATE GRAZING ANGLES TO INCREASE WITH THE £x°£
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GRAZING ANGLE AND THE WIND SPEED OR SEA STATE AND GENERALLY TO BE GREATER FOR VERTICAL POLARIZATION AND IN UPWINDDOWNWIND DIRECTIONS &OR OTHER REVIEWS OF SEA CLUTTER AND ITS HISTORY SEE 3KOLNIK .ATHANSON AND ,ONG 3EA CLUTTER IS HOWEVER A COMPLEX PHENOMENON PRESENTING VARIOUS FACES DEPENDING ON THE WAY THE RADAR VIEWS THE SCENE &OR EXAMPLE IT IS COMMONLY NOTED THAT WHEN VIEWED ON AN ! SCOPE SIGNAL AMPLITUDE VERSUS RANGE THE APPEARANCE OF SEA CLUTTER DEPENDS STRONGLY ON THE SIZE OF THE RESOLUTION CELL OR RADAR FOOTPRINT &OR LARGE CELLS IT APPEARS DISTRIBUTED IN RANGE AND MAY BE CHARACTERIZED BY A SURFACE AVERAGED CROSS SECTION WITH RELATIVELY MODEST FLUCTUATIONS ABOUT A MEAN VALUE !S THE SIZE OF THE RESOLUTION CELL IS REDUCED CLUTTER INCREASINGLY APPEARS TO CONTAIN SEQUENCES OF ISO LATED TARGET LIKE OR DISCRETE RETURNS THAT VARY IN TIME !T THE HIGHER RESOLUTIONS THE DISCRETE RETURNS TEND TO STAND WELL OUT OF THE BACKGROUND OCCURRING FOR BOTH POLARIZATIONS BUT MOST CLEARLY EVIDENT WITH HORIZONTAL POLARIZATION AT SMALL GRAZING ANGLES 4HESE ISOLATED RETURNS ARE CALLED SEA SPIKES AND ARE A COMMON CLUTTER COM PONENT IN THIS RADAR OPERATING REGIME 1UITE CLEARLY AN UNDERSTANDING OF SEA CLUTTER IN ALL ITS ASPECTS WILL BE A CONSIDERABLE UNDERTAKING &ORTUNATELY A CLOSE RELATION SHIP BETWEEN RADAR AND OCEANOGRAPHY HAS GROWN UP IN THE FIELDS OF REMOTE SENSING LEADING TO THE ACCUMULATION OF A LARGE AMOUNT OF INFORMATION BOTH EXPERIMENTAL AND THEORETICAL ABOUT HOW SCATTERING AT RADAR FREQUENCIES RELATES TO OCEANOGRAPHIC VARIABLES )N MANY WAYS THIS INFORMATION SERVES AS THE BASIS OF MUCH OF OUR CURRENT UNDERSTANDING OF SEA CLUTTER )N MODELING SEA CLUTTER THERE IS A DIFFERENCE BETWEEN A THEORY WHICH RELATES THE PHYSICAL SCATTERING PROPERTIES OF THE SEA SURFACE TO THE RECEIVED SIGNAL AND A CHARAC TERIZATION WHICH PROVIDES A DESCRIPTION OF THE SEA CLUTTER DATA IN TERMS OF A STATISTICAL MODEL EG 2AYLEIGH LOGNORMAL 7EIBULL AND + DISTRIBUTION THAT ALTHOUGH SOME TIMES SUGGESTIVE OF PHYSICAL PROCESSES IN THE UNDERLYING SCATTERING IS OF GREATER DIRECT INTEREST TO THE RADAR SYSTEM DESIGNER IN PROVIDING DETECTION PROBABILITIES AND FALSE ALARM RATES (ISTORICALLY ATTEMPTS TO PROVIDE A THEORETICAL EXPLANATION OF THE OBSERVED BEHAV IOR OF CLUTTER SIGNALS TRACE ESSENTIALLY FROM THE WORK PURSUED DURING 7ORLD 7AR )) AND DESCRIBED IN THE WELL KNOWN -)4 2ADIATION ,ABORATORY BOOK MENTIONED ABOVE 5NFORTUNATELY THE SCATTERING MODELS DEVELOPED DURING THIS PERIOD ALONG WITH MOST OF THOSE PUBLISHED OVER THE FOLLOWING DECADE FAILED TO ACCOUNT IN ANY CONVINCING WAY FOR THE BEHAVIOR OF SEA BACKSCATTER )N HOWEVER #ROMBIE OBSERVED THAT AT HIGH FREQUENCY (& WAVELENGTHS TENS OF METERS SCATTERING APPEARED TO ARISE FROM A RESONANT INTERACTION WITH SEA WAVES OF ONE HALF OF THE INCIDENT WAVELENGTH IE TO BE OF THE "RAGG TYPE 2EINFORCED BY THE THEORETICAL IMPLICATIONS OF VARIOUS SMALL WAVEHEIGHT APPROXIMATIONS AND WAVE TANK MEASUREMENTS UNDER IDEALIZED CONDI TIONS THE "RAGG MODEL WAS INTRODUCED INTO THE MICROWAVE REGIME BY MANY WORKERS IN THE MID Sn 4HIS PRODUCED A REVOLUTION IN THINKING ABOUT THE ORIGINS OF SEA CLUTTER BECAUSE IT INVOLVED THE SEA WAVE SPECTRUM THUS FORGING A LINK BETWEEN CLUTTER PHYSICS AND OCEANOGRAPHY IN WHAT BECAME THE FIELD OF RADIO OCEANOGRAPHY (OWEVER FUNDAMENTAL CONCEPTUAL PROBLEMS IN APPLYING THE "RAGG HYPOTHESIS IN MICROWAVE SCATTERING ALONG WITH ITS INABILITY TO ADDRESS SIGNIFICANT ASPECTS OF MEA SURED SEA CLUTTER HAVE LED THROUGH THE YEARS TO CONTINUING INQUIRY INTO THE PHYSICAL ORIGINS OF SEA SCATTER AND HOW BEST TO MODEL ITn 4HIS BEING THE CASE SPECULATION ABOUT PHYSICAL MODELS WILL BE KEPT TO A MINIMUM IN THE SECTIONS ON THE EMPIRICAL BEHAVIOR OF SEA CLUTTER 4HE PROBLEM OF MODELING SEA SCATTER WILL BE DISCUSSED SEPA RATELY IN A LATER SECTION
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#LOSE OBSERVATION OF THE SEA SURFACE DISCLOSES A VARIETY OF FEATURES DESCRIBABLE AS WEDGES CUSPS WAVES FOAM TURBULENCE AND SPRAY AS WELL AS BREAKING EVENTS OF ALL SIZES AND MASSES OF FALLING WATER !NY OR ALL OF THESE MIGHT CONTRIBUTE TO THE SCATTER ING OF ELECTROMAGNETIC WAVES RESPONSIBLE FOR SEA CLUTTER 4HE BASIC OCEANOGRAPHIC DESCRIPTOR OF THE SEA SURFACE HOWEVER IS THE WAVE SPECTRUM WHICH SAYS LITTLE ABOUT THE DETAILS OF THESE FEATURES BUT CONTAINS A GREAT DEAL OF INFORMATION ABOUT THE SEA SURFACE IN GENERAL AND IS CENTRAL TO THE APPLICATION OF THE "RAGG SCATTERING HYPOTHESIS !CCORDINGLY SOME TUTORIAL MATERIAL DESCRIBING THE SPECTRAL CHARACTERIZATION OF THE SEA SURFACE IS INCLUDED IN THIS SECTION ALONG WITH A BRIEF DISCUSSION OF SURFACE EVENTS SUCH AS WAVE BREAKING AND OTHER SURFACE EFFECTS THOUGHT TO CONTRIBUTE TO THE PRODUCTION OF SEA SPIKES 4HERE ARE BASICALLY TWO TYPES OF SURFACE WAVES CAPILLARY AND GRAVITY DEPENDING ON WHETHER SURFACE TENSION OR GRAVITY IS THE DOMINANT RESTORING FORCE 4HE TRANSITION BETWEEN ONE AND THE OTHER TAKES PLACE AT A WAVELENGTH OF ABOUT CM SO THE SMALLER CAPILLARY WAVES SUPPLY THE SURFACE FINE STRUCTURE WHILE GRAVITY WAVES MAKE UP THE LARGER AND MOST VISIBLE SURFACE STRUCTURES 3EA WAVES HAVE THEIR ORIGIN PRIMARILY IN THE WIND BUT THIS DOES NOT MEAN THAT THE hLOCALv WIND IS A PARTICULARLY GOOD INDICATOR OF WHAT THE WAVE STRUCTURE BENEATH IT WILL BE )N ORDER TO AROUSE THE SURFACE TO ITS FULLY DEVELOPED OR EQUILIBRIUM STATE THE WIND MUST BLOW FOR A SUFFICIENT TIME DURATION OVER A SUFFICIENT DISTANCE FETCH 4HAT PART OF THE WAVE STRUCTURE DIRECTLY PRODUCED BY THESE WINDS IS CALLED SEA "UT WAVES PROPAGATE SO EVEN IN THE ABSENCE OF LOCAL WIND THERE CAN BE SIGNIFICANT LOCAL WAVE MOTION DUE TO WAVES ARRIVING FROM FAR AWAY PERHAPS FROM A DISTANT STORM 7AVES OF THIS TYPE ARE CALLED SWELL AND SINCE THE SURFACE OVER WHICH THE WAVES TRAVEL ACTS AS A LOW PASS FILTER SWELL COMPONENTS OFTEN TAKE THE FORM OF LONG CRESTED LOW FREQUENCY SINUSOIDS 4HE 7AVE 3PECTRUM 4HE OCEAN WAVE SPECTRUM DESCRIBING THE SEA SURFACE APPEARS IN SEVERAL FORMS )F THE TIME HISTORY OF THE SURFACE ELEVATION IS MONITORED AT A FIXED POINT THE RESULTING TIME SERIES MAY BE PROCESSED TO PROVIDE A FREQUENCY SPECTRUM 3 F OF THE SURFACE ELEVATION WHERE 3 F DF IS A MEASURE OF THE ENERGY IE SQUARE OF THE WAVEHEIGHT OF THE WAVES IN THE FREQUENCY INTERVAL BETWEEN F AND F DF 7AVE SPECTRA HAVE BEEN MEASURED IN THE OPEN OCEAN PRIMARILY FOR GRAVITY WAVES DOWN TO WAVELENGTHS OF ABOUT M /PEN OCEAN MEASUREMENTS OF CAPILLARY WAVE SPECTRA ARE ESPECIALLY DIFFICULT TO PERFORM &OR A GRAVITY WAVE THE FREQUENCY F AND THE WAVENUMBER + ARE RELATED BY THE DIS PERSION RELATION
F O G+
WHERE G IS THE ACCELERATION OF GRAVITY AND + O , WITH , BEING THE WAVELENGTH !LTHOUGH EACH INDIVIDUAL GRAVITY WAVE OBEYS THIS RELATION THE WAVES AT A POINT ON THE SEA SURFACE COULD COME FROM ANY DIRECTION SO THEY ARE CHARACTERIZED BY A TWO DIMENSIONAL PROPAGATION VECTOR WITH ORTHOGONAL COMPONENTS +X AND +Y WHERE THE + TO BE USED IN %Q IS THE MAGNITUDE + +X +Y 4HE WAVENUMBER SPECTRUM ASSOCIATED WITH 3 F IS A FUNCTION OF THE TWO COMPONENTS OF + AND IS COMMONLY WRIT TEN AS 7+X +Y 4HIS IS CALLED THE DIRECTIONAL WAVE SPECTRUM AND EXPRESSES THE ASYM METRIES ASSOCIATED WITH WINDS CURRENTS REFRACTION ISOLATED SWELL COMPONENTS ETC
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&OR A GIVEN SOURCE OF ASYMMETRY SUCH AS THE WIND VARIOUS PARTS OF THE SPECTRUM WILL DISPLAY DIFFERENT DIRECTIONAL BEHAVIORS &OR EXAMPLE IN A FULLY DEVELOPED SEA THE LARGER WAVES WILL TEND TO MOVE IN THE DIRECTION OF THE WIND WHILE THE SMALLER WAVES WILL BE MORE ISOTROPIC $IRECTIONAL SPECTRA ARE MORE DIFFICULT TO MEASURE AND ARE OBTAINED BY A VARIETY OF EXPERIMENTAL METHODS SUCH AS AN ARRAY OF WAVE STAFFS TO MEASURE SURFACE HEIGHTS OVER A MATRIX OF POINTS A MULTIAXIS ACCELEROMETER BUOY STEREO PHOTOGRAPHY AND EVEN BY PROCESSING RADAR BACKSCATTER SIGNALS (OWEVER A FREQUENCY SPECTRUM MEASURED AT A POINT CAN CONTAIN NO KNOWLEDGE OF WAVE DIRECTION SO A WAVENUMBER SPECTRUM 7+ IS OFTEN DEFINED IN TERMS OF THE FREQUENCY SPECTRUM 3 F BY THE RELATION
7+ 3 F + DF D+
WITH THE RELATION BETWEEN F AND + GIVEN BY %Q 4O ACCOUNT FOR THE WIND DIRECTION 7+ IS SOMETIMES MULTIPLIED BY AN EMPIRICAL FUNCTION OF + AND DIRECTION E RELATIVE TO THE UP WIND DIRECTION /CEANOGRAPHERS HAVE NOT ALWAYS BEEN IN COMPLETE AGREEMENT ABOUT THE FORM OF THE FREQUENCY SPECTRUM .ONEQUILIBRIUM WAVE CONDITIONS INADEQUATE SAMPLING TIMES POOR GROUND TRUTH ETC CAN CONTAMINATE THE DATA SET FROM WHICH EMPIRICAL SPECTRA ARE DERIVED (OWEVER BY CAREFUL SELECTION OF DATA FROM MANY SOURCES ENSURING THAT ONLY EQUILIBRIUM FULLY DEVELOPED SEA CONDITIONS WERE REPRESENTED AND THE WIND WAS ALWAYS MEASURED AT THE SAME REFERENCE HEIGHT USUALLY TAKEN AS METERS 0IERSON AND -OSKOWITZ ESTABLISHED A SIMPLE EMPIRICAL SPECTRUM THAT HAS PROVEN POPULAR AND USEFUL )T HAS THE FORM
3 F !F E " F M F
WHERE G IS THE ACCELERATION OF GRAVITY AND FM GO 5 CORRESPONDING TO THE FREQUENCY OF A WAVE MOVING WITH A VELOCITY EQUAL TO THE WIND SPEED 5 ! AND " ARE EMPIRICAL CONSTANTS 4HIS SPECTRUM IS ILLUSTRATED IN &IGURE FOR SEVERAL WIND SPEEDS 4HE EFFECT OF INCREASING WIND SPEED IS SIMPLY TO MOVE THE LOW FREQUENCY CUTOFF TO LOWER FREQUENCIES ALONG THE HIGH FREQUENCY F ASYMPTOTE )T SHOULD BE NOTED THAT MOST OF THE OCEANOGRAPHERS SPECTRA ARE BASED ON MEASUREMENTS AT RELATIVELY LOW FREQUENCIES AND SO CANNOT BE TAKEN SERIOUSLY AT FREQUENCIES ABOVE ABOUT (Z .EVERTHELESS THESE SPECTRAL FORMS ARE OFTEN USED UP TO (Z OR GREATER IN PREDICTING RADAR CLUTTER UNDER THE "RAGG HYPOTHESIS #ONVERTING THIS FREQUENCY SPECTRUM INTO AN ISOTROPIC WAVENUMBER SPECTRUM THROUGH %Q RESULTS IN A SPECTRUM OF SIMILAR FORM ONLY WITH A + ASYMPTOTE 0HILLIPS DERIVED THIS ASYMPTOTIC BEHAVIOR ON DIMENSIONAL GROUNDS AND A WIDELY USED SIMPLIFICATION OBTAINED BY REPLACING THE SMOOTH PEAK IN &IGURE BY A SHARP CUTOFF IS GENERALLY REFERRED TO AS THE 0HILLIPS 3PECTRUM
7+ + + G5
+ G5
WHERE THE CUTOFF WAVENUMBER CORRESPONDS TO THE FREQUENCY FM OF THE PEAK IN %Q /PPOSED TO THIS HIGHLY SIMPLIFIED FORM ARE INCREASINGLY COMPLEX SPECTRA BASED ON MORE CAREFUL EMPIRICAL STUDIES AS WELL AS MORE SOPHISTICATED THEORETICAL CONSIDERATIONS )N DISCUSSING THE CHARACTERIZATION OF THE SEA SURFACE BY ITS SPECTRUM IT MUST BE KEPT IN MIND THAT THE SPECTRUM IS A HIGHLY AVERAGED DESCRIPTION OF HOW THE ENERGY OF THE SUR FACE IS DISTRIBUTED AMONG THE WAVENUMBERS OR FREQUENCIES OF THE WAVES PRESENT ON IT
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&)'52% 3EA WAVE FREQUENCY SPECTRA OF THE 0IERSON -OSKOWITZ TYPE REPRESENTING FULLY DEVELOPED SEAS AFTER 7 * 0IERSON AND , -OSKOWITZ Ú !MERICAN 'EOPHYSICAL 5NION
3INCE THE PHASES OF THESE WAVES ARE LOST THE SPECTRUM GIVES NO INFORMATION ABOUT THE DETAILED MORPHOLOGY OF THE SURFACE ITSELF IE ABOUT THE COMPLEX SURFACE FEATURES THAT ARE RESPONSIBLE FOR THE SCATTERED FIELD 4HIS POINT WILL BE RAISED AGAIN AS WE GO ALONG 'ENERAL 3EA $ESCRIPTORS 4HE SHAPE OF THE CURVES IN &IGURE INDICATES THAT THE SEA WAVE SYSTEM IS SHARPLY PEAKED SO IT SHOULD BE POSSIBLE TO GET A ROUGH IDEA OF THE BEHAVIOR OF THE MAJOR WAVES ON THE SURFACE BY TAKING THE VALUES OF PERIOD F AND WAVELENGTH O + DEFINED AT THE SPECTRAL PEAK 4HESE VALUES ARE ASSIGNED TO A WAVE SATISFYING THE DISPERSION RELATION %Q AND HAVING A PHASE VELOCITY # O F + EQUAL TO THE WIND SPEED 5 "Y USING %Q THE PERIOD 4 ` AND WAVELENGTH ,` THEREBY DEFINED TAKE THE FORM
4 ` 5 ,` 5
WHERE 5 IS IN METERS PER SECOND &OR EXAMPLE THE LARGEST WAVES IN A FULLY DEVELOPED SEA FOR A KT MS WIND WILL HAVE A WAVELENGTH OF ABOUT FT M WITH A PERIOD OF S 4HE STATISTICAL DISTRIBUTION OF WAVEHEIGHTS ON THE OCEAN SURFACE IS QUITE CLOSE TO GAUSSIAN WITH A MEAN SQUARE HEIGHT THAT CAN BE OBTAINED BY INTEGRATING THE WAVE HEIGHT SPECTRUM OVER ALL FREQUENCIES OR WAVENUMBERS &OR SPECTRA RESEMBLING THOSE IN &IGURE THE RMS WAVEHEIGHT IS GIVEN APPROXIMATELY BY HRMS 5 M
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4HE RMS WAVEHEIGHT CONTAINS CONTRIBUTIONS FROM ALL THE WAVES ON THE SURFACE BUT VERY OFTEN IT IS THE PEAK TO TROUGH HEIGHT FOR THE HIGHER WAVES THAT IS OF MAJOR INTEREST 4HIS IS CERTAINLY THE CASE FOR A SHIP IN A SEAWAY OR IN THE SHADOWING OF THE SURFACE AT LOW RADAR GRAZING ANGLES 4HE SIGNIFICANT HEIGHT OR PEAK TO TROUGH HEIGHT OF THE ONE THIRD HIGHEST WAVES PROVIDES SUCH A MEASURE )T IS DENOTED BY ( AND IS TAKEN TO BE ABOUT SIX TIMES THE SPECTRAL RMS AMPLITUDE SEE EG +INSMAN &IG &OR A KT WIND THIS IS ONLY ABOUT FT BUT FOR GALE FORCE WINDS OF KT IT RISES TO ALMOST FT WHICH IS A RATHER FORMIDABLE SEA ,OOKING AT THE SEA AN OBSERVER MIGHT DESCRIBE WHAT IS SEEN IN TERMS OF A SUBJECTIVE STATE OF THE SEA EG hSMOOTH v hROUGH v OR hTERRIFYINGv )F THESE DESCRIPTIONS ARE LISTED IN ORDER OF SEVERITY AND ASSIGNED NUMBERS THESE NUMBERS DEFINE A SEA STATE ! SIMILAR NUMERICAL SCALE EXISTS FOR WIND SPEEDS THE "EAUFORT WIND SCALE WITH NUMBERS ABOUT AN INTEGER HIGHER THAN THE CORRESPONDING SEA STATE "UT IT IS SELDOM USED IN REFERENCE TO SEA CLUTTER 4HERE ARE THEN TWO NUMBERS COMMONLY USED TO INDICATE THE ACTIVITY OF THE SEA SURFACE A SUBJECTIVE SEA STATE AND A MEASURED WIND SPEED /NLY WHEN THE WIND HAS SUFFICIENT FETCH AND DURATION TO EXCITE A FULLY DEVELOPED SEA CAN A WAVEHEIGHT BE UNAM BIGUOUSLY ASSOCIATED WITH IT 4HE SURFACE DESCRIPTORS GENERALLY USED IN CONNECTION WITH SEA CLUTTERSEA STATE WIND SPEED AND ITS ASSOCIATED EQUILIBRIUM WAVEHEIGHTARE GIVEN IN 4ABLE WITH THE WIND SPEED IN KNOTS THE SIGNIFICANT WAVEHEIGHT IN FEET AND THE DURATIONFETCH REQUIRED FOR A FULLY DEVELOPED SEA IN HOURSNAUTICAL MILE )T IS OF INTEREST TO NOTE THAT THE MEDIAN WIND SPEED OVER THE WORLDS OCEANS IS ABOUT KT CORRESPONDING TO SEA STATE "REAKING 7AVES AND /THER 3URFACE $ISTURBANCES 4HE OBSERVABLE FEATURES OF THE SEA SURFACE THAT BEST SUGGEST AN ORIGIN FOR THE SHARP LOCALIZED RADAR RETURNS CALLED SEA SPIKES ARE SURFACE EVENTS THAT ARE THEMSELVES SHARPLY LOCALIZED EVENTS INCLUDING BREAK ING WAVES OF ALL SIZES INDUCED EITHER BY THE WIND OR BY NONLINEAR INTERACTIONS AMONG WAVE SYSTEMS ,ARGE SCALE BREAKING WAVES DISPLAY TWO CHARACTERISTIC BEHAVIORS SPILLING IN WHICH AN UNSTABLE WAVE PEAK UNRAVELS AND PLUNGING WHERE THE PEAK CURLS OVER ON ITSELF AND CRASHES ONTO THE FRONT FACE AS A CASCADE OF WATER MASSES ENDING IN A CHAOTIC JUMBLE !NOTHER DIFFERENT EVENT IS THE MICROBREAKER A SMALL TRANSIENT SHOCK FRONT INDUCED BY A PUFF OF WIND OR ANOTHER WAVE !S NOTED EARLIER HIGHLY AVERAGED WAVE SPECTRA CANNOT DISCLOSE THE MORPHOLOGY OF SUCH SURFACE FEATURES AND UNFORTUNATELY PHYSICAL OCEANOGRAPHY IS STILL UNABLE TO PROVIDE A GENERALLY SATISFACTORY DESCRIPTION OR CHARACTERIZATION OF WAVE BREAKING .EVERTHELESS THERE ARE TWO USEFUL HEURISTIC PARAM ETERS RELATING ELEMENTS OF A BREAKING WAVE SCENE TO WIND SPEED 7HITECAP DENSITY IS A VISIBLE TRACER OF BREAKING WAVE ACTIVITY AND HAS A POWER LAW DEPENDENCE ON WIND SPEED 4!",% 3EA 3URFACE $ESCRIPTORS
3EA 3TATE SMOOTH SLIGHT MODERATE ROUGH VERY ROUGH HIGH VERY HIGH
7IND 3PEED KT
7AVEHEIGHT ( FT
$URATIONFETCH HNMI
n n n n n n
n n n n n n
3%! #,544%2
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GIVEN BY Q WB ^ 5 4HE AVERAGE LENGTH OF A BREAKING WAVEFRONT MOVING AT SPEED C ALSO DEPENDS ON WIND SPEED AND IS GIVEN BY A PARAMETER ,C 4HESE PARAMETERS WILL APPEAR AGAIN LATER WHEN WE DISCUSS SOME OF THE MORE RECENT MODELS FOR SEA CLUTTER !N ADDITIONAL FEATURE OF SMALL SCALE BREAKING OR OTHER STRONGLY NONLINEAR EVENTS IS THE APPEARANCE OF hPARASITICv OR hBOUNDv CAPILLARIES ATTACHED TO THE EVENT AND MOVING WITH IT 4HEY TEND TO BE SMALL AMPLITUDE FEATURES LOCALIZED AND NARROW BAND
£x°ÎÊ *, Ê 6",Ê"Ê- Ê 1// , 3EA CLUTTER IS A FUNCTION OF MANY PARAMETERS SOME OF THEM SHOWING A COMPLICATED INTERDEPENDENCE SO WE EMPHASIZE AGAIN THAT IT IS NOT AN EASY TASK TO ESTABLISH ITS DETAILED BEHAVIOR WITH A GREAT DEAL OF CONFIDENCE OR PRECISION &OR EXAMPLE IN A PROPER SEA CLUTTER MEASUREMENT THE POLARIZATION RADAR FREQUENCY GRAZING ANGLE AND RESOLUTION CELL SIZE WILL HAVE BEEN SPECIFIED 4HEN THE WIND SPEED AND DIRECTION MUST BE MEASURED AT A REFERENCE ALTITUDE AND IF THE RESULTS ARE TO BE COMPARED WITH THOSE OF OTHER EXPERIMENTERS THE PROPER DURATION AND FETCH SHOULD BE AVAILABLE TO ENSURE STANDARDIZATION TO EQUILIBRIUM SEA CONDITIONS 3INCE THESE MEASURED WINDS ARE RELATED TO THE WIND STRUCTURE AT THE SURFACE THROUGH THE ATMOSPHERIC BOUNDARY LAYER THE SHAPE OF THIS LAYER MUST BE DETERMINED BY MEASURING THE AIR AND SEA TEMPERATURES 4O COM PLICATE THE PICTURE STILL FURTHER IT HAS BEEN FOUND THAT SEA CLUTTER CAN BE DEPENDENT ON THE DIRECTION OF THE LONG WAVES WHICH INCLUDES SWELL IN THE MEASUREMENT AREA SO IDEALLY THE DIRECTIONAL WAVE SPECTRUM SHOULD BE MEASURED AS WELL /BVIOUSLY IT IS UNLIKELY THAT ALL OF THESE ENVIRONMENTAL PARAMETERS WILL BE RECORDED WITH PRECISION IN EVERY OR EVEN ANY SEA CLUTTER MEASUREMENT SO CONSIDERABLE VARIABILITY IN THE BASIC CONDITIONS UNDER WHICH SEA CLUTTER DATA ARE COLLECTED BY DIFFERENT EXPERIMENTERS CAN BE EXPECTED )T IS OF INTEREST TO NOTE THAT IN MANY OF THE REPORTED MEASUREMENTS OF SEA CLUTTER PARTICULARLY IN THE OLDER LITERATURE WIDE INCONSISTENCIES BETWEEN WIND SPEED AND WAVEHEIGHT MAY BE FOUND &OR EXAMPLE A WIND SPEED OF KT MIGHT BE REPORTED WITH WAVEHEIGHTS OF FT OR KT WINDS WITH FT WAVES 4HESE PAIRINGS ARE NOT CONSISTENT WITH THE VALUES FOR AN EQUILIBRIUM SEA DESCRIBED IN 4ABLE AND INDICATE THE UNNOTICED OR UNRECORDED PRESENCE OF HEAVY SWELL OR HIGHLY NONEQUILIBRIUM WIND CONDITIONS OR BOTH %VEN WITH ALL THE VARIABLES PROPERLY SPECIFIED RECORDED CLUTTER DATA CAN BE SPREAD OVER A WIDE DYNAMIC RANGE ESPECIALLY AT LOW GRAZING ANGLES 3INCE SEA CLUTTER IS GENERALLY VIEWED AS A SURFACE DISTRIBUTED PROCESS THE BASIC CLUTTER PARAMETER IS TAKEN TO BE THE NORMALIZED RADAR CROSS SECTION .2#3 R OF THE SURFACE COMMONLY REFERRED TO AS SIGMA ZERO AND EXPRESSED IN DECIBELS RELATIVE TO MM )T IS OBTAINED EXPERIMENTALLY BY DIVIDING THE MEASURED RADAR CROSS SECTION OF AN ILLUMINATED PATCH OF THE SURFACE BY A NORMALIZING AREA SO DIFFERENCES IN THE DEFINITION OF THIS AREA CAN LEAD TO INCONSISTENCIES AMONG VARIOUS REPORTS OF .2#3 MEASUREMENTS 3CATTERING FROM ANY DISTRIBUTED TARGET INVOLVES THE PRODUCT OF THE TRANSMITTING AND RECEIVING SYS TEM FOOTPRINTS INTEGRATED OVER THE TARGET 4HESE FOOTPRINTS COVER EXACTLY THE SAME AREA FOR A MONOSTATIC RADAR AND WILL DEPEND ON THE PULSE AND BEAMWIDTHS THE RANGE AND THE GRAZING ANGLE )F THE FOOTPRINTS ARE ASSUMED TO BE OF THE COOKIE CUTTER TYPE CONSTANT AMPLITUDE FALLING SHARPLY TO ZERO AT THE HALF POWER POINTS THEN THE RELATION BETWEEN THE ACTUAL RADAR CLUTTER CROSS SECTION R C AS INFERRED FROM THE RECEIVED POWER VIA THE RADAR EQUATION AND THE .2#3 R IS GIVEN BY
R R C !F
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WHERE FOR A RADAR WITH AN ANTENNA BEAMWIDTH " AND RECTANGULAR PULSE OF LENGTH S VIEWING THE SURFACE AT RANGE 2 AND GRAZING ANGLE X THE AREA !F IS EITHER
!F O "2 SINX
FOR BEAM LIMITED CONDITIONS EG CONTINUOUS WAVE #7 OR LONG PULSE RADAR AT HIGH GRAZING ANGLES OR
!F CS "2COSX
FOR PULSE WIDTH LIMITED CONDITIONS EG SHORT PULSE RADAR AT LOW GRAZING ANGLES 2EAL RADARS DO NOT PRODUCE COOKIE CUTTER FOOTPRINTS HOWEVER SINCE THE ANTENNA BEAM WILL HAVE A COMPLEX PROFILE AND THE PULSE MIGHT BE SHAPED &OR THIS REASON AN EFFECTIVE ! MUST BE OBTAINED FROM A SURFACE INTEGRATION OF THE ACTUAL AMPLITUDE PROFILE OF THE FOOTPRINT WHICH WILL TEND TO RESULT IN A SMALLER VALUE OF ! THAN THAT DEFINED BY %Q OR %Q 4HIS WILL PRODUCE LARGER VALUES OF R AS DERIVED FROM MEASURED VALUES OF RC BY %Q -OST EXPERIMENTERS USE THE HALF POWER BEAMWIDTH IN %Q OR %Q WITH AN ERROR THAT IS USUALLY ONLY OR D" #LUTTER 3TATISTICS 3UMMARIES OF CLUTTER MEASUREMENTS MADE BEFORE ABOUT MAY BE FOUND IN SEVERAL OF THE STANDARD REFERENCE BOOKS ON RADAR AND RADAR CLUTTER !MONG THE PROGRAMS OF THIS PERIOD THE MOST AMBITIOUS WAS THAT PURSUED IN THE LATE S AT THE .AVAL 2ESEARCH ,ABORATORY .2, IN WHICH AN AIRBORNE FOUR FREQUENCY RADAR &2 OPERATING WITH BOTH HORIZONTAL AND VERTICAL POLARIZATIONS AT 5(& -(Z , BAND -(Z # BAND -(Z AND 8 BAND -(Z MADE CLUTTER MEASUREMENTS UPWIND DOWNWIND AND CROSSWIND IN WINDS FROM TO KT FOR GRAZING ANGLES BETWEEN AND 4HE SYSTEM WAS CALIBRATED AGAINST STAN DARD METAL SPHERES DROPPED FROM AIRCRAFT AND WIND SPEEDS AND WAVEHEIGHTS WERE RECORDED IN THE MEASUREMENT AREAS FROM SHIP INSTRUMENTS 4YPICALLY SAMPLES OF R FOR A GIVEN SET OF RADAR AND ENVIRONMENTAL PARAMETERS ARE SCATTERED OVER A WIDE RANGE OF VALUES AND IN THE .2, MEASUREMENTS WERE ORGANIZED INTO PROBABILITY DISTRIBUTIONS OF THE TYPE SHOWN IN &IGURE 4HE DATA REPRESENTED BY THE SOLID LINE ARE PLOTTED ON NORMAL PROBABILITY PAPER WITH 2AYLEIGH AND LOG NORMAL DISTRIBUTIONS SHOWN FOR COMPARISON DASHED LINES 4HE ORDINATE IS THE PERCENT OF TIME FOR WHICH THE ABSCISSA IS EXCEEDED AND THE ABSCISSA IS THE VALUE OF R AS DEFINED BY %Q WITH ! TAKEN FROM %Q OR %Q AS APPROPRIATE 4HIS PARTICULAR DISTRI BUTION IS REPRESENTATIVE OF CLUTTER FROM A RELATIVELY LARGE RADAR FOOTPRINT PULSE LENGTH ABOUT L SEC OR METERS MEASURED AT INTERMEDIATE GRAZING ANGLES TO FOR MODERATE WIND SPEEDS ABOUT KT )T IS 2AYLEIGH LIKE BUT SHOWS A TENDENCY TOWARD LOG NORMAL BEHAVIOR FOR THE LARGER CROSS SECTIONS &ROM A DETAILED STATISTICAL ANALYSIS OF THE .2, &2 DATA 6ALENZUELA AND ,AING CONCLUDED THAT FOR THIS DATA AT LEAST THE DISTRIBUTIONS OF SEA CLUTTER CROSS SECTIONS WERE INTERMEDIATE BETWEEN THE 2AYLEIGH AND LOG NORMAL DISTRIBUTIONS /RGANIZING THE DATA SAMPLES INTO PROBABILITY DISTRIBUTIONS MAKES THE MEDIAN VALUE A CONVENIENT STATISTICAL MEASURE OF THE CLUTTER CROSS SECTION "UT MANY INVES TIGATORS PROCESS THEIR DATA TO PROVIDE THE MEAN VALUE AND BECAUSE THE CONVERSION OF A MEDIAN TO A MEAN REQUIRES KNOWLEDGE OF THE PROBABILITY DISTRIBUTION FUNCTION CARE MUST BE TAKEN TO AVOID AMBIGUITY IN COMPARING THE MEASUREMENTS OF DIFFERENT EXPERIMENTERS 4HE ORIGINAL ANALYSIS OF THE .2, &2 DATA WAS BASED ON MEDIAN CROSS SECTIONS AND THE ASSUMPTIONS OF THE COOKIE CUTTER ANTENNA BEAM EMBODIED IN %QS AND n )N LATER PRESENTATIONS OF THIS DATA THE MEDIAN VALUES OF R
3%! #,544%2
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&)'52% !N EXAMPLE OF THE PROBABILITY DISTRIBUTION OF SEA CLUTTER DATA FROM * # $ALEY ET AL
WERE REPLACED BY MEANS RAISING THEM BY ABOUT D" AND THE AREA ! IN %Q WAS REDEFINED IN TERMS OF A MORE REALISTIC TAPERED FOOTPRINT ADDING ANOTHER TO D" 4HIS MEANS THAT THERE CAN BE A DIFFERENCE OF TO D" BETWEEN THE EARLIER AND LATER PRESENTATIONS OF THE SAME DATA AND SINCE THESE RESULTS HAVE BEEN WIDELY USED AND QUOTED IT IS IMPORTANT TO ENSURE THAT THE PROPER DEFINITION OF R IS BEING USED WHEN COMPARING THEM WITH CLUTTER DATA THAT HAS BEEN TAKEN BY OTHER EXPERIMENTERS OR IN USING THESE RESULTS IN CLUTTER PREDICTIONS &IGURE SHOWS THAT EVEN FOR INTERMEDIATE GRAZING ANGLES IN THE RANGE n THE SEA CLUTTER DISTRIBUTION DEPARTS FROM STRICTLY 2AYLEIGH !T LOWER GRAZING ANGLES AND PARTICULARLY FOR NARROW PULSE WIDTHS THE PRESENCE OF SEA SPIKES OR OTHER NON GAUSSIAN BEHAVIOR MAY BE ACCOMMODATED BY ONE OF THE MULTIPARAMETER OR COMPOUND DISTRIBU TIONS THAT EXPRESS AN EXCESS OF HIGHER RETURNS SUCH AS THE 7EIBULL AND + DISTRIBUTIONS 4HE LATTER WAS INTRODUCED TO CHARACTERIZE THE PARTICULAR BEHAVIOR OF LOW GRAZING ANGLE CLUTTER SEEN IN A MARINE ENVIRONMENT )TS SUCCESS IS VERY LIKELY DUE TO ITS RELATION TO THE 2ICE DISTRIBUTION WHICH DESCRIBES THE STATISTICS OF STEADY SIGNALS IN NOISE THUS REFLECTING THE STATISTICS OF hTARGET LIKEv SEA SPIKE RETURNS IN A 2AYLEIGH BACKGROUND
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'ENERAL 4RENDS "EING THE FIRST REALLY COMPREHENSIVE COLLECTION OF CLUTTER DATA OVER A WIDE RANGE OF RADAR FREQUENCIES THE &2 PROGRAM PRODUCED MANY PLOTS SHOW ING THE DEPENDENCE OF SEA CLUTTER ON GRAZING ANGLE FREQUENCY POLARIZATION WIND DIRECTION AND WIND SPEED (OWEVER COMPARISON OF THESE PLOTS WITH OTHERS MADE BOTH EARLIER AND LATER SHOWS THE EXTENT OF THE VARIATIONS TO BE FOUND IN SEA CLUTTER MEASURE MENTS REPORTED BY DIFFERENT INVESTIGATORS FOR EXACTLY THE SAME SET OF PARAMETERS 4HIS IS SEEN CLEARLY IN &IGURE A AND B WHICH COMPARES THE GRAZING ANGLE DEPENDENCE OF 8 BAND CLUTTER DATA FOR WIND SPEEDS IN THE NEIGHBORHOOD OF KT OBTAINED FROM FOUR SOURCES .2, &2 THESE ARE MEAN RESULTS FOR UPWIND DIRECTIONS AND INCLUDE THE ANTENNA CORRECTIONS MENTIONED ABOVE AIRCRAFT MEASUREMENTS BY -ASUKO ET AL ALSO IN THE UPWIND DIRECTION AND SUMMARIES OF DATA TAKEN FROM BOOKS ON RADAR SYSTEMS BY 3KOLNIK AND .ATHANSON 4HE DISCREPANCIES BETWEEN THE DIFFERENT DATA SETS CAN BE ACCOUNTED FOR AT LEAST IN PART AS FOLLOWS 4HE OLDER DATA SUMMARIES WERE BASED ON PUBLISHED MEASUREMENTS FROM VARIOUS SOURCES IN WHICH THERE IS NO SPECI FICATION OF WIND DIRECTION )T MAY THEREFORE BE ASSUMED THAT THESE DATA REPRESENT SOME KIND OF AVERAGE OF UPWIND DOWNWIND AND CROSSWIND DIRECTIONS !S WILL BE SEEN THIS AVERAGE IS ABOUT TO D" SMALLER THAN THE UPWIND RETURNS -OREOVER THE EARLY .2, &2 DATA WAS USED LIBERALLY IN THE OLDER DATA SUMMARIES AND IT WAS NOTED ABOVE THAT THERE IS A DIFFERENCE OF TO D" BETWEEN THE EARLY AND LATER PRESENTATIONS OF THE SAME .2, &2 DATA THE LATTER BEING USED IN &IGURE A AND B 7ITH THESE CORRECTIONS THE CURVES MIGHT SHOW CLOSER AGREEMENT .EVERTHELESS IT IS CLEAR THAT UNCRITICAL USE OF PUBLISHED CLUTTER DATA COULD LEAD RADAR SYSTEMS DESIGNERS TO CHOOSE SEA CLUTTER ESTIMATES MANY D" APART FOR THE SAME CONDITIONS 4HE .2, &2 DATA SET IS UNIQUE IN THAT NO OTHER PROGRAM HAS REPORTED MEASURE MENTS MADE OVER SO WIDE A RANGE OF FREQUENCIES GRAZING ANGLES AND WIND SPEEDS AT THE SAME TIME &IGURE SHOWS THE TRENDS FOR BOTH VERTICALLY AND HORIZONTALLY POLARIZED
&)'52% #OMPARISON OF 8 BAND CLUTTER DATA FROM DIFFERENT SOURCES FOR A NOMINAL WIND SPEED OF KN A VERTICAL POLARIZATION AND B HORIZONTAL POLARIZATION BASED ON DATA FROM ( -ASUKO ET AL .2, &2 - ) 3KOLNIK AND & % .ATHANSON
3%! #,544%2
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SEA CLUTTER OVER A RANGE OF GRAZING ANGLES DOWN TO n 4HE CURVES REPRESENT THE CENTERS OF o D" BANDS THAT CONTAIN THE MAJOR RETURNS FOR THE THREE HIGHER FREQUENCIES , # AND 8 BANDSTHE 5(& RETURNS WERE A FEW DECIBELS LOWER AND WIND SPEEDS ABOVE ABOUT KT 4HE MAJOR DIFFERENCES IN SEA CLUTTER FOR THE TWO POLARIZATIONS ARE SEEN TO LIE IN THE RANGE OF GRAZING ANGLES BETWEEN ABOUT n AND n WHERE THE HORIZONTALLY POLARIZED RETURNS ARE SMALLER 4HIS DIFFERENCE IS FOUND TO BE EMPHASIZED AT BOTH LOWER WIND SPEEDS AND LOWER FREQUENCIES 4HE CROSS SECTIONS APPROACH EACH OTHER AT HIGH ANGLES n AND FOR THE HIGHER MICROWAVE FREQUENCIES AT LOW ANGLES n AS WELL )N FACT FOR GRAZING ANGLES LESS THAN A FEW DEGREES AND MODERATE TO STRONG WIND SPEEDS OBSERVERS HAVE REPORTED THAT AT 8 BAND AND AT THE HIGHER SEA STATES THE HORIZONTALLY POLARIZED RETURNS CAN EXCEED THE VERTICALLY POLARIZED RETURNS 4HE .2, &2 SYSTEM PERMITTED TRANSMISSION AND RECEPTION ON ORTHOGONAL POLAR IZATIONS SO THAT DATA COULD BE COLLECTED FOR CROSS POLARIZED SEA CLUTTER 4HESE RETURNS TENDED TO HAVE A WEAK DEPENDENCE ON GRAZING ANGLE AND WERE ALWAYS SMALLER THAN EITHER OF THE LIKE POLARIZED RETURNS LYING IN THE CROSS HATCHED REGION SHOWN ON &IGURE )T IS INFORMATIVE TO COMPARE MEASUREMENTS AT DIFFERENT FREQUENCIES BY DIFFERENT INVESTIGATORS IN DIFFERENT PARTS OF THE WORLD UNDER SIMILAR WIND CONDITIONS &IGURE DISPLAYS MEASUREMENTS OF VERTICALLY POLARIZED SEA CLUTTER DOWN TO A GRAZING ANGLE OF FOR WIND SPEEDS OF ABOUT KT FROM THREE INDEPENDENT EXPERIMENTS USING AIRBORNE RADARS AT # 8 AND + BAND FREQUENCIES !LTHOUGH THERE IS NO ASSURANCE THAT
&)'52% 'ENERAL TRENDS IN CLUTTER BEHAVIOR FOR AVERAGE WIND SPEEDS ABOUT KT BASED ON .2, &2 DATA 0LOTS REPRESENT , # AND 8 BAND DATA WITHIN o D"
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&)'52% &REQUENCY DEPENDENCE OF SEA CLUTTER FOR WIND SPEEDS OF ABOUT KT '(Z &EINDT '(Z 3CHROEDER AND '(Z -ASUKO
ALL THESE MEASUREMENTS WERE MADE OVER FULLY DEVELOPED SEAS IT IS CLEAR THAT THERE IS A RATHER STRONG CONSISTENCY AMONG THEM WHICH REINFORCES THE OBSERVATION MADE IN REFERENCE TO &IGURE THAT THE FREQUENCY DEPENDENCE OF SEA CLUTTER AT INTERMEDIATE GRAZING ANGLES IS WEAK AT MICROWAVE FREQUENCIES FROM , TO + BAND $EPENDENCE ON 7IND 3PEED AND $IRECTION %XPERIMENTALLY THE RELATION BETWEEN SEA CLUTTER AND WIND SPEED IS COMPLEX AND UNCERTAIN IT HAVING BEEN FOUND TO DEPEND ON ALMOST ALL OF THE PARAMETERS THAT CHARACTERIZE SEA CLUTTER FREQUENCY GRAZING ANGLE POLARIZATION THE STATE OF THE SEA SURFACE THE DIRECTION AND SPEED OF THE WIND ITSELF AND EVEN ON WHETHER THE MEASUREMENTS ARE MADE FROM AN AIRCRAFT OR A TOWER PLATFORM ! COMMON WAY TO ORGANIZE CLUTTER DATA IS TO SEEK THE BEST STRAIGHT LINE FIT LINEAR REGRESSION BETWEEN CLUTTER CROSS SECTIONS IN DECIBELS AND THE LOG OF THE WIND SPEED OR SOME OTHER PARAMETER 4HIS OF COURSE IMPOSES A POWER LAW RELATION BETWEEN THE VARIABLES R ^ 5N WHERE N IS DETERMINED BY THE SLOPE OF THE LINE !N EXAMPLE IS SHOWN IN &IGURE /N THE OTHER HAND WHILE THE TOTALITY OF THE .2, &2 RESULTS APPEARED TO SHOW SATURATION FOR WIND SPEEDS ABOVE ABOUT KT THE HIGH AND LOW TO MODERATE WIND SPEED DATA WERE COLLECTED AT DIFFERENT TIMES IN DIFFERENT PLACES UNDER DIFFERENT CONDITIONS OF SEA SURFACE DEVELOPMENT AND DISCREPANCIES BETWEEN THE TWO DATA SETS FOR COMMON WIND SPEEDS HAVE WEAKENED THE EVIDENCE FOR SATURATION /THER INVESTIGATORS DENY THAT IT IS EVEN POSSIBLE TO EXPRESS WIND DEPENDENCE IN THE FORM OF A POWER LAW PROPOSING THE EXISTENCE OF A KIND OF THRESHOLD WIND SPEED BELOW WHICH CLUTTER VIRTUALLY VANISHES AND ABOVE WHICH THE CLUTTER LEVEL RISES RAPIDLY TOWARD A SATURATION VALUE 4HIS IS INDICATED BY THE CURVES IN &IGURE WHERE THE STRAIGHT LINES CORRESPOND TO VARIOUS POWER LAWS AND THE CURVED LINES DERIVE FROM
3%! #,544%2
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&)'52% 3EA CLUTTER FROM A TOWER PLATFORM WITH POWER LAW WIND SPEED DEPENDENCE DEFINED BY LINEAR REGRESSION ANGLE OF INCIDENCE GRAZING ANGLE AFTER ! ( #HAUDHRY AND 2 + -OORE Ú )%%%
WAVE SPECTRUM CONSIDERATIONS )T IS POSSIBLE TO FIND EXAMPLES OF DATA THAT APPEAR TO FOLLOW SUCH BEHAVIOR WHILE AT THE SAME TIME BEING EXPRESSED AS A POWER LAW BY BRUTE LINEAR REGRESSION AS ILLUSTRATED IN THE TOWER DATA SHOWN IN &IGURE 4HIS BEHAVIOR IS NOT UNCOMMON
&)'52% ! HYPOTHETICAL WIND SPEED DEPENDENCE OF SEA CLUTTER CURVED TRACES COMPARED WITH VARIOUS POWER LAWS STRAIGHT LINES DERIVED FROM 7 * 0IERSON AND - ! $ONELAN Ú !MERICAN 'EOPHYSICAL 5NION
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&)'52% %XAMPLE OF FORCING A POWER LAW FIT COMPARE DATA POINTS WITH THOSE IN &IGURE AFTER ! ( #HAUDHRY AND 2 + -OORE Ú )%%%
.EVERTHELESS THE IMPOSITION OF A POWER LAW RELATION PROVIDES A CONVENIENT WAY TO VISUALIZE TRENDS IN THE BEHAVIOR OF SEA CLUTTER WITH WIND SPEED 4HE VARIOUS AIR CRAFT MEASUREMENTS REFERRED TO ABOVE AUGMENTED BY DATA FROM A TOWER IN THE .ORTH 3EA WERE USED AS THE BASIS OF THE POWER LAW PLOTS OF R AS FUNCTIONS OF WIND SPEED AND GRAZING ANGLE SHOWN IN &IGURE A B 4HESE PLOTS SUGGEST HOW SEA CLUTTER FOR A GIVEN FREQUENCY 8 BAND WIND DIRECTION UPWIND AND POLARIZATION BEHAVES WITH WIND SPEED AND GRAZING ANGLE (OWEVER EXAMINATION OF THE ACTUAL DATA POINTS UNDERLYING THESE LINEAR REGRESSIONS SHOW POINT SCATTER THAT SOMETIMES RESEM BLES &IGURE SOMETIMES &IGURE AND SOMETIMES NEITHER SO THESE STRAIGHT LINES COVER UP CONSIDERABLE UNCERTAINTY )N FACT IT APPEARS THAT THERE IS NO SIMPLE FUNCTIONAL DEPENDENCE OF SEA CLUTTER ON WIND SPEED THAT CAN BE ESTABLISHED WITH ANY CONFIDENCE FROM EXISTING DATA ALTHOUGH MOST INVESTIGATORS WOULD PROBABLY AGREE THAT THE BEHAVIOR OF MICROWAVE SEA CLUTTER WITH WIND SPEED AT INTERMEDIATE GRAZING ANGLES CAN BE ROUGHLY DESCRIBED AS FOLLOWS FOR LIGHT WINDS LESS THAN TO KT SEA CLUTTER IS WEAK VARIABLE AND ILL DEFINED FOR INTERMEDIATE WINDS ABOUT TO KT IT CAN BE DESCRIBED ROUGHLY BY A POWER LAW OF THE TYPE FOUND IN &IGURE AND FOR STRONG WINDS ABOVE ABOUT KT THERE IS A TENDENCY FOR IT TO LEVEL OFF )N FACT THE CONVERGENCE OF THE LINES IN &IGURE A B WITH INCREASING WIND SPEED SUGGESTS THAT THE REFLECTIVITY OF THE SEA SURFACE IS TENDING TOWARD ,AMBERTS LAW FOR WHICH THERE IS NO DEPENDENCE ON GRAZING ANGLE FREQUENCY OR POLARIZATION BUT ONLY ON SURFACE ALBEDO OR AVERAGE REFLECTIVITY )N SEVERAL OF THE EXPERIMENTS REFERENCED ABOVE THE DEPENDENCE OF SEA BACKSCATTER ON ANGLE RELATIVE TO THE WIND DIRECTION WAS FOUND BY RECORDING THE RADAR RETURN FROM A SPOT ON THE SURFACE WHILE FLYING AROUND IT IN A CIRCLE &IGURE A B GIVES AN EXAMPLE OF THIS BEHAVIOR FOR GRAZING ANGLES OF ABOUT AND WIND SPEEDS CLOSE TO KT 4HE FIGURES CONTAIN RESULTS OBTAINED INDEPENDENTLY BY THREE DIFFERENT GROUPS 4HE BEHAVIOR SHOWN HERE IS REPRESENTATIVE OF THAT FOUND GENERALLY SEA CLUTTER IS STRONGEST VIEWED UPWIND WEAKEST VIEWED CROSSWIND AND OF INTERMEDIATE STRENGTH VIEWED DOWNWIND THE TOTAL VARIATION BEING ABOUT D" /THER STUDIES CORROBORATE THIS BEHAVIOR
3%! #,544%2
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&)'52% ! REPRESENTATION OF 8 BAND UPWIND CLUTTER BEHAVIOR WITH WIND SPEED AND GRAZING ANGLE A VERTICAL POLARIZATION AND B HORIZONTAL POLARIZATION
&)'52% $EPENDENCE OF CLUTTER ON WIND DIRECTION NOMINAL WIND SPEED KT GRAZING ANGLE ABOUT UPWIND AND DOWNWIND AFTER ( -ASUKO ET AL Ú !MERICAN 'EOPHYSICAL 5NION
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3EA #LUTTER AT (IGH 'RAZING !NGLES 4HE TOP LINES IN &IGURE A B CORRE SPOND TO CLUTTER AT A GRAZING ANGLE OF THAT IS FOR A RADAR LOOKING STRAIGHT DOWN /N A STRICTLY EMPIRICAL BASIS THE CLUTTER CROSS SECTION AT THIS ANGLE IS ONLY WEAKLY DEPENDENT ON FREQUENCY HAS A MAXIMUM OF ABOUT D" AT ZERO WIND SPEED AT LEAST FOR THE ANTENNA BEAMWIDTHS AND EXPERIMENTAL CONFIGURATIONS REPORTED AND FALLS OFF GRADUALLY AS THE WIND PICKS UP 3CATTERING AT HIGH GRAZING ANGLES IS COMMONLY REGARDED AS A FORM OF SPECULAR SCATTERING FROM TILTED FACETS OF THE SURFACE SO IT IS OF INTEREST TO NOTE THAT THERE APPEARS TO BE A SMALL RANGE OF ANGLES IN THE NEIGHBORHOOD OF FOR WHICH THE CROSS SECTION IS ALMOST COMPLETELY INDEPENDENT OF WIND SPEED 3INCE THESE ANGLES CORRESPOND TO COMPLEMENTS OF THE COMMON RMS SEA SLOPE ANGLES OF ABOUT IT MIGHT BE ARGUED THAT AS THE WIND INCREASES THE CLUTTER DECREASE DUE TO INCREASING SURFACE ROUGHNESS IS BALANCED BY A CLUTTER INCREASE DUE TO AN INCREASING POPULATION OF SCATTERING FACETS 4HIS LINE COULD THEREFORE BE REGARDED AS THE BOUND ARY SEPARATING THE SPECULAR REGIME WHERE THE CROSS SECTION IS DECREASED BY SURFACE ROUGHNESS FROM THE ROUGH SURFACE REGIME WHERE THE CROSS SECTION INCREASES WITH SURFACE ROUGHNESS )T SHOULD FURTHER BE NOTED THAT CLUTTER MEASUREMENTS AT THESE HIGH GRAZING ANGLES WILL BE RELATIVELY SENSITIVE TO THE AVERAGING EFFECTS OF WIDE ANTENNA BEAMWIDTHS WHICH COULD BECOME A SOURCE OF AMBIGUITY IN AIRCRAFT MEASUREMENTS AT THE LOWER RADAR FREQUENCIES !T ,OW 'RAZING !NGLES !T LOW GRAZING ANGLES BELOW MEAN SEA SLOPE ANGLES OF ABOUT SEA CLUTTER TAKES ON A DIFFERENT CHARACTER 4HE SHARP TARGET LIKE CLUTTER PEAKS KNOWN AS SEA SPIKES BEGIN TO APPEAR ON ! SCOPE PRESENTATIONS AND THE PROBABILITY DISTRIBUTIONS ASSUME A DIFFERENT FORM &IGURE A AND B SHOW THE PRESENCE OF SEA SPIKES IN SECOND TIME HISTORIES OF RETURNS FROM A FIXED SPOT MEASURED OFF THE COAST OF &LORIDA WITH A VARIABLE RESOLUTION 8 BAND RADAR LOOKING INTO MODERATE A AND CALM B SEAS AT A GRAZING ANGLE .OTICE THAT THE APPEAR ANCE OF THE SEA SPIKES IS VERY SIMILAR FOR BOTH MODERATE AND WEAK WIND CONDITIONS ALTHOUGH THE AMPLITUDES DIFFER BY ALMOST D" AND THE VERTICALLY POLARIZED RETURNS APPEAR TO BE SOMEWHAT BROADER WHILE THE HORIZONTALLY POLARIZED RETURNS ARE MORE SPIKY PARTICULARLY FOR SHORT PULSES IN CALM SEAS 4HESE ARE ALL CHARACTERISTICS OF SEA CLUTTER AT LOW GRAZING ANGLES 4HE PROBABILITY DISTRIBUTIONS OF LOW GRAZING ANGLE SEA CLUTTER CHANGE WITH WIND SPEED %XAMPLES MAY BE FOUND IN THE MEASUREMENTS BY 4RIZNA OF LOW ANGLE SEA CLUT TER USING HIGH RESOLUTION NS SHIPBOARD RADAR IN BOTH THE !TLANTIC AND THE 0ACIFIC OCEANS 4HE PROBABILITY DISTRIBUTIONS OF THE CLUTTER CROSS SECTIONS WERE PLOTTED IN THE MANNER SHOWN IN &IGURE WHICH SHOWS THE DISTRIBUTIONS OF HORIZONTALLY POLAR IZED 8 BAND DATA AT A GRAZING ANGLE FOR LOW MEDIUM AND HIGH WIND SPEEDS IN ORDER FROM LEFT TO RIGHT 4HE LOW WIND TRACE CORRESPONDS TO A 2AYLEIGH DISTRIBUTION THE OTHER SEGMENTED TRACES ARE TWO PARAMETER 7EIBULL DISTRIBUTIONS DEFINED BY DIFFERENT PARAMETER PAIRS )T IS CLEAR THAT THE BEHAVIOR IS DIFFERENT AND CONSIDERABLY MORE COM PLEX THAN THAT SHOWN IN &IGURE FOR HIGHER GRAZING ANGLES AND WIDER PULSES &ROM THE CHARACTER OF THE DATA 4RIZNA INTERPRETS THESE THREE SEGMENT TRACES AS SHOWING PRI MARILY RECEIVER NOISE IN THE LOWEST BRANCH DISTRIBUTED SPATIALLY HOMOGENEOUS CLUTTER IN THE MIDDLE BRANCH AND GENUINE SEA SPIKES IN THE BRANCH CONTAINING THE HIGHEST CROSS SECTIONS SOME OF WHICH EXCEED M &OR THE HIGHER WIND SPEEDS AND FULLY DEVELOPED SEAS ENCOUNTERED IN THE .ORTH !TLANTIC THE PERCENTAGE OF SEA SPIKES IN THIS POPULATION WAS FOUND TO GROW AS THE TH POWER OF THE WIND SPEED WHICH INTEREST INGLY IS THE SAME WIND SPEED DEPENDENCE SHOWN BY THE PERCENTAGE OF WHITECAPS SEEN ON THE SURFACE WHICH AS NOTED IN 3ECTION ARE TRACERS FOR BREAKING WAVES
3%! #,544%2
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&)'52% 3EA SPIKES AT 8 BAND GRAZING ANGLE AND VARIOUS PULSE WIDTHS A SEA STATE AND B SEA STATE .OTE EQUAL AMPLITUDES AT THE TWO POLARIZATIONS AND A D" DIFFERENCE IN CLUTTER STRENGTH BETWEEN MODERATE AND WEAK WINDS FROM *0 (ANSEN AND 6 & #AVALERI
&)'52% %XAMPLES OF CLUTTER PROBABILITY DISTRIBUTIONS AT LOW GRAZING ANGLES AFTER $ 4RIZNA
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)N COMPARING STATISTICAL RESULTS IT SHOULD BE KEPT IN MIND THAT TO THE EXTENT THAT THE SEA SURFACE MAY BE VIEWED AS A STATIONARY HOMOGENEOUS PROCESS AS IT GENERALLY IS OVER THE DURATION AND SPATIAL EXTENT OF ANY PARTICULAR EXPERIMENTAL EVENT THE SCAT TERING CROSS SECTION MAY BE SAID TO BE ERGODIC WHICH MEANS THAT THE STATISTICAL RESULTS OBTAINED BY TIME AVERAGING FROM A SMALL CELL ARE EQUIVALENT TO AN ENSEMBLE AVERAGE FROM A LARGER CELL PROVIDED THAT THE NUMBER OF hSAMPLESv IS THE SAME IN THE TWO CASES &OR THIS REASON THE STATISTICAL IMPLICATIONS OF EXPERIMENTAL DATA CAN BE PROP ERLY COMPARED ONLY IF THE DETAILS OF THE SAMPLING PROCEDURE ARE SPECIFIED (OWEVER THE NUMBER OF SAMPLES IN MOST OF THE EXPERIMENTAL RESULTS SHOWN THUS FAR HAVE BEEN SUFFICIENTLY LARGE THAT THE DIFFERENCES BETWEEN FOR EXAMPLE &IGURES AND MAY BE CONSIDERED REAL AND RELATED TO DIFFERENCES IN GRAZING ANGLE RATHER THAN IN RESO LUTION CELL SIZE )N FACT DISTRIBUTIONS CLOSELY RESEMBLING THOSE IN &IGURE WERE OBTAINED MUCH EARLIER FROM SIMILAR MEASUREMENTS WITH CONSIDERABLY BROADER PULSE WIDTHS /THER MEASUREMENTS HAVE CONTINUED TO CONFIRM THE DIFFERENCES THAT EMERGE IN ! SCOPE APPEARANCE AND STATISTICAL DESCRIPTION OF THE CLUTTER IN THIS REGIME OF LOW GRAZING ANGLES 3OME ATTEMPTS TO DESCRIBE THE PHYSICAL ORIGIN OF THESE PHENOMENA WILL BE DISCUSSED IN 3ECTION BELOW !T 6ERY ,OW 'RAZING !NGLES 4HERE IS SOME EVIDENCE THAT SEA CLUTTER MIGHT DROP OFF MORE SHARPLY BELOW A CRITICAL ANGLE IN THE NEIGHBORHOOD OF A DEGREE OR SO 4HIS CRITICAL ANGLE OR CRITICAL RANGE FOR A RADAR AT A FIXED HEIGHT HAS BEEN OBSERVED FROM TIME TO TIME SINCE FIRST NOTED IN EARLY OBSERVATIONS OF SEA CLUTTER 4HE CRITICAL ANGLE HAS BEEN ASCRIBED TO INTERFERENCE BETWEEN DIRECT AND PERFECTLY REFLECTED RAYS AT THE SCATTERING TARGETS RESPONSIBLE FOR THE CLUTTER SIGNAL ALTHOUGH THESE TARGETS REMAIN UNSPECIFIED !LTHOUGH THIS SIMPLE PICTURE COULD PRODUCE THE 2n DECAY THAT IS SOME TIMES OBSERVED A CRITICAL ANGLE OFTEN FAILS TO MATERIALIZE AND WHEN IT DOES IT NEED NOT SHOW AN 2n DECREASE WITH RANGE EQUIVALENT TO A FOURTH POWER DEPENDENCE ON GRAZING ANGLE !N ALTERNATIVE EXPLANATION FOR THIS BEHAVIOR APPLICABLE AT THE HIGHER MICROWAVE FREQUENCIES HAS BEEN SUGGESTED BASED ON A THRESHOLD SHADOWING MODEL FOR UPWIND AND DOWNWIND DIRECTIONS 4HIS MODEL IMPLIES A SHARP DECREASE IN THE AVERAGE CROSS SECTION FOR GRAZING ANGLES BELOW A FEW DEGREES )N CROSSWIND DIRECTIONS WITH THE RADAR LOOKING ALONG THE TROUGHS OF THE MAJOR WAVES A MUCH MILDER SHADOW ING FUNCTION WILL APPLY SO THERE SHOULD BE A CLEAR DISTINCTION BETWEEN THE UPWIND DOWNWIND AND CROSSWIND BEHAVIOR OF SEA CLUTTER AT VERY LOW GRAZING ANGLES %XAMPLES OF CLUTTER BEHAVIOR AT THESE VERY LOW ANGLES MAY BE FOUND IN INDEPENDENT MEASUREMENTS AT RELATIVELY HIGH WIND SPEEDS BY (UNTER AND 3ENIOR OFF THE SOUTH COAST OF %NGLAND AND BY 3ITTROP OFF THE WEST COAST OF .ORWAY 4HEIR RESULTS FOR ORTHOGONAL DIRECTIONS RELATIVE TO THE WIND ARE SHOWN IN &IGURE ALONG WITH THE PREDICTIONS OF A CONVENTIONAL SHADOWING FUNCTION AND THE THRESHOLD SHADOWING FUNCTION )T WOULD APPEAR THAT A COMBINATION OF CONVENTIONAL SHADOWING WHICH GOES AS THE FIRST POWER OF THE GRAZING ANGLE ACROSS THE WIND AND THRESHOLD SHADOWING IN UPWIND AND DOWN WIND DIRECTIONS CAN ACCOUNT FOR THE OBSERVED BEHAVIOR OF THIS VERY LOW ANGLE CLUTTER QUITE WELL 4HE DECAY LAW FOR VERY LOW ANGLE CLUTTER SHOULD THEREFORE DEPEND ON THE VIEWING ANGLE RELATIVE TO THE WIND DIRECTION SO IT MIGHT OCCUR WITH POWERS BETWEEN THE FIRST AND THE FOURTH 4HIS IS JUST WHAT HAS BEEN OBSERVED )T SHOULD BE REMARKED HOWEVER THAT SHADOWING AT LOW GRAZING ANGLES IS A COMPLEX PHENOMENON SEE BELOW AND THE PHYSICAL ORIGIN OR EVEN THE EXISTENCE OF A CRITICAL ANGLE IS STILL OPEN TO QUES TION -OREOVER THERE IS RELATIVELY LITTLE GOOD DATA ON VERY LOW ANGLE CLUTTER FOR OTHER THAN 8 BAND FREQUENCIES SO THE GENERAL BEHAVIOR OF SEA CLUTTER IN THIS ANGULAR REGIME REMAINS UNCERTAIN
3%! #,544%2
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&)'52% $IFFERENTIAL BEHAVIOR OF VERY LOW ANGLE CLUTTER FOR ORTHOGONAL WIND DIRECTIONS 3C IS A CONVENTIONAL SHADOWING FUNCTION 34 IS A THRESHOLD SHADOWING FUNCTION AFTER DATA FROM ) - (UNTER AND 3ENIOR Ú )%%% AND ( 3ITTROP
!T (& AND -ILLIMETER 7AVE &REQUENCIES !LL THE MEASUREMENTS DESCRIBED ABOVE WERE MADE AT MICROWAVE FREQUENCIES BETWEEN 5(& -(Z AND +A BAND '(Z (IGH FREQUENCY (& RADARS USUALLY OPERATE IN THE FREQUENCY RANGE BETWEEN ABOUT AND -(Z CORRESPONDING TO WAVELENGTHS BETWEEN AND M RESPECTIVELY 3INCE THE OPERATION OF SUCH RADARS TAKES PLACE EITHER BY THE GROUND WAVE OR OVER IONOSPHERIC SKY WAVE PATHS SPANNING GREAT RANGES THE GRAZING ANGLES TEND TO BE SMALL BETWEEN AND &OR THESE WAVELENGTHS AND GRAZING ANGLES MEASUREMENTS BY #ROMBIE INDICATE THAT THE SCATTERING FROM THE SEA SURFACE WAS THE RESULT OF SCATTERING FROM SEA WAVES OF ONE HALF THE RADAR WAVELENGTH IE h"RAGGv SCATTER )N THE YEARS SINCE THESE EARLY MEASUREMENTS THERE HAS BEEN CONSIDERABLE ACTIVITY IN THE FIELD OF (& RADAR AND (& CLUTTER AND THE RESULTS CAN BE SUM MARIZED AS FOLLOWS &OR VERTICAL POLARIZATION THE MAJOR ENERGY OF THE (& CLUTTER SIGNAL APPEARS IN SPECTRAL LINES DISPLACED TO EITHER SIDE OF THE CARRIER FREQUENCY BY THE FREQUENCY OF SEA WAVES HAVING A WAVELENGTH EQUAL TO HALF THE (& WAVELENGTH K IN METERS 4HE RELATIVE STRENGTHS OF THE PLUS AND MINUS LINES ARE DETERMINED BY THE PROPORTION OF ADVANCING AND RECEDING "RAGG RESONANT WAVE COMPONENTS IN THE CLUT TER CELL 0ROVIDED THE WIND SPEED IS GREATER THAN ABOUT L KT WITH K IN METERS AND THE SEA IS FULLY DEVELOPED THE CLUTTER CROSS SECTION R IS ABOUT n D" AND IS RELA TIVELY INDEPENDENT OF WIND SPEED AND FREQUENCY 4HE DEFINITION OF R IN (& RADAR IS COMPLICATED BY PROBLEMS IN PROPERLY DEFINING ANTENNA GAINS FOR GROUND WAVE AND SKY WAVE PATHS AND BY PROPAGATION EFFECTS DUE TO THE IONOSPHERE 4HE CLUTTER SPECTRUM TENDS TO FILL IN AROUND AND BETWEEN THE LINES AS THE WIND PICKS UP &OR HORIZONTAL POLARIZATION WHICH IS POSSIBLE ONLY FOR SKY WAVE PATHS OVER WHICH THE PLANE OF POLARIZATION CAN BE ROTATED BY THE %ARTHS MAGNETIC FIELD THE CROSS SECTION IS MUCH SMALLER AND SHOWS THE CHARACTERISTIC FOURTH POWER DECAY WITH A DECREASING GRAZING ANGLE &OR THESE (& WAVELENGTHS OF TENS OF METERS THE SEA IS RELATIVELY FLAT AND THE SCATTERING LAWS ARE SIMPLE ! DETAILED DISCUSSION OF (& RADAR MAY BE FOUND IN #HAPTER
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!T THE OTHER END OF THE POTENTIALLY USEFUL RADAR SPECTRUM IN THE MILLIMETER WAVE BAND THE FEW PUBLISHED MEASUREMENTS OF RADAR CLUTTER LEAD TO THE CONCLUSION THAT MILLIMETER WAVE BACKSCATTER BEHAVES IN MUCH THE SAME MANNER AS BACKSCATTER AT THE LOWER MICROWAVE FREQUENCIES 4HIS WAS SUGGESTED BY THE + BAND CURVES SHOWN IN &IGURE FOR MODERATE WIND SPEEDS AND FURTHER SUPPORTED BY SOME OLDER SHIPBOARD DATA AT FREQUENCIES BETWEEN AND '(Z )T SHOULD BE NOTED THAT FOR MARITIME RADARS CLUTTER SIGNAL PATHS LIE CLOSE TO THE SEA SURFACE WHERE THE ATMOSPHERIC AND WATER VAPOR DENSITIES ARE HIGHEST 4HIS MEANS THAT AT THESE HIGHER FREQUENCIES THE CLUTTER SIGNAL WILL BE STRONGLY AFFECTED BY ATMOSPHERIC ABSORPTION EFFECTS AND CONSE QUENTLY THE SURFACE RELATED CROSS SECTION INFERRED FROM THE RECEIVED SIGNAL STRENGTH IN ANY GIVEN MEASUREMENT WILL DEPEND UPON THE PATH LENGTH -OREOVER THE ROLE OF SEA SPRAY IN BOTH SCATTERING AND ABSORPTION WILL CERTAINLY BE MORE IMPORTANT THAN AT THE LOWER MICROWAVE FREQUENCIES )T IS DIFFICULT TO FIND CLUTTER DATA AT FREQUENCIES ABOVE +A BAND ALTHOUGH ( AND 6 POLARIZED RETURNS AT '(Z AT A GRAZING ANGLE OF WERE REPORTED BOTH WITH VALUES CLOSE TO n D" 4HE 3PECTRUM OF 3EA #LUTTER 4HE SCATTERING FEATURES PRODUCING SEA CLUTTER ARE ASSOCIATED WITH A SURFACE SUBJECT TO SEVERAL TYPES OF MOTION 4HE FEATURES THEMSELVES MAY BE MOVING WITH SMALL GROUP OR PHASE VELOCITIES OVER THIS SURFACE WHILE THE SURFACE ITSELF IS MOVED IN TURN BY THE ORBITAL VELOCITIES OF THE LARGER WAVES PASSING ACROSS IT OR THE FEATURE MAY BE ADVECTED AT THE VELOCITY OF THE WAVE SYSTEM SUPPORTING IT 4HE SCATTERERS MIGHT EVEN BE DETACHED FROM THE UNDERLYING SURFACE AS IN THE PLUMES EMIT TED AT THE CRESTS OF BREAKING WAVES AND MOVE AT SPEEDS GREATER THAN THE WAVE SYSTEM ITSELF !T HIGHER RADAR FREQUENCIES AND IN STRONG WINDS THE POSSIBILITY OF SCATTERING FROM SPRAY CARRIED BY THE WIND FIELD ABOVE THE SURFACE MUST BE CONSIDERED !LL OF THIS COMPLEX MOTION SHOWS UP IN A DOPPLER SHIFT IMPARTED TO THE SCATTERED ELECTROMAGNETIC WAVE 5NFORTUNATELY THERE IS AS YET LITTLE DETAILED PHYSICAL UNDERSTANDING OF THE COM PLICATED PHENOMENOLOGY OF SEA CLUTTER SPECTRA -EASUREMENTS OF MICROWAVE CLUTTER SPECTRA FOR REAL SEAS HAVE BEEN REPORTED IN THE LITERATURE FOR AIRCRAFT MEASUREMENTS OF THE SPECTRAL SHAPE ALONE FIXED SITE SHORE MEASUREMENTS SHOWING A SHIFT IN THE SPECTRAL PEAK AND MEASUREMENTS FROM SHIPS AT INTERMEDIATE GRAZING ANGLES /THER MEASUREMENTS OF SEA CLUTTER SPECTRA INCLUDE THOSE MADE AT MUCH LOWER FREQUENCIES IN THE (& BAND AS DESCRIBED IN THE LAST SECTION THOSE MADE UNDER ARTIFICIAL CONDITIONS IN WAVE TANKS WHOSE APPLICATION TO REAL SEA CONDITIONS IS UNCERTAIN AND THOSE FROM OTHER FIXED SITES AT HIGH RESOLUTION AND SHORT AVERAGING TIMES TO BE DISCUSSED LATER !S IT TURNS OUT MICROWAVE SEA CLUTTER SPECTRA HAVE A RATHER SIMPLE FORM AT THE LOWER GRAZING ANGLES &IGURE ILLUSTRATES TYPICAL SPECTRAL BEHAVIOR AT THE TWO POLARIZA TIONS BASED ON DATA COLLECTED BY 0IDGEON FOR # BAND CLUTTER LOOKING UPWIND AT A FEW DEGREES GRAZING 4HE PEAK FREQUENCY OF THE UPWIND SPECTRUM APPEARS TO BE DETERMINED BY THE PEAK ORBITAL VELOCITY OF THE LARGEST SEA WAVES PLUS A WIND DEPENDENT VELOCITY INCREMENT CONTAINING BUT NOT ENTIRELY EXPLAINED BY WIND INDUCED SURFACE CURRENTS 4HIS PEAK ORBITAL VELOCITY IS TAKEN TO BE THAT OF THE MAJOR WAVES AND MAY BE OBTAINED IN TERMS OF THE SIGNIFICANT HEIGHT ( AND PEAK PERIOD 4 ` 3ECTION FROM THE EXPRESSION
6ORB O ( 4 ` 5 MS
4HE APPROXIMATE DEPENDENCE ON WIND SPEED 5 WAS FOUND BY SUBSTITUTING ( HRMS FROM %Q ASSUMING A FULLY DEVELOPED SEA AND 4 ` FROM %Q 4O THIS THERE MUST
3%! #,544%2
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&)'52% 1UALITATIVE BEHAVIOR OF DOPPLER SPECTRA OF SEA CLUTTER LOOKING UPWIND AT LOW GRAZING ANGLES AFTER # BAND MEASUREMENTS BY 6 7 0IDGEON Ú !MERICAN 'EOPHYSICAL 5NION
BE ADDED A WIND DRIFT VELOCITY OF ABOUT OF 5 AND A FIXED SCATTERER VELOCITY WHICH APPEARS TO BE ABOUT MS IN THE 8 AND # BAND MEASUREMENTS 3UMMING THESE COMPONENTS YIELDS THE VIRTUAL DOPPLER VELOCITY AT THE PEAK OF THE CLUTTER SPECTRUM FOR THE PARTICULAR CASE OF A VERTICALLY POLARIZED 8 OR # BAND RADAR LOOKING UPWIND AT LOW GRAZING ANGLES
6VIR 5 MS
!S NOTED EARLIER CARE MUST BE TAKEN WHENEVER WIND SPEED IS USED TO PARAMETERIZE A PROCESS THAT DEPENDS ON WAVEHEIGHT 4HERE IS AN UNAMBIGUOUS RELATION ONLY FOR A FULLY DEVELOPED SEA IN THE ABSENCE OF SWELL 4HE REMAINING PROPERTIES OF THE CLUTTER SPECTRUM CAN NOW BE DISCUSSED IN TERMS OF 6ORB AND 6VIR &OR EXAMPLE THE SPECTRAL PEAK FOR HORIZONTAL POLARIZATION FOLLOWS A SIMILAR LINEAR DEPENDENCE ON 5 ONLY WITH A COEFFICIENT LYING SOMEWHERE BETWEEN AND AS MAY BE NOTED IN THE SKETCH SHOWN IN &IGURE 4HE REASONS FOR THE DIFFERENCES BETWEEN THE SPECTRA FOR THE TWO POLARIZATIONS ARE NOT AS YET CLEAR ALTHOUGH THE TENDENCY OF THE ( POLARIZATION SPECTRA TO LIE AT A HIGHER FREQUENCY IS LIKELY DUE TO THE PREFERENTIAL SOURCE OF ( POLARIZATION RETURNS IN FASTER MOVING WAVE STRUCTURES 4HE HALF POWER WIDTH $ OF THE CLUTTER VELOCITY SPECTRUM IS QUITE VARIABLE DEPENDING ON SUCH THINGS AS RADAR POLARIZATION AND SEA CONDITIONS )T SEEMS MOST CLOSELY RELATED TO THE PEAK ORBITAL VELOCITY GIVEN BY %Q .ATHANSON SHOWS A PLOT CONTAINING SPECTRAL WIDTHS AT BOTH POLARIZATIONS FROM SEVERAL INVESTIGATORS OVER A WIDE ASSORTMENT OF UNSPECIFIED SEA CONDITIONS 4HE POINTS ARE WIDELY SCATTERED BUT THE DEPENDENCE ON WIND SPEED IS GIVEN ROUGHLY WITH A RATHER LARGE VARIANCE BY THE EXPRESSION $ ^ 5 MS WHICH IS JUST THE ORBITAL VELOCITY IN %Q WITH A COEFFICIENT ABOUT HALFWAY BETWEEN THE VALUES FOR VERTICAL ^ AND HORIZONTAL ^ POLARIZATION &OR LOOK DIRECTIONS AWAY FROM UPWIND THE PEAK DOPPLER FOLLOWS A COSINE DEPENDENCE QUITE CLOSELY GOING TO ZERO AT CROSSWIND ASPECTS AND TURNING NEGATIVE DOWNWIND 4HE WIDTH OF THE SPECTRUM APPEARS TO REMAIN RELATIVELY CONSTANT
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4HE DETAILS OF THE CLUTTER SPECTRUM SHOW LITTLE DEPENDENCE ON EITHER THE RADAR FRE QUENCY OR THE GRAZING ANGLE AT LEAST FOR ANGLES LESS THAN ABOUT )N REVIEWING THE RESULTS OF MEASUREMENTS AT FOUR FREQUENCIES5(& , # AND 8 BANDS6ALENZUELA AND ,AING NOTED A RELATIVELY WEAK TENDENCY OF CLUTTER BANDWIDTH TO DECREASE WITH INCREASES IN FREQUENCY BETWEEN THE 5(& AND 8 BANDS AND GRAZING ANGLES BETWEEN AND 3INCE BOTH OF THESE VARIATIONS CAN LIKELY BE ACCOMPANIED BY A CHANGE IN THE SIZE OF THE RADAR FOOTPRINT ON THE SURFACE THEY MIGHT BE DUE TO A DEPENDENCE ON RESOLU TION CELL DIMENSIONS ALTHOUGH THE OTHER WORKERS FOUND THAT THE PULSE LENGTH HAD LITTLE EFFECT ON CLUTTER BANDWIDTH FOR VALUES BETWEEN ABOUT AND §SEC 3PECTRA OBTAINED WITH SHORT AVERAGING TIMES DISCLOSE SOMETHING OF THE ORIGINS OF THE CLUTTER SPECTRUM &IGURE IS A SEQUENCE OF SECOND SPECTRA OBTAINED BY +ELLER ET AL WITH A COHERENT VERTICALLY POLARIZED 8 BAND RADAR OPERATING AT A GRAZING ANGLE OF AND A RESOLUTION CELL SIZE OF ABOUT M 4HE ZERO DOPPLER REF ERENCE IN THIS FIGURE WAS LOCATED ARBITRARILY AT n (Z 4HE SPREAD ALONG EACH LINE
&)'52% 3HORT TIME AVERAGED DOPPLER SPECTRA AT 8 BAND FOR AN INTERMEDIATE GRAZING ANGLE OF SPECTRA COMPUTED AT SEC INTERVALS SHALLOW WATER DATA IS FROM A FIXED SITE ON A PIER FROM 7 # +ELLER ET AL
3%! #,544%2
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IS DUE TO THE SMALL SCALE WAVE MOTIONS ON THE SURFACE WHILE THE LARGER MEANDERS ARE INDUCED BY THE VELOCITIES OF LARGE WAVES MOVING THROUGH THE MEASUREMENT CELL 4HE WIND SPEED WAS ABOUT MS AND A DOPPLER SHIFT OF (Z CORRESPONDS TO A RADIAL VELOCITY OF MS 4HE AVERAGE CLUTTER SPECTRUM EXPECTED FOR THIS WIND SPEED AND GRAZING ANGLE WITH BANDWIDTH ESTIMATED FROM %Q IS INCLUDED IN THE SKETCH SHOWN IN &IGURE 4HE LARGE SPECTRAL SPIKE APPEARING IN THE CENTER OF THE DISPLAY IS NO DOUBT DUE TO A WAVE BREAKING IN OR CLOSE TO THE MEASUREMENT CELL 4HE DOPPLER VELOCITY FOR THIS SPIKE SUGGESTS A PEAK SCATTERER VELOCITY ABOUT EQUAL TO THE WIND SPEED WHICH WOULD CORRESPOND TO THE VELOCITY OF THE LONGEST WAVES ON THE SURFACE !LTHOUGH SUCH EVENTS ARE RELATIVELY RARE IN A FIXED AREA OF M THEY SHOULD OCCUR QUITE FREQUENTLY WITHIN A LARGE SURVEILLANCE CELL AND MIGHT OFTEN HAVE LARGE SCATTER ING CROSS SECTIONS ASSOCIATED WITH THEM 3IMILAR RECORDS MAY BE FOUND IN REFERENCE 7ARD ET AL /THER %NVIRONMENTAL %FFECTS 2AIN %ARLY EVIDENCE OF THE EFFECT OF RAIN ON SEA CLUTTER WAS MAINLY ANECDOTAL FOR EXAMPLE RADAR OPERATORS WOULD REPORT THAT SEA CLUTTER TENDS TO DECREASE WHEN IT STARTS TO RAIN (OWEVER THERE HAS BEEN LITTLE IN THE WAY OF RELIABLE QUANTITATIVE EXPERIMENTAL INFORMATION ABOUT THE INTERACTION BETWEEN RAIN AND WIND DRIVEN SEA CLUTTER IN THE OPEN OCEAN ,ABORATORY MEASUREMENTS BY -OORE ET AL WITH ARTIFICIAL hRAINv SUGGESTED THAT FOR LIGHT WINDS THE BACKSCATTER LEVEL INCREASED WITH THE RAIN RATE WHILE FOR HEAVY WINDS RAIN MADE LITTLE DIFFERENCE %XTENSIVE MEASUREMENTS AT +U BAND IN THE OPEN OCEAN TENDED TO CONFIRM THIS BEHAVIOR )N MEASUREMENTS IN NATURAL RAIN OVER #HESAPEAKE "AY (ANSEN FOUND THAT EVEN A LIGHT RAIN MMH CHANGES THE SPECTRAL CHARACTER OF SEA CLUTTER AT MODERATE WIND SPEEDS MS BY INTRODUCING A SIGNIFICANT HIGH FREQUENCY COMPONENT (E ALSO FOUND SOME EVIDENCE IN SUPPORT OF THE RADAR OPERATORS AT LEAST FOR THE LOW GRAZ ING ANGLES AND HORIZONTAL POLARIZATIONS WITH WHICH MOST SHIPBOARD RADARS OPERATE &IGURE COMPARES THE CORRELATION FUNCTION OF SEA CLUTTER 8 BAND LOW GRAZING ANGLE ( POLARIZATION WITH AND WITHOUT RAIN FOR A KT WIND SPEED AND A RAIN RATE OF MMH 4HE SHARP DECREASE IN CORRELATION TIME IN THE PRESENCE OF RAIN REFLECTS THE BROADENING OF THE CLUTTER SPECTRUM ALTHOUGH GENERALLY THERE APPEARS TO BE LITTLE QUANTITATIVE INFORMATION ABOUT THE EFFECT OF RAIN ON THE SPECTRUM OF SEA CLUTTER
&)'52% %FFECT OF RAIN ON THE CORRELATION FUNCTION OF WIND DRIVEN SEA CLUTTER 8 BAND HORIZONTAL POLARIZATION WIND SPEED KT RAIN RATE MMH FROM * 0 (ANSEN
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4HE PRODUCTION OF SEA CLUTTER BY RAIN FALLING ON A hCALMv SURFACE IN THE ABSENCE OF WIND WAS ALSO INVESTIGATED BY (ANSEN WITH THE RESULTS SHOWN IN &IGURE ! HIGH RESOLUTION 8 BAND RADAR NS PULSE BEAMWIDTH OPERATING AT A GRAZING ANGLE OF ABOUT VIEWED THE BACKSCATTER FROM A FIXED SPOT ON THE WINDLESS SURFACE OF #HESAPEAKE "AY AS THE RAIN STEADILY INCREASED FROM TO MMH 4HE CROSS SECTIONS FOR VERTICAL AND HORIZONTAL POLARIZATIONS WERE QUITE DIFFERENT FOR LOW RAIN RATES BUT TENDED TO MERGE AT A RAIN RATE OF ABOUT MMH 4HE MAGNITUDE OF THIS SPLASH CROSS SECTION ROSE TO A R OF ABOUT n D" CORRESPONDING TO HIGHLY AVERAGED WIND INDUCED CROSS SEC TIONS AT THIS GRAZING ANGLE FOR WINDS OF ABOUT KT &URTHER LABORATORY AND THEORETI CAL STUDIES HAVE SHOWN THAT THE MAJOR SCATTERING FEATURE UNDER THESE CONDITIONS IS THE VERTICAL STALK THAT EMERGES SHORTLY AFTER DROP IMPACT -OREOVER THESE STUDIES SUGGEST THAT THE 6 POLARIZED RETURNS FROM RAINDROP SPLASHES SHOULD BE ONLY MILDLY SENSITIVE TO THE RAIN RATE WHILE THE ( POLARIZED RETURNS SHOULD SHOW A STRONG DEPENDENCE ON BOTH THE RAIN RATE AND THE DROP SIZE DISTRIBUTION 3OMETHING OF THIS BEHAVIOR MAY BE SEEN IN THE DATA IN &IGURE /PEN OCEAN MEASUREMENTS AT +U BAND AND AT MUCH HIGHER GRAZING ANGLES SHOW SUFFICIENT VARIABILITY WITH WIND SPEED RAIN RATE AND GRAZING ANGLE TO LEAVE THE UNCERTAINTIES THAT OPENED THIS SECTION LARGELY UNRESOLVED )N ADDITION TO SCATTERING FROM THE RAINDROP IMPACTS THE DISTRIBUTION OF RAINDROPS IN THE VOLUME OF THE ATMOSPHERE ABOVE THE SURFACE CAN HAVE TWO ADDITIONAL EFFECTS ON SEA CLUTTERAS AN ABSORBERSCATTERER OVER THE RADAR PROPAGATION PATH WHICH IS WELL UNDERSTOOD AND AS A MASS ADDITIVE TO THE WIND AFFECTING MOMENTUM TRANSFER TO THE SURFACE AND THUS THE EXCITATION OF WIND WAVES THEMSELVES WHICH IS LESS WELL UNDERSTOOD !TMOSPHERIC $UCTING !NOTHER TOPIC IN SEA CLUTTER THAT HAS BEEN LITTLE EXPLORED IS THE ROLE PLAYED BY PROPAGATION EFFECTS WITHIN THE ATMOSPHERIC BOUNDARY LAYER LYING OVER THE SEA SURFACE 4HE EFFECTS OF ATMOSPHERIC ABSORPTION HAVE BEEN NOTED ABOVE IN CONNECTION WITH MILLIMETER WAVE CLUTTER BUT AT VERY LOW GRAZING ANGLES THE RAY PATHS JOINING THE RADAR TO THE SURFACE BECOME VERY SENSITIVE TO REFRACTIVE INHOMOGENEITIES IN THE ATMOSPHERIC BOUNDARY LAYER /VER DISTANCES APPROACHING AND
&)'52% 3EA CLUTTER PRODUCED BY RAIN SPLASHES ALONE ON A CALM SURFACE D" CORRESPONDS TO ABOUT R D" FROM (ANSEN
3%! #,544%2
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BEYOND THE CONVENTIONAL OPTICAL HORIZON SUCH PERTURBATIONS COULD PRODUCE STRONG FOCUS DEFOCUS VARIATIONS ALONG THE SURFACE ILLUMINATION PROFILE OR A GENERAL RISE IN THE LOCAL GRAZING ANGLE &IGURE GIVES AN EXPERIMENTAL EXAMPLE OF THE EFFECT OF DUCTING ON VERY LOW ANGLE SEA CLUTTER 4HE GRAZING ANGLE GIVEN AS THE ABSCISSA IS ACTUALLY A PLOT OF INVERSE RANGE SO THE LIFTING OF THE CROSS SECTION BY DUCTING OVER AN ORDER OF MAGNITUDE SPAN OF RANGES IS VERY LIKELY DUE TO A RISE IN THE LOCAL GRAZING ANGLE PRODUCED BY REFRACTION IN THE EVAPORATIVE LAYER FIRST METERS OR SO ABOVE THE SURFACE 3UCH EFFECTS SHOULD BE SUSPECTED WHENEVER THE RADAR PROPAGATION PATH EXTENDS BEYOND THE OPTICAL HORIZON 3HADOWING 4HE POSSIBILITY OF SHADOWING MUST BE CONSIDERED SERIOUSLY WHENEVER THE SEA IS VIEWED AT GRAZING ANGLES SMALLER THAN THE RMS SLOPE ANGLE OF THE SEA SURFACE 3OME EXAMPLES WERE DISCUSSED EARLIER IN CONNECTION WITH THE BEHAVIOR OF SEA CLUTTER AT LOW GRAZING ANGLES IN &IGURE )N FACT THE SHARP FALLOFF OF THE NONDUCTING DATA IN &IGURE MIGHT BE FURTHER EVIDENCE OF THE THRESHOLD SHADOWING MENTIONED EARLIER (OWEVER THE COMMON IDEA OF SHADOWING DERIVES FROM THE GEOMETRICAL OPTICS CONCEPT OF A SHARP TRANSITION BETWEEN LIGHT AND DARKNESS "Y CONSIDERING THE IMPLICATIONS OF DIFFRACTION AT THE WAVE PEAKS IT IS POSSIBLE TO DETERMINE THE DOMAIN OF RADAR FREQUEN CIES AND WIND SPEEDS OVER WHICH THE CONCEPTS OF GEOMETRICAL OPTICS MAY BE APPLIED 4HIS WAS DONE IN 7ETZEL WHERE IT IS SHOWN HOW DIFFRACTION RATHER THAN GEOMETRICAL SHADOWING CONTROLS PROPAGATION INTO AND OUT OF THE TROUGHS OF THE WAVES UNDER MANY OF THE USUAL FREQUENCIES AND WIND SPEEDS ENCOUNTERED IN PRACTICAL RADAR OPERATIONS AT LOW GRAZING ANGLES &OR EXAMPLE SHADOWING WILL TAKE PLACE AT +A BAND FOR ANY WINDS ABOVE KT YET WILL HARDLY EVER OCCUR AT , BAND FREQUENCIES ,ATER ANALYTICAL SOLU TIONS BASED ON NUMERICAL METHODS EXPLORED AND EXPANDED THE IDEA OF SHADOWING OVER THE SEA SURFACE UNDER HIGHLY IDEALIZED AND MORE GENERAL CONDITIONS 3URFACE #URRENTS 4HE MOST OBVIOUS EFFECT OF A CURRENT ON SEA CLUTTER WOULD BE A SHIFT IN THE PEAK OF THE DOPPLER SPECTRUM ANALOGOUS TO THE CONTRIBUTION OF THE WIND DRIFT CURRENT MENTIONED IN CONNECTION WITH %Q !NOTHER EFFECT IS RELATED TO
&)'52% %FFECT OF DUCTING ON LOW ANGLE CLUTTER WIND SPEED ABOUT KT AFTER & " $YER AND . # #URRIE Ú )%%%
£x°ÓÈ
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THE FACT THAT THE EXCITATION OF THE SURFACE WAVE SYSTEM DEPENDS ON THE LOCAL APPARENT WIND AT THE SURFACE SO THERE CAN BE SIGNIFICANT DIFFERENCES IN WAVEHEIGHT ACCORDING TO WHETHER THE WIND IS BLOWING WITH OR AGAINST THE CURRENT !CCORDING TO %Q WAVEHEIGHT IS PROPORTIONAL TO THE SQUARE OF THE WIND SPEED SO IN THE 'ULF 3TREAM FOR EXAMPLE WITH A CURRENT OF KT FLOWING NORTH A KT NORTHERLY BLOWING AGAINST THE CURRENT WILL RAISE A SEA THREE TIMES AS HIGH AS A KT SOUTHERLY BLOWING WITH THE CURRENT %VEN WITH NO WIND THE PRESENCE OF STRONG CURRENT SHEARS CAN PRODUCE HIGHLY AGITATED SURFACES 3HIPBOARD OBSERVERS HAVE REPORTED BANDS OF ROARING BREAKERS PASS ING BY ON AN OTHERWISE SMOOTH SURFACE PRESUMABLY PRODUCED BY POWERFUL SURFACE CURRENT SHEARS ASSOCIATED WITH LARGE AMPLITUDE INTERNAL WAVES )N A MORE SUBTLE WAY MODULATED CURRENTS ARE HELD RESPONSIBLE FOR SYNTHETIC APERTURE RADAR 3!2 IMAGES THAT CONTAIN THE EXPRESSION OF BOTTOM TOPOGRAPHY PRODUCED BY THE "ERNOULLI %FFECT IN SHALLOW WATERS )N EACH OF THE EXAMPLES CITED ABOVE THE CURRENT PRODUCES A CHANGE IN THE SURFACE ROUGHNESS WHICH CAN BE EXPECTED TO GIVE RISE TO A CHANGE IN SEA CLUTTER CROSS SECTION #ONTAMINANTS 4HE IDEA OF POURING OIL ON TROUBLED WATERS IS A FAMILIAR ONE THE ANGRY SURFACE WILL SMOOTH AND SUBSIDE )N ANOTHER AGE THE SURVIVAL GEAR LOCKER OF EVERY SAILING SHIP WOULD CONTAIN A BOTTLE OF OIL TO QUIET THE SEA IN A STORM !LTHOUGH THE EFFECTIVENESS OF THIS PROCEDURE HAS ALWAYS BEEN SOMEWHAT CONTROVERSIAL THERE IS NO QUESTION THAT OIL CAN PRODUCE A SLICK OF SMOOTH WATER AT RELATIVELY LOW WIND SPEEDS )N FACT BIOLOGICAL OILS PRODUCED BY BACTERIA ALGAE AND PLANKTON CAN BE FOUND EVERYWHERE ON THE WORLDS OCEANS AND FORM NATURAL SLICKS IN THOSE REGIONS THAT COMBINE THE GREATEST OIL CONCENTRATION WITH THE LOWEST WIND SPEEDS EG CLOSE TO CONTINENTAL SHORELINES -AN MADE CONTAMINANTS CAN OF COURSE HAVE THE SAME EFFECT ! LAYER OF OIL ONLY ONE MOLECULE THICK WILL SIGNIFICANTLY AFFECT THE ABILITY OF THE SURFACE TO SUPPORT WAVE MOTIONS BUT THIS LAYER MUST BE CONTINUOUS 4HE ADJA CENT MOLECULES THEN SENSE EACH OTHER AND FORM A FILM THAT IS RESISTANT TO HORIZONTAL COMPRESSION 4HE SURFACE ELASTICITY IS CHANGED A TYPE OF LONGITUDINAL VISCOSITY IS INTRODUCED AND THE SURFACE BECOMES STABILIZED AGAINST THE GROWTH OF SHORT WAVES UP TO SEVERAL INCHES IN LENGTH 4O THE EXTENT THAT RADAR SEA CLUTTER IS PRODUCED BY SMALL SCALE SURFACE ROUGHNESS AT GRAZING ANGLES LESS THAN ABOUT THE PRESENCE OF OIL ON THE SURFACE SHOULD LEAD TO A MEASURABLE DECREASE IN CLUTTER CROSS SECTION "UT AS NOTED ABOVE THE REDUCTION OF SMALL WAVE MOTIONS REQUIRES THE EXISTENCE OF A CONTINUOUS MONOLAYER SLICK FORMATION IS A GOnNO GO PROCESS AND SO SLICKS WILL TEND TO HAVE RELATIVELY SHARP BOUNDARIES )N OPERATING THE .2, &2 SYSTEM AS A SYNTHETIC APERTURE RADAR TO OBTAIN IMAGES OF THE SLICKS PRODUCED BY OIL SPILLS 'UINARD FOUND THAT THE SLICKS WERE WELL DEFINED THAT IT TOOK VERY LITTLE OIL TO MAINTAIN A VISIBLE SLICK THAT VERTICAL POLARIZATION PROVIDED MUCH GREATER CONTRAST THAN DID HORIZONTAL AND THAT THE SLICKS WERE QUENCHED BY WINDS AND CURRENTS !LTHOUGH SIGNAL STRENGTH WAS NOT RECORDED IN THIS IMAGING EXPERIMENT LATER MEASUREMENTS AT 8 AND , BANDS BY OTHERS INDICATED THAT AT THE HIGHER GRAZING ANGLES ABOUT THE CLUTTER REDUCTION PRODUCED BY THE TYPES OF OIL OCCURRING IN NATURAL SLICKS WAS RATHER SMALL ON THE ORDER OF A PERCENT 3INCE SLICKS ARE DISPERSED BY THE WIND AND ASSOCIATED WAVE ACTION AT WIND SPEEDS GREATER THAN ABOUT KT THE EFFECT OF NATURAL SLICKS ON CLUTTER MAY NOT BE CLEAR BECAUSE THEY TEND TO OCCUR IN THE REGIME OF LOW WIND SPEEDS WHERE THE SEA SURFACE IS ALREADY ILL DEFINED 4HE CELEBRATED SUN GLITTER MEASUREMENTS BY #OX AND -UNK GAVE A QUANTITATIVE MEASURE OF THE EFFECT OF CONTAMINANTS ON THE SURFACE SLOPES IN OPEN WATER SHOWING THAT THE WIND GENERATED COMPONENT OF THE RMS SLOPE OF hOILEDv WATERS IS SIGNIFICANTLY
3%! #,544%2
£x°ÓÇ
SMALLER THAN THAT OF hCLEANv WATER 4HE HEAVY COMMERCIAL OILS USED IN THEIR EXPERIMENT WERE EFFECTIVE IN SUPPRESSING SMALL SCALE WAVES OVER A RANGE OF WIND SPEEDS WELL BEYOND THOSE WHICH WOULD NORMALLY DISPERSE THE LIGHTER NATURAL OILS SO THE EFFECT OF OIL SPILLS ON SEA CLUTTER SHOULD BE EXPECTED TO EXTEND TO THE HIGHER WIND SPEEDS )N FACT AT THESE HIGHER WIND SPEEDS THE DEPRESSION OF RADAR BACKSCATTER BY SUCH OILS AT 8 AND +A BANDS CAN REACH TO D" AT INTERMEDIATE GRAZING ANGLES BETWEEN AND
£x°{Ê / ", -Ê Ê " -Ê"Ê- Ê 1// , )N ADDITION TO PROVIDING AN INTELLECTUAL BASIS FOR hUNDERSTANDINGv SEA CLUTTER PHENOM ENA A COMPLETE THEORY OF SEA CLUTTER SHOULD IDEALLY PROVIDE ACCURATE A PRIORI PREDIC TIONS OF ALL ASPECTS OF CLUTTER BEHAVIOR UNDER ALL POSSIBLE ENVIRONMENTAL CONDITIONS )N SPITE OF OVER YEARS OF EFFORT THE THEORY OF SEA CLUTTER DOES NEITHER OF THESE TASKS VERY WELL AS WE WILL SEE IN THIS SECTION )N THE DEVELOPMENT OF MODELS OF SEA SCATTER BASED ON PHYSICAL THEORY THERE ARE ESSENTIALLY TWO BASIC AND DISTINCT APPROACHES (ISTORICALLY THE FIRST APPROACH ASSUMED SEA SCATTER TO HAVE ITS ORIGIN IN SCATTERING FEATURES OR OBSTACLES ACTUALLY PRESENT ON OR NEAR THE SEA SURFACE %ARLY SCATTERING MODELS INCLUDED RAIN TO MODEL SPRAY SMOOTH CIRCULAR METALLIC DISKS ARRAYS OF SEMI INFINITE PLANES AND FIELDS OF HEMISPHERI CAL BOSSES TO NAME A FEW /BVIOUSLY THE CHOICE OF THESE SCATTERING OBSTACLES RELATED MORE TO THE PREEXISTENCE OF CONVENIENT SCATTERING SOLUTIONS FOR THESE SHAPES THAN TO INSIGHTS GAINED FROM OBSERVING THE SEA 3INCE THEN FEATURE MODELS HAVE SOUGHT GREATER REALITY BY CONSIDERING WEDGE SHAPES AS SUGGESTED BY THE SHARP CRESTS OF 3TOKES WAVES OBSERVED ON MOST NATURAL WATER SURFACES AND THE SHOCKS AND PLUMES SUGGESTED BY THE PROPERTIES OF WAVE GROUPS AND THE HYDRODYNAMICS OF BREAKING WAVES 4HE OTHER APPROACH TO THEORETICAL MODELING DERIVES THE SCATTERED FIELD FROM A GLOBAL BOUNDARY VALUE PROBLEM '"60 IN WHICH THE SEA AS A WHOLE IS CONSIDERED A BOUNDARY SURFACE WHOSE CORRUGATIONS ARE DESCRIBED BY SOME KIND OF STATISTICAL PRO CESS !N ENORMOUS LITERATURE IS DEVOTED TO THE THEORY OF SURFACE SCATTER FROM THIS POINT OF VIEW STEMMING FROM THE IMPORTANCE NOT ONLY OF RADAR SEA SCATTER BUT ALSO RADAR GROUND SCATTER AND SONAR REVERBERATION THE ACOUSTIC EQUIVALENT OF RADAR CLUTTER FROM BOTH THE SURFACE AND THE BOTTOM OF THE SEA "ECAUSE THE '"60 APPROACH LEADS TO THE ANALYTICAL EXPRESSION OF THE "RAGG SCATTERING HYPOTHESIS THAT HAS DOMINATED THE THEORY OF SEA SCATTER SINCE THE LATE S A BRIEF EXPLANATION OF SOME OF THE CENTRAL IDEAS IS INCLUDED BELOW 4HEORIES "ASED ON 'LOBAL "OUNDARY 6ALUE 0ROBLEMS 'ENERAL FORMULATIONS OF THE '"60 THOUGH ELEGANT ARE OF LITTLE PRACTICAL VALUE AND SOME KIND OF APPROXI MATION IS NECESSARY TO OBTAIN USEFUL QUANTITATIVE RESULTS FROM THEM 4HE METHODS OF APPROXIMATION RELATE TO THE TWO METHODS OF FORMULATING THE '"60 3MALL AMPLITUDE APPROXIMATIONS SEA WAVEHEIGHTS MUCH SMALLER THAN THE RADAR WAVELENGTH ARE USED AB INITIO WITH 2AYLEIGHS HYPOTHESIS IN WHICH THE SURFACE BOUNDARY CONDITIONS ARE EMPLOYED TO MATCH AN ANGULAR SPECTRUM OF OUTGOING PLANE WAVES TO THE INCIDENT FIELDn ! GENERAL INTEGRAL FORMULATION BASED ON 'REENS THEOREM IS PURSUED EITHER IN A SMALL AMPLITUDE APPROXIMATION OR UNDER THE ASSUMPTIONS OF PHYSICAL OPTICS SURFACE CURVATURES MUCH GREATER THAN THE RADAR WAVELENGTH n
£x°Ón
2!$!2 (!.$"//+
)N FORMULATION SOMETIMES CALLED THE SMALL PERTURBATION METHOD 30- AND ASSO CIATED MOST OFTEN WITH THE WORK OF 2ICE THE SURFACE DISPLACEMENTS ARE ASSUMED EVERYWHERE TO BE MUCH SMALLER THAN THE RADAR WAVELENGTH SO THE METHOD IS DIRECTLY APPLICABLE ONLY TO SUCH CASES AS (& SCATTERING WITH WAVELENGTHS OF TENS OF METERS AT LOW TO INTERMEDIATE WIND SPEEDS AND WITH WAVEHEIGHTS OF A FEW METERS AT MOST 4HE SOLUTION IS IN THE FORM OF A POWER SERIES IN THE RATIO OF SEA WAVEHEIGHT TO RADAR WAVELENGTH AND IT PREDICTS THE FIRST ORDER "RAGG LINES AND SECOND ORDER SPECTRAL FILLING AROUND THE LINES THAT WERE MENTIONED IN THE EARLIER SECTION ON (& SEA CLUTTER /N THE OTHER HAND THE VARIOUS INTEGRAL FORMULATIONS REFERENCED ABOVE USUALLY BEGIN WITH A VERY GENERAL EXPRESSION FOR THE FIELDS SCATTERED FROM THE SEA SURFACE WHICH ARE SQUARED AND ENSEMBLE AVERAGED OVER REALIZATIONS OF THE SEA SURFACE TO PROVIDE THE AVERAGE POWER RETURNED TO THE RADAR ANTENNA AND THEN NORMALIZED TO THE ILLUMINATED AREA AS IN %Q $ESPITE THE GENERALITY OF THE INITIAL FORMULATIONS MOST OF THE FINAL EXPRESSIONS FOR R EITHER APPEAR IN OR CAN BE PUT INTO A FORM REPRESENTED SCHEMATI CALLY BY THE FOLLOWING SIMPLIFIED ONE DIMENSIONAL EXPRESSION SEE (OLIDAY ET AL "ECHMANN AND 3PIZZICHINO &UNG AND 0AN AND 6ALENZUELA FOR EXAMPLE c
; # Y =
S Y !K &P Y ¯ DY EI KY ;E K H
E K H =
c
WHERE ! IS A CONSTANT K K COSX AND K K SINX WHERE K IS THE RADAR WAVE NUMBER O K &P X IS A FUNCTION OF POLARIZATION P GRAZING ANGLE X AND THE ELECTRICAL PROPERTIES OF SEAWATER H IS THE RMS SEA WAVEHEIGHT AND #Y IS THE SURFACE CORRELATION COEFFICIENT /F COURSE THE REDUCTION OF A COMPLICATED BOUNDARY VALUE PROBLEM TO SO SIMPLE A FORM REQUIRES ASSUMPTIONS ABOUT BOTH THE SURFACE FIELDS AND THE DISTRIBUTION OF THE SEA HEIGHTS WHICH IS GAUSSIAN TO A GOOD APPROXIMATION "UT WHILE THE 30- APPROACH MENTIONED ABOVE REQUIRES THE RATIOS HK TO BE SMALL RIGHT AT THE START '"60 THEORIES DERIVED FROM EXPRESSIONS RESEMBLING %Q HAVE NO A PRIORI RESTRICTIONS ON SURFACE HEIGHTS 4HE STATISTICAL PROPERTIES OF THE SEA SURFACE ENTER THROUGH THE CORRELATION COEFFI CIENT #Y APPEARING UNDER THE INTEGRAL SIGN IN THE EXPONENTIAL IN THE BRACKETS AND BY EXPANDING THIS EXPONENTIAL IN %Q IT MAY BE WRITTEN
S Y !K &P Y E
K H
c
£
N
K N 7 N K N
WHERE c
7 N K ¯ DT EI KT ;H # T =N
c
3MALL AMPLITUDE !PPROXIMATION )N THE LIMIT OF SMALL RATIOS OF RMS WAVEHEIGHT TO RADAR WAVELENGTH OR MORE SPECIFICALLY
KH
ONLY THE FIRST TERM IN THE SERIES IN %Q SURVIVES AND THE CROSS SECTION ASSUMES THE VERY SIMPLE FORM
S Y P K &P` Y 7 K COSY
3%! #,544%2
£x°Ó
WHERE THE CONSTANT ! HAS BEEN MADE EXPLICIT AND &P HAS ABSORBED A SIN TERM FROM THE SERIES 7 IS THE &OURIER TRANSFORM OF THE SURFACE CORRELATION FUNCTION WHICH MAKES IT THE SEA WAVENUMBER SPECTRUM DISCUSSED IN 3ECTION EVALUATED AT TWICE THE SURFACE PROJECTED RADAR WAVENUMBER WHICH DEFINES A "RAGG OR HALF WAVELENGTH RESONANCE %XCEPT POSSIBLY FOR THE DETAILS OF THE ANGLE FACTOR &P %Q IS EQUIVA LENT TO THE RESULT OBTAINED BY THE 30- DISCUSSED ABOVE AND ALTHOUGH IT IS SOMETIMES FELT THAT ITS DERIVATION FROM A SURFACE INTEGRAL PROVIDES SOME POTENTIAL FOR GREATER GENERALIZATION IT CARRIES WITH IT ALL OF THE SAME RESTRICTIONS "EFORE PROCEEDING FURTHER IT IS INSTRUCTIVE TO LOOK A LITTLE MORE CLOSELY AT THE IMPLI CATIONS OF THE MATHEMATICAL EXPRESSIONS IN THESE FORMULATIONS .OTE THAT IN %Q THE EXPRESSION IN THE BRACKETS UNDER THE INTEGRAL IS THE ONLY PLACE AT WHICH THE SURFACE WAVE PROPERTIES OF THE SEA APPEAR 4HAT IS THE CROSS SECTION IS SIMPLY PROPORTIONAL TO THE &OURIER TRANSFORM OF A SEA SURFACE FUNCTIONAL SO THE RADAR ACTS AS A FILTER TUNED TO THE hSPATIAL FREQUENCYv K COSX EXTRACTING THAT LINE FROM THE SPECTRUM OF WHATEVER ASSORTMENT OF SCATTERERS THE SEA SURFACE FUNCTIONAL EXPRESSES WHETHER THEY BE LONG SWELL COMPONENTS SHORT WAVELENGTH NOISE LOCALIZED SCATTERING FEATURES OR A CHAOTIC TUMBLE OF WATER BALLS /NLY UNDER QUITE SPECIAL CIRCUMSTANCES WILL THERE ACTUALLY BE AN IDENTIFIABLE SURFACE WAVE AT THAT hFREQUENCYv THAT WOULD JUSTIFY THE TERM "RAGG RESONANCE IN ITS ORIGINAL SENSE WHICH AFTER ALL WAS A RESONANCE IN AN ORDERED CRYSTAL LATTICE OF DISCRETE SCATTERERS !LTHOUGH AUTHORS OFTEN REFER TO hFREE "RAGG WAVES v SUCH OBJECTS ARE FOUND PRIMARILY AMONG THE PARASITIC CAPILLARIES REFERRED TO IN 3ECTION OR AMONG THE RING WAVES PROPAGATING OUT FROM THE IMPACT OF A FALLING DROP 4HIS RAISES A QUESTION ABOUT THE MEANING OF SUCH OFTEN USED TERMS AS "RAGG WAVELETS "RAGG PATCHES AND SO ON AS IF SUCH THINGS HAD A REAL EXISTENCE OUTSIDE OF THEIR EMERGENCE AS AN ARTIFACT OF A FILTER OPERATION 4HIS CONFUSION OF CONCEPTS MIGHT BE AVOIDED BY VISUALIZING THE RADAR AS EXTRACTING THE h"RAGG LINEv FROM THE SPECTRAL COMPOSITIONS OF THOSE SURFACE FEATURES THAT CONTAIN A WAVE OF LENGTH K COSX IN THEIR &OURIER REPRE SENTATION INDEPENDENT OF THE EXISTENCE OF SUCH A WAVE AS A REAL OBJECT .EVERTHELESS THIS DIRECT LINEAR RELATION BETWEEN RADAR CROSS SECTION AND THE OCEAN OGRAPHERS DESCRIPTOR OF THE SEA SURFACE HAS HAD A POWERFUL INFLUENCE ON THINKING ABOUT THE PHYSICAL ORIGINS OF SEA CLUTTER )T IS APPEALING IN ITS SIMPLICITY AND IT SUGGESTS A DIRECT WAY BOTH TO PREDICT RADAR CLUTTER FROM MEASUREMENTS OR FORECASTS OF THE SEA SPEC TRUM AND INVERSELY TO USE RADAR BACKSCATTER MEASUREMENTS TO PROVIDE REMOTE SENSING OF THE SEA SURFACE FOR OCEANOGRAPHIC AND METEOROLOGICAL APPLICATIONSPROVIDED OF COURSE THAT IT CORRECTLY DESCRIBES THIS RELATIONSHIP !LTHOUGH %Q SUCCESSFULLY PREDICTS TO ST ORDER THE CLUTTER RETURNS AT (& FREQUENCIES AT MICROWAVE FREQUENCIES THE SMALL WAVEHEIGHT ASSUMPTION ON WHICH THIS MODEL RESTS IS VIOLATED ON ANY REAL SEA SURFACE 4HE SMALL WAVEHEIGHT CONDITION EXPRESSED BY %Q MEANS THAT AT 8 BAND FOR EXAMPLE THE MAXIMUM DEPARTURE OF THE SEA SURFACE FROM A FLAT PLANE MUST BE MUCH SMALLER THAN MM /THER #ALCULATIONAL 3TRATEGIES )NSTEAD OF EXPANDING THE EXPONENTIAL IN THE INTE GRAND OF %Q IT SHOULD BE POSSIBLE AT LEAST IN PRINCIPLE TO REPLACE #Y DIRECTLY BY THE &OURIER TRANSFORM OF 7+ THE INVERSE OF %Q FOR N THUS PROVIDING A DIRECT FUNCTIONAL RELATIONSHIP BETWEEN THE RADAR CROSS SECTION AND THE SEA WAVE SPEC TRUM WITHOUT THE RESTRICTIONS OF A SMALL AMPLITUDE APPROXIMATION 4HIS CUMBERSOME APPROACH INVOLVES EXTENSIVE COMPUTATIONS EVEN TO OBTAIN LIMITED RESULTS IN INDIVIDUAL CASES AS SHOWN IN WORK BY (OLLIDAY ET AL )N ANOTHER LIMITING CASE THE BASIC INTEGRAL FORMULATION OF THE '"60 IS SOLVED IN THE OPTICAL APPROXIMATION LARGE K RESULTING IN AN EXPRESSION COMMONLY CALLED THE
£x°Îä
2!$!2 (!.$"//+
SPECULAR RETURN BECAUSE ITS ORIGIN MAY BE TRACED TO PIECES OF THE SURFACE THAT PROVIDE A REFLECTION POINT FOR THE INCIDENT WAVE 4HIS EXPRESSION IS WRITTEN FOR A GAUSSIAN SEA SURFACE IN THE FORM
S Y \ 2 \ S CSC Y EXP; COT Y S =
WHERE S IS THE RMS SURFACE SLOPE AND 2 IS THE FLAT SURFACE REFLECTION COEFFICIENT FOR NOR MAL INCIDENCE 4HIS IS THE TYPE OF SCATTERING ALLUDED TO IN CONNECTION WITH THE HIGH GRAZ ING ANGLE RETURNS DISCUSSED IN 3ECTION THE TENDENCY OF R TO LEVEL OFF FOR GRAZING ANGLES CLOSE TO SEE &IGURES AND MAY BE ASCRIBED TO THIS MECHANISM &ROM WHAT HAS BEEN SAID THUS FAR IT CAN BE SEEN THAT STRICT ANALYTICAL SOLUTIONS VIA THE '"60 APPROACH APPEAR TO RUN INTO DEAD ENDS INTRACTABLE FORMAL EXPRESSIONS IN THE FORM OF %Q SMALL AMPLITUDE APPROXIMATIONS IN THE FORM OF %Q THAT MAKE LITTLE SENSE FOR MICROWAVE SCATTERING FROM REAL SEA SURFACES OR OPTICAL LIMITS SUCH AS %Q THAT RELATE TO THE PROBABILITY DENSITIES OF SPECULARLY REFLECTING SURFACE SLOPES )T APPEARS THEREFORE THAT THE USE OF INTEGRAL FORMULATIONS IN THE PRACTICAL SOLUTION OF THE SEA CLUTTER PROBLEM AT MICROWAVE FREQUENCIES WILL REQUIRE SOMETHING MORE #OMPOSITE 3URFACE (YPOTHESES 3INCE IT IS NOT CLEAR HOW TO EXTEND STRAIGHTFOR WARD '"60 SOLUTIONS BEYOND THE LIMITING APPROXIMATIONS DESCRIBED ABOVE A HEURISTIC MODEL WAS DEVELOPED THAT VIEWED THE SEA AS A CARPET OF "RAGG SCATTERING hWAVELETSv MODULATED BY THE MOTIONS OF THE LARGER WAVES ON THE SURFACEn 4HIS COMPOSITE SURFACE MODEL IS OFTEN REFERRED TO AS THE TWO SCALE MODEL IN WHICH IT IS IMAGINED THAT THE SURFACE WAVE SPECTRUM CAN SOMEHOW BE SEPARATED INTO TWO PARTS ONE CONTAINING LOW AMPLITUDE h"RAGG SCATTERING WAVELETSv WHOSE INTEGRATED RMS WAVEHEIGHT SATISFIES THE CONDITIONS OF %Q AND ANOTHER THAT CONTAINS ONLY THE LONGER WAVES THAT TILT AND STRETCH AND OTHERWISE MODULATE THE "RAGG WAVES AFFECTING THE "RAGG SCATTERERS THROUGH A MODULATION TRANSFER FUNCTION AS WELL AS PROVIDING A SPECULAR COMPONENT RESEMBLING %Q /THER ASSUMPTIONS INCLUDE THAT THE CORRELATION LENGTHS OF THE SHORT "RAGG WAVES BE LONG ENOUGH THAT A RESONANT INTERACTION IS POSSIBLE BUT SHORT ENOUGH THAT ADJACENT AREAS ON THE SURFACE CONTRIBUTE TO THE TOTAL SIGNAL IN RANDOM PHASE NOTE HOW h"RAGG WAVESv ARE VIEWED HERE AS PHYSICAL OBJECTS AND THE LONG WAVES THAT TILT AND MODULATE THE SHORT WAVES HAVE RADII OF CURVATURE SUFFICIENTLY LARGE THAT THE CURVATURE OVER THE CORRELATION LENGTH OF THE h"RAGG PATCHESv IS SMALL IN SOME SENSE )N ITS SIMPLEST AND MOST COMMONLY USED hTILTv FORM IT INTERPRETS R X IN %Q AS THE CROSS SECTION OF A PATCH WITH LOCAL GRAZING ANGLE X R @ WHERE @ IS THE LOCAL WAVE SLOPE AND X IS THE MEAN GRAZING ANGLE &OR THE SIMPLE ONE DIMENSIONAL CASE THIS QUANTITY IS AVERAGED OVER THE SEA SLOPE ANGLE DISTRIBUTION P@ YIELDING c
S Y ¯ S Y A PA DA
c
&OR A MORE GENERAL TWO DIMENSIONAL SEA THE LOCAL GRAZING ANGLE IS A FUNCTION OF THE SLOPES IN AND NORMAL TO THE PLANE OF INCIDENCE SO FOR EACH POLARIZATION P THE ANGLE FUNCTION &PX IN R X BECOMES A COMPLEX MIXTURE OF THE ANGLE FUNCTIONS OF BOTH POLARIZATIONS 0LANT PROVIDES A COMPREHENSIVE DISCUSSION OF THIS MODEL %XTENSIONS OF THIS MODEL INTO WHAT MIGHT BE CALLED A THREE SCALE MODEL ARE GUIDED BY THE SAME IDEAS THAT LED TO THE TWO SCALE MODEL !N ADDITIONAL AD HOC SPECTRAL PARTITION IS INTRODUCED BETWEEN THE LONGEST AND SHORTEST WAVE COMPONENTS OF THE SEA SPECTRUM BUT THIS PRODUCED ONLY MODEST IMPROVEMENT
3%! #,544%2
£x°Î£
!LTHOUGH SUCH COMPOSITE SURFACE MODELS MAY LEAVE THE IMPRESSION THAT THEY HAVE EMERGED AS A RIGOROUS PRODUCT OF AN INTEGRAL FORMULATION OF THE '"60 IT IS CLEAR THAT THEY ARE NOT REALLY SCATTERING THEORIES BUT INSTEAD SCATTERING PICTURES ASSEMBLED FROM A GROUP OF MORE OR LESS PLAUSIBLE ASSUMPTIONS "UT WITH THE FAILURE OF THE MORE FORMAL '"60 THEORIES TO PROVIDE A GENERAL FRAMEWORK FOR PREDICTING AND UNDERSTANDING SEA CLUTTER THESE MODELS HAVE BECOME THE BASIS FOR MOST ANALYTICAL APPROACHES TO MICRO WAVE SCATTERING FROM THE SEA &IGURE COMPARES A SAMPLE OF .2, &2 DATA TAKEN AT HIGH WIND SPEEDS KN WITH THE PREDICTIONS OF THE PURE 30- "RAGG MODEL IN THE FORM OF %Q FOR 6 POLARIZATION AND THE TWO SCALE MODEL IN THE FORM OF %Q FOR ( POLARIZATION 4HE WAVE SPECTRUM USED WAS THE 0HILLIPS SPECTRUM GIVEN IN %Q (ISTORICALLY COMPARISONS OF THIS TYPE HAVE BEEN USED OFTEN TO PROVIDE SUPPORT FOR THE "RAGG SCAT TERING HYPOTHESIS AND THE AGREEMENT OFTEN LOOKS GOOD ESPECIALLY FOR VERTICAL POLARIZATION AT THE HIGHER WIND SPEEDS 9ET WHY THIS IS SO REMAINS A PUZZLING CURIOSITY )N THIS EXAMPLE THE WIND SPEEDS ARE HIGH SO THE SEA WILL BE ROUGH BUT IT WAS NOTED ABOVE THAT THE 30- APPROXIMATION USED IN &IGURE REQUIRES WAVEHEIGHTS MUCH LESS THAN A CENTIMETER SO THIS APPROXIMATION IS TOTALLY INVALID FOR THESE DATA -OREOVER THE 0HILLIPS SPECTRUM WAS USED AS THE SEA SURFACE SPECTRUM BUT THERE IS NO EVIDENCE THAT THIS SPECTRUM HOLDS DOWN TO THE REQUIRED CAPILLARY WAVELENGTH OF ABOUT CM )N FACT THE NATURE OF THE SEA SPECTRUM IN THIS RANGE REMAINS UNCERTAIN AND HAS BEEN REFERRED TO AS hONE OF THE MOST EXCITING UNSOLVED PROBLEMS OF THE SEA SURFACEv 4HE PRIMARY EFFECT OF THE TWO SCALE MODEL IS SIMPLY TO RAISE THE INAPPLICABLE 30- VALUES FOR ( POLARIZATION WHICH ARE DROPPING SHARPLY WITH GRAZING ANGLE BY INCLUDING HIGHER LOCAL ANGLES VIA %Q 4HERE WOULD BE LITTLE SENSIBLE EFFECT ON THE MORE CONSTANT VERTICAL RETURNS &INALLY THE POLARIZATION DIFFERENCES THEMSELVES HAVE BEEN SHOWN TO DERIVE ENTIRELY FROM THE BEHAVIOR OF THE REFLECTION COEFFICIENTS AT THE UNDERLYING SURFACE SEE FOR EXAMPLE 7RIGHT AND 7ETZEL AND SO ARE NOT AN INTRINSIC PART OF THE "RAGG HYPOTHESIS AND WOULD APPLY TO ANY SMALL PERTURBATION ON THE SURFACE .EVERTHELESS AGREEMENT BETWEEN MEASUREMENT AND PREDICTION OF THE TYPE ILLUSTRATED IN &IGURE
&)'52% #OMPARISON OF THE PREDICTIONS OF THE "RAGG HYPOTHESIS WITH .2, &2 DATA HEAVY LINES FOR HIGHER WIND SPEEDS KT DASH DOTTED LINES 30- "RAGG DASHED LINE TWO SCALE MODEL FOR ( POLARIZATION ONLY ASSUMING MEAN SEA SLOPES AFTER 6ALENZUELA
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HAS KEPT ALIVE CREDIBILITY IN THE "RAGG SCATTERING HYPOTHESIS IN SPITE OF THE CLEAR VIOLA TIONS OF CONDITIONS AND NONSEQUITURS NOTED ABOVE AS WELL AS THE LACK OF A PROPER THEORY ARGUED FROM FIRST PRINCIPLES 4HE FAILURE OF THIS MODEL TO ACCOUNT FOR SEA SPIKES AND OTHER NON 2AYLEIGH RETURNS NOTED IN 3ECTION HAS LED TO AN AUGMENTATION OF THE TWO SCALE COMPOSITE SURFACE TO INCLUDE BREAKING WAVES A PRESUMED SOURCE OF THESE RETURNS /NE OF THE LATEST OF THESE TWO SCALE PLUS MODELS MAY BE FOUND IN +UDRYAVTSEV ET AL WHERE BREAKING WAVE EFFECTS ARE INCORPORATED ANALYTICALLY THROUGH THE 0HILLIPS EXPRESSION FOR THE DENSITY OF BREAKING FRONTS AS A FUNCTION OF WIND SPEED THE PARAMETER ,C NOTED IN 3ECTION WITH THE SCATTERING BEHAVIOR BASED ON 7ETZELS PLUME MODEL SEE h3CATTERING BY 3URFACE &EATURESv 4HE RESULT IS A SIGNIFICANT IMPROVEMENT IN SEA SCATTER PREDICTIONS EMPHASIZING THE IMPORTANCE OF BREAKING IN THE SCATTERING SCENE !N EXAMPLE OF THIS IMPROVEMENT IS SHOWN IN &IGURE WHERE EXPERIMENTAL DATA FOR THE POLARIZATION RATIO RELATIVE TO WIND DIRECTION WAS OBTAINED FROM THE 0OLRAD PROGRAM /NE OF THE MAJOR CLAIMS FOR "RAGG MODELS HAS BEEN THEIR APPARENT ABIL ITY TO AGREE LOOSELY WITH THE OBSERVED POLARIZATION RATIOS OF SEA CLUTTER RETURNS AND IN &IGURE AS IN &IGURE THE DATA WERE COMPARED TO THE PREDICTIONS OF THE 30- PURE "RAGG MODEL AND THE TWO SCALE MODEL WHILE ADDING THE TWO SCALE PLUS MODEL WHICH INCORPORATES THE EFFECTS OF BREAKING WAVES )N THIS CASE THE "RAGG MODEL AND THE TWO SCALE MODEL DERIVED FROM IT CLEARLY FAIL TO DESCRIBE THE OBSERVED BEHAVIOR OF THE POLARIZATION RATIO WHILE THE INCLUSION OF BREAKING WAVES FULL MODEL PROVIDES A SURPRISINGLY FAITHFUL REPRODUCTION OF THE DATA EVEN AT THE HIGH GRAZING ANGLE OF 4HE 8 BAND DATA ILLUSTRATED PREVIOUSLY IN &IGURE A B CAN ALSO BE SHOWN TO CORROBORATE THE PREDICTIONS OF THIS MODEL FOR A SIMILAR WIND SPEED AND GRAZING ANGLE THUS FURTHER SUPPORTING THE SUSPICION THAT BREAKING WAVE EVENTS WILL CONTRIBUTE IMPORTANTLY TO SEA CLUTTER OVER MOST OF THE hROUGH SURFACEv REGIME OF GRAZ ING ANGLES AT THESE WIND SPEEDS
&)'52% 0OLARIZATION RATIO VERSUS WIND DIRECTION FOR 8 BAND RADAR AT GRAZING ANGLE AND WIND ABOUT KT 0OINTS EXPERIMENTAL DATA FROM 0OLRAD EXPERIMENT DASHED LINE PURE 30- "RAGG DASHED DOTTED LINE TWO SCALE "RAGG SOLID LINE TWO SCALE PLUS MODEL INCLUDING BREAKING WAVES AFTER +UDRYATSEV ET AL Ú 4HE !MERICAN 'EOPHYSICAL 5NION
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3CATTERING BY 3URFACE &EATURES ! BREAKING WAVE WITH PLUMES OF WATER CAS CADING DOWN ITS FACE AND PERHAPS A HALO OF SPRAY ABOVE IS ONLY ONE OF THE RICH ASSORT MENT OF SCATTERING ELEMENTS APPEARING ON THE SEA SURFACEINCLUDING WEDGES CUSPS MICROBREAKERS HYDRAULIC SHOCKS PATCHES OF TURBULENCE AND GRAVITY CAPILLARY WAVES BOTH WIND DRIVEN AND PARASITIC ANY OR ALL OF WHICH COULD CONTRIBUTE TO THE SCATTERED CLUTTER SIGNAL &OR EXAMPLE THE COMMON 3TOKES WAVE HAS A QUASI TROCHOIDAL STRUCTURE THAT RESEM BLES A WEDGE ON THE SURFACE SO WEDGE SCATTER MIGHT DESCRIBE AN IMPORTANT ASPECT OF SEA CLUTTER 4HE SCATTERING MODEL IS USUALLY SOME VARIANT OF THE FAMILIAR GEOMETRICAL THEORY OF DIFFRACTION '4$ WHICH IS STRICTLY APPLICABLE TO THE BACKSCATTER PROBLEM ONLY WHEN THE EDGE OF THE WEDGE IS NORMAL TO THE PLANE OF INCIDENCE .EVERTHELESS THE CROSS SECTION PREDICTIONS AT THE LOWER GRAZING ANGLES FOR BOTH POLARIZATIONS SHOW TRENDS SIMILAR TO THE PREDICTIONS OF THE "RAGG OR COMPOSITE SURFACE MODELS /NE MAJOR PROBLEM WITH ALL MODELS BASED ON SCATTERING FEATURE SIMULATIONS IS THE LACK OF RELIABLE INFORMATION ABOUT THE SHAPES SIZES ORIENTATIONS SPEEDS LIFETIMES AND STATISTICS OF THE FEATURES THEMSELVES 4HUS ALTHOUGH THERE IS OFTEN GUIDANCE FROM EITHER OBSERVATION OR THEORY THE PREDICTIONS OF SUCH MODELS WILL BE BASED ON UNCERTAIN ASSUMPTIONS ABOUT THESE CRUCIAL PARAMETERS !S AN EXAMPLE WATER SURFACE STABILITY ARGUMENTS PREVENT THE INTERIOR ANGLE OF A SHARPENING WAVE CREST FROM FALL ING BELOW WHICH THEN BECOMES A CONVENIENT MEASURE OF THE WEDGE ANGLE IN WEDGE SCATTERING MODELS )N &IGURE THE OVERALL SCALE OF WEDGE SCATTERING AS CALCULATED BY THE '4$ WAS ADJUSTED TO LOCATE THE CLUSTER OF CROSS SECTIONS AT THE LEVEL OF THE EXPERIMENTAL VALUES 7EDGES APPEAR TO MODEL THE QUALITATIVE BEHAVIOR WITH BOTH POLARIZATIONS FAIRLY WELL AT THE LOWER GRAZING ANGLES &IGURE ALSO INCLUDES TWO ADDITIONAL SIMPLE SCATTERING MODELS FOR COMPARISON ,AMBERTS LAW MENTIONED IN CONNECTION WITH &IGURE A B EXPRESSES THE CROSS SEC TION IN THE FORM R ! SINX WHERE ! IS THE SURFACE ALBEDO #HOOSING ! D" A REASONABLE VALUE FOR MICROWAVE FREQUENCIES GIVES A FAIRLY GOOD MATCH TO THE VERTI CALLY POLARIZED RETURNS OVER A WIDE RANGE OF GRAZING ANGLES 4HE FACET MODEL EXPRESSED
&)'52% #OMPARISON OF SEVERAL AD HOC FEATURE MODELS WITH .2, &2 DATA DATA THE SAME AS SHOWN IN &IGURE
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BY %Q AND THOUGHT TO DESCRIBE CLUTTER AT THE HIGHER GRAZING ANGLES IS SHOWN FOR KT SEAS 4HE GENERAL BEHAVIOR DESCRIBED BY THESE TWO MODELS SEEMS TO AGREE ABOUT AS WELL AS ANY OTHER ALTHOUGH THEY TOO MUST EMPLOY ARBITRARY ASSUMPTIONS TO OBTAIN REASONABLE FITS TO THE DATA SO THE SIGNIFICANCE OF THIS AGREEMENT IS DIFFICULT TO ASSESS (OWEVER ONE MIGHT DEDUCE FROM &IGURE THAT SHARP THINGS LIKE WEDGES DOMINATE THE CLUTTER AT SMALL GRAZING ANGLES FLAT THINGS LIKE FACETS AT LARGE ANGLES AND GENERALLY ROUGH THINGS AT THE INTERMEDIATE ANGLES 4HE THEORY OF SCATTERING FROM BREAKING WAVES REFERENCED IN CONNECTION WITH &IGURE WAS ORIGINALLY MOTIVATED BY AN ATTEMPT TO EXPLAIN THE COMPLEX BEHAVIOR OF SEA SPIKES AT LOW GRAZING ANGLES OBSERVED BY ,EWIS AND /LIN 4HIS THEORY WAS BASED ON THE PLUME MODEL OF THE MOST COMMON SPILLING BREAKER IN WHICH A WATER PLUME IS EMITTED AT THE SPILLING CREST AND MOVES DOWN THE FRONT FACE THE SCATTERING BEHAVIOR WAS SUPPLIED BY MULTIPATH ILLUMINATION INVOLVING REFLECTIONS FROM THE FACE OF THE WAVE 4HE ELABORATION OF THIS MODEL EXPLAINED MUCH OF THE COMPLEX BEHAVIOR OF THE OBSERVED SEA SPIKES HOWEVER LIKE ALL OTHER MODELS BASED ON SCATTERING FEATURES IT WAS NECESSARY TO MAKE ASSUMPTIONS ABOUT THE SIZES SHAPES AND LIFETIMES OF THE SCATTERING PLUMES 4HESE PARAMETERS WERE ALL INFERRED FROM OBSERVATION OF REAL SEA SURFACES AND THE RESULTING PREDICTIONS WERE SURPRISINGLY GOOD !DDITIONALLY ITS SUCCESS IN THE TWO SCALE PLUS MODEL MENTIONED ABOVE PROVIDES FURTHER CREDIBILITY !LTHOUGH SCATTERING FEATURES HAVE BEEN INTRODUCED MAINLY IN CONNECTION WITH LOW GRAZING ANGLE SEA CLUTTER SEE 7ETZEL FOR A DETAILED DISCUSSION THERE IS EVI DENCE AS NOTED ABOVE TO BELIEVE THAT FEATURE SCATTERING OPERATES AT ALL GRAZING ANGLES #ONSIDERING THE FAILURE OF SCATTERING THEORIES FORMULATED AS A '"60 TO PROVIDE ANY PREDICTIONS BEYOND THOSE IN CERTAIN LIMITING CASE APPROXIMATIONS AND THE PRECARIOUS NATURE OF THE LOGICAL INFRASTRUCTURE OF THE "RAGG HYPOTHESIS IN MICROWAVE SCATTERING FROM A NATURAL SEA IT IS QUITE POSSIBLE THAT FURTHER CAREFUL CONSIDERATION OF THE ACTUAL SCATTERING FEATURES PRESENT ON THE SEA SURFACE WILL IMPROVE OUR UNDERSTANDING OF SEA CLUTTER IN THE FUTURE )MPLICATIONS OF 3URFACE 'EOMETRY 4HE APPROXIMATIONS TO THE '"60 DIS CUSSED ABOVE WERE ALL FORMULATED IN THE FREQUENCY DOMAIN BUT A TIME DOMAIN MODEL FOR SEA SCATTER POINTS TO A POSSIBLE GENERAL SURFACE GEOMETRIC ORIGIN FOR THE SURFACE RETURNS 4HE MODEL INTRODUCES THE IDEA THAT THE BASIC SCATTERING ELEMENTS OF A SURFACE ARE LOCALIZED AT POINTS OF HIGH SURFACE CURVATURE AS AT THE SHARP TIPS OF SMALL 3TOKES WAVES OR AT THE CORNER OF A PLUME INTERSECTING THE FRONT FACE OF A BREAKING WAVE 5SING A C FUNCTION AS A PROBING PULSE AN APPROXIMATE EXPRESSION FOR THE SCAT TERING CROSS SECTION WAS FOUND AS A FUNCTION OF SURFACE CURVATURE # RTO WHERE TO IS THE ROUND TRIP TIME FROM THE RADAR TO A POINT RTO ON THE SURFACE
R TO "X S TO # CTO COSX
WITH " A COMPLICATED TRIGONOMETRIC FUNCTION OF GRAZING ANGLE X SURFACE SLOPE S AND TO 4HE FACTOR " PEAKS AT POINTS OF SPECULAR REFLECTION SO %Q EXPRESSES THE EFFECTS OF SPECULAR GLINTS AS WELL AS SHARP CURVATURES !LTHOUGH THE ORIGINAL THEORY IS BASED ON A PHYSICAL OPTICS FORMULATION FOR A SCALAR FIELD SEE 3ANGSTON FOR THE VECTOR FORM SOME SUPPORT FOR ITS IMPLICATIONS CAN BE GAINED FROM A PLOT OF THE SQUARE OF SURFACE CURVATURE OVER A REAL SEA SURFACE &IGURE A SHOWS THE SURFACE SLOPE MEASURED OVER A SHORT SEGMENT OF SURFACE IN THE 'ULF 3TREAM WITH THE CORRESPOND ING CURVATURE SQUARED PROFILE BELOW 4HE CLUTTER CROSS SECTION DEFINED FOR THIS PROFILE
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&)'52% A -EASURED SLOPE TOP CURVE OVER A SAMPLED SURFACE IN THE 'ULF 3TREAM WITH THE COR RESPONDING SQUARE OF THE SURFACE CURVATURE BELOW B 7AVE TANK MEASUREMENT OF RADAR SCATTERING FROM AN EVOLVING BREAKING WAVE CORRELATED WITH WAVE SURFACE HEIGHT VARIATIONS FROM - ! 3LETTEN AND * # 7EST Ú 4HE !MERICAN 'EOPHYSICAL 5NION
BY %Q CLEARLY BEARS A RESEMBLANCE TO SOME OF THE HIGH RESOLUTION RETURNS SHOWN IN &IGURE -OREOVER THESE SPIKY RETURNS ARE CORRELATED WITH JUST THE KIND OF SURFACE BUMPS AND WRINKLES AND SLOPE DISCONTINUITIES THAT HAVE BEEN IDENTIFIED AS SOURCES OF SEA SPIKES IN LABORATORY TANK MEASUREMENTS !N EXAMPLE IS SHOWN IN &IGURE B WHERE AN ULTRA HIGH RESOLUTION RADAR LOOKS AT THE RETURN FROM A BREAKING WAVE WHOSE SURFACE IS EVOLVING AS PLOTTED ABOVE THE RADAR SIGNAL 7E SEE THAT THE SPIKES APPEAR AT THE POINTS OF MAXIMUM SURFACE CURVATURE ALTHOUGH THE LARGE SIGNAL PEAK IS PROBABLY A SPECULAR REFLECTION FROM THE INITIAL BREAKING FRONT )T IS OFTEN OVERLOOKED THAT THE PRESUMED ORIGIN OF SEA SCATTER IS SUGGESTED BY THE KIND OF MEASURING INSTRUMENT BEING USED WHICH IN TURN DETERMINES THE MOST APPRO PRIATE THEORETICAL BASISIE THE hTHEORY OF THE EXPERIMENTv )F YOU GO TO SEA WITH A #7 RADARAN hAVERAGING WAVE SPECTROMETERvYOU WILL BE SELECTING A SPECTRAL LINE BY LONG INTEGRATION TIMES AND INTERPRET THE ORIGIN AS A WAVE EFFECT NAMELY A h"RAGG RESONANCEv /N THE OTHER HAND IF YOU USE A HIGH RESOLUTION PROBEA RADAR MICROSCOPETHE CLUTTER SCENE WILL BE POPULATED BY HIGHLY LOCALIZED SCATTER ING EVENTS OR SEA SPIKES ISOLATED BY A SHORT PULSE WIDE BANDWIDTH SIGNAL )N THIS CASE THE MOST APPROPRIATE hTHEORY OF THE EXPERIMENTv IS THE TIME DOMAIN FORMALISM DESCRIBED ABOVE /THER WAYS OF VIEWING SEA CLUTTER IN TERMS OF SURFACE GEOMETRY CHARACTERIZE THE SEA AND THE CLUTTER AS FRACTAL PROCESSES OR SEEK PARAMETERS DESCRIBING ITS COMPLEXITY BY DEFINING A hSTRANGE ATTRACTORv 5NFORTUNATELY THESE STUDIES DO NOT SEEM TO CONTAIN ANY USEFUL INSIGHTS INTO THE PHYSICAL SCATTERING PROCESSES AT THE SURFACE EXCEPT PER HAPS TO CONCLUDE THAT SEA CLUTTER ARISES FROM MULTIPLE SOURCES WHICH WE ALREADY KNOW /N THE OTHER HAND THE IDENTIFICATION OF CHANGES IN THE CHARACTERISTIC MEASURES OF THESE PROCESSES EG FRACTAL DIMENSION AND EMBEDDING DIMENSION HAVE BEEN PROPOSED AS A WAY TO IDENTIFY THE PRESENCE OF TARGETS IN CLUTTER
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.UMERICAL -ETHODS 7ITH RAPID INCREASES IN COMPUTER SPEED IT HAS BECOME PRACTICAL TO SOLVE CERTAIN SCATTERING PROBLEMS BY NUMERICAL METHODS THEREBY SIDE STEPPING THE INTRODUCTION OF THE APPROXIMATIONS REQUIRED BY THE ANALYTICAL SOLUTIONS DESCRIBED ABOVE )N SURFACE SCATTERING PARTICULARLY FOR THE CONTINUOUS SEA SURFACE THE METHOD OF CHOICE APPEARS TO BE SOME VARIANT OF THE -ETHOD OF -OMENTS !N EXACT INTEGRAL EQUATION FOR THE SURFACE CURRENTS EXCITED BY AN ILLUMINATING FIELD IS SOLVED NUMERICALLY OVER A GRID OF POINTS WHERE THE FLEXIBILITY AND ACCURACY OF THE SOLUTION DEPENDS ESSENTIALLY ON THE GRID SPACING THE SIZE OF THE SURFACE FEATURES COMPARED TO THE ILLUMINATING WAVELENGTH THE EXTENT OF THE SURFACE OVER WHICH THE GRID IS LAID AND THE EFFICIENCY OF THE COMPUTING ALGORITHMS USED IN WHAT ARE EXTENSIVE CALCULATIONS /NCE FOUND FOR AN ENSEMBLE OF SURFACE REALIZATIONS THESE CURRENTS CAN BE USED IN A SCATTERING INTEGRAL OVER EACH OF THE SURFACES TO GENERATE AN ENSEMBLE OF SCATTERED FIELDS WHICH ARE FINALLY AVERAGED INTO A SURFACE SCATTERING CROSS SECTION !LTHOUGH THESE METHODS ARE OFTEN VIEWED AS THE hGOLD STANDARDv FOR DOING SCATTERING CALCULATIONS THEIR COMPLEXITY AND DIFFICULTY GENERALLY RESTRICT THEIR APPLICATION TO IDEALIZED OR LABORATORY SURFACE STRUCTURES WHERE THEY SIMPLY CONFIRM THAT -AXWELLS EQUATIONS CONTINUE TO BE VERIFIED IN SCATTERING EXPERIMENTS .EVERTHELESS SUCH NUMERICAL SIMULATIONS CAN BE INFORMATIVE IN IDENTIFYING THE SOURCE OF PARTICULAR SCATTERING EVENTS SUCH AS SEA SPIKES ALONG WITH THEIR DEPENDENCE ON SUCH RADAR PARAMETERS AS GRAZING ANGLE POLARIZATION AND FREQUENCY 2OLE OF ,ABORATORY 3TUDIES 4HE SEA SURFACE IS A NATURAL SYSTEM CONTROLLED BY THE LAWS OF HYDRODYNAMICS "UT SO IS A BOWL OF SOUP OR A TANK OF WATER OR A RUSHING STREAMALL OF WHICH MIGHT SHARE CERTAIN BEHAVIORS WITH A SEA SURFACE WHILE PRE SENTING A VENUE MUCH MORE AMENABLE TO THE COMFORTABLE INVESTIGATION OF SCATTERING PHENOMENOLOGY 7HILE THERE IS THE OBVIOUS MATTER OF SCALE ONE MIGHT ENTERTAIN THE NOTION THAT WHAT IS FOUND TO HOLD IN THE SMALL COMPASS OF A LABORATORY WAVE TANK MIGHT TRANSFER WITH LITTLE ALTERATION TO THE OPEN OCEAN "UT THIS CERTAINLY CANNOT BE TRUE THE SEA SURFACE IS STRUCTURED BY LARGE SCALE WIND SYSTEMS IMPOSSIBLE TO DUPLICATE UNDER LABORATORY CONDITIONS 4HEREFORE THE LABORATORY IS USED ALMOST EXCLUSIVELY TO STUDY IN DETAIL HOW AN ELECTROMAGNETIC WAVE INTERACTS WITH SOME RESTRICTED AND WELL CONTROLLED ASPECT OF SURFACE PHENOMENOLOGY THAT IS THOUGHT TO BE INVOLVED IN THE OPEN SEA 4HERE IS A VAST LITERATURE EXTENDING OVER ALMOST YEARS REPORTING A WIDE VARIETY OF LABORATORY EXPERIMENTS ON MICROWAVE SCATTERING FROM A DISTURBED WATER SURFACE 4HE EARLIEST APPEAR TO BE CAREFUL SMALL SCALE EXPERIMENTS IN THE MID S TO CONFIRM THE EXISTENCE OF "RAGG SCATTER AT CENTIMETER WAVELENGTHS WHILE AT THE OTHER END OF THE EXPERIMENTAL SCALE THE CHAOS OF A FULL SCALE BREAKER WAS SIMULATED BY SUBMERGING A HYDROFOIL ACROSS A METER WIDE CIRCULATING WATER CHANNEL DRIVEN BY MEGAWATTS OF TURBINE POWER "UT MOST LABORATORY EXPERIMENTS ARE MORE MODEST INVOLVING A LONG WAVE TANK PERHAPS A METER OR TWO ACROSS WITH THE WAVE SYSTEM PRODUCED BY EITHER A CONTROLLED WIND OR A PROGRAMMED WAVEMAKER 4O ILLUSTRATE A FEW OF THE EXPERIMENTS AND THEIR RESULTS +WOH AND ,AKE MEASURED 8 BAND RETURNS FROM GENTLE BREAKING WAVES IN A WAVE TANK AND FOUND THAT SPECULAR AND CURVATURE SCATTERING APPEARED TO DOMINATE OVER "RAGG SCATTERING FOR SUCH SUR FACES +ELLER ET AL MEASURED 8 BAND RETURNS AND SURFACE SPECTRUM SIMULTANEOUSLY IN A WAVE TANK AND FOUND "RAGG BASED THEORIES MIGHT HAVE CREDENCE AT INTERMEDIATE GRAZING ANGLES AND STRONG WINDS BUT WERE UNABLE TO ACCOUNT FOR SCATTERING BEHAVIOR UNDER OTHER CONDITIONS 3LETTEN AND 7EST MADE A TWO PRONGED APPROACH TO BREAK ING WAVE SCATTER CONSTRUCTING A METALLIC MODEL OF A BREAKING WAVE COMPARING ITS
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SCATTERING PROPERTIES WITH NUMERICAL CALCULATIONS AND THEN GOING TO THE WAVE TANK TO VERIFY THE SCATTERING BEHAVIOR FOR REAL WATER WAVES %RICSON ET AL GENERATED A STATIONARY BREAKER IN A SMALL FLOW TUNNEL AND COMPARED ITS SCATTERING PROPERTIES WITH A SPECULAR POINT CALCULATION #OAKLEY ET AL SET UP A HYDROFOIL IN A POWERFUL WATER CHANNEL GENERATING A LARGE BREAKING WAVE FRONT THAT PRODUCED RADAR RETURNS CONSISTENT WITH ,AMBERTS ,AW ALONG WITH THE POLARIZATION RATIOS IMPLIED BY MULTIPATH REFLEC TIONS FROM THE UNDISTURBED FRONT FACE 4HESE INVESTIGATORS ALONG WITH MANY OTHERS HAVE BEEN EXPLORING RADAR SCATTERING FROM WATER SURFACES IN WAYS THAT CAN BE EXPECTED TO CONTRIBUTE SIGNIFICANTLY TO OUR GROWING UNDERSTANDING OF SEA CLUTTER
£x°xÊ -1 ,9Ê Ê " 1-" )N THE EARLY DAYS OF RADAR THE IMPORTANCE OF KNOWING THE SEA CLUTTER ENVIRONMENT LED TO MANY EXPERIMENTS UNDER A VARIETY OF CONDITIONS 6ARIATIONS IN QUALITY AND COMPLETE NESS OF GROUND TRUTH CALIBRATION OF THE EQUIPMENT AND THE EXPERIMENTERS EXPERI ENCE LED TO RESULTS THAT OFTEN SHOWED CONSIDERABLE INCONSISTENCY AND SUGGESTED CLUTTER BEHAVIOR THAT WAS SOMETIMES MORE A FUNCTION OF THE VAGARIES OF THE EXPERIMENT THAN OF THE PHYSICS OF THE CLUTTER !S DATA OF INCREASINGLY BETTER QUALITY ACCUMULATED IT MIGHT HAVE BEEN EXPECTED THAT THE BEHAVIOR OF SEA CLUTTER WOULD BE ESTABLISHED WITH INCREAS ING CONFIDENCE 4HIS HAS NOT ALWAYS BEEN SO LEAVING OUR GENERAL KNOWLEDGE ABOUT SEA CLUTTER TO BE SUMMARIZED ROUGHLY AS FOLLOWS &OR THE HIGHER OF WIND SPEEDS ENCOUNTERED OVER THE WORLDS OCEANS GREATER THAN ABOUT KT MICROWAVE SEA CLUT TER AT INTERMEDIATE TO HIGH GRAZING ANGLES HAS LITTLE DEPENDENCE ON FREQUENCY AND THE EFFECTS OF WIND SPEED ARE UNCERTAIN SEEMING TO DEPEND ON POLARIZATION WIND DIRECTION AND GRAZING ANGLE IN OFTEN CONFUSING WAYS 9ET VARIOUS EMPIRICAL DESCRIPTIONS AND STA TISTICAL CHARACTERIZATIONS ARE AVAILABLE THAT ALLOW MUCH OF THE USEFUL SEA CLUTTER REGIME TO BE DESCRIBED IN WAYS THAT CAN BE OF PRACTICAL VALUE TO THE RADAR COMMUNITY PROVIDED THAT SOME CARE IS TAKEN IN DEFINING AND OBSERVING THE PERTINENT PARAMETERS (OWEVER THERE ARE MAJOR AREAS OF UNCERTAINTY PRESENT AT ANY WIND SPEED WHENEVER THE GRAZING ANGLE GOES BELOW A FEW DEGREES AND THE SURFACE ILLUMINATION BEGINS TO FEEL THE EFFECTS OF REFRACTION AND DIFFRACTION AND AT ANY GRAZING ANGLE WHENEVER THE WIND SPEED IS LESS THAN ABOUT KT WHERE PECULIARITIES AND UNCERTAINTIES IN THE GENERATION OF SURFACE ROUGHNESS BEGIN TO EMERGE MOST STRONGLY !T THE LOW GRAZING ANGLES ENCOUNTERED IN MARITIME RADAR OPERATIONS SEA CLUTTER BECOMES SPIKY AND INTERMITTENT REQUIRING SPE CIAL ATTENTION TO SIGNAL PROCESSING AND THE INTERPRETATION OF THE RADAR SIGNAL -OREOVER FEATURES OF THE SEA ENVIRONMENT SUCH AS RAIN CURRENTS SLICKS AND REFRACTIVE ANOMALIES CAN CONFUSE THE RELIABLE SEPARATION OF TARGET RETURNS FROM CLUTTER ARTIFACTS 4HE QUESTION OF MICROWAVE SEA CLUTTER THEORY REMAINS UNSETTLED 4HE MOST POP ULAR MODEL THE TWO SCALE "RAGG MODEL IS ACTUALLY AN ASSEMBLAGE OF ASSUMPTIONS SUPPORTED BY CIRCUMSTANTIAL EVIDENCE THERE IS STILL NO CLEAR REASON WHY IT SHOULD WORK WHEN IT DOES )N FACT THERE IS INCREASING EVIDENCE FROM BOTH THE TANK AND THE OPEN OCEAN THAT THIS MODEL FAILS TO ACCOUNT FOR MANY ASPECTS OF MEASURED SEA SCATTER BEHAVIOR !UGMENTING IT WITH A TERM EXPRESSING THE EFFECT OF BREAKING WAVES IN ACTIVE SEAS HAS IMPROVED PREDICTIONS BUT STILL PERPETUATES THE AD HOC CHARACTER OF COM POSITE SURFACE MODELS 4HEORIES BASED ON SCATTERING BY SURFACE FEATURES HAVE BEGUN TO SHOW PROMISE AND AT LEAST ONE OF THESE FEATURESTHE BREAKING WAVE AT VARIOUS SCALES MACRO TO MICROIS INCREASINGLY RECOGNIZED AS AN IMPORTANT CONTRIBUTOR TO
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SEA CLUTTER FOR LOW GRAZING ANGLES AND SHORT PULSES IN PARTICULAR 4HE MAJOR PROBLEM OF CHARACTERIZING THESE FEATURES IN A MANNER USEFUL TO QUANTITATIVE PREDICTIONS IS STILL BEING ADDRESSED 0ERHAPS THE EXPRESSION OF THE SCATTERING PROPERTIES OF THE SURFACE IN TERMS OF AN INTRINSIC SURFACE PROPERTY LIKE ITS FINE SCALE CURVATURE MIGHT INTRODUCE AN ORGANIZING PRINCIPLE FOR THE MANY BITS AND PIECES THAT PRESENTLY MAKE UP THE THEORY OF SEA SCATTER )N THE LAST EDITION OF THIS (ANDBOOK THE FINAL STATEMENT IN THIS CHAPTER WAS h)T WILL BE INTERESTING TO SEE WHAT PROGRESS WILL HAVE BEEN MADE IN THE THEORY OF SEA CLUTTER BY THE PUBLICATION OF THE NEXT EDITION OF THIS HANDBOOKv )T APPEARS THAT THE ANSWER ISNOT MUCH "UT THERE IS SOME EVIDENCE THAT THE THEORY OF SEA SCATTER IS GRADUALLY BEING FREED FROM THE PARALYZING MONOTHEISM OF "RAGG SCATTER SO THERE IS HOPE FOR THE FUTURE
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>À`Ê °Ê Ài 4HE 5NIVERSITY OF +ANSAS
£È°£Ê /," 1 /" 2ADAR GROUND RETURN IS DESCRIBED BY R THE DIFFERENTIAL SCATTERING CROSS SECTION OR SCATTERING COEFFICIENT SCATTERING CROSS SECTION PER UNIT AREA RATHER THAN BY THE TOTAL SCATTERING CROSS SECTION R USED FOR DISCRETE TARGETS 3INCE THE TOTAL CROSS SECTION R OF A PATCH OF GROUND VARIES WITH THE ILLUMINATED AREA THAT IS DETERMINED BY THE GEOMETRIC RADAR PARAMETERS PULSE WIDTH BEAMWIDTH ETC R WAS INTRODUCED TO OBTAIN A COEF FICIENT INDEPENDENT OF THESE PARAMETERS 5SE OF A DIFFERENTIAL SCATTERING CROSS SECTION IMPLIES THAT THE RETURN FROM THE GROUND IS CONTRIBUTED BY A LARGE NUMBER OF SCATTERING ELEMENTS WHOSE PHASES ARE INDEPENDENT 4HIS IS PRIMARILY BECAUSE OF DIFFERENCES IN DISTANCE THAT ALTHOUGH SMALL FRACTIONS OF TOTAL DISTANCE ARE MANY WAVELENGTHS 3UPERPOSITION OF POWER IS POSSIBLE FOR THE COM PUTATION OF AVERAGE RETURNS )F THIS CONDITION IS NOT APPLICABLE TO A PARTICULAR GROUND TARGET THE DIFFERENTIAL SCATTERING CROSS SECTION CONCEPT HAS NO MEANING FOR THAT TARGET &OR EXAMPLE A VERY FINE RESOLUTION RADAR MIGHT BE ABLE TO RESOLVE A PART OF A CAR THE SMOOTH SURFACES ON THE CAR WOULD NOT BE PROPERLY REPRESENTED BY R /N THE OTHER HAND A COARSER RADAR MIGHT LOOK AT MANY CARS IN A LARGE PARKING LOT AND A VALID R FOR THE PARKING LOT COULD BE DETERMINED )F A REGION ILLUMINATED AT ONE TIME BY A RADAR CONTAINS N SCATTERING ELEMENTS AND THE ABOVE CRITERION IS SATISFIED SO THAT POWER MAY BE ADDED THE RADAR EQUATION FOR AVERAGE POWER BECOMES N
0R £ I
N 0TI'TI !RIS I 0TI'TI !RI S I $!I $!I £ P 2I P 2I I
(ERE $!I IS AN ELEMENT OF SURFACE AREA AND 0TI POWER TRANSMITTED TOWARD POINT I 'TI GAIN IN DIRECTION OF POINT I AND !RI RECEIVING EQUIVALENT APERTURE IN DIRECTION OF POINT I ARE VALUES OF 0T 'T AND !R APPROPRIATE FOR AN ELEMENT AT THE LOCATION OF $ !I 4HE FACTOR IN PARENTHESES IN THE NUMERATOR OF THE RIGHT HAND EXPRESSION IS THE INCRE MENTAL SCATTERING CROSS SECTION FOR ELEMENT I BUT THIS CONCEPT IS MEANINGFUL ONLY IN AN AVERAGE 4HUS THE AVERAGE POWER RETURNED IS GIVEN BY N
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(ERE R HAS BEEN USED TO DENOTE THE AVERAGE VALUE OF RI $ !I )N THIS FORMULATION WE MAY PASS IN THE LIMIT FROM THE FINITE SUM TO THE INTEGRAL GIVEN BY
0R
P
0' T T !RS D! ¯)LLUMINATED AREA 2
4HIS INTEGRAL IS NOT REALLY CORRECT FOR THERE IS A MINIMUM SIZE FOR REAL INDEPENDENT SCATTERING CENTERS .EVERTHELESS THE CONCEPT IS WIDELY USED AND IS APPLICABLE AS LONG AS THE ILLUMINATED AREA IS LARGE ENOUGH TO CONTAIN MANY SUCH CENTERS &IGURE ILLUSTRATES THE GEOMETRY ASSOCIATED WITH %Q .OTE THAT FOR A RECTAN GULAR PULSE 0T IS EITHER ZERO OR THE PEAK TRANSMITTER POWER BUT FOR OTHER PULSE SHAPES THE VARIATION WITH T OR 2 IS SIGNIFICANT !CTUAL PULSES ARE OFTEN APPROXIMATED BY RECTANGULAR PULSES WITH WIDTHS EQUAL TO THEIR HALF POWER WIDTHS 2EAL PULSES CANNOT BE RECTANGULAR AFTER PASSING THROUGH REAL TRANSMITTER ANTENNA AND RECEIVER BANDWIDTHS 4HE TRANSMITTING ANTENNA GAIN AND RECEIVING ANTENNA APERTURE ARE FUNCTIONS OF THE ELEVATION AND AZIMUTH ANGLES
'T 'TP E !R !RP E
A
4HE DIFFERENTIAL SCATTERING CROSS SECTION ITSELF IS A FUNCTION OF BOTH LOOK ANGLE P E AND GROUND LOCATION
R R P E LOCATION
B
4HE INTEGRAL OF %Q MUST BE INVERTED WHEN R IS MEASURED 7ITH NARROW BEAMS AND SHORT PULSES THE INVERSION IS RELATIVELY EASY BUT WITH THE WIDER BEAMS AND LON GER PULSES USED IN MANY MEASUREMENTS THE VALUES OBTAINED ARE SOMETIMES POORLY DEFINED 3OME AUTHORS USE A SCATTERING CROSS SECTION PER UNIT PROJECTED AREA RATHER THAN PER UNIT GROUND AREA &IGURE ILLUSTRATES BY USING A SIDE VIEW THE DIFFERENCE
&)'52% 'EOMETRY OF THE RADAR EQUATION
'2/5.$ %#(/
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&)'52% 'ROUND AREA AND PROJECTED AREA
BETWEEN GROUND AREA AND PROJECTED AREA 4HE GROUND AREA IS PROPORTIONAL TO $Q AND THE PROJECTED AREA IS SMALLER 4HUS
S ! G D PROJECTED AREA G COSQ D! OR
S G COSQ
3INCE BOTH F AND R ARE CALLED SCATTERING COEFFICIENTS READERS OF THE LITERATURE MUST BE ESPECIALLY CAREFUL TO DETERMINE WHICH IS BEING USED BY A PARTICULAR AUTHOR 2ADAR ASTRONOMERS USE A DIFFERENT R
TOTAL RETURN POWER FROM ENTIRE SURFACE POWER RETURNNED FROM PERFECT ISOTROPICSPHERE OF SAME RADIUS
4HE RESULTING VALUE FOR R IS USUALLY MUCH SMALLER THAN R FOR THE PLANET AT VERTICAL INCIDENCE AND IS LARGER THAN THE VALUES OF R NEAR GRAZING INCIDENCE RETURN FROM THE LIMB OF THE PLANET 2ELATIVE )MPORTANCE OF 4HEORY AND %MPIRICISM 4HE THEORY OF RADAR GROUND RETURN HAS BEEN THE SUBJECT OF MANY PUBLICATIONS 4HE VARIOUS THEORIES INSOFAR AS THEY CAN BE CONFIRMED BY EXPERIMENT PROVIDE BASES FOR JUDGING THE EFFECTS OF VARIA TIONS IN THE DIELECTRIC PROPERTIES OF THE GROUND OF THE ROUGHNESS OF THE GROUND AND NATURE OF VEGETATIVE OR SNOW COVER OF RADAR WAVELENGTH AND OF ANGLE OF INCIDENCE 6IEWED AS AIDS TO INSIGHT RADAR GROUND RETURN THEORIES CAN BE EXTREMELY USEFUL 4HE VALIDITY OF ANY GROUND RETURN THEORY MUST DEPEND ON THE MATHEMATICAL MODEL USED TO DESCRIBE THE SURFACE AS WELL AS ON THE APPROXIMATIONS REQUIRED TO OBTAIN ANSWERS %VEN THE SIMPLEST GROUND SURFACE THE SEA IS EXTREMELY DIFFICULT TO DESCRIBE ACCURATELY IT IS HOMOGENEOUS TO BEYOND THE SKIN DEPTH CONTAINS RELATIVELY MODEST SLOPES AND EXCEPT FOR SPRAY HAS NO PART ABOVE ANOTHER PART OF THE SURFACE !T GRAZING ANGLES SHADOWING OF ONE WAVE BY ANOTHER MIGHT OCCUR ,AND SURFACES ARE MUCH MORE DIFFICULT TO DESCRIBE )MAGINE AN ADEQUATE MATHEMATICAL DESCRIPTION OF THE SHAPE OF A FOREST WHEN EVERY LEAF AND PINE NEEDLE MUST BE DESCRIBED &URTHERMORE LAND SURFACES ARE SELDOM HOMOGENEOUS EITHER HORIZONTALLY OR WITH DEPTH 3INCE A TRUE MATHEMATICAL DESCRIPTION OF THE GROUND SURFACE APPEARS OUT OF THE QUES TION EMPIRICAL MEASUREMENTS ARE NECESSARY TO DESCRIBE THE RADAR RETURN FROM NATURAL SURFACES 4HE ROLE OF THEORY IS TO AID IN INTERPRETING THESE MEASUREMENTS AND TO SUGGEST HOW THEY MAY BE EXTRAPOLATED
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!VAILABLE 3CATTERING )NFORMATION 0RIOR TO THE LACK OF COORDINATED RESEARCH PROGRAMS OVER THE NECESSARY LONG PERIOD RESULTED IN ONLY ONE REALLY USABLE SET OF MEASUREMENTS DEVELOPED AT /HIO 3TATE 5NIVERSITY 3INCE THAT TIME EXTEN SIVE MEASUREMENTS HAVE BEEN MADE FROM TRUCKS AND HELICOPTERS BY THE 5NIVERSITY OF +ANSAS GROUPS IN THE .ETHERLANDS AND SEVERAL GROUPS IN &RANCE 4HESE MEASUREMENTS CONCENTRATED ESPECIALLY ON VEGETATION WITH THE +ANSAS MEASUREMENTS ALSO INCLUDING SOME WORK ON SNOW AND EXTENSIVE WORK ON SEA ICE -OST OF THESE MEA SUREMENTS WERE IN THE TO RANGE OF INCIDENCE ANGLES -EASUREMENTS NEAR VERTI CAL ARE SCARCER 7ELL CONTROLLED EXPERIMENTS NEAR GRAZING ARE ALSO SCARCE EXCEPT FOR A MAJOR ,INCOLN ,ABORATORY PROGRAM !IRBORNE MEASUREMENTS ARE NECESSARY TO MAKE LARGER SCATTERING AREAS ACCESSIBLE !LTHOUGH AIRBORNE PROGRAMS FOR SPECIAL PURPOSES HAVE BEEN LEGION CURVES OF SCATTER ING COEFFICIENT VERSUS ANGLE FOR A KNOWN HOMOGENEOUS AREA ARE SCARCE 4HE WORK AT THE -)4 2ADIATION ,ABORATORY WAS EARLY 7ORK BY 0HILCO #ORPORATION 'OODYEAR !EROSPACE #ORPORATION 'ENERAL 0RECISION ,ABORATORY AND THE 53 .AVAL 2ESEARCH ,ABORATORY .2, n PROGRAMS WERE IMPORTANT EARLY ON 4HE #ANADA #ENTRE FOR 2EMOTE 3ENSING ##23 HAS MADE NUMEROUS AIRBORNE AND GROUND BASED SCATTEROM ETER MEASUREMENTS ESPECIALLY OVER SEA ICE 4HE %NVIRONMENTAL 2ESEARCH )NSTITUTE OF -ICHIGAN %2)- ##23 THE %UROPEAN 3PACE !GENCY %3! AND THE *ET 0ROPULSION ,ABORATORY *0, USED IMAGING SYNTHETIC APERTURE RADARS 3!2S FOR SOME SCATTERING MEASUREMENTS BUT MOST WERE NOT WELL CALIBRATED 3INCE THE ADVENT OF SPACEBORNE 3!2S 3)2 ! " AND # %23 AND 2ADARSAT %NVISAT *%23 AND OTHERS HUNDREDS OF PAPERS HAVE APPEARED DEALING WITH MEASUREMENTS OF SCATTERING AND RADAR APPLICATIONS -OREOVER THE *0, !)23!2 HAS FLOWN AROUND THE WORLD AND SEVERAL OTHER AIRBORNE 3!2S FOR REMOTE SENSING HAVE APPEARED IN VARIOUS COUN TRIES WITH HUNDREDS OF RESULTING PAPERS 4HE READER SHOULD SEARCH THE LITERATURE FOR THESE RESULTS WHICH ARE FAR TOO NUMEROUS TO REFERENCE HERE -ANY OF THE MORE RECENT 3!2Sn ALSO PROVIDE INFORMATION ON POLARIMETRIC RESPONSES 2ESULTS OF MOST OF THESE MEASUREMENTS ARE SUMMARIZED IN 5LABY -OORE AND &UNG AND 5LABY AND $OBSON -ORE COMPLETE SUMMARIES OF THE EARLIER WORK AND NEAR GRAZING STUDIES ARE IN ,ONG AND IN THE WORK OF "ILLINGSLEY -ANY APPLICA TION SUMMARIES ARE ALSO IN THE -ANUAL OF 2EMOTE 3ENSING 2EADERS REQUIRING MORE DETAILED INFORMATION SHOULD CONSULT THESE BOOKS
£È°ÓÊ *, / ,-Ê / ÊÊ ,"1 Ê, /1, 2ADAR RETURN DEPENDS UPON A COMBINATION OF SYSTEM PARAMETERS AND GROUND PARAMETERS 2ADAR SYSTEM PARAMETERS %QS AND A AND B 7AVELENGTH 0OWER )LLUMINATED AREA $IRECTION OF ILLUMINATION BOTH AZIMUTH AND ELEVATION 0OLARIZATION INCLUDING THE FULL POLARIZATION MATRIX WHEN AVAILABLE 'ROUND PARAMETERS #OMPLEX PERMITTIVITY CONDUCTIVITY AND PERMITTIVITY 2OUGHNESS OF SURFACE )NHOMOGENEITY OF SUBSURFACE OR COVER TO DEPTH WHERE ATTENUATION REDUCES WAVES TO NEGLIGIBLE AMPLITUDE
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$IFFERENT WAVELENGTHS ARE SENSITIVE TO DIFFERENT ELEMENTS ON THE SURFACE /NE OF THE EARLIEST KNOWN AND MOST STRIKING DIRECTIONAL EFFECTS IS THE CARDINAL POINT EFFECT IN RETURNS FROM CITIES 2ADARS LOOKING IN DIRECTIONS ALIGNED WITH PRIMARY STREET GRIDS OBSERVE STRON GER REGULAR RETURNS THAN RADARS AT OTHER ANGLES (ORIZONTALLY POLARIZED WAVES ARE REFLECTED BETTER BY HORIZONTAL WIRES RAILS ETC THAN ARE VERTICALLY POLARIZED WAVES 6ERTICALLY POLARIZED WAVES ARE REFLECTED BETTER FROM VERTICAL STRUCTURES SUCH AS TREE TRUNKS AT LEAST WHEN THE WAVELENGTH IS COMPARABLE OR LARGER THAN THE TRUNK DIAMETER )F THE GEOMETRY OF TWO RADAR TARGETS WERE THE SAME THE RETURNS WOULD BE STRONGER FROM THE TARGET WITH HIGHER COMPLEX PERMITTIVITY BECAUSE LARGER CURRENTS DISPLACEMENT OR CONDUCTION WOULD BE INDUCED IN IT "ECAUSE IDENTICAL GEOMETRIES WITH DIFFERING PERMIT TIVITIES DO NOT OCCUR IN NATURE THIS DISTINCTION IS NOT EASY TO MEASURE %FFECTIVE PERMITTIV ITY FOR GROUND TARGETS IS VERY STRONGLY INFLUENCED BY MOISTURE CONTENT SINCE THE RELATIVE PERMITTIVITY OF LIQUID WATER IS FROM ABOUT AT 8 BAND TO ABOUT AT 3 BAND AND LONGER WAVELENGTHS WHEREAS MOST DRY SOLIDS HAVE PERMITTIVITIES LESS THAN !TTENUATION IS ALSO STRONGLY INFLUENCED BY MOISTURE SINCE WET MATERIALS USUALLY HAVE HIGHER CONDUCTIVITY THAN THE SAME MATERIALS DRY &IGURES AND SHOW THE EFFECT OF MOISTURE CONTENT ON PROPERTIES OF PLANTS AND OF SOIL 4HE HIGH PERMITTIVITY OF PLANTS WITH MUCH MOISTURE MEANS THAT RADAR RETURN FROM CROPS VARIES AS THE PLANTS MATURE EVEN WHEN GROWTH IS NEGLECTED
&)'52% -EASURED MOISTURE DEPENDENCE OF THE DIELECTRIC CONSTANT OF CORN LEAVES AT AND '(Z 3 IS THE SALINITY OF WATER CONTENT IN PARTS PER THOUSAND DV DV JDVp IS THE COMPLEX DIELECTRIC CONSTANT IN &M AND MV IS THE VOLUMETRIC MOISTURE CONTENT IN KGM AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
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&)'52% !PPARENT RELATIVE DIELECTRIC CONSTANT VERSUS MOISTURE CONTENT 2ICHFIELD SLIT LOAM AFTER * 2 ,UNDIEN
4HE ROUGHNESS OF SURFACES ESPECIALLY NATURAL ONES IS DIFFICULT TO DESCRIBE MATH EMATICALLY BUT EASY TO UNDERSTAND QUALITATIVELY 4HUS IT IS EASY TO SEE THAT A FRESHLY PLOWED FIELD IS ROUGHER THAN THE SAME FIELD AFTER RAIN AND WIND HAVE BEEN AT WORK ON IT ! FOREST IS INHERENTLY ROUGHER THAN EITHER A FIELD OR A CITY )T IS HARDER TO SEE THE DIFFERENCE BETWEEN THE ROUGHNESS OF NATURAL AREAS AND THE ROUGHNESS OF A CITY THAT HAS FLAT WALLS INTERSPERSED WITH WINDOW SILLS AND WITH CURBS CARS AND SIDEWALKS 3URFACES THAT ARE RELATIVELY SMOOTH TEND TO REFLECT RADIO WAVES IN ACCORDANCE WITH THE &RESNEL REFLECTION DIRECTION SO THEY GIVE STRONG BACKSCATTER ONLY WHEN THE LOOK ANGLE IS NEARLY NORMAL TO THE SURFACES 2OUGH SURFACES ON THE OTHER HAND TEND TO RERADIATE NEARLY UNIFORMLY IN ALL DIRECTIONS AND SO THEY GIVE RELATIVELY STRONG RADAR RETURNS IN ANY DIRECTION 4HE PROBLEM OF RADAR SCATTER IS COMPLICATED BECAUSE WAVES PENETRATE SIGNIFICANT DISTANCES INTO MANY SURFACES AND VEGETATION CANOPIES AND INTERNAL REFLECTION AND SCATTER CONTRIBUTE TO THE RETURN -EASUREMENTS OF ATTENUATION FOR FIELD CROPS AND GRASSES SHOW THAT MOST OF THE RETURN IS FROM THE UPPER LAYERS WITH SOME CONTRIBUTION BY THE SOIL AND LOWER LAYERS IF THE VEGETATION IS NOT VERY DENSE !T # BAND AND HIGHER FREQUENCIES MOST OF THE SIGNAL RETURNED FROM TREES IS USUALLY FROM THE UPPER AND MIDDLE BRANCHES WHEN THE TREES ARE IN LEAF n ALTHOUGH IN WINTER THE SURFACE IS A MAJOR CONTRIBUTOR TO THE SIGNAL !T , BAND AND ESPECIALLY AT 6(& THE SIGNAL PENETRATES FARTHER SO TRUNKS AND THE GROUND CAN BE MAJOR CONTRIBUTORS EVEN WHEN THE TREES ARE LEAFED OUT !DDITIONAL PROBLEMS OCCUR NEAR GRAZING INCIDENCE "ECAUSE OF THE LOW ANGLE WITH THE SURFACE SHADOWING FREQUENTLY OCCURSSOME PARTS OF THE TARGET ARE OBSCURED BY INTERVENING PROJECTIONS SUCH AS HILLS AND BUILDINGS 0ARTS OF THE AREA THAT ARE SOME WHAT ELEVATED HAVE THE SIGNAL MODIFIED BY THE EFFECT OF MULTIPATH INTERFERENCE BETWEEN
!NGLE OF REFLECTION EQUALS ANGLE OF INCIDENCE
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THE DIRECT RAY AND ONE REFLECTED OFF THE GROUND 3INCE THE SCATTERING FROM RELATIVELY LEVEL SURFACES IS VERY SMALL ANY PROJECTION MAY GIVE A RETURN MUCH STRONGER THAN THE BACKGROUND THEREBY SKEWING THE STATISTICS SO A 2AYLEIGH DISTRIBUTION NO LONGER APPLIES TO THE AVERAGE SIGNAL /BJECTS SUCH AS TREES BUILDINGS FENCE POSTS AND POWER LINES GIVE LOCALIZED ECHOES STRONG RELATIVE TO THEIR SURROUNDINGS -OREOVER THE SIGNAL FROM SURFACES WITHOUT PROJECTIONS FALLS OFF VERY RAPIDLY FOR DEPRESSION ANGLES WITHIN A FEW DEGREES OF GRAZING 4HIS MEANS THAT THE EFFECT OF SMALL LOCAL SLOPES CAN BE VERY SIGNIFICANT IN MODULATING THE RETURN SIGNAL NOT JUST IN SHADOWING
£È°ÎÊ / ", / Ê " -ÊÊ Ê/ ,Ê //" $ESCRIPTIONS OF A 3URFACE -ANY THEORETICAL MODELS FOR RADAR RETURN FROM THE GROUND ASSUME A ROUGH BOUNDARY SURFACE BETWEEN AIR AND AN INFINITE HOMOGENEOUS HALF SPACE 3OME INCLUDE EITHER VERTICAL OR HORIZONTAL HOMOGENEITIES IN THE GROUND PROPERTIES AND IN VEGETATIVE OR SNOW COVERS 3URFACE DESCRIPTIONS SUITABLE FOR USE IN MATHEMATICAL MODELS ARE NECESSARILY GREATLY IDEALIZED &EW NATURAL GROUNDS ARE TRULY HOMOGENEOUS IN COMPOSITION OVER VERY WIDE AREAS $ESCRIPTIONS OF THEIR DETAILED SHAPE MUST BE SIMPLIFIED IF THEY ARE TO BE HANDLED ANALYTICALLY ALTHOUGH COMPUTERS PERMIT THE USE OF TRUE DESCRIPTIONS 6ERY FEW SUR FACES HAVE EVER BEEN MEASURED TO THE PRECISION APPROPRIATE FOR CENTIMETER WAVELENGTH RADARS EVEN FOR THESE THERE IS NO ASSURANCE THAT SCATTERING BOUNDARIES DO NOT EXIST WITHIN A SKIN DEPTH BENEATH THE SURFACE 3URFACES CONTAINING VEGETATION AND CONGLOM ERATE ROCKS ALMOST COMPLETELY DEFY DESCRIPTION 3TATISTICAL DESCRIPTIONS OF SURFACES ARE USED FOR MOST THEORIES SINCE A THEORY SHOULD BE REPRESENTATIVE OF SOME KIND OF SURFACE CLASS RATHER THAN OF A PARTICULAR SURFACE AND SINCE EXACT DESCRIPTION IS SO DIFFICULT 4HE STATISTICAL DESCRIPTIONS THEMSELVES MUST BE OVERSIMPLIFIED HOWEVER -ANY THEORIES ASSUME ISOTROPIC STATISTICS CERTAINLY NOT APPROPRIATE FOR PLOWED FIELDS OR GRIDDED CITIES -OST THEORIES ASSUME SOME KIND OF MODEL INVOLVING ONLY TWO OR THREE PARAMETERS STANDARD DEVIATION MEAN SLOPE CORRELA TION DISTANCE ETC WHEREAS NATURAL OR HUMAN MADE SURFACES SELDOM ARE SO SIMPLY DESCRIBED 4HE THEORIES FOR VEGETATION AND OTHER VOLUME SCATTERS HAVE MORE PARAMETERS &OR NEAR GRAZING CONDITIONS THE MODELS MUST ACCOUNT FOR SHADOWING 3IMPLIFIED -ODELS %ARLY RADAR THEORIES FOR GROUND RETURN ASSUMED AS IN OPTICS THAT MANY TARGETS COULD BE DESCRIBED BY A ,AMBERT LAW VARIATION OF INTENSITY THAT IS THE DIFFERENTIAL SCATTERING COEFFICIENT VARIES AS COSP WITH P BEING THE ANGLE OF INCI DENCE 4HIS hPERFECTLY ROUGHv ASSUMPTION WAS SOON FOUND WANTING ALTHOUGH IT IS A FAIR APPROXIMATION FOR THE RETURN FROM MANY VEGETATED SURFACES OVER THE MIDRANGE OF ANGLES OF INCIDENCE #LAPP DESCRIBED THREE MODELS INVOLVING ASSEMBLIES OF SPHERES WITH DIFFERENT SPACINGS AND EITHER WITH OR WITHOUT A REFLECTING GROUND PLANE 4HESE MODELS YIELD VARIATIONS FROM R INDEPENDENT OF ANGLE THROUGH R s COS P TO R s COS P 3INCE THE SPHERE MODELS ARE HIGHLY ARTIFICIAL ONLY THE RESULTING SCATTER LAWS NEED BE CONSID ERED -OST TARGETS GIVE RETURNS THAT VARY MORE RAPIDLY OVER PART OF THE INCIDENCE ANGLE REGIME THAN THESE MODELS ALTHOUGH FORESTS AND SIMILAR ROUGH TARGETS OF SOME DEPTH SOMETIMES GIVE SUCH SLOWLY VARYING RETURNS
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3INCE THESE ROUGH SURFACE MODELS USUALLY FAIL TO EXPLAIN THE RISE IN RETURN NEAR VERTICAL INCIDENCE OTHER SIMPLIFIED MODELS COMBINE ,AMBERTS LAW AND OTHER ROUGH SURFACE SCATTERING MODELS WITH SPECULAR REFLECTION AT VERTICAL INCIDENCE AND A SMOOTH CURVE IS DRAWN BETWEEN THE SPECULAR VALUE AND THE ROUGH SURFACE PREDICTION 3PECULAR REFLECTION IS DEFINED AS REFLECTION FROM A SMOOTH PLANE AND OBEYS THE &RESNEL REFLECTION LAWS !T NORMAL INCIDENCE THE SPECULAR REFLECTION COEFFICIENT IS THEREFORE
'2
HG H HG H
WHERE G AND GG ARE THE INTRINSIC IMPEDANCES OF AIR AND EARTH RESPECTIVELY 4HE FRACTION OF TOTAL INCIDENT POWER SPECULARLY REFLECTED FROM A ROUGH SURFACE IS
E PS H L
WHERE RH STANDARD DEVIATION OF SURFACE HEIGHT VARIATIONS AND K WAVELENGTH 3INCE THIS PROPORTION IS DOWN TO WHEN RH K O AND TO WHEN S H L P SIGNIFICANT SPECULAR REFLECTION IS SELDOM FOUND FOR THE CENTIMETER WAVELENGTHS GENERALLY USED FOR RADAR .EVERTHELESS A SIMPLIFIED MODEL LIKE THIS IS CONVENIENT FOR SOME PURPOSES /BSERVATION OF REFLECTED SUNLIGHT FROM RIPPLED WATER FROM ROADS AND FROM OTHER SMOOTH SURFACES LEADS TO THE POSTULATION OF A FACET THEORY 4HE ONLY SUNLIGHT REACH ING THE OBSERVER FROM SMOOTH SURFACES SUCH AS WATER IS THAT FROM FACETS FOR WHICH ANGLE OF INCIDENCE EQUALS ANGLE OF REFLECTION 4HUS THE OBSERVED LIGHT MAY BE DESCRIBED BY METHODS OF GEOMETRIC OPTICS 7HEN GEOMETRIC OPTICS IS USED TO DESCRIBE RADAR SCATTER THE SURFACE OF THE GROUND IS REPRESENTED BY SMALL FLAT PLANE SEGMENTS 2ADAR RETURN IS ASSUMED TO OCCUR ONLY FOR FACETS ORIENTED NORMAL TO THE RADAR NORMAL ORIENTATION IS REQUIRED FOR BACKSCATTER SO THAT THE REFLECTED WAVE RETURNS TO THE SOURCE 4HUS IF THE SLOPE DISTRIBUTION OF SUCH FACETS IS KNOWN THE FRACTION NORMAL TO A GIVEN DIVERGING BEAM CAN BE ESTABLISHED AND FROM THIS THE RETURN CAN BE OBTAINED 'EOMETRIC OPTICS ASSUMES ZERO WAVELENGTH AND SO THE RESULTS OF SUCH A THEORY ARE WAVELENGTH INDEPENDENT CLEARLY NOT IN ACCORD WITH OBSERVATION 4HE FACET MODEL FOR RADAR RETURN IS EXTREMELY USEFUL FOR QUALITATIVE DISCUSSIONS AND SO MODIFICATION TO MAKE IT FIT BETTER WITH OBSERVATION IS APPROPRIATE 4WO KINDS OF MODIFICATION MAY BE USED SEPARATELY OR JOINTLY CONSIDERING THE ACTUAL RERADIATION PATTERN OF FINITE SIZE FACETS AT FINITE WAVELENGTHS AND CONSIDERING THE EFFECT OF WAVE LENGTH ON ESTABLISHING THE EFFECTIVE NUMBER OF FACETS 4HUS THE SCATTER FROM A FACET MAY ACTUALLY OCCUR IN DIRECTIONS OTHER THAN THAT REQUIRING THAT ANGLE OF INCIDENCE EQUAL ANGLE OF REFLECTION &IGURE ILLUSTRATES THIS &OR LARGE FACETS COMPARED WITH WAVE LENGTH MOST OF THE RETURN OCCURS ALMOST AT NORMAL INCIDENCE WHEREAS FOR SMALL FACETS THE ORIENTATION MAY BE OFF NORMAL BY A CONSIDERABLE AMOUNT WITHOUT GREAT REDUCTION IN SCATTER !S THE WAVELENGTH IS INCREASED THE CATEGORY OF A GIVEN FACET CHANGES FROM LARGE TO SMALL EVENTUALLY THE FACET IS SMALLER THAN A WAVELENGTH AND ITS RERADIATION PATTERN SHAPE REMAINS ALMOST ISOTROPIC FROM THAT POINT -ANY FACETS THAT WOULD BE SEPARATE AT SAY A CM WAVELENGTH ARE COMBINED AT A M WAVELENGTH THE RESULT MAY BE A TRANSITION FROM ROUGH TO SMOOTH SURFACE BEHAVIOR &IGURE A SHOWS A NUMBER OF FACETS OF DIFFERENT SIZES CONTRIBUTING TO A RADAR RETURN
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&)'52% .ORMAL INCIDENCE RERADIATION PATTERNS OF FACETS
0HYSICAL /PTICS -ODELS 4HEORIES BASED ON APPLICATIONS OF THE +IRCHHOFF (UYGENS PRINCIPLE HAVE BEEN THOROUGHLY DEVELOPED n 4HE +IRCHHOFF APPROXI MATION IS THAT THE CURRENT FLOWING AT EACH POINT IN A LOCALLY CURVED OR ROUGH SURFACE IS THE SAME AS WOULD FLOW IN THE SAME SURFACE IF IT WERE FLAT AND ORIENTED TANGENT TO THE ACTUAL SURFACE 4HIS ASSUMPTION PERMITS CONSTRUCTION OF SCATTERED FIELDS BY ASSUMING THAT THE CURRENT OVER A ROUGH PLANE SURFACE HAS THE SAME MAGNITUDE AS IF THE SURFACE WERE SMOOTH BUT WITH PHASE PERTURBATIONS SET BY THE DIFFERING DISTANCES OF INDIVIDUAL
&)'52% A &ACET MODEL OF A RADAR RETURN
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POINTS FROM THE MEAN PLANE &OR SURFACES ASSUMED TO BE AZIMUTHALLY ISOTROPIC THE USUAL APPROACH YIELDS INTEGRALS OF THE FORM E KS H COSQ ; R X =* KX COSQ X DX COS Q ¯
WHERE QX P RH K *
SPATIAL AUTOCORRELATION FUNCTION OF SURFACE HEIGHTS ANGLE WITH VERTICAL STANDARD DEVIATION OF SURFACE HEIGHTS O K FIRST ORDER FIRST KIND "ESSEL FUNCTION
4HE AUTOCORRELATION FUNCTION OF HEIGHT WITH DISTANCE IS SELDOM KNOWN FOR TERRAIN ALTHOUGH IT CAN BE DETERMINED ON A LARGE SCALE BY ANALYSIS OF CONTOUR MAPS AND IT HAS BEEN FOUND FOR SOME AREAS BY CAREFUL CONTOURING AT CLOSE INTERVALS AND SUBSEQUENT ANALYSIS "ECAUSE OF LACK OF KNOWLEDGE OF ACTUAL AUTOCORRELATIONS MOST THEORY HAS BEEN DEVELOPED WITH ARTIFICIAL FUNCTIONS THAT ARE CHOSEN MORE FOR THEIR INTEGRABILITY THAN FOR THEIR FIT WITH NATURE SELECTION AMONG THEM HAS BEEN ON THE BASIS OF WHICH ONES YIELD THE BEST FIT BETWEEN THEORETICAL AND EXPERIMENTAL SCATTER CURVES 4HE CORRELATION FUNCTION FIRST USED WAS GAUSSIAN
QX E X ,
WHERE , IS THE CORRELATION LENGTH .OT ONLY IS THIS A FUNCTION THAT MAKES THE INTEGRAL ANALYTICALLY TRACTABLE BUT IT ALSO GIVES EXACTLY THE SAME RESULTS AS GEOMETRIC OPTICS 3INCE IT FAILS LIKE GEOMETRIC OPTICS TO EXPLAIN FREQUENCY VARIATION IT CANNOT BE A TRULY REPRESENTATIVE CORRELATION FUNCTION ALTHOUGH IT GIVES A SCATTERING CURVE THAT FITS SEVERAL EXPERIMENTAL CURVES NEAR THE VERTICAL 4HE NEXT MOST FREQUENTLY USED FUNCTION IS THE EXPONENTIAL
RX E \X\ ,
4HIS HAS SOME BASIS IN CONTOUR MAP ANALYSIS THE RESULTS FIT BOTH %ARTH AND LUNAR RADAR RETURN OVER A WIDER RANGE OF ANGLES THAN THE GAUSSIAN BUT SOMETIMES NOT AS WELL NEAR VERTICAL &URTHERMORE IT HAS THE MERIT THAT IT EXHIBITS FREQUENCY DEPEN DENCE 2ESULTING EXPRESSIONS FOR POWER SCATTERING COEFFICIENT VARIATIONS APPEAR IN 4ABLE
4!",% 3CATTERING #OEFFICIENT 6ARIATION
#ORRELATION COEFFICIENT
E X
,
E \X\ ,
0OWER %XPRESSION
2EFERENCE
+ , S H TAN Q E SIN Q
$AVIES
¤ +Q SIN Q ³ ! ¥ COS Q ´µ COS Q SIN Q ¦
6ORONOVICH
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3MALL 0ERTURBATION AND 4WO 3CALE -ODELS 2ECOGNITION THAT EXISTING MODELS WERE INADEQUATE FOR DESCRIBING OCEAN SCATTER LED TO RECOGNITION THAT RESONANCE OF THE SIGNAL WITH SMALL STRUCTURES ON THE SURFACE HAS A POWERFUL INFLUENCE ON THE STRENGTH OF THE SIGNAL RECEIVED 4HUS A SMALL PERTURBATION METHOD ORIGINALLY PROPOSED BY 2ICE BECAME THE MOST POPULAR WAY TO DESCRIBE OCEAN SCATTER )TS APPLICATION TO LAND SCATTER WAS NOT FAR BEHIND 4HE TERM "RAGG SCATTER IS OFTEN USED TO DESCRIBE THE MECHANISM FOR THE SMALL PERTURBATION MODEL 4HE IDEA COMES FROM THE CONCEPT ILLUSTRATED IN &IGURE B ! SINGLE SINUSOIDAL COMPONENT OF A COMPLEX SURFACE IS SHOWN WITH AN INCOMING RADAR WAVE AT ANGLE OF INCIDENCE P 4HE RADAR WAVELENGTH IS K AND THE SURFACE COMPONENT WAVELENGTH IS , 7HEN THE SIGNAL TRAVELS AN EXTRA DISTANCE K $2 BETWEEN THE SOURCE AND TWO SUCCESSIVE WAVE CRESTS THE PHASE DIFFERENCE BETWEEN THE ECHOES FROM SUCCESSIVE CRESTS IS SO THE ECHO SIGNALS ALL ADD IN PHASE )F THIS CONDITION IS SATISFIED FOR A PARTICULAR , AND P IT FAILS TO BE SATISFIED FOR OTHERS 4HUS THIS IS A RESONANT SELECTION FOR A GIVEN P OF A PARTICULAR COMPONENT OF THE SURFACE , 4HE STRENGTH OF THE RECEIVED SIGNAL IS PROPORTIONAL TO THE HEIGHT OF THIS COMPONENT AND TO THE NUMBER OF CRESTS ILLUMINATED BY THE RADAR )F THE SURFACE HAS AN UNDERLYING CURVATURE THE NUMBER OF ILLUMINATED CRESTS SATISFYING THE RESONANCE CRITERION MAY BE LIMITED BY THE LENGTH OF THE ESSENTIALLY FLAT REGION OTHERWISE IT IS LIMITED BY THE RADAR RESOLUTION 4HE THEORETICAL EXPRESSION FOR THE SCATTERING COEFFICIENT IS
S PQ K S COS Q \ A PQ \ 7 K SIN Q
WHERE P Q POLARIZATION INDICES ( OR 6 K O K THE RADAR WAVENUMBER @(( 2 &RESNEL REFLECTION COEFFICIENT FOR HORIZONTAL POLARIZATION
A 66 E R
SIN Q E R SIN Q ;E R COSQ E R SIN Q =
WHERE DR IS THE RELATIVE PERMITTIVITY D ` JD p AND @6( @(6 7K SIN P IS THE NORMALIZED ROUGHNESS SPECTRUM THE &OURIER TRANSFORM OF THE SURFACE AUTOCORRELATION FUNCTION )T MAY BE WRITTEN AS 7+ WHERE + IS THE WAVENUMBER FOR THE SURFACE )N TERMS OF THE WAVELENGTH ON THE SURFACE ,
+ O,
&)'52% B )N PHASE ADDITION FOR "RAGG SCATTERING $2 NK
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4HUS THE COMPONENT OF THE SURFACE THAT SATISFIES THE "RAGG RESONANCE CONDITION IS
, K SIN P
4HIS MEANS THAT THE MOST IMPORTANT CONTRIBUTOR TO A SURFACE RETURN IS THE COMPONENT OF SURFACE ROUGHNESS WITH WAVELENGTH , %VEN THOUGH OTHER COMPONENTS MAY BE MUCH LARGER THE "RAGG RESONANCE MAKES THIS COMPONENT MORE IMPORTANT /N THE OCEAN THIS MEANS THAT TINY RIPPLES ARE MORE IMPORTANT THAN WAVES THAT ARE METERS HIGH THE SAME APPLIES FOR LAND SURFACE SCATTER !S ORIGINALLY DEVELOPED THIS THEORY WAS FOR PERTURBATIONS TO HORIZONTAL FLAT SUR FACES BUT IT WAS SOON MODIFIED TO HANDLE SURFACES WITH LARGE SCALE ROUGHNESS 4HE LARGE SCALE ROUGHNESS WAS ASSUMED TO CAUSE A TILTING OF THE FLAT SURFACE TO WHICH THE SMALL PERTURBATION THEORY COULD BE APPLIED 4HE PRINCIPAL PROBLEM WITH THIS APPROACH IS DECIDING WHERE IN THE SURFACE SPECTRUM LIES THE BOUNDARY BETWEEN THE LARGER COMPO NENTS THAT DO THE TILTING AND SMALLER COMPONENTS THAT ARE "RAGG RESONANT -ANY PAPERS HAVE BEEN WRITTEN TO DESCRIBE THE EVOLUTION OF THIS THEORY FOR A COMPLETE SUMMARY THE READER IS REFERRED TO &UNGS DEVELOPMENT /THER -ODELS 4HE THEORY FOR VOLUME SCATTER HAS LED TO MANY PAPERS AND CON TINUES TO EVOLVE &OR A REVIEW OF SOME OF THE APPROACHES THE READER SHOULD CONSULT &UNGS SUMMARY AND PAPERS BY +ONG ,ANG &UNG AND 4SANG 4HESE MODELS HAVE BEEN USED REASONABLY SUCCESSFULLY TO DESCRIBE SCATTER FROM VEGETATION SNOW AND SEA ICE -ODELS OF STRAIGHT VEGETATION SUCH AS WHEAT IN TERMS OF CYLINDERS HAVE HAD SOME SUCCESS #ORNER REFLECTOR EFFECTS HAVE BEEN USED TO DESCRIBE STRONG RETURNS FROM BUILDINGS AT NON NORMAL INCIDENCE ANGLES /THER SPECIALIZED MODELS HAVE BEEN USED FOR PARTICULAR PURPOSES ,ATER THEORETICAL WORK FOR SURFACES INVOLVES SOLVING INTEGRAL EQUATIONS FOR THE SCAT TERED FIELDS 4HIS HAS BEEN USED BOTH TO VALIDATE OTHER MODELS AND TO BETTER DESCRIBE THE TRUE SCATTERING FROM A KNOWN ROUGH SURFACE 4HIS METHOD TENDS TO BE COMPUTATION ALLY EXTENSIVE .UMERICAL SCATTERING COMPUTATIONS ARE ALSO IN VOGUE 2EGARDLESS OF THE MODEL USED AND THE APPROACH APPLIED TO DETERMINING THE FIELD STRENGTH THEORETICAL WORK ONLY GUIDES UNDERSTANDING !CTUAL %ARTH SURFACES ARE TOO COM PLEX TO BE DESCRIBED ADEQUATELY IN ANY OF THE MODELS AND THE EFFECTS OF SIGNALS THAT PEN ETRATE THE GROUND AND ARE SCATTERED THEREIN ARE TOO LITTLE KNOWN TO PERMIT ITS EVALUATION
£È°{Ê Ê"Ê,"1 Ê " 4HE AMPLITUDE OF GROUND ECHOES RECEIVED BY RADARS ON MOVING VEHICLES FLUCTUATES WIDELY BECAUSE OF VARIATIONS IN PHASE SHIFT FOR RETURN FROM DIFFERENT PARTS OF THE ILLUMI NATED AREA )N FACT EVEN FIXED RADARS FREQUENTLY OBSERVE FLUCTUATIONS IN GROUND ECHOES BECAUSE OF MOTIONS OF VEGETATION WIRES BLOWING IN THE WIND ETC 4HIS FLUCTUATION IS REFERRED TO AS FADING &ADING IS SIGNIFICANT FOR THE RADAR ENGINEER BECAUSE ONE MUST ACCOUNT FOR THE FACT THAT A SINGLE SAMPLE OF THE RADAR RETURN MAY VARY WIDELY FROM THE MEAN DESCRIBED BY R 4HUS THE SYSTEM MUST BE ABLE TO HANDLE THE DYNAMIC RANGE OF FADING WHICH MAY EXCEED D" 2EGARDLESS OF THE MODEL USED TO DESCRIBE A GROUND SURFACE SIGNALS ARE IN FACT RETURNED FROM DIFFERENT POSITIONS NOT ON A PLANE !S A RADAR MOVES PAST A PATCH OF GROUND
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WHILE ILLUMINATING IT THE LOOK ANGLE CHANGES AND THIS CHANGES THE RELATIVE DISTANCES TO DIFFERENT PARTS OF THE SURFACE THE RESULT IS THAT RELATIVE PHASE SHIFT IS CHANGED 4HIS IS THE SAME KIND OF RELATIVE PHASE SHIFT CHANGE WITH DIRECTION THAT IS PRESENT FOR AN ANTENNA ARRAY AND RESULTS IN THE ANTENNA PATTERN &OR GROUND ECHO THE DISTANCE IS DOUBLED SO THE PATTERN OF AN ECHOING PATCH OF LENGTH , HAS LOBES OF WIDTH K, 4HIS COMPARES WITH K, FOR AN ANTENNA OF THE SAME CROSS RANGE LENGTH "ECAUSE THE EXCITATION OF THE ELEMENTS OF THE SCATTERING ARRAY IS RANDOM THE SCATTERING PATTERN IN SPACE IS ALSO RANDOM 4HIS FADING PHENOMENON IS USUALLY DESCRIBED IN TERMS OF THE DOPPLER SHIFT OF THE SIGNAL 3INCE DIFFERENT PARTS OF THE TARGET ARE AT SLIGHTLY DIFFERENT ANGLES THE SIGNALS FROM THEM EXPERIENCE SLIGHTLY DIFFERENT DOPPLER SHIFTS 4HE DOPPLER SHIFT OF COURSE IS SIMPLY THE RATE OF CHANGE OF PHASE DUE TO MOTION 4HUS THE TOTAL RATE OF CHANGE OF PHASE FOR A GIVEN TARGET IS
W W C W DI
DFI D W CT K2I DT DT
WHERE VC CARRIER ANGULAR FREQUENCY VDI DOPPLER ANGULAR FREQUENCY FOR ITH TARGET EI PHASE FOR ITH TARGET 2I RANGE FROM RADAR TO ITH TARGET 4HE DOPPLER SHIFT CAN BE EXPRESSED IN TERMS OF THE VELOCITY VECTOR V AS
W DI K
D2I 2 KV I KV COS V 2 I DT 2I
WHERE BOLD FACED LETTERS ARE VECTORS (ENCE THE TOTAL FIELD IS GIVEN BY
T ª § ¶¹ 2 % £ !I EXP « J ¨W C T ¯ K V I DT K2I ·º 2I ·¸» I ¬ ¨©
WHERE !I IS THE FIELD AMPLITUDE OF THE ITH SCATTERER AND 2I IS THE RANGE AT TIME ZERO 4HE ONLY REASON THE SCALAR PRODUCT VARIES FOR DIFFERENT SCATTERERS IS THE DIFFERENT ANGLE BETWEEN THE VELOCITY VECTOR AND THE DIRECTION TO THE SCATTERER 4HIS RESULTS IN A SEPARATE DOPPLER FREQUENCY FOR EACH SCATTERER )F WE ASSUME THE LOCATIONS TO BE RANDOM AS MOST THEORIES DO THE RECEIVED SIGNAL IS THE SAME AS ONE COMING FROM A SET OF OSCIL LATORS WITH RANDOM PHASES AND UNRELATED FREQUENCIES 4HIS SAME MODEL OF A GROUP OF RANDOMLY PHASED DIFFERENT FREQUENCY OSCILLATORS IS USED TO DESCRIBE NOISE THUS THE STATISTICS OF THE FADING SIGNAL AND THE STATISTICS OF RANDOM NOISE ARE THE SAME 4HIS MEANS THAT THE ENVELOPE OF THE RECEIVED SIGNAL IS A RANDOM VARIABLE WITH ITS AMPLITUDE DESCRIBED BY A 2AYLEIGH DISTRIBUTION 3UCH DISTRIBUTIONS HAVE BEEN MEA SURED FOR MANY GROUND TARGET ECHOES !LTHOUGH THE ACTUAL DISTRIBUTIONS VARY WIDELY NO BETTER DESCRIPTION CAN BE GIVEN FOR RELATIVELY HOMOGENEOUS TARGETS 7ITH A 2AYLEIGH DISTRIBUTION THE RANGE OF FADING IS ABOUT D" SO AN INDIVIDUAL PULSE RETURN MAY BE ANYWHERE IN THIS RANGE 7HEN A TARGET IS DOMINATED BY ONE LARGE ECHO SUCH AS A METAL ROOF ORIENTED TO GIVE A STRONG RETURN THE DISTRIBUTION IS BETTER DESCRIBED BY THAT FOR A SINE WAVE IN NOISE )F THE LARGE ECHO IS CONSIDERABLY STRONGER THAN THE MEAN OF THE REMAINING CONTRIBUTORS TO THE RETURN THIS APPROACHES A NORMAL DISTRIBUTION ABOUT THE VALUE FOR THE LARGE ECHO 4HIS SITUATION IS PARTICULARLY COMMON FOR NEAR GRAZING CONDITIONS
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&OR REFERENCE THE TWO DISTRIBUTIONS ARE GIVEN
P V DV
V V Y E DV Y
2AYLEIGH
P V DV
V V A Y ¤ AV ³ E ) ¥ ´ Y ¦Y µ
SINE WAVE 2AYLEIGH
WHERE V ENVELOPE VOLTAGE X MEAN SQUARE VOLTAGE ! SINE WAVE PEAK VOLTAGE )X "ESSEL FUNCTION FIRST KIND ZERO ORDER IMAGINARY ARGUMENT )N PRACTICE THE DISTRIBUTION FROM LARGE TARGETS MAY BE MORE COMPLICATED THAN EITHER OF THE SIMPLE MODELS DESCRIBED )NDEED PARTICULARLY NEAR GRAZING INCIDENCE THE SIGNAL IS OFTEN DESCRIBED BY A + A 7EIBULL OR A LOG NORMAL DISTRIBUTIONn 4HESE DISTRIBU TIONS ARE MORE OFTEN USED TO DESCRIBE THE VARIATIONS BETWEEN DIFFERENT RETURNS FROM AN AREA RATHER THAN FADING 4HEY MAY BE THOUGHT OF AS DESCRIBING WHAT HAPPENS WHEN THE AREA CONTAINS DIFFERENT R S AND THE DISTRIBUTION FOR EACH IS 2AYLEIGH "ECAUSE OF THIS THE RANGE OF VARIABILITY MAY BE EVEN GREATER THAN THE D" FOR A 2AYLEIGH DISTRIBUTION &ADING 2ATE #OMPUTATIONS $OPPLER FREQUENCY CALCULATION IS THE EASIEST WAY TO FIND FADING RATES 4O COMPUTE THE SIGNAL AMPLITUDE RETURNED WITH A PARTICULAR RANGE OF DOPPLER SHIFTS ALL SIGNALS HAVING SUCH SHIFTS MUST BE SUMMED 4HIS REQUIRES KNOW ING THE CONTOURS OF CONSTANT DOPPLER SHIFT ISODOPS ON THE SCATTERING SURFACE 4HESE CONTOURS MUST BE ESTABLISHED FOR EACH PARTICULAR GEOMETRIC ARRANGEMENT ! SIMPLE EXAMPLE IS PRESENTED HERE HORIZONTAL MOTION OVER A PLANE EARTH 4HIS IS TYPICAL OF AN AIRCRAFT IN ORDINARY CRUISING FLIGHT #ONSIDER TRAVEL IN THE Y DIRECTION WITH Z VERTICAL AND THE ALTITUDE FIXED Z H 4HEN
V Y V
2 X X Y Y Z H WHERE X Y Z ARE UNIT VECTORS (ENCE
VR V
2 2
VY
X Y H
WHERE VR IS THE RELATIVE SPEED #URVES OF CONSTANT RELATIVE SPEED ARE ALSO CURVES OF CONSTANT DOPPLER SHIFT 4HE EQUATION OF SUCH A CURVE IS
X Y
V VR H VR
4HIS IS A HYPERBOLA 4HE LIMITING CURVE FOR ZERO RELATIVE SPEED IS A STRAIGHT LINE PERPENDICULAR TO THE VELOCITY VECTOR &IGURE SHOWS SUCH A SET OF CONSTANT DOPPLER SHIFT CONTOURS
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&)'52% #ONTOURS OF CONSTANT DOPPLER FREQUENCY SHIFT ON A PLANE EARTH DUE TO HORIZONTAL MOTION
4HE SPECTRUM OF FADING CAN BE CALCULATED BY A SLIGHT REARRANGEMENT OF THE RADAR EQUATION %Q 4HUS IF 7R FD IS THE POWER RECEIVED BETWEEN FREQUENCIES FD AND FD DFD THE RADAR EQUATION BECOMES
7R FD DFD
P
AREAA ¯)LLUMINATED BETWEEN F AND F DF D
D
D
DFD 0' T T !R S D! 2 P
¯
0' T T !R S 2
¤ D! ³ ¥¦ DF ´µ D
4HIS IS AN INTEGRAL IN WHICH THE AREA ELEMENT BETWEEN FD AND FD DFD IS EXPRESSED IN TERMS OF COORDINATES ALONG AND NORMAL TO THE ISODOPS 3UCH COORDINATES MUST BE ESTABLISHED FOR EACH PARTICULAR CASE &IGURE SHOWS THE GEOMETRY FOR HORIZONTAL TRAVEL 4HE COORDINATE W IS ALONG THE ISODOP AND G IS NORMAL TO IT 7E CAN EXPRESS %Q IN TERMS OF THESE COORDINATES AS
7R FD
DH § L ¶ DFD ¨© P ·¸
§ 0' S DX ¶ T · 2 ¸
¯STRIPP ¨©
.OTE THAT 0T THE TRANSMITTED POWER IS NON ZERO IN THE INTEGRAL ONLY FOR THE TIME IT ILLU MINATES THE GROUND )N PULSE RADARS ONLY THAT PART OF THE GROUND AREA PROVIDING SIGNALS BACK TO THE RADAR AT A PARTICULAR TIME CAN BE CON SIDERED TO HAVE FINITE 0T AND SO THE RANGE OF FREQUENCIES THAT CAN BE PRESENT IS LIMITED BY THE PULSE AS WELL AS BY THE ANTENNAS AND THE MAXIMUM VELOCITY !NOTHER EXAMPLE IS SHOWN IN &IGURE 4HIS IS THE SMALL ILLUMINATED AREA FOR A NARROW BEAM SHORT PULSE SYSTEM WITH THE ANTENNA POINTED STRAIGHT AHEAD (ERE WE CAN MAKE LINEAR APPROXIMATIONS WITHOUT TOO MUCH ERROR
&)'52% 'EOMETRY OF COMPLEX FADING CALCULATIONS AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
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&)'52% 'EOMETRY OF DOPPLER SHIFT CALCULA TIONS FOR AN AIRBORNE SEARCH RADAR
! PULSE OF LENGTH S IS TRANSMITTED FROM AN ANTENNA OF BEAMWIDTH E 7E MAY SIMPLIFY THE PROBLEM BY ASSUMING A RECTANGULAR ILLUMINATED AREA 2E CS SIN P &URTHERMORE THE CURVATURE OF THE ISODOPS MAY BE NEGLECTED SO THE DOPPLER FREQUENCY IS ASSUMED TO BE THE SAME FOR ALL MAXIMUM RANGE POINTS AND THE SAME FOR ALL MINIMUM RANGE POINTS 7ITH THIS ASSUMPTION FD MAX FD MIN
V SIN Q MAX L
V SIN Q MIN L
4HUS THE TOTAL WIDTH OF THE DOPPLER SPECTRUM IS
$ FD
V SIN Q MAX SIN Q MIN L
&OR SHORT PULSES AND ANGLES AWAY FROM VERTICAL THIS IS
$ FD y
V $Q COSQ L
)N TERMS OF PULSE LENGTH IT BECOMES VCT COS Q HL SIN Q )F THE ANGULAR DIFFERENCE ACROSS THE ILLUMINATED RECTANGLE IS SMALL ENOUGH SO THAT R IS ESSENTIALLY CONSTANT THE DOPPLER SPECTRUM IS A RECTANGLE FROM FMIN TO FMAX
$ FD
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)N PRACTICE ANTENNA BEAMS ARE NOT RECTANGULAR 4HE RESULT IS THAT THE DOPPLER SPEC TRUM FOR A SIDE LOOKING RADAR LIKE THAT SHOWN IN THE EXAMPLE IS NOT RECTANGULAR BUT RATHER HAS THE SHAPE OF THE ANTENNA ALONG TRACK PATTERN 4HUS IF THE ANTENNA PATTERN IN THE ALONG TRACK DIRECTION IS ' ' A WITH A THE ANGLE OFF THE BEAM CENTER WE CAN EXPRESS A IN TERMS OF THE DOPPLER FREQUENCY FD AS A FD KV
AND THE SPECTRUM IS
7 FD
L 0TS RX § L FD ¶ ' ¨ · P 2 © V ¸
WHERE RX IS THE HORIZONTAL RESOLUTION IN THE RANGE DIRECTION /F COURSE THE HALF POWER BEAMWIDTH MAY BE USED AS AN APPROXIMATION RESULTING IN THE BANDWIDTH GIVEN BY %Q %FFECT OF $ETECTION 4HE EFFECT OF DETECTING NARROWBAND NOISE HAS BEEN TREATED EXTENSIVELY IN THE LITERATURE (ERE IT IS NECESSARY ONLY TO SHOW THE POSTDETECTION SPECTRUM OF THE PRECEDING EXAMPLE AND TO CONSIDER THE NUMBER OF INDEPENDENTLY FADING SAMPLES PER SECOND &IGURE SHOWS THE SPECTRUM BEFORE AND AFTER SQUARE LAW DETECTION &OR SQUARE LAW DETECTION THE POST DETECTION SPECTRUM IS THE SELF CONVOLUTION OF THE PREDETECTION SPECTRUM /NLY THE PART THAT PASSES THE LOW PASS FILTERS IN A DETECTOR IS SHOWN IN THE FIGURE 4HE RECTANGULAR 2& SPECTRUM HAS BECOME A TRIANGULAR VIDEO SPECTRUM 4HIS SPECTRUM DESCRIBES THE FADING OF THE DETECTOR OUTPUT FOR A #7 RADAR &OR A PULSE RADAR THE SPECTRUM IS SAMPLED BY THE PULSE REPETITION FREQUENCY 02& )F THE 02& IS HIGH ENOUGH SO THAT THE ENTIRE SPECTRUM CAN BE REPRODUCED THE 02& IS HIGHER THAN THE .YQUIST FREQUENCY $FD THE DIAGRAM INDICATED IS THAT OF THE SPECTRUM OF THE SAMPLES OF A RECEIVED PULSE AT A GIVEN RANGE &IGURE SHOWS A SERIES OF ACTUAL PULSES FROM A MOVING RADAR FOLLOWED BY A SERIES OF SAMPLES AT RANGE 2 4HE SPECTRUM SHOWN IN &IGURE IS THE SPECTRUM OF THE ENVELOPE OF SAMPLES AT 2 AFTER LOW PASS FILTERING 4HE SPECTRUM OF FADING AT ANOTHER RANGE OR VERTICAL ANGLE IS DIFFERENT IN ACCORD WITH %Q &OR MANY PURPOSES THE NUMBER OF INDEPENDENT SAMPLES IS IMPORTANT BECAUSE THESE MAY BE TREATED BY USING THE ELEMENTARY STATISTICS OF UNCORRELATED SAMPLES &OR CONTINU OUS INTEGRATION THE EFFECTIVE NUMBER OF INDEPENDENT SAMPLE IS
&)'52% 3PECTRUM OF FADING FROM A HOMOGENEOUS SMALL PATCH A BEFORE AND B AFTER DETECTION
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&)'52% &ADING FOR SUCCESSIVE PULSES OF A MOVING RADAR WITH GROUND TARGET
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0E4 4§ X¶ ¯ ¨ · 2SF X DX © 4¸
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WHERE 0E IS THE MEAN ENVELOPE POWER 4 IS THE INTEGRATION AVERAGING TIME AND 2SF T IS THE AUTOCOVARIANCE FUNCTION FOR THE DETECTED VOLTAGE &OR MANY PRACTICAL PURPOSES IF . IS LARGE IT MAY BE APPROXIMATED BY
. y "4
WHERE " IS THE EFFECTIVE )& BANDWIDTH &OR THE EFFECT OF SHORT INTEGRATION TIME SEE 5LABY ET AL &ADING SAMPLES CAN OF COURSE ALSO BE INDEPENDENT BECAUSE MOTION OF THE VEHICLE CAUSES THE BEAM TO ILLUMINATE A DIFFERENT PATCH OF GROUND 4HUS IN A PARTICULAR CASE THE INDEPENDENT SAMPLE RATE MAY BE DETERMINED EITHER BY THE MOTION OF THE ILLUMINATED PATCH OVER THE GROUND OR BY THE DOPPLER EFFECT OR BY SOME COMBINATION OF THE TWO 4HE NUMBER OF INDEPENDENT SAMPLES DETERMINES THE WAY IN WHICH THE 2AYLEIGH OR OTHER DISTRIBUTIONS MAY BE APPLIED 4HUS IF PULSES GIVE ONLY INDEPENDENT SAMPLES THE VARIANCE OF THE MEAN OBTAINED BY INTEGRATING THESE PULSES IS MUCH GREATER THAN WOULD BE TRUE IF ALL PULSES WERE INDEPENDENT $OPPLER BASED SYSTEMS SUCH AS DOPPLER NAVIGATORS MOVING TARGET INDICATORS AND SYNTHETIC APERTURE RADAR SYSTEMS DEPEND ON THE PREDETECTION SPECTRUM FOR THEIR OPERA TION BECAUSE THEY ARE COHERENT AND DO NOT USE AMPLITUDE OR SQUARE LAW DETECTION -OVING 4ARGET 3URFACES 3OMETIMES CLUTTER HAS INTERNAL MOTION 4HIS CAN OCCUR WHEN FIXED RADARS ARE USED TO OBSERVE MOVEMENT OF THE SEA AND THE LAND /N LAND CLUTTER MOTION IS USUALLY DUE TO MOVING VEGETATION ALTHOUGH MOVING ANIMALS AND MACHINES CREATE SIMILAR EFFECTS 4HE RADAR RETURN FROM AN ASSEMBLY OF SCATTERERS LIKE THOSE SHOWN IN &IGURE CAN CHANGE BECAUSE OF MOTION OF THE INDIVIDUAL SCATTERERS JUST AS IT CHANGES BECAUSE OF MOTION OF THE RADAR 4HUS IF EACH SCATTERER IS A TREE THE WAVING OF THE TREES AS THE WIND BLOWS CAUSES RELATIVE PHASE SHIFTS BETWEEN THE SEPARATE SCATTERERS THE RESULT IS FADING &OR A FIXED RADAR THIS MAY BE THE ONLY FADING OBSERVED EXCEPT FOR VERY SLOW FADING DUE TO CHANGES IN REFRACTION )F THE SURFACE ELEMENTS ARE STIFF THEY MAY NOT MOVE ENOUGH TO GET SIGNIFICANT DOPPLER SPREADING AND THE FADING DISTRIBUTION MAY NOT BE CLOSE TO 2AYLEIGH 3EE "ILLINGSLEY AND OTHER PAPERS BY HIM FOR MORE DISCUSSION OF THE SITUATION FOR FIXED RADARS OBSERVING GROUND TARGETS &OR A MOVING RADAR THIS MOTION OF THE TARGET CHANGES THE RELATIVE VELOCITIES BETWEEN TARGET ELEMENT AND RADAR SO THAT THE SPECTRUM IS DIFFERENT FROM THAT FOR A FIXED SURFACE 4HE WIDTH OF THE SPECTRUM DUE TO VEHICLE MOTION DETERMINES THE ABILITY OF THE RADAR TO DETECT THIS TARGET MOTION
£È°xÊ -1, /Ê/ +1 -ÊÊ ",Ê,"1 Ê, /1, 3PECIAL PURPOSE INSTRUMENTATION RADARS AND MODIFIED STANDARD RADARS MAY BE USED TO DETERMINE THE GROUND RETURN 3INCE THE GROUND RETURN IS ALMOST INVARIABLY DUE TO SCATTER ING THESE SYSTEMS ARE TERMED SCATTEROMETERS 3UCH SYSTEMS MAY USE #7 SIGNALS WITH OR WITHOUT DOPPLER PROCESSING BUT THEY MAY ALSO USE BOTH PULSE AND &- TECHNIQUES
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3CATTEROMETERS CAPABLE OF MEASURING RESPONSE OVER A WIDE RANGE OF FREQUENCIES ARE CALLED SPECTROMETERS 6ARIOUS ANTENNA PATTERNS FROM PENCIL BEAMS TO FAN BEAMS MAY BE USED 3YSTEMS TO MEASURE THE FULL POLARIZATION MATRIX MUST USE VERY CAREFUL ANTENNA DESIGNS SO THAT THE PHASES OF THE DIFFERENT TRANSMITTED AND RECEIVED POLARIZATIONS ARE WELL CONTROLLED AND LEAKAGE BETWEEN POLARIZATIONS IS THOROUGHLY SUPPRESSED #7 AND &- #7 3YSTEMS 4HE SIMPLEST SCATTEROMETER USES A STATIONARY #7 RADAR 3UCH SYSTEMS ARE NOT VERY FLEXIBLE BUT THEY ARE DISCUSSED HERE IN SOME DETAIL TO ILLUSTRATE CALIBRATION TECHNIQUES THAT ALSO APPLY TO THE MORE COMPLEX SYSTEMS 4HE #7 SCATTEROMETER IS SHOWN IN BLOCK FORM IN &IGURE 4O EVALUATE R THE RATIO OF TRANSMITTED TO RECEIVED POWER IS REQUIRED 4HE SYSTEM DEPICTED IN &IGURE A MEASURES TRANSMITTER POWER AND RECEIVER SENSITIVITY SEPARATELY 4HE TRANSMITTER FEEDS AN ANTENNA THROUGH A DIRECTIONAL COUPLER SO THAT A PORTION OF THE ENERGY MAY BE FED TO A POWER METER 4HE RECEIVER OPERATES FROM A SEPARATE ANTENNA ELECTRICALLY ISOLATED 4HE OUTPUT OF THE RECEIVER IS DETECTED AVERAGED AND DIGITALLY RECORDED )TS SENSITIVITY MUST BE CHECKED BY USE OF A CALIBRATION SOURCE 4HE CALIBRATED SIGNAL MAY BE FED THROUGH THE RECEIVER AT A TIME WHEN THE TRANSMITTER IS OFF &IGURE B SHOWS A SIMILAR ARRANGE MENT IN WHICH THE SIGNAL FROM THE TRANSMITTER IS ATTENUATED A KNOWN AMOUNT AND USED TO CHECK THE RECEIVER GAIN "Y COMPARING THE OUTPUT FROM THE ATTENUATED TRANSMITTER SIGNAL WITH THAT RECEIVED FROM THE GROUND THE SCATTERING CROSS SECTION MAY BE DETERMINED WITHOUT ACTUALLY KNOWING THE TRANSMITTED POWER AND THE RECEIVER GAIN 4HE CALIBRATIONS SHOWN IN &IGURE ARE INCOMPLETE WITHOUT KNOWING THE ANTENNA PATTERNS AND ABSOLUTE GAINS 3INCE ACCURATE GAIN MEASUREMENTS ARE DIFFICULT ABSOLUTE CALIBRATIONS MAY BE MADE BY COMPARING RECEIVED SIGNALS WITH PROPER RELA TIVE CALIBRATION FROM THE TARGET BEING MEASURED AND FROM A STANDARD TARGET 3TANDARD TARGETS MAY BE METAL SPHERES ,UNEBURG LENS REFLECTORS METAL PLATES CORNER REFLECTORS OR ACTIVE RADAR CALIBRATORS !2#SACTUALLY REPEATERS /F THE PASSIVE CALIBRATORS THE ,UNEBURG LENS REFLECTOR IS BEST BECAUSE IT HAS A LARGE CROSS SECTION FOR ITS VOLUME AND HAS A VERY WIDE PATTERN SO THAT ALIGNMENT IS NOT CRITICAL ,UNEBURG LENS REFLECTORS ARE USED FOR MAKING STRONG RADAR TARGETS OF SMALL VESSELS AND THEY MAY BE OBTAINED
&)'52% #7 SCATTEROMETER SYSTEM BLOCK DIAGRAM A SEPARATE TRANSMITTER AND RECEIVER CALIBRATION AND B CALIBRATION OF THE RATIO OF RECEIVED TO TRANSMITTED POWER
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FROM COMPANIES THAT SUPPLY THAT MARKET &OR DISCUSSION OF THE RELATIVE MERITS OF DIFFERENT PASSIVE CALIBRATION TARGETS SEE 5LABY ET AL 4HE IDEAL RECEIVER WOULD RESPOND LINEARLY TO ITS INPUT SO THAT A SINGLE CALIBRATION AT ONE INPUT LEVEL WOULD SUFFICE FOR ALL LEVELS 4HE USUAL RECEIVER HOWEVER HAS SOME NON LINEARITIES DUE TO DETECTOR PROPERTIES AND TO SATURATION OF ITS AMPLIFIERS BY LARGE SIGNALS &IGURE SHOWS A TYPICAL INPUT OUTPUT CURVE FOR A RECEIVER 4WO EQUAL INCREMENTS IN INPUT SIGNAL $I AS SHOWN PRODUCE DIF FERENT INCREMENTS IN OUTPUT BECAUSE OF THE &)'52% 4YPICAL RECEIVER INPUT OUTPUT NONLINEARITY OF THIS CURVE &OR THIS REASON CURVE )LLUSTRATED IS THE EFFECT OF NONLINEARITY RECEIVER CALIBRATION MUST BE PERFORMED OVER A RANGE OF INPUT LEVELS AND THE NONLINEARI TIES MUST BE COMPENSATED FOR IN THE DATA PROCESSING #7 SCATTEROMETERS DEPEND ON ANTENNA BEAMS TO DISCRIMINATE DIFFERENT ANGLES OF INCIDENCE AND DIFFERENT TARGETS 5SUALLY ASSUMPTIONS ARE MADE THAT THE ANTENNA PAT TERN HAS CONSTANT GAIN WITHIN THE ACTUAL D" POINTS AND ZERO GAIN OUTSIDE BUT THIS CLEARLY IS NOT AN ACCURATE DESCRIPTION )F LARGE TARGETS APPEAR IN THE LOCATIONS ILLUMI NATED BY THE SIDE OF THE MAIN BEAM OR THE MINOR LOBES THEIR SIGNALS MAY CONTRIBUTE SO MUCH TO THE RETURN THAT IT IS SIGNIFICANTLY CHANGED 3INCE THIS CHANGED SIGNAL IS CHARGED TO THE DIRECTION OF THE MAJOR LOBE BY THE DATA REDUCTION PROCESS THE RESULTING VALUE FOR R IS IN ERROR 2ESPONSES AT VERTICAL INCIDENCE FREQUENTLY CAUSE TROUBLE FOR VERTICAL INCIDENCE SIGNALS ARE USUALLY FAIRLY STRONG 4HUS THE ANTENNA PATTERN MUST BE ACCURATELY KNOWN AND TAKEN INTO ACCOUNT IN THE DATA ANALYSIS ! PATTERN WITH STRONG MINOR LOBES MAY BE SIMPLY INADMISSIBLE 4HE SCATTERING COEFFICIENT IS DETERMINED BY APPLYING
0R
0T L P
¯)LLUMINATED AREA
'TS D! 2
4HE INTEGRATION IS OVER WHATEVER AREA IS ILLUMINATED SIGNIFICANTLY INCLUDING THE REGIONS HIT BY THE MINOR LOBES 4HE USUAL ASSUMPTION IS THAT R IS CONSTANT OVER THE ILLUMINATED AREA SO THAT
0R
0T L S P
¯)LLUMINATED AREA
'T D! 2
4HIS ASSUMPTION WOULD BE TRUE ONLY IF THE ANTENNA CONFINED THE RADIATED ENERGY TO A VERY SMALL SPREAD OF ANGLES AND TO A FAIRLY HOMOGENEOUS REGION 4HE RESULTING EXPRESSION IS
S
P 0R
0T L ¯)LLUMINATED 'T 2 D! AREA
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.OTE THAT ONLY THE RATIO OF TRANSMITTED TO RECEIVED POWER IS REQUIRED SO THE TECH NIQUE SHOWN IN &IGURE B IS JUSTIFIED 3OMETIMES 2 'T OR BOTH ARE ASSUMED CON STANT OVER THE ILLUMINATED AREA BUT SUCH AN APPROXIMATION TO %Q SHOULD BE ATTEMPTED ONLY AFTER CHECKING ITS VALIDITY FOR A PARTICULAR PROBLEM )F THE RESULT OF APPLYING THE TECHNIQUE OF %Q TO A SET OF MEASUREMENTS INDI CATES THAT R PROBABLY DID VARY ACROSS THE SIGNIFICANTLY ILLUMINATED AREA THIS VARIATION MAY BE USED AS A FIRST APPROXIMATION TO DETERMINE A FUNCTION FP DESCRIBING THE P VARIATION OF R AND A NEXT ORDER APPROXIMATION THEN BECOMES
S
P 0R 0T L ¯)LLUMINATED §© F Q 'T 2 ¶¸ D!
AREEA
0ROPER SCATTERING MEASUREMENTS DEMAND AN ACCURATE AND COMPLETE MEASUREMENT OF ANTENNA GAIN 'T 4HIS CAN BE A VERY TIME CONSUMING AND EXPENSIVE PROCESS PARTICU LARLY WHEN THE ANTENNA IS MOUNTED ON AN AIRCRAFT OR OTHER METALLIC OBJECT .EVERTHELESS COMPLETE PATTERNS ARE A MUST FOR GOOD SCATTER MEASUREMENTS 2ANGE -EASURING 3YSTEMS 2ADARS ABILITY TO SEPARATE RETURNS FROM DIFFERENT RANGES CAN BE USED ADVANTAGEOUSLY ALONG WITH DIRECTIVE ANTENNA BEAMS TO SIMPLIFY THE SCATTERING MEASUREMENTS -OST RANGING SCATTEROMETERS USE EITHER PULSE MODULATION OR &- ALTHOUGH MORE EXOTIC MODULATIONS COULD ALSO BE USED 4HE DISCUSSION HERE TREATS PULSE SYSTEMS BUT SINCE ALL OTHER RANGE MEASURING SYSTEMS CAN BE REDUCED TO EQUIVA LENT PULSE SYSTEMS MOST RESULTS ARE GENERAL &IGURE SHOWS THE WAY IN WHICH PULSE MEASUREMENT OF RANGE IS USED &IGURE A SHOWS A CIRCULAR PENCIL BEAM !T ANGLES NEAR GRAZING THE ILLUMI NATED PATCH SET BY THE CIRCULAR ANTENNA PATTERN BECOMES RATHER LONG THE PATCH IS AN ELLIPSE AND USE OF THE PULSE LENGTH TO CONFINE ILLUMINATION TO A PART OF THE PATCH IS HELPFUL )NDEED FOR ANGLES VERY NEAR GRAZING THIS IS THE ONLY SATISFACTORY WAY TO RESOLVE SMALL REGIONS -ANY SYSTEMS THAT USE BEAMWIDTH TO SET THE MEASURED AREA NEAR VERTICAL USE RANGE RESOLUTION FOR ANGLES BEYOND SAY
&)'52% 2ANGE RESOLUTION APPLIED TO SCATTEROMETRY A IMPROVING ONE DIMENSION OF A CIRCULAR BEAM ILLUMINATION PATTERN AND B USE WITH A FAN BEAM
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&IGURE B SHOWS AN ANTENNA PATTERN THAT TAKES BETTER ADVANTAGE OF THE POSSIBILI TIES OF RANGE MEASUREMENT ! FAN BEAM IS USED TO ILLUMINATE A NARROW STRIP ALONG THE GROUND AND THE RANGE RESOLUTION PERMITS SEPARATING THE RETURNS FROM DIFFERENT ANGLES BY THE TIME THEY RETURN 4HIS TECHNIQUE IS ESPECIALLY EFFECTIVE AT ANGLES AWAY FROM THE VERTICAL FOR THE RESOLUTION NEAR THE VERTICAL IS MUCH POORER THAN NEAR GRAZING )F WE ASSUME THAT R IS ESSENTIALLY CONSTANT THE GAIN IS CONSTANT THE PULSE IS RECTAN GULAR AND THE DIFFERENCE IN RANGE ACROSS A RESOLUTION ELEMENT IS NEGLIGIBLE THE EXPRES SION FOR R BECOMES
S
0R P 2 SIN Q 0T L 'FR2
WHERE R2 IS THE SHORT RANGE RESOLUTION *ANZA HAS REPORTED DETAILS OF CALIBRATION PROBLEMS WITH A RANGE MEASURING PULSED RADAR SCATTEROMETER #7 $OPPLER 3CATTEROMETERS ! CONVENIENT WAY FOR AN AIRBORNE MEASUREMENT IS TO MEASURE THE SCATTERING COEFFICIENT AT MANY ANGLES SIMULTANEOUSLY WITH A #7 SYS TEM IN WHICH THE RELATIVE VELOCITIES CORRESPONDING TO DIFFERENT ANGLES ARE SEPARATED BY SEPARATING THEIR DOPPLER FREQUENCIES 4HE USE OF A FAN BEAM WITH SUCH A SYSTEM PERMITS THE SIMULTANEOUS MEASUREMENT OF SCATTERING COEFFICIENTS AT POINTS AHEAD OF AND BEHIND THE AIRCRAFT CARRYING THE RADAR &IGURE SHOWS THIS 4HE PATTERN OF THE ANTENNA ILLU MINATION ON THE GROUND IS SHOWN INTERSECTED BY TWO ISODOPS LINES OF CONSTANT DOPPLER FREQUENCY WITH THE WIDTH OF THE SPECTRUM BETWEEN THEM SHOWN ON THE DIAGRAM 4HE DISTANCE BETWEEN THEM CAN BE SEEN TO BE $R 2SIN Q SIN Q AND
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V SIN Q SIN Q L
4HUS THE WIDTH OF THE ELEMENT ON THE GROUND IS RELATED TO THE DOPPLER FREQUENCY BANDWIDTH BY
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&)'52% 2ESOLUTION IN A FAN BEAM #7 DOPPLER SCATTEROMETER
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WHERE THIS TECHNIQUE IS APPLIED TO THE RADAR EQUATION AND THE FOLLOWING ARE ASSUMED R CONSTANT IN THE ILLUMINATED AREA !NTENNA GAIN CONSTANT OVER ITS BEAMWIDTH & AND ZERO ELSEWHERE 2ANGE VARIATION ACROSS THE SMALL ILLUMINATED AREA NEGLIGIBLE
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AND SO
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$OPPLER SCATTEROMETERS NEED NOT USE FORE AND AFT BEAMS 4HE 3EASAT AND .3#!44 SPACEBORNE DOPPLER SCATTEROMETERS WERE DESIGNED WITH BEAMS POINTED SQUINTED AHEAD AND BEHIND THE NORMAL TO THE GROUND TRACK )NDEPENDENT 3AMPLES 2EQUIRED FOR -EASUREMENT !CCURACY 4HE 2AYLEIGH DISTRIBUTION DESCRIBES THE FADING SIGNAL FAIRLY WELL )F WE ASSUME A 2AYLEIGH DISTRIBUTION OF FADING THE NUMBER OF INDEPENDENT SAMPLES REQUIRED FOR A GIVEN ACCURACY IS SHOWN IN &IGURE 4HE RANGE DEFINED IN THIS FIGURE IS THE RANGE OF MEAN VALUES LYING BETWEEN AND OF POINTS ON THE DISTRIBUTION 4HIS ACCURACY RANGE IS INDEPENDENT OF ANY ACCU RACY PROBLEMS ASSOCIATED WITH CALIBRATION AND KNOWLEDGE OF THE ANTENNA PATTERN 4HE PRECISION OF THE MEASUREMENT DEPENDS UPON THE NUMBER OF INDEPENDENT SAM PLES NOT ON THE TOTAL NUMBER OF SAMPLES 4HE NUMBER OF INDEPENDENT SAMPLES CAN BE FOUND FROM %Q OR %Q AFTER SUITABLE ANALYSIS 4HIS ANALYSIS ASSUMES THAT ONLY DOPPLER FADING CONTRIBUTES TO INDEPENDENCE BUT MOTION FROM ONE CELL TO ANOTHER ALSO ADDS INDEPENDENT SAMPLES 4HUS THE TOTAL NUMBER OF SUCH SAMPLES IS APPROXI MATELY THE PRODUCT OF THE NUMBER CALCULATED FROM %Q AND THE NUMBER OF GROUND CELLS AVERAGED &IGURE SHOWS SOME EXAMPLES OF THE EFFECT OF THE ANGLE OF INCI DENCE ON THE NUMBER OF INDEPENDENT SAMPLES FOR A HORIZONTALLY TRAVELING SCATTEROMETER WITH A FORWARD POINTED BEAM 3TUDY OF THE RESULTS OBTAINED IN THIS TYPE OF ANALYSIS INDICATES THAT IN REGIONS WHERE THE SCATTERING COEFFICIENT DOES NOT CHANGE RAPIDLY WITH ANGLE THE WIDEST POS SIBLE ANGULAR WIDTH OBTAINED BY A LONGER PULSE OR A WIDER FILTER FOR A #7 DOPPLER SYSTEM GIVES THE MAXIMUM NUMBER OF INDEPENDENT SAMPLES FOR A GIVEN DISTANCE TRAVELED ALONG THE GROUND
&)'52% !CCURACY OF AVERAGES FOR FADING SIGNALS
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&)'52% %XAMPLES OF THE VARIATION WITH ANGLE OF INCIDENCE OF THE NUMBER OF INDEPENDENT SAMPLES FOR A SCATTEROMETER
.EAR 6ERTICAL 0ROBLEM -OST PUBLISHED RADAR RETURN DATA PURPORTING TO INCLUDE VERTICAL INCIDENCE GIVE VERTICAL INCIDENCE SCATTERING COEFFICIENTS THAT ARE TOO SMALL 4HIS IS A CONSEQUENCE OF A FUNDAMENTAL PROBLEM IN MEASURING NEAR THE VERTICAL WITH A FINITE BEAMWIDTH OR PULSE LENGTH .EAR VERTICAL RADAR RETURNS FROM MOST TARGETS DROP OFF RAPIDLY AS THE ANGLE WITH THE VERTICAL IS INCREASED 4HUS THE MEASURING BEAMWIDTH OR PULSEWIDTH USUALLY ENCOMPASSES SIGNALS FROM REGIONS HAVING VALUES FOR R MANY DECIBELS APART 3INCE THE SCATTERING COEFFICIENT VARIES MUCH MORE RAPIDLY NEAR THE VERTI CAL THAN AT ANGLES BEYOND OR FROM THE VERTICAL THE PROBLEM IS MUCH MORE SEVERE AT THE VERTICAL &URTHERMORE THE PROBLEM IS COMPLICATED AT THE VERTICAL BY THE FACT THAT THE ANGULAR SCALE TERMINATES THERE SO THAT A BEAM CENTERED AT THE VERTICAL ILLUMINATES WEAKER TARGETS R ON BOTH SIDES OF ITS PATTERN WHEREAS A BEAM AWAY FROM THE VERTICAL ILLUMINATES STRONGER SIGNALS ON ONE SIDE AND WEAKER SIGNALS ON THE OTHER &IGURE SHOWS WHAT HAPPENS FOR A STEEPLY DESCENDING CURVE OF R VERSUS P 4HE RADAR RETURN INTEGRAL FROM %Q IS A CONVOLUTION INTEGRAL THE FIGURE SHOWS THE CONVOLUTION OF THE BEAM PATTERN WITH THE R CURVE #LEARLY THE AVERAGE AT THE VERTICAL IS LOWER THAN IT SHOULD BE TO INDICATE PROPERLY THE VARIATION OF R NEAR THE VERTICAL &IGURE SHOWS AN EXAMPLE BASED ON THE THEORETICAL SCATTERING COEFFICIENT FOR THE SEA DERIVED FROM THE SPECTRA REPORTED BY THE 3TEREO 7AVE /BSERVATION 0ROJECT 4HE EFFECT OF DIFFERENT BEAMWIDTHS IS CLEARLY SHOWN 7ITH A PULSE OR OTHER RANGE MEASURING SYSTEM REPORTED VALUES ARE ALWAYS IN ERROR BECAUSE AS INDICATED ABOVE IT IS ALMOST IMPOSSIBLE TO RESOLVE A NARROW RANGE OF ANGLES NEAR THE VERTICAL &OR SHORT RANGES ONE CAN CONFIGURE THE ANTENNA SO THAT A PLANE WAVE IMPINGES ON THE SURFACE 7HEN THIS IS DONE THE NEAR VERTICAL SCATTERING COEFFICIENT CAN HAVE ITS ANGULAR VARIATION PROPERLY DESCRIBED
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&)'52% (OW FINITE BEAMWIDTH CAUSES A NEAR VERTICAL ERROR IN MEASURING THE SCATTERING COEFFICIENT
'ROUND AND (ELICOPTER 3CATTEROMETERS AND 3PECTROMETERS -ANY GROUND SCATTERING MEASUREMENTS HAVE BEEN MADE WITH SYSTEMS MOUNTED ON BOOM TRUCKS AND HELICOPTERS -OST OF THESE ARE &- #7 SYSTEMS THAT USE WIDE BANDWIDTH TO OBTAIN EXTRA INDEPENDENT SAMPLES RATHER THAN FOR FINE RESOLUTION 3OME USE VERY WIDE BANDWIDTH TO OBTAIN FINE RANGE RESOLUTION TO LOCATE SOURCES OF SCATTERING -OST HAVE MULTIPLE POLARIZATION CAPABILITY AND SOME ARE CAPABLE OF POLARIMETRY BECAUSE THE PHASE OF TWO RECEIVED SIGNALS WITH ORTHOGONAL POLARIZATION CAN BE MEASURED 4HE BASIC ELEMENTS OF AN &- #7 SCATTEROMETER ARE SHOWN IN &IGURE 4HE SWEPT OSCILLATOR MUST PRODUCE A LINEAR SWEEP THIS IS EASY WITH YTTRIUM IRON GARNET 9)' nTUNED OSCILLATORS BUT REQUIRES LINEARIZING CIRCUITS IF TUNING USES A VARACTOR
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&)'52% %FFECT OF ANTENNA BEAMWIDTH ON THE MEASURED SCATTERING COEFFICIENT AS A FUNCTION OF ANGLE OF INCIDENCE
-ANY SYSTEMS USE DIGITAL WAVEFORM SYNTHESIS TO OBTAIN THE SWEPT WAVEFORM )F DUAL ANTENNAS ARE USED AS SHOWN THE OVERLAP OF THE BEAMS MUST BE CONSIDERED 3INGLE ANTENNA SYSTEMS ARE SOMETIMES USED WITH A CIRCULATOR ISOLATING TRANSMITTER AND RECEIVER THEIR PERFORMANCE IS SOMEWHAT POORER THAN THAT OF DUAL ANTENNA SYSTEMS BECAUSE OF INTERNAL REFLECTIONS AND LEAKAGE THROUGH THE CIRCULATOR &IGURE SHOWS THE KIND OF SYSTEM THAT MAY BE USED TO MEASURE SCATTERING FROM WITHIN A VOLUME "Y DETERMINING THE SPECTRUM OF THE RETURN THE USER CAN ESTABLISH THE SCATTERING FROM DIFFERENT RANGES 4HIS SYSTEM HAS BEEN USED IN DETERMINING THE SOURCES OF SCATTER IN VEGETATIONn AND SNOW 5LTRASONIC WAVES IN WATER CAN BE USED TO SIMULATE ELECTROMAGNETIC WAVES IN AIRn "ECAUSE OF THE DIFFERENCE IN VELOCITY OF PROPAGATION AN ACOUSTIC FREQUENCY OF -(Z CORRESPONDS WITH A WAVELENGTH OF MM 3UCH A WAVELENGTH IS OF A CONVENIENT SIZE FOR MANY MODELING MEASUREMENTS AND OF COURSE EQUIPMENT IN THE -(Z REGION IS IN MANY WAYS EASIER TO OPERATE THAN EQUIPMENT IN THE MICROWAVE REGION CERTAINLY IT IS MUCH EASIER TO OPERATE AND LESS EXPENSIVE THAN MICROWAVE EQUIPMENT OPERATING AT A MM WAVELENGTH !COUSTIC PLANE WAVES AND ELECTROMAGNETIC PLANE WAVES SATISFY THE SAME BOUNDARY CONDITIONS 7HEN THE SCATTERING SURFACES ARE NOT PLANE AND WHEN ANGLES OF INCIDENCE ARE RATHER OBLIQUE THE ANALOGY BETWEEN ACOUSTIC AND ELECTROMAGNETIC WAVES IS LESS VALID /F COURSE ACOUSTIC SYSTEMS CANNOT SIMULATE CROSS POLARIZATION
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&)'52% "ASIC BLOCK DIAGRAM OF AN &- #7 SCATTEROMETER 2& SECTION
3CATTERING #OEFFICIENTS FROM )MAGES 2ADAR IMAGES PRODUCED BY REAL OR SYNTHETIC APERTURE RADARS CAN BE USED FOR SCATTERING COEFFICIENT MEASUREMENT 5NFORTUNATELY MOST SUCH SYSTEMS ARE UNCALIBRATED OR POORLY CALIBRATED SO THE RESULTS ARE SOMEWHAT DUBIOUS EVEN ON A RELATIVE BASIS WHEN IMAGES ARE PRODUCED ON DIF FERENT DAYS 2ELATIVE CALIBRATION HAS BEEN INTRODUCED INTO SOME SYSTEMS n !BSOLUTE CALIBRATION WHICH ALSO SERVES AS RELATIVE CALIBRATION IN SOME CASES CAN BE ACHIEVED BY USING STRONG REFERENCE TARGETS WITH THE ACTIVE RADAR CALIBRATOR !2# REPEATERS ESPECIALLY SUITABLE !NOTHER APPROACH THAT HAS BEEN USED IS TO MEASURE SCATTERING FROM REFERENCE AREAS WITH A GROUND BASED OR HELICOPTER SYSTEM THAT IS WELL CALIBRATED AND TO COMPARE THE IMAGES TO THESE MEASURED VALUES
&)'52% "ASIC BLOCK DIAGRAM OF AN &- #7 RANGE DISCRIMINATING SCATTEROMETER CONTROL AND DATA HANDLING SYSTEM
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"ISTATIC -EASUREMENTS -EASUREMENTS OF GROUND RETURN WHEN THE RECEIVER AND TRANSMITTER ARE SEPARATED ARE COMPARATIVELY RARE 4HESE MEASUREMENTS ARE VERY DIFFICULT TO MAKE FROM AIRCRAFT BECAUSE IT IS NECESSARY THAT BOTH TRANSMITTER AND RECEIVER ANTEN NAS LOOK AT THE SAME GROUND POINT AT THE SAME TIME AND THAT THE SIGNAL BE CORRELATED WITH KNOWN ANTENNA LOOK ANGLES &URTHERMORE IT IS DIFFICULT TO KNOW THE POLARIZATION AND THE EXACT SIZE AND SHAPE OF THE COMMON AREA ILLUMINATED BY THE ANTENNA BEAMS ARE SOMETIMES DIFFICULT TO DETERMINE &OR THIS REASON FEW BISTATIC MEASUREMENTS FROM AIRCRAFT HAVE BEEN REPORTED IN THE LITERATURE ,ABORATORY BISTATIC MEASUREMENTS HAVE BEEN MADE BY BOTH THE 7ATERWAYS %XPERIMENT 3TATION AND 4HE /HIO 3TATE 5NIVERSITY GROUPS USING ELECTROMAGNETIC WAVES AND BY THE 5NIVERSITY OF +ANSAS GROUP USING ACOUSTIC WAVES "ISTATIC MEA SUREMENTS OF LASER RADIATION HAVE BEEN MADE AT "ELL 4ELEPHONE ,ABORATORIES AND # BAND MEASUREMENTS OF BUILDINGS HAVE BEEN MADE AT THE 5NIVERSITY OF +ANSAS /THER SURFACE BASED MEASUREMENTS HAVE ALSO BEEN REPORTED "ISTATIC MEASUREMENTS CALL FOR COMPLICATIONS WHEN MADE OUTSIDE THE LABORATORY BECAUSE AN ABSOLUTE REFERENCE FOR BOTH TRANSMITTER POWER AND RECEIVER SENSITIVITY MUST BE USED )N THE LABORATORY HOWEVER IT IS POSSIBLE TO USE TECHNIQUES SIMILAR TO THOSE FOR MONOSTATIC MEASUREMENTS
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" /Ê 1// ,Ê " -®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
S !I E Q QI
A
S D" LOG !I Q QI
B
WHERE !I AND PI ARE CONSTANTS THAT DIFFER FOR THE NEAR VERTICAL AND MIDRANGE REGIONS &IGURE SHOWS AN EXAMPLE OF THIS VARIATION .O THEORY GIVES EXACTLY THIS RESULT
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&)'52% 'ENERAL CHARACTERISTICS OF SCATTERING COEFFICIENT VARIATION WITH ANGLE OF INCIDENCE AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
BUT NEARLY ALL MEASUREMENTS FIT SUCH A MODEL CLOSELY AND THE MODEL APPROXIMATES MOST THEORETICAL CURVES WELL OVER THE RELEVANT REGIONS 4HIS SIMPLE RESULT MEANS THAT SIMPLE CLUTTER MODELS MAY BE DEVELOPED AND USED ALTHOUGH MORE COMPLEX MODELS MAY BE NECESSARY FOR SOME REMOTE SENSING APPLICATIONS
&)'52% 2EGRESSION OF AVERAGE OF ALL '(Z CROPLAND DATA FOR TWO YEARS OBTAINED WITH A MICROWAVE ACTIVE SPECTROMETER AFTER 2 + -OORE + ! 3OOFI AND 3 - 0URDUSKI Ú )%%%
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4HE BASIS FOR THE LINEAR MODEL IS A COMBINATION OF THE 3KYLAB RESULTS OVER .ORTH !MERICA AND THOSE FROM +ANSAS CROPLAND MEASUREMENTS OVER THREE COMPLETE SEASONS WITH THE MICROWAVE ACTIVE SPECTROMETER -!3 4HE '(Z 3KYLAB 2!$3#!4 HAD A GROUND FOOTPRINT OF A KM CIRCLE AT VERTICAL TO AN ELLIPSE OF BY KM AT 4HE -!3 HAD FOOTPRINTS AT RANGING FROM BY M AT '(Z TO BY M AT '(Z BUT MILLIONS OF MEASUREMENTS WERE AVERAGED FOR THE MODEL "ECAUSE THE 3KYLAB DATA WAS AT ONLY ONE FREQUENCY AND THE RESPONSES FOR THE TWO EXPERIMENTS WERE ESSENTIALLY THE SAME AT THAT FREQUENCY THE FREQUENCY RESPONSE SHOWN IN THE MODEL DEPENDS ENTIRELY ON THE -!3 MEASUREMENTS 4HE SUMMER 3KYLAB OBSERVATIONS INCLUDED DESERTS GRASSLAND CROPLAND AND FORESTS WHEREAS THE +ANSAS MEASUREMENTS WERE ONLY OF CROPLAND (OWEVER EARLY AND LATE IN THE GROWING SEASON THE CROPLAND WAS ESSENTIALLY BARE SIMILAR TO THE SUMMER DESERT EXCEPT FOR SOIL MOISTURE CONTENT $URING THE HEIGHT OF THE GROWING SEASON THE CROPS WERE DENSE ENOUGH SO THAT SCATTER WAS SIMILAR TO THAT FROM FORESTS 4HUS THE OVERALL MODEL SEEMS REPRESENTATIVE OF SUMMER CONDITIONS AVERAGED OVER ALL OF .ORTH !MERICA 4HE MODEL TAKES THE FORM S D" F Q ! "Q #F $F Q
n a Q a n
A
WHERE ! " # AND $ TAKE ON DIFFERENT VALUES FOR DIFFERENT POLARIZATIONS ABOVE AND BELOW '(Z 4HE FREQUENCY RESPONSE BELOW '(Z IS MUCH MORE RAPID THAN ABOVE '(Z -OREOVER AT FREQUENCIES ABOVE '(Z THE FREQUENCY RESPONSE IS INDEPENDENT OF ANGLE SO THAT $ &OR LOWER FREQUENCIES THE FREQUENCY RESPONSE IS ANGLE DEPENDENT &OR ANGLES LESS THAN ONLY TWO POINTS WERE AVAILABLE AND SO SEPARATE FREQUENCY REGRESSIONS WERE RUN AT EACH OF THESE ANGLES 4HE MODEL FOR THESE ANGLES IS
S D" F Q - Q . Q F
Q n n
B
4HE FREQUENCY RESPONSES BELOW '(Z DIFFERED FOR THE TWO YEARS SO THE MOD ELS HAVE SEPARATE VALUES OF THE CONSTANTS FOR AND 4HE YEAR WAS VERY DRY IN +ANSAS THEREFORE THE VALUES ARE PROBABLY MORE REPRESENTATIVE BUT BOTH ARE GIVEN HERE 6ALUES OF THE CONSTANTS ARE IN 4ABLE &IGURE SHOWS THE CLUTTER MODEL FOR THE MIDRANGE OF ANGLES AS A FUNCTION OF FREQUENCY 4!",% #ONSTANTS FOR ,INEAR 3CATTERING -ODEL 3UMMER
&REQUENCY 2ANGE '(Z
!NGLE &REQUENCY #ONSTANT 3LOPE " 3LOPE # ! OR - D" OR . D" D"'(Z
3LOPE #ORRECTION $ D" ¾ '(Z
%Q
0OLARIZATION
!NGULAR 2ANGE
A
6 6 6 ( ( (
n n n n n n
n n n n n n
B
6 AND ( 6 AND ( 6 AND ( 6 AND ( 6 AND ( 6 AND (
n n n n n n
!FTER 2 + -OORE + ! 3OOFI AND 3 - 0URDUSKI Ú )%%%
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&)'52% 'ENERAL LAND SCATTERING CLUTTER MODEL VERTICAL POLARIZATION (ORIZONTAL POLARIZATION IS VERY SIMILAR AFTER 2 + -OORE + ! 3OOFI AND 3 - 0URDUSKI Ú )%%%
4HE FIGURE IS ONLY FOR VERTICAL POLARIZATION BECAUSE RESULTS ARE SO SIMILAR FOR VERTICAL AND HORIZONTAL 5LABY DEVELOPED A DIFFERENT MORE COMPLEX MODEL FROM THE +ANSAS VEGETATION DATA 4HIS MODEL FITS CURVES RATHER THAN STRAIGHT LINES TO THE MEASURED DATA &OR MOST PURPOSES THE STRAIGHT LINE MODEL IS ADEQUATE AND IT IS MUCH EASIER TO USE ! STRAIGHT LINE MODEL FOR SNOW COVERED GRASSLAND SIMILAR TO THAT FOR VEGETATION DEPENDS ON A MORE LIMITED DATA SET 4HE DATA WAS FOR ONLY ONE SEASON IN #OLORADO WHEN THE SNOW WAS ONLY ABOUT CM DEEP 4HIS MEANS THAT THE SIGNAL PROBABLY PENE TRATED TO THE GROUND SURFACE AT FREQUENCIES BELOW ABOUT '(Z .EVERTHELESS THE MODEL INDICATES THE KIND OF RESULTS TO BE EXPECTED FOR THIS IMPORTANT SITUATION 4ABLE GIVES THE RESULTING CONSTANTS TO USE IN %Q A 4!",% 2EGRESSION 2ESULTS FOR 'ROUND "ASED -EASUREMENTS OF 3NOW #OVERED 'ROUND
4IME OF $AY $AY $AY $AY $AY .IGHT .IGHT .IGHT .IGHT
0OLARIZATION
&REQUENCY #ONSTANT 2ANGE '(Z ! D"
&REQUENCY !NGLE 3LOPE 3LOPE # " D" D"'(Z
3LOPE #ORRECTION $ D" r '(Z
6 6 ( ( 6 6 ( (
n n n n n n n n
n
!FTER 2 + -OORE + ! 3OOFI AND 3 - 0URDUSKI ¡ )%%% ./4% P TO n 6ALUES OF COEFFICIENTS IN THIS TABLE ARE ALSO CONSIDERED THOSE OF THE MODEL
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3NOW SCATTER DEPENDS STRONGLY ON THE FREE WATER CONTENT OF THE UPPER LAYER OF SNOW SO SCATTER IS MUCH LOWER FROM THE WET DAYTIME SNOW WHERE SOLAR MELTING HAS COM MENCED THAN FOR THE DRY NIGHTTIME SNOW (ENCE DIFFERENT MODELS MUST BE USED FOR DAY AND NIGHT COMPARE THE DAY AND NIGHT MEASUREMENTS SHOWN IN &IGURE 4HE DIFFER ENCE BETWEEN DAY AND NIGHT SCATTER FROM SNOW IS EVEN MORE PRONOUNCED AT '(Z BUT THE MODEL DOES NOT INCLUDE '(Z BECAUSE NO DATA EXISTS BETWEEN AND '(Z !LTHOUGH NO SPECIFIC CLUTTER MODEL HAS BEEN DEVELOPED FOR FORESTS RESULTS FROM THE 3KYLAB 2!$3#!4 AND 3EASAT SCATTEROMETER SHOW THAT THE !MAZON RAINFOREST SCATTERS ALMOST INDEPENDENTLY OF THE ANGLE OF INCIDENCE EVEN NEAR VERTICAL 4HE MEAN MEASURED VALUE AT WAS
o D" AT '(Z 3IMILAR RESULTS WERE FOUND AT # BAND /BSERVATIONS WITH 3)2 " 3)2 # AND *%23 INDICATED THAT THIS LACK OF ANGULAR VARIATION OF R ALSO IS PRESENT AT '(Z 4HE MODELS DESCRIBED ABOVE ARE BASED ON AVERAGES OVER VERY LARGE AREAS &OR THIS SITUATION THE VARI ABILITY FROM PLACE TO PLACE IS SMALL PARTICULARLY IN THE MIDRANGE OF ANGLES &IGURE SHOWS THE MEAN AND UPPER AND LOWER DECILE VALUES MEA SURED BY THE 3KYLAB 2!$3#!4 OVER .ORTH !MERICA 4HE LARGE VARIATION NEAR VERTICAL APPARENTLY RESULTS FROM THE EFFECT OF NEARLY SPECULAR REFLEC TION FROM WATER BODIES 7HEN THE FOOTPRINT IS SMALLER MORE VARIABILITY OCCURS 4HIS IS SHOWN IN &IGURE FROM A STUDY OF THE VARIATION OF SCAT TER OBSERVED BY 3)2 " WITH AVERAGES OVER DIFFERENT SIZED FOOTPRINTS &OR SMALL FOOTPRINTS THE SCATTER VARIES OVER A WIDE RANGE AND SYSTEM DESIGN ERS MUST ACCOUNT FOR THIS
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&)'52% 2EGRESSIONS FOR VERTICAL POLARIZATION CLUTTER MODEL FOR SNOW A DAY AND B NIGHT .OTE THE LARGE DIFFERENCES (ORIZONTAL POLARIZATION IS SIMILAR AFTER 2 + -OORE + ! 3OOFI AND 3 - 0URDUSKI Ú )%%%
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&)'52% !NGULAR PATTERNS OF THE MEAN UPPER DECILE AND LOWER DECILE OF 3KYLAB SCATTEROMETER OBSERVATIONS OVER .ORTH !MERICA DURING THE SUMMER SEASON FROM -OORE ET AL 5NIVERSITY OF +ANSAS 2EMOTE 3ENSING ,ABORATORY 4ECHNICAL 2EPORT
&)'52% RANGE OF PIXEL AMPLITUDE VERSUS RESOLUTION
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£È°ÇÊ - // , Ê " /Ê / .UMEROUS PROGRAMS TO GATHER SCATTERING COEFFICIENT DATA EXISTED PRIOR TO BUT SIZABLE DATA COLLECTIONS WITH ACCOMPANYING hGROUND TRUTHv WERE RARE 3INCE HOWEVER SEVERAL MAJOR PROGRAMS HAVE CHANGED THE SITUATION SO THAT MUCH INFORMATION IS NOW AVAILABLE )NDEED THIS INFORMATION IS SO WIDESPREAD THAT AN ADEQUATE SUMMARY OF THE LITERATURE IS IMPOSSIBLE (ENCE THIS SECTION CAN ONLY GIVE HIGHLIGHTS OF THE RESULTS AND MAJOR PROGRAMS 4HE READER SHOULD CONSULT THE THREE MAJOR COMPENDIA OF SUCH DATA FOR MORE INFORMATION BOTH ON RESULTS AND ON BIBLIOGRAPHY NOTE THAT INFORMATION IS SPREAD THROUGH MANY CHAPTERS OF THESE VOLUMES 3OME EARLY SCATTERING COEFFICIENT MEASUREMENT PROGRAMS WORTH MENTIONING INCLUDE THOSE OF THE .AVAL 2ESEARCH ,ABORATORY 'OODYEAR !EROSPACE #ORPORATION 3ANDIA #ORPORATION NEAR VERTICAL DATA AND PARTICULARLY 4HE /HIO 3TATE 5NIVERSITY &ROM TO THE LARGEST PROGRAM WAS AT THE 5NIVERSITY OF +ANSAS %XTENSIVE PROGRAMS WERE ALSO IN &RANCE #ENTRE .ATIONAL D%TUDES 3PATIALES #ENTRE .ATIONAL D%TUDES DES 4£L£COMMUNICATIONS 5NIVERSIT£ 0AUL 3ABATIER THE .ETHERLANDS #ANADA #ENTRE FOR 2EMOTE 3ENSING ##23 ESPECIALLY SEA ICE AND 3WITZERLAND AND !USTRIA SNOW -ANY OF THE RESULTS FROM THESE PROGRAMS APPEAR IN DIGESTS OF THE )NTERNATIONAL 'EOSCIENCE AND 2EMOTE 3ENSING 3YMPOSIA )'!233 )%%% 'EOSCIENCE AND 2EMOTE 3ENSING 3OCIETY AND JOURNALS SUCH AS )%%% 4RANSACTIONS ON 'EOSCIENCE AND 2EMOTE 3ENSING AND ON /CEAN %NGINEERING )NTERNATIONAL *OURNAL OF 2EMOTE 3ENSING 2EMOTE 3ENSING OF %NVIRONMENT AND 0HOTOGRAMMETRIC %NGINEERING AND 2EMOTE 3ENSING !LTHOUGH CALIBRATIONS FOR SOME OF THE OLDER DATA WERE DOUBTFUL SUMMARY PRESEN TATIONS ARE NOT AVAILABLE FOR NEWER DATA !CCORDINGLY &IGURE SHOWS AN EARLIER SUMMARY BASED MOSTLY ON 8 BAND DATA /NE SHOULD BE CAUTIOUS IN USING THIS DATA BUT THE FIGURE GIVES A FEEL FOR THE OVERALL VARIATIONS &IGURE IS A SIMILAR PRESENTATION FOR NEAR VERTICAL DATA #ALIBRATION OF THE SYSTEMS WAS GOOD BUT THE ANTENNA EFFECT DISCUSSED IN 3ECTION MAKES THE VALUES FROM TO LOW %FFECTS OF 2OUGHNESS -OISTURE #ONTENT AND 6EGETATION #OVER 3CATTERING FALLS OFF MORE RAPIDLY WITH ANGLES FOR SMOOTH SURFACES THAN FOR ROUGH SURFACES 3INCE THE ROUGHNESS THAT AFFECTS RADAR MUST BE MEASURED IN WAVELENGTH UNITS A SURFACE SMOOTH AT LONG WAVELENGTHS MAY BE ROUGH AT SHORTER ONES 4HIS IS ILLUSTRATED IN &IGURE WHICH SHOWS THESE EFFECTS WITH MEASUREMENTS FROM PLOWED FIELDS !T '(Z THE SIGNAL CHANGED D" BETWEEN AND FOR THE SMOOTHEST FIELD AND ONLY D" FOR THE ROUGHEST !T '(Z THE SMOOTHEST FIELD WAS ROUGH ENOUGH TO REDUCE THE VARIATION TO D" &OR MOST SURFACES CROSS POLARIZED SCATTER IS LOWER THAN LIKE POLARIZED SCATTER OFTEN BY ABOUT D" #ROSS POLARIZED SCATTER FROM SMOOTH SURFACES IS MUCH LESS NEAR VERTI CAL THAN ELSEWHERE &IGURE SHOWS THIS EFFECT #ROSS POLARIZED RETURNS FROM VOLUME SCATTERERS WITH ELEMENTS THAT ARE LARGE COMPARED WITH A WAVELENGTH ARE STRON GER THAN FOR SURFACES SOMETIMES BEING ONLY D" DOWN 3CATTER DEPENDS ON THE DIELECTRIC CONSTANT WHICH DEPENDS ON MOISTURE CONTENT 4HUS SCATTER FROM WET SOILS AT ANGLES OFF VERTICAL IS USUALLY MUCH HIGHER THAN FROM DRY SOILS &IGURE SHOWS THIS 4HE EFFECT CAN BE MANY DECIBELS D" IN THE FIGURE 6EGETATION CANOPIES OVER SOIL CAN CONTRIBUTE TO SCATTER IN THE VARIOUS WAYS SHOWN IN &IGURE &IGURE SHOWS AN EXAMPLE -OST OF THE SCATTER FROM THE ENTIRE PLANT CAME FROM THE TOP LEAVES WITH ENOUGH ATTENUATION THERE TO REDUCE
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&)'52% "OUNDARIES OF MEASURED RADAR DATA A HORIZONTAL POLAR IZATION AND B VERTICAL POLARIZATION #OURTESY OF ) +ATZ
THE SCATTER FROM STEM BOTTOM LEAVES AND SOIL TO MEASURABLE BUT NEGLIGIBLE SIZE 7HEN THOSE LEAVES WERE ABSENT THE SIGNALS SCATTERED FROM THE SOIL AND LOWER PARTS OF THE PLANT WERE ABOUT EQUAL TO EACH OTHER AND WERE MUCH LARGER THAN WHEN LEAVES WERE PRESENT
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&)'52% "OUNDARIES OF MEASURED RADAR RETURN NEAR VERTICAL INCIDENCE BASED ON 3ANDIA #ORPORATION DATA FROM & * *ANZA 2 + -OORE AND " $ 7ARNER
&)'52% !NGULAR RESPONSE OF THE SCATTERING COEFFICIENT FOR FIVE MOIST FIELDS WITH DIFFERENT ROUGHNESS AT A '(Z B '(Z AND C '(Z AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
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&)'52% !NGULAR DEPENDENCE OF THE DEPOLARIZATION RATIO OF A SMOOTH SURFACE AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
&)'52% -EASURED SCATTERING COEFFICIENT R LEFT SCALE AS A FUNCTION OF SOIL MOISTURE CONTENT FOR THREE SURFACE ROUGHNESSES 4HE SOLID CURVE IS THE REFLECTIVITY ' RIGHT SCALE CALCULATED ON THE BASIS OF DIELECTRIC MEASUREMENTS AFTER 4 ,E4OAN Ú )%%%
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&)'52% #ONTRIBUTIONS TO BACKSCATTER FROM A VEGETATION CANOPY OVER A SOIL SURFACE DIRECT BACKSCATTERING FROM PLANTS DIRECT BACKSCAT TERING FROM SOIL INCLUDES TWO WAY ATTENUATION BY CANOPY AND PLANT SOIL MULTIPLE SCATTERING AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
&)'52% &- #7 PROBING SCATTEROMETER MEASUREMENTS OF A CORN PLANT AT 4HE SOLID CURVE IS THE FULL PLANT THE DOT DASH CURVE LEAF REMOVED THE DOTTED CURVE LEAF REMOVED AFTER , + 7U ET AL
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"ECAUSE VOLUME SCATTER DOMINATES FOR DENSE VEGETATION ESPECIALLY TREES R IS NEARLY INDEPENDENT OF THE ANGLE OF INCIDENCE &IGURE SHOWS THIS WITH RESULTS FROM 8 BAND IMAGING OF A FOREST 4HE FIGURE IS A PLOT OF F RATHER THAN R F R COS P !T LOW FREQUENCIES SUCH AS 6(& THIS CONDITION CHANGES BECAUSE THE ATTENUATION THROUGH THE LEAVES AND BRANCHES IS LESS 3OIL -OISTURE &IGURE SHOWS THE SIZE OF THE EFFECT OF SOIL MOISTURE ON R 3OIL MOISTURE EFFECTS DIFFER FOR DIFFERENT SOILS $OBSON AND 5LABY SHOWED THAT THIS USE OF MOISTURE EXPRESSED IN PERCENT OF FIELD CAPACITY IMPROVED THE FIT BETWEEN R AND MOISTURE CONTENT &IELD CAPACITY IS A MEASURE OF HOW TIGHTLY THE SOIL PARTICLES BIND THE WATER THE UNBOUND WATER AFFECTS D MORE !N EMPIRICAL EXPRESSION FOR FIELD CAPACITY &# IS
&# 3 # PERCENT BY WEIGHT
WHERE 3 AND # ARE THE PERCENTAGES BY WEIGHT OF SAND AND CLAY IN THE SOIL 4HE SOIL MOISTURE CONTENT IN TERMS OF FIELD CAPACITY IS
MF MG &# PERCENT
WITH MG THE PERCENT MOISTURE IN THE SOIL BY WEIGHT 7HEN WE USE THIS MEASURE THE RELA TION BETWEEN R IN D" AND MF IS LINEAR EVEN IN THE PRESENCE OF MODERATE VEGETATION COVER AS SHOWN IN &IGURE 4HE SLOPE OF THIS CURVE IS SOMEWHAT DIFFERENT WITH VEGETA TION COVER THAN IT IS WITHOUT HOWEVER !LTHOUGH MF IS APPARENTLY AT LEAST AS GOOD AS THE VOLUMETRIC MOISTURE CONTENT FOR RELATING TO R ITS USE HAS BEEN QUESTIONED 3OIL MOISTURE CAN AFFECT A RADAR IMAGE AS HAS BEEN DEMONSTRATED IN IMAGERY OBTAINED FROM THE 3EASAT , BAND 3!2 ! SIMULATION EXPERIMENT SHOWED THAT ONE CAN ESTIMATE SOIL MOISTURE WITHIN FOR OF THE PIXELS IN AN IMAGE -OREOVER IT SHOWED THAT RESOLUTIONS BETWEEN AND M WERE SUPERIOR TO FINER RESOLUTIONS
&)'52% -EASURED SCATTERING VARIATION OF A FOREST PARCEL OF OLD BEECH TREES .OTE USE OF F WITH AN ARBITRARY REFERENCE INSTEAD OF R FOR THE ORDINATE AFTER $ ( (OEKMAN
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&)'52% '(Z SCATTERING COEFFICIENT VERSUS SOIL MOISTURE PERCENT OF FIELD CAPACITY FOR VEGETATION COVERED SOIL AFTER & 4 5LABY ET AL
FOR THIS PURPOSE -OST OF THE SPACEBORNE 3!2S THAT FOLLOWED 3EASAT HAVE BEEN USED IN SOIL MOISTURE STUDIES 6EGETATION "ACKSCATTER FROM VEGETATION DEPENDS ON MANY PARAMETERS AND VAR IES WIDELY 4HUS ALTHOUGH WE CAN DEVELOP AVERAGE MODELS LIKE THOSE DESCRIBED IN 3ECTION DETAILS ARE MUCH MORE COMPLEX 4HE R VARIES WITH SEASON MOISTURE CONTENT STATE OF GROWTH AND TIME OF DAY &IGURE SHOWS THE SEASONAL VARIATION FOR CORN COMPARED WITH A MODEL PRESENTED IN THE REFERENCE 4HE MUCH LARGER VARIATION AT R APPARENTLY RESULTS FROM THE LARGER EFFECT AT VERTICAL OF THE SOIL AND CONSEQUENTLY ITS MOISTURE CONTENT 4HE RAPID D" SWING BETWEEN -AY AND *UNE RESULTS FROM DRYING OF THE SOIL %VEN AT WHERE ATTENUATION THROUGH THE CANOPY MASKS THE SOIL EFFECT THE SEASONAL VARIATION EXCEEDS D" $IURNAL VARIATIONS ARE RELATIVELY SMALL BUT FINITE 4HEY RESULT BOTH FROM PLANT MOISTURE CHANGES AND FROM MORPHOLOGICAL CHANGES A CORN PLANT ACTUALLY LIFTS ITS LEAVES hTO MEET THE SUNv MORNING GLORIES CLOSE THEIR FLOWERS AT NIGHT -OST CROPS ARE PLANTED IN ROWS 4HIS CAUSES AN AZIMUTHAL VARIATION OF R AS SHOWN IN &IGURE 4HE MODULATION SHOWN IS THE RATIO OF R LOOKING PARALLEL TO THE ROWS MORE VEGETATION TO THAT LOOKING NORMAL 4HIS PHENOMENON IS MUCH MORE PRONOUNCED AT THE LOWER FREQUENCIES 3OME GENERAL PROPERTIES OF VEGETATION SCATTER ARE VISIBLE IN &IGURE !T LOW FREQUENCIES THE DECAY WITH P IS RAPID OUT TO ABOUT AND THEN MORE GRADUAL MOST OF THE STEEP PART RESULTS FROM SURFACE ECHO !T HIGHER FREQUENCIES THE PLANT ATTENU ATION PREVENTS A SIGNIFICANT SURFACE ECHO SO THE ANGULAR VARIATION IS MORE UNIFORM
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&)'52% 4IME VARIATION OF SCATTER FROM A CORN AND B ALFALFA AT INCIDENCE ANGLES OF VERTICAL AND AFTER % !TTEMA AND & 4 5LABY
#ROSS POLARIZED SIGNALS AT VERTICAL ARE NEGLIGIBLE SO EVEN AT LOW FREQUENCIES THE CROSS POLARIZED R VARIES UNIFORMLY !T BOTH HIGH AND LOW FREQUENCIES IT IS ABOUT D" BELOW THE LIKE POLARIZED R 3NOW 7HEN SNOW COVERS THE GROUND MUCH OF THE SCATTER IS FROM THE SNOW RATHER THAN THE UNDERLYING GROUND 3NOW IS BOTH A VOLUME SCATTERING AND AN ATTENUAT ING MEDIUM 7HEN THE SNOW IS DRY SCATTER COMES FROM A LARGE VOLUME WHEN IT IS WET THE SCATTERING VOLUME IS MUCH LESS BECAUSE OF HIGHER ATTENUATION !S A RESULT
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&)'52% &REQUENCY RESPONSE OF THE LOOK DIRECTION MODULATION RATIO FOR A SOYBEAN FIELD WITH HORIZONTAL POLARIZATION AT INCIDENCE ANGLES OF AND AFTER & 4 5LABY 2 + -OORE AND ! + &UNG
R DECREASES RAPIDLY AS THE SUN MELTS THE TOP LAYER &IGURE ILLUSTRATES HOW FAST THIS CAN BE AND ALSO SHOWS THAT THE EFFECT IS MUCH GREATER AT THE HIGHER FREQUENCIES WHERE ATTENUATION IS GREATER &IGURE SHOWS THE ANGULAR VARIATION SEEN FOR SNOW COVERED GROUND /FF VERTICAL SCATTERING IS MUCH GREATER AT HIGHER FREQUENCIES &OR THE CM DEPTH SHOWN MUCH OF THE SCATTER AT AND '(Z IS PROBABLY FROM THE UNDERLYING SURFACE 3OME REPORTS STATE THAT THERE ARE RADAR HOT SPOTS IN SNOW COVER PARTICULARLY AT '(Z 4HESE REPORTS RESULT FROM IMPROPER INTERPRETATION OF VARIATIONS THAT ARE DUE TO NORMAL 2AYLEIGH FADING OF THE SIGNAL 3CATTER FROM SNOW COMES FROM MANY CEN TERS WITHIN THE ILLUMINATED VOLUME SO THE CONDITIONS FOR 2AYLEIGH FADING ARE MET
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&)'52% #OMPARISON OF MODEL CALCULATIONS WITH MEASUREMENTS AT A '(Z AND B '(Z AFTER ( %OM AND ! + &UNG
-EASUREMENTS WITH SUITABLE AVERAGING IN FREQUENCY OR ILLUMINATION ANGLE DEMONSTRATE THAT SNOW COVERED SURFACES SCATTER ESSENTIALLY UNIFORMLY EXCEPT FOR THE EFFECTS OF THE MULTIPATH FADING 3EA )CE 3EA ICE IS A VERY COMPLEX MEDIUM )CE OBSERVERS CHARACTERIZE IT IN MANY DIFFERENT CATEGORIES THAT DEPEND ON THICKNESS AGE AND HISTORY OF FORMATION (ENCE ONE CANNOT CHARACTERIZE ITS RADAR RETURN IN ANY SIMPLE WAY IN THIS SENSE IT IS LIKE VEGETATION 4HE MOST IMPORTANT ICE TYPES FROM A RADAR POINT OF VIEW ARE FIRST YEAR &9 TO M THICK MULTIYEAR -9 M THICK AND A CONGLOMERATION OF THINNER TYPES M THICK ,IKE SNOW SEA ICE INFLUENCED BY SOLAR MELTING AND ABOVE FREEZING TEMPERATURES SCATTERS MICROWAVES VERY DIFFERENTLY FROM THE MORE NORMAL COLD SURFACE ICE )N WIN TER THE COLD -9 ICE SCATTERS MUCH MORE THAN COLD &9 ICE )N SUMMER R FOR -9 ICE DECREASES TO ABOUT THE SAME LEVEL AS THAT OF &9 ICE &IGURE SHOWS THIS AND TYPI CAL ANGULAR RESPONSES 4HESE CURVES ARE FOR '(Z BUT THE RESULTS WOULD BE SIMILAR AT ANY FREQUENCY DOWN TO 3 BAND &IGURE SHOWS THE FREQUENCY VARIATION OF R FOR VARIOUS KINDS OF ICE 3HORE FAST ICE IS GROUNDED TO THE BOTTOM AT THE SHORELINE IN THIS CASE IT IS PROBABLY -9 'RAY ICE IS ONE OF THE TYPES THINNER THAN &9 +IM DEVELOPED A THEORY THAT EXPLAINS A WIDE RANGE OF SEA ICE R MEASUREMENTS &ROM THIS AND EXTENSIVE DATA FROM THE LITERATURE ON ICE PROPERTIES &IGURE SHOWS THE RANGES OF &9 AND -9 SCATTERING UNDER WINTER CONDITIONS #LEARLY HIGHER FREQUENCIES ARE BETTER FOR IDENTIFYING ICE TYPES THAN LOWER FREQUENCIES AND
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&)'52% $IURNAL PATTERNS OF R AND LIQUID WATER CONTENT FOR SNOW AT SEVERAL FREQUENCIES .OTE THE EXTREME VARIATION OF THE +A BAND AS THE SUN STARTS TO MELT THE SURFACE AFTER 7 ( 3TILES AND & 4 5LABY
DISCRIMINATION IS NOT POSSIBLE BELOW ABOUT '(Z !T , BAND AND BELOW THE DIFFER ENCES BETWEEN -9 AND &9 ICE ARE SMALL EVEN IN WINTER 4HIS MEANS THAT IMAGING RADARS CAN EASILY DISTINGUISH ICE TYPES BY INTENSITY ALONE AT THE HIGHER FREQUENCIES IN WINTER BUT NOT IN SUMMER 4HIS FACT IS THE BASIS FOR OPERATIONAL ICE MONITORING SYSTEMS BY THE 3OVIET 5NION ;USING THE 4OROS +U BAND SIDE LOOKING AIRBORNE RADAR 3,!2 = AND #ANADA USING A MODIFIED 8 BAND !03 3,!2 AND THE 34!2 8 BAND 3!2 ! PRIME MOTIVATION FOR THE #ANADIAN 2ADARSAT 3!2 WAS MONITOR ING OF SEA ICE WHICH THE SYSTEM HAS BEEN DOING SUCCESSFULLY SINCE 4HE 2USSIAN 8 BAND REAL APERTURE RADARS IN THE /KEAN SERIES HAVE BEEN USED FOR SIMILAR PURPOSESn 3NOW COVER ON ICE CAN MASK ICE SCATTER ITSELF AS WITH SNOW ON LAND 3INCE THE ARCTIC IS RELATIVELY DRY MOST AREAS HAVE LITTLE SNOW BUT SNOW DOES MAKE DISTINGUISHING ICE TYPES DIFFICULT AT TIMES 4HIS IS PARTICULARLY TRUE IN THE !NTARCTIC WHERE SNOW IS MORE PREVALENT ON THE SEA ICE
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&)'52% !NGULAR RESPONSE OF R OF DRY SNOW AT DIFFERENT FREQUENCIES 2APID FALLOFF AT LOWER FREQUENCIES APPARENTLY RESULTS FROM PENETRATION TO THE SMOOTH GROUND SURFACE AFTER 7 ( 3TILES ET AL
0ROGRAMS TO LEARN MICROWAVE PROPERTIES OF SEA ICE HAVE BEEN NUMEROUS BECAUSE OF THE IMPORTANCE OF ARCTIC OPERATIONS AND METEOROLOGY -ICROWAVE REMOTE SENSING IS NECESSARY TO MONITOR ICE PROPERTIES IN THE ARCTIC OWING TO THE LONG WINTER NIGHT FREQUENT CLOUD COVER AND INACCESSIBILITY
£È°nÊÊ *" , /,9 3EVERAL SYNTHETIC APERTURE IMAGING RADARS ARE CAPABLE OF MEASURING THE FULL COM PLEX POLARIZATION MATRIX 0ROBABLY THE FIRST OF THESE WAS AN AIRBORNE SYSTEM BUILT BY .!3!S *ET 0ROPULSION ,ABORATORY 4HE FIRST ONE IN SPACE WAS THE 3HUTTLE )MAGING 2ADARn# 3)2 # !LTHOUGH USE OF MULTIPLE POLARIZATIONS DATES FROM THE EARLY DAYS OF IMAGING RADARS THE MEASUREMENT OF PHASE BETWEEN THE RECEIVED SIGNAL WITH DIFFERENT POLARIZATIONS IS MORE RECENT DATING FROM THE LATE S &EW IF ANY FULL POLARIMETRIC DATA SETS EXIST OF THE TYPE DESCRIBED ABOVE FOR SINGLE POLARIZATIONS &OR MORE COMPLETE DISCUSSIONS OF RADAR POLARIMETRY CONSULT REFERENCES 5LABY AND %LACHI 3LETTEN AND -C,AUGHLIN AND VAN :YL AND +IM 3INCE POLARIMETRIC RADARS USE DEFINED PHASES FOR BOTH TRANSMIT AND RECEIVE THE SIGNALS MUST BE DESCRIBED IN THE FORM USED FOR ELLIPTICAL POLARIZATION 4HIS IS ILLUSTRATED IN &IGURE
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&)'52% #OMPARISON OF SEA ICE SCATTERING AT '(Z IN SUMMER AND WINTER AFTER ! , 'RAY ET AL Ú )%%%
7HEN B THE POLARIZATION IS LINEAR WITH THE % VECTOR IN THE DIRECTION GIVEN BY X 7HEN B on THE POLARIZATION IS CIRCULAR WITH n FOR LEFT HAND AND n FOR RIGHT HAND 7HEN \ B \ n THE POLARIZATION IS ELLIPTICAL !NALYTICALLY THE ELECTRIC FIELD MAY BE DESCRIBED AS
% %HH %VV
WHERE H AND V ARE UNIT VECTORS IN THE H AND V DIRECTIONS 4HE INSTANTANEOUS FIELDS ARE GIVEN BY %Q WHERE THE DS SHOW THE DIFFERENT PHASES FOR THE COMPONENTS OF % AND K IS THE WAVENUMBER
EH T 2E %H E J WT KX D H
A
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&)'52% %XAMPLE OF FREQUENCY RESPONSE OF R FOR DIFFERENT KINDS OF SEA ICE FROM 9 3 +IM
AND EV T 2E %V J WT KZ D V
B
)N COMPLEX FORMAT
%H %H E JD H AND %V %V E JD V )F WE TAKE C CV n CH AND SET CV AS A REFERENCE WE CAN WRITE
% %H E JD %V V
4HUS FOR A SINGLE WAVE WE NEED ONLY HAVE THREE INDEPENDENT PARAMETERS )N RADAR WE MUST CONSIDER BOTH TRANSMITTED AND RECEIVED POLARIMETRIC SIGNALS SO THE NEED FOR FOUR MAGNITUDES AND TWO PHASES !NOTHER WAY TO DESCRIBE POLARIMETRIC SIGNALS IS TO USE THE MATRIX OF 3TOKES PARAMETERS
§ ¶ §) ¶ ¨ %H %V · ¨1· ¨ · & ¨ · ¨ %H %V · 5
¨ · ¨ 2E %H %V · ©¨6 ¸· ¨ )M % % · H V ¸ ©
4HE INDIVIDUAL 3TOKES PARAMETERS ) 1 5 AND 6 ARE DEFINED AS SHOWN IN %Q
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&)'52% -EASUREMENT BASED THEORETICAL R VARIATIONS FOR FIRST YEAR AND MULTIYEAR SEA ICE 2ANGES ARE DETERMINED BY USING KNOWN VARIATIONS OF ICE CHARAC TERISTICS AFTER 9 3 +IM ET AL
3OME OF THE RETURN SIGNALS FROM A RESOLUTION CELL MAINTAIN THEIR POLARIZATION CHARAC TERISTICS OVER TIME AND SPACE WHEREAS OTHERS HAVE A RANDOM POLARIZATION 4HIS OCCURS AS FOR SUNLIGHT WHEN THE POLARIZATION ELLIPSE CHANGES ITS PROPERTIES RANDOMLY AND RAPIDLY WITH TIME OR WITH SMALL DIFFERENCES IN ANGLE 7HEN BOTH THE PERSISTENT AND RANDOM PARTS
&)'52% 0OLARIMETRIC ELLIPSE B IS THE ELLIPTICITY ANGLE AND X IS THE ORIENTATION ANGLE 4HE ELLIPSE IS THE LOCUS OF THE END OF THE % VECTOR THROUGHOUT A CYCLE
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ARE PRESENT THE TARGET IS SAID TO BE PARTIALLY POLARIZED WHEN NO RANDOM COMPONENT IS PRESENT THE TARGET IS FULLY POLARIZED 2ADAR SIGNALS ARE FREQUENTLY ONLY PARTIALLY POLARIZED ESPECIALLY WHERE MULTIPLE BOUNCES OCCUR WITHIN THE TARGET AREA &OR THE NONRANDOM PART WE MUST DEFINE A 3TOKES VECTOR USING AN ENSEMBLE AVERAGE OF EACH COMPONENT THE AVERAGING MAY BE OVER TIME OR LOOK ANGLE 4HUS WE HAVE § ¨ ¨ & ¨ ¨ ¨ ¨ ©
%H %V ¶ · · %H %V · · 2E%H %V · )M%H %V ·¸
WHEN THE WAVE IS COMPLETELY POLARIZED
) 1 5 6
) 1 5 6
BUT WHEN IT IS PARTIALLY POLARIZED
)N FACT WHEN THE WAVE IS COMPLETELY UNPOLARIZED SUNLIGHT FOR EXAMPLE %V AND %H ARE UNCORRELATED SO 5 AND 6 ARE BOTH ZERO 7AVES OF THIS TYPE ARE USED IN POLARIMETRIC RADAR HOWEVER TO SEE HOW THE SCATTER ING COEFFICIENT WORKS WE NEED TO CONSIDER BOTH THE INCIDENT AND SCATTERED WAVE !T THIS POINT WE MUST INTRODUCE THE SCATTERING MATRIX 3 4HE RECEIVED FIELD MAY BE REPRESENTED BY
JK2 %R E 3 %T 2
WHERE
§% T ¶ §% R ¶ % R ¨ VR · AND %T ¨ VT · ©%H ¸ ©%H ¸
AND
§3 3 ¨ VV ©3HV
3VH ¶ 3HH ·¸
)N THE USUAL RECIPROCAL MEDIA 3VH 3HV 3INCE THE CHOICE OF A PHASE REFERENCE IS ARBITRARY THERE ARE THEN THREE INDEPENDENT MAGNITUDES \3VV\ \3HH\ \3HV\ BUT ONLY TWO INDEPENDENT PHASES 3HH 3HV 4HESE QUANTITIES CAN BE USED TO DESCRIBE THE PROPER TIES OF THE POLARIZED PART OF THE ECHO FROM A TARGET 7E CAN ALSO DESCRIBE THE SCATTERING USING THE -UELLER MATRIX THAT IS RELATED TO THE 3TOKES MATRIX 4HE READER IS REFERRED TO THE LITERATURE FOR FURTHER DESCRIPTIONS OF THE -UELLER MATRIX
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4HE USUAL WAY TO OBTAIN POLARIZED RESPONSES IS TO TRANSMIT ALTERNATE VERTICALLY AND HORIZONTALLY POLARIZED PULSES 0RESUMING THERE IS ALMOST NO CHANGE IN THE TARGET DUR ING THE INTERPULSE INTERVAL THE RESPONSES MAY BE COMBINED TO PRODUCE THE SCATTERING MATRIX OR -UELLER MATRIX "Y COMBINING THE SIGNALS IN PROCESSING THIS METHOD PERMITS SYNTHESIZING EQUIVALENT TRANSMITTED POLARIZATIONS WITH ANY ELLIPTICITY AND ORIENTATION ! COMMONLY USED WAY TO DESCRIBE THE POLARIZATION CHARACTERISTICS OF A TARGET IS THE POLARIZATION SIGNATURE 4HIS CONSISTS OF TWO THREE DIMENSIONAL GRAPHS &OR THE FIRST GRAPH CALLED COPOLARIZED ONE USES THE COMPONENTS OF THE RECEIVED SIGNAL THAT ARE THE SAME AS THE TRANSMITTED SIGNAL POLARIZATION 4HE SECOND GRAPH USES COMPONENTS OF THE RECEIVED SIGNAL THAT ARE ORTHOGONAL TO THE TRANSMITTED SIGNAL &IGURE GIVES A WIDELY QUOTED EXAMPLE OF THIS TYPE OF DISPLAY FOR IMAGES OF 3AN &RANCISCO 4HE AXES IN THE HORIZONTAL PLANE ARE THE ORIENTATION ANGLE FOR THE SYNTHESIZED TRANSMITTED SIGNAL XT AND ITS ELLIPTICITY ANGLE BT 4HE VERTICAL AXIS IS RELATIVE POWER 6ALUES OF XT n AND n ARE HORIZONTAL POLARIZATION WHEREAS XT n IS VER TICAL POLARIZATION ,INEAR POLARIZATION OCCURS WHEN BT n AND RIGHT AND LEFT CIRCULAR POLARIZATIONS OCCUR WHEN BT on 7HEN THE MINIMUM IS ABOVE ZERO THE PEDESTAL BENEATH IT CORRESPONDS TO THE UNPOLARIZED SIGNAL 4HE OCEAN IMAGE IN &IGURE A SHOWS THAT THE POLARIZATION IS ESSENTIALLY LIN EAR WITH THE 66 SIGNAL STRONGER THAN THE (( 4HE CROSS POLARIZED RESPONSE SHOWS ESSENTIALLY NO CROSS POLARIZED SIGNAL FOR LINEAR TRANSMISSION BUT SOME FOR CIRCULARLY POLARIZED TRANSMISSION &OR THE PARK SHOWN IN &IGURE B THE VERTICALLY POLARIZED LINEAR SIGNAL IS SLIGHTLY HIGHER THAN THE HORIZONTALLY POLARIZED ONE 4HERE IS SOME CROSS POLARIZED RESPONSE FOR THE LINEAR SIGNAL AND SOME UNPOLARIZED SIGNAL &OR THE URBAN AREA SHOWN THE STRONGEST RESPONSES ARE TILTED IN ORIENTATION IN BOTH THE COPOLARIZED AND CROSS POLARIZED CASES !# )"+! %,!' %'"-%$) # !')" # ) "' *# ' ) "$! '
! !() # *$&%# '"-!
&)'52% 3ELECTION OF POLARIZATION SIGNATURES FROM 3!2 IMAGE OF 3AN &RANCISCO A AN OCEAN AREA B A LARGE PARK AND C ONE OF SEVERAL URBAN AREAS AFTER $ , %VANS Ú )%%%
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4HE ACTUAL NUMBERS FOR THE COPOLARIZED RESPONSE FOR THIS CASE ARE B n 66 AND X n 4HE REFERENCE PRESENTS SIMILAR PLOTS SHOWING SEPARATELY THE POLARIZED AND UNPOLARIZED RESPONSES "ECAUSE OF THE COMPLEXITY OF THIS REPRESENTATION AND OTHERS FOR POLARIMETRIC SIGNALS ONE CANNOT AS READILY PROVIDE CURVES OF RESPONSE AS FOR SINGLE POLARIZATION IMAGES (ENCE WE DO NOT FIND MANY CATALOGS OF POLARIMETRIC SCATTERING RESPONSES .EVERTHELESS MANY AUTHORS HAVE DESCRIBED THE USE OF POLARIMETRIC IMAGES 3OME OF THE PAPERS USING THE TERM POLARIMETRIC REALLY REFER TO THE USE OF JUST (( 66 AND (6 POLARIZATIONS WITHOUT REGARD FOR THE PHASE )N THIS SENSE THEY ARE USING THESE IMAGES IN THE WAY THAT LIKE AND CROSS POLARIZED IMAGES HAVE BEEN USED SINCE THE START OF IMAGING RADARS /THERS HOWEVER TAKE FULL ADVANTAGE OF THE FULL POLARIZATION MATRIX /NE WAY TO USE THE FULL MATRIX IS TO SYNTHESIZE POLARIZATIONS THAT EITHER EMPHASIZE OR SUPPRESS PARTICULAR CLASSES OF TARGETS &OR EXAMPLE IN &IGURE C ONE COULD SYN THESIZE A n ORIENTATION ANGLE FOR A LINEAR POLARIZATION TO EMPHASIZE THIS CLASS OR USE VERTICAL POLARIZATION TO SUPPRESS THE DOMINANT CLASS IN THE IMAGE 6ARIOUS AUTHORS HAVE SHOWN THAT ONE CAN SYNTHESIZE AN ELLIPTICAL POLARIZATION THAT INCREASES THE TARGET TO CLUTTER RATIO WHERE THE TARGET IS FOR EXAMPLE A MANMADE OBJECT 3WARTZ ET AL FOUND A POLARIZATION THAT GAVE A D" TARGET TO CLUTTER RATIO WHERE THE TARGET WAS AN URBAN AREA AND THE CLUTTER WAS REPRESENTED BY A PARK IN THE 3AN &RANCISCO IMAGE USED TO PRODUCE &IGURE (E FOUND THIS WAS OBTAINED WITH TRANSMITTER POLARIZATION HAVING XE BT n n AND RECEIVER POLARIZATION OF XE BT 4HIS COMPARES WITH THE BEST RESULT USING LIKE AND CROSS POLARIZATIONS WITHOUT PHASE COHERENCE OF D" /THERS USE THE THREE INDEPENDENT MAGNITUDES OF THE SCATTERING MATRIX AND THE PHASE ANGLE D BETWEEN THE (( AND 66 RESPONSES 2ESEARCH HAS SHOWN THERE IS LITTLE USEFUL INFORMATION IN THE PHASE ANGLE RELATING (( TO CROSS POLARIZATION ! COMMON USE OF THESE DATA IS IN PRODUCING STATE VECTORS TO EMPLOY IN DISCRIMINATION OF TARGET AREAS WITH THE COMPONENTS OF THE VECTORS BEING THE THREE MAGNITUDES AND THE PHASE ANGLES FOR EACH FREQUENCY USED 4HESE VECTORS ARE THEN USED IN VARIOUS STATISTICAL ALGORITHMS TO IDENTIFY DIFFERENT TARGET CLASSES 4HIS APPROACH HAS ALSO BEEN USED IN OTHER FORESTS AGRICULTURAL AREAS SEA ICE AND SNOW AND TO IDENTIFY SURFACE CLASSES OF GEOLOGIC SIGNIFICANCE !N EXAMPLE OF THE USE OF PHASE DIFFERENCE IN DISCRIMINATING SURFACE CLASSES IN THE !MAZON BASIN IS ILLUSTRATED IN &IGURE .OTE THE SIGNIFICANT DIFFERENCES BETWEEN # AND 8 BAND FOR -ACROPHYTE AND &LOODED FOREST 4HESE DIFFERENCES COULD BE USED AS DISCRIMINATORS TO IDENTIFY THESE CLASSES BUT NORMALLY THEY WOULD SIMPLY BE ADDITIONAL ELEMENTS IN THE STATE VECTORS USED IN STATISTICAL ALGORITHMS
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4HE RESULTS WERE DESCRIBED IN TERMS OF R & WHICH WAS CALLED CLUTTER STRENGTH & IS A PROPAGATION FACTOR THAT ACCOUNTS FOR MULTIPATH ATTENUATION ETC BUT COULD NOT BE MEASURED SEPARATELY 7HEREAS ANGLE OF INCIDENCE IS USED TO DESCRIBE RESULTS IN STUDIES WHERE POINTING IS NEARER VERTICAL DEPRESSION OR GRAZING ANGLE IS A MORE APPROPRIATE DESCRIPTION WHEN DEALING WITH ANGLES WHERE INCIDENCE IS CLOSER TO HORIZONTAL 'RAZING ANGLE IS THE COM PLEMENT OF INCIDENCE ANGLE 4HE MEASUREMENTS WERE ALL AT LOW DEPRESSION ANGLES WITH THIS TERM USED IN LIEU OF GRAZING ANGLE BECAUSE IT CAN BE DEFINED IN TERMS OF ANTENNA POINTING WHEREAS GRAZING ANGLE ALSO DEPENDS ON LOCAL SLOPE WHICH IS BOTH VARIABLE AND IN GENERAL UNKNOWN )MAGES TAKEN AT NEAR GRAZING ANGLES TEND TO BE EXTREMELY hPATCHYv BECAUSE ANY PROJECTIONS ABOVE THE SURFACE TREES HILLS BUILDINGS FENCES POWER LINES MACHINERY AND VEHICLES PRESENT SURFACES MORE NEARLY NORMAL TO THE BEAM 4HUS NEARBY PIXELS MAY HAVE CLUTTER STRENGTH DIFFERING BY TENS OF D" -OREOVER SMALL SLOPES FACING THE RADAR INCREASE THE GRAZING ANGLE RESULTING IN STRONGER ECHOES WHEREAS SLOPES AWAY FROM THE RADAR DECREASE THE SIGNAL OR MAY OBLITERATE IT BY SHADOWING "ECAUSE OF THIS EFFECT THE PROBABILITY DISTRIBUTIONS OF NEAR GRAZING ECHOES ARE VERY DIF FERENT FROM THOSE AT MORE MODERATE INCIDENCE ANGLES !LTHOUGH SOME SMALL REGIONS WITHOUT SIGNIFICANT PROJECTIONS OR FORWARD SLOPES MAY HAVE 2AYLEIGH DISTRIBUTIONS OR IF ONLY ONE LARGE SCATTERER IS PRESENT 2ICEAN DISTRIBUTIONS MOST AREAS HAVE OTHER DISTRIBUTIONSOFTEN 7EIBULL OR EVEN LOG NORMAL 4HE RESULT IS THAT THE MEAN ESTIMATED R & IS OFTEN MUCH HIGHER THAN THE MEDIAN A FEW TARGETS OR D" HIGHER CAN RAISE THE MEAN A LOT EVEN THOUGH THE TARGETS OCCUPY ONLY A TINY FRACTION OF THE AREA 4HUS ONE SHOULD BE CAREFUL IN USING MEAN VALUES FOR RADAR DESIGN THE MEDIAN VALUES ARE MORE REPRESENTATIVE "ILLINGSLEY PRESENTED HIS RESULTS BOTH IN TERMS OF MEAN VALUES AND MEDIAN VALUES (ERE WE REPORT ONLY THE MEDIAN VALUES BECAUSE THEY TEND TO BE MORE MEANINGFUL FOR RADAR DESIGN THAN THE VALUES DISTORTED BY OCCASIONAL STRONG TARGETS &OR MOST AREAS LITTLE DIFFERENCE WAS FOUND BETWEEN VERTICAL AND HORIZONTAL POLARIZATIONS SO THE RESULTS WERE REPORTED FOR DATA GROUPS INCLUDING BOTH POLARIZATIONS &IGURE SHOWS THE RESULTS GROUPED BY TARGET CLASS
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&OR &IGURE A AND B THE DEPRESSION ANGLE AND TYPE ARE THE PARAMETERS WHEREAS FOR &IGURE C THE TERRAIN SLOPE IS THE PARAMETER 4HE LINES ARE BASED ON LINEAR REGRESSION ON THE LOGARITHMIC FREQUENCY SCALE WITH THE EXCEPTION OF DESERT AND GRASS AT VERY LOW DEPRESSION ANGLES WHERE A QUADRATIC REGRESSION WAS USED .OTE THAT URBAN MOUNTAIN AND FOREST TEND TO HAVE RELATIVELY HIGH VALUES COMPARED WITH AGRICULTURE AND UNCULTIVATED LAND WITH MODERATE SLOPES
£È°£äÊ Ê, ,Ê / ,*, //" 3IDE LOOKING FINE RESOLUTION IMAGING RADARS WITH REAL OR SYNTHETIC APERTURES PRO DUCE IMAGES THAT CLOSELY RESEMBLE AERIAL PHOTOGRAPHS "OTH SHADOWS AND DIFFER ENCES IN R FOR DIFFERENT PARTS OF THE GROUND PRODUCE IMAGE INTENSITY VARIATIONS LIKE THOSE IN PHOTOGRAPHS &OR THIS REASON PHOTOINTERPRETERS CAN EASILY LEARN TO INTERPRET RADAR IMAGES (OWEVER SINCE THE RADAR IMAGES ARE DUE TO MICROWAVE REFLECTIVITY NOT OPTICAL REFLECTIVITY THE INTERPRETERS MUST UNDERSTAND THE DIFFERENCES AND THAT THE IMAGES AT THE DIFFERENT WAVELENGTHS ARE IN FACT COMPLEMENTARY -OREOVER THE GEOMETRICAL DISTORTIONS FOR RADAR IMAGES ARE THOSE OF A SIDE LOOKING RANGE MEASURE MENT SYSTEM WHEREAS THOSE OF AERIAL PHOTOS ARE THOSE OF A DOWN LOOKING ANGLE MEASUREMENT SYSTEMA DIFFERENCE THAT THE INTERPRETER MUST UNDERSTAND !T LOW GRAZING ANGLES THE DISTORTIONS ARE SMALL FOR RADAR BUT AT LOW INCIDENCE ANGLES THEY ARE LARGE -OREOVER THE SPECKLE IN RADAR IMAGES IS NOT PRESENT IN PHOTOGRAPHS -ODERN IMAGING RADARS USE DIGITAL RECORDING AND PROCESSING AND THE IMAGES ARE PRODUCED ON FILM OR MANIPULATED DIGITALLY "ECAUSE THE SIDE LOOKING CONFIGURATION PRODUCES A STRIP IMAGE THE OUTPUT FILMS ARE USUALLY IN THE FORM OF LONG STRIPS -OST CAMERAS PRODUCE SEPARATE IMAGES THAT ARE APPROXIMATELY SQUARE 3TRIP FILM CAMERAS AND OPTICAL INFRARED SCANNERS PRODUCE STRIP IMAGES LIKE THOSE OF RADARS BUT WITH DIFFER ENT DISTORTIONS BECAUSE THEY ARE ANGLE NOT RANGE MEASURING DEVICES %VERY PURE AND APPLIED SCIENCE THAT USES AERIAL PHOTOGRAPHY CAN ALSO USE RADAR IMAGES 4HIS IS PARTICULARLY USEFUL IN CLOUDY ENVIRONMENTS BUT RADAR IS ALSO USEFUL EVEN IN CLEAR WEATHER BECAUSE PERFORMANCE IS INDEPENDENT OF TIME OF DAY SO SUN ANGLE DOES NOT MATTER -OREOVER RADAR GROUND SIGNATURES DIFFER FROM THOSE IN THE VISIBLE AND INFRARED 2ADAR HAS BEEN APPLIED TO AGRICULTURE FORESTRY GEOLOGY HYDROLOGY URBAN GEOGRAPHY REGIONAL STUDIES OCEANOGRAPHY AND ICE MAPPING &ADING COMPLICATES THE INTERPRETATION OF IMAGES BY PRODUCING SPECKLE 4HIS MEANS THAT AVERAGING OF THE SPECKLED IMAGE USUALLY IS NECESSARY 3OMETIMES THE PROCESSOR DOES THE AVERAGING AND SOMETIMES THE INTERPRETER DOES IT MENTALLY IT MUST BE DONE TO INTERPRET AN IMAGE 4HE IMAGE INTENSITY FOR INDIVIDUAL PIXELS WITH A SINGLE LOOK 3!2 FOLLOWS THE 2AYLEIGH DISTRIBUTION ACTUALLY THE EXPONENTIAL DISTRIBUTION IF SQUARE LAW DETECTION IS USED -OST 3!2 PROCESSORS SACRIFICE SOME SPATIAL RESOLUTION BY AVER AGING SAY FOUR PIXELS TOGETHER AFTER DETECTION 4RANSMITTING MORE BANDWIDTH THAN NEEDED FOR RANGE RESOLUTION ACCOMPLISHES THIS PURPOSE WITHOUT LOSS OF NEEDED SPA TIAL RESOLUTION BUT IT TAKES MORE TRANSMITTER POWER 3UITABLE FREQUENCY AGILITY CAN ACCOMPLISH THE SAME RESULT 4RADEOFFS EXIST BETWEEN SPATIAL RESOLUTION AND MEASUREMENT PRECISION 4HE LATTER CAN BE USED TO DEFINE A GRAY LEVEL RESOLUTION /NE CAN THEN THINK OF IMAGE RESOLUTION IN TERMS OF A VOLUME
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WHERE RA IS THE ALONG TRACK RESOLUTION RY IS THE GROUND RANGE RESOLUTION AND RG IS THE GRAY LEVEL RESOLUTION 4HE REFERENCED STUDY SHOWED THAT INTERPRETABILITY DEPENDS ON 6 SO TRADEOFFS BETWEEN THE THREE ELEMENTS OF 6 ARE POSSIBLE "EST RESULTS FOR A HUMAN INTERPRETER OCCUR WHEN THREE INDEPENDENT SAMPLES OF THE FADING ARE AVERAGED )GNORING THIS FADING SPECKLE CAN LEAD TO ERRONEOUS CONCLUSIONS ON THE SPATIAL RESOLUTION NEEDED FOR A GIVEN APPLICATION 3INGLE FREQUENCY SINGLE POLARIZATION RADAR IMAGES ARE USEFUL (OWEVER USE OF MULTIPLE POLARIZATIONS PARTICULARLY INCLUDING CROSS POLARIZATION AND MULTIPLE FREQUEN CIES CLEARLY INCREASES THEIR VALUE $IFFERENT ANGLES OF INCIDENCE ARE MOST SUITABLE FOR DIFFERENT APPLICATIONS &OR EXAMPLE SOIL MOISTURE MONITORING IS BEST WITHIN OF VER TICAL AT FREQUENCIES NEAR '(Z 6EGETATION DISCRIMINATION IS BETTER HOWEVER AT HIGHER FREQUENCIES AND ANGLES OF INCIDENCE &OR SOME APPLICATIONS USE OF THE FULL POLARIZATION MATRIX INCLUDING THE PHASE IS USEFUL 4HE PHASE INFORMATION IS PARTICULARLY HELPFUL IN ASSESSING SCATTERING MECHANISMS AS IN FORESTS "ECAUSE THE LITERATURE IN THIS FIELD IS SO MASSIVE THE RADAR ENGINEER WISHING TO LEARN MORE ABOUT THE SUBJECT SHOULD CONSULT THE -ANUAL OF 2EMOTE 3ENSING -ICROWAVE 2EMOTE 3ENSING ESPECIALLY 6OL ))) AND #HAPTER OF 6OL )) AND THE JOURNALS OUTLINED EARLY IN 3ECTION
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-OST OF THE DISCUSSION IN THIS (ANDBOOK CONCERNS REAL APERTURE RADAR 2!2 WHERE THE ANTENNA IS A PHYSICAL OBJECT THAT FIRST EMITS AND THEN COLLECTS THE RADIA TION 7E TURN OUR ATTENTION TO THE CASE WHERE THE ANTENNA MOVES TO COVER A SYN THETIC APERTURE THUS PRODUCING SYNTHETIC APERTURE RADAR 3!2 4HIS OVERVIEW IS BASED ON 3ULLIVAN AND #UTRONAo MORE DETAILED TREATMENTS ARE ALSO PROVIDED IN THE LITERATUREn
£Ç°£Ê - Ê*, * Ê"Ê-, &OR AIRBORNE OR SPACEBORNE GROUND MAPPING RADAR THERE HAS BEEN CONTINUOUS DESIRE TO ACHIEVE FINER RESOLUTION 7E SHALL USE THE TERM RANGE RESOLUTION TO MEAN THE RESOLU TION ALONG THE LINE OF SIGHT ,/3 FROM THE RADAR TO THE TARGET REGION AND CROSSRANGE RESOLUTION TO MEAN THE RESOLUTION ALONG THE DIRECTION PERPENDICULAR TO THE ,/3 AND PARALLEL TO THE GROUND 4HE FORMER IS ALSO FREQUENTLY TERMED DOWNRANGE RESOLUTION TO EMPHASIZE THAT IT IS ALONG THE ,/3 #ROSSRANGE RESOLUTION IS ALSO FREQUENTLY CALLED AZI MUTH RESOLUTION SINCE IT IS MEASURED ALONG A LINE OBTAINED BY HOLDING RANGE CONSTANT AND VARYING THE AZIMUTH AS MEASURED FROM THE PHYSICAL ANTENNA OF THE ,/3 )F AND ONLY IF THE ,/3 REMAINS PERPENDICULAR TO THE DIRECTION OF FLIGHT RANGE RESOLUTION IS SOMETIMES CALLED CROSS TRACK RESOLUTION AND CROSSRANGE RESOLUTION IS SOMETIMES CALLED ALONG TRACK RESOLUTION 7ITH RESPECT TO 3!2 RESOLUTION THE PREFERRED TERMS ARE FINE AND COARSE "ETTER RESOLUTION IS FINER NOT GREATER POORER RESOLUTION IS COARSER NOT LESS )N THIS WAY AMBIGUITY IN TERMINOLOGY CAN BE AVOIDED /F COURSE IN PRACTICE THE TERMS HIGH RESOLUTION FINE RESOLUTION AND LOW RESOLUTION COARSE RESOLUTION ARE OFTEN USED WITHOUT AMBIGUITY #ROSSRANGE RESOLUTION WAS INITIALLY ACHIEVED BY USE OF A NARROW BEAM 4HE BEAM WIDTH IN RADIANS P" OF AN APERTURE ANTENNA IS GIVEN APPROXIMATELY BY THE WAVELENGTH
4HE PRESENT CHAPTER DRAWS SIGNIFICANTLY FROM $R 3ULLIVANS BOOK 2ADAR &OUNDATIONS FOR )MAGING AND !DVANCED #ONCEPTS 2ALEIGH .# 3CI4ECH 0UBLISHING $R 3ULLIVAN IS GRATEFUL TO 3CI4ECH FOR PERMISSION TO QUOTE CONSIDERABLE MATERIAL FROM THE CHAPTERS ON 3!2 (E IS ALSO GRATEFUL TO -R -ICHAEL 4ULEY )NSTITUTE FOR $EFENSE !NALYSES FOR REVIEWING THE MANUSCRIPT PRIOR TO PUBLICATION AND SUGGESTING MANY IMPROVEMENTS o )N THE FIRST TWO EDITIONS OF THIS (ANDBOOK THE CHAPTER ON 3!2 WAS WRITTEN BY $R ,OUIS * #UTRONA WHO IS NOW DECEASED )N $R 3ULLIVAN HAD THE PRIVILEGE OF WORKING WITH $R #UTRONA AT THE %NVIRONMENTAL 2ESEARCH )NSTITUTE OF -ICHIGAN !NN !RBOR NOW 'ENERAL $YNAMICS 9PSILANTI AND IS GRATEFUL FOR HAVING LEARNED MUCH FROM HIM CONCERNING 3!2
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K DIVIDED BY THE APERTURE DIAMETER P" y K $ 4HE CORRESPONDING LINEAR CROSSRANGE RESOLUTION AT RANGE 2 IS THEN
D CR y
2L REAL APERTURE $
&OR EXAMPLE IF K CM 8 BAND AND $ M P" y RADIANS !T A RANGE OF 2 KM THE CROSSRANGE RESOLUTION WOULD BE 2 P" y KM HARDLY FINE ENOUGH TO RESOLVE SUCH TARGETS AS BUILDINGS AND VEHICLES (OWEVER BY USING APPROPRIATE COHERENT PROCESS ING AN APERTURE OF MODEST SIZE MAY BE MOVED EG BY AN AIRCRAFT OR SPACECRAFTREFERRED TO AS THE PLATFORM ALONG A PATH IN SPACEA SYNTHETIC APERTUREAND MAY ACHIEVE CROSS RANGE RESOLUTION COMPARABLE TO WHAT WOULD IN PRINCIPLE BE ACHIEVED BY A REAL APERTURE WITH A LENGTH EQUAL TO THE PATH LENGTH SYNTHETIC APERTURE ,3!
D CR y
2L L y SYNTHETIC APERTURE ,3! $P
WHERE $P IS THE SYNTHETIC APERTURE ANGLE IE THE ANGLE SUBTENDED BY THE SYNTHETIC APERTURE AS SEEN FROM THE TARGET AREA 4HE ADDITIONAL FACTOR OF TWO IN THE DENOMINATOR COMPARED WITH %Q OCCURS BECAUSE OF THE 3!2 PROCESSING AND WILL BE DISCUSSED &OR EXAMPLE FOR A PATH LENGTH OF KM THE CROSSRANGE RESOLUTION FOR THE CASE DISCUSSED ABOVE WOULD BE y CM CLEARLY A SUPERB IMPROVEMENT OVER THE REAL APERTURE CASE
£Ç°ÓÊ , 9Ê-/",9Ê"Ê-, 4HE ORIGINAL CONCEPT OF 3!2 WAS FIRST DESCRIBED BY #ARL 7ILEY OF 'OODYEAR IN (E CALLED IT DOPPLER BEAM SHARPENING $"3 ,ATER THE DOPPLER BEAM SHARPENING MODE OF 3!2 WAS INTRODUCED AS THE NAME FOR A VARIABLE SQUINT ANGLE MODE THAT PRODUCED A PARTIAL PLAN POSITION INDICATOR 00) DISPLAY 4HUS $"3 REALLY HAS TWO MEANINGS IN 3!2 THE NAME FOR 3!2 INVENTED BY 7ILEY BEFORE IT WAS CALLED 3!2 AND THE NAME FOR A 00) LIKE MODE BASED ON SQUINTED 3!2 )N THE 5NIVERSITY OF )LLINOIS DEMONSTRATED THE 3!2 CONCEPT )N DURING A SUMMER STUDY THAT LAUNCHED A PROGRAM KNOWN AS 0ROJECT -ICHIGAN IDEAS RELATED TO SYNTHETIC APERTURES WERE DISCUSSED BY , * #UTRONA OF THE 5NIVERSITY OF -ICHIGAN 7ILLOW 2UN ,ABORATORIES # 7 3HERWIN OF THE 5NIVERSITY OF )LLINOIS 7 (AUSZ OF 'ENERAL %LECTRIC AND * +OEHLER OF 0HILCO #ORPORATION 4HIS RESULTED IN A SUCCESSFUL 3!2 PROGRAM BY THE -ICHIGAN GROUP 4HE )LLINOIS GROUP ALSO DEMONSTRATED SUCCESS FUL 3!2 IMAGING 4HE WORK OF #UTRONA ET AL AND 3HERWIN ET AL PLUS MANY OTHER EARLY 3!2 PAPERS ARE COMPILED IN A VERY USEFUL BOOK BY +OVALY -ORE DETAILED HISTORIES OF 3!2 DEVELOPMENT ARE GIVEN BY #URLANDER AND -C#ONOUGH *ACKSON AND !PEL AND !USHERMAN ET AL
£Ç°ÎÊ /9* -Ê"Ê-, 7HEN WE REFER TO 3!2 WE USUALLY MEAN FOCUSED 3!2 THE TERM INDICATES THAT THE PHASE INFORMATION HAS BEEN OPTIMALLY PROCESSED TO PRODUCE RESOLUTION COMPARABLE TO THE THEORETICAL LIMIT )N THE DEVELOPMENT OF 3!2 SEVERAL INTERESTING TECHNIQUES
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PRECEDED THE DEVELOPMENT OF FOCUSED 3!2 4HESE TECHNIQUES ARE DISCUSSED IN ORDER OF PROGRESSIVELY FINER RESOLUTION 0RECURSORS TO &OCUSED 3!2 3IDE ,OOKING !IRBORNE 2ADAR 3,!2 3,!2 CONSISTED OF AN AIRCRAFT MOUNTED 2!2 POINTED PERPENDICULAR TO THE DIRECTION OF FLIGHT HENCE hSIDE LOOKINGv WITH CROSSRANGE RESOLUTION ^ 2K$ $OPPLER "EAM 3HARPENING $"3 !S PREVIOUSLY MENTIONED WHEN 7ILEY FIRST CONCEIVED OF THE CONCEPT THAT WE NOW CALL 3!2 HE TERMED IT DOPPLER BEAM SHARP ENING 7ILEY EXPLAINED IT AS FOLLOWS h) HAD THE LUCK TO CONCEIVE OF THE BASIC IDEA WHICH ) CALLED $OPPLER "EAM 3HARPENING $"3 RATHER THAN 3YNTHETIC !PERTURE 2ADAR 3!2 ,IKE ALL SIGNAL PROCESSING THERE IS A DUAL THEORY /NE IS A FREQUENCY DOMAIN EXPLANATION 4HIS IS $OPPLER "EAM 3HARPENING )F ONE PREFERS ONE CAN ANA LYZE THE SYSTEM IN THE TIME DOMAIN INSTEAD 4HIS IS 3!2 4HE EQUIPMENT REMAINS THE SAMEnJUST THE EXPLANATION CHANGES #ONCEPTION WAS REPORTED IN A 'OODYEAR !IRCRAFT REPORT IN v 3UBSEQUENTLY AS DESCRIBED IN 3ECTION OF 3CHLEHER $"3 CAME TO REFER TO AN AIRBORNE SCANNING MODE IN WHICH THE ECHOES FROM THE SCANNING REAL BEAM ARE DOPPLER PROCESSED TO PRODUCE CROSSRANGE RESOLUTION FINER THAN THAT PROVIDED BY THE REAL BEAM ALONE BROADSIDE CROSSRANGE RESOLUTION IS y 2K ,$"3 WHERE ,$"3 IS THE SYNTHETIC APER TURE LENGTH GENERATED DURING A TARGET DWELL 3TIMSON EXPLAINS h4YPICALLY THE ANTENNA CONTINUOUSLY SCANS THE REGION OF INTEREST"ECAUSE THE INTEGRATION TIME IS LIMITED TO THE LENGTH OF TIME A GROUND PATCH IS IN THE ANTENNA BEAMOR IF YOU PREFER THE LENGTH OF THE ARRAY THAT CAN BE SYNTHESIZED IS SO LIMITEDTHE RESOLUTION IS COARSER THAN CAN BE ACHIEVED WITH A NON SCANNING ANTENNAv P 5NFOCUSED 3!2 4HIS TYPE OF EARLY 3!2 IS DESCRIBED BY #UTRONA AS FOLLOWS h4HE COHERENT SIGNALS RECEIVED AT THE SYNTHETIC ARRAY POINTS ARE INTEGRATED WITH NO ATTEMPT MADE TO SHIFT THE PHASES OF THE SIGNALS BEFORE INTEGRATION 4HIS LACK OF PHASE ADJUST MENT IMPOSES A MAXIMUM UPON THE SYNTHETIC ANTENNA LENGTH THAT CAN BE GENERATED 4HIS MAXIMUM SYNTHETIC ANTENNA LENGTH OCCURS AT A GIVEN RANGE WHEN THE ROUND TRIP DISTANCE FROM A RADAR TARGET TO THE CENTER OF THE SYNTHETIC ARRAY DIFFERS BY K FROM THE ROUND TRIP DISTANCE BETWEEN THE RADAR TARGET AND THE EXTREMITIES OF THE ARRAYv #UTRONA SHOWS THAT THE CROSSRANGE RESOLUTION IS APPROXIMATELY K 2 5NFOCUSED 3!2 IS TYPICALLY NOT USED TODAY AND IS INCLUDED HERE ONLY FOR HISTORICAL REASONS )T WAS USED IN THE EARLY DAYS OF 3!2 SINCE THE TECHNOLOGY OF THAT TIME DID NOT SUPPORT FOCUSED 3!2 4YPES OF &OCUSED 3!2 )N FOCUSED 3!2 A PHASE CORRECTION IS MADE FOR EACH RETURNING PULSE ECHO 4HIS ESSENTIALLY RESULTS IN THE THEORETICAL CROSSRANGE RESOLUTION OF %Q 3TRIPMAP 3!2 3TRIPMAP 3!2 OR hSTRIPv 3!2 IS ALSO SOMETIMES CALLED hSEARCHv 3!2 SINCE IT IS USEFUL FOR IMAGING LARGE AREAS AT RELATIVELY COARSE RESOLUTION )N STRIP MAP 3!2 THE BEAM REMAINS NORMAL TO THE FLIGHT PATH THE LATTER IS ASSUMED TO BE A STRAIGHT LINE AT CONSTANT ALTITUDE AND CONTINUOUSLY OBSERVES A SWATH OR STRIP OF TERRAIN PARALLEL TO THE FLIGHT PATH EXTENDING FROM SOME MINIMUM RANGE 2MIN TO SOME MAXIMUM RANGE 2MAX FROM THE FLIGHT PATH
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2!$!2 (!.$"//+
&OR STRIPMAP 3!2 THE SYNTHETIC APERTURE ANGLE $P IS ESSENTIALLY EQUAL TO THE REAL APERTURE BEAMWIDTH P"
$P y P " y
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5NDER IDEAL CONDITIONS AS LONG AS $ K AND SIGNAL TO NOISE RATIO 3.2 THEN THE SMALLER THE PHYSICAL ANTENNA THE FINER THE CROSSRANGE RESOLUTION INDEPENDENT OF RANGE !S THE PHYSICAL ANTENNA MOVES ALONG THE SYNTHETIC APERTURE THE RETURN FROM A POINT TARGET AT A PARTICULAR RANGE WILL EXHIBIT A QUADRATIC PHASE BEHAVIOR IE PHASE VARIES AS THE SQUARE OF THE TIME REFERENCED TO THE CLOSEST APPROACH THAT IS UNIQUE TO THE TARGETS LOCATION ON THE GROUND 3OME STRIPMAP 3!2S USE A FILTERING APPROACH TO TAKE ADVANTAGE OF THIS PHENOMENON )N FACT FOR THE ECHO FROM A POINT TARGET IN THE SCENE A CLOSE ANALOGY EXISTS BETWEEN ITS QUADRATIC PHASE VARIATION DURING A SINGLE PULSE FROM A LINEAR &- ;,&-= PULSE ECHO AND ITS QUADRATIC PHASE VARIATION OVER MANY PULSES DUE TO PLATFORM MOTION 3TIMSON P /THER STRIPMAP 3!2S DIVIDE THE STRIP INTO SUBPATCHES AND USE SPOTLIGHT 3!2 PROCESSING NEXT SECTION FOR EACH SUBPATCH SEE ALSO 3ECTION OF !USHERMAN ET AL 4HE NEWER 2ANGE -IGRATION !LGORITHM 2-! SEE #HAPTER OF #ARRARA ET AL ORIGINALLY DEVELOPED FOR SEISMIC APPLICATIONS PROVIDES THE MOST THEORETICALLY CORRECT SOLUTION TO THE STRIPMAP IMAGE PROBLEM )T DOES NOT MAKE A FAR FIELD APPROXIMATION BUT TREATS THE WAVEFRONTS AS SPHERICAL )T IS PARTICULARLY APPLICABLE TO 3!2 WITH VERY WIDE FRACTIONAL BANDWIDTH ANDOR WIDE SYNTHETIC APERTURE ANGLE 2-! INVOLVES SUBSTAN TIAL COMPUTATIONAL COMPLEXITY HOWEVER AS PROCESSORS BECOME MORE SOPHISTICATED THIS LIMITATION IS DISAPPEARING ! SIMPLER FASTER VERSION OF 2-! IS THE #HIRP 3CALING !LGORITHM #3! SEE #HAPTER OF #ARRARA ET AL 3QUINTED 3TRIPMAP 3!2 )N THIS CASE THE ANTENNA BORESIGHT IS NOT NORMAL TO THE FLIGHT PATH !S SEEN FROM A TOP VIEW THE SQUINT ANGLE PSQ IS THE ANGLE BETWEEN THE ANTENNA BORESIGHT AND THE NORMAL TO THE FLIGHT PATH THUS FOR A BROADSIDE BEAM PSQ AND CCR $ -ORE GENERALLY
$P
D CR
P!
L $P
L $ COSP SQ $ COSP SQ
)T IS ASSUMED HERE THAT THE SYNTHETIC APERTURE LENGTH ,3! 2 AND PSQ IS ESSENTIALLY CONSTANT DURING A DATA COLLECTION $EPENDING ON DETAILS THIS CONDITION IS VALID ONLY FOR PSQ LESS THAN ABOUT SINCE FOR A GIVEN CROSSRANGE RESOLUTION AS PSQ INCREASES ,3! INCREASES AND THE CONDITION BECOMES NO LONGER VALID 3POTLIGHT 3!2 3POTLIGHT 3!2 SOMETIMES CALLED hSPOT 3!2v IS USED TO OBTAIN A RELATIVELY FINE RESOLUTION IMAGE OF A KNOWN LOCATION OR TARGET OF INTEREST !S THE
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PLATFORM PASSES BY THE TARGET THE BEAM DIRECTION MOVES TO KEEP POINTING AT THE TARGET )N THIS WAY $P MAY BE MADE CONSIDERABLY GREATER THAN P" AND CCR SPOTLIGHT CCR STRIPMAP 7E MAY WISH TO MAKE A CORRECTION FOR THE VARIATION IN RECEIVED POWER ^2 AS THE RANGE TO THE TARGET VARIES SLIGHTLY OVER THE SYNTHETIC APERTURE 4HIS IS USUALLY NEGLIGIBLE FOR MOST SPOTLIGHT 3!2 APPLICATIONS BUT MIGHT NOT BE NEGLIGIBLE WHEN COLLECTION ANGLES ARE LARGE SUCH AS FOR THE CASE OF FOLIAGE PENETRATION 3!2 3ECTION 4HE SYNTHETIC APERTURE TIME T! REQUIRED TO COLLECT THE DATA FOR A SPOTLIGHT 3!2 IMAGE IS FOUND AS FOLLOWS
D CR y
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T! y
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WHERE 6 IS THE PLATFORM SPEED )NTERFEROMETRIC 3!2 )NTERFEROMETRIC 3!2 )N3!2 SOMETIMES ALSO CALLED h)&3!2v REFERS TO THE USE OF TWO ANTENNAS WHOSE SIGNALS ARE COMBINED COHERENTLY )N3!2 WAS ORIGINALLY DEVELOPED BY THE *ET 0ROPULSION ,ABORATORY *0, TO DETECT OCEAN CURRENTS OR MOVING TARGETS 4HE TWO ANTENNAS WERE DISPLACED HORIZONTALLY ON THE PLATFORM ALONG A LINE PARALLEL TO THE GROUND SO THAT THE RECEIVED ECHOES FROM A MOVING TARGET WOULD BE DIFFERENT FROM THE CORRESPONDING ECHOES FROM FIXED TAR GETS AND THUS MOVERS COULD BE DETECTED AND ANALYZED ,ATER RESEARCHERS EG !DAMS ET AL USED TWO ANTENNAS DISPLACED VERTICALLY ON THE PLATFORM SO THAT THE RECEIVED ECHOES FROM A TARGET ABOVE THE SURFACE ASSUMED FLAT WOULD BE DIFFERENT FROM THE CORRESPONDING ECHOES FROM A TARGET ON THE SURFACE AND THUS TARGET HEIGHT COULD BE ESTI MATED "OTH TYPES OF )N3!2 ARE DISCUSSED IN 3ECTION 4HE FORMER IS DISCUSSED IN h)NTERFEROMETRIC 3!2 FOR -OVING 4ARGET )NDICATION -4) v AND THE LATTER IS DISCUSSED IN h)NTERFEROMETRIC 3!2 FOR 4ARGET (EIGHT -EASUREMENTv )NVERSE 3!2 3KOLNIK PRESENTS A DISCUSSION OF )NVERSE 3!2 )3!2 (E STATES h)N 3!2 THE TARGET IS ASSUMED STATIONARY AND THE RADAR IS IN MOTION )N )3!2 THE TARGET MOTION PROVIDES THE CHANGES IN RELATIVE VELOCITY THAT CAUSE DIFFERENT DOPPLER SHIFTS TO OCCUR ACROSS THE TARGETv PP n 3KOLNIK ALSO INCLUDES A DISCUSSION OF )3!2 IMAGES OF SHIPS OBTAINED BY THE 5 3 .AVAL 2ESEARCH ,ABORATORY .2, -USMAN ET AL !N AIRBORNE RADAR OBTAINS A SERIES OF IMAGES OF A SHIP THAT IS EXPE RIENCING PITCHROLLYAW IN THE WAVES AND THE USER IS ABLE TO IDENTIFY THE SHIP TYPE AND CHARACTERISTICS -USMAN ET AL DISCUSS FEATURE EXTRACTION MULTIFRAME PROCESSING AND A CAPABILITY FOR AUTOMATIC TARGET RECOGNITION !42 OF SHIPS )3!2 IS ALSO WIDELY USED FOR DIAGNOSTIC MEASUREMENTS ON INDOOR AND OUTDOOR RADAR CROSS SECTION 2#3 RANGES +NOTT ET AL P )MPROVEMENTS IN 3!2 2ESOLUTION 4HE FOLLOWING EXAMPLE ILLUSTRATES HOW 3!2 CROSSRANGE RESOLUTION HAS IMPROVED AS THE PRECEDING TYPES OF AIRBORNE MAPPING RADAR WERE DEVELOPED ,ET US ASSUME THAT K M 8 BAND $ APERTURE DIAMETER M 2 KM PSQ 6 MSEC ,$"3 M CORRESPONDING TO AN ANGULAR SCAN RATE OF SEC AND SPOTLIGHT SYNTHETIC APERTURE LENGTH KM $P y DEG
£Ç°È
2!$!2 (!.$"//+
4HEN CROSSRANGE RESOLUTION IS APPROXIMATELY AS FOLLOWS FOR THE DIFFERENT MODES DIS CUSSED PREVIOUSLY 3,!2 M $"3 M 5NFOCUSED STRIPMAP 3!2 M 3TRIPMAP 3!2 M 3POTLIGHT 3!2 M
£Ç°{Ê -,Ê, -" 1/" )N THIS SECTION WE DISCUSS 3!2 RESOLUTION IN MORE DETAIL "Y hRESOLUTION v IN KEEPING WITH COMMON USAGE WE MEAN THE PRECISION TO WHICH WE CAN MEASURE THE LOCATION OF A POINT TARGET AND NOT NECESSARILY THE ABILITY TO RESOLVE TWO POINT TARGETS &OR A DISCUSSION OF THIS ISSUE SEE 7OLFE AND :ISSIS (OW WE DO THIS WILL BE DISCUSSED IN MORE DETAIL BELOW 3INCE FINE RANGE RESOLUTION IS TYPICALLY ACHIEVED WITH A SINGLE PULSE THE CORRE SPONDING PROCESSING IS OFTEN TERMED FAST TIME PROCESSING /N THE OTHER HAND FINE CROSSRANGE RESOLUTION REQUIRES MULTIPLE PULSES AND THE CORRESPONDING PROCESSING IS THEREFORE OFTEN TERMED SLOW TIME PROCESSING #ARRARA 2ICHARDS AND +LEMM 2ANGE 2ESOLUTION 3TRICTLY SPEAKING 3!2 REFERS TO A METHOD FOR IMPROVING CROSSRANGE RESOLUTION NOT RANGE RESOLUTION (OWEVER BECAUSE FINE RANGE RESOLUTION IS SO NECESSARY TO A SUCCESSFUL 3!2 AND ALSO BECAUSE OF AN ANALOGY BETWEEN RANGE AND CROSSRANGE RESOLUTION WE DISCUSS RANGE RESOLUTION BRIEFLY HERE &INE RANGE RESOLUTION IS ACHIEVED BY TRANSMITTING AND RECEIVING RADAR WAVES CHAR ACTERIZED BY A FAIRLY WIDE BANDWIDTH " !S AN EXAMPLE CONSIDER A CARRIER FREQUENCY F '(Z AND A BANDWIDTH " '(Z /NE WAY TO ACHIEVE THIS BANDWIDTH NOT THE BEST WAY IN GENERAL BUT A WAY THAT IS EASY TO DESCRIBE IS TO USE A STEP FREQUENCY WAVEFORM CONSISTING OF A SERIES OF hSINGLE FREQUENCYv PULSES EACH WITH A FREQUENCY SOMEWHAT GREATER THAN THAT OF THE PREVIOUS PULSE "Y A hSINGLE FREQUENCYv PULSE WE MEAN A PULSE CONSISTING OF A PURE SINUSOIDAL TONE MULTIPLIED BY A RECTANGULAR FUNCTION OF DURATION hWIDTHv S MUCH LONGER THAN THE PERIOD OF THE TONE 3UCH A PULSE IS NOT TRULY SINGLE FREQUENCY BUT HAS A BANDWIDTH OF y S &OR EXAMPLE IF S MICROSECOND "PULSE -(Z 4HIS IS FAR LESS THAN THE BANDWIDTH OF THE OVERALL STEP FREQUENCY WAVEFORM EQUAL TO THE DIFFERENCE BETWEEN THE FREQUENCIES OF THE LAST AND FIRST PULSES IN THE SEQUENCE WHICH IS TYPICALLY HUNDREDS OF -(Z 3TEP FREQUENCY PULSE COMPRESSION HAS NOT PROVEN SUCCESSFUL IN AIRBORNE OR SPACE BORNE APPLICATIONS AS COMPARED TO THE LINEAR &- ,&- WAVEFORM SEE 3ECTION OF #ARRARA AND IS SELDOM USED ,INEAR &- ,&- IS A COMMON WAVEFORM USED IN OPERATIONAL HIGH POWER RADARS BECAUSE EACH PULSE CONTAINS THE FULL BANDWIDTH THEREBY ENABLING THE FULL BANDWIDTH TO BE TRANSMITTED AND RECEIVED MUCH MORE QUICKLY THAN WITH STEP FREQUENCYA GREAT ADVANTAGE WHEN THE RADAR IS MOVING SUCH AS FOR 3!2AND THE HARDWARE IS RELATIVELY INEXPENSIVE AND MATURE ,&- HAS BEEN SUCCESSFULLY EMPLOYED OPERATIONALLY EG IN THE 5 3 .AVY !.!03 AND !.!03 SINCE THE S 4HE ONLY APPARENTLY SUCCESSFUL APPLICATION OF STEP FREQUENCY HAS BEEN IN GROUND BASED INSTRUMENTATION RADARS WHERE IT IS LESS EXPENSIVE TO IMPLEMENT AND MORE TIME IS AVAILABLE FOR DATA COLLECTION +NOTT ET AL PP .EVERTHELESS FOR THE MOMENT WE ASSUME THE STEP FREQUENCY WAVEFORM BECAUSE IT PROVIDES A MUCH SIMPLER EXAMPLE FOR EXPLAINING THE PRINCIPLE OF RANGE RESOLUTION
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,ET US ASSUME THAT THE RADAR TRANSMITS A STEP FREQUENCY WAVEFORM CONSISTING OF IDEN TICAL GROUPS OF PULSES EACH GROUP CONSISTING OF . hSINGLE FREQUENCYv PULSES OF WIDTH S 7ITHIN A PULSE GROUP THE FREQUENCY OF A PULSE IS $F GREATER THAN THAT OF THE PREVIOUS PULSE AND THE RADAR TRANSMITS 02& . GROUPS PER SECOND WHERE 02& IS THE PULSE REPETITION FREQUENCY 4HE WAVEFORM BANDWIDTH IS . $F S 4HE PHASE AND AMPLITUDE OF EACH PULSE ECHO IS DIGITALLY RECORDED BY THE RADAR !S SHOWN IN &IGURE A A DISCRETE &OURIER TRANSFORM $&4 TYPICALLY A FAST &OURIER TRANS FORM &&4 IS APPLIED TO THIS SET OF . COMPLEX SAMPLES OF FREQUENCY DOMAIN DATA RESULTING IN A SET OF . COMPLEX NUMBERS IN THE TIME DOMAIN CORRESPONDING TO ECHOES MAGNITUDE AND PHASE THAT WOULD BE RETURNED FROM A VERY SHORT PULSE OF WIDTH y " SAMPLED AT TIME INTERVALS $T " 4HIS IS A SIMPLE EXAMPLE OF PULSE COMPRESSION 3INCE AN INCREMENTAL DELAY $T CORRESPONDS TO AN INCREMENTAL DOWNRANGE DISTANCE $R C$T WE MULTIPLY THE $&4 OUTPUT BY C AND OBTAIN THE ECHOES CORRESPONDING TO A SET OF DOWNRANGE DISTANCES SEPARATED BY A PIXEL WIDTH OF C$T C" 4HUS THE RANGE RESOLUTION STRICTLY SPEAKING PIXEL SEPARATION OF A STEP FREQUENCY WAVEFORM OF BANDWIDTH " IS
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!LTHOUGH IT IS BEYOND THE SCOPE OF THIS CHAPTER IT CAN BE SHOWN THAT SUCH A RANGE RESOLUTION OF y C" MAY BE OBTAINED USING A WIDE VARIETY OF WAVEFORM TYPES AS LONG AS THE OVERALL TRANSMITTED BANDWIDTH IS " &OR EXAMPLE 3ECTION OF 3ULLIVAN SHOWS THAT THIS IS TRUE FOR THE ,&- WAVEFORM #ROSSRANGE 2ESOLUTION ,ET US NOW ASSUME THAT THE AIRBORNE OR SPACEBORNE 3!2 IS OBSERVING A SCENE ON THE %ARTHS SURFACE CONSISTING OF A FEW POINT TARGETS AND THAT IT TRANSMITS AND RECEIVES . IDENTICAL PULSES EACH OF BANDWIDTH " PRESUMABLY THOUGH NOT NECESSARILY VIA THE ,&- WAVEFORM AND DETERMINES THE DOWNRANGE POSITION OF EACH
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&)'52% 2ANGE AND CROSSRANGE RESOLUTION 3IMILAR DISCRETE &OURIER TRANSFORM $&4 PROCESSES MAY BE USED TO OBTAIN RANGE AND CROSSRANGE RESOLUTION
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TARGET WITH A RANGE RESOLUTION OF C" ,ET US ALSO ASSUME THAT THE 3!2 IS MOVING IN A STRAIGHT LINE AT A CONSTANT ALTITUDE ( AND CONSTANT SPEED 6 FOR A TIME 4 ALONG A DIRECTION NORMAL TO THE ,/3 4HE SYNTHETIC APERTURE ,3! 64 IS ASSUMED SMALL COMPARED WITH THE RANGE 2 TO THE CENTER OF THE TARGET REGION !S VIEWED FROM THE TARGET REGION ALSO ASSUMED SMALL COMPARED TO 2 THE SYNTHETIC APERTURE SUBTENDS THE SYNTHETIC APERTURE ANGLE y ,3!2 642 !S THE RADAR MOVES THROUGH ITS SYNTHETIC APERTURE IT VIEWS THE SCENE FROM SLIGHTLY DIFFERENT ANGLES &OR SIMPLICITY LET US ASSUME THAT DURING THIS TIME THE TARGETS DO NOT LEAVE THEIR hRANGE BINSv OF WIDTH C" 4HIS ASSUMPTION WILL BE DIS CUSSED IN 3ECTION h2ANGE -IGRATIONv &ROM THE VIEWPOINT OF THE 3!2 THE SCENE APPEARS TO BE ROTATING WITH ANGULAR VELOCITY 7 62 $URING THE DATA COLLECTION THE TOTAL ANGLE THROUGH WHICH THE SCENE APPEARS TO ROTATE IS $P 74 642 ! SPECIFIC POINT TARGET APPEARS TO HAVE A ,/3 VELOCITY OF 7R RELATIVE TO THE 3!2 WHERE R IS THE CROSSRANGE DISTANCE OF THE TARGET FROM THE ,/3 4HESE APPARENT ,/3 VELOCITIES WILL RESULT IN DOPPLER FREQUENCIES IN ABSOLUTE VALUE OF VAPPARENT K 7RK WHERE K IS THE WAVELENGTH CORRESPONDING TO THE CARRIER FREQUENCY &OR EACH RANGE BIN WE NOW HAVE . COMPLEX NUMBERS CORRESPONDING TO DIFFERENT RADAR ECHOES IN THE TIME DOMAIN !S SHOWN IN &IGURE B THESE . TIME DOMAIN ECHOES MAY BE PROCESSED USING A $&4 TO PRODUCE A SET OF . FREQUENCY DOMAIN RETURNS 4HE FREQUENCY INTERVAL BETWEEN SUCCESSIVE RETURNS IS $F 4 AND THE OVERALL FRE QUENCY INTERVAL IS . 4 y .4 02& F2 7E ASSUME OPERATION AT BASEBAND AND THUS THE FREQUENCY IN QUESTION IS THE APPARENT DOPPLER FREQUENCY OF THE TARGETS 7E CONVERT THIS TO CROSSRANGE BY MULTIPLYING BY K7 K26
D CR y
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.OTE THAT OUR ASSUMPTION THAT 2 64 PERMITS THE USE OF SMALL ANGLE APPROXIMA TIONS FOR SMALL $P 7HEN $P IS NOT SMALL %Q MUST BE APPROPRIATELY MODIFIED 3UMMARY OF 3!2 2ESOLUTION 7E HAVE THEREFORE NOW DERIVED THE TWO BASIC FORMULAS FOR 3!2 RESOLUTION
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4HE PROCESSING DESCRIBED PRODUCES A TWO DIMENSIONAL ARRAY OF COMPLEX NUMBERS IE EACH CONSISTS OF A MAGNITUDE AND A PHASE 4HIS ORDERED ARRAY OF COMPLEX NUMBERS AS A FUNCTION OF DOWNRANGE AND CROSSRANGE PRODUCES A COMPLEX RADAR IMAGE IE EACH PIXEL CONSISTS OF A MAGNITUDE AND A PHASE 4YPICALLY THE MAGNITUDE SQUARED REPRESENT ING PIXEL ENERGY IS DISPLAYED !S SHOWN IN #HAPTER OF 3ULLIVAN A POINT TARGET IN THE SCENE TRANSFORMS TO A TWO DIMENSIONAL POINT SPREAD FUNCTION 03& IN THE RADAR IMAGE SO CALLED BECAUSE A POINT TARGET IS DISPLAYED IN THE IMAGE AS SOMEWHAT hSPREAD OUTv 4HIS 03& IS CHARACTERIZED BY A MAINLOBE AND SIDELOBES IN BOTH RANGE AND CROSSRANGE 5SUALLY WEIGHTING ALSO CALLED TAPERING OR APODIZATION IS APPLIED IN THE PROCESSING RESULTING IN CONSIDERABLY LOWER SIDE LOBES BUT AT THE EXPENSE OF A SOMEWHAT BROADER MAINLOBE A PRICE THAT THE USER IS TYPICALLY WILLING TO PAY -ANY TYPES OF WEIGHTING EXIST )F NO WEIGHTING IS APPLIED THE 03& IS A SINC FUNCTION OF THE FORM SINX X )N THAT CASE THE FORMULAS ABOVE FOR 3!2 RESOLUTION
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REPRESENT THE DISTANCE FROM THE MAINLOBE PEAK TO THE FIRST NULL .OTE THAT THIS DEFINITION OF 3!2 RESOLUTION IS DIFFERENT FROM THE MORE COMMON DEFINITION OF THE HALF POWER WIDTH OF THE MAINLOBE 7ITH NO WEIGHTING THE LATTER IS TIMES THE VALUES GIVEN ABOVE THUS THE TWO DEFINITIONS ARE NOT VERY DIFFERENT 7E PREFER THE FORMER DEFINITION BECAUSE FOR NO WEIGHTING IT RESULTS IN A SIMPLER FORMULA WITHOUT THE INTRODUCTION OF THE FACTOR OF -ORE DETAILS CONCERNING WEIGHTING ARE GIVEN IN 3ECTION 4HERE ARE AT LEAST TWO MATHEMATICALLY EQUIVALENT WAYS OF CONSIDERING 3!2 !S WE HAVE DEVELOPED THE CONCEPT SO FAR THE CROSSRANGE RESOLUTION MAY BE CONSIDERED TO RESULT FROM THE DOPPLER SHIFTS RESULTING FROM THE DIFFERENT APPARENT LINE OF SIGHT VELOCITIES OF DIFFERENT PARTS OF THE SCENE (OWEVER THE CROSSRANGE RESOLUTION MAY ALSO BE CONSIDERED TO RESULT FROM THE LARGE SYNTHETIC APERTURE MUCH AS FINE CROSSRANGE RESOLUTION WOULD ALSO RESULT FROM A LARGE REAL APERTURE 0ER %Q THE CROSSRANGE RESOLUTION PEAK TO FIRST NULL OF A 3!2 IS FINER BY A FACTOR OF TWO THAN THE RESOLUTION FOR A 2!2 OF EQUAL APERTURE !N INTUITIVE EXPLANATION FOR THIS INTERESTING RESULT IS THAT FOR 2!2 THE ECHO RECEIVED AT A PARTICULAR APERTURE LOCATION RESULTS FROM ENERGY TRANSMITTED FROM ALL LOCATIONS IN THE APERTURE WHEREAS FOR 3!2 THE ECHO RECEIVED AT A PARTICULAR APERTURE LOCATION RESULTS FROM ENERGY TRANSMITTED FROM THAT KNOWN LOCATION IN THE APERTURE IE MORE INFORMATION IS RECEIVED #ARRARA ET AL P 3TIMSON PROVIDES A DETAILED EXPLANATION FOR THIS RESULT PP n &IGURE PRESENTS A COMPARISON OF 2!2 AND 3!2
&)'52% #OMPARISON OF 2!2 AND 3!2 4HE CROSSRANGE RESOLUTION PEAK TO FIRST NULL OF ANTENNA PATTERN OF A 3!2 IS ONE HALF THAT OF A REAL APERTURE RADAR 2!2 OF THE SAME APERTURE DIAMETER #OURTESY OF 3CI4ECH 0UBLISHING )NC
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4HE SIDELOBES ARE ALSO DIFFERENT FOR 2!2 AND 3!2 &OR A 2!2 WITH AN UNWEIGHTED APERTURE FUNCTION THE TRANSMITTED INTENSITY AT THE PEAK OF THE FIRST ANGULAR SIDELOBE IS REDUCED BY n D" AND THE RECEIVED INTENSITY FROM A TARGET IN THAT DIRECTION IS THUS REDUCED BY n D" &OR A 3!2 TYPICALLY THE ENTIRE REGION OF THE IMAGE IS IN THE MAIN BEAM DURING THE DATA COLLECTION AND THERE ARE NO EFFECTS FROM THE SIDELOBES OF THE PHYSICAL ANTENNA 4HE SIDELOBES RESULT SOLELY FROM THE PROCESSING AND WITH NO WEIGHTING THE FIRST SIDELOBE IS REDUCED BY n D" RELATIVE TO THE MAIN BEAM
£Ç°xÊ 9Ê-* /-Ê"Ê-, 2ANGE AND 6ELOCITY #ONTOURS 5SING FINE RANGE RESOLUTION A RADAR CAN DISTIN GUISH BETWEEN TARGETS AT DIFFERENT RANGES ! PARTICULAR TARGET MAY BE DETERMINED TO BE LOCATED ON A CONSTANT RANGE CONTOUR )N $ SPACE THESE CONTOURS ARE CONCENTRIC SPHERES WITH THE RADAR AT THE CENTER &IGURE A 3IMILARLY USING DOPPLER PROCESSING THE RADAR CAN DISTINGUISH BETWEEN TARGETS OF DIFFERENT APPARENT VELOCITIES )F 6 IS THE PLATFORM VELOCITY AND P IS THE ANGLE BETWEEN 6 AND THE ,/3 TO A STATIONARY TARGET THEN THE APPARENT ,/3 SPEED OF THE TARGET IS 6,/3
6 COS P &IGURE B )N $ SPACE SURFACES OF CONSTANT 6,/3 ARE CIRCULAR CONES WITH AXIS 6 AND GENERATING ANGLE P WITH THE RADAR AT THE VERTEX 4HE NEGATIVE SIGN OCCURS
&)'52% 2ANGE AND VELOCITY CONTOURS IN $ SPACE A #ONSTANT RANGE CON TOURS ARE CONCENTRIC SPHERES WITH THE RADAR AT THE CENTER B #ONSTANT APPARENT VELOCITY CONTOURS ARE CIRCULAR CONES WITH THE RADAR AT THE VERTEX AND THE AXIS ALONG THE PLATFORM VELOCITY VECTOR #OURTESY OF 3CI4ECH 0UBLISHING )NC
39.4(%4)# !0%2452% 2!$!2
£Ç°££
BECAUSE WE DEFINE ,/3 VELOCITY AS D2DT WHERE 2 IS THE RANGE TO THE TARGET 4HUS A POSITIVE D2DT CORRESPONDS TO A RECEDING TARGET AND RESULTS IN A NEGATIVE DOPPLER FRE QUENCY SHIFT AND A NEGATIVE D2DT CORRESPONDS TO AN INCOMING TARGET AND RESULTS IN A POSITIVE DOPPLER FREQUENCY SHIFT #ONSIDER AN AIRBORNE RADAR WITH AN ISOTROPIC ANTENNA PATTERN WITH CONSTANT VELOCITY ALONG A STRAIGHT LINE PARALLEL TO A FLAT GROUND &IGURE A /N THE GROUND THE CON STANT RANGE CONTOURS ARE THE INTERSECTIONS OF CONCENTRIC SPHERES WITH THE GROUNDA SET OF CONCENTRIC CIRCLES WITH THE SUBRADAR POINT AT THE CENTER &IGURE B 4HE CONTOURS OF CONSTANT ,/3 VELOCITY CALLED ISODOPS CORRESPOND TO THE INTERSECTIONS BETWEEN THE SET OF CONES AND THE FLAT GROUNDA SET OF NESTED HYPERBOLAS &IGURE C &IGURE D SHOWS THE COMBINATION OF CONSTANT RANGE CIRCLES AND THE ISODOPS 4HE hNADIR LINEv SHOWN IN &IGURE IS THE LOCUS OF SUBRADAR POINTS AS THE PLATFORM FLIES ALONG ITS PATH
&)'52% 2ANGE AND VELOCITY CONTOURS ON THE %ARTHS SURFACE A #OLLECTION GEOMETRY B #ONSTANT RANGE CONTOURS ARE CONCENTRIC CIRCLES WITH THE SUBRADAR POINT AT THE CENTER hNADIR LINEv REFERS TO THE LOCUS OF SUBRADAR POINTS C #ONSTANT APPARENT VELOCITY CONTOURS hISODOPSv ARE CONFOCAL HYPERBOLAS WITH THE AXIS PARALLEL TO THE PLATFORM VELOCITY VECTOR D 3ET OF INTERSECTING CONCENTRIC CIRCLES AND CONFOCAL HYPERBOLAS #OURTESY OF 3CI4ECH 0UBLISHING )NC
£Ç°£Ó
2!$!2 (!.$"//+
4HROUGH APPROPRIATE RANGE DOPPLER PROCESSING RETURNS FROM EACH INTERSECTION CELL MAY BE DISTINGUISHED /VER A SMALL ANGLE ABOUT THE BROADSIDE DIRECTION THE RANGE CONTOURS AND THE ISODOPS ARE ESSENTIALLY ORTHOGONAL TO EACH OTHER 4HE RESULT ING RADAR RETURNS MAY BE DISPLAYED TO YIELD AN IMAGE OF THE GROUND !T A NONZERO SQUINT ANGLE THE ISODOPS ARE NOT ORTHOGONAL TO THE RANGE CONTOURS HOWEVER ADDI TIONAL PROCESSING CORRECTIONS CAN STILL USUALLY RESULT IN AN ESSENTIALLY UNDISTORTED GROUND IMAGE -OTION #OMPENSATION 4HE BASIC THEORY OF 3!2 RELIES ON THE ASSUMPTION THAT THE PLATFORM AND THEREFORE THE 3!2 ANTENNA IS TRAVELING ALONG A STRAIGHT LINE FLIGHT PATH AT CONSTANT VELOCITY PARALLEL TO THE GROUND AT CONSTANT ALTITUDE 4HIS IS NOT EXACTLY TRUE AND FOR SUCCESSFUL 3!2 IMAGING IT IS NECESSARY THAT THE DEVIATIONS OF THE ANTENNA FROM THIS NOMINAL FLIGHT PATH BE MEASURED RECORDED AND COMPENSATED FOR IN THE PRO CESSING 4HIS PROCEDURE IS KNOWN AS MOTION COMPENSATION SOMETIMES ABBREVIATED MOCOMP &OR EXAMPLE AT A PARTICULAR MOMENT AS A PARTICULAR FREQUENCY IS TRANSMIT TED IF THE ANTENNA IS ESTIMATED TO HAVE DEVIATED A DISTANCE D AWAY FROM THE NOMINAL FLIGHT PATH ALONG THE ,/3 THE PHASE CORRECTION
$F
P D P DF L C
WITH APPROPRIATE SIGN IS ADDED TO THE MEASURED PHASE AT THE FREQUENCY F TO PRODUCE THE BEST ESTIMATE OF WHAT THE RECORDED PHASE WOULD HAVE BEEN IF THE PLATFORM HAD NOT DEVIATED FROM THE NOMINAL FLIGHT PATH 3IMILARLY IF THE PLATFORM SPEED IS NOT CONSTANT THE RECEIVED DATA ARE INTERPOLATED TO PRODUCE THE BEST ESTIMATE OF WHAT THEY WOULD HAVE BEEN IF THE SPEED HAD BEEN CONSTANT 7HEN THE PLATFORM IS AN AIRCRAFT AN ON BOARD )NERTIAL .AVIGATION 3YSTEM ).3 USES ACCELEROMETERS AND GYROSCOPES TO MEASURE THE DEVIATIONS 3OMETIMES A SMALLER )NERTIAL -EASUREMENT 5NIT )-5 RELYING ON THE SAME GENERAL PRINCIPLES IS hSTRAPPED DOWNv VERY NEAR THE ANTENNA 7ITHOUT AN ABSOLUTE REFERENCE FRAME THE OUTPUTS OF ANY ).3 OR )-5 WILL DRIFT WITH TIME AS ERRORS ACCUMULATE !N ABSOLUTE FRAME FOR POSITION AND VELOCITY MAY BE OBTAINED FROM THE GLOBAL POSITIONING SYSTEM '03 A CONSTELLA TION OF AT LEAST SATELLITES IN POLAR %ARTH ORBIT PROVIDING CONTINUOUS REFERENCE SIGNALS FOR DETERMINATION OF PRECISE POSITION AND VELOCITY 3LANT AND 'ROUND 0LANES 7HEN A 3!2 IMAGE IS INITIALLY PRODUCED THE RANGE PIXEL SIZE CR IS USUALLY A CONSTANT )T IS GENERALLY CHOSEN TO BE SOMEWHAT LESS THAN C" EG C" TO ENSURE ADEQUATE SAMPLING !S ILLUSTRATED IN &IGURE THE ACTUAL GROUND LOCATIONS THAT CORRESPOND TO THESE RANGE SAMPLES ARE NOT SPACED AT CONSTANT INTERVALS IN GROUND RANGE .EAR THE SCENE CENTER THEY ARE SPACED AT
CG CR COS X
WHERE X IS THE GRAZING ANGLE !T GROUND RANGES CLOSER TO THE RADAR THEY ARE SPACED STILL FARTHER APART BECAUSE OF THE SPHERICAL RANGE CONTOURS .EAR THE SCENE CENTER THE IMAGE CORRESPONDS TO THE PROJECTION OF THE GROUND ONTO A SLANT PLANE THIS PLANE IS DETERMINED BY THE ,/3 AND ITS PERPENDICULAR IN THE GROUND PLANE 7E OFTEN REFER TO THIS TYPE OF IMAGE AS A SLANT PLANE IMAGE "Y APPROPRIATE INTERPOLATION AND RESAMPLING A GROUND PLANE IMAGE WITH CG CONSTANT CCR MAY BE PRODUCED 'ROUND PLANE IMAGERY WITH MINIMAL DISTORTION IS NECESSARY IF COMPARISON IS TO BE MADE WITH MAPS OR WITH IMAGING TAKEN FROM OTHER SENSORS SUCH AS OPTICAL SENSORS OR OTHER 3!2S
39.4(%4)# !0%2452% 2!$!2
£Ç°£Î
&)'52% 3LANT AND GROUND PLANES 4HE SLANT PLANE IS DETERMINED BY THE RADAR LINE OF SIGHT AND ITS PERPENDICULAR IN THE GROUND PLANE 'ROUND PLANE RANGE RESOLUTION IS COARSER THAN SLANT PLANE RANGE RESOLU TION #OURTESY OF 3CI4ECH 0UBLISHING )NC
0ULSE 2EPETITION &REQUENCY 02& 2EQUIREMENTS FOR 3!2 &OR BROADSIDE OPERATION THE APPARENT ANGULAR VELOCITY OF THE SCENE ROTATION IS
7
6 2
7ITH RESPECT TO THE RADAR THE RELATIVE VELOCITY OF POINT ! SEE &IGURE AT THE FIRST NULL OF THE MAIN BEAM IS
L6 ¤ 6 ³ ¤ L 2³ V! 7R ¥ ´ ¥ ´ $ ¦ 2µ ¦ $ µ
&)'52% -INIMUM 02& FOR 3!2 4HE APPARENT LINE OF SIGHT VELOCITY OF POINT ! IS TOWARD THE RADAR WHEREAS THE APPARENT LINE OF SIGHT VELOCITY OF POINT " IS AWAY FROM THE RADAR 4HESE DETERMINE THE MINIMUM 02& OF 6$ WHERE 6 PLATFORM SPEED AND $ ANTENNA PHYSICAL DIAMETER #OURTESY OF 3CI4ECH 0UBLISHING )NC
£Ç°£{
2!$!2 (!.$"//+
3IMILARLY THE RELATIVE VELOCITY OF POINT " ON THE OPPOSITE SIDE OF THE BEAM IS ¤ 6 ³ ¤ L 2 ³ L6 V" 7R ¥ ´ ¥ ´ ¦ 2µ ¦ $ µ $
4HUS THE RANGE OF RELATIVE VELOCITIES IN THE SCENE IS
$V 7R 7R 7R
L6 $
4HE RANGE OF DOPPLER FREQUENCIES RECEIVED FROM THE SCENE IS
$FD
L6 6 L $ $
4HUS TO AVOID VELOCITY AMBIGUITY THE 02& MUST BE AT LEAST 6$ 7RITING
F2 MIN
6 $ T 2 MAX
$
WE HAVE
6T 2 MAX
4HUS THE DISTANCE TRAVELED BY THE PLATFORM DURING THE TIME BETWEEN PULSES T2 MUST BE NO MORE THAN $ AND THE 3!2 MUST TRANSMIT AT LEAST TWO PULSES AS ITS PHYSICAL ANTENNA PASSES A STATIONARY POINT IN SPACE 7E ALSO FREQUENTLY WANT RANGE UNAMBIGUOUS OPERATION WHICH IMPLIES
6 C a F2 $ 2
&OR EXAMPLE IF 6 MS y KTS $ M AND 2 KM THEN (Z F2 (Z %Q IS REALLY TWO EQUATIONS 7E USE FOR THE SECOND EQUATION INSTEAD OF a BECAUSE WHEN THE EQUALITY IS USED A PULSE IS BEING TRANSMITTED JUST AS THE ECHO FROM THE PREVIOUS PULSE IS BEING RECEIVED RESULTING IN ECLIPSING AND CONSEQUENT LOSS OF THE RECEIVED INFORMATION 3KOLNIKPP n POINTS OUT THAT SINCE FOR STRIPMAP 3!2 THE CROSSRANGE RESOLUTION CCR $ %Q %Q BECOMES
6 C a F2 D CR 2
4HIS LEADS TO THE CONDITION
2 C a D CR 6
4HUS THE UNAMBIGUOUS RANGE 2U AND THE RESOLUTION OF A STRIPMAP 3!2 CANNOT BE SELECTED INDEPENDENTLY OF ONE ANOTHER 3KOLNIK FURTHER POINTS OUT QUOTING "AYMA AND -C)NNES THAT MORE SOPHISTICATED REASONING LEADS TO THE CONDITION
2U C a D CR 6
39.4(%4)# !0%2452% 2!$!2
£Ç°£x
3KOLNIK CONTINUES h7HEN A 3!2 IMAGES THE GROUND FROM AN ELEVATED PLATFORM THE UNAMBIGUOUS RANGE CAN CORRESPOND TO THE DISTANCE BETWEEN THE FORWARD EDGE AND THE FAR EDGE OF THE REGION TO BE MAPPED 4HIS REQUIRES THAT THE ELEVATION BEAMWIDTH BE TAILORED TO ILLUMINATE ONLY THE SWATH 3 THAT IS TO BE IMAGED BY THE RADAR 4HE SWATH 3 IS OFTEN MUCH SMALLER THAN THE MAXIMUM RANGE SO THAT THE 02& CAN BE INCREASED TO ALLOW THE UNAMBIGUOUS RANGE 2U TO ENCOMPASS THE DISTANCE 3 COS X WHERE X IS THE GRAZING ANGLEv P &OR A STRIPMAP 3!2 %Q THEN BECOMES 3 C a D CR 6 COSY
2ANGE -IGRATION !S WE HAVE SEEN A 3!2 MAY OBTAIN RANGE RESOLUTION OF CR C" WHERE " SIGNAL BANDWIDTH AND OBTAIN CROSS RANGE RESOLUTION THROUGH DOPPLER PROCESSING WITH CCR K$P )F WE WISH TO PREVENT RANGE MIGRATION MOVEMENT OF A POINT TARGET FROM ONE RANGE BIN TO THE NEXT DURING THE TIME REQUIRED TO COLLECT THE DATA FOR IMAGE FORMATION WE WOULD REQUIRE THAT $2 THE VARIATION OF RANGE DURING THE DATA COLLECTION OVER THE SYNTHETIC APERTURE BE LESS THAN CR 7E CONSIDER THE FORMATION OF A 3!2 IMAGE AFTER COLLECTING DATA OVER AN APERTURE TIME T! 4HE 3!2 FLIGHT PATH IS A STRAIGHT LINE AT CONSTANT SPEED AND ALTITUDE OVER A FLAT GROUND &ROM ,EVANON WE HAVE
2MAX
2
6 T ! 2
2MIN 2
WHERE 2 DISTANCE FROM THE RADAR TO THE SCENE CENTER IN THE MIDDLE OF THE DATA COLLEC TION INTERVAL AND 2MAX DISTANCE FROM THE RADAR TO THE SCENE CENTER AT THE BEGINNING AND END OF THE DATA COLLECTION INTERVAL 4HEN
$2 2MAX 2MIN
6T ! ,3! 2 $Q 2 L DR 2 2 D CR
4HE LAST INEQUALITY IS NECESSARY FOR THE CONDITION OF NO RANGE MIGRATION &OR EXAM PLE PARAMETERS FOR A 3!2 MIGHT BE 2 KM K M AND CR CCR M THEN $2 M CR AND THE CONDITION IS NOT SATISFIED 4HUS THE PROCESSOR MUST USUALLY CORRECT FOR RANGE MIGRATION (OWEVER THIS IS TYPICALLY ACCOMPLISHED BY MODERN 3!2 PROCESSING METHODS &OR SPOTLIGHT 3!2 THE POLAR FORMAT ALGORITHM IS OFTEN USED TO ACCOMPLISH THIS CORRECTION /THER 0ROCESSING &UNCTIONS #URLANDER ET AL PROVIDE A DETAILED DISCUSSION OF SEVERAL KEY OPTIONS FOR 3!2 PROCESSING BEYOND SIMPLE IMAGE FORMATION L
L
L
L
#LUTTERLOCK #URLANDER ET AL #HAPTER REFERS TO THE USE OF INFORMATION IN THE RECEIVED SIGNALS TO ASCERTAIN THE CENTER FREQUENCY OF THE ECHOES FROM THE GROUND CLUTTER AND COMPENSATE FOR SIDEWAYS DRIFT OF THE PLATFORM !UTOFOCUS #URLANDER ET AL #HAPTER DESCRIBES THE USE OF INFORMATION IN THE COMPLEX IMAGE ITSELF TO ESTIMATE AND CORRECT PHASE ERRORS AND THEN REPROCESS AND SHARPEN THE IMAGE SEE ALSO #ARRARA ET AL #ALIBRATION #URLANDER ET AL #HAPTER REFERS TO THE USE OF TARGETS OF KNOWN RADAR CROSS SECTION 2#3 IN THE SCENE TO OBTAIN THE ABSOLUTE LEVEL OF 2#3 PER PIXEL AND THUS R THE GROUND 2#3 PER UNIT AREA 'EOLOCATION #URLANDER ET AL #HAPTER IS THE PROCESS OF DETERMINING THE ABSOLUTE LATITUDE AND LONGITUDE OF PIXELS IN THE 3!2 IMAGE TYPICALLY USING INFORMATION FROM THE '03
£Ç°£È
2!$!2 (!.$"//+
£Ç°ÈÊ -,Ê Ê+1 /9 )T IS CLEARLY IMPORTANT FOR A 3!2 TO PRODUCE HIGH QUALITY IMAGERY )MAGE QUALITY IS TYPICALLY MEASURED USING SEVERAL IMAGE QUALITY METRICS )1-S DESCRIBED IN THE FOL LOWING SECTIONS -ORE DETAILED DISCUSSION OF 3!2 IMAGERY IS GIVEN BY (ENDERSON AND ,EWIS AND /LIVER AND 1UEGAN 0OINT 3PREAD &UNCTION 03& ! POINT TARGET MAY BE CONSIDERED AN IMPULSE INPUT TO A 3!2 PROCESSOR AND THE 03& IN THE IMAGE MAY BE REGARDED AS AN IMPULSE RESPONSE )02 4HE PRIMARY )1- FOR MOST 3!2S IS THE WIDTH METERS OF THE 03& MAINLOBE AT ITS hHALF POWER POINTS v OR POINTS WHERE THE INTENSITY POWER PROPORTIONAL TO VOLTAGE SQUARED IS ONE HALF OR D" RELATIVE TO THE MAINLOBE PEAK 4HIS )1- IS TYPICALLY REFERRED TO AS THE h D" WIDTHv 4O OBTAIN FINE RESOLUTION IN EITHER RANGE OR CROSSRANGE A &OURIER TRANSFORM &4 IS PERFORMED ON A SET OF COLLECTED DATA 3INCE ALL DATA SAMPLES HAVE ESSENTIALLY THE SAME MAGNITUDE FOR EITHER RANGE OR CROSSRANGE WE ESSENTIALLY PERFORM A &4 ON A RECT ANGULAR FUNCTION WHICH PRODUCES A SINC FUNCTION SINX X WITH A D" WIDTH OF CPN WHERE CPN PEAK TO FIRST NULL INTERVAL AND A FIRST SIDELOBE n D" BELOW THE PEAK !S MENTIONED IN 3ECTION WHEN A TAPERING OR WEIGHTING FUNCTION MULTI PLIES THE RECTANGULAR INPUT THE RESULT IS TYPICALLY A FUNCTION WITH BROADER MAINLOBE AND LOWER SIDELOBES THAN THE SINC SEE 3ECTION OF 3ULLIVAN ! TYPICAL WEIGHTING FUNCTION USED IN 3!2 PROCESSING IS 4AYLOR WEIGHTING WITH THE FIRST SIDELOBE CONSTRAINED TO BE n D" BELOW THE PEAK AND hNBAR v SEE 3ECTION $ OF #ARRARA ET AL WHICH PRODUCES A WIDENED MAIN BEAM OF D" )02 VALUE L CPN !NOTHER CHOICE IS (ANN OR h(ANNINGv WEIGHTING WHICH RESULTS IN AN EVEN WIDER MAIN BEAM OF CPN THE FIRST SIDELOBE IS n D" BELOW THE PEAK AND THE FAR SIDELOBES ARE VERY LOW COMPARED WITH UNIFORM OR 4AYLOR WEIGHTING !N EXCELLENT DISCUSSION OF OVER WEIGHTING FUNCTIONS NOT INCLUDING 4AYLOR IS GIVEN BY (ARRIS 3IGNAL 4O .OISE 2ATIO 3.2 &OR A REAL RADAR FOR WHICH THE EXACT PHASE OF THE TARGET ECHO CAN NEVER BE KNOWN IN ADVANCE THE GREATEST ACHIEVABLE SIGNAL TO NOISE RATIO 3.2 IS 3ULLIVAN 3ECTION
3.2
% K4 &
% 02X AVGT !
WHERE % COLLECTED ENERGY K "OLTZMANNS CONSTANT ¾ n JOULE+ELVIN 4 STANDARD TEMPERATURE + & hNOISE FIGURE v WHICH IS TYPICALLY ABOUT 02X AVG AVERAGE RECEIVED POWER AND T! TIME TO FORM THE SYNTHETIC APERTURE 4HE DENOMINATOR OF %Q IS CORRECT ONLY IF THE TEMPERATURE OF THE RADAR IS THE SAME AS THAT OF THE SCENE WHICH WE ASSUME SEE #HAPTER AND 3ECTION OF 3ULLIVAN
%
04X AVG' L S 04X AVG !H S T! T! P 2 ,OSS P 2 L ,OSS
39.4(%4)# !0%2452% 2!$!2
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WHERE 04X AVG AVERAGE TRANSMITTED POWER ' ANTENNA GAIN R TARGET RADAR CROSS SECTION 2#3 ! ANTENNA APERTURE AREA G ANTENNA EFFICIENCY AND THE RADAR LOSSES ARE REPRESENTED BY ,OSS &OR 3!2 AT PSQ FROM %Q
T!
L2 6D CR
4HUS
3.2
04X AVG' L S 04X AVG !H S P 2K4 & ,OSS 6D CR P 2L K4 & ,OSS 6D CR
)F A FLAT GROUND IS BEING OBSERVED THEN
S S D CRD R COSY
WHERE R CHARACTERIZES THE GROUND 2#3 PER UNIT AREA AND CR PIXEL WIDTH IN SLANT RANGE 4HEN THE SIGNAL TO NOISE RATIO 3.2 IS
3.2
04X AVG !H S D R 04X AVG' L S D R P 2K4 & ,OSS 6 COSY P 2L K4 & ,OSS 6 COSY
4HIS AGREES WITH 3KOLNIK %Q AND #URLANDER ET AL %Q )T IS VERY USEFUL TO CONSIDER THE NOISE EQUIVALENT SIGMA ZERO .%R DEFINED AS THE LEVEL OF R THAT PRODUCES A RECEIVED POWER EQUAL TO THE THERMAL NOISE POWER IE AN 3.2 OF UNITY 7E SET 3.2 AND HAVE
.%S
P 2K4 & ,OSS 6 COSY P 2L K4 & ,OSS 6 COSY 04X AVG' L D R 04X AVG !H D R
&OR EXAMPLE IF 2 KM 4 + & ,OSS 6 MS X O 0AVG 7 ' D" K M 8 BAND AND CR M THEN .%R D" ! CLEAR 3!2 IMAGE MUST HAVE AN 3.2 GREATER THAN ABOUT D" &ROM "ARTON AND SUMMARIZED IN 3ECTION OF 3ULLIVAN WE SEE THAT THIS EXAMPLE 3!2 COULD IMAGE hWOODED HILLS v IE R y D" WITH 3.2 y D" BUT COULD NOT IMAGE hFLATLANDv PERHAPS DESERT AT R y D" SINCE 3.2 y D" )NTEGRATED 3IDELOBE 2ATIO )3,2 !N ACTUAL 03& TYPICALLY RESEMBLES THE THEO RETICAL 03& BUT IS SOMEWHAT DIFFERENT FROM IT ESPECIALLY IN THE SIDELOBES DUE TO PHASE NOISE MOTION COMPENSATION IMPERFECTIONS AND OTHER hREAL WORLDv EFFECTS ! USEFUL FIGURE OF MERIT IS THE INTEGRATED SIDELOBE RATIO )3,2 DEFINED AS
)3,2
)NTEGRAL OVER 03& 3IDELOBES )NTEGRAL OVEER 03& -AINLOBE
)3,2 IS USUALLY MEASURED IN D" A TYPICAL VALUE MIGHT BE D" ,OW )3,2 IS CLEARLY DESIRED -ULTIPLICATIVE .OISE 2ATIO -.2 4HERMAL NOISE GENERALLY INTERNAL WHEN THE RADAR IS A 3!2 IS OFTEN REFERRED TO AS ADDITIVE NOISE SINCE IT ADDS TO THE SCENE INDE PENDENT OF THE SCENE CONTENT !NOTHER TYPE OF UNWANTED BACKGROUND IN A 3!2 IMAGE
£Ç°£n
2!$!2 (!.$"//+
IS OFTEN CALLED MULTIPLICATIVE NOISE NOT REALLY NOISE IN THE STRICT SENSE WHICH IS PRO PORTIONAL TO THE AVERAGE SCENE INTENSITY #ARRARA ET AL DEFINE MULTIPLICATIVE NOISE AS FOLLOWS h4HE PRINCIPAL CONTRIBUTORS TO MULTIPLICATIVE NOISE ARE THE INTEGRATED SIDELOBES OF THE SYSTEM IMPULSE RESPONSE THE ENERGY PRESENT IN THE SCENE AS A RESULT OF RANGE AND AZIMUTH AMBIGUITIES AND DIGITAL ;IE FROM QUANTIZATION IN THE ANALOG TO DIGITAL CONVERTER= NOISEv P 4HE MULTIPLICATIVE NOISE RATIO -.2 OF A 3!2 IMAGE IS DEFINED AS THE RATIO OF THE IMAGE INTENSITY IN NO RETURN AREA .2! NOT INCLUDING THERMAL NOISE DIVIDED BY THE AVERAGE IMAGE INTENSITY IN A RELATIVELY BRIGHT SURROUNDING AREA IN PRINCIPLE NOT INCLUD ING THERMAL NOISE !N .2! IS AN AREA WITH ESSENTIALLY ZERO RETURNFOR EXAMPLE A SHADOW AREA A VERY SMOOTH AREA SUCH AS A CALM LAKE OR A SPECIALLY CONSTRUCTED LARGE SHEET OF ALUMINUM !NOTHER SIMILAR 3!2 IMAGE QUALITY METRIC )1- IS THE CONTRAST RATIO #2 DEFINED AS THE RATIO OF THE AVERAGE INTENSITY OF A TYPICAL BRIGHT REGION IN A 3!2 IMAGE TO THE INTENSITY OF AN .2! )F THERMAL NOISE IS NEGLIGIBLE THEN #2 -.2 #OMPARISON OF 3!2 )MAGERY AND /PTICAL )MAGERY 4HE HUMAN EYE IS OF COURSE A SYSTEM FOR PRODUCING IMAGES USING VISIBLE LIGHT 4HE LIGHT HITS THE LENS AND IS FOCUSED UPON THE RETINA AND THE RESULTING IMAGE IS TRANSMITTED TO THE BRAIN /VER MANY MILLENNIA HUMANS HAVE BECOME FULLY ACCUSTOMED TO SEEING AND PROCESSING THIS VIS IBLE IMAGERY 4HEREFORE UPON SEEING A 3!2 IMAGE WE MAY INSTINCTIVELY ASSUME THAT IT HAS CERTAIN PROPERTIES OF A VISIBLE IMAGE WHICH IN FACT IT DOES NOT POSSESS /PTICAL IMAGERY IS BASED ON AN hANGLE ANGLEv PRINCIPLE WHEREAS 3!2 IMAGERY IS BASED ON A VERY DIFFERENT hRANGE CROSSRANGEv PRINCIPLE 4HE TOP ILLUSTRATION IN &IGURE ILLUSTRATES THE APPEARANCE OF A FLAT LANDSCAPE TO THE HUMAN EYE OR A CAMERA 4HE TERRAIN IS ILLUMINATED BY SUNLIGHT AT LEAST PARTIALLY DIFFUSED THROUGH THE ATMOSPHERE !T THE EYE EACH PIXEL SUBTENDS THE SAME AZIMUTH AND ELEVATION ANGLES 4HUS PIXELS FARTHER FROM THE EYE ARE LARGER COARSER RESOLUTION IN BOTH DOWNRANGE AND CROSSRANGE THAN PIXELS CLOSER TO THE EYE 4HE BOTTOM ILLUSTRATION IN &IGURE SHOWS THAT FOR A 3!2 IMAGE THE SITUATION IS QUITE DIFFERENT ASSUMING ADEQUATE 3.2 4HE RANGE PIXEL SIZE CR IS
DR
C " COS Y
0IXELS FARTHER FROM THE 3!2 ARE SMALLER IN RANGE SMALLER GRAZING ANGLE AND FINER DOWNRANGE RESOLUTION THAN PIXELS CLOSER TO THE 3!2 AND CROSSRANGE RESOLUTION IS INDEPENDENT OF RANGE 7HEN WE DISPLAY A 3!2 IMAGE ESPECIALLY OF A LARGE LANDSCAPE IT IS USUALLY MOST SATISFYING TO DISPLAY IT WITH THE 3!2 DIRECTION AT THE TOP 4HE FINER RESOLUTION PIXELS ARE AT THE BOTTOM JUST AS THEY ARE WITH A NATURALLY ORIENTED OPTICAL IMAGE 4HIS ORIENTATION TENDS TO LOOK MOST NATURAL TO A HUMAN OBSERVER "ECAUSE 3!2 IMAGERY AND OPTICAL IMAGERY ARE COLLECTED USING ENTIRELY DIFFERENT PHYSICAL PRINCIPLES WE SHOULD NOT BE SURPRISED IF THEY LOOK DIFFERENT ! GOOD EXAMPLE OF THIS IS PROVIDED IN A 3!2 IMAGE OF THE 7ASHINGTON -ONUMENT COURTESY OF THE %NVIRONMENTAL 2ESEARCH )NSTITUTE OF -ICHIGAN NOW 'ENERAL $YNAMICS 9PSILANTI -) 4HE TOP ILLUSTRATION IN &IGURE ILLUSTRATES THE COLLECTION GEOMETRY AND THE SCHE MATIC RESULT OF OPTICAL IMAGERY OF THE 7ASHINGTON -ONUMENT WITH THE -ONUMENTS SHADOW POINTED TOWARD THE OBSERVER 7E ASSUME THAT THE SUN IS TO THE SOUTH OF THE -ONUMENT AND THE OBSERVER IS TO THE NORTH 4HE IMAGE SHOWS A SHADOW ON THE NORTH
39.4(%4)# !0%2452% 2!$!2
£Ç°£
&)'52% #OMPARISON OF 3!2 AND OPTICAL IMAGERY /PTICAL IMAGERY IS BASED ON AN hANGLE ANGLEv PRINCIPLE 3!2 IMAGERY IS BASED ON A hRANGE CROSSRANGEv PRINCIPLE /FTEN OPTICAL AND 3!2 IMAGES OF THE SAME TARGET REGION DO NOT LOOK THE SAME TO A HUMAN OBSERVER #OURTESY OF 3CI4ECH 0UBLISHING )NC
SIDE CAST BY THE SUN 4HE PORTION OF THE -ONUMENT VISIBLE IN THE IMAGE IS THE NORTH SIDE ILLUMINATED BY DIFFUSELY SCATTERED SUNLIGHT )N COMPARISON THE BOTTOM ILLUSTRATION IN &IGURE SHOWS THE GEOMETRY AND RESULT OF 3!2 IMAGERY AGAIN WITH THE SHADOW ON THE NORTH SIDE 4HIS TIME THE SHADOW IS CAST BY THE 3!2 ITSELF 4HE PORTION OF THE MONUMENT VISIBLE IN THE IMAGE IS THE SOUTH SIDE &IGURE SHOWS THE 3!2 IMAGE )T DOES NOT LOOK ENTIRELY LIKE AN OPTICAL IMAGE NOR SHOULD IT !NOTHER DIFFERENCE BETWEEN 3!2 AND OPTICAL IMAGES IS THE PRESENCE OF SPECKLE SEE 3ECTION IN (ENDERSON AND ,EWIS IN THE FORMER ,ET US CONSIDER A PARTICU LAR PIXEL OF A COMPLEX IMAGE OF COMPLICATED TERRAIN SUCH AS VEGETATION "Y hPIXELv WE MEAN THE COMPLEX NUMBERMAGNITUDE AND PHASETHAT AFTER 3!2 PROCESSING CORRESPONDS TO A PARTICULAR LOCATION ON THE GROUND )F ONLY ONE SCATTERER WERE IN THE REGION OF GROUND REPRESENTED BY THE PIXEL THEN THE PIXEL MAGNITUDE AND PHASE WOULD BE A FUNCTION OF THE SCATTERERS EXACT POSITION 3INCE THE REGION REPRESENTED BY THE PIXEL TYPICALLY CONTAINS MANY SCATTERERS THE COMPLEX PIXEL VALUE IS THE SUM OF THE
£Ç°Óä
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&)'52% 0RINCIPLES OF IMAGING THE 7ASHINGTON -ONUMENT &OR THE GEOMETRY SHOWN THE OPTICAL IMAGE SHOWS THE SIDE OF THE -ONUMENT ON THE SAME SIDE AS THE SHADOW WHEREAS THE 3!2 IMAGE SHOWS THE SIDE OF THE -ONUMENT ON THE OPPOSITE SIDE OF THE SHADOW #OURTESY OF 3CI4ECH 0UBLISHING )NC
COMPLEX NUMBERS THAT EACH RESULTS FROM ONE OF THE SCATTERERS 4HUS WHEN TERRAIN ESPECIALLY VEGETATION IS IMAGED THE AMPLITUDE VOLTAGE OF A PARTICULAR PIXEL IS THE MAGNITUDE OF THE COMPLEX SUM OF THE COHERENT RETURNS FROM MANY SCATTERERS WITHIN THE PIXEL )N ANOTHER NEARBY PIXEL EVEN IF THE TERRAIN IS NOMINALLY THE SAME AS IN THE FIRST PIXEL THE COHERENT RETURNS WILL ADD DIFFERENTLY AND THE PIXEL MAGNITUDE WILL BE SOMEWHAT DIFFERENT 4HIS PHENOMENON CHARACTERISTIC OF COHERENT IMAGERY CAUSES 3!2 IMAGERY OF TERRAIN TO EXHIBIT MORE PIXEL TO PIXEL FLUCTUATION SPECKLE THAN COR RESPONDING OPTICAL IMAGERY 3TIMSON POINTS OUT h3OMETIMES THE BEAM OF THE REAL ANTENNA MAY BE WIDE ENOUGH TO ENABLE THE SAME AREA TO BE MAPPED SEVERAL TIMES WITHOUT CHANGING THE ANTENNAS LOOK ANGLE 4HIS IS CALLED MULTILOOK MAPPING 7HEN THE MAPS ARE SUPERIMPOSED IE WHEN ;THE MAGNITUDES OF= SUCCESSIVE RETURNS FROM EACH RESOLUTION CELL ARE AVERAGED THE EFFECTS OF SCINTILLATION ;IE SPECKLE= ARE REDUCEDv P
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&)'52% 3!2 IMAGE OF THE 7ASHINGTON -ONUMENT 4HE 3!2 IMAGE SHOWS THE SIDE OF THE -ONUMENT THAT IS ON THE OPPOSITE SIDE OF THE SHADOW WHICH MAY APPEAR COUNTERINTUITIVE TO A HUMAN OBSERVER #OURTESY OF 'ENERAL $YNAMICS 9PSILANTI -ICHIGAN
£Ç°ÇÊ -1 ,9Ê"Ê 9Ê-,Ê +1/" ! REVIEW OF THE BASIC EQUATIONS OF 3!2 FOLLOWS 2ANGE RESOLUTION CR C" C SPEED OF LIGHT " PULSE BANDWIDTH #ROSSRANGE RESOLUTION CCR K $P K WAVELENGTH $P ANGLE SUBTENDED BY SYNTHETIC APERTURE 0HYSICAL BEAMWIDTH K $ $ ANTENNA DIAMETER
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#ROSSRANGE RESOLUTION FOR STRIPMAP 3!2
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&OR STRIPMAP 3!2
3 C a D CR 6 COSY
3IGNAL TO NOISE RATIO 3.2
04X AVG !H S D R 04X AVG' L S D R P 2 K4 & ,OSS 6 COSY P 2 L K4 & ,OSS 6 COSY
£Ç°nÊ -* Ê-,Ê** /" )N THIS SECTION WE BRIEFLY DISCUSS SEVERAL SPECIFIC ASPECTS OF 3!2 SPECIFICALLY POLARI METRIC 3!2 MOVING TARGETS VIBRATING TARGETS MEASUREMENT OF OBJECT HEIGHT AND FOLI AGE PENETRATION 3!2 0OLARIMETRIC 3!2 5SUALLY WHEN A RADAR TRANSMITS A PULSE AT A PARTICULAR POLARIZA TION EG HORIZONTAL( IT RECEIVES THE ECHOES AT THE SAME POLARIZATION 3OME RADARS ARE CAPABLE OF TRANSMITTING AT ONE POLARIZATION AND RECEIVING AT TWO ORTHOGONAL POLAR IZATIONS EG HORIZONTAL ;(= AND VERTICAL ;6= OR RIGHT CIRCULAR ;2= AND LEFT CIRCULAR ;,= &URTHERMORE SOME RADARS CAN TRANSMIT AT EITHER OF TWO ORTHOGONAL POLARIZATIONS AND RECEIVE AT EITHER OF THE TRANSMITTED POLARIZATIONS AND THE CHOICE OF TRANSMITTED AND RECEIVED POLAR IZATIONS CAN BE VARIED FROM PULSE TO PULSE )F THE PHASES AS WELL AS THE MAGNITUDES OF THE ECHOES ARE OBTAINED THEN SUCH A RADAR IS FULLY POLARIMETRIC 7E MAY DESIGNATE THE CHOICE OF POLARIZATIONS AS FOLLOWS (6 IS hTRANSMIT ( RECEIVE 6 v AND SO FORTH &ULLY POLARIMETRIC 3!2S HAVE BEEN DEMONSTRATED 3ULLIVAN ET AL AND (ELD ET AL &OR EXAMPLE 3ULLIVAN ET AL INCLUDES (( AND (6 8 BAND 3!2 IMAGES TAKEN OF THE SAME SCENE AT THE SAME TIME USING (( AND (6 MODES INTERLEAVED ON A PULSE TO PULSE BASIS 4HE 3!2 DESCRIBED COULD USING PULSE TO PULSE INTERLEAVING TRANSMITRECEIVE FIRST (( THEN (6 THEN 6( AND THEN 66 DATA AND PRODUCE FOUR CORRESPONDING SIMULTANE OUSLY COLLECTED COMPLEX IMAGES SUCH THAT THE PHASES OF THE CORRESPONDING PIXELS IN THE FOUR IMAGES BEAR A SPECIFIC RELATIONSHIP TO EACH OTHER DEPENDING ON THE TARGET TYPE .OVAK ET AL DEVELOPED AN OPTIMAL POLARIMETRIC WHITENING FILTER FOR ENHANCED TAR GET DETECTION IN SUCH SETS OF FULLY POLARIMETRIC 3!2 IMAGES 5SING FULLY POLARIMETRIC DATA FROM A '(Z 3!2 THEY SHOWED THAT DIHEDRAL REFLECTORS LOOK QUITE DIFFERENT FROM TRIHEDRAL REFLECTORS IN FULLY POLARIMETRIC 3!2 IMAGERY &EW DIHEDRALS EXIST IN +A BAND NATURAL CLUTTER THUS IF A PORTION OF A 3!2 IMAGE CORRESPONDS CLOSELY TO A DIHEDRAL THEN THE REGION IS LIKELY TO CONTAIN CULTURAL HUMAN MADE OBJECTS
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-OVING 4ARGETS IN A 3!2 )MAGE $ISPLACEMENT OF A -OVING 4ARGET 4HE BASIC THEORY OF 3!2 ASSUMES THAT THE GROUND SCENE IS STATIONARY ! MOVING TARGET IN THE SCENE WILL HAVE A hWRONGv RELA TIONSHIP BETWEEN ITS LOCATION AND ITS LINE OF SIGHT VELOCITY )F THE TARGET MOTION IS IN A STRAIGHT LINE AT CONSTANT SPEED THE TARGET IMAGE WILL BE DISPLACED IN CROSSRANGE BY
RDISPL
6,/3 6,/3 2 6 7
WHERE 7 IS THE APPARENT ROTATION RATE OF THE SCENE RELATIVE TO THE RADAR AND 6,/3 IS THE TARGET VELOCITY COMPONENT ALONG THE RADAR LINE OF SIGHT )N GENERAL COMPLICATED MOTION OF A TAR GET DURING A 3!2 DATA COLLECTION PREVENTS FORMATION OF A CLEAR 3!2 IMAGE OF THE TARGET $ETECTION OF -OVING 4ARGETS IN 3!2 )MAGES 6ARIOUS PROCESSING METHODS HAVE BEEN DEVELOPED TO DETECT AND REPOSITION MOVING TARGETS 3INGLE !PERTURE -OVING 4ARGET )NDICATION -4) 3!2 7ITH RESPECT TO CON VENTIONAL SINGLE APERTURE 3!2 KEY RESULTS HAVE BEEN OBTAINED BY SEVERAL AUTHORS INCLUDING 2ANEY &REEMAN &REEMAN AND #URRIE AND 7ERNESS ET AL )F THE 02& IS GREATER THAN THE MINIMUM NECESSARY TO PRODUCE A 3!2 IMAGE THEN FURTHER DOPPLER BANDS ARE AVAILABLE 4HESE BANDS CAN BE USED FOR ADDITIONAL INFORMATION AND PROCESSING RESULTS FOR MOVING TARGETS WILL BE DIFFERENT FROM THOSE FOR FIXED TARGETS &REEMAN PRESENTS A SUMMARY OF POTENTIAL RESULTS FOR MOVING TARGETS COV ERING SUCH ISSUES AS AZIMUTH SHIFT RANGE WALK AND AZIMUTH DEFOCUS h0ROBABLY THE WORST DEFECTWILL BE DISPLACEMENT OF MOVING TARGETS IN THE AZIMUTH DIRECTION AWAY FROM THEIR TRUE POSITION ON THE GROUND 4HE PREFILTER WE HAVE DESCRIBED IS OPTIMISED FOR TARGETS TRAVELING RADIALLY3UCH TARGETS WILL APPEAR AT THEIR CORRECT POSITION IN THE -4) IMAGEv )NTERFEROMETRIC 3!2 )N3!2 FOR -OVING 4ARGET )NDICATION -4) !S MENTIONED IN 3ECTION )NTERFEROMETRIC 3!2 )N3!2 SOMETIMES ALSO CALLED )&3!2 REFERS TO THE USE OF TWO ANTENNAS WHOSE SIGNALS ARE COMBINED COHERENTLY 4HE TWO ANTENNAS ARE DISPLACED HORIZONTALLY ALONG A LINE PARALLEL TO THE GROUND TO DETECT AND ANALYZE MOVING TARGETS AND ARE DISPLACED VERTICALLY TO ESTIMATE TERRAIN HEIGHT "OTH TYPES OF )N3!2 ARE DISCUSSED HEREIN 4HE FORMER IS DISCUSSED IN THIS SECTION AND THE LATTER IS DISCUSSED LATER IN h)NTERFEROMETRIC 3!2 )N3!2 FOR 4ARGET (EIGHT -EASUREMENTv )N3!2 TO DETECT MOVING TARGETS WAS ORIGINALLY DEVELOPED BY THE *ET 0ROPULSION ,ABORATORY *0, TO DETECT OCEAN CURRENTS AND HAS BEEN IMPROVED BY SEVERAL AUTHORS /NE OF THE MOST SOPHISTICATED TECHNIQUES HAS BEEN DEVELOPED FOR THE *OINT 34!23 AIRCRAFT AND USES AN INTERESTING COMBINATION OF 3!2 AND -4) TECH NIQUES TO DETECT AND EVALUATE MOVING TARGETS 4HE *OINT 34!23 3!2 MODE INVOLVES A CLASSICAL SINGLE RECEIVER CHANNEL SPOTLIGHT 3!2 THAT DWELLS ON A DESIGNATED GROUND REFERENCED COORDINATE FOR A DURATION THAT RESULTS IN A NOMINALLY SQUARE POINT SPREAD FUNCTION IE DOWNRANGE RESOLUTION CROSSRANGE RESOLUTION 4HE -4) MODE IS CAPABLE OF DETECTING AND ACCURATELY GEO LOCATING BOTH EXOCLUTTER IE TARGET MOVING FASTER THAN APPARENT TERRAIN MOTION AND ENDOCLUTTER IE TARGET MOVING MORE SLOWLY THAN APPARENT TERRAIN MOTION RETURNS FROM MOVING TARGETS THAT IN GENERAL HAVE RADAR CROSS SECTIONS THAT ARE SMALLER THAN
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THE CORRESPONDING MAIN BEAM CLUTTER ONLY CELLS )T ACCOMPLISHES THIS BY TRANSMITTING A COHERENT BURST OF PULSES THAT ARE SUBSEQUENTLY RECEIVED BY EACH OF THREE LINEARLY DIS PLACED SUBARRAYS OR INTERFEROMETER PORTS )N EACH CHANNEL THE PULSES ARE FAST TIME AND SLOW TIME PROCESSED INTO A SET OF RANGE AND DOPPLER CELLS WHOSE INTENSITIES MAY BE CONSIDERED AS A 3!2 IMAGE OF THE SCENE ALTHOUGH NOT AS FINE IN RANGE OR DOPPLER RESOLUTION AS IN THE 3!2 MODE AND GENERALLY NOT WITH A NOMINALLY SQUARE 03& %ACH OF THE INTERFEROMETER PORTS PRODUCES A COMPLEX VALUED RANGE DOPPLER hIMAGEv THAT COULD BE CALLED A h3!2v IMAGE SINCE IT WAS FORMED FROM A COHERENT SEQUENCE OF PULSES AND THE SUBSEQUENT COMPLEX PAIR WISE COMBINING OF THESE IMAGES WITH THE PROPER RELATIVE COMPLEX WEIGHTING TO NULL THE CLUTTER CAN BE CONSIDERED AS AN )N3!2 PROCESS /N THE OTHER HAND TO AVOID CONFUSION WITH THE TYPE OF INTERFEROMETRIC 3!2 THAT IS USED FOR TARGET HEIGHT MEASUREMENT THE *OINT 34!23 TEAM TYPICALLY REFERS TO THEIR PROCESS AS h#LUTTER 3UPPRESSION )NTERFEROMETRYv OR SIMPLY h#3)vp "ARBAROSSA AND &ARINA SHOW THAT BY USING MULTIPLE SUBAPERTURES DETECTION AND REPOSITIONING OF MOVING TARGETS CAN BE CONSIDERABLY IMPROVED IN AN EXTENSION OF THE REAL BEAM $ISPLACED 0HASE #ENTER !NTENNA $0#! TECHNIQUE 3TAUDAHER 4HEY DEVELOPED A PROCEDURE FOR 3!2 PROCESSING USING AN ARBITRARY NUMBER OF SUBAPER TURES SEPARATED HORIZONTALLY TO CANCEL GROUND CLUTTER AND IMAGE A MOVING TARGET 4HEIR APPROACH IS A COMBINATION OF SPACE TIME PROCESSING SEE THE LITERATURE FOR A DISCUSSION OF 3PACE 4IME !DAPTIVE 0ROCESSING OR 34!0 AND TIME FREQUENCY PROCESSING &IGURE A SHOWS A SIMULATED POINT SPREAD FUNCTION 03& OF A MOVING POINT TARGET AFTER CLUTTER CANCELLATION AND &IGURE B SHOWS THE FINAL SIMU LATED 03& AFTER RANGE MIGRATION COMPENSATION 4HE AUTHORS STATE h4HE ;POINT= TARGET IS SUPPOSED MOVING ON THE TERRAIN SHADOW ING EFFECTS HAVE BEEN NEGLECTED AT A CONSTANT VELOCITY IN A DIRECTION OBLIQUE WITH RESPECT TO THE RADAR MOTION 4HE VELOCITY PARAMETERS HAVE BEEN CHOSEN IN ORDER TO MAKE EVIDENT THE PRESENCE OF RANGE MIGRATION AND OF CROSS RANGE SMEARING OF THE TAR GET IMAGE 4HE GROUND REFLECTIVITY HAS BEEN ASSUMED EQUAL TO THE TARGET REFLECTIVITY THIS IS QUITE A PESSIMISTIC ASSUMPTION BECAUSE IN MANY CASES OF PRACTICAL INTEREST THE TARGET REFLECTIVITY IS HIGHER ! RECEIVER THERMAL NOISE D" BELOW THE TARGET RETURN HAS ALSO BEEN SUMMED TO THE RECEIVED SIGNAL 4HE GROUND ECHO IS FIRST CAN CELED BY USING A TWO ELEMENT ANTENNA AND TWO TIME SAMPLES 4HE TWO ANTENNAS ARE SEPARATED BY D V4 ;V PLATFORM SPEED 4 PULSE REPETITION INTERVAL= ! 3!2 IMAGE IS THEN FORMED BY CONVENTIONAL TECHNIQUES 4HE RESULT IS SHOWN IN &IGURE ;A= 4HE SMEARING OF THE MOVING POINTLIKE TARGET IS EVIDENT 'IVEN THE MOTION PARAM ETERS THE TARGET HAS MIGRATED OVER SIX RANGE CELLS 4HIS IS THE CAUSE FOR THE BROADEN ING OF THE TARGET IMAGE EVEN IN RANGE AS WELL AS IN CROSS RANGE 4HE TARGET ECHO CAUSES A DETECTION AND INITIALIZES THE MOTION ESTIMATION CHANNEL 4HE HIGH ;FINE= RESOLUTION DATA ARE INITIALLY SMOOTHED IN RANGE TO DECREASE ;COARSEN= THE RANGE RESO LUTION 4HEN THE PROCESSOR LOOKS FOR THE RANGE CELL WITH THE MAXIMUM ENERGY CONTENT AND COMPUTES THE 76$ ;7IGNER 6ILLE $ISTRIBUTION= OF THAT CELL ONLY 4HE PHASE HISTORY IS THEN USED FOR COMPENSATING THE RANGE MIGRATION AND THE PHASE SHIFT ON THE HIGH ;FINE= RESOLUTION RANGE DATA 4HE FINAL IMAGE IS SHOWN IN &IGURE ;B= 4HE SHARPENING OF THE TARGET IMAGE IS QUITE EVIDENTv "ARBAROSSA AND &ARINA ASSUMED A POINT TARGET IN THEIR SIMULATION 4HEY OBTAIN A PRECISE LOCATION OF A SIMULATED MOV ING POINT TARGET BUT DO NOT CLAIM TO HAVE PRODUCED A SIMULATED IMAGE OF AN EXTENDED MOVING TARGET SUCH AS A VEHICLE p 0ARAGRAPH COURTESY OF $R -ARSHALL 'REENSPAN .ORTHROP 'RUMMAN #ORPORATION
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&)'52% 3!2 IMAGE OF A MOVING TARGET USING MULTIPLE SUBAPERTURES FOR CLUTTER CANCELLATION SIMULATED DATA A ADAPTIVE PROCESSING AND B ADAPTIVE PROCESSING PLUS 3!2 AFTER 3 "ARBAROSSA AND ! &ARINA Ú )%%%
'UARINO AND )BSEN DESCRIBE AN EXPERIMENT USING THE !.!0' RADAR h4HE RADAR PROVIDES A UNIQUE SIMULTANEOUS 3!2'-4) ;'ROUND -OVING 4ARGET )NDICATIONSCANNING REAL APERTURE RADAR= MODE IN WHICH DETECTED TARGETS ARE DIS PLAYED ON THE 3!2 MAP AS MOVING TARGET SYMBOLS 4HE SYMBOLS ARE ACCURATELY LOCATED AT THEIR TRUE AZIMUTH POSITION RELATIVE TO THE MAP CENTER4HE ;3!2= MAP ON WHICH THE MOVING TARGET SYMBOL IS DISPLAYED IS COLLECTED AND PROCESSED SIMUL TANEOUSLY WITH THE '-4)v 4HE AUTHORS ALSO MAKE CLEAR THAT 'LOBAL 0OSITIONING 3YSTEM '03 INPUTS WERE ESSENTIAL TO THEIR ACCURATE LOCATION OF TARGETS FIXED TAR GETS WERE GEOLOCATED TO AN ABSOLUTE ACCURACY OF BETTER THAN METERS AND MOVING TARGET VEHICLES TO AN ABSOLUTE ACCURACY OF ABOUT METERS 3TIMSON ALSO DISCUSSES THESE !.!0' RESULTS PP )MAGING OF -OVING 4ARGETS IN 3!2 )MAGES 0ERRY ET AL HAVE DEVELOPED A METHOD FOR 3!2 IMAGING OF GROUND MOVING TARGETS THAT HAVE UNKNOWN STRAIGHT LINE CONSTANT SPEED MOTION 4HEY PROCESS THE RECEIVED PHASE HISTORY WITH A hKEYSTONE FORMATTINGv PROCEDURE THAT ELIMINATES THE EFFECTS OF LINEAR RANGE MIGRATION FOR ALL GROUND MOVING TARGETS REGARDLESS OF THEIR UNKNOWN VELOCITY 4HE PROCESSING PROCEDURE THEN AUTOMATI CALLY FOCUSES THE MOVING TARGETS &IGURE A SHOWS A CONVENTIONALLY PROCESSED 3!2 IMAGE CONTAINING THREE MOVING TARGETSA MILITARY TRUCK TYPE - A TRACTOR TRAILER TRUCK AND A SURROGATE IE A FULL SIZE REPLICA OF A MISSILE TRANSPORTER ERECTOR LAUNCHER 4%, &IGURE B SHOWS THE FOCUSED IMAGE OF THE TRACTOR TRAILER RESULTING FROM THE PROCESSING 4HE TWO FOOT RESOLUTION CLEARLY SHOWS THE OUTLINE OF THE CAB AND TRAILER OF THE TRUCK 6IBRATING 4ARGETS IN A 3!2 )MAGE #ONSIDER A 3!2 OBSERVING A SCENE THAT CON TAINS A POINT TARGET WHOSE POSITION IS OSCILLATING SINUSOIDALLY VIBRATING SEE 3ECTION OF #ARRARA ET AL 4HE COMPONENT OF THE VIBRATION AMPLITUDE THAT IS PARALLEL TO THE LINE OF SIGHT ,/3 IS D 4HE VARIABLE COMPONENT OF THE RADAR TARGET DISTANCE IS THEN
$2TGTT D SIN O FVIBT
WHERE FVIB IS THE VIBRATION FREQUENCY ,ET THE NORMALIZED COMPLEX ECHO CORRESPONDING TO A STATIONARY PIXEL BE E J P FD T WHERE FD IS THE DOPPLER FREQUENCY CHARACTERISTIC OF THE PIXEL 7E ASSUME LOW FRACTIONAL BANDWIDTH IN WHICH CASE THIS IS EQUIVALENT TO THE DOPPLER FREQUENCY CORRESPONDING TO THE CENTER FREQUENCY OF THE TRANSMITTED BANDWIDTH SEE 3ECTION OF 3ULLIVAN
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&)'52% )MAGING A MOVING TARGET IN A 3!2 IMAGE A #ONVENTIONAL 3!2 IMAGE REAL DATA SHOWING BLURRED MOVING VEHICLES AN - MILITARY TRUCK A TRACTOR TRAILER TRUCK AND A SURROGATE MOCKUP OF A MISSILE TRANSPORTER ERECTOR LAUNCHER B )MAGE OF TRACTOR TRAILER TRUCK USING hKEYSTONEv PROCESSING THE TRUCKS CAB IS AT THE BOTTOM AND THE TRAILER IS ABOVE IT AFTER 2 0 0ERRY ET AL Ú )%%%
)N ADDITION TO THIS ECHO THE PIXEL CONTAINING THE TARGET WILL PRODUCE AN ADDITIONAL ECHO WITH A PERIODIC PHASE ERROR
FE
P D SIN P FVIBT FO SIN P FVIBT L
7E ASSUME O D K THUS EO 4HE NORMALIZED COMPLEX ECHO CORRESPONDING TO THE PHASE ERROR IS
E JFE E JF SIN P FVIBT
y JF SIN P FVIBT
F E J P FVIBT E J P FVIBT 4HE NORMALIZED COMPLEX ECHO CORRESPONDING TO THE VIBRATING TARGET IS THEN THE COMPLEX PRODUCT OF THE ECHO CORRESPONDING TO THE STATIONARY PIXEL AND THE ECHO COR RESPONDING TO THE PHASE ERROR
E JFDOP E J P FD T E JFE
AND
E JFDOP E J P FD T
FO J P T FD FVIB E
E J P T FD FVIB
)N THE 3!2 IMAGE THE VIBRATING POINT TARGET WILL APPEAR IN THREE CROSSRANGE LOCATIONS -OST OF THE TARGET ENERGY STILL APPEARS AT THE CORRECT LOCATION WHEREAS A SMALL FRACTION OF THE ENERGY WILL APPEAR IN EACH OF TWO PIXELS SEPARATED IN CROSSRANGE BY FVIB IN DOPPLER FREQUENCY 4HUS A VIBRATING TARGET CAN GIVE RISE TO A PAIR OF DISTINCTIVE ECHOES
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4HE CORRESPONDING VELOCITY SEPARATION IS $V o FVIB K AND THE CROSSRANGE DISPLACEMENT IS THEN
$R
FVIBLAVG 2 $V $V 2 o 6 6 7
WHERE K AVG AVERAGE WAVELENGTH ASSUMING LOW FRACTIONAL BANDWIDTH 4HE RELATIVE AMPLITUDE OF EACH OF THE PAIRED ECHOES IS
6OLTAGE
FO P D LAVG
¤ P D ³ F 0OWER ¤¥ O ³´ ¥ ¦ µ ¦ LAVG ´µ
4HUS THE AMPLITUDE OF THE PAIRED ECHOES IS PROPORTIONAL TO THE SQUARE OF THE VIBRA TION AMPLITUDE AND CROSSRANGE DISPLACEMENT IS PROPORTIONAL TO THE VIBRATION FREQUENCY SEE 3ECTION OF 3ULLIVAN &OR BRIGHT POINT LIKE TARGETS OR FOR TARGETS SUCH THAT O D IS NOT SMALL COMPARED TO K ADDITIONAL TERMS SHOULD BE RETAINED IN %Q DESCRIBING THE FACT THAT A SERIES OF PAIRED ECHOES OF DECREASING AMPLITUDE MAY APPEAR IN CROSSRANGE &IGURE SHOWS A 3!2 IMAGE OF A SCENE INCLUDING A VIBRATING TARGETA TRUCK WITH ITS ENGINE RUNNING 4HE IMAGE CONTAINS TWO SETS OF PAIRED ECHOES CORRESPONDING TO TWO VIBRATION FREQUENCIES CHARACTERISTIC OF THE PARTICULAR TRUCK USED FOR THE OBSERVATION -EASUREMENT OF /BJECT (EIGHT 4HE BASIC THEORY OF 3!2 ASSUMES THAT THE SCENE IS FLAT 4O THE EXTENT THAT THE SCENE IS NOT FLAT DISTORTIONS IN THE 3!2 IMAGE WILL RESULT )N SOME CASES THEY CAN BE USED TO MEASURE THE HEIGHT OF ELEVATED OBJECTS ABOVE A FLAT TERRAIN
&)'52% 3!2 SCENE CONTAINING VIBRATING TARGET #ROSSRANGE IS HORI ZONTAL RANGE IS VERTICAL 4HE PAIRED ECHOES IN CROSSRANGE ARE CHARACTERISTIC OF A VIBRATING TARGET TRUCK WITH ENGINE RUNNING IN A 3!2 IMAGE 4HE FREQUENCIES (Z AND (Z ARE PECULIAR TO THE SPECIFIC TRUCK THAT WAS IMAGED #OURTESY OF .ORTHROP 'RUMMAN #ORPORATION
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3HADOWS 4HE SIMPLEST METHOD OF MEASURING OBJECT HEIGHT IS TO OBSERVE THE LENGTH ,SHADOW OF THE SHADOW OF THE OBJECT CAST BY THE 3!2 AND CALCULATE THE OBJECT HEIGHT H FROM THE KNOWN 3!2 ALTITUDE ( AND GROUND RANGE 2G
H ,SHADOW
( 2G
4HIS EXPRESSION ASSUMES FLAT EARTH AND MAY BE GENERALIZED TO CURVED EARTH IF 2G IS RELATIVELY LARGE SEE 3ECTION OF 3ULLIVAN (OWEVER THE SHADOW METHOD WORKS ONLY FOR AN ISOLATED RELATIVELY HIGH OBJECT ON ESSENTIALLY FLAT TERRAIN EG &IGURE ,AYOVER 3!2 PROCESSING SORTS TARGET RETURNS INTO BINS PIXELS DEPENDING ON THE RANGE 2 AND VELOCITY V OF THE TARGET RELATIVE TO THE PLATFORM )F TWO OR MORE TARGETS HAVE THE SAME 2 AND V THEN THEY WILL BE PLACED AT THE SAME LOCATION IN THE 3!2 IMAGE 7E SHALL DEFINE A LAYOVER CONTOUR AS THE LOCUS OF POINTS IN $ SPACE SUCH THAT AN OBJECT AT ANY OF THE POINTS WILL BE ASSIGNED TO THE SAME LOCATION IN A 3!2 IMAGE !S SHOWN IN &IGURE A LAYOVER CONTOUR IS THE INTERSECTION OF A CONSTANT RANGE SPHERE OF RANGE 2 AND A CONSTANT VELOCITY CONE OF GENERATING ANGLE A COSn V6 WITH AXIS ALONG THE PLATFORM DIRECTION IE A CIRCLE OF RADIUS 2 SINA AHEAD OF THE PLATFORM A n CORRESPONDS TO TARGETS BEHIND THE PLATFORM 7E SHALL THERE FORE CALL THE CONTOUR THE LAYOVER CIRCLE )F THE TOP OF AN ELEVATED OBJECT SUCH AS A TOWER IS ON THE LAYOVER CIRCLE AND IF THE GROUND IS FLAT THEN THE TOP OF THE TOWER WILL APPEAR IN THE 3!2 IMAGE AT THE SAME POSITION AS A POINT ON THE GROUND WHERE THE LAYOVER CIRCLE INTERSECTS THE GROUND 4HE TOWER WILL BE hLAID OVER v HENCE THE NOMENCLATURE !S SHOWN IN &IGURE LET US CONSIDER A PLATFORM IN STRAIGHT LINE CONSTANT SPEED MOTION AT ALTITUDE ( OVER A FLAT EARTH FORMING A 3!2 IMAGE THE CENTER OF WHICH IS AT SLANT RANGE 2S ( AND SQUINT ANGLE PSQ 3UPPOSE THAT A TOWER OF HEIGHT H H ( IS IN THE AREA THAT IS IMAGED 7E DESCRIBE LOCATIONS WITHIN THE IMAGE BY A COORDINATE SYSTEM X Y )F THE BASE OF THE TOWER IS AT X Y WE WISH TO ASCERTAIN THE IMAGE COORDINATES OF THE TOP OF THE TOWER &IGURE A ILLUSTRATES A PERSPECTIVE VIEW "ECAUSE 2G ( THE ISODOP Y n AXIS MAKES AN ANGLE PSQ WITH THE Y AXIS 4HE IMAGE CENTER IS A DISTANCE 3 2G COS PSQ FROM THE X AXIS WHERE 2G GROUND RANGE &IGURE B SHOWS A VIEW FROM THE X AXIS INDICATING THE LAYOVER CIRCLE NORMAL TO THE X AXIS AND SHOWING THAT THE IMAGE LOCATION OF THE TOWER TOP IS LOCATED A DISTANCE THE LAYOVER DISTANCE D H(2G COS PSQ FROM THE IMAGE LOCATION OF THE TOWER BASE &IGURE C THEN DEPICTS THE VIEW IN IMAGE COORDINATES X Y 4HE IMAGE COORDINATES OF THE TOWER TOP ARE
X X D SIN PSQ Y Y D COS PSQ
&OR EXAMPLE IF 2G KM ( KM H M AND PSQ THEN D M X X AND Y Y n M 4HE TOWER TOP APPEARS IN THE IMAGE M CLOSER TO THE RADAR THAN THE TOWER BASE 4HIS PRINCIPLE MAY SOMETIMES BE USED TO ESTIMATE THE HEIGHT OF ISOLATED TOWER LIKE STRUCTURES ON RELATIVELY LEVEL GROUND
H
D2G COSQSQ (
4HE INTERSECTION OF THE CONSTANT VELOCITY CONE AND THE GROUND IS A HYPERBOLA )F ( IS NOT 2 THE ISODOP DIRECTION WILL NOT BE PARALLEL TO THE DOWN RANGE DIRECTION
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&)'52% ,AYOVER A 0ERSPECTIVE VIEW B VIEW ALONG PLATFORM FLIGHT PATH AND C VIEW IN COORDINATE SYSTEM OF 3!2 IMAGE #OURTESY OF 3CI4ECH 0UBLISHING )NC
4HE GEOMETRY IS MORE COMPLICATED BUT LAYOVER DISTANCE AND OBJECT HEIGHT MAY STILL BE ESTIMATED 3TEREO 3!2 4WO 3!2 IMAGES OF THE SAME SCENE MAY BE OBTAINED FROM SOMEWHAT DIFFERENT LOCATIONS SEE 3ECTION IN #ARRARA ET AL .ONCOHERENT COMPARISON
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OF THE TWOTHE STEREO TECHNIQUEMAY ENABLE ESTIMATION OF OBJECT HEIGHT 4HE TECH NIQUE IS ANALOGOUS TO THE METHOD BY WHICH WE HUMANS USE OUR TWO EYES TO HELP ESTIMATE THE DISTANCE OF THE OBJECTS THAT WE SEE )N FACT THE TWO 3!2 IMAGES MAY BE PRINTED ON THE SAME PAGE USING TWO DIFFERENT COLORS WITH THE VIEWER USING SPECIAL GLASSES SO THAT THE LEFT EYE SEES ONLY ONE IMAGE AND THE RIGHT EYE ONLY THE OTHER AND THE BRAIN PROCESSING THE TWO TOGETHER SO THAT THE SCENE IS PERCEIVED IN $ )NTERFEROMETRIC 3!2 )N3!2 FOR 4ARGET (EIGHT -EASUREMENT )NTERFEROMETRIC 3!2 )N3!2 ALSO CALLED )&3!2 SEE 3ECTION OF #ARRARA ET AL AND !DAMS ET AL WHEN USED FOR TERRAIN HEIGHT MEASUREMENT INVOLVES TWO 3!2 IMAGES TAKEN FROM ANTEN NAS AT SLIGHTLY DIFFERENT ALTITUDES AND COMPARED COHERENTLY TO OBTAIN FINE RESOLUTION INFOR MATION REGARDING THE HEIGHT OF TERRAIN OR TARGETS IN THE IMAGE )N THIS CASE IT IS SOMETIMES CALLED )&3!2% WHERE % EMPHASIZES ELEVATION MEASUREMENT )N3!2 MAY BE PERFORMED USING A SINGLE PLATFORM WITH TWO ANTENNAS SINGLE PASS )N3!2 OR BY THE SAME PLATFORM MAKING TWO PASSES OVER THE SAME TERRAIN TWO PASS )N3!2 !LLEN GIVES SEVERAL EXAM PLES OF FIELDED SYSTEMS USING EACH TYPE )T IS ESSENTIAL THAT THE RELATIVE LOCATIONS OF THE TWO ANTENNAS BE RATHER PRECISELY KNOWN !DVANTAGES AND DISADVANTAGES OF THE TWO TYPES OF )N3!2 ARE AS FOLLOWS 4WO PASS )N3!2 L
L
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.O SPECIAL HARDWARE IS REQUIRED A CONVENTIONAL 3!2 MAY BE FLOWN TWICE OVER THE DESIGNATED TERRAIN -OTION COMPENSATION IS CHALLENGING THE POSITION OF THE ANTENNA VERSUS TIME IN EACH PASS MUST BE KNOWN WITH GREAT PRECISION ! LONG BASELINE VERTICAL DISTANCE BETWEEN ANTENNA PATHS PROVIDES FINE VERTICAL RESOLUTION BUT CHALLENGING AMBIGUITIES 4HE SCENE MAY CHANGE BETWEEN PASSES DUE TO WIND ETC %XAMPLE RESULTS ARE GIVEN BY 3CHULER ET AL WHO PERFORM hTERRAIN TOPOGRAPHY MEASUREMENT USING MULTIPASS POLARIMETRIC 3!2v
3INGLE PASS )N3!2 "ASELINE IS RELATIVELY WELL KNOWN PROVIDING CONSISTENCY THROUGHOUT SYNTHETIC APERTURE 3CENE IS SAME FOR BOTH IMAGES SINCE DATA FOR EACH ARE COLLECTED SIMULTANEOUSLY /N BOARD REAL TIME PROCESSING IS A POSSIBILITY -ORE SOPHISTICATED EXPENSIVE HARDWARE IS REQUIRED TWO ANTENNAS TWO RECEIVER CHANNELS AND TWO SETS OF ANALOG TO DIGITAL !$ CONVERTERS %XAMPLE RESULTS ARE GIVEN BY !DAMS ET AL WHO INCLUDE AN )N3!2 IMAGE OF THE STADIUM AT THE 5NIVERSITY OF -ICHIGAN IN !NN !RBOR VIEWABLE WITH TWO COLOR GLASSES
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4O UNDERSTAND THE THEORY OF )N3!2 WE FIRST CONSIDER TWO ANTENNAS ! AND " SEPARATED VERTICALLY BY A BASELINE , OBSERVING A POINT TARGET A THAT IS ON A FLAT GROUND AT RANGE 2 THE RADAR LINE OF SIGHT ,/3 INTERSECTS THE FLAT GROUND AT GRAZING ANGLE X &IGURE 7E CONSIDER TWO POSSIBILITIES ONE ANTENNA TRANSMITS AND EACH RECEIVES N AND ANTENNA ! TRANSMITS AND THEN RECEIVES THEN ANTENNA " TRANSMITS AND THEN RECEIVES N
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&OR A hSINGLE FREQUENCYv PULSE OF WAVELENGTH K THE DIFFERENCE IN THE PHASES OF THE ECHOES RECEIVED FROM THE POINT TARGET OBSERVED BY THE TWO ANTENNAS IS FROM &IGURE
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7E NOW CONSIDER THE SAME ANTENNAS ! AND " OBSERVING A SECOND POINT TARGET B THAT IS A DISTANCE H ABOVE THE FLAT GROUND ALSO AT RANGE 2 THE RADAR LINE OF SIGHT ,/3 INTER SECTS THE PARALLEL TO THE FLAT GROUND AT GRAZING ANGLE X 4HE DIFFERENCE IN THE PHASES OF THE ECHOES RECEIVED FROM THE POINT TARGET OBSERVED BY THE TWO ANTENNAS IS NOW
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)N3!2 FOR TERRAIN ELEVATION MEASUREMENT CAN ALSO BE PERFORMED BY AN AIRCRAFT WITH TWO ANTENNAS SEPARATED HORIZONTALLY PERPENDICULAR TO THE FLIGHT PATH BY , 4HE AIRCRAFT IS BANKING AT ANGLE F AND COLLECTING DATA FROM THE FLAT GROUND AT GRAZING ANGLE X &IGURE 4HEN THE EFFECTIVE APERTURE PERPENDICULAR TO THE ,/3 IS , SIN X F INSTEAD OF ,COS X &ROM &IGURE WE HAVE
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&URTHERMORE WHEN THE PHASE MOVES THROUGH AN INTERVAL OF O AN AMBIGUITY OCCURS IN TERRAIN ALTITUDE MEASUREMENT 4HE CORRESPONDING ALTITUDE DIFFERENCE IS COMPUTED BY REPLACING C $E BY O IN %QS AND 6ERTICAL ANTENNA SEPARATION NO BANKING
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! NUMBER OF AUTHORS REPORT SUCCESSFUL RESULTS WITH &/0%. 3!2 USING SUCH 3!2S AS THE %NVIRONMENTAL 2ESEARCH )NSTITUTE OF -ICHIGAN 0 3!2 THE 3WEDISH .ATIONAL $EFENSE 2ESEARCH %STABLISHMENT #!2!"!3 SENSOR AND THE 32) )NTERNATIONAL 5LTRA 7IDEBAND 3!2 &URTHERMORE -OYER PRESENTS IMAGES FROM CONVENTIONAL AND &/0%. 3!2S SHOWING THAT VEHICLES UNDER TREES MAY BE IMAGED SIGNIFICANTLY BETTER WITH &/0%. 3!2 THAN WITH CONVENTIONAL 3!2 EXAMPLE IMAGERY IS GIVEN IN &IGURE
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2 * 3ULLIVAN 2ADAR &OUNDATIONS FOR )MAGING AND !DVANCED #ONCEPTS 2ALEIGH .# 3CI4ECH PREVIOUSLY PUBLISHED AS -ICROWAVE 2ADAR )MAGING AND !DVANCED #ONCEPTS .ORWOOD -! !RTECH (OUSE , * #UTRONA h3YNTHETIC APERTURE RADAR v IN - 3KOLNIK 2ADAR (ANDBOOK ND %D .EW 9ORK -C'RAW (ILL ST %D .EW 9ORK -C'RAW (ILL 7 ' #ARRARA 2 3 'OODMAN AND 2 - -AJEWSKI 3POTLIGHT 3YNTHETIC !PERTURE 2ADAR .ORWOOD -! !RTECH (OUSE * #URLANDER AND 2 -C$ONOUGH 3YNTHETIC !PERTURE 2ADAR .EW 9ORK *OHN 7ILEY AND 3ONS ' 7 3TIMSON )NTRODUCTION TO !IRBORNE 2ADAR ND %D -ENDHAM .* 3CI4ECH # * *AKOWATZ *R $ % 7AHL 0 ( %ICHEL $ # 'HIGLIA AND 0 ! 4HOMPSON 3POTLIGHT -ODE 3!2 ! 3IGNAL 0ROCESSING !PPROACH "OSTON +LUWER !CADEMIC 0UBLISHERS 3 ! (OVANESSIAN )NTRODUCTION TO 3YNTHETIC !RRAY AND )MAGING 2ADARS .ORWOOD -! !RTECH (OUSE
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£n°£Ê * ,-* /6 -OTIVATION 7ORLDWIDE THE RATE OF INVESTMENT IN SPACE BASED RADAR 3"2 DUR ING THE TIME THE RADARS IN THIS CHAPTER WERE OPERATING WAS ON THE ORDER OF ONE BILLION DOLLARS PER YEAR 3PACE BASED SYNTHETIC APERTURE RADAR 3!2 SYSTEMS CAPABLE OF M RESOLUTION HAVE BECOME THE NORM WITH SYSTEMS UNDER DEVELOPMENT OR ALREADY LAUNCHED BY AT LEAST SEVEN COUNTRIES !S EXPANDED IN THE APPROPRIATE SECTIONS OF THIS CHAPTER THE RANGE MEASUREMENT PRECISION OF SURFACE HEIGHT CHANGE IS NOW ON THE ORDER OF MILLIMETER PER YEAR AS ESTABLISHED BY TWO DIFFERENT CLASSES OF %ARTH OBSERVING 3"2S 3!2S AND RADAR ALTIMETERS 3EVERAL NATIONS ARE SPONSORING RADARS FOR EXPLORATION AT THE -OON AND BEYOND 3"2 RELATED PATENT APPLICATIONS CONTINUE APACE )N SHORT 3"2 IS AN EXCITING EXACTING EXTENSIVE AND EXPANDING TOPIC 3PACE BASED RADAR SYSTEMS FACE FUNDAMENTAL CHALLENGES 4HE PERMISSIBLE OPTIONS FOR THE VALUE OF SEVERAL PARAMETERS SUCH AS PULSE REPETITION FREQUENCY ARE MORE RESTRICTED FOR 3"2 THAN FOR AIRBORNE SYSTEMS ,IKEWISE THE HARDWARE ENVIRONMENT IMPOSES MORE RIGOROUS CONSTRAINTS ON IMPLEMENTATION AND 3"2 SYSTEMS DO NOT ENJOY THE LUXURIES OF HANDS ON MAINTENANCE NOR IN FIELD PARTS REPLACEMENT (OWEVER THE PAYOFF FROM RADARS IN SPACE MORE THAN COMPENSATES FOR THESE CHALLENGES SINCE SPACE OFFERS A UNIQUE PERSPECTIVE FOR %ARTH OBSERVATION AND IS AN ESSENTIAL VIEWPOINT FOR LUNAR OR PLANETARY EXPLORATION #OVERED AND /MITTED 4OPICS 4HIS CHAPTER INTRODUCES SPACE BASED REMOTE SENSING RADARS 4HE FOCUS IS ON 4YPE )) 3"2S AS OUTLINED IN THE PREVIOUS EDITION OF THIS (ANDBOOK INCLUDING BOTH %ARTH ORBITING AND PLANETARY SYSTEMS 4HE MATERIAL IN THIS CHAPTER IS DESIGNED TO BE REASONABLY COMPLETE AT A SURVEY LEVEL THE DISCUSSION ZOOMS IN ON SELECTED CASE EXAMPLES TO ILLUSTRATE APPLICATION SPECIFIC IMPLEMENTA TIONS OR TECHNOLOGICAL INNOVATIONS !N OUTSTANDING EARLY EXAMPLE IS THE 3EASAT SATEL LITE LAUNCHED IN &IGURE WHICH AS ITS NAME SUGGESTS WAS DESIGNED FOR OCEANIC OBSERVATIONS 4HREE OF ITS SENSORS WERE 3"2SA SYNTHETIC APERTURE RADAR AN ALTIMETER AND A SCATTEROMETER !S THE READER WILL DISCOVER IN THIS CHAPTER THESE THREE 3EASAT INSTRUMENTS ESTABLISHED THE INITIAL PARADIGM FOR VIRTUALLY ALL SUBSEQUENT RADARS OF THEIR RESPECTIVE CLASSES
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4HIS CHAPTER DOES NOT COVER THE 4YPE ) SHORT RANGE SPECIALIZED 3"2 SYSTEMS REVIEWED IN EARLIER EDITIONS SUCH AS TERMINAL GUIDANCE OR RENDEZVOUS RADARS !LSO NOT COVERED ARE 4YPE ))) 3"2S SUCH AS MULTI SPACECRAFT SYSTEMS FOR SPACE BASED RADAR SURVEILLANCE OF THE %ARTHS SURFACE OR AIRSPACE !LTHOUGH THESE LARGE 3"2 CONCEPTS ARE INTERESTING IN PRINCIPLE THEIR IMPLIED COSTS REMAIN A DISINCENTIVE PARTICULARLY IF THEIR ERSTWHILE SPONSORS EXPECT THEIR PERFORMANCE TO APPROACH THE CURRENT STATE OF THE ART IN AIRBORNE SEARCH OR SURVEILLANCE RADARS %XCEPT FOR THE MENTION OF A FEW BASIC CONCEPTS THIS CHAPTER DOES NOT DELVE INTO THE EXTENSIVE SUBJECTS OF ORBITOLOGY IMPLEMENTATION OF SPACE QUALIFIED HARDWARE NOR SYSTEM INTEGRATION AND TEST FOR WHICH THE INTERESTED READER IS DIRECTED TO STANDARD REFERENCES "ASIC /RBIT #HARACTERISTICS 5NLIKE AN AIRBORNE PLATFORM THAT CAN GO ANYWHERE AT ANY TIME SUBJECT TO FUEL AND AIR SPACE LIMITATIONS A SATELLITES POSITION AND VELOC ITY WHEN IN ORBIT ABOUT A PLANETARY BODY ARE RIGIDLY GOVERNED BY ORBITAL DYNAMICS SUMMARIZED COMPACTLY BY +EPLERS LAWS &URTHER ACCESS BY AN 3"2 TO A GIVEN AREA OF INTEREST DEPENDS ON THE ROTATION RATE OF THE PLANET AS WELL AS THE SATELLITES POSITION ALONG ITS ORBIT AND THE RADARS VIEWING GEOMETRY 4HUS THE PRIMARY PARAMETERS TO BE INCLUDED IN 3"2 MISSION DESIGN INCLUDE ORBITAL ALTITUDE SPACECRAFT ON ORBIT VELOCITY AND HENCE PERIOD ORBIT INCLINATION AND THE ROTATION RATE OF THE PLANET %ARTH OBSERVING 3"2S SUCH AS 3!2S TEND TO OPERATE FROM SPACECRAFT IN NEAR CIRCULAR LOW %ARTH ORBITS ,%/ 4YPICAL ,%/ ALTITUDES SPAN KM TO KM ,OWER ALTITUDES INCUR LARGER ATMOSPHERIC DRAG WHEREAS HIGHER ALTITUDES IMPLY HIGHER RADIA TION LEVELS AND LONGER RADAR RANGES NEITHER OF WHICH ARE DESIRABLE IN MOST SITUATIONS 3PACECRAFT VELOCITIES AT THESE ,%/ ALTITUDES ARE ON THE ORDER OF KMS THEIR COR RESPONDING PERIODS ARE ABOUT MINUTES %ARTH ROTATION AT A RATE OF ^ DEGREE MIN SHIFTS THE SUB SATELLITE POINT AT THE EQUATOR BY ^ KM ORBIT TO ORBIT 4HE ORBIT ALTITUDE NORMALLY MAY BE CHOSEN TO TUNE THE PERIOD AND %ARTH ROTATION RATE SO THAT AN EXACT REPEAT PATTERN DEVELOPS THAT HAS A STIPULATED NUMBER OF DAYS 4HE REPEAT PERIOD
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OFTEN IS AN INTEGRAL NUMBER SUCH AS THE DAY REPEAT OF 2!$!23!4 ALTHOUGH A NON INTEGRAL PERIOD MAY BE PREFERRED SUCH AS THE DAY REPEAT OF THE 4/0%8 0OSEIDON RADAR ALTIMETER /RBIT PARAMETERS SUCH AS REPEAT PERIOD MUST BE MAINTAINED REQUIRING SMALL BOOSTS FROM SPACECRAFT THRUSTER MANEUVERS TYPICALLY APPLIED EVERY SEVERAL WEEKS FOR ,%/ MISSIONS 4HE REVISIT TIME OF A GIVEN 3"2 ASSET DEPENDS ON THE RANGE SWATH WIDTH COVERED BY THE RADAR IN QUESTION AS WELL AS THE ORBITS EXACT REPEAT PERIOD AND THE LATITUDE OF THE SITE OF INTEREST 4HE OFF NADIR LOOK ANGLE OF CERTAIN 3"2S CAN BE ADJUSTED TO INCREASE THE EFFECTIVE REVISIT RATE .OTE THAT ORBIT MANEUVERS ARE NOT A PRACTICAL MEANS TO IMPROVE THE FREQUENCY OF SITE COVERAGE SINCE A LARGE CHANGE IN ALTITUDE HENCE VELOCITY OR ESPECIALLY ANY CHANGE OF ORBIT INCLINATION THE ANGLE OF THE INERTIAL ORBIT PLANE WITH RESPECT TO THE %ARTHS EQUATOR WOULD REQUIRE A SUBSTANTIAL EXPENDITURE OF PRECIOUS ONBOARD FUEL RESOURCES 4HE %ARTH IS FLATTENED AT THE POLES DUE PRIMARILY TO ITS RELATIVELY RAPID ROTATION 4HE RESULTING LACK OF SPHERICAL SYMMETRY IN THE GRAVITY FIELD AT ORBITAL ALTITUDE IMPOSES SMALL LATERAL FORCES ON AN INCLINED ORBIT PLANE WHICH CONSEQUENTLY PRECESSES IN INERTIAL SPACE 4HE AMOUNT DIRECTION AND RATE OF ORBIT PRECESSION CAN BE CONTROLLED BY CHOICE OF THE INCLINATION AND THE MEAN ALTITUDE OF THE ORBIT -ANY SATELLITE PLATFORMS USE THIS DEGREE OF FREEDOM TO GENERATE A SUN SYNCHRONOUS ORBIT WHICH IS ONE THAT MAINTAINS A CONSTANT ANGLE OF ITS ORBIT PLANE RELATIVE TO SOLAR ILLUMINATION OVER THE ENTIRE YEAR 4HE %UROPEAN 3PACE !GENCYS %NVISAT SPACECRAFT IS A GOOD EXAMPLE OF A SUN SYNCHRONOUS ,%/ HAVING ^n INCLINATIONo AND KM ALTITUDE 3UN SYNCHRONOUS SPACECRAFT THAT HOST OPTICAL INSTRUMENTS SUCH AS *APANS !,/3 CHOOSE THE PHASE OF THE SUN ANGLE TO FAVOR ILLUMINATION OF THE SURFACE WHICH USUALLY LEADS TO A MIDDAY ORBIT FROM WHICH MOST OF THE %ARTHS SURFACE IS VIEWED AT ABOUT THE SAME LOCAL TIME NEAR MIDDAY 3UCH ORBITS IMPLY THAT THE SPACECRAFT MUST PASS THROUGH THE %ARTHS SHADOW ABOUT HALF THE TIME WHICH HAS CONSEQUENCES ON THE DESIGN OF THE THERMAL AND POWER SUBSYSTEMS IN PARTICULAR )N CONTRAST SPACECRAFT THAT CARRY ONLY RADARS SUCH AS 2!$!23!4 TEND TOWARD FAVORABLE ILLUMINATION OF THE SPACECRAFT 4HE NATURAL RESULT IN THIS CASE IS THE SO CALLED DAWN DUSK ORBIT IN WHICH THE SATELLITEAND ITS SOLAR PANEL DEPENDENT POWER SYSTEMAVOIDS THE SHADOW OF THE %ARTH ALMOST ALWAYS FOR ALMOST ALL SEASONS #ERTAIN APPLICATIONS ARE PARTICULARLY WELL SERVED BY EXACT REPEAT ORBITS &OR EXAM PLE IF A GROUP OF ORBITAL TRAJECTORIES FALLS WITHIN A SMALL RADIUS OF EACH OTHER WHEN OVER AN AREA OF INTEREST THEN RADAR MEASUREMENTS FROM SEVERAL ORBITS MAY BE COMPARED COHERENTLY THUS POTENTIALLY SENSITIVE AT THE ORDER OF A WAVELENGTH TO CHANGES IN THE SCENE BETWEEN OBSERVATIONS 3UCH COHERENT CHANGE DETECTION IS A STANDARD TECHNIQUE IN THE FIELD OF SPACE BASED 3!2 INTERFEROMETRY REVIEWED IN THE FOLLOWING SECTION %XACT REPEAT ORBITS ARE STANDARD FOR MOST RADAR ALTIMETERS BUT FOR GEOPHYSICAL REASONS NOT FOR MUTUAL COHERENCY 3UN SYNCHRONICITY PRESENTS ITS OWN PROBLEMS FOR OCEAN SENSING ALTIMETERS 4HESE COMMENTS ARE ELABORATED IN 3ECTION !S DISCUSSED IN SEVERAL CHAPTERS OF THIS BOOK THE PERFORMANCE OF DOPPLER SENSITIVE RADARS IS CONDITIONAL UPON THE VELOCITY OF THEIR HOST PLATFORM 4HE VELOCITY OF A SPACE CRAFT IN ORBIT AT ALTITUDE H ABOVE A PLANET OF RADIUS 20 AND MASS -0 IS GIVEN BY
63# - 0 ' 20 H
.ADIR IS THE POINT BELOW THE SPACECRAFT ON THE SURFACE INTERSECTED BY THE RADIUS VECTOR FROM THE %ARTHS CENTER TO THE SPACECRAFT o )NCLINATIONS GREATER THAN n ARE RETROGRADE BECAUSE THEIR % 7 VELOCITY COMPONENT IN THE ASCENDING PASS IS CONTRARY TO THE DIRECTION OF THE %ARTHS ROTATION IN CONTRAST TO PROGRADE ORBITS WHOSE INCLINATIONS ARE LESS THAN n
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WHERE ' IS THE UNIVERSAL GRAVITY CONSTANTp r n .MKGn 4ABLE LISTS REP RESENTATIVE SPACECRAFT VELOCITIES FOR BODIES IN THE SOLAR SYSTEM THAT HAVE BEEN VISITED OR ARE LIKELY TO BE OBSERVED BY RANGE DOPPLER RADARS &EASIBLE SATELLITE ALTITUDES ARE LIMITED BELOW BY THE PREVAILING ATMOSPHERIC DENSITY 4HE FINAL COLUMN OF THE TABLE LISTS THE ALTITUDE VELOCITY PRODUCT H63# CORRESPONDING TO EACH ENTRY 4HIS PRODUCT IS A SCALING FACTOR THAT CHARACTERIZES THE RANGE DOPPLER SPACE CONFRONTING AN 3"2 INTENDED TO BE DEPLOYED IN THAT ENVIRONMENT 4HERE IS APPROXIMATELY A FOLD SPREAD IN THE VALUE OF THIS PARAMETER FROM THE %ARTH TO *UPITERS MOON %UROPA )T FOLLOWS THAT RADAR DESIGNS THAT WORK IN ONE SITUATION MAY NOT BE AT ALL APPROPRIATE IF MIGRATED TO A DIFFER ENT PLANETARY BODY )T IS OFTEN SAID THAT RADAR IS hALL WEATHER v BUT THIS GENERALIZATION CLEARLY IS NOT UNIVERSALLY TRUE ESPECIALLY FOR 3"2S &ROM SPACE THE IONOSPHERE ANDOR ATMOSPHERE MAY CORRUPT OR EVEN PREVENT RADAR PROPAGATION 4HE IONOSPHERE MAY INDUCE &ARADAY ROTATION e THUS DEGRADING OR DESTROYING THE POLARIZATION PROPERTIES OF THE TRANSMIT TED AND RECEIVED SIGNALS 4HE &ARADAY ROTATION A OF A LINEARLY POLARIZED % VECTOR IS PROPORTIONAL TO 2- K WHERE THE ROTATION MEASURE 2- IS A FUNCTION OF IONOSPHERIC ELECTRON DENSITY 4HE IONOSPHERE ALSO INTRODUCES DISPERSION AND UNDER CERTAIN UNFA VORABLE CIRCUMSTANCES EFFECTIVELY CUTS OFF PROPAGATION 4HUS FOR EXAMPLE IT WAS NOT POSSIBLE FOR THE -(Z -!23)3 RADAR SOUNDER TO PROBE THE -ARTIAN SURFACE DUR ING DAYLIGHT HOURS BECAUSE THE CUTOFF FREQUENCY UNDER THOSE CONDITIONS INCREASED TO ABOUT -(Z 4HUS -!23)3 WORKED AS A SURFACE SOUNDER DURING DARK HOURS AND AS AN IONOSPHERIC SOUNDER DURING DAYLIGHT HOURS -ORE ON THE -!23)3 RADAR MAY BE FOUND IN 3ECTION 4HE CM WAVELENGTH OF THE -AGELLAN 6ENUS RADAR REVIEWED IN 3ECTION WAS CHOSEN IN RESPONSE TO THE TRADE OFF BETWEEN PROPAGATION THROUGH 6ENUS VERY DENSE ATMOSPHERE FOR WHICH LONGER WAVELENGTHS WOULD BE BETTER AND SYNTHETIC APERTURE RADAR SYSTEM CONSIDERATIONS FOR WHICH SHORTER WAVELENGTHS WOULD BE BETTER 0ROPAGATION SPEED IS RETARDED ALONG THE PATH LENGTH FROM AN OCEAN VIEWING ALTIMETER TO THE %ARTH BY A VERY SMALL FRACTION OF THE SPEED OF LIGHT BUT SUFFICIENT NEV ERTHELESS TO IMPOSE RANGE MEASUREMENT ERRORS OF MANY METERS 4HESE ERRORS MUST BE ESTIMATED AND COMPENSATED BEFORE THE REQUIRED CM LEVEL ACCURACY CAN BE ACHIEVED AS SUMMARIZED IN 3ECTION #OMMENTS ON (ARDWARE /N A POPULAR !MERICAN CHILDRENS TELEVISION PRO GRAM ONE IS TOLD THAT h)T IS NOT EASY BEING GREENv ,IKEWISE IT IS NOT EASY BEING p . IS THE STANDARD SYMBOL FOR .EWTON FORCE WITH THE UNITS M KG Sn e 4HE PLANE OF POLARIZATION OF AN %- WAVE IS PERTURBED BY INTERACTION WITH THE MAGNETIC FIELD THROUGH WHICH IT PASSES AN EFFECT DISCOVERED BY &ARADAY
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A RADAR ESPECIALLY ABOARD A SPACECRAFT "ECAUSE A RADAR BY DEFINITION MUST TRANSMIT ITS NEAR FIELD RADIATION IS A POTENTIAL THREAT TO ALL OTHER INSTRUMENTS AND SUBSYSTEMS OF THE HOST SPACECRAFT AND ITS PAYLOAD /NCE HAVING GOT PAST THE RISK OR PARANOIA OF NEAR FIELD RADIATION NORMAL SPACECRAFT DESIGN PRINCIPLES KICK IN 4HE FIRST ORDER CON SIDERATIONS ON HARDWARE THAT ARE CHARACTERISTIC OF AND ESSENTIALLY UNIQUE TO THE SPACE ENVIRONMENT INCLUDE RADIATION AND ENERGETIC PARTICLES VIBRATION ESPECIALLY DURING THE LAUNCH PHASE HARSH AND CONTRASTING THERMAL ENVIRONMENTS OFTEN CHALLENGING MASS LIMITATIONS AND A PREMIUM ON PAYLOAD POWER )N %ARTH ORBIT AND PERHAPS SUR PRISINGLY ALSO AT THE -OON A SPACE BASED RADAR MUST COMPLY WITH INTERNATIONALLY AGREED SPECTRAL ALLOCATIONS 4HESE LIMIT BOTH THE AVAILABLE BANDS AND THE BANDWIDTHS WHICH IMPACT SYSTEM DESIGN AND MAY CONSTRAIN CERTAIN PERFORMANCE OBJECTIVES SUCH AS RESOLUTION 3INCE IT IS EXPENSIVE TO GET TO ORBIT 3"2S LIKE OTHER SPACE BASED SYSTEMS MUST BE DESIGNED TO MINIMIZE MASS AND TO MAXIMIZE EFFICIENCY AND LONGEVITY -ASS POWER AND LIFETIME EMERGE AS DRIVING THEMES THAT DICTATE CONSERVATIVE DESIGN GENEROUS MARGINS DURING SYSTEM IMPLEMENTATION AND REDUNDANCY OFTEN REALIZED BY DUAL STRING HARDWARE IN MOST IF NOT ALL SUBSYSTEMS OTHER THAN THE ANTENNA /RGANIZATION OF THE #HAPTER 4HE CHAPTER SECTIONS ARE ORGANIZED BY MEASURE MENT THEME TAKEN IN A BROAD SENSE 4HESE THEMES ARE %ARTH ORBITING SYNTHETIC APERTURE RADAR 3!2 RADAR ALTIMETRY WHICH IN THE 3"2 CONTEXT ALMOST ALWAYS IMPLIES OBSER VATION OF THE %ARTHS OCEANS AND LARGER SURFACE WATER BODIES PLANETARY RADARS WHERE hPLANETv INCLUDES PLANETOIDS SUCH AS LARGE MOONS SCATTEROMETERS WHOSE DATA ASSOCI ATE A GEOPHYSICAL PARAMETER SUCH AS OCEANIC WIND SPEED TO THE OBSERVED CALIBRATED RADAR BACKSCATTER PROPERTIES OF THE ILLUMINATED SURFACE AND SOUNDERS WHICH INCLUDES BOTH ATMOSPHERIC AND SUBSURFACE RADAR SYSTEMS %ACH SECTION INCLUDES AN OVERVIEW OF ALL RELEVANT 3"2S NOTING KEY TURNING POINTS OR WATERSHED INNOVATIONS IN THE THEMES HISTORY 3ELECTED EXAMPLES HAVE BEEN CHOSEN FOR MORE IN DEPTH REVIEW /NLINE WEB SITES ARE SUGGESTED FOR EACH CITED INSTRUMENT THESE WEB SITES WERE ACCESSIBLE AT THE DATE OF PUBLICATION OF THIS BOOK
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4HE FIELD OF SPACE BASED REMOTE SENSING RADARS IS SUBJECT TO RAPID CHANGE 4HIS CHAPTER PROVIDES THE VIEW FROM THE EARLY ST CENTURY 2EADERS ARE ENCOURAGED TO SEEK CURRENTLY TOPICAL INFORMATION THROUGH ONLINE RESOURCES +EYWORDS SUCH AS THE NAMES OF THE MISSION NATIONALITY AND RADAR ARE USUALLY SUFFICIENT TO LOCATE SEVERAL REFER ENCES !LERT .OT ALL ONLINE RESOURCES ARE ACCURATE THE READER IS ADVISED TO SEEK OUT MORE THAN ONE AND TO VERIFY INFORMATION BY CROSS COMPARISON
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3!2 IMAGES ARE DEGRADED BY A MULTIPLICATIVE SELF NOISE KNOWN AS SPECKLE WHICH IS A DIRECT CONSEQUENCE OF THE COHERENCE REQUIRED BY THE RADAR PROCESSOR COMBINATION TO FORM THE SYNTHETIC APERTURE AND THE RESULTING ENHANCED RESOLUTION 3PECKLE CAN BE REDUCED ONLY THROUGH SUPPLEMENTAL INCOHERENT PROCESSING MULTI LOOKING IN 3!2 JARGON !DDITIONAL LOOKS REQUIRE PROPORTIONALLY MORE BANDWIDTH )T FOLLOWS THAT LARGE TWO DIMENSIONAL BANDWIDTH RANGE AND AZIMUTH IS THE DRIVING REQUIREMENT FOR THIS CLASS OF RADAR 3PACE BASED 3!2 SYSTEMS HAVE MOTIVATED FRUITFUL SPECIALIZATIONS IN QUANTITATIVE APPLICATIONS IN A WIDE VARIETY OF AREAS COMPREHENSIVELY REVIEWED IN THE 0RINCIPLES AND !PPLICATIONS OF )MAGING 2ADAR 4OPICS SUCH AS 3POT3!2 3CAN3!2 POLARIMETRY AND INTERFEROMETRY THAT HAVE INFLUENCED RADAR SYSTEM AND MISSION DESIGN ARE OUTLINED IN CLOSING PARAGRAPHS OF THIS SECTION &LIGHT 3YSTEMS 4HE CONCEPT OF 3!2 INTRODUCED IN BY #ARL 7ILEY WAS REDUCED TO PRACTICE IN SUBSEQUENT YEARS FIRST THROUGH SIMULATIONS THEN THROUGH AIR BORNE PROOF OF CONCEPT SYSTEMS 1UILL THE FIRST SPACE BASED 3!2 SEE 4ABLE WAS LAUNCHED ONLY A DECADE LATER 4HAT WAS A REMARKABLE ACHIEVEMENT CONSIDERING THAT IN THE MODERN ERA IT OFTEN TAKES NEARLY YEARS TO GO FROM CONCEPT TO LAUNCH OF A NEW 3!2 EVEN THOUGH THE PRINCIPLES AND TECHNOLOGY FOR THESE 3"2S ARE BY NOW WELL ESTABLISHED 1UILL WAS RUDIMENTARY BUT DID SUCCEED IN GENERATING DATA SUFFICIENT TO FORM IMAGES 4HE NOMINAL M RESOLUTION WAS SPECTACULAR FOR ITS TIME GIVEN THAT THE BEST RESOLUTION THAT COULD BE EXPECTED FROM AN OTHERWISE COMPARABLE REAL APERTURE 3"2 WOULD BE ON THE ORDER OF KILOMETERS .EVERTHELESS THE RESULTS DID NOT MEET THE NEEDS OF THE SPONSOR AND SO THE NOTIONAL SECOND AND THIRD MISSIONS WERE NEVER LAUNCHED 1UILL WAS THE ONLY !MERICAN 3"2 WHOSE DATA WERE OPTICALLY RECORDED ONBOARD EVENTUALLY RETURNED TO %ARTH BY EJECTED CAPSULE AND THEN COLLECTED BY AN AIRBORNE RETRIEVAL MANEUVER 4!",% 3YNTHETIC !PERTURE 2ADARS %ARTH VIEWING
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ANALOG -(Z OFFSET VIDEO TO BE CONVERTED ON THE GROUND TO EITHER OPTICAL MEDIA TRANSPARENT FILM STRIPS OR DIGITIZED BIT QUANTIZATION )MAGERY WAS GENERATED BUT NOT IMMEDIATELYo BY EITHER OPTICAL OR DIGITAL PROCESSING METHODS 4HE 3EASAT SATEL LITE SUFFERED A MASSIVE SHORT CIRCUIT IN ITS PRIMARY POWER SYSTEM IN THE SOLAR PANEL SLIP RING ASSEMBLY WHICH ENDED ITS MISSION IN /CTOBER AFTER ONLY THREE MONTHS OF OPERATION 3)2 3!2 3ERIES 4HE 3HUTTLE IMAGING RADARS 3)2 ! WHICH FLEW ON THE FIRST 3HUTTLE THAT CARRIED A SCIENCE PAYLOAD 3)2 " AND 3)2 #8 3!2 WERE ESSENTIALLY TECHNOLOGY AND SCIENCE DEMONSTRATIONS MISSIONS EACH LASTING ABOUT ONE WEEK OR LESS )N SEQUENCE THESE RADARS HAD INCREASINGLY MORE CAPABILITY IN TERMS OF INCIDENCE FREQUENCY AND POLARIZATION 3)2 #8 3!2 OPERATED AT THREE BANDS # AND , 53! AND 8 CONTRIBUTED THROUGH AN INTERNATIONAL PARTNERSHIP WITH 'ERMANY AND )TALY $ATA FROM 3)2 # CONTINUES IN DEMAND THANKS TO ITS FULLY POLARIMETRIC MULTIBAND COVERAGE OF A WIDE VARIETY OF SCENES 4HE 3HUTTLE 2ADAR 4ERRAIN -APPER 324- WAS AN OUTGROWTH OF 3)2 # USING A SMALL RECEIVING ANTENNA AT 8 AND # BAND MOUNTED ON A M LONG EXTENDABLE STRUT TO COLLECT SIMULTANEOUS BACKSCATTER SUBSEQUENTLY PRO CESSED INTO TOPOGRAPHIC MAPS 4HIS WAS THE FIRST DEMONSTRATION OF SINGLE PASS SPACE BASED INTERFEROMETRIC 3!2 CAPABILITY )N3!2 $ATA WERE COLLECTED OVER A VERY LARGE FRACTION OF THE GLOBAL LANDMASS +OSMOS !LTHOUGH NOT CLASSIFIED IN THE STRICT SENSE +OSMOS CAME TO VIEW LARGELY AFTER THE LAUNCH OF ITS TECHNICAL SUCCESSOR !LMAZ 2USSIAN AND !RABIC FOR DIAMOND IN THE ROUGH 0RECEDING THESE 3OVIET 3!2S WERE A SERIES OF REAL APERTURE RADARS KNOWN AS /KEAN AND BY OTHER NAMES !LMAZ WAS A VERY INTERESTING RADAR IN THAT IT PROVIDED UNIQUE 3 BAND 3"2 IMAGERY OF THE %ARTHS SURFACE 4HE TECHNOLOGY BEHIND THIS AND RELATED 2USSIAN SYSTEMS CONTINUED TO BE DEVELOPED CULMINATING IN THE +ONDOR % RADAR AND THROUGH A BILATERAL TECHNOLOGY EXCHANGE PROGRAM THE (* # 3!2 OF #HINA "OTH OF THESE RADARS USE THE M PARABOLIC REFLECTOR DEVELOPED ORIGINALLY FOR 0RIRODA THE FINAL MODULE FOR THE 2USSIAN -)2 COMPLEX 4RAVERS THE RADAR ABOARD 0RIRODA WAS AN EXPERIMENTAL DEMONSTRATION MISSION 4HERE ARE AT LEAST THREE MEMBERS OF THE 8 BAND NATIONAL ASSET 3!2 FLEET INCLUDING 4EC3!2 )SRAEL AND THE )'3 2 SERIES *APAN 4HE FIRST )'3 2 WAS LAUNCHED IN 4HE LAUNCH OF A SEQUEL FAILED %23 AND %23 4HE # BAND 3!2S FROM THE %UROPEAN 3PACE !GENCY %3! INTRODUCED OPERATIONAL SPACE BASED 3!2 CAPABILITY 3INCE THE LAUNCH OF THE FIRST %UROPEAN 2ADAR 3ATELLITE %23 %3! 3!2S HAVE MAINTAINED A CONTINUOUS RECORD OF OUTSTANDING PERFORMANCE %23 AND ITS FOLLOWERS HAVE HAD ONBOARD DATA RECORDING CAPABILITY %23 AND %23 HAD IN COMMON ^ M RESOLUTION AT LOOKS KM SWATH WIDTH AND ^n INCIDENCE ALL IN THE PATTERN OF THE 3EASAT 3!2 4HE TWO %23 3!2S WERE VIRTUALLY IDENTICAL %23 AND %23 ENJOYED ABOUT ONE YEAR OF SIMULTANEOUS OPERA TION ORGANIZED BY %3! TO CHASE EACH OTHER SO THAT THEIR JOINT REPEAT VISIT WAS ONLY ONE DAY 4HIS LEAD TO THE ACCUMULATION OF A UNIQUE DATA SET ESPECIALLY VALUABLE FOR COHERENT CHANGE DETECTION MEASUREMENTS TWO PASS )N3!2 4HE %23 3!2 INSTRUMENT WAS A SUBSET OF A COMBINED RADAR GROUP THE !CTIVE -ICROWAVE )NSTRUMENT !-) COM PRISED OF A SCATTEROMETER AND A WINDWAVE MINI 3!2 MODE AS WELL AS THE 3!2 ITSELF o 4HE FIRST DIGITALLY PROCESSED IMAGES FROM THE 3EASAT 3!2 REQUIRED HOURS FOR A QUARTER FRAME KM SQUARE ON A MAINFRAME COMPUTER
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4HE SCATTEROMETER MODE IS DESCRIBED IN 3ECTION 4HE WINDWAVE MODE BASED ON THE 3!2 WAS DESIGNED TO GRAB KM SQUARE SNAPSHOT IMAGES OF THE OCEAN SURFACE WHICH COULD BE PROCESSED ONBOARD OR LATER IN A GROUND FACILITY TO ESTIMATE WIND SPEED AND DIRECTION FROM THE RADAR BRIGHTNESS AND WAVE PATTERN IN THE DATA 4HIS MODE WAS MOTIVATED BY A REQUIREMENT TO GATHER 3!2 QUALITY DATA OVER A LARGE AREA WITHIN TIGHT DATA VOLUME LIMITS /NE CONSEQUENCE OF THE OCEAN VIEWING REQUIREMENTS WAS THAT 66p EMERGED AS THE FAVORED POLARIZATION SINCE VERTICALLY POLARIZED OCEANIC BACKSCATTER TENDS TO BE LARGER AT # BAND AT STEEP INCIDENCEe THAN HORIZONTALLY POLARIZED OCEANIC BACKSCATTER %23 AND ALSO CARRIED RADAR ALTIMETERS 3ECTION 4HE %3! SERIES OF SATELLITES USE MIDDAY SUN SYNCHRONOUS ORBITS BECAUSE THEIR PAYLOADS INCLUDE OPTICAL SENSORS 4HE RESULTING HALF ORBIT ECLIPSE CONTRIBUTES TO THEIR PER ORBIT 3!2 OPERATIONAL LIMIT OF TEN MINUTES * %23 4HE 3!2 ABOARD THE *APANESE %ARTH 2ESOURCES 3ATELLITE * %23 WAS SIMILAR TO 3EASAT BEING AT , BAND WITH AN ( POLARIZED M BY M ANTENNA )TS n INCIDENT ANGLE WHICH IS LARGER THAN THAT OF 3EASAT WAS ENABLED BY ITS LOWER ALTITUDE AND LARGER ANTENNA APERTURE )TS K7 PEAK POWER WAS COMPARABLE TO THAT OF 3EASAT /NE CONSEQUENCE OF THE LARGER ANTENNA VERTICAL DIMENSION IS THE KM SWATH WHICH IS NARROWER THAN THAT OF 3EASAT * %23 WAS CRIPPLED BY ANTENNA AND CONNEC TOR PROBLEMS SO THAT ITS SENSITIVITY NOISE EQUIVALENT SIGMA ZERO .%QR WAS ONLY n D" D" SHY OF ITS n D" DESIGN !S A RESULT * %23 IMAGE PRODUCTS WERE FAR NOISIER THAN THOSE OF 3EASAT WHOSE SENSITIVITY WAS n D" )N SPITE OF THAT HANDICAP HOWEVER * %23 DATA AT CM WAVELENGTH PROVIDED THE FIRST SYNOPTIC COVERAGE OF THE TROPICAL FORESTS OF "RAZIL AND NEIGHBORING COUNTRIES 4HESE DATA ESTABLISHED AN EARLY hGOLD STANDARDv FOR TROPICAL FOREST SURVEYS SINCE , BAND IS SO MUCH BETTER SUITED TO THIS APPLICATION THAN SHORTER WAVELENGTHS * %23 HAD M RESOLUTION AT LOOKS ABOUT hBETTERv THAN 3EASAT BASED ON COMPARISON OF THEIR RESPECTIVE 3!2 IMAGE QUALITY FACTORS 3ECTION * %23 OPERATED FOR EIGHT YEARS CONSIDERABLY LONGER THAN ITS TWO YEAR DESIGN LIFE 2!$!23!4 3HOWN IN &IGURE 2!$!23!4 MARKED A MAJOR MILESTONE IN SPACE BASED 3!2 )T WAS THE FIRST SYSTEM TO OFFER THE USER A CHOICE OF RESOLUTIONS INCIDENT ANGLES AND SWATH WIDTHS 4HE EVOLUTION OF THESE CHARACTERISTICS MERITS A BRIEF REVIEW 4HE #ANADIAN REQUIREMENTS SPANNED A VARIETY OF APPLICATIONS FROM OCE ANIC SURVEILLANCE VESSELS AND OIL PLATFORMS AS WELL AS SEA STATE LAND AND SEA ICE AGRICULTURE AND FORESTS AMONG MANY OTHERS 4HE SEA ICE APPLICATION HAD HIGH PRI ORITY WHICH DROVE THE CHOICE OF POLARIZATION (ORIZONTAL WAS CHOSEN BECAUSE THAT
p )T IS COMMON IN RADAR REMOTE SENSING THAT THEIR POLARIZATIONS ARE ABBREVIATED AS AN ALPHABETIC PAIR IN THIS CASE INDICATING VERTICAL POLARIZATION ON BOTH TRANSMIT AND RECEIVE e 3PACE BASED 3!2S TEND TO LOOK TOWARD THE SURFACE AT ANGLES THAT ARE MUCH CLOSER TO VERTICAL THAN DO AIRBORNE 3!2S 4HE MOST COMMONLY USED TERMINOLOGY IS INCIDENCE THE ANGLE AT THE ILLUMINATED SURFACE BETWEEN THE LOCAL VERTICAL AND THE INCOMING ILLUMINATION 4HE ANGLE OF INCIDENCE IS THE COMPLEMENT OF THE GRAZING ANGLE THE CUSTOMARY NOMENCLATURE FOR AIRBORNE RADARS )NCIDENCE DIFFERS FROM ELEVATION THE ANGLE AT THE SPACECRAFT BETWEEN VERTICAL AND THE DIRECTION FROM THE SPACECRAFT TO THE SCENE WHERE THE DIFFERENCE IS DUE TO THE %ARTHS CURVATURE
!LERT 4HE *APANESE 3!2S USUALLY SPECIFY THE LOOK ANGLE AS THE ELEVATION ANGLE AT THE SPACECRAFT ALTHOUGH CALLING THAT ANGLE hINCIDENCEv 4HUS MOST OF THE LITERATURE CITES n FOR * %23 S INCIDENCE WHICH CAN LEAD TO CONFUSION IF THE VALUE OF THIS PARAMETER IS IMPORTANT IN A GIVEN APPLICATION 4HE SAME CAVEAT APPLIES TO 0!,3!2 DESCRIBED IN A SUBSEQUENT PARAGRAPH
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&)'52% 2!$!23!4 IS OUTWARDLY SIMILAR TO ITS PREDECESSOR 4HE SOLAR PANELS ARE PARALLEL TO THE ALONG TRACK AXIS OF THE ANTENNA INDICATIVE OF A DAWN DUSK SUN SYNCHRONOUS ORBIT #OURTESY OF THE #ANADIAN 3PACE !GENCY
OFFERED AN ADVANTAGE WHEN ATTEMPTING TO DISTINGUISH NEW ICE FROM CALM SEA AT # BAND AND MODERATE INCIDENCE 4HE APPLICATIONS DIVERSITY IMPLIED A SPAN OF PREFERRED INCI DENCE FROM ^n TO MORE THAN n )N RESPONSE THE ANTENNA WAS REQUIRED TO STEER ITS BEAM IN ELEVATION WHICH EVOLVED INTO SEVEN DIFFERENT STANDARD ELEVATION BEAM PAT TERNS ELECTRONICALLY STEERED AND SHAPED !S MIGHT BE EXPECTED NO APPLICATIONS THEME WOULD ACCEPT DEGRADED RESOLUTION 4O SATISFY THAT DEMAND THE RADAR DESIGN ADOPTED THREE BANDWIDTHS SO THAT THE NOMINAL GROUND RANGE RESOLUTION WOULD BE MAINTAINED AT ^ M OVER ALL BASELINE INCIDENT ANGLES !S A COROLLARY THE WIDER BANDWIDTH AT SHALLOWER INCIDENCE WOULD RESULT IN FINER RANGE RESOLUTION 4HE ANTENNA DESIGN WAS BASED ON HORIZONTAL RUNS OF WAVEGUIDES EACH CENTER FED &ERRITE PHASE SHIFTERS ONE FOR EACH WAVEGUIDE CONTROLLED THE TRANSMIT AND RECEIVE BEAM SHAPE AND BORESIGHT IN ELEVATION 4HE ELECTRONIC BEAM SELECTION ENABLED 2!$!23!4 TO INCORPORATE 3CAN3!2o 4HUS THE RESOLUTION OPTIONS FOR 2!$!23!4 RANGE FROM M BY M SINGLE LOOK KM SWATHS FINE MODE TO M BY M LOOKS KM SWATHS 3CAN3!2 7IDE )NCIDENCE RANGES FROM n TO n INCLUDING THE EXTENDED MODES 4HERE ARE SEVEN STANDARD MODES EACH HAVING ITS OWN ELEVATION BEAM THESE MODES HAVE NOMINALLY M BY M LOOKS KM SWATHS 4HE .%QR IS n D" OR BETTER AND MODE DEPENDENT "Y THE END OF 2!$!23!4 HAD COMPLETED ITS TH YEAR LOGGING MORE THAN ORBITS AND COLLECTING ENOUGH DATA TO MAP THE ENTIRE SURFACE OF THE %ARTH AN EQUIVALENT OF TIMES 4HE #ANADIAN )CE 3ERVICE RELIES ON 2!$!23!4 DATA FOR ITS ROUTINE OPERATIONS WHICH REQUIRE MORE THAN FRAMES OF DATA PER YEAR 3INCE THE 3!2 IS THE ONLY 2!$!23!4 PAYLOAD INSTRUMENT A SUN SYNCHRONOUS DAWN DUSK ORBIT WAS CHOSEN TO MAXIMIZE ILLUMINATION OF THE SOLAR PANELS WHICH ALLOWS MINUTES OF 3!2 OPERATION PER ORBIT 2!$!23!4 LOOKS TO THE RIGHT SIDE OF THE ORBIT PLANE WHICH GIVES IT ACCESS TO THE #ANADIAN !RCTIC UP TO THE .ORTH 0OLE 4WICE DURING ITS MISSION THE SPACECRAFT WAS YAWED n FOR SEVERAL WEEKS WHICH ENABLED FULL COVERAGE OF !NTARCTICA 4HE RESULTING DATA WERE MERGED TO YIELD THE FIRST HIGH RESOLUTION IMAGERY OF THE WHOLE CONTINENT AND OVER SEVERAL REGIONS REPEAT PASS COVERAGE SUPPORTED INTERFEROMETRIC 3!2 MEASUREMENT OF !NTARCTIC GLACIAL FLOW RATES 2!$!23!4 IS AN ENHANCED VERSION OF 2!$!23!4 4ABLE CHARTS A SUM MARY OF ITS MANY MODES
o $ISCUSSED LATER IN THIS SECTION
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3ELECTIVE POLARIZATION 3TANDARD 7IDE &INE 3CAN3!2 7IDE 3CAN3!2 .ARROW 3INGLE POLARIZATION ,OW INCIDENCE (IGH INCIDENCE 0OLARIMETRY 3TANDARD 1UAD0OL &INE 1UAD0OL 3ELECTIVE 3INGLE 0OL -ULTI LOOK &INE 5LTRA &INE %XPERIMENTAL -/$%8 '-4) 6ERY (IGH 2ESOLUTION
%.6)3!4 4HE ADVANCED 3!2 !3!2 ABOARD %3!S %NVISAT TAKES 2!$!23!4 S VERSATILITY ONE STEP FURTHER WITH THE ADDITION OF TWO POLARIZATIONS ( AND 6 ON EITHER TRANSMIT OR RECEIVE )TS M BY M ACTIVE ARRAY ANTENNA COM PRISES TRANSMITRECEIVE MODULES )N OTHER REGARDS ITS MODES REFLECT THE BASIC 2!$!23!4 DESIGN DUE IN LARGE PART TO THE PARTICIPATION BY KEY RADAR SPECIALISTS FROM #ANADAA MEMBER OF %3!S %ARTH /BSERVATION 0ROGRAM "OARDON THE !3!2 CONCEPTUAL DESIGN TEAM 4HE TRANSMIT AND RECEIVE POLARIZATIONS ARE INDEPENDENT OF EACH OTHER SO THAT AT FULL RESOLUTION THE POLARIZATION CHOICES ARE (( 66 OR (6 .OTE THAT THIS DUAL POLARIZATION MODE IS ACTUALLY ALTERNATING POLARIZATION IN WHICH THE POLARIZATION STATES ARE SWITCHED BETWEEN TRANSMISSIONS OR RECEPTIONS BUT THE PULSE REPETITION FREQUENCY IS NOT INCREASED 3UCH A hDUAL POLARIZEDv PAIR BY DEFINITION CANNOT BE MUTUALLY COHERENT SINCE IT CORRESPONDS TO INTERLEAVED SAMPLES OF THE BACK SCATTER TIME MULTIPLEXED AT LESS THAN THE .YQUIST RATE !S A CONSEQUENCE THE PHASE DIFFERENCE BETWEEN COMPLEX SAMPLES AT EACH PIXEL IS NOT AVAILABLE 4HE !3!2 ALTER NATING POLARIZATION MODE PROVIDES DUAL POLARIZED IMAGES THAT ARE SIMILAR TO THOSE THAT HAVE BEEN AVAILABLE FROM MANY AIRBORNE SYSTEMS FOR DECADES ALTHOUGH NOT AVAILABLE FROM AN 3"2 EXCEPT FOR 3)2 " AND 3)2 # UNTIL %.6)3!4 0!,3!2 )N CONTRAST TO THE INCOHERENT POLARIMETRIC OPTIONS OF !3!2 THE 0HASED !RRAY , BAND 3YNTHETIC !PERTURE 2ADAR 0!,3!2 ABOARD *APANS !,/3p LAUNCHED IN *ANUARY INCLUDES FULL QUADRATUREe POLARIMETRY 4HE 0!,3!2 MODES INCLUDE STANDARD SINGLE POLARIZATION MAPPING MODES A 3CAN3!2 MODE A VARIETY OF DUAL AND QUADRATURE POLARIZED MODES AND EXPERIMENTAL MODES INCLUDING 3POT3!2 %ARLY MISSION CALIBRATION AND VALIDATION STUDIES VERIFIED THAT THE RADAR IS PERFORMING AS INTENDED -ORE ON 0!,3!2 APPEARS LATER IN THIS SECTION p !DVANCED ,AND /BSERVATION 3ATELLITE *!8! *APAN e $ISCUSSED LATER IN THIS SECTION
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*IAN"ING +NOWN ALTERNATIVELY AS 2EMOTE 3ENSING 3ATELLITE *IANBING IS #HINAS FIRST SYNTHETIC APERTURE RADAR MISSION 4HE SPACECRAFT MASS IS KG LAUNCHED INTO A SUN SYNCHRONOUS ORBIT AT ^ KM ALTITUDE -ISSION OBJECTIVES INCLUDE POLARIMETRIC DIVERSITY AND INTERFEROMETRY 4HE TWO BASELINE MULTI LOOK RESOLUTIONS ARE M KM SWATH AND M KM SWATH OVER A VARIETY OF INCIDENT ANGLES )TS ANTENNA IS AN ACTIVE PHASED ARRAY 4ERRA3!2 8 4ERRA3!2 8 IS THE FIRST CIVILIAN DEDICATED SPACE BASED 3!2 AT 8 BAND )TS M BY M ANTENNA IS A TWO DIMENSIONAL ACTIVE ARRAY OF 42 MODULES )T HAS A VARIETY OF MODES FROM 3CAN3!2 M RESOLUTION OVER KM SWATHS TO 3POT3!2 M RESOLUTION OVER A KM BY KM IMAGE FRAME )TS STRIP MAPPING MODE IS BASELINED AT M RESOLUTION ACROSS KM SWATHS 4HE ARRAY IS PARTITIONED IN THE ALONG TRACK DIRECTION WHICH CAN BE EXERCISED IN A TWO APERTURE ALONG TRACK INTERFEROMETRIC MODE FOR '-4) EXPERIMENTS AMONG OTHER APPLICATIONS &ULL QUADRATURE POLARIZATION IS ONE OF THE MODE OPTIONS 4HE ONLY PAYLOAD INSTRUMENT IS THE RADAR SO THE SPACECRAFT IS DESIGNED FOR A SUN SYNCHRONOUS DAWN DUSK ORBIT DAY REPEAT 3EVERAL YEARS AFTER THE LAUNCH OF 4ERRA3!2 8 IT WILL BE JOINED BY A COMPANION 4ANDEM 8 WHICH IS MEANT TO BE A FUNCTIONAL COPY 4HESE TWO WILL CO ORBIT AS A CLOSELY COORDINATED PAIR TO SUPPORT A VARIETY OF BISTATIC AND INTERFEROMETRIC APPLICATIONS /THER 3PACE BASED 3!2S 3PACE BASED 3!2 CONTINUES TO UNDERGO CONSID ERABLE EXPANSION ON AN INTERNATIONAL FRONT 4HIS SECTION PROVIDES AN OVERVIEW OF PROGRAMS KNOWN AT THE TIME OF PUBLICATION OF THIS (ANDBOOK TO HAVE PROGRESSED THROUGH 0HASE ! WHICH IS EVIDENCE OF FUNDING THAT IS SUFFICIENTLY SERIOUS THAT MOST ARE LIKELY TO CULMINATE IN THE LAUNCH AND OPERATION OF A FLIGHT SYSTEM 4HE ARCHI TECTURE OF THESE EMERGING SYSTEMS IS DOMINATED BY ONE OF TWO ANTENNA PARADIGMS ACTIVE TWO DIMENSIONAL PHASED ARRAYS OR REFLECTORS -OST MISSIONS ARE MULTIMODE IN RESOLUTION HENCE SWATH AND COVERAGE AND POLARIMETRY RANGING FROM INCOHERENT DUAL POLARIZATION TO FULL QUADRATURE POLARIMETRY !T LEAST FOUR OF THESE INITIATIVES IMPLY SEVERAL SATELLITES EITHER IN CONSTELLATION OR IN SERIES !LL TOGETHER SOMETHING IN EXCESS OF NEW 3!2S ARE BEING LAUNCHED IN THE FIRST DECADE OF THE ST CENTURY FROM AT LEAST EIGHT DIFFERENT COUNTRIES (IGHLIGHTS OF SEVERAL OF THESE SYSTEMS ARE SUMMARIZED IN THE FOLLOWING PARAGRAPHS #/3-/ 3KY-ED )TALY HAS A SERIES OF FOUR #/3-/ 3KY-ED 8 BAND 3!2 SATELLITES 4HE #/3-/ 3!2S HAVE MULTIPOLARIZATION ACTIVE PHASED ARRAY ANTENNAS THAT SUPPORT A VARIETY OF MODES INCLUDING M 3POT3!2 STRIP MAP 3CAN3!2 AND KM WIDE SWATH 4HE #/3-/ BUS IS BASED ON THE DESIGN BUILT AND FLIGHT PROVEN FOR #ANADAS 2!$!23!4 4EC3!2 4HE FIRST SPACE BASED 3!2 FROM )SRAEL 4EC3!2 IS A FEATURED ELEMENT OF THEIR NATIONAL SATELLITE TECHNOLOGY DEVELOPMENT PROGRAM ,AUNCHED BY )NDIA 4EC3!2S NOMINAL STRIP MAP MODE IS MULTI LOOK M RESOLUTION AT 8 BAND -AJOR ADDITIONAL OBJECTIVES INCLUDE LARGE AREA COVERAGE AS WELL AS HIGH RESOLUTION WHICH IMPLY 3CAN3!2 AND 3POT3!2 MODES RESPECTIVELY 4HE M 3POT3!2 RESOLUTION CONSTRAINS THE DESIGN ONE CONSEQUENCE OF WHICH IS THE SYMMETRICAL BODY MOUNTED M DIAMETER UMBRELLA STYLE MESH REFLECTOR KG DRIVEN BY ONE OF TEN FEED HORNS SLIGHTLY OFFSET FROM THE FOCAL POINT 4HIS UNITY ASPECT RATIO ANTENNA IS A NOTABLE DEPAR TURE FROM THE RECTANGULAR ANTENNAS SO TYPICAL OF MOST SPACE BASED 3!2 PRECEDENTS
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&)'52% 4EC3!2 FEATURES A SYMMETRICAL REFLECTOR ANTENNA IN CONTRAST TO THE CLASSIC HIGH ASPECT RATIO hBILLBOARDv STYLE PIONEERED BY 3EASAT #OURTESY OF )!) )SRAEL
3CAN3!2 COVERAGE M RESOLUTION KM SWATH TO M RESOLUTION KM SWATH INCIDENCE DEPENDENT IS EXECUTED BY SEQUENTIAL SELECTION OF THE APPROPRIATE FEEDS 4HE FEED HORNS ARE ( OR 6 POLARIZED SO THAT POLARIMETRIC DIVERSITY IS ALSO SUPPORTED BY THIS ARRANGEMENT -ISSION DESIGN INCLUDES SPACECRAFT STEERING TO SUPPORT SQUINTED ASPECTS RELATIVE TO THE REFERENCE SIDE LOOKING ORTHOGONAL VIEWING 4HE HIGH POWER STAGE IS COMPRISED OF TEN CHANNELED 474!S EIGHT OF WHICH ARE REQUIRED IN COMBINATION LEAVING TWO AS REDUNDANT BACKUP 4HE RADAR MASS IS KG INCLUDING THE REFLECTOR AND FEEDS SATELLITE DRY MASS INCLUDING THE RADAR IS ^ KG WHICH AT THE TIME SET THE STANDARD AS THE SMALLEST 3!2 SATELLITE IN %ARTH ORBIT 4HE POWER SUBSYSTEM DELIVERS UP TO K7 DURING IMAGING OPERATIONS 4HE SPACECRAFT ORBIT IS n INCLINATION ^ KM ALTITUDE DAY REPEAT PERIOD 3INCE THIS IS NOT A SUN SYNCHRONOUS ORBIT AND SINCE THE ANTENNA PATTERN TO FIRST ORDER IS SYMMETRIC THE SPACECRAFT MAY BE ROTATED ABOUT THE RADARS LINE OF SIGHT TO HELP SUSTAIN NEAR FULL ILLUMINATION OF THE TWO SOLAR PANEL ARRAYS IN ALL SUN ORBIT PLANE CONFIGURATIONS 2ADAR DATA ARE RECORDED IN A 'BIT SOLID STATE UNIT FOLLOWING TO BLOCK FLOATING POINT QUANTIZATION 3PACECRAFT DESIGN LIFE IS FIVE YEARS (* # (* # IS THE FIRST OF FIVE 3!2 SATELLITES IN #HINAS SMALL SATELLITE PROGRAM ANNOUNCED IN FOR ENVIRONMENT AND DISASTER MONITORING 4HE ARCHI TECTURE OF THESE SYSTEMS IS CLOSELY PARALLEL TO 2USSIAS +ONDOR % SERIES SINCE THEY ARE BOTH OUTGROWTHS OF A BILATERAL DEVELOPMENT PROGRAM BASED ON THE ARCHITECTURE OF THE 0RIRODA 3 BAND RADAR 4HE (* #S ANTENNA IS A REFLECTOR THAT HAS AN EFFEC TIVE APERTURE OF M BY M FOLLOWING DEPLOYMENT )N STRIP MAP MODE THE (* # HAS A MULTI LOOK M RESOLUTION OVER A KM SWATH AND M RESOLUTION IN 3CAN3!2 MODE AT KM SWATH WIDTH 3POT3!2 MODE IS SUPPORTED BY CONTROLLED YAW MANEUVERS OF THE SPACECRAFT !LL OF THE SPACECRAFT IN THE SERIES FIVE RADARS AND SIX OPTICAL SYSTEMS USE SUN SYNCHRONOUS ORBITS AT ^ KM ALTITUDE 4HE RADARS MASS IS ^ KG 3!2 ,UPE 'ERMANY HAS FIVE IDENTICAL 8 BAND SATELLITES DISTRIBUTED IN THREE KM HIGH ORBITS INCLINED AT ABOUT n 4HE ASPECT RATIO OF THEIR M BY M
4RAVELING WAVE TUBE AMPLIFIER 3EE #HAPTER FOR MORE DISCUSSION
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ANTENNAS SUGGESTS THAT THE DOMINANT OBJECTIVE IS FINE RESOLUTION WHICH NECESSITATES A RELATIVELY NARROW RANGE SWATH 0UBLISHED SPECIFICATIONS NOTE THAT THE INTENDED RESO LUTION IN THE SLIP 3!2o MODE IS M OVER A KM BY KM IMAGE FRAME 4HESE INNOVATIVE 3"2S ARE RELATIVELY SMALL AT LEAST BY %ARTH OBSERVING SATELLITE 3!2 STAN DARDS 4HEIR KG MASS TOTAL DRY MASS OF THE SPACECRAFT AND THE RADAR IS LESS THAN THE MASS OF 2!$!23!4 S ANTENNA 4HE 3!2 ,UPE DESIGN ALSO IS COST CONSCIOUS BASED ON RIGID NONDEPLOYED REFLECTOR ANTENNAS hBORROWEDv FROM A COMMERCIAL COMMUNICATIONS SATELLITE PRODUCTION LINE THAT ARE INHERENTLY MORE EFFICIENT AND LESS MASSIVE THAN AN ACTIVE ARRAY 4HE RADAR ELECTRONICS ARE DIRECTLY DESCENDED FROM A COMMERCIAL PRODUCT LINE 2)3!4 4HE 2ADAR )MAGING 3ATELLITE OR 2)3!4 IS )NDIAS FIRST SPACE BASED 3!2 FOLLOWING EXTENSIVE PROGRAMS IN OPTICAL REMOTE SENSING SATELLITES AND AIRBORNE IMAGING RADAR DEVELOPMENT 2)3!4S DEPLOYABLE ANTENNA M BY M IS AN ACTIVE PHASED ARRAY COMPRISED OF # BAND 'HZ 42 MODULES EACH CAPABLE OF 7 PEAK POWER 4HE AVERAGE OUTPUT POWER 7 REQUIRES AN AVERAGE INPUT DC POWER OF K7 %ACH 42 MODULE IS CONNECTED TO SEPARATE DISTRIBUTION NETWORKS FEEDING ( AND 6 POLARIZED ELEMENTS WHICH SUPPORT POLARIZATION DIVERSITY AS WELL AS ELEVA TION BEAM STEERING 4HERE ARE TWO PARALLEL RECEIVE CHANNELS DEDICATED TO THE ( AND 6 POLARIZED ANTENNA ELEMENTS 2)3!4 HAS FIVE MODES EACH OF WHICH MAY OPERATE AT A VARIETY OF INCIDENT ANGLES 4HE MODES ARE FINE RESOLUTION STRIP MAP M RESOLU TION KM SWATH DUAL POLARIZATION FINE RESOLUTION STRIP MAP M AT KM QUADRATURE POLARIZATION MEDIUM RESOLUTION 3CAN3!2 M AT KM DUAL POLAR IZATION COARSE RESOLUTION 3CAN3!2 M AT KM DUAL POLARIZATION AND HIGH RESOLUTION 3POT3!2 BETTER THAN M KM SQUARE IMAGE FRAME DUAL POLARIZATION 4HE 3POT3!2 MODE REQUIRES YAWPITCH STEERING OF THE SPACECRAFT TO on #OVERAGE TO EITHER SIDE OF THE GROUND TRACK REQUIRES A ROLL MANEUVER OF THE SPACECRAFT TO DIRECT THE ANTENNA PATTERN TO THE OPPOSITE SIDE OF NADIR AN APPROACH THAT IS SIMILAR TO THAT OF 2!$!23!4 4HE VARIETY OF RESOLUTIONS IS SUPPORTED BY FOUR BANDWIDTHS -(Z -(Z -(Z AND -(Z THROUGH A PROGRAMMABLE DIGITAL CHIRP GENERATOR 4HE RECEIVED DATA ARE DOWNCONVERTED TO BASEBAND DIGITIZED TO BITS ) AND 1 AND QUANTIZED BY BLOCK FLOATING POINT MEANS TO FEWER BITS TO AT THE USERS OPTION WITHIN MODE DEPENDENT LIMITS !LL SUBSYSTEMS SAVE FOR THE ANTENNA ARE DUAL REDUN DANT .OMINAL 02& IS (Z o (Z $ATA RATES SPAN -BITSS TO -BITSS DEPENDING ON MODE 4HE ON ORBIT MASS OF THE SPACECRAFT WILL BE ^ KG OF WHICH THE 3!2 PAYLOAD INCLUDING THE ANTENNA CLAIMS ^ KG /NBOARD DATA STORAGE CAPAC ITY IS 'BITS DOWNLINK MAXIMUM DATA RATE IS -BITSS 8 BAND DUAL CIRCULARLY POLARIZED 4HE 2)3!4 ORBIT IS SUN SYNCHRONOUS DAWN DUSK AT ^ KM ALTITUDE AND DAY REVISIT PERIOD -!03!2 4HE -ULTI !PPLICATION 0URPOSE 3!2 IS A JOINT "RAZILIAN 'ERMAN ENTERPRISE AIMED PRIMARILY AT ASSESSING AND MONITORING "RAZILS NATURAL RESOURCES !FTER SEVERAL YEARS OF TRADE STUDIES , BAND WAS SELECTED 'HZ 4HE RADAR IS BUILT AROUND A NEAR SYMMETRICAL REFLECTOR M BY M WITH TEN FEEDS OFFSET FROM THE FOCAL POINT SO THAT THE BEAM CAN BE ELECTRONICALLY SCANNED IN ELEVATION 3PATIAL RESOLU TION AND SWATH SPAN M TO M AND KM TO KM RESPECTIVELY MODE DEPENDENT o 3LIP 3!2 IS A MODIFIED 3CAN3!2 MODE IN WHICH THE ANTENNA PATTERN IS DRAGGED ALONG THE SURFACE AT A SLOWER RATE THAN IN THE CONVENTIONAL STRIP MAP MODE 4HE RESULT IS LARGER DOPPLER BANDWIDTH HENCE ENHANCED AZIMUTH RESOLU TION AND ALSO A WIDER IMAGED AREA THAN A PURE 3POT3!2 CAN SUPPORT
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4HE HIGH RESOLUTION SPECIFICATION RESULTS FROM AN EXTERNAL CONSTRAINT THE MAXIMUM -(Z BANDWIDTH STIPULATED BY INTERNATIONAL SPECTRAL ALLOCATION AGREEMENTS 4HERE IS PROVISION FOR ALL POLARIMETRIC CONFIGURATIONS 4HE SUN SYNCHRONOUS ORBIT WILL BE CON TROLLED TO ASSURE RELIABLE DAY REVISIT BASELINES TO SUPPORT INTERFEROMETRY .OMINAL INSTRUMENT MASS IS KG 0!,3!2 !LTHOUGH BASED ON * %23 HERITAGE 0!,3!2 IS AN EXCELLENT EARLY EXAMPLE OF MULTIMODE SPACE BASED 3!2S 0!,3!2S MODES &IGURE INCLUDE STANDARD SINGLE POLARIZATION MAPPING 3CAN3!2 A VARIETY OF DUAL AND QUADRATURE POLARIZED MODES p AND EXPERIMENTAL OR DEMONSTRATION MODES INCLUDING 3POT3!2 4HE , BAND CM BASELINE FREQUENCY -(Z HAS TWO BANDWIDTHS -(Z FINE BEAM SINGLE POLARIZATION MODE AND -(Z DUAL QUAD POL AND 3CAN3!2 MODES 4HE SPAN OF MID SWATH INCIDENT ANGLES IS n nn .OTE THAT THE *APANESE USUALLY CITE THESE ANGLES AS hOFF NADIRv nnn WHICH REFERS TO THEIR ELEVATION WITH RESPECT TO VERTICAL IN SPACECRAFT COORDINATES RATHER THAN THEIR INTERSECTION RELA TIVE TO A LOCAL VERTICAL AT THE %ARTHS MEAN OBLATE SPHEROIDAL SURFACE
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&)'52% /VERVIEW OF 0!,3!2S VIEWING GEOMETRIES %ACH OF THESE BEAM POSITIONS SUPPORTS A VARIETY OF POLARIZATION COMBINATIONS LEADING TO A VERY LARGE NUMBER OF AVAILABLE MODES 4HE SOLAR PANEL IS ORTHOGONAL TO THE ORBIT PLANE INDICATIVE OF A MIDDAY SUN SYNCHRONOUS ORBIT $IAGRAM COURTESY OF *!8! *APAN
p 4HE SEVERAL FORMS OF POLARIMETRIC DIVERSITY COMMON IN REMOTE SENSING SYSTEMS ARE REVIEWED LATER IN THIS SECTION
£n°£È
2!$!2 (!.$"//+
-ODERN SPACE BASED 3!2S OWE THEIR LARGE MODE VARIETY TO ACTIVE ELECTRONIC STEERED ANTENNA ARRAYS 0!,3!2S ANTENNA CONSISTS OF SOLID STATE 42 MODULES DISTRIBUTED ON FOUR PANELS WHOSE DEPLOYED DIMENSIONS ARE M BY M VERTICAL AND HORIZONTAL RESPECTIVELY 3PACECRAFT VELOCITY AND ANTENNA LENGTH DICTATE A LOWER BOUND ON PULSE REPETITION FREQUENCY WHICH FOR 0!,3!2 SPANS K(Zn K(Z DEPENDING ON MODE 0EAK TRANSMITTED POWER IS ^ K7 TWICE THAT OF THE 3EASAT 3!2 4HE RESULTING SENSITIVITY NOISE EQUIVALENT SIGMA ZERO IS VERY GOOD n D" OR BETTER FOR MOST MODES 0!,3!2S HOST !,/3 SPACECRAFT IS YAW STEERED TO MAINTAIN AZIMUTH ANTENNA BORESIGHT POINTING AT ZERO DOPPLER WHICH INCREASES THE LIKELIHOOD OF PASS TO PASS INTERFEROMETRIC COHERENCE AND SIMPLIFIES SOMEWHAT 3!2 IMAGE FORMATION PROCESSING 4HE NOMINAL DATA RATE IN MOST MODES IS -BITS WHICH IS DOWNLINKED VIA *APANS $ATA 2ELAY 4EST 3ATELLITE $243 4HE 3CAN3!2 MODE REQUIRES ONLY HALF THAT RATE -BITS WHICH CAN BE DOWNLINKED DIRECTLY TO GROUND STATIONS !,/3 HAS AN ONBOARD 'BYTE SOLID STATE RECORDER TO BUFFER DATA OUTPUT FROM THE RADAR AS WELL AS FROM THE REST OF THE PAYLOAD 0!,3!2S VOLUMINOUS VARIETY OF MODES IS A CURSE AS WELL AS A BLESSING -ISSION MANAGEMENT MUST COPE WITH DATA COLLECTION IN EACH OF THESE MODES AS WELL AS PHAS ING THE RESULTING DATA BURDEN TO SHARE THE COMMUNICATIONS LINK WITH THE TWO OTHER HIGH DATA RATE INSTRUMENTS IN THE !,/3 PAYLOAD 4HE STANDARD POLICY FOR THE EARLY YEARS OF 0!,3!2S ON ORBIT SCHEDULING IS TO FOCUS ON SIX hDEFAULTv MODESFOUR hOPERATIONALv AND TWO hSEMI OPERATIONALv 4HE RESULTING TERMS ARE FIXED hSTANDARDv OFF NADIR ANGLE OF n FOR A GREAT MAJORITY OF THE DATA TAKES POLARIZATION OPTIONS TO BE SINGLE POL (( AND DUAL POL (( (6 QUAD POL AT n OFF NADIR FOR 2$ DEM ONSTRATIONS OVER PRESELECTED hSUPERSITESv AND FIVE BEAM 3CAN3!2 IN (( POLARIZA TION )N ADDITION THE FOLLOWING CONSTRAINTS APPLY ONLY ONE MODE IS EXERCISED DURING ONE DAY REPEAT CYCLE PREFERRED OPERATIONS ARE DURING THE HOURS OF DARKNESS IN THE ASCENDING PASSES FOR MOST MODES EXCEPTING LOWER DATA RATE 3CAN3!2 DATA TAKES DUR ING DESCENDING PASSES IN COORDINATION WITH THE OPTICAL SENSORS AND ALSO EXCEPTING EXTRAORDINARY )N3!2 AND MARINE APPLICATIONS AT NONSTANDARD INCIDENCE AND RECURRENT REPEAT PASS COVERAGE OF SELECTED SITES IN GROUPS OF EIGHT OR MORE DAY CYCLES IN SUP PORT OF )N3!2 OBJECTIVES 3PACE BASED 3!2 $ESIGN )SSUES 4HE OPTIONS FOR SPACE BASED 3!2 DESIGN ARE MORE LIMITED THAN FOR AIRBORNE SYSTEMS DUE PRIMARILY TO THE CONSTRAINTS IMPOSED BY VIABLE ORBITS INCLUDING ESPECIALLY SENSOR VELOCITY RADAR RANGE 2 AND SYSTEM COST 4HE FOLLOWING PARAGRAPHS REVIEW THE MAJOR THEMES 02& #ONSTRAINTS 4HE RULES THAT GOVERN THE PULSE REPETITION FREQUENCY 02& OF A SPACE BASED 3!2 ARE THE SAME AS THOSE APPLICABLE TO AIRBORNE SYSTEMS ALTHOUGH THEY PLAY OUT RATHER DIFFERENTLY 4HE FUNDAMENTAL REQUIREMENT IS THAT THE 02& FP BE SUFFICIENTLY HIGH TO SAMPLE UNAMBIGUOUSLY THE DOPPLER SPECTRUM OF WIDTH "$OP AND ALSO SUFFICIENTLY LOW SO THAT THERE IS TIME BETWEEN TRANSMISSIONS TO RECEIVE THE DATA BACKSCATTERED FROM THE INTENDED SWATH OF SLANT RANGE TIME DOMAIN WIDTH 42 4HUS
"$OP F0 42
)N PRACTICE SUFFICIENT MARGIN MUST BE INCLUDED IN BOTH THE UPPER AND LOWER LIMITS TO ACCOUNT FOR THE LENGTH OF THE TRANSMITTED PULSE AND FOR THE FACT THAT NEITHER THE DOPPLER SPECTRUM NOR THE ANTENNAS ELEVATION PATTERN HAVE SHARP CUTOFFS
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
£n°£Ç
4HE LOWER BOUND OFTEN IS RECAST AS
"$OP
B63# 63# F0 $!Z L
WHICH STATES THAT THE 02& MUST BE SUFFICIENTLY HIGH SUCH THAT THERE ARE TWO TRANSMIS SIONS PER ANTENNA APERTURE LENGTH $!Z AS THE RADAR MOVES ALONG ITS TRAJECTORY (ERE 63# IS SPACECRAFT VELOCITY ALONG ITS ORBIT A IS THE WIDTHe OF THE AZIMUTH ANTENNA PATTERN AND K IS THE RADAR WAVELENGTH 4HIS FORM IS INTUITIVELY SATISFYING SINCE THE SINGLE LOOK AZIMUTH RESOLUTION IS APPROXIMATELY ONE HALF OF THE ANTENNAS ALONG TRACK WIDTH HENCE THIS INEQUALITY REQUIRES THAT EACH RESOLVED ALONG TRACK RANGE LINE MUST BE SAMPLED AT LEAST ONCE 5SUALLY THE 02& LOWER BOUND IS SET SO THAT THERE IS A MARGIN OF OR MORE WITH RESPECT TO THIS CONSTRAINT )N AN AIRBORNE 3!2 THE 02& CONSTRAINT IS DERIVED TO SATISFY THE DOPPLER BANDWIDTH FROM WHICH FOLLOWS THE MAXIMUM RANGE THAT THE RADAR CAN OPERATE WITHOUT INTRODUC ING AMBIGUITIES (OWEVER BY DEFAULT THE MINIMUM RANGE FOR A SPACE BASED 3!2 IS ITS ORBITAL ALTITUDE USUALLY KM OR HIGHER 4HE TYPICAL SLANT RANGE TO THE INTENDED SCENE MAY BE KM AND MORE 4HUS THE UPPER BOUND ON THE 02& SHOULD NOT BE SET BY THE RANGE TO THE SCENE BUT RATHER BY THE RANGE WIDTH OF THE AREA TO BE IMAGED !S A CONSEQUENCE THE RESULTING HIGH 02& WILL GENERATE A SEQUENCE OF PULSES AT ANY MOMENT THAT ARE DISTRIBUTED BETWEEN THE RADAR AND THE SCENE 4HE SPACE BETWEEN PULSES MUST BE LARGER THAN THE INTENDED SWATH WIDTH &OR EXAMPLE IN CERTAIN MODES 2!$!23!4 GENERATES SEVEN PULSES hIN FLIGHTv SIMULTANEOUSLY !T THE BEGINNING OF SUCH A DATA COL LECTION BACKSCATTER FROM THE INTENDED SCENE WOULD ARRIVE ONLY AFTER THE SEVENTH PULSE HAD BEEN TRANSMITTED )N MANY AIRBORNE SYSTEMS THE 02& IS CHOSEN TO BE RATHER HIGHER THAN THE LIMIT IMPOSED BY THE RANGE TO THE INTENDED TARGET SPACE )N SUCH CASES THE EXTRA 02& CON TRIBUTES TO IMPROVED 3.2 BUT AT THE COST OF INCREASED AVERAGE DATA RATE $ATA RATE CAN BE DECREASED BY hPRE SUMMINGvCOHERENTLY ADDING N ADJACENT RETURNS 4HE CON SEQUENCE OF COURSE IS THAT THE EFFECTIVE 02& IS REDUCED BY THE SAME FACTOR N 4HIS PRACTICE IS SELDOM ACCEPTABLE FOR SPACE BORNE 3!2S BECAUSE IT LEADS TO AZIMUTH AMBI GUITIES UNLESS THE DOPPLER SPECTRUM IS LIMITED PRIOR TO 02& REDUCTION !MBIGUITIES 4HE 02& GENERATES A TWO DIMENSIONALLY SAMPLED SPACE WHEN THE DATA ARE DECOMPOSED INTO hSLOW TIMEv IN THE AZIMUTH DIRECTION AND hFAST TIMEv IN THE RANGE DIRECTION )N AZIMUTH THE 02& CREATES ALIASED VERSIONS OF THE DATA ILLUMINATED BY THE MAIN BEAM OF THE ANTENNA 4HE SPECTRA OF THESE ALIASES ARE LOCATED AT MULTIPLES OF THE 02& TO EITHER SIDE OF THE DOPPLER CENTROID OF THE MAIN BEAM /F COURSE WHEN SAMPLED THEY ARE FOLDED BACK INTO THE .YQUIST PASSBAND 4HESE ALIASES ARE AZIMUTH AMBIGUITIES WHICH ARE SUPPRESSEDHENCE NOT VISIBLEIN A WELL DESIGNED SYSTEM SUPPORTED BY A WELL TUNED PROCESSOR 7HEN THEY DO APPEAR AZIMUTH AMBIGUITIES ARE RELATIVELY EASY TO IDENTIFY &IGURE BECAUSE THEY ARE WEAKER GHOST DUPLICATES OF IMAGE FEATURES THAT WERE COLLECTED THROUGH THE MAIN BEAM AND THEREFORE AT EARLIER OR LATER POSITIONS ALONG THE IMAGE STRIP 4HE AZIMUTH SHIFT OF THE AMBIGUITIES RELATIVE TO THE CENTRAL IMAGE IS AN INTEGRAL MULTIPLE OF $8 2L F0 63# WHICH IS THE SPATIAL
e &OR A UNIFORMLY ILLUMINATED APERTURE THE D" BEAMWIDTH IS A K $ )T IS CUSTOMARY FOR ANALYSIS OF 3!2 !Z SYSTEMS TO APPROXIMATE THIS EXPRESSION BY A ^ K $!Z AND TO INTERPRET A AS THE WIDTH OF THE RECTANGLE THAT HAS THE SAME PEAK VALUE AND AREA AS THE ANTENNA PATTERN
£n°£n
2!$!2 (!.$"//+
OFFSET CORRESPONDING TO THE 02& !ZIMUTH AMBIGUITIES ESPECIALLY FROM POINT TARGETS HAVE THE SAME DOPPLER &- RATE AS SCATTERERS WITHIN THE MAIN BEAM AND SO THEIR FOCUS IS PRESERVED THROUGH THE PROCESSOR )N THE RANGE DIRECTION ONE OF THE CONSEQUENCES OF HAVING MANY PULSES IN FLIGHT AT ONCE IS THAT THERE ARE ECHOES FROM SEVERAL DIFFERENT RANGES THAT ARRIVE BACK AT THE RADAR AT THE SAME RELATIVE DELAY WITHIN THE RANGE GATE AS THE REFLECTIONS FROM THE INTENDED SWATH )F THESE EXTRA ECHOES ARE SUFFICIENTLY STRONG THE RESULTING IMAGE ARTIFACTS ARE RANGE AMBI GUITIES 2ANGE AMBIGUITIES ARE NOT AS EASY TO IDENTIFY AS AZIMUTH AMBIGUITIES BECAUSE THEY ARISE FROM RANGES OUTSIDE OF THE NOMINAL SWATH HENCE NOT OTHERWISE IMAGED 2ANGE AMBIGUITIES BY DEFINITION ARISE FROM RANGES THAT ARE DIFFERENT FROM THOSE FOR WHICH THE PROCESSOR IS SET SO THAT RANGE AMBIGUOUS POINT TARGETS TEND TO BE DEFOCUSED 4HE PRINCIPAL MEANS OF SUPPRESSING AMBIGUITIES IS TO CONFINE THE MAIN BEAM OF THE ANTENNA SO THAT THE POTENTIAL SOURCES OF AZIMUTH OR RANGE AMBIGUITIES ARE NOT ILLU MINATED OR AT LEAST ARE ILLUMINATED ONLY VERY WEAKLY 4HIS REQUIREMENT IMPOSES A MINIMUM AREA CONSTRAINT ON THE 3!2S ANTENNA 4HE LOWER AND UPPER BOUND 02& CONSTRAINTS OF "$OP AND 42 LEAD TO
$%L $!Z 263# L C TANP )NC
WHERE THE ANTENNA AREA IS THE PRODUCT OF ITS LENGTH $!Z AND HEIGHT $%L AND P )NC IS THE MEAN INCIDENT ANGLE IN THE IMAGED SWATH 4HE RANGE VELOCITY PRODUCT IN THIS EXPRES SION IS DETERMINED BY THE PARAMETERS PECULIAR TO THE PARTICULAR PLANET OR MOON ABOUT WHICH THE 3!2 IS TO OPERATE 4ABLE !S A CONSEQUENCE AN ANTENNA OF AREA M AT THE -OON WOULD HAVE BE M FOR THE SAME RADAR AT -ARS AND NEARLY M FOR OPERATION IN %ARTH ORBIT )T ALWAYS IS TEMPTING TO PUSH THIS CONSTRAINT SINCE MOST SPACE BASED 3!2S USE AS MUCH OF THE AMBIGUITY FREE SPACE AS CAN BE TOLERATED )N PRACTICE THE ANTENNA AREA USUALLY IS CHOSEN TO BE AT LEAST A FACTOR OF TWO LARGER THAN THIS MINIMUM WOULD SUG GEST !MBIGUITIES ARE PROPORTIONAL TO THE STRENGTH OF THE OFFENDING BACKSCATTER AND AS SUCH THEY CONTRIBUTE TO THE MULTIPLICATIVE NOISE RATIO -.2 OF THE SYSTEM !NTENNA SIDELOBES AND AMBIGUITIES ARE FURTHER SUPPRESSED BY APPROPRIATE WEIGHTING IN THE PROCESSOR 4HE TRADE OFF IS LOWER -.2 AT THE EXPENSE OF BROADER IMPULSE RESPONSE WIDTH )27 4YPICAL DESIGNS PROVIDE ^ EXCESS RANGE AND DOPPLER BANDWIDTH RELATIVE TO THOSE IMPLIED BY THE REQUIRED RANGE AND AZIMUTH RESOLUTIONS TO ACCOM MODATE SUCH WEIGHTING .ADIR 2ETURN ! POTENTIALLY TROUBLESOME RANGE AMBIGUITY ARISES FROM THE SURFACE DIRECTLY BELOW THE SPACECRAFT 4HIS NADIR RETURN IS ALWAYS RELATIVELY STRONG PARTICULARLY IF THERE ARE SPECULAR BACKSCATTERING COMPONENTS 3INCE ANY REALISTIC ANTENNA PATTERN HAS A NON ZERO SIDELOBE DIRECTED TOWARD NADIR THE RESULTING REFLECTION COULD APPEAR IN THE IMAGE 4HE MAIN STRATEGY IS TO AVOID THE AMBIGUITY BY CHOOSING THE 02& SO THAT THE NADIR RETURN ARRIVES AT THE SAME TIME THAT THE RADAR IS TRANSMITTING 4HIS TIMING PLACES A FURTHER CONSTRAINT ON THE PULSE REPETITION FREQUENCY )T TURNS OUT THAT THE NADIR RETURN MAY NOT BE AVOIDABLE IF OTHER CONSTRAINTS OVERRIDE THE AVAILABLE 02& OPTIONS 4HIS OCCURS FOR EXAMPLE IF THE DRIVING REQUIREMENT IS 3CAN3!2 WHICH HAS ITS OWN SET OF CONSTRAINTS ON 02&
-ULTIPLICATIVE NOISE A STANDARD SPECIFICATION IN SYNTHETIC APERTURE RADAR INCLUDES UNWANTED CONTRIBUTIONS SUCH AS AMBIGUITIES AND QUANTIZATION NOISE THAT ARE PROPORTIONAL TO THE STRENGTH OF THE RECEIVED SIGNAL
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
£n°£
&)'52% %XAMPLE OF ARTIFACTS AS THEY APPEARED IN EARLY 2!$!23!4 FOUR SUB SWATH 3CAN3!2 IMAGERY 4HE DIRECTION OF FLIGHT IS VERTICAL IN THIS PRESENTATION NEAR EDGE RANGE AT THE LEFT OF THE FRAME #OURTESY OF THE #ANADIAN 3PACE !GENCY AND THE #ANADA #ENTRE FOR 2EMOTE 3ENSING
!NTENNAS AND 4RANSMITTERS !NTENNAS FOR THE PIONEERING SPACE BASED 3!2 SYS TEMS WERE EXCLUSIVELY PASSIVE SUCH AS THE , BAND PATCH ARRAY ON 3EASAT OR THE SLOT TED WAVEGUIDE ARRAYS USED ON %23 AND !LMAZ 4HE FIRST EXCEPTION TO THIS RULE WAS 2!$!23!4 DESIGNED AROUND AN ARRAY OF HORIZONTAL SLOTTED WAVEGUIDES EACH OF WHICH WAS CENTER FED THROUGH A PHASE SHIFTER SO THAT THE ELEVATION BEAM PAT TERN COULD BE SELECTED AND SHAPED ELECTRONICALLY -ORE AMBITIOUS READ hMASSIVE AND EXPENSIVEv SYSTEMS TEND TO USE TWO DIMENSIONALLY ACTIVE ELECTRONIC SCANNED ARRAYS %3!S 4HESE ARE POPULATED BY TRANSMITRECEIVE 42 MODULES OFTEN INCORPORATING TWO POLARIZATIONS ( AND 6 %XAMPLES INCLUDE 2!$!23!4 %.6)3!4S !3!2 0!,3!2 #/3-/ 4ERRA3!2 8 AND 2)3!4 )T IS ARGUED THAT ACTIVE ARRAYS SET THE STAGE FOR hGRACEFUL FAILUREv SINCE THE LOSS OF A FEW 42 ELEMENTS WOULD HAVE LITTLE EFFECT ON THE NET PERFORMANCE OF THE SYSTEM )N PARALLEL AN ALTERNATIVE 3!2 ANTENNA PARADIGM STRESSES SIMPLICITY AND LOWER MASS AND LOWER COST OVER TWO DIMENSIONAL ELECTRONIC BEAM STEERING 4HESE ARE REFLECTORS OF WHICH #HINAS (* # 'ERMANYS 3!2 ,UPE )SRAELS 4EC3!2 AND "RAZILS -AP3!2 ARE GOOD EXAMPLES )F A REFLECTOR IS DRIVEN BY MULTIPLE FEEDS THEN ONE MAY STILL EFFECT BEAM STEERING ALTHOUGH WITH RATHER LESS BEAM SHAPE VARIETY AND CONTROL THAN THROUGH AN %3! 3PACE BASED RADAR TRANSMITTERS NATURALLY FALL INTO TWO CLASSES INTIMATELY COUPLED WITH THE ANTENNAS ARCHITECTURE )F THE ANTENNA IS ACTIVE THEN THE TRANSMITTER AS WELL AS THE FRONT END OF THE RECEIVER IS DISTRIBUTED OVER THE ARRAY )N THIS CASE SEVERAL HUNDRED 42 ELE MENTS OF A FEW WATTS PEAK POWER EACH ADD UP TO MANY HUNDREDS OF PEAK RADIATED POWER 0HASE CONTROL OF THE ELEMENTS IS A CRITICAL PARAMETER USUALLY REQUIRING ADAPTIVE TEMPERA TURE COMPENSATION TO ASSURE COHERENCY OF THE RADIATED WAVEFRONT 4HE ALTERNATIVE IS ALMOST ALWAYS LIMITED TO TRAVELING WAVE TUBE AMPLIFIERS 474!S ALTHOUGH RECENT DEVELOPMENTS IN HIGH POWER SOLID STATE DEVICES IS INFLUENCING 3"2 3!2 DESIGN 2ADARS BUILT AROUND 474!S HAVE ESTABLISHED IMPRESSIVE LONGEVITY RECORDS WITNESS 2!$!23!4 AND %23 BOTH OF WHICH REMAINED IN OPERATION FOR MORE THAN TEN YEARS
£n°Óä
2!$!2 (!.$"//+
$ATA 2ATE $ATA RATE IS PROPORTIONAL TO THE PRODUCT OF PULSE REPETITION FREQUENCY F0 THE NUMBER OF RANGE SAMPLES .2 WHICH IS PROPORTIONAL TO SLANT RANGE SWATH PLUS THE UNCOMPRESSED PULSE LENGTH AND INVERSELY PROPORTIONAL TO RANGE RESOLUTION THE NUMBER OF QUANTIZATION BITS .3 RETAINED IN EACH SAMPLE OF THE DATA AND A FACTOR OF THAT ACCOUNTS FOR THE IN PHASE ) AND QUADRATURE 1 COMPONENTS SINCE BOTH THE AMPLITUDE AND THE PHASE OF THE SIGNAL STREAM ARE REQUIRED /NCE RESOLUTION AND SWATH ARE ESTAB LISHED THE NUMBER OF BITS PER SAMPLE IS THE ONLY PARAMETER OPEN TO CHOICE %XCELLENT RESULTS MAY BE OBTAINED FOR .3 AS SMALL AS BITS PER ) AND PER 1 BY ADAPTING THE QUANTIZATION THRESHOLDS TO THE MEAN SIGNAL LEVEL 2EFER TO 3ECTION FOR MORE ON THIS TOPIC 1UANTIZATION NOISE WHICH IS LARGER FOR FEWER BITS IS PROPORTIONAL TO SIGNAL STRENGTH HENCE IT IS A FACTOR IN THE -.2 BUDGET %XACTING APPLICATIONS SUCH AS INTERFER OMETRY ARE BETTER SERVED BY MORE BITS PER SAMPLE SUBJECT TO THE RATE AND VOLUME LIMITS OF THE DATA HANDLING SUBSYSTEMS 0ROCESSING !LTHOUGH SIMILAR IN PRINCIPLE TO AIRBORNE SYSTEMS PROCESSING FOR SPACE BASED 3!2S DIFFERS IN SEVERAL KEY REGARDS 4HE HIGHLIGHTS ARE REVIEWED HERE &OR MORE COMPLETE COVERAGE SEE THE STANDARD REFERENCES ! SIMPLIFIED INTRODUC TION TO THE KEY PARAMETERS MAY BE HELPFUL 4HE NATURAL STARTING POINT IS THE RANGE EQUATION FROM WHICH SEVERAL PROPERTIES EMERGE THAT ARE UNIQUE TO THE SPHERICAL GEOMETRY OF RADARS IN ORBIT )N THE NARROW BEAM SIDE LOOKING CASE AND NEGLECTING THE EFFECTS OF %ARTH ROTATION THE RADAR TO TARGET RANGE VARIATION GENERATES A PHASE TIME HISTORY OVER A SYNTHETIC APERTURE LENGTH OF 4 SECONDS FROM A POINT REFLECTOR AT MINIMUM SLANT RANGE 2
1T
P ¤ T ³ 2 6 6 3# "EAM L ¥¦ 2 ´µ
WHERE 6"EAM IS THE VELOCITY ON THE SURFACE OF THE ILLUMINATING FOOTPRINT OF THE AZIMUTH ANTENNA PATTERN 4HE TIME DERIVATIVE OF THE PHASE YIELDS THE SCATTERERS DOPPLER HISTORY
F$ T
63#6"EAM T L 2
IN WHICH THE &- RATE IS PROPORTIONAL TO THE EFFECTIVE VELOCITY 6%FF 63# 6"EAM 4HIS IS IN CONTRAST TO THE AIRBORNE CASE FOR WHICH THE &- RATE OF THE AZIMUTH DOPPLER MODULATION IS PROPORTIONAL TO THE SQUARE OF THE AIRCRAFT VELOCITY 7HY THE DIFFERENCE 2ATHER THAN A STRAIGHT LINE WHICH IS THE BASELINE SITUATION FOR AN AIRBORNE SYSTEM THE SYNTHETIC APERTURE OF A SPACE BORNE 3!2 IS FORMED ALONG AN ARC 4HIS IMPOSES A SMALL BUT SIGNIFICANT INCREASE IN THE EFFECTIVE LENGTH OF THE SYNTHETIC APERTURE AND ALSO MODI FIES THE &- RATE !S A CONSEQUENCE THE NOMINAL SINGLE LOOK AZIMUTH RESOLUTION FROM A SPACE BASED 3!2 IS R!Z 6"EAM 63# $!Z RATHER THAN THE FAMOUS hONE HALF OF THE APERTURE LENGTHv OF AIRBORNE 3!2S .OTE THAT 6"EAM IS ALWAYS SMALLER THAN THE SPACE CRAFT VELOCITY AND DECREASES WITH INCREASING SPACECRAFT ALTITUDE AND INCIDENT ANGLE !LERT )N CERTAIN 3!2 PROCESSING LITERATURE THE EFFECTIVE VELOCITY FOR THE ORBITAL CASE IS DENOTED hRADAR VELOCITY v A RATHER MISLEADING AND INAPPROPRIATE TERM 4HE AVERAGE DATA RATE FROM SPACE BASED 3!2S IN %ARTH ORBIT IS ON THE ORDER OF -BS MEGABITS PER SECOND WITH HIGHER RESOLUTION AND POLARIZATION DIVERSITY SYS TEMS GENERATING SEVERAL TIMES THAT 4HE DRIVERS ARE THE SPACECRAFT VELOCITY ^ KMS RANGE RESOLUTION AND SWATH WIDTH -ANY USERS WOULD LIKE TO HAVE IMMEDIATE ACCESS TO PROCESSED DATA WHICH LEADS TO THE QUESTION OF ONBOARD PROCESSING 3PACE BASED
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
£n°Ó£
3!2 SYSTEMS AS A RULE DO NOT IMPLEMENT IMAGE FORMATION ONBOARD FOR SEVERAL REASONS INCLUDING HIGH DATA RATES 0ROCESSING FROM RAW 3!2 DATA TO IMAGERY INCREASES DATA VOLUME SUBSTANTIALLY THUS INCREASING THE DOWNLINK DATA TRANSFER BURDEN 0ERHAPS MORE PERSUASIVE ONCE PROCESSED INTO DETECTED IMAGES THE OPTIONS ARE LIMITED FOR SPECIAL IZED APPLICATION SPECIFIC POST PROCESSING )N CONTRAST TO AIRBORNE SYSTEMS THE DYNAMICS OF MOST SPACECRAFT ARE SUCH THAT NO MOTION COMPENSATION IS REQUIRED FOR SPACE BASED 3!2S UNLESS EXTREMELY FINE RESOLU TION IS TO BE GENERATED (OWEVER DETERMINING THE DOPPLER CENTROID OF THE AZIMUTH SPECTRUM WITH RESPECT TO ZERO DOPPLER EMERGES AS A DOMINANT ISSUE )F THE AZIMUTH ANTENNA BORESIGHT IS PERFECTLY ORTHOGONAL TO THE INERTIAL ORBIT PLANE THE %ARTHS ROTA TION IMPOSES A DOPPLER SHIFT ONTO THE RECEIVED DATA &ROM LOW %ARTH ORBIT ,%/ THE MAGNITUDE OF THIS SHIFT IS ON THE ORDER OF n AND TO FIRST ORDER VARIES SINUSOIDALLY WITH LATITUDE WITH MAXIMUM MAGNITUDE AT THE EQUATOR AND WITH ZERO AT THE EXTREME . AND 3 LATITUDES 4HE EFFECT CAN BE OFFSET BY YAW STEERING THE SPACECRAFT SO THAT THE ANTENNAS BORESIGHT IS ALWAYS DIRECTED TOWARD ZERO DOPPLER 4HIS ORIENTS THE VERTICAL PLANE OF THE AZIMUTH BORESIGHT TO BE ORTHOGONAL TO THE NADIR TRACK ON THE SURFACE RATHER THAN TO THE ORBIT PLANE 7HEREAS 3!2 DATA FROM BOTH ARRANGEMENTS CAN BE PROCESSED INTO SATISFACTORY IMAGERY MORE DEMANDING APPLICATIONS SUCH AS RADAR INTERFEROMETRY ARE BETTER SERVED BY YAW STEERED SYSTEMS 9AW STEERING IMPOSES NEGLIGIBLE ADDITIONAL DEMANDS ON THE SPACECRAFT ATTITUDE CONTROL SYSTEM SINCE IT REQUIRES MANEUVERS OF ONLY on OVER EACH ORBITAL PERIOD .OTE THAT A 3!2 LOOKS DOWN AS WELL AS TO THE SIDE SO THAT VERTICAL VELOCITY COMPONENTS IN THE SATELLITES ORBIT ALSO LEAD TO DOPPLER SHIFTS IN THE DATA )N PRINCIPLE A DOPPLER SHIFT FROM A VERTICAL VELOCITY COMPONENT ALSO COULD BE OFFSET BY ATTITUDE ADJUSTMENTS OF THE SPACECRAFT ALTHOUGH THIS STRATEGY IS NOT IN GENERAL PRACTICE $OPPLER CENTROID ESTIMATION IS A CENTRAL FUNCTION IMPLEMENTED IN ALL PROCESS ING ALGORITHMS FOR 3"2 3!2 DATA $ATA 0RODUCTS 4HE NOTIONAL DATA PRODUCT FROM A SPACE BASED 3!2 IS IMAG ERY USUALLY VISUALIZED AS A BLACK AND WHITE MAPPING OF THE SCENE ILLUMINATED BY THE RADAR "Y DEFINITION THE DIGITAL NUMBERS AT EACH PIXEL IN SUCH AN IMAGE ARRAY ARE REAL AND NON NEGATIVE )N THEORY THESE NUMBERS CORRESPOND TO THE MAGNITUDE SQUARED OF THE FOCUSED AND DETECTED BACKSCATTERED FIELD )N PRACTICE MOST IMAGE PRODUCTS SUCH AS THOSE FROM THE %UROPEAN 3PACE !GENCYS 3!2S USE MAGNITUDE BECAUSE THE RESULTING IMAGERY HAS AN ACCEPTABLE APPEARANCE AND THE SIZE OF THE DATA FILE IS SMALLER THAN IF IN \MAGNITUDE\ )F SEVERAL DATA SETS OVER THE SAME SCENE ARE COMBINED OFTEN THESE ARE INDIVIDUALLY COLOR CODED LEADING TO MULTICOLOR IMAGE PRODUCTS %ACH CONSTITUENT DATA SET MIGHT BE FROM A DIFFERENT POLARIZATION WAVE LENGTH OR OBSERVATION TIME )T IS COMMON PARLANCE TO REFER TO IMAGERY AS MAPPINGS OF THE NORMALIZED BACKSCAT TER POWER R X Y !LERT )N FACT THIS IS SELDOM IF EVER TRUE "ACKSCATTERED POWER IS PROPORTIONAL TO \MAGNITUDE\ NOT MAGNITUDE (ENCE THE USER MUST ASSURE THAT THE DATA ARE INDEED MAGNITUDE SQUARED BEFORE APPLYING TOOLS SUCH AS SPECKLE FILTERS THAT ARE DESIGNED FOR R DIMENSIONALITY 3ECOND R IMPLIES THAT THE DATA ARE CALIBRATED NOT ONLY WITH RESPECT TO THE RADIOMETRIC PARAMETERS OF THE RADAR AND PROCESSOR BUT ALSO WITH RESPECT TO THE LOCAL INCIDENT ANGLE AT THE PIXEL LOCATION X Y !LTHOUGH DATA FROM %23 ARE CORRECTED TO ACCOUNT FOR THE MEAN INCIDENCE WITHIN THE IMAGED SWATH THERE IS NO ATTEMPT TO CORRECT FOR SLOPES LOCALLY WITHIN THE SWATH TO THE PIXEL LEVEL !N ALTERNATIVE IS TO DENOTE THE MAGNITUDE SQUARED DIGITAL NUMBERS AS A WHICH INDICATES SIMPLY RADAR POWER PER PIXEL 4HIS HAS BECOME STANDARD PRACTICE WITH 2!$!23!4 DATA FOR EXAMPLE
£n°ÓÓ
2!$!2 (!.$"//+
3TANDARD IMAGE PRODUCTS USUALLY ARE hMULTI LOOKv )N JARGON COMMON IN THE SPACE BASED 3!2 FIELD hLOOKSv REFER TO STATISTICALLY INDEPENDENT VERSIONS OF THE SAME SCENE 7HEN THESE ARE ADDED TOGETHER THE NET RESULT IS TO REDUCE THE SPECKLE NOISE WHILE REINFORCING THE IMAGED FEATURES %ACH SUCH LOOK IS FORMED FROM A SPECTRAL BAND THAT DOES NOT OVERLAP SPECTRA CORRESPONDING TO THE OTHER LOOKS 4HUS FOR A GIVEN BAND WIDTH INCREASING THE NUMBER OF LOOKS REDUCES SPECKLE BUT AT THE COST OF COMPROMISING RESOLUTION -ORE ON THIS TRADE OFF MAY BE FOUND IN 3ECTION )N CONTRAST TO CONVENTIONAL POST DETECTION IMAGERY FOCUSED 3!2 DATA MAY BE PRE SENTED AS SINGLE LOOK COMPLEX 3,# PRODUCTS 4HESE DATA RETAIN THE FULL RESOLUTION OF THE RADAR AND MOST IMPORTANT RETAIN THE RELATIVE PHASE OF THE BACKSCATTERED FIELD "Y DEFINITION 3,# FILES ARE IN AMPLITUDE AND PHASE OFTEN REPRESENTED AS AN ARRAY OF IN PHASE ) AND QUADRATURE 1 SIGNED NUMBER PAIRS AT EACH PIXEL 3,# DATA ARE REQUIRED FOR 3!2 INTERFEROMETRY POLARIMETRY AND COHERENT CHANGE DETECTION 0USHING !MBIGUITY ,IMITS 4HE BASELINE SINGLE LOOK 3!2 AZIMUTH RESOLUTION IS PROPORTIONAL TO ONE OVER THE DOPPLER BANDWIDTH GENERATED BY THE AZIMUTH BEAM WIDTH OF THE SIDE LOOKING ANTENNA 4HE CORRESPONDING LENGTH OF THE SYNTHETIC APERTURE IS EQUIVALENT TO THE ALONG TRACK SPREAD OF THE ANTENNA PATTERN WHICH OF COURSE IS PROPORTIONAL TO RANGE ,ET THIS BE THE CANONICAL CASE !ZIMUTH RESOLUTION MAY BE SHARPENED ONLY BY INCREASING DOPPLER BANDWIDTH WHICH CAN BE DONE IN ONE OF TWO WAYS INCREASING THE ANTENNAS BEAMWIDTH OR INCREASING THE SPREAD OF ASPECT ANGLES WITHIN WHICH THE ANTENNA ILLUMINATES A GIVEN PORTION OF THE SCENE 4HE LATTER IS THE BASIS FOR 3POTLIGHT 3!2 o IN WHICH THE ANTENNA IS STEERED TO DWELL ON THE INTENDED AREA AS THE RADAR PASSES THUS CREATING A WIDER TOTAL DOPPLER BANDWIDTH AND A LONGER SYN THETIC APERTURE 4HE TRADE OFF IS THAT ADJACENT AREAS ALONG TRACK MAY NOT BE IMAGED AT ALL )NCREASING AZIMUTH RESOLUTION BY BROADENING THE ANTENNA PATTERN EITHER BY REDUCING THE APERTURE LENGTH OR SPOILING THE BEAM HAS THE DISADVANTAGE OF REDUCING THE ANTENNAS GAIN WHICH USUALLY IS NOT DESIRABLE FOR SPACE BASED 3!2S )N ADDITION THE 02& MUST BE LARGER THAN THE INSTANTANEOUS DOPPLER BANDWIDTH THUS REDUCING THE ALLOWABLE UNAMBIGUOUS RANGE SWATH 'OING THE OTHER DIRECTIONSMALLER DOPPLER BANDWIDTHLEADS TO MORE COARSE AZI MUTH RESOLUTION 4HE DOPPLER BANDWIDTH OF THE ORIGINAL SIGNAL HISTORY FROM A GIVEN BACKSCATTERER MAY BE REDUCED BY THE SIMPLE EXPEDIENT OF GENERATING A SHORTER SYN THETIC APERTURE THAN THE CANONICAL CASE 4HIS LOGIC LEADS TO THE hBURST MODE v WHICH FIGURES PROMINENTLY IN TWO FORMS IN SPACE BASED 3!2S "URST MODE ALONG A SINGLE IMAGED SWATH IMPLIES A REDUCED DATA RATE WHICH MAY BE NECESSARY TO MEET THE STRIN GENT DATA RATE REQUIREMENTS CONFRONTING PLANETARY OR LUNAR MISSIONS !LTERNATIVELY THE INTERVALS BETWEEN BURSTS MAY BE USED TO ILLUMINATE SEVERAL DIFFERENT RANGE SWATHS THUS EXPANDING THE AREA THAT MAY BE IMAGED UNAMBIGUOUSLY 4HIS IS THE PRINCIPLE BEHIND THE 3CAN3!2 MODE !MBIGUITY 3PACE 4RADE OFFS )T IS EASY TO SHOW THAT THESE RESOLUTION AND COVERAGE OPTIONS ARE CONSISTENT WITH THE PRINCIPLES THAT GOVERN RANGE AND AZIMUTH AMBIGUITIES 4HE FUNDAMENTAL RULE IS THAT THE IMAGE SPACE ILLUMINATED BY THE ANTENNA MUST BE hUNDERSPREADv IF AMBIGUITIES ARE TO BE AVOIDED 4HE UNDERSPREAD CONDITION IS THAT o !LTERNATIVELY KNOWN AS 3POT3!2
42 "$OP
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
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WHERE 42 IS THE SLANT RANGE SWATH DEPTH OF THE ANTENNA PATTERN AND "$OP IS THE COR RESPONDING DOPPLER BANDWIDTH 4O FIRST ORDER THE AZIMUTH RESOLUTION IS GIVEN BY
R!Z
A 2. , 3 !Z "$OP
WHERE A IS THE AZIMUTH BEAMWIDTH 2 IS SLANT RANGE ., IS THE NUMBER OF LOOKS HERE ASSUMED TO BE TAKEN IN THE AZIMUTH DOMAIN AND 4!Z "$OP IS THE AZIMUTH TIME BANDWIDTH PRODUCT COMPRISED OF THE ILLUMINATION TIME OF THE TARGET AND ITS DOPPLER BANDWIDTH 3UBSTITUTING FOR DOPPLER BANDWIDTH IN THE UNDERSPREAD CONDITION LEADS TO THE CONSTRAINT
42 A 2. , 3 !Z R!Z
WHICH SHOWS HOW RESOLUTION AND TARGET ILLUMINATION TIME MAY BE TRADED AGAINST EACH OTHER WHILE STILL RESPECTING THE FUNDAMENTAL AMBIGUITY CONSTRAINT 4HE FOLLOWING FOUR CASES ARE IMPORTANT IN PRACTICE 3TRIP -AP 4HE STANDARD APPROACH IS STRIP MAPPING IN WHICH THE AMBIGUITY FREE SPACE IS NEARLY FILLED WITH THE ALLOWABLE SWATH RESOLUTION AND NUMBER OF LOOKS /F COURSE AZIMUTH RESOLUTION CAN BE INCREASED WITHIN THE ALLOWED SPACE AT NO LOSS OF SWATH WIDTH IF THE NUMBER OF LOOKS IS DECREASED IN PROPORTION 3POT3!2 )F AZIMUTH RESOLUTION IS THE DRIVING OBJECTIVE THEN R!Z MAY BE REDUCED AS LONG AS THE INTEGRATION TIME 4!Z IS INCREASED IN PROPORTION 'IVEN THAT THE BEAMWIDTH OF THE ANTENNA IS FIXED THE INTEGRATION TIME CAN BE INCREASED ONLY IF THE BEAM IS POINTED TO MAINTAIN ILLUMINATION OF THE DESIRED TARGET MUCH AS A SPOTLIGHT FROM A MOVING VEHICLE DWELLS ON AN AREA OF INTEREST 4HE USUAL CONSEQUENCE OF FINE RESOLUTION IN 3POT3!2 MODE IS SMALLER RANGE SWATH AND AN AZIMUTH SIZE THAT IS LIMITED ABOVE BY THE WIDTH OF THE ANTENNAS FOOTPRINT 4HE REQUIRED STEERING RATE IS RELATIVELY SLOW TYPICALLY A FEW DEGREES OVER A FEW SECONDS IMPLEMENTED EITHER BY MOVING THE ANTENNA BEAM OR BY YAW STEERING THE SPACECRAFT .OTE THAT THE RADARS 02& NEEDS TO BE ONLY ABOVE THE .YQUIST LIMIT SET BY THE ANTENNA BEAMWIDTH NOT BY THE TOTAL SPAN OF DOPPLER FREQUENCIES COLLECTED 2ANGE RESOLUTION IS IMPROVED IN THE USUAL WAY BY INCREASING THE RADARS BANDWIDTH FOR WHICH THE 3TRETCH TECHNIQUE IS OFTEN HELPFUL ! VARIATION OF THIS MODE 3LIP3!2 IS TO DRAG THE ANTENNA FOOTPRINT RATHER THAN TO STARE AT ONE AREA THUS TRADING POORER AZIMUTH RESOLUTION THAN A PURE 3POT3!2 WOULD DELIVER TO GAIN INCREASED AZIMUTHAL COVERAGE (OW FAR CAN THIS BE PUSHED 5NDER THE ASSUMPTION THAT A TARGETS SCATTERING IS COHERENT OVER A FULL n SECTOR IT CAN BE SHOWN THAT THE ULTIMATE AZIMUTH RESOLU TION IS K "Y THE WAY SUCH PHENOMENAL RESULTS HAVE BEEN APPROACHED IN THE FIELD OF SEISMOLOGY "URST -ODE )F AVERAGE DATA RATE IS THE DRIVING CONSIDERATION THEN THE INTEGRA TION TIME 4!Z MAY BE REDUCED BELOW THE CANONICAL LIMIT SET BY THE AZIMUTH ANTENNA BEAMWIDTH 4HIS IS ACCOMPLISHED BY TURNING OFF THE TRANSMITTER AFTER ENOUGH PULSES HAVE BEEN COLLECTED TO SATISFY THE AZIMUTH RESOLUTION REQUIREMENT %ACH SUCH BURST HAS AN INSTANTANEOUS DOPPLER CORRESPONDING TO THE ANTENNA BEAMWIDTH WHICH DETERMINES THE .YQUIST 02& LIMIT BUT A SHORTER SYNTHETIC APERTURE LENGTH "URST MODE IS STANDARD
£n°Ó{
2!$!2 (!.$"//+
OPERATING PROCEDURE FOR PLANETARY OR LUNAR RADARS FOR WHICH HIGH IMAGE RESOLUTION IS NOT REQUIRED AND THE SPACECRAFT TO %ARTH DATA LINK IS SEVERELY LIMITED 7HILE IN BURST MODE IT IS CUSTOMARY TO USE EACH BURST AS A SINGLE LOOK DATA TAKE SETTING THE BURST REP ETITION FREQUENCY SO THAT THE DESIRED NUMBER OF LOOKS IS COLLECTED DURING THE SYNTHETIC APERTURE LENGTH OF THE AZIMUTH BEAM PATTERN 4HE CHALLENGE IS TO CALIBRATE THE ANTENNA PATTERN SUCH THAT THE FRAMELETS FROM ALL BURSTS MAY BE COMBINED TO ASSEMBLE A CONTINU OUS IMAGE ALONG TRACK -ISMATCHES APPEAR AS hSCALLOPINGvSYSTEMATIC BRIGHTNESS MODULATIONS AT BOUNDARIES BETWEEN EACH OF THE FRAMELETS 3CAN3!2n )F SWATH WIDTH IS THE DRIVING REQUIREMENT THEN AZIMUTH RESOLUTION CAN BE TRADED FOR RANGE COVERAGE 4HE TRICK IS TO MULTIPLEX SEVERAL BURST MODE DATA SETS WHERE EACH SET OF BURSTS CORRESPONDS TO A DIFFERENT RANGE SUB SWATH )N THIS FORM OF BURST MODE THE TRANSMITTER IS ALWAYS hONv THE BURST RANGE SUB SWATH ALLOCATION BURDEN FALLS ONTO THE ANTENNA 3CAN3!2 REQUIRES RAPID ELEVATION BEAM STEERING SUCH AS THROUGH A PHASED ARRAY EG 4ERRA3!2 8 OR SELECTION OF ONE AMONG SEVERAL RANGE OFFSET FEEDS FACING A REFLECTOR EG (* # )N ADDITION TO SUPPRESSING SCALLOPING GOOD 3CAN3!2 IMAGERY REQUIRES THAT THE SEVERAL RANGE SUB SWATHS BE KNITTED TOGETHER SUCH THAT THE CROSSOVERS BETWEEN ANTENNA PATTERNS ARE NOT EVIDENT 2!$!23!4 WAS THE FIRST MISSION TO IMPLEMENT THEN TO PERFECT OPERATIONAL 3CAN3!2 WHICH HAS BEEN ADOPTED AS A STANDARD MODE ON MANY SPACE BASED 3!2S 3WATH WIDTHS ACHIEVED ARE AS MUCH AS FIVE TIMES THE NOMINAL STRIP MAP WIDTH WHICH IS CONSIDERABLY LARGER THAN THE CONVENTIONAL AMBIGUITY CONSTRAINT WOULD ALLOW .ORMALLY THE TRADE OFF IN AZIMUTH RESOLUTION IS BALANCED WITH A CORRESPONDING COMPROMISE IN RANGE RESOLUTION LEAVING EXCESS RANGE BANDWIDTH THAT MAY BE CONVERTED INTO LOOKS 3TARTING FROM A KM SWATH M r M LOOK SYSTEM A REASONABLE 3CAN3!2 MODE COULD BE KM SWATH M r M r LOOKS WITH NO INCREASE IN AVERAGE DATA RATE OR TRANSMITTED POWER .OTE THAT ALL OF THESE AMBIGUITY SPACE TRADES START WITH THE CANONICAL CASE 4HE TRADE OFFS ARE RELATIVE TO THAT STARTING POSITION ! RADAR HAVING AN INHERENTLY SMALL RANGE SWATH FOR EXAMPLE WOULD REQUIRE 3CAN3!2 TO EXPAND THE RANGE SWATH TO A FEW TENS OF KM WHICH MAY STILL BE MUCH LARGER THAN THE SAME RADAR COULD COVER WITHOUT AMBIGUITIES IN A STRIP MAP MODE -ULTIPLE #HANNELS )NTERFEROMETRY AND 0OLARIZATION 0HASE COMPARISON BETWEEN TWO OR MORE MUTUALLY COHERENT DATA SETS LEADS TO RICH NEW POSSIBILITIES ESPE CIALLY INCLUDING INTERFEROMETRY AND POLARIMETRY 4HIS IS PARTICULARLY RELEVANT TO SPACE BASED 3!2S WHICH HAVE BEEN AND WILL CONTINUE TO BE RICH SOURCES OF QUANTITA TIVE MICROWAVE MEASUREMENTS OF A WIDE VARIETY OF SURFACE FEATURES ENABLED BY THESE MULTICHANNEL CAPABILITIES 4HE FOLLOWING PARAGRAPHS PROVIDE ONLY A GLIMPSE INTO THESE TOPICS THE DISCUSSION IS MEANT TO WHET THE APPETITE OF THE READER AND TO PROVIDE LEADS TO THE VOLUMINOUS LITERATURE )NTERFEROMETRY )NTERFEROMETRY BY RADAR &IGURE IMPLIES MEASUREMENTS THAT ARE BASED ON PHASE DIFFERENCES SENSED THROUGH TWO DIFFERENT OBSERVATIONS OF THE SAME PHENOMENAn 0HASE DIFFERENCES ARISE FROM MICROWAVE SCALE CHANGES THAT ARE DUE EITHER TO DIFFERENTIAL VIEWING ASPECT OR TO ELEMENTS OF MOTION IN THE SCENE )N GENERAL TERMS THE SENSITIVITY OF PHASE MEASUREMENTS DEPENDS TO FIRST ORDER ON THE RADARS WAVELENGTH THE SPATIAL OR TEMPORAL BASELINE OF THE CONTRIBUTING DATA SETS AND THE SCALE OF SPATIAL OR TEMPORAL DIFFERENTIAL SIGNALS 4HE INTERFEROMETRIC BASELINE INCREASES WITH RANGE AND WITH PLATFORM VELOCITY )T FOLLOWS THAT FOR SPACE BASED RADARS
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
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&)'52% 2ADAR INTERFEROMETRY EXPRESSES THE INTERFERENCE CREATED BETWEEN TWO MUTUALLY COHERENT BACKSCATTERED FIELDS 4HE PHASE DIFFERENCE INTERFEROGRAM MODULO O CORRESPONDS TO THE RELATIVE ELEVATION OF THE ILLUMINATED TERRAIN AFTER REMOVAL OF THE SYSTEMATIC SLANT RANGE AND %ARTH CURVATURE SIGNATURES
CONVENTIONAL INTERFEROMETRIC 3!2 MEASUREMENTS FROM ONE SPACECRAFT PLATFORM USUALLY ARE NOT PRACTICAL SINCE THE IMPLIED SPATIAL OR TEMPORAL SEPARATIONS OF THE MEASUREMENTS ARE MUCH LARGER THAN ONE SATELLITE COULD SUPPORT !N ALERT READER MAY NOTE THE OBVIOUS EXCEPTION TO THIS RULE 324- DESCRIBED PREVIOUSLY WHICH MOUNTED ITS SECOND INTER FEROMETRIC ANTENNA ON A M EXTENDABLE STRUT 3ATELLITE ORBITS TEND TO BE WELL KNOWN AND FOLLOW VERY SIMILAR TRAJECTORIES OVER SUBSEQUENT REPEAT PERIODS )T FOLLOWS THAT THE SPACE BASED ENVIRONMENT OFFERS AN ATTRACTIVE ALTERNATIVE REPEAT PASS INTERFEROMETRY ORIGINALLY SUGGESTED BY 'OLDSTEIN )F THE PASS TO PASS OBSERVATIONS ARE SEPARATED IN THE VERTICAL PLANE THEN INTERFEROM ETRY LEADS TO RELATIVE TERRAIN HEIGHT ESTIMATION )F TWO OBSERVATIONS HAVE A TIME DELAY CORRESPONDING TO THE REPEAT PERIOD OF THE ORBIT TYPICALLY TO DAYS THEN SUB WAVELENGTH MOVEMENTS IN THE LINE OF SIGHT DIRECTION OF THE RADAR MAY BE MEA SURED 4HE TECHNIQUE CAN BE EXTENDED TO MULTIPLE PASSES WITH PROPORTIONATE INCREASE IN THE TEMPORAL BASELINE LEADING TO QUITE REMARKABLE RESULTS 2EPEAT PASS TECHNIQUES ARE WELL SUITED TO MAPPING TOPOGRAPHIC RELIEF AND TO LONG TERM COHERENT CHANGE DETEC TION FOR MAPPING GLACIER MOVEMENT OR TERRESTRIAL SUBSIDENCE )F SHORTER TIME SCALES ARE OF INTEREST TO DETECT MOVING VEHICLES FOR EXAMPLE '-4) THEN A SHORTER INTER FEROMETRIC BASELINE IS REQUIRED WHICH IMPLIES TWO OR MORE 3"2S IN RELATIVELY TIGHT CO ORBITING FORMATION 4HE BASIC 3!2 INTERFEROMETRIC ENVIRONMENT IS ONE IN WHICH THERE IS A PAIR OF MUTUALLY COHERENT IMAGES THAT HAVE EMBEDDED PHASES THAT DEPEND ON THE DETAILS OF VIEWING GEOMETRY AND SCENE STRUCTURE 4HE COHERENTLY COMBINED IMAGES ARE KNOWN AS AN INTERFEROGRAM WHICH TYPICALLY CONTAINS FRINGES THAT EXPRESS THE INTERACTIONS BETWEEN THE PHASE STRUCTURE OF THE TWO DATA SETS 3IGNAL PROCESSING IS DESIGNED TO ESTIMATE THESE PHASE DIFFERENCES AND TO DEDUCE GEOPHYSICAL PARAMETERS OF INTEREST FROM THE RESULTING MEASUREMENT 4HE INTERFEROMETRIC SIGNAL MODEL IS SIMPLE IN CONCEPT &OR ANY NEIGHBORHOOD IN THE SCENE THE INPUT SIGNAL PAIR MAY BE DESCRIBED BY
S T ' A EXP; JJ =
£n°ÓÈ
2!$!2 (!.$"//+
AND
S T ' A EXP; JJ J$J R T T =
WHERE THE SUBSCRIPTS ON THE REFLECTIVITY ' SUGGEST THAT THE TWO SIGNALS MAY BE OBTAINED AT TWO DIFFERENT POINTS IN TIME AS WELL AS FROM TWO DIFFERENT SPATIAL PERSPECTIVES 4HE OBJECTIVE IS TO ESTIMATE THE RELATIVE PHASE DIFFERENCE $I USUALLY FOUND THROUGH THE CROSS CORRELATION
%;S T S T = 2 T T A EXP; J$J R T T =
WHICH IS PRESENTED AS IT WOULD BE CALCULATED USING COMPLEX IMAGE DATA (ERE %;= IS THE EXPECTATION AVERAGING OPERATOR 4HE PHASE DIFFERENCE $I MAY BE DUE EITHER TO GEOMETRIC OR TO TEMPORAL DIFFERENCES BETWEEN THE TWO OBSERVATIONS 3UCCESSFUL INTER FEROMETRY DEPENDS ON THE CROSS CORRELATION 2T T OF THE SCATTERING FUNCTIONS 'T AND 'T 4HE NORMALIZED CROSS CORRELATION FUNCTION IS THE MUTUAL COHERENCE FUNCTION
G T T
2 T T %;\S \ = %;\S \ =
IN PARALLEL TO THAT ENCOUNTERED IN PHYSICAL OPTICS 'AMMA IS A QUANTITATIVE MAPPING OF THE COHERENCE BETWEEN THE TWO OBSERVATIONS )N GENERAL SCENE COHERENCE DECREASES WITH SHORTER WAVELENGTH AND LONGER TIME BETWEEN OBSERVATIONS -UTUAL COHERENCE IS AN ESSENTIAL INGREDIENT FOR RADAR INTERFEROMETRY #OHERENCE IMPLIES TWO CONSTRAINTS SPATIAL AND TEMPORAL 4HE SPATIAL CONSTRAINT APPLIES TO THE SPAC ING BETWEEN THE ORBITAL PASSES )DEALLY THE RADAR WAVELENGTH PROJECTED ONTO EACH AREA OF THE SURFACE MUST BE THE SAME FROM BOTH ORBITS 3INCE THE TWO ORBITS ARE SEPARATED EACH AREA IS OBSERVED AT A SLIGHTLY DIFFERENT INCIDENT ANGLE 4HIS IMPLIES THAT THE EFFEC TIVE WAVELENGTH PROJECTED ONTO THE GROUND PLANE IS SLIGHTLY DIFFERENT FOR THE TWO CASES )NTERFERENCE IS SUPPORTED ONLY IF THE RANGE BANDWIDTH OF THE RADAR SIGNAL IS SUFFICIENT TO SPAN THE PROJECTED WAVELENGTHS WHICH BECOMES MORE DEMANDING AS THE ORBIT SEPARA TION INCREASES &ORTUNATELY THE RANGE PULSE HAS SUFFICIENT BANDWIDTH USUALLY MORE THAN -(Z SO THAT MUTUALLY COHERENT RANGE BANDWIDTHS CAN BE CHOSEN FROM THE DATA AT THE TIME OF PROCESSING ,OSS OF MUTUAL COHERENCE THROUGH INCREASING ORBIT SPACING IS KNOWN AS BASELINE DECORRELATION /NE MAY SHOW FOR REASONABLY LEVEL TERRAIN THAT THE UPPER BOUND CONSTRAINT ON THE DIFFERENCE $P 2AD IN ELEVATION ANGLE BETWEEN THE TWO ORBITS IS $P 2AD L TANP 2AD R2 WHERE R2 IS SLANT RANGE RESOLUTION WHICH IS INVERSELY PROPORTIONAL TO RANGE BANDWIDTH !LERT )N THE 3!2 INTERFEROMETRIC LITERATURE IT IS CUSTOMARY TO USE ELEVATION ANGLE DEFINED AS THE ANGLE BETWEEN THE RADAR LINE OF SIGHT AND THE %ARTH RADIUS VECTOR AS SEEN FROM THE RADAR &OR TYPICAL LARGE TIME BANDWIDTH PRODUCT SIGNALS THE ELEVATION ANGLE CONSTRAINT IMPLIES THAT CORRELATION OF THE PAIR OF RETURN SIGNALS IS MAINTAINED FOR ORBITAL SEPARATIONS ON THE ORDER OF A KILOMETER &OR ABSOLUTE ELEVATION MAPS TO BE DERIVED HOWEVER PRECISE KNOWLEDGE TO THE LEVEL OF ONE METER IS REQUIRED OF THE SPATIAL SEPARATION BETWEEN OBSERVATION TRACKS 4EMPORAL COHERENCE APPLIES PRIMARILY TO THE SCENE )N ORDER FOR THE TWO SIGNALS TO ACT AS AN INTERFEROMETRIC PAIR THEIR RESPECTIVE PHASE STRUCTURES MUST BE RELATIVELY STABLE OVER THE TIME INTERVAL BETWEEN SATELLITE OBSERVATIONS )N SHORT THERE MUST EXIST MUTUAL COHERENCE BETWEEN THE TWO SCATTERING SIGNALS EVEN THOUGH THEY ARE OBSERVED AT DIFFER ENT TIMES 4HIS REQUIREMENT IS READILY SATISFIED FOR SHORT INTEROPPORTUNITY INTERVALS SUCH
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
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AS FROM THE THREE DAY REPEAT ORBIT FIRST USED WITH 3EASAT DATA TO PROVE THE CONCEPT AND FOR STABLE TERRAIN FEATURES SUCH AS UNVEGETATED ROCKY MOUNTAIN SLOPES )T IS NOT NECES SARILY SATISFIED FOR SCENES SUCH AS ICE OR VEGETATION THAT MAY UNDERGO CHANGES IN THE DETAILS OF REFLECTION AND SCATTERING BETWEEN OBSERVATIONS )N CERTAIN NATURAL AND MOST URBAN SCENES THERE WILL BE MANY CORNER REFLECTOR SHAPED FEATURES WHOSE PHASE REMAINS STABLE OVER VERY LONG TIME SCALES 4HESE SO CALLED PER MANENT OR PERSISTENT SCATTERERS SUPPORT DIFFERENTIAL INTERFEROMETRIC MEASUREMENTS THAT MAY SPAN MANY REPEAT VISITS OF THE RADAR LEADING TO REMARKABLE SENSITIVITY TO SLOW MOTION PHENOMENA &OR EXAMPLE MULTIFRAME $)N3!2p ANALYSIS OF 2!$!23!4 DATA HAS LED TO MAPS OF .EW /RLEANS SUBSIDENCE RATES WHICH VARY FROM ^ MMY TO MORE THAN MMY WITH A SENSITIVITY ON THE ORDER OF MMY !NY APPROACH TO PHASE DIFFERENCE MEASUREMENT IS SUBJECT TO THE FUNDAMENTAL O AMBIGUITY CHARACTERISTIC OF PHASE ESTIMATION ALGORITHMS )N MANY RADAR SITUATIONS KNOWLEDGE OF THE PHYSICAL CONSTRAINTS OF THE SITUATION COUPLED WITH PHASE UNWRAPPING ALGORITHMS IS SUFFICIENT FOR THE PURPOSE 0OLARIMETRY &OR ANY GIVEN POLARIZATION OF THE TRANSMITTED WAVE THE REFLECTIVITY PROCESS IN GENERAL WILL GIVE RISE TO A DIVERSITY OF POLARIZATIONS IN THE BACKSCATTERED WAVE 4O OBSERVE THESE THE RADAR MUST BE DUAL POLARIZED 3IMILARLY THE REFLECTIVITY IS A FUNCTION OF THE POLARIZATION OF THE TRANSMITTED WAVE 4HUS IF THE SCATTERING FUNC TION ITSELF IS TO BE FULLY CHARACTERIZED TWO ORTHOGONAL POLARIZATIONS MUST BE TRANSMIT TED AS WELL )NCREASINGLY POLARIMETRIC DIVERSITY IS BEING IMPLEMENTED IN SPACE BASED 3!2S )MPLEMENTATION OF A FULLY POLARIMETRIC RADAR ALWAYS IMPLIES GREATER DATA CHANNEL CAPACITY MORE TRANSMITTED POWER AND LESS RANGE SWATH COVERAGE /F COURSE THE ANTENNATHE RADARS hPOLARIZATION GATEWAYvMUST BE ABLE TO RECEIVE AND POS SIBLY ALSO TO TRANSMIT ON MORE THAN ONE POLARIZATION )N GENERAL TERMS THERE ARE FOUR OPTIONS AVAILABLE FOR POLARIMETRIC DIVERSITY IN A SPACE BASED 3!2 4HESE ARE 3INGLE MONOSTATIC POLARIZATION 4YPICAL OF ALL DEDICATED SPACECRAFT 3!2S UNTIL THE LAUNCH OF %.6)3!4 WITH EITHER (( OR 66 POLARIZATIONS 4HIS CUSTOM ARY NOTATION INDICATES HORIZONTAL OR VERTICAL LINEAR POLARIZATIONS ON BOTH TRANS MISSION AND RECEPTION FOR THESE SINGLE POLARIZED RADARS $UAL POLARIZATION 4HE TRADITIONAL DEFINITION IS TRANSMISSION ON ONE POLARIZATION USUALLY LINEAR SUCH AS ( AND RECEPTION ON THE LIKE POLARIZED AND THE CROSS POLARIZED COMPONENTS SUCH AS ( AND 6 )N A TRADITIONAL DUAL POLARIZED RADAR THE RELATIVE PHASE BETWEEN THE TWO POLARIZED DATA SETS IS DISCARDED )N %ARTH ORIENTED REMOTE SENSING RADARS TYPICAL COMBINATIONS INCLUDE (( AND (6 FOR EXAMPLE OR (( AND 66 WHICH REQUIRES TWO SEPARATE TRANSMIT POLARIZATIONS 4HE !3!2 ABOARD %.6)3!4 IS THE FIRST SPACE BASED EXAMPLE OF THIS TYPE OF POLARIZATION DIVERSITY )F THE FOUR LINEAR POLARIZATION POSSIBILITIES ARE EXPLOITED NONCOHER ENTLY THEN THE BACKSCATTERING FUNCTION OF THE SCENE MAY BE CHARACTERIZED BY THE THREE BACKSCATTER COEFFICIENTS R (( R 6( R 66 WHICH OF COURSE ARE DEVOID OF PHASE .OTE THAT RECIPROCITY IMPLIES THAT R (6 R 6( #OHERENT DUAL POLARIZATION ! DUAL POLARIZED RADAR THAT RETAINS THE RELATIVE PHASE BETWEEN THE TWO RECEIVED POLARIZATIONS IS A SIGNIFICANT DEPARTURE FROM TRADITIONAL DUAL POLARIZED SYSTEMS 4HE MODIFIER hCOHERENTv HELPS TO DISTINGUISH p $IFFERENTIAL INTERFEROMETRIC SYNTHETIC APERTURE RADAR
£n°Ón
2!$!2 (!.$"//+
SUCH RADARS FROM THEIR MORE COMMON COUNTERPARTS DESCRIBED IN THE PRECEDING PARAGRAPH #OHERENT DUAL POLARIZATION HAS NOT BEEN EXPLOITED IN ORBITAL 3!2S ALTHOUGH IT IS STANDARD PRACTICE IN %ARTH BASED RADAR ASTRONOMY THROUGH FACILI TIES SUCH AS THE !RECIBO RADAR TELESCOPE %XPERIENCE HAS SHOWN THAT THERE IS RELATIVELY LITTLE ADDED VALUE IN THE PHASE BETWEEN THE LIKE POLARIZED AND CROSS POLARIZED RETURNS UNDER THE CONDITION OF ( OR 6 TRANSMIT POLARIZATION (OWEVER AN INNOVATIVE ALTERNATIVE IS TO TRANSMIT CIRCULAR POLARIZATION AND RECEIVE COHER ENTLY TWO ORTHOGONAL LINEARLY POLARIZED COMPONENTS 3EE 3ECTION FOR FUR THER DISCUSSION &ULL OR QUADRATURE POLARIZATION 4HIS IS THE RICHEST OPTION BECAUSE IT ALLOWS FULL CHARACTERIZATION OF THE COMPLEX MATRIX OF THE BACKSCATTER AT ALL RESOLVED POINTS IN THE SCENE )T HAS BEEN DEVELOPED EXTENSIVELY IN THEORY AND IN PRACTICE WITH DATA FROM AIRBORNE SYSTEMS AND 3)2 # *APANS 0!,3!2 IS THE FIRST OPERATIONAL SPACE BASED SYSTEM TO INCORPORATE A QUAD POL MODE 0RIMARY INTEREST IN FULLY POLARIMETRIC RADARS DERIVES FROM THE ENRICHED SCATTERING OBSERVATION POSSIBILITIES REVEALED THROUGH REPLACEMENT OF THE SCALAR FORM OF REFLECTIV ITY BY ITS COMPLEX VECTOR COUNTERPART 4HUS WHEN EITHER ( OR 6 POLARIZATIONS ARE INCIDENT ON A SCATTERING ELEMENT BOTH POLARIZATIONS ARE BACKSCATTERED ACCORDING TO
§%(" ¶ §3(( ¨% " · ¨3 © 6 ¸ © 6(
3(6 ¶ §%(4 ¶ 366 ·¸ ¨©%64 ·¸
WHERE THE SUPERSCRIPT " DENOTES THE FIELD COMPONENTS REFLECTED BACK TOWARD THE RADAR 4HE NEW TERMS OF INTEREST REPRESENT THE SCENES r SCATTERING MATRIX AN ARRAY OF FOUR COMPLEX NUMBERS %ACH ELEMENT IN THIS BACKSCATTERING MATRIX EXPRESSES THE MAGNI TUDE AND PHASE IMPOSED ONTO THE BACKSCATTERED FIELD SUPERSCRIPT " IN RESPONSE TO THE ILLUMINATION FROM THE TRANSMITTED FIELD SUPERSCRIPT 4 ACCORDING TO THEIR RESPECTIVE POLARIZATIONS 4HUS THE SCATTERING MATRIX IS A QUANTITATIVE DESCRIPTION OF THE TRANSFOR MATION OF POLARIZATION STATE UPON REFLECTION AS WELL AS THE MAGNITUDE AND PHASE OF EACH REFLECTION COEFFICIENT )T IS OFTEN TRUE THAT THE FIELD POLARIZATIONS ARE NOT CHANGED DURING PROPAGATION THE IRROTATIONAL ASSUMPTION )N THIS CASE THE POLARIZATIONS OF THE BACKSCATTERED WAVES ARE EQUIVALENT TO THOSE THAT ARRIVE AT THE RADAR 4HIS PROPERTY CHARACTERIZES MOST OF THE POLARIMETRY LITERATURE AT LEAST IN REMOTE SENSING APPLICATIONS AND IS REFLECTED IN THESE PARAGRAPHS 4HE PRINCIPAL EXCEPTION TO THIS RULE IS &ARADAY ROTATION WHICH MAY BE A SIGNIFICANT FACTOR FOR LONGER WAVELENGTH SYSTEMS SUCH AS 0 BAND AND TO A LESSER EXTENT , BAND &OR IRROTATIONAL PROPAGATION THE PORTION OF THE BACKSCATTERED FIELD CAPTURED BY THE RADAR IS DETERMINED BY THE POLARIZATION VECTOR OF THE RECEIVING ANTENNA ;% 2= 4HE SIG NAL VOLTAGE VREC ENTERING THE SYSTEM MAY BE WRITTEN IN VECTOR MATRIX FORM AS
VREC §©%(2
§% " ¶ %62 ¶¸ ¨ (" · ©%6 ¸
4HIS IS THE STARTING POINT FOR 3!2 QUADRATURE POLARIMETRY %SSENTIALLY A QUAD POL 3!2 IS MANAGED SO THAT THE TRANSMITTER GENERATES BOTH ORTHOGONAL POLARIZATIONS 4HE RESULTING QUAD POL DATA SET CAN BE TRANSFORMED TO REPRESENT ALL POSSIBLE COMBINATIONS OF TRANSMIT ANDOR RECEIVE POLARIZATIONS 0ITFALLS AWAIT THE UNWARY HOWEVER INCLUDING TRICKY COORDINATE CONVENTIONS AN INITIALLY CONFUSING VARIETY OF hSTANDARDv FORMS FOR
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REPRESENTING THE DATA AND SEVERAL ALTERNATIVE METHODS FOR DATA ANALYSIS /NCE MAS TERED HOWEVER QUAD POL 3!2 DATA IS THE UNDOUBTED GOLD STANDARD FOR QUANTITATIVE SCENE CHARACTERIZATION BY AN IMAGING RADAR ! SPACE BASED QUAD POL CAPABILITY IMPLIES A SIGNIFICANT COST 4HE DRIVING REQUIRE MENT IS THAT THE DATA MUST BE MUTUALLY COHERENT 4HAT IS RELATIVELY EASY FOR THE RECEIVER WHICH ONLY NEEDS TO HAVE TWO CHANNELS THAT CAPTURE SIMULTANEOUSLY THE PHASE AND AMPLITUDE OF TWO ORTHOGONAL POLARIZATIONS OF THE BACKSCATTERED FIELD /N THE OTHER HAND ONLY ONE POLARIZATION CAN BE TRANSMITTED AT A TIME )LLUMINATING THE SCENE WITH TWO POLARIZATIONS REQUIRES THE TRANSMITTER TO BE TOGGLED BETWEEN ORTHOGONAL POLARIZA TION STATES 4HIS MULTIPLEXED TRANSMISSION SCHEME IMPLIES THAT THE RADARS 02& MUST BE DOUBLED TO SATISFY THE MINIMUM .YQUIST SAMPLING RATE SIMULTANEOUSLY FOR EACH PAIR OF TRANSMISSIONS $OUBLED 02& IMPLIES THAT THE AVERAGE RADIATED POWER MUST BE DOUBLED AND THE UNAMBIGUOUS RANGE SWATH IS HALVED BOTH IN COMPARISON TO THE STANDARD CASE OF TRANSMITTING ONLY ONE POLARIZATION .OTE THAT THE AVERAGE DATA RATE IS THE SAME AS THE DUAL POLARIZED CASE SINCE TWICE AS MUCH DATA ARE COLLECTED BY A QUAD POL MODE FOR EACH RESOLVED POINT IN THE SCENE BUT THE SWATH WIDTH IS SMALLER BY A FACTOR OF TWO #ONSIDERABLE PROGRESS CONTINUES TO BE MADE IN THE DEVELOPMENT OF TOOLS FOR QUANTI TATIVE ANALYSIS OF POLARIMETRIC 3!2 DATA 7HEN IN COMBINATION WITH INTERFEROMETRIC DATA THE FIELD IS KNOWN AS 0OL)N3!2 FOR WHICH DEDICATED SPECIALIST MEETINGS ARE CONVENED FREQUENTLY !N IMPORTANT METHODOLOGY IS TARGET DECOMPOSITION THROUGH WHICH SPECIFIC BACKSCATTER CLASSES SUCH AS DOUBLE BOUNCE "RAGG OR VOLUME OF A SCENE MAY BE SEPARATED FROM OTHER TYPES THENCE SUBJECTED TO INTERFEROMETRIC ANALYSIS 5SING SUCH TECHNIQUES IT IS POSSIBLE TO ESTIMATE THE TOPOGRAPHY OF THE SURFACE BENEATH A VEGETATED CANOPY FOR EXAMPLE !PPLICATIONS 3!2S ARE THE LARGEST CLASS OF SPACE BASED REMOTE SENSING RADARS PRIMARILY AS A RESULT OF THEIR PRACTICAL UTILITY -ANY APPLICATIONS ARE ENERGIZED BY RADARS NATURAL ABILITY TO OPERATE AT NIGHT OR THROUGH CLOUD FOG SMOKE AND HAZE AND ITS INHERENT SENSITIVITY TO CHANGES WITHIN THE SCENE AT WAVELENGTH SCALES 2ADAR IMAG ERY HAS PROVEN TO BE VALUABLE FOR A WIDE VARIETY OF APPLICATIONS FROM OCEANOGRAPHIC OBSERVATIONS THE THEME THAT MOTIVATED 3EASAT TO MEASUREMENT OF MILLIMETER SCALE DISPLACEMENT SUCH AS THE SUBSIDENCE OF URBAN AREAS OR THE SWELLING OF VOLCANOES PRIOR TO THEIR ERUPTION #ANADAS REQUIREMENT TO MAINTAIN NEAR CONTINUOUS MONITORING OF ITS NORTHERN AND COASTAL ICE IS MET PRIMARILY BY THOUSANDS OF FRAMES OF 2!$!23!4 DATA PER YEAR )NDIA IS THE SECOND LARGEST CONSUMER OF SPACE BASED IMAGING RADAR DATA USED FOR AGRICULTURE AND FOREST MANAGEMENT AND FOR MEASURING CHANGES IN ITS ALPINE GLA CIERS #OUNTRIES SUCH AS "RAZIL GRACED WITH TROPICAL FORESTS RELY ON SPACE BASED RADAR IMAGERY TO MAINTAIN SURVEILLANCE AND TO COMPILE ANNUAL STATISTICS OF DEFORESTATION 3INCE RADAR IMAGERY IS A RELIABLE METHOD OF MAPPING SLICKS ON THE OCEANS SURFACE IT IS THE PRINCIPAL MEANS OF MONITORING OIL SPILLS THAT MAY RESULT FROM A GROUNDED TANKER OR A VESSEL ILLEGALLY PUMPING ITS BILGES IN A COASTAL AREA 4HE IMAGING RADAR REFERENCE CITED EARLIER PROVIDES AN EXCELLENT REVIEW OF MANY OF THESE APPLICATIONS
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MAIN OBJECTIVE OF A SPACE BASED ALTIMETER IS ALSO TO MEASURE THE DISTANCE BETWEEN THE RADAR AND THE SURFACE THE MOST COMMON APPLICATION IS DETERMINATION OF THE LOCAL SEA LEVEL RELATIVE TO THE %ARTHS GEOID e RATHER THAN THE HEIGHT OF THE SPACECRAFT 4HE REFERENCE FOR THIS MEASUREMENTTHE ORBITAL HEIGHT OF THE SPACECRAFTMUST BE KNOWN BY OTHER MEANS TO WITHIN A FEW CENTIMETERS 3EA SURFACE HEIGHT IS A FUNCTION OF MANY GEOPHYSICAL PARAMETERS SUCH AS CURRENT FLOW AN %L .I¶O EVENT AND VARIATIONS IN THE OCEANS DEPTH 2ELATIVELY SMALL CHANGES ON THE ORDER OF CM IN MEAN SEA SURFACE HEIGHT MAY CORRESPOND TO SUBSTANTIAL DIFFERENCES IN THE CORRESPONDING GEOPHYSICAL PARAMETERS )T FOLLOWS THAT RANGE MEASUREMENT ACCURACY AND PRECISION ARE THE DRIVING REQUIREMENTS FOR THIS CLASS OF RADAR 4HE ACCURACY OF AN ALTIMETERS HEIGHT MEASUREMENT DEPENDS TO FIRST ORDER ON KNOWLEDGE OF THE SPACECRAFTS HEIGHT ALONG ITS ORBIT AND ON CORRECTION OF THE PROPAGATION DELAYS SUFFERED BY THE RADARS ROUND TRIP WAVEFORM 4HE PRECISION OF AN OCEAN VIEWING ALTIMETER IS PROPORTIONAL TO THE RADARS RANGE RESOLUTION AND INVERSELY PROPORTIONAL TO THE SQUARE ROOT OF THE NUMBER OF STATISTICALLY INDEPENDENT MEASUREMENTS LOOKS COMBINED FOR EACH DATA POINT /CEAN VIEWING ALTIMETERS IN GENERAL HAVE LARGE 3.2 4HUS BANDWIDTH AND LOOKS BECOME THE DRIVING REQUIREMENTS ON SYSTEM DESIGN 4HE EMPHASIS IN THIS SECTION IS ON ALTIMETER PRECISION 3EA SURFACE HEIGHT MEASUREMENTS HAVE BECOME ESSENTIAL FOR A WIDE VARIETY OF APPLI CATIONS IN OCEANOGRAPHY GEODESY GEOPHYSICS AND CLIMATOLOGY 7ITH THE EXCEPTION OF NEAR POLAR ICE %ARTH ORBITING OCEANOGRAPHIC ALTIMETERS HAVE SEEN RELATIVELY LITTLE APPLICATION OVER NONAQUATIC SURFACES ! SATELLITE BASED ALTIMETER SYSTEMATICALLY CIRCLES THE %ARTH GENERATING SURFACE HEIGHT MEASUREMENTS ALONG ITS NADIR TRACK 4HESE MEASUREMENTS ACCUMULATE PROVID ING UNIQUE SYNOPTIC DATA THAT HAVE REVOLUTIONIZED OUR KNOWLEDGE AND UNDERSTANDING OF BOTH GLOBAL AND LOCAL PHENOMENA FROM %L .I¶O TO BATHYMETRY 3"2 ALTIMETER DATA ALSO PROVIDE MEASUREMENTS OF SIGNIFICANT WAVE HEIGHT AND WIND SPEED !LTHOUGH ONE MIGHT CONSIDER ALTIMETERS TO BE RELATIVELY SIMPLE ONE DIMENSIONAL RANGE MEASURE MENT INSTRUMENTS THEIR PHENOMENAL ACCURACY AND PRECISION REQUIRES ELEGANT MICRO WAVE IMPLEMENTATION AND INNOVATIVE SIGNAL PROCESSING /VERVIEW 4HE SURFACE HEIGHT MEASUREMENT OBJECTIVES OF SPACE BASED ALTIMETERS CAN BE GROUPED INTO FOUR BROAD CATEGORIES LARGE SCALE DYNAMIC SEA SURFACE TOPOGRA PHY DYNAMIC MESOSCALE OCEANIC FEATURES STATIC MESOSCALE SEA SURFACE TOPOGRAPHY AND ICESEA ICE AS WELL AS CONTINENTAL ICE SHEETS %ACH OF THESE MEASUREMENT THEMES IMPLIES NARROWED CONSTRAINTS ON CHOICE OF ORBIT AND ON THE TOP LEVEL INSTRUMENT AND MISSION DESIGN 3ATELLITE ALTIMETERS DEDICATED TO DETERMINING THE OCEANS LARGE SCALE DYNAMIC SURFACE TOPOGRAPHY ARE CHARACTERIZED BY ABSOLUTE SEA SURFACE HEIGHT 33( SEC AVERAGED MEASUREMENT ACCURACY ON THE ORDER OF CENTIMETERS ALONG TRACKS OF MORE THAN KM AND ORBITS THAT RETRACE THEIR SURFACE TRACKS EVERY TO DAYS )N CONTRAST MESOSCALE MISSIONS FOCUS ON SEA SURFACE HEIGHT SIGNALS OF LESS THAN ^ KM IN LENGTH 2ATHER THAN ABSOLUTE 33( ACCURACY THESE SHORTER SCALE APPLICATIONS REQUIRE PRECISION SUFFICIENT TO SUSTAIN SURFACE SLOPE MEASUREMENT ACCURACY ON THE ORDER OF MICRORADIAN ONE MM SEA LEVEL CHANGE OVER A KM DISTANCE &OR GEODETIC SIGNALS THAT ARE EXPRESSED THROUGH STATIC SEA SURFACE TOPOGRAPHIC VARIATIONS ORBITS ARE REQUIRED THAT GENERATE DENSE TRACK TO TRACK SPACING /BSERVATION OF OCEANIC AND e 4HE AVERAGE SEA LEVEL IN THE ABSENCE OF DYNAMIC PERTURBATIONS OF THE SURFACE ELEVATION DUE TO TIDES AND CURRENTS
)N THE FIELD OF OCEANOGRAPHY MESOSCALE FEATURES HAVE SCALES OF SEVERAL HUNDRED KILOMETERS AS OPPOSED TO THE MUCH LARGER BASIN SCALE THE .ORTH !TLANTIC OCEAN FOR EXAMPLE
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POLAR ICE SHEETS REQUIRES THAT THE ALTIMETER HAVE ROBUST RANGE AND SPATIAL RESOLUTION ACCURACY AND PRECISION REGARDLESS OF THE NON ZERO AVERAGE SURFACE SLOPE IN BOTH THE ALONG TRACK AND CROSS TRACK DIRECTION OF THE CONTINENTAL GLACIERS 3UITABLE ORBITS FOR ICE SHEET MISSIONS MUST HAVE NEAR POLAR INCLINATION AND MULTIYEAR RELATIVE ACCURACY OF A FEW CENTIMETERS 7HEREAS THE METHODOLOGY OF THESE INSTRUMENTS IS TO DETERMINE THE DISTANCE BETWEEN THE RADAR AND THE SURFACE LIKE ANY RADAR AN ALTIMETER ACTUALLY MEASURES ROUND TRIP DELAY NOT DISTANCE !T THE ACCURACY REQUIRED OF A SPACE BASED OCEANOGRAPHIC ALTIMETER THE DECEPTIVELY SIMPLE PROPORTIONALITY OF RANGE TO DELAY TIME MUST TAKE INTO ACCOUNT THE SMALL BUT SIGNIFICANT RETARDATION OF THE RADARS MICROWAVES AS THEY PROPAGATE 4HE CM LEVEL 33( ACCURACY REQUIRED OF THESE INSTRUMENTS IS MUCH SMALLER THAN THE RANGING ERRORS INTRODUCED BY DELAYS THROUGH THE IONOSPHERE AND THE ATMOSPHERE 4HE DELAYS IMPOSED BY THE IONOSPHERE ARE A FUNCTION OF FREQUENCY )N PRACTICE THESE CAN BE ESTI MATED AND THEN CORRECTED IF THE ALTIMETER MEASURES ROUND TRIP RANGE AT TWO DIFFERENT FREQUENCIES 4HE DELAYS IMPOSED BY THE ATMOSPHERE ARE COMPRISED OF TWO COMPONENTS THE DRY ATMOSPHERE AND WATER VAPOR 4HE DRY ATMOSPHERE COMPONENT IS WELL KNOWN AND STABLE AT LONG SPATIAL SCALES IN PRACTICE THE RESULTING DELAY IS COMPENSATED BY RECOURSE TO MODEL PREDICTIONS $ELAYS DUE TO WATER VAPOR IN THE ATMOSPHERE ARE VARI ABLE DOWN TO SCALES OF SEVERAL HUNDRED KILOMETERS AND MUCH SMALLER WHEN TRAVERSING A STORM FRONT 3TANDARD PRACTICE IS TO MEASURE THE INTEGRATED WATER VAPOR CONTRIBUTION IN THE VERTICAL COLUMN BELOW THE ALTIMETER BY A MICROWAVE RADIOMETER FOR WHICH TWO OR THREE FREQUENCIES ARE REQUIRED -EASUREMENT ERRORS ARE DOMINATED BY THE ACCURACY OF ORBIT HEIGHT DETERMINATION AND BY THE INTRINSIC PRECISION OF THE INSTRUMENT &IGURE SHOWS A SUMMARY HISTORY OF THESE FACTORS 4HE DATA SHOW THAT CM INSTRUMENT ACCURACY IS THE STATE OF THE ART FOR CONVENTIONAL ALTIMETERS 4HE DELAY DOPPLER INSTRUMENT SEE BELOW WOULD FURTHER IMPROVE INSTRUMENT PRECISION TO CM
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&)'52% (ISTORY OF PRECISION ORBIT DETERMINATION 0/$ AND INTRIN SIC INSTRUMENT PRECISION OF THE LEADING RADAR ALTIMETERS OF THE PAST YEARS 6ERTICAL AXIS IN CM -ODERN 0/$ ACCURACY RELIES ON '03 AND THE &RENCH $/2)3 SYSTEM 0RECISION IS LIMITED BY THE ALTIMETERS DEGREES OF FREEDOM INCOHERENT WAVEFORM AVERAGING AFTER $UDLEY #HELTON /REGON 3TATE 5NIVERSITY PERSONAL COMMUNICATION
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#ENTIMETER SCALE RANGE ACCURACY IS SUPPORTED IN THE OCEANOGRAPHIC APPLICATION BY AVERAGING OVER THE RANGE RESPONSE OF MANY RETURNS 4HE RANGE RESOLUTION OF EACH RETURN WAVEFORM IS TYPICALLY ON THE ORDER OF METERS 4HESE WAVEFORMS ARE ACCU MULATED AND AVERAGED PULSE TO PULSE WHOSE SHAPE CONVERGES ON THE FLAT SURFACE IMPULSE RESPONSE &IGURE 3EA SURFACE HEIGHT 33( IS DERIVED FROM THE TIME DELAY TO THE MIDPOINT OF THE WAVEFORMS LEADING EDGE RISE /NE THOUSAND OR MORE SUCH WAVEFORMS AVERAGED OVER ONE SECOND CORRESPOND TO A MEAN RANGE ESTI MATE WHOSE STANDARD DEVIATION IS ON THE ORDER OF CENTIMETERS WHICH IN PRACTICE DEGRADES WITH INCREASING SIGNIFICANT WAVE HEIGHT /NE SECOND AVERAGES ARE STANDARD FOR OPERATIONAL ALTIMETERS WHICH IMPLIES AN ALONG TRACK RESOLUTION ON THE ORDER OF KILOMETERS DETERMINED PRIMARILY BY SATELLITE VELOCITY !VERAGING IS hTHE NAME OF THE GAMEv IN RADAR ALTIMETRY &OR EXAMPLE GLOBAL DATA SETS FROM INSTRUMENTS SUCH AS 4/0%8 AND *ASON HAVE BEEN ANALYZED TO ESTIMATE THE RATE OF MEAN SEA LEVEL RISE TO AN ACCURACY OF MILLIMETER PER YEAR )N ADDITION TO SEA SURFACE HEIGHT THE SATELLITE RADAR ALTIMETERS WAVEFORM SUPPORTS TWO OTHER OCEANOGRAPHIC MEASUREMENTS SIGNIFICANT WAVE HEIGHT 37( AND SURFACE WIND SPEED 73 /VER A QUASI FLAT SEA A PULSE LIMITED ALTIMETERS IDEALIZED MEAN
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!! &)'52% A 4HE ALTIMETERS PULSE TYPICALLY M LONG AFTER COMPRESSION SEQUENTIALLY ENCOUNTERS OCEANIC SURFACE WAVES OF HEIGHT UP TO M OR MORE B 3EA SURFACE HEIGHT 33( CORRESPONDS TO THE MIDPOINT OF THE WAVEFORMS LEADING EDGE SIGNIFICANT WAVE HEIGHT 37( TO THE SLOPE OF THE LEADING EDGE AND WIND SPEED 73 TO THE INVERSE BACKSCATTERED POWER 4HE WAVEFORMS DEPICTED HERE ARE IDEAL IZED USEFUL hSMOOTHNESSv REQUIRES OR MORE INCOHERENTLY AVER AGED RADAR RETURNS
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WAVEFORM IS A STEP FUNCTION WHOSE RISE TIME IS EQUAL TO THE COMPRESSED PULSE LENGTH AND WHOSE POSITION ON THE TIME DELAY AXIS IS DETERMINED BY THE ALTIMETERS HEIGHT )F THE SEA SURFACE IS MODULATED BY WAVES THE ALTIMETRIC DEPTH OF THE SURFACE INCREASES WHICH REDUCES THE SLOPE OF THE WAVEFORMS LEADING EDGE (ENCE 37( IS PROPORTIONAL TO THE WAVEFORM RISE TIME )F THE SEA SURFACE IS DISTURBED BY THE WIND THE RESULTING FINE SCALE ROUGHNESS DECREASES THE POWER OF THE PULSE REFLECTED BACK TO THE ALTIMETER (ENCE FOR WIND SPEEDS OF MORE THAN ABOUT TWO KNOTS 73 IS INVERSELY RELATED TO MEAN WAVEFORM POWER )N PRACTICE THE INFLECTIONS OF THE IDEALIZED FLAT SURFACE RESPONSE FUNCTION WAVEFORM ARE SOFTENED BY THE PULSE WEIGHTING AND THE WAVEFORM IS ATTENU ATED OVER TIME BY THE WEIGHTING OF THE ANTENNA PATTERN 4O EXTRACT 37( AND 73 FROM WAVEFORM DATA FINELY TUNED ALGORITHMS HAVE BEEN DEVELOPED AND VALIDATED AGAINST IN SITU BUOY MEASUREMENTS &OR EXAMPLE THE 4/0%8 +U BAND ALTIMETER MEASURES 37( TO WITHIN o M UP TO MORE THAN M AND 73 WITHIN o MS UP TO MORE THAN MS 4HESE FIGURES CORRESPOND TO AVERAGES OVER SECOND OR ABOUT KM ALONG THE SUB SATELLITE PATH OF THE ALTIMETERS FOOTPRINT WHICH TYPICALLY IS KMn KM WIDE DETERMINED BY MEAN SEA STATE &LIGHT 3YSTEMS +EY ATTRIBUTES OF SATELLITE RADAR ALTIMETERS ARE SUMMARIZED IN 4ABLE 3INCE OCEANIC HEIGHT MEASUREMENT ACCURACY HAS IMPROVED DUE PRIMARILY TO MORE EFFECTIVE MEANS OF ESTIMATING AND CORRECTING SYSTEMATIC ERRORS 0ERFORMANCE ALSO HAS BENEFITED FROM INNOVATIVE ONBOARD HARDWARE AND ALGORITHMS AND MORE PRECISE DETERMINATION OF THE RADIAL COMPONENT OF THE ORBIT 4HE *ASON ALTIMETER REPRESENTS THE STATE OF THE ART IN ABSOLUTE SEA SURFACE HEIGHT MEASUREMENT ACCURACY AS OF THE YEAR 3 AND '%/3 4HE FIRST SATELLITE RADAR ALTIMETER WAS THE PROOF OF CONCEPT 3 INSTRUMENT THAT FLEW ON THREE 3KYLAB MISSIONS )TS OBJECTIVES WERE TO VERIFY PREDICTED WAVEFORM RESPONSE TO WIND AND WAVES TO MEASURE THE RADAR CROSS SECTION OF THE SEA AT VERTICAL INCIDENCE TO MEASURE INTER PULSE CORRELATION PROPERTIES AND TO OBSERVE THE EFFECT OF OFF NADIR ANTENNA ORIENTATION A SCATTEROMETER EXPERIMENT 'EOS PROVIDED THE FIRST GEODETIC AND GEOPHYSICAL RESULTS OF SIGNIFICANCE WITHIN THE .ATIONAL 'EODETIC 3ATELLITE 0ROGRAM INCLUDING THE FIRST MAPS OF SEA LEVEL VARIABILITY AND THE 4!",% !LTIMETERS
3PACECRAFT #OUNTRY 3KYLAB '%/3 3EASAT 'EOSAT %23 4/0%8 0OSEIDON %23 '&/ *ASON %NVISAT *ASON !LTIKA #RYO3AT 3ENTINEL
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MARINE GEOID 'EOS AND THE 3 ALTIMETERS USED CONVENTIONAL PULSE COMPRESSION TECHNIQUES !S SUGGESTED IN THE TABLE NEITHER OF THESE TWO EARLY ALTIMETERS INCLUDED A WATER VAPOR RADIOMETER AND EACH USED ONLY ONE FREQUENCY SO THAT THEY HAD NO IN BUILT MEANS TO CORRECT FOR IONOSPHERIC OR ATMOSPHERIC PROPAGATION DELAYS 3EASATS !LTIMETER 3EASATS WAS THE FIRST TO USE FULL DERAMPo PULSE COMPRESSION WHICH OPENED THE WAY FOR THE VERY SMALL RANGE RESOLUTION REQUIRED FOR MANY OCEANOGRAPHIC APPLICATIONS 4HE DERAMP TECHNIQUE DESCRIBED BELOW HAS BEEN ADOPTED BY ALL RADAR ALTIM ETERS SINCE THEN 3EASAT WAS DESIGNED TO MEASURE GLOBAL OCEAN DYNAMIC TOPOGRAPHY AS WELL AS WAVE HEIGHT AND SURFACE WIND SPEED 'EOSAT 4HIS ALTIMETERS DESIGN WAS PATTERNED CLOSELY AFTER THAT OF THE 3EASAT ALTIMETER 'EOSAT WAS A 53 .AVY MILITARY SATELLITE WHOSE PRIMARY MISSION WAS TO MAP THE %ARTHS MARINE GEOID TO THEN UNPRECEDENTED ACCURACY FOR WHICH A NON REPEAT ORBIT WAS REQUIRED 3INCE ITS PUBLIC RELEASE IN THE DATA SET FROM THE FIRST MONTH GEODETIC MISSION HAS BECOME THE BACKBONE OF THE GLOBAL BATHYMETRIC CHART THAT IS THE INDUSTRY STANDARD 'EOSATS SECONDARY MISSION WAS TO OBSERVE DYNAMIC MESOSCALE OCEANO GRAPHIC PHENOMENA FOR WHICH IT WAS MANEUVERED INTO AN EXACT REPEAT ORBIT PERIOD DAYS 'EOSATS GEO DETIC MISSION AND EXACT REPEAT MIS SION ARE KNOWN AS '- AND %2- RESPECTIVELY !S A SPACECRAFT 'EOSAT WAS ONE OF THE FEW %ARTH OBSERVING MISSIONS TO RELY ON THE PURELY PASSIVE GRAVITY GRADIENT MEANS OF ATTITUDE CON TROL AS EVIDENCED BY THE EXTENDED VERTICAL BOOM IN &IGURE 4HE ATTITUDE WAS STABLE TO LESS THAN n TO WHICH THE ALTIMETERS PULSE LIMITED RANGE MEASUREMENT WAS ROBUST 'EOSAT &OLLOW /N '&/ '&/ WAS DESIGNED TO REPLICATE AS MUCH AS POSSIBLE THE 'EOSAT EXACT REPEAT MISSION IN SUPPORT OF OPERATIONAL REQUIREMENTS FOR THE 53 .AVY '&/ REPRESENTS THE CURRENT STATE OF THE ART IN SMALL DEDICATED RADAR ALTIMETER MISSIONS )T INCLUDES A DUAL FREQUENCY WATER VAPOR RADIOMETER 762 AT AND '(Z DATA FROM WHICH ARE USED TO REDUCE THE CORRESPONDING PROPAGATION UNCERTAINTY TO CM
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4HE RADARS MASS IS KG INCLUDING FULL REDUNDANCY AND THE 762 ITS PRIME POWER CONSUMPTION IS LESS THAN 7 4OTAL SPACECRAFT DRY MASSp IS ABOUT KG 4/0%80OSEIDON )N THE LATE S PROGRAM PLANNING FOR SATELLITE RADAR ALTIM ETER MISSIONS SPLIT INTO TWO THEMES DETERMINED BY THE RELATIVE PRIORITY OF THEIR MEA SUREMENTS )F THE ALTIMETER WERE THE PRIME PAYLOAD INSTRUMENT THEN THE ORBIT AND MISSION DESIGN COULD BE OPTIMIZED ACCORDINGLY 4HIS THEME WAS FOLLOWED BY 4/0%8 0OSEIDON 40 A JOINT 5NITED 3TATES .!3! AND &RENCH #.%3 MISSION 4/0%8 WAS DESIGNED TO MEASURE AND MAP THE DYNAMIC OCEAN TOPOGRAPHY WITH SUFFICIENT ACCU RACY TO DETERMINE LARGE SCALE CIRCULATION PATTERNS 4/0%8 MOST FAMOUS CONTRIBUTION IS EARLY OBSERVATION AND NEAR REAL TIME MONITORING OF %L .I¶O EVENTS WHOSE HEIGHT SIGNATURE OVER THE EQUATORIAL EASTERN 0ACIFIC OCEAN TYPICALLY IS AN INCREASE ON THE ORDER OF n CM WITH RESPECT TO THE MEAN 0OSEIDON CONTRIBUTED BY &RANCE WAS A SMALL PROOF OF CONCEPT INSTRUMENT THAT HAD A SOLID STATE TRANSMITTER 0OSEIDON WAS THE PRE CURSOR OF THE *ASON ALTIMETERS AND THE 3)2!, INSTRUMENT ABOARD #RYO3AT 4HE 40 ORBIT REPEAT PERIOD WAS CHOSEN CAREFULLY TO SATISFY ADEQUATE OBSERVATION OF THE DOMINANT ALIASED TIDAL CONSTITUENTS !LL SOLAR TIDAL CONSTITUENTS WOULD BE AMBIGU OUS WITH OTHER HEIGHT SIGNALS IF THE REPEAT PERIOD WERE AN INTEGRAL NUMBER OF DAYS &OR 40 THE TIME OF DAY FOR EACH SUBSEQUENT OBSERVATION SLIPS BY ABOUT TWO HOURS 4HE 40 REPEAT PASS FOOTPRINT LOCATION ACCURACY IS BETTER THAN o KM A REQUIREMENT THAT IS BOUNDED BY THE CROSS TRACK GRADIENT OF THE OCEANIC GEOID 4HE 40 INSTRUMENT PACK AGE INCLUDED A THREE FREQUENCY RADIOMETER 4/0%8 WAS THE FIRST ALTIMETER TO USE TWO FREQUENCIES TIME MULTIPLEXED TO ESTIMATE AND COMPENSATE FOR PROPAGATION DELAYS IMPOSED BY IONOSPHERIC ELECTRONS $ESIGNED FOR AN INITIAL THREE YEAR MISSION SUBSE QUENTLY STRETCHED TO FIVE YEARS 40 PROVIDED VALUABLE DATA FOR AN IMPRESSIVE THIRTEEN YEARS 40 WAS FORMALLY DECOMMISSIONED IN $ECEMBER !S IS TRUE FOR MOST RADARS THE RECEIVED WAVEFORM PRODUCED BY AN INDIVIDUAL PULSE FROM 4/0%8 WAS CORRUPTED BY COHERENT SELF NOISE KNOWN AS SPECKLE 4HE STANDARD DEVIATION OF SPECKLE IS REDUCED BY SUMMING AVERAGING MANY STATISTICALLY INDEPENDENT WAVEFORMS TOGETHER 3TATISTICAL INDEPENDENCE BETWEEN SEQUENTIAL RETURNS OBSERVED BY A RADAR ALTIMETER DEPENDS PRIMARILY ON THE RADAR PULSE REPETITION RATE THE ANTENNA SIZE THE SPACECRAFT VELOCITY AND ON THE SEA SURFACE CONDITIONS 4HE ANTENNA WAS A M REFLECTOR THAT SERVED BOTH ALTIMETER BANDS AND ALSO THE RADIOMETER 3ELECTED PARAM ETERS ASSOCIATED WITH THE ALTIMETERS DESIGN ARE LISTED IN 4ABLE 4HE PULSE TO PULSE 4!",% 4/0%8 0ARAMETERS
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STATISTICAL INDEPENDENCE REQUIREMENT EVALUATED FOR THE 4/0%8 INDICATES THAT THE MAXI MUM 02& SHOULD BE K(Z YET IT WAS K(Z IN PRACTICE 4HE PULSE RATE ABOVE THE THRESHOLD IMPROVED THE ADDITIVE 3.2 BUT DID NOT CONTRIBUTE TO SPECKLE REDUCTION 4HE 02& STATISTICAL INDEPENDENCE LIMIT DECREASES WITH INCREASING SIGNIFICANT WAVE HEIGHT *ASON *ASON FOLLOWED IN THE FOOTSTEPS OF 4/0%8 FIGURATIVELY AND LITERALLY !FTER THE LAUNCH OF *ASON INTO THE 40 ORBIT 4/0%8 WAS MANEUVERED INTO A hTAN DEMv PHASING SO THAT THE MEASUREMENTS OF THE TWO ALTIMETERS COULD BE CROSS CALIBRATED *ASON IS ESSENTIALLY IDENTICAL TO *ASON %23 %23 AND %.6)3!4 )F THE ALTIMETER IS NOT THE PRIMARY PAYLOAD THEN THE RESULTING MISSION AND ORBIT ARE LIKELY TO BE DETERMINED BY OTHER REQUIREMENTS WHICH MAY COMPROMISE ALTIMETRY 4HE %UROPEAN 3PACE !GENCYS SATELLITE ALTIMETERS ON %23 AND %23 AS WELL AS THE ADVANCED RADAR ALTIMETER 2! ON %3!S %.6)3!4 ARE OF SECOND PRIORITY WITH RESPECT TO THE OTHER INSTRUMENTS ON THEIR RESPECTIVE SPACECRAFT 4HEIR SUN SYNCHRONOUS ORBITS ARE LESS THAN OPTIMUM FOR MOST ALTIMETRIC APPLICATIONS DUE PRIMARILY TO THE FACT THAT FOUR OF THE EIGHT DOMINANT TIDAL CONSTITUENTS ARE SUN SYNCHRONOUS 4HESE ORBITS ARE ALSO AT LOWER ALTITUDES THAN THE 40 ORBIT WHICH IMPLIES THAT ORBIT MAINTENANCE MANEUVERS MUST BE MORE FREQUENT THUS COMPROMISING PRECISION ORBIT DETERMINATION $URING A PORTION OF ITS MISSION THE ORBIT OF %23 WAS REPHASED TO A LONG REPEAT PERIOD DAYS 4HAT LONG REPEAT PERIOD GENERATED A RELATIVELY DENSE SURFACE SAMPLING GRID USEFUL FOR ESTIMATING SEA ICE COVER GEODESY AND BATHYMETRY 4HE %23 MISSION DID NOT VARY ITS REPEAT PERIOD 4HE CONSEQUENCE OF THESE ORBIT PROPERTIES IS THAT THE RESULTING DATA ARE NOT WELL SUITED TO MEASURING THE ANNUAL RATE OF SEA LEVEL RISE WHICH IS A KEY CLIMATE RELATED VARIABLE #RYO3AT 4HIS WAS THE FIRST %ARTH %XPLORER /PPORTUNITY -ISSIONS WHICH WAS PART OF THE %UROPEAN 3PACE !GENCYS ,IVING 0LANET 0ROGRAMME 4HE MISSION CONCEPT WAS SELECTED IN AND SUBSEQUENTLY LAUNCHED IN /CTOBER 5NFORTUNATELY THE LAUNCH VEHICLE MALFUNCTIONED %3! AND ITS MEMBER STATES AUTHORIZED A REPLACEMENT 4HE #RYO3AT ORBIT HAS A HIGH INCLINATION n AND A LONG REPEAT PERIOD DAYS WITH A DAY SUBCYCLE DESIGNED TO PROVIDE DENSE INTERLOCKING COVERAGE OVER THE POLAR REGIONS )TS AIM IS TO STUDY POSSIBLE CLIMATE VARIABILITY AND TRENDS BY DETERMINING THE VARIATIONS IN THICKNESS OF THE %ARTHS CONTINENTAL ICE SHEETS AND MARINE SEA ICE COVER #RYO3AT IS DESCRIBED IN MORE DETAIL IN A SUBSEQUENT SECTION !LTI+A !LTI+A DIFFERS FROM OTHER OCEAN VIEWING ALTIMETERS IN THIS SECTION DUE PRIMARILY TO ITS USE OF +A BAND '(Z RATHER THAN +U BAND 4HE FIRST INSTRUMENT FROM &RANCE IS PART OF THE PAYLOAD ON )NDIAS /CEANSAT !LTI+A IS SINGLE FREQUENCY SINCE AT +A BAND THE RETARDATION DUE TO THE IONOSPHERE IS SUFFICIENTLY SMALL THAT IT DOES NOT HAVE TO BE MEASURED AND COMPENSATED (OWEVER THE ^ CM WAVELENGTH IS VULNERABLE TO ATMOSPHERIC MOISTURE IT IS PREDICTED THAT AS MUCH AS OF THE DATA WILL BE COMPROMISED BY RAIN 4HE KG INSTRUMENT REQUIRES AN INPUT POWER OF 7 4HE OFFSET FED REFLECTOR ANTENNA IS M IN DIAMETER RESULTING IN A BEAMWIDTH LESS THAN HALF THAT OF ITS +U BAND COUNTERPARTS 3EVERAL ADVANTAGES ARE CLAIMED FOR THE SMALLER BEAMWIDTH INCLUDING OPERATION CLOSER TO LAND /N THE OTHER HAND THE NARROWER BEAM IMPLIES THAT THE WAVEFORM IS MORE SENSITIVE TO SPACECRAFT ATTITUDE ERRORS !LTI+AS -(Z BANDWIDTH LEADS TO A PULSE LIMITED FOOTPRINT ABOUT SMALLER THAN USUAL
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4HE 02& IS K(Z APPROXIMATELY TWICE THAT OF MOST CONVENTIONAL ALTIMETERS SLIGHTLY LARGER THAN THE PULSE TO PULSE STATISTICAL INDEPENDENCE CONDITION OF K(Z /RBIT #ONSIDERATIONS 'IVEN AN ARBITRARILY GOOD RADAR ALTIMETER ITS ORBIT BECOMES THE DOMINANT FACTOR THAT MAY LIMIT SEA SURFACE HEIGHT MEASUREMENT ACCU RACY /RBIT SELECTION FOR AN OCEAN ALTIMETER REQUIRES CONSIDERATION OF THE IMPACT OF AN ORBITS INCLINATION REPEAT PERIOD AND ALTITUDE &OR EXAMPLE IF THE OBJECTIVE IS ABSOLUTE SEA SURFACE HEIGHT ACCURACY OVER LARGER SPATIAL SCALES AND LONG TIME SCALES THEN A HIGHER ALTITUDE ORBIT HAVING A RELATIVELY MODERATE PROGRADE INCLINATION AND RELATIVELY SHORT NON SUN SYNCHRONOUS REPEAT PERIOD IS THE ONLY SENSIBLE STARTING POINT !N ALTIMETERS REVISIT PERIOD IS TEN DAYS OR MORE IN CONTRAST TO TIDES WITH APPROXI MATELY OR CYCLES PER DAY DRIVEN PRIMARILY BY LUNAR AND SOLAR GRAVITY !S A RESULT ALL TIDAL SIGNALS SENSED BY AN ALTIMETER ARE UNDERSAMPLED !LTIMETRIC DATA RETAIN THE RESULTING ALIASES WHICH OVER THE COURSE OF A YEAR OR SO CAN BE IDENTIFIED QUANTIFIED AND CALIBRATED OUT !N ALTIMETERS ORBIT MUST BE CHOSEN SO THAT THE TIDAL ALIASES DO NOT GET CONFUSED WITH SIGNALS OF GEOPHYSICAL INTEREST 4HE 40 /RBIT 4HE STATE OF THE ART AT LEAST IN ACCURACY AND LARGE SCALE CIRCULATION STUDIES IS *ASON OPERATING IN THE ORBIT ORIGINALLY DESIGNED FOR 4/0%80OSEIDON 4HE ORBIT PARAMETERS INCLUDE REPEAT PERIOD CALENDAR DAYS UNFORTUNATELY OFTEN STATED AS DAYS INCLINATION n REPEAT TRACK SEPARATION AT THE EQUATOR KM AND ALTITUDE KM 4HE RADIAL COMPONENT OF PRECISION ORBIT DETERMINATION 0/$ IS ON THE ORDER OF CM FOR 40 AND *ASON RESULTS SHOW 0/$ TO A LEVEL OF CM !LTHOUGH THESE PARAMETERS REFLECT THE FRUITS OF MULTIPLE YEARS OF TRADE STUDIES BY MANY INDIVIDU ALS AT LEAST ONE UNWANTED CHARACTERISTIC REMAINS 4HE + TIDAL ALIAS IS VERY NEARLY TWO CYCLES PER YEAR THUS APPEARING CLOSE TO GEOPHYSICAL SIGNALS ASSOCIATED WITH SEASONAL EFFECTS + CANNOT BE IGNORED AS IT IS THE LARGEST DIURNAL CONSTITUENT AND IS SECOND IN MAGNITUDE ONLY TO THE DOMINANT LUNAR CONSTITUENT 4HE CONSTRAINT ON THE EXACTNESS OF AN ORBITS REPEATING GROUND TRACK IS DETERMINED TO FIRST ORDER BY THE FINE STRUCTURE IN THE LOCAL GEOID EXPRESSED AT THE OCEANS SURFACE &OR EXAMPLE CROSS TRACK SURFACE SLOPES GRADIENTS IN THE GEOID MAY BE AS LARGE AS r n NEAR THE DEEPER OCEANIC TRENCHES )N SUCH AN EXTREME CASE A CROSS TRACK DRIFT OF ONLY KM WOULD GIVE RISE TO A CM CHANGE IN SEA SURFACE HEIGHT 33( )N RESPONSE ALGO RITHMS HAVE BEEN DEVELOPED THAT CORRECT 33( DATA FOR THE EFFECTS OF THE LARGER CROSS TRACK GEOID GRADIENTS )T ALSO IS STANDARD PRACTICE TO CONSTRAIN AN ALTIMETERS CROSS TRACK DRIFT TO LESS THAN KM 2EPEAT TOLERANCE USUALLY IS THE CONDITION THAT MOTIVATES ACTIVE ORBIT MAINTENANCE MANEUVERS .ON 2EPEAT /RBIT 4HE PRECEDENT FOR THIS IS 'EOSAT ITS FIRST MONTHS WERE DEVOTED TO GEODESY FOR WHICH A NON REPEAT ORBIT IS OPTIMAL 'EODETIC MISSIONS MAP GRAVITY ANOMALIES REFLECTED IN SUBTLE LOCAL TILTS OF THE MEAN OCEAN SURFACE 4HESE ARE STATIC MESOSCALE FEATURES OF SPATIAL SCALES LESS THAN ABOUT KM DETERMINED BY THE TOPOGRAPHIC FEATURES COMPOSITION OF THE SEA BOTTOM AND STATIONARY OCEANIC CURRENTS $ATA FROM 'EOSAT HAVE BEEN USED TO DERIVE THE STANDARD BATHYMETRIC CHARTS AVAILABLE FOR THE GLOBAL OCEANS 'EOSAT %2- /RBIT 4HE ONLY OTHER FAMILY OF DEDICATED MISSIONS IS THAT IN THE 'EOSAT n %XACT 2EPEAT -ISSION %2- ORBIT THE SAME ORBIT USED BY '&/ 4HIS ORBIT HAS A PERIOD OF CALENDAR DAYS SOMETIMES INAPPROPRIATELY
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ABBREVIATED TO DAYS n INCLINATION CONSEQUENTLY KM TRACK TO TRACK SPAC ING AT THE EQUATOR AND KM ALTITUDEe &ROM THE 'EOSAT ORBIT HALF OF THE PRINCI PAL TIDAL CONSTITUENTS ALIAS INTO UNWANTED FREQUENCIES NEAR ZERO ONE OR TWO CYCLES PER YEAR )N PARTICULAR THE DOMINANT TIDAL CONSTITUENT THE COMMON TWICE DAILY LUNAR TIDE IS ALIASED TO DAYS WHICH IS CLOSE TO THE ANNUAL CYCLE 0RECISION ORBIT DETERMINATION IS GOOD TO ONLY ABOUT CM WHICH IS RELATIVELY LARGE DUE IN NO SMALL MEASURE TO FAILURE OF THE PRIMARY ONBOARD '03 NAVIGATION SUBSYSTEM 3UN 3YNCHRONOUS /RBITS 3UN SYNCHRONOUS SATELLITES HOST %UROPEAN 3PACE !GENCY %3! ALTIMETERS ON %23 %23 AND 2! ON %.6)3!4 !LL SHARE THE SAME ORBIT CALENDAR DAYS REPEAT PERIOD n INCLINATION AND KM MEAN EQUATORIAL ALTITUDE 2ADIAL KNOWLEDGE OF THESE SUN SYNCHRONOUS ORBITS IS GOOD TO ABOUT CM BASED ON THE $ELFT MODEL !S SUN SYNCHRONOUS ALTIMETERS THE LARGEST SOLAR CONSTITUENT TWICE DAILY ALIASES TO ZERO AND ALL TIDAL CONSTITUENTS THAT ARE PRIMARILY DEPENDENT ON SOLAR FORCES ALIAS TO FREQUENCIES CLOSE TO ZERO 4HEORETICAL &OUNDATIONS 4HE FOLLOWING PARAGRAPHS PROVIDE A SUMMARY OF THE KEY CHARACTERISTICS OF A SPACE BASED RADAR ALTIMETER %XAMPLES ARE DRAWN FROM THE DESIGN OF 4/0%8 0ULSE LIMITED !LTIMETERS &IGURE ILLUSTRATES THE PULSE LIMITED CONDITION 4HE RADIUS R0 OF THE AREA DELIMITED ON A QUASI FLAT SURFACE BY A PULSE OF LENGTH S SEC ONDS ON THE %ARTH OF MEAN RADIUS 2% SEEN FROM A RELATIVE ALTITUDE OF H KILOMETERS IS
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WHERE @ 2 2% H 2% IS A CONSEQUENCE OF THE SPHERICAL OBSERVATION GEOMETRY &OR TYPICAL SATELLITE RADAR ALTIMETERS THE PULSE LIMITED FOOTPRINT OVER A QUASI FLAT SURFACE IS ON THE ORDER OF TWO KILOMETERS IN DIAMETER 4HE PULSE LIMITED AREA !P IS
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!S THE PULSE CONTINUES TO IMPINGE AND SPREAD OVER THE SURFACE THE RESULTING PULSE LIMITED ANNULI ALL HAVE AREAS EQUAL TO THAT OF THE INITIAL PULSE LIMITED FOOTPRINT (ENCE THE RECEIVED POWER TENDS TO MAINTAIN THE LEVEL CORRESPONDING TO THE PEAK OF THE INITIAL RESPONSE &IGURE 4HE PULSE LIMITED AREAS EXPAND IN RESPONSE TO INCREASING LARGE SCALE SURFACE ROUGHNESS WHICH IN THE OCEANOGRAPHIC CONTEXT IS EXPRESSED AS SIGNIFICANT WAVE HEIGHT 37( 4HE HEIGHT ACCURACY OF A PULSE LIMITED ALTIMETER IS MUCH LESS SENSITIVE TO SMALL ANGULAR POINTING ERRORS THAN IS THE CASE FOR A BEAM LIMITED ALTIMETER !DAPTIVE 4RACKING ! SATELLITE BASED RADAR ALTIMETER NEEDS TO MEASURE THE DIS TANCE ACCURATELY BUT ONLY FOR AN ESSENTIALLY PLANAR SURFACE ORIENTED ORTHOGONALLY TO THE RADARS LINE OF SIGHT #ONSERVATIVE DESIGN SUGGESTS THAT THE MEASUREMENT SHOULD BE CONCENTRATED NEAR THE REFLECTION FROM THAT SURFACE (ENCE OCEAN VIEWING ALTIM ETERS HAVE A SMALL RANGE WINDOW WHOSE POSITION TRACKS THE DELAY AND STRENGTH OF THE
e 4HE 'EOSAT %2- ORBIT WAS CHOSEN FOR POLITICAL AS MUCH AS FOR TECHNICAL REASONS )T FOLLOWED THE 3EASAT ORBIT THAT HAD ESTABLISHED A WELL KNOWN PRECEDENT
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SURFACE REFLECTION 4HE OCEANS SURFACE HAS A SIGNIFICANT WAVE HEIGHT OF LESS THAN M OR SO 2ADAR BACKSCATTER IS PRIMARILY SPECULAR TYPICALLY SPANNING D" TO D" TO CITE PARAMETERS USED IN THE TESTING OF THE 4/0%8 ALTIMETER )N PRACTICE RANGE GATE DELAY AND BACKSCATTER TRACKING ARE MET WITH TWO SERVO REGULATOR FEEDBACK LOOPS &IGURE 4HE FIRST LOOP IS A SECOND ORDER HEIGHT TRACKER CONSISTING OF RANGE POSITION ALPHA TRACKER AND RANGE RATE BETA TRACKER 4HE SECOND LOOP IS THE RECEIVER GAIN CONTROL !'# !LTIMETER HEIGHT MEASUREMENT IS GIVEN BY THE SETTING OF THE
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RANGE DELAY COARSE AND FINE VALUES CORRECTED BY THE REMAINING HEIGHT ERROR MEASURED FROM THE WAVEFORMS POSITION IN THE TRACKER 3URFACE WIND SPEED AND SIGNIFICANT WAVE HEIGHT ARE DERIVED FROM THE !'# VALUES AND THE WAVEFORMS SHAPE RESPECTIVELY 4HE PRECISION OF AN INDIVIDUAL HEIGHT MEASUREMENT IS DETERMINED BY THE COMBINATION OF RANGE RESOLUTION AND INCOHERENT WAVEFORM AVERAGING )F A SINGLE SIMPLE SHORT PULSE WERE TRANSMITTED THEN THE HEIGHT RESOLUTION WOULD EQUAL THE PULSE LENGTH 4HE PRINCIPAL DISADVANTAGE OF A SHORT PULSE IS THAT IT CONTAINS LITTLE ENERGY 4HE INHERENT RESOLUTION OF A PULSE IS INVERSELY PROPORTIONAL TO ITS BANDWIDTH 3PACE BASED RADAR ALTIMETERS USE SOME FORM OF MODULATION ON THE TRANSMITTED SIGNAL TO MAINTAIN A LARGE BANDWIDTH WITHIN A LONGER PULSE THUS INCREASING THE TRANSMITTED ENERGY AT NO LOSS OF RESOLUTION $ERAMP ON 2ECEIVE 3ATELLITE BASED RADAR ALTIMETERS PRESENT AN ELEGANT EMBODI MENT OF THE 3TRETCH TECHNIQUE WHICH IS KNOWN AS FULL DERAMP IN THE FIELD OF SPACE BASED RADAR ALTIMETRY 4HIS METHOD WAS FIRST EMPLOYED BY -AC!RTHUR IN THE 3EASAT ALTIMETER AND HAS BEEN ADOPTED AS THE STANDARD TECHNIQUE SINCE THEN FOR THIS TYPE OF RADAR 4HE DISTINGUISHING FEATURE OF THIS TECHNIQUE IS A CLEVER TRADE BETWEEN THE TWO KEY
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PARAMETERS IN A LARGE TIME BANDWIDTH PRODUCT 4"0 SIGNAL !FTER RECEPTION DEMODU LATION IS APPLIED THAT TRANSFORMS THE hSHORT TIME LARGE BANDWIDTHv NATURE OF THE ORIGI NAL PULSE TO hLONG TIME SMALL BANDWIDTHv SIGNALS 3INCE THE SAME 4"0 IS MAINTAINED THE ORIGINAL RESOLUTION IS PRESERVED 4HE METHOD IS IDEAL FOR ALTIMETRY SINCE THE RANGE DEPTH OF THE OCEANS SURFACE IS VERY MUCH SMALLER THAN THE TIME AVAILABLE IN THE PULSE REPETITION PERIOD #LEARLY THE FULL DERAMP TECHNIQUE OFFERS A CONSIDERABLE SAVINGS IN SYSTEM BANDWIDTH AT ALL SUBSEQUENT STAGES AND AT NO COST IN RANGE RESOLUTION 4HE FIG URES CITED IN 4ABLE SHOW THAT THE RATIO OF WAVEFORM BANDWIDTH TO 2& BANDWIDTH FOR 4/0%8 IS ON THE ORDER OF 4HE 4/0%8 ALTIMETER DESIGN IS DESCRIBED MORE COMPLETELY IN THE OPEN LITERATURE 'EOSAT 'EODETIC -ISSION 2ADAR ALTIMETRIC DATA ARE THE BASIS FOR STATE OF THE ART GRAVIMETRIC VARIATIONS EXPRESSED AT THE OCEANS SURFACE AND CONSEQUENTLY OCEANIC BATHYMETRY 4HE PRINCIPAL OBJECTIVE OF A GEODETIC SATELLITE RADAR ALTIMETER IS TO MEASURE THE ALONG TRACK SLOPE OF THE SEA SURFACE CAUSED BY GRAVITY DEFLECTIONS OVER SPATIAL SCALES LESS THAN A FEW HUNDREDS OF KILOMETERS &IGURE 4HESE SLOPES ARE DERIVED FROM THE 33( MEASUREMENTS SUMMARIZED ABOVE BUT THIS APPLICA TION HAS ITS OWN UNIQUE IMPLICATIONS FOR SYSTEM DESIGN 4HE HIGHLIGHTS ARE REVIEWED IN THE FOLLOWING PARAGRAPHS 3EA SURFACE SLOPE IS DERIVED BY TAKING THE DIFFERENCE BETWEEN TWO NEIGHBORING HEIGHT MEASUREMENTS WHERE THE SLOPE TANGENT EQUALS hRISE OVER RUNv 4HE KEY WORD FOR THESE MEASUREMENTS IS PRECISION THE STANDARD DEVIATION NOISE OF THE SEA SURFACE HEIGHT MEASUREMENT ABOUT ITS MEAN VALUE (EIGHT MEASUREMENT PRECISION IS DETER MINED BY THE RADAR ALTIMETERS POST PROCESSING RANGE RESOLUTION AND BY THE AMOUNT OF AVERAGING AVAILABLE FOR EACH ESTIMATE .OTE THAT A PRECISION MEASUREMENT MAY STILL HAVE POOR ACCURACY IF ITS MEAN VALUE IS BIASED AWAY FROM THE CORRECT VALUE 7HEN COMPARING TWO NEIGHBORING HEIGHT MEASUREMENTS ANY CONSTANT BIAS IS CANCELLED BY SUBTRACTION AS LONG AS THE ERROR IS THE SAME FOR BOTH MEASUREMENTS 4HE SEA SURFACE SLOPE MEASUREMENT PROBLEM IS CHALLENGING BECAUSE THE DESIRED SLOPE SIGNALS ARE AS SMALL AS ONE MICRORADIAN EQUIVALENT TO A MM HEIGHT DIFFERENTIAL RISE FOR EACH KM ALONG TRACK SEPARATION RUN )N ADDITION TO HEIGHT PRECISION GEODETIC ALTIMETRY REQUIRES SMALLER ALONG TRACK RESOLUTION THAN A CONVENTIONAL ALTIMETER AND AN ORBIT THAT ACCUMULATES DENSE CROSS TRACK COVERAGE 4HE ALTIMETERS FOOTPRINT RESOLUTION SHOULD BE SMALLER THAN ABOUT KM
&)'52% 7HEN AVERAGED AND STRIPPED OF DYNAMIC CURRENT DRIVEN FEATURES THE MEAN OCEAN SURFACE IS A DIRECT EXPRESSION OF THE LOCAL GRAVITY GRA DIENT 3TATE OF THE ART RADAR ALTIMETERS CAN MEASURE THE RESULTING SLOPES TO A MICRORADIAN PRECISION
,ITERALLY MEASUREMENT OF THE DISTANCE BETWEEN THE MEAN OCEAN SURFACE AND THE LOCAL SEA FLOOR
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WHICH CORRESPONDS TO THE MINIMUM HALF WAVELENGTH SCALE OF THE OBSERVABLE PERTUR BATIONS IN THE OCEANS MEAN SURFACE DUE TO SPATIAL VARIATIONS IN THE %ARTHS GRAVITY 4HE ORBIT SHOULD NOT REPEAT FOR ^ YEARS TO YIELD AN AVERAGE GROUND TRACK SPAC ING OF KM AGAIN IN RESPECT OF THE GRAVITY SIGNAL AT THE OCEANS SURFACE 4HE ORBITS INCLINATION SHOULD BE NEAR nnn TO RESOLVE NORTH AND EAST SLOPES NEARLY EQUALLY AND TO COVER THE LOWER LATITUDES WHERE EXISTING DATA ARE INADEQUATE .OTE THAT OCEANO GRAPHIC RADAR ALTIMETER MISSIONS 4/0%80OSEIDON *ASON %23 %.6)3!4 AND 'EOSAT %2-'&/ ARE NORMALLY PLACED INTO EXACT REPEAT ORBITS TO DAYS AND AS A CONSEQUENCE HAVE WIDELY SPACED KM TO KM GROUND TRACKS 3UCH ORBITS CANNOT RESOLVE THE SHORT WAVELENGTH TWO DIMENSIONAL SURFACE SLOPES REQUIRED FOR USE FUL GEODESY 3INCE ABSOLUTE HEIGHT ACCURACY IS NOT REQUIRED GEODETIC RADAR ALTIMETERS CAN BE RELATIVELY BASIC INSTRUMENTS 4HEY DO NOT NEED TO COMPENSATE FOR PROPAGATION DELAYS HENCE THEY NEED ONLY ONE FREQUENCY AND THEY DO NOT NECESSARILY NEED A WATER VAPOR RADIOMETER 762 )NDEED A SIMPLE INSTRUMENT IS PREFERRED IT HAS BEEN SHOWN THAT EFFORTS TO CORRECT FOR PATH DELAYS USUALLY ADD NOISE TO SLOPE ESTIMATES 'EODETIC MEA SUREMENTS PROVIDED BY THE 'EOSAT AND %23 BOTH SINGLE FREQUENCY ALTIMETERS WITH NO 762 FURNISHED THE BEST RESOLUTION OCEANIC GEODESY AND BATHYMETRY AVAILABLE UP THROUGH AT LEAST FOR THE OPEN OCEAN 4HEIR RESULTING BATHYMETRIC RESOLUTION IS LIM ITED TO ABOUT KM NORTH SOUTH AND POORER RESOLUTION OF EAST WEST SLOPE COMPONENTS 4HESE RESULTS REFLECT THE LESS THAN OPTIMUM RESOLUTION WAVEFORM PRECISION AND ORBIT INCLINATION OF THOSE TWO ALTIMETERS 'EODETIC RESOLUTION AT THE OCEANS SURFACE CAN BE NO FINER THAN ABOUT KM HALF A WAVELENGTH A LIMIT THAT IS DETERMINED BY THE AVERAGE DEPTH OF THE OCEAN #RYO3AT )CE 3HEET -ISSION 0ULSE LIMITED SPACE BASED RADAR ALTIMETERS WORK BEST OVER RELATIVELY MILD TOPOGRAPHIC RELIEF OF MEAN SLOPE ZERO SUCH AS THE OCEANS SURFACE /VER ICE SHEETS OR TERRESTRIAL SURFACES PERFORMANCE IS DEGRADED 5NWANTED CHARACTERISTICS INCLUDE FOOTPRINT DILATION OVER ROUGHER TERRAIN HEIGHT ERRORS IN PROPOR TION TO SURFACE MEAN SLOPE AND THE TENDENCY OF THE MINIMUM RANGE MEASUREMENT TO HOP FROM ONE ELEVATED REGION TO ANOTHER WITHOUT THE CONTROL OR KNOWLEDGE OF THE DATA ANALYST "EAM LIMITED TECHNIQUES OF WHICH LASER ALTIMETERS ARE EXTREME EXAMPLES CIRCUMVENT THESE PROBLEMS BUT MAY IMPLY THEIR OWN SET OF DISADVANTAGES ! MAJOR POTENTIAL APPLICATION OF RADAR ALTIMETRY IS TO MONITOR THE HEIGHT OF EXTENSIVE ICE SHEETS AS FOUND IN 'REENLAND OR !NTARCTICA !PPROXIMATELY OF THESE LAND ICE SURFACES HAVE SLOPES LESS THAN ^n WHICH ALTHOUGH SMALL IS SUFFICIENT TO TRICK A CON VENTIONAL ALTIMETER INTO VERY LARGE HEIGHT ERRORS &OR EXAMPLE AN UNKNOWN n SLOPE WOULD LEAD TO A M SURFACE HEIGHT ERROR WHICH IS UNACCEPTABLE IF CM LEVEL INTER ANNUAL CHANGES ARE THE OBJECTIVE 4HE #RYO3AT ALTIMETER IS THE FIRST SPACE BASED RADAR ALTIMETER DESIGNED TO OPER ATE OVER ICE &IGURE )TS PAYLOAD INSTRUMENT IS THE 3!2)NTERFEROMETRIC 2ADAR !,TIMETER 3)2!, WHICH HAS THREE MODES #ONVENTIONAL 3!2 AND )NTERFEROMETRIC 4HE #ONVENTIONAL MODE PULSE LIMITED DESCRIBED IN THE FORGOING PARAGRAPHS REFLECTS ITS 0OSEIDON HERITAGE 4HE 3!2 MODE IS BASED ON THE DELAY DOPPLER ARCHITECTURE WHICH OFFERS ADVANTAGES IN PRECISION RESOLUTION AND ALONG TRACK SURFACE SLOPE TOLER ANCE 4HE )NTERFEROMETRIC MODE IS DESIGNED TO MEASURE THE CROSS TRACK SURFACE SLOPE COMPONENT "OTH OF THESE ADVANCED ALTIMETER MODES HAVE BEEN DEMONSTRATED WITH THE $0 AIRBORNE ALTIMETER 5NLIKE PREVIOUS RADAR ALTIMETER MISSIONS #RYO3AT WILL DOWNLINK ALL ALTIMETRIC DATA WITH ESSENTIALLY NO ONBOARD PROCESSING $ATA FROM EACH OF THE THREE MODES ARE
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&)'52% 4HE #RYO3AT SATELLITE AND ITS 3)2!, ALTIMETER 4HE TWO ANTENNAS )NTERFEROMETRIC MODE ARE ATHWART THE VELOCITY VECTOR SO THAT THE DIFFERENTIAL PHASE MODULO O OF THE FIRST RETURN INDICATES THE CROSS TRACK POSITION OF THE MINIMUM RANGE REFLECTING SURFACE WHICH IN EFFECT IS A MEASURE OF THE CROSS TRACK COMPONENT OF THE MEAN SURFACE GRADIENT #OURTESY OF %UROPEAN 3PACE !GENCY
PROCESSED IN GROUND BASED FACILITIES SINCE THE MORE COMPLICATED WAVEFORMS FROM ICY SURFACES REQUIRE ITERATIVE DEVELOPMENT OF SUITABLE PROCESSING ALGORITHMS BY INVESTIGA TORS PRIOR TO RETRIEVING THE DESIRED INFORMATION 4HE CONVENTIONAL MODE IS USED FOR THE OPEN OCEAN FOR CALIBRATION AND SEA SURFACE HEIGHT REFERENCE PURPOSES AND THE CENTRAL CONTINENTAL ICE SHEETS THAT ARE RELATIVELY LEVEL 4HE INTERFEROMETRIC MODE IS RESERVED FOR THE MORE STEEPLY SLOPING MARGINS OF THE ICE SHEETS 4HE SYNTHETIC APERTURE MODE IS USED PRIMARILY OVER SEA ICE WHERE ITS SHARPER SPATIAL RESOLUTION AND PRECISION SUP PORT MEASURING THE DIFFERENCE BETWEEN THE SEA LEVEL AND THE TOP SURFACE OF FLOATING ICE FREEBOARD "ECAUSE THE DENSITY OF ICE IS RELATIVELY WELL KNOWN SUCH FREEBOARD MEASUREMENTS CAN BE INVERTED TO ESTIMATE ICE THICKNESS
£n°{Ê * /,9Ê, ,4HE HISTORY OF PLANETARY IMAGING RADARS IS SUMMARIZED IN 4ABLE 6ENUS HAS BEEN THE MOST POPULAR DESTINATION LARGELY BECAUSE IT IS CLOUD COVERED HENCE ITS SURFACE IS NOT OBSERVABLE BY OPTICAL MEANS ITS MASS AND SIZE ARE SIMILAR TO THOSE OF %ARTH AND SPECTRAL OBSERVATIONS HAVE SHOWN THAT ITS ATMOSPHERE IS ^ #/ SUGGESTING THAT A GREENHOUSE EFFECT COULD HAVE OVERWHELMED WHAT MIGHT HAVE BEEN A MORE HOSPITABLE PLANET ! POPULAR THEME FOR PLANETARY EXPLORATION BY RADAR IS THE SEARCH FOR EVIDENCE OF WATER ESPECIALLY WATER ICE $ATA FROM RADAR MISSIONS ARE AVAILABLE THROUGH .!3!S 0LANETARY $ATA 3YSTEM &LIGHT 3YSTEMS 6ENERA PERFORMED THE FIRST SIMPLE RADAR MEASUREMENTS OF 6ENUS FROM A SPACECRAFT 6ENERA CARRIED A PULSE MODULATED RADAR ALTIMETER WHICH RETURNED READINGS DURING ITS DESCENT FROM ORBIT TO ITS DEMISE ON THE SURFACE OF 6ENUS
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2ADAR 2ADAR ALTIMETRY /2!$ !LTIMETER ALSO COARSE IMAGERY CM 3!2 AND ALTIMETER CM WAVELENGTH 3!2 CM M M PIXELS COVERAGE "ISTATIC SCATTEROMETER EXPERIMENT CM 42- CM 3!2 RESOLUTION n KM AND ALTIMETER &ORERUNNER -INI 2& 53! CM 3!2 SCATTEROMETER -INI 2& 3!2 CM AND CM IMAGER AND INTERFEROMETER
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4HE CAPSULES TRAJECTORY WAS ESTIMATED BY DOPPLER RADIO READINGS AND AERODYNAMIC CALCULATIONS AND BY SUBTRACTING THIS FROM THE ABSOLUTE RADAR ALTITUDE READINGS A GROUND PROFILE COULD BE MEASURED 2EADINGS SPAN A VERTICAL RANGE OF KM DOWN TO KM DURING WHICH TIME THE CAPSULE DRIFTED HORIZONTALLY FOR A DISTANCE OF ABOUT KM !NALYSIS OF THE RETURN PULSES YIELDED ESTIMATES OF ELEVATION VARIATIONS OF THE OVER FLOWN SURFACE 6ENERA DEMONSTRATED THE FIRST BISTATIC PLANETARY RADAR OBSERVATIONS 4HE 6ENERA ORBITERS MAPPED STRIPS OF THE SURFACE OF 6ENUS RANG ING FROM n KM LONG AND n KM WIDE ! CM WAVELENGTH RADIO WAVE WAS BEAMED AT THE SURFACE BY THE TELEMETRY ANTENNA AND BOTH THE DIRECT AND REFLECTED SIGNALS WERE RECORDED BY %ARTH BASED RECEIVERS 4HE FIRST ANALYSIS OF THESE DATA GAVE ONE DIMENSIONAL MEASUREMENTS OF TERRAIN SHAPE WITH A RESOLUTION OF n KM 0IONEER 6ENUS WAS HOST TO EXPERIMENTS WITH A TOTAL MASS OF KG INCLUDING A RADAR ALTIMETER /2!$ WHICH ALSO PRODUCED RUDIMENTARY SURFACE MAPS AS THE RADAR BEAM WAS SCANNED IN THE PLANE ORTHOGONAL TO THE ORBIT BY THE SPACECRAFTS 20- SPIN STABILIZATION 4HE RADAR PACKAGE REQUIRED AN AVERAGE 7 INPUT POWER AND HAD A MASS OF KG 0EAK TRANSMITTED POWER WAS 7 4HE 8 BAND AND 3 BAND COMMUNICATIONS SYSTEM USED A DESPUN ANTENNA ^ M DIAMETER DISH 4HE RADAR ALTIMETER PROVIDED MANY YEARS OF DATA WITH A HEIGHT ACCURACY OF M WHICH WAS THE BEST AVAILABLE INFORMATION ON 6ENUS SURFACE FIGURE UNTIL -AGELLAN 4HE ALTIMETERS WAVEFORM STRENGTH AND SHAPE WERE ANALYZED TO ESTIMATE SURFACE ELECTRICAL CONDUCTIVITY AND METER SCALE ROUGHNESS PROPERTIES 4HE SPACECRAFTS HOUR ORBIT WAS HIGHLY ELLIPTICAL ^ KM PERIAPSIS AND ^ KM APOAPSISo FOR MOST OF THE MISSION 2ADAR DATA WERE COLLECTED ONLY BELOW KM ALTITUDES WITH A RESOLVED FOOTPRINT ON THE SURFACE OF KM ALONG TRACK AND KM ACROSS TRACK o 0ERIAPSIS AND APOAPSIS ARE RESPECTIVELY THE POINTS ALONG AN ELLIPTICAL ORBIT THAT ARE CLOSEST TO AND FARTHEST FROM THE GRAVITATIONAL CENTER OF THE SYSTEM
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6ENERA SIMULTANEOUS hTWINv MISSIONS WERE THE FIRST SPACE BASED 3!2 MAP PERS OF ANOTHER PLANET 4HEY IMAGED THE AREA FROM THE NORTH POLE DOWN TO ABOUT n. LATITUDE OVER MONTHS OF OPERATIONS 4HEIR RADARS HAD TWO MODES IMAGING AND ALTIM ETRY OPERATING AT CM WAVELENGTHS )MAGING RESOLUTION WAS ^ KM %ACH KG SPACECRAFT WAS A CYLINDER M IN LENGTH 4HE SYNTHETIC APERTURE RADAR ANTENNA WAS A r METER PARABOLIC CYLINDER REFLECTOR POWERED BY AN WATT TRAVELING WAVE TUBE AMPLIFIER 2ATHER THAN PULSE OR CHIRP MODULATION 6ENERA USED A CONTINUOUS TRANSMISSION MODULATED BY A CODED SEQUENCE OF n PHASE SHIFTS 4HE RECEIVED SIGNAL WAS DIGITIZED INTO COMPLEX NUMBERS BITS ) BITS 1 ! RADAR LOOK WAS TAKEN EVERY SECONDS AND STORED IN A 2!- MEMORY BUFFER 4O KEEP UP WITH THIS DATA RATE RECORDING ALTERNATED BETWEEN TWO ONBOARD TAPE RECORDERS $ATA WERE DOWNLINKED EACH ORBIT ^ -"YTES AND THEN PROCESSED IN GROUND BASED FACILITIES %ACH IMAGING PASS GENERATED RADAR IMAGES THAT WERE COMBINED INTO A SURVEY STRIP OF KM WIDE BY KM LONG 4HESE WERE SUBSEQUENTLY COMBINED INTO MOSAICS 4HE SPACECRAFT INCLUDED A M DIAMETER PARA BOLIC DISH ANTENNA FOR THE RADAR ALTIMETER !FTER THE ORBITS WERE ACCURATELY DETERMINED THE ALTIMETERS WERE SWITCHED TO HIGH RESOLUTION MODE ! ELEMENT PHASE MODULATION WAS USED WITH A HEIGHT AMBIGUITY OF KM )N LATER PHASES OF PROCESSING DOPPLER FREQUENCY ANALYSIS NARROWED THE EFFECTIVE FOOTPRINT TO KM BY KM 4HE ALTIMETER OPERATIONS INTERLEAVED WITH THOSE OF THE IMAGER RESULTED IN THE FIRST RADAR ALTIMETRIC MAP OF THE NORTHERN OF 6ENUS COMPRISED OF MORE THAN INDIVIDUAL MEASUREMENTS 4HE COMMUNICATIONS SYSTEM USED A DEDICATED M RADIO DISH ANTENNA 4HE 6ENERA SPACECRAFT WERE IN APPROXIMATELY ^ HOUR POLAR ORBITS WITH A PERIAPSIS ^ KM AT n. LATITUDE AND APOAPSIS ^ KM -AGELLAN MAPPED OVER OF THE SURFACE OF 6ENUS &IGURE WITH IMAG ING RESOLUTION AN ORDER OF MAGNITUDE BETTER THAN THE EARLIER 6ENERA MISSIONS
&)'52% 4HE IMPACT CRATER 'OLUBKINA ON THE SURFACE OF 6ENUS IMAGED BY -AGELLAN 3 BAND (( POLARIZED 4HE KM MILE DIAMETER CRATER IS CHARACTERIZED BY TERRACED INNER WALLS AND A CENTRAL PEAK TYPICAL OF LARGE IMPACT CRATERS ON %ARTH THE -OON AND -ARS 2OUGH EJECTA GIVE RISE TO STRONG RADAR RETURN A BLESSING FOR THOSE INTERESTED IN PLANETARY GEOLOGY #OURTESY OF .!3!
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!LTIMETRY AND RADIOMETRY DATA ALSO MEASURED THE SURFACE TOPOGRAPHY AND ELECTRI CAL CHARACTERISTICS -AGELLANS ELLIPTICAL ORBIT WAS INCLINED AT n WHICH ALLOWED VIRTUALLY FULL ACCESS TO THE SURFACE BY THE SIDE LOOKING 3!2 "Y THE END OF THE MIS SION -AGELLAN HAD RETURNED MORE DATA THAN ALL PRIOR PLANETARY MISSIONS COMBINED 4HE RADAR OPERATED IN THREE MODESIMAGER ALTIMETER AND RADIOMETERINTERLEAVED DURING EACH PASS 4HE 8 BAND DATA DOWNLINK SUPPORTED DATA RATES OF KBITS OR KBITS 4HE M DIAMETER HIGH GAIN ANTENNA WAS USED FOR BOTH THE RADAR AND FOR TELECOMMUNICATIONS 3PACECRAFT MASS WAS KG THE RADAR MASS WAS KG )NPUT POWER WAS 7 AT 6$# -AGELLAN OPERATED AT 3 BAND 'HZ RADIATING A PEAK POWER OF 7 .OMINAL PULSE LENGTH WAS §SEC WITH 02& (Zn (Z SELECTABLE TO ACCOMMODATE THE WIDE VARIATIONS IN RANGE AND INCIDENCE NECESSITATED BY THE ELLIPTICAL ORBIT )T ACHIEVED M RESOLUTION IN 3!2 MAPPING MODE M HEIGHT RESOLUTION IN ALTIMETER MODE AND n# IN RADIOMETER MODE !LL -AGELLAN DATA ARE AVAILABLE THROUGH THE 0LANETARY $ATA 3YSTEM #ASSINI A MULTIMODE RADAR MAPPER LEVERAGED FROM -AGELLANS HERITAGE WAS INCLUDED IN THE INSTRUMENT PAYLOAD OF THE #ASSINI (UYGENS -ISSION WHICH WAS LAUNCHED IN /CTOBER AND STARTED ITS FOUR YEAR TOUR OF 3ATURN AND ITS MOONS IN *ULY 4HE MOTIVATION FOR THE #ASSINI MAPPER WAS THE SAME AS THAT FOR -AGELLAN NAMELY TO MAKE MEASUREMENTS OF THE SURFACE OF 4ITAN THROUGH ITS DENSE CLOUD COVER $URING ITS EXTENSIVE TOUR OF THE 3ATURNIAN SYSTEM THE #ASSINI (UYGENS MISSION WAS TO COMPLETE FLYBYS OF 4ITAN OF WHICH WILL BE AT THE CLOSEST APPROACH OF LESS THAN KM OF WHICH WILL HAVE MINIMUM ALTITUDES OF ^ KM 4HE FIRST CLOSE FLYBY WAS IN .OVEMBER FROM WHICH THE FIRST RADAR IMAGES OF THE SURFACE WERE COL LECTED 4HE RADAR ANTENNA USES THE M ( POLARIZED HIGH GAIN TELECOMMUNICATIONS ANTENNA A STRATEGY SIMILAR TO THAT PIONEERED ON -AGELLAN 3EVEN BEAMS EACH AT DIF FERENT FREQUENCY WIDTH AND BORESIGHT ORIENTATION ARE REQUIRED TO SUPPORT MULTIPLEXED ALTIMETRY AND SCATTEROMETRY AS WELL AS IMAGING AND RADIOMETRY 4HE RADARS MASS IS ^ KG AND ITS INPUT POWER REQUIREMENT IS ^ 7 0EAK DATA RATES ARE ON THE ORDER OF KBITS !LL MODES OPERATE AT +U BAND '(Z )N ITS MOST FAVORABLE LOWER ALTITUDE IMAGING GEOMETRY GROUND RANGE AND AZIMUTH RESOLUTIONS ARE ON THE ORDER OF KM AT LOOKS !T HIGHER ALTITUDES MORE LOOKS ARE GATHERED TO PARTIALLY OFFSET THE DEGRADED RESOLUTION 4HE RADARS NOISE EQUIVALENT R RANGES FROM ^ D" AT LOW ALTITUDE TO ^ D" AT KM ALTITUDE )N CONTRAST TO THE SCHEME USED ON -AGELLAN SMALLER ANGLES OF INCIDENCE AND LOWER BANDWIDTH ARE USED FOR THE HIGHER ALTITUDES 4HE LOWER BANDWIDTH HELPS TO REDUCE THE MEAN NOISE LEVEL WHEREAS THE SHALLOWER INCIDENT ANGLE HELPS TO MAINTAIN RANGE RESOLUTION WITH SMALLER RADIATED PULSE BANDWIDTH #LEMENTINE ONE OF THE FIRST hFASTER BETTER CHEAPERv MISSIONS HAD PRIMARY OBJECTIVES INCLUDING LASER ALTIMETRY AND OPTICAL SURFACE MAPPING OF THE -OON AS WELL AS TECHNOL OGY DEMONSTRATION 4HE MAIN PAYLOAD INSTRUMENTATION WAS COMPRISED OF FOUR OPTICAL CAMERAS INCLUDING ONE WITH A LASER ALTIMETER -AJOR NEW INFORMATION ABOUT THE -OON WAS PROVIDED FROM #LEMENTINES DATA COLLECTED DURING ITS DAYS IN LUNAR ORBIT #LEMENTINE IS RELEVANT TO THIS CHAPTER BECAUSE OF A UNIQUE BISTATIC RADAR EXPERIMENT CONDUCTED WITH THE 3 BAND CM 2& DATA SYSTEM 4HE LUNAR SOUTH POLE WAS ILLU MINATED BY #LEMENTINES COMMUNICATIONS ANTENNA WATTS CIRCULARLY POLARIZED AND THE REFLECTIONS FROM THE SPECULAR POINT WERE TRACKED BY AN ANTENNA OF THE $EEP 3PACE .ETWORK $3. OVER FOUR PASSES 4HE OBSERVED REFLECTED SIGNAL CHARACTERISTICS WERE CONSISTENT WITH NORMAL LUNAR REGOLITHp ON THREE PASSES BUT DATA FROM THE FOURTH PASS p &OUND VIRTUALLY EVERYWHERE ON THE -OONS SURFACE REGOLITH IS A LAYER OF GRANULAR ROCKY MATERIAL COVERING SOLID ROCK
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SEEMED TO SHOW AN ENHANCED STRENGTH THAT CORRESPONDED TO THE SPECULAR POINT PASS ING ACROSS THE FLOOR OF THE CRATER 3HACKELTON 3UCH ENHANCED REFLECTIONS ESPECIALLY IN THE hUNEXPECTEDv SENSE OF CIRCULAR POLARIZATION ARE INDICATIVE OF VOLUMETRIC RADAR RESPONSE FROM VERY COLD FROZEN VOLATILES SUCH AS WATER ICE BEST ILLUSTRATED BY %ARTH BASED RADAR OBSERVATIONS OF *UPITERS ICY MOONS 4HE SUBSEQUENT CLAIM THAT WATER ICE HAD BEEN DISCOVERED AT THE -OON PRECIPITATED WIDE INTEREST 7HEN INDEPENDENT ANALY SES OF THE #LEMENTINE DATA FAILED TO REPRODUCE THE ORIGINAL RESULT CONSIDERABLE CONTROVERSY WAS GENERATED AS WELL $ISCOVERY ANDOR VERIFICATION OF POLAR ICE DEPOSITS ON THE -OON EMERGED AS A MAJOR OBJECTIVE OF .!3!S EXPLORATION PROGRAM AND IF PROVEN WOULD BE AN ESSENTIAL RESOURCE FOR HABITABLE OUTPOSTS AT THE -OON 2ADAR %XPLORATION FOR 0LANETARY )CE 6OLUMETRIC ICE GIVES RISE TO TWO UNUSUAL RADAR RESPONSES 7HEN ILLUMINATED BY A CIRCULARLY POLARIZED FIELD THE PREDOMINANT BACKSCATTER FROM MOST NATURAL SURFACES HAS THE OPPOSITE SENSE OF CIRCULAR POLARIZATION )N THE CASE OF VOLUMETRIC ICE HOWEVER THE BACKSCATTER HAS THE SAME SENSE OF CIRCU LAR POLARIZATION 4HE CLASSICAL MEASURE OF THIS EFFECT IS THE CIRCULAR POLARIZATION RATIO #02 R3# R/# OR hSAME SENSE OVER OPPOSITE SENSEv CIRCULARLY POLARIZED BACKSCATTER STRENGTHS 4HE TOTAL REFLECTED POWER FROM VOLUMETRIC ICE IS RELATIVELY STRONG AT LEAST FOR hCLEANv DEPOSITS "OTH THE POLARIZATION AND RADAR BRIGHTNESS EFFECTS ARE EXPLAINED BY THE COHERENT OPPOSITION BACKSCATTER EFFECT #/"% 7ATER ICE WAS PREDICTED MANY YEARS AGO TO HAVE ACCUMULATED OVER SOME TWO BILLION YEARS IN THE FLOOR OF LUNAR CRATERS OR OTHER FEATURES WHOSE DEPTH AND LATITUDE KEPT THEM IN PERMANENT SOLAR SHADOW 4HE ONLY SOURCE OF HEAT FOR THOSE REGIONS WOULD BE BACK GROUND STARLIGHT AND ENERGY FROM THE -OONS INTERIOR SO THAT THE AMBIENT TEMPERATURE WOULD BE NO MORE THAN ^ + !S WATER ICE ENTERS SUCH A COLD SPACE FROM COMETS IT ACCUMULATES 4HIS PROCESS GENERALLY IS ACCEPTED AS AN EXPLANATION OF THE RADAR BRIGHT RESPONSE FROM -ERCURYS POLAR CRATERS FOR EXAMPLE AS OBSERVED BY %ARTH BASED RADAR TELESCOPES $UE TO THE SMALL AXIAL TILT OF THE -OON HOWEVER RADAR TELESCOPES SUCH AS !RECIBO HAVE NO SIMILAR OPPORTUNITY TO EXPLORE THE FLOORS OF THE LUNAR POLAR CRATERS 4HE PROBLEM IS THAT RELATIVELY LARGE #02 IS NOT UNIQUE TO VOLUMETRIC ICE DEPOSITS $IHEDRAL TWO DIMENSIONAL CORNERS ALSO REFLECT MOST STRONGLY IN THE SAME SENSE AS THE INCIDENT CIRCULAR POLARIZATION .ATURALLY OCCURRING DIHEDRALS SUCH AS ROUGH ROCK FOR MATIONS CREATED BY A LARGE IMPACT COULD GENERATE FALSE WATER ICE SIGNATURES 4O REDUCE THE POTENTIAL AMBIGUITY OF #02 AND BRIGHTNESS MEASUREMENTS THE RADAR OBSERVATIONS MUST BE REPEATABLE AND SHOULD BE CORRELATED WITH OTHER INDICATORS #HANDRAYAAN AND THE ,UNAR 2ECONNAISSANCE /RBITER ,2/ INCLUDE IN EACH OF THEIR PAYLOADS A h-INI 2&v RADAR 4HE VERSION FOR #HANDRAYAAN IS AT 3 BAND CM WAVELENGTH WITH M RESOLUTION AT LOOKS 4HE -INI 2& FOR ,2/ HAS TWO FREQUEN CIES 3 BAND CM AND 8 BAND CM AND TWO RESOLUTIONS M AT LOOKS AND M AT LOOKS 4HE ,2/ RADAR ALSO INCLUDES AN INTERFEROMETRIC MODE WHICH REQUIRES A CONTINUOUS 02& IN CONTRAST TO THE BURST PLAN USED FOR THE OTHER MODES "OTH HAVE MODERATE INCIDENT ANGLES ^ DEGREES MODERATE SWATH WIDTHS KM TO KM AND OPERATE FROM LOW ALTITUDES KM AND KM RESPECTIVELY 'IVEN THE APPLICABLE SMALL RANGE VELOCITY PRODUCT 4ABLE THE ANTENNA AREA NEEDS TO BE ONLY ^ M TO SATISFY THE MINIMUM AREA CONSTRAINT %Q 4HESE RADARS ARE INDEED LOW MASS AT ABOUT KG AND KG RESPECTIVELY INCLUDING IN EACH CASE THEIR ANTENNA ! MAJOR OBJECTIVE FOR BOTH OF THESE RADARS IS TO LOOK FOR EVIDENCE OF ICE DEPOSITS IN THE PERMANENTLY SHADOWED AREAS OF THE -OONS POLAR REGIONS 4HIS REQUIRES THAT THEY MUST MEASURE THE CIRCULAR POLARIZATION RATIO #02 (ENCE THEY TRANSMIT CIRCULAR POLARIZATION AND THEY ARE DUAL POLARIZED ON RECEIVE 4HEIR ANTENNAS ARE COMPRISED OF PASSIVE ARRAYS OF ( AND 6 POLARIZED ELEMENTS DRIVEN SIMULTANEOUSLY n OUT OF
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PHASE SO THAT THE RADIATED POLARIZATION IS CIRCULAR EITHER LEFT OR RIGHT 4HE RECEIVED LINEAR POLARIZATIONS ARE MAINTAINED THROUGH THE REMAINDER OF THE SYSTEM TO THE IMAGE PROCESSOR OUTPUT PRODUCTS 4HIS RESULTS IN THE HYBRID POLARITY ARCHITECTURE THAT IS OUTLINED BELOW -AGELLAN )NNOVATIVE 6ENUS -APPER -AGELLAN &IGURE HAD TO FACE UP TO TWO DRIVING MISSION RESTRAINTS COST AND DATA RATE 4HE FIRST WAS SET BY .!3! AND THE 53 GOVERNMENT BUDGET AUTHORITIES 4HE SECOND WAS SET BY PHYSICS CONDITIONAL UPON THE DATA RATE CAPABILITIES OF THE $EEP 3PACE .ETWORK 4HE LESSON OF COURSE IS THAT IT IS NOT ENOUGH TO DO GOOD READ hBIG BUDGET 3"2 BASEDv SCIENCE IT MUST BE DONE EFFICIENTLY AND RELATIVELY PATIENTLY )N THE CASE OF -AGELLAN HOWEVER THESE TOP LEVEL RESTRAINTS MOTIVATED A SUPERB INNOVATIVE RADAR DESIGN #OST 4HERE WERE SEVERAL CONSEQUENCES TO THE SEVERE REDUCTION IN APPROVED FUNDS RELATIVE TO FUNDS REQUESTED FOR THE ORIGINAL 6ENUS /RBITING )MAGING 2ADAR 6/)2 MISSION 2ATHER THAN A CONVENTIONAL CIRCULAR ORBIT -AGELLAN WAS REDESIGNED FOR AN ELLIPTICAL ORBIT &IGURE WHICH HAD CONSIDERABLY LESS ASSOCIATED COSTS AND RISK !LSO RATHER THAN THE ORIGINAL LARGE HIGH ASPECT RATIO ANTENNA TYPICAL OF SPACE BASED 3!2S -AGELLAN WAS OBLIGED TO USE A SPARE CIRCULAR COMMUNICATIONS ANTENNA LEFT OVER FROM A PREVIOUS MISSION 7HEREAS THESE MAY SOUND LIKE BENIGN IF NOT TRIVIAL MODIFICATIONS THEY NECESSITATED PARADIGM SHIFTING INNOVATIONS BY THE 3!2 DESIGN TEAM !NTENNA 4HE KEY ELEMENT IN ANY SPACE BASED 3!2 DESIGN IS THE ANTENNA )T DETERMINES RANGE SWATH COVERAGE AND REQUIRED MINIMUM TRANSMITTER POWER AND HAS A MAJOR INFLUENCE ON RESOLUTION AND DATA RATE 4HE -AGELLAN ANTENNA A M DIAMETER DISH WAS A SIGNIFICANT DEPARTURE FROM THE CONVENTIONAL HIGHLY ASYMMETRIC RECTANGULAR ANTENNAS THAT WERE THEN IN FAVOR FOR 3!2S
&)'52% !RTISTS IMPRESSION OF -AGELLAN OBSERVING THE SURFACE OF 6ENUS BACKLIT BY THE SUN FEATURING THE RADAR AND HIGH GAIN COMMUNI CATIONS ANTENNA AND THE SMALLER HORN ANTENNA FOR THE ALTIMETER #OURTESY OF .!3!
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&)'52% $ETAILS OF -AGELLANS ELLIPTICAL ORBIT DOMINATED BY ^ MINUTES OF DATA TAKE AND HOURS OF DATA DOWNLINK DURING EACH HOUR ORBIT PERIOD 'RAPHIC COURTESY OF .!3!
4HE VERTICAL DIMENSION OF THE ANTENNA TOGETHER WITH RANGE INCIDENCE AND WAVE LENGTH DETERMINED THE WIDTH OF THE ILLUMINATED SWATH ON THE SURFACE 4HIS PROVIDED AN UPPER BOUND ON THE IMAGED SWATH WIDTH WHICH IN THE CASE OF -AGELLAN WAS LESS THAN THE SWATH ACTUALLY ILLUMINATED 4HE IMAGED SWATH WIDTH WAS CHOSEN TO BE SOMEWHAT WIDER THAN THE ORBIT TO ORBIT TRANSLATION OF 6ENUS SURFACE DUE TO PLANET ROTATION 4HE PERIOD OF THE ELLIPTICAL ORBIT WAS SELECTED TO BE ABOUT THREE HOURS SO THAT IN SUCCESSION EACH IMAGING PASS OVERLAPPED AND EXTENDED THE SURFACE IMAGED ON PREVIOUS PASSES )N THE ALONG TRACK DIRECTION THE ANTENNA SIZE HAD FAR REACHING CONSEQUENCES 4HE THEORETICAL SINGLE LOOK AZIMUTH RESOLUTION AVAILABLE FROM THE -AGELLAN ANTENNA COULD BE ABOUT METERS 3ECTION 4HIS IS ON THE ORDER OF TIMES SMALLER THAN THE SCI ENCE REQUIREMENT OF METERS AZIMUTH RESOLUTION )T FOLLOWED THAT SINGLE LOOK M DATA COULD BE COLLECTED BY OPERATING THE RADAR ONLY OF THE TIME )F ., LOOKS WERE REQUIRED THEN THE IMPLIED OPERATING DUTY FACTOR WOULD BE ., LARGER BY A FACTOR OF ., 4HE RESULT IS THE BURST MODE 3ECTION IN WHICH THE RADAR OPERATES AT MUCH LESS THAN OF THE TIME "URST MODE IS A STANDARD STRATEGY FOR 3!2S DESIGNED TO EXPLORE THE -OON OR OTHER PLANETARY BODIES USING ANTENNAS WHOSE ALONG TRACK DIMENSION IS MUCH SMALLER THAN THE AZIMUTH RESOLUTION REQUIRED OF THE DATA 4HE LOOKS PARAMETER ., DESERVES SPECIAL COMMENT IN THE 3"2 CONTEXT SUMMARIZED BELOW 4HE -AGELLAN ANTENNA WAS USED AS THE HIGH GAIN ANTENNA FOR DATA DOWNLINK AS WELL AS FOR THE 3!2 $URING THE HIGH ALTITUDE SEGMENT OF EACH ORBIT THE SPACECRAFT WAS ORIENTED TO POINT THE ANTENNA TOWARD %ARTH 4HE ANTENNA HAD TWO FEEDS ONE AT 3 BAND (( POLARIZATION FOR THE RADAR AND 8 BAND CIRCULAR POLARIZATION FOR TELEMETRY !FTER EACH POLE TO POLE DATA COLLECTION THE TELEMETRY TRANSFERRED THE ACCUMULATED DATA TO ONE OF THE THREE $EEP 3PACE .ETWORK $3. RECEIVING STATIONS SO THAT IN CONSE QUENCE THE DATA DUMP KEPT PACE WITH THE DATA TAKE PER ORBIT /RBIT &OR REASONS DIRECTLY ATTRIBUTABLE TO PRINCIPLES OF ORBITAL MECHANICS IT WAS MUCH LESS COSTLY TO GO INTO AN ELLIPTICAL ORBIT AT 6ENUS RATHER THAN A CIRCULAR ONE 4HE FACT THAT IT WOULD BE CONSIDERABLY MORE DIFFICULT TO GET DECENT IMAGERY SUCCESSFULLY
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FROM AN ELLIPTICAL ORBIT WAS OF LITTLE CONCERN TO THE BUDGET MASTERS ALTHOUGH THE ELLIP TICAL ORBIT CONSTRAINT ATTRACTED MORE THAN A LITTLE ATTENTION FROM THE 3!2 DESIGN TEAM 4HE -AGELLAN RADAR HAD TO ADAPT TO VARIATIONS IN RELATIVE ALTITUDE FROM APPROXIMATELY KM NEAR THE EQUATOR TO MORE THAN KM OVER THE POLES 1UITE REASONABLY ONE MIGHT EXPECT THAT THE RESULTING IMAGERYLET ALONE THE IMPLIED TIMING AND SCAL ING ISSUESWOULD SUFFER AS A CONSEQUENCE 4HANKS TO THE MISSION DESIGN HOWEVER -AGELLAN IMAGE QUALITY IS SURPRISINGLY CONSISTENT POLE TO POLE 4HE REASONS PROVIDE AN IMPORTANT OBJECT LESSON 3INCE THE -AGELLAN RADAR WAS OPERATED IN BURST MODE IT WAS CONVENIENT AS WELL AS NECESSARY PRIOR TO EACH BURST TO SET THE MODE PARAMETERS WHICH IN GENERAL VARIED FROM BURST TO BURST #RITICAL PARAMETERS INCLUDED 02& RANGE GATE BURST LENGTH BURST PERIOD AND SPACECRAFT ROLL 4HE PARAMETER FILES WERE PREPARED IN ADVANCE BASED ON THE DATA COLLECTION GEOMETRY AND TURNED INTO COMMANDS TO BE GENERATED BY THE RADAR MAP PING SEQUENCING SOFTWARE 4HE RESULT WAS A SET OF ABOUT UNIQUE CONFIGURATIONS EACH TIED TO SPECIFIC SEGMENTS OF THE ORBIT )N OPERATION SUITABLE COMMANDS WERE PRE LOADED INTO THE ONBOARD 3!2 CONTROL PROCESSOR FOR EACH THREE DAY MAPPING INTERVAL )N ORDER TO OFFSET THE TENFOLD ALTITUDE CHANGE ON 3!2 IMAGE QUALITY THE 3!2 OPER ATING PROFILE WAS DESIGNED TO EXPLOIT A VARIETY OF INCIDENT ANGLES !T THE START OF EACH IMAGING PASS AT HIGH ALTITUDE THE INCIDENCE WAS SLEWED FROM STEEP NEAR THE POLE TO SHALLOW IN THE NEIGHBORHOOD OF THE EQUATOR BACK TO STEEP WHEN APPROACHING THE OPPOSITE POLE 4HIS INCIDENCE VARIATION HELPED TO OFFSET THE LARGE CHANGE IN RADAR RANGE TO THE IMAGED SWATH BUT IT MEANT ALSO THAT THE RANGE RESOLUTION AS EXPRESSED ON THE SURFACE VARIED AS A FUNCTION OF LATITUDE &OR A CONSTANT RADAR BANDWIDTH THE EFFEC TIVE SURFACE RANGE RESOLUTION AT SHALLOWER INCIDENCE IS IMPROVED OVER THAT ACHIEVED AT STEEPER INCIDENCE &ORTUNATELY AT STEEPER INCIDENCE AND HENCE AT LONGER RANGES THERE WAS MORE TIME AVAILABLE TO GATHER MORE LOOKS )MAGE 1UALITY ,OOKS AND RESOLUTION WORK TOGETHER TO DETERMINE THE IMAGE QUAL ITY READ hGEOPHYSICAL INFORMATION POTENTIALv OF 3!2 IMAGERY OVER NATURAL TERRAIN COMPOSED OF DISTRIBUTED SCATTERERS 4HE GOVERNING EXPRESSION IS THE 3!2 IMAGE QUAL ITY PARAMETER
13!2
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WHERE ., IS THE NUMBER OF STATISTICALLY INDEPENDENT LOOKS AND R2G AND R!Z ARE THE RANGE AND AZIMUTH RESOLUTION RESPECTIVELY ON THE SURFACE (ERE THE IMPORTANT GENERAL IZABLE LESSON IS THAT AN INCREASE IN NUMBER OF LOOKS CAN BE APPLIED TO OFFSET A DECREASE IN RANGE RESOLUTION WITHIN REASON AND IN THIS KIND OF EXPLORATORY SPACE BASED 3!2 DATA .OTE THAT BOTH LOOKS AND RESOLUTION REQUIRE SUPPORT IN BANDWIDTH )T FOLLOWS THAT 13!2 IS PROPORTIONAL TO THE PRODUCT OF THE RANGE AND AZIMUTH BANDWIDTHS HENCE PROPORTIONAL TO THE TWO DIMENSIONAL INFORMATION CAPACITY OF THE RADAR IN THE 3HANNON SENSE 4HIS PRINCIPLE WAS APPLIED WITH GREAT PROFIT TO THE -AGELLAN 3!2 DESIGN AS ILLUSTRATED BY 4ABLE &ROM THAT TABLE ONE CAN VERIFY THAT THE IMAGE QUALITY OF -AGELLAN DATA VARIED BY NO MORE THAN ^o POLE TO POLE IN SPITE OF LARGE VARIATIONS IN RADAR RANGE INCIDENT ANGLE AND GROUND RANGE RESOLUTION $ATA 2ATE -AGELLAN 3!2 DATA WERE RELAYED FROM 6ENUS TO %ARTH VIA THE $3. 4HIS MAJOR COMMUNICATION SYSTEM IMPOSED A WORKING LIMIT OF ABOUT KBITS ON THE 3!2 DATA TELEMETRY 7HEREAS THIS MAY SEEM RATHER LARGE IT IS MINUSCULE BY
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SPACE BASED 3!2 STANDARDS &OR EXAMPLE THE DIGITAL DATA RATE FOR THE %23 AND 2!$!23!4 %ARTH OBSERVING 3!2S IS ON THE ORDER OF -BITS .EWER DESIGNS CLAIM UP TO -BITS 3INCE THE -AGELLAN OBJECTIVE WAS TO IMAGE A SUBSTANTIAL POR TION OF THE SURFACE OF THE ENTIRE PLANET AT M RESOLUTION WITHIN THE LENGTH OF THE PRIMARY MISSION THE $3. DATA RATE CAPABILITY EMERGED AS THE TOUGHEST REQUIREMENT ON THE ENTIRE SYSTEM 2AW 3!2 DATA RATE IS PROPORTIONAL TO THE IMAGE QUALITY FACTOR SWATH WIDTH SPACE CRAFT VELOCITY AND THE NUMBER OF DIGITAL BITS PER DATA SAMPLE /F COURSE MEAN DATA RATE CAN BE RELAXED IF THE DATA FROM ANY GIVEN PASS CAN BE COLLECTED AND THEN PLAYED BACK AT A SLOWER RATE !LTHOUGH THIS STRATEGY WAS EXPLOITED BY THE -AGELLAN DESIGN TOLERANCE FOR WHICH WAS SET UP BY THE ELLIPTICAL ORBIT IT WAS NOT SUFFICIENT TO SOLVE THE LIMITED DATA RATE PROBLEM 4HE ONLY DEGREE OF FREEDOM REMAINING IN THE DATA RATE BUDGET WAS THE NUMBER OF BITS RETAINED FOR EACH SAMPLE IN THE RAW 3!2 DATASTREAM 7ORKING BACK THROUGH THE $3. CONSTRAINT IT TURNED OUT THAT THERE WERE ONLY TWO BITS AVAILABLE FOR -AGELLANS RAW 3!2 DATA 9ESA BIT 3!2 !ND AGAIN THE UNIQUE CHARACTERISTICS OF AN ORBITAL 3!2 MADE THIS AN ACCEPTABLE SOLUTION FOR THE -AGELLAN DESIGN 4HE KEY REQUIREMENTS FOR THIS PARADIGM ARE TWO AN EFFECTIVE SIGNAL ENCODING THAT IS VERY LARGE AND AN IMAG ING ENVIRONMENT THAT IS DENSE AND DOMINATED BY DISTRIBUTED RANDOM BACKSCATTER 0LANETARY 3!2S AND MANY %ARTH OBSERVING SPACE BASED RADARS EASILY SATISFY THESE REQUIREMENTS /NE MEASURE OF AN IMAGING RADARS EXTENSIVE SIGNAL ENCODING IS THE PRODUCT OF ITS RANGE AND AZIMUTH TIME BANDWIDTH PRODUCTS OR EQUIVALENTLY ITS POTEN TIAL TWO DIMENSIONAL COMPRESSION RATIO )N THE CASE OF 3!2 DATA THIS RATIO IS GIVEN BY THE AREA OF THE INSTANTANEOUS PULSE FOOTPRINT ANTENNA WIDTH BY PROJECTED PULSE LENGTH DIVIDED BY THE RESOLVED CELL AREA THE PRODUCT OF AZIMUTH AND RANGE RESOLU TION 4HIS RATIO VARIED BY MODE FOR -AGELLAN BUT IN GENERAL WAS WELL IN EXCESS OF WHICH TURNS INTO A GAIN IN DYNAMIC RANGE FROM THE SIGNAL DOMAIN TO THE IMAGE DOMAIN OF D" 4HE h BIT METHODv WAS BASED ON A "LOCK !DAPTIVE 1UANTIZER "!1 4HIS IN EFFECT IMPLEMENTED AN AUTOMATIC GAIN CONTROL !'# THAT SELECTED THE MOST INFLUENTIAL DIGITAL SAMPLES BITS FROM THE RAW 3!2 DATASTREAM !S DESIGNED FOR -AGELLAN THE DATA WERE DIGITIZED INTO BITS IN PHASE AND QUADRATURE )1 4HE ANALOG TO DIGITAL STAGE WAS FOLLOWED BY THE "!1 OPERATION WHICH SELECTED THE TWO MOST SIGNIFICANT BITS IN EACH )1 DATA PAIR RELATIVE TO A MEAN SIGNAL LEVEL THAT HAD BEEN ESTABLISHED FROM THE PREVIOUS BURST OF RECEIVED DATA 4HE MEAN SIGNAL LEVEL VARIED VERY SLOWLY BURST TO BURST SINCE ADJACENT BURSTS COVERED ESSENTIALLY THE SAME SCENE ELEMENTS 4HE MEAN SIGNAL LEVEL !'# SETTING WAS INCLUDED IN THE HEADER FOR EACH BURSTS DATA RECORD TO BE USED IN SUBSEQUENT 3!2 IMAGE FORMATION
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!LTHOUGH THE DYNAMIC RANGE OF THE RAW 3!2 DATA OUT OF A "!1 OPERATOR IS SEVERELY LIMITED THE POTENTIAL DYNAMIC RANGE OF THE RESULTING IMAGE DATA IS MUCH LARGER IT IS BOUNDED ABOVE BY THE PRODUCT OF THE INPUT DYNAMIC RANGE AND THE TWO DIMENSIONAL COMPRESSION RATIO OF THE 3!2 DATA 4HUS THE DYNAMIC RANGE CAPACITY AFTER PROCESSING FOR -AGELLAN IMAGERY WAS IN EXCESS OF D" 4HIS WAS WELL ILLUSTRATED IN THE MANY THOUSANDS OF IMAGE FRAMES FORMED FROM -AGELLANS 3!2 DATA (YBRID POLARITY !RCHITECTURE ! LEADING HIGH LEVEL OBJECTIVE OF A RADAR DES TINED FOR THE -OON -ARS OR ANY OTHER PLANETARY BODY IS TO MAXIMIZE ITS MEASUREMENT POTENTIAL WHILE ALSO MINIMIZING ITS RESOURCE DEMANDS PRINCIPALLY POWER AND MASS )F SENSITIVITY TO FROZEN VOLATILES IS A REQUIREMENT LEVIED ON A PLANETARY EXPLORATORY RADAR THEN THE SYSTEM SHOULD BE DUAL POLARIZED AND MUST TRANSMIT CIRCULAR POLARIZATION !S REVIEWED IN 3ECTION A DUAL POLARIZED RADAR MAXIMIZES ITS MEASUREMENT CAPABILI TIES ONLY IF IT RETAINS THE RELATIVE PHASE AS WELL AS THE MAGNITUDES OF THE TWO RECEIVED AMPLITUDES SUCH AS %( AND %6 IN THE LINEAR POLARIZATION BASIS )T HAS BEEN KNOWN SINCE THAT A QUASI MONOCHROMATIC %- FIELD CAN BE FULLY CHARACTERIZED BY THE FOUR 3TOKES PARAMETERS )N TERMS OF LINEARLY POLARIZED RECEIVED DATA THE 3TOKES PARAMETERS ARE 3 \ %( \ \ %6 \
3 \ %( \ \ %6 \
3 2E %( %6
3 )M %( %6
WHERE DENOTES COMPLEX CONJUGATE AND THE CARATS INDICATE AN AVERAGE TAKEN OVER SEVERAL SAMPLES #LEARLY THE RELATIVE PHASE BETWEEN THE TWO POLARIZATIONS IS AN ESSENTIAL FACTOR FOR TWO OF THE FOUR 3TOKES PARAMETERS $ATA EXPRESSED THROUGH THE 3TOKES PARAM ETERS ARE WELL SUITED TO BEING EXPLOITED BY MATRIX DECOMPOSITION METHODOLOGY &OR A GIVEN TRANSMITTED POLARIZATION THE VALUES OF THESE 3TOKES PARAMETERS ARE INVARIANT WITH RESPECT TO THE POLARIZATION BASIS OF THE RECEIVER )T FOLLOWS THAT THE OPTI MUM ARCHITECTURE IS HYBRID POLARITY CIRCULARLY POLARIZED ON TRANSMIT AND LINEARLY DUAL POLARIZED ON RECEIVE &IGURE 4HIS ARCHITECTURE REQUIRES LESS MASS AND OFFERS GREATER EFFICIENCY THAN ALTERNATIVES WHILE CAPTURING ALL OF THE POTENTIAL INFORMA TION IN THE BACKSCATTERED FIELD !N ANTENNA COMPRISED OF TWO LINEAR ARRAYS SUCH AS ( AND 6 WILL RADIATE A CIRCULARLY POLARIZED FIELD IF THE SETS OF ELEMENTS ARE DRIVEN SIMULTANEOUSLY AND n OUT OF PHASE AS SHOWN IN &IGURE )N PRACTICE THE AMPLITUDE WEIGHTING AND RELATIVE PHASING OF THE ARRAYS WILL SELDOM BE PERFECT !S A RESULT THE RADIATED FIELD WILL BE SOMEWHAT ELLIPTICAL RATHER THAN PURELY CIRCULAR 4HE HYBRID POLARITY ARCHITECTURE IS SELF CALIBRATING AND THEREFORE RELATIVELY ROBUST IN RESPONSE TO SUCH IMPERFECTIONS )N BRIEF UNDER THE CONDITION THAT R (( R 66 THE MEAN SIGNAL LEVEL IN THE TWO RECEIVE CHANNELS SHOULD BE EQUAL )N TERMS OF THE 3TOKES PARAMETERS 3 4HE ( AND 6 BACKSCATTER COEFFICIENTS WILL ALWAYS BE EQUIVALENT WHEN THE RADARS ILLUMINATION IS PERPENDICULAR TO THE SURFACE (ENCE ANY HYBRID POLARITY RADAR CAN SET UP THIS CONDITION BY THE SIMPLE EXPEDIENT OF LOOKING DOWN ON A HORIZONTAL SURFACE DURING A CALIBRATION EXERCISE $ISCREPANCIES IN EITHER AMPLITUDE OR PHASE WILL BE EVIDENT FROM SUCH DATA COLLECTED OVER A RANDOM DIS TRIBUTED SCENE 4HERE IS NO NEED FOR A KNOWN POINT TARGET REFERENCE IN THE FIELD OF VIEW 4HE 3TOKES PARAMETERS THAT CORRESPOND TO SUCH MEASUREMENTS ARE SUFFICIENT TO CHARAC TERIZE THE RELATIVE (6 PHASE OF THE TRANSMITTED FIELD AS WELL AS THAT OF THE RECEIVERS
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
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&)'52% 4HE HYBRID POLARITY 3!2 ARCHITECTURE FIRST USED BY THE -INI 2& LUNAR RADARS ON #HANDRAYAAN AND ,2/
£n°xÊ - // ," / ,3PACE BASED REMOTE SENSING SCATTEROMETERS MEASURE THE NORMALIZED BACKSCATTER WITH SUFFICIENT PRECISION AND ACCURACY TO DEDUCE THE VALUE OF ONE OR MORE PARAMETERS OF GEOPHYSICAL SIGNIFICANCE &OR EXAMPLE THE POWER REFLECTED FROM THE OCEAN BACK TO A RADAR IS A FUNCTION OF SURFACE ROUGHNESS AT THE SCALE OF THE RADARS WAVELENGTH WHICH IN TURN IS A FUNCTION OF THE LOCAL WIND %STIMATION OF WIND SPEED AND DIRECTION OVER THE OPEN OCEAN IS THE MOST COMMON APPLICATION FOR THESE INSTRUMENTS ! WIND SCAT TEROMETER WAS ADOPTED BY %5-%43!4 IN THE EARLY S AS A REQUIRED OPERATIONAL CAPABILITY WITH OPERATIONAL ACCURACIES OF o MS IN WIND SPEED AND on IN DIRECTION )N ADDITION TO OPEN OCEAN OBSERVATIONS CALIBRATED DATA FROM THIS CLASS OF 3"2 HAVE BEEN APPLIED TO A VARIETY OF LARGE AREA SURFACE FEATURES SUCH AS DETERMINATION OF SEA ICE COVERAGE MAPPING THE BOUNDARIES BETWEEN THE PRINCIPAL ICE ZONES OF 'REENLAND OR GLOBAL ESTIMATION OF TROPICAL DEFORESTATION )N ALL SUCH APPLICATIONS THE EMPHASIS IS ON MEASUREMENT OF MEAN REFLECTIVITY OVER LARGE AREAS RATHER THAN MAPPING FINE SPATIAL DETAIL 4HESE RADARS TYPICALLY HAVE RESOLUTIONS ON THE SCALE OF S OF KILOMETERS SUP PORTED OVER SWATHS OF KILOMETERS OR MORE )N THE OCEAN APPLICATION RELATIVELY SMALL CHANGES IN RADAR BACKSCATTER MAY COR RESPOND TO SUBSTANTIAL DIFFERENCES IN THE RETRIEVED WIND INFORMATIONe )T FOLLOWS THAT THE DOMINANT REQUIREMENT FOR THIS CLASS OF RADAR IS THE ACCURACY AND PRECISION OF THE RECEIVED POWER MEASUREMENT (OWEVER THE NEXT STEP VECTOR WIND RETRIEVALS TRANSFORMING THE RADAR BACKSCATTERED POWER INTO ACCURATE ESTIMATES OF WIND SPEED AND DIRECTIONIS FAR FROM TRIVIAL )NDEED THE TECHNIQUE FAILS FOR THE VERY LOW WIND SPEEDS THAT DO NOT GENERATE WAVELENGTH SCALE SURFACE ROUGHNESS )N THE LIMIT
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.OTE THAT BOTH ACCURACY AND PRECISION ARE REQUIRED 2ADAR BACKSCATTER BY ITS VERY NATURE IS A QUANTITY HAVING A LARGE STANDARD DEVIATION THAT CAN BE REDUCED ONLY BY EXTENSIVE AVERAGING "ECAUSE THE GEOPHYSICAL INTERPRETATION OF SCAT TEROMETRIC DATA OFTEN DEPENDS ON DISTINGUISHING BETWEEN TWO SIMILAR VALUES OF R THE RESULTS DEPEND CRITICALLY ON REDUCING THE UNCERTAINTY IN THE ESTIMATED VALUE AS WELL AS GETTING THE AVERAGE VALUE RIGHT
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AN OBLIQUE VIEWING RADAR SUCH AS A SCATTEROMETER WILL GENERATE VIRTUALLY NO BACK SCATTER FROM THE SEA SURFACE IN THE ABSENCE OF WIND DRIVEN WAVES EVEN IF THERE IS A SUBSTANTIAL SWELL IN THE REGION 6ECTOR 7IND 2ETRIEVAL 4HE NORMALIZED BACKSCATTER COEFFICIENT R FROM A WIND ROUGHENED OCEANIC SURFACE DEPENDS FOREMOST ON THE RADARS WAVELENGTH THE LOCAL ANGLE OF INCIDENCE AND THE POLARIZATION RESPECTIVELY 4HE WIND PARAMETERS TO BE ESTIMATED ARE ITS SPEED THE RELATIVE ANGLE IN THE HORIZONTAL PLANE BETWEEN THE WIND DIRECTION AND THE RADAR LINE OF SIGHT 4HE OCEANS REFLECTIVITY IS ALSO A FUNCTION OF OTHER FACTORS INCLUDING SURFACTANTS SUCH AS OIL SLICKS EITHER NATURAL OR ANTHROPOGENIC THE AIR SEA TEMPERATURE DIFFERENCE OR THE PRESENCE OF LARGE WAVES SUCH AS OCEANIC SWELL BUT THESE ARE OF LESS SIGNIFICANCE FOR THE PRESENT DISCUSSION 4HE REFLECTION COEFFICIENT R IS NONLINEAR WITH RESPECT TO THE WIND PARAMETERS &IGURE ILLUSTRATES THE RESPONSE FOR ONE POLARIZATION WHERE THE HORIZONTAL AXIS IS THE RELATIVE WIND DIRECTION AND THE VERTICAL AXIS IS THE NORMALIZED RADAR CROSS SEC TION 4HE SEVERAL CURVES EACH CORRESPOND TO A SPECIFIC WIND SPEED )N GENERAL UPWIND AND DOWNWIND ASPECTS PROVIDE STRONGER BACKSCATTER THAN CROSS WIND AND THE UPWIND ASPECT USUALLY IS A BIT STRONGER THAN DOWNWIND 7IND VECTOR DATA HAVE BEEN COLLECTED BY AIRBORNE SCATTEROMETERS FLYING IN CIRCLES LITERALLY OVER INSTRUMENTED TEST SITES 4HERE HAVE BEEN MANY ATTEMPTS OVER THE YEARS TO CONVERGE ON A SUITABLE MATHEMATI CAL MODEL FOR THIS BEHAVIOR WITH REASONABLE SUCCESS 4HERE ARE SEVERAL VECTOR WIND RETRIEVAL METHODS IN CURRENT USE INCLUDING #-/$ AND A NEURAL NETWORK MODEL 4HE DATA CLEARLY SHOW THAT MEASUREMENT OF RADAR BACKSCATTER AT ONLY ONE ASPECT ANGLE IS NOT SUFFICIENT TO DETERMINE WIND SPEED AND DIRECTION 4HE 3EASAT SCATTEROMETER USED TWO LOOK ANGLES SEPARATED BY n BUT THE RESULTING RETRIEVALS HAD AS MANY AS
&)'52% 4YPICAL BACKSCATTER STRENGTH VERTICAL AXIS FROM A WIND DRIVEN SEA SURFACE AS A FUNCTION OF WIND SPEED MODELED DATA AND THE WIND DIRECTION RELATIVE TO THE RADARS LOOK DIRECTION HORIZONTAL AXIS 3IMILAR FAMILIES OF CURVES CORRESPOND TO THE RADARS POLARIZATION USUALLY (( OR 66 AND ANGLE OF INCIDENCE #URVES SUCH AS THESE ARE DERIVED FROM A MODEL SUCH AS #-/$ SUBSEQUENTLY VERIFIED BY EXTENSIVE AIRBORNE MEASUREMENTS
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FOUR POTENTIAL SOLUTIONS WHICH PRESENTED AS DIRECTIONAL AMBIGUITIES 3PACE BASED WIND SCATTEROMETERS ARE CHARACTERIZED BY DIFFERING VIEWING GEOMETRIES EACH MOTI VATED BY THE NEED TO SUPPRESS DIRECTIONAL AMBIGUITIES WITHIN THE CONSTRAINT OF A PHYSI CALLY OR FINANCIALLY FEASIBLE IMPLEMENTATION -EASUREMENT 0RECISION #LEARLY R MUST BE MEASURED WITH AN ACCURACY AND PRECISION OF LESS THAN D" IF USEFUL WIND RETRIEVALS ARE TO BE DERIVED !CCURACY DEPENDS ON THE RADARS STABILITY AND ITS CALIBRATION 4HE CHALLENGE FOR SPACE BORNE SCATTEROMETRY IS TO DESIGN THE RADAR SUCH THAT THE PRECISIONTHE NORMALIZED STANDARD DEVIATION OF THE R MEASUREMENTSIS SUFFICIENTLY SMALL )N THE STANDARD TERMINOLOGY OF SCATTEROMETRY THE CLASSICAL PARAMETER IS +0 THE NORMALIZED STANDARD DEVIATION OF THE MEASUREMENT )N THE CASE OF A FAN BEAM SCATTEROMETER THAT EMPLOYS DOPPLER FILTERING THE GOVERNING EXPRESSION IS
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WHERE . IS THE NUMBER OF STATISTICALLY INDEPENDENT PULSES SUMMED INTO EACH R MEA SUREMENT 4 IS THE TRANSMITTED PULSE LENGTH " IS THE DOPPLER BANDWIDTH OF THE MEA SUREMENT CELL AND 3.2 IS THE SIGNAL TO NOISE RATIO +0 USUALLY IS CITED AS A PERCENT WHERE VALUES OF OR BETTER ARE THE OBJECTIVE .OTE FOR HIGH 3.2 THAT +0 CONVERGES TO .4" !T LOWER WIND SPEEDS +0 DEPENDS ON 3.2 AS WELL AS ON THE NUMBER OF STATISTICALLY INDEPENDENT LOOKS 4HE DETAILS OF ANY EXPRESSION SUCH AS THIS DEPEND ON THE UNDERLYING STATISTICAL MODEL WHICH IS GAUSSIAN IN THIS CLASSIC EXPRESSION (OWEVER THE GENERAL PRINCIPLE IS THAT THE SCATTEROMETER MUST PROVIDE MANY INDEPENDENT LOOKS TO REDUCE THE STANDARD DEVIATION OF THE R MEASUREMENT REGARDLESS OF THE STATISTICAL DISTRIBUTION OF THE OCEANS BACKSCATTER 4RENDS 6ECTOR WIND DATA HAVE BEEN ADOPTED BY OPERATIONAL METEOROLOGICAL AGENCIES SUCH AS %5-%43!4 )T IS LIKELY THAT SPACE BASED MICROWAVE ASSETS WILL CONTINUE TO BE USED FOR THE FORESEEABLE FUTURE TO PROVIDE THESE DATA 4HE SUCCESS OF 3EA7INDS DISCUSSED LATER IN THIS SECTION SUGGESTS THAT THE CONICAL SCAN PARADIGM WILL BE THE BASIS FOR FUTURE VECTOR WIND SCATTEROMETER DESIGN 4HAT SAID THERE ARE TWO SPACE BASED ALTERNATIVES FOR MEASURING VECTOR WINDS BY MICROWAVE MEANS ACTIVE AND PASSIVE 2ADARS OFTEN ARE UNPOPULAR ON SPACECRAFT THAT HOST OTHER INSTRUMENTS OF WHICH SOME MAY BE COMPROMISED BY RADIO FREQUENCY INTER FERENCE 2&) GENERATED BY A NEARBY MICROWAVE TRANSMITTER 2ADARS ALSO REQUIRE MORE POWER FROM THEIR HOST SPACECRAFT THAN PASSIVE SYSTEMS 4HESE AND RELATED CONSIDER ATIONS MOTIVATED THE DEVELOPMENT OF 7IND3AT A PASSIVE INSTRUMENT THAT ESTIMATES NEAR SURFACE VECTOR WINDS BY 3TOKES PARAMETER ANALYSIS OF THE MICROWAVE EMISSIVITY FROM THE OCEAN SURFACE 7IND3AT IS ONE OF TWO INSTRUMENTS ABOARD THE #ORIOLIS SATEL LITE LAUNCHED IN 4HE OPERATIONAL RELIABILITY OF PASSIVE VECTOR WIND DATA RELATIVE TO SCATTEROMETRIC MEASUREMENTS REMAINS AN OPEN ISSUE 3CATTEROMETRIC DATA ARE BEING EXPLOITED FOR MANY PURPOSES OTHER THAN OCEANIC VEC TOR WINDS !LTHOUGH THE hIMAGESv GENERATED BY A SPACE BASED SCATTEROMETER MAY HAVE ONLY KM RESOLUTION THEIR WIDE SWATH AND FREQUENT REVISIT INTERVALS ARE WELL SUITED TO SYNOPTIC COVERAGE OF GLOBAL SCALE PHENOMENA 4HE MULTI YEAR HISTORY OF SCATTEROMET RIC RADARS PROVIDES AN IMPORTANT DATA SET FOR CLIMATE CHANGE STUDIES AS WELL AS MONI TORING SEASONAL VARIATIONS 3UITABLE APPLICATIONS INCLUDE SEA ICE COVER LARGE ICEBERGS CONTINENTAL ICE SHEETS VEGETATION AND SOIL MOISTUREn
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&LIGHT 3YSTEMS 2AD3CAT 4ABLE WAS THE NAME GIVEN TO THE RADIOMETER SCATTEROMETER PORTION OF THE 3 +U BAND INSTRUMENT ABOARD 3KYLAB 4HE TOP LEVEL OBJECTIVES OF THIS EXPERIMENT WERE TO PROVIDE THE NEAR SIMULTANEOUS MEASUREMENT OF MICROWAVE BACKSCATTER AND EMISSIVITY OF LAND AND OCEAN ON A GLOBAL SCALE AND TO PROVIDE ENGINEERING DATA FOR USE IN DESIGNING SPACE RADAR ALTIMETERS 4HE EQUIP MENT SHARED A COMMON GIMBALED ANTENNA 4HE SCATTEROMETER MEASURED THE NORMALIZED BACKSCATTER COEFFICIENT OF OCEAN AND TERRAIN AS A FUNCTION OF INCIDENCE RANGING FROM n TO n !LTHOUGH ONLY SPARSE COVERAGE OF SELECTED SITES WAS POSSIBLE THE DATA WERE SUFFICIENT TO DEMONSTRATE THE POTENTIAL OF SPACE BASED RADAR MEASUREMENT OF SURFACE WIND VECTORS OVER THE OCEAN 4HE 3 ZONE OF ACCESS WAS FORWARD AND TO EITHER SIDE OF THE SPACECRAFT GROUND TRACK &OR SELECTED MEASUREMENTS THE BEAM WAS POINTED IN THE ALONG TRACK DIRECTION TO FIXED ANGLES OF AND WITH SUFFICIENT DWELL TIME AT EACH ANGLE TO PERMIT AVERAGING TO ACHIEVE APPROXIMATELY PRECISION 2AD3CAT DATA COLLECTED OVER THE !MAZON RAIN FOREST SUGGESTED THAT THE UNIFORMITY OF THE OBSERVED BACKSCATTER WOULD BE A STABLE CALIBRATION REFERENCE FOR SPACE BASED RADARS WHICH HAS SINCE BEEN VALIDATED AS A STANDARD TECHNIQUE 3!33 THE 3EASAT ! 3ATELLITE 3CATTEROMETER WAS THE FIRST SPACE BASED RADAR DESIGNED SPECIFICALLY TO MEASURE OCEANIC WINDS )T WAS A MULTI FAN BEAM INSTRUMENT COMPRISED OF TWO SETS OF TWO DUAL POLARIZED ANTENNAS (( AND 66 EACH ^ M IN LENGTH WHOSE FAN SHAPED BEAMS POINTED TO n AND n TO EITHER SIDE OF THE ORBIT PLANE )NCIDENCE SPANNED n TO n COVERING A KM WIDE SWATH ON EACH SIDE #ALIBRATION DATA TAKEN OVER THE RAIN FOREST WERE USED TO REDUCE ANTENNA GAIN UNCER TAINTY TO LESS THAN D" 3INCE 3EASAT WAS NOT YAW STEERED THE FORE AND AFT FOOTPRINTS WERE MISREGISTERED DUE TO %ARTH ROTATION WHICH REDUCED THE USEFUL SWATH AT LOWER LATITUDES TO ABOUT KM 4HE VALUE OF +P VARIED FROM TO OVER THE OCEAN UNDER MODERATE TO HIGH SEA STATES BUT DEGRADED TO FOR LOWER WIND SPEEDS AND TO FOR VERY LOW BACKSCATTER FROM NON OCEANIC SURFACES 4HE ACCURACIES OF WIND SPEED AND DIRECTION OVER n MS WERE o MS AND o O RESPECTIVELY 4HE DATA WERE NOT SUFFICIENT TO AVOID DIRECTIONAL AMBIGUITIES HOWEVER .OMINAL RESOLUTION WAS KM DETERMINED BY THE INTERSECTION OF THE ANTENNA PATTERN AND ISO DOPPLER CONTOURS 4HE RADAR OPERATED AT '(Z RADIATING A PEAK POWER OF 7 AT DUTY FACTOR FROM A TRAVELING WAVE TUBE AMPLIFIER 474! 4HE WAVEFORM WAS MODULATED #7 4HE RECEIVER FRONT END WAS A TUNNEL DIODE AMPLIFIER WHICH MAINTAINED THE NOISE FIGURE TO BE LESS THAN D" AT ALL OPERATING TEMPERATURES -EAN INPUT POWER WAS 7 DC THE INSTRUMENT MASS WAS KG
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73 ABOARD THE %23 AND %23 SPACECRAFT OF %3! DENOTES THE SCATTEROMETER MODE EMBEDDED IN THEIR # BAND !-) RADAR INSTRUMENTATION 4HESE SCATTEROMETERS USED THREE FAN BEAM ANTENNAS WHOSE FOOTPRINTS WERE ORIENTED AT n n AND n WITH RESPECT TO THE SATELLITE TRACK 4HE TWO OUTER ANTENNAS ARE M LONG .OTE THAT THE SPACECRAFT HAD TO BE YAW STEERED TO MAINTAIN THIS FOOTPRINT GEOMETRY OVER THE ROTATING %ARTH 4HE # BAND OPERATING FREQUENCY ALTHOUGH A DEPARTURE FROM SPACE BASED PRECEDENT RESULTED FROM USE OF THE SAME 2& HARDWARE AS THE 3!2 MODE !S A CONSEQUENCE SIMULTANEOUS 3!2 AND SCATTEROMETER OPERATIONS WERE NOT POSSIBLE )N CONTRAST TO +U BAND THE # BAND DATA WERE LESS DEGRADED BY RAIN AND PROVED TO BE MORE RELIABLE FOR HIGHER WIND SPEEDS 4HE ANTENNA SWATHS SPANNED KM FROM WHICH THE AVERAGED DATA FROM THE THREE LOOK DIRECTIONS WERE COLOCATED INTO KM RESOLUTION CELLS POSTED ON A KM GRID !3#!4 THE !DVANCED 3CATTEROMETER ABOARD -ET/P IS ESSENTIALLY AN IMPROVED VERSION OF THE %23 INSTRUMENTS )T IS A STAND ALONE RADAR DESIGNED FOR OPERATIONAL USE IT DOES NOT HAVE TO TIME SHARE ONBOARD ELECTRONICS AS WAS THE CASE WITH THE SCAT TEROMETER IN THE !-) SUITE )T COVERS SWATHS ON BOTH SIDES OF THE SATELLITE GROUND TRACK 4HE NEAR EDGE OF THESE KM SWATHS ARE OFFSET KM FROM NADIR SPANNING nnn n INCIDENCE 4HE D" RADIOMETRICALLY ACCURATE DATA ARE AVERAGED TO ACHIEVE +P FROM HIGH UP WIND SPEED TO LOW SPEED CROSS WIND ASPECT 4HE RESULT ING VECTORS FOR NEAR SURFACE WINDS COVER n MS WITH ACCURACY o MS AND o n 4HE RADAR OPERATES AT '(Z RADIATING MS LINEAR FREQUENCY MODULATED ,&- PULSES AT 7 PEAK POWER FROM COMBINED 'A!S &%4 DEVICES /NLY ONE ANTENNA IS ACTIVE FOR S AT A TIME THE OPERATION CYCLES AROUND THE SIX ANTENNAS IN SEQUENCE 4HE INSTRUMENT MASS IS KG INPUT POWER REQUIRED IS 7 4HANKS TO ONBOARD PROCESSING THE INHERENT DATA RATE IS REDUCED FROM -BITS TO AN AVERAGE OF KBITS TO THE -ET/P PAYLOAD DATA HANDLING SYSTEM .3#!4 THE .!3! 3CATTEROMETER PROVIDED TO *APAN AS PART OF THE !DVANCED %ARTH /BSERVING 3ATELLITE !$%/3 PAYLOAD WAS AN UPGRADED VERSION OF 3!33 .3#!4 USED SIX DUAL POLARIZED STICK ANTENNAS M LONG FOUR OF WHICH WERE AIMED AT o n ( POLARIZED AND on 6POLARIZED FROM THE SURFACE TRACK AND THE TWO MIDBEAM ANTENNA PATTERNS WERE ALIGNED AT n AND n EACH ( AND 6 POLARIZED 4HE THIRD BEAM ON EACH SIDE HELPED TO REMOVE THE FOURFOLD DIRECTIONAL AMBIGUITIES THAT PLAGUED 3!33 WIND RETRIEVALS 4WO KM WIDE SWATHS WERE COVERED AT KM RESOLUTION )N ORDER TO SUPPORT KM ALONG TRACK RESOLUTION THE RADARS SEQUENCER HAD TO CYCLE THROUGH ALL ANTENNA PATTERNS WITHIN S RESULTING IN A MAXIMUM DWELL TIME OF MS WITHIN EACH OF THE EIGHT FOOTPRINTS #ROSS BEAM RESOLUTION WAS DETERMINED BY DOPPLER ANALYSIS (OWEVER SINCE THE MEAN DOPPLER OFFSET WAS A FUNCTION OF ANTENNA ORIENTATION AS WELL AS INCIDENCE THE RETURN FROM EACH DIRECTION NEEDED ITS OWN ,/ OFFSET 4HE ANTENNAS PEAK GAIN WAS D" DIRECTED TOWARD MAXIMUM RANGE .3#!4S MASS WAS KG REQUIRED INPUT POWER WAS 7 4HE 2& SYSTEM WAS BUILT AROUND REDUNDANT 474!S TRANSMITTING MODULATED MS PULSES AT A 02& OF (Z PEAK POWER 7 3EA7INDS MARKS A SIGNIFICANT DEPARTURE FROM THE hSTICK ANTENNASv OF PRIOR WIND SCATTEROMETERS RELYING INSTEAD ON A DISH ANTENNA ROTATING AT 20- TO SWEEP ITS TWO BEAMS OVER A NADIR CENTERED SWATH KM WIDE &IGURE 4HE FIRST 3EA7INDS MISSION WAS ABOARD 1UIK3#!4 MOBILIZED BY .!3! AND LAUNCHED IN *UNE AS A RAPID RESPONSE TO THE PREMATURE LOSS OF !$%/3 IN *UNE 4HE SECOND 3EA7INDS WAS EMBARKED ON *APANS !$%/3 )) "OTH INSTRUMENTS OPERATE AT +U BAND K(Z RADIATING 7 MS PULSES AT (Z 02& SPLIT EQUALLY BETWEEN THE TWO ANTENNA BEAMS 4HE TRANSMITTER IS A 474! BASED ON .3#!4 HERITAGE 4HE MODULATED PULSE BANDWIDTH IS K(Z WHICH IS MAINTAINED WITHIN AN K(Z FILTER IN THE RECEIVER 4HE RECEIVED DATA MUST BE COMPENSATED TO OFFSET THE DOPPLER SHIFT WHICH VARIES
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&)'52% 4HE 3EAWINDS SCATTEROMETER AS EMBARKED ON *APANS !$%/3 )) SPACECRAFT 4HE RADAR DRIVES THE CONICALLY SCANNED REFLECTOR ANTENNA WHICH TAKES UP MOST OF THE REAL ESTATE ON THE %ARTH VIEWING FACE OF THE SATELLITE
SINUSOIDALLY OVER -(Z DURING EACH ANTENNA ROTATION )NSTRUMENT MASS IS KG REQUIRED INPUT POWER IS 7 4HESE NUMBERS ILLUSTRATE THE PRINCIPAL ADVANTAGES OF THE ARCHITECTURE PROVIDING GREATER COVERAGE WITH LESS MASS AND POWER IN CONTRAST TO THE STICK ANTENNA ARCHITECTURE 3YSTEM SENSITIVITY ACCOMMODATES R IN THE RANGE n D" TO n D" 4HE ANTENNA IS A M REFLECTOR GAIN ^ D" WITH TWO FEEDS RESULT ING IN A PAIR OF PENCIL BEAMS AT n ( POLARIZATION AND n INCIDENCE 6 POLARIZATION 4HE ILLUMINATION GEOMETRY ALSO IS ADVANTAGEOUS BECAUSE THE INCIDENCE IS THE SAME FOR ALL ASPECT ANGLES 4HE BEAM LIMITED FOOTPRINTS ARE APPROXIMATELY KM BY KM &OLLOWING ONBOARD PROCESSING THE AVERAGE DATA RATE IS KBITSS 3EA7INDS PERFOR MANCE IS AT LEAST COMPARABLE TO OTHER WIND SCATS WIND SPEED AND DIRECTION ACCURACY BEING MS TO MS AT MS AND n RESPECTIVELY .OMINAL SURFACE RESOLUTION IS KM ADVANCED PROCESSING REDUCES THIS TO ^ KM !LTHOUGH THE SWATH IS KM WIDE THE VARIETY OF ASPECT AND POLARIZATION COVERAGE LIMITS THE SCIENCE COMPLIANT WIND VECTOR RETRIEVALS TO STRIPS FROM KM TO KM EITHER SIDE OF THE GROUND TRACK !QUARIUS 4HE !QUARIUS MISSION IS DESIGNED TO MAP SEA SURFACE SALINITY FOR WHICH , BAND RADIOMETRIC SENSING OF THE OCEANS EMISSIVITY IS THE PRIMARY MEASURE MENT (OWEVER EMISSIVITY IS A FUNCTION OF THE ROUGHNESS OF THE SURFACE AS WELL AS ITS TEMPERATURE AND DIELECTRIC CONSTANT WHICH IS THE VARIABLE OF INTEREST 4HE !QUARIUS PAYLOAD INCLUDES AN , BAND -(Z SCATTEROMETER TO MEASURE SURFACE ROUGHNESS 4HE SCATTEROMETER AND RADIOMETER SHARE THE SAME M DIAMETER REFLECTOR ILLUMINATED BY THREE OFFSET FEEDS WHICH GENERATE THREE SIDE LOOKING BEAMS AT n n AND n INCIDENCE THUS SWEEPING OUT STRIPS OF COVERAGE AS THE SPACECRAFT MOVES ALONG ITS ORBIT 4HE SCATTEROMETER IS FULLY POLARIZED (( (6 6( AND 66 0EAK TRANSMITTED POWER IS ^ 7 PULSE LENGTH IS MS SUFFICIENT TO SUPPORT SEA SURFACE R OVER THE RANGE D" TO n D" 2ESOLUTION IS MODEST AT ^ KM 4HE SCATTEROMETER AND RADI OMETER SHARE ELECTRONICS #OMBINED INSTRUMENT MASS IS ^ KG AND REQUIRED PRIME POWER IS ^ 7
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£n°ÈÊ , ,Ê-"1 ,)N ITS MOST GENERAL FORM A RADAR SOUNDER IS A DEVICE WHOSE TRANSMISSIONS ARE DESIGNED TO PENETRATE THE VOLUME OF A TARGET MEDIUM FROM WHICH THE WAVEFORM OF THE RESULTING BACKSCATTER INDICATES VARIATIONS IN DIELECTRIC CONTRASTS AS A FUNCTION OF DEPTHo !S A SOUNDER PASSES OVER AN ILLUMINATED REGION THE SEQUENCE OF RANGING WAVEFORMS GENER ATES A PROFILE WHICH IS A TWO DIMENSIONAL REFLECTIVITY CROSS SECTION OF THE SURVEYED VOLUME 0ENETRATION DEPTH IN GENERAL INCREASES WITH WAVELENGTH AND ALSO WITH RADIATED POWER /N THE OTHER HAND REFLECTIVITY DEPENDS ON THE DIELECTRIC CONTRASTS BETWEEN INTERNAL LAYERS A MATERIALS DIELECTRIC CONSTANT IS ALSO A FUNCTION OF WAVELENGTH )T FOLLOWS THAT SPACE BASED RADAR SOUNDERS MUST CHOOSE A FREQUENCY AND BANDWIDTH THAT BALANCE THE OFTEN CONFLICTING REQUIREMENTS OF PENETRATION REFLECTIVITY AND RESOLUTION UNDER THE CONSTRAINTS OF AVAILABLE POWER AND ANTENNA APERTURE 4HE SPACE BASED RADAR SOUNDERS HIGHLIGHTED IN 4ABLE FALL NATURALLY INTO TWO GROUPS SUBSURFACE AND ATMOSPHERICIONOSPHERIC )T IS EVIDENT THAT THE SUBSURFACE SOUNDERS ALL ARE AT RELATIVELY LOW FREQUENCY IN CONTRAST TO THE ATMOSPHERIC SOUNDERS AT MUCH HIGHER FREQUENCY 4HE IONOSPHERIC SOUNDING MODE OF -!23)3 IS A SPECIAL CASE ELABORATED BELOW 3UBSURFACE 3OUNDINGnFLIGHT 3YSTEMS 3UBSURFACE SOUNDING FROM A SPACE BASED RADAR IS CONSIDERABLY MORE CHALLENGING THAN FROM A SURFACE MOUNTED '02 #HAPTER OR A VERY LOW ALTITUDE AIRCRAFT /F COURSE ONCE RADAR SIGNALS PENETRATE THE SURFACE THE USUAL VOLUMETRIC ATTENUATIONS AND REFLECTIONS OCCUR !S WITH ANY '02 LARGE DYNAMIC RANGE IS REQUIRED SINCE THE SIGNALS OF INTEREST MAY BE WEAKER THAN COMPETING RETURNS BY D" OR MORE 2ADAR SOUNDING TO APPRECIABLE DEPTH IS POSSIBLE ONLY IN DRY MATERIALS SUCH AS LUNAR REGOLITH OR IN VERY COLD LOW LOSS ICE 4!",% 2ADAR 3OUNDERS
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!POLLO -ARS %XPRESS -2/ 3%,%.% 42--ARS %XPRESS #LOUD3AT '0-
n n n n n
,UNAR SUBSURFACE -ARS SUBSURFACE -ARS SUBSURFACE ,UNAR SUBSURFACE 2AIN -ARS IONOSPHERE %ARTH CLOUD PROFILES 2AIN
-(Z -(Z -(Z -(Z '(Z n -(Z '(Z '(Z
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o 4HE TERM SOUNDER USUALLY ASSOCIATED WITH ACOUSTIC ECHO SOUNDING DERIVES FROM MANY CENTURIES OF OCEANIC DEPTH MEASUREMENTS USING LEAD LINES AND THE LIKE 4HE LOGICAL EXTENSION FROM ACOUSTIC TO ELECTROMAGNETIC METHODOLOGY IS A SMALL STEP IN COMPARISON
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)N ADDITION TO THE USUAL '02 CONSIDERATIONS TWO SPACE SPECIFIC ISSUES ARISE NEITHER OF WHICH CAN BE SOLVED BY THE USUAL EXPEDIENT OF INCREASING THE RADARS TRANSMITTED POWER 4HE FIRST PROBLEM IS CLUTTER &ROM ORBITAL ALTITUDE SCATTERERS ON THE SURFACE FAR FROM NADIR MAY GENERATE STRONG BACKSCATTER THAT APPEARS AT THE SAME RADAR RANGE AS THE SIGNALS REFLECTED FROM DEPTH AS SUGGESTED IN &IGURE 4HE PROBLEM IS COM POUNDED WITH INCREASING ALTITUDE AND BY THE FACT THAT AT THE LONG WAVELENGTHS REQUIRED FOR DEEPER PENETRATION THE SIZE CONSTRAINTS ON A SPACECRAFT MOUNTED ANTENNA DICTATE THAT THE ILLUMINATION PATTERN WILL HAVE LITTLE OR NO DIRECTIVITY 0ROCESSING OVER GROUPS OF RETURNS TO REDUCE THE EFFECTIVE WIDTH OF THE BEAM CAN BE HELPFUL $OPPLER BASED TECHNIQUES ARE APPLICABLE TO THE ALONG TRACK DIRECTION (OWEVER THE ORBITS ALTI TUDE VELOCITY PARAMETER 4ABLE MAY BE SO LARGE THAT THE AVAILABLE AMBIGUITY FREE RANGE DOPPLER WINDOW IS TOO SMALL TO BE USEFUL .ARROWING THE EFFECTIVE ANTENNA PAT TERN IN THE CROSS TRACK DIRECTION PRESENTS EVEN MORE OF A CHALLENGE 4HE SECOND PROBLEM IS RANGE SIDELOBES &ROM ORBITAL ALTITUDES AND FROM A REALISTIC SPACECRAFT IT IS NOT FEASIBLE TO TRANSMIT A SIMPLE SHORT PULSE THAT HAS SUFFICIENT ENERGY TO GENERATE USEFUL REFLECTIONS FROM DEPTH ,ONG MODULATED PULSES ARE THE ONLY PRACTICAL METHOD 5NFORTUNATELY THE SPECULAR COMPONENT OF SURFACE REFLECTION USUALLY IS VERY STRONG AT THE LONG WAVELENGTHS REQUIRED FOR SUBSURFACE SOUNDING 0ULSE COMPRESSION OF THE SURFACE RETURN GENERATES RANGE SIDELOBES WHICH APPEAR AT DEPTHS THAT COULD EASILY OVERWHELM THE WEAKER REFLECTIONS FROM THE INTERNAL STRUCTURE 4HE STANDARD STRATEGY TO MITIGATE THIS PROBLEM IS RIGOROUS SIDELOBE CONTROL REQUIRING SEVERE PULSE AMPLITUDE WEIGHTING AND STRICT CONTROL OF PHASE AND AMPLITUDE LINEARITY $UE TO THE LARGE FOOTPRINT OF A SPACE BASED SOUNDER AND THE NEED TO SALVAGE ALL POSSIBLE CONTRIBUTIONS OF SIGNALS FROM DEPTH IT IS STANDARD PRACTICE TO ASSUME THAT THE DOMINANT IN SITU RETURNS ARISE FROM SPECULAR SCATTERING HENCE FROM EXTENDED HORIZONTAL LAYERS 4HE CONTRIBUTING AREA IS DETERMINED BY THE RADIUS R& OF THE FIRST &RESNEL ZONE R& HL IN FREE SPACE WHERE H IS THE ALTITUDE OF THE RADAR ABOVE THE SURFACE 4HE RADIUS IS SOMEWHAT LARGER WITHIN THE MEDIUM SINCE THE SPHERICAL WAVEFRONT IS FLAT TENED DUE TO THE SLOWER SPEED OF IN SITU PROPAGATION !,3% 4HE !POLLO ,UNAR 3OUNDER %XPERIMENT WAS A COMBINATION IMAGER AND SOUNDER OPERATING AT WAVELENGTHS OF M M AND M 4HE !,3% SOUNDER
&)'52% 4WO PROBLEMS THAT CHALLENGE SPACE BASED SUB SURFACE SOUNDING ARE RANGE COINCIDENT COMPETITION BETWEEN THE DESIRED RETURN FROM DEPTH AND SURFACE CLUTTER AND RANGE SIDELOBES FROM THE VERY STRONG RETURN FROM THE TOP SURFACE AT NADIR
30!#% "!3%$ 2%-/4% 3%.3).' 2!$!23
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MODE WAS DESIGNED TO MEASURE SUBSURFACE HORIZONS IN THE LUNAR DIELECTRIC CONSTANT IN BOTH SIDE LOOKING AND DOWN LOOKING VIEWING GEOMETRY 4HE INSTRUMENT WAS BASED ON SYNTHETIC APERTURE RADAR 3!2 PRINCIPLES 4HE DATA WERE RECORDED DIRECTLY ONTO MM PHOTOGRAPHIC FILM WHICH WAS PROCESSED THROUGH A COMBINATION OF OPTICAL AND DIGITAL MEANS FOLLOWING RETURN OF !POLLO TO %ARTH /PTICAL PROCESSING WAS THE STATE OF THE ART BACK IN FOR 3!2 DATA 0ENETRATION DEPTHS PROVED TO BE APPROXI MATELY PROPORTIONAL TO WAVELENGTH 4HE RADARS WAVEFORM WAS CONSTRAINED SO THAT ALL SIDELOBES WERE AT LEAST D" BELOW THE MAIN BEAM PEAK FOR ALL RESPONSES BEYOND THREE IMPULSE WIDTHS OF THE COMPRESSED SIGNAL !MPLITUDE AND PHASE LINEARITY WERE CON STRAINED TO BE BETTER THAN AND RADIAN RESPECTIVELY 4HE TRANSMITTED PULSES WERE LINEAR &- AT BANDWIDTH IN ALL THREE BANDS .OMINAL FREE SPACE RESOLUTIONS WERE M M AND M !NTENNA GAINS WERE D" D" AND D" 4HESE LOW NUMBERS FOLLOW FROM THE POOR DIRECTIVITY OF THE ANTENNA 4RANSMITTED AVER AGE POWER WAS 7 7 AND 7 0ENETRATION DEPTHS WERE PREDICTED TO BE M M AND M WHICH TURNED OUT TO BE CONSISTENT WITH !,3%S PERFORMANCE -!23)3 4HE %UROPEAN 3PACE !GENCYS -ARS %XPRESS SPACECRAFT INCLUDES THE -ARS !DVANCED 2ADAR FOR 3UBSURFACE AND )ONOSPHERIC 3OUNDING INSTRUMENT THE FIRST ORBITAL SOUNDER TO FLY SINCE !,3% -!23)3 IS A MULTIFREQUENCY DOWN LOOKING RADAR THAT RADIATES -(Z PULSES IN ONE OF FOUR BANDS CENTERED ON THE FREQUENCIES CITED IN 4ABLE -ARS %XPRESS IS IN AN ELLIPTICAL ORBIT SUBSURFACE SOUNDING OPERATIONS ARE RESTRICTED TO THE LOWER KM TO KM ALTITUDES 3OUNDING IS FURTHER LIMITED BY THE IONOSPHERE WHICH PREVENTS EFFECTIVE RADIO WAVE PROPAGATION TO THE SURFACE AT FREQUENCIES BELOW THE PLASMA FREQUENCY F WHICH AT -ARS IS ^ -(Z ON THE SUNLIT SIDE AND ^ -(Z ON THE DARK SIDE 4HE IONOSPHERE INDUCES A FREQUENCY DEPENDENT TIME DELAY ON THE SIGNAL ACCORDING TO THE INDEX OF REFRACTION N WHERE N ; F F = 4HE RESULTING DISPERSION DISTORTS THE RADAR MODULATION WHICH MUST BE COMPENSATED BEFORE PULSE COMPRESSION 4HE M DIPOLE ANTENNA ORIENTED ORTHOGONAL TO THE ORBIT PLANE IS ONLY WEAKLY DIRECTIVE WITH A D" GAIN 4HE TWO M LONG ELEMENTS WERE NOT UNFURLED UNTIL TWO YEARS INTO THE MISSION DUE TO CONCERNS ABOUT THEIR POTENTIAL FOR DAMAGING THE SPACECRAFT DURING DEPLOYMENT 4HE EFFECTIVE CROSS TRACK FOOTPRINT IS ON THE ORDER OF KM 4HE ALONG TRACK FOOTPRINT IS ABOUT KM WHICH IS THE RESULT OF ONBOARD COHERENT DOPPLER PROCESSING 4HIS STRATEGY REDUCES THE IMPACT OF OFF NADIR CLUTTER ARISING FROM SOURCES IN THE ALONG TRACK DIRECTION 4HE TECHNIQUE IMPROVES THE SUBCLUTTER VISIBILITY BY D" OR MORE 4HE RADARS MASS AND INPUT POWER ARE KG AND 7 0EAK RADIATED POWER IS 7 4HE SYSTEM NOISE FLOOR IS ABOUT D" BELOW THE MEAN SURFACE RETURN WHICH ESTABLISHES THE DYNAMIC RANGE THAT LIMITS DEPTH OF PENETRA TION -!23)3 HAS PERFORMED AS INTENDED WITH EARLY RESULTS FROM THE POLAR LAYERED DEPOSITS FOR EXAMPLE 3(!2!$ 4HE 3HALLOW 2ADAR SOUNDER WAS DESIGNED TO COMPLEMENT -!23)3 )N GENERAL TERMS IT HAS HIGHER RESOLUTION AT A HIGHER FREQUENCY DESIGNED TO PROVIDE SHARPER DIFFERENTIATION OF THE UPPER SEVERAL HUNDRED METERS OF THE SURFACE OF -ARS 3(!2!$ TRANSMITS A -(Z LINEAR &- SIGNAL CENTERED AT -(Z 4HEORETICAL VERTI CAL RESOLUTION IS M IN MATERIAL HAVING A PERMITTIVITY OF 4HE M DIPOLE ANTENNA HAS A FREQUENCY DEPENDENT TWO WAY GAIN OF D" TO D" 4HE EFFECTIVE BEAM FOOTPRINT AFTER DOPPLER PROCESSING IS ^ KM ALONG TRACK AND ^ KM ACROSS TRACK .OMINAL 3.2 WITH RESPECT TO THE SURFACE RETURN IS IN EXCESS OF D" )NSTRUMENT MASS IS ^ KG INPUT POWER IS ^ 7 3(!2!$ MEASUREMENTS STARTED LATE ONLY WHEN THE -2/ ORBIT WAS CIRCULARIZED AFTER SIX MONTHS OF AEROBRAKING
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3%,%.% 4HE *APANESE LUNAR MISSION 3%,%.% INCLUDES A -(Z ,UNAR 2ADAR 3OUNDER ,23 AS ONE OF ITS PAYLOAD INSTRUMENTS 4HE ORBIT IS CIRCULAR AT KM ALTITUDE 4HE RADAR TRANSMITS §SEC LINEAR &- SIGNALS THAT ARE DEMODU LATED USING THE STRETCH TECHNIQUE SIMILAR TO RADAR ALTIMETERS %ACH PULSE IS AMPLITUDE WEIGHTED BY A SINE FUNCTION O TO SUPPRESS SIDELOBES BY ^ D" FROM THE SURFACE RETURN THAT OTHERWISE WOULD MASK THE DESIRED RETURNS FROM DEPTH 4HE IN SITU RESOLUTION IS NOMINALLY ^ M WITHIN A MEDIUM OF PERMITTIVITY ^ 4HE RADAR DYNAMIC RANGE IS ^ D" TO PERMIT OBSERVATION OF SUBSURFACE PROFILES TO A DEPTH OF SEVERAL KM 4HE ANTENNA IS COMPRISED OF TWO SETS OF DIPOLES M TIP TO TIP WITH AN EFFECTIVE FOOTPRINT OF SEVERAL TENS OF KM 0EAK OUTPUT POWER IS 7 )NSTRUMENT MASS IS KG AND INPUT POWER 7 !TMOSPHERIC )ONOSPHERIC 3OUNDINGn&LIGHT 3YSTEMS 4HE OBJECTIVE OF THIS CLASS OF RADAR SOUNDERS IS TO GENERATE A CROSS SECTION PROFILE OF THE WATER OR ELEC TRON DENSITY IN THE ORBIT PLANE BENEATH THE SPACECRAFT !TMOSPHERIC SOUNDING BY RADAR REQUIRES SENSITIVITY TO RELATIVELY WEAK BACKSCATTER EFFECTIVE SUPPRESSION OR AVOID ANCE OF THE STRONG RETURN FROM NADIR MODEST RANGE RESOLUTION AND RELATIVELY NARROW FIELDS OF VIEW 4HESE REQUIREMENTS LEAD TO HIGH POWER RADARS AT +U BAND OR ABOVE A SIMPLE PULSE WAVEFORM AND SUBSTANTIAL ANTENNA AREA 2ADAR SOUNDERS SHOULD NOT BE CONFUSED WITH PASSIVE MICROWAVE RADIOMETERS ALSO CALLED SOUNDERS UNFORTUNATELYTHAT ARE USED BY OPERATIONAL METEOROLOGICAL SATELLITES TO ESTIMATE ATMOSPHERIC WATER DISTRIBUTION ! MULTIFREQUENCY RADIOMETER GENERATES COARSE WATER VAPOR DENSITY PROFILES FOR WHICH ALTITUDE IS A FUNCTION OF FRE QUENCY 0ASSIVE MICROWAVE SOUNDING UNITS HAVE MASS AND POWER REQUIREMENTS ON THE ORDER OF KG AND 7 MUCH LESS THAN THEIR ACTIVE RADAR COUNTERPARTS 42-- 4HE 4ROPICAL 2AINFALL -EASURING -ISSION WAS A JOINT UNDERTAKING BETWEEN .!3! AND THE *APANESE !EROSPACE %XPLORATION !GENCY *!8! 4HE FIVE INSTRUMENT PAYLOAD INCLUDES THE 0RECIPITATION 2ADAR 02 WHICH WAS DESIGNED AND BUILT BY *!8! THEN .!3$! AND WAS THE FIRST OF ITS KIND ON A SPACE BASED PLATFORM )TS PRECESSING KM ORBIT INCLINED AT n SUPPORTS TEMPORALLY AND SPATIALLY SPARSE ATMOSPHERIC COVERAGE OVER TROPICAL LAND AND SEA 4HE RADAR PROVIDES A THREE DIMEN SIONAL STRUCTURE OF RAINFALL FROM THE SURFACE TO AN ALTITUDE OF KM 7HEN COMBINED WITH DATA FROM THE PASSIVE MICROWAVE RADIOMETER 4-) 02 DATA SUPPORT IMPROVED ACCURACY OF RAINFALL RETRIEVALS 4HE RADARS +U BAND ^ CM FREQUENCY IS ABOUT THREE TIMES HIGHER THAN MOST SURFACE BASED METEOROLOGICAL RADARS BUT WAS SELECTED TO ACHIEVE A REASONABLY NARROW n BEAMWIDTH FROM AN ANTENNA AREA CONSTRAINED BY SPACECRAFT ACCOMMODATION TO BE NO MORE THAN M BY M (ORIZONTAL RESOLUTION AT NADIR IS ABOUT KM 4HE ANTENNA A ELEMENT SLOTTED WAVEGUIDE PHASED ARRAY WITH D" GAIN IS ELECTRONICALLY SCANNED OVER on ACROSS TRACK COVERING A SWATH KM WIDE CENTERED AT NADIR 0EAK TRANSMITTED POWER IS 7 GENERATED FROM SOLID STATE POWER AMPLIFIERS 330!S ONE FOR EACH WAVEGUIDE 4HE M RANGE RESOLUTION IS SET BY THE UNITY TIME BANDWIDTH PRODUCT §SEC PULSE 4HE RADAR HAS SUFFICIENT SENSITIVITY TO RESPOND TO RAIN RATES AS SMALL AS MMHR )NSTRUMENT MASS IS KG REQUIRED INPUT POWER IS 7 4HE IONOSPHERIC SOUNDING MODE ON -!23)3 DESCRIBED ABOVE IS AIMED PRIMAR ILY AT CHARACTERIZATION OF THE -ARTIAN IONOSPHERE DURING DAYLIGHT CONDITIONS FROM ALTITUDES BELOW KM 4HE RADAR IS OPERATED AS A STEPPED FREQUENCY INSTRUMENT SWEEPING K(Z TO -(Z IN K(Z INTERVALS OVER SECONDS &ROM KM THE NOMINAL 3.2 IS D" INCREASING TO D" AT -(Z
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#LOUD3AT ,AUNCHED IN !PRIL #LOUD3AT INCLUDES AS ITS PRIMARY PAYLOAD THE #LOUD 0ROFILING 2ADAR #02 #LOUD3AT FLIES IN A SUN SYNCHRONOUS ORBIT IN CLOSE FORMATION WITH #!,)03/ WHICH CARRIES A CLOUD PROFILING LIDAR AND IN SOME WHAT LOOSER FORMATION WITH !QUA !URA 4ERRA AND 0!2!3/, 4AKEN TOGETHER THESE SIX ENVIRONMENTAL SATELLITES CONSTITUTE THE SO CALLED ! 4RAIN 4HE AVERAGE SEPARATION BETWEEN #LOUD3AT AND #!,)03/ IS ABOUT KM WHICH CORRESPONDS TO A ONE MINUTE DELAY BETWEEN THE RADAR AND LIDAR CLOUD PROFILING MEASUREMENTS 4HE #02 WAS DEVEL OPED JOINTLY BY .!3! AND THE #ANADIAN 3PACE !GENCY )T IS A '(Z NADIR VIEWING REAL APERTURE RADAR TRANSMITTING §SEC PULSES AT A 02& OF K(Z TO FILL A WINDOW FROM THE SURFACE TO KM ALTITUDE WITH M VERTICAL RESOLUTION SOUNDING DATA 4HE ANTENNA DIAMETER LIMITED BY THE LAUNCH VEHICLE SHROUD IS M WHICH SUPPORTS ACROSS TRACK AND ALONG TRACK RESOLUTIONS OF KM AND KM RESPECTIVELY 4HE LARGER ALONG TRACK RESOLUTION REFLECTS THE SEC INTEGRATION TIME OF THE RETURNS !NTENNA GAIN IS D" !VERAGE DATA RATE IS KBITSS $YNAMIC RANGE IS D" MINIMUM DETECTABLE VOLUMETRIC RETURN IS n D": 4HE 02 MASS IS KG INPUT POWER REQUIRED IS 7 0EAK POWER TRANSMITTED IS K7 4HE #02S HIGH POWER AMPLIFIER (0! IS THE FIRST OF ITS KIND FOR A SPACE BASED RADAR AN EXTENDED INTERACTION KLYSTRON 4HE KLYSTRON IS DRIVEN BY M7 SIGNALS FROM A SOLID STATE PREAMPLIFIER 4HE KLYSTRON REQUIRES K6 PROVIDED BY A HIGH VOLTAGE POWER SUPPLY SYSTEM THAT ALSO IS A SPACE FIRST 4HE (0! IS FULLY REDUNDANT $02 4HE DUAL FREQUENCY PRECIPITATION RADAR IS THE ACTIVE MICROWAVE INSTRU MENT FOR THE 'LOBAL 0RECIPITATION -EASUREMENT '0- #ORE /BSERVATORY $02 IS BASED ON A +U BAND INSTRUMENT +U02 SIMILAR TO ITS PREDECESSOR ON 42-- AUGMENTED BY A +A BAND '(Z RADAR +A02 4HEIR TWO PHASED ARRAY SLOTTED WAVEGUIDE ANTENNAS ARE SIZED AND ORIENTED SO THAT THEIR FOOTPRINTS ARE THE SAME 4HEIR RESPECTIVE STEERED BEAMS ARE SYNCHRONIZED SO THAT FOR THE CENTRAL KM SWATH WITHIN WHICH THEY BOTH HAVE COVERAGE THEIR VERTICAL PROFILES ARE NEAR SIMULTANEOUS 4HE +U02 AND +A02 ANTENNAS ARE SIZED AT M r M AND M r M RESPECTIVELY EACH COMPRISED OF SLOTTED WAVEGUIDES DRIVEN BY INDIVIDUAL SOLID STATE POWER AMPLIFIERS 0EAK TRANSMITTED POWERS ARE 7 AND 7 -ASS AND INPUT POWER OF THE TWO RADARS ARE KG AND KG AND 7 AND 7 4HE ONLY OTHER INSTRUMENT IN THE PAYLOAD IS A MICROWAVE RADIOMETER 4O PROVIDE COVERAGE AT MORE LATITUDES THE SPACECRAFT HAS A HIGHER INCLINATION ORBIT THAN 42--S n 4HE MAIN ADVANTAGES OF THE SECOND FRE QUENCY AND INCREASED POWER ARE TO DISTINGUISH BETWEEN RAIN AND SNOW AND TO INCREASE SENSITIVITY TO RAIN RATES AS LOW AS MMHR
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#HAPTER
iÌiÀ}V>Ê,>`>À ,°ÊivvÀiÞÊ iiiÀÊ>`Ê,LiÀÌÊ°Ê-iÀ>v .ATIONAL #ENTER FOR !TMOSPHERIC 2ESEARCH
£°£Ê /," 1 /" 3TANDARD OPERATIONAL METEOROLOGICAL DOPPLER RADARS HAVE BECOME FAMILIAR OBSERVA TIONAL TOOLS TO RADAR ENGINEERS AS WELL AS THE GENERAL PUBLIC SINCE THEIR INTRODUCTION BY THE 5NITED 3TATES .ATIONAL 7EATHER 3ERVICE .73 IN THE S AND ARE WIDELY USED BY WEATHER FORECASTERS IN THE PUBLIC AND PRIVATE SECTORS -AJOR TECHNICAL IMPROVEMENTS WERE INTRODUCED IN THE S WHEN THE .73 THE &EDERAL !VIATION !GENCY &!! AND THE 53 !IR &ORCE JOINED TOGETHER TO INSTALL THE NEXT GENERATION NATIONAL NETWORK OF 732 $ DOPPLER RADARS COMMONLY CALLED .EXRAD RADARS !LSO IN THE S THE &!! INSTALLED THE 4ERMINAL $OPPLER 7EATHER 2ADAR 4$72 SYSTEM AT MAJOR AIRPORTS IN THE 53 4HE FEDERAL AGENCIES HAVE SUBSEQUENTLY IMPLEMENTED MANY TECHNICAL UPGRADES TO THE .EXRAD AND 4$72 NETWORKS TO IMPROVE THEIR PERFORMANCE FOR PUBLIC WARNINGS AND AVIATION SAFETY )N CONTRAST TO THE 732 AND 732 # RADARS THEY REPLACED THE 732 $ SYSTEMS PROVIDE QUANTITATIVE AND AUTOMATED REAL TIME INFORMATION ON STORMS PRECIPITATION HURRICANES TORNADOES AND A HOST OF OTHER IMPORTANT WEATHER PHE NOMENA WITH HIGHER SPATIAL AND TEMPORAL RESOLUTION THAN EVER BEFORE )N THE AVIATION COMMUNITY 4$72 RADARS PROVIDE CRUCIAL INFORMATION FOR PROVIDING SAFE DEPARTURES AND LANDINGS AT THE MAJOR AIRPORTS BY DETECTING HAZARDOUS WIND SHEAR EVENTS SUCH AS MICROBURSTS STRONG GUST FRONTS AND OTHER PERFORMANCE REDUCING WIND HAZARDS 6ARIOUS OTHER TYPES OF METEOROLOGICAL RADARS EXIST 4HE .EXRAD LONG RANGE WEATHER SUR VEILLANCE RADARS ARE FREQUENTLY SUPPLEMENTED BY TYPICALLY SMALLER MEDIUM RANGE WEATHER RADARS OPERATED BY 46 STATIONS FOR LOCAL OBSERVATIONS )N ADDITION TO THE FAMILIAR COM MERCIAL AIRBORNE WEATHER AVOIDANCE AND OBSERVATION RADARS AIRBORNE HURRICANE MONITORING PROVIDES DETAILED FORECASTS AND WARNINGS FOR APPROACHING COASTAL HURRICANES !ND VERTI CAL POINTING WIND PROFILING FIXED BEAM SYSTEMS ARE ROUTINELY USED TO OBTAIN CONTINUOUS PROFILES OF HORIZONTAL WINDS WHEREAS SPACED BASED METEOROLOGICAL RADARS ARE MEASURING WIDESPREAD EQUATORIAL PRECIPITATION FIELDS AND CLOUD PROPERTIES -ETEOROLOGICAL RESEARCH RESULTS ARE REGULARLY TRANSFERRED TO THE OPERATIONAL WEATHER RADAR COMMUNITY FOR ACHIEV ING HIGHER SPACE AND TIME RESOLUTION FOR IMPROVED DATA QUALITY AND FOR THE PRODUCTION OF NEW WEATHER RADAR PRODUCTS ALL OF WHICH HAVE LED TO DRAMATIC IMPROVEMENTS IN WEATHER FORECASTING $OPPLER WEATHER RADARS MEASURE DETAILED VECTOR WIND FIELDS AS WELL AS PRECIPI TATION FIELDS 3MALL HIGHLY MOBILE RESEARCH RADARS PROVIDE MANY OF THE SAME CAPABILITIES AS THE FIXED RADARS $UAL POLARIZATION TECHNIQUES ARE USED FOR IMPROVED QUANTITATIVE
4HE .ATIONAL #ENTER FOR !TMOSPHERIC 2ESEARCH IS SPONSORED BY THE .ATIONAL 3CIENCE &OUNDATION £°£
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PRECIPITATION MEASUREMENT FOR DETECTING HAIL AND FOR DISCRIMINATING ICE PARTICLES SNOW FROM WATER RAIN &URTHERMORE GROUND BASED RESEARCH RADARS CAN NOW MEASURE ATMO SPHERIC MOISTURE IN THE SURFACE BOUNDARY LAYER !IRBORNE RESEARCH RADARS PROVIDE MANY OF THESE SAME CAPABILITIES WITH INCREASED COVERAGE AND GREATER MOBILITY 4HIS VARIETY OF APPLICATIONS IN BOTH RESEARCH AND OPERATIONS ILLUSTRATES THE VITALITY OF METEOROLOGICAL RADAR TECHNOLOGY AND ITS EVOLUTION 4HIS CHAPTER IS INTENDED TO INTRODUCE THE READER TO METEOROLOGICAL RADAR PARTICULARLY THOSE SYSTEM CHARACTERISTICS THAT ARE UNIQUE TO METEOROLOGICAL APPLICATIONS )N THIS REGARD IT SHOULD BE NOTED THAT MOST METEOROLOGICAL RADARS APPEAR SIMILAR TO RADARS USED FOR OTHER PURPOSES 0ULSED DOPPLER SYSTEMS ARE FAR MORE PREVALENT THAN #7 RADARS 0RIMARILY CENTER FED PARABOLIC DISH ANTENNAS WITH FOCAL POINT FEED AND LOW NOISE SOLID STATE DIGITAL RECEIVERS ARE USED -AGNETRONS KLYSTRONS TRAVELING WAVE TUBES AND OTHER FORMS OF TRANSMITTER FORMS ARE ROUTINELY USED 4HE DISTINGUISHING FACTOR BETWEEN METEOROLOGICAL RADAR AND OTHER KINDS OF AVIATION OR MILITARY RADARS LIES IN THE NATURE OF WEATHER TARGETS THE RESULTING CHARACTERISTICS OF THE RADAR SIGNAL AND THE MEANS BY WHICH THESE WEATHER ECHOES ARE PROCESSED TO SUP PRESS ARTIFACTS AND GENERATE ONLY THE SIGNIFICANT AND ESSENTIAL WEATHER INFORMATION )MPORTANT METEOROLOGICAL TARGETS OCCUPY A WIDE RANGE OF SCATTERING ECHO INTENSITIES TO D": THAT ARE DISTRIBUTED IN SPACE FROM SHORT RANGE KM TO LONG RANGE KM CLOSE TO THE SURFACE M TO THE TOP OF THE ATMOSPHERE WHERE WEATHER IS IMPORTANT KM AND TYPICALLY OCCUPY A LARGE FRACTION OF THE SEVERAL MILLIONS OF SPATIAL RESOLUTION CELLS OBSERVED BY THE RADAR -OREOVER IT IS NECESSARY TO MAKE QUANTITATIVE MEASUREMENTS OF THE RECEIVED SIGNAL CHARACTERISTICS IN EACH OF THESE CELLS OR hWEATHER TARGETS v TO ESTIMATE SUCH PARAMETERS AS PRECIPITATION RATE PRECIPITATION TYPE AIR MOTION TURBULENCE AND WIND SHEAR )N ADDITION BECAUSE A HIGH PERCENTAGE OF RADAR RESOLUTION CELLS CONTAIN USEFUL INFORMATION METEOROLOGICAL RADARS REQUIRE FAST DIGITAL SIGNAL PROCESSORS EFFECTIVE MEANS FOR SUPPRESSING ARTIFACTS CAUSED BY THE DATA DENSITY HIGH DATA RATE RECORDING SYSTEMS AND INFORMATIVE DISPLAYS OF THIS INFORMA TION 4HUS WHEREAS MANY NON WEATHER RADAR APPLICATIONS CALL FOR DETECTION TRACKING AND DETAILED CHARACTERIZATION OF RELATIVELY FEWER NUMBER OF DESIRED TARGETS IN A FIELD OF WIDESPREAD WEATHER GROUND SEA DECOY AND BIRD CLUTTER THE METEOROLOGICAL RADARS FOCUS ON MAKING ACCURATE ESTIMATES OF THE NATURE OF THE hWEATHER CLUTTERv ITSELF "OTH AVIATIONMILITARY AND WEATHER RADARS REQUIRE HEAVY PROCESSING ACTIVITY BUT THE VOLUME OF DATA FOR ASSIMILATION RECORDING AND DISPLAY OF WEATHER RADARS IS OFTEN MUCH LARGER SINCE DIFFERENT ESSENTIAL INFORMATION MUST BE EXTRACTED FOR A LARGE NUMBER OF ANTICI PATED USERS WHEN MEASURING WIDESPREAD WEATHER SYSTEMS 4HE DISCUSSION HEREIN REFERS TO A NUMBER OF USEFUL TEXTS AND REFERENCES FOR THE READER (OWEVER THE CLASSIC 2ADAR /BSERVATION OF THE !TMOSPHERE BY ,OU "ATTAN DESERVES SPECIAL MENTION FOR ITS CLARITY AND COMPLETENESS AND REMAINS A STANDARD FOR COURSES IN RADAR METEOROLOGY 4HE "ATTAN -EMORIAL AND TH !NNIVERSARY 2ADAR -ETEOROLOGY #ONFERENCE PRODUCED A COLLECTION OF REVIEW PAPERS 2ADAR IN -ETEOROLOGY COVERING THE FIRST FOUR DECADES OF RADAR METEOROLOGY FROM THE HISTORICAL TECHNOLOGICAL SCIENTIFIC AND OPERATIONAL PERSPECTIVES "EAN ET AL IN 3KOLNIKS FIRST 2ADAR (ANDBOOK ADDRESSED THE PROBLEM OF WEATHER EFFECTS ON RADAR $OVIAK AND :RNIC| PLACE SPECIAL EMPHASIS ON DOPPLER ASPECTS OF METEOROLOGICAL RADAR WHEREAS "RINGI AND #HANDRA EMPHASIZE ALL ASPECTS OF POLARIMETRIC RADARS AND ,HERMITTE FOCUSES ON MILLIMETER WAVE CLOUD RADARS 2INEHARTS 2ADAR FOR -ETEOROLOGISTS GIVES A BROAD AND EASILY COMPREHENDIBLE OVER VIEW OF ALL ASPECTS OF WEATHER RADAR 4HE )%%% 'EOSCIENCE AND %LECTRONICS 3PECIAL )SSUE ON 2ADAR -ETEOROLOGY !TLASS 2ADAR IN -ETEOROLOGY 7AKIMOTO AND 3RIVASTIVAS 2ADAR AND !TMOSPHERIC 3CIENCE ! #OLLECTION OF %SSAYS IN (ONOR OF $AVID !TLAS AND
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-EISCHNERS 7EATHER 2ADAR PROVIDE AN EVOLVING PERSPECTIVE ON MANY ASPECTS OF METEO ROLOGICAL RADARS BY TECHNOLOGICAL AND SCIENTIFIC LEADERS &INALLY PERHAPS THE BROADEST AND MOST COMPLETE SET OF REFERENCES ON PROGRESS IN THE FIELD CAN BE FOUND IN THE SERIES OF 0ROCEEDINGS AND 0REPRINTS OF THE )NTERNATIONAL #ONFERENCES ON 2ADAR -ETEOROLOGY SPONSORED BY THE !MERICAN -ETEOROLOGICAL 3OCIETY !-3 4HESE DOCUMENTS CAN BE FOUND IN MANY TECHNICAL LIBRARIES AND ALSO CAN BE OBTAINED ONLINE )N ADDITION THE 0ROCEEDINGS OF THE %UROPEAN #ONFERENCES ON 2ADAR -ETEOROLOGY PROVIDES EXCELLENT REFERENCE MATERIAL
£°ÓÊ / Ê, ,Ê +1/" Ê",Ê / "," " Ê/, /4HE RECEIVED POWER 0R FROM A RADAR POINT TARGET CAN BE DERIVED FROM ANY OF A VARIETY OF EXPRESSIONS THAT ARE APPLICABLE TO RADAR IN GENERAL &OR A SINGLE POINT TARGET A SIMPLE FORM THAT IS READILY DERIVED IS
0R
BS R
WHERE A IS A CONSTANT DEPENDENT UPON RADAR SYSTEM PARAMETERS TRANSMITTED POWER 0T ANTENNA SYSTEM GAIN ' AND WAVELENGTH K R IS THE RANGE TO THE POINT TARGET AND R IS THE RADAR CROSS SECTION 2#3
)T IS IN THE CALCULATION OF R FOR DISTRIBUTED METEOROLOGICAL TARGETS THAT THE RADAR EQUATION DIFFERS FROM THAT FOR POINT TARGETS &OR DISTRIBUTED TARGETS LIKE RAINFALL THE 2#3 MAY BE WRITTEN
R G6
WHERE G IS THE RADAR REFLECTIVITY IN UNITS OF CROSS SECTIONAL AREA PER UNIT VOLUME AND 6 IS THE VOLUME SAMPLED BY THE RADAR G CAN ITSELF BE WRITTEN AS .
H £S I
I
WHERE . IS THE NUMBER OF SCATTERERS PER UNIT VOLUME AND R I IS THE BACKSCATTERING CROSS SECTION OF THE ITH POINT SCATTERER )N GENERAL THE METEOROLOGICAL SCATTERERS CAN TAKE ON A VARIETY OF FORMS WHICH INCLUDE WATER DROPLETS ICE CRYSTALS HAIL SNOW AND MIXTURES OF THE ABOVE -IE DEVELOPED A GENERAL THEORY FOR THE ENERGY BACKSCATTERED BY AN OPTICAL PLANE WAVE IMPINGING ON CONDUCTING SPHERES IN COLLOIDAL SUSPENSION 4HE SAME THEORY APPLIES TO SPHERICAL RAINDROPS FALLING THROUGH THE ATMOSPHERE FOR WHICH THE BACKSCATTERED ENERGY IS A FUNCTION OF THE WAVELENGTH K OF THE INCIDENT ENERGY AND THE RADIUS A AND COMPLEX INDEX OF REFRACTION M OF THE PARTICLE 4HE RATIO O AK DETERMINES THE DOMINANT SCATTER ING PROPERTIES OF THE PARTICLE 3PHERICAL WATER DROPLETS IN AIR THAT ARE LARGE RELATIVE TO THE WAVELENGTH SCATTER IN THE SO CALLED OPTICAL REGION DROPLETS ON THE ORDER OF THE SAME SIZE AS THE WAVELENGTH SCATTER IN THE SO CALLED RESONANT SCATTERING REGION AND DROPLETS SMALL RELATIVE TO THE WAVELENGTH SCATTER IN THE SO CALLED 2AYLEIGH REGION
"Y CONVENTION IN THIS CHAPTER WE SHALL USE R FOR RANGE AND 2 FOR RAINFALL RATE
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7HEN THE RATIO PAL THE 2AYLEIGH APPROXIMATION MAY BE APPLIED AND RI BECOMES
P \ + \ $I L
SI
WHERE $I IS THE DIAMETER OF THE ITH DROP AND
\ + \
M M
WHERE M IS THE COMPLEX INDEX OF REFRACTION !T TEMPERATURES BETWEEN AND n# AND CENTIMETER WAVELENGTHS \+\ y FOR THE WATER PHASE AND \+\ y FOR THE ICE PHASE %QUATION CAN NOW BE WRITTEN AS
H
P \ + \ L
.
£ $I
I
AND WE DEFINE THE RADAR REFLECTIVITY FACTOR : AS .
: £ $I I
)N RADAR METEOROLOGY IT IS COMMON TO USE THE DIMENSIONS OF MILLIMETERS FOR DROP DIAMETER $I AND TO CONSIDER THE SUMMATION TO TAKE PLACE OVER A UNIT VOLUME OF SIZE M TO YIELD A VOLUME DENSITY EXPRESSION 4HEREFORE THE CONVENTIONAL UNIT OF : IS IN MMM &OR ICE PARTICLES $I IS SOMETIMES EXPRESSED AS THE DIAMETER OF THE WATER DROPLET THAT WOULD RESULT IF THE ICE PARTICLE WERE TO MELT COMPLETELY (OWEVER THE RADAR SCATTERING PROCESS FOR THE MANY SHAPES AND TEMPERATURES OF ICE PARTICLES IS EXTREMELY COMPLICATED AND A DEFINITIVE GENERALIZED EXPRESSION CANNOT BE GIVEN )T IS OFTEN CONVENIENT TO TREAT THE DROP OR PARTICLE SIZE DISTRIBUTION AS A CONTINUOUS FUNCTION WITH A NUMBER DENSITY .$ WHERE .$ IS THE NUMBER OF DROPS PER UNIT VOLUME HAVING DIAMETERS BETWEEN $ AND $ D$ )N THIS CASE : IS GIVEN BY THE SIXTH MOMENT OF THE PARTICLE SIZE DISTRIBUTION
c
: ¯ N $ $ D$
)F THE RADAR BEAM IS FILLED WITH SCATTERERS THE SAMPLE VOLUME OF 6 IS GIVEN APPROXIMATELY BY
6y
P QF R CT
WHERE P AND E ARE THE AZIMUTH AND ELEVATION BEAMWIDTHS C IS THE VELOCITY OF LIGHT AND S IS THE RADAR PULSE WIDTH 3UBSTITUTING %QS AND INTO %Q WE SEE THAT THE 2#3 FOR THE DISTRIBUTED WEATHER SCATTERER IS DIRECTLY PROPORTIONAL TO THE PULSE VOLUME AS DETERMINED BY THE PULSE LENGTH AND ANTENNA BEAM AT THE TARGET RANGE 4HEN COMBINING %QS AND AND SUBSTITUTING INTO %Q GIVES
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B P QF R CT P \ + \ L R
BP QF C T \ + \ : L R
B `: R
£°x
.
£ $I I
4HIS EXPRESSION ILLUSTRATES THAT FOR THE DISTRIBUTED WEATHER TARGET THE RECEIVED POWER IS A FUNCTION ONLY OF A ` A CONSTANT DEPENDENT UPON ALL THE RADAR SYSTEM AND PHYSI CAL PARAMETERS DIRECTLY PROPORTIONAL TO THE RADAR REFLECTIVITY FACTOR : AND MOST SIGNIFICANT INVERSELY PROPORTIONAL TO R NOT R AS IN THE CASE OF POINT TARGETS 4HE RADAR SYSTEM PARAMETERS INCLUDED IN A IN %Q INCLUDE THE PEAK TRANSMIT POWER 0T THE ANTENNA SYSTEM GAIN ' TWICE ONCE FOR TRANSMITTING AND ONCE FOR RECEIV ING AND THE WAVELENGTH K 7E INCLUDE ALL ANTENNA SYSTEM LOSSES IN THIS ANTENNA SYS TEM GAIN FACTOR RADOME WAVEGUIDE ROTARY JOINTS ETC SINCE ALL THE MEASUREMENTS MUST BE REFERENCED TO THE SAME POINT IN THE RADAR SYSTEMUSUALLY AT A COUPLER NEAR THE CIRCULATOR "ECAUSE THE ANTENNA GAIN IS NOT UNIFORM OVER THE BEAMWIDTH ASSUMING A UNIFORM GAIN CAN LEAD TO ERRORS IN THE CALCULATION OF : 5SING A SIMILAR DERIVATION 0ROBERT *ONES TOOK THIS INTO ACCOUNT ASSUMED A GAUSSIAN SHAPE FOR THE ANTENNA BEAM AND DERIVED THE FOLLOWING EQUATION FOR THE RECEIVED POWER
0R
0' L QF CT . T SI LN P R £ I
WHERE LN IS THE CORRECTION FOR THE GAUSSIAN SHAPED BEAM "Y SUBSTITUTING %QS AND INTO %Q THE RECEIVED POWER CAN BE EXPRESSED IN TERMS OF THE REFLECTIVITY FACTOR : AND RANGE R AS
0R
0' QF CTP \ + \ : T LN L R
"ECAUSE THE RECEIVING FILTER SUPPRESSES SOME OF THE RECEIVED SIGNAL POWER 0R MUST BE REDUCED BY ,R WHICH DEPENDS ON THE DETAILS OF THE TRANSMITTED SPECTRUM AND THE RECEIVER FILTER BUT IS USUALLY A FACTOR OF ABOUT D" FOR A TYPICAL WAVEFORM AND hMATCHED FILTERv 3OLVING FOR THE RADAR REFLECTIVITY FACTOR : GIVES
: ; LN K ,R 0T ' P E C S O \+\= 0R R
WHERE THE REFLECTIVITY FACTOR IS EXPRESSED IN TERMS OF THE RECEIVED POWER AND RANGE /NE MUST BE CAREFUL TO USE CONSISTENT UNITS IN %Q )F METER KILOGRAM SECONDS MKS UNITS ARE USED THE CALCULATION OF : WILL HAVE DIMENSIONS OF MM #ONVERSION TO THE MORE CONVENIENT UNITS OF MMM REQUIRES THAT : BE MULTIPLIED BY THE FACTOR &URTHERMORE EXPRESSING 0R AND R IN COMMON UNITS OF D"M D" RELATIVE TO MILLIWATT AND KM REQUIRES THAT : ALSO BE MULTIPLIED BY "ECAUSE : VALUES OF INTEREST CAN RANGE OVER SEVERAL ORDERS OF MAGNITUDE A LOGARITHMIC SCALE IS OFTEN USED 4HUS
D": # 0R D"M LOG R KM
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WHERE # ISOLATED IN BRACKETS IN %Q IS THE SO CALLED 7EATHER 2ADAR #ONSTANT WITH 0R EXPRESSED IN D"M AND R IN KM 4YPICAL VALUES OF # ARE TO D" FOR THE OPERATIONAL WEATHER RADARS )T IS CLEAR THAT FOR FIXED RANGE AND RECEIVED POWER A LOWER VALUE OF THE RADAR CONSTANT # ALLOWS A SMALLER REFLECTIVITY VALUE IN D": TO BE OBSERVED 4HUS SMALLER VALUES OF # CORRESPOND TO MORE SENSITIVE RADARS 4HIS EQUATION CAN BE USED TO MEASURE THE REFLECTIVITY FACTOR : WHEN THE ANTENNA BEAM IS FILLED WHEN THE SMALL SCATTERING PARTICLE 2AYLEIGH APPROXIMATION IS VALID AND WHEN THE SCATTERERS ARE IN EITHER THE ICE OR THE WATER PHASE "ECAUSE ALL THESE CONDI TIONS ARE NOT ALWAYS SATISFIED IT IS COMMON TO USE THE TERM :E THE EFFECTIVE REFLECTIVITY FACTOR IN PLACE OF : 7HEN :E IS USED IT IS GENERALLY UNDERSTOOD THAT THE ABOVE CONDI TIONS ARE ASSUMED 0RACTITIONERS IN THE FIELD OF RADAR METEOROLOGY OFTEN USE :E AND : INTERCHANGEABLY ALBEIT INCORRECTLY !NOTHER FACTOR WE HAVE IGNORED IN THE DERIVATION OF THE RADAR EQUATION IS ATTENUA TION BY PRECIPITATION AND ATMOSPHERIC GASSES !T CM WAVELENGTHS THE ATTENUATION IS USUALLY NOT SIGNIFICANT HOWEVER AT AND CM AND ESPECIALLY THE YET SHORTER MM WAVELENGTHS ATMOSPHERIC ATTENUATION MUST BE ACCOUNTED FOR IN THE RADAR EQUATION BY ADDING AN ADDITIONAL RANGE DEPENDENT TERM ,A 4HE FOLLOWING SECTION GIVES DETAILS ON ESTIMATING THIS ATTENUATION IN COMMONLY ENCOUNTERED CONDITIONS &INALLY IT IS IMPORTANT TO NOTE THE : VALUES ARE OF METEOROLOGICAL SIGNIFICANCE BECAUSE THEY ARE DIRECTLY RELATED TO CLOUD PROPERTIES AND ACTUAL RAINFALL RATES 2 AS DESCRIBED LATER IN THIS CHAPTER : VALUES IN NONPRECIPITATING CLOUDS AS SMALL AS n D": ARE OF INTEREST FOR CLOUD PHYSICS STUDIES )N THE OPTICALLY CLEAR LOWER ATMO SPHERIC BOUNDARY LAYER hCLEAR AIRv : VALUES OF THE ORDER n D": TO D": ARE TYPICAL AND FREQUENTLY ORIGINATE FROM INSECTS AND BIRDS )N RAIN : MAY RANGE FROM ABOUT n D": TO AS MUCH AS D": WITH A TO D": RAIN BEING OF THE TYPE THAT CAN CAUSE SEVERE FLOODING 3EVERE HAILSTORMS MAY PRODUCE : VALUES HIGHER THAN D": -ANY OPERATIONAL RADAR TYPES ARE DESIGNED TO DETECT THOSE : VALUES THAT PRODUCE MEA SURABLE PRECIPITATION TO D": AND hCLEAR AIRv ECHOES TO KM WHERE THE %ARTHS CURVATURE PREVENTS SURFACE BASED MEASUREMENTS 4HUS BEING ABLE TO MEASURE STRONG PRECIPITATION ECHOES AT SHORT RANGE AND ALSO WEAK PRECIPITATION ECHOES AT LONG RANGE REQUIRES RADAR RECEIVERS HAVING A TOTAL DYNAMIC RANGE OF n D" WHEREAS MEASURING WEAK ECHOES IN THE PRESENCE OF STRONG GROUND CLUTTER REQUIRES AS LARGE AN INSTANTA NEOUS DYNAMIC RANGE D" AS POSSIBLE -ORE RECENT OPERATIONAL RADARS AND MOST RESEARCH RADARS ATTEMPT TO ACHIEVE THE MOST SENSITIVITY POSSIBLE AND CAN DETECT MINI MUM REFLECTIVITY VALUES OF n D": OR LESS AT SHORT RANGES EG KM /PERATIONAL RADARS IN THE PAST HAVE EMPLOYED SENSITIVITY TIME CONTROL 34# TO REDUCE GAIN AT SHORT RANGE AND COMPENSATE FOR STRONG NEARBY ECHOES HOWEVER RECENT RADARS TEND NOT TO USE 34# TECHNIQUES SINCE RECEIVER DYNAMIC RANGES ARE ADEQUATE TO COVER IMPORTANT WEATHER ECHO INTENSITIES AT THE NECESSARY RANGES 2ESEARCH RADARS HAVE RARELY USED 34# OWING TO THE ATTENDANT LOSS OF SENSITIVITY AT SHORT RANGES
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!TTENUATION %FFECTS !TTENUATION HAS AT LEAST TWO NEGATIVE EFFECTS ON METEORO LOGICAL RADAR SIGNALS &IRST MAKING ACCURATE QUANTITATIVE MEASUREMENTS OF THE BACK SCATTERED ENERGY FROM PRECIPITATION AT RANGES FARTHER THAN ANY INTERVENING PRECIPITATION BECOMES VERY DIFFICULT 4HIS INABILITY TO PRECISELY MEASURE THE TRUE BACKSCATTERING CROSS SECTION REQUIRES THAT QUANTITATIVE MEASUREMENTS OF PRECIPITATION RATES BE CORRECTED FOR ATTENUATION WHEN POSSIBLE 3ECOND IF THE ATTENUATION DUE TO PRECIPITATION OR THE INTERVENING MEDIUM IS SUF FICIENTLY GREAT THE SIGNAL FROM A PRECIPITATION CELL BEHIND A REGION OF STRONG ABSORP TION MAY BE TOTALLY SUPPRESSED /NE EXAMPLE OF THE POTENTIALLY SERIOUS CONSEQUENCES OF VERY STRONG ABSORPTION IS THE IMPACT IT MIGHT HAVE ON AVIATION STORM AVOIDANCE RADARS MOST OF WHICH ARE IN THE CM BAND )T IS COMMON FOR SHORT WAVELENGTH ON BOARD AVIATION WEATHER RADARS TO NOT DETECT INTENSE CONVECTIVE CELLS BEHIND CLOSER HIGH ATTENUATION THUNDERSTORMS 3EVERE STORMS WITH HIGH PRECIPITATION RATES ALSO CAUSE HIGH ATTENUATION EVEN AT CM WAVELENGTHS AS NOTED BY (ILDEBRAND AND !LLEN ET AL )N SOME METEOROLOGICAL RADAR APPLICATIONS IT IS DESIRABLE TO ATTEMPT TO MEASURE ATTENUATION ALONG SELECTED PROPAGATION PATHS 4HIS IS DONE BECAUSE ABSORPTION IS RELATED TO LIQUID WATER CONTENT AND CAN PROVIDE USEFUL INFORMATION FOR THE DETECTION OF SUCH PHENOMENA AS HAIL IN ACCORDANCE WITH THE DUAL WAVELENGTH TECHNIQUE DESCRIBED BY %CCLES AND !TLAS AND 6IVEK ET AL )N THE FOLLOWING SUBSECTIONS QUANTITATIVE EXPRESSIONS RELATING ATTENUATION TO PRECIPITATION ARE GIVEN -UCH OF THIS IS TAKEN FROM "EAN $UTTON AND 7ARNER AND ,HERMITTE "ATTAN AND /GUCHI ARE ALSO EXCELLENT SOURCES FOR ADDITIONAL INFORMA TION ON THE ABSORBING PROPERTIES OF PRECIPITATION !TTENUATION BY 7ATER 6APOR !TMOSPHERIC WATER VAPOR MAY TAKE ON VALUES UP TO GM AND GIVE VARIABLE ATTENUATION DEPENDING ON THE WATER VAPOR CONTENT (OWEVER AT TYPICAL WEATHER RADAR WAVELENGTHS LONGER THAN CM THE ATTENUATION IS LESS THAN A FEW HUNDREDTHS D"KM AND IS USUALLY IGNORED 'ASEOUS OXYGEN CONTRIBUTES ONLY A MINOR ABSORPTION EFFECT AT THESE CENTIMETER WAVELENGTHS AND IS ALSO USUALLY IGNORED !TTENUATION IN #LOUDS #LOUD DROPLETS ARE REGARDED HERE AS THOSE WATER OR ICE PARTICLES HAVING RADII SMALLER THAN MM CM &OR WAVELENGTHS OF INCIDENT RADIATION WELL IN EXCESS OF CM THE ATTENUATION DEPENDS PRIMARILY ON THE LIQUID WATER CONTENT AND IS INDEPENDENT OF THE DROP SIZE DISTRIBUTION 4HE GENERALLY ACCEPTED EQUATIONS FOR ATTENUATION BY CLOUDS USUALLY SHOW THE MOISTURE COMPONENT OF THE EQUA TIONS IN THE FORM OF THE LIQUID WATER CONTENT GRAMS PER CUBIC METER /BSERVATIONS INDICATE THAT THE LIQUID WATER CONCENTRATION IN CLOUDS GENERALLY RANGES FROM TO GM ALTHOUGH 7EICKMANN AND +AMPE HAVE REPORTED ISOLATED INSTANCES OF CUMU LUS CONGESTUS CLOUDS HIGH TOWERING CONVECTIVE CLOUDS THAT FREQUENTLY PRODUCE HEAVY PRECIPITATION WITH WATER CONTENTS OF GM IN THE UPPER LEVELS )N ICE CLOUDS THE WATER CONTENT RARELY EXCEEDS AND IS OFTEN LESS THAN GM 4HE ATTENUATION DUE TO CLOUD DROPLETS MAY BE WRITTEN
+ +-
WHERE + ATTENUATION D"KM + ATTENUATION COEFFICIENT D"KM GM - LIQUID WATER CONTENT GM
-
PR . AI £ I
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P ¤ M ³ )M ¥ L ¦ M ´µ
WHERE THE AI ARE DROPLET RADII Q IS THE DENSITY OF WATER AND )M IS THE IMAGINARY PART 6ALUES OF + FOR ICE AND WATER CLOUDS ARE GIVEN FOR VARIOUS WAVELENGTHS AND TEMPERA TURES BY 'UNN AND %AST IN 4ABLE 3EVERAL IMPORTANT FACTS ARE DEMONSTRATED BY 4ABLE 4HE DECREASE IN ATTENUA TION WITH INCREASING WAVELENGTH IS CLEARLY SHOWN 4HE VALUES CHANGE BY ABOUT AN ORDER OF MAGNITUDE FOR A CHANGE OF K FROM TO CM 4HE DATA PRESENTED HERE ALSO SHOWS THAT ATTENUATION IN WATER CLOUDS INCREASES WITH DECREASING TEMPERATURE )CE CLOUDS GIVE ATTENUATIONS ABOUT TWO ORDERS OF MAGNITUDE SMALLER THAN WATER CLOUDS OF THE SAME WATER CONTENT 4HE ATTENUATION OF MICROWAVES BY ICE CLOUDS CAN BE NEGLECTED FOR PRACTICAL PURPOSES !TTENUATION BY 2AIN 2YDE AND 2YDE CALCULATED THE EFFECTS OF RAIN ON MICROWAVE PROPAGATION AND SHOWED THAT ABSORPTION AND SCATTERING EFFECTS OF RAINDROPS BECOME MORE PRONOUNCED AT THE HIGHER MICROWAVE FREQUENCIES WHERE THE WAVELENGTHS AND THE RAINDROP DIAMETERS ARE MORE NEARLY COMPARABLE )N THE CM BAND AND AT SHORTER WAVELENGTHS THE EFFECTS ARE APPRECIABLE BUT AT WAVELENGTHS IN EXCESS OF CM THE EFFECTS ARE GREATLY DECREASED )T IS ALSO CLEAR THAT SUSPENDED WATER CLOUD DROPLETS AND RAIN HAVE AN ABSORPTION RATE IN EXCESS OF THAT OF THE COMBINED OXYGEN AND WATER VAPOR ABSORPTION )N PRACTICE IT HAS BEEN CONVENIENT TO EXPRESS RAIN ATTENUATION AS A FUNCTION OF THE PRECIPITATION RATE 2 WHICH DEPENDS ON THE LIQUID WATER CONTENT AND THE FALL VELOCITY OF THE DROPS THE LATTER IN TURN DEPENDING ON THE SIZE OF THE DROPS 2YDE STUDIED THE ATTENU ATION OF MICROWAVES BY RAIN AND DEDUCED BY USING ,AWS AND 0ARSONSS DROP SIZE DISTRIBUTIONS THAT THIS ATTENUATION IN DECIBELS PER KILOMETER CAN BE APPROXIMATED BY R
+ 2 ¯ + ; 2R =A DR
WHERE +2 TOTAL ATTENUATION D" 2R RAINFALL RATE ALONG PATH R R LENGTH OF PROPAGATION PATH KM + CONSTANT DEPENDENT ON FREQUENCY AND TEMPERATURE A CONSTANT DEPENDENT ON FREQUENCY 4!",% /NE WAY !TTENUATION #OEFFICIENT + IN #LOUDS IN D"KM PER GM ,IQUID 7ATER
7AVELENGTH CM 4EMPERATURE n# 7ATER CLOUD
)CE CLOUD
EXTRAPOLATED VALUE
n n n
r n r n r n
r n r n r n
r n r n r n
r n r n r n
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-EDHURST SHOWS THAT A IS A GOOD ASSUMPTION IN MANY CASES 4HE PATH LOSS PER MILE FOR THE THREE FREQUENCY BANDS OF AND '(Z IS SHOWN IN &IGURE ,HERMITTE EXTENDS THIS EARLY WORK TO HIGHER FREQUENCIES CONFIRMING THE RELATIONSHIP AND DESCRIBING THE EFFECT OF THE DROP SIZE DISTRIBUTION ON THE ATTENUATION RATE (E ALSO REVIEWS MORE RECENT EMPIRICAL DATA 4HE GREATEST UNCERTAINTY IN PREDICTION OF ATTENUATION RATES CAUSED BY RAINFALL WHEN THEORETICAL FORMULAS ARE USED AS A BASIS FOR CALCULATION IS THE EXTREMELY LIM ITED KNOWLEDGE OF DROP SIZE DISTRIBUTIONS IN RAIN OF VARYING FALL RATES UNDER DIFFER ING CLIMATIC AND WEATHER CONDITIONS ,HERMITTE AND 5IJLENHOET ET AL THOROUGHLY REVIEW THE EVOLUTION OF ANALYTIC EXPRESSIONS FOR DROP SIZE DISTRIBUTIONS DESCRIBING THE -ARSHALL 0ALMER EXPERIMENT AND THEIR RESULTING EXPONENTIAL DISTRIBUTION AND THE MORE GENERAL THREE PARAMETER 'AMMA DISTRIBUTION 4HEY ALSO REVIEW THE DEPEN DENCE OF THE PARAMETERS DEFINING THE DISTRIBUTION TO THE RAIN RATE AND TO THE TYPE OF RAINFALL 4HERE IS LITTLE EVIDENCE THAT RAIN WITH A KNOWN RATE OF FALL HAS A UNIQUE DROP SIZE DISTRIBUTION ALTHOUGH "URROWS AND !TTWOODS STUDIES SEEM TO INDICATE THAT A CERTAIN MOST PROBABLE DROP SIZE DISTRIBUTION CAN BE ATTACHED TO RAIN OF A GIVEN RATE OF FALL 2ESULTS OF THIS STUDY ARE SHOWN IN 4ABLE WHICH GIVES THE PERCENTAGE OF TOTAL VOLUME OF RAINFALL OCCUPIED BY RAINDROPS OF DIFFERENT DIAMETERS AND VARYING RAINFALL RATES MILLIMETERS PER HOUR )N THE BASIS OF THESE RESULTS THE ABSORPTION CROSS SECTION OF DIFFERENT RAIN RATES IS SHOWN IN 4ABLE 4HIS TABLE GIVES THE DECIBEL ATTENUATION PER KILOMETER FOR DIFFERENT RAINFALL RATES FOR RADAR WAVELENGTHS BETWEEN AND CM
&)'52% 4HEORETICAL RAIN ATTENUATION IN D"MILE STATUTE VERSUS RAINFALL RATE AFTER * 7 2YDE AND $ 2YDE
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4!",% $ROP 3IZE $ISTRIBUTIONS AT $IFFERENT 0RECIPITATION 2ATES
0RECIPITATION 2ATE 2 MMH $ROP $IAMETER $ CM
0ERCENTAGE OF A 'IVEN 6OLUME #ONTAINING $ROPS OF $IAMETER $
3INCE THE TOTAL ATTENUATION CROSS SECTION DEPENDS ON THE TEMPERATURE BECAUSE OF ITS EFFECTS ON THE DIELECTRIC PROPERTIES OF WATER IT IS IMPORTANT TO EVALUATE THE ATTENU ATION OF RAINS WHOSE DROPS ARE AT DIFFERENT TEMPERATURES FROM THOSE IN THE PRECEDING TABLES 4ABLE CONTAINS THE NECESSARY DATA RELATIVE TO THE CHANGE OF ATTENUATION WITH TEMPERATURE AND CAN BE USED WITH 4ABLE 4O DETERMINE TOTAL ATTENUATION CAUSED BY RAINFALL THROUGH A PARTICULAR PRECIPITATION PATH SOMETHING MUST BE KNOWN OR ASSUMED ABOUT THE NATURE OF THE PRECIPITATION ITSELF AND CONSEQUENTLY ABOUT HOW ITS RAINFALL RATES AND DROP SIZES ARE DISTRIBUTED IN THREE DIMENSIONS ! SYSTEMATIC VERTICAL VARIATION OF 2 DECAYING WITH HEIGHT ABOVE A MEASURED SUR FACE VALUE SEEMS TO BE APPROPRIATE IN STRATIFORM RAINFALL WHICH IS RAIN HAVING A WIDESPREAD AND CONTINUOUS NATURE 3UCH WIDESPREAD RAINFALL IS USUALLY TRIGGERED BY 4!",% !TTENUATION IN $ECIBELS PER +ILOMETER FOR $IFFERENT 2ATES OF 2AIN 0RECIPITATION AT A
4EMPERATURE OF n# 5SING THE $ROP SIZE $ISTRIBUTIONS IN 4ABLE 7AVELENGTH K CM 0RECIPITATION 2ATE 2 MMH K K K K K K K
K K
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4!",% #ORRECTION &ACTOR -ULTIPLICATIVE FOR 2AINFALL !TTENUATION
0RECIPITATION 2ATE 2 MMH
K CM
n#
n#
n#
n#
n#
A RELATIVELY LARGE SCALE MECHANISM SUCH AS A FRONTAL OR MONSOON SITUATION ! VERTICAL VARIATION OF 2 OF THE FORM
2 2 E DH
CAN BE ASSUMED TO BE APPROPRIATE UNDER CONTINUOUS RAINFALL CONDITIONS 2 IS THE SUR FACE RAINFALL RATE H IS THE HEIGHT ABOVE THE %ARTHS SURFACE AND D IS A CONSTANT EQUAL TO ABOUT #ONVECTIVE PRECIPITATION HOWEVER SHOWS A QUITE DIFFERENT NATURE &OR EXAMPLE THE PRESENCE OF VIRGA PRECIPITATION ALOFT BUT EVAPORATING BEFORE REACHING THE SURFACE ASSOCIATED WITH SO MANY SHOWER TYPE CLOUDS IN DRY CLIMATES INDICATES THAT CONVECTIVE SHOWER RAINFALL PROFILES ARE MUCH MORE DIFFICULT TO MODEL !TTENUATION BY (AIL 2YDE CONCLUDED THAT THE ATTENUATION CAUSED BY HAIL IS ONE HUNDREDTH OF THAT CAUSED BY RAIN AND THAT ICE CRYSTAL CLOUDS CAUSE NO SENSIBLE ATTENUATION AND SHOW VERY SMALL ATTENUATION EVEN AT THE EXCESSIVE RATE OF FALL OF INH (OWEVER THE SCATTERING BY ICE SPHERES SURROUNDED BY A CONCENTRIC FILM OF LIQUID WATER HAVING A DIFFERENT DIELECTRIC CONSTANT DOES NOT GIVE THE SAME EFFECT THAT 2YDES RESULTS FOR DRY PARTICLES WOULD INDICATE &OR EXAMPLE WHEN ONE TENTH OF THE RADIUS OF AN ICE SPHERE OF RADIUS CM MELTS SCATTERING OF CM RADIATION IS APPROXIMATELY OF THE VALUE THAT WOULD BE SCATTERED BY AN ALL WATER DROP !T WAVELENGTHS OF AND CM WITH A A RADIUS OF DROP +ERKER ,ANGLEBEN AND 'UNN FOUND THAT PARTICLES ATTAINED TOTAL ATTENUATION CROSS SECTIONS CORRESPONDING TO ALL MELTED PARTICLES WHEN LESS THAN OF THE ICE PARTICLES WAS MELTED 7HEN THE MELTED
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MASS REACHED ABOUT TO THE ATTENUATION WAS ABOUT TWICE THAT OF A COMPLETELY MELTED PARTICLE 4HESE CALCULATIONS SHOW THAT THE ATTENUATION IN THE MELTING OF ICE IMME DIATELY UNDER THE n# ISOTHERM CAN BE SUBSTANTIALLY GREATER THAN IN THE SNOW REGION JUST ABOVE AND UNDER SOME CIRCUMSTANCES GREATER THAN IN THE RAIN BELOW THE MELTING LEVEL &URTHER MELTING CANNOT LEAD TO MUCH FURTHER ENHANCEMENT APPARENTLY AND MAY LEAD TO A LESSENING OF THE REFLECTIVITY OF THE PARTICLE BY BRINGING IT TO SPHERICITY OR BY BREAKING UP THE PARTICLE -ELTING OF ICE PARTICLES PRODUCES ENHANCED BACKSCATTER AND THIS EFFECT GIVES RISE TO THE OBSERVED ELEVATED BRIGHT BAND NEAR THE n# ISOTHERM ,HERMITTE DISCUSSES HAIL ATTENUATION FOR SHORTER WAVELENGTH RADARS WHEN RESONANT REGION -IE SCATTERING IS THE DOMINANT SCATTERING MECHANISM 5SING ACCEPTED SIZE DISTRIBUTIONS OF DRY HAIL HE SHOWS ATTENUATION RATES OVER THE FREQUENCY INTERVAL OF n '(Z THAT ARE NEGLIGIBLE AT THE LOWER FREQUENCIES BUT RISE ASYMPTOTICALLY TO ABOUT D"KM AT FREQUENCIES ABOVE '(Z !TTENUATION BY &OG 4HE CHARACTERISTIC FEATURE OF A FOG IS THE REDUCTION IN VISIBIL ITY 6ISIBILITY IS DEFINED AS hTHE GREATEST DISTANCE IN A GIVEN DIRECTION AT WHICH IT IS JUST POSSIBLE TO SEE AND IDENTIFY WITH THE UNAIDED EYE IN THE DAYTIME A PROMINENT DARK OBJECT AGAINST THE SKY AT THE HORIZON AND AT NIGHT A KNOWN PREFERABLY UNFOCUSED MODERATELY INTENSE LIGHT SOURCEv !LTHOUGH THE VISIBILITY DEPENDS UPON BOTH DROP SIZE AND NUMBER OF DROPS AND NOT ENTIRELY UPON THE LIQUID WATER CONTENT IN PRACTICE THE VISIBILITY IS AN APPROXIMATION OF THE LIQUID WATER CONTENT AND THEREFORE MAY BE USED TO ESTIMATE RADIO WAVE ATTENUATION /N THE BASIS OF 2YDES WORK 3AXTON AND (OPKINS GIVE THE FIGURES IN 4ABLE FOR THE ATTENUATION IN A FOG OR CLOUDS AT n# TEMPERATURE 4HE ATTENUATION VARIES WITH THE TEMPERATURE BECAUSE THE DIELECTRIC CONSTANT OF WATER VARIES WITH TEMPERATURE THEREFORE AT n# AND n# THE FIGURES IN 4ABLE SHOULD BE MULTIPLIED BY AND RESPECTIVELY )T IS IMMEDIATELY NOTED THAT CLOUD OR FOG ATTENUATION IS AN ORDER OF MAGNITUDE GREATER AT CM THAN AT CM AND THAT NEARLY ANOTHER ORDER OF MAGNITUDE INCREASE OCCURS BETWEEN AND CM 2ANGE AND 6ELOCITY !MBIGUITIES 7EATHER RADARS UTILIZE A SEQUENCE OF PULSES TO MEASURE THE RADAR REFLECTIVITY AND DOPPLER CHARACTERISTICS "ECAUSE THE PULSING RATE TYPICALLY DETERMINES THE SAMPLING FREQUENCY FOR DOPPLER QUANTITIES ON A CONSTANT PULS ING RATE RADAR THE UNAMBIGUOUS DOPPLER FREQUENCY .YQUIST FREQUENCY FOR A FIXED PULSE REPETITION FREQUENCY 02& RADAR IS GIVEN BY
&.YQ o 02&
WHERE 02& IS THE PULSE REPETITION FREQUENCY 3IMULTANEOUSLY THE UNAMBIGUOUS RANGE INTERVAL IS GIVEN BY
2A
C 02&
4!",% !TTENUATION #AUSED BY #LOUDS OR &OG 4EMPERATURE n#
!TTENUATION D"KM 6ISIBILITY M
K CM
K CM
K CM
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AND THE PRODUCT &.YQ 2A IS SIMPLY C 3INCE THE DOPPLER SHIFT F AND THE TARGET RADIAL VELOCITY V ARE LINEARLY RELATED THE UNAMBIGUOUS VELOCITY IS RELATED TO THE .YQUIST FREQUENCY BY
&.YQ 2A
6A
L & .YQ
)T FOLLOWS THAT THE PRODUCT OF UNAMBIGUOUS VELOCITY AND UNAMBIGUOUS RANGE IS
6A 2A
LC
&OR CONSTANT 02& RADARS THIS PRODUCT IS MAXIMIZED BY MAXIMIZING K THE TRANSMIT TED WAVELENGTH 4HUS USING LONGER WAVELENGTHS ALLOWS OPTIMIZING THE 02& BY TRAD ING UNAMBIGUOUS RANGE FOR UNAMBIGUOUS VELOCITY &OR STANDARD CONSTANT 02& RADARS CM WAVELENGTHS HAVE BEEN WIDELY CHOSEN FOR MOST PRECIPITATION MEASUREMENTS OF INTEREST IN WHICH DESIGN PARAMETERS SUCH AS RADAR BEAMWIDTH SIZE OF ANTENNA AND ATTENUATION EFFECTS MAY BE MADE ACCEPTABLE 'ROUND #LUTTER %FFECTS -ANY METEOROLOGICAL RADAR APPLICATIONS CALL FOR THE DETECTION OF PRECIPITATION ECHOES IN THE PRESENCE OF GROUND CLUTTER 3PECIFICALLY PRE CIPITATION MEASUREMENTS NEAR THE GROUND ARE OF EXTREME INTEREST IN AGRICULTURAL AND HYDROLOGICAL APPLICATIONS AS WELL AS INFORMATION FOR THE GENERAL PUBLIC !PPLICATIONS IN WHICH GROUND CLUTTER IS SERIOUS RELATES TO THE GROUND BASED RADAR DETECTION OF LOW LEVEL WIND SHEAR AT AIRPORTS AND MEASURING PRECIPITATION NEAR THE GROUND IN MOUNTAIN OUS TERRAIN FOR FLASH FLOOD WARNINGS "OTH THE .EXRAD AND 4ERMINAL $OPPLER 7EATHER 2ADAR 4$72 NETWORK RADARS HAVE BEEN DESIGNED TO ASSURE CLUTTER SUPPRESSION IN EXCESS OF D" !LTHOUGH GROUND CLUTTER CANNOT BE ELIMINATED ITS EFFECT CAN BE MITIGATED THROUGH CAREFUL DESIGN 4HE PRIMARY APPROACH IS TO USE AN ANTENNA WITH LOW SIDELOBES PAR TICULARLY IN ELEVATION WHICH WILL SUPPRESS THE CLUTTER COMPONENT OF THE INPUT ECHO WHEN THE MAIN BEAM IS SLIGHTLY ABOVE THE HORIZON ! SECOND APPROACH IS USING SHORTER WAVELENGTHS 3HORTER WAVELENGTHS RESULT IN IMPROVED SIGNAL TO CLUTTER RATIOS OWING TO THE FACT THAT THE 2AYLEIGH SCATTERED WEATHER SIGNAL POWER IS INVERSELY PROPORTIONAL TO K WHEREAS THE GROUND CLUTTER RETURN IS ONLY WEAKLY DEPENDENT ON WAVELENGTH )F ONE ASSUMES THAT THE CLUTTER SIGNAL IS WAVELENGTH INDEPENDENT AND THE ANTENNA BEAM WIDTH IS FIXED IT CAN BE SHOWN THAT THE WEATHER SIGNAL POWER TO CLUTTER POWER RATIO IS INVERSELY PROPORTIONAL TO K 7EATHER RADARS TYPICALLY USE DIGITAL SIGNAL PROCESSING TECHNIQUES TO IMPLEMENT CLUTTER FILTERS THAT SUPPRESS NEAR ZERO VELOCITY CLUTTER ECHOES 4HESE FILTERS MAY BE IMPLEMENTED USING EITHER A TIME DOMAIN CLUTTER FILTER APPLIED TO THE ) AND 1 RADAR VIDEO DATA ONE FORM OF WHICH IS SOMETIMES CALLED A DELAY LINE CANCELER FROM ITS EARLY ANALOG IMPLEMENTATION TO SUPPRESS THE ZERO VELOCITY GROUND CLUTTER COMPONENTS OR A FREQUENCY DOMAIN DOPPLER POWER SPECTRUM A DIGITAL hFILTER BANKv TO ACHIEVE THE SAME EFFECT 4HE TIME DOMAIN FILTERS FOR MECHANICALLY SCANNED WEATHER RADARS ARE USUALLY INFINITE IMPULSE RESPONSE ))2 FILTERS WITH NARROW BUT ADJUSTABLE WIDTHS UP TO A FEW MS AND HAVING SUPPRESSION LEVELS OF n D" AND VERY STEEP TRANSITION REGIONS 4HESE TIME DOMAIN FILTERS WITH A FREQUENCY NOTCH CENTERED AT ZERO VELOCITY FREQUENCY
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WILL ALSO SUPPRESS WEATHER ECHO POWER THAT MAY EXIST IN THE SAME VELOCITY REGION AND BIAS ALL THE ESTIMATES OF REFLECTIVITY VELOCITY AND WIDTH 3PECTRAL DOMAIN CLUTTER FILTERS IMPLEMENTED BY A DISCRETE &OURIER TRANSFORM $&4 ON THE OTHER HAND SUPPRESS THE NEAR ZERO CLUTTER COMPONENTS IN THE FREQUENCY DOMAIN AND MAY INTERPOLATE THE REMAINING SPECTRUM ACROSS THIS REGION TO RETAIN MOST OF THE UNDERLYING SIGNAL OR NOISE SPECTRAL INFORMATION !N ALTERNATIVE FREQUENCY DOMAIN TECHNIQUE FOR THE .EXRAD RADAR SEPARATELY MODELS THE CLUTTER AND WEATHER SIGNAL AS GAUSSIAN SHAPED SPECTRA AND SEPARATES THESE TWO COMPONENTS OF THE DOPPLER SPECTRUM USING DIGITAL SEARCH ALGORITHMS AND THEN REMOVES THESE CLUTTER COMPONENTS WHILE LEAV ING THE UNDERLYING WEATHER SIGNAL UNPERTURBED 4HUS WHEN THE GAUSSIAN ASSUMPTIONS APPLY THE REMAINING WEATHER SIGNAL SPECTRUM PROVIDES AN UNBIASED ESTIMATOR FOR ALL THE WEATHER PARAMETER SPECTRUM MOMENT ESTIMATES 4YPICAL 7EATHER 2ADAR $ESIGNS 4HERE IS NO UNIVERSAL WEATHER RADAR SYSTEM DESIGN THAT CAN SERVE ALL PURPOSES !IRBORNE WEATHER RADARS ARE CONSTRAINED BY SIZE AND WEIGHT LIMITATIONS 'ROUND BASED RADARS MAY BE CONSTRAINED BY COST AND SITING CONSIDERATIONS 3EVERE STORM WARNING RADARS REQUIRE LONG RANGE AND HIGH UNAMBIGU OUS VELOCITY AND THEN MUST PENETRATE VERY HEAVY RAIN THUS DICTATING LONG WAVELENGTHS 2ADARS DESIGNED FOR STUDIES OF NONPRECIPITATING CLOUDS TYPICALLY USE SHORT WAVE LENGTHS MM AND MM IN ORDER TO ACHIEVE SUFFICIENT SENSITIVITY TO DETECT SMALL CLOUD PARTICLES OF THE ORDER OF n MM AT SUFFICIENTLY SMALL RESOLUTION VOLUMES 3ENSITIVE SHORT RANGE &- #7 RADARS HAVING HIGH AVERAGE POWER CAN BE USED TO OBTAIN VERY HIGH RANGE RESOLUTION FOR DETECTING VERY THIN SCATTERING LAYERS IN THE CLEAR AIR BOUNDARY LAYER -OST METEOROLOGICAL RADARS ARE PULSED RADARS HAVING DOPPLER CAPABILITY 'ROUND BASED RADARS USED FOR SEVERE STORM RESEARCH AND WARNINGS NORMALLY USE 3 BAND ^ '(Z OR # BAND ^ '(Z TRANSMITTERS !IRBORNE WEATHER AVOIDANCE AND PRECIP ITATION RADARS PRIMARILY USE 8 BAND ^ '(Z DUE TO SIZE LIMITATIONS AND OCCASIONALLY # BAND TRANSMITTERS TO MINIMIZE ATTENUATION !IRBORNE AND GROUND CLOUD RADARS AND SPACEBORNE RADARS ENCOMPASS THE MM WAVELENGTHS AT +U BAND ^ '(Z +A BAND ^ '(Z AND 7 BAND ^ '(Z "EAMWIDTHS OF a n ARE COMMONLY USED FOR LONGER RANGE RADARS !DMITTEDLY THIS IS SOMEWHAT ARBITRARY BUT THE CHOICE OF n IS BASED UPON SEVERAL DECADES OF EXPERI ENCE ! n BEAM WILL PROVIDE A CROSS RANGE RESOLUTION OF KM AT A RANGE OF KM "ECAUSE THUNDERSTORMS CONTAIN IMPORTANT SPATIAL FEATURES SUCH AS HEAVY PRECIPITA TION SHAFTS AND UPDRAFT CORES WITH HORIZONTAL DIMENSIONS OF THE ORDER TO KM A n BEAM IS REASONABLY WELL MATCHED TO THESE ATMOSPHERIC PHENOMENA BEING OBSERVED OUT TO RANGES OF A FEW HUNDRED KM 3HORTER RANGE AIRBORNE WEATHER RADARS OFTEN EMPLOY BEAMWIDTHS OF nn AS A COMPROMISE BETWEEN WAVELENGTH REQUIREMENTS AND ANTENNA SIZE CONSTRAINTS WHEREAS SPACEBORNE RADARS MAY USE A FRACTION OF A DEGREE BEAMWIDTH TO RETAIN USABLE HORIZONTAL RESOLUTION AT TYPICAL LONG RANGES n KM /PERATIONAL WEATHER RADARS NORMALLY ARE CAPABLE OF SHORT AND LONG PULSE OPERATION IN THE RANGE OF MS TO ABOUT MS AND 02&S BETWEEN AND (Z FOR LONG RANGE PRECIPITATION RADARS 4HROUGH PULSE WIDTH DIVERSITY HIGH RESOLUTION IS OBTAINED USUALLY AT SHORT RANGE WHEREAS FOR LONG RANGE DETECTION LONGER PULSES PROVIDE INCREASED SENSITIVITY AND TEND TO EQUALIZE THE ALONG BEAM AND CROSS BEAM RESOLUTIONS 4HE SHORTER WAVELENGTH +U +A AND 7 BAND RADARS TYPICALLY USE PULSE LENGTHS LESS THAN MS TO ACHIEVE IMPROVED RANGE RESOLUTION AND 02&S BETWEEN AND (Z BECAUSE OF THE SHORT RANGE CLOUD MEASUREMENTS THAT ARE LIMITED BY ATTENUATION
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AT THESE WAVELENGTHS 3PACE BORNE RADARS ALSO USE THESE HIGHER 02&S BUT KEEP TRACK OF MULTIPLE PULSES EN ROUTE TO THEIR WEATHER REGIONS FAR BELOW THE ORBITAL ALTITUDES %QUATION SHOWS THAT THE RECEIVED POWER IS DIRECTLY PROPORTIONAL TO THE PULSE LENGTH S 4HE NOISE POWER 0N IS CONVENTIONALLY GIVEN BY
0N J 4"
WHERE J "OLTZMANNS CONSTANT r n 7(Z + 4 RECEIVER NOISE TEMPERATURE + " RECEIVER NOISE BANDWIDTH (Z &OR A RECEIVER FILTER MATCHED TO THE PULSE LENGTH T 3OMETIMES WEATHER RADARS WILL USE A SHORT PULSE FOR HIGH 02& DOPPLER PROCESSING AT SHORT RANGES AND A LONGER PULSE AT LOW 02& FOR GREATER SENSITIVITY WHEN PERFORM ING LONG RANGE SURVEILLANCE SCANS TO MONITOR DISTANT WEATHER 3INCE THE TRANSMITTED PEAK POWER IS TYPICALLY CONSTRAINED TO BE FIXED THEN THE TRANSMITTED AVERAGE POWER INCREASES LINEARLY WITH S !LSO THE MATCHED FILTER BANDWIDTH AND ASSOCIATED NOISE POWER DECREASES INVERSELY WITH S )F THE RADAR PULSE VOLUME IS FILLED WITH DISTRIB UTED METEOROLOGICAL SCATTERERS THEN THE RADAR CROSS SECTION OF THE WEATHER TARGET ALSO INCREASES WITH S AS DETERMINED BY %QUATIONS AND AND THE SIGNAL TO NOISE RATIO 3.2 OF RECEIVED POWER IS PROPORTIONAL TO S
"y
0R T T s y 0N K 4" K 4
4HUS UNDER THESE COMMON CONDITIONS INCREASING THE PULSE LENGTH WILL INCREASE THE 3.2 AND THE EFFECTIVE RADAR RANGE )T IS IMPORTANT TO NOTE THAT THE DISTRIBUTED TARGET RADAR DEPENDENCE OF 3.2 ON S IS DIFFERENT FROM THE POINT TARGET RADAR IN WHICH THE MATCHED FILTER 3.2 EQUALS THE RATIO OF PULSE ENERGY TO NOISE SPECTRAL DENSITY %. 0T S . A LINEAR DEPENDENCE ON S 4HE SQUARED DEPENDENCE FOR DISTRIBUTED SCATTER ERS IS BECAUSE THE TRANSMIT PULSE SCATTERS POWER FROM ALL SCATTERERS IN THE CS PULSE VOLUME NOT JUST A SINGLE POINT TARGET THEREBY INCREASING THE RADAR CROSS SECTION OF THE WEATHER SCATTERER 02&S FOR METEOROLOGICAL RADARS RANGE FROM AS LOW AS SEVERAL HUNDRED Sn FOR LONG RANGE DETECTION TO SEVERAL THOUSAND Sn FOR SHORTER WAVELENGTH SYSTEMS ATTEMPTING TO ACHIEVE HIGH UNAMBIGUOUS VELOCITIES 'ENERALLY SPEAKING MOST METEOROLOGICAL DOP PLER RADARS ARE OPERATED IN A SINGLE 02& MODE COMPROMISING THE RADARS ABILITY TO UNAMBIGUOUSLY RESOLVE EITHER RANGE OR VELOCITY (OWEVER THE PULSING SEQUENCE MAY USE A hDUAL 02&v MODE IN WHICH GROUPS OF CONSTANT 02& PULSES ARE TRANSMITTED OR A hDUAL STAGGERED 024v PULSE REPETITION TIME TO RESOLVE BOTH RANGE AND VELOCITY AMBIGUITIES !NOTHER APPROACH IS TO EMPLOY A TRANSMITTED PULSE SEQUENCE WITH RAN DOM OR DETERMINISTIC PHASES FROM PULSE TO PULSE WHICH ALLOWS OVERLAID ECHOES TO BE SEPARATED -ULTIPLE 024 TECHNIQUES HAVE ALSO BEEN EXPLORED BUT ARE NOT IN COMMON USE 2ANGE AMBIGUITIES CANNOT BE TOTALLY ELIMINATED BUT THEIR EFFECTS CAN BE SIGNIFI CANTLY MITIGATED THROUGH THESE APPROACHES 4O DISCUSS DESIGN DETAILS OF THE COMMON TYPES OF METEOROLOGICAL RADARS IS BEYOND THE SCOPE OF THIS CHAPTER 2INEHART GIVES A DETAILED TABLE OF SYSTEM CHARACTERISTICS OF
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4!",% 2ELEVANT .EXRAD 3YSTEM #HARACTERISTICS
4RANSMITTED 0EAK!VERAGE 0OWER KLYSTRON 0ULSE LENGTH 0OLARIZATION 7AVELENGTH 2ECEIVER NOISE TEMPERATURE $YNAMIC RANGE !NTENNA GAIN "EAMWIDTH 3IDELOBE LEVELS -AXIMUM RANGE REFLECTIVITY DATA -AXIMUM RANGE DOPPLER DATA 5NAMBIGUOUS VELOCITY #LUTTER SUPPRESSION MAXIMUM 3YSTEM SENSITIVITY 2OTATION RATE
K7 7 M MS ,INEAR HORIZONTAL CM + D" D" n n D" KM KM o MS D" n D": AT KM n DEGSEC
A VARIETY OF WEATHER RADARS (OWEVER IT WILL BE USEFUL HEREIN TO INCLUDE SOME OF THE IMPORTANT CHARACTERISTICS OF THE .EXRAD 732 $ RADAR WHICH ILLUSTRATE THE PERFOR MANCE OF MODERN OPERATIONAL WEATHER RADARS 4ABLE CONTAINS SOME OF THE MORE RELEVANT ORIGINAL .EXRAD DESIGN FEATURES &IGURE SHOWS A TYPICAL .EXRAD INSTALLATION AT -ISSOULA -ONTANA 4HE ANTENNA IS MOUNTED ON A TOWER TO CLEAR SURROUNDING OBSTACLES SUCH AS BUILDINGS AND TREES 4HE ELEC TRONIC EQUIPMENT IS HOUSED IN ONE SHELTER AND THE STANDBY GENERATOR IS HOUSED IN ANOTHER
&)'52% .EXRAD 732 $ RADAR AT -ISSOULA -ONTANA MOUNTED ON M TOWER WITH TWO EQUIPMENT SHELTERSONE CONTAINING THE TRANS MITTER RECEIVER PROCESSOR AND COMMUNICATIONS EQUIPMENT AND THE OTHER CONTAINING A STANDBY GEN ERATOR 0HOTO COURTESY OF ./!!.73
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&)'52% .EXRAD REFLECTIVITY DATA FROM &REDERICK /KLAHOMA RADAR ON !PRIL SHOWING LINE OF INTENSE CON VECTIVE CELLS AND SURROUNDING PRECIPITATION 0HOTO COURTESY OF ./!!.73
&IGURE SHOWS AN EXAMPLE OF RADAR REFLECTIVITY DATA FROM THE &REDERIC /KLAHOMA RADAR AS A LINE OF INTENSE THUNDERSTORMS AND ASSOCIATED RAINFALL PASS THROUGH THE COVER AGE AREA 4HE PROCESSING TECHNIQUES USED TO GENERATE THE VARIOUS WEATHER IMAGES AND PRODUCTS ARE DISCUSSED LATER IN THIS CHAPTER &IGURE SHOWS THE 3 BAND CM AND +A BAND CM DUAL POLARIZATION DOPPLER RESEARCH RADAR OPERATED BY THE .ATIONAL #ENTER FOR !TMOSPHERIC 2ESEARCH .#!2 4HE SYSTEM PERMITS SIMULTANEOUS MEASUREMENTS OF THE REFLECTIVITY FACTOR ON TWO WAVELENGTHS DOPPLER PARAMETERS ON THE 3 BAND WAVELENGTH AND EXTENSIVE POLARI METRIC MEASUREMENTS AT BOTH WAVELENGTHS 4HE TECHNICAL CHARACTERISTICS ARE SIMILAR TO THE .EXRAD SPECIFICATIONS 4HE ANTENNA BEAMS ARE MATCHED WITH APPROXIMATELY n BEAMWIDTH AND THE LARGE 3 BAND DISH IS M IN DIAMETER 4HE PEAK TRANSMITTED POWER
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IS -7 AT 3 BAND AND +7 AT +A BAND 4HE PULSE WIDTHS ARE APPROXIMATELY MS 4HE 02& IS TYPICALLY Sn AT 3 BAND AND A FEW TIMES LARGER AT +A BAND 4HIS RADAR SYSTEM IS CHARACTERISTIC OF THE TECHNOLOGIES CURRENTLY IN PLACE IN THE RESEARCH COMMUNITY 0OLARIMETRIC 2ADAR -ETEOROLOGICAL RADARS USING DUAL POLARIZATION TRANSMIT AND RECEIVE BOTH HORIZONTAL AND VERTICAL POLARIZATIONS TO ESTIMATE ADDITIONAL CHARACTERIS TICS OF THE WEATHER TARGETS 4RANSMITTING THE TWO ORTHOGONAL POLARIZATIONS EITHER SIMULTANEOUSLY 3(6 OR TRANSMITTING THEM SEPARATELY IN A PREDETERMINED SEQUENCE AND USING DUAL PARALLEL DIGITAL RECEIVERS ONE ON EACH POLARIZATION CHANNEL ALLOW ESTI MATION OF THE DIFFERENTIAL QUANTITIES BETWEEN ECHOES FROM THE TWO POLARIZATIONS /NE CAN DERIVE IMPROVED RAINFALL RATES AS WELL AS OTHER PHYSICAL INFORMATION ON THE TYPE OF PRECIPITATION AS FUNCTIONS OF POLARIMETRIC MEASUREMENTS THAT RELATE THE DIFFERENCES IN THE HORIZONTALLY AND VERTICALLY POLARIZED SIGNALS "Y FAR THE MOST COMMON POLARIMET RIC PARAMETERS ARE THE hDIFFERENTIAL REFLECTIVITYv :DR AND hDIFFERENTIAL PHASEv &DP WHICH GIVE BULK SCATTERING AND PROPAGATION CHARACTERISTICS OF THE METEOROLOGICAL TAR GETS ,ETTING %H AND %V DENOTE THE COMPLEX RECEIVED SIGNAL VOLTAGES THAT ALSO REPRE SENT THE RECEIVED ELECTRIC FIELDS AT HORIZONTAL AND VERTICAL POLARIZATIONS THE IMPORTANT POLARIMETRIC PARAMETERS TO BE ESTIMATED ARE GIVEN BELOW
$IFFERENTIAL REFLECTIVITY :DR :H :V
$IFFERENTIAL PHASE &DP &V &H
3PECIFIC DIFFERENTIAL PHASE +DP D &DP DR
#O POLAR CORRELATION RATIO QHV \ %H %V \ % H%H % V%V ,INEAR DEPOLARIZATION RATIO ,$2 :CX V :CO H
:H AND :V ARE THE MEASURED REFLECTIVITIES OF THE HORIZONTAL AND VERTICAL CO POLAR IZED RECEIVED SIGNALS AND :DR IS EXPRESSED IN D" WHEREAS &H AND &V ARE THE MEASURED PHASES OF THE SAME POLARIZED RECEIVED SIGNALS +DP IS THE SUITABLY SMOOTHED RANGE DERIVATIVE OF THE MEASURED DIFFERENTIAL PHASE &DP AND IS USUALLY EXPRESSED IN DEGKM QHV IS THE CO POLAR CORRELATION COEFFICIENT OF %H AND %V WHERE THE PHASE MEASUREMENTS ARE ASSUMED TO BE TIME COINCIDENT WHICH IS THE CASE WITH 3(6 TRANSMISSION AND RECEP TION ,$2 IS A RATIO OF THE CROSS POLAR VERTICAL REFLECTIVITY :CX V NORMALIZED BY THE CO POLAR HORIZONTAL REFLECTIVITY :CO H "ECAUSE POLARIMETRIC MEASUREMENTS ADD NEW DIMENSIONS OF RADAR INFORMATION AND BECAUSE THESE MEASUREMENTS ARE RELATED TO THE PHYSICAL CHARACTERISTICS OF THE SCATTERERS SUITABLE COMBINATIONS OF THESE DATA GIVE A STRONG INDICATION OF PRECIPITATION TYPE RAIN SNOW ICE PARTICLES SLEET HAIL ETC AS WELL AS RADAR ECHO CLASSIFICATION INTO VARIOUS CATEGORIES PRECIPITATION GROUND OR SEA CLUTTER BIRDS AND INSECTS CHAFF ETC 2ADAR #ALIBRATION 4O EFFECTIVELY USE RADARS FOR ACCURATE PRECIPITATION ESTI MATES THE CONVERSION OF MEASURED REFLECTIVITY FACTOR TO RECEIVED ECHO POWER MUST BE WELL KNOWN 4HE GAINS OR CONVERSION CONSTANTS OF THE VARIOUS RADAR COMPONENTS CAN BE MEASURED USING ENGINEERING TEST EQUIPMENT MANUFACTURER SPECIFICATIONS AND FIELD MEASUREMENTS #ALIBRATING WEATHER RADAR USUALLY MEANS TO ACCURATELY SPECIFY THE RADAR CONSTANT IN THE RADAR EQUATION AND TO ACCURATELY ESTIMATE THE RECEIVED POWER
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MEASURED BY THE RADAR SYSTEM )T ALSO ENCOMPASSES ITEMS SUCH AS KNOWING WHERE THE SCATTERING VOLUME IS IN $ SPACE BY KNOWING ANTENNA POINTING ANGLES AND ACCURATELY DETERMINING RANGE !LTHOUGH FLOATING SPHERES TETRAHEDRAL REFLECTORS AND OTHER TARGETS OF KNOWN RADAR CROSS SECTION MAY BE USED THE IMPORTANT hSOLAR CALIBRATIONv TECHNIQUE USES THE SOLAR POSITION TO ADJUST ANTENNA POINTING AND THE RADIATED SOLAR FLUX TO DETERMINE ANTENNA GAIN !LONG WITH OTHER RADAR PARAMETER MEASUREMENTS ONE CAN READ ILY DETERMINE THE RADAR CONSTANT "Y INJECTING TEST SIGNALS OF KNOWN POWER ONE CAN DETERMINE THE RECEIVER GAIN TRANSFER FUNCTION &OR POLARIMETRIC RADARS SPECIAL CARE IS REQUIRED )T HAS BEEN DEMONSTRATED THAT BY MEASURING THE CROSS POLAR POWERS IN ADDITION TO THE SOLAR FLUX AN ACCURATE ESTIMATE OF THE DIFFERENTIAL CHANNEL CALIBRA TION CAN BE OBTAINED 4HE !-3 HELD A VERY SUCCESSFUL 7EATHER 2ADAR #ALIBRATION 3YMPOSIUM DOCUMENTING ALL ASPECTS OF METEOROLOGICAL RADAR CALIBRATION
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-- 4O COMPUTE THE VARIOUS WEATHER PRODUCTS NECESSARY FOR FORECASTING WARNING AND OTHER OPERATIONAL ACTIVITIES THE FIRST THREE SPECTRUM MOMENTS CORRESPONDING TO RECEIVED POWER MEAN RADIAL VELOCITY AND DOPPLER SPECTRUM OR VELOCITY WIDTH MUST BE ESTIMATED +EELER AND 0ASSARELLI REVIEW STANDARD ESTIMATION TECHNIQUES AND ERRORS FOR SPECTRUM MOMENT ESTIMATION &OR THE HIGHEST RESOLUTION MEASUREMENTS THESE SPECTRAL MOMENTS MUST BE COMPUTED AT EACH RANGE GATE SENSED BY THE RADAR AND CONVERTED INTO MEANINGFUL METEOROLOGICAL INFORMATION 4HE NATURE OF THE DISTRIBUTED METEOROLOGICAL TARGET WHICH SHALL BE DISCUSSED NEXT IMPOSES SOME SPECIAL REQUIREMENTS NOT GENERALLY CONSIDERED FOR HARD NONFLUCTUATING TARGETS ON THE PROCESSING TECHNIQUES TO ESTIMATE THESE MOMENTS )T CAN BE SHOWN THAT THE RECEIVED SIGNAL FROM METEOROLOGICAL TARGETS IS WELL REPRE SENTED BY A NARROWBAND GAUSSIAN PROCESS 4HIS IS A DIRECT CONSEQUENCE OF THE FACT THAT THE NUMBER OF SCATTERERS IN THE PULSE VOLUME IS LARGE THE PULSE VOLUME IS LARGE COMPARED WITH THE TRANSMITTED WAVELENGTH THE PULSE VOLUME CONTAINS MULTIPLE POINT SCATTERING SOURCES CAUSING ALL PHASES ON THE RANGE FROM TO O TO BE COMBINED AND RETURNED AND THE PARTICLES ARE IN RELATIVE MOTION DUE TO TURBULENCE WIND SHEAR AND THEIR VARYING FALL SPEEDS 4HE SUPERPOSITION OF THE SCATTERED ELECTRIC FIELDS FROM SUCH A LARGE NUMBER OF PAR TICLES EACH WITH DIFFERENT AMPLITUDE AND RANDOM PHASE GIVES RISE THROUGH THE CENTRAL LIMIT THEOREM TO A SIGNAL WITH BIVARIATE OR A TWO DIMENSIONAL GAUSSIAN PROBABILITY DENSITY FUNCTION 4HUS THE FLUCTUATING AMPLITUDE OF THE RETURN SIGNAL HAS A 2ALEIGH STA TISTICAL DISTRIBUTION AND ITS PHASE IS UNIFORMLY DISTRIBUTED BETWEEN nO &URTHERMORE ITS INTENSITY POWER IS EXPONENTIALLY DISTRIBUTED "ECAUSE ALL THE PARTICLES WITHIN THE SAMPLE VOLUME ARE MOVING WITH SOME MEAN OR AVERAGE RADIAL VELOCITY THERE IS A MEAN FREQUENCY OF THE DOPPLER SPECTRUM THAT IS SHIFTED FROM THE TRANSMITTED FRE QUENCY &INALLY SINCE THE PARTICLES ARE IN MOTION WITH RESPECT TO ONE ANOTHER THERE IS ALSO A DOPPLER SPREAD OFTEN REFERRED TO AS THE WIDTH OF THE DOPPLER SPECTRUM :RNIC DESCRIBES A STRAIGHTFORWARD TECHNIQUE OF SYNTHESIZING DIGITAL WEATHER RADAR SIGNALS FROM A PARAMETERIZED DOPPLER SPECTRUM CHARACTERIZING A SPECIFIC PULSE VOLUME $OVIAK AND :RNIC AS WELL AS "RINGI AND #HANDRASEKAR GIVE DETAILED DERIVATIONS OF THESE RELATIONSHIPS WHEREAS +EELER AND 0ASSARELLI SUMMARIZE DISTRIBUTED TARGET DATA CHARACTERISTICS AND RELATE THEM TO THE SAMPLED DATA SETS REPRESENTATIVE OF WEATHER RADAR AND OTHER ATMOSPHERIC SOUNDING SYSTEMS
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3PECTRUM -OMENT %STIMATION ! COMMON 'AUSSIAN MODEL OF THE MEAN RECEIVED POWER SPECTRAL DENSITY OF A METEOROLOGICAL SIGNAL IS DEPICTED IN &IGURE AND CAN BE INTERPRETED AS FOLLOWS 4HE RECEIVED POWER IS SIMPLY THE INTEGRAL UNDER THE CURVE THE ZEROTH MOMENT AND IS GIVEN BY
0R ¯ 3 F DF ¯ 3 V DV
WHERE F AND V ARE RELATED BY F K V 4HE MEAN VELOCITY V IS GIVEN BY THE FIRST MOMENT OF THE SPECTRUM
V
¯ V3V DV ¯ 3V DV
4HE SPECTRUM VELOCITY WIDTH R V IS GIVEN BY TAKING THE SQUARE ROOT OF THE SECOND CENTRAL MOMENT
S V
¯ V V 3V DV ¯ 3V DV
2ADAR METEOROLOGISTS SOMETIMES REFER TO S V AS THE SPECTRUM VARIANCE BECAUSE OF ITS COMPUTATIONAL EQUIVALENCE TO THE VARIANCE OF A CONTINUOUSLY DISTRIBUTED RANDOM VARIABLE )N SHORT 3V IS ANALOGOUS TO A PROBABILITY DENSITY FUNCTION FOR V SINCE IT IS ACTUALLY A REFLECTIVITY WEIGHTED DISTRIBUTION OF PARTICLE VELOCITIES WITHIN THE SCATTERING VOLUME 4HE TERM SPECTRUM WIDTH WILL BE USED TO REFER TO RV )T IS CLEAR THEREFORE THAT THE DOPPLER SPECTRUM CONTAINS THE INFORMATION NECESSARY TO MEASURE METEOROLOGICALLY IMPORTANT SIGNAL PARAMETERS 4HESE FIRST THREE MOMENTS ARE USUALLY REFERRED TO AS BASE DATA AND OFTEN LABELED : 6 AND 7 WITH THE APPROPRIATE CONVERSIONS AND UNITS )N THE MOST GENERAL CASE QUADRATURE PHASE DETECTION IS USED TO OBTAIN THE REAL AND IMAGINARY PARTS OF THE COMPLEX SIGNAL 4HESE ARE USUALLY DIGITIZED IN A LARGE NUMBER OF RANGE GATES y AT THE RADARS PULSE REPETITION FREQUENCY 4HE RESULTANT COMPLEX TIME SERIES IN EACH GATE CAN THEN BE PROCESSED BY USING A FAST &OURIER TRANSFORM &&4 TO OBTAIN AN ESTIMATE OF THE DOPPLER POWER SPECTRUM FROM WHICH THE ECHO POWER MEAN VELOCITY AND SPECTRUM WIDTH CAN BE OBTAINED
&)'52% 'AUSSIAN MODEL OF THE MEAN DOPPLER POWER SPECTRUM 4HE THREE SPECTRAL MOMENTS RECEIVED POWER RADIAL VELOCITY AND SPECTRUM WIDTH CAN BE ESTIMATED FROM THE SPECTRUM AND ARE DIRECTLY RELATED TO THE METEOROLOGICAL VARIABLES OF INTEREST
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!N EFFICIENT MOMENT ESTIMATION TECHNIQUE WAS ORIGINALLY DESCRIBED BY 2UMMLER AND REINTERPRETED BY $OVIAK AND :RNIC 4HIS ESTIMATOR MAKES USE OF THE FACT THAT THE COMPLEX AUTOCORRELATION FUNCTION OF THE RECEIVED SIGNAL HAS THE GENERAL FORM
§ P V ¶ 2 N4 0R R N4 EXP ¨ J N4 · © L ¸
WHERE QN4 IS THE CORRELATION COEFFICIENT OF THE TIME SERIES DATA AND N4 IS THE TIME LAG )T CAN BE SHOWN THAT V THE MEAN VELOCITY IS A FUNCTION OF THE FIRST LAG 24
V
L ARG; 24 = P 4
)T CAN ALSO BE SHOWN THAT
S V y
L P 4
24 ¶ § ¨ 2 0N · © ¸
WHERE 0N IS THE NOISE POWER 4HIS ESTIMATOR HAS BEEN WIDELY USED IN THE PAST FOR MEAN FREQUENCY ESTIMATION WITH DOPPLER METEOROLOGICAL RADARS 4HE ESTIMATES ARE UNBIASED IN THE PRESENCE OF NOISE WHEN THE DOPPLER SPECTRUM IS SYMMETRICAL )TS GREATEST APPEAL HOWEVER IS DUE TO ITS COMPUTATIONAL SIMPLICITY &OR A PULSED RADAR WITH A PULSE REPETITION PERIOD 4 24 IS OBTAINED FROM ADJACENT PAIRS OF PULSES USING THE SIMPLE EXPRESSION
24
.
.
£ SK SK K
WHERE THE SK ARE THE COMPLEX IN PHASE ) AND QUADRATURE 1 SIGNAL SAMPLES SAMPLED AT THE RADAR 024 AT A GIVEN RANGE AND SK IS ITS COMPLEX CONJUGATE )T IS CLEAR THAT THIS ALGORITHM REQUIRES . COMPLEX MULTIPLICATIONS FOR A TIME SERIES OF . SAMPLES WHEREAS THE &&4 REQUIRES . LOG . 4HIS SO CALLED PULSE PAIR ALGORITHM THEREFORE IS AN EFFI CIENT SPECTRAL MOMENT ESTIMATION TECHNIQUE (OWEVER IT SHOULD BE APPLIED ONLY WHEN ONE IS CERTAIN TO HAVE A PURE WEATHER SIGNAL IN WHITE NOISE OTHERWISE OTHER SPECTRAL COMPONENTS OR NON WHITE NOISE WILL BIAS THE SPECTRAL MOMENT ESTIMATES &OR MANY PAST OPERATIONAL RADARS THE PULSE PAIR PROCESSOR WAS THE TECHNIQUE OF CHOICE (OWEVER IN MANY RESEARCH APPLICATIONS IT REMAINS ADVANTAGEOUS FOR IMPROVED DATA QUALITY CONTROL PURPOSES TO ACCESS THE FULL DOPPLER SPECTRUM AND REMOVE ARTIFACTS PRIOR TO COMPUTING THE SPECTRAL MOMENTS CORRESPONDING TO THE METEOROLOGICAL DATA OF INTEREST 4HE WIND PROFILING RADAR COMMUNITY HAS MADE EXTENSIVE USE OF SPEC TRAL PROCESSING FOR ARTIFACT REMOVAL AND SENSITIVITY IMPROVEMENT /NE OF THE MORE IMPORTANT TASKS IS ESTIMATING THE NOISE FLOOR SO AS TO REMOVE ITS EFFECT ON THE SPECTRAL MOMENT ESTIMATES 4WO OBJECTIVE TECHNIQUES ARE COMMON #ONSTANTLY IMPROVING PROGRAMMABLE DIGITAL SIGNAL PROCESSING CHIPS AND SIGNAL PROCESSING COMPUTERS MAKE IT POSSIBLE FOR RADAR METEOROLOGISTS TO IMPLEMENT VARIOUS TYPES OF SPECTRUM PROCESS ING TECHNIQUES THAT VASTLY IMPROVE DATA QUALITY OVER THE SIMPLE PULSE PAIR PROCESSING ALGORITHM &URTHERMORE PROCESSORS THAT ADAPT THEMSELVES TO A VARIABLE ENVIRONMENT IN WHICH THEY USUALLY OPERATE ARE FEASIBLE &LEXIBLE PROGRAMMING OF DIGITAL SIGNAL PROCES SORS PERMITS TAILORING OF THE PROCESSORS CHARACTERISTICS TO THE APPLICATION FROM DAY TO DAY OR EVEN BEAM TO BEAM AND GATE TO GATE
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-EASUREMENT !CCURACY "ECAUSE THE RECEIVED SIGNALS ARE SAMPLE FUNCTIONS FROM GAUSSIAN RANDOM PROCESSES THE DOPPLER SPECTRUM AND ITS MOMENTS CANNOT BE MEASURED EXACTLY IN ANY FINITE PERIOD OF TIME #ONSEQUENTLY ALL MEASUREMENTS WILL BE SOMEWHAT IN ERROR WITH THE ERROR BEING A FUNCTION OF THE PROPERTIES OF THE ATMOSPHERE THE RADAR WAVELENGTH AND THE TIME ALLOCATED TO THE MEASUREMENT 4HE THEORETICAL DEVELOPMENT OF SIGNAL ESTIMATOR STATISTICS IS FOUND IN $ENENBERG 3ERAFIN AND 0EACH FOR THE &&4 TECHNIQUE $OVIAK AND :RNIC` COVER THE SUBJECT QUITE COMPLETELY WHILE +EELER AND 0ASSARELLI PROVIDE A GOOD SUMMARY OF ALL THESE ESTIMATION TECHNIQUES AND THE RESPECTIVE MEASUREMENT ERROR EXPRESSIONS &OLLOWING ARE SOME USE FUL EXPRESSIONS FOR THE MEAN SQUARE ERROR OF MEAN POWER AND MEAN VELOCITY ESTIMATES 0OWER %STIMATION )T IS WELL KNOWN THAT FOR A GAUSSIAN RANDOM PROCESS USING SQUARE LAW SIGNAL DETECTION SAMPLES OF THE MEAN POWER 0R OF THE PROCESS ARE EXPO NENTIALLY DISTRIBUTED WITH VARIANCE 0R 4HE VARIATION IS DUE TO THE PROCESS ITSELF NOT ANY NOISE ASSOCIATED WITH THE MEASUREMENT 'IVEN A TIME 4 SEC ALLOCATED TO THE MEASURE MENT AND A SIGNAL BANDWIDTH R F (Z THERE WILL BE APPROXIMATELY R F4 INDEPENDENT SAMPLES OF THE SQUARE OF THE SIGNAL ENVELOPE )T FOLLOWS THEREFORE THAT FOR THE HIGH 3.2 CASE AN ESTIMATE OF THE MEAN POWER FOR THIS PROCESS 0}R WILL HAVE A VARIANCE OR MEAN SQUARE ERROR GIVEN BY
VAR 0}R y
0R S F 4
3UBSTITUTING FOR R F FROM THE EXPRESSION R F R V K WHERE R V IS THE WIDTH OF THE DOPPLER SPECTRUM %Q BECOMES
VAR 0}R y
L 0R S V4
4HIS EXPRESSION IS VALID FOR HIGH SIGNAL TO NOISE CASES 6ELOCITY %STIMATION 4HE VARIANCE OF THE MEAN FREQUENCY ESTIMATE OF THE DOPPLER SPECTRUM IS
VAR F}
0R4
¯ F 3 F F DF
} 4HIS IS AN INTERESTING RESULT SHOWING THAT THE VARIANCE OF THE ESTIMATE F IS A FUNC TION ONLY OF THE SHAPE OF THE DOPPLER SPECTRUM PRIMARILY ITS SPECTRUM WIDTH AND THE INTEGRATION TIME 4 ALLOCATED FOR PROCESSING )F THE SPECTRUM CAN BE ACCURATELY MODELED BY A GAUSSIAN SHAPE WITH VARIANCE S F %Q REDUCES TO
VAR F}
SF
LS V P 4
P 4
.OTING THAT VAR V} L VAR F} WE CAN WRITE
VAR V}
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)F WE MULTIPLY THE NUMERATOR AND DENOMINATOR BY R V %Q BECOMES VAR V
LS V S V P S V4 P S F 4
4HUS IT IS SEEN THAT THE VARIANCE OF THE MEAN VELOCITY ESTIMATE V} IS DIRECTLY PROPOR TIONAL TO THE VARIANCE OF THE DOPPLER SPECTRUM AND INVERSELY PROPORTIONAL TO THE NUMBER OF INDEPENDENT SAMPLES R F 4 .OTE ALSO THAT VAR V} IS PROPORTIONAL TO K INDICATING THAT FOR THE SAME PROCESSING TIME 4 AND FOR THE SAME R V THE VARIANCE OF THE ESTIMATE CAN BE REDUCED BY REDUCING THE WAVELENGTH WHICH INCREASES THE NUMBER OF INDEPEN DENT SAMPLES %QUATIONS n ARE APPLICABLE IN HIGH SIGNAL TO NOISE RATIO CASES 5NCERTAINTIES IN THE SPECTRAL MOMENT ESTIMATES RESULT FROM THE LIMITED OBSERVATION TIME OF THE NARROW BAND RANDOM PROCESS CHARACTERIZING THE METEOROLOGICAL ECHO !NY NOISE IN THE MEASUREMENT FURTHER INCREASES THE UNCERTAINTY :RNIC` GIVES THE MORE GENERAL FOLLOWING EXPRESSION FOR THE VARIANCE OF THE MEAN FREQUENCY ESTIMATE F FOR THE PULSE PAIR ESTIMATION TECHNIQUE AND A GAUSSIAN SHAPED SPECTRUM ª ¹ . . «P S F 4 3 ; R 4 =º 3 ¬ » WHERE Q IS THE CORRELATION COEFFICIENT AND .3 IS THE NOISE TO SIGNAL RATIO %QUATION APPLIES A SINGLE 02& WITH INTERPULSE PERIOD 4 AND ASSUMES THAT ALL PULSES IN THE INTERVAL 4 ARE USED IN THE ESTIMATION ALGORITHM )T REDUCES EXACTLY TO %Q FOR A LARGE 3.2 AND FOR NARROW SPECTRA IE Q4 y 4HE READER IS REFERRED TO :RNIC` FOR FURTHER DETAILS REGARDING THE ESTIMATION OF OTHER MOMENTS OF THE DOPPLER SPECTRUM
VAR F}
P 4 R 4 4
0ULSE #OMPRESSION 0ULSE COMPRESSION HAS BEEN INFREQUENTLY USED FOR METEO ROLOGICAL APPLICATIONS BECAUSE SHORT PULSE PEAK POWER HAS NOT BEEN A LIMITATION ON WEATHER RADAR SYSTEM PERFORMANCE +EELER AND &RUSH HOWEVER DESCRIBED HOW ATMO SPHERIC DISTRIBUTED TARGETS MAY BE TREATED AS FROZEN FIXED hSLABSv OF SCATTERING CENTERS SUCH THAT THEY APPROXIMATE LAYERS OF NONFLUCTUATING SCATTERERS AS THE CODED RADAR PULSE PROPAGATES THROUGH THEM 4HUS EACH SCATTERING SLAB PRODUCES A RETURN SIGNAL THAT CAN BE COMPRESSED BY THE COMPRESSION FILTER IN THE SAME WAY AS FOR INDIVIDUAL POINT TARGETS 4HEY POINTED OUT THAT PULSE COMPRESSION CAN BENEFIT RAPID SCANNING RADAR APPLICATIONS IN WHICH THE DESIRED DWELL TIME OF EACH SCATTERING VOLUME IS MUCH SHORTER THAN THE DECORRELATION TIME OF THE WEATHER ECHOES )N THESE CASES AVERAGING PULSE COMPRESSED RANGE MEASUREMENTS INSTEAD OF INTEGRATING OVER A LONGER DWELL TIME PROVIDES THE LARGE NUMBER OF INDEPENDENT SAMPLES NEEDED FOR ACCURATE MEASUREMENT IN A VERY SHORT BEAM OBSERVATION TIME 3IMILARLY THE EFFECTIVE RANGE RESOLUTION OVER WHICH AVERAG ING IS PERFORMED CAN BE FLEXIBLE TO MEET CHANGING OBSERVATIONAL REQUIREMENTSSHORT RANGE INTERVALS FOR HIGHLY STRUCTURED HEAVY RAINFALL STORMS TYPICALLY CONVECTIVE AND LONGER RANGE INTERVALS FOR MORE UNIFORM BUT WEAKER RAINFALL TYPICALLY STRATIFORM )N OTHER SITUATIONS WHERE SIGNALS ARE VERY WEAK SUCH AS FOR WIND PROFILER APPLICATIONS AND CLEAR AIR BOUNDARY LAYER OBSERVATIONS PULSE COMPRESSION MAY BE USED TO INCREASE SYSTEM SENSITIVITY BY INCREASING THE AVERAGE POWER OF THE SYSTEM USING LONG PULSES WHILE PROCESSING FOR ANY DESIRED RANGE RESOLUTION 2ANGE RESOLUTION AND 3.2 ARE INDE PENDENTLY DETERMINED BY THE PULSE COMPRESSION WAVEFORM DESIGN PARAMETERS ! NOTE OF CAUTION IS IN ORDER WHEN CONSIDERING PULSE COMPRESSION FOR METEORO LOGICAL RADARS RELATING TO THE MATTER OF RANGE SIDELOBES #AREFUL DESIGN IS NECESSARY TO MINIMIZE THESE SIDELOBES JUST AS ANTENNA SIDELOBES SHOULD BE MINIMIZED IN ORDER
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TO MITIGATE THE EFFECTS OF INTERPRETIVE ERRORS CAUSED BY WIDE DYNAMIC RANGE DISTRIBUTED WEATHER TARGETS !MPLITUDE FREQUENCY AND PHASE SHAPING OF THE TRANSMITTED PULSE ALONG WITH SPECIAL SIDELOBE SUPPRESSIONCOMPRESSION FILTERS IN THE RECEIVER PROCESSOR ALLOW RANGE SIDELOBES TO BE SUPPRESSED BY MORE THAN D" OVER A SIGNIFICANT DOPPLER INTERVALTENS OF METERS PER SECOND 4HESE COMPRESSION FILTERS ARE NOT MATCHED TO THE TRANSMIT WAVEFORM THEREFORE THE 3.2 DEGRADES SOMEWHAT AND POSSIBLE LOSS OF RANGE RESOLUTION IN THE MAIN BEAM MAY OCCUR (OWEVER THESE LOSSES ARE TOLERABLE FOR MANY METEOROLOGICAL MEASUREMENTS OF INTEREST 7HITENING 0ULSE COMPRESSION INVOLVES INCREASED TRANSMIT BANDWIDTH THAT IS FREQUENTLY DIFFICULT TO HAVE ALLOCATED AND MAY LIMIT ITS USE AT 3 BAND AND # BAND FOR OPERATIONAL APPLICATIONS ! FIXED BANDWIDTH TECHNIQUE FOR INCREASING RANGE RESOLUTION AND THE NUMBER OF INDEPENDENT SAMPLES IS THE PROCESS OF SAMPLING THE TRANSMIT PULSE AT AN INTERVAL SEVERAL TIMES SHORTER THAN ITS DURATION AND USING A LINEAR PREDICTIVE WHITENING FILTER TO REMOVE THE CORRELATED INFORMATION FROM THE OVERSAMPLED DATA 4HIS WHIT ENING PROCESS INCREASES THE NUMBER OF INDEPENDENT SAMPLES FOR RANGE AVERAGING THAT ALLOWS IMPROVED PARAMETER ESTIMATION ACCURACY BUT AT A COST OF SIGNIFICANTLY REDUCED 3.2 4HE HIGHER NOISE BANDWIDTH IN THE RECEIVER REQUIRED BY THE HIGHER RATE SAMPLING AND THE WHITENING FILTER NOISE ENHANCEMENT CAUSE THE 3.2 TO BE REDUCED BY A FACTOR OF APPROXIMATELY , WHERE , IS THE INCREASED SAMPLING FACTOR 3TATED ANOTHER WAY THE WHITENING FILTER EFFECTIVELY SHORTENS THE TRANSMIT PULSE BY , WHILE PASSING THE INCREASED RECEIVER NOISE POWER BY , THEREBY TRADING RANGE RESOLUTION FOR 3.2 &ORTUNATELY FOR PRECIPITATION ECHOES AND TYPICAL WEATHER RADARS THE 3.2 IS QUITE HIGH AND EVEN AFTER THE WHITENING PROCESS IT REMAINS HIGH ENOUGH TO EFFECTIVELY UTILIZE THE LARGER NUMBER OF INDEPENDENT SAMPLES FOR IMPROVED BASE DATA ESTIMATES OR IMPROVED RANGE RESOLU TION MEASUREMENTS /N THE OTHER HAND IF THE SIGNAL IS WEAK NOISE ENHANCEMENT WILL DOMINATE THE WHITENING PROCESS AND ANY ADVANTAGE IS LOST (IGHLY IMPORTANT IS THE FACT THAT THE TRANSMIT PULSE AND ITS BANDWIDTH ARE NOT CHANGED CONSEQUENTLY INCREASED FRE QUENCY ALLOCATION TO MAKE USE OF THE HIGHER RANGE RESOLUTION IS NOT AN ISSUE 3HORT $WELL 4IME 3PECTRA -AXIMUM %NTROPY 3PECTRAL PROCESSING OF WEATHER ECHOES ADDS ANOTHER DEGREE OF FREEDOM THE FREQUENCY DIMENSION TO THE ABIL ITY TO DISCRIMINATE SIGNAL FROM GROUND CLUTTER OTHER ARTIFACTS AND NOISE AND TO ESTIMATE METEOROLOGICAL PARAMETERS OF INTEREST -OST FREQUENCY DOMAIN PROCESSING REQUIRES RELATIVELY LONG )1 DATA SAMPLE SETS FOR DISCRETE &OURIER TRANSFORM ANALYSES WINDOW FUNCTIONS AND POSSIBLE SPECTRAL AVERAGING TO OBTAIN SPECTRA SUITABLE FOR QUANTITA TIVE PROCESSING &ASTER SCANNING RADARS USED FOR SAMPLING RAPIDLY EVOLVING STORMS REQUIRES SPECTRUM ANALYSIS TECHNIQUES THAT USE SHORT DWELL TIME DATA SETS OF MANY FEWER )1 DATA SAMPLES -ODERN SPECTRUM ANALYSIS TECHNIQUES SUCH AS THE "URG MAXIMUM ENTROPY AND THE #APON MAXIMUM LIKELIHOOD ESTIMATORS ALLOW USING SHORT DWELL SAMPLED DATA TO OBTAIN STABLE SPECTRUM ESTIMATORS 4HESE TECHNIQUES BELONG TO THE GENERAL CLASS OF AUTOREGRESSIVE !2 ESTIMATORS WHEREBY THE OBSERVED DATA ARE MOD ELED AS ALL POLE FILTERED WHITE NOISE RATHER THAN A WEIGHTED SUM OF SINUSOIDS ACCORDING TO THE &OURIER MODEL -ULTIPLE SIGNALS AND GROUND CLUTTER MAY BE RESOLVED THE SAME AS USING &OURIER ESTIMATORS 4HESE SHORT DWELL TIME !2 SPECTRA MAY THEN BE USED TO ESTIMATE WEATHER SPECTRAL MOMENTS THE SAME AS THE &OURIER DATA MODEL SPECTRUM ESTI MATORS FROM WHICH THE WEATHER PARAMETERS ARE DERIVED 0ROCESSOR )MPLEMENTATIONS -ODERN METEOROLOGICAL RADARS USE DIGITAL SIGNAL PROCESSING TECHNIQUES ON PROGRAMMABLE PLATFORMS AND INTERACTIVE COLOR DISPLAYS
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FOR QUANTITATIVE PRECISION IN INTERPRETING THE WEATHER ECHOES -ODERN WEATHER RADARS REQUIRE LARGE DYNAMIC RANGE TO SENSE STRONG ECHO AT SHORT RANGE AND WEAK ECHO AT LONG RANGE 4HUS THE RECEIVER AND PROCESSOR DESIGNS ATTEMPT TO MAINTAIN AMPLITUDE AND PHASE LINEARITY THROUGHOUT THAT RANGE BY USING A DYNAMIC AUTOMATIC GAIN CONTROL !'# WHEREBY THE RECEIVER GAIN AND PHASE ARE ADJUSTED ALONG THE RANGE INTERVAL THROUGH THE USE OF RAPIDLY SWITCHED ATTENUATORS OR MORE OFTEN DIGITAL COMPENSATION #LEARLY SUCH RAPID SWITCHING IN THE RECEIVER REQUIRES CAREFUL DESIGN IN ORDER TO AVOID THE AFFECTS OF SWITCHING TRANSIENTS !N APPROACH THAT AVOIDS TRANSIENT EFFECTS IS TO USE TWO PARALLEL )& RECEIVER CHANNELS EACH WITH MODERATE DYNAMIC RANGE AND FIXED GAINS AND TO SAMPLE THE SIGNAL IN THE CHANNEL THAT IS BEST MATCHED TO THE SIGNAL STRENGTH )N ALL THOSE APPROACHES IT IS POSSIBLE TO ACHIEVE LINEAR DYNAMIC RANGE OF GREATER THAN D" AND TO USE FLOATING POINT DIGITAL PROCESSING 4HE REFLECTIVITY MEAN DOPPLER VELOCITY AND SPECTRUM WIDTH CAN ALL BE ESTIMATED DIGITALLY FROM THE FLOATING POINT SAMPLES 4HE PROCESSING CAN BE PERFORMED WITH A DEDICATED DIGITAL SIGNAL PROCESSING COMPUTER OR BY FAST GENERAL PURPOSE COMPUTERS COMBINED WITH SPECIAL SIGNAL PROCESSING COMPONENTS USING $IGITAL 3IGNAL 0ROCESSING $30 CHIPS OR FIELD PROGRAMMABLE GATE ARRAY &0'! DEVICES #ONTINUED TECHNOLOGY ADVANCES WILL PERMIT ADVANCED BUT MATURE SIGNAL PROCESSING ALGO RITHMS SUCH AS MODERN SPECTRAL PROCESSING AND ADAPTIVE FILTERING TO BE IMPLEMENTED
£°xÊ "* ,/" Ê** /" !S HAS BEEN DEMONSTRATED METEOROLOGICAL RADARS MEASURE BACKSCATTERED POWER AND RADIAL VELOCITY PARAMETERS 4HE CHALLENGE TO THE RADAR METEOROLOGIST IS TO TRANSLATE THESE MEASUREMENTS THEIR SPATIAL DISTRIBUTIONS AND THEIR TEMPORAL EVOLUTION INTO QUANTITATIVE ASSESSMENTS OF THE WEATHER 3ERAFIN AND 7ILSON AMONG OTHERS SHOW HOW MODERN METEOROLOGICAL RADARS ARE USED FOR FORECASTING THE WEATHER 4HE LEVEL OF SOPHISTICATION USED IN INTERPRETATION VARIES BROADLY RANGING FROM HUMAN INTERPRETATION OF RUDIMEN TARY DISPLAYS TO AUTOMATIC ALGORITHMS AND MODERN MULTIDIMENSIONAL DISPLAYS TO ASSIST HUMAN INTERPRETATION %XPERT SYSTEM APPROACHES THAT ATTEMPT TO REPRODUCE HUMAN INTERPRETIVE LOGICAL PROCESSES HAVE BEEN EMPLOYED EFFECTIVELY 4HE DEGREE TO WHICH AUTOMATION CAN BE APPLIED IS EVIDENT IN THE .EXRAD RADAR SYSTEM DESIGN THAT PRODUCES THE AUTOMATED METEOROLOGICAL PRODUCTS SHOWN IN 4ABLE 4!",% 0ARTIAL ,IST OF .EXRAD !UTOMATED 0RODUCTS
"ASE RADAR REFLECTIVITY ALL RANGES EACH SCAN "ASE RADIAL VELOCITY "ASE SPECTRUM WIDTH #OMPOSITE MAXIMUM AT ALL HEIGHTS REFLECTIVITY 0RECIPITATION ECHO TOPS 3EVERE WEATHER PROBABILITY 6ELOCITY !ZIMUTH $ISPLAY 6!$ 7IND 0ROFILE 3TORM RELATIVE MEAN RADIAL VELOCITY 6ERTICAL INTEGRATED LIQUID 3TORM TRACKING INFORMATION (AIL POTENTIAL -ESOCYCLONE AND 4ORNADO 6ORTEX 3IGNATURE 3URFACE RAINFALL ACCUMULATION HR HR TOTAL STORM 2ADAR %CHO #LASSIFIER
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0RECIPITATION -EASUREMENT !MONG THE MORE IMPORTANT PARAMETERS TO BE MEASURED IS RAINFALL HAVING SIGNIFICANCE TO A NUMBER OF WATER RESOURCE MANAGEMENT PROBLEMS RELATED TO AGRICULTURE FRESH WATER SUPPLIES STORM DRAINAGE AND WARNING OF POTENTIAL FLOODING 4HE RAINFALL RATE CAN BE EMPIRICALLY RELATED TO THE REFLECTIVITY FACTOR BY AN EXPRESSION OF THE FORM
: A2B
WHERE A AND B ARE CONSTANT AND 2 IS THE RAINFALL RATE USUALLY IN MILLIMETERS PER HOUR "ATTAN DEVOTES THREE FULL PAGES OF HIS BOOK TO THE LISTING OF DOZENS OF : 2 RELATION SHIPS DERIVED BY INVESTIGATORS AT VARIOUS LOCATIONS THROUGHOUT THE WORLD FOR VARIOUS WEATHER CONDITIONS AND IN ALL SEASONS OF THE YEAR 4HE FACT THAT NO UNIVERSAL EXPRESSION CAN BE APPLIED TO ALL WEATHER SITUATIONS IS NOT SURPRISING WHEN ONE NOTES THAT RAINFALL DROP SIZE DISTRIBUTIONS ARE HIGHLY VARIABLE &OR MANY CONDITIONS THE DROP SIZE DISTRI BUTION CAN BE REPRESENTED BY AN EXPONENTIAL FUNCTION
.$ . E n,$
WHERE . AND , ARE CONSTANTS AND ,$ WHERE $ IS THE MEDIAN DROP DIAMETER )F .$ IS KNOWN THE REFLECTIVITY FACTOR CAN BE CALCULATED FROM %Q "Y USING THE TERMINAL FALL SPEED DATA OF 'UNN AND +INZER THE RAINFALL RATE CAN ALSO BE OBTAINED AND : RELATED TO 2 AS SHOWN IN %Q 4HE EXPONENTIAL FORM OF THE DROP SIZE DISTRI BUTION GENERALLY FITS THE AVERAGE OF SEVERAL DROP SIZE DISTRIBUTIONS THAT OCCUR OVER DIF FERENT PHASES OF CONVECTIVE AND TROPICAL RAINFALL AND ARE AVERAGED OVER SPACE OR TIME (OWEVER THE hGAMMAv DROP SIZE DISTRIBUTION REPRESENTS A BETTER FIT TO INSTANTANEOUS NATURAL VARIATIONS OF THE DROP SIZE DISTRIBUTION UNDER DIFFERENT CONDITIONS 4HE GAMMA DROP SIZE DISTRIBUTION IS GIVEN AS
.$ . $L E n,$
WITH L n AND ,$ L 4HE L PARAMETER CONTROLS THE SHAPE OF THE DISTRIBUTION AND WHEN L THE DISTRIBUTION IS EXPONENTIAL #LEARLY A SINGLE WAVELENGTH SINGLE POLARIZATION RADAR CAN MEASURE ONLY A SINGLE PARAMETER : AND MUST ASSUME 2AYLEIGH SCATTERING 3INCE THE RAINFALL RATE DEPENDS UPON TWO PARAMETERS . AND , IT IS NOT SURPRISING THAT %Q IS NOT UNIVERSAL $ESPITE THIS FACT "ATTAN LISTS FOUR EXPRESSIONS AS BEING hFAIRLY TYPICALv FOR THE FOLLOWING FOUR TYPES OF RAIN
3TRATIFORM RAIN : 2
/ROGRAPHIC RAIN : 2
4HUNDERSTORM RAIN : 2
3NOW : 2
3TRATIFORM REFERS TO WIDESPREAD RELATIVELY UNIFORM RAIN AND USES THE WELL KNOWN -ARSHALL 0ALMER DROP SIZE DISTRIBUTION /ROGRAPHIC RAIN IS PRECIPITATION THAT IS INDUCED OR INFLUENCED BY HILLS OR MOUNTAINS WHEREAS 4HUNDERSTORM RAIN IS TYPICAL OF CONVECTIVE PRECIPITATION SYSTEMS )N EACH OF THE ABOVE EXPRESSIONS : IS IN MMM AND 2 IS IN MMH )N %Q 2 IS THE PRECIPITATION RATE OF THE WATER EQUIVALENT MELTED SNOW "ATTAN GIVES A MORE COMPLETE TREATMENT OF THIS IMPORTANT TOPIC
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7ILSON AND "RANDES GIVE A COMPREHENSIVE TREATMENT OF HOW RADAR AND RAIN GAUGE DATA CAN BE USED TO COMPLEMENT ONE ANOTHER IN MEASUREMENTS OF PRECIPITATION OVER LARGE AREAS 4HEY STATE THAT THE RADAR DETERMINED STORM CUMULATIVE PRECIPITATION MEASUREMENTS ARE EXPECTED TO BE ACCURATE WITHIN A FACTOR OF FOR OF THE TIME !CCURACIES OVER LARGE AREAS CAN BE IMPROVED TO ABOUT WITH THE ADDITION OF A SURFACE RAIN GAUGE NETWORK !LTHOUGH RADAR MEASURES REFLECTIVITY ALOFT THE PRIMARY CONCERN IS RAINFALL ESTIMATION AT THE SURFACE 2AIN GAUGE MEASUREMENTS ARE FREQUENTLY USED TO ADJUST THE RADAR REFLECTIVITY VALUES :AWADZKI DESCRIBES MANY FACTORS THAT INFLUENCE RAINFALL MEASUREMENT BY RADAR *OSS AND ,EEAND OTHERS USE THE 6ERTICAL 0ROFILE OF 2EFLECTIVITY 602 TO ESTIMATE THE SURFACE RAINFALL RATE WITH SOME SUCCESS "RIDGES AND &ELDMAN DISCUSS HOW TWO INDEPENDENT MEASUREMENTS REFLEC TIVITY FACTOR AND ATTENUATION CAN BE USED TO OBTAIN BOTH PARAMETERS OF THE DROP SIZE DISTRIBUTION AND MORE PRECISELY DETERMINE THE RAINFALL RATE 0OLARIMETRIC %STIMATES $UAL POLARIZATION RADAR HAS BEEN PROVEN TO YIELD IMPROVED RAINFALL ESTIMATES AS WELL AS OTHER ADVANTAGES FOR WEATHER RADAR 0OLARIMETRIC RADAR MEASUREMENTS TAKE ADVANTAGE OF THE FLATTENED RAINDROP SHAPE APPROXIMATED BY AN OBLATE SPHEROID A FLATTENED SPHERE HAVING A HORIZONTAL DIMENSION GREATER THAN ITS VERTI CAL DIMENSION AND ITS PROPAGATION AND SCATTERING CHARACTERISTICS TO OBTAIN ACCURATE RAIN RATE ESTIMATORS 3ELIGA AND "RINGI AND 3ACHIDANANDA AND :RNIC SHOW HOW THE CO POLAR MEASUREMENTS OF : AT HORIZONTAL :H AND VERTICAL :V POLARIZATIONS CAN PRO DUCE TWO INDEPENDENT MEASUREMENTS AND THEREFORE PROVIDE MORE ACCURATE RAINFALL RATE MEASUREMENTS THAN THOSE RELATED TO SIMPLE REFLECTIVITY "RINGI AND #HANDRA GIVE THE FOLLOWING RAIN RATE ESTIMATORS FOR MEASUREMENTS AT CM 3 BAND /THER WAVELENGTHS HAVE DIFFERENT CONSTANTS BECAUSE OF -IE FACTORS ENTERING INTO THE CALCULATIONS AND THE WAVELENGTH DEPENDENCE OF PHASE MEASUREMENTS
2:H :DR :H :DRn
2+DP +DP
2+DP :DR +DP :DRn
4HE REFLECTIVITY BASED RAIN RATE ESTIMATORS CORRESPONDING TO THE -ARSHALL 0ALMER : 2 AND THE COMMON .EXRAD 732 $ : 2 RELATIONS ARE
2-0 : : FOR -ARSHALL 0ALMER
2$ : : FOR .EXRAD 732 $
4HE POLARIMETRIC PRECIPITATION MEASUREMENTS BRING UNIQUE CHARACTERISTICS THAT ADDRESS NOT ONLY IMPROVED PRECIPITATION MEASUREMENTS BUT ALSO IMPROVED DATA QUAL ITY CHARACTERISTICS 4HE DIFFERENTIAL REFLECTIVITY BETWEEN THE HORIZONTAL AND VERTI CAL POLARIZATIONS :DR ALLOWS ESTIMATING THE EFFECTIVE DROP SIZE WHEREAS DIFFERENTIAL PHASE +DP GIVES ADDITIONAL SOMEWHAT INDEPENDENT INFORMATION ON ESTIMATION OF RAINFALL RATES +DP IS AN ESPECIALLY IMPORTANT PARAMETER WHEN THE RADAR IS CONFRONTED WITH TYPICAL CONTAMINANTS AS BEAM BLOCKAGE GROUND CLUTTER DOMINATION AND CALIBRA TION ERRORS &URTHERMORE 2YZHKOV AND :RNIC HAVE SHOWN THAT +DP BASED RAINFALL MEASUREMENTS ARE LESS DEPENDENT ON THE UNKNOWN AND VARIABLE DROP SIZE DISTRIBU TION $3$ THAN POWER BASED MEASUREMENTS &URTHERMORE OTHER INFERENCES FROM THE
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POLARIMETRIC MEASUREMENTS ALLOW ONE TO ESTIMATE THE PARAMETERS OF THE GAMMA FUNC TION FORM OF THE $3$ WHICH MAY FURTHER IMPROVE RAINFALL ESTIMATION !ND SELF CONSISTENCY CONSTRAINTS OF THE POLARIMETRIC PRECIPITATION COVARIANCE MATRIX IMPOSE RELATIVELY STRICT BOUNDS ON THE ABSOLUTE REFLECTIVITY MEASUREMENTS ALLOWING ONE TO CALIBRATE THE REFLECTIVITY MEASUREMENT AND MAKE IMPROVED RAINFALL RATE ESTIMATES &OR SHORT WAVELENGTH RADARS ONE MUST CONSIDER -IE SCATTERING EFFECTS WHEN MEASUR ING RAINFALL RATE BY REFLECTIVITY MEASUREMENT ,HERMITTE AND +OLLIAS ET AL GIVE AN ANALYSIS OF -IE SCATTERING AND SHOW THAT IF THE SCATTERING IS PROPERLY ACCOUNTED THE RAINFALL MEASUREMENTS ARE ACCURATE 0OLARIMETRIC RADARS MAY BE CONFIGURED IN DIFFERENT WAYS FOR DIFFERENT MEASURE MENTS 2ESEARCH RADARS EXPLORE THE DEPOLARIZATION RATIOS BY ALTERNATING HORIZONTALLY AND VERTICALLY POLARIZED PULSES (OWEVER THE PREFERRED CONFIGURATION FOR OPERA TIONAL RADARS IS TO TRANSMIT BOTH HORIZONTAL AND VERTICAL POLARIZATIONS SIMULTANEOUSLY WHILE INDEPENDENTLY RECEIVING BOTH ORTHOGONAL SIGNALS FOR POLARIMETRIC PROCESSING ALLOWING RECEPTION OF THE IMPORTANT CO POLAR QUANTITIES 4HE RELATIVE PHASE OF EACH TRANSMITTED POLARIZATION IS ARBITRARY BUT THE DIFFERENTIAL MAGNITUDE AND PHASE OF THE CO POLAR RECEIVED SIGNALS IN EACH POLARIZATION ARE SUFFICIENT FOR THE POLARIMETRIC MEASUREMENTS )T IS OUR OPINION THAT NO SINGLE TOPIC IN RADAR METEOROLOGY HAS RECEIVED MORE ATTENTION THAN RAINFALL RATE MEASUREMENT !LTHOUGH USEFUL EMPIRICAL EXPRESSIONS HAVE EVOLVED AND DUAL POLARIZATION TECHNIQUES SHOW SIGNIFICANT IMPROVEMENTS IN ACCU RACY A COMPLETELY SATISFACTORY APPROACH REMAINS TO BE DEVELOPED 0OLARIMETRIC MEASUREMENTS BY THE 732 $ RADARS WILL ALLOW MORE ACCURATE PRECIPITATION MEASUREMENTS AND ICE WATER PHASE KNOWLEDGE THAT IS IMPORTANT FOR MAKING IMPROVED FORECASTS SEPARATING WINTER PRECIPITATION INTO REGIONS OF RAIN AND SNOW AND DETECTING HAZARDOUS AIRCRAFT ICING CONDITIONS )MPLEMENTATION OF PHASE CODING ALGORITHMS ALLOW THESE RADARS TO SEPARATE MULTIPLE TIME AROUND OR MULTI PLE TRIP ECHOES AND TO COMPUTE DEALIASED VELOCITIES IN THE RANGE DEALIASED ECHOES TO CLASSIFY AND SEPARATE PRECIPITATION ECHOES FROM ARTIFACTS AS GROUND CLUT TER SEA CLUTTER AND INSECTS ECHOES TO ACCOMMODATE FLEXIBLE SCAN STRATEGIES AND TO INCORPORATE IMPROVED DATA RESOLUTION IN RANGE AND AZIMUTH 4HESE PERFORMANCE ENHANCEMENTS ARE READILY ACHIEVED BY INSTALLING GREATER AND MORE FLEXIBLE SIGNAL AND DATA PROCESSING POWER 3EVERE 3TORM 7ARNING /NE OF THE PRIMARY PURPOSES OF WEATHER RADARS IS TO PROVIDE TIMELY WARNINGS OF SEVERE WEATHER PHENOMENA SUCH AS TORNADOES DAMAGING WINDS FLASH FLOODS AND LANDFALLING HURRICANES !CCURATE LONG TERM FORECASTING OF THE PRECISE LOCATION AND LEVEL OF SEVERITY OF THESE PHENOMENA THROUGH DATA ASSIMILATION AND NUMERICAL WEATHER PREDICTION TECHNIQUES IS BEYOND THE PRESENT STATE OF THE ART /PERATIONAL RADARS HOWEVER CAN DETECT THESE PHENOMENA AND PROVIDE LOCAL WARN INGS OF APPROACHING SEVERE EVENTS THEY CAN ALSO DETECT THE ROTATING MESOCYCLONES IN SEVERE STORMS THAT ARE PRECURSORS TO THE DEVELOPMENT OF TORNADOES AT THE %ARTHS SURFACE 'ROUND BASED COASTAL AND AIRBORNE RADARS CAN ALSO MEASURE THE SEVERITY OF APPROACHING HURRICANES AND DEFINE THEIR MOST INTENSE LANDFALL POSITIONS FOR EVACU ATION WARNINGS 4ORNADO $ETECTION ! SINGLE DOPPLER RADAR CAN MEASURE ONLY THE RADIAL COMPO NENT OF THE VECTOR WIND FIELD (ENCE EXACT MEASUREMENTS OF VECTOR WINDS AT A POINT ARE GENERALLY NOT POSSIBLE (OWEVER ROTATING WINDS OR VORTICES CAN BE DETECTED AND
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THEIR INTENSITIES MEASURED BY SIMPLY MEASURING THE CHANGE IN RADIAL VELOCITY WITH AZIMUTH ANGLE AS SHOWN IN &IGURE 4HE RADAR SCANS IN AZIMUTH AND DETECTS A COUPLET IN RADIAL VELOCITY AT CONSTANT RANGE 4HE AZIMUTH SHEAR IS GIVEN SIMPLY BY THE EXPRESSION
DVR VR y DX RA
WHERE X IS IN THE DIRECTION ORTHOGONAL TO THE RADIUS OF THE CIRCULATION AND @ IS THE ANGLE SUBTENDED BY THE CIRCULATION AT RANGE R "ECAUSE MESOCYCLONES MAY SPAWN TORNADOES AND CAN BE MANY KILOMETERS IN DIAM ETER RADARS WITH ABOUT n BEAMWIDTH HAVE THE SPATIAL RESOLUTION TO DETECT MESOCY CLONES AT RANGES IN EXCESS OF KM )T SHOULD BE CLEAR THAT ANY MEAN TRANSLATIONAL MOTION WOULD CHANGE THE ABSOLUTE VALUES OF THE MEASURED RADIAL VELOCITIES BUT WOULD NOT AFFECT THE SHEAR MEASUREMENT !ZIMUTHAL SHEAR VALUES OF THE ORDER OF n Sn OR GREATER AND WITH VERTICAL EXTENT GREATER THAN THE DIAMETER OF THE MESOCYCLONE ARE DEEMED NECESSARY FOR A TORNADO TO OCCUR $ETECTION OF THE TORNADO VORTEX ITSELF IS NOT GENERALLY POSSIBLE BEYOND ABOUT KM USING TYPICAL WEATHER RADAR BEAMWIDTHS SINCE ITS HORIZONTAL EXTENT MAY BE ONLY A FEW HUNDRED METERS $ETECTION OF THE RADIAL SHEAR THEREFORE IS NOT POSSIBLE UNLESS THE TOR NADO IS CLOSE ENOUGH TO THE RADAR TO BE RESOLVED BY THE BEAMWIDTH (OWEVER IN CASES WHERE THE TORNADO FALLS ENTIRELY WITHIN THE BEAM THE DOPPLER SPECTRUM WIDTH MAY BE USED TO ESTIMATE TORNADIC INTENSITY )N SOME CASES BOTH A MESOCYCLONE AND ITS INCIPIENT TORNADO CAN BE DETECTED 7ILSON AND 2OESLI SHOW AN EXCELLENT EARLY EXAMPLE OF A TORNADO VORTEX SIGNATURE 463 EMBEDDED WITHIN A LARGER MESOCYCLONE -ICROBURSTS &UJITA AND #ARACENA FIRST IDENTIFIED THE MICROBURST PHENOMENON AS THE CAUSE OF AN AIRLINER CRASH THAT TOOK PLACE IN 4HE MICROBURST AND ITS EFFECTS ON AN AIRCRAFT DURING TAKEOFF OR LANDING ARE DEPICTED IN &IGURE 4HE MICROBURST IS SIMPLY A SMALL SCALE SHORT DURATION DOWNDRAFT EMANATING FROM A CONVECTIVE STORM 4HIS hBURSTv OF AIR SPREADS OUT RADIALLY AS IT STRIKES THE GROUND FORMING A RING OF DIVERGINGAIR ABOUT TO KM DEEP AND OF THE ORDER OF TO KM IN DIAMETER WITH DIVERGENT WINDS GREATER THAN MS AND LASTING LESS THAN MINUTES !IRCRAFT PEN ETRATING A MICROBURST FIRST EXPERIENCE AN INCREASE IN HEAD WIND AND THEN A CONTINU OUS PERFORMANCE ROBBING DECREASE IN HEAD WIND WHICH CAN CAUSE THE PLANE TO CRASH IF ENCOUNTERED SHORTLY BEFORE TOUCHDOWN OR JUST AS THE AIRCRAFT IS TAKING OFF -ORE COMPLETE DESCRIPTIONS OF MICROBURSTS AND THEIR EFFECTS ON AVIATION SAFETY ARE GIVEN BY &UJITA AND -C#ARTHY AND 3ERAFIN
&)'52% -EASUREMENT OF ROTATION OR AZIMUTHAL WIND SHEAR IN A MESOCYCLONE A ROTATING WIND PARCEL 4HE AZIMUTHAL SHEAR IS GIVEN BY #V#X VR R@ #OURTESY OF 5NIVERSITY #ORPORATION FOR !TMOSPHERIC 2ESEARCH Ú "OULDER #/
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&)'52% $EPICTION OF A MICROBURST AND ITS EFFECT ON AN AIRCRAFT DURING TAKEOFF 4HE LOSS OF AIRSPEED IN THE DIVERGENT WIND FIELD NEAR TO THE GROUND IS EXTREMELY HAZ ARDOUS ! SIMILAR LOSS OF AIRSPEED NEAR THE GROUND OCCURS DURING LANDING #OURTESY OF 5NIVERSITY #ORPORATION FOR !TMOSPHERIC 2ESEARCH Ú "OULDER #/
-ICROBURST DETECTION LIKE TORNADO DETECTION IS ACCOMPLISHED BY ESTIMATING SHEAR (OWEVER IN THE CASE OF THE MICROBURST IT IS THE RADIAL SHEAR OF THE RADIAL VELOCITY THAT IS TYPICALLY MEASURED (UMAN INTERPRETATION OF MICROBURST SIGNATURES IN COLOR ENHANCED RADIAL VELOCITY DISPLAYS IS EASILY ACCOMPLISHED WITH TRAINED OBSERVERS AND AUTOMATIC DETECTION HAS BEEN IMPLEMENTED ON THE 4$72 RADAR SYSTEM 2ADIAL VELOCITY DIFFER ENCES OF TO MS ARE OBSERVED IN MICROBURSTS ! RADIAL VELOCITY DIFFERENCE OF MORE THAN MS OVER THE LENGTH OF A JET RUNWAY y KM IS A SERIOUS CONCERN /NE PRINCIPAL PROBLEM CONCERNING MICROBURSTS IS THEIR SHORT LIFETIMES WHICH ARE ON THE ORDER OF n MINUTES BUT THE DURATION OF PEAK INTENSITY IS ONLY OR MIN UTES &IELD RESEARCH HAS CLEARLY DEMONSTRATED THAT A FEW MINUTES ADVANCE WARNING USING DOPPLER RADAR CAN BE ACHIEVED /PERATIONAL MICROBURST DETECTION RADARS USE THIS AUTOMATED DETECTION ALGORITHM WITH HIGH PERFORMANCE GROUND CLUTTER MITIGATION TECH NIQUES SINCE THE PHENOMENON OCCURS NEAR THE GROUND AND OFTENTIMES IN VERY LIGHT OR NO PRECIPITATION # BAND IS THE PREFERRED OPERATIONAL FREQUENCY FOR SEVERAL REASONS &IRST A # BAND ANTENNA WILL HAVE A SMALLER BEAMWIDTH THAN AN 3 BAND ANTENNA OF THE SAME SIZE AND ALLOW IMPROVED AIR FLOW MEASUREMENTS WITH STRONG CLUTTER SUPPRESSION NEAR THE AIRPORT SURFACE 3ECOND SINCE SHORT RANGE DETECTION IS IMPORTANT RADAR ATTENUATION EFFECTS ARE NOT A PRIMARY CONCERN 4HIRD # BAND OFFERS IMPROVED SIGNAL TO CLUTTER
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PERFORMANCE SINCE THE LARGE CLUTTER TARGETS ARE LIMITED IN RADAR CROSS SECTION BY -IE SCATTERING WHEREAS THE ATMOSPHERE BORNE WIND TRACING SCATTERERS ARE SMALL AND OBEY 2AYLEIGH SCATTERING CROSS SECTION PHYSICS 8 BAND RADARS HAVE BEEN CONSIDERED TO SOME DEGREE BUT THE MORE SEVERE ATTENUATION THAT CAN OCCUR IN VERY HEAVY RAIN WILL LIMIT PERFORMANCE UNLESS THE RADAR IS LOCATED VERY NEAR TO THE AIRPORT RUNWAYS )N THE MID S THE # BAND 4ERMINAL $OPPLER 7EATHER 2ADAR 4$72 SYSTEM WAS INSTALLED AT MAJOR AIRPORTS TO DETECT AND WARN AIRCRAFT OF HAZARDOUS WIND SHEAR CONDITIONS APPROACHING GUST FRONTS THAT MAY AFFECT THE AIRPORT APPROACH AND DEPARTURE CONFIGURATION AND MICROBURSTS 4HIS NETWORK OF RADARS ALONG WITH MUCH IMPROVED PILOT TRAINING AND AWARENESS HAS ALL BUT ELIMINATED AIRCRAFT ACCIDENTS CAUSED BY MICRO BURSTS AND STRONG WIND SHEAR (AIL 4HE .EXRAD RADAR MAKES USE OF A HAIL DETECTION ALGORITHM THAT COMBINES A HIGH REFLECTIVITY FACTOR WITH ECHO HEIGHT AND UPPER LEVEL DIVERGENT RADIAL VELOCITY WINDS TO DETECT THE OCCURRENCE OF HAIL 0OLARIMETRIC RADAR TECHNIQUES IMPROVE QUANTITA TIVE HAIL DETECTION "RINGI ET AL !YDIN ET AL AND )LLINGWORTH ET AL PROPOSED A HAIL DETECTION TECHNIQUE USING DIFFERENTIAL REFLECTIVITY MEASUREMENTS 4HIS TECHNIQUE DEPENDS UPON THE FACT THAT FOR TUMBLING HAIL THE DIFFERENTIAL REFLECTIVITY THE RATIO OF HORIZONTAL TO VERTICAL REFLECTIVITY IS NEAR UNITY y D" 4HIS DIFFERS SHARPLY FROM HEAVY RAIN WHERE THIS RATIO CAN BE AS LARGE AS D" BECAUSE LARGE WATER DROPLETS ARE HORIZONTALLY ORIENTED 4HE COMBINATION OF ABSOLUTE REFLECTIVITY FACTOR AND THE DUAL POLARIZATION DIFFERENTIAL REFLECTIVITY GIVES UNIQUE SIGNATURES FOR HAIL AND HEAVY RAIN EACH OF WHICH IS CHARACTERIZED BY A HIGH REFLECTIVITY FACTOR 4HE DIFFERENCE IN THE DIFFER ENTIAL REFLECTIVITY SIGNATURES IS EASILY EXPLAINED ,ARGE RAINDROPS ASSUME FLATTER SHAPES APPROXIMATED BY OBLATE SPHEROIDS AS THEY FALL AND THUS SCATTER BACK THE HORIZON TALLY POLARIZED ELECTRIC FIELD MORE STRONGLY THAN THE VERTICALLY POLARIZED ELECTRIC FIELD (AILSTONES HAVING AN IRREGULAR SHAPE PHYSICALLY TUMBLE WHILE THEY FALL AND THEREFORE EXHIBIT NO PREFERRED ORIENTATION ON AVERAGE 4HUS THE HORIZONTAL AND VERTICAL SCATTERED FIELDS HAVE NEARLY THE SAME AVERAGE VALUE 7IND -EASUREMENT ,HERMITTE AND !TLAS WERE THE FIRST TO SHOW HOW A SINGLE DOPPLER RADAR CAN BE USED TO MEASURE VERTICAL PROFILES OF THE HORIZONTAL WIND FIELD WHEN PRECIPITATION IS PRESENT 4HIS TECHNIQUE IS MOST ACCURATE IF THE WIND FIELD IS UNIFORM IN THE REGION SCANNED BY THE RADAR 4HE METHOD DEPENDS UPON AN ANALYSIS OF THE RADIAL VELOCITY MEASURED DURING A COMPLETE SCAN IN AZIMUTH WITH A SINGLE FIXED ELEVATION ANGLE !T ANY SLANT RANGE R THE HEIGHT OF THE MEASUREMENT IS R SIN @ AND THE RADIUS OF THE REGION SCANNED IS R COS @ WHERE @ IS THE ELEVATION ANGLE AS DEPICTED IN &IGURE )F A IS THE AZIMUTH ANGLE 6H IS THE HORIZONTAL WIND SPEED AND 6F IS THE FALL SPEED OF THE PARTICLES THEN THE RADIAL VELOCITY AT RANGE R IS GIVEN BY
6R A 6H COS A COS @ 6F SIN @
! HARMONIC ANALYSIS LEAST SQUARE FITTING THE AMPLITUDE PHASE AND OFFSET OF A SINU SOID CAN BE USED TO OBTAIN 6H THE HORIZONTAL WIND SPEED THE WIND DIRECTION WHERE COS A IS MAXIMUM AND 6F THE MEAN PARTICLE FALL SPEED ALL PLOTTED AS A FUNCTION OF HEIGHT 4HIS TECHNIQUE IS REFERRED TO AS THE 6ELOCITY !ZIMUTH $ISPLAY 6!$ "ROWNING AND 7EXLER LATER SHOWED HOW THE 6!$ TECHNIQUE COULD BE EXTENDED TO MEASURE OTHER PARAMETERS OF THE WIND FIELD INCLUDING WIND FIELD DIVERGENCE AND WIND FIELD DEFORMA TION BY EMPLOYING AN EXTENDED HARMONIC OR &OURIER SERIES ANALYSIS 4HE 6!$ HAS BEEN IMPLEMENTED ON THE .EXRAD AS A STANDARD PRODUCT THAT CAN BE USED IN PRECIPITATION AND
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&)'52% 6ELOCITY !ZIMUTH $ISPLAY GEOMETRY FOR MEASURING HORIZONTAL WIND WITH A SINGLE DOPPLER RADAR -EASUREMENT OF THE RADIAL VELOCITY FOR A COMPLETE AZIMUTHAL SCAN A AT ELEVATION ANGLE @ PERMITS AN ESTIMATE OF THE VERTICAL PROFILE OF HORIZONTAL WINDS #OURTESY OF 5NIVERSITY #ORPORATION FOR !TMOSPHERIC 2ESEARCH Ú "OULDER #/
FREQUENTLY IN CLEAR AIR 4HE 6!$ TECHNIQUE IS MOST OFTEN APPLIED TO WIND PROFILER RADARS THAT POINT VERTICALLY AND STEP SCAN AT RELATIVELY LARGE ELEVATION ANGLES !N ALTERNATIVE DETERMINATION OF BOUNDARY LAYER WIND FIELDS USING A SINGLE WEATHER RADAR HAS FOUND SUCCESS USING AN ECHO TRACKING TECHNIQUE 4HUNDERSTORM 0REDICTION 7ILSON AND 3CHREIBER ILLUSTRATE HOW METEOROLOGI CAL DOPPLER RADAR CAN BE USED TO DETECT LOCATIONS WHERE NEW THUNDERSTORM DEVELOP MENT IS LIKELY TO OCCUR -ANY WEATHER RADARS HAVE SUFFICIENT SENSITIVITY TO DETECT DISCONTINUITIES OF CLEAR AIR ECHOES IN THE LOWER TO KM OF THE ATMOSPHERE OUT TO OR KM 4HIS DETECTION OCCURS PRINCIPALLY IN THE SUMMER MONTHS WHEN THE BACKSCATTERING MECHANISM IS CAUSED BY INSECTS IN THE LOWER LEVELS OF THE ATMOSPHERIC BOUNDARY LAYER AND SOMETIMES MAY ALSO BE DUE TO "RAGG SCATTERED REFRACTIVE INDEX INHOMOGENEITIES 7ILSON AND 3CHREIBER HAVE FOUND THAT ABOUT OF THE THUNDER STORMS THAT OCCUR IN THE &RONT 2ANGE OF THE 2OCKIES IN THE SUMMERTIME DEVELOP OVER SUCH hBOUNDARIESv BETWEEN TWO DIFFERENT AIR MASSES 3INCE THESE BOUNDARIES CAN BE DETECTED BEFORE ANY CLOUDS ARE PRESENT AND IT IS POSSIBLE TO INFER THE AIR MASS CONVERGENCE OR COMING TOGETHER OF TWO AIR MASSES WHERE INSECTS ARE FORCED TO ACCUMULATE ALONG THESE BOUNDARIES BY DOPPLER RADAR MEASUREMENTS MORE PRECISE PREDICTION OF THUNDERSTORM OCCURRENCE IS POSSIBLE &ROM THE RADAR DESIGNERS STAND POINT SUCH APPLICATIONS DICTATE THE USE OF ANTENNAS WITH VERY LOW SIDELOBES ALONG WITH LOW PHASE NOISE TRANSMITTERS AND RECEIVER COMPONENTS AND SIGNAL PROCESSORS HAVING SIGNIFICANT GROUND CLUTTER REJECTION CAPABILITY 4HE .EXRAD RADAR SYSTEM WITH ITS HIGH QUALITY ANTENNA AND D" OF CLUTTER REJECTION IS WELL SUITED TO THIS IMPORTANT OPERATIONAL TASK 2EFRACTIVITY AND 7ATER 6APOR -EASUREMENTS #ONVENTIONAL WEATHER RADAR PRO CESSING IS GENERALLY DESIGNED TO EMPHASIZE PRECIPITATION AND WIND FIELD MEASUREMENTS
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AND TO SUPPRESS GROUND CLUTTER (OWEVER IT IS KNOWN THAT RADAR BEAM BENDING CAUSED BY ATMOSPHERIC REFRACTION AND THE RESULTING ANOMALOUSLY PROPAGATED GROUND CLUTTER ECHO GIVES AN INDICATION OF THE VERTICAL PROFILES OF TEMPERATURE AND MOISTURE IN THE INTERVENING LOWER ATMOSPHERE -OREOVER MEASURING THE PROPAGATION SPEED OF THE RADAR PULSE BETWEEN NORMALLY PROPAGATED CLUTTER TARGETS THOSE DIRECTLY VIEWED BY THE RADAR GIVES AN ESTIMATE OF THE REFRACTIVE INDEX OF AIR ALONG THIS PROPAGATION PATH "Y MEASURING THE ABSOLUTE PHASE OF THE RADAR SIGNAL RECEIVED FROM STATIONARY GROUND CLUTTER TARGETS AND COMPARING THEM WITH REFERENCE ABSOLUTE PHASE MEASUREMENTS UNDER KNOWN REFRACTIVE CONDITIONS ONE CAN MEASURE THE NEAR SURFACE PROPAGATION SPEEDS OF THE RADAR PULSE ALONG THESE PATHS 4HEN THE REFRACTIVE INDEX OR REFRACTIVITY OF THE ATMOSPHERE OF THESE ATMOSPHERIC PATHS MAY BE DETERMINED 2EFRACTIVITY IS A FUNC TION OF TEMPERATURE PRESSURE AND MOISTURE CONTENT #ONSEQUENTLY IF SURFACE TEM PERATURE AND PRESSURE ARE INDEPENDENTLY AVAILABLE AS THEY FREQUENTLY ARE THEN THE REFRACTIVE INDEX MEASUREMENTS MAY BE CONVERTED TO SPATIAL FIELDS OF WATER VAPOR IN THE SURFACE BOUNDARY LAYER 3UCH WATER VAPOR MEASUREMENTS ARE CRITICAL FOR OBTAINING ACCURATE FORECASTS USING NUMERICAL MODELS AND SIMULATIONS OF THE ATMOSPHERE 4HIS EXPERIMENTAL MEASUREMENT TECHNIQUE CAN BE USED TO RANGES OF ABOUT KM WHERE THE %ARTHS CURVATURE PREVENTS ROUTINE OBSERVATION OF GROUND CLUTTER TARGETS AND IS BEING CONSIDERED FOR OPERATIONAL USE IN .EXRAD
£°ÈÊ , - , Ê** /" /PERATIONAL METEOROLOGICAL RADARS ARE DESIGNED FOR RELIABILITY AND SIMPLICITY OF OPERA TION WHILE PROVIDING THE PERFORMANCE NEEDED FOR OPERATIONAL APPLICATIONS 2ESEARCH RADARS ARE CONSIDERABLY MORE COMPLEX SINCE CUTTING EDGE RESEARCH REQUIRES MORE DETAILED AND MORE SENSITIVE MEASUREMENTS OF A MULTIPLICITY OF VARIABLES SIMULTANE OUSLY )N THE RESEARCH COMMUNITY MULTIPLE PARAMETER POLARIZATION AND WAVELENGTH RADAR STUDIES MULTIPLE DOPPLER RADAR NETWORK STUDIES AND A NEW GENERATION OF AIRBORNE AND SPACEBORNE RADARS ARE RECEIVING CONSIDERABLE ATTENTION $UAL 0OLARIZATION7AVELENGTH 2ADAR )T IS CLEAR THAT POLARIMETRIC DOPPLER RADARS PROVIDE A SIGNIFICANT INCREASE IN THE USEFUL INFORMATION THAT CAN BE OBTAINED FROM METEOROLOGICAL TARGETS 4HE DETECTION OF HAIL AND MORE ACCURATE RAINFALL ESTI MATES HAS PRIMARY SIGNIFICANCE $UAL POLARIZATION MEASUREMENTS AT MULTIPLE WAVE LENGTHS PROVIDE EVEN MORE INFORMATION RELATED TO THE EVENTUAL INTERPRETATION OF THE SIZE DISTRIBUTIONS WATER PHASE STATES AND HYDROMETEOR WATER OR ICE PARTICLES TYPES IN DIFFERENT CLASSES OF PRECIPITATION AND CLOUDS 4HE CAPABILITIES OF MULTIPLE PARAMETER METEOROLOGICAL RADARS ARE PRESENTED IN "RINGI AND (ENDRY "RINGI AND #HANDRA AND IN THE COLLECTION OF PAPERS EDITED BY (ALL 7HEREAS LONGER WAVELENGTH RADARS ARE NECESSARY FOR THE STUDY OF SEVERE STORMS SHORTER WAVELENGTH MILLIMETER WAVE RADARS ARE USEFUL FOR SENSING AND PROBING NEWLY DEVELOPING CLOUDS 2ESEARCHERS OFTEN NEED A WIDE RANGE OF THESE CAPABILITIES SIMULTANEOUSLY &ROM THE RADAR ENGINEERING STAND POINT THE CHALLENGE IS CONSIDERABLE REQUIRING RADAR DESIGNERS TO DEVELOP COHERENT WAVEFORM POLARIZATION DIVERSE AND WAVELENGTH DIVERSE RADARS !S NOTED THERE EXIST SEVERAL POLARIMETRIC RESEARCH RADARS AND OPERATIONAL RADARS IN THE WORLD -ULTIPLE 2ADARS ! SINGLE DOPPLER RADAR MEASURES ONLY A SINGLE RADIAL COMPO NENT OF VELOCITY ,HERMITTE WAS AMONG THE FIRST TO DESCRIBE HOW TWO OR MORE DOPPLER RADARS COULD BE USED SCANNING TOGETHER TO OBTAIN THE FULL THREE DIMENSIONAL AIR MOTION
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FIELDS IN PRECIPITATION 4HIS PIONEERING WORK LED THE WAY TOWARD THE USE OF NETWORKS OF DOPPLER RADARS FOR STUDIES OF INDIVIDUAL CLOUDS TO EXAMINE THE THREE DIMENSIONAL STRUCTURE OF VECTOR AIR MOTION IN PRECIPITATION ! POINT SHOULD BE MADE HERE REGARDING THE USE OF TWO DOPPLER RADARS FOR MEASUREMENTS OF THREE DIMENSIONAL WINDS 3INCE IN PRINCIPLE TWO INDEPENDENT LOOKS CAN MEASURE ONLY TWO COMPONENTS OF VECTOR AIR MOTION THE ASSUMPTION OF ATMOSPHERIC MASS CONTINUITY IS INVOKED 4HIS EQUATION OF MASS CONTINUITY 6 IS USED TO OBTAIN THE THIRD DIMENSIONAL COMPONENT WHERE 6 IS THE VECTOR AIR MOTION AND IS CONSTRAINED TO BE ZERO AT THE SURFACE 4HE VERTICAL AIR MOTION IS CALCULATED FROM VERTICAL INTEGRATION OF THE MASS CONTINUITY EQUATION &IGURE ILLUSTRATES AN AIR MOTION FIELD OBTAINED BY TWO DOPPLER RADAR OBSERVA TIONS IN AN INDIVIDUAL CONVECTIVE STORM CELL 3HOWN ARE THE HORIZONTAL VECTOR FIELDS IN A PLANE APPROXIMATELY M ABOVE THE SURFACE 4HE PHENOMENON BEING MEASURED IS A LOW LEVEL DIVERGENT OUTFLOW OR MICROBURST JUST TO RIGHT OF THE CENTER &IGURE SHOWS ANOTHER EXAMPLE OF PRECIPITATION INTENSITY AND AIR MOTION FIELDS SUPERPOSED ON A PHOTOGRAPH OF A CONVECTIVE THUNDERSTORM CELL 4HE DATA ARE TAKEN FROM THREE DOPPLER RADARS SPACED ABOUT KM APART ! DEVELOPING NETWORK OF SHORT RANGE DOPPLER RADARS NOT RANGE LIMITED BY THE %ARTHS CURVATURE WILL PROVIDE MORE DETAILED OBSERVATIONS CLOSE TO THE SURFACE THAN THE RELA TIVELY WIDELY SPACED 732 $ NETWORK 4HE #OLLABORATIVE !DAPTIVE 3ENSING OF THE !TMOSPHERE #!3! RADAR NETWORK WILL INCLUDE MANY INEXPENSIVE LOW POWER SCAN NING SHORT WAVELENGTH RADARS MOUNTED ON TOWERS OF OPPORTUNITY PRIMARILY CELL PHONE TOWERS THAT BLANKET MUCH OF THE 53 %XISTING EQUIPMENT ON THESE TOWERS WILL
&)'52% 6ECTOR WIND FIELDS IN A HORIZONTAL PLANE DERIVED FROM DUAL DOPPLER RADAR OBSERVATIONS OF A SUMMERTIME CONVECTIVE STORM NEAR $ENVER #OLORADO 4HE DARK SOLID LINE IS SHOWN TO INDICATE THE LENGTH OF A TYPICAL JET AIRCRAFT RUNWAY 4HE DIVERGENT OUTFLOW FROM A MICROBURST SHOWS A STRONG MS HEADWIND CHANG ING TO A SIMILARLY STRONG TAILWIND OVER THE LENGTH OF THE RUNWAY #0 IS THE FORMER RESEARCH RADAR OPERATED BY .#!2 #OURTESY OF 5NIVERSITY #ORPORATION FOR !TMOSPHERIC 2ESEARCH Ú "OULDER #/
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&)'52% 2ADAR REFLECTIVITY CONTOURS AND AIR FLOW VECTORS SUPERPOSED ON PHOTOGRAPH OF A RAP IDLY GROWING !LABAMA THUNDERSTORM CELL 4HE DATA DEPICTS A MS UPDRAFT ORIGINATING IN AN EXTREMELY STRONG D": RAIN OR HAIL CORE 4HE WIND VECTORS ARE TAKEN FROM COMBINING DATA FROM THREE NEARBY DOP PLER RADARS #OURTESY OF !MERICAN -ETEOROLOGICAL 3OCIETY &ROM $% +INGSMILL AND 2 - 7AKIMOTO h+INEMATIC $YNAMIC AND 4HERMODYNAMIC !NALYSIS OF A 7EAKLY 3HEARED 3EVERE 4HUNDERSTORM OVER .ORTHERN !LABAMA v -ONTHLY 7EATHER 2EVIEW VOL P
PROVIDE A SHARED INFRASTRUCTURE FOR THE #!3! RADARS 4HIS RADAR SYSTEM WILL INCLUDE INTELLIGENT DECISION MAKING FOR SCANNING AND TRACKING IMPORTANT LOW LEVEL ATMOSPHERIC FEATURES THAT ARE DEEMED CRITICAL FOR THE AVIATION WEATHER FORECASTING TRANSPORTATION AND LOCAL EMERGENCY RESPONSE USERS 4HE #!3! RADARS CAN COMMUNICATE WITH EACH OTHER FOR COLLABORATIVE USE OF THE DATA AND ADAPTIVELY CHANGE THEIR OPERATING PARAM ETERS TO BEST MEET THE PRESCRIBED NEEDS AT A GIVEN TIME $EPENDING ON THE FINAL COSTS OF DEPLOYMENT AND OPERATION #!3! NETWORKS MAY BE DEVELOPED ONLY AROUND CRITICAL AREAS SUCH AS URBAN AREAS AIRPORTS ETC 2APID 3CAN 0HASED !RRAY 2ADAR $OPPLER WEATHER RADARS THAT USE PHASED ARRAY ANTENNAS AND COMPLEX WAVEFORM DESIGN MAY BE APPLIED TO SOME OF THE MORE DIFFICULT RADAR METEOROLOGY OBSERVATIONS 4HE USE OF MULTIPLE DOPPLER RADARS HAS PROVIDED DRA MATIC NEW INFORMATION ON THE INTERNAL WINDS IN LARGE PRECIPITATING SYSTEMSINFORMATION THAT CAN BE OBTAINED IN NO OTHER WAY $ESPITE THE POWER OF THIS TECHNIQUE THE SPATIAL RESOLUTION IN THE DERIVED THREE DIMENSIONAL MOTION FIELDS IS GENERALLY NOT BETTER THAN
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OF THE ORDER OF KM 4HERE ARE SEVERAL REASONS FOR THIS 4HE FINITE BEAMWIDTH LIMITS THE RESOLUTION AVAILABLE AT LONGER RANGES !T SHORTER RANGES THE LARGE SOLID ANGLE THAT MUST BE SCANNED IN ORDER TO COVER ALL REGIONS OF A STORM REQUIRES TOTAL SCANNING TIMES OF THE ORDER OF TO MIN EVEN FOR WELL SITUATED STORMS 4HIS IS A CONSEQUENCE OF THE ON TARGET DWELL TIME NECESSARY FOR ACCURATE MEASUREMENTS &INALLY THE STORM ITSELF IS EVOLVING AND MOVING DURING THIS MEASUREMENT TIME THUS COMPLICATING THE DATA REGISTRATION IN SPACE AND TIME 3OME OPERATIONAL AND MANY RESEARCH APPLICATIONS REQUIRE FASTER SCANNING THAN CONVENTIONAL MECHANICALLY SCANNED RADARS CAN PROVIDE 4HESE APPLICATIONS INCLUDE LONGER LEAD TIMES FOR TORNADO WARNINGS THE STUDY OF FINER SCALE STORM FEATURES INTERAC TIONS BETWEEN THE INTERNAL MOTIONS AND HYDROMETEOR GROWTH PROCESSES IN THE STORMS AND STUDIES OF ELECTRIC CHARGE SEPARATION IN CLOUDS "ROOK AND +REHBIEL WERE AMONG THE FIRST TO DISCUSS A VERY RAPID SCANNING RADAR ALTHOUGH NONDOPPLER FOR EFFECTIVELY OBTAINING SNAPSHOTS OF CONVECTIVE STORMS +EELER AND &RUSH DISCUSS DESIGN CONSID ERATIONS FOR A MORE CAPABLE RAPID SCANNING DOPPLER RADAR !NY RAPID SCANNING APPROACH GENERALLY MUST ENCOMPASS TWO FEATURES THE TRANS MIT WAVEFORM MUST HAVE A RELATIVELY LARGE BANDWIDTH TO INCREASE THE NUMBER OF INDE PENDENT SAMPLES AVAILABLE IN THE DESIRED SPATIAL RESOLUTION CELL AND THE ANTENNA MUST BE RAPIDLY SCANNED THROUGHOUT THE DESIRED ATMOSPHERIC VOLUME EITHER MECHANICALLY OR ELECTRONICALLY -ECHANICALLY SCANNED SINGLE FREQUENCY STANDARD WEATHER RADARS USE A LONG DWELL TIME TO ACQUIRE AN ADEQUATE NUMBER OF INDEPENDENT SAMPLES TO ACCURATELY ESTIMATE THE SPECTRAL MOMENT DATA USED FOR METEOROLOGICAL MEASUREMENTS ! LARGE BANDWIDTH SYSTEM EG PULSE COMPRESSION RADAR CAN ACQUIRE INDEPENDENT SAMPLES IN RANGE IN A SHORT DWELL TIME THAT CAN BE AVERAGED THUS REDUCING THE DWELL TIME FOR EACH BEAM AND REDUCING THE TOTAL VOLUME COVERAGE SCAN TIME &AST MECHANICAL SCANNING DEGSEC PRODUCES DELETERIOUS SPECTRUM BROADENING EFFECTS THAT ELECTRONIC STEP SCANNING EASILY AVOIDS SINCE THE BEAM IS FIXED IN SPACE DURING THE DWELL TIME ! FAVORED APPROACH IS TO UTILIZE A ONE DIMENSIONAL PHASED ARRAY THAT IS ELECTRONICALLY SCANNED IN ELEVATION WHILE SLOWLY ROTATING IN AZIMUTH )N THIS WAY A FULL HEMISPHERIC VOLUME CAN BE COVERED IN n MINUTES AND SMALLER SECTOR VOLUMES MAY BE COVERED IN LESS THAN MINUTE 3EVERAL MILITARY RADARS AND AVIATION RADARS UTILIZE ELECTRONICALLY SCANNED BEAMS BUT THE EXPENSE OF A FULLY CAPABLE SYSTEM HAS PREVENTED MORE THAN ONLY A FEW METEOROLOGICAL RADAR SYSTEMS FROM BEING DESIGNED AND BUILT 2APID SCANNING PHASED ARRAY RADARS HAVE ALSO BEEN STUDIED EXTENSIVELY IN %UROPE !N ALTERNATIVE APPROACH IS TO EMPLOY DIGITAL BEAMFORMING OR FREQUENCY STEERING TECHNIQUES TO TRANSMIT AND SIMULTANEOUSLY RECEIVE MULTIPLE BEAMS USING PARALLEL RECEIVERS 3UCH MILITARY RADARS HAVE BEEN OPERATED FOR SEVERAL DECADES BUT NONE OF THESE SYSTEMS WERE EVER DESIGNED OR USED FOR WEATHER MEASUREMENTS ! MECHANICALLY SCANNED MULTIPLE BEAM WEATHER RADAR SYSTEM USING SIMULTANEOUS FREQUENCY SCANNED BEAMS HAS BEEN DESIGNED AND CONSTRUCTED ON A SMALL TRUCK 4HE 2APID $OPPLER ON 7HEELS 2APID $/7 8 BAND RADAR SHOWN IN &IGURE USES SIX SIMULTANEOUS FREQUENCY STEERED BEAMS SEPARATED BY A FEW DEGREES EMANATING FROM A SLOTTED WAVE GUIDE PHASED ARRAY AND INDEPENDENT RECEIVERS TO ACQUIRE A VOLUMETRIC COVERAGE OF CONVECTIVE STORMS IN n MINUTES 0ULSE COMPRESSION IS NOT USED 4HE RAPID DATA ACQUISITION SPEED OF THIS SYSTEM HAS THE POTENTIAL TO GIVE NEW INSIGHTS INTO THUNDER STORM EVOLUTION HURRICANES AT LANDFALL HAIL FORMATION PLUS MICROBURST GUST FRONT AND TORNADO GENESIS MECHANISMS THAT MAY LIKELY EVOLVE INTO AN OPERATIONAL CAPABILITY )N THE EARLY S THE &!! LED AN EFFORT TO DEVELOP DUAL USE WEATHER AND AIRCRAFT SURVEILLANCE RADAR BASED ON ELECTRONIC SCANNING AND PULSE COMPRESSION TECHNIQUES
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&)'52% 2APID $/7 $OPPLER ON 7HEELS IS A MOBILE 8 BAND RADAR THAT USES SIX SIMULTANEOUS BEAMS TO COVER A VOLUME OF ATMOSPHERE IN A MUCH SHORTER VOLUME COVERAGE TIME THAN A MECHANICALLY SCANNED SINGLE BEAM RADAR 4HIS RAPID UPDATE SCAN IS IMPORTANT FOR MEASURING VIOLENT CONVECTIVE STORMS ESPE CIALLY TORNADOES AS SHOWN IN PHOTO 0HOTO COURTESY OF 5NIVERSITY #ORPORATION FOR !TMOSPHERIC 2ESEARCH Ú "OULDER #/
AND AN EFFORT BEGINNING A DECADE LATER CONTINUED THE DEVELOPMENT OF PHASED ARRAY RADARS FOR CIVIL APPLICATIONS 2ADARS INITIALLY DESIGNED FOR MILITARY APPLICATIONS WERE MODIFIED FOR WEATHER DETECTION AND SUCCESSFULLY DEMONSTRATED THE CONCEPT )N THE EARLY S A JOINT EFFORT BETWEEN THE 53 .AVY THE .ATIONAL 7EATHER 3ERVICE THE .ATIONAL 3EVERE 3TORMS ,ABORATORY AND THE 5NIVERSITY OF /KLAHOMA LED TO THE DEVELOPMENT OF THE SO CALLED .ATIONAL 7EATHER 2ADAR 4ESTBED FACILITY IN .ORMAN /KLAHOMA BY COMBINING A SINGLE PANEL 309 PHASED ARRAY RADAR ON A ROTATING PEDES TAL WITH A 732 $ TRANSMITTER AND CUSTOM RECEIVER !LTHOUGH THIS PARTICULAR RADAR IS NOT LIKELY TO BE THE PREFERRED DESIGN FOR A FUTURE WEATHER RADAR THE /KLAHOMA 0HASED !RRAY 2ADAR TESTBED CAN BE USED TO EXPLORE ELECTRONIC SCANNING STRATEGIES TOGETHER WITH NEW PULSING AND PROCESSING CONCEPTS THAT MAY LEAD TO FUTURE DEVELOPMENT OF A PHASED ARRAY WEATHER RADAR SYSTEM !IRBORNE 2ADARS 7HEREAS COMMERCIAL AVIATION WEATHER RADARS ARE NOSE MOUNTED 8 BAND RADARS FOR SEVERE WEATHER AND TURBULENCE DETECTION AND AVOIDANCE AIRBORNE RESEARCH RADARS MUST HAVE RELATIVELY MORE COMPLEX ARCHITECTURES IN ORDER TO MAKE MORE SENSITIVE HIGH RESOLUTION MEASUREMENTS 4HIS POWERFUL TECHNIQUE PERMITS THE USE OF A MOBILE PLATFORM WHICH THEREFORE ALLOWS MEASUREMENTS OVER REGIONS NOT ACCESSIBLE BY GROUND BASED SYSTEMS -OREOVER THE MOBILITY OF THE AIRCRAFT PERMITS LONGER TERM OBSERVATIONS OF RAPIDLY MOVING BUT LONG LIVED STORMS AND CLOUD SYSTEMS THEREBY ALLOWING MORE COMPLETE STUDIES OF EVOLUTION DURING VARIOUS PHASES OF THE SYSTEM .#!2S %LDORA AIRBORNE DOPPLER RADAR SYSTEM SHOWN IN &IGURE CONSISTS OF TWO SLOTTED WAVEGUIDE FIXED BEAM ANTENNAS MOUNTED IN THE TAIL OF THE 0 AIR CRAFT WHICH IS OPERATED BY THE .AVAL 2ESEARCH ,ABORATORY AND COVERED BY A ROTATING
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&)'52% 4AIL MOUNTED %,$/2! DOPPLER WEATHER RADAR OPERATED BY THE .ATIONAL #ENTER FOR !TMOSPHERIC 2ESEARCH ON THE .AVAL 2ESEARCH ,ABORATORY 0 RESEARCH AIRCRAFT #OURTESY OF 5NIVERSITY #ORPORATION FOR !TMOSPHERIC 2ESEARCH Ú "OULDER #/
RADOMEA ROTO DOME /NE BEAM POINTS FORWARD ABOUT n AND THE OTHER AFT BY THE SAME ANGLE THEREBY OBTAINING TWO RADIAL COMPONENTS OF COMMON TARGET VOLUMES 7ITH SUCH A SYSTEM EACH ANTENNA SCANS IN A CONICAL SURFACEONE CONE POINTING FORWARD THE OTHER ONE REARWARDTHUS PERMITTING SYNTHESIS OF A DUAL DOPPLER RADAR SYSTEM ALONG THE AIRCRAFT TRACK 4HE AIRCRAFT IS FLOWN ALONGSIDE STORMS TO SYNTHESIZE DUAL DOP PLER OBSERVATIONS AND THEREFORE TO OBTAIN VECTOR WINDS "ECAUSE THE AIRCRAFT NEED NOT FLY ORTHOGONAL TRACKS THE TIME REQUIRED FOR MEASUREMENTS OF CLOUD SYSTEMS IS DRAMATI CALLY REDUCED AS ARE THE ERRORS IN THESE MEASUREMENTS -OREOVER SEVERE STORMS WHICH COULD OTHERWISE NOT BE PENETRATED ALONG AN ORTHOGONAL TRACK AND HURRICANES WHICH CAN BE PENETRATED BY SUCH AIRCRAFT CAN BE OBSERVED FULLY BY AN AIRCRAFT OUTSIDE THE REGIONS OF SEVERE WEATHER 6ARIOUS AIRBORNE RADARS EXIST IN THE RESEARCH COMMUNITY FOR DIFFERENT APPLICATIONS AND USER GROUPS .!3! HAS DEVELOPED THE DUAL WAVELENGTH CM AND MM %$/0 RADAR FOR THE HIGH ALTITUDE %2 AIRCRAFT AND A 7 BAND '(Z AIRBORNE CLOUD RADAR FOR THE $# RESEARCH AIRCRAFT ./!! HAS OPERATED TWO 8 BAND RADARS SIMILAR TO THE %,$/2! RADAR FOR HURRICANE TRACKING AND RESEARCH *0, DEVELOPED THE !2-!2 RADAR TO TEST SPACE RADAR CONCEPTS FOR THE 4ROPICAL 2AINFALL -EASUREMENTS -ISSION 42-- 4HE 5NIVERSITY OF 7YOMING USES A MM CLOUD RADAR MOUNTED ON A +ING !IR AIRCRAFT )N THE MID S .#!2 ACQUIRED THE (IGH PERFORMANCE )NSTRUMENTED !IRBORNE 0LATFORM FOR %NVIRONMENTAL 2ESEARCH (!)0%2 A 'ULF 3TREAM ' MEDIUM SIZE JET AIRCRAFT AND DESIGNED A DUAL WAVELENGTH AND MM REMOVABLE POD MOUNTED RADAR FOR CLOUD STUDIES 4HE #ANADIAN .ATIONAL 2ESEARCH #OUNCIL HAS DEVELOPED A SIMILAR AIRBORNE RADAR SYSTEM 3PACEBORNE 2ADARS !MONG THE MORE SIGNIFICANT CHALLENGES FACING RESEARCHERS TODAY IS THE NEED TO MAKE GLOBAL MEASUREMENTS OF PRECIPITATION 5NDERSTANDING GLOBAL CLIMATE REQUIRES THAT QUANTITATIVE MEASUREMENTS OF PRECIPITATION BE MADE THROUGHOUT THE WORLD PARTICULARLY IN THE TROPICS AND OVER THE OCEANS 3ATELLITE OBSERVATIONS APPEAR
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TO OFFER THE ONLY PRACTICAL MECHANISM FOR OBTAINING THESE MEASUREMENTS 4HE 42-- SATELLITE WAS LAUNCHED IN CARRYING THE +U BAND SINGLE FREQUENCY 0RECIPITATION 2ADAR 02 AND A M SINGLE BEAM ARRAY ANTENNA THAT IS STEERED n ON EITHER SIDE OF THE SPACECRAFT TRACK )TS RELATIVELY LOW INCLINATION ORBIT AT KM ALTITUDE PROVIDES TROPICAL PRECIPITATION MEASUREMENTS WITH M RANGE RESOLUTION AND A KM FOOT PRINT OVER A KM SWATH ! 42-- FOLLOW ON PROGRAM THE 'LOBAL 0RECIPITATION -EASUREMENT '0- PROGRAM ENVISIONS EXTENDING PRECIPITATION COVERAGE TO THE MID LATITUDE n . AND 3 LATITUDE FLYING IN A KM ALTITUDE ORBIT AND USING DUAL WAVELENGTH PRECIPITATION RADAR $02 AT +U AND +A BANDS FOR MORE ACCURATE RAINFALL ESTIMATES USING ATTENUATION TECHNIQUES 4HE TWO RADARS WILL HAVE MATCHED BEAMS FROM TWO SLOTTED WAVEGUIDE ARRAY ANTENNAS AND PROVIDE COVERAGE UNDER THE SPACECRAFT TRACK SIMILAR TO 42-- #LOUD3AT IS A SATELLITE LAUNCHED IN FLYING A 7 BAND MM CLOUD PROFILING RADAR #02 ORBITING THE %ARTH IN A SUN SYNCHRONOUS ORBIT AT AN ALTITUDE OF ABOUT KM 4HE TRANSMITTER IS AN %XTENDED )NTERACTION +LYSTRON %)+ HIGH POWER AMPLIFIER GENERATING A LSEC MONOCHROMATIC PULSE HAVING PEAK POWER OF K7 4HE ANTENNA IS A M DIAMETER REFLECTOR OFFSET FED BY A QUASI OPTICAL TRANSMISSION LINE AND PRODUCES A n BEAM WITH EXTREMELY LOW SIDELOBES 4HESE RADAR DESIGN PARAMETERS ALLOW AN EXCEPTIONAL SENSITIVITY OF n D": AT THE %ARTH SURFACE #LOUD3AT ORBITS IN FORMATION WITH FOUR OTHER SATELLITES AS PART OF THE SO CALLED ! TRAIN CONSTEL LATION OF SATELLITES THAT PROVIDE COMBINED RADAR LIDAR AND RADIOMETRIC MEASUREMENTS FOR %ARTH STUDIES 4HE #02 ON BOARD #LOUD3AT HAS M VERTICAL RESOLUTION WITH A KM FOOTPRINT AND IS SIMILAR TO THE .!3! !IRBORNE #LOUD 2ADAR THAT HAS FLOWN FOR SEVERAL YEARS ON BOARD THE .!3! $# AIRCRAFT #OMBINING THESE HIGH RESOLUTION CLOUD MEASUREMENTS WITH HIGH SENSITIVITY IS ONE OF THE TECHNICAL GOALS FOR ACQUIRING NEW INFORMATION REGARDING CLOUD EFFECT ON THE %ARTHS CLIMATE #LEAR !IR 7IND 0ROFILING 2ADARS !NOTHER FORM OF DOPPLER RADAR THAT HAS BECOME WIDELY USED ESPECIALLY IN THE RESEARCH COMMUNITY IS THE SO CALLED WIND PRO FILING RADAR OR hWIND PROFILERv 7IND PROFILERS USUALLY TAKE THE FORM OF 6(& AND 5(& MULTIPLE FIXED BEAM SYSTEMS POINTING VERTICALLY AND AT ANGLES APPROXIMATELY n FROM THE ZENITH TO INFER PROFILES OF THE HORIZONTAL WIND AVERAGED OVER THE AREA OF MEASUREMENT 3UCH RADARS CAN MAKE DOPPLER MEASUREMENTS THROUGHOUT THE RANGE OF ALTITUDES FROM A FEW HUNDRED METERS TO KM OR MORE ABOVE THE SURFACE DEPENDING UPON THE WAVELENGTH SELECTED AND THE POWER APERTURE PRODUCT AVAILABLE 4HESE RADARS HAVE THE ABILITY TO MEASURE HIGH RESOLUTION WINDS CONTINUOUSLY WHICH PERMITS THE OBSERVATION OF SMALLER SCALE TEMPORAL AND SPATIAL WIND FIELD FEATURES THAT CANNOT BE OBTAINED FROM THE GLOBAL HOUR RAWINSONDE BALLOON LAUNCH NETWORK 4HESE SMALLER SCALE MEASUREMENTS ARE IMPORTANT FOR UNDERSTANDING LOCAL AND REGIONAL WEATHER AND FOR EFFECTIVE FORECASTING ON THESE SCALES 6ERY POWERFUL RADARS OF THIS TYPE ARE REFERRED TO AS -ESOSPHERE 3TRATOSPHERE 4ROPOSPHERE -34 RADARS BECAUSE OF THEIR ABILITY TO MAKE MEASUREMENTS THROUGHOUT MOST OF THESE ATMOSPHERIC REGIONS UP TO n KM IN ALTITUDE 3EVERAL MAJOR -34 RADAR FACILITIES LOCATED AT FACILITIES AROUND THE WORLD OPERATE AT 6(& FREQUENCIES AROUND -(Z AND OBSERVE UPPER ATMOSPHERIC TROPOSPHERIC AND LOWER STRATOSPHERIC WINDS OR THE HIGHER LEVEL STRATOSPHERIC AND MESOSPHERIC WINDS 3HORTER WAVELENGTH 5(& WIND PROFILERS OPERATING AT n -(Z SENSE ATMOSPHERIC WINDS UP TO n KM AND THESE hTROPOSPHERIC WIND PROFILERSv ARE THE MOST WIDELY USED FOR OPERATIONAL WEATHER OBSER VATIONS 5(& WIND PROFILERS OPERATING AT -(Z IN THE 53 AND n -(Z
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IN %UROPE COVER THE LOWER ATMOSPHERIC WINDS UP TO n KM OR A FEW KM HIGHER WITH LARGER ANTENNAS WHERE THE STRONG MOISTURE FLUCTUATIONS PRESENT IN THE ATMOSPHERIC BOUNDARY LAYER PROVIDE STRONG SCATTERING SIGNATURES AT THESE SHORTER WAVELENGTHS 4HESE 5(& BOUNDARY LAYER WIND PROFILERS ARE TYPICALLY USED FOR AIR POLLUTION MONI TORING AND WARNINGS AS WELL AS VARIOUS RESEARCH APPLICATIONS 4HESE CLEAR AIR RADARS RECEIVE ENERGY BACKSCATTERED FROM REFRACTIVE INDEX INHO MOGENEITIES CAUSED BY NATURALLY OCCURRING ATMOSPHERIC TURBULENCE 4HE ANTENNA SYSTEMS USUALLY TAKE THE FORM OF PHASED ARRAYS THAT FORM BEAMS SEVERAL DEGREES WIDE THAT ARE SWITCHED TO OR NEARLY VERTICAL BEAMS FOR n MINUTES EACH AND MEASURE VERTICAL PROFILES OF WIND EVERY n MINUTES 4HE ANTENNAS ARE FREQUENTLY OF THE COAXIAL COLLINEAR CO CO STYLE FOR THOSE RADARS AND 9AGI ARRAY ELEMENTS FOR THOSE AT THE HIGHER FREQUENCIES 4HE HIGHER FREQUENCY 5(& PROFILERS TYPICALLY USE EITHER 9AGI OR MICROSTRIP PATCH ARRAY ANTENNAS 4RANSMITTERS ARE GENERALLY IN THE FORM OF HIGH POWERED COHERENT TRANSMITTING TUBES OR SOLID STATE AMPLIFIERS !T THE 5NIVERSITY OF +YOTO *APAN THE ANTENNA TRANSMITTER SYSTEM CONSISTS OF CROSSED 9AGI RADIATING ELEMENTS EACH WITH ITS OWN SOLID STATE TRANSMITTER 4HIS APPROACH ALLOWS FOR VERY FLEXIBLE ELECTRONIC SCANNING OF THE BEAM ./!! OPERATES A NET WORK OF OVER THIRTY AND -(Z WIND PROFILERS IN THE CENTRAL 5NITED 3TATES USING SOLID STATE TRANSMITTERS THAT SUPPLY CONTINUOUS WIND PROFILES UP TO KM FOR IMPROVED WEATHER FORECASTS AND CURRENT UPPER AIR WIND INFORMATION FOR AVIATION APPLICATIONS )T IS IMPORTANT TO RECOGNIZE THAT THREE BEAM DOPPLER SYSTEMS CAN ACCURATELY MEASURE HORIZONTAL WINDS IN ALL THREE VELOCITY COMPONENTS IF THE WIND IS UNIFORM &OUR AND FIVE BEAM SYSTEMS ALLOW ONE TO DETERMINE THE QUALITY OF THE MEASURE MENTS BY DETECTING THE PRESENCE OF A NONUNIFORM WIND FLOW #ARBONE 3TRAUCH AND (EYMSFIELD AND 3TRAUCH ET AL ADDRESS THE ISSUE OF WIND MEASUREMENT ERROR IN DETAIL 4HE READER IS REFERRED TO THE REVIEW PAPER BY 2TTGER AND ,ARSEN FOR A THOROUGH TREATMENT OF WIND PROFILER TECHNOLOGY AND TO THE SEQUENCE OF 4ROPOSPHERIC 0ROFILING 3YMPOSIA FOR TROPOSPHERIC PROFILING APPLICATIONS OF WINDS AND OTHER METE OROLOGICAL PARAMETERS 3PACED !NTENNA 4ECHNIQUES !N ADDITIONAL ADVANTAGE OF THESE LONG WAVELENGTH RADARS IS THEIR ABILITY TO MEASURE NOT ONLY THE RADIAL VERTICAL WIND COMPONENTS DIRECTLY BUT ALSO THE MEAN HORIZONTAL WIND THAT IS TRANSVERSE TO THE VERTICAL BEAM WITHOUT SCANNING THAT BEAM OFF ZENITH 4HESE PROFILERS USE THE SO CALLED SPACED ANTENNA TECH NIQUES WITH MULTIPLE RECEIVERS TO PROCESS THE AMPLITUDE AND PHASE DIFFERENCES OF THE ECHO STRUCTURES AS THEY TRANSLATE OVER TWO ADJACENT ANTENNAS USUALLY SUBARRAYS OF THE SAME ARRAY ANTENNA TO MEASURE COMPONENTS OF THE HORIZONTAL OR TRANSVERSE WIND )N THIS MANNER TWO ORTHOGONAL SUBARRAYS CAN MEASURE COMPONENTS OF THE HORIZONTAL WIND USING CROSS SPECTRAL OR CORRELATION PROCESSING TECHNIQUES 3INCE THE MEASUREMENT IS MADE IN PAIRS OF OVERLAPPING BEAMS DIRECTLY ABOVE THE RADAR IT IS NO LONGER NECESSARY TO ASSUME OR REQUIRE HORIZONTAL HOMOGENEITY OF THE WIND FIELD IN THE LARGER AREA ABOVE THE RADAR ANDOR THE LONG INTEGRATION TIMES NECESSARY TO ASSURE THIS HOMOGENEITY 4HESE SPACED ANTENNA TECHNIQUES ARE MOST FREQUENTLY USED WHEN HIGH SPATIAL AND TEMPORAL RESOLUTION MEASUREMENTS ARE REQUIRED SUCH AS ESTIMATING DETAILED BOUNDARY LAYER TURBULENCE FIELDS :HANG AND $OVIAK HAVE INVESTIGATED USING THE DUAL BEAMnSPACED ANTENNA TECHNIQUE IMPLEMENTED WITH AN ELECTRONICALLY SCANNED PHASED ARRAY RADAR TO ESTIMATE THE TRANSVERSE AS WELL AS THE RADIAL WIND COMPONENTS AT ARBITRARY SCAN ANGLES
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Óä°£Ê /," 1 /" "EYOND THE HORIZON DETECTION OF TERRESTRIAL TARGETS AT RANGES OF THOUSANDS OF KILOMETERS CAN BE ACHIEVED BY RADARS OPERATING IN THE HIGH FREQUENCY (& BAND TO -(Z 4HIS VERY LONG RANGE COVERAGE IS OBTAINED BY USING SKYWAVE PROPAGATION THAT IS REFLECTING THE RADAR SIGNALS FROM THE IONOSPHERE (& GROUND WAVE SURFACE WAVE PROPAGATION OVER THE SEA HAS BEEN USED FOR INTERMEDIATE BUT STILL OVER THE HORIZON DISTANCES UP TO SEVERAL HUNDRED KILOMETERS /CCASIONALLY (& RADAR SYSTEMS ALSO FIND APPLICATIONS IN LINE OF SIGHT APPLICATIONS AT SHORT RANGE 4HIS CHAPTER FOCUSES PREDOMINANTLY ON SKYWAVE RADAR THOUGH MUCH OF THE DISCUSSION APPLIES EQUALLY TO SURFACE WAVE RADAR 2ATHER THAN AMALGAMATE DISCUSSION OF THE TWO RADAR CONFIGURATIONS THROUGHOUT THE CHAPTER THE DISTINCTIVE FEATURES OF (& SURFACE WAVE RADAR ARE TREATED SEPARATELY IN AN APPENDIX AT THE END OF THE CHAPTER )N ONE SENSE THE DEVELOPMENT OF (& SKYWAVE RADAR CAN BE TRACED BACK TO THE S WHEN SKYWAVE ECHOES WERE IDENTIFIED BUT THE FIRST (& RADAR SYSTEMS WERE NOT DEPLOYED UNTIL THE S 3INCE THEN SKYWAVE RADAR HAS EVOLVED TO ADDRESS APPLICATIONS SUCH AS THE DETECTION AND TRACKING OF AIRCRAFT BALLISTIC AND CRUISE MISSILES AND SHIPSn )N ADDITION TO DETECTING hSKINv ECHOES FROM TARGETS OF INTEREST (& RADAR IS USEFUL FOR OBSERV ING VARIOUS FORMS OF HIGH ALTITUDE ATMOSPHERIC IONIZATION BOTH NATURAL INCLUDING THOSE ASSOCIATED WITH AURORAE AND METEORS AND ARTIFICIAL INCLUDING THE INTERACTION OF SPACE CRAFT AND BALLISTIC MISSILES WITH THE IONOSPHERIC PLASMAn &URTHER THE WAVELENGTHS USED ARE OF THE SAME ORDER AS OCEAN SURFACE GRAVITY WAVES AND THIS CORRESPONDENCE CAN BE EXPLOITED TO PROVIDE INFORMATION ON THE WAVE DIRECTIONAL SPECTRUM OCEAN CURRENTS AND BY INFERENCE SURFACE WINDS )NDEED SCATTERING FROM THE SEA CAN OFTEN BE EMPLOYED AS A RADAR CROSS SECTION 2#3 AMPLITUDE REFERENCE AND IS A WIDELY USED DIAGNOSTIC TOOL 4HE NARROW BAND WAVEFORMS EMPLOYED THE LOW FREQUENCIES AND THE NATURE OF THE TRANS MISSION PATH MAKE THE SPATIAL RESOLUTION COARSE WHEN COMPARED WITH HIGHER FREQUENCY RADARS BUT THE DOPPLER RESOLUTION CAN BE EXCEEDINGLY FINE 4HE MAGNITUDE AND DOPPLER DISTRIBUTION OF THE ECHOES FROM THE DISTANT %ARTHS SURFACE OFTEN TERMED BACKSCATTER THOUGH THAT TERM SHOULD BE RESERVED FOR MONOSTATIC RADARS ARE MAJOR FACTORS IN SETTING SYSTEM DYNAMIC RANGE SPECTRAL PURITY AND SIGNAL PROCESSING REQUIREMENTS Óä°£
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&)'52% 2AY TRACING THROUGH A MODEL IONOSPHERE SHOWING THE VARIATION OF THE RADAR FOOTPRINT WITH CARRIER FREQUENCY 4HE CONTOURS MAP THE PLASMA FREQUENCY OR ELECTRON DENSITY
&OR EFFECTIVE RADAR OPERATION ENVIRONMENTAL PARAMETERS THAT AFFECT RADAR PERFORMANCE NEED TO BE DETERMINED IN REAL TIME DEFINED AS THAT INTERVAL IN WHICH THERE ARE NO LARGE SCALE CHANGES IN THE IONOSPHERE 4YPICALLY THIS IS OF THE ORDER OF n MINUTES 4RANSMISSION PATH INFORMATION IS GENERALLY DERIVED FROM ADJUNCT VERTICAL AND OBLIQUE SOUNDERS AS WELL AS BY USING THE RADAR ITSELF AS A SOUNDER !N IONOSPHERIC ELECTRON DENSITY MODEL COMPLEX ENOUGH TO ENABLE ADEQUATE SOUNDING INTERPRETATION IS REQUIRED )ONOSPHERIC OR TRANSMIS SION PATH STATISTICAL CLIMATOLOGIES AND FORECASTS ARE NECESSARY FOR RADAR DESIGN AND FOR DEVELOPMENT OF SITE SPECIFIC MODELS )N ADDITION OTHER USERS IN THE (& SPECTRUM MUST BE OBSERVED CONTINUOUSLY AND OPERATING FREQUENCIES SELECTED TO AVOID INTERFERENCE 4HE ESSENTIAL FEATURES OF SKYWAVE PROPAGATION CAN BE SEEN IN &IGURE 4HE IONOSPHERE BEING AN IONIZED GAS WITH FREE ELECTRONS WILL REFLECT ALL RADAR SIGNALS WHEN THE RADAR FREQUENCY IS LESS THAN THE PLASMA FREQUENCY GIVEN BY
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&)'52% .UMERICALLY COMPUTED RAYS ILLUSTRATING MULTIPLE HOP PROPAGATION ACROSS THE EQUATORIAL ZONE 4HE ELEVATED PEAK ELECTRON DENSITY NEAR THE EQUATOR AT ^ KM IS THE !PPLETON ANOMALY
WHERE F0 IS IN -(Z AND .E IS IN ELECTRONS PER CUBIC METER &OR A GIVEN ELEVATION ANGLE @ IF THE RADAR FREQUENCY EXCEEDS F P SIN A AT THE HEIGHT OF MAXIMUM IONIZATION RAYS LAUNCHED AT HIGHER ELEVATION ANGLES WILL ESCAPE RESULTING IN A SO CALLED SKIP OR DEAD ZONE WITHIN WHICH THE %ARTHS SURFACE IS NOT ILLUMINATED "EYOND THIS SKIP ZONE ENERGY IS RETURNED TO THE %ARTH REACHING A MAXIMUM RANGE WHEN THE RAYS LEAVING THE ANTENNA ARE HORIZONTAL 5SEFUL RANGE COVERAGE WILL LIE BETWEEN THESE LIMITS WHICH DEFINE THE ONE HOP ZONE !S SHOWN IN &IGURE A MULTIPLICITY OF HOPS MAY EXIST AND ENERGY MAY EVEN CIRCLE THE EARTH CLUTTER ECHOES FROM THESE LONG RANGES CAN SERIOUSLY DEGRADE RADAR PERFORMANCE ! COMPARISON OF &IGURES A B AND C REVEALS THAT DIFFERENT RANGE EXTENTS ARE ILLUMINATED BY USING DIFFERENT OPERATING FREQUENCIES WITH LONGER STARTING RANGES REQUIRING HIGHER FREQUENCIES )N THE EXAMPLES SHOWN -(Z ILLUMI NATES RANGES FROM TO KM WHEREAS -(Z ILLUMINATES RANGES FROM TO KM WHEREAS -(Z ILLUMINATES FROM TO KM (ENCE THE FARTHEST EDGE OF THE FOOTPRINT NEED NOT INCREASE WITH FREQUENCY DEPENDING ON THE PREVAILING IONO SPHERIC CONDITIONS )N THIS EXAMPLE A SINGLE IONOSPHERIC LAYER IS CONSIDERED .ORMALLY THERE ARE TWO OR THREE DISTINCT LAYERS SUCH THAT SIGNALS MAY PARTIALLY PENETRATE THE LOWER LAYERS TO BE REFLECTED BY A HIGHER LAYER !S A CONSEQUENCE THE RELATIONSHIP BETWEEN THE RANGE TO A TARGET AND THE MEASURED ECHO TIME DELAY BECOMES MULTIVALUED WITH UNKNOWN PARAMETERS SUCH AS LAYER HEIGHTS THAT MUST BE ESTIMATED BY VARIOUS TECH NIQUES AS DESCRIBED LATER IN THIS CHAPTER 4O ILLUSTRATE THE OPERATING PRINCIPLES OF A SKYWAVE RADAR &IGURE PRESENTS A MAP SHOWING MULTIPLE SURVEILLANCE TASKS ASSIGNED TO A HYPOTHETICAL RADAR WITH n AZIMUTHAL COVERAGE &IVE SECTORS OF CURRENT SURVEILLANCE ACTIVITY ARE SHOWN EACH ADDRESSING A PARTICULAR MISSION AS INDICATED EACH MISSION CONSISTING OF A NUMBER OF DWELL INTERROGATION REGIONS $)2S 4HE ELECTRONICALLY STEERED RADAR TRANSMIT BEAM STEPS THROUGH THESE $)2S IN SOME ASSIGNED SEQUENCE ILLUMINATING EACH $)2 WITH AN APPROPRIATE WAVEFORM FOR A CORRESPONDING INTERVAL DURING WHICH THE RECEIVING SYSTEM ACQUIRES A COHERENT TIME SERIES OF ECHO SAMPLES 4HE COHERENT INTEGRATION TIME #)4 DEPENDS ON THE TYPE OF OBSERVATION BUT IS ALMOST ALWAYS IN THE RANGE OF n SECONDS %ACH TRANSMITTER FOOTPRINT IS ANALYZED BY FORMING SIMULTANEOUS CONTIGUOUS RECEIVE BEAMS ON THE ORDER OF n WIDE AT -(Z IN THE CASE OF THE 53 .AVY 2/4(2 AND THE !USTRALIAN *INDALEE AND */2. RADARS WHICH EQUATES TO A KM CROSS RANGE RESOLU TION AT A KM RANGE 4HE TASK SPECIFIC REQUIREMENTS ON $)2 REVISIT RATES DETERMINE THE SEQUENCING OF THE $)2 INTERROGATIONS AND OF COURSE SET THE LIMIT ON HOW MANY TASKS CAN BE ADDRESSED
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&)'52% 3OME COVERAGE AND TASKING OPTIONS FOR HYPOTHETICAL (& RADARS ON A FICTITIOUS MID !TLANTIC ISLAND 4HE COVERAGE REGIONS NUMBERED n CORRESPOND TO SKYWAVE RADAR MISSIONS AS FOLLOWS AIR ROUTE MONITORING BARRIER SURVEILLANCE STRATEGIC WATERWAY MONITORING BALLISTIC MISSILE LAUNCH DETECTION AND REMOTE SENSING AND HURRICANE TRACKING 4HE SECTOR DESIGNATED IS REPRESENTATIVE OF (& SURFACE WAVE RADAR COVERAGE
#ONSIDER THE SET OF TASKS AND $)2S SHOWN IN &IGURE 4ASK WOULD REQUIRE ONLY SHORT #)4S n S SAY IF THE AIRCRAFT IS ASSUMED TO BE LARGE AND WOULD NEED REVISITS PERHAPS EVERY MINUTE AS THE FLIGHT IS NOT EXPECTED TO MANEUVER SO THE TRACK WILL BE WELL BEHAVED AND OBSERVED POSITION ERRORS WOULD BE DUE TO IONOSPHERIC FLUCTUATIONS /NLY THE SINGLE $)2 CONTAINING THE AIRCRAFT NEED BE INTERROGATED 4ASK BARRIER SUR VEILLANCE IF CONCERNED WITH SHIP TRAFFIC CAN AFFORD TO RELAX THE REVISIT TIME TO TENS OF MINUTES AS SHIPS MOVE SO SLOWLY BUT IN ORDER TO ACHIEVE DETECTION LONG #)4S OF n S ARE REQUIRED TO SEPARATE THE SHIP ECHOES FROM THE SEA CLUTTER IN THE DOPPLER SPECTRUM %VEN SO THE RADAR CAN STEP ACROSS THE BARRIER ARC WITH PLENTY OF TIME TO INTERLEAVE A 4ASK DWELL BETWEEN ADDRESSING SUCCESSIVE $)2S IN 4ASK )F THE BARRIER 4ASK WERE CONCERNED WITH AIRCRAFT WITH A #)4 OF n S THE REVISITS WOULD NEED TO BE FREQUENT ENOUGH TO ACHIEVE THE DESIRED PROBABILITY OF DETECTION BEFORE THE AIRCRAFT HAD TIME TO CROSS THE BARRIER /NE APPROACH IS TO WIDEN THE BARRIER BY PROCESSING MORE RANGE CELLS OR BY REDUCING THE WAVEFORM BANDWIDTH AND ALLOWING THE RANGE CELLS TO GROW WIDER BUT THIS MAY FAIL IF THE IONOSPHERE DOES NOT SUPPORT PROPAGATION OVER THE INCREASED RANGE DEPTH !NOTHER POSSIBILITY IS TO INCREASE THE REVISIT INTERVAL OVER A SUBSET OF THE $)2S 4HE RELATIVE PRIORITY OF 4ASKS AND WOULD ALSO NEED TO BE TAKEN INTO ACCOUNT 4ASK BALLISTIC MISSILE LAUNCH DETECTION WOULD REQUIRE MUCH MORE FREQUENT SUR VEILLANCE IF A LAUNCH WERE BELIEVED TO BE IMMINENT OR ELSE THE MISSILE MIGHT ESCAPE FROM THE RADAR FOOTPRINT WITHOUT BEING DETECTED !SSUME A #)4 OF SECONDS AND A TOLERABLE REVISIT INTERVAL OF S 4ASKS AND COULD BE INTERLEAVED FOR EXAMPLE BY CARRYING OUT FIVE DWELLS OF 4ASK AND THEN ONE OF 4ASK AND THEN REPEATING THIS PAT TERN 4ASK IS CONCERNED WITH SLOW MOVING SHIPS SO THE REVISIT INTERVAL COULD BE TENS
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OF MINUTES BUT A LONG #)4 OF PERHAPS n S IS REQUIRED IN ORDER TO SEPARATE THE SHIP ECHOES FROM THE SEA CLUTTER IN THE DOPPLER SPECTRUM $URING THIS TIME 4ASK S REQUIRE MENTS WOULD BE VIOLATED 4ASKS AND AS DEFINED ARE INCOMPATIBLE 4ASK REMOTE SENSING OF OCEAN CONDITIONS WOULD HAVE A MUCH LOWER PRIORITY AS IT DEALS WITH SLOWLY VARYING PHENOMENA SO IT WOULD NEED ONLY OCCASIONAL REVISITING 4HE SMALLER SECTOR SHOWN AS 4ASK EXTENDING TO A RANGE OF KM IS REPRESENTATIVE OF THE COVERAGE OF AN (& SURFACE WAVE RADAR AS USED FOR PROTECTING THE APPROACHES TO A PORT FOR EXAMPLE 4HIS EXAMPLE IS TYPICAL OF THE SCHEDULING AND RESOURCE ALLOCATION PROBLEM THAT IS CENTRAL TO (& SKYWAVE RADAR OPERATIONS #OMPROMISES ARE OFTEN UNAVOIDABLE 4HE SITUATION IS FURTHER COMPLICATED BY THE CONTINUOUS VARIATION OF IONOSPHERIC PROPAGA TION CONDITIONS WHICH MUST BE MONITORED AND USED TO GUIDE TASKING AS WHEN BAD IONOSPHERIC hWEATHERv IS LIKELY TO PRECLUDE CERTAIN MISSIONS !LMOST INVARIABLY THE SECTORS AND INDEED THE INDIVIDUAL $)2S WITHIN A SECTOR WILL REQUIRE DIFFERENT CARRIER FREQUENCIES EVEN FOR A GIVEN RANGE AS THE IONOSPHERE MAY VARY SUBSTANTIALLY ACROSS THE FULL RANGE AND AZIMUTH EXTENT OF THE ACTIVE COVERAGE 4HE DEFINING CHARACTERISTIC OF (& SKYWAVE RADAR IS THAT THE RADAR OPERATOR MUST SELECT FREQUENCIES THAT ARE OPTIMUM FOR THE VARIOUS TASKS AND ADAPT THESE FREQUENCIES TO THE EVER CHANGING IONOSPHERE 4HIS CHAPTER SETS OUT TO EXPLAIN THE PRINCIPAL FEATURES OF (& SKYWAVE RADAR AS IT IS PRESENTLY IMPLEMENTED EMPHASIZING THE PHYSICAL CONSIDERATIONS THAT GOVERN SYSTEM DESIGN AND PERFORMANCE
Óä°ÓÊ / Ê, ,Ê +1/" ! FORM OF THE RADAR EQUATION %Q CAN BE USED TO POINT TO ASPECTS OF (& RADAR THAT ARE SIGNIFICANTLY DIFFERENT FROM RADARS THAT USE HIGHER FREQUENCIES 4HESE DIFFER ENCES INCLUDE ADAPTATION TO ENVIRONMENT FREQUENCY AND WAVEFORM SELECTION RADAR CROSS SECTION PATH LOSSES MULTIPATH EFFECTS NOISE INTERFERENCE ANTENNA GAIN SPATIAL RESOLUTION AND CLUTTER &OR THE CASE OF NOISE LIMITED DETECTION THE RADAR EQUATION TAKES THE FORM 3 0AV 'T 'R 4K S &P . P , P ,S . 2
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3. OUTPUT SIGNAL TO NOISE RATIO 0AV AVERAGE TRANSMITTED POWER 'T TRANSMITTER ANTENNA GAIN 'R RECEIVER ANTENNA GAIN 4 COHERENT PROCESSING TIME K WAVELENGTH R TARGET RADAR CROSS SECTION &P PROPAGATION PATH FACTOR . NOISE POWER PER UNIT BANDWIDTH ,P ,S TRANSMISSION PATH AND SYSTEM LOSSES 2 DISTANCE BETWEEN RADAR AND TARGET
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4HESE PARAMETERS ARE EXPLAINED BRIEFLY AS FOLLOWS !NTENNAS 'T AND 'R ! COMMON CONVENTION FOR (& BAND RADARS IS TO INCLUDE THE EFFECT OF THE GROUND IN THE ANTENNA PERFORMANCE CHARACTERIZATION AND THAT CON VENTION WILL BE USED HERE &OR EXAMPLE A HALF WAVE DIPOLE IN FREE SPACE HAS A MAXIMUM GAIN OVER AN ISOTROPE OF D" )F THAT ANTENNA IS ORIENTED VERTICALLY JUST ABOVE BUT NOT TOUCHING A PERFECTLY CONDUCTING EARTH ITS MAXIMUM GAIN WILL BE INCREASED BY A FACTOR OF OR D" TO D" AT n ELEVATION ANGLE "ECAUSE THE %ARTH IS NEVER PERFECT ITS CONDUCTIVITY AND DIELECTRIC CONSTANT ARE FACTORS IN DETERMINING ANTENNA PERFORMANCE 4HE ELECTRICAL PROPERTIES OF THE %ARTH ARE A MUCH STRONGER FACTOR FOR VERTICAL POLARIZATION THAN FOR HORIZONTAL HOWEVER TERRAIN FEA TURES AND SURFACE ROUGHNESS ARE IMPORTANT FOR BOTH POLARIZATIONS #OHERENT PROCESSING TIME 4 &OR RANGES BEYOND THE SKIP DISTANCE (& RADAR RETURNS ALMOST INVARIABLY CONTAIN %ARTH BACKSCATTER AT THE SAME RANGES AS TARGETS $OPPLER PROCESSING IS USED TO SEPARATE TARGETS FROM %ARTH BACKSCATTER HENCE COHERENT SAM PLES ARE ACQUIRED OVER AN INTERVAL 4 WHICH MAY EXCEED S THOUGH IT IS USUALLY IN THE RANGE OF n S 7AVELENGTH K 4HE WAVELENGTH OR OPERATING FREQUENCY MUST BE SELECTED SO THAT THE TRANSMITTED ENERGY IS REFLECTED BY THE IONOSPHERE TO ILLUMINATE THE DESIRED AREA OF THE %ARTH 4HE SPECTRUM OF THE EMISSIONS MUST BE CONSTRAINED NOT TO INTERFERE WITH OTHER USERS "ECAUSE BOTH THE IONOSPHERE AND THE (& BAND OCCUPANCY DISTRIBU TIONS ARE TIME VARYING PARAMETERS ADAPTIVE RADAR MANAGEMENT IS REQUIRED 2ADAR CROSS SECTION 2#3 R 4HE RADAR CROSS SECTION OF CONVENTIONAL TARGETS WILL GENERALLY BE A FUNCTION OF FREQUENCY POLARIZATION AND ASPECT ANGLE BUT AT (& THE TARGET DIMENSIONS ARE TYPICALLY OF THE SAME ORDER AS THE WAVELENGTH SO SCATTER ING BEHAVIOR IS DIFFERENT FROM THAT OBSERVED AT HIGHER FREQUENCIES 3CATTERING ALSO OCCURS FROM THE ENVIRONMENTCLUTTERSO MODELS OF THE SCATTERING COEFFICIENT PER UNIT AREA OF LAND AND OCEAN SURFACES OR PER UNIT VOLUME OF THE TURBULENT IONOSPHERE ARE USED TO PROVIDE EFFECTIVE 2#3 VALUES FOR %Q WHEN THOSE NATURAL SCATTER ERS ARE THE hTARGETSv OF INTEREST 4HUS FOR THE 2#3 OF %ARTH CLUTTER THE NORMALIZED SURFACE SCATTERING COEFFICIENT R n IS MULTIPLIED BY THE RESOLUTION CELL SIZE ! 4HE IMPORTANT RESOLUTION CELL SIZE FACTORS VIZ RECEIVER ANTENNA BEAMWIDTH AND SPECTRAL BANDWIDTH ARE NOT EXPLICITLY CONTAINED IN %Q #LUTTER FREQUENTLY SETS THE LIMIT TO TARGET DETECTABILITY IN WHICH CASE IT IS THE SIGNAL TO CLUTTER RATIO RATHER THAN THE SIGNAL TO NOISE RATIO THAT IS OF INTEREST !CCORDINGLY A DIFFERENT FORM OF THE RADAR EQUATION MUST THEN BE EMPLOYED 0ROPAGATION FACTORS &P 3EVERAL PROPAGATION PHENOMENA INCLUDING &ARADAY POLARIZATION ROTATION GROUND REFLECTION MULTIPATH MULTIPLE HOP PROPAGATION AND IONOSPHERIC FOCUSING MAY NEED TO BE INCLUDED IN THE EQUATION DEPENDING ON THE SCENARIO OF INTEREST &ARADAY ROTATION REFERS TO THE VARIATION OF THE POLARIZATION OF THE SIGNAL INCIDENT ON THE TARGET AS A FUNCTION OF TIME AND DISTANCE ARISING FROM ITS PROPAGATION THROUGH THE MAGNETIZED IONOSPHERIC PLASMA LINEARLY POLARIZED TRANS MITTED SIGNALS OFTEN ARRIVE IN THE TARGET ZONE WITH A ROTATED AXIS OF POLARIZATION BUT STILL ESSENTIALLY LINEARLY POLARIZED 3INCE MANY TARGETS HAVE 2#3 THAT VARY WITH POLARIZATION AN IMPORTANT RESULT IS THAT THE MOST FAVORABLE POLARIZATION WILL ILLU MINATE THE TARGET RECURRENTLY 4HE SPATIAL SCALE OF THE POLARIZATION hFRINGESv IN THE RADAR FOOTPRINT IS TYPICALLY IN THE RANGE n KM AND THE CHANGE OF FREQUENCY NEEDED TO ROTATE THE PLANE OF POLARIZATION BY n AT A GIVEN LOCATION IN THE RADAR FOOTPRINT THE POLARIZATION BANDWIDTH IS OF THE ORDER OF K(Z SO DIFFERENTIAL
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EFFECTS MAY BE SIGNIFICANT /F COURSE POLARIZATION WILL ALSO FLUCTUATE AT THE RECEIV ING ANTENNA AS A CONSEQUENCE OF THE TIME VARYING RETURN PATH .OISE .O &OR RADARS OPERATING IN THE (& BAND THE RECEIVER INTERNAL NOISE IS ALMOST ALWAYS LESS THAN THE EXTERNAL NOISE ,OSSES ,P ,S 4HE LOSS TERM ,P CONTAINS THE TWO WAY LOSSES ALONG THE PATH TRAVERSED INCLUDING IONOSPHERIC ABSORPTION AND GROUND REFLECTION LOSSES ,S REPRE SENTS ANY RADAR SYSTEM LOSSES )ONOSPHERIC LOSSES WHILE PREDICTED ON A STATISTICAL BASIS CAN CONSTITUTE A MAJOR UNKNOWN IN REAL TIME RADAR OPERATION 2ANGE 2 4HE RANGE IN %Q IS THE hSLANT RANGE v THAT IS THE LENGTH OF THE SKY WAVE PATH BETWEEN TARGET AND RADAR NOT THE DISTANCE AS MEASURED ALONG THE %ARTHS SURFACE 4HE IONOSPHERIC REFLECTION HEIGHT NEEDS TO BE USED TO CONVERT THIS SLANT RANGE TO GREAT CIRCLE GROUND DISTANCE 4HE APPARENT RANGE TO A PARTICULAR TARGET MAY TAKE ON MORE THAN ONE VALUE SINCE MULTIPLE PATHS MAY EXIST 7ITH THESE INTERPRETATIONS THE RADAR EQUATION %Q CAN BE USED TO MODEL THE PERFORMANCE OF SKYWAVE RADARS WHEN NOISE NOT CLUTTER IS SETTING THE LIMIT TO TARGET DETECTABILITY NOTING THAT THE COMPLEXITY AND STATISTICAL NATURE OF IONOSPHERIC PROPAGATION AND THE EXTERNAL NOISE ENVIRONMENT MEANS THAT IT IS OFTEN NECESSARY TO APPLY THE EQUATION TO PROBABILITY DISTRIBUTIONS NOT SCALAR VALUES OF THE PARAM ETERS 7HEN THE TARGETS VELOCITY PLACES ITS DOPPLER SHIFT BEYOND THOSE OF ANY CLUT TER RETURNS THE NOISE LIMITED MODEL IS APPROPRIATE BUT THERE ARE TWO IMPORTANT SITUATIONS WHERE THIS IS NOT THE CASE 4HE FIRST IS SHIP DETECTION WHERE THE INTRINSIC DOPPLER SPREAD OF SEA CLUTTER ROUTINELY EXTENDS BEYOND THE TYPICAL DOPPLER SHIFTS OF MOST SHIP ECHOES 4HE SECOND CASE IS THE PHENOMENON OF SPREAD DOPPLER CLUTTER WHICH ARISES FROM PLASMA INSTABILITIES AND TURBULENCE ESPECIALLY POST SUNSET AND AT HIGH AND LOW LATITUDES 4HE EQUIVALENT VELOCITY OF THIS TYPE OF CLUTTER CAN EXTEND TO HUNDREDS OF METERS PER SECOND MASKING EVEN FAST AIRCRAFT RETURNS 4HESE TOPICS ARE ADDRESSED IN 3ECTION $EALING WITH CLUTTER LIMITED SITUATIONS IS A VITAL PART OF THE RADAR DESIGNERS TASK REQUIRING A DETAILED UNDERSTANDING OF THE PHENOMENA AND THEIR DISTRIBUTIONS
Óä°ÎÊ /",-Ê 1 ÊÊ - 976 Ê, ,Ê - 0RINCIPAL $IFFERENCES "ETWEEN (& AND -ICROWAVE 2ADAR "EFORE ANALYZING (& SKYWAVE RADAR SYSTEMS IN DETAIL IN THE SECTIONS THAT FOLLOW AND DESCRIBING THOSE PROPERTIES OF THE ENVIRONMENT THAT IMPACT THEIR DESIGN AND PERFORMANCE IT IS INSTRUC TIVE TO SUMMARIZE THE PRINCIPLE DIFFERENCES BETWEEN SKYWAVE RADAR AND CONVENTIONAL MICROWAVE RADAR 4HIS PROVIDES A CAUTIONARY REMINDER NOT TO EXTRAPOLATE TOO READILY FROM THE FAMILIAR CHARACTERISTICS OF THE MICROWAVE DOMAIN TO THE (& BAND (& SKYWAVE RADARS OPERATE AT RANGES ABOUT AN ORDER OF MAGNITUDE GREATER THAN MICROWAVE LONG RANGE AIR SURVEILLANCE RADARS 4HE (& RADAR WAVELENGTH IS HUNDREDS OF TIMES GREATER SO THE ANTENNAS ARE PROPORTIONATELY LARGER AS MUCH AS TWO OR THREE KILOMETERS IN LENGTH IF THEY ARE TO SEE SHIPS BUT CONSIDERABLY LESS IF ONLY AIRCRAFT ARE TO BE DETECTED 4RANSMITTER AVERAGE POWER MIGHT BE ON THE ORDER OF SEVERAL HUNDRED KILOWATTS FOR A SKYWAVE RADAR BUT ON THE ORDER OF A FEW KILOWATTS FOR A MICROWAVE !4# RADAR 4HE OBSERVATION TIME #)4 FOR SKYWAVE SYSTEMS CAN RANGE FROM ONE TO MANY TENS OF SECONDS BUT IS ON THE ORDER OF TENS OF MILLISECONDS FOR MICROWAVE RADAR
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4HE LONG OBSERVATION TIME FOR A SKYWAVE RADAR IS NEEDED TO OBTAIN THE NECESSARY ECHO SIGNAL ENERGY TO ENSURE RELIABLE TARGET DETECTION AS WELL AS TO OBTAIN THE LONG INTEGRA TION TIMES NEEDED FOR EFFECTIVE DOPPLER PROCESSING 4HE IONOSPHERE HAS A DOMINATING INFLUENCE ON SKYWAVE RADAR WHEREAS THE NORMAL ATMOSPHERE HAS VERY LITTLE EFFECT ON MICROWAVE RADAR 4HE SKYWAVE RADARS FREQUENCY AND OTHER PARAMETERS ARE DRIVEN PRIMARILY BY THE NEED TO PROPAGATE VIA THE IONOSPHERE #ONSTRAINTS IMPOSED BY PROPA GATION AND THE AVAILABILITY OF UNOCCUPIED FREQUENCY CHANNELS DICTATE THAT THE RANGE RESOLUTION OF (& RADARS IS NOT NEARLY AS GOOD AS THAT OF MICROWAVE SYSTEMS 4HE (& TRANSMITTER HAS TO MAINTAIN STRINGENT CONTROL OF ITS RADIATED SIGNAL SPECTRUM SO AS TO AVOID INTERFERENCE TO OTHER USERS OF THE (& SPECTRUM ! SIMILAR CONSIDERATION APPLIES TO MICROWAVE RADARS BUT NOT TO THE EXTENT THAT IT DOES AT (& -ILITARY MICROWAVE RADARS LIKE TO HAVE AVAILABLE A WIDE SPECTRAL WIDTH FOR PURPOSES OF ELECTRONIC PROTECTION AND TO EXTRACT MORE DETAILED TARGET INFORMATION BUT THE INCREASING DEMANDS OF CIVILIAN WIRE LESS SERVICES HAVE REDUCED THE AVAILABLE SPECTRUM AVAILABLE TO MICROWAVE RADARS TO THE POINT WHERE IT IS LIMITING PERFORMANCE 4HE SENSITIVITY OF MICROWAVE RADARS IS LIMITED BY RECEIVER NOISE BUT THE SENSITIVITY OF (& RADARS IS LIMITED BY EXTERNAL NOISE THAT ENTERS THE RECEIVER THROUGH THE ANTENNA 4HIS EXTERNAL NOISE IS DUE NOT ONLY TO NATURAL MECHANISMS SUCH AS THUNDERSTORMS BUT TO THE SIG NALS FROM THE MANY (& TRANSMITTERS THROUGHOUT THE WORLD "OTH MICROWAVE AND (& RADARS CAN BE LIMITED BY THE LARGE ECHO SIGNALS FROM LAND OR SEA THOUGH IN (& SKYWAVE RADARS THE PROBLEM IS PARTICULARLY SEVERE $OPPLER PROCESSING IS ESSENTIAL UNDER SUCH CONDITIONS &OR SOME AIRCRAFT THE RADAR CROSS SECTION AT (& IS SIGNIFICANTLY LARGER THAN THAT AT MICRO WAVES -ANY (& /4( RADARS UTILIZE AN &- #7 WAVEFORM SO WIDELY SEPARATED SITES ARE NEEDED TO MINIMIZE THE LEAKAGE OF THE TRANSMITTER INTO THE RECEIVER -ICROWAVE RADARS HAVE USED &- #7 WAVEFORMS IN THE PAST BUT IN MOST CASES THESE HAVE BEEN REPLACED BY WAVEFORMS THAT DONT REQUIRE SEPARATE TRANSMITTER AND RECEIVER SITES 4ABLE PRESENTS A COMPARISON OF SOME KEY RADAR PARAMETERS FOR REPRESENTATIVE RADAR SYSTEMS OF EACH TYPE AND CONTRASTS THE WAYS IN WHICH THE RESPECTIVE MODES OF PROPAGATION SCATTERING NOISE AND DEPLOYMENT CONSTRAIN THE FORM AND FUNCTION OF RADAR SYSTEMS )MPLICATIONS FOR 3KYWAVE 2ADAR $ESIGN &ROM AN EXAMINATION OF 4ABLE IT IS CLEAR THAT A SKYWAVE RADAR IS NOT SIMPLY A MICROWAVE RADAR SCALED UP IN SIZE BY A FACTOR OF ^ THAT IS IN PROPORTION TO THE WAVELENGTH 2EFERRING TO THE RADAR EQUATION THE 2n LOSS TERM MEANS THAT FOR A REPRESENTATIVE TENFOLD INCREASE IN DETEC TION RANGE OF (& OVER MICROWAVE D" EXTRA RANGE LOSS ACCUMULATES 4HIS CANNOT ALL BE RECOVERED BY RADIATING MORE POWER AND INCREASING ANTENNA GAIN FOR PRACTICAL ENGINEERING REASONS AND COST APART FROM CONSTRAINTS IMPOSED BY IONOSPHERIC PROPA GATION #OHERENT DOPPLER PROCESSING PROVIDES THE NECESSARY PROCESSING GAIN BUT THE PROCESSING TIMES REQUIREDFROM TO SMEAN THAT REVISIT RATES WHEN CONDUCTING SURVEILLANCE OVER AN EXTENDED REGION WILL FALL BELOW ACCEPTABLE LEVELS UNLESS MULTIPLE RECEIVE BEAMS ARE PROCESSED IN PARALLEL $ESIGNERS HAVE EXPLORED DIFFERENT TRADE OFFS IN MOST CASES CONVERGING ON SCHEMES IN WHICH n RECEIVE BEAMS ARE FORMED WITHIN A BROADER TRANSMITTED BEAM FOOTPRINT 4HE REDUCED TRANSMITTING ANTENNA GAIN MAY BE COMPENSATED BY INCREASING POWER OR COHERENT PROCESSING TIME %VEN UNDER BENIGN CONDITIONS THE IONOSPHERE SELDOM SUPPORTS HIGHLY COHER ENT PROPAGATION OVER BANDWIDTHS GREATER THAN ^ K(Z EVEN WHEN CLEAR CHANNELS WIDE ENOUGH TO ACCOMMODATE SUCH WAVEFORMS ARE AVAILABLE WHICH IS INFREQUENTLY -ORE TYPICALLY CLEAR CHANNELS RANGE FROM n K(Z SO THE WAVEFORM BANDWIDTH IS NORMALLY CHOSEN TO LIE IN THIS RANGE 4HE CORRESPONDING RANGE RESOLUTIONS EXTEND
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FROM n KM 4HE CROSS RANGE RESOLUTION CELL DIMENSION ,2 AT RANGE 2 IS GIVEN BY , y 2$K WHERE $ IS THE RECEIVING ARRAY APERTURE AND K IS THE RADAR WAVELENGTH 4!",% +EY $IFFERENCES "ETWEEN -ICROWAVE 2ADAR AND (& 3KYWAVE 2ADAR
4HE PARAMETER VALUES QUOTED HERE ARE INTENDED TO BE BROADLY REPRESENTATIVE RATHER THAN AN ATTEMPT TO SPAN ALL KNOWN SYSTEMS ) -)#2/7!6% 2!$!2 4YPE CHOSEN FOR COMPARISON
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*OINT AIRCRAFT AND SHIP DETECTION TWO SITE RADAR SUCH AS *INDALEE */2. AND 2/4(2 -AJOR ANTENNA DIMENSION M n n !VERAGE TRANSMIT POWER K7 !NTENNA RADIATION PATTERN &ULLY DEFINED BY ANTENNA 3TRONGLY INFLUENCED BY GROUND CONSTRUCTION PROPERTIES AROUND ANTENNA 4YPICAL OPERATING RANGE KM n n -INIMUM RANGE KM 2ANGE RESOLUTION M n u 3 TRUCTURED HORIZONTALLY AND 0ROPAGATION MEDIUM u (OMOGENEOUS OR VERTICALLY BOTH DETERMINISTICALLY AND STRATIFIED RANDOMLY ON MANY SCALES u &REQUENCY DISPERSIVE u .ONDISPERSIVE u !NISOTROPIC MAGNETOIONIC u )SOTROPIC u (IGHLY DYNAMIC u 3TABLE u 7EAKLY NONLINEAR u ,INEAR u 6 ARIES DRAMATICALLY WITH TIME OF u .EARLY CONSTANT DAY SEASON ETC u 2EFLECTED FROM IONOSPHERE 2ADAR SIGNAL PROPAGATION PATH u ,INE OF SIGHT u ULTIPLE PATHS RESULTING IN MULTIPLE u 5SUALLY UNIQUE MAY ECHOES FROM A SINGLE TARGET AT HAVE SIMPLE GROUND DIFFERENT APPARENT RANGES BEARINGS REFLECTION MULTIPATH ELEVATION ANGLES AND DOPPLER SHIFTS u 2ELATIVELY STABLE u 5NSTABLE u 0 OORLY KNOWN MUST BE INFERRED FROM ANCILLARY SOUNDING SYSTEMS $OMINANT PROPAGATION EFFECTS u -ULTIPATH INTERFERENCE u !TTENUATION u &OCUSING AND DEFOCUSING ON THE RADAR SIGNAL BETWEEN DIRECT AND SURFACE REFLECTED SIGNALS u 0OLARIZATION TRANSFORMATION u 0HASE MODULATION u 7AVEFRONT DISTORTION 4ARGET SCATTERING REGIME /PTICAL HIGH FREQUENCY 2AYLEIGH n RESONANCE IE TARGET SIZE OR ^ RADAR WAVELENGTH IE TARGET SIZE RADAR WAVELENGTH ,OOK DOWN VIEWING GEOMETRY #LUTTER u #AN BE SERIOUS INEVITABLY RESULTS IN STRONG GROUND ESPECIALLY AT SHORT ECHOES AT THE SAME RANGE AS THE TARGET RANGES u -INIMIZED BY NARROW TYPICALLY n D" STRONGER THAN THE BEAM SHORT PULSE AND TARGET ECHO DOPPLER PROCESSING $OPPLER PROCESSING 7IDELY USED FOR DETECTION %SSENTIAL TO SEPARATE MOVING TARGETS OF MOVING TARGETS IN CLUTTER FROM STRONG CLUTTER RETURNS
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4!",% +EY $IFFERENCES "ETWEEN -ICROWAVE 2ADAR AND (& 3KYWAVE 2ADAR
4HE PARAMETER VALUES QUOTED HERE ARE INTENDED TO BE BROADLY REPRESENTATIVE RATHER THAN AN ATTEMPT TO SPAN ALL KNOWN SYSTEMS #ONTINUED ) -)#2/7!6% 2!$!2 &REQUENCY CONSTRAINTS
.OISE FLOOR DOMINATED BY 3ITING CONSTRAINTS
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u "OUNDED ABOVE BY THE STATISTICAL #AN BE SERIOUS AVAILABILITY OF SKYWAVE PROPAGATION BECAUSE OF THE NEED FOR TO RANGES OF INTEREST WIDEBAND RADAR SYSTEMS u "OUNDED BELOW BY SPECTRUM AND BY COMPETITION AVAILABILITY ANTENNA SIZE AND THE FOR THE MICROWAVE RAPID FALL OFF IN TARGET 2#3 FREQUENCY SPECTRUM BY COMMUNICATIONS AND OTHER u -UST NOT INTERFERE WITH OTHER USERS IN THE CROWDED (& SPECTRUM THUS ELECTROMAGNETIC SERVICES LIMITING CHOICE OF FREQUENCY AND BANDWIDTH u -UST ADAPT CONTINUALLY TO THE CHANGING IONOSPHERE SO AS TO MAINTAIN ILLUMINATION OF CURRENT TARGET REGION )NTERNAL RECEIVER NOISE 3OURCES ATMOSPHERIC GALACTIC THERMAL ETC ANTHROPOGENIC ETC u 5NOBSTRUCTED ELEVATED u 2ECEIVE ARRAY SITE MUST BE %- SITES PREFERRED QUIET GENERALLY RURAL TO AVOID CITY AND INDUSTRIAL NOISE AT (& FREQUENCIES u (UGE ARRAYS REQUIRE FLAT OPEN SPACES TO MINIMIZE TOPOGRAPHIC EFFECTS ON BEAM PATTERNS u )F A BISTATIC OR TWO SITE QUASI MONOSTATIC DESIGN IS ADOPTED IT NEEDS TWO SITES WITH ADEQUATE SEPARATION ^ KM AND THE CORRECT GEOGRAPHICAL RELATIONSHIP RELATIVE TO THE COVERAGE ARC u ,OCATION ON THE %ARTH MUST BE SUCH THAT AURORAL AND EQUATORIAL SPREAD DOPPLER ECHOES DONT MASK TARGETS
(ENCE TO ACHIEVE , KM AT KM RANGE WHEN THE FREQUENCY IS -(Z AND THUS A RESOLUTION CELL NOT TOO ECCENTRIC IN SHAPE REQUIRES AN ARRAY APERTURE OF ABOUT M &EEDING ARRAYS OF THIS SIZE CAN REQUIRE HUNDREDS OF KILOMETERS OF CABLES OR IN SOME SYSTEMS FIBER OPTICS AND RAISES CHALLENGING PROBLEMS IN ARRAY CALIBRATION 4HE TRANSMITTING ARRAY APERTURE ASSUMING y RECEIVE BEAMS TO BE FITTED INTO THE TRANSMIT BEAM NEED BE ONLY ^ M AT THIS FREQUENCY )T FOLLOWS FROM THE RADAR EQUATION AND THE CONSIDERATIONS JUST DISCUSSED THAT TRANS MIT POWER IN THE RANGE OF n K7 IS GENERALLY APPROPRIATE FOR DETECTING SMALL AIRCRAFT TARGETS OVER A WIDE RANGE OF CONDITIONS )N ORDER TO RADIATE POWER EFFICIENTLY THE TRANSMITTING ANTENNA ELEMENTS TEND TO BE LARGE RESONANT STRUCTURES FOR EXAMPLE THE VERTICAL LOG PERIODIC ANTENNAS USED IN THE */2. SYSTEM ARE UP TO M TALL )N CONTRAST THE CHOICE OF RECEIVING ANTENNA ELEMENT HAS TRADITIONALLY BEEN BASED ON THE
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PRECEPT THAT EFFICIENCY IS OF LOW IMPORTANCE FOR (& RECEPTION BECAUSE EXTERNAL NOISE IS ALMOST ALWAYS FAR STRONGER THAN INTERNAL NOISE ! MORE EFFICIENT RECEIVING ELEMENT ACCEPTS MORE SIGNAL POWER BUT EQUALLY MORE EXTERNAL NOISE SO PRIMA FACIE NOTHING IS GAINED IN TERMS OF THE SIGNAL TO NOISE RATIO #OST IS THUS REDUCED BY EMPLOYING A SMALL RECEIVING ANTENNA ELEMENT (EIGHTS OF n M ARE COMMON 4HE LOOK DOWN GEOMETRY OF SKYWAVE ILLUMINATION RESULTS IN STRONG CLUTTER RETURNS IN THE SAME RANGE CELL AS THE TARGET DEMANDING A HIGH DYNAMIC RANGE ABLE TO SUPPORT CLUTTER TO TARGET ENERGY RATIOS IN EXCESS OF D" 4HIS PLACES SEVERE DEMANDS ON THE SPECTRAL PURITY AND DYNAMIC RANGE OF THE RADAR WAVEFORM GENERATOR TRANSMITTING AND RECEIVING SYSTEMS (IGH SENSITIVITY HAS THE SIDE EFFECT OF REVEALING THE ECHOES FROM MANY NATURAL SCATTERERS IN THE IONOSPHERE AS WELL AS THE SPECTRUM OF GROUND CLUTTER THAT HAS BEEN SPREAD IN DOPPLER BY THE FLUCTUATIONS OF THE SIGNAL PROPAGATION PATH )N ORDER TO RECOGNIZE AND SUPPRESS THESE UNWANTED RETURNS WHICH CAN OBSCURE TARGET ECHOES AN UNDERSTANDING OF THE UNDERLYING PHYSICS IS ESSENTIAL ! DISTINCTIVE REQUIREMENT OF A SKYWAVE RADAR IS A SUITE OF AUXILIARY SYSTEMS TO MON ITOR THE STATE OF THE IONOSPHERE AND THE AVAILABILITY OF UNOCCUPIED CHANNELS IN WHICH TO OPERATE 4HIS RELIANCE ON CONTINUOUS ENVIRONMENTAL MONITORING AND THE ASSOCIATED ABILITY TO ADAPT THE RADAR PARAMETERS AND TASKING TO MAKE BEST USE OF THE PREVAILING CONDITIONS CANNOT BE SATISFIED WITH SIMPLE LOW DYNAMIC RANGE EQUIPMENT FOR THAT WOULD FAIL TO REVEAL MANY OF THE PHENOMENA THAT ARE SETTING THE THRESHOLD FOR TARGET DETECTION AND TRACKING &URTHER A HIGH DEGREE OF AUTOMATION IS ESSENTIAL TO KEEP UP WITH THE CHANGING ENVIRONMENT ! COMPARISON OF PRINCIPLE DESIGN PARAMETERS OF SEVERAL CURRENT AND FORMER OPERA TIONAL (& SKYWAVE RADARS IS PRESENTED IN 4ABLE ILLUSTRATING THE DIVERSITY OF ENGI NEERING SOLUTIONS THAT HAVE BEEN IMPLEMENTED TO MEET SPECIFIC MISSION OBJECTIVES
4!",% 0RINCIPAL $ESIGN 0ARAMETERS FOR 3OME -AJOR (& 3KYWAVE 2ADAR 3YSTEMS
0AST AND 0RESENT 4HIS INFORMATION HAS BEEN COMPILED FROM SOURCES THAT IN SOME CASES ARE INCOMPLETE 7HERE ONLY PARTIAL INFORMATION IS PROVIDED IT MAY STILL BE USEFUL FOR COMPARISON PURPOSES .OTES I 6,0! DENOTES VERTICAL LOG PERIODIC ANTENNA AND II BAND N BAND LINEAR ARRAYS ARE USUALLY CONSTRUCTED AS CONTIGUOUS COLLINEAR ARRAYS
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4ELECOM 'ENERAL %LECTRIC 2AYTHEON !USTRALIA 53! 53! '%# -ARCONI 5+ 2,- 53! !USTRALIA
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1UASI MONOSTATIC
1UASI MONOSTATIC
1UASI MONOSTATIC
4RUE MONOSTATIC
1UASI MONOSTATIC
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n D"7
D"7
D"7
9EAR OF FIRST TARGET DETECTIONS #ONFIGURATION 1UASI MONOSTATIC 4X n 2X SITE SEPARATION KM -AX TRANSMITTER POWER K7 4X GAIN D" %20 D"7
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3TEEL 9ARD +OMSOMOLSK .OSTRADAMUS NA !MUR
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4!",% 0RINCIPAL $ESIGN 0ARAMETERS FOR 3OME -AJOR (& 3KYWAVE 2ADAR 3YSTEMS
0AST AND 0RESENT 4HIS INFORMATION HAS BEEN COMPILED FROM SOURCES THAT IN SOME CASES ARE INCOMPLETE 7HERE ONLY PARTIAL INFORMATION IS PROVIDED IT MAY STILL BE USEFUL FOR COMPARISON PURPOSES .OTES I 6,0! DENOTES VERTICAL LOG PERIODIC ANTENNA AND II BAND N BAND LINEAR ARRAYS ARE USUALLY CONSTRUCTED AS CONTIGUOUS COLLINEAR ARRAYS #ONTINUED *INDALEE 3TAGE " 4X ARRAY DESIGN BAND LINEAR ARRAY OF LOW BAND AND HIGH BAND 6,0! ANTENNAS
&REQUENCY n RANGE -(Z 4X APERTURES M
*/2. ,AVERTON
ADJACENT CONTIGUOUS BAND LINEAR BAND LINEAR ARRAYS OF 6,0! ARRAYS OF ANTENNAS CANTED DIPOLES ARRAYS ORIENTED WITH M TALL AT n TO EACH BACKSCREENS OTHER ELEMENTS PER BAND ARRAYS ORIENTED AT n n n
4X AZIMUTH o n o n BEAM STEER DEG 2X ARRAY DESIGN ,INEAR ARRAY LINEAR ARRAYS OF M FAN OF TWIN MONOPOLE PAIRS MONOPOLE GROUPED AS ELEMENTS OVERLAPPED ARRAYS AT n SUBARRAYS 2X APERTURE M
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9 SHAPED ARRAY OF r BICONICAL ELEMENTS RANDOMLY DISTRIBUTED
r VERTICAL CURTAIN ARRAYS OF MASTS r VERTICALLY STACKED HORIZONTAL CAGE DIPOLES
n n
n
n
ARMS r LONG r WIDE n
o n
o n
CONTIGUOUS LINEAR ARRAYS OF r M VERTICAL MONOPOLES WITH M BACKSCREENS ARRAYS AT n
,INEAR ARRAY 9 SHAPED r VERTICAL OF r M ARRAY OF r CURTAIN ARRAYS VERTICAL TWIN M BICONICAL OF MASTS r MONOPOLES ELEMENTS VERTICALLY GROUPED AS r STACKED SUBARRAYS HORIZONTAL WITH RANDOM CAGE DIPOLES DISTRIBUTION LONG r ARMS r LONG r HIGH WIDE
.O OF RECEIVE CHANNELS 2X AZIMUTH o n o n o n o n BEAM STEER 7AVEFORM TYPE ,INEAR &-#7 ,INEAR &-#7 ,INEAR &-#7 ,INEAR &- #7 ,INEAR &-#7 7AVEFORM ^ n ^ n n n REPETITION FREQUENCY (Z 7AVEFORM n TYPICAL n TYPICAL n n BANDWIDTHK(Z #OHERENT n !IR n !IR n n INTEGRATION MODE MODE TIME S n 3HIP n 3HIP MODE MODE 0RIMARY MISSION !IRCRAFT !IRCRAFT !IRCRAFT !IRCRAFT DETECTION DETECTION DETECTION DETECTION 3ECONDARY MISSIONS
3TEEL 9ARD +OMSOMOLSK .OSTRADAMUS NA !MUR
3HIP DETECTION 3HIP DETECTION #RUISE MISSILE 2EMOTE 2EMOTE DETECTION SENSING SENSING
3HIP DETECTION
n #ODED PULSE
"INARY PHASE CODED PULSE
!IRCRAFT DETECTION
"ALLISTIC MISSILE DETECTION 3HIP DETECTION !IRCRAFT 2EMOTE DETECTION SENSING #RUISE MISSILE DETECTION
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4HE TERM QUASI MONOSTATIC IS USED TO DENOTE CONFIGURATIONS IN WHICH THE TRANSMIT AND RECEIVE SITES ARE SEPARATED AS IS OFTEN DONE WITH RADARS EMPLOYING &- #7 WAVE FORMS BUT NOT SO FAR APART THAT THE ANGLE SUBTENDED AT THE TARGET IS MORE THAN ^n SO THE SCATTERING BEHAVIOR IS CLOSE TO WHAT IS OBSERVED FOR EXACTLY MONOSTATIC GEOMETRY
Óä°{Ê / Ê" "-* , ÊÊ Ê, "76 Ê*,"*/" 4HE SOLAR ACTIVITY THAT DRIVES THE IONIZATION OF THE %ARTHS UPPER ATMOSPHERE IS VARIABLE ON A DIURNAL SEASONAL AND LONG TERM BASIS WITH A SUPERIMPOSED RANDOM COMPONENT AND OCCASIONAL MAJOR STORMS AND OTHER DISTURBANCES &URTHER THE %ARTHS LOWER ATMOSPHERE IS COUPLED TO THE IONOSPHERE BY A VARIETY OF UPWARD PROPAGATING WAVE AND RADIATION PROCESSES WHEREAS THE %ARTHS MAGNETOSPHERE THE REGION BEYOND THE IONOSPHERE WHERE THE SOLAR WIND INTERACTS WITH THE %ARTHS MAGNETIC FIELD IS THE SOURCE OR CONDUIT FOR CORRESPONDING PERTURBATIONS FROM ABOVE 4HE IONOSPHERIC RESPONSE TO ALL THESE EXTERNAL FORCES IS GOVERNED NOT ONLY BY INERTIAL EFFECTS BUT ALSO BY CHEMICAL REACTIONS AND BY THE EMBEDDED TIME VARYING ELECTRIC AND MAGNETIC FIELDS THAT LINK THE IONOSPHERIC PLASMA TO THE %ARTH AND TO THE INTERPLANETARY MEDIUM !S A CONSEQUENCE THE STRUCTURE OF THE IONOSPHERE UNDERGOES CHANGES ON A WIDE VARIETY OF SPATIAL AND TEMPORAL SCALES WHICH DRASTICALLY AFFECT ITS PROPERTIES AS A MEDIUM FOR RADIOWAVE PROPAGATION 4HE PRIMARY REQUIREMENT FOR RADAR SYSTEM DESIGN IS A QUANTITATIVE DESCRIPTION OF THE PROPAGATION CHARACTERISTICS OVER THE PROPOSED COVERAGE REGION 3PECIFICALLY THE RADAR DESIGNER NEEDS A STATISTICAL DESCRIPTION THAT WILL ENABLE MATCHING THE TRANSMITTED SIGNAL POWER LEVEL AND ANTENNA GAIN PATTERN TO THE SUPPORTED FREQUENCY SPAN NOISE LEVELS PROPAGATION LOSS CHARACTERISTICS AND RAY PATHS TO THE TARGET REGION )N ADDITION THE RADAR OPERATOR NEEDS A MODEL WITH ENOUGH SOPHISTICATION TO PERMIT FULL INTERPRETA TION OF THE REAL TIME SOUNDINGS FOR OPERATING PARAMETER SELECTION SIGNAL PROCESSING AND DATA ANALYSIS 7ITH THIS LATTER REQUIREMENT A STATISTICAL DESCRIPTION IS USUALLY NOT ADEQUATE AS IMPORTANT FEATURES MAY BE LOST &OR EXAMPLE UNDER RAPIDLY CHANGING IONOSPHERIC CONDITIONS THE RADAR ECHOES WILL EXPERIENCE A TIME VARYING DOPPLER SHIFT !VERAGING OVER TIME WOULD RESULT IN A DOPPLER SHIFT TENDING TO ZERO #LEARLY THIS IS OF NO VALUE TO THE OPERATOR WISHING TO COMPENSATE FOR IONOSPHERIC MOTION AND HENCE TO RETRIEVE A MEANINGFUL ESTIMATE OF TARGET RADIAL VELOCITY !S A SECOND EXAMPLE CONSIDER THE SITUATION WHERE AN ATMOSPHERIC GRAVITY WAVE !'7 IS PROPAGATING THROUGH THE IONOSPHERE IN THE VICINITY OF THE CONTROL POINT IONOSPHERIC REFLECTION POINT WHILE A TARGET IS BEING TRACKED 4HE IONOSPHERE IS ONLY ^ IONIZED AT THE ALTITUDES OF INTEREST TO (& RADAR BUT WAVES IN THE NEUTRAL GAS UNDER THE RESTORING FORCE OF GRAVITY TRANSFER THEIR MOTION TO THE FREE ELECTRONS VIA COLLISIONS !S THE DISTRIBUTION OF ELECTRONS DEFINES THE hREFLECTING SURFACEv EXPERIENCED BY THE RADAR SIGNALS THE APPARENT BEARING AND RANGE OF THE TARGET WILL FLUCTUATE AS THE IONOSPHERIC hREFLECTING SURFACEv UNDULATES IN RESPONSE TO THE !'7 4HIS UNDULATION IS KNOWN AS A TRAVELING IONOSPHERIC DISTUR BANCE 4)$ 4)$S MAY HAVE WAVELENGTHS OF HUNDREDS OF KILOMETERS AND SPEEDS UP TO KILOMETERS PER HOUR 5NLESS THE RADAR MAKES APPROPRIATE REAL TIME CORRECTIONS TO THE TARGET COORDINATES TRACKING ACCURACY WILL BE SEVERELY IMPAIRED 4O ADDRESS THESE VARIOUS NEEDS IT IS ADVANTAGEOUS TO ADOPT CORRESPONDING DESCRIP TIONS OR MODELS EMPHASIZING DIFFERENT ASPECTS OF THE IONOSPHERE AND ITS INFLUENCE ON RADIOWAVE PROPAGATION AND HENCE (& RADAR PERFORMANCE )N MANY CASES OF PRACTICAL INTEREST IONOSPHERIC MODELS DEVELOPED ORIGINALLY FOR (& COMMUNICATIONS PURPOSES
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CAN BE ADAPTED TO THE RADAR CONTEXT WHERE THE MAIN DIFFERENCE IS THE GREATER SENSITIV ITY OF RADAR OBSERVATIONS TO DYNAMICAL PROCESSES 4HIS ARISES PRIMARILY BECAUSE OF THE EXTREMELY HIGH DYNAMIC RANGE REQUIRED TO ACCOMMODATE AND PRESERVE TARGET ECHOES IN THE PRESENCE OF STRONG CLUTTER AND EXTERNAL NOISE )ONOSPHERIC 3TRUCTURE 4HE BASIC PHYSICS OF IONIZATION AND RECOMBINATION PRO CESSES LEADS TO A NATURAL DIVISION OF THE IONOSPHERE INTO A NUMBER OF REGIONS $ 2EGION 4HIS REGION OCCUPIES THE LOWEST ALTITUDES CONSIDERED )T EXTENDS FROM TO KM WITH ELECTRON DENSITY INCREASING RAPIDLY WITH ALTITUDE IN THE DAYTIME )TS PROPERTIES REFLECT THE BALANCE BETWEEN FREE ELECTRON PRODUCTION BY THE INCIDENT SOLAR RADIATION FLUX AND FREE ELECTRON LOSS VIA VARIOUS ELECTRON ION AND ELECTRON NEUTRAL RECOMBINATION PROCESSES !CCORDINGLY THE MAXIMUM IONIZATION IN THE $ REGION OCCURS NEAR THE SUBnSOLAR POINT AND WILL BE GREATEST DURING PERIODS OF HIGHEST SOLAR ACTIVITY SUNSPOT MAXIMUM THOUGH IT DOES NOT ACHIEVE DENSITIES SUFFICIENT TO REFLECT OR EVEN SIGNIFICANTLY REFRACT (& RADIO WAVES 4HE KEY ROLE OF THE $ REGION IN (& RADIOWAVE PROPAGATION IS SIGNAL ATTENUATION VIA ELECTRON NEUTRAL COLLISIONS THAT ARE FREQUENT AT THESE MODERATE ALTITUDES WHERE THE NEUTRAL SPECIES DENSITY IS STILL RELATIVELY HIGH )T IS NOT REPRESENTED EXPLICITLY IN SOME IONOSPHERIC MODELS WHERE ITS EFFECTS ARE ACCOUNTED FOR WITH AN EMPIRICALLY DERIVED PATH LOSS CALCULATION % 2EGION 4HIS IONIZATION REGION EXTENDS BETWEEN ABOUT AND KM IN ALTI TUDE WITH A MAXIMUM NEAR KM WHEN SUNLIT )N ADDITION THERE MAY BE ANOMALOUS IONIZATION REFERRED TO AS SPORADIC % 4HIS LATTER IONIZATION LAYER IS TYPICALLY ONLY A FEW KILOMETERS THICK AND USUALLY SHORT LIVED OFTEN LASTING LESS THAN AN HOUR IT MAY BE EITHER SMOOTH OR PATCHY IS SEASONALLY AND DIURNALLY VARIABLE WEAKLY CORRELATED WITH SOLAR ACTIVITY SHOWING A TENDENCY TO FAVOR LOW SUNSPOT NUMBERS AND HAS MARKED VARIATION WITH LATITUDE &ROM THE PROPAGATION PERSPECTIVE SPORADIC % HOLDS A SPECIAL PLACE AS THE LAYER PROVIDING THE MOST STABLE PROPAGATION OVER COHERENT INTEGRATION TIMES TYPICAL OF SKYWAVE RADAR "ECAUSE IT IS ONLY ^ KM ABOVE THE %ARTHS SURFACE THE MAXIMUM RANGE THAT CAN BE REACHED VIA ONE HOP % LAYER PROPAGATION IS ONLY ^ KM THOUGH NORMALLY THE LAYER IS NOT TOTALLY REFLECTING SO SOME ENERGY CONTINUES UPWARD TO THE & LAYER WHERE IT IS REFLECTED TO REACH THE %ARTHS SURFACE AT MUCH GREATER RANGES & 2EGION 4HIS IS THE HIGHEST ALTITUDE REGION OF INTEREST FOR SKYWAVE PROPAGATION AND IT IS ALSO THE REGION OF GREATEST ELECTRON DENSITY )N THE DAYLIGHT HOURS THE & REGION SOMETIMES MANIFESTS TWO COMPONENT LAYERS ESPECIALLY IN SUMMER 4HE &L REGION LIES BETWEEN AND KM AND LIKE THE % REGION IS DIRECTLY DEPENDENT UPON SOLAR RADIATION IT REACHES MAXIMUM INTENSITY ABOUT H AFTER LOCAL NOON 4HE & REGION IS VARIABLE IN BOTH TIME AND GEOGRAPHICAL LOCATION 4HE ALTITUDE OF THE & REGION PEAK LIES TYPICALLY BETWEEN AND KM AT MIDDLE LATITUDES 4HE & REGION IONIZATION SHOWS MARKED DAY TO DAY VARIATIONS AND IN GENERAL IS NOT THE REGULAR SUN FOLLOWER THAT THE % AND & REGIONS ARE 4HE SIMPLE PHYSICAL PICTURE OF THE IONOSPHERE AS CONSISTING OF SEVERAL MORE OR LESS CONCENTRIC LAYERS MUST BE MODIFIED SUBSTANTIALLY AT BOTH LOW AND HIGH LATITUDES TO TAKE INTO ACCOUNT THE EFFECTS OF THE IMPRESSED ELECTRIC AND MAGNETIC FIELDS 4O BEGIN WITH THE DISPLACEMENT OF THE %ARTHS MAGNETIC AXIS FROM ITS ROTATIONAL AXIS MEANS THAT THE IONOSPHERE DOES NOT PRESERVE A MORE OR LESS CONSTANT FORM ENVELOPING A ROTATING EARTH .EAR THE MAGNETIC EQUATOR WHERE THE GEOMAGNETIC FIELD IS CLOSE TO HORIZON TAL ATMOSPHERIC TIDES AND ASSOCIATED WINDS DRIVE THE SO CALLED % REGION AND & REGION
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DYNAMOS RESULTING IN AN UPWARD DRIFT OF THE IONOSPHERIC PLASMA AND ITS SUBSEQUENT DESCENT ALONG THE GEOMAGNETIC FIELD LINES 4HE RESULTING ELECTRON DENSITY DEPLETION AT THE EQUATOR AND ROUGHLY SYMMETRIC ENHANCEMENTS IN THE VICINITY OF ^ n .3 LATITUDE IS KNOWN AS THE !PPLETON OR EQUATORIAL ANOMALY "ESIDES CAUSING ERRORS IN ESTIMATED TARGET RANGE AND BEARING THE TILTED IONOSPHERIC hREFLECTING SURFACEv NEAR THE EQUATOR CAN SUPPORT SCATTERING OF INCIDENT RADIOWAVES INTO LOW LOSS ELEVATED TRANS EQUATORIAL MODES CHORDAL MODES THAT RETURN STRONG CLUTTER FROM THE OPPOSITE HEMISPHERE OFTEN WITH HIGHLY UNSTABLE PHASE CHARACTERISTICS )N THE POLAR ZONES THE NEAR VERTICAL GEOMAGNETIC FIELD LINES PROVIDE A PATHWAY FOR CHARGED PARTICLES AND DISTURBANCES OF SOLAR AND MAGNETOSPHERIC ORIGIN TO REACH IONOSPHERIC HEIGHTS AND CONTRIBUTE TO IONIZATION PROCESSES AND PLASMA TRANSPORT 4HE BEST KNOWN PHENOMENA HERE ARE THE AURORAE WHICH ARE CONCENTRATED IN OVALS POLE WARD OF THE BOUNDARY WHERE THE %ARTHS GEOMAGNETIC FIELD LINES CHANGE FROM CLOSED CONNECTED TO THEIR IMAGES IN THE OPPOSITE HEMISPHERE TO OPEN THAT IS CONNECTED TO THE INTERPLANETARY MAGNETIC FIELD ! WIDE VARIETY OF PLASMA WAVES AND INSTABILITIES POPULATE THESE REGIONS PRODUCING IRREGULARITIES THAT ACHIEVE HIGH ELECTRON DENSITIES AND HENCE PROVIDE STRONG SOURCES OF SPREAD DOPPLER CLUTTER 4HEY HAVE BEEN KNOWN TO IMPACT SKYWAVE RADAR SYSTEMS SEVERELY )ONOSPHERIC 6ARIABILITY 7HILE ALL IONOSPHERIC PROPERTIES ARE TIME VARYING FROM AN /4(2 PERSPECTIVE IT IS USEFUL TO SEPARATE THE hFASTv PROCESSES OR hDYNAMICSv FROM THE hSLOWv OR hSTRUCTURALv VARIABILITY ! PHENOMENON IS TERMED DYNAMICAL RELATIVE TO A RADAR OBSERVATION PROCESS IF IT OCCURS ON A TIMESCALE COMMENSURATE WITH THE CORRE SPONDING PROCESS TIMESCALE SUCH AS I PULSEWAVEFORM REPETITION INTERVAL II COHERENT INTEGRATION DWELL TIME III SCAN REVISIT TIME OR IV MISSION TRACK LIFETIME $YNAMICAL PROCESSES IMPACT DIRECTLY ON HOW ONE SHOULD PROCESS THE RECEIVED SIGNALS OR PERFORM TRACKING 3LOW PROCESSES SUCH AS THE YEAR SOLAR CYCLE SEASONAL CHANGES AND THE DIURNAL CYCLE OF THE % AND & LAYERS CAN GENERALLY BE TREATED AS QUASI STATIONARY BACKGROUND PROCESSES THAT SET UP THE IONOSPHERIC STRUCTURE AT ANY GIVEN TIME WITHIN WHICH FAST PROCESSES MAY OCCUR !N EXCEPTION TO THIS CLASSIFICATION ARISES WITH THE DAWN AND DUSK TERMINATORS THAT IS THE DAY NIGHT BOUNDARIES SWEEPING AROUND THE %ARTH AT KMHR THEY PRODUCE ABRUPT CHANGES IN THE IONOSPHERE AND TRIGGER LARGE SCALE INSTABILITIES 3TRUCTURAL 6ARIABILITY 4HE DAY NIGHT CYCLE PRODUCES DRASTIC CHANGES IN THE ION IZATION DISTRIBUTION WITHIN THE IONOSPHERE !T NIGHT THE $ LAYER DISAPPEARS THE % AND & REGIONS EXPERIENCE A SUBSTANTIAL DECREASE IN IONIZATION AND THE EQUATORIAL AND POLAR REGIONS ARE MORE PRONE TO LARGE SCALE PERTURBATIONS 4HE EXTENT OF DIURNAL VARIATION CAN BE SEEN BY EXAMINING &IGURE WHICH SHOWS MEASURED ELECTRON DENSITY EXPRESSED IN TERMS OF PLASMA FREQUENCY AS DEFINED IN %Q VERSUS VIRTUAL HEIGHT AND TIME OF DAY AT A MID LATITUDE LOCATION 4YPICALLY THE DIURNAL VARIATION REQUIRES A RADAR TO VARY ITS OPERATING FREQUENCY BY MORE THAN AN OCTAVE IN FREQUENCY TO MAINTAIN HOUR SURVEILLANCE OVER A FIXED TARGET LOCATION
6IRTUAL HEIGHT IS THE REFLECTION HEIGHT COMPUTED FROM SIGNAL TIME DELAY BY ASSUMING THAT THE RADIOWAVE TRAVELS AT THE SPEED OF LIGHT AS IF IN FREE SPACE IN FACT THE RADIOWAVE GROUP VELOCITY IN THE PLASMA IS LOWER SO THE TRUE HEIGHT IS LESS &OR MOST PURPOSES IT IS MORE CONVENIENT TO DEAL WITH VIRTUAL HEIGHT BECAUSE THERE ARE TWO THEOREMS THAT DRAMATICALLY SIMPLIFY PRACTICAL CALCULATIONS -ARTYNS THEOREM SHOWS THAT COMPLICATED OBLIQUE SKYWAVE RAY PATHS VIA THE TRUE REFLECTION POINT CAN BE REPLACED TO GOOD APPROXIMATION WITH SIMPLE RECTILINEAR GEOMETRY VIA THE VIRTUAL REFLECTION POINT 4HE THEOREM OF "REIT AND 4UVE DEMONSTRATES THAT TO GOOD APPROXIMATION THE TIME OF FLIGHT IS UNCHANGED BY THIS SUBSTITUTION $AVIES PROVIDES A CLEAR EXPLANATION OF THESE USEFUL THEOREMS
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&)'52% $IURNAL VARIATION OF THE ELECTRON DENSITY PROFILE AS MEASURED BY THE PLASMA FREQUENCY PLOTTED FOR VARIOUS VIRTUAL HEIGHTS IN KM 4HE DATA WAS RECORDED BY A VERTICAL INCIDENCE SOUNDER AT LATITUDE 3 LONGITUDE % ON 3EPTEMBER 33.
7HAT IS MORE SURPRISING IS THE DAY TO DAY VARIABILITY EVEN AT MID LATITUDES WHICH IMPACTS SIGNIFICANTLY ON (& RADAR PERFORMANCE 4HE INABILITY TO PREDICT RELIABLY EVEN A DAY IN ADVANCE IS A SERIOUS CONSIDERATION IN RADAR DESIGN AND SCHEDULING !N ILLUSTRATION OF DAY TO DAY VARIABILITY IS PRESENTED IN &IGURE WHICH OVER LAYS VERTICAL INCIDENCE SOUNDINGS RECORDED AT THE SAME TIME OF DAY FOR A MONTH
&)'52% #OMPARISON OF MEASURED VERTICAL INCIDENCE IONOGRAMS FOR A FIXED TIME OF DAY OVER A MONTH WITH A MODEL BASED PREDICTION OF THE MEDIAN DENOTED BY THE SMALL CIRCLES
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4HE TRACES PLOT THE VIRTUAL HEIGHT VERSUS RADIOWAVE FREQUENCY FOR THE ORDINARY RAY SEE SUBSECTION BELOW ON RADIOWAVE PROPAGATION 3OUNDINGS OF THIS TYPEIONOGRAMS MEASURE THE RETURN TRIP TIME DELAY FOR A SIGNAL TO TRAVEL UP TO THE HEIGHT AT WHICH THE ELECTRON DENSITY IS SUFFICIENT TO REFLECT IT THAT IS WHERE THE PLASMA FREQUENCY FP EQUALS THE INCIDENT RADIOWAVE FREQUENCY !LSO SHOWN IN &IGURE IS THE CORRESPONDING MONTHLY MEDIAN TAKEN FROM THE MODEL OF 4HOMASON ET AL #ONSIDER THE CRITICAL FREQUENCY THAT IS THE HIGHEST REFLECTED FREQUENCY CORRESPONDING TO THE IONOSPHERES PEAK ELECTRON DENSITY 4HE UPPER AND LOWER DECILES DEPART FROM THE MEDIAN BY TYPICALLY o /VER SUCH A RANGE OF FRE QUENCY TERMS IN THE RADAR EQUATION SUCH AS ANTENNA GAINS TARGET 2#3 AND SLANT RANGE MAY VARY SUBSTANTIALLY SO RADAR PERFORMANCE IS INEVITABLY STATISTICALLY DISTRIBUTED !LTHOUGH IT MAKES SENSE TO USE MEDIAN VALUES FOR MANY RADAR PERFORMANCE MODELING CALCULATIONS THE RADAR DESIGNER SHOULD ADOPT A CONSERVATIVE APPROACH AND ASSUME THE LOWEST CRITICAL FREQUENCY 0ERHAPS THE MOST INTRIGUING MAJOR CAUSE OF SYSTEMATIC VARIATION IS THE YEAR CYCLE OF SOLAR ACTIVITY 6ARIOUS CORRELATED PARAMETERS HAVE BEEN DEFINED TO MEASURE THIS ACTIVITY INCLUDING THE CM SOLAR FLUX SUNSPOT NUMBER AND VARIOUS MAGNETIC INDICES &IGURE SHOWS THE SMOOTHED AVERAGE SUNSPOT NUMBER PLOTTED FROM THE YEAR OF THE FIRST VALIDATED /4(2 DETECTIONS OF MILITARY TARGETS ACHIEVED BY THE -53)# RADAR AT .2, %NHANCED SOLAR ACTIVITY IMPACTS ON THE IONOSPHERE IN MANY WAYS BUT ITS MOST SIG NIFICANT ACTION FROM A RADAR PERSPECTIVE IS TO PRODUCE SUBSTANTIALLY HIGHER IONIZATION LEVELS THAT PERSIST AT USABLE LEVELS THROUGH THE NIGHT SO HIGHER RADAR FREQUENCIES CAN BE EMPLOYED AND THE MINIMUM ACHIEVABLE RANGE DECREASES )N ADDITION THE HEIGHT OF THE MAXIMUM ELECTRON DENSITY INCREASES SO ONE HOP PROPAGATION CAN REACH GREATER RANGES
&)'52% 4HE VARIATION OF THE MONTHLY MEDIAN SUNSPOT NUMBER SINCE THE YEAR OF THE FIRST OPERA TIONAL SKYWAVE RADAR DETECTIONS
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$AYTIME ABSORPTION INCREASES FOR A GIVEN FREQUENCY BECAUSE OF HIGHER $ LAYER DENSI TIES BUT THIS IS COMPENSATED BY ACCESS TO HIGHER OPERATING FREQUENCIES !N INCREASE IN THE NUMBER AND SEVERITY OF MAGNETIC STORMS AND SUDDEN IONOSPHERIC DISTURBANCES IS ANOTHER CONSEQUENCE OF HIGHER SOLAR ACTIVITY AS ARE INCREASED POST SUNSET PLASMA BUB BLE ACTIVITY AND ASSOCIATED SCINTILLATION IN EQUATORIAL REGIONS SOLAR FLARES AND CORONAL MASS EJECTIONS ALL OF WHICH DISRUPT STABLE PROPAGATION 3OLAR FLARES ARE GIANT EXPLOSIONS ON THE SUNS SURFACE GENERALLY OCCURRING NEAR SUNSPOTS WHICH EMIT IONIZING RADIATION THAT PENETRATES INTO THE $ REGION AND DRAMATICALLY INCREASES ABSORPTION 4HE RESULTING SUDDEN IONOSPHERIC DISTURBANCE 3)$ OR SHORT WAVE FADE OUT CAN COMPLETELY INCA PACITATE A SKYWAVE RADAR FOR A PERIOD FROM MINUTES TO HOURS 0ERHAPS MORE IMPORTANTLY ALTHOUGH THE FLARE ITSELF IS NOT PREDICTABLE THE ASSOCIATED BURST OF PARTICLES WILL START TO ARRIVE A FEW HOURS LATER WITH MOST EJECTED MATERIAL REACHING %ARTH SEVERAL DAYS LATER SERIOUSLY DISRUPTING (& PROPAGATION 4HE CRITICAL IMPORTANCE OF SOLAR ACTIVITY WILL BE DEMONSTRATED IN 3ECTION IN THE CONTEXT OF RADAR PERFORMANCE PREDICTION )ONOSPHERIC $YNAMICS !S THE RADAR SIGNALS TRAVERSE THE IONOSPHERE MOTIONS OF THE PLASMA MEDIUM ALONG THE PROPAGATION PATH IMPRINT THEMSELVES ON THE SIGNALS IN WAYS THAT CAN DEGRADE OR OBLITERATE THE TARGET INFORMATION OF INTEREST 3KYWAVE RADARS CAN BE DESIGNED TO RECOGNIZE THE SIGNATURES OF THESE PHENOMENA ADJUSTING THE RADAR FREQUENCY CHOICE OF WAVEFORM AND PROCESSING TO MITIGATE THEIR EFFECTS WHERE NECESSARY 3OMETIMES THE IONOSPHERIC MOTIONS ACTUALLY HELP THE RADAR FOR EXAMPLE BY ENABLING IT TO DISCRIMI NATE BETWEEN NATURAL NOISE AND SOME FORMS OF DELIBERATE INTERFERENCE 4HUS IT IS VITALLY IMPORTANT TO UNDERSTAND NOT ONLY THE STRUCTURE OF THE IONOSPHERE AND THE OPPORTUNITIES IT PROVIDES FOR PROPAGATION BUT ALSO THE MOTIONS AND DISTURBANCES THAT INHABIT IT 4HE VARIETY OF WAVE TYPES AND IRREGULARITY OF PRODUCTION MECHANISMS IN THE ION OSPHERE IS ENORMOUS AND INCLUDES NOT ONLY THOSE ARISING NATURALLY BUT ALSO MANY INDUCED PHENOMENA SUCH AS THOSE RESULTING FROM GROUND BASED IONOSPHERIC 2& HEAT ERS OR ROCKET INTERACTIONS WITH THE AMBIENT PLASMA !MONG THE MOST IMPORTANT FROM THE RADAR POINT OF VIEW ARE THE FOLLOWING u 4RANSIENT PLASMA STRUCTURES ASSOCIATED WITH IONIZED METEOR TRAILS AT ANY GIVEN LOCA TION METEORS HAVE A STRONG DIURNAL VARIATION AND DIRECTIONALITY 4HEY ARE EVER PRES ENT AND CONSTITUTE A MAJOR SOURCE OF CLUTTER FOR (& RADARS u ,ARGE AND MEDIUM SCALE ATMOSPHERIC GRAVITY WAVES !'7 PRODUCED BY ENERGETIC PHENOMENA IN THE LOWER ATMOSPHERE PROPAGATE UPWARD WITH INCREASING AMPLITUDE UNTIL NONLINEAR PROCESSES BEGIN TO DOMINATE RESULTING IN WAVE BREAKING ,ARGE !'7S MAY PERSIST FOR HOURS AND PROPAGATE OVER GLOBAL DISTANCES CAUSING SERIOUS DEVIATION OF INCIDENT RADIOWAVES 4HEY ARE SOMETIMES THE MAJOR CAUSE OF TRACKING ERRORS u -AGNETIC DISTURBANCES ORIGINATING WHERE THE SOLAR WIND IMPACTS ON THE MAGNETO SPHERE THEY PROPAGATE EARTHWARD AND CAUSE RESONANT OSCILLATIONS OF THE GEOMAGNETIC FIELD LINES PERMEATING THE IONOSPHERE 4HE FIELD LINES ARE hFROZEN INv TO THE IONO SPHERIC PLASMA AND HENCE THE IONOSPHERE VIBRATES LOCALLY AT FREQUENCIES TYPICALLY IN THE RANGE OF nn (Z IMPOSING A CORRESPONDING MODULATION ON ANY TRANSITING RADIOWAVES 3HIP ECHOES CAN BE OBSCURED BY THIS MODULATION u 4HE EQUATORIAL ELECTROJET PART OF THE GLOBAL SYSTEM OF FIELDS AND CURRENTS DRIVEN BY THE DYNAMO ACTION OF WINDS AND TIDES IS HOST TO SMALL SCALE FIELD ALIGNED IRREGULARI TIES WITH CHARACTERISTIC VELOCITY DISTRIBUTIONS 3OME SMALL SCALE PLASMA INSTABILITIES MAY ENDURE FOR A FRACTION OF A SECOND OTHERS FOR TENS OF SECONDS EVIDENT TO RADARS AS SPREAD DOPPLER CLUTTER THAT PREVENTS THE DETECTION OF SMALL TARGETS
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u %QUATORIAL PLASMA BUBBLES OFTEN APPEAR AFTER SUNSET AND CONVECT UPWARD THROUGH THE & REGION WHERE THEY CONTRIBUTE TO STRONG DIFFUSE DOPPLER SPREAD SCATTERING REFERRED TO AS SPREAD & $ETECTION OF ALL TARGETS IS DIFFICULT WHEN THIS EFFECT OCCURS u 4HE AURORAE ARE DYNAMIC STRUCTURES GOVERNED BY FIELDS AND PLASMA FLOWS IN THE MAG NETOSPHERE STRONG ELECTRIC FIELDS ALIGNED WITH THE MAGNETIC FIELD ACCELERATE ELECTRONS DOWN INTO THE IONOSPHERE WHERE THEY PRODUCE HIGHLY IONIZED FORMATIONS THAT REFLECT RADIO WAVES VERY EFFICIENTLY 4HE RESULTING DOPPLER SPREAD ECHOES ARE SO STRONG THEY CAN INCAPACITATE A RADAR THROUGH ITS SIDELOBES u 'EOMAGNETIC STORMS AND SUB STORMS RESULT FROM SOLAR FLARES AND CORONAL MASS EJEC TIONS !S MENTIONED EARLIER HARD 8 RAYS AND ULTRAVIOLET RADIATION RAISE $ LAYER ION IZATION DRAMATICALLY WITH CONSEQUENT INCREASES IN RADIOWAVE ABSORPTION 7ITHIN AN HOUR AND FOR A DAY OR SO AFTER FLARE GENERATED PARTICLE BURSTS START TO ARRIVE AND ARE CHANNELED DOWN THE MAGNETIC FIELD LINES AT HIGH LATITUDES CAUSING IONOSPHERIC HEAT ING AND ASSOCIATED DIFFUSION TO LOWER LATITUDES TOGETHER WITH A VARIETY OF MAGNETIC FIELD PERTURBATIONS (& PROPAGATION IS OFTEN SEVERELY DISRUPTED -ODELS AND 4HEIR 5SES +NOWLEDGE OF THE CONDITIONS TO BE EXPECTED FOR A PAR TICULAR RADAR DEPLOYMENT IS VITAL TO RADAR DESIGN AS WELL AS PROVIDING A GUIDE TO ECHO INTERPRETATION AND A MEANS TO SIMULATION AND PERFORMANCE PREDICTION 4HIS TYPE OF INFORMATION BASED ON DECADES OF IONOSPHERIC OBSERVATIONS AND THEORY IS CONVENIENTLY DISTILLED IN MODELS THAT ARE WIDELY AVAILABLE AND USED EXTENSIVELY "UT EVEN MORE IMPORTANTLY FROM THE OPERATIONAL PERSPECTIVE (& RADARS MUST MAINTAIN A REAL TIME IONOSPHERIC MODEL 24)- THAT IS INTIMATELY LINKED WITH THE RADAR SUBSYSTEMS SERVING TO GUIDE FREQUENCY SELECTION RADIATED POWER TASK SCHEDULING COORDINATE REGISTRATION CONVERTING FROM THE RADAR COORDINATES OF TIME DELAY AND ANGLE OF ARRIVAL TO GEOGRAPHI CAL COORDINATES IONOSPHERIC MODE STRUCTURE INTERPRETATION AND ASSOCIATION OF MUL TIPLE TRACKS FROM A SINGLE TARGET 5NLIKE THE CLIMATOLOGICAL MODELS 24)-S MUST BE UPDATED CONTINUOUSLY WITH INFORMATION FROM AN AUXILIARY NETWORK OF BEACONS /BLIQUE AND VERTICAL INCIDENCE SOUNDERS AND TRANSPONDERS HAVE BEEN DEPLOYED FOR THIS PURPOSE &OR INSTANCE THE */2. RADARS EXPLOIT APPROXIMATELY SOUNDERS AND RELATED FACILITIES DISTRIBUTED AROUND THE COAST OF !USTRALIA 2ADAR PERFORMANCE IN MOST OPERATIONAL ROLES IS GOVERNED BY THE FIDELITY OF THE ADOPTED 24)- )T IS IMPORTANT TO DIFFERENTIATE BETWEEN MODELS THAT DESCRIBE THE PHYSICAL OR PHYSICO CHEMICAL STATE OF THE IONOSPHERE AND MODELS THAT DESCRIBE RADIOWAVE PROPA GATION CHARACTERISTICS THOUGH THE LATTER ARE OFTEN DERIVED FROM THE FORMER BY APPLY ING RAY TRACING METHODS AND THE FORMER ARE PREDOMINANTLY DERIVED FROM RADIOWAVE PROPAGATION MEASUREMENTS SUCH AS POINT TO POINT LINK STATISTICS AND VERTICAL INCIDENCE SOUNDINGS "OTH CLASSES ARE OF GENERAL APPLICABILITY TO (& COMMUNICATIONS AND GEO PHYSICAL INVESTIGATIONS AS WELL AS SKYWAVE RADAR -ODELS OF THE )ONOSPHERIC -EDIUM -ODELS OF THE IONOSPHERE FALL INTO TWO CATEGORIES u #LIMATOLOGICAL MODELS BASED ON SOUNDER ROCKET AND SATELLITE MEASUREMENTS "EING DERIVED FROM STATISTICS THEY PROVIDE NO EXPLICIT INFORMATION ON REAL TIME h@WEATHERv THAT IS IRREGULARITIES WAVES AND OTHER DYNAMIC PROCESSES THOUGH MEASURES OF VARI ABILITY MAY BE PROVIDED -ANY EARLY MODELS HAD THEIR GENESIS IN THE LARGE DATABASE OF RECORDED IONOSPHERIC SOUNDINGS MADE DURING THE )NTERNATIONAL 'EOPHYSICAL 9EAR OF n AND THE )NTERNATIONAL 9EAR OF THE 1UIET 3UN OF n 4HESE MODELS
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WHICH FOCUSED ON THE SPATIAL DISTRIBUTION OF ELECTRON DENSITY WERE USED EXTENSIVELY IN EARLY (& RADAR PERFORMANCE ANALYSES AND INCLUDE )43! )43 2!$!2 # )/.#!0 AND !-"#/-n ,UCAS PROVIDES DETAILS OF THESE MODELS AND THEIR ORIGINS 3OME OF THE PREDICTION METHODS HAVE NOT BEEN WELL DOCUMENTED ALTHOUGH WIDELY DISTRIBUTED ALSO USERS FREQUENTLY hIMPROVEv UPON A MODEL AND PREDICTION METHOD TO SUIT THEIR SPECIFIC NEEDS !S AN EXAMPLE THE MODEL 2!$!2 # IS THE BASIC BUILDING BLOCK OF 4HOMASON ET AL IN .2, 2EPORT HOWEVER THEY ADDED A $ REGION A COLLISION FREQUENCY DISTRIBUTION AN %ARTHS MAGNETIC FIELD A TOPSIDE ELEC TRON DISTRIBUTION AN AURORAL ELECTRON DENSITY MODIFICATION AND OTHER FEATURES THAT MAKE THE MODEL MORE GENERALLY USEFUL 4HE IONOSPHERIC MODEL AS DESCRIBED IN .2, 2EPORT HAS BEEN USED FOR SOME OF THE EXAMPLES PRESENTED IN 3ECTION 4HE )NTERNATIONAL 2EFERENCE )ONOSPHERE )2) IS PERHAPS THE FOREMOST MODERN EXAM PLE PRESENTLY AVAILABLE AS VERSION )2) n /THER CLIMATOLOGICAL MODELS USED IN (& RADAR APPLICATIONS ARE 0)- 02)3- AND &!)- u 0HYSICS BASED OR FIRST PRINCIPLES MODELS SUCH AS 535 '!)- *0,53# '!)- 3!-) DEVELOPED BY (UBA AND *OYCE AND +HATTATOVS MODEL SOLVE THE PLASMA DYNAMICS AND COMPOSITION EQUATIONS GOVERNING EVOLUTION OF DENSITY VELOCITY AND TEMPERATURE FOR VARIOUS ION SPECIES ON A GLOBAL $ GRID SUBJECT TO THE %ARTHS MAG NETIC FIELD AND PREVAILING SOLAR INDICES 4HESE MODELS REQUIRED SEEDING WITH INITIAL CONDITIONS OFTEN A LIMITING CONSIDERATION &OR BOTH CLASSES IMPROVED ACCURACY OF FORECASTING IS ACHIEVED BY ASSIMILATING DATA FROM GROUND BASED SOUNDERS TOTAL ELECTRON CONTENT 4%# DERIVED FROM '03 56 AIRGLOW DATA AND IN SITU MEASUREMENTS OF ELECTRON DENSITY FROM SATELLITES AND OTHER SOURCES /FTEN THE ASSIMILATION IS PERFORMED WITHIN AN EXTENDED +ALMAN FILTER FRAME WORK SO ACCURACY ESTIMATES ARE A BYPRODUCT &URTHER SITE SPECIFIC APPLICATIONS MAY BENEFIT FROM ADAPTATION OF THE UNDERLYING MODEL PARAMETERS AND COEFFICIENTS 4HE COMPLEX STRUCTURE AND DYNAMICS OF THE IONOSPHERIC MEDIUM GOVERN (& SKY WAVE PROPAGATION PRIMARILY THROUGH THE SPACE TIME VARIATION OF THE FREE ELECTRON DENSITY DISTRIBUTION ! USEFUL SIMPLIFICATION IS TO REGARD THE LARGE SCALE IONOSPHERIC STRUCTURE AS DEFINING THE PROPAGATION GEOMETRY THROUGHOUT THE ILLUMINATION VOLUME WHEREAS THE DYNAMICAL PROCESSES IMPOSE THEIR RESPECTIVE MODULATIONS ON THE TRANSIT ING SIGNALS #OMPUTATIONAL !SPECTS AND 2AY TRACING &OR MANY /4(2 PURPOSES IT SUFFICES TO EMPLOY A RAY THEORETIC REPRESENTATION OF THE RADIOWAVE FIELD 2AY TRACING TECHNIQUES FALL INTO TWO CATEGORIES ANALYTIC AND NUMERICAL !NALYTIC METHODS ARE FAST BUT RELY ON FIT TING PARAMETRIC MODELS TO THE ELECTRON DENSITY PROFILES AND ARE HENCE OF LIMITED USE FOR OPERATIONAL APPLICATIONS WHERE ACCURACY IS CRITICAL 4HEY ARE ALSO LIMITED BY THEIR INABILITY TO HANDLE MAGNETOIONIC EFFECTS ON PROPAGATION .EVERTHELESS THEY PROVIDE CLOSED FORM EXPRESSIONS FOR GROUP RANGE PHASE PATH GROUND RANGE AND OTHER PARAMETERS AND THERE FORE CAN BE VERY USEFUL FOR COMPUTATIONALLY INTENSIVE STUDIES SUCH AS SYSTEM OPTIMIZA TION 4HE MULTI QUASI PARABOLIC -10 MODEL OF (ILL BASED ON #ROFTS 10 TECHNIQUE IS WIDELY USED WHILE QUASI CUBIC MODELS HAVE BEEN PROPOSED BY .EWTON ET AL .UMERICAL RAY TRACING CODES ARE VERSATILE AND ABLE TO ACCOMMODATE ALMOST ARBI TRARY IONOSPHERIC STRUCTURE AT THE EXPENSE OF COMPUTATIONAL BURDEN /F THE MANY NUMERICAL RAY TRACING CODES DEVELOPED OVER THE YEARS THE IMPLEMENTATION BY *ONES AND 3TEPHENSON BASED ON INTEGRATION OF THE FIRST ORDER (ASELGROVE EQUATIONS REMAINS THE MOST WIDELY USED #OLEMAN HAS DEVELOPED AN ALTERNATIVE IMPLEMENTATION
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-ODELS OF )ONOSPHERIC 2ADIOWAVE 0ROPAGATION &ROM THE (& SKYWAVE RADAR PER SPECTIVE INTEREST IS USUALLY CENTERED NOT ON THE IONOSPHERE PER SE BUT ON HOW IT DETER MINES RADIOWAVE PROPAGATION -ODELS SUCH AS 6/!#!0 AND !3!03 GENERATE PREDICTIONS OF POINT TO POINT CIRCUIT PARAMETERS INCLUDING MAXIMUM AND MINIMUM USABLE FREQUENCY ELEVATION ANGLE GROUP PATH MODE PROBABILITY PATH LOSS AND SIGNAL TO NOISE RATIO FOR USER SPECIFIED TERMINAL CHARACTERISTICS ! MORE GENERAL CAPABILITY IS AVAILABLE WITH 0ROPLAB !S THESE MODELS ARE BASED ON THEIR RESPECTIVE CLIMATOLOGICAL DATABASES THEY ARE OF NO USE FOR REAL TIME APPLICATIONS SUCH AS 24)- AND ARE INADEQUATE FOR SERIOUS RADAR DESIGN WHICH SHOULD BE BASED ON MEASUREMENTS TAKEN AT THE PROPOSED DEPLOYMENT SITE BUT THEY CAN BE USEFUL FOR ANSWERING CERTAIN QUESTIONS SUCH AS h#AN MY SIGNAL BE HEARD AT 8 AND IF SO AT WHAT 3.2 v &OR CALCULATIONS REQUIRING MODERATE ACCURACY GEOMETRICAL OPTICS OR VIRTUAL RAY TRACING BASED ON -ARTYNS 4HEOREM CAN BE APPLIED TO STORED SEMI EMPIRICAL ELECTRON DENSITY PROFILES OR BETTER STORED hSNAPSHOTSv OF THE IONOSPHERE GENERATED BY AN 24)- !LTERNATIVELY ANALYTIC RAY TRACING CAN BE PERFORMED ON ANALYTIC PROFILES FITTED TO 24)- DATABASES 4HE MOST ACCURATE PREDICTIONS COME FROM THE APPLICATION OF SOPHISTICATED RAY TRACING ROUTINES TO A DATABASE OF 24)- SNAPSHOTS 7HEN A RADIOWAVE PROPAGA TION MODEL IS COMBINED WITH RADAR SYSTEM PARAMETERS TARGET SCATTERING CHARACTERISTICS AND (& NOISE DISTRIBUTIONS THE RADAR EQUATION %Q CAN BE SOLVED TO PREDICT THE RADARS PERFORMANCE AS TREATED IN 3ECTION 4HIS IS THE BASIC APPROACH EMPLOYED WITHIN 2!$!2 # FOR INSTANCE &ROM THE OPERATIONAL (& RADAR VIEWPOINT USE OF THESE PROPAGATION MODELS IS LIMITED TO STATISTICAL STUDIES OF RADAR PERFORMANCE NOT REAL TIME RADAR SUPPORT APPLICATIONS SUCH AS COORDINATE REGISTRATION BECAUSE OF THE POOR FIDELITY OF THE ASSUMED ELECTRON DENSITY DISTRIBUTIONS AND THE SHORTCOMINGS OF GEOMETRIC RAY TRACING /THER -ODELS AND 0ROPAGATION )SSUES 3TUDIES OF (& RADAR PERFORMANCE AT LOW LATITUDES HAVE SHOWN THAT IT IS OFTEN NECESSARY TO INCORPORATE MODELS OF DYNAMICAL PROCESSES EITHER BECAUSE THEY MANIFEST THEMSELVES DIRECTLY IN THE DOPPLER STRUCTURE OF RADAR ECHOES OR BECAUSE THEY ARE INDICATORS OF OTHER PHENOMENA THAT DO 5SEFUL MODELS IN THIS CATEGORY INCLUDE (7- WHICH DESCRIBES THE STRUCTURE OF THE ZONAL AND MERIDIONAL NEUTRAL WINDS THROUGHOUT THE IONOSPHERE AND 7"-/$ WHICH DESCRIBES SCINTILLATION ARISING FROM SMALL SCALE IRREGULARITIES SUCH AS THOSE ASSOCIATED WITH SPREAD & IN THE POST SUNSET IONOSPHERE 4HESE MODELS FIND IMPORTANT APPLICATIONS TO THE ANALYSIS AND INTERPRETATION OF DOPPLER SPREAD CLUTTER ! NUMBER OF PHENOMENA HAVE BEEN IGNORED IN THE PRECEDING DISCUSSION THOUGH THEIR EFFECTS CAN BE OBSERVED IN SOME SKYWAVE RADAR SYSTEMS 4HEY INCLUDE I A VARIETY OF NONLINEAR PROCESSES THAT CAN OCCUR DURING IONOSPHERIC PROPAGATION II DELAYED ECHOES FOCUSING AT THE ANTIPODE AND III ROUND THE WORLD PROPAGATION 4HE MOST SIGNIFICANT PRACTICAL EXPLOITATION OF SUCH PHENOMENA CAN BE FOUND IN EXPERIMENTS DIRECTED AT IONOSPHERIC MODIFICATION
Óä°xÊ 76 ", -Ê",ÊÊ, , 4HE FACTORS THAT GOVERN THE CHOICE OF WAVEFORM IN (& RADAR SYSTEMS CAN BE GROUPED INTO TWO CLASSES &IRST THERE ARE THE CONSIDERATIONS COMMON TO MICROWAVE RADAR THAT IS RANGE AND DOPPLER RESOLUTION AS DESCRIBED BY THE AMBIGUITY FUNCTION AND OPTIMIZED
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FOR TARGET DETECTION AND ESTIMATION REALIZABILITY IN HARDWARE SUSCEPTIBILITY TO INTERFER ENCE EFFICIENCY AND THE ELECTRICAL PROPERTIES OF THE SCATTERERS OF INTEREST )N ADDITION u (& RADAR WAVEFORMS MUST FIT WITHIN AVAILABLE CLEAR CHANNELS IN THE (& FREQUENCY BAND COMPLYING WITH STRINGENT CONSTRAINTS ON LEAKAGE INTO CHANNELS OCCUPIED BY OTHER USERS u 4HEY MUST BE COMPATIBLE WITH THE FACT THAT THE RADAR IS OPERATING IN A hWAVEGUIDE v NAMELY THE VOLUME BETWEEN THE %ARTHS SURFACE AND THE IONOSPHERE WITH UNIQUE POSSIBILITIES FOR MULTIPLE PROPAGATION PATHS INCLUDING ROUND THE WORLD PROPAGATION SIGNIFICANTLY MODIFYING THE EFFECTIVE AMBIGUITY FUNCTION u 4HEY MUST BE ABLE TO ACHIEVE THE DESIRED MEASUREMENT CAPABILITY IN THE PRESENCE OF EXTREMELY STRONG GROUND CLUTTER u 4HEY MUST BE DESIGNED SO AS TO MINIMIZE DISTORTION OR CORRUPTION BY THE IONOSPHERIC MEDIUM OR AT LEAST ENABLE SUCH DISTORTION TO BE ESTIMATED AND MITIGATED BY SIGNAL PROCESSING AFTER RECEPTION u 4HEY MUST HEED THE CONSTRAINTS ON PEAK VERSUS AVERAGE POWER IMPOSED BY THE (& TRANSMITTING EQUIPMENT AND ANTENNAS 4HE WAVEFORMS USED IN MOST OPERATIONAL (& SKYWAVE RADARS ARE VARIATIONS ON THE PERIODIC LINEAR FREQUENCY MODULATED CONTINUOUS WAVE ,&- #7 SIGNAL /FTEN THERE IS SOME PROVISION FOR AMPLITUDE SHAPING NORMALLY AT THE COMMENCEMENT AND END OF EACH SWEEP 4HE *INDALEE RADAR WAS DESIGNED WITH THE FACILITY TO APPLY A NUM BER OF AMPLITUDE NOTCHES WITHIN THE SWEEP THEREBY ENABLING THE RADAR TO SWEEP AT ZERO AMPLITUDE ACROSS NARROW BAND USERS IN THE SAME FREQUENCY BAND WITHOUT CAUSING INTERFERENCE !NOTHER CLASS OF VARIATIONS INVOLVES DEPARTING FROM A LINEAR FREQUENCY MODULATION "Y VARYING THE FREQUENCY TIME CHARACTERISTIC OF THE WAVEFORM RANGE SIDE LOBES CAN BE REDUCED AND SPECTRAL LEAKAGE CAN BE CONTROLLED #ONTROLLING THE PHASE DISCONTINUITY FROM THE END OF ONE SWEEP TO THE BEGINNING OF THE NEXT PROVIDES ANOTHER DIMENSION IN WHICH THE WAVEFORM PROPERTIES CAN BE OPTIMIZED &URTHER GENERALIZATION OF THE &- #7 WAVEFORM IS POSSIBLE BY RELAXING THE CONDITION THAT THE WAVEFORM BE PERIODIC 4HIS IS A POWERFUL TOOL FOR CONTROLLING RANGE AMBIGUOUS ECHOES WHICH CAN BE SHIFTED ABOUT IN THE RANGE DOPPLER PLANE TO UNCOVER PREVIOUSLY OBSCURED TARGET ECHOES !ND PERHAPS MOST IMPORTANTLY IN THE CONGESTED (& SPECTRUM WHERE CLEAR CHANNELS OF ADEQUATE BANDWIDTH TO ACHIEVE THE DESIRED RESOLUTION MAY BE SCARCE &- #7 WAVE FORMS DEFINED OVER TWO OR MORE SEPARATE SUBBANDS ARE READILY SYNTHESIZED -OST EARLY (& SKYWAVE RADARS EMPLOYED PULSE WAVEFORMS IN PART BECAUSE THE TECH NOLOGY OF THE DAY DID NOT SUPPORT &- #7 WAVEFORMS WITH THE REQUIRED LEVEL OF SPEC TRAL PURITY FOR THIS DEMANDING APPLICATION BUT ALSO BECAUSE PULSE WAVEFORMS ENJOY SOME UNDENIABLE ADVANTAGES &IRST THEY CAN BE EMPLOYED FROM A SINGLE TRANSMIT RECEIVE SITE AVOIDING THE COST AND COMPLEXITY OF ACQUIRING SUITABLE LAND DUPLICATING MANY FACILITIES AND SYNCHRONIZING TWO WIDELY SEPARATED SITES 3ECOND THE ABILITY TO GATE THE ECHOES IN TIME MEANS THAT THE ONLY CLUTTER POWER THAT IMPACTS ON THE RANGE FOOTPRINT SPANNED BY A PULSE IS CLUTTER ORIGINATING IN THAT FOOTPRINT 4HIS RELAXES THE WAVEFORM GENERATOR DYNAMIC RANGE REQUIREMENTS SOMEWHAT ESPECIALLY WHEN PHENOMENA SUCH AS AURORAL CLUTTER MAY CAUSE PROBLEMS THOUGH TO ACHIEVE THE SAME PROBABILITY OF DETECTION PEAK POWER MUST INCREASE TO MAINTAIN EQUIVALENT AVERAGE POWER 4HIRD AS A CONSEQUENCE OF REDUCED DYNAMIC RANGE REQUIREMENTS AND ASSUMING FOR THE MOMENT THAT STRICT SPECTRAL EMISSION CONTROLS ARE NOT AN ISSUE MORE EFFICIENT AMPLIFIERS CAN BE USED AS DISCUSSED IN THE FOLLOWING SECTION &OURTH PULSE WAVEFORMS MAY BE LESS SUSCEPTIBLE TO SOME FORMS OF JAMMING
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"UT THERE ARE DISADVANTAGES &IRST EMISSION CONTROLS ARE ALMOST INVARIABLY A SERI OUS MATTER WHEN IT COMES TO OBTAINING A LICENSE TO RADIATE 3ECOND THERE ARE RADAR APPLICATIONS BEYOND BASIC TARGET DETECTION WHERE EXTREMELY HIGH SPECTRAL PURITY IS ESSENTIAL AS WITH DETECTION OF SMALL SHIPS AT LOW SPEEDS 4HIRD THE ANTENNA DESIGN MUST BE ABLE TO HANDLE HIGHER FIELD STRENGTHS WITHOUT ARCING AND SPARKING WHICH INTRODUCES NOISE &OURTH UNLIKE THE &- #7 CASE IT IS NOT GENERALLY FEASIBLE TO SYNTHESIZE SUITABLE PULSE WAVEFORMS FROM SEPARATE SUBBANDS OF THE (& SPECTRUM WHEN WIDE CLEAR CHANNELS ARE NOT AVAILABLE &IFTH THERE ARE FEWER OPTIONS FOR RADI ATING MULTIPLE WAVEFORMS SIMULTANEOUSLY FROM THE SAME TRANSMITTING FACILITY !ND SIXTH FOR HIGH POWER (& RADARS THE ADDITIONAL POWER DENSITY ASSOCIATED WITH PULSE WAVEFORMS IN THE IONOSPHERE MAY IN PRINCIPLE CAUSE SELF MODULATION FROM NON LINEAR EFFECTS
Óä°ÈÊ / Ê/, - // Ê-9-/ 4RANSMITTERS -OST OF THE RADAR DESIGNS AND MISSIONS REQUIRE TRANSMITTER AVER AGE POWER LEVELS BETWEEN K7 AND -7 !NTENNAS ARE GENERALLY ARRAYS OF RADIAT ING ELEMENTS AND THE COMMON PRACTICE WITH (& RADAR IS TO DRIVE EACH ELEMENT WITH A SEPARATE AMPLIFIER 4HIS APPROACH PERMITS BEAM STEERING AT A LOW POWER LEVEL IN THE AMPLIFIER CHAIN 4HE ACTIVE ELEMENT IN EACH FINAL TRANSMITTER STAGE CAN BE EITHER A TRA DITIONAL VACUUM TUBE OR A SOLID STATE DEVICE -OST OPERATIONAL (& RADARS EMPLOY SOLID STATE AMPLIFIERS BASED ON A HIERARCHY OF MODULES STARTING WITH ELEMENTAL AMPLI FIERS OF PERHAPS 7 AND COMBINING THESE PROGRESSIVELY VIA PASSIVE NETWORKS UNTIL THE FINAL OUTPUT POWER IS ATTAINED 2ELATIVE PHASE SHIFTS OR TIME DELAYS ARE INSERTED IN THE AMPLIFIER CHAIN DRIVING EACH ANTENNA ELEMENT TO STEER THE RESULTANT BEAM 4HIS ARCHITECTURE ENHANCES RELIABILITY AND PROVIDES GRACEFUL DEGRADATION IN THE EVENT OF MODULE FAILURE 3OLID STATE (& RADAR TRANSMITTERS OPERATE AT POWER EFFICIENCIES LOWER THAN THOSE BASED ON VACUUM TUBE AMPLIFIERS 6ACUUM TUBE AMPLIFIERS ARE ALSO MORE ROBUST AND HAVE BEEN USED SUCCESSFULLY IN A NUMBER OF (& SKYWAVE RADARS INCLUDING THE !.&03 4HE ADOPTION OF SOLID STATE AMPLIFIERS IN RADARS SUCH AS 2/4(2 AND *INDALEE */2. IS DRIVEN BY THE NEED TO ACCOMMODATE INSTANTANEOUS FREQUENCY SWITCHING OVER WIDE BANDWIDTHS WHILE MAINTAINING HIGH LINEARITY AND SPECTRAL PURITY 4HESE RADARS ROUTINELY INTERLEAVE DIFFERENT SURVEILLANCE TASKS WITH WIDELY SEPARATED CARRIER FREQUEN CIES AND -(Z FOR EXAMPLESWITCHING AS OFTEN AS EVERY ONE OR TWO SECONDS WHILE CONFORMING TO STRICT SPECTRAL EMISSION STANDARDS 3UCH INSTANTANEOUS FREQUENCY CHANGES WOULD PLACE UNACHIEVABLE SWITCHING DEMANDS ON THE HIGH LEVEL VACUUM TUBE RADIO FREQUENCY CIRCUITS -EETING POWER CONTROL AND AMPLITUDE SHAPING OF WAVEFORM REQUIREMENTS DICTATES LINEAR OPERATION OF AMPLIFIERS !PART FROM THE REQUIREMENT TO MEET EMISSION GUIDELINES LAID DOWN BY NATIONAL AND INTERNATIONAL SPECTRUM MANAGEMENT AUTHORITIES HIGH SPECTRAL PURITY IS ESSENTIAL BECAUSE SKYWAVE RADAR USES DOPPLER PROCESSING TO SEPARATE THE TARGETS FROM THE CLUT TER AND HENCE THE CLUTTER RETURNED ON THE PHASE AND AMPLITUDE NOISE SIDEBANDS RADI ATED BY THE TRANSMITTER MUST BE KEPT BELOW THE ECHO POWER OF DESIRED TARGETS 4HIS CAN IMPOSE A STRINGENT CONDITION ON THE EMITTED SIGNAL TO NOISE RATIO OF THE TRANSMIT TER AND HENCE ON THE SIGNAL TO NOISE RATIO OF THE WAVEFORM GENERATOR &OR EXAMPLE NOISE SPECTRAL DENSITY AT (Z FROM A CARRIER MAY NEED TO BE AS LOW AS n D"C IN ORDER TO DETECT SOME TARGETS OF INTEREST &OR DESIGNS EMPLOYING AN AMPLIFIER FOR EACH
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ANTENNA ELEMENT THE RADIATED PHASE NOISE WILL GENERALLY ADD NONCOHERENTLY AND THUS BE SUPPRESSED BY ^ D" RELATIVE TO BEAMFORMED NOISE POWER FOR A ELEMENT ARRAY "UT THAT IS NOT THE END OF THE MATTERTRANSMITTER PHASE NOISE WILL BE REFLECTED BY THE DISTANT %ARTH SURFACE AND INTEGRATED ACROSS THE RECEIVER PASSBAND RAISING THE PHASE NOISE CONTRIBUTIONS TO THE NOISE FLOOR BY A FACTOR THAT FOR AN &- #7 WAVEFORM IS ROUGHLY EQUAL TO THE RATIO OF THE WAVEFORM BANDWIDTH TO THE WAVEFORM REPETITION FREQUENCY 4HE LOWER LEVEL STAGES OF SIGNAL AMPLIFICATION CAN GENERALLY BE DESIGNED TO ADD ESSENTIALLY ZERO NOISE BUT MECHANICAL VIBRATION IN THE HIGH POWER AMPLIFIERS CAN ADD APPRECIABLE AMOUNTS SO CARE MUST BE EXERCISED IN THE AIR OR LIQUID COOLANT FLOW SYSTEM DESIGN )F THE RADAR IS TO PERFORM WIDE AREA SURVEILLANCE FREQUENT FREQUENCY CHANGES ARE REQUIRED IN ORDER TO COVER THE VARIOUS RANGE EXTENTS )N ADDITION RELATIVE PHASE OR TIME DELAY CHANGES ARE REQUIRED IN EACH AMPLIFIER CHAIN TO ACCOMPLISH AZIMUTHAL STEERING ! BROAD BANDWIDTH PERFORMANCE AND A TOLERANCE TO A VARIABLE VOLTAGE STANDING WAVE RATIO LOAD ARE THEREFORE ESSENTIAL FEATURES IN AN (& RADAR TRANSMITTER 4YPICALLY ONE MIGHT SPECIFY 6372 AT FULL POWER OVER AN OPERATING RANGE OF n -(Z SAY WITH AN ABILITY TO TOLERATE HIGHER 6372S AT FRACTIONAL POWER OUTPUTS 3INCE THE ANTENNA ELE MENTS WILL BE WIDEBAND HARMONIC FILTERS MAY BE REQUIRED &OR EXAMPLE ONE TRANSMIT TER AND HARMONIC FILTER COMBINATION MIGHT HAVE A TO -(Z PASSBAND AND A STOPBAND FOR -(Z AND HIGHER FREQUENCIES A SECOND COMBINATION MIGHT PASS UP TO -(Z AND REJECT -(Z AND HIGHER AND THE DESIGN WOULD CONTINUE IN THIS MANNER TO THE HIGHEST FREQUENCY OF OPERATION 3OME SKYWAVE RADAR DESIGNS CALL FOR UP TO SIX BANDS ! RELATED ISSUE IS THE OCCURRENCE OF MUTUAL COUPLING BETWEEN ANTENNA ELEMENTS IN THE TRANSMIT ARRAY %NERGY COUPLED BACK INTO AN AMPLIFIER FROM ITS NEIGHBORS CAN REACH LEVELS THAT RESULT IN INTERMODULATION DISTORTION AS WELL AS CAUSING LOAD RESONANCES THAT STRESS THE AMPLIFIER CHAIN !NTENNAS 4HE CHOICE OF ANTENNA CONFIGURATION IS INTIMATELY LINKED TO THE RADAR MISSION GENERALLY DEFINED IN TERMS OF TARGET TYPES RADAR COVERAGE AND COVERAGE RATE 4HE .AVAL 2ESEARCH ,ABORATORY MAGNETIC DRUM RECORDING EQUIPMENT -!$2% RADAR EMPLOYED A SINGLE ANTENNA DUPLEXED AND USED FOR BOTH TRANSMIT AND RECEIVE 4HIS M WIDE BY M HIGH APERTURE PROVIDED SUFFICIENT GAIN AND ANGULAR RESOLU TION FOR AIRCRAFT TRACKING IN THE UPPER PART OF THE (& BAND 4HE EXPERIMENTAL &RENCH /4( RADAR .OSTRADAMUSn LIKEWISE EMPLOYS A SINGLE ANTENNA ARRAY CONFIGURED AS THREE HORIZONTAL ARMS OF LENGTH M RADIATING FROM A CENTRAL CONTROL CENTER THOUGH ONLY A SUBSET OF ELEMENTS ARE USED TO TRANSMIT WHEREAS ALL OF THE ELEMENTS ARE USED FOR RECEPTION 3UCH TRULY MONOSTATIC DESIGNS HAVE THE SPECIAL ADVANTAGE THAT THE OUT BOUND PROPAGATION PATH TO A TARGET IS ALMOST IDENTICAL TO THE IN BOUND PATH -ONOSTATIC RADARS WITH SEPARATE TRANSMIT AND RECEIVE ANTENNAS EXPERIENCE DECORRELATION BETWEEN THE PATHS AS THE SEPARATION INCREASES AND DIFFERENT PARTS OF THE IONOSPHERE BECOME INVOLVED %ITHER FORM OF MONOSTATIC RADAR AVOIDS THE COSTS OF MULTIPLE SITES AND ASSO CIATED COMMUNICATIONS INFRASTRUCTURE AND THE CHALLENGE OF FINDING SUITABLE SITES WITH AN APPROPRIATE GEOGRAPHICAL RELATIONSHIP BUT THEY ARE CONSTRAINED IN WAVEFORM CHOICE ANDOR RADIATED POWER BY THE NEED TO AVOID SIMULTANEOUS TRANSMISSION AND RECEPTION AS WELL AS BEING POTENTIALLY SUSCEPTIBLE TO RANGE FOLDED CLUTTER )N PARTICULAR THE CLASS OF &- #7 WAVEFORMS HAS BEEN WIDELY ADOPTED DRIVEN MAINLY BY CONSTRAINTS ON SPEC TRAL EMISSIONS OUTSIDE THE NOMINAL RADAR BANDWIDTH &OR THESE REASONS CONFIGURATIONS EMPLOYING SEPARATE TRANSMIT AND RECEIVE ANTENNA SITES ARE EMPLOYED IN RADARS SUCH AS *INDALEE */2. AND 2/4(2 USUALLY IN A QUASI MONOSTATIC ARRANGEMENT WHERE THE
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INTERSITE SEPARATION IS ABOUT n NAUTICAL MILES MUCH LESS THAN THE RANGE TO THE TARGET ZONE BUT SUFFICIENT TO PREVENT SELF JAMMING WHEN USING CONTINUOUS WAVEFORMS AND TO SEPARATE THE TRANSMIT AND RECEIVE RANGE AMBIGUITY ZONES IN AZIMUTH 4RANSMIT RADIATING ELEMENT CHOICE IS DRIVEN PRIMARILY BY THE RANGE OF FREQUENCIES TO BE RADIATED AND THE WAVEFORM BANDWIDTH BUT IT MUST ALSO TAKE INTO ACCOUNT THE RANGE AND AZIMUTH COVERAGE REQUIRED THE ASSOCIATED COVERAGE RATE AND CONCERNS ABOUT CLUTTER ESPECIALLY SPREAD DOPPLER CLUTTER 4HE VERTICAL RADIATION PATTERN CON TROLS THESE ISSUES 4HE POWER HANDLING CAPABILITIES OF THE ANTENNA ELEMENTS ARE ALSO A CONSIDERATION ! LOWER BOUND ON THE TRANSMIT ARRAY APERTURE IS SET BY THE NEED TO ACHIEVE ADEQUATE DIRECTIVITY AND HENCE POWER DENSITY ON THE TARGET THE SENSITIVITY REQUIRED DEPENDS ON THE SIZE OF THE TARGETS OF INTEREST 4HE UPPER BOUND IS OFTEN SET BY THE REVISIT REQUIREMENTIN GENERAL THE RADAR WILL STEP OVER A WIDE ARC BUT IT MUST SAMPLE EACH REGION FREQUENTLY TO MAINTAIN TRACKS ON MANEUVERING TARGETS SO THE TRANSMIT BEAMWIDTH SHOULD NOT BE TOO NARROW 4HE NEED TO KEEP 6372 TO MODEST LEVELS IS USUALLY ADDRESSED BY HAVING TO ARRAYS ADDRESSING SUBBANDS OF ABOUT ONE OCTAVE OF FREQUENCY EACH 3OME OF THESE CONSIDERATIONS ARE INFLUENCED BY THE ADVANTAGES THAT ATTACH TO EMPLOY ING MULTIPLE SIMULTANEOUS RECEIVE BEAMS SO A BROAD BUT WELL SHAPED TRANSMIT BEAM THAT CAN BE FILLED BY PERHAPS TO NARROW RECEIVE BEAMS IS A POPULAR CHOICE )N THE LIMITING CASE THE TRANSMIT ARRAY MAY FLOODLIGHT THE ENTIRE SECTOR OF COVERAGE WHICH IS FILLED WITH RECEIVE BEAMS THAT STARE CONTINUOUSLY 4HE NONUNIFORMITY OF CLUTTER SOURCES CAN CAUSE SERIOUS PROBLEMS WITH ANY DESIGN THAT DOES NOT HAVE CONTROL OVER THE ARRAY PATTERN &URTHER (& ANTENNAS SELDOM ACHIEVE HIGH FRONT TO BACK RATIOS SO THE RISK OF SIGNAL MASKING BY BACKLOBE CLUTTER CANNOT BE IGNORED &OR LINEAR ARRAYS OFFSETTING THE TRANSMIT AND RECEIVE ARRAY BORESIGHTS IS A MODERATELY EFFECTIVE MEASURE THAT MUST BE TRADED OFF AGAINST THE CONCOMITANT REDUCTION IN MAIN BEAM OVERLAP ,INEAR ARRAYS OF VERTICALLY POLARIZED LOG PERIODIC ANTENNAS VERTICAL PLANAR ARRAYS OF HORIZONTAL DIPOLES STACKED 9AGI ANTENNAS ELEVATED RHOMBIC ELEMENTS LINEAR ARRAYS OF TILTED MONOPOLES AND A TWO DIMENSIONAL ARRAY OF BICONICAL ANTENNAS HAVE ALL BEEN USED IN SKYWAVE RADAR TRANSMIT SYSTEMS IN SOME CASES WITH BACKSCREENS TO IMPROVE THE OTHERWISE MEDIOCRE FRONT TO BACK RATIOS )N THE ELEVATION PLANE DESIRABLE RADIATION ANGLES RUN BETWEEN n AND n FOR COM MON VALUES OF RANGE AND REFLECTION HEIGHT 4HE VERTICAL BEAMWIDTH NEEDS TO BE SUF FICIENT TO ILLUMINATE THE REQUIRED RANGE DEPTH IN GENERAL THIS IS AUTOMATICALLY SATISFIED OWING TO THE COST AND COMPLEXITY OF AN ANTENNA ABLE TO FORM A BEAM NARROWER THAN THIS IN THE VERTICAL PLANE &OR MOST SCENARIOS ANY SENSITIVITY GAINED BY DIRECTIVITY IN ELEVATION DIRECTLY IMPROVES RADAR PERFORMANCE SINCE INSTANTANEOUS RANGE DEPTH IS GENERALLY LIMITED BY IONOSPHERIC EFFECTS 4HIS IS IN CONTRAST WITH AZIMUTH DIRECTIVITY FOR TRANSMITTING WHERE AN INCREASE IN DIRECTIVE GAIN IS ACCOMPANIED BY A DECREASE IN AREA COVERAGE &OR NOISE LIMITED DETECTION THIS CAN BE COMPENSATED BY A REDUCTION IN DWELL TIME BUT FOR CLUTTER LIMITED DETECTION THERE MAY BE A PENALTY FOR COVERAGE RATE 3OME RADARS USE HORIZONTAL TWO DIMENSIONAL ARRAYS WITH UP TO ^ RECEIVE CHANNELS TO ACHIEVE QUITE HIGH VERTICAL DIRECTIVITY ON BOTH TRANSMIT AND RECEIVE )N THE PAST OTHERS SUCH AS -!$2% AND SOME FORMER 3OVIET 5NION SKYWAVE RADARS EMPLOYED VERTICAL TWO DIMENSIONAL ARRAYS UP TO M HIGH AND M WIDE IN THE CASE OF THE 3OVIET RADARS !T LOW ELEVATION ANGLES THE ANTENNA PATTERN IS STRONGLY INFLUENCED BY THE ELECTRI CAL AND MAGNETIC PROPERTIES OF THE GROUND AROUND AND IN FRONT OF THE ARRAY 4O ACHIEVE
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GAIN AT LOW ANGLES IT IS STANDARD PRACTICE TO INSTALL A GROUND MESH SCREEN THIS HAS THE SECONDARY BENEFIT OF AVOIDING PATTERN DISTORTION DUE TO INHOMOGENEITIES IN THE SOIL &OR EXAMPLE THE *INDALEE TRANSMIT ARRAYS SIT ON ^ HECTARES ^ ACRES OF STEEL MESH EXTENDING ^ M IN FRONT OF THE ARRAYS .OTWITHSTANDING THE MERITS OF VERTICAL DIRECTIVITY MOST SKYWAVE RADARS DO NOT EMPLOY STEERABLE DIRECTIVITY IN ELEVATION BUT COVER ALL NECESSARY RADIATION ANGLES WITH ONE BROAD ELEVATION BEAM 4HIS CHOICE PERMITS THE ANTENNA TO HAVE A RELATIVELY SMALL VERTICAL DIMENSION AND HENCE REDUCED COST THOUGH DEMANDS ON ANTENNA RADIATION EFFICIENCY IMPOSE A LOWER LIMIT !NOTHER ISSUE IS THE CHOICE OF TRANSMIT POLARIZATION .EARLY ALL OPERATIONAL SKYWAVE RADARS RADIATE WITH VERTICAL POLARIZATION BASED ON THE EASE OF ACHIEVING GOOD VERTI CAL COVERAGE AT MODERATE COST BY MEANS OF THE WIDELY USED LOG PERIODIC BROADBAND ANTENNA 4HE LARGE CURTAIN ARRAYS OF THE FORMER 3OVIET RADARS USED HORIZONTAL DIPOLE ELEMENTS WHEREAS THE 53!& !.!03 USED INCLINED DIPOLES TO ADAPT TO GROUND CONDITIONS 4HE POTENTIAL BENEFITS OF FULL POLARIZATION CONTROL ON TRANSMIT HAVE BEEN ASSESSED AND A NUMBER OF EXPERIMENTAL STUDIES CARRIED OUT BUT NO OPERATIONAL SYSTEM HAS GONE DOWN THIS PATH 4HE ANTENNAS AND POWER AMPLIFIERS USED IN (& BROADCAST STATIONS HAVE MUCH IN COMMON WITH (& RADAR THAT IS TO MAINTAIN A SPECIFIED LEVEL OF ILLUMINATION OVER A DESIGNATED AREA 4O ACHIEVE THIS GOAL MANY MULTIBAND AND STEERABLE BROADCAST ANTEN NASn EMPLOY LARGE VERTICAL APERTURES !NTENNAS USED FOR (& RADAR HAVE AN ADDITIONAL SEVERE CONSTRAINT THE NEED TO MINIMIZE MECHANICAL MOTION DUE TO THE WIND !EOLIAN VIBRATION THAT WOULD CAUSE SIGNAL PHASE MODULATION THAT WOULD THEN BE IMPOSED ON THE TRANSMITTED SIGNALS THIS REQUIREMENT IS EASIER TO MEET WITH LOW ANTENNA HEIGHT DESIGNS !N UNDER EXPLOITED ADVANTAGE OF BROAD BEAMS IN ELEVATION IS THE ABILITY TO ILLUMINATE AN EXTENDED RANGE DEPTH WHEN CONDITIONS PERMIT PROVIDING CLUTTER MAPS OUTSIDE THE RANGE BAND OF IMMEDIATE INTEREST FOR TARGET DETECTION THESE CAN BE USED TO SCHEDULE SUBSEQUENT SURVEILLANCE TASKS
Óä°ÇÊ , ,Ê ,"--Ê- /" 4HE RADAR SCATTERING PROPERTIES OF TARGETS DETERMINE BOTH THEIR DETECTABILITY AND THE PROSPECTS FOR TARGET CLASSIFICATION THEREFORE MUCH EFFORT HAS GONE INTO ESTABLISHING PRECISELY HOW TO DESCRIBE THOSE PROPERTIES FOR A GIVEN RADAR CONTEXT )N THE (& SKYWAVE RADAR CASE THE INEVITABILITY OF &ARADAY ROTATION THAT OCCURS DURING IONOSPHERIC PROPA GATION HAS BEEN USED TO ARGUE THAT A FULLY POLARIMETRIC TREATMENT IS UNNECESSARY SO IT IS COMMON PRACTICE TO REPRESENT THE SCATTERING BEHAVIOR IN TERMS OF SCALAR RADAR CROSS SECTION 2#3 &ULLY POLARIMETRIC FORMULATIONS ARE RELEVANT WHEN MODELING COMPLEX SCATTERING PROCESSES AND FOR TARGET CLASSIFICATION STUDIES )N GENERAL AIRCRAFT AND SHIPS HAVE DIMENSIONS THAT PUT THEM WITHIN THE RESONANT SCATTERING REGIME THOUGH THE SMALLEST AIRCRAFT AND CRUISE MISSILES WILL LIE IN THE 2AYLEIGH SCATTERING REGIME FOR THE LOWER HALF OF THE (& BAND (ERE THE 2#3 DISPLAYS LIMITED ASPECT SENSITIVITY AND A STRONG DEPENDENCE ON THE TARGETS GROSS DIMENSIONS &OR AN AIRCRAFT THE SPAN OF THE WINGS THE FUSELAGE LENGTH THE TAIL AND ELEVATOR SPAN THE VERTICAL STABILIZER AND RUDDER HEIGHT AND THEIR RELATIVE LOCATIONS ARE THE MAIN FEATURES THAT INFLUENCE THE 2#3 4ARGET SHAPING ON A SCALE SIZE MUCH LESS THAN A WAVELENGTH WILL HAVE LITTLE EFFECT !CCURATE MEASUREMENTS OF RADAR SCATTERING AT (& FREQUENCIES IS CHALLENGING BUT FACILITIES FOR MAKING SCALE MODEL MEASUREMENTS ARE
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WIDELY AVAILABLE INCLUDING ANECHOIC CHAMBERS INDOOR COMPACT RANGES AND OUTDOOR TEST FIELDS &ULL SCALE EXPERIMENTAL MEASUREMENTS CAN BE MADE IN SOME CIRCUM STANCES BY MEANS OF CALIBRATED REFERENCE SCATTERERS OR TRANSPONDERS DEPLOYED IN THE TARGET ZONE AND MODULATED TO SEPARATE THEIR RETURNS FROM THE TARGET AND CLUTTER ECHOES &OR BODIES WITH HIGHLY CONDUCTIVE SURFACES THE SCATTERING CROSS SECTION CAN BE CALCU LATED QUITE ACCURATELY BY NUMERICAL METHODS SUCH AS THE METHOD OF MOMENTS CODE .%# !S A RULE OF THUMB THE (& 2#3 OF AIRCRAFT CAN USUALLY BE COMPUTED TO AN ACCURACY OF ABOUT OR D" WITH RESPECT TO MEASURED VALUES WITHOUT RESORTING TO HIGHLY SOPHISTICATED TECHNIQUES 7HEN PRECISE 2#3 INFORMATION IS NOT ESSENTIAL ROUGH BUT USEFUL 2#3 ESTIMATES CAN BE MADE BY EXAMINING THE SCATTERING BEHAVIOR OF A FEW hCANONICALv SHAPES &IGURE IS A FAMILY OF PLOTS GIVING 2#3 VERSUS RADAR FREQUENCY FOR AN OBLONG SHAPED CONDUCTING BODY 4HE STRAIGHT LINE MARKED n L DIPOLE GIVES THE 2#3 OF A RESONANT CONDUCTING HALF WAVELENGTH ROD WHERE THE ROD IS PARALLEL WITH THE ELECTRIC FIELD 4HIS GEOMETRY GIVES THE MAXIMUM 2#3 FOR THE ROD 4HE UPPER SCALE OF THE ABSCISSA GIVES THE ONE HALF WAVELENGTH DIMENSION OF THE FREQUENCY GIVEN ON THE LOWER SCALE 4HE CURVE MARKED n IS THE 2#3 OF THE OBLONG SHAPED CONDUCTING BODY OF M LENGTH AND M THICKNESS AGAIN THE TARGET LONG DIMENSION IS ALIGNED WITH THE ELECTRIC FIELD 4HE MAXIMUM 2#3 COINCIDES WITH THE NOMINAL HALF WAVELENGTH DIMENSION OR WITH THE FIRST RESONANCE
&)'52% 4HE FREQUENCY DEPENDENCE OF THE 2#3 FOR AN M LONG BY M DIAMETER PERFECTLY CONDUCTING CYLINDER PRESENTED FOR VARIOUS ILLUMINATION GEOMETRIES 4HE % VECTOR AND THE M DIMEN SION ARE IN THE SAME PLANE n NOSE ON n AND n BROADSIDE CURVES ARE SHOWN 4HE TOP DASHED CURVE IS FOR A RESONANT DIPOLE AT n 4HE SMALL SKETCHES AT THE FIRST SECOND AND THIRD RESONANCES SHOW THE 2#3 ANGULAR PATTERN NEAR THESE FREQUENCIES
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&)'52% 2#3 FREQUENCY DEPENDENCE OF A ROD MONOPOLE AND A HEMISPHERE ON A PERFECTLY CONDUCTING PLANE FOR VERTICAL INCIDENT AND SCATTERED POLARIZATION
4HE CURVES MARKED AND n GIVE THE 2#3 AS THE TARGET IS ROTATED TO THESE ANGLES IN THE PLANE THAT CONTAINS THE ELECTRIC VECTOR 4HE LITTLE SKETCHES GIVE AT THE LEFT THE BODY SHAPE AND THEN THE 2#3 PATTERNS AT NOMINAL WAVELENGTH WAVELENGTH AND WAVELENGTH IN ORDER TO HELP VISUALIZE HOW THE 2#3 WILL CHANGE AS THE ASPECT ANGLE IS VARIED &OR TARGETS OF OTHER LENGTHS WITH APPROXIMATELY THE SAME SHAPE FACTOR THE RESPONSE CAN BE DETERMINED BY SLIDING THE CURVE ALONG THE L LINE AND MAKING THE FIRST RESONANCE COINCIDE WITH THE LINE AT THE WAVELENGTH POINT !S HAS BEEN MEN TIONED &ARADAY ROTATION RESULTS IN VARYING INCIDENT POLARIZATION SO OVER TIME A TARGET WILL EXPERIENCE BOTH FAVORABLE AND MISMATCHED POLARIZATION WITH RESULTANT FADING OF THE SCATTERED SIGNAL /F COURSE ADDITIONAL FADING OF THE SCATTERED SIGNAL OCCURS DUE TO TIME VARYING POLARIZATION MISMATCH AT THE RECEIVING ANTENNA &IGURE GIVES THE VERTICAL POLARIZATION 2#3 OF A ROD AND A HEMISPHERE MOUNTED ON A PERFECTLY CONDUCTING SURFACE 7ITH THESE CANONICAL SHAPES AN ESTIMATE OF 2#3 CAN BE MADE FOR SURFACE CRAFT BY MATCHING , AND 2 TO THE PRINCIPLE DIMENSIONS TO THE TARGET &OR SMALL VESSELS THE MAST HEIGHT WILL BE OF MOST IMPORTANCE &OR SURFACE TARGETS WHERE THE MAXIMUM 2#3 OCCURS WITH VERTICAL POLARIZATION A D" SKYWAVE 2#3 ENHANCEMENT RESULTS FROM THE IMAGE FIELD 4O ILLUSTRATE THE 2#3 BEHAVIOR OF A TYPICAL AIRCRAFT IN MORE DETAIL &IGURE SHOWS THE 2#3 OF THE & FIGHTER AS COMPUTED HERE BY .%# APPLIED TO A WIRE GRID REPRESENTATION OF THE AIRCRAFT DERIVED FROM A PLASTIC KIT MODEL 4HE 2#3 SHOWN IS FOR MONOSTATIC BACKSCATTER GEOMETRY AND HORIZONTAL COPOLAR (( POLARIZATION #ALCULATIONS ARE PRESENTED FOR FREQUENCIES OF AND -(Z !LTHOUGH THE FIDELITY OF SUCH 2#3 CALCULATIONS OF CONVENTIONAL PLATFORMS HAS BEEN CONFIRMED ON MANY OCCASIONS IT IS NOT CLEAR THAT STANDARD COMPUTATIONAL METHODS ARE APPLICABLE TO THE PROBLEM OF ESTIMATING THE 2#3 OF AIRCRAFT TARGETS THAT CANNOT BE MODELED AS SIMPLE PERFECT ELECTRICAL CONDUCTORS 0%# OR TO SMALL hGO FASTv BOATS IN DYNAMIC INTERACTION WITH THE SEA SURFACE
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&)'52% -ONOSTATIC 2#3 OF THE & FIGHTER AIRCRAFT AT AND -(Z COMPUTED FOR (( POLAR IZATION AT A LOOK DOWN ANGLE OF
Óä°nÊ 1// ,\Ê " -Ê," ÊÊ / Ê 6," / %ARTH 3URFACE #LUTTER 4HE GEOMETRY OF SKYWAVE ILLUMINATION ENSURES THAT TAR GET ECHOES WILL BE IMMERSED IN RETURNS FROM THE %ARTHS SURFACE THAT IS CLUTTER )N ORDER TO DETECT THE TARGETS THE PROPERTIES OF THIS CLUTTER NEED TO BE UNDERSTOOD SO THAT THE CHOICE OF FREQUENCY WAVEFORM AND SIGNAL PROCESSING ARE COMPATIBLE WITH THE NEED TO SEPARATE TARGET ECHOES FROM CLUTTER AND ALSO SO THAT THE REQUIRED DYNAMIC RANGE OF THE RADAR CAN BE CORRECTLY SPECIFIED %ARLY (& RADAR EXPERIMENTS ESTABLISHED THAT THE STRONG GROUND CLUTTER OBSERVED VIA SKYWAVE PROVIDED AN INDICATION OF THE PHYSICAL CHARACTERISTICS OF THE ILLUMINATED TERRESTRIAL SURFACE %XTENSIVE OBSERVATIONS MADE AT THE .AVAL 2ESEARCH ,ABORATORY VIEWING ALTERNATELY !TLANTIC /CEAN AREAS AND CENTRAL 5NITED 3TATES AREAS INDICATED THAT AVERAGED OVER A WIDE AREA SEA CLUTTER POWER LEVELS WERE USUALLY ABOUT AN ORDER OF MAGNITUDE HIGHER THAN THOSE FROM AN AREA OF SIMILAR SIZE IN THE CENTRAL 5NITED 3TATES ,ATER OBSERVERS NOTED EXTREMELY LOW BACKSCATTER FROM ICE COVERED AREAS OF 'REENLAND 4HESE RESULTS ARE CONSISTENT WITH PREDICTED SCATTERING COEFFICIENT VARIATIONS BASED ON THE TOPOGRAPHY AND THE ELECTRICAL PROPERTIES OF THE SURFACES 3UBSEQUENTLY OBSERVA TIONS OVER THE )NDIAN /CEAN WITH THE *INDALEE RADAR EMPLOYING CAREFULLY CALIBRATED TRANSPONDERS REVEALED ^ D" VARIATIONS IN THE OCEAN SCATTERING COEFFICIENT DEPEND ING ON SEA STATE ,AND #LUTTER -APPING OF SKYWAVE BACKSCATTER FROM TERRESTRIAL LAND SURFACES IS OF INTEREST FOR TWO MAIN REASONS &IRST A LOCALIZED AREA OF ENHANCED BACKSCATTER SUCH AS A CITY IN THE CENTRAL PLAINS OF THE 53 OR A MOUNTAIN RISING FROM A TROPICAL
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RAINFOREST PROVIDES A GEOGRAPHICAL REFERENCE THAT CAN ASSIST WITH THE EVER PRESENT PROBLEM OF COORDINATE REGISTRATION UNCERTAINTIES IN THE RAY PATH TRAVERSED BY THE RADAR SIGNALS CAN LEAD TO TARGET POSITIONING ERRORS OF OVER KM UNDER SOME CIRCUM STANCES 3ECOND SOME REGIONS EXPERIENCE STRONG SEASONAL VARIATIONS IN VEGETATION AND SOIL MOISTURE CONTENT WHICH MAY BE REFLECTED IN MEASURABLE CHANGES TO SCATTERING BEHAVIOR )T IS ALSO IMPORTANT TO UNDERSTAND THE EFFECT OF THE GROUND SCATTERING COEF FICIENT AND THE TOPOGRAPHY WHEN INTERPRETING ECHOES FROM TARGETS ABOVE THE GROUND 3EA #LUTTER )N CONTRAST WITH THE ABRUPT CHANGES IN SCATTERING BEHAVIOR THAT OCCUR AT COASTLINES OR OVER COMPLEX TERRAIN THE MAGNITUDE OF THE RADAR ECHO FROM THE OPEN OCEAN THAT IS THE SCATTERING COEFFICIENT R n TENDS TO VARY SLOWLY WITH RANGE AND AZIMUTH AS A CONSEQUENCE OF THE SCALE LENGTHS OF TYPICAL OCEANIC METEOROLOGICAL SYSTEMS AND THE RESPONSE TIME OF THE OCEAN SURFACE TO VARYING WIND STRESS -OREOVER MUCH OF THE TIME TO A REASONABLE APPROXIMATION THE ECHO POWER IS PROPORTIONAL TO THE RESOLUTION CELL AREA AND CAN BE USED AS AN ABSOLUTE AMPLITUDE REFERENCE WHEN CARE IS EXERCISED 4HE REASON FOR THIS IS EXPLAINED LATER IN THE DISCUSSION OF RADAR OCEANOGRAPHY /F FAR GREATER INTEREST THAN THE AVERAGE MAGNITUDE OF THE SEA ECHO IS THE WEALTH OF INFORMATION EMBEDDED IN ITS DOPPLER SPECTRUM 4HE WAVES ON THE SEA SURFACE INTRODUCE A COMPLEX MODULATION ON THE REFLECTED RADAR SIGNAL WHICH IS MANIFESTED IN THE SIGNALS DOPPLER SPECTRUM %STIMATION AND INTERPRETATION OF THIS MODULATION YIELDS INFORMATION ON THE TIME VARYING SEA SURFACE GEOMETRY WITH MAJOR IMPLICATIONS FOR SHIP DETECTION AS DISCUSSED BELOW )T TRANSPIRES THAT A RELATIVELY SIMPLE MODEL ACCOUNTS FOR THE OBSERVED PROPERTIES OF SEA CLUTTER WITH REMARKABLE FIDELITY PROVIDED THE SEA IS NOT TOO ROUGH 4HIS MODEL IS BASED ON TWO ASSUMPTIONS 4HE SEA SURFACE CAN BE REPRESENTED TO A GOOD APPROXIMATION AS A SUPERPOSITION OR F SPECTRUM 3J OF SURFACE GRAVITY WAVES SATISFYING THE DISPERSION RELATION
V GJ TANHJ D
WHERE V IS THE WAVE ANGULAR FREQUENCY G IS THE ACCELERATION DUE TO GRAVITY J IS THE WAVE NUMBER OF THE WATER WAVE AND D IS THE WATER DEPTH &OR DEEP WATER THIS REDUCES TO V GJ
FROM WHICH THE WATER WAVE PHASE VELOCITY CAN BE WRITTEN
Vx
V § G, ¶ J ¨© P ·¸
WHERE , IS THE WAVELENGTH OF THE WATER WAVE )N TERMS OF (& WAVELENGTHS THE SEA SURFACE CAN BE REGARDED AS ONLY SLIGHTLY ROUGH THEREFORE ADMITTING AN APPROXIMATE SOLUTION FOR THE SCATTERED FIELD IN THE FORM OF A PERTURBATION SERIES EXPANSION IN THE PARAMETER KA WHERE K IS THE RADIO WAVENUM BER AND A IS A REPRESENTATIVE OCEAN WAVE AMPLITUDE 4HIS APPROACH FORMULATED BY 2ICE FOR THE CASE OF A STATIC SURFACE AND EXTENDED BY "ARRICK TO THE CASE WHERE THE SURFACE IS EVOLVING ACCORDING TO THE DISPERSION RELATION %Q LEADS TO AN EQUATION FOR THE DOPPLER SPECTRUM OF THE REFLECTED RADIOWAVES
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F
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£ 3 MKSCAT KINC C V V "
M o
P K
F
F
F
F F C V M GJ M GJ DJ DJ
F
£ ¯¯ 'MJ MJ 3MJ 3MJ M M o
F F F WHERE KINC AND KSCAT ARE THE INCIDENT AND SCATTERED RADIO WAVE VECTORS K \ KINC \ F V IS THE DOPPLER FREQUENCY 3J IS THE SEA DIRECTIONAL WAVE SPECTRUM C IS THE F F $IRAC DELTA FUNCTION AND THE "RAGG FREQUENCY V " IS GIVEN BY V " G K K 4HE F F KERNEL ' J J IS DISCUSSED BELOW %Q REVEALS THAT THE "ARRICK 2ICE SOLU TION HAS A SIMPLE INTERPRETATION IN TERMS OF SPATIAL RESONANCE OR "RAGG SCATTERING !LTHOUGH THE DISORGANIZED LOOKING OCEAN SURFACE IS REPRESENTED AS THE &OURIER SUM OF AN INFINITE NUMBER OF SINUSOIDAL WAVE TRAINS EACH WITH ITS CHARACTERISTIC WAVE NUMBER AND DIRECTION THE PRINCIPAL hFIRST ORDERv CONTRIBUTIONS TO THE SCATTERED FIELD ARISE FROM ONLY TWO OCEAN WAVE TRAINS NAMELY THOSE WHOSE WAVE VECTORS SATISFY THE RELATION SCAT
F F F J o o KSCAT KINC
INC
&OR THE SIMPLE CASE OF BACKSCATTER AT GRAZING INCIDENCE THE GEOMETRY FOR MONO F F STATIC SURFACE WAVE RADAR KSCAT KINC SO THESE RESONANT OCEAN WAVES HAVE A WAVE LENGTH EQUAL TO ONE HALF OF THE RADAR WAVELENGTH WITH ONE SOLUTION CORRESPONDING TO A WAVE DIRECTLY APPROACHING THE RADAR AND THE OTHER RECEDING FROM IT 4HE CORRE SPONDING DOPPLER SHIFTS ARE THOSE ASSOCIATED WITH THE PHASE VELOCITY OF THE RESONANT WAVES THAT IS
FD o
G GF o y o F -(Z PK PC
WHERE THE DOPPLER SHIFT FD IS IN (Z G IS THE GRAVITATIONAL ACCELERATION MS F IS THE RADAR FREQUENCY AND C THE VELOCITY OF LIGHT 7ITH THIS INSIGHT THE SECOND ORDER TERM IN %Q CAN BE INTERPRETED AS hDOUBLE BOUNCEv PROCESSES INVOLVING "RAGG SCATTER FROM FIRST ONE AND THEN ANOTHER WAVE TRAIN WITH THE TWICE SCATTERED RADIOWAVE DIRECTED TOWARD THE RECEIVER /F COURSE THERE ARE IN PRINCIPLE INFINITELY MANY PAIRS OF WAVE TRAINS THAT CAN SATISFY THIS CONDITION HENCE THE INTEGRAL !ND THERE IS ANOTHER COMPLICATION 4HE INDIVIDUAL OCEAN WAVE TRAINS ARE NOT COMPLETELY INDEPENDENTTHEY INTERACT WEAKLY AND PRODUCE EVANESCENT NONLINEAR PRODUCT WAVES THAT WHILE NOT FREELY PROPAGATING CHANGE THE GEOMETRY OF THE SEA SURFACE AND CONTRIBUTE TO THE SCATTERED FIELD AT SECOND ORDER ALSO VIA "RAGG SCATTERING 4HUS AS SHOWN FIRST BY "ARRICK THE SECOND ORDER SCATTERING KERNEL IS MADE UP OF ELECTROMAGNETIC AND HYDRODYNAMIC TERMS ' ' %- ' (9$ 4HE RESULTING PIECEWISE CONTINUOUS SECOND ORDER DOPPLER SPECTRUM IS USUALLY SOME n D" WEAKER THAN THE FIRST ORDER "RAGG PEAKS BUT BEING SPREAD IN DOPPLER HAS THE POTENTIAL TO MASK SHIP ECHOES OVER MUCH MORE OF DOPPLER SPACE &IGURE IS AN EXAMPLE OF THE NUMERICAL EVALUATION OF %Q FOR A SPECIFIC OCEAN WAVE SPECTRUM 0OLARIZATION DEPENDENCE ARISES THROUGH ' &OR A HIGHLY CONDUCTING MEDIUM SUCH AS SEAWATER VIEWED AT TYPICAL (& RADAR GEOMETRIES THE COPOLAR SURFACE SCATTERING
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&)'52% #OMPUTED DOPPLER SPECTRA OF SEA CLUTTER FOR VARIOUS POLARIZATIONS THE RADAR FREQUENCY HERE IS -(Z WHILE THE DIRECTIONAL WAVE SPECTRUM ADOPTED IS A 0IERSON -OSKOWITZ WAVE NUMBER SPECTRUM COMBINED WITH A COS I ANGULAR SPREADING PATTERN
COEFFICIENT OR 2#3 PER UNIT SURFACE AREA IS MUCH LARGER FOR VERTICAL THAN FOR HORIZONTAL POLARIZATION WITH THE CROSSPOLAR SCATTERING COEFFICIENTS TYPICALLY ASSUMING INTERMEDI ATE VALUES FOR MODERATE BISTATIC SCATTERING GEOMETRIES R nVV R nHV y R nVH R nHH AS ILLUSTRATED IN &IGURE %Q IS OF FUNDAMENTAL IMPORTANCE TO MANY (& RADAR APPLICATIONS INCLUDING SHIP DETECTION REMOTE SENSING SEE FOLLOWING SECTION WAVEFORM SELECTION AND OTHER RADAR MANAGEMENT FUNCTIONS &OR EXAMPLE &IGURE SHOWS A MEASURED DOPPLER SPEC TRUM AND SUPERIMPOSED REPRESENTATIVE ESTIMATES OF THE MAGNITUDES OF THE ECHOES THAT MIGHT BE RECEIVED FROM A NUMBER OF DIFFERENT SHIP TYPES FOR THE SAME RADAR DESIGN AND WAVEFORM PARAMETERS !LSO SHOWN AT LEFT ARE THE SPEED BANDS WITHIN WHICH THE SHIP ECHOES WOULD BE OBSCURED BY THE CLUTTER 4HE ABILITY TO PREDICT THESE OBSCURED BANDS BY MEANS OF %Q CAN BE EXPLOITED FOR (& RADAR DESIGN AND SITING AND FOR SCHEDULING SHIP DETECTION OPERATIONS 4HUS COMBINING %Q WITH AN OCEAN WAVE CLIMATOLOGY FOR ANY REGION ENABLES THE STATISTICAL PREDICTION OF RADAR SHIP DETECTION PERFORMANCE
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&)'52% 3CHEMATIC REPRESENTATION OF BLIND SPEED BANDS IN WHICH SHIP ECHOES ARE OBSCURED BY SEA CLUTTER
3IMILARLY CHOICE OF THE WAVEFORM FREQUENCY AND BANDWIDTH CAN BE GUIDED BY CALCULA TION OF THE CLUTTER POWER SPECTRAL DENSITY AS A FUNCTION OF THESE PARAMETERS FOR ANY GIVEN SEA STATE TAKING INTO ACCOUNT ANY INFORMATION ABOUT TARGET COURSE SPEED AND 2#3 ! VERY IMPORTANT OPERATIONAL CONSIDERATION HERE IS THE POTENTIAL FOR AN ADVERSARY TO EXPLOIT THE SEA CLUTTER SPECTRUM BY CONTRIVING TO PLACE HIS SHIP ECHO AT THE "RAGG FREQUENCY WHERE IT WOULD BE OBSCURED BY SEA CLUTTER 4HE ADVERSARY CAN ACHIEVE THIS BY CHOOSING ANY COMBINATION OF COURSE AND SPEED THAT MAKES THE VELOCITY COMPONENT TOWARD THE RADAR EQUAL TO THE EQUIVALENT PHASE VELOCITY OF THE "RAGG PEAK 4HE RADAR OPERATOR MUST COUNTER THIS BY EXPLOITING HIS UNDERSTANDING OF THE DETAILED STRUCTURE OF THE SPECTRUM AND ITS VARIATION WITH RADAR FREQUENCY TO UNMASK THE TARGET 2ADAR /CEANOGRAPHY 4HE EXISTENCE OF THE RELATION EXPRESSED IN F %Q BETWEEN THE SEA SURFACE REPRESENTATION AS A DIRECTIONAL WAVE SPECTRUM 3J AND THE DOPPLER SPECTRUM MEASURED BY AN (& RADAR PROVIDES AN OPPORTUNITY TO DETERMINE THE DETAILED STATE OF THE SEA SURFACE BY REMOTE SENSING WITH SKYWAVE OR SURFACE WAVE RADAR )N ORDER TO EXTRACT SEA PARAMETERS FROM RADAR DOPPLER SPECTRA AND TO OPTIMIZE THE CHOICE OF RADAR PARAMETERS FOR THE RADARS SURVEILLANCE MISSIONS IT IS HELPFUL TO UNDERSTAND SOME ELEMENTARY OCEANOGRAPHY 4HE OCEAN WAVES THAT CONTRIBUTE MOST TO THE (& RADAR RETURNS HAVE WAVELENGTHS IN THE RANGE OF n M THESE WAVES ARE EXCITED BY THE SURFACE WINDS )F A WIND BLOWS AT A CONSTANT VELOCITY LONG ENOUGH AND OVER SUFFICIENT FETCH THE DISTANCE OVER WHICH THE WIND IS BLOWING A STEADY STATE CONDITION WILL BE ACHIEVED WHERE THE WIND PROVIDES JUST ENOUGH ENERGY TO THE WAVES TO BALANCE THAT LOST BY BREAKING AND OTHER DISSIPATION MECHANISMS -OREOVER IN THIS STATE OF DYNAMIC EQUILIBRIUM ENERGY WILL BE TRANSFERRED
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&)'52% .ONDIRECTIONAL WAVEHEIGHT POWER SPECTRAL DENSITY AS MEASURED WITH A WAVE BUOY SHOW ING POWER LAW BEHAVIOR 4HE STRAIGHT LINE IS THE ORIGINAL 0HILLIPS SATURATION ASYMPTOTE WHICH IS APPROACHED AT HIGH FREQUENCIES IN THIS EXAMPLE 4HE SCALE MARKED hWIND VELOCITYv CAN BE USED TO DEDUCE THAT WINDS UP TO KT HAVE EXCITED WAVES WITH FREQUENCIES AS LOW AS (Z BUT THAT EITHER THE DURATION OR FETCH OR BOTH HAVE NOT BEEN SUFFICIENT FOR FULL DEVELOPMENT 4HE SCALE ACROSS THE TOP GIVES THE RADAR FREQUENCY CORRESPOND ING TO RESONANT BACKSCATTER
PREDOMINANTLY TO WAVES WHOSE VELOCITIES ARE FAIRLY CLOSELY MATCHED TO THE WIND VELOC ITY AND UNDERGO REDISTRIBUTION ACROSS WAVENUMBER SPACE THROUGH THE MECHANISM OF NONLINEAR WAVE INTERACTIONS TO PRESERVE THE EQUILIBRIUM SPECTRAL FORM 4HERE ARE A NUMBER OF MODELS THAT HAVE BEEN PROPOSED TO DESCRIBE THE EQUILIBRIUM SPECTRAL FORM AND INDEED MODELS THAT ATTEMPT THE MORE AMBITIOUS TASK OF MODELING NONEQUILIBRIUM SPECTRA -OST OF THESE MODELS ARE BASED ON EXPERIMENTAL MEASURE MENTS ILLUSTRATED HERE BY &IGURE WHICH SHOWS AN EXAMPLE OF THE FREQUENCY SPECTRUM DERIVED FROM WAVE BUOY MEASUREMENTS ! COMMON FEATURE OF SUCH WAVE SPECTRA IS THAT WAVES OF A GIVEN WAVELENGTH TEND TO REACH A LIMITING SPECTRAL DENSITY BEYOND WHICH THE PROCESSES OF DISSIPATION AND NONLINEAR TRANSFER OF ENERGY TO OTHER WAVENUMBERS PREVENTS FURTHER GROWTH 4HIS CONDITIONKNOWN AS SATURATION OR BEING FULLY DEVELOPEDIS REACHED AT QUITE MODEST WIND SPEEDS FOR THOSE WAVES RESPONSIBLE FOR FIRST ORDER SCATTER AT (& THAT IS n KNOTS /F THE VARIOUS NONDIRECTIONAL OCEAN WAVE MODELS REPORTED IN THE LITERATURE THAT OF 0IERSON AND -OSKOWITZ HAS BEEN MOST WIDELY USED BY THE RADAR COMMUNITY 4HEY DERIVED THE FOLLOWING RELATION FOR A FULLY DEVELOPED NONDIRECTIONAL SPECTRUM BASED UPON EMPIRICAL DATA
& J
§ ¤J ³ ¶ AE C EXP ¨ N ¥ J ´ · P J ¦ µ · ©¨ ¸
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OR EQUIVALENTLY IN TERMS OF WAVE FREQUENCY
§ ¤ G ³ ¶ A G & V E EXP ¨ N ¥ ´ · V ¨© ¦ V Uµ ·¸
WHERE
U WIND SPEED JC GU M AND AE
4HE EXPONENTIAL TERM APPROXIMATES THE DECAY IN THE SPECTRUM FOR WAVE SPEEDS ABOVE THE WIND MAXIMUM VELOCITY -ODELS THAT TAKE ACCOUNT OF THE CONSEQUENCES OF FINITE FETCH AND FINITE DURATION OF THE WIND STRESS INCLUDE THE */.37!0 SPECTRUM AND THE MODEL OF %LFOUHAILY ET AL SUCH EFFECTS CAN LEAD TO SUBSTANTIAL CHANGES IN THE (& DOPPLER SPECTRUM AND HENCE TARGET DETECTABILITY SO THESE MODELS SHOULD BE USED WHEN APPLICABLE 4HE DECREASE OF WAVE SPECTRAL DENSITY WITH WAVENUMBER IS OBSERVED TO LIE CLOSE TO A Kn POWER LAW AS ADOPTED BY MOST MODELS AND BY A NATURAL COINCIDENCE THIS IS BALANCED BY THE K FACTOR IN THE FIRST ORDER SCATTERING COEFFICIENT IN %Q SO THE RESULTING S IS ROUGHLY INDEPENDENT OF FREQUENCY OVER THE RANGE OF FREQUENCIES FOR WHICH THE POWER LAW BEHAVIOR IS OBSERVED !N IMPORTANT CONSEQUENCE IS THAT WITH SUCH A REFERENCE PROPAGATION PATH LOSSES MAY BE ESTIMATED 4O TEST THIS IDEA THE MAGNITUDE AND VARIABILITY OF RVVn WAS EXAMINED WITH THE 3AN #LEMENTE )SLAND (& SURFACE WAVE RADAR 4HIS RADAR FACILITY HAD SEVERAL VALUABLE AND UNIQUE FEATURES A TRANSMISSION PATH OUT OVER THE OPEN SEA MULTIPLE FREQUENCY OPERATION WITHIN A REPETITION PERIOD CALIBRATED ANTENNAS KNOWN TRANSMITTER POWER AND GROUND TRUTH IN THE FORM OF OCEAN WAVEHEIGHT RECORDINGS 7HEN LOOKING INTO AN APPROXIMATELY KNOT WIND VALUES OF RVVn WERE FOUND TO BE CONSTANT WITHIN A FEW DECIBELS FOR OPERAT ING FREQUENCIES WHERE THE OCEAN WAVE SPECTRUM WAS APPROXIMATELY FULLY DEVELOPED THESE OBSERVATIONS PROVIDED A CONFIRMATION OF "ARRICKS FIRST ORDER THEORY "Y USING THE ANTENNA GAIN CONVENTIONS STATED EARLIER AND ASSUMING A SEMI ISOTROPIC SEA DIRECTIONAL SPECTRUM THE VALUE OF RVVn WAS CALCULATED AS n D" THE MEASURED VALUES WERE GROUPED BETWEEN AND D" OF THIS VALUE OVER A TO -(Z FREQUENCY SPAN 4HIS EXPERIMENT PROVIDED THE FIRST DIRECT MEASUREMENTS OF THE SEA SURFACE SCATTERING COEFFICIENT /F COURSE WHEN THE "RAGG RESONANT WAVES ARE NOT FULLY DEVELOPED THE SCATTERING COEFFICIENT WILL BE PROPORTIONATELY LESS AS SHOWN IN &IGURE COMPILED FROM DATA SETS RECORDED LOOKING UPWIND OR DOWNWIND WITH THE *INDALEE RADAR /CCASIONS WHEN THE WIND SPEED WAS INSUFFICIENT TO AROUSE THE "RAGG RESONANT WAVES TO SATURATION LEVELS YIELDED SCATTERING COEFFICIENT VALUES UP TO D" BELOW THE PEAK VALUES ,OW SCATTERING COEFFICIENT VALUES CAN ALSO ARISE BECAUSE THE ANGULAR SPECTRUM OF THE WAVE SYSTEM IS NOT BEING SAMPLED ALONG A DIRECTION THAT PRESENTS THE MAXIMUM AMPLITUDE COMPONENT AT THE "RAGG RESONANT WAVENUMBER 4HE DIRECTIONAL WAVE SPEC TRUM CAN BE WRITTEN AS F 3 K x 3 K E & K ' E K WHERE & K IS THE NONDIRECTIONAL SPECTRUM
& K ¯
P
3 K E DE
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&)'52% #ALIBRATED MEASUREMENTS OF THE RATIO OF THE MEASURED SCATTERING COEFFICIENT TO THE SATURATED SEA SCATTERING COEFFICIENT PLOTTED AS A FUNCTION OF THE RATIO OF WIND SPEED TO THE PHASE SPEED OF THE "RAGG RESONANT WAVES FOR UPWINDDOWNWIND OBSERVATIONS
AND 'E K IS THE NORMALIZED ANGULAR SPREADING FUNCTION THAT DESCRIBES HOW THE WAVE ENERGY IS DISTRIBUTED IN AZIMUTH
P
¯
' E K DE
4HE NON ZERO WAVE SPECTRUM IS NOT CONFINED TO DIRECTIONS HAVING A COMPONENT PAR P P ALLEL TO THE WIND DIRECTION E IE 'E K FOR a E a NOR IS IT SEMI ISOTROPIC ' E K P FOR P a E a P )N GENERAL THE ANGULAR SPECTRUM IS NON ZERO THROUGH n WITH THE SPREADING FUNCTION DEPENDING ON MANY VARIABLES INCLUDING THE RECENT SURFACE WIND HISTORY (& RADAR HAS SUFFICIENT SENSITIVITY TO MEASURE THE RELATIVE AMPLITUDE OF THE WAVES RUNNING AGAINST THE WIND EVEN THOUGH THEY MAY HAVE A POWER SPECTRAL DENSITY AND HENCE AN 2#3 SEVERAL ORDERS OF MAGNITUDE BELOW THOSE RUNNING WITH THE WIND 4HESE UPWIND PROPAGATING OCEAN WAVES ARE CAUSED PREDOMINANTLY BY THIRD ORDER NONLINEAR WAVE WAVE INTERACTIONS REFLECTION PROCESSES WAVE CURRENT INTERAC TIONS AND PROPAGATION FROM NEIGHBORING REGIONS WITH DIFFERENT WIND STRESS 4HEY ARE VERY IMPORTANT FOR REMOTE SENSING AND IMPACT STRONGLY ON TARGET DETECTION BECAUSE THE SECOND ORDER SCATTERING PROCESSES ARE HEAVILY DEPENDENT ON 'E K 4HEY ALSO SERVE AS A SENSITIVE INDICATOR OF BACKSCATTER COEFFICIENT ESTIMATION SINCE TAKING ACCOUNT OF ONLY THE FIRST ORDER SCATTERED FIELD
R s ;' E E7 K ' E E7 P =
WHERE E 7 IS THE WIND DIRECTION 4O QUANTIFY THIS IF THE WAVE ANGULAR SPECTRUM MODEL OF ,ONG AND 4RIZNA IS USED THE MAXIMUM VALUE OF R n FOR A SATURATED SEA IS n D" IN THE UPWIND OR DOWNWIND DIRECTION LONGITUDINAL SEA AND ONLY n D" IN THE CROSSWIND DIRECTION TRANSVERSE SEA &IGURE SHOWS THE SCATTERING COEFFICIENT FOR THIS AND SOME SIMPLE PARAMETRIC ANGULAR SPREADING FUNCTIONS VERSUS ANGLE WITH RESPECT TO WIND DIRECTION AS COMPUTED FROM THE FIRST ORDER CONTRIBUTIONS
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&)'52% 6ARIATION OF THE PEAK BACKSCATTER COEFFICIENT AS A FUNCTION OF WIND DIRECTION RELATIVE TO THE RADAR LOOK DIRECTION FOR VARIOUS SPREADING FUNCTIONS ASSUMING A SEA FULLY DEVELOPED AT THE "RAGG RESONANT WAVE FREQUENCY
)N SUMMARY THE SEA ECHO POWER IN A RESOLUTION CELL IS GENERALLY THE LARGEST ECHO SIGNAL GENERALLY EXISTS IN THE OPEN OCEAN EVEN IN RELATIVE CALM VARIES AS THE SQUARE OF RESONANT WAVEHEIGHT WHICH IS FREQUENTLY SATURATED AT THE HIGHER FREQUEN CIES AND VARIES WITH DIRECTION BEING GREATEST FOR SEAS RUNNING TOWARD OR AWAY FROM THE RADAR 4HE DOPPLER SPECTRUM OF THE ECHO HAS SHARP VARIATIONS THAT REQUIRE CAREFUL PROCESSING TO PRESERVE 4HE RECEIVER AND PROCESSOR MUST BE ABLE TO HANDLE BOTH THE HIGH LEVEL SIGNAL DUE TO THIS LARGE 2#3 AND THOSE MUCH SMALLER SIGNALS DUE TO TARGETS ESPECIALLY WHEN THE LATTER ARE ADJACENT TO THE STRONGEST CLUTTER COMPONENTS !N (& RADAR MUST BE DESIGNED TO ACCOMMODATE SUCH CLUTTER LEVELS EVEN THOUGH THEY WILL NOT EXIST ALL THE TIME OR AT ANY ONE TIME OVER ALL AREAS ESPECIALLY AT THE LOWER OPERATING FREQUENCIES %STIMATION OF 3EA 3TATE 7AVE 3PECTRA AND 3URFACE 7INDS 4ECHNIQUES FOR EXTRACTING OCEAN WAVE FIELD INFORMATION FROM MEASURED DOPPLER SPECTRA HAVE BEEN REPORTED BY NUMEROUS AUTHORS WORKING IN ALMOST ALL CASES FROM THE "ARRICK SOLUTION FOR THE SCATTERED FIELD AND DEALING ALMOST EXCLUSIVELY WITH (& SURFACE WAVE RADAR DATA UNCORRUPTED BY IONOSPHERIC PROPAGATION )NVERSION OF THE RELATION IN %Q F TO OBTAIN AN ESTIMATE OF 3J IS MATHEMATICALLY NONTRIVIAL REQUIRING SOME ADDITIONAL ASSUMPTIONS TO OBTAIN A UNIQUE STABLE SOLUTION 3OME OF THESE METHODS ADDRESS THE PROBLEM OF FULL DIRECTIONAL WAVE SPECTRUM ESTIMATION n WHEREAS OTHERS PROPOSE ESTIMATORS FOR INTEGRATED MEASURES OF SEA ROUGHNESS SUCH AS SIGNIFICANT WAVEHEIGHT
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/CEAN CURRENTS CAN BE DETERMINED WHEN A ZERO DOPPLER REFERENCE SUCH AS AN ISLAND IS IN THE RADAR FOOTPRINT 4HE ./!! 7AVEWATCH WEBSITE PROVIDES ACCESS TO ARCHIVED MAPS OF SIGNIFICANT WAVEHEIGHT DOMINANT WAVE PERIOD AND OTHER PARAM ETERS SUCH INFORMATION IS EXTREMELY HELPFUL WHEN DESIGNING A RADAR FOR REMOTE SENS ING APPLICATIONS )N ADDITION TO PROVIDING INFORMATION ABOUT THE SEA SURFACE (& RADAR CAN BE USED TO INFER SURFACE WIND SPEED AND DIRECTION 7IND DIRECTION IS COMMONLY ESTIMATED BY TAKING THE RATIO OF THE FIRST ORDER RESONANT "RAGG PEAKS AND EMPLOYING AN EMPIRICAL RELATIONSHIP BETWEEN THIS RATIO AND THE WIND DIRECTION RELATIVE TO THE RADAR LOOK AXIS AS PIONEERED BY ,ONG AND 4RIZNA "Y SCANNING OVER A RADARS COVERAGE AREA A MAP OF INFERRED WIND DIRECTION CAN BE CONSTRUCTED SURFACE WIND DIRECTION MAPS ARE A ROUTINE BYPRODUCT OF THE *INDALEE RADAR 7HILE WAVEHEIGHT AND WAVE SPECTRUM ESTIMATES CAN IN PRINCIPLE BE EXTRACTED FROM HIGHER ORDER FEATURES OF SKYWAVE RADAR SEA ECHO SPECTRA A MAJOR DIFFICULTY ARISES DUE TO THE MYRIAD FORMS OF CONTAMINATION AND DISTORTION INTRODUCED BY THE IONOSPHERE 4HIS HAS LED TO THE DEVELOPMENT OF NUMEROUS TECHNIQUES FOR ESTIMATING AND REMOVING THE VARIOUS FORMS OF SIGNAL CORRUPTIONn !S AN ALTERNATIVE 4RIZNA AND 0ILON AND (EADRICK HAVE REPORTED A METHOD FOR ESTIMATING R n FROM SIMPLE MEA SUREMENTS MADE DIRECTLY ON THE CORRUPTED RADAR ECHO SPECTRUM 7HILE THIS APPROACH MAY BE RELATIVELY INSENSITIVE TO SOME FORMS OF CORRUPTION IT IS NOT APPLICABLE TO SEAS FAR FROM EQUILIBRIUM !LL THE METHODS FOR ESTIMATING SEA STATE OR SCATTERING COEFFICIENTS REQUIRE LONG COHERENT INTEGRATION TIMES USUALLY COMBINED WITH NONCOHERENT AVERAGING OF A NUMBER OF #)4S IN ORDER TO ACHIEVE A DISTINCT AND STABLE SPECTRUM 4HIS TYPE OF RADAR OPERATION WILL FREQUENTLY BE INCOMPATIBLE WITH OTHER RADAR MISSIONS "UT BECAUSE THE SEA ECHO IS GENERALLY A VERY LARGE SIGNAL IT MAY BE OBTAINED WITH AN ADJUNCT OBLIQUE SOUNDER OPERATING IN AN APPROPRIATE RADAR MODE 3CATTERING FROM -ETEOR 4RAILS AND /THER )RREGULARITIES IN THE )ONOSPHERE #LUTTER FROM IONOSPHERIC IRREGULARITIES SUCH AS THOSE MENTIONED IN 3ECTION CAN SEVERELY LIMIT RADAR PERFORMANCE 5NLIKE THE TERRESTRIAL OR OCEAN ENVIRONMENTS WHERE VELOCITIES OF NATURAL SCATTERERS TEND TO BE LOW THE IONOSPHERE IS HOME TO PHENOMENA WITH APPARENT SPEEDS OF n MSn AND MORE OBSCURING MUCH OF THE RELEVANT DOPPLER DOMAIN WHERE MANMADE TARGETS MIGHT BE FOUND -ANY OF THESE SCATTERERS HAVE A TRANSIENT EXISTENCE MUCH LESS THAN THE COHERENT INTEGRATION TIME SO CONVENTIONAL SIGNAL PROCESSING CAUSES THEIR ECHOES TO APPEAR SPREAD IN DOPPLER AS WELL AS DOPPLER SHIFTED 4HE GENERIC TERM SPREAD DOPPLER CLUTTER IS USED TO COVER ALL THESE PHENOMENA WHERE THE SCATTERERS RESPONSIBLE FOR THE CLUTTER DO NOT HAVE A WELL DEFINED DOPPLER SHIFT 4HE SAME TERM IS USED TO DESCRIBE THE ENTIRELY DIFFERENT MECHANISM WHERE CLUTTER SMEARING IN DOPPLER OCCURS AS A CONSEQUENCE OF RAPID VARIATIONS IN THE PROPAGATION PATH RATHER THAN IN THE MOTION OF THE SCATTERER -ETEORS AND THEIR TRAILS ARE THE MOST UBIQUITOUS SOURCE OF TRANSIENT ECHOESn 4HEY DISPLAY A REASONABLY WELL DEFINED DIURNAL AND GEOGRAPHICAL DISTRIBUTION SPECIFIC TO ANY GIVEN RADAR SITE BUT THEY CAN CAUSE PROBLEMS OVER A WIDE RANGE EXTENT BECAUSE THEY CAN BE ILLUMINATED BY A VARIETY OF PROPAGATION MODES AS SHOWN SCHEMATICALLY IN &IGURE .ORMAL INCIDENCE AS SHOWN YIELDS THE LARGEST ECHO BUT OBLIQUE INCIDENCE ECHOES AND SCATTERING FROM THE METEOR hHEADv ARE ALSO OBSERVED &IGURE COMPARES A SIMPLE PREDICTIVE MODEL WITH MEASUREMENTS CONFIRMING THAT THE OBSERVED BEHAVIOR IS UNDERSTOOD AND THUS CAN BE TAKEN INTO ACCOUNT IN RADAR DESIGN AND OPERATIONS
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&)'52% -ETEOR TRAIL SPECULAR SCATTERING GEOMETRY FOR SEVERAL PROPAGA TION MODES
-ETEORS ARE USUALLY CLASSIFIED AS SPORADIC OCCURRING MORE OR LESS RANDOMLY AS THE %ARTH MOVES AROUND THE SUN AND SHOWERS SUCH AS THE ,EONIDS AND THE %TA !QUARIDS WHICH OCCUR ON PREDICTABLE DATES WHERE THEIR ORBITS INTERSECT THE %ARTHS ORBIT #%'#$&$ $&# &%%#$%#&% $
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&)'52% 0REDICTED RANGE DEPENDENCE OF METEOR ECHO STRENGTH COMPARED WITH MEASUREMENTS GROUND CLUTTER RETURNS ARE ALSO SHOWN 4HE DISTRIBUTION OF METEOR RADIANTS DETERMINES THIS VARIATION
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/N THESE OCCASIONS THE FLUX OF METEORS CAN BE SO HIGH THAT THEY CAN CAUSE SERIOUS OBSCURATION OF TARGET ECHOES !S RADARS BECOME MORE SENSITIVE THEY REGISTER SMALLER AND SMALLER METEORS WHICH ARE FAR MORE ABUNDANT SO AT TIMES THE FLUX OF COUNTLESS SMALL METEOR TRAILS SETS THE EFFECTIVE DETECTION THRESHOLD -ETEOR ECHO SUPPRESSION CAN BE ATTEMPTED IN THE SPATIAL DOMAIN IF THE RECEIVING ARRAY HAS VERTICAL DIRECTIVITY BUT FOR MOST RADARS THE ONLY OPTION IS REJECTION BY SIGNAL PROCESSING EXPLOITING THE TRANSIENT NATURE OF THE ECHOES TO DETECT AND CENSOR THEM IN THE TIME DOMAIN %CHOES FROM THE AURORAE SIMILARLY INVOLVE TRANSIENT SCATTERING PROCESSES THAT APPEAR IN THE RADAR DATA AS HIGHLY DOPPLER SPREAD ECHOES WITH THE POTENTIAL TO OBSCURE TARGETS 3CATTERING FROM THE AURORAL REGION HAS BEEN STUDIED EXTENSIVELY USING THE 3UPER$!2. (& RADAR NETWORK INITIATED BY 'REENWALD AND AN AURORAL ECHO SCATTERING MODEL HAS BEEN DEVELOPED BY %LKINS THIS CAN BE USED TO PREDICT TARGET OBSCURATION WHEN THE TRANSMISSION PATH IS THROUGH THE AURORAL REGION 0ROVIDED THE RADAR IS WELL REMOVED FROM THE AURORAL ZONE THE WAVEFORM CAN OFTEN BE CHOSEN SO AS TO MANIPULATE THE CLUT TER ECHOES WITHIN RANGE DOPPLER SPACE UNMASKING TARGETS HITHERTO OBSCURED /FTEN SEVERAL WAVEFORMS WITH DIFFERENT REPETITION FREQUENCIES ARE INTERLEAVED TO ACHIEVE THIS &OR RADARS CLOSE TO THE AURORAL ZONE THE OPTIONS ARE GENERALLY MORE LIMITED )ONOSPHERIC IRREGULARITIES THAT SCATTER BACK TO THE RADAR RECEIVER OCCUR MUCH MORE OFTEN AT NIGHT THAN BY DAY AT ANY LATITUDE 3ENSIBLE SITING OF THE RADAR ENSURING GOOD FRONT TO BACK RATIOS ON THE ANTENNAS EMPLOYING VERTICAL NULLING IF AVAILABLE AND USING ADAPTIVE SIGNAL PROCESSING TECHNIQUES OR AT LEAST MAINTAINING LOW RECEIVE ARRAY SIDELOBES ARE ALL EFFECTIVE TOOLS FOR MITIGATING AURORAL METEOR AND OTHER IONOSPHERIC CLUTTER
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1* 9 )N THE (& BAND THE AVERAGE NOISE POWER SPECTRAL DENSITY AT MID BAND NEAR -(Z SAY MAY EXCEED n D"7(Z AND WILL GENERALLY EXCEED n D"7(Z COMPARED WITH TYPICAL RECEIVER INTERNAL NOISE SPECTRAL DENSITIES OF PERHAPS n D"7(Z 4HUS UNLIKE THE MICROWAVE RADAR CASE EXTERNAL NOISE IS ALMOST ALWAYS DOMINANT 4HIS HAS FUNDAMENTAL IMPLICATIONS FOR RECEIVING SYSTEM DESIGN AND SIGNAL PROCESSING !NOTHER CRITICAL ISSUE IS THE OBSERVED SYSTEMATIC VARIATION OF THE EXTERNAL NOISE LEVEL WHICH HAS A DIRECT IMPACT ON RADAR PERFORMANCE 4HE MAJOR SOURCE OF QUASI CONTINUUM BACKGROUND NOISE AT THE LOWER FREQUENCIES IS LIGHTNING DISCHARGES IONOSPHERICALLY PROPAGATED FROM ALL OVER THE WORLD SFERICS !T THE HIGH END OF THE BAND EXTRATERRESTRIAL OR GALACTIC NOISE MAY BE GREATER THAN THAT DUE TO SFERICS 2ECEIVE SITES IN AN AREA OF EXTENSIVE ELECTRICAL EQUIPMENT USE CAN FIND ANTHROPOGENIC NOISE DOMINANT "UT MOST IMPORTANTLY THE (& BAND IS DENSELY OCCUPIED BY OTHER USERS ESPECIALLY POWERFUL (& BROADCASTERS RELYING ON THE PREVAILING FRE QUENCY WINDOW FOR SATISFACTORY PROPAGATION %VEN OUT OF BAND SIGNAL LEVELS ARE A CON SIDERATION IN RECEIVER FRONT END DESIGN WHERE IT IS COMMON TO HAVE BANDWIDTHS MUCH WIDER THAN THAT OF THE RADAR SIGNAL 4HERE ARE A LARGE NUMBER OF BROADCAST STATIONS THAT HAVE K7 TRANSMITTERS AND ANTENNAS WITH MORE THAN D" GAIN -EASUREMENTS MADE ON THE MIDDLE !TLANTIC COAST OF THE 5NITED 3TATES SHOW (& BROADCAST BAND SIG NALS WITH STRENGTHS OF TO M6M 4HESE AMBIENT LEVELS MUST BE ACCOMMODATED IN RECEIVER DESIGN BECAUSE A WIDEBAND FRONT END IS DESIRABLE FOR RAPID AND FREQUENT FREQUENCY CHANGES
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4HE PRACTICE IN ALLOCATIONS FOR (& RADAR OPERATION IS TO PERMIT USE OF BROAD BANDS OF THE SPECTRUM WITH A REQUIREMENT TO CAUSE NO DISCERNIBLE INTERFERENCE TO AN EXISTING SERVICE AND TO PROVIDE A LOCKOUT FEATURE FOR CHANNELS THAT NEED PROTECTION 4HUS AN INTEGRAL PART OF AN (& RADAR IS A CHANNEL OCCUPANCY ANALYZER THAT PROVIDES A REAL TIME DESCRIPTION OF SPECTRUM AVAILABILITY AS ILLUSTRATED IN &IGURES AND
&)'52% ! SNAPSHOT OF THE (& SPECTRUM AT NOON IN SUMMER AND AT A LOW SUNSPOT NUMBER ZOOM ING IN PROGRESSIVELY TO SHOW A SECTION OF THE SPECTRUM WHERE A K(Z CLEAR CHANNEL IS EVIDENT CENTERED ON -(Z 4HE DATA WAS RECORDED AT LATITUDE 3 LONGITUDE %
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!LMOST WITHOUT EXCEPTION (& RADARS HAVE OPERATED ON THIS PRINCIPLE OF NONINTER FERENCE MAKING DO WITH hCLEARv CHANNELS BETWEEN OTHER USERS 0ATTERNS IN 3PECTRUM /CCUPANCY 7HEN THE (& BAND IS SCANNED WITH A SPEC TRUM ANALYZER IT CAN BE SEEN THAT THE GROSS FEATURES OF OCCUPANCY AT ANY PARTICULAR HOUR ARE REMARKABLY STATIONARY OVER THE DAYS OF A SEASON 4HIS IS DUE TO BROADCAST STATIONS FIXED SERVICE POINT TO POINT TRANSMITTERS AND MANY OTHER SPECTRUM USERS HAVING REGULAR SCHEDULES AS IS EVIDENT FROM &IGURE WHICH PLOTS THE POWER SPECTRAL DENSITY AT K(Z RESOLUTION FOR HIGH AND LOW SOLAR ACTIVITY SUMMER AND WINTER DAY AND NIGHT
&)'52% (& ACTIVITY OVER THE n -(Z FOR LOW AND HIGH SUNSPOT NUMBERS L H SUMMER AND WINTER S W AND DAY AND NIGHT D N AS MEASURED AT LATITUDE 3 LONGITUDE % 4HE DATA IS TAKEN FROM *ULIAN DAYS AND OF AND
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!S REMARKED EARLIER THE MAXIMUM FREQUENCY THAT WILL REFLECT ENERGY BACK TO THE %ARTH DURING THE DAY MAY BE MORE THAN TWICE THAT AT NIGHT THEREFORE THE OCCUPANCY TENDS TO BE DENSER AT NIGHT THAN DURING THE DAYA PROBLEM COMPOUNDED BY THE LOWER ABSORPTION AND HENCE RECEPTION OF MORE DISTANT SIGNALS ,OOKED AT OVER LONGER TIMESCALES VARIOUS PATTERNS AND TRENDS EMERGE -OST OBVI OUSLY THE YEAR SOLAR CYCLE FORCES CHANGES TO SPECTRUM USAGE AND THE DENSITY OF USERS WITH A RESULTANT IMPACT ON (& RADAR CHANNEL SELECTION !NOTHER TREND THAT HAS BECOME APPARENT IN RECENT YEARS IS THE GRADUAL REDUCTION IN (& USERS AS SERVICES MOVE TO SATEL LITE COMMUNICATIONS MICROWAVE LINKS FIBER OPTICS AND OTHER MEDIA .EVERTHELESS THE INCREASED NUMBER OF (& RADARS HAS LED TO A NEW CHALLENGE INTER RADAR INTERFERENCE AND THE NEED FOR FREQUENCY ARBITRATION .OISE -ODELS 4HE WIDELY USED REFERENCE ON NOISE IS THE )NTERNATIONAL 2ADIO #ONSULTATIVE #OMMITTEE ##)2 2EPORT 4HIS REPORT IS BASED UPON MEA SUREMENTS MADE AT LOCATIONS THROUGHOUT THE WORLD 4HE MEASUREMENT AND DATA ANALYSIS WERE PERFORMED TO EXCLUDE INDIVIDUAL COLLECTION SITE LOCAL THUNDERSTORM CON TRIBUTIONS 3PAULDING AND 7ASHBURN ADDED DATA FROM THE FORMER 5332 FOR TWO REVISED ##)2 REPORTS .OISE LEVEL MEDIANS AS A FUNCTION OF FREQUENCY ARE GIVEN IN THE FORM OF WORLDWIDE MAPS BY SEASON AND H TIME BLOCKS ,UCAS AND (ARPER HAVE PROVIDED A NUMERICAL REPRESENTATION OF ##)2 2EPORT WHICH IS USEFUL FOR COM PUTER COMPUTATIONS AND THIS HAS BEEN REVISED BY ADDING THE WORK OF 3PAULDING AND 7ASHBURN 4HE MAPS OF MEDIAN VALUES ARE ACCOMPANIED BY DECILE VALUES TO INDICATE DISTRIBUTIONS OVER DAYS OF THE SEASON ##)2 2EPORT HAS A SIGNIFICANT DISCREPANCY AS POINTED OUT BY 3AILORS SO IT SHOULD BE USED WITH CAUTION 4HESE NOISE MAPS PROVIDE THE LEVEL THAT AN OMNIDIRECTIONAL ANTENNA WOULD RECEIVE %VEN THOUGH ASSUMING ISOTROPIC ##)2 NOISE HAS LIMITATIONS IT DOES PROVIDE A REFERENCE LEVEL FOR INITIAL RADAR DESIGN ! NUMBER OF OPERATIONAL AND EXPERIMENTAL (& SYSTEMS HAVE ACCUMULATED THEIR OWN NOISE DATABASES AND COMPARED THEM WITH ##)2 MODEL DATA THE REPORT OF .ORTHEY AND 7HITHAM GIVES A DETAILED ANALYSIS !N (& RADAR IS GENERALLY DESIGNED TO TAKE ADVANTAGE OF WHAT THE ENVIRONMENT PER MITS THAT IS THE RECEIVER NOISE FIGURE SHOULD BE GOOD ENOUGH TO MAKE ENVIRONMENTAL NOISE THE LIMITATION !N EXAMPLE OF THE ##)2 2EPORT DATA WILL NOW BE DISCUSSED &IGURE WAS DRAWN FROM ,UCAS AND (ARPER .OISE POWER IN A (Z BAND RELATIVE TO 7 D"7 IS GIVEN AS A FUNCTION OF FREQUENCY FOR THREE DIFFERENT SOURCES OF NOISE GALACTIC ATMOSPHERIC AND ANTHROPOGENIC 4HE PRACTICE IN USE IS TO SELECT THE LARGEST 4HIS IS A WINTER DAYTIME EXAMPLE AT A 5NITED 3TATES EAST COAST LOCATION 4HE THREE STRAIGHT LINES ARE ESTIMATES OF ANTHROPOGENIC NOISE FOR THREE DIFFERENT TYPES OF SITES 4HE SHAPE OF THE ANTHROPOGENIC CURVES IS DESCRIBED BY THE EQUATIONS
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WHERE THE FREQUENCY F IS IN MEGAHERTZ AND LN INDICATES THE NATURAL LOGARITHM 4HESE FREQUENCY TRENDS APPROXIMATE MANY MEASUREMENTS OF HUMAN MADE NOISE BUT IDEALLY THE CURVE WOULD BE BASED ON MEASUREMENTS AT THE PARTICULAR RADAR SITE 4HE GALACTIC NOISE CURVE SHOULD BE SELECTED WHEN IT IS THE LARGEST AND WHEN THERE IS A PATH THROUGH THE IONOSPHERE THE PATH WILL NOT EXIST FOR THE LOWER OPERATING FREQUENCIES IN THE DAYTIME 4HE ATMOSPHERIC NOISE RISES FROM LOW FREQUENCIES TO ABOUT -(Z AND
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&)'52% .OISE POWER PER HERTZ IS GIVEN FOR g NORTH LATITUDE AND g WEST LONGITUDE IN WINTER A 54# IS GIVEN AS A DAYTIME EXAMPLE AND B 54# IS GIVEN AS A NIGHTTIME EXAMPLE
THEN RAPIDLY FALLS &IGURE B IS FOR NIGHTTIME !LL THE CURVES ARE THE SAME AS IN &IGURE A EXCEPT FOR ATMOSPHERIC NOISE !T -(Z THE NIGHT AND DAY LEVELS ARE THE SAME BELOW -(Z THE NOISE DECREASES WITH DECREASING FREQUENCY IN DAYTIME AND INCREASES AT NIGHT !BOVE -(Z DAYTIME LEVELS ARE GREATER THAN THOSE AT NIGHT 4HESE EFFECTS CAN BE PARTIALLY EXPLAINED BY THE VERY LOSSY LONG RANGE PATHS IN DAY THAT ATTENUATE THE LONG RANGE NOISE AT THE LOWER FREQUENCIES AND BY THERE BEING FEW OR NO SKYWAVE PATHS TO NOISE TERRESTRIAL SOURCES AT THE HIGHER FREQUENCIES AT NIGHT )N GENERAL NIGHTTIME NOISE WILL BE GREATER THAN DAYTIME NOISE FOR SKYWAVE ILLUMINATION OF A SELECTED RANGE 4HIS IS EVIDENT IN &IGURE RECORDED AT TIME ZONE 54 4HE GENERAL TRENDS OF ATMOSPHERIC NOISE IN OTHER SEASONS ARE SIMILAR TO THOSE IN WINTER (OWEVER THERE CAN BE LARGE DIFFERENCES IN LEVELS AT OTHER LOCATIONS ON THE %ARTH &OR MORE DETAILED ANALYSIS AND SYSTEM OPTIMIZATION IT IS NO LONGER ACCEPTABLE TO TREAT THE NOISE AS AN ISOTROPIC FIELD 3TRONG AZIMUTH AND ELEVATION ANGLE DEPENDENCE OF THE SFERICS FIELD IS INEVITABLE EXAMINATION OF MAPS PRODUCED BY SATELLITES INDI CATES THAT TROPICAL RAIN FORESTS AND OTHER REGIONS OF CONCENTRATED THUNDERSTORM ACTIVITY ARE MAJOR SOURCES OF NOISE AND THESE REGIONS ARE CONNECTED WITH A GIVEN RADAR SITE BY THE CONSTRAINTS OF SKYWAVE PROPAGATION #OLEMAN COMBINED THE THUNDERSTORM ACTIVITY MAPS OF +OTAKI WITH NUMERICAL RAY TRACING AND MODELED ANTENNA PATTERNS TO DEMONSTRATE THAT THE DIRECTIONAL VARIABILITY OF NOISE COUPLED WITH THE DIRECTIONAL CHARACTERISTICS OF DIFFERENT ANTENNAS CAN LEAD TO MARKED CHANGES IN NOISE OUTCOMES AND HENCE IN OPTIMAL RADAR DESIGN !NOTHER IMPORTANT ISSUE IS THE BEHAVIOR OF THE EXTERNAL NOISE FIELD AS A FUNCTION OF TIME THAT IS WITHIN THE COHERENT INTEGRATION INTERVAL SINCE THIS IMPACTS STRONGLY ON SIGNAL PROCESSING FOR INTERFERENCE REJECTION /THER EFFECTS THAT CAN INFLUENCE RADAR PERFORMANCE ARE SOMETIMES MISTAKEN FOR THE ADDITIVE NOISE DISCUSSED ABOVE /NE OF
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&)'52% $IURNAL VARIATION OF (& NOISE MEASURED IN D"7(Z AT LATITUDE 3 LONGITUDE % .OVEMBER
THESE IS THE SPREAD DOPPLER CLUTTER DISCUSSED IN 3ECTION SOMETIMES REFERRED TO AS ACTIVE OR MULTIPLICATIVE NOISE 4HE OCCURRENCE OF THIS TYPE OF CLUTTER IS GREATER AT NIGHT AND IS MUCH MORE PREVALENT IN THE AURORAL ZONES AND AROUND THE MAGNETIC EQUATOR
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HAVE BEEN SHOWN TO SUPPORT SPATIALLY COHERENT PROCESSING (ENCE THE RECEIVING ARRAY APERTURES OF SKYWAVE RADARS MAY RANGE FROM ^ KM FOR SYSTEMS CONCERNED ONLY WITH AIRCRAFT AND BALLISTIC MISSILES TO MORE THAN KM IN SYSTEMS DESIGNED FOR SHIP DETECTION AND TRACKING 4AKING KM AS A RECEIVE APERTURE CONVENTIONAL BEAMWIDTH AT -(Z IS ^ SO SIMULTANEOUS BEAMS SPAN ^ WHICH SETS THE REQUIRED TRANSMIT APERTURE IN THIS EXAMPLE AT n M DEPENDING ON THE VARIATION IN GAIN THAT CAN BE TOLERATED ACROSS THE SET OF RECEIVE BEAMS 4HE MOST VERSATILE BEAMFORM ING TECHNIQUES RELY ON HAVING A RECEIVER FOR EACH ARRAY ELEMENT BUT AS THE NUMBER OF ELEMENTS MAY APPROACH THE COST OF SUCH A SOLUTION MAY BE PROHIBITIVE )T IS THEN ADVANTAGEOUS TO CONFIGURE THE ARRAY ELEMENTS INTO SUBARRAYS POSSIBLY OVERLAPPED OR SHARING ELEMENTS WITH ONE RECEIVER PER SUBARRAY &OR INSTANCE THE ORIGINAL *INDALEE RADAR GROUPED ELEMENTS SPANNING KM INTO OVERLAPPED SUBARRAYS 7HILE THIS CONSTRAINS THE RESULTANT BEAMS TO LIE WITHIN THE SUBARRAY ANGULAR RESPONSE PATTERN IT HAS THE ADVANTAGE OF REDUCING RECEIVER DYNAMIC RANGE REQUIREMENTS BY SUPPRESSING INTERFERENCE FROM OTHER ANGULAR SECTORS ,INEAR ARRAYS PROVIDE THE MOST ECONOMICAL ROUTE TO HIGH SPATIAL RESOLUTION IN AZI MUTH BUT THE EXISTENCE OF MULTIPLE PATHS FOR SIGNAL RECEPTION TYPICALLY VIA THE % & AND & LAYERS HAS MOTIVATED SOME DESIGNERS TO EMPLOY TWO DIMENSIONAL ARRAYS HORI ZONTALLY OR AT GREATER COST VERTICALLY DEPLOYED 4HE RELATIVE MERITS OF THESE DESIGNS CAN BE MEASURED ONLY WITH RESPECT TO THE PRIORITIES ACCORDED TO THE VARIOUS MISSIONS ASSIGNED TO A GIVEN RADAR 4HE CHOICE OF RECEIVING ANTENNA ELEMENT HAS TRADITIONALLY BEEN BASED ON THE PRECEPT THAT AT (& THE EXTERNAL NOISE ALMOST ALWAYS EXCEEDS THE INTERNAL NOISE BY A SUBSTANTIAL MARGIN /N THIS LOGIC IMPROVING ANTENNA EFFICIENCY INCREASES THE OUTPUT EXTERNAL NOISE AND INTERFERENCE AMPLITUDE AT THE SAME RATE THAT IT IMPROVES THE WANTED SIGNALS THEREBY GAINING NO ADVANTAGE IN 3.2 3ELECTION OF ANTENNA ELEMENT TYPE SUCH AS MONOPOLES DIPOLES "EVERAGE ANTENNAS PHASED ENDFIRE ROWS OF MONOPOLES OR BICONICAL ANTEN NAS FOR INSTANCE CAN THEN BE BASED ON FREQUENCY RESPONSE OVER THE ANTICIPATED BAND OF INTEREST AND SUITABILITY FOR THE CHOSEN ARRAY GEOMETRY AS WELL AS TERRAIN CONSTRAINTS SUCH AS THE SOIL CONDUCTIVITY 3TUDIES HAVE SHOWN THAT THIS ARGUMENT IS NOT NECES SARILY VALID WHEN ADVANCED ADAPTIVE SPATIAL AND TEMPORAL PROCESSING TECHNIQUES ARE EMPLOYED BECAUSE INTERFERENCE REJECTION EFFICACY IS ENHANCED BY HIGHER INTERFERENCE TO INTERNAL NOISE RATIOS )T HAS BEEN WIDELY ARGUED THAT THE INEVITABILITY OF TIME VARYING POLARIZATION TRANS FORMATION IN THE COURSE OF IONOSPHERIC PROPAGATION GREATLY REDUCES THE POSSIBLE UTILITY OF BEING ABLE TO MEASURE THE POLARIZATION STATE OF THE SIGNALS ARRIVING AT THE RECEIVING ARRAY 4HIS IS AN OPEN QUESTION AT THIS TIME THOUGH EXPERIMENTS AIMED AT ASSESSING SKYWAVE RADAR POLARIMETRY ARE UNDERWAY 2ECEIVERS 4HERE ARE MANY DEMANDS ON THE RECEIVERS FOR /4( RADAR INCLUDING HIGH DYNAMIC RANGE LINEARITY WIDE BANDWIDTH AND UNIFORMITY BETWEEN RECEIVERS WHEN USED IN MULTIRECEIVER SYSTEMS &OR MOST CIVIL AIRCRAFT AND SHIPS TARGET RADAR CROSS SECTION 2#3 AT (& IS ROUGHLY OF THE SAME ORDER AS THE MICROWAVE 2#3 THAT IS ^n D"SM FOR AIRCRAFT AND ^n D"SM FOR SHIPS BUT THE RANGE IS n TIMES GREATER SO THE EXTRA LOSS ASSOCIATED WITH 2n IS IN THE RANGE n D" -OREOVER EACH TARGET ECHO IS IMMERSED IN CLUTTER FROM THE ILLUMINATED FOOTPRINT WHICH MAY HAVE AN AREA OF MANY THOUSANDS OF SQUARE KILOMETERS &URTHER THE (& SIGNAL ENVIRONMENT INCLUDES ONE WAY TRANSMISSIONS FROM POWERFUL RADIO STATIONS AROUND THE WORLD AS DISCUSSED IN THE PREVIOUS SECTION )MPERFECTIONS IN THE RECEIVER RESULT IN SOME OF THIS
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NOISE AND CLUTTER ENERGY BEING SUPERIMPOSED ON THE WANTED RADAR ECHOES EITHER ADDI TIVELY OR MULTIPLICATIVELY (ENCE CAREFUL ATTENTION TO RECEIVER DESIGN IS IMPERATIVE IF THE RADAR DESIGNER WISHES TO AVOID SELF INFLICTED PERFORMANCE LIMITATIONS !TTEMPTS TO REDUCE CONTAMINATION FROM EXTERNAL BROADCAST SIGNALS BY INSERTING NAR ROW BAND FILTERS AT THE RECEIVER FRONT END SACRIFICE THE HIGH AGILITY THAT IS NEEDED WHEN THE RADAR IS CHANGING FREQUENCY TYPICALLY BY SEVERAL -(Z SECOND BY SECOND AS IT JUMPS BETWEEN TASKS 4HERE ARE ALSO PENALTIES FROM I FILTER SWITCHING TIME II SET TLING TIME III DISTORTION CAUSED BY GROUP DELAY DISPERSION AND IV REDUCED RELIABILITY WHEN THERE ARE HUNDREDS OF RECEIVERS &URTHER EACH CHANNEL WILL NEED TO ACCOUNT FOR THE GAIN AND PHASE VARIATION FOR EACH FILTER INCREASING THE OVERHEADS ON BAND SWITCH ING )T IS BETTER TO ZERO IN ON THE BANDWIDTH OF INTEREST BY NONSWITCHED FILTERS LATER IN THE RECEIVER USING A VARIABLE FREQUENCY LOCAL OSCILLATOR TO POSITION THE DESIRED SUBBANDS OVER THE SELECTIVE FILTERS /F COURSE THE SWITCHED ,/ CAN ALSO SUFFER FROM IMPERFEC TIONS BUT ONLY ONE LOCAL OSCILLATOR IS NEEDED AS OPPOSED TO HUNDREDS OF RECEIVERS 7HICHEVER DESIGN PATH IS FOLLOWED THE DEMANDS ON RECEIVER LINEARITY AND SPURIOUS FREE DYNAMIC RANGE ARE EXTREME 4HERE ARE FIVE DOMINANT MECHANISMS KNOWN TO DEGRADE (& RADAR RECEIVERS THE NONLINEAR PROCESSES OF ANALOG TO DIGITAL CONVERSION OUT OF BAND INTER MODULATION )-$ CROSS MODULATION AND IN BAND INTER MODULATION AND THE PSEUDO LINEAR PRO CESS OF RECIPROCAL MIXING !NALOG TO DIGITAL #ONVERSION !NALOG TO DIGITAL CONVERSION INVOLVES TWO STAGES SAMPLING AND QUANTIZATIONEACH WITH POTENTIAL FOR DISTORTING THE RECEIVED SIGNAL 4HE RECEIVED SIGNALS MUST BE SAMPLED WITH SUFFICIENT PRECISION AND UNIFORMITY TO PRESERVE THE INHERENT SPECTRAL CONTENT ACROSS THE DYNAMIC RANGE SPANNED BY THE SIG NAL COMPONENTSTARGET ECHOES CLUTTER AND EXTERNAL NOISEAFTER TAKING ACCOUNT OF THE ARTIFACTS INTRODUCED BY QUANTIZATION AND TIMING JITTER ESPECIALLY IN MULTI RECEIVER SYSTEMS /UT OF BAND )NTER MODULATION /UT OF BAND )-$ ARISES FROM NONLINEAR MIXING OF TWO OR MORE STRONG INTERFERERS SUCH AS BROADCAST STATIONS WHERE THE POWERFUL SIGNALS ENTER THE FRONT END OF THE RECEIVING SYSTEM AND GENERATE )-$ PRODUCTS WITHIN THE RADAR SIGNAL BANDWIDTH BEFORE THEY THE ORIGINAL INTERFERERS ARE REJECTED BY SELEC TIVE FILTERING #ROSS MODULATION #ROSS MODULATION INVOLVES NONLINEAR MIXING OF A STRONG INTERFERER WITH THE RECEIVED RADAR ECHOES TRANSFERRING THE INTERFERER MODULATION ONTO THE RADAR SIGNAL )N BAND )NTER MODULATION ! SINGLE RESOLUTION CELL IN THE RADAR FOOTPRINT MAY HAVE AN AREA OF n SQUARE KILOMETERS AND THERE MAY BE HUNDREDS OF CELLS IN THE RADAR FOOTPRINT SO USING REPRESENTATIVE VALUES OF TARGET 2#3 &IGURE AND SURFACE SCATTERING COEFFICIENT Sn &IGURE THE SIGNAL TO CLUTTER RATIO IN AN /4( RADAR RECEIVER MAY BE AS LOW AS n D" FOR SYSTEMS EMPLOYING &- #7 WAVEFORMS .ONLINEARITY AT ANY STAGE HAS THE POTENTIAL TO MASK TARGET ECHOES BY MIXING THE CLUTTER ECHO WITH ITSELF GENERATING )-$ PRODUCTS THAT EXTEND BEYOND THE INTRINSIC DOPPLER BAND OF THE CLUTTER 5NLIKE THE OUT OF BAND )-$ IN BAND )-$ CAN OCCUR AT ANY STAGE THROUGH THE RECEIVER AND HENCE EVEN SECOND ORDER PRODUCTS MAY CAUSE PROBLEMS
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2ECIPROCAL -IXING !NALOG RECEIVERS OF HETERODYNE DESIGN GENERALLY INVOLVE A NUMBER OF LOCAL OSCILLATORS FOR SIGNAL MIXING AND PERHAPS A WAVEFORM GENERATOR USED TO IMPLEMENT A MATCHED FILTER 4HESE ANCILLARY SOURCES ARE INEVITABLY OF FINITE SPECTRAL PURITY WITH A PHASE NOISE FLOOR THAT MAY EXTEND OVER A WIDE BAND OF FREQUENCIES ALBEIT AT A VERY LOW LEVEL !NY POWERFUL INTERFERING SIGNALS ENTERING THE FIRST MIXER STAGE OF THE RECEIVER WILL COMBINE WITH THE PHASE NOISE FLOOR AND POTENTIALLY GENERATE PRODUCTS IN THE RADAR SIGNAL BANDWIDTH )N THE CASE OF DIGITAL RECEIVERS SAMPLING NOISE WILL HAVE AN EQUIVALENT EFFECT $IGITAL 2ECEIVER 4ECHNOLOGY (& RECEIVERS CAN EMPLOY DIRECT DIGITAL CONVER SION AT 2& AVOIDING SOME OF THE LIMITATIONS OF ANALOG DEVICES )SSUES SUCH AS RECIP ROCAL MIXING ARE STILL PRESENT THOUGH IN SLIGHTLY MODIFIED FORM #OMPARISONS WITH ANALOG RECEIVERS HAVE DEMONSTRATED THAT LITTLE OR NO PENALTY IS INCURRED WITH SUCH DESIGNS IF A BAND PRESELECTOR FILTER IS INSTALLED AT THE FRONT END /N THE OTHER HAND THERE ARE MAJOR ADVANTAGES TO BE HAD SUCH AS SIMULTANEOUS RECEPTION OF SEVERAL RADAR SIGNALS ON DIFFERENT FREQUENCIES SO A SINGLE RECEIVER CAN SERVICE MORE THAN ONE RADAR TRANSMITTER #ALIBRATION 4HE CONVENTIONAL BEAMFORMING PROCESS IN AN IDEAL MULTI CHANNEL RECEIVING SYSTEM SHOULD DELIVER A SINGLE OUTPUT ASSIGNED TO THE CORRECT DIRECTION FOR A PLANE WAVE INCIDENT ON THE ANTENNA ARRAY )NEVITABLE VARIATIONS IN GAIN AND PHASE ARIS ING FROM SMALL ANTENNA POSITIONING ERRORS GROUND SCREEN INHOMOGENEITIES DIFFERENCES BETWEEN PREAMPLIFIERS MUTUAL COUPLING CABLE MISMATCH THERMAL AND OTHER VARIATIONS OF CABLE CHARACTERISTICS AND ALL THE ANALOG STAGES OF THE RECEIVER RESULT IN DISTORTION OF THE BEAM SHAPE AND HENCE DEGRADED RADAR RESOLUTION ELEVATED SIDELOBES AND HENCE VULNERABILITY TO CLUTTER AND INTERFERENCE POINTING ERRORS AND HENCE INCREASED TRACKING ERRORS AND INTERFERER WAVEFRONT GEOMETRY PERTURBATIONS AND HENCE WASTED DEGREES OF FREEDOM IN ADAPTIVE BEAMFORMING 4O MITIGATE THESE EFFECTS (& RADARS MUST EMPLOY SOPHISTICATED CALIBRATION SCHEMES 3EVERAL APPROACHES HAVE BEEN TRIED u 5SE OF AN EXTERNAL RADIATING ELEMENT IN THE NEAR FIELD IN FRONT OF THE ARRAY 4HIS SCHEME IS VULNERABLE TO VARIATIONS IN THE SOIL ELECTRICAL AND MAGNETIC PROPERTIES SUCH AS THOSE RESULTING FROM SEASONAL CHANGES IN SOIL MOISTURE LEVELS u )NJECTION OF A CALIBRATION WAVEFORM AT THE ANTENNAS OR AT THE RECEIVER INPUTS BEHIND THE ANTENNA ARRAY BY MEANS OF AN INDEPENDENT hOPEN LOOPv SIGNAL FEEDER NETWORK 4HIS SCHEME CANNOT CALIBRATE THE ANTENNAS AND INITIAL FEEDERS IT APPLIES ONLY FROM THE POINT WHERE THE SIGNAL IS INJECTED u 5SE OF A DISTANT RADIATING SOURCE THAT ILLUMINATES THE ARRAY VIA SKYWAVE OR EVEN A DISCRETE TARGET ECHO 4HIS SCHEME PRESUMES THAT THE ARRIVING SIGNAL WAVEFRONTS ARE ESSENTIALLY PLANAR OR SMOOTH AFTER IONOSPHERIC REFLECTION WHICH IS NOT ALWAYS THE CASE u *OINT ANALYSIS OF MULTIPLE DISCRETE METEOR ECHOES 4HIS SCHEME IS APPEALING BUT RELIES ON HAVING ENOUGH IDENTIFIABLE DISCRETE ECHOES &OR A ELEMENT ARRAY IT MAY BE GENERALLY VIABLE BUT LESS FREQUENTLY FOR A ELEMENT ARRAY u 2ECEIVER AND PLANE WAVE REJECTION TESTS APPLIED TO INJECTED BROADBAND NOISE 4HIS APPROACH PROVIDES USEFUL METRICS OF CALIBRATION PERFORMANCE AND RELATIVE PERFORMANCE BUT DOES SO ONLY DOWNSTREAM FROM THE RECEIVER INPUTS AS WITH II ABOVE
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%ACH OF THESE APPROACHES HAS ITS ADVANTAGES AND DRAWBACKS IN THE CONTEXT OF CON VENTIONAL &OURIER BEAMFORMING 7HEN ADAPTIVE PROCESSING TECHNIQUES ARE BEING EMPLOYED IT IS ALSO IMPORTANT THAT THE EFFECTIVE LOOK DIRECTION MATCHES THE ARRAY STEER ING VECTOR OR ELSE CANCELLATION OF THE WANTED SIGNAL WILL OCCUR
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-- Ê Ê/, 3IGNAL !NALYSIS AND 4ARGET $ETECTION 4HE OBJECTIVE OF SIGNAL PROCESSING IS TO DETECT AND CHARACTERIZE ECHOES FROM SCATTERERS OF INTEREST EITHER DISCRETE AIRCRAFT OR SHIPS OR EXTENDED THE SEA SURFACE AND THIS IS CUSTOMARILY ACHIEVED BY DECOMPOS ING THE TIME SERIES DATA FROM THE RECEIVERS INTO THE NATURAL RADAR DOMAIN DIMENSIONS OF GROUP RANGE BASED ON TIME DELAY DIRECTION OF ARRIVAL BEAM SPACE AND DOPPLER FREQUENCY HOPEFULLY SEPARATING THE ECHOES OF INTEREST FROM UNWANTED CLUTTER AND NOISE 4HE STANDARD TOOL FOR THIS DECOMPOSITION IS THE &&4 AT LEAST IN OPERATIONAL SKYWAVE RADARS IN PART BECAUSE IT IS COMPUTATIONALLY QUITE FEASIBLE TO ANALYZE THE INCOMING SIG NAL INTO TYPICALLY ^ RANGE BINS n BEAMS AND ^ DOPPLER CELLS IN PERHAPS ^ SECONDS USING GENERAL PURPOSE COMPUTING HARDWARE 4HUS THE &&4 OR $&4 FOR SHORT TRANSFORMS IS COMMONLY USED FOR THE THREE DIMENSIONS OF ANALYSIS !LTERNATIVE ANALYSIS TECHNIQUES HAVE BEEN IMPLEMENTED IN SOME SYSTEMS FOR APPLICATIONS SUCH AS DETECTION OF ACCELERATING TARGETS n THE DETECTION OF HARMONICALLY RELATED SIGNALS AND WHEN HIGH DOPPLER RESOLUTION IS REQUIRED BUT ONLY SHORT COHERENT INTEGRATION TIMES CAN BE ACCOMMODATED IN THE RADAR TIMELINE 3OME IMPORTANT PROCESSOR DESIGN CONSIDERATIONS EMERGE FROM AN ANALYSIS OF HIGH QUALITY (& RADAR DATA AS ILLUSTRATED BY THE FOLLOWING EXAMPLE &IGURE SHOWS A SEQUENCE OF SEA CLUTTER DOPPLER SPECTRA FROM THE !.&03 RADAR PRE SENTED AS RECEIVED POWER AMPLITUDE VERSUS DOPPLER FREQUENCY 4O GENERATE THIS PLOT POWER SPECTRA FROM A SINGLE RANGE BIN WERE COMPUTED FROM NONOVERLAPPING TIME INTERVALS AND THEN GROUPED INTO BLOCKS OF FIVE AND AVERAGED NONCOHERENTLY 4HE WAVEFORM REPETITION FREQUENCY 72& IN THIS CASE WAS (Z WITH A COHERENT INTE GRATION TIME OF S RESULTING IN A NOMINAL DOPPLER FILTER BANDWIDTH OF (Z .OISE . SAMPLES WERE TAKEN FROM THE MAXIMUM DOPPLER BIN TARGET SAMPLES 4 ON THE TARGET PEAK AND "RAGG LINE AMPLITUDES ! AND 2 FROM THE CLUTTER PEAKS CORRESPONDING TO THE APPROACHING AND RECEDING RESONANT OCEAN WAVES AS DESCRIBED IN 3ECTION . 4 ! AND 2 ARE PLOTTED IN &IGURE A 4HE SUB CLUTTER VIS IBILITY 3#6 WIDELY USED IN (& RADAR AS A MEASURE OF SENSITIVITY AND DEFINED AS 2. IS D" IN THIS EXAMPLE )N MICROWAVE RADAR THE TERM SUB CLUTTER VISIBILITY IS SENSIBLY DEFINED AS THE RATIO BY WHICH THE TARGET ECHO POWER MAY BE WEAKER THAN THE CLUTTER POWER AND STILL BE DETECTED )N THE (& RADAR LITERATURE HISTORICALLY THE DETECTION THRESHOLD COMPONENT HAS NOT BEEN INCLUDED SO 3#6 IS ESSENTIALLY THE CLUTTER TO NOISE RATIO &OR A REPRESENTATIVE EFFECTIVE CLUTTER 2#3 OF D"SM PER RESOLUTION CELL THE TARGET 2#3 CAN BE ESTIMATED AS
2#3 2D" 4D" D"SM
AND SUPPOSING THAT THE 3.2 REQUIRED FOR REGISTERING A DETECTION IS D" THE MINIMUM DETECTABLE 2#3 -$2#3 IN THIS EXAMPLE CAN BE COMPUTED AS
-$2#3 2 . D"SM
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&)'52% .ONCOHERENTLY AVERAGED POWER SPECTRA FROM THREE CONTIGUOUS TIME INTERVALS PLOTTED WITH AN OFFSET FOR CLARITY 4HE TARGET LIES WELL OUTSIDE THE CLUTTER REGION WHERE THE "RAGG LINES ARE CLEARLY VISIBLE SO THE SIGNAL TO NOISE RATIO NOT THE SIGNAL TO CLUTTER RATIO DETERMINES DETECTABILITY .OTE THE ^ D" VARIATION IN TARGET ECHO STRENGTH DUE TO CHANGES IN THE IONOSPHERE OVER SECONDS
4HIS IS A QUITE LOW 2#3 AT (& INDICATING THAT WHEN CONDITIONS ARE FAVORABLE VERY SMALL TARGETS ARE POTENTIALLY DETECTABLE 4HE EXPERIMENTAL DEMONSTRATION THAT ON OCCASION THE ENVIRONMENT SUPPORTS ^ D" SUB CLUTTER VISIBILITY OBLIGES THE RADAR DESIGNER TO ENSURE THAT THE RECEIVING SYSTEM AND SIGNAL PROCESSING OPERATIONS DO NOT UNWITTINGLY DEGRADE THE RADAR PERFOR MANCE 3OME APPROPRIATE DESIGN CONSIDERATIONS ARE u !N ANALOG TO DIGITAL !$ CONVERTER OF AT LEAST BIT PRECISION IS IN ORDER FOR (& RADARS WITH HIGH POWER GAIN PRODUCTS 0AV'4 '2 u 2ECEIVING APERTURES WAVEFORM BANDWIDTHS AND COHERENT INTEGRATION TIMES SHOULD PROVIDE ENOUGH SAMPLES AND HIGH ENOUGH SAMPLING RATES TO RESOLVE UNAMBIGUOUSLY DISTINCT FEATURES OF THE CLUTTER SPECTRUM WHERE SUCH RESOLUTION IMPACTS ON TARGET DETECTABILITY OR THE EXTRACTION OF IMPORTANT INFORMATION u 4HE WINDOW FUNCTIONS USED TO CONTROL LEAKAGE DURING CONVENTIONAL SPECTRUM ANALY SIS MUST HAVE SUFFICIENTLY LOW SIDELOBES WHEN TRANSFORMS ARE TO BE APPLIED DIRECTLY TO HIGH DYNAMIC RANGE DATA 4HE BASIC STEPS OF RANGE AZIMUTH AND DOPPLER ANALYSIS ARE NOT THE ONLY STAGES OF SIGNAL PROCESSING !S EXPLAINED IN 3ECTION (& SKYWAVE RADAR SIGNALS ARE SUBJECT
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&)'52% A 4EMPORAL FADING AND B DISTRIBUTION PROPERTIES OF THE TARGET CLUTTER PEAKS AND NOISE FEATURES IN THE DOPPLER SPECTRUM OF &IGURE COMPUTED FROM AN EXTENDED DATA SEQUENCE
TO VARIOUS FORMS OF CONTAMINATION AND DISTORTION MANY IONOSPHERICALLY INDUCED SO METHODS TO DEAL WITH THESE HAVE LONG BEEN PART OF THE RADAR SIGNAL PROCESSING TOOLBOX -OREOVER THE NEED TO DEAL WITH THESE DELETERIOUS EFFECTS HAS BECOME MORE PRESSING AS THE ACHIEVABLE DYNAMIC RANGE OF RECEIVING SYSTEMS HAS INCREASED REVEALING A GREATER VARIETY OF SIGNAL DISTORTION MECHANISMS (ENCE IN ADDITION TO PER FORMING THE BASIC DECOMPOSITION DESCRIBED ABOVE AND CALIBRATING THE RECEIVER CHAIN FOR THE CURRENT WAVEFORM THE SIGNAL PROCESSING STAGE MAY BE TASKED WITH A NUMBER OF SIGNAL CONDITIONING OPERATIONS 3IGNAL CONDITIONING HERE REFERS TO FILTERING AND SCALING PROCESSES AIMED AT REMOVING CONTAMINATION AND DISTORTION THAT IF LEFT ON THE SIGNAL WOULD DEGRADE THE RESULTS OF THE PRIMARY PROCESSING OPERATIONS SUCH AS DOPPLER ANALY SIS AND BE MORE DIFFICULT TO REMOVE AFTER THAT PRIMARY PROCESSING 4YPICALLY THERE ARE OPTIONAL PROCESSING ALGORITHMS AVAILABLE TO REMOVE IMPULSIVE NOISE ORIGINATING FROM LIGHTNING TRANSIENT ECHOES FROM METEORS AND FIELD ALIGNED IRREGULARITIES IN THE IONO SPHERE STRONG DIRECTIONAL INTERFERENCE AND CLUTTER ECHOES FROM BEYOND THE MAXIMUM UNAMBIGUOUS RANGE )N ADDITION THE RADAR DESIGNER NOW HAS THE OPTION TO COMPENSATE FOR SIGNAL PATH FLUCTUATIONS IN BOTH SPATIAL AND TEMPORAL DOMAINS WITHIN LIMITS BY EMPLOYING PROCESSING SCHEMES THAT DIAGNOSE THE NATURE OF THE SIGNAL CORRUPTION ON A FIRST PASS AND THEN REPROCESS WITH ALGORITHMS THAT COMPENSATE FOR THE OBSERVED CORRUPT ING MECHANISMS 4HE SIGNAL PROCESSING STAGE MAY ALSO BE TASKED WITH EXTRACTING ENVIRONMENTAL INFORMATION FROM THE RADAR ECHOES AS MENTIONED IN 3ECTION 4HIS INCLUDES REMOTE SENSING OF OCEAN WINDS AND SEA STATE LAND SEA MAPPING FOR COAST LINE RECOGNITION TO ASSIST WITH COORDINATE REGISTRATION MEASUREMENTS OF THE IONOSPHERE FOR ASSIMILATION INTO IONOSPHERIC MODELS EXTRACTION OF ECHOES FROM REMOTE BEACONS DEPLOYED TO ASSIST WITH COORDINATE REGISTRATION AND CALIBRATION AND MANY OTHER BYPROD UCTS OF THE BASIC DETECTION MISSION
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!T PRESENT THE MOST POWERFUL TOOLS FOR DEALING WITH ADDITIVE INTERFERENCE AS WELL AS SOME CLASSES OF SPREAD DOPPLER CLUTTER ARE THE TECHNIQUES OF ADAPTIVE PROCESSING /RIGINALLY THESE TECHNIQUES WERE DEVELOPED FOR AIRBORNE MICROWAVE RADARS BUT THEY HAVE BEEN SHOWN TO HAVE WIDE APPLICABILITY IN (& RADARn 4HE PRIMARY DOMAIN WHERE MAJOR PERFORMANCE GAINS ARE REALIZED IS SPATIAL ANALYSIS THAT IS BEAMFORMING )N THIS CONTEXT A hSNAPSHOTv OF THE OUTPUTS FROM THE ALL THE RECEIVERS ACROSS THE ARRAY IS TAKEN AND USED TO COMPUTE A SET OF COMPLEX VALUED WEIGHTS FOR EACH DESIRED BEAM DIRECTION THESE ARE THEN APPLIED TO THE RECEIVER OUTPUTS BEFORE SUMMING TO FORM THE ADAPTED BEAMS 4HE REASON FOR THE EFFICACY OF ADAPTIVITY HERE IS THAT AS REMARKED PREVIOUSLY (& RADARS ARE ALMOST ALWAYS EXTERNAL NOISEnLIMITED 4HE AZIMUTHAL DIS TRIBUTION OF NOISE FROM THUNDERSTORMS INDUSTRIAL SITES AND OTHER SOURCES IS FAR FROM UNIFORMLY DISTRIBUTED &URTHERMORE EVEN SO CALLED CLEAR CHANNELS SELECTED FOR RADAR OPERATIONS ARE CONTAMINATED WITH DIRECTIONAL NOISE OF NATURAL OR INDUSTRIAL ORIGIN ALBEIT AT A MUCH LOWER LEVEL #ONVENTIONAL &&4 TYPE BEAMFORMING MAKES NO ALLOWANCE FOR THIS SO A LOT OF NOISE ENERGY LEAKS INTO EACH COMPUTED BEAM THROUGH THOSE OF ITS REGU LARLY SPACED SIDELOBES THAT ARE POINTING TOWARD STRONG NOISE SOURCES 3PATIALLY ADAP TIVE PROCESSING 3!0 REDUCES THIS PROBLEM BY ADJUSTING THE AMPLITUDE AND PHASE OF THE SAMPLED RECEIVER OUTPUTS IN SUCH A WAY AS TO MINIMIZE THE INTEGRATED NOISE POWER LEAKAGE WHILE PRESERVING THE GAINSENSITIVITY OF THE BEAM BEING SYNTHESIZED &IGURE COMPARES CONVENTIONAL PROCESSING AND 3!0 APPLIED TO THE SAME BLOCK OF RADAR DATA ! REDUCTION OF SOME D" IS ACHIEVED IN THIS EXAMPLE WHERE NOISE NOT CLUTTER IS THE PROBLEM 4HE PATTERN HERE HAS ADAPTED TO MINIMIZE THE TOTAL ENERGY COLLECTED IN THE DOPPLER BANDS ;n n= (Z AND ; = (Z WHILST MAINTAINING THE ARRAY
&)'52% #OMPARISON OF DOPPLER SPECTRA ESTIMATED BY I CONVENTIONAL BEAM FORMING #"& AND II SPATIALLY ADAPTIVE PROCESSING DESIGNED TO MINIMIZE ENERGY OUT SIDE THE LOW DOPPLER CLUTTER 4HE NOISE AND ANY FAST CLUTTER HAS BEEN REDUCED BY ^ D" WHICH IMPROVES DETECTABILITY OF FAST TARGETS NOTE THAT THE SEA CLUTTER SPECTRUM CHANGES AS A CONSEQUENCE OF THE NEW ARRAY PATTERN IE THE CLUTTER SPECTRUM DOES NOT NECESSARILY REPRESENT THE CLUTTER SPECTRUM FROM THE CELL OF INTEREST
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RESPONSE IN THE SPECIFIED DIRECTION /F COURSE DEPENDING ON THE ANGULAR DISTRIBUTION OF THE NOISE SOURCES THE ARRAY RESPONSE PATTERN MAY HAVE VERY HIGH SIDELOBES BUT THEY WILL LIE IN DIRECTIONS WHERE THE NOISE LEVELS ARE LOWEST 4HE SAME MAY NOT BE TRUE OF THE CLUTTER THAT OCCUPIES THE LOW DOPPLER BAND ;n = (Z WHICH HAS NOT BEEN USED TO GUIDE THE ADAPTATION OF THE ARRAY RESPONSE )NDEED THE RESULTANT CLUTTER SPECTRUM MAY WELL HAVE CHARACTERISTICS VERY DIFFERENT FROM THOSE FOUND IN THE STEER DIRECTION 4HIS IS THE CASE IN THE EXAMPLE SHOWN IN &IGURE WHERE THE "RAGG LINE RATIO HAS CHANGED DRAMATICALLY AND EVEN REVERSED IN SIGN )N THE EXAMPLE JUST GIVEN THE 3!0 WEIGHTS WERE KEPT FIXED FOR THE ENTIRE #)4 7HEN THE EXTERNAL NOISE FIELD IS CHANGING RAPIDLY AS HAPPENS WHEN THE IONOSPHERE IS DISTURBED IT IS NECESSARY TO ADAPT THE WEIGHTS DURING THE #)4 TO MAINTAIN EFFECTIVE REJECTION OF THE NOISE AS ITS AZIMUTHAL DISTRIBUTION CHANGES EVEN FOR SHORT ^ S DWELLS AS USED FOR AIRCRAFT DETECTION 4HIS IS THE PROVINCE OF SPACE TIME ADAPTIVE PROCESSING OR 34!0 (ERE THE DATA USED TO DETERMINE THE WEIGHTS REQUIRES NOT JUST A SINGLE SNAP SHOT OR AVERAGE OF SNAPSHOTS BUT A NUMBER OF SNAPSHOTS OF THE ARRAY OUTPUTS THIS BLOCK OF DATA IS THEN USED TO CONSTRUCT WEIGHTS THAT ARE APPLIED TO THE BLOCK OF DATA BEFORE BEAMFORMING AND DOPPLER ANALYSIS 34!0 IS OF PARTICULAR IMPORTANCE TO SHIP DETECTION WHERE THE EXTERNAL NOISE FIELD ALMOST INVARIABLY CHANGES SUBSTANTIALLY DURING THE LONG #)4 4HE COMPLEXITY OF 34!0 IN THIS CONTEXT ARISES FROM THE FACT THAT EACH TIME THE WEIGHTS ARE CHANGED ACCORDING TO THE 3!0 RULES THE MAIN BEAM EXPERIENCES A PHASE SHIFT EVEN THOUGH ITS AMPLITUDE GAINSENSITIVITY IS PRESERVED 4HUS OVER THE ENTIRE #)4 A SEQUENCE OF PHASE SHIFTS IS APPLIED THAT IS A MODULATION WHICH IS IMPOSED ON THE RECEIVED SIGNAL !S A CONSEQUENCE THE STRONG CLUTTER ECHOES ARE SPREAD IN DOPPLER MASKING TARGETS 4O OVERCOME THIS PROBLEM !BRAMOVICH ET AL DEVELOPED A TECH NIQUE KNOWN AS THE METHOD OF STOCHASTIC CONSTRAINTS WHICH USES DIFFERENT RULES FOR WEIGHT ADJUSTMENT PRESERVING NOT ONLY THE GAIN BUT ALSO TO A GOOD APPROXIMATION THE PHASE OF THE CLUTTER RECEIVED VIA THE MAIN BEAM RESPONSE !LTHOUGH THESE MODERN SPATIO TEMPORAL ADAPTIVE PROCESSING TECHNIQUES HAVE BEEN PROVEN TO BE HIGHLY EFFECTIVE THE COMPUTATIONAL AND DATA REQUIREMENTS ARE SO HIGH THAT MOST OF THEM CANNOT BE IMPLEMENTED IN THEIR MOST POWERFUL FORMS FOR REAL TIME PROCESSING )NSTEAD SIMPLIFIED ALGORITHMS WITH IMPRESSIVE BUT NONETHELESS SUBOPTI MUM PERFORMANCE ARE EMPLOYED )N VIEW OF THE NUMBER OF SIMULTANEOUS SPATIAL CELLS TO BE CONSIDERED DETECTION IS GENERALLY BASED ON A CONSTANT FALSE ALARM RATE #&!2 ALGORITHM ADAPTED TO THE PARTICULAR CLUTTER ENVIRONMENT )N MOST IMPLEMENTATIONS THE #&!2 DETECTION THRESH OLD IS COMPUTED FOR EACH RESOLUTION CELL AS A LINEAR COMBINATION OF ORDER STATISTICS EXTRACTED FROM RANKED SAMPLE VALUES OVER A WINDOW SPANNING NEIGHBORING RANGE BINS ANTENNA BEAMS AND DOPPLER CELLS WITH PROVISIONS FOR ADAPTING THE WINDOW SHAPE NEAR STRONG VARIATIONS IN NOISE OR CLUTTER POWER /FTEN THE RESULTS ARE SIMILAR TO THOSE PREDICTED BY THE LOG NORMAL DISTRIBUTION AS EVIDENCED BY THE EXPERIMENTAL DATA SHOWN IN &IGURE B WHICH GIVES THE POWER LEVEL DISTRIBUTIONS FOR THE EXAMPLE SHOWN IN &IGURE 4HESE APPROXIMATELY LOG NORMAL DISTRIBUTIONS ARE TYPICAL FOR BENIGN CONDITIONS 4RACKING 0ERHAPS THE MOST FUNDAMENTAL DIFFERENCE BETWEEN SKYWAVE RADAR AND OTHER RADARS IS THE EXISTENCE OF MULTIPLE PROPAGATION PATHS WITH DISTINCT TIME DELAYS ANGLES OF INCIDENCE DOPPLER SHIFTS AND FLUCTUATION PROPERTIES 4HE TRACKING STAGE MUST DEAL WITH THE MULTIPLICITY OF ECHOES ASSOCIATED WITH EACH INDIVIDUAL TARGET AND BY EXTRACTING AND ASSIMILATING INFORMATION ABOUT THE PREVAILING IONOSPHERE INFER THE NUMBER OF GENUINE TARGETS THEIR TRUE LOCATIONS AND VELOCITIES AND PERHAPS
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OTHER INFORMATION SUCH AS TARGET ALTITUDE %STIMATES OF AIRCRAFT TARGET ALTITUDE ARE VERY USEFUL BUT SKYWAVE RADAR HAS NOT PROVED TO BE A RELIABLE MEANS OF OBTAINING ACCURATE ESTIMATES 4HE PROBLEM OF CONVERTING FROM RADAR COORDINATES TO GEOGRAPHICAL COORDINATES IS REFERRED TO AS COORDINATE REGISTRATION #2 $OZENS OF #2 TECHNIQUES HAVE BEEN EXPLORED INCLUDING I INFERENCE FROM A REGIONAL IONOSPHERIC MODEL II DEPLOYING A NETWORK OF REPEATERS OR BEACONS IN THE RADAR FOOTPRINT III CORRELATING COASTLINES WITH LAND CLUTTER SEA CLUTTER BOUNDARIES IN THE RADAR DATA IV CORRELATING OTHER PARAMETERS SUCH AS SCATTER ING COEFFICIENT V USING KNOWN TARGET INFORMATION SUCH AS REPORTS FROM SHIPS AND COM MERCIAL AIRLINE FLIGHTS AND VI REGISTERING AIRPORTS WHERE TRACKS ORIGINATE OR TERMINATE 4HE KEY TO ROBUST #2 IS THE FUSION OF ALL AVAILABLE INFORMATION IN A CONSISTENT PROBABILIS TIC FRAMEWORK -OST RADARS IMPLEMENT TARGET TRACKING AS A SEPARATE STAGE THAT OPERATES ON THE CANDIDATE TARGETS AFTER THEY HAVE BEEN REGISTERED INITIATING UPDATING OR TERMINAT ING TRACKS AS APPROPRIATE %XPERIENCE WITH MANY DIFFERENT TYPES OF TRACKING SCHEMES HAS LED A NUMBER OF OPERATIONAL RADARS TO CONVERGE ON ALGORITHMS BASED ON VARIANTS OF PROBABILISTIC DATA ASSOCIATION 0$! SOMETIMES GENERALIZED TO MAINTAIN MULTIHYPOTH ESIS MODELS 5NLIKE TRADITIONAL TRACKING FILTERS SUCH AS THE +ALMAN FILTER WHICH SELECTS A SINGLE DETECTION IE PEAK OR PLOT TO ASSOCIATE WITH EACH MAINTAINED TRACK 0$! FILTERS COMBINE THE INFLUENCE OF ALL THE CANDIDATE PEAKS WITHIN A PRESCRIBED RADIUS TO COMPUTE A TRACK UPDATE )N THE SKYWAVE RADAR CONTEXT THIS HAS YIELDED SUPERIOR RESULTS !N IMPORTANT DECISION RELATES TO WHERE THE COORDINATE REGISTRATION IS IMPLEMENTED 3OME SYSTEMS ESTABLISH TRACKS IN RADAR COORDINATES AND THEN PASS THE TRACKS INCLUDING MULTIPLE TRACKS FROM A SINGLE TARGET TO THE #2 SYSTEM WHICH MUST IDENTIFY AND RECON CILE ANY MULTIPLE TRACKS AS WELL AS PERFORM THE REGISTRATION !LTERNATIVELY THE PROBLEM OF TARGET TRACKING CAN BE INTEGRATED WITH THE PROBLEM OF DETERMINING THE IONOSPHERIC PROPAGATION PATHS "Y AUGMENTING THE STATE VECTOR USED FOR REPRESENTING A TARGET WITH ADDITIONAL PARAMETERS THAT CHARACTERIZE THE PROPAGATION PATH STRUCTURE A JOINT ESTIMA TION PROBLEM CAN BE FORMULATED AND SOLVEDn )N THIS WAY THE TARGETS CONTRIBUTE TO REGISTERING THEIR OWN COORDINATES
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Ê / 4HE COMPLEXITY OF THE (& RADAR OPERATING ENVIRONMENTTHE IONOSPHERE CLUTTER NOISE AND OTHER USERS OF THE BANDNECESSITATES A COMMENSURATE COMPLEXITY IN SYS TEM DESIGN SO THAT THE RADAR CAN ADAPT TO PREVAILING CONDITIONS BY SELECTING THE BEST FREQUENCY OR COMBINATION OF FREQUENCIES WAVEFORM SIGNAL PROCESSING DETECTION THRESHOLDS AND SO ON FOR THE TASK AT HAND !CHIEVING THIS OPTIMUM CONTROL IS IMPORTANT BECAUSE EXPERIENCE HAS SHOWN THAT (& SKYWAVE RADAR PERFORMANCE MAY DEGRADE DRA MATICALLY WITH ONLY MODEST DEPARTURES FROM OPTIMUM SETTINGS 4HUS THERE IS A DEMAND FOR TWO INGREDIENTS I INFORMATION ABOUT THE ENVIRONMENT AND II A MECHANISM OR AT LEAST A STRATEGY FOR USING THAT INFORMATION TO CONTROL THE RADAR PARAMETERS !T THE VERY MINIMUM (& SKYWAVE RADARS MUST MAINTAIN A REAL TIME AWARENESS OF PROPAGATION CONDITIONS AS A FUNCTION OF FREQUENCY RANGE AND BEARING AZIMUTH AS WELL AS A DETAILED KNOWLEDGE OF SPECTRUM OCCUPANCY 4HIS IS USUALLY ACHIEVED BY PRO VIDING AUXILIARY FACILITIES INCLUDING SOME OR ALL OF THE FOLLOWING I #ONVENTIONAL ION OSPHERIC SOUNDERS VERTICAL AND OBLIQUE INCIDENCE WHICH DETERMINE THE IONOSPHERIC ELECTRON DENSITY PROFILE BY MEASURING THE TIME OF FLIGHT OF REFLECTED RADIOWAVES OVER A RANGE OF FREQUENCIES THIS ELECTRON DENSITY PROFILE INFORMATION IS ASSIMILATED INTO
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LOCAL REAL TIME IONOSPHERIC MODELS II ! WIDEBAND BACKSCATTER SOUNDER THAT IS A LOW POWER LOW RESOLUTION RADAR THAT SWEEPS ACROSS THE (& BAND MEASURING ECHO STRENGTH VERSUS TIME DELAY GROUP RANGE TO SEE WHICH FREQUENCIES ARE ILLUMINATING ANY GIVEN REGION III ! MINI RADAR SIMILAR TO A BACKSCATTER SOUNDER THAT EMPLOYS A NARROWBAND WAVEFORM TO STUDY THE DOPPLER STRUCTURE OF THE ECHOES AS A FUNCTION OF GROUP RANGE FOR SELECTED FREQUENCIES IV ! NETWORK OF REMOTE BEACONS OR TRANSPONDERS TO PROVIDE COORDINATE REGISTRATION V 3PECTRUM MONITORING RECEIVERS TO LOCATE CLEAR CHANNELS FOR POSSIBLE USE AND TO ASSESS THEIR PROPERTIES ! DETAILED DESCRIPTION OF THE SUITE OF AUXIL IARIES FOR THE *INDALEE RADAR CAN BE FOUND IN %ARL AND 7ARD 4RADITIONALLY THE CONTROL MECHANISM HAS BEEN THE EXPERT RADAR OPERATOR &OR MANY REASONS THIS IS NOT WHOLLY SATISFACTORY SO VARIOUS ALTERNATIVES HAVE BEEN EXPLORED INCLUDING PACKAGED hRECIPESv THAT CAN BE INVOKED BY LESS SKILLED OPERATORS AND EXPERT SYSTEMS IMPLEMENTED WITH ARTIFICIAL INTELLIGENCE CONSTRUCTS !PART FROM THE NEED TO ADAPT TO THE CHANGING IONOSPHERE AND NOISE ENVIRONMENT (& RADARS ARE FREQUENTLY TASKED WITH A VARIETY OF MISSIONS TO BE CONDUCTED MORE OR LESS CONCURRENTLY WITH TIME VARYING PRIORITIES 4HESE WILL GENERALLY INVOLVE DIFFERENT WAVEFORMS TASK SPECIFIC CONSTRAINTS ON FREQUENCY IN ADDITION TO PROPAGATION CON SIDERATIONS DIFFERING REQUIREMENTS IN TERMS OF ACCEPTABLE PROPAGATION QUALITY AND SO ON ! COMMON EXAMPLE IS THE DESIRE TO SEARCH FOR SHIPS AND AIRCRAFT CONCURRENTLY !CCORDINGLY OPTIMIZATION OF THE ALLOCATION OF RESOURCES BECOMES A CRITICAL ISSUE WITH SIGNIFICANT IMPLICATIONS FOR THE WAY SKYWAVE RADARS OPERATE /NE APPROACH TO FITTING MORE TASKS INTO THE TIME AVAILABLE IS TO PARTITION THE RADAR TRANSMIT AND RECEIVE ARRAYS TOGETHER WITH THE TRANSMITTER MODULES AND RECEIVERS SO THAT WHEN CONDITIONS ARE FAVORABLE THE PARTITIONS CAN OPERATE AS INDEPENDENT RADARS WITH REDUCED SENSITIVITY AND RESOLUTION &OR EXAMPLE THE *INDALEE AND */2. RADARS ARE DYNAMICALLY RECONFIGURABLE AS FULL OR HALF RADARS !LTERNATIVELY IT MAY BE ACCEPT ABLE TO EMPLOY A DUAL PURPOSE WAVEFORM ABLE TO SUPPORT TWO DISTINCT MISSIONS THOUGH WITH SUBOPTIMAL PERFORMANCE OR FOR THE TRANSMIT SYSTEM TO RADIATE MULTIPLE ORTHOGONAL WAVEFORMS FOR SIMULTANEOUS RECEPTION AND PROCESSING AT A PROPORTIONAL LOSS OF AVERAGE POWER ON EACH TRANSMISSION BUT WITHOUT LOSS OF SPATIAL DIRECTIVITY "UT EVEN IF THESE APPROACHES ARE SOMETIMES APPLICABLE IT IS ALMOST ALWAYS NECESSARY TO SCHEDULE THE VARIOUS TASKS SUCH THAT ACCEPTABLE REVISIT TIMES ARE MAINTAINED ON IMPORTANT MISSIONS WITH LOW PRIORITY TASKS SUCH AS WEATHER MONITORING ACTIVATED LESS FREQUENTLY AND CHALLENGING TASKS ACTIVATED WHEN SUITABLE PROPAGATION CONDITIONS OCCUR /NE OTHER IMPORTANT ISSUE ARISES WITH RESOURCE MANAGEMENT AND THAT IS THE ABIL ITY TO DIAGNOSE FAULTS AND FAILURES AS SOON AS THEY OCCUR .OT ONLY IS THIS NECESSARY TO HASTEN THE REPAIR PROCEDURE BUT ALSO IT ENABLES THE RADAR TO ADAPT ITS CONFIGURATION TO DO THE BEST IT CAN WITH IMPAIRED EQUIPMENT &OR EXAMPLE IF THE RECEIVER CONNECTED TO THE MIDDLE ELEMENT IN AN ANTENNA ARRAY WERE TO FAIL BEAMFORMING WOULD BE MORE SERI OUSLY DEGRADED THAN IF THE FAILURE WERE TO OCCUR IN A RECEIVER CONNECTED TO AN ELEMENT AT THE END OF THE ARRAY !UTOMATIC DETECTION OF SUCH A FAILURE AND REALLOCATION OF AN END ELEMENT RECEIVER TO THE MIDDLE ELEMENT OF THE ARRAY WOULD MINIMIZE THE DEGRADATION
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Ê " -ODELING IS AN ESSENTIAL PART OF THE RADAR DESIGN PROCESS AND ALSO AS A MEANS TO PREDICT THE PERFORMANCE OF EXISTING OR PROPOSED RADARS TO WHICH ONE DOES NOT EXPECT ACCESS )N THESE ROLES THE EMPHASIS IS ON FIDELITY )N (& SKYWAVE RADAR SYSTEMS MODELING HAS
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ANOTHER ROLEAS A REAL TIME MONITOR OF WHAT IS EXPECTED UNDER THE PREVAILING CONDI TIONS SO AS TO ALERT THE RADAR OPERATOR IF A DISCREPANCY EMERGES WHICH MIGHT BE INDICA TIVE OF NATURAL EQUIPMENT RELATED OR INTENTIONAL EVENTS WARRANTING ATTENTION !N ISSUE ONE ENCOUNTERS WHEN DISCUSSING RADAR PERFORMANCE IS THE CHOICE OF PERFORMANCE CRITERION &ROM THE USERS PERSPECTIVE IT MAY SEEM LOGICAL TO MEASURE PERFORMANCE IN TERMS OF TIME TAKEN TO ESTABLISH A TRACK ON A GIVEN TARGET AVERAGED OVER TIME AND COVERAGE SINCE TRACKS ARE THE ESSENTIAL PRODUCT DELIVERED TO USERS BY THE RADAR /F COURSE THIS PLACES THE ONUS ON THE TRACKING SYSTEM SO ONE MIGHT STEP BACK A LITTLE AND CHOOSE INSTEAD 3.2 ACHIEVABLE ON A GIVEN TARGET AGAIN AVER AGED OVER TIME AND COVERAGE "UT THIS IGNORES THE PRECISION OF THE MEASUREMENT ASSOCIATED WITH BOTH RESOLUTION WHICH MAY IMPACT ON THE UTILITY OF THE DETECTIONS AND ACCURACY IN THE SENSE OF REGISTRATION IN ABSOLUTE GEOGRAPHICAL COORDINATES !ND WHAT OF THE SMALLEST DETECTABLE TARGET #OVERAGE AND COVERAGE RATE 3HIP DETECTION CAPABILITY VERSUS AIRCRAFT DETECTION CAPABILITY #LEARLY THERE IS NO SINGLE PREFERRED METRIC 4HE MEASURE ADOPTED HERE FOR ILLUSTRATIVE PURPOSES IS THE ACHIEVABLE SIGNAL TO NOISE RATIO 3.2 AS DEFINED BY THE RADAR EQUATION %Q 4HE CONSTITUENT VARIABLES THAT APPEAR IN THE EQUATION HAVE BEEN DISCUSSED IN 3ECTIONS n EMPHASIZING THE UNIQUE CONSIDERATIONS THAT ARISE WITH (& SKYWAVE RADAR SO THE TOOLS FOR PERFORMANCE MODELING AND ANALYSIS ARE AVAILABLE "Y CONSIDERING THE CASE OF NOISE LIMITED DETECTION AS APPLIES ESPECIALLY TO AIRCRAFT TARGETS THE ADDITIONAL COM PLICATIONS OF CLUTTER LIMITED DETECTION ARE AVOIDED )N THE FOLLOWING PARAGRAPHS TWO DIFFERENT APPROACHES TO PERFORMANCE MODELING FOR THE CASE OF NOISE LIMITED DETECTION ARE DESCRIBED IN SOME DETAIL 4HE .2, )43 2ADAR 0ERFORMANCE -ODEL 4HE .2, )43 2ADAR 0ERFORMANCE -ODEL DEVELOPED BY ,UCAS ET AL PROVIDES A NUMBER OF TOOLS FOR RADAR PER FORMANCE ESTIMATION )T DOES NOT EMPLOY FULL $ RAY TRACING SUCH AS THE CODE DESCRIBED BY *ONES AND 3TEPHENSON WHICH CAN PROVIDE PATHS IN THREE DIMENSIONS INCLUDING DELAYS AND LOSSES FOR BOTH ORDINARY AND EXTRAORDINARY RAYS SEE 3ECTION !RGUING THAT SUCH COMPREHENSIVE CALCULATIONS ARE EXCESSIVE WHEN THERE ARE SIGNIFICANT UNCERTAINTIES IN THE ELECTRON DENSITY DISTRIBUTION .2, -EMORANDUM 2EPORT DESCRIBES THE BASIC TECHNIQUE USED FOR PATH DETERMINATIONS ! SIMPLE CLOSED FORM VIRTUAL PATH TRACE 3NELLS LAW FOR A SPHERICALLY SYMMETRIC MEDIUM IS SEQUENCED THROUGH ELEVATION RADIATION ANGLES IN n INCREMENTS 4HIS PROCESS IS INCREMENTED IN -(Z STEPS OVER THE RADARS OPERATING BAND )N THE PRESENT EXAM PLE A VERTICAL SOUNDING OF THE IONOSPHERE KM DOWNRANGE HAS BEEN USED AS THE ELECTRON DISTRIBUTION FOR ALL ONE HOP PATHS AND A SOUNDING KM DOWNRANGE IS USED FOR TWO HOP PATHS &IGURE GIVES NIGHT AND DAY EXAMPLES OF IONOGRAMS SHOWING THE IONOSPHERE KM DOWNRANGE FROM A RADAR LOCATED AT n. AND n7 LOOKING EAST IN SUMMER AT A MEDIAN SUNSPOT NUMBER OF 4HE COR RESPONDING WINTER CASE IS PRESENTED IN &IGURE 3UCH PLOTS CAN BE USED TO DETERMINE THE MAXIMUM FREQUENCY THAT WILL PROPAGATE TO A GIVEN RANGE IN MOST CASES THE OPTIMUM FREQUENCY IS JUST BELOW THE MAXIMUM FREQUENCY &OR THE LITTLE TABLES SHOWN IN &IGURE AND &# IS THE CRITICAL FREQUENCY IN MEGAHERTZ (# IS THE HEIGHT OF MAXIMUM IONIZATION OR THE NOSE OF THE PARABOLA IN KILOMETERS AND 9- IS THE SEMILAYER THICKNESS IN KILOMETERS %S DESCRIBES THE STATISTICAL RANGE OF VARIATION OF SPORADIC % AS - MEDIAN , LOWER DECILE AND 5 UPPER DECILE CRITICAL FREQUENCIES IN MEGAHERTZ
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&)'52% 4HE VIRTUAL SOLID LINE AND TRUE DASHED LINE REFLECTION HEIGHTS ARE GIVEN FOR *ULY 33. AND A MID !TLANTIC COAST REFRACTION AREA A 54 IS A DAYTIME EXAMPLE SINGLE HOP AND B 54 IS A NIGHTTIME EXAMPLE 3EE TEXT FOR AN EXPLANATION OF THE TABLE IN THE LOWER RIGHT OF THE FIGURE
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&)'52% 0REDICTED IONOGRAMS AS IN &IGURE BUT FOR *ANUARY A 54# FOR DAY AND B 54# FOR NIGHT 3EE TEXT FOR AN EXPLANATION OF THE TABLE IN THE LOWER RIGHT OF THE FIGURE
#ONSTANT PLASMA FREQUENCY CONTOURS VERSUS RANGE FROM THE RADAR FOR 54# 33. *ANUARY NIGHT AND 54# DAY ARE PRESENTED IN &IGURES AND TO ILLUSTRATE THE TILT OF THE IONOSPHERE &OR THE NIGHT CASE THE CONCENTRIC
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&)'52% 0LASMA FREQUENCY CONTOURS ARE GIVEN IN -(Z EXTENDING FROM THE RADAR TO A POINT EAST NMI DOWNRANGE FOR A *ANUARY NIGHT EXAMPLE
&)'52% 0LASMA FREQUENCY CONTOURS ARE GIVEN IN -(Z EXTENDING FROM THE RADAR TO A POINT EAST NMI DOWNRANGE FOR A *ANUARY DAY EXAMPLE
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SPHERICAL ASSUMPTION FROM THE KM DOWNRANGE POSITION WILL GIVE PATHS THAT ARE SLIGHTLY LONG FOR ONE HOP RANGES )N THE TWO HOP RANGES THE NO GRADIENT ASSUMP TION CAUSES MORE DISTORTION )N GENERAL ERRORS OF THIS NATURE HAVE LITTLE IMPACT ON PERFORMANCE PREDICTION (OWEVER NEAR REAL TIME ANALYSIS FOR VIRTUAL RANGE AND AZIMUTH CORRECTION TO GREAT CIRCLE DISTANCE AND BEARING GRID REGISTRATION REQUIRES THAT TILT OR GRADIENT EFFECTS BE TAKEN INTO ACCOUNT 4HE DAYTIME EXAMPLE HAS LITTLE HORIZONTAL GRADIENT AND THE SIMPLIFYING ASSUMPTION MAKES LITTLE DIFFERENCE 7HEN BETTER ACCURACY IS DESIRED THE CORRECT VERTICAL PROFILE CAN BE USED FOR EACH RADIATION ANGLE ALSO GRADIENTS CAN BE SIMULATED BY MAKING THE IONOSPHERE NONCONCENTRIC WITH THE %ARTH ! MORE COMPLETE PATH ANALYSIS SHOULD BE USED IN RADAR PERFORMANCE ASSESSMENT AND MANAGEMENT BUT THESE PLASMA DENSITY CONTOURS CAN BE USED TO ESTIMATE THE MAGNITUDE OF THE ERRORS INTRODUCED BY THE ASSUMPTION OF A SPHERICALLY SYMMETRIC IONOSPHERE &IGURE SHOWS A PERFORMANCE PREDICTION FOR A HYPOTHETICAL RADAR IN THE FORM OF AN OBLIQUE SOUNDING ! TYPICAL SKYWAVE RADAR IS SUPPORTED BY ONE OR MORE VERTI CAL SOUNDERS AND OBLIQUE BACKSCATTER SOUNDERS FOR TRANSMISSION PATH ANALYSIS AND TO AID IN RADAR FREQUENCY MANAGEMENT /F COURSE THE RADAR ITSELF IS AN OBLIQUE SOUNDER BUT ITS SOUNDING DATA IS RESTRICTED TO THE FREQUENCY WAVEFORM AND SCAN PROGRAM OF ITS PRIMARY SURVEILLANCE TASK !N ADJUNCT OBLIQUE SOUNDER CAN PROVIDE INFORMATION IN
&)'52% 4HE NUMBERS IN THIS FIGURE SHOW THE 3.2 IN D" AS A FUNCTION OF FREQUENCY AND RANGE IN THE FORM OF A TYPICAL OBLIQUE BACKSCATTER SOUNDING *ANUARY '-4 DAY 33. LOCATION n. AND n7 BEARING n 3EE THE TEXT FOR A DESCRIPTION OF RADAR PARAMETERS
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THE FORM OF &IGURE ON %ARTH BACKSCATTER ECHO POWER %STIMATES FOR NOISE POWER SPECTRAL DENSITY ARE DERIVED FROM ##)2 2EPORT AS DESCRIBED IN 3ECTION )N THIS PREDICTION 3.2 IN DECIBELS IS PLOTTED AS A FUNCTION OF OPERATING FREQUENCY AND GREAT CIRCLE TIME DELAY OR GROUND RANGE 4HE NUMBERS JUST ABOVE THE ABSCISSA AT MS DELAY ARE THE NOISE POWERS IN DECIBELS BELOW 7(Z &OR THIS PLOT THE 54# TIME IS 33. 0AV K7 'T'R D" 4 S AND R D"SM &IGURE GIVES THE CORRESPONDING NIGHT PLOT 4HE SHAPE OF THESE DISPLAYS IS QUITE SIMILAR TO WHAT WOULD BE SEEN WITH A DIAGNOSTIC OBLIQUE SOUNDING THE LEVELS WOULD GENERALLY BE GREATER BECAUSE THE RESOLUTION CELL AREA TIMES THE SURFACE SCATTERING COEFFICIENT IS GENERALLY MUCH LARGER THAN D"SM 3OME OF THE NIGHT DAY CONTRASTS SUCH AS AVAILABLE FREQUENCIES AND DIFFERENCE IN NOISE LEVEL FOR THE SAME RANGE ARE EVIDENT !LSO NOTE THAT AT NIGHT THE -(Z LOWER FREQUENCY LIMIT DOES NOT PROVIDE COVERAGE CLOSER THAN ABOUT KM )T SHOULD BE REMEMBERED THAT THIS IS A MEDIAN 33. CALCULATION AND IF CONSISTENT PERFORMANCE FOR RANGES AS CLOSE AS KM IS REQUIRED DURING NIGHTS A LOWER FREQUENCY LIMIT SHOULD BE SELECTED TO DEAL WITH PERIODS OF LOWER SOLAR ACTIVITY AND THE CRITICAL FREQUENCY DISTRIBUTION 4HE PLOTS SHOW THAT OPERATION ON A SINGLE FREQUENCY MAY EXPERIENCE LESS THAN o D" VARIA TION OVER A RANGE INTERVAL OF KM !LSO IF FREQUENCY SELECTION HAD BEEN MADE WITH A -(Z GRANULARITY INSTEAD OF THE -(Z USED THE 3.2 WOULD BE REDUCED BY ONLY A DECIBEL OR SO
&)'52% 4HE NUMBERS IN THIS FIGURE SHOW THE 3.2 IN D" AS A FUNCTION OF FREQUENCY AND RANGE IN THE FORM OF AN OBLIQUE SOUNDING AS IN &IGURE BUT FOR '-4 NIGHT 3EE THE TEXT FOR A DESCRIPTION OF RADAR PARAMETERS
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4HE PERFORMANCE ESTIMATION CHARTS THAT FOLLOW COME FROM ANALYSES AS DESCRIBED ABOVE !FTER PERFORMING OBLIQUE SOUNDING CALCULATIONS A RANGE INDEXED TABLE OF PROPAGATION AND NOISE PARAMETERS IS COMPILED 0ARAMETER SELECTIONS ARE MADE ON THE BASIS OF THE BEST 3.2 IN EACH NOMINAL NMI INTERVAL BUT THE SELECTION IS ADJUSTED TO COME FROM THE ADJACENT LOWER FREQUENCY TO AVOID AN OPTIMISTIC BIAS 4HEN PARAMETER PLOTS ARE GENERATED AS A FUNCTION OF RANGE 4HE VARIABLES ADOPTED HERE AS PARAMETERS ARE PROPAGATION LOSSES FREQUENCY NOISE AND ELEVATION RADIATION ANGLE 4HE CHOICE OF RANGE AS THE INDEPENDENT VARIABLE MAY SEEM ARTIFICIAL BUT IT IS A USEFUL APPROACH FOR PERFORMANCE EXAMINATION 7ITH THESE CURVES THE IMPACT ON RADAR 3.2 PERFORMANCE CAN BE ESTIMATED FOR SELECTED ANTENNA GAIN PATTERNS TRANSMITTED POWERS TARGET 2#3 AND COHERENT INTEGRATION TIMES #)4 &IGURE IS AN EXAMPLE FOR *ANUARY WITH MODERATE SOLAR ACTIVITY 33. IN DAYTIME 4HE 2 LOSS IS THE FOURTH POWER OF RANGE TO THE TARGET IN METERS EXPRESSED IN DECIBELS 2 , ADDS NONDEVIATIVE ABSORPTION DEVIATIVE ABSORPTION SPORADIC % OBSCU RATION AND GROUND REFLECTION LOSSES IF THERE IS MORE THAN ONE HOP 4HE SHARP INCREASE IN LOSS JUST BEFORE NMI IS CAUSED BY TRANSITION FROM ONE TO TWO HOPS FOR TWO HOPS THE LOSSY $ REGION IS TRANSITED TWICE AS MANY TIMES GROUND REFLECTION LOSS IS ADDED AND REQUIRED OPERATION AT A LOWER FREQUENCY INCREASES LOSS 4HE JAGGED CURVE IN THE TRANSI TION REGION IS DUE TO THE PARAMETER SELECTION PROCESS IN RADAR OPERATION THE FREQUENCY WOULD BE SELECTED TO MINIMIZE TRANSITION EFFECTS 4HE FREQUENCY RADIATION ANGLE AND NOISE POWER PER HERTZ THAT GO WITH THIS SITE AND LOOK DIRECTION ARE ALSO PLOTTED
&)'52% 2ADAR PERFORMANCE CONTROLLING VARIABLES PLOTTED AS A FUNCTION OF RANGE FOR *ANUARY 54# 33.
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!N EXAMPLE WILL SERVE TO ILLUSTRATE THE USE OF SUCH PLOTS 3ELECT NMI AS THE RANGE 4HEN THE FREQUENCY IS -(Z WAVELENGTH M AND L D" NOISE POWER n D" AND 2 , D" #HOOSE D"7 FOR 0AV D" FOR 'T D" FOR 'R D"S FOR 4 D"SM FOR 2#3 AND D" FOR &P 3UBSTITUTING IN %Q
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&IGURE SHOWS THE PERFORMANCE INDICATED WITH THESE ASSUMPTIONS FOR ALL RANGES ! PATH FACTOR ENHANCEMENT OF D" HAS BEEN CHOSEN AS A REPRESENTATIVE VALUE OF CONSTRUC TIVE MULTIPATH INTERFERENCE FOR AN AIRCRAFT TARGET 4HE BEAMWIDTH HAS BEEN TAKEN TO BE n AND THE SURFACE SCATTERING COEFFICIENT TO BE n D" AND WITH A D" PATH ENHANCE MENT THE CLUTTER LEVEL HAS BEEN PLOTTED 4HE CLUTTER TO NOISE RATIO #.2 AT NMI IS ABOUT D" &OR THE CONSTANT BEAMWIDTH ASSUMED THE CLUTTER TO SIGNAL RATIO INCREASES WITH RANGE AND IS D" AT NMI ,ARGE CLUTTER TO SIGNAL RATIOS ARE TYPICAL OF (& RADAR SOME FORM OF DOPPLER FILTERING IS USED TO SEPARATE TARGETS FROM CLUTTER )N &IGURES AND PERFORMANCE ESTIMATION CURVES ARE GIVEN FOR WINTER AND SUMMER SEASONS NIGHT AND DAY AND LOW SOLAR ACTIVITY 4HE PERMIS SIBLE FREQUENCY SELECTION IS SET BETWEEN AND -(Z AND ANTENNA RADIATION IS NOT CONSIDERED BELOW AN ELEVATION ANGLE OF n 4HE ANALYSES WERE MADE FOR A RADAR OFF THE MID !TLANTIC COAST OF THE 5NITED 3TATES AND SHOULD BE A GOOD APPROXIMATION FOR ANY LOCATION WHERE TRANSMISSION PATHS ARE THROUGH THE MIDDLE MAGNETIC LATITUDES
&)'52% ! SPECIFIC EXAMPLE OF 3.2 AND CLUTTER TO NOISE RATIO #.2 AS DETERMINED BY USING &IGURE 4HE TARGET 2#3 IS LABELED hSIZEv AND IS TREATED AS CONSTANT
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&)'52% 2ADAR PERFORMANCE ESTIMATE FOR *ANUARY 54# 33.
&)'52% 2ADAR PERFORMANCE ESTIMATE FOR *ANUARY 54# 33.
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&)'52% 2ADAR PERFORMANCE ESTIMATE FOR *ULY 54# 33.
&)'52% 2ADAR PERFORMANCE ESTIMATE FOR *ULY 54# 33.
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4HESE PERFORMANCE ESTIMATION CURVES CAN BE USED TO SHOW EXTREMES IN 3.2 VARIATION ANTENNA ELEVATION ANGLES REQUIRED AND EXPECTED CLUTTER TO NOISE RATIOS 4HE EXPECTED PERFORMANCE OF A PARTICULAR RADAR DESIGN CAN BE EXPLORED WITH THESE GRAPHS BECAUSE SUMMER AND WINTER DO GIVE GOOD COVERAGE OF THE IMPORTANT VARIABLES 4HE PERFOR MANCE CURVES HAVE BEEN LIMITED IN ALMOST ALL EXAMPLES TO THE CASE OF LOW SOLAR ACTIVITY SINCE IN GENERAL THIS IS THE MOST DIFFICULT TIME 4HE HIGHER FREQUENCY AVAILABILITY AND PERFORMANCE AFFORDED AT HIGH SOLAR ACTIVITY IS ILLUSTRATED IN &IGURE WHICH TREATS THE CASE OF *ULY 54# FOR 33. !NALYSIS OF PERFORMANCE ESTIMATION CURVES FOR ALL COMBINATIONS OF I THE FOUR SEASONS II DAY AND NIGHT AND III HIGH AND LOW SOLAR ACTIVITY REVEALS CONSISTENT BEHAVIOR I 3UMMER SHOWS MUCH GREATER LOSSES THAN WINTER II %XCEPT FOR SUMMER NIGHT LOSSES ARE ONLY SLIGHTLY LESS THAN DAY LOSSES III .IGHT NOISE IS MUCH GREATER THAN DAY NOISE IV &OR A SPECIFIC RANGE OPTIMUM FREQUENCIES VARY BY 4HIS /4( PERFORMANCE PRESENTATION FORMAT CAN BE USED TO DECIDE ON THE ANTENNA PATTERNS AND POWERS REQUIRED FOR SPECIFIC TARGETS AND MISSIONS OR IT CAN BE USED TO EXHIBIT PERIODS OF ENHANCED OR DEGRADED PERFORMANCE FOR AN EXISTING DESIGN
&)'52% 2ADAR PERFORMANCE ESTIMATE FOR *ULY 54# 33.
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3EVERAL QUALIFIERS SHOULD BE KEPT IN MIND !T OTHER GEOGRAPHIC LOCATIONS THE APPRO PRIATE ##)2 NOISE SHOULD BE SELECTED OR BETTER YET NOISE MEASUREMENTS MADE IN SITU &OR RADARS THAT USE AURORAL ZONE PATHS SPECIFIC ANALYSES ARE REQUIRED AND TARGET OBSCURA TION BY SPREAD IN DOPPLER CLUTTER MUST BE CONSIDERED 4HE PERFORMANCE ESTIMATES SHOWN IN THE FIGURES ASSUME THAT THE RADAR DESIGN AND WAVEFORMS ARE SUCH THAT EXTERNAL NOISE IS THE CONTROL 4HE USE OF A SINGLE DESCRIPTION FOR NIGHT AND DAY GIVES A FAIR REPRESENTATION BUT THE TRANSITION FROM NIGHT TO DAY IS VERY ABRUPT AND REQUIRES CAREFUL FREQUENCY MAN AGEMENT IN RADAR OPERATION 4HE IONOSPHERIC DESCRIPTION THAT HAS BEEN USED IS FOR WHAT HAS BEEN TERMED THE QUIET IONOSPHERE CONDITIONS THAT APPLY MOST OF THE TIME 5NDER DISTURBED CONDITIONS PERFORMANCE MAY BE MARKEDLY INFERIOR TO THAT PREDICTED 4HE *INDALEE 2ADAR 0ERFORMANCE -ODEL 4HE *INDALEE 2ADAR 0ERFORMANCE -ODEL DRAWS ON SEVERAL UNIQUE DATABASES 3INCE OBLIQUE BACKSCATTER SOUND INGS HAVE BEEN RECORDED ON A MINUTE CYCLE SCANNING FROM TO OR OPTIONALLY -(Z %IGHT SIMULTANEOUS BEAMS SPANNING A n ARC ARE FORMED 0RIOR TO THE SYSTEM USED A SINGLE RECEIVER SCANNING THE RECEIVE BEAMS SERVICING EACH RECEIVE BEAM FOR K(Z OF EACH K(Z PORTION OF A BACKSCATTER IONOGRAM 0OST EACH BEAM HAS BEEN SERVICED CONTINUOUSLY WITH ITS OWN RECEIVER "ACKGROUND NOISE DATA USED IN CONJUNCTION WITH THE BACKSCATTER DATA FOR THE %XCESS 0OWER ANALYSIS IS COL LECTED USING THE SAME EIGHT DIRECTIONAL BEAMS AS THE BACKSCATTER SOUNDER 7HILE THERE ARE A FEW SIGNIFICANT GAPS IN THESE TIME SERIES THEY SPAN TWO SOLAR CYCLES FURTHER INTEGRITY HAS BEEN MAINTAINED BY EXTENSIVE VETTING BEFORE ENTERING NEW DATA INTO THE DATABASE 4HE UNIQUE ADVANTAGE OF THIS DATABASE IS THAT THE NOISE AND PROPAGATION DATA ARE RECORDED UNDER IDENTICAL IONOSPHERIC CONDITIONS WHEREAS COM BINING INDEPENDENT CLUTTER AND NOISE STATISTICAL MODELS SUCH AS )2) WITH ##)2 PRESERVES NO CORRELATIONS HOWEVER STRONG THEY MAY BE 3EVERAL FORMS OF DATA ANALYSIS AND DISPLAY ARE ACCESSIBLE BUT PERHAPS THE MOST USE FUL ARE THE MAPS OF I %XCESS 0OWER AND II /PTIMUM &REQUENCY 4HE %XCESS 0OWER PARAMETER IS CONSTRUCTED AS FOLLOWS #ONSIDER A SPECIFIC TARGET WHOSE 2#3 IS KNOWN OR ESTIMATED AS A FUNCTION OF FREQUENCY 3UPPOSE A PREDICTION OF MEDIAN RADAR DETEC TION PERFORMANCE IS REQUIRED FOR A SPECIFIC MONTH OF THE YEAR AND A PARTICULAR SUNSPOT NUMBER OR YEAR OF SOLAR CYCLE !NALYSIS IS INITIATED BY SELECTING FROM THE DATABASE A MONTH THAT MATCHES THE REQUIREMENTS )NDIVIDUAL BACKSCATTER IONOGRAMS ARE PAIRED WITH THE CONCURRENT BACK GROUND NOISE DATA AND THE RATIO TAKEN TO YIELD A POPULATION OF ESTIMATES OF TRUE SUB CLUTTER VISIBILITY 3#6 FOR EACH FREQUENCY STEP EACH BEAM AND EACH RANGE BIN .EXT USING A SPECIFIED TIME GRANULARITYTYPICALLY ONE HOURMEDIAN VALUES OF 3#6 ARE CALCULATED FOR EACH SPATIAL CELL AND TIME INTERVAL FROM THE STATISTICAL POPULATION OF INDIVIDUAL 3#6 ESTIMATES .OTE AGAIN THAT THESE MEDIAN VALUES ARE THE MEDIAN VALUES OF THE 3#6 POPULATION NOT A STATISTIC DERIVED BY COMBINING MEDIAN VALUES OF CLUTTER WITH MEDIAN VALUES OF NOISE 4HE MEDIAN 3#6 VALUES ARE RELATED DIRECTLY TO THE BACKSCATTER SOUNDER TRANSMIT POWER AND THE TRANSMIT ANTENNA GAIN &ROM THE RADAR EQUATION %Q THE 3#6 CAN BE SCALED TO THAT WHICH WOULD BE EXPECTED FOR THE MAIN RADAR WITH ITS DIFFERENT RADIATED POWER 04 APERTURE RADAR BANDWIDTH ETC #OMBINING THESE SCALED 3#6 VALUES WITH I A MODEL OF THE SURFACE BACKSCATTERING COEFFICIENT VERSUS FREQUENCY ALMOST ALL THE /4( RADAR COVERAGE IS OCEAN SO BASED ON REGIONAL WAVE STATISTICS THE CONSTANT VALUE n D" IS USED II THE TARGET 2#3 VERSUS FREQUENCY MODEL AND III AN ESTIMATE OF THE TARGET ECHO SIGNAL PROCESSING LOSS TYPICALLY ^ D" WHICH ARISES PREDOMINANTLY FROM &&4 ANALYSIS YIELDS THE PREDICTED MEDIAN TARGET 3.2 AT EACH SPATIAL LOCATION AS
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A FUNCTION OF FREQUENCY 4HIS CAN BE USED DIRECTLY BUT IT IS CONVENIENT TO DEFINE THE %XCESS 0OWER AT EACH FREQUENCY AS FOLLOWS 3UPPOSE u !N 3.2 THRESHOLD OF - D" IS REQUIRED BEFORE THE SIGNAL PROCESSING WILL REGISTER A DETECTION AND u 4HE 3.2 CALCULATED FOR A PARTICULAR RANGE AZIMUTH CELL IN THE COVERAGE IS 3.2 F D" WHICH MAY BE NEGATIVE 4HEN IN D"
%XCESS 0OWER F - 3.2 F 04 02%&
IS THE AMOUNT OF EXTRA POWER RELATIVE TO ANY CHOSEN REFERENCE POWER 02%& NEEDED TO ACHIEVE DETECTION AS A FUNCTION OF FREQUENCY ! NEGATIVE VALUE INDICATES THAT THE RADAR HAS GREATER SENSITIVITY THAN REQUIRED &IGURE SHOWS AN EXAMPLE PRESENTED AS A CONTOUR PLOT 4HE SECOND PARAMETER OF SPECIAL INTEREST IS OPTIMUM FREQUENCY DEFINED AS THE VALUE OF THE FREQUENCY AT EACH RANGE TIME LOCATION THAT MAXIMIZES THE 3.2 FOR THE GIVEN TARGET TAKING ALL RADAR EQUATION FACTORS INTO ACCOUNT !GAIN A CONTOUR PLOT FORMAT IS USED HERE IN &IGURE /THER -ODELING !PPROACHES 4HE MODELS DESCRIBED ABOVE ARE FORMULATED IN THE CONTEXT OF THE RADAR EQUATION %Q !N ALTERNATIVE IS TO EMPLOY A COHERENT hPRO CESS MODEL v IN WHICH THE FIELD AMPLITUDE AND PHASE ARE TRACKED FROM TRANSMITTER TO RECEIVER 4HIS APPROACH HAS BEEN USED TO SIMULATE THE EFFECTS OF MULTIPATH DIFFUSE SCAT TERING POLARIZATION EFFECTS AND NONLINEARITY &OR EXAMPLE &IGURE SHOWS
&)'52% 2ANGE TIME MAP OF POWER REQUIRED RELATIVE TO A 02%& OF K7 TO DETECT A SPECIFIC TARGET AS A FUNCTION OF RANGE AND TIME OF DAY FOR A PARTICULAR MONTH AND LEVEL OF SOLAR ACTIVITY
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&)'52% 2ANGE TIME MAP OF OPTIMUM FREQUENCY IN -(Z TO DETECT A SPECIFIC TARGET AS A FUNCTION OF RANGE AND TIME OF DAY FOR A PARTICULAR MONTH AND LEVEL OF SOLAR ACTIVITY
THE PREDICTED DISTRIBUTION OF THE RESULTANT RADAR CROSS SECTION WHEN MULTIPATH AND &ARADAY ROTATION ARE TAKEN INTO ACCOUNT 4HE RELEVANT PHYSICSROUGH SURFACE FORWARD SCATTERING COEFFICIENT BISTATIC IN THE VERTICAL PLANE FREE SPACE TARGET SCATTERING CROSS
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SECTION FOR HYBRID MULTIPATH &ARADAY ROTATION AND DIFFERENTIAL &ARADAY ROTATIONARE INCORPORATED VIA PARAMETRIC MODELS DERIVED FROM MEASUREMENTS OR COMPUTATIONAL ELECTROMAGNETICS AND THE DISTRIBUTION OBTAINED BY -ONTE #ARLO SIMULATION
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Ê76 Ê, , 'ENERAL #HARACTERISTICS AND #APABILITIES !LTHOUGH SKYWAVE PROPAGATION PROVIDES THE UNIQUE CAPABILITY OF LOW ALTITUDE TARGET DETECTION AT RANGES OF THOUSANDS OF KILOMETERS OTHER FORMS OF PROPAGATION AT (& CAN BE EXPLOITED IN RADAR APPLICATIONS "Y FAR THE MOST COMMON OF THESE IS GROUND WAVE OR SURFACE WAVE PROPAGATION WHICH IS MOST EFFECTIVE FOR VERTICALLY POLARIZED RADIOWAVES TRAVELING OVER HIGHLY CONDUCTIVE SURFACES SUCH AS SEAWATER )N ADDITION THERE ARE APPLICATIONS FOR WHICH LINE OF SIGHT OR SPACEWAVE PROPAGATION IS APPROPRIATE SUCH AS MEASUREMENT OF THE (& 2#3 OF AEROSPACE VEHICLES &URTHERMORE IN MANY INSTANCES BISTATIC CONFIGURATIONS CAN BE EMPLOYED WITH THE POSSIBILITY OF USING DIFFERENT PROPAGATION MECHANISMS FOR TRANS MITTER TARGET AND TARGET RECEIVER PATHS )N VIEW OF THE FAMILIARITY OF SPACE WAVE PROPA GATION AND THE PRECEDING DISCUSSION OF SKYWAVE SYSTEMS IT SUFFICES HERE TO ADDRESS THE MAIN FEATURES OF (& SURFACE WAVE OR GROUND WAVE RADAR (&372 (&372 SYSTEMS TEND TO FALL INTO TWO CATEGORIES I LOW POWER RADARS INTENDED PRIMARILY FOR OCEANOGRAPHIC REMOTE SENSING ESPECIALLY OF OCEAN CURRENTS AND II LARGER AND MORE POWERFUL SYSTEMS WITH TARGET DETECTION AS THEIR PRIMARY MISSION 4HE FORMER ARE IN WIDESPREAD OPERATION AROUND THE WORLD ONLY A FEW OF THE LATTER ARE OPERATIONAL IN SURVEILLANCE ROLES 4HE ABILITY OF THE LOW POWER REMOTE SENSING RADARS TO DETECT SHIPS AT OVER THE HORIZON RANGES ALTHOUGH MODEST HAS BEEN EXPLOITED IN SOME DUAL PURPOSE DEPLOYMENTS 4HE PRINCIPAL VIRTUE OF (&372 AS AN OCEAN SURVEILLANCE RADAR LIES IN ITS ABILITY TO DETECT SMALL SURFACE VESSELS AND LOW FLYING AIRCRAFT AT RANGES FAR BEYOND THE VISIBLE HORIZON !S WITH SKYWAVE RADAR PERFORMANCE DEPENDS STRONGLY ON ENVIRONMENTAL AND TARGET PARAMETERS AS WELL AS RADAR DESIGN THE DETECTION RANGES CITED IN 4ABLE PROVIDE SOME INDICATION OF CAPABILITY AGAINST SURFACE VESSELS AND LOW FLYING AIRCRAFT AS CLAIMED OR REPORTED FOR SEVERAL ESTABLISHED (&372 SYSTEMS 4!",% .OMINAL OR #LAIMED -AXIMUM $ETECTION 2ANGES KILOMETERS OF 3OME (&372
3YSTEMS 3EA3ONDE IS A COMPACT LOW POWER RADAR DESIGNED PRIMARILY FOR REMOTE SENSING IT IS AVAILABLE WITH AN UPGRADED PERFORMANCE OPTION 4HE OTHER RADARS SHOWN WERE DESIGNED FOR SURVEILLANCE )N ALL CASES PERFORMANCE MAY FALL FAR SHORT OF THE CITED VALUES UNDER INCLEMENT ENVIRONMENTAL CONDITIONS
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-UCH OF THE DISCUSSION RELATING TO SKYWAVE RADAR CARRIES OVER DIRECTLY TO (&372 BUT THERE ARE A FEW AREAS WHERE DIFFERENCES ARE SIGNIFICANT u 4HE ANTENNAS MUST BE DESIGNED AND POSITIONED TO ACHIEVE HIGH EFFICIENCY IN COUPLING TO THE SURFACE WAVE MODE %XPERIMENTS HAVE SHOWN THAT HIGHER FIELD STRENGTHS ARE GENERATED AT OVER THE HORIZON RANGES WHEN THE TRANSMITTING ANTENNA IS LOCATED CLOSE TO SEA LEVEL RATHER THAN IN AN ELEVATED POSITION PLACING THE ANTENNA EVEN JUST ONE OR TWO WAVELENGTHS ABOVE SEA LEVEL CAN INTRODUCE SEVERAL D" OF ADDITIONAL LOSS u -OST (&372 SYSTEMS USE A VERY BROAD hFLOODLIGHTv TRANSMIT BEAM TO ILLUMINATE THE ENTIRE COVERAGE ARC MULTIPLE SIMULTANEOUS RECEIVE BEAMS ARE FORMED TO FILL THE ARC AND UPDATE ALL TRACKS SIMULTANEOUSLY 4HIS REDUCES COST AND COMPLEXITY BUT INCURS SOME LOSS OF SENSITIVITY FOR NOISE LIMITED TARGET DETECTION u #OHERENT INTEGRATION TIMES MAY EXTEND TO HUNDREDS OF SECONDS AS (&372 IS NOT RELIANT ON THE IONOSPHERE AS A MEDIUM FOR PROPAGATION u /NLY VERTICALLY POLARIZED ELECTROMAGNETIC WAVES PROPAGATE EFFECTIVELY IN THE SURFACE WAVE MODE OVER THE SEA SO THE (&372 SIGNAL RECEIVING ANTENNAS ARE NECESSARILY VERTICALLY POLARIZED /N THE OTHER HAND UNWANTED SIGNALS AND INTERFERENCE ARRIVING BY SKYWAVE MAY HAVE ANY POLARIZATION 4HIS PRESENTS A MEANS FOR REJECTION OF INTER FERENCE BY FILTERING IN POLARIZATION SPACE ANY SIGNALS CORRELATED WITH THOSE RECEIVED ON AN AUXILIARY HORIZONTALLY POLARIZED RECEIVE ANTENNA CAN BE CANCELLED FROM THE OUTPUTS OF THE VERTICALLY POLARIZED ARRAY u 4HE INCREASINGLY RAPID ATTENUATION OF PROPAGATION TO RANGES BEYOND ABOUT KM AS SHOWN IN &IGURE MEANS THAT AT LONGER RANGES RELATIVELY LITTLE DETECTION PERFORMANCE IMPROVEMENT IS GAINED BY LARGE INCREASES IN TRANSMITTED POWER u 4HE RATE OF DECAY OF THE SURFACE WAVES RISES SHARPLY WITH INCREASING FREQUENCY AS SHOWN IN &IGURE WHEREAS THE 2#3 OF SMALL TARGETS TENDS TO INCREASE RAPIDLY AND EXTERNAL NOISE DECREASES )T FOLLOWS THAT RADAR DESIGN IS SENSITIVE TO THE CLASSES OF TARGETS TO BE DETECTED u 7HILE (&372 DOES NOT RELY ON THE IONOSPHERE ECHOES FROM IRREGULARITIES IN THE IONOSPHERE MAY APPEAR AT RANGES IN EXCESS OF ^ KM 3IMILARLY GROUND REFLEC TIONS RECEIVED VIA OBLIQUE SKYWAVE PROPAGATION MAY APPEAR AT RANGES IN EXCESS OF ^ KM 3UCH ECHOES MAY BE SPREAD IN DOPPLER AND CAN CONSTITUTE A SERIOUS PROB LEM FOR (&372 SYSTEMS !CCORDINGLY ANTENNAS SHOULD BE DESIGNED WITH LOW GAIN AT HIGHER ELEVATION ANGLES 4HE MAIN DESIGN PARAMETERS OF A REPRESENTATIVE (&372 SYSTEMTHE $ARONMONT 3%#!2 RADARARE LISTED IN 4ABLE 4HE CORRESPONDING VALUES FOR SKYWAVE RADARS CAN BE FOUND IN 4ABLE 0ROPAGATION #ONSIDERATIONS IN (&372 3YSTEMS 4O A GOOD APPROXIMATION WHEN A TARGET OF INTEREST IS ABOVE THE OPTICAL HORIZON OF AN (&372 THE FIELD INCI DENT ON THE TARGET CAN BE DECOMPOSED INTO TERMS THAT CORRESPOND TO I DIRECT LINE OF SIGHT II SEA SURFACE REFLECTION AND III A LATERAL OR hSURFACE ATTACHEDv WAVE "EYOND THE HORIZON THE SURFACE WAVE IS THE DOMINANT CONTRIBUTOR BUT AT SHORTER RANGES ALL THREE MECHANISMS MUST BE TAKEN INTO ACCOUNT !CCORDINGLY THE RELATIONSHIP BETWEEN I TARGET ECHO STRENGTH AND II THE RANGE AND ALTITUDE OF THE TARGET IS NOT A SIMPLE ONE -OREOVER THE CALCULATION OF THE FIELD DISTRIBUTION IS COMPUTATIONALLY EXPENSIVE IF
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4!",% 3PECIFICATIONS OF 3%#!2 AN (& 3URFACE 7AVE 2ADAR $ESIGNED FOR 3URVEILLANCE OF
THE NMI %XCLUSIVE %CONOMIC :ONE 2ADAR -ANUFACTURER 4YPE 4X 2X SITE SEPARATION KM 0OWER AVERAGE K7 0OWER PEAK K7 &REQUENCY BAND -(Z 7AVEFORM "ANDWIDTH K(Z 7AVEFORM REPETITION FREQUENCY (Z 4X ANTENNA DESIGN 2X ANTENNA DESIGN 2X APERTURE M "EAMWIDTH -(Z -(Z .O OF SIMULTANEOUS BEAMS )NSTANTANEOUS RANGE DEPTH KM .O OF RANGE BINS #OHERENT INTEGRATION TIME #)4 S .O OF DOPPLER CELLS -AX VELOCITY RESOLUTION MSn 0RIMARY MISSION 2EVISIT TIME FOR ENTIRE COVERAGE AREA 3ECONDARY MISSIONS .UMBER OF SIMULTANEOUS TARGETS TRACKED
3%#!2 $ARONMONT 4ECHNOLOGIES "ISTATIC (& SURFACE WAVE RADAR n n LINEAR &- #7 n n 3INGLE VERTICAL LOG PERIODIC ANTENNA WITH GROUND SCREEN OR ENDFIRE MONOPOLE DOUBLETS WITH GROUND SCREEN n n n OR n n n n 3HIP DETECTION %QUAL TO #)4 !IRCRAFT DETECTION 2EMOTE SENSING
ACCURATE PREDICTIONS ARE REQUIRED 4HE DIFFICULTIES ARE COMPOUNDED WHEN MIXED PATHS ARE INVOLVED THAT IS WHEN PART OF THE PROPAGATION PATH LIES OVER LAND AS HAPPENS WHERE ISLANDS ARE PRESENT IN THE COVERAGE AREA &OCUSING ATTENTION HERE ON OVER THE HORIZON DETECTION &IGURE SHOWS HOW THE SURFACE WAVE DECAYS WITH RANGE PARAMETRIC IN FREQUENCY FOR THE CASE IN WHICH BOTH THE RADAR ANTENNA AND THE TARGET ARE NEAR THE SEA SURFACE 4HESE CURVES ARE FOR A SMOOTH SURFACE AND USE A EARTH RADIUS TO APPROXIMATE ATMOSPHERIC REFRACTION EFFECTS 4HE PROPAGATION CODE USED HERE IS DUE TO "ERRY AND #HRISMAN AND IT IS QUITE FLEXIBLE PERMITTING ANTENNA AND TARGET ALTITUDES SURFACE CONDUCTIVITY AND PERMITTIVITY POLARIZA TION AND FREQUENCY TO BE SPECIFIED 4HE KEY POINTS TO BE DRAWN FROM THIS EXAMPLE ARE I THE APPARENT ADVANTAGE TO BE GAINED BY OPERATING AT LOW FREQUENCIES WHERE PROPAGA TION LOSSES ARE MINIMIZED THOUGH THIS BENEFIT MUST BE BALANCED AGAINST ANTENNA SIZE THE HIGHER NOISE ENVIRONMENT AND OFTEN REDUCED TARGET 2#3 AND II THE RAPIDLY ACCELERATING FALL OFF IN SIGNAL STRENGTH AT RANGES BEYOND A FEW HUNDRED KILOMETERS WHERE D" OF EXTRA TRANSMIT POWER MAY BUY ONLY ON THE ORDER OF KILOMETERS OF ADDITIONAL DETECTION RANGE ! MORE WIDELY USED PROPAGATION CODE IS '27!6% WHICH EMPLOYS DIFFERENT MATHEMATICAL REPRESENTATIONS FOR THE FIELD DEPENDING ON RANGE AND OTHER PARAMETERS SO AS TO MAXIMIZE COMPUTATIONAL EFFICIENCY 3OME INDICATION OF THE ACCURACY OF THIS MODEL
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&)'52% #URVES OF PROPAGATION LOSS VERSUS RANGE AS USED FOR ESTI MATING SURFACE WAVE RADAR PERFORMANCE 4HE SURFACE IS ASSUMED TO BE SMOOTH TARGET AND ANTENNA HEIGHTS ARE M CONDUCTIVITY IS TAKEN AS 3M AND THE DIELECTRIC CONSTANT IS
CAN BE FOUND IN &IGURE WHICH COMPARES '27!6% PREDICTIONS WITH EXPERIMEN TAL MEASUREMENTS OF THE SIGNAL STRENGTH RECEIVED AT A SHORE BASED (&372 WHEN THE TRANSMITTER WAS CARRIED BY A SMALL BOAT TRAVELING OUT TO A RANGE OF ^ KM 4O AVOID PERIPHERAL ISSUES CONCERNING ANTENNAS THE '27!6% CURVES HAVE BEEN ARBITRARILY NOR MALIZED HERE TO ALIGN WITH THE MEASUREMENTS AT A RANGE OF KM )T IS CLEAR THAT WITH THIS NORMALIZATION THE PREDICTIONS MATCH REASONABLY WELL OVER THE WHOLE RANGE EXTENT WITH SMALL BUT SYSTEMATIC DEPARTURES '27!6% SEEMS TO UNDERESTIMATE ATTENUATION SLIGHTLY AT -(Z BUT OVER ESTIMATE AT -(Z 4HE SEA ROUGHNESS IN THIS CASE WAS LOW SEA STATE n 4HE IMPACT OF SEA ROUGHNESS ON SIGNAL AMPLITUDE CAN BE TAKEN INTO ACCOUNT BY USING THE EXPRESSIONS FOR ROUGHNESS LOSS DERIVED BY "ARRICK !NOTHER SURFACE WAVE PROPAGATION MODELING CODE HAS BEEN DEVELOPED BY 3EVGI PAYING PARTICULAR ATTENTION TO THE CALCULATION OF PROPAGATION OVER HYBRID PATHS WITH MULTIPLE ISLANDS 4HE EFFECT OF THE TIME VARYING SEA ROUGHNESS ON THE SIGNAL PHASE AND WAVEFRONT STRUCTURE MANIFESTED IN THE TIME DELAY DOPPLER SPECTRUM AND DIRECTION OF ARRIVAL SPECTRUM OF THE RECEIVED SIGNAL CAN BE COMPUTED USING THE MULTIPLE SCATTERING THEORY OF !NDERSON ET AL
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3CATTERING 4ARGETS AND #LUTTER 4HE DISCUSSION OF (& 2#3 AND SEA CLUTTER IN 3ECTIONS AND APPLIES EQUALLY TO (&372 INDEED THE ABSENCE OF THE COR RUPTING EFFECTS OF THE IONOSPHERE PROVIDES EVEN GREATER SCOPE FOR EXPLOITING THE SCAT TERED SIGNALS &URTHERMORE ALTHOUGH THE INCREASED RATE OF DECAY OF THE SURFACE WAVE AT HIGHER FREQUENCIES IMPOSES A LIMIT ON THE RANGE OF FREQUENCIES THAT MIGHT BE USED TO DETECT A TARGET AT A GIVEN RANGE THE SITUATION IS BY NO MEANS AS RESTRICTIVE AS FOR SKY WAVE PROPAGATION 4HIS RAISES THE POSSIBILITY OF EXPLOITING MULTIPLE FREQUENCIES MORE EFFECTIVELY SO AS TO EXTRACT ADDITIONAL TARGET AND SEA STATE INFORMATION AND UNMASK TARGETS HIDDEN IN CLUTTER ! COMPELLING EXAMPLE IS PRESENTED IN &IGURE WHERE A RANGE CELL CONTAINING A SHIP TARGET TRAVELING AT A SPEED OF KNOTS HAS BEEN INTERROGATED AT EIGHT RADAR FREQUEN CIES AND THE RESULTING DOPPLER SPECTRA PLOTTED IN A NESTED DISPLAY 4HE TWO COLUMNS OF PLOTS SHOW RECEIVED POWER VERSUS DOPPLER FREQUENCY FOR THE EIGHT OPERATING FREQUENCIES AS LABELED AND FOR THE TARGET APPROACHING RIGHT COL UMN AND RECEDING LEFT COLUMN 4HE ABSCISSA UNITS ARE IN DOPPLER NORMALIZED TO
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&)'52% -ULTIFREQUENCY (&372 DOPPLER SPECTRA SHOWING THE DIFFERENT FREQUENCY DEPENDENCE OF I TARGET AND II CLUTTER SPECTRUM CHARAC TERISTICS 4HE TARGET 4 IS SHOWN WHEN APPROACHING RIGHT AND RECEDING LEFT IN THE PRESENCE OF THE SEA ECHO WITH "RAGG PEAKS MARKED ! FOR APPROACH ING AND 2 FOR RECEDING 4HE CURVES PLOT RECEIVED POWER VERSUS NORMAL IZED DOPPLER IE IN UNITS OF THE "RAGG FREQUENCY FOR EIGHT RADAR OPERATING FREQUENCIES 4HE PEAK AT ZERO FREQUENCY IS DUE TO A STATIONARY TARGET IN AN ANTENNA SIDELOBE
THE RESONANT WAVE OR "RAGG FREQUENCY THEREFORE THE RESONANT WAVE RESPONSES PEAK AT o 4HE AMPLITUDE RANGE FOR EACH PLOT IS D" 4HE NARROW PEAKS AT ZERO DOPPLER FREQUENCY ARE DUE TO LAND IN AN ANTENNA SIDELOBE 4HE TARGET DOPPLER AND "RAGG LINE FREQUENCY COINCIDE AT A RADAR FREQUENCY OF -(Z THE TARGET DOPPLER LIES BETWEEN THE "RAGG LINES FOR RADAR FREQUENCIES BELOW THAT FREQUENCY AND OUTSIDE THEM FOR
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FREQUENCIES ABOVE 4HE POSITIVE DOPPLER RESONANT WAVE PEAK IS ABOUT D" LARGER THAN THE NEGATIVE DOPPLER PEAK INDICATING A SEA DRIVEN BY WINDS BLOWING TOWARD THE RADAR 4HE PROCESSING USED IN DEVELOPING THESE DISPLAYS WAS S #)4 AND MIN AVERAGING 0ERFORMANCE -ODELING %XAMPLES OF (&372 SYSTEM PERFORMANCE MODEL ING GENERALLY FOLLOW THE PRECEPTS DESCRIBED IN 3ECTION 4HE MAIN DIFFERENCE HERE IS THE AVAILABILITY OF PATH LOSS DESCRIPTORS SUCH AS THOSE SHOWN IN &IGURE &OR EXAMPLE CONSIDER A RADAR AT -(Z WITH AN AVERAGE POWER OF K7 D"7 A TRANSMIT RECEIVE ANTENNA GAIN PRODUCT OF D" AND A TARGET AT NMI WITH AN 2#3 OF D"SM THEN THE RECEIVED POWER IS
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Ó£°£Ê /," 1 /" 4HE TERMS GROUND PENETRATING RADAR '02 GROUND PROBING RADAR SUBSURFACE RADAR OR SURFACE PENETRATING RADAR 302 REFER TO A RADAR BASED ELECTROMAGNETIC TECHNIQUE DESIGNED PRIMARILY FOR THE LOCATION OF OBJECTS OR INTERFACES BURIED BENEATH THE %ARTHS SURFACE OR LOCATED WITHIN A VISUALLY OPAQUE STRUCTURE '02 IS A SUCCESSFUL EXAMPLE OF THE EXPLOITATION OF ULTRAWIDEBAND RADAR AND TYPICALLY A '02 WITH A RANGE OF M WOULD OPERATE OVER THE RANGE '(Z TO '(Z !LTHOUGH '02 HAS MANY SIMILARITIES TO RADAR SYSTEMS THERE ARE SOME KEY DIFFER ENCES WHICH NEED TO BE APPRECIATED WHEN COMPARING THEM WITH CONVENTIONAL RADAR SYSTEMS '02 SYSTEMS ARE A SPECIAL CLASS OF ULTRAWIDEBAND 57" RADAR SYSTEM AND CAN RADIATE ENERGY IN THE RANGE OF FREQUENCIES FROM A FEW -(Z UP TO '(Z WITH A BANDWIDTH OF UP TO A DECADE BUT MORE USUALLY n OCTAVES 4HE TYPICAL AVERAGE RADI ATED POWER INTEGRATED OVER THE BAND OF INTEREST MAY BE IN THE ORDER OF A MILLIWATT BUT THE POWER PER (Z MAY BE AS LOW AS PICOWATTS '02 IS USUALLY OPERATED SO THAT THE TARGET WHICH IS WITHIN A LOSSY DIELECTRIC IS ONLY A FEW WAVELENGTHS FROM THE APERTURE OF ANTENNA 4HE TOTAL PATH LOSSES WITHIN A FEW WAVELENGTHS MAY REACH D" OR MORE DEPENDING ON THE MATERIAL -ANY '02 SYSTEMS OPERATE IN A REGION WHERE THE WAVELENGTHS RADIATED ARE GREATER OR IN THE SAME ORDER OF MAGNITUDE AS THE TARGET DIMENSIONS 4HUS '02 OPERATES BETWEEN THE 2AYLEIGH REGION AND -IE OR RESONANCE REGION OF THE TARGET DIMENSIONS 4HIS IS VERY DIFFERENT FROM CONVENTIONAL RADAR SYSTEMS WHERE THE TARGET DIMENSIONS ARE MUCH LARGER THAN THE WAVELENGTH OF THE INCIDENT RADIATION IE THE OPTICAL REGION 4HE TECHNOLOGY OF '02 IS LARGELY APPLICATIONS ORIENTED AND THE OVERALL DESIGN PHI LOSOPHY AS WELL AS THE HARDWARE IS USUALLY DEPENDENT ON THE TARGET TYPE AND THE MATE RIAL OF THE TARGET AND ITS SURROUNDINGS '02 IS VULNERABLE TO EXTREMELY HIGH LEVELS OF CLUTTER AT SHORT RANGES AND THIS RATHER THAN SIGNALNOISE RECOVERY IS ITS MAJOR TECHNICAL CHALLENGE 4HE SYSTEM TO BE SPECIFIED SHOULD TAKE THIS INTO ACCOUNT !LL THESE ASPECTS POSE SPECIAL DESIGN PROBLEMS FOR '02 WHICH IS DESCRIBED IN DETAIL BY $ANIELS 4HIS CHAPTER IS A SUMMARY OF THAT MATERIAL AND IS REFERENCED BY COURTESY OF THE )%% ! TYPICAL '02 SYSTEM IS SHOWN IN &IGURE AND CONSISTS OF A PAIR OF ANTENNAS ONE FOR TRANSMIT AND ONE FOR RECEIVE CONNECTED TO THE TRANSMITTER RECEIVER AND PROCES SOR AND CONTAINED WITHIN A SEALED ENCLOSURE A BATTERY AND CONTROL PROCESSOR AND DIS PLAY UNIT 4HE WHEELS DRIVE A SHAFT ENCODER THAT TRIGGERS DATA ACQUISITION AND HENCE THE DISPLAY THAT IS SYNCHRONISED TO THE MOVEMENT OF THE SYSTEM !N EXAMPLE OF THE DISPLAY Ó£°£
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&)'52% 4YPICAL '02 SYSTEM #OURTESY 53 2ADAR
WHICH TAKES THE FORM OF A CROSS SECTION OF THE GROUND SURVEYED BY THE '02 IS SHOWN IN &IGURE 4HE HORIZONTAL SCALE IS CM PER MARKER AND THE VERTICAL SCALE IS TIME IN NANOSECONDS NS !N EXPLANATION OF THE IMAGE IS PROVIDED LATER IN THIS CHAPTER '02 SYSTEM DESIGN CAN BE CLASSIFIED INTO TWO GROUPS '02 SYSTEMS THAT TRANSMIT AN IMPULSE AND RECEIVE THE REFLECTED SIGNAL FROM THE TARGET USING A SAMPLING RECEIVER CAN BE CONSIDERED TO OPERATE IN THE TIME DOMAIN '02 SYSTEMS THAT TRANSMIT INDIVIDUAL FRE QUENCIES IN A SEQUENTIAL MANNER AND RECEIVE THE REFLECTED SIGNAL FROM THE TARGET USING A FREQUENCY CONVERSION RECEIVER CAN BE CONSIDERED TO OPERATE IN THE FREQUENCY DOMAIN 4HE FIRST USE OF ELECTROMAGNETIC SIGNALS TO DETERMINE THE PRESENCE OF REMOTE TERRES TRIAL METAL OBJECTS IS GENERALLY ATTRIBUTED TO (ÓLSMEYER IN BUT THE FIRST DESCRIPTION OF THEIR USE FOR LOCATION OF BURIED OBJECTS APPEARED SIX YEARS LATER IN A 'ERMAN PATENT BY ,EIMBACH AND ,WY 4HE WORK OF (ÓLSENBECK IN APPEARS TO BE THE FIRST USE OF PULSED TECHNIQUES TO DETERMINE THE STRUCTURE OF BURIED FEATURES (E NOTED THAT ANY
&)'52% 4YPICAL DISPLAY FROM '02
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DIELECTRIC VARIATION NOT NECESSARILY INVOLVING CONDUCTIVITY WOULD ALSO PRODUCE REFLEC TIONS AND THAT THE TECHNIQUE THROUGH THE EASIER REALIZATION OF DIRECTIONAL SOURCES HAD ADVANTAGES OVER SEISMIC METHODS 0ULSED TECHNIQUES WERE DEVELOPED FROM THE S ONWARD AS A MEANS OF PROBING TO CONSIDERABLE DEPTHS IN ICE 3TEENSON AND %VANS IN FRESH WATER AND SALT DEPOSITS 5NTERBERGER IN DESERT SAND AND ROCK FORMATIONS +ADABA AND -OREY 0ROBING OF ROCK AND COAL WAS ALSO INVESTIGATED BY #OOK AS WELL AS 2OE ALTHOUGH THE HIGHER ATTENUATION IN THE LATTER MATERIAL MEANT THAT DEPTHS GREATER THAN A FEW METERS WERE IMPRACTICAL .ILSSON GIVES A MORE EXTENDED ACCOUNT OF THE HISTORY OF '02 AND ITS GROWTH UP TO THE MID S &ROM THE S THE RANGE OF APPLICATIONS HAS BEEN EXPANDING STEADILY AND NOW INCLUDES THOSE GIVEN IN 4ABLE 0URPOSE BUILT EQUIPMENT FOR EACH OF THESE APPLICATIONS HAS BEEN BEING DEVELOPED AND THE USER NOW HAS A BETTER CHOICE OF EQUIPMENT AND TECHNIQUES '02 HAS ADVANCED RAPIDLY AS A RESULT OF A VARIETY OF APPLICATIONS BUT AS THE REQUIRE MENTS HAVE BECOME MORE DEMANDING SO THE EQUIPMENT TECHNIQUES AND DATA PROCESS ING METHODS HAVE BEEN DEVELOPED AND REFINED ! '02 TRANSMITS A REGULAR SEQUENCE OF LOW POWER PULSES OF ELECTROMAGNETIC ENERGY INTO THE MATERIAL OR GROUND AND THEN RECEIVES AND DETECTS THE WEAK REFLECTED SIGNAL FROM THE BURIED TARGET 4HE ENERGY IS IN THE FORM OF EITHER A VERY SHORT DURA TION IMPULSE A SWEEP OVER A RANGE OF FREQUENCIES RADIATION OF NOISE OVER A DEFINED BAND OR A PSEUDORANDOM CODED SEQUENCE OF PULSES -OST '02 SYSTEMS ALL OF WHICH NEED TO COMPLY WITH THE RELEVANT NATIONAL AND INTERNATIONAL REGULATIONS REGARDING RADIO TRANSMITTERS OPERATE WITHIN THE RANGE OF FREQUENCIES FROM -(Z TO '(Z AND CAN HAVE A BANDWIDTH OF SEVERAL '(Z 4HE &## REQUIREMENT FOR 57" LIMITS THE RADIATED POWER TO n D"M (Zn 4HE TOPIC OF RADAR SYSTEM DESIGN IS COVERED IN MANY TEXTS AND USEFUL INFORMATION WILL BE FOUND IN THE FOLLOWING REFERENCES $ANIELS #OOK AND "ERNFELD 3KOLNIK .ATHANSON 7EHNER 'ALATI AND !STANIN AND +OSTYLEV 4HE BURIED TARGET CAN BE A CONDUCTOR A DIELECTRIC OR COMBINATIONS OF BOTH 4HE SURROUNDING HOST MATERIAL CAN BE SOIL EARTH MATERIALS WOOD ROCKS ICE FRESH WATER OR MANMADE MATERIALS SUCH AS CONCRETE OR BRICK ! TYPICAL '02 ACHIEVES A RANGE OF UP TO A FEW METERS BUT SOME SPECIAL SYSTEMS CAN PENETRATE UP TO HUNDREDS OF METERS OR EVEN KILOMETERS ! FEW '02 SYSTEMS HAVE BEEN OPERATED FROM AIRCRAFT AND FROM SATELLITES TO IMAGE GEOLOGICAL FEATURES BURIED BENEATH THE 3AHARAN DESERTS AS WELL AS MEASURING THE DEPTH OF THE -OON AND FEATURES ON -ARS OR COMETS 4HE RANGE OF THE '02 IN THE GROUND IS LIMITED BECAUSE OF THE ABSORPTION THE SIGNAL UNDERGOES WHILE IT TRAVELS ON ITS TWO WAY PATH THROUGH THE GROUND MATERIAL '02 WORKS WELL THROUGH MATERIALS SUCH AS GRANITE DRY SAND SNOW ICE AND FRESH WATER BUT WILL NOT PENETRATE CERTAIN CLAYS THAT
4!",% -AIN !PPLICATIONS OF '02
!RCHAEOLOGICAL INVESTIGATIONS "RIDGE DECK ANALYSIS $ETECTION OF BURIED MINES ANTI PERSONNEL AND ANTI TANK &ORENSIC INVESTIGATIONS DETECTING BURIED BODIES 'EOPHYSICAL INVESTIGATIONS 0IPES AND CABLE DETECTION 2AIL TRACK AND BED INSPECTION 2OAD CONDITION SURVEY 3NOW ICE AND GLACIER
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ARE HIGH IN SALT CONTENT OR SALT WATER BECAUSE OF THE HIGH ABSORPTION OF ELECTROMAGNETIC ENERGY OF SUCH MATERIALS &OR COMPARISON THE TOTAL TWO WAY PATH LOSS FROM %ARTH TO THE -OON USING A '(Z RADAR WOULD BE GREATER THAN D" FOR A RANGE OF KM AND A TARGET RADAR CROSS SECTION IN THE ORDER OF M WHEREAS A '02 RADAR OFTEN ENCOUNTERS A PATH LOSS IN EXCESS OF D" FOR RANGES OF LESS THAN A METER )N AIR THE '02 SIGNAL TRAVELS AT THE SPEED OF LIGHT BUT IS SLOWED DOWN IN GROUND MATERIALS BY THEIR DIELECTRIC CONSTANT HENCE TRUE RANGE NEEDS CALIBRATING FOR EACH MATERIAL '02 WILL NOT PENETRATE METAL BECAUSE OF THE LATTERS CONDUCTIVITY 4HERE ARE NOW A NUMBER OF COMMERCIALLY AVAILABLE EQUIPMENTS AND THE TECHNIQUE IS GRADUALLY DEVELOPING IN SCOPE AND CAPABILITY -ANY '02 SYSTEMS ARE MOBILE AND MOUNTED ON WHEELS OR SKIDS TO BE MOVED BY HAND BUT SYSTEMS CAN BE USED ON VEHICLES FOR RAPID SURVEY BY MEANS OF AN ARRAY OF ANTENNAS /THER '02 SYSTEMS ARE DESIGNED TO BE INSERTED INTO BOREHOLES TO PROVIDE IMAGES OF THE INTERVENING ROCK 4YPICAL '02 SYSTEM ATTRIBUTES ARE GIVEN IN 4ABLE -OST '02 SYSTEMS USE SEPARATE MAN PORTABLE TRANSMIT AND RECEIVE ANTENNAS WHICH ARE PLACED ON THE SURFACE OF THE GROUND AND MOVED IN A KNOWN PATTERN OVER THE SURFACE OF THE GROUND OR MATERIAL UNDER INVESTIGATION AND AN IMAGE CAN BE GENERATED IN REAL TIME ON A DISPLAY EITHER IN GREY SCALE OR IN COLOR "Y SYSTEMATICALLY SURVEYING THE AREA IN A REGULAR GRID PATTERN A RADAR IMAGE OF THE GROUND CAN BE BUILT UP '02 IMAGES ARE DISPLAYED EITHER AS TWO DIMENSIONAL REPRESENTATIONS USING HORIZONTAL X OR Y AND DEPTH Z AXES OR A HORIZONTAL PLANE REPRESENTATION X Y AT A GIVEN DEPTH Z OR AS A THREE DIMENSIONAL RECONSTRUCTION '02 DATA MAY BE CLASSIFIED AS ! SCAN " SCAN OR # SCAN DEPENDING ON THE PLANE OF IMAGE NOTE THESE ARE NOT THE SAME AS CONVENTIONAL RADAR ! " AND # SCANS ! '02 ! SCAN IS A MEASUREMENT AT A SINGLE FIXED POINT IN SPACE AND IS DISPLAYED IN AMPLITUDE Y AND RANGE X ! " SCAN IS A REPRESENTATION USUALLY IN GRAYSCALE OR COLOR CODED IMAGE INTENSITY OF A PLANE X Z OR Y Z OF SCAN WHEREAS A # SCAN REPRESENTS A HORIZONTAL PLANE X Y AT A GIVEN DEPTH Z !LTERNATIVELY THE '02 MAY BE DESIGNED TO PROVIDE AN AUDIBLE WARNING OF TARGET PRESENCE WHILE THE '02 IS MOVED 4HE '02 IMAGE OF A TARGET IS VERY DIFFERENT FROM ITS OPTICAL IMAGE BECAUSE THE WAVELENGTHS OF THE ILLUMINATING RADIATION ARE SIMILAR IN DIMENSION TO THE TARGET 4HIS RESULTS IN A MUCH LOWER DEFINITION IN THE '02 IMAGE AND ONE THAT IS HIGHLY DEPENDENT ON THE PROPAGATION CHARACTERISTICS OF THE GROUND 4HE BEAM PATTERN OF THE ANTENNA IS WIDELY SPREAD IN THE DIELECTRIC AND THIS DEGRADES THE SPATIAL RESOLUTION OF THE IMAGE UNLESS CORRECTED 2EFRACTION AND ANISOTROPIC CHARACTERISTICS OF THE GROUND MAY ALSO DISTORT THE IMAGE &OR SOME LONGER RANGE SYSTEMS SYNTHETIC APERTURE PROCESSING TECH NIQUES ARE USED TO OPTIMIZE THE RESOLUTION OF THE IMAGE AND WILL BE DISCUSSED LATER 4!",% #HARACTERISTICS OF '02 3YSTEMS IN A 3OIL OF 2ELATIVE $IELECTRIC #ONSTANT OF AND
,OSS 4ANGENT OF 0ULSE $URATION IN NS
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5NPROCESSED '02 IMAGES OFTEN SHOW hBRIGHT SPOTSv CAUSED BY MULTIPLE INTER NAL REFLECTIONS AS WELL AS A DISTORTION OF THE ASPECT RATIO OF THE IMAGE OF THE TARGET CAUSED BY VARIATIONS IN THE VELOCITY OF PROPAGATION 3YMMETRICAL TARGETS SUCH AS SPHERES OR PIPES CAUSE MIGRATION OF THE REFLECTED ENERGY TO A HYPERBOLIC PATTERN '02 IMAGES CAN BE PROCESSED TO COMPENSATE FOR THESE EFFECTS AND THIS IS USUALLY CARRIED OUT OFFLINE ! '02 CAN BE DESIGNED TO DETECT SPECIFIC TARGETS SUCH AS INTERFACES IN ROADS PIPES AND CABLES BY MEANS OF POLARIZED RADIATION AND LOCALIZED OBJECTS SUCH AS CUBES SPHERES AND CYLINDERS '02 IS CAPABLE OF DETECTING FEATURES MANY HUNDREDS OF YEARS OLD HENCE A PROSPECTIVE SITE SHOULD REMAIN UNEXCAVATED PRIOR TO SURVEY SO AS TO PRESERVE ITS INFORMATION ! SIMPLIFIED DIAGRAM OF THE VARIOUS SOURCES OF CLUTTER IN A '02 ENVIRONMENT IS GIVEN IN &IGURE AND IT CAN BE SEEN THAT SEPARATION OF THE VARIOUS SIGNALS IS THE KEY TO IDENTIFYING THE WANTED SIGNAL )NEVITABLY THERE HAVE BEEN SOME CLAIMS FOR '02 CAPABILITY THAT ARE SIMPLY OUT SIDE THE REALMS OF KNOWN PHYSICS AND THESE SEEM TO HAVE BEEN SEIZED ON BY SOME SECTIONS OF THE MEDIA ! CLAIM WAS MADE THAT A PARTICULAR '02 AND ITS OPERATOR COULD DETECT TARGETS THE SIZE OF GOLF BALLS AT A DEPTH OF EIGHT METERS #LEARLY THE WAVELENGTHS CAPABLE OF PROPAGATING TO EIGHT METERS IN SOIL WOULD BE SO MUCH LARGER THAN A GOLF BALLnSIZED TARGET THAT THE RADAR CROSS SECTIONAL AREA OF THE LATTER WOULD FADE INTO INSIGNIFICANCE EVEN NOISE 4HE PERSUASIVENESS OF THE CLAIMANT AND THE LACK OF UNDERSTANDING OF BASIC PHYSICS ON THE PART OF SOME POTENTIAL USERS ENABLED THIS KIND OF CLAIM TO BE SERIOUSLY CONSIDERED #LAIMS WERE MADE THAT A '02 HAD BEEN DEVELOPED hTHAT CAN PROVIDE THREE DIMENSIONAL IMAGES OF OBJECTS UP TO METERS BELOW THE SURFACE OF LAND AND SEA 3UCH A DEVICE WOULD ALLOW VERIFIERS TO IDENTIFY UNDERGROUND WEAPONS FACILITIES LIKE THOSE OF CONCERN IN ,IBYA )RAQ AND .ORTH +OREA 4HE UNDERWATER DETECTION CAPABILITY COULD ALSO BE USED TO VERIFY TREATIES DEALING WITH SUBMARINES AND NUCLEAR WEAPONS POSITIONED ON THE SEABEDv (OW WELL
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'02 WOULD PROPAGATE THROUGH SEAWATER IS AN INTERESTING QUESTION GIVEN THE KNOWN ATTENUATION OF SEAWATER AT RADAR FREQUENCIES ! CAREFUL ANALYSIS OF SOME OF THE CLAIMS ABOUT THE SAME RADAR WAS PUBLISHED BY 4ULEY AND IS INTERESTING READING
Ó£°ÓÊ *9- -Ê"Ê*,"*/" Ê Ê / , )NTRODUCTION #ONVENTIONAL RADAR SYSTEMS ARE GENERALLY NOT SIGNIFICANTLY AFFECTED BY THE PROPAGATION CHARACTERISTICS OF THE MEDIUM THE RADAR SIGNALS TRAVEL THROUGH APART FROM RAIN ABSORPTION SPECTRA OF THE ATMOSPHERE OR IONIZED ATMOSPHERIC LAYERS 4HIS IS DEFINITELY NOT THE CASE WITH '02 WHERE THE TRANSMISSION MEDIUM MAY BE NON ISOTRO PIC HIGH DIELECTRIC AND HIGH LOSS AND MAY BE LAYERED 4HEREFORE AN UNDERSTANDING OF SOIL AND MATERIAL PROPAGATION CHARACTERISTICS IS IMPORTANT AND THIS SECTION DESCRIBES THE KEY FEATURES OF THE PHYSICS OF PROPAGATION IN MATERIALS -AXWELLS EQUATIONS ARE THE FOUNDATION FOR THE CONSIDERATION OF THE PROPAGATION OF ELECTROMAGNETIC WAVES )N FREE SPACE THE MAGNETIC SUSCEPTIBILITY AND ELECTRIC PERMITTIVITY ARE CONSTANTS THAT IS THEY ARE INDEPENDENT OF FREQUENCY AND THE MEDIUM IS NOT DISPERSIVE )N A DIELECTRIC WITH A ZERO LOSS TANGENT NO LOSSES DUE TO ATTENUATION ARE ENCOUNTERED AND HENCE THERE IS NO CONSIDERATION OF THE ATTENUATION WHICH OCCURS IN REAL DIELECTRIC MEDIA )F AN ALTERNATING ELECTRIC FIELD IS APPLIED TO A MATERIAL THE INDIVIDUAL MOLECULES WILL BE INDUCED TO ROTATE IN AN OSCILLATORY MANNER ABOUT AN AXIS THROUGH THEIR CENTERS THE INERTIA OF THE MOLECULES PREVENTING THEM FROM RESPONDING INSTANTANEOUSLY 3IMILAR TRANSLATIONAL EFFECTS CAN OCCUR 4HE POLARIZATION PRODUCED BY AN APPLIED FIELD SUCH AS A PROPAGATING RADAR WAVE IS CLOSELY RELATED TO THE THERMAL MOBILITY OF THE MOLECULES AND IS THEREFORE STRONGLY TEMPERATURE DEPENDENT .OTE THAT POLARIZATION IN THIS CONTEXT IS DIFFERENT FROM THE POLARIZATION OF %- WAVES )N GENERAL THE RELAXATION TIME WHICH MAY BE EXPRESSED AS A RELAXATION FREQUENCY DEPENDS ON ACTIVATION ENERGY THE NATURAL FREQUENCY OF OSCILLATION OF THE POLARIZED PARTICLES AND ON TEMPERATURE 2ELAXATION FREQUENCIES VARY WIDELY BETWEEN DIFFERENT MATERIALS &OR EXAMPLE MAXIMUM ABSORPTION OCCURS AT VERY LOW FREQUENCIES IN ICE (Z WHEREAS IT TAKES PLACE IN THE MICROWAVE REGION IN WATER (Zn (Z THUS THE EFFECTS OF THIS PHENOMENON CAN HAVE A DIRECT BEARING UPON THE DIELECTRIC PROPERTIES OF MATERIALS AT THE FREQUENCIES EMPLOYED BY '02S ESPECIALLY IF MOISTURE IS PRESENT WITHIN A MATERIAL 4HERE ARE A NUMBER OF OTHER MECHANISMS WHICH CAUSE A SEPARA TION OF POSITIVELY AND NEGATIVELY CHARGED IONS RESULTING IN ELECTRIC POLARIZATION 4HESE MECHANISMS CAN BE ASSOCIATED WITH IONIC ATMOSPHERES SURROUNDING COLLOIDAL PARTICLES PARTICULARLY CLAY MINERALS ABSORBED WATER AND PORE EFFECTS AS WELL AS INTERFACIAL PHENOMENON BETWEEN PARTICLES 4HE GENERAL FORM OF THE MODEL THAT DESCRIBES THE FREQUENCY DEPENDENCE OF SUCH SYSTEMS IS THE $EBYE RELAXATION EQUATION
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D ` IS THE REAL PART OF THE DIELECTRIC PERMITTIVITY D ` REAL PART OF THE DIELECTRIC PERMITTIVITY D p IMAGINARY PART OF THE DIELECTRIC PERMITTIVITY D c HIGH FREQUENCY LIMITING VALUE OF THE PERMITTIVITY
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D S LOW FREQUENCY LIMITING VALUE OF THE PERMITTIVITY V RADIAN FREQUENCY O F S RELAXATION TIME CONSTANT
4HE FREQUENCY OF MAXIMUM MOVEMENT AND LOSS OCCURS AT V S )N GENERAL SINGLE RELAXATIONS ARE RARELY OBSERVED IN NATURAL SYSTEMS )NSTEAD THERE ARE DISTRIBUTIONS OF RELAXATIONS CORRESPONDING TO DISTRIBUTIONS OF SIZE SCALES THAT INFLUENCE MOVEMENT OF CHARGE 4HERE ARE SEVERAL EQUATIONS DESCRIBING SUCH DISTRIBUTED SYSTEMS WITH THE MOST COMMON EXPERIMENTAL OBSERVATIONS IN AGREEMENT WITH THE MODEL FROM #OLE AND #OLE
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WHERE @ DESCRIBES THE BREADTH OF THE TIME CONSTANT DISTRIBUTION FROM A SINGLE RELAXATION @ TO AN INFINITELY BROAD DISTRIBUTION @ WITH A COMMON PROCESS $IFFERENT POLARIZATION PROCESSES MAY BE DESCRIBED BY A SERIES OF #OLE #OLE EQUATIONS WITH DIF FERENT VALUES OF @ AND OTHER PARAMETERS 4HE ELECTROMAGNETIC PROPERTIES OF A BURIED TARGET MUST BE DIFFERENT FROM THE SUR ROUNDING SOIL OR MATERIAL AND THIS MEANS THAT TO A FIRST ORDER ITS RELATIVE DIELECTRIC CON STANT SHOULD BE SIGNIFICANTLY LESSER OR GREATER THAN THE HOST SOIL 4YPICALLY MOST SOILS EXHIBIT A RELATIVE DIELECTRIC CONSTANT WHICH RANGES BETWEEN TO &RESH WATER HAS A RELATIVE DIELECTRIC CONSTANT OF APPROXIMATELY )T SHOULD BE NOTED THAT THE GROUND AND SURFACE ARE QUITE LIKELY TO BE INHOMOGENEOUS AND CONTAIN INCLUSIONS OF OTHER ROCKS OF VARIOUS SIZE AS WELL AS MANMADE DEBRIS 4HIS SUGGESTS THAT THE SIGNAL TO CLUTTER PER FORMANCE OF THE SENSOR IS LIKELY TO BE AN IMPORTANT PERFORMANCE FACTOR #LUTTER MAY BE REGARDED AS ANY RADAR RETURN THAT IS NOT ASSOCIATED WITH THE WANTED TARGET AND NEEDS TO BE DEFINED WITH RESPECT TO A PARTICULAR APPLICATION !TTENUATION %LECTROMAGNETIC WAVES PROPAGATING THROUGH NATURAL MEDIA EXPERI ENCE LOSSES TO BOTH THE ELECTRIC % OR MAGNETIC ( FIELDS 4HIS CAUSES ATTENUATION OF THE ORIGINAL ELECTROMAGNETIC WAVE 0LANE WAVES ARE GOOD APPROXIMATIONS TO REAL WAVES IN MANY PRACTICAL SITUATIONS -ORE COMPLICATED ELECTROMAGNETIC WAVEFRONTS CAN BE CONSIDERED AS A SUPERIMPOSITION OF PLANE WAVES AND THIS METHOD MAY BE USED TO GAIN AN INSIGHT INTO MORE COMPLEX SITUATIONS &OR MOST SOILS OF INTEREST IN '02 THE MAGNETIC RESPONSE IS WEAK AND NEED NOT BE CONSIDERED AS A COMPLEX QUANTITY UNLIKE THE PERMITTIVITY AND CONDUCTIVITY (OWEVER IN CERTAIN SOIL TYPES SUCH AS THOSE DERIVED FROM VOLCANIC ROCKS OR OTHERWISE HIGH IN IRON CONTENT FULL CONSIDERATION OF THE MAG NETIC PROPERTIES IS NECESSARY )N THE CASE OF LOSSY DIELECTRIC MATERIALS BOTH CONDUCTION AND DIELECTRIC EFFECTS CAUSE ABSORPTION OF ELECTROMAGNETIC RADIATION 4HE ELECTROMAGNETIC MATERIAL PROPERTIES THAT DESCRIBE SUCH A SYSTEM ARE IN THE COM PLEX PROPAGATION CONSTANT F
G IK A IA
WHERE F PROPAGATION CONSTANT K WAVE NUMBER O K @ ATTENUATION CONSTANT ;NEPERSM= A PHASE CONSTANT ;RADIANSM=
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4HE FIELD AT A DISTANCE Z FROM THE SOURCE IS GIVEN BY % Z T % E A Z E J W T A Z
4HE WAVELENGTH K IN THE MEDIUM IS IN METERS
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WHERE F IS FREQUENCY IN (ERTZ 4HE LOSSES IN SUCH SYSTEMS ARE DESCRIBED IN TERMS OF TANGENTS OF LOSS ANGLES C BETWEEN ELECTRIC AND MAGNETIC FIELDS 4HE ELECTRICAL LOSS TANGENT IS GIVEN BY
E `` S S TAN D E WHICH CAN BE SIMPLIFIED TO TAN D E y FOR LOW LOSS MATERIALS E` WE` WE` REPRESENTING THE SUM OF THE CHARGE TRANSPORT AND POLARIZATION RELAXATION LOSSES AND THE PHASE ANGLE BETWEEN ELECTRIC FIELD AND CURRENT DENSITY 4HE SKIN DEPTH OR ATTENUATION LENGTH IS @ ;M= THE DISTANCE ELECTROMAGNETIC ENERGY TRAVELS WHILE BEING ATTENUATED BY E IN AMPLITUDE 4HIS DISTANCE IS KNOWN AS THE SKIN DEPTH D AND PROVIDES AN INITIAL GUIDE TO THE USEFUL PENETRATION DEPTH OF A '02 SYSTEM ALTHOUGH IN SOME MEDIA THE USEFUL RANGE MAY BE GREATER 4HE INDIVIDUAL PROPAGATION CONSTANTS CAN BE WRITTEN AS WHERE
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@ ATTENUATION FACTOR A PHASE CONSTANT
AND THE DIMENSIONLESS FACTOR D pD ` IS MORE COMMONLY TERMED THE MATERIAL LOSS TANGENT 4HIS DISCUSSION HAS NOT CONSIDERED THE ELECTROMAGNETIC AND MAGNETIC LOSS TANGENT AND THESE MAY NEED TO BE CONSIDERED IN SPECIAL CASES )T CAN BE SEEN FROM THE ABOVE EXPRESSIONS THAT THE ATTENUATION CONSTANT OF A MATE RIAL IS TO A FIRST ORDER LINEARLY RELATED IN D"Mn TO FREQUENCY )T IS NOT SUFFICIENT TO CONSIDER ONLY THE LOW FREQUENCY CONDUCTIVITY WHEN ATTEMPTING TO DETERMINE THE LOSS TANGENT OVER THE FREQUENCY RANGE TO (Z )N THE CASE OF A MATERIAL THAT IS DRY AND RELATIVELY LOSSLESS IT MAY BE REASONABLE TO CONSIDER THAT TAN CE IS CONSTANT OVER THAT FREQUENCY RANGE (OWEVER FOR MATERIALS THAT ARE WET AND LOSSY SUCH AN APPROXIMATION IS INVALID (OWEVER THERE ARE A NUMBER OF OTHER FACTORS THAT INFLUENCE THE EFFECTIVE PENETRATION DEPTH NOTABLY THE STRENGTH OF REFLECTION FROM THE TARGET SOUGHT AND THE DEGREE OF CLUTTER SUPPRESSION OF WHICH THE SYSTEM IS CAPABLE ! FIRST ORDER ESTIMATE OF THE VARIOUS CONTRIBUTIONS TO SIGNAL LOSS CAN BE CARRIED OUT USING THE STANDARD RADAR RANGE EQUATION ALTHOUGH THIS IS ONLY APPLICABLE FOR FAR FIELD CONDITIONS AND THUS HAS RESTRICTIONS
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TRANSMITTED POWER IN WATTS RECEIVED POWER IN WATTS ANTENNA GAIN ANTENNA EFFECTIVE APERTURE RANGE IN METERS TARGET RADAR CROSS SECTION CALIBRATION COEFFICIENT
4HE CUMULATIVE LOSSES INCLUDE THE TRANSMISSION COEFFICIENTS INTO THE GROUND THE SPREADING LOSSES DESCRIBE THE 2n LOSSES FOR A TARGET OF M AND THE ATTENUATION LOSSES ARE FOR A SOIL WITH A DR OF AND TAN C OF &IXED LOSSES INCLUDE THE TRANS MISSION LOSSES INTO THE SOIL AND THE EFFECTIVE RADAR CROSS SECTION OF THE TARGET WHICH COMPRISES ITS TRUE RADAR CROSS SECTION AND REFLECTION LOSS FROM THE TARGET .OTE THAT A CONDUCTING REFLECTOR WILL HAVE LOW RETURN LOSS WHEREAS A NONCONDUCTING REFLECTOR WILL HAVE A HIGH RETURN LOSS )N &IGURE THE CALCULATION HAS BEEN DERIVED FROM METER TO METERS AS THE RADAR RANGE EQUATION IS NOT AN ACCURATE MODEL IN THIS RANGE LESS THAN METER AND THE PURPOSE OF THE EXPLANATION IS TO PROVIDE A BASIC INTRODUCTION TO FIRST ORDER SIGNAL ESTIMATION
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2EFLECTION )N ANY ESTIMATION OF RECEIVED SIGNAL LEVEL IT IS NECESSARY TO CONSIDER THE COEFFICIENTS OF REFLECTION AND TRANSMISSION AS THE WAVE PASSES THROUGH THE DIELECTRIC TO THE TARGET AND 3NELLS ,AWS DESCRIBE THE ASSOCIATED ANGLES OF INCIDENCE REFLECTION TRANSMISSION AND REFRACTION 7HERE LOSSY MATERIALS ARE INVOLVED COMPLEX ANGLES OF REFRACTION MAY OCCUR UNLIKE THE SIMPLE CLASSICAL CASE AND POLARIZATION AND THE 3TOKES MATRIX MAY ALSO BE REQUIRED FOR ORIENTED HIGH ASPECT RATIO FEATURES LIKE PIPES WIRES AND FRACTURES
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4HE INTRINSIC IMPEDANCE G OF A MEDIUM IS THE RELATIONSHIP BETWEEN THE ELECTRIC FIELD % AND THE MAGNETIC FIELD ( AND IS A COMPLEX QUANTITY GIVEN BY
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!T THE BOUNDARY BETWEEN TWO MEDIA SOME ENERGY WILL BE REFLECTED AND THE REMAINDER TRANSMITTED 4HE REFLECTED FIELD STRENGTH IS DESCRIBED BY THE REFLECTION COEFFICIENT R
R
H H H H
WHERE G AND G ARE THE IMPEDANCES OF MEDIUM AND RESPECTIVELY 4HE REFLECTION COEFFICIENT HAS A POSITIVE VALUE WHEN G G SUCH AS WHERE AN AIR FILLED VOID EXISTS IN A DIELECTRIC MATERIAL 4HE EFFECT ON A PULSE WAVEFORM IS TO CHANGE THE PHASE OF THE REFLECTED WAVELET SO THAT TARGETS WITH DIFFERENT RELATIVE DIELEC TRIC CONSTANTS TO THE HOST MATERIAL SHOW DIFFERENT PHASE PATTERNS OF THE REFLECTED SIGNAL (OWEVER THE PROPAGATION PARAMETERS RELATIVE DIELECTRIC CONSTANT AND LOSS TANGENT OF THE HOST MATERIAL THE GEOMETRIC CHARACTERISTICS OF THE TARGET AND ITS DIELECTRIC PARAM ETERS AFFECT THE AMPLITUDE OF THE REFLECTED SIGNAL #LUTTER ! MAJOR DIFFICULTY FOR OPERATION OF '02 SYSTEMS IS THE PRESENCE OF CLUTTER WITHIN THE MATERIAL #LUTTER IS DEFINED AS SOURCES OF UNWANTED REFLECTIONS THAT OCCUR WITHIN THE EFFECTIVE BANDWIDTH AND SEARCH WINDOW OF THE RADAR AND PRESENT AS SPATIALLY COHERENT REFLECTORS 4HE DEFINITION OF CLUTTER VERY MUCH DEPENDS ON THE WANTED TARGET 4HE OPERATOR OF A '02 SYSTEM SEARCHING FOR PIPES MAY CLASSIFY THE INTERFACES BETWEEN ROAD LAYERS AS CLUTTER WHEREAS THE OPERATOR OF A SYSTEM MEASURING ROAD LAYER THICKNESS MIGHT CONSIDER PIPES AND CABLES AS SOURCES OF CLUTTER #AREFUL DEFINITION AND UNDERSTANDING ARE CRITICALLY IMPORTANT IN SELECTING AND OPERATING THE BEST SYSTEM AND PROCESSING ALGORITHMS #LUTTER CAN COMPLETELY OBSCURE THE BURIED TARGET AND A PROPER UNDERSTANDING OF ITS SOURCE AND IMPACT ON THE RADAR IS ESSENTIAL 0OLARIZATION ! COMPLETE DESCRIPTION OF THE RADAR SCATTERING CROSS SECTION OF A TARGET INCLUDES A DESCRIPTION OF ITS POLARIZATION SCATTERING CHARACTERISTICS NOT THE SAME AS MOLECULAR POLARIZATION 4HE POLARIZING PROPERTIES OF TARGETS ARE DESCRIBED BY THE 3TOKES PARAMETERS AND THE POLARIZATION COORDINATES CAN BE REPRESENTED ON THE 0OINCARE 3PHERE !LL OF THESE ARE WELL DESCRIBED IN STANDARD TEXTS ON OPTICS AND ELECTROMAGNETIC THEORY )N SUMMARY THESE DESCRIPTIONS ALLOW THE STATE OF AN ELECTRO MAGNETIC WAVE TO BE DESCRIBED IN TERMS OF LINEAR ELLIPTICAL AND CIRCULAR POLARIZATION LEFT HANDED OR RIGHT HANDED )T IS WELL KNOWN THAT LINEAR TARGETS SUCH AS WIRES ACT AS DEPOLARIZING FEATURES AND THAT A LINEARLY POLARIZED CROSSED DIPOLE ANTENNA ROTATED ABOUT AN AXIS NORMAL TO A LINEAR TARGET SUCH AS A WIRE OR PIPE PRODUCES A SINUSOIDAL VARIATION IN RECEIVED SIGNAL (OWEVER THE NULL POINTS ARE A DISTINCT DISADVANTAGE BECAUSE THE OPERATOR IS REQUIRED TO MAKE TWO SEPARATE AXIALLY ROTATED MEASUREMENTS AT EVERY POINT TO BE SURE OF DETECTING PIPES AT UNKNOWN ORIENTATIONS !N ATTRACTIVE TECHNIQUE IS TO RADIATE A CIRCULARLY POLARIZED WAVE WHICH AUTOMATICALLY ROTATES THE POLARIZED VECTOR IN SPACE AND HENCE REMOVES THE DIRECTION OF SIGNAL NULLS 4HESE TECHNIQUES CAN BE USED TO DISCRIMINATE IN FAVOR OF THE TARGET &OR EXAMPLE A RIGHT HANDED CIRCULARLY POLARIZED 2(#0 WAVE WILL BE REFLECTED AS A LEFT HANDED CIRCULARLY
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POLARIZED ,(#0 WAVE FROM A PLANAR SURFACE BUT SOME PROPORTION OF 2(#0 WILL BE REFLECTED FROM A THIN PIPE OR WIRE 4HIS ENABLES THE GROUND SURFACE REFLECTION TO BE REDUCED WHILE ENHANCING THAT FROM THE THIN PIPE OR WIRE 6ELOCITY 4HE VELOCITY OF PROPAGATION OF ELECTROMAGNETIC WAVES IN FREE SPACE IS APPROXIMATELY r MSn BUT SLOWS IN A MATERIAL DEPENDING ON ITS RELATIVE PERMITTIV ITY AND RELATIVE MAGNETIC PERMEABILITY 4HE VELOCITY OF PROPAGATION OF ELECTROMAGNETIC WAVES IN A SOIL WITH A VALUE FOR DR OF WOULD BE SLOWED TO r MSn 4HE TIME TO A TARGET AT A RANGE OF METER IS THEREFORE NS AND '02 SYSTEMS OPERATE AT TIME RANGES BETWEEN A FEW NANOSECONDS UP TO NS ALTHOUGH SOME SYSTEMS FOR PROBING THROUGH ICE MAY USE RANGES UP TO SEVERAL TENS OF MILLISECONDS )N GENERAL IT IS NOT POSSIBLE TO MAKE A RELIABLE ESTIMATE OF PROPAGATION VELOCITY OR RELA TIVE PERMITTIVITY IN A MEDIUM FROM A SINGLE MEASUREMENT WITHOUT TRIAL HOLING INSERTING A PROBE INTO A PREDRILLED HOLE OR OTHER SUPPLEMENTARY INFORMATION %VEN IN THE CASE WHERE A MEASUREMENT IS CARRIED OUT AT ONE LOCATION IT IS OFTEN FOUND THAT SIGNIFICANT VARIATIONS IN VELOCITY WILL OCCUR WITHIN COMPARATIVELY SHORT DISTANCES FROM THE ORIGINAL LOCATION 4HIS CAN LEAD TO SIGNIFICANT ERRORS IN THE ESTIMATION OF DEPTHS OF REFLECTORS /NE PROCEDURE THAT OVERCOMES THIS LIMITATION IS KNOWN AS COMMON DEPTH POINT SURVEYING WHICH UTILIZES TWO ANTENNAS IN BISTATIC OPERATION AT A NUMBER OF TRANSMIT AND RECEIVE POSITIONS 4HE VELOCITY OF PROPAGATION IS GIVEN BY M LN LR DN DR n HENCE IN A MATERIAL WITH LR THE VELOCITY BECOMES M CER 4HE PHASE VELOCITY IS GIVEN BY M V A AND AS
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4HE PHASE VELOCITY IS ALSO DEPENDENT ON THE FACTOR D pD ` WHICH IS ALSO TAN C )T IS ALSO POSSIBLE TO DERIVE VELOCITY FROM MULTIPLE MEASUREMENTS SCANNING OVER A TARGET BUT THIS WORKS WELL ONLY IN RELATIVELY UNCLUTTERED SITUATIONS WHERE THE MEDIA HAS NO ANISOTROPIC CHARACTERISTICS $ISPERSION 4HE FREQUENCY DEPENDENT NATURE OF THE DIELECTRIC PROPERTIES OF THE MATE RIAL CAUSES THE PHASE VELOCITY OF THE COMPONENT FREQUENCIES OF A WIDEBAND SIGNAL TO SUFFER DIFFERENTIAL PROPAGATION VALUES (ENCE THERE WILL BE VARIATION IN THE VELOCITY OF PROPA GATION WITH FREQUENCY $IELECTRICS EXHIBITING THIS PHENOMENON ARE TERMED DISPERSIVE )N THIS SITUATION THE DIFFERENT FREQUENCY COMPONENTS WITHIN A BROADBAND RADAR PULSE WOULD TRAVEL AT SLIGHTLY DIFFERENT SPEEDS CAUSING THE PULSE SHAPE TO CHANGE WITH TIME (OWEVER THE PROPAGATION CHARACTERISTICS OF OCTAVE BAND RADAR SIGNALS IN MOST EARTH MATERIALS REMAIN LARGELY UNAFFECTED BY DISPERSION )N MANY INSTANCES THE POTENTIAL VARIATION IN THE VELOCITY OF WAVE PROPAGATION OVER THE FREQUENCY RANGE OF INTEREST IS SMALL AND CAN BE IGNORED $EPTH 2ESOLUTION &OR TRADITIONAL RADAR SYSTEMS IT IS ACCEPTED THAT TWO IDENTICAL TARGETS CAN BE SEPARATED IN RANGE IF THEY ARE OF A PULSE WIDTH APART )N OPTICS ,ORD 2AYLEIGH PROPOSED THAT THE RESOLVING POWER OF AN INSTRUMENT IS WHEN THE PRINCIPAL INTENSITY OF ONE COMPONENT COINCIDES WITH THE FIRST INTENSITY MINIMUM OF THE OTHER COM PONENT -ANY '02 PULSES TAKE THE FORM OF A 2ICKER WAVELET THE SECOND DIFFERENTIAL OF A GAUSSIAN IMPULSE AND AN EXAMPLE OF TWO PULSES FROM TARGETS IS SHOWN IN &IGURE WHERE BOTH THE IMPULSES AND THEIR ENVELOPES ARE SHOWN 7HEN THE TARGETS ARE CLOSER AS
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SHOWN IN &IGURE ALTHOUGH IT IS POSSIBLE TO DISTINGUISH THEIR ENVELOPES IT BECOMES INCREASINGLY DIFFICULT TO RESOLVE THE ACTUAL PULSES BECAUSE THE SIGNAL MIGHT BE DUE TO A RESONANCE GENERATED BY A SINGLE TARGET HENCE IN THE CASE OF PULSES WITH AN ENVELOPE THAT HAS NO MINIMA THE PULSE WIDTH RESOLUTION CRITERIA MAY NOT BE OPTIMAL %SSENTIALLY RANGE RESOLUTION IS DEFINED BY THE BANDWIDTH OF THE RECEIVED SIGNAL ! RECEIVER BANDWIDTH IN EXCESS OF -(Z AND TYPICALLY '(Z IS REQUIRED TO PROVIDE A TYPICAL RESOLUTION OF BETWEEN AND CM DEPENDING ON THE RELATIVE PERMITTIVITY OF THE MATERIAL 7HEN A NUMBER OF FEATURES MAY BE PRESENT A SIGNAL HAVING A LARGER BANDWIDTH IS REQUIRED TO BE ABLE TO DISTINGUISH BETWEEN THE VARIOUS TARGETS AND TO SHOW THE DETAILED STRUCTURE OF A TARGET )N THIS CONTEXT IT IS THE BANDWIDTH OF THE RECEIVED SIGNAL THAT IS IMPORTANT RATHER THAN THAT OF THE TRANSMITTED WAVELET 4HE MATERIAL ACTS AS A LOW PASS FILTER WHICH MODIFIES THE TRANSMITTED SPECTRUM IN ACCORDANCE WITH THE ELECTRICAL PROP ERTIES OF THE PROPAGATING MEDIUM 4HERE ARE SOME APPLICATIONS OF '02 SUCH AS ROAD LAYER THICKNESS MEASUREMENT WHERE THE FEATURE OF INTEREST IS A SINGLE INTERFACE 5NDER SUCH CIRCUMSTANCES IT IS POSSIBLE TO DETERMINE THE DEPTH SUFFICIENTLY ACCURATELY BY MEASURING THE ELAPSED TIME BETWEEN THE LEADING EDGE OF THE RECEIVED WAVELET PROVIDED THE PROPAGATION VELOCITY IS ACCURATELY KNOWN !LTHOUGH A GREATER DEPTH RESOLUTION IS ACHIEVED IN WETTER MATERIALS FOR A GIVEN TRANSMITTED BANDWIDTH BECAUSE OF THE REDUCED WAVELENGTH IN HIGH DIELECTRIC MATERIALS EARTH MATERIALS WITH SIGNIFICANT WATER CONTENT TEND TO HAVE HIGHER ATTENUATION PROPER TIES 4HIS CHARACTERISTIC REDUCES THE EFFECTIVE BANDWIDTH TENDING TO BALANCE OUT THE CHANGE SO THAT WITHIN CERTAIN BOUNDS THE RESOLUTION IS APPROXIMATELY INDEPENDENT OF LOSS WITHIN THE PROPAGATING MATERIAL
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7HERE INTERFACES ARE SPACED MORE CLOSELY THAN ONE HALF WAVELENGTH THE REFLECTED SIGNAL FROM ONE INTERFACE WILL BECOME DIFFICULT TO RESOLVE WITH THAT FROM ANOTHER )T SHOULD BE NOTED THAT THE NORMAL RADAR CRITERIA FOR RANGE RESOLUTION IS LESS APPROPRI ATE FOR THE CASE OF A WEAK TARGET ADJACENT TO A STRONG TARGET AND THERE IS NO ACCEPTED DEFINITION OF RESOLUTION FOR THE CASE OF UNEQUAL SIZE TARGETS 0LAN 2ESOLUTION 4HE PLAN PLAN IS DEFINED AS A PLANE NORMAL TO THE DIRECTION OF PROPAGATION RESOLUTION OF A '02 SYSTEM IS IMPORTANT WHEN LOCALIZED TARGETS ARE SOUGHT AND WHEN THERE IS A NEED TO DISTINGUISH BETWEEN MORE THAN ONE AT THE SAME DEPTH 7HERE THE REQUIREMENT IS FOR LOCATION ACCURACY WHICH IS PRIMARILY A TOPO GRAPHIC SURVEYING FUNCTION THE SYSTEM REQUIREMENT IS LESS DEMANDING 4HE PLAN RESOLUTION IS DEFINED BY THE CHARACTERISTICS OF THE ANTENNA AND THE SIG NAL PROCESSING EMPLOYED )N GENERAL RADAR SYSTEMS APART FROM 3!2 TO ACHIEVE AN ACCEPTABLE PLAN RESOLUTION REQUIRES A HIGH GAIN ANTENNA 4HIS NECESSITATES A SUFFICIENTLY LARGE APERTURE AT THE LOWEST FREQUENCY TO BE TRANSMITTED 4O ACHIEVE SMALL ANTENNA DIMENSIONS AND HIGH GAIN THEREFORE REQUIRES THE USE OF A HIGH CARRIER FREQUENCY WHICH MAY NOT PENETRATE THE MATERIAL TO SUFFICIENT DEPTH 7HEN SELECTING EQUIPMENT FOR A PARTICULAR APPLICATION IT IS NECESSARY TO COMPROMISE BETWEEN PLAN RESOLUTION SIZE OF ANTENNA THE SCOPE FOR SIGNAL PROCESSING AND THE ABILITY TO PENETRATE THE MATERIAL 0LAN RESOLUTION IMPROVES AS ATTENUATION INCREASES PROVIDED THAT THERE IS SUFFICIENT SIG NAL TO DISCRIMINATE UNDER THE PREVAILING CLUTTER CONDITIONS )N LOW ATTENUATION MEDIA THE RESOLUTION OBTAINED BY THE HORIZONTAL SCANNING TECHNIQUE IS DEGRADED BUT ONLY UNDER THESE CONDITIONS DO SYNTHETIC APERTURE TECHNIQUES INCREASE THE PLAN RESOLUTION %SSENTIALLY THE GROUND ATTENUATION HAS THE EFFECT OF PLACING A hWINDOWv ACROSS THE 3!2 APERTURE AND THE HIGHER THE ATTENUATION THE MORE SEVERE THE WINDOW (ENCE IN HIGH ATTENUATION SOILS 3!2 TECHNIQUES MAY NOT PROVIDE ANY USEFUL IMPROVEMENT TO '02 SYSTEMS 3!2 TECHNIQUES HAVE BEEN APPLIED TO '02 BUT VERY OFTEN IN DRY SOILS WITH LOW ATTENUATION 3!2 TECHNIQUES TYPICALLY REQUIRE MEASUREMENTS MADE USING TRANSMITTER AND RECEIVER PAIRS AT A NUMBER OF ANTENNA POSITIONS TO GENERATE A SYNTHETIC APERTURE OR TO FOCUS THE IMAGE 5NLIKE CONVENTIONAL RADARS WHICH GENERALLY USE A SINGLE ANTENNA MOST '02 SYSTEMS USE SEPARATE TRANSMIT AND RECEIVE ANTENNAS TO PROVIDE RECEIVER ISOLATION 4HE '02 COMMUNITY REFERS TO THIS AS A BISTATIC MODE ALTHOUGH ACTUALLY THE ANTENNA SYSTEM IS CLOSELY SPACED AND MOBILE 4HIS IS DIFFERENT FROM THE TRADITIONAL RADAR COMMUNITY THAT ASSOCIATES THE TERM BISTATIC WITH LARGE SEPARATIONS
Ó£°ÎÊ " -ODELS OF THE '02 SITUATION RANGE FROM A SIMPLE SINGLE FREQUENCY EVALUATION OF PATH LOSSES TO COMPLETE $ TIME DOMAIN DESCRIPTIONS OF THE '02 AND ITS ENVIRON MENT -ODELING TECHNIQUES INCLUDE SINGLE FREQUENCY MODELS TIME DOMAIN MODELS RAY TRACING INTEGRAL TECHNIQUES METHOD OF MOMENTS -O- AND DISCRETE ELEMENT METHODS 4HE &INITE $IFFERENCE 4IME $OMAIN &$4$ TECHNIQUE HAS BECOME ONE OF THE POPULAR TECHNIQUES AND CAN BE DEVELOPED TO RUN ON MOST DESKTOP COMPUTERS WITH RELATIVE EFFICIENCY )T SHOULD BE NOTED THAT '02 SYSTEMS OFTEN OPERATE IN INTIMATE CONTACT WITH THE GROUND AND VERY CLOSE TO THE TARGET 4HUS THE ANTENNA RADIATES IN THE NEAR FIELD WHEREAS SOME GEOPHYSICAL '02 SYSTEMS OPERATE AT LONGER RANGES M TO KM AND THEY
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COULD BE CONSIDERED TO OPERATE IN THE &RESNEL AND EVEN &RAUNHOFER FAR FIELD REGION 7HEN THE TARGET IS SO CLOSE TO THE ANTENNA IT INTERACTS WITH THE REACTIVE FIELDS OF THE ANTENNA AND ACCURATE MODELS WOULD REFLECT THIS MODE OF OPERATION 4HE MOST BASIC MODEL USES THE RADAR RANGE EQUATION AND ENABLES AN ESTIMATE OF RECEIVED SIGNAL LEVEL DYNAMIC RANGE AND PROBABILITY OF DETECTION TO BE ASSESSED )T HAS SIGNIFICANT WEAKNESSES IN THAT MOST CLOSE RANGE '02 SYSTEMS ARE OPERATING IN THE NEAR FIELD OR EVEN THE REACTIVE FIELD OF THE ANTENNA WHEREAS THE MODEL ASSUMES A FAR FIELD MODEL )T IS PROBABLY MORE RELEVANT TO THE LONGER RANGE GEOPHYSICAL APPLICATIONS WHERE THE TARGET IS MANY TENS OF METERS FROM THE RADAR -ANY '02 RECEIVERS WERE ORIGINALLY BASED ON SAMPLING OSCILLOSCOPE TECHNOL OGY AND THE USE OF VOLTAGE BECAME EXPERIMENTALLY MORE USEFUL 4HE MOST BASIC MODEL FOR ASSESSMENT OF VOLTAGE SIGNAL LEVEL IS DERIVED FROM THE RADAR RANGE EQUA TION WHICH DOES HAVE THE LIMITATIONS PREVIOUSLY NOTED (OWEVER IT DOES ENABLE A FIRST ORDER ASSESSMENT OF ANTICIPATED SIGNAL LEVELS AND AN EXAMPLE IS GIVEN IN THIS SECTION 4HE MODEL IS BASED ON THE EQUATION FOR THE VOLTAGE AT THE RECEIVER AS A FUNCTION OF RANGE R AND TARGET RADAR CROSS SECTION R AND GIVEN BY REFERENCE 2UTLEDGE AND -UHA )N THE FIRST MODEL SHOWN IN &IGURE THE ANTENNA IS SET AT A HEIGHT OF CM ABOVE THE TARGET DIELECTRIC CYLINDERS OF CM THICKNESS RANGING IN SIZE FROM M DIAMETER TO M DIAMETER 4HE TARGET HAS A VALUE OF DR OF AND THE SOIL DR AND TANC 4HE RADIATED PULSE HAS A CENTER FREQUENCY OF '(Z AND AN OUTPUT PULSE PEAK VOLTAGE OF VOLTS 4HE RADAR RECEIVER HAS AN EQUIVALENT BANDWIDTH OF -(Z TO '(Z AND AN EQUIVALENT RECEIVER NOISE VOLTAGE OF n VOLTS 4HE PROBABILITY OF DETECTION 0$ IS DERIVED FROM THE ERROR FUNCTION OF THE SIGNAL TO NOISE RATIO AS SHOWN IN &IGURE .OTE THAT THESE VALUES ONLY RELATE TO THE RECEIVER NOISE AND DO NOT INCLUDE EXTERNAL SOURCES OF FALSE ALARMS DUE TO CLUTTER 4HE MOST BASIC MODEL IS THAT OF THE TRANSMISSION LINE EQUIVALENT AND IS USEFUL FOR ASSESSING THE TIME DOMAIN SIGNATURE OF A PHYSICAL SITUATION ! CONCEPTUALLY SIMPLE MODEL CAN BE USED TO GAIN AN INSIGHT INTO THE OPTIMUM CENTER FREQUENCY OF OPERATION AND IS SHOWN IN &IGURE %ACH LAYER IS MODELED AS EQUIVALENT IMPEDANCE AND THE TRANSMISSION AND REFLEC TION COEFFICIENTS ARE CALCULATED FOR EACH INTERFACE 4HE VELOCITY OF PROPAGATION AND THE MATERIAL LOSSES ARE INCLUDED ALTHOUGH NOT THE SPREADING LOSSES 4HE REASON FOR THIS IS THAT THE RECEIVED ! SCAN WOULD NORMALLY HAVE TIME VARYING GAIN APPLIED IN THE RECEIVER AND SIGNAL PROCESSING AND TO INTRODUCE SPREADING LOSS AND THEN COM PENSATE IS AN INEFFICIENT MODELING EXERCISE )N THE MODEL ONLY THE FIRST REFLECTION IS COMPUTED ALTHOUGH MULTIPLE INTERNAL REFLECTIONS WITHIN EACH LAYER WILL BE GENERATED AND A FULL REPRESENTATION SHOULD INCLUDE THESE 4HE PARAMETERS OF THE LAYERS ARE GIVEN IN 4ABLE
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4HE OUTPUT FROM THE MODEL IS SHOWN IN &IGURE AND &IGURE &INITE $IFFERENCE 4IME $OMAIN &$4$ METHODS CAN BE USED TO MODEL THE FIELD PROPAGATION OF A TYPICAL '02 SYSTEM 4HE ANTENNA USED FOR THIS PURPOSE IS A RESISTIVELY LOADED 4%- HORN AS DESCRIBED BY -ARTEL ET AL )T IS CM LONG WITH AN APERTURE OF CM BY CM 4HE 4%- HORN HAS ULTRAWIDEBAND CAPABILITIES FROM -(Z TO '(Z )T IS POSITIONED ABOVE A METALLIC TARGET BURIED IN THE GROUND AS SHOWN IN &IGURE 4HE DISTANCE BETWEEN THE HORN APERTURE AND THE AIR GROUND INTERFACE IS CM DIFFERENT FROM THE EARLIER MODEL 4HE MODELED TARGET IS A CYLINDER WITH A RADIUS OF CM AND A HEIGHT OF CM )T IS SHALLOWLY BURIED AT ABOUT CM BELOW THE AIR GROUND INTERFACE
&)'52% 3IMULATION OF ! SCAN USING -(Z CENTER FREQUENCY #OURTESY )%%
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&)'52% %LECTRIC FIELD PLOT ON A VERTICAL CUT PLANE AFTER THE MAIN GROUND REFLECTION #OURTESY )%%
4HE GROUND IS MODELED AS A UNIFORM LOSSY MATERIAL WITH A RELATIVE PERMITTIVITY OF AND A CONDUCTIVITY OF 3M 3IEMENSMETER 4HE AIR GROUND INTERFACE IS ASSUMED TO BE PERFECTLY FLAT &ROM THE FIELD PLOT ONE CAN RECOGNIZE THE ANTENNA STRUCTURE AND THE STRONG FIELD REGION ON AND INSIDE THE HORN PLATE 4HE BURIED OBJECT IS ALSO VISIBLE 4HE MAIN REFLEC TION CAUSED BY THE AIR GROUND INTERFACE CAN CLEARLY BE SEEN COMING BACK TOWARD THE ANTENNA SYSTEM )N ADDITION A WEAKER REFLECTION COMING FROM THE BURIED OBJECT IS STARTING TO FORM AND FOLLOWS THE AIR GROUND INTERFACE REFLECTION IN TIME 4HIS IS A TYPICAL TIME DOMAIN CHARACTERISTIC OF STANDOFF '02 SYSTEM -OREOVER OTHER PHYSICAL PHE NOMENA CAN BE OBSERVED SUCH AS THE FREE SPACE PATH LOSS AND THE REDUCTION IN VELOCITY OF PROPAGATION IN THE GROUND )T SHOULD BE NOTED THAT THE PROCESS OF PHYSICALLY SCANNING THE ANTENNA SYSTEM OVER THE TARGET CREATES A HYPERBOLIC IMAGE OF THE TARGET AS SHOWN IN &IGURE &OR THE TWO DIMENSIONAL CASE X POSITION ON SURFACE AND Z DEPTH TO THE TARGET OF A MATERIAL WITH KNOWN CONSTANT VELOCITY THE MEASURED TIME TO THE POINT REFLECTOR IS GIVEN BY T AND THEN THE DISTANCE TO THE POINT REFLECTOR IS GIVEN BY Z VT !T ANY POSITION ALONG THE X AXIS THE DISTANCE Z IS ALSO GIVEN BY
ZI XI X Z
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&)'52% 4YPICAL HYPERBOLIC IMAGE OF '02 DATA FROM A REFLECTOR OF CIRCULAR CROSS SECTION #OURTESY )%%
4HIS EQUATION SHOWS THAT THE MEASURED WAVEFRONT APPEARS AS A HYPERBOLIC IMAGE OR A CURVE OF MAXIMUM CONVEXITY -IGRATION TECHNIQUE MAY BE USED TO MOVE OR MIGRATE A SEGMENT OF AN ! SCAN TIME SAMPLE TO THE APEX OF A CURVE OF MAXIMUM CONVEXITY 4HE HYPERBOLIC CURVE NEEDS TO BE WELL SEPARATED FROM OTHER FEATURES AND A GOOD SIGNAL TO NOISE RATIO IS NEEDED FOR THIS TECHNIQUE TO WORK WELL
Ó£°{Ê *,"* ,/ -Ê"Ê / , 4HE DETERMINATION OF THE DIELECTRIC PROPERTIES OF EARTH MATERIALS REMAINS LARGELY EXPER IMENTAL 2OCKS SOILS AND CONCRETE ARE COMPLEX MATERIALS COMPOSED OF MANY DIFFERENT MINERALS IN WIDELY VARYING PROPORTIONS AND THEIR DIELECTRIC PARAMETERS MAY DIFFER GREATLY EVEN WITHIN MATERIALS THAT ARE NOMINALLY SIMILAR -OST EARTH MATERIALS CONTAIN MOISTURE USUALLY WITH SOME MEASURE OF SALINITY 3INCE THE RELATIVE PERMITTIVITY OF WATER IS IN THE ORDER OF EVEN SMALL AMOUNTS OF MOISTURE CAUSE A SIGNIFICANT INCREASE OF THE RELATIVE PERMITTIVITY OF THE MATERIAL ! LARGE NUMBER OF WORKERS HAVE INVESTI GATED THE RELATIONSHIPS BETWEEN THE PHYSICAL CHEMICAL AND MECHANICAL PROPERTIES OF MATERIALS AND THEIR ELECTRICAL AND IN PARTICULAR MICROWAVE PROPERTIES )N GENERAL THEY HAVE SOUGHT TO DEVELOP SUITABLE MODELS TO LINK THE PROPERTIES OF THE MATERIAL TO ITS ELEC TROMAGNETIC PARAMETERS 3UCH MODELS PROVIDE A BASIS FOR UNDERSTANDING THE BEHAVIOR OF ELECTROMAGNETIC WAVES WITHIN THESE MEDIA 4HE REAL AND IMAGINARY DIELECTRIC LOSSES
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&)'52% $IELECTRIC PROPERTIES D ` UPPER AND D p LOWER OF LOSSY SOIL AS A FUNCTION OF FREQUENCY #OURTESY )%%
AS A FUNCTION OF FREQUENCY CAN BE PLOTTED OVER A WIDE FREQUENCY RANGE AND A TYPICAL RESULT IS SHOWN IN &IGURE )NFORMATION ON THE GEOLOGICAL PROPERTIES OF EARTH SOILS CAN BE FOUND IN THE $IGITAL 3OIL -AP OF THE 7ORLD AND $ERIVED 3OIL 0ROPERTIES #$ PUBLISHED BY THE &OOD AND !GRICULTURE /RGANIZATION OF THE 5NITED .ATIONS 4HIS ENABLES THE TEN MAP SHEETS OF THE WORLD TO BE CLASSIFIED IN TERMS OF PARAMETERS SUCH AS P( CONCENTRATION OF HYDRO GEN IONS ORGANIC CARBON CONTENT #. CARBON TO NITROGEN RATIO CLAY MINERALOGY SOIL DEPTH SOIL MOISTURE CAPACITY AND SOIL DRAINAGE CLASS 3UCH INFORMATION IS USEFUL IN ASSESSING THE POTENTIAL OF 2& TECHNIQUES AND PARTICULARLY '02 FOR PARTICULAR GEO GRAPHIC REGIONS 4HERE ARE TWO BENEFITS TO UNDERSTANDING SOIL PROPERTIES IN RELATION TO '02 4HE FIRST IS TO UNDERSTAND THE APPLICABILITY OF '02 TO PARTICULAR SOILS AND HENCE THE POSSIBILITY OF USING '02 TO DETECT BURIED TARGETS SUCH AS PIPE CABLES LANDMINES ETC 4HE SECOND IS TO USE '02 TO CHARACTERIZE SOILS AND SOIL PROPERTIES '02 CAN PROVIDE A DETAILED MAP OF THE SUBSURFACE WHICH WHEN COMBINED WITH TRADITIONAL SOIL SURVEY METHODS CAN PROVIDE INFORMATION ON THE TYPE OF SOIL ITS EXTENT LATERALLY AND IN DEPTH THE WATER TABLE THE LAYERING AND FEATURES OF THE SOIL AND HENCE ITS LOCAL GEOLOGY AND HISTORY '02 HAS BEEN USED IN THE 53 BY THE $EPARTMENT OF !GRICULTURE .ATURAL 2ESOURCES #ONSERVATION 3ERVICE 53$! .2#3 AS A QUALITY CONTROL TOOL FOR SOIL MAPPING AND INVESTIGATIONS 4HE USE OF '02 IN SOIL SURVEY ACTIVITIES HAS PROVIDED INFORMATION ABOUT SOIL RESOURCES THAT WOULD HAVE BEEN UNOBTAINABLE BY OTHER MEANS OR WOULD HAVE BEEN UNECONOMICAL TO OBTAIN !N EXAMPLE OF THE RESULTS OF THIS WORK IS SHOWN IN &IGURE
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Ó£°xÊ *,Ê-9-/ 4HE CHOICE OF SYSTEM DESIGN IS TO A LARGE EXTENT GOVERNED BY THE TYPE OF TARGET THE RES OLUTION REQUIRED AND THE ANTICIPATED GROUND ATTENUATION AND CLUTTER 4HE DEPTH RANGE OF THE RADAR SYSTEM IS LIKELY TO BE PRIMARILY DEFINED BY THE SOIL ATTENUATION ONCE A PARTICU LAR RANGE OF FREQUENCIES HAS BEEN CHOSEN (OWEVER IT CAN BE SHOWN THAT CONSIDERABLE VARIATIONS n D" IN THE SENSITIVITY OF COMPETING SYSTEM DESIGNS ACTUALLY TRANSLATE TO RELATIVELY SMALL CHANGES IN DEPTH PERFORMANCE IN LOSSY SOILS 4HE SELECTION OF A SUITABLE WAVEFORM FOR TRANSMISSION AT LEAST IN TERMS OF RESOLU TION CAN BE CONSIDERED A FUNCTION OF THE DURATION OF THE COMPLEX ENVELOPE OF THE SIG NAL 4HE OUTPUT FROM MOST ULTRAWIDEBAND RADAR SYSTEMS CAN BE COMPARED IN TERMS OF A TIME DOMAIN REPRESENTATION OF THE WAVEFORM !LMOST ALL TYPES OF RADAR CAN BE ASSESSED NOT JUST BY THEIR SIGNAL TO NOISE AND SIGNAL TO CLUTTER RATIOS BUT ALSO BY COMPARING THEIR INHERENT RANGE SENSITIVITY 3UCH A PROCEDURE REVEALS THE CHARACTERISTICS THAT CONTROL THE RADAR PERFORMANCE 4HE DESIGN OF A '02 SYSTEM IS DEFINED BY THE MODULATION TECH NIQUE AND TIME DOMAIN FREQUENCY DOMAIN AND PSEUDO RANDOM CODED DOMAIN RADAR DESIGNS ARE MOST LIKELY TO BE ENCOUNTERED &REQUENCY DOMAIN RADARS MAY USE EITHER STEPPED FREQUENCY OR CONTINUOUSLY SWEPT FREQUENCY MODULATION 4HEY TRANSMIT ON A REPETITIVE BASIS A NOMINALLY CONSTANT AMPLITUDE SIGNAL WHOSE FREQUENCY INCREASES IN A LINEAR PROGRESSION FROM THE LOWEST TO THE HIGHEST VALUE 2ECOVERY OF THE RECEIVER SIGNAL FROM NOISE MAY BE ACHIEVED BY EITHER CONVENTIONAL BANDPASS FILTERS OR BY THE MATCHED FILTER OR 7IENER FILTER 4HE FUNDAMENTAL OPERATION OF A MATCHED FILTER IS CORRELATION 4HE AMPLITUDE OF EACH POINT IN THE OUTPUT SIGNAL IS A MEASURE OF HOW WELL THE FILTER KERNEL MATCHES THE CORRESPONDING SECTION OF THE INPUT SIGNAL 4HE OUTPUT OF A MATCHED FILTER DOES NOT NEC ESSARILY LOOK LIKE THE SIGNAL BEING DETECTED BUT IF A MATCHED FILTER IS USED THE SHAPE OF THE TARGET SIGNAL MUST ALREADY BE KNOWN 4HE MATCHED FILTER IS OPTIMAL IN THE SENSE
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THAT THE PEAK SIGNAL OUTPUT TO MEAN NOISE RATIO IS GREATER THAN CAN BE ACHIEVED WITH ANY OTHER LINEAR FILTER 4HIS IS NOT ALWAYS THE BEST FILTER TO USE FOR TIME DOMAIN WAVEFORMS WHERE THE FIDELITY OF THE OUTPUT MAY BE A REQUIREMENT 4HE 7IENER FILTER SEPARATES SIGNALS BASED ON THEIR FREQUENCY SPECTRA 4HE GAIN OF THE 7IENER FILTER AT EACH FREQUENCY IS DETERMINED BY THE RELATIVE AMOUNT OF SIGNAL AND NOISE AT THAT FREQUENCY 4HE 7IENER AND MATCHED FILTER MUST BE CARRIED OUT BY CONVOLU TION MAKING THEM EXTREMELY SLOW TO EXECUTE 4HE MATCHED FILTER RADAR RECEIVER PROVIDES AN OPTIMUM LINEAR PROCESSING OF RADAR IN THE PRESENCE OF NOISE 4HE RADAR SIGNAL IS PROCESSED BY A FILTER THAT CROSS CORRELATES THE RECEIVED WAVEFORM WITH A SUITABLY TIME DELAYED VERSION OF THE TRANSMITTED WAVEFORM 4HE OUTPUT RESULTS IN AN OUTPUT IN WHICH THE AMPLITUDE OF THE LATTER AND ITS POSITION IN DELAY TIME IS RELATED TO THE TARGET RADAR CHARACTERISTIC 4HIS TYPE OF RECEIVER IS WIDELY USED TO PROCESS CHIRP STEP FREQUENCY AND PSEUDO RANDOM CODED WAVEFORMS AND THE DESIGN OF SUCH WAVEFORMS IS EXTENSIVELY DESCRIBED IN THE LITERATURE -ANY COMMERCIAL TIME DOMAIN RADAR SYSTEMS USE A SAMPLING RECEIVER TO DOWN CONVERT THE RADAR SIGNALS FROM THE NANOSECOND TIME FRAME TO A MILLISECOND TIME FRAME THAT IS EASIER TO POST PROCESS (OWEVER A REAL DISADVANTAGE OF THE SAMPLING RECEIVER IS ITS LIMITED DYNAMIC RANGE DUE TO THE SAMPLING DIODES AND INHERENTLY HIGH NOISE LEVEL DUE TO ITS WIDE BANDWIDTH $ETAILS OF TYPICAL SAMPLING RECEIVERS WHICH ARE ESSENTIALLY THE SAME AS SAMPLING OSCILLOSCOPES CAN BE FOUND IN THE LITERATURE AND ONCE ISSUES OF SAMPLING LINEARITY IN TIME ARE ADDRESSED THE GENERIC DESIGN HAS FORMED THE BASIS FOR THE MAJORITY OF COMMERCIAL '02 SYSTEMS ! KEY PARAMETER FOR MOST '02 SYSTEMS IS THE MEAN POWER 4HE TIME DOMAIN RADAR TRANSMITS ON A REPETITIVE BASIS A SHORT DURATION IMPULSE #ONSEQUENTLY ITS PEAK POWER IS SIGNIFICANTLY GREATER THAN ITS MEAN POWER 4HIS IS NOT THE CASE WITH STEPPED FREQUENCY WHOSE RADIATED POWER PER SPECTRAL LINE IS HIGHER THAN THE TIME DOMAIN RADAR THAT GIVES AN ADVANTAGE IN TERMS OF TRANSMITTER PEAK SIGNAL CAPABILITY COMPARED WITH THE IMPULSE '02
Ó£°ÈÊ " 1 /" Ê/ +1 4HERE ARE THREE MAIN MODULATION TECHNIQUES TIME DOMAIN FREQUENCY DOMAIN AND PSEUDO RANDOM CODED RADAR '02 SYSTEMS THAT TRANSMIT AN IMPULSE AND RECEIVE THE REFLECTED SIGNAL FROM THE TARGET USING A SAMPLING RECEIVER CAN BE CONSIDERED TO OPERATE IN THE TIME DOMAIN '02 SYSTEMS THAT TRANSMIT INDIVIDUAL FREQUENCIES IN A SEQUENTIAL MAN NER AND RECEIVE THE REFLECTED SIGNAL FROM THE TARGET USING A FREQUENCY CONVERSION RECEIVER CAN BE CONSIDERED TO OPERATE IN THE FREQUENCY DOMAIN 4HE LATTER SYSTEMS OFTEN RECON STRUCT THE DOWNCONVERTED FREQUENCIES TO RECOVER A TIME DOMAIN REPLICA OF THE SIGNAL !LL '02S MAY HAVE TO DETECT SIGNALS FROM A TARGET THAT MAY BE n TO n D" LOWER THAN THE RADIATED SIGNAL AT RANGES IN THE ORDER OF A METER NS IN FREE SPACE )N ADDITION THE RECEIVED SIGNAL WILL CONTAIN TEMPORAL SCATTERING INFORMATION ON THE TARGET THAT CAN BE EXPLOITED 4HE TEMPORAL FIDELITY OF RECEIVED SIGNAL NEEDS TO BE PRESERVED AND THUS DESIGNERS OF '02 HAVE TO ENSURE THAT THE RECEIVER IS NOT SATURATED BY THE TRANSMITTED SIGNAL THE ANTEN NAS DO NOT CAUSE TIME SIDELOBES AND THE RECEIVER DOES NOT DISTORT THE RECEIVED SIGNAL 4IME $OMAIN -OST COMMERCIALLY AVAILABLE '02 SYSTEMS USE SHORT PULSES OR IMPULSES SUCH AS THE 2ICKER WAVELET AS SHOWN PREVIOUSLY IN &IGURE 4HE HIGH SPEED SEQUENTIAL SAMPLING APPROACH USED TO ACQUIRE 2& WAVEFORMS PRODUCES A LOW
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3.2 BECAUSE THE SPECTRUM OF THE SAMPLING PULSE IS A POOR MATCH FOR THAT OF THE RECEIVED PULSE )N GENERAL THE DYNAMIC RANGE OF THE SAMPLING RECEIVER IS TYPICALLY D" WITHOUT RANGE TIME VARYING GAIN 4HE EFFECT OF THE RANGE VARYING GAIN IS TO ENABLE THE LOWER AMPLITUDE SIGNALS FROM TARGETS AT A GREATER RANGE TO BE AMPLIFIED SO AS TO BE ABOVE THE MINIMUM SAMPLING THRESHOLD SIGNAL LEVEL 4HIS IS EQUIVALENT TO A LINEAR RECEIVER WITH A D" OR MORE DYNAMIC RANGE 3IGNAL AVERAGING OR INTEGRATION OF THE SAMPLES CAN INCREASE THE EFFECTIVE SENSITIVITY BY THE AMOUNT OF AVERAGING AND THIS CAN BE TYPICALLY TO D" 4HE RATIO OF THE PEAK TRANSMITTED SIGNAL TO THE MEAN RECEIVER NOISE LEVEL CAN BE UP TO D" 4HE ANTENNAS THAT CAN BE USED WITH TIME DOMAIN '02 ARE LIMITED TO LINEAR PHASE DESIGNS SUCH AS RESISTIVELY LOADED DIPOLES 4%- HORNS OR )MPULSE 2ADIATING !NTENNAS )2!S )T SHOULD BE NOTED THAT ULTRAWIDEBAND ANTENNAS FALL INTO TWO CLASSES THOSE THAT RADIATE A REASONABLY SHORT IMPULSE WITH LOW TIME SIDELOBES AND FUNDAMENTALLY POS SESS A LINEAR PHASE FREQUENCY CHARACTERISTIC 4HE ALTERNATIVE CLASS OF ANTENNAS SUCH AS LOG PERIODICS HAVE WIDEBAND FREQUENCY CHARACTERISTICS BUT NONLINEAR PHASE FREQUENCY CHARACTERISTICS %SSENTIALLY THE LATTER CLASS WILL CAUSE THE DIFFERENT FREQUENCY COMPO NENTS OF AN IMPULSE TO BE RADIATED AT DIFFERENT TIMES HENCE DISPERSING THE IMPULSE )F SUCH ANTENNAS ARE USED WITH TIME DOMAIN RADAR THE DISPERSIVE PROPERTIES OF THE ANTENNA USED MUST BE COMPENSATED BY SUITABLE POST PROCESSING FILTERING 4HE TIME DOMAIN RADAR SYSTEM TRANSMITS A SEQUENCE OF PULSES TYPICALLY OF AMPLI TUDES WITHIN THE RANGE BETWEEN 6 TO 6 AND PULSE WIDTHS WITHIN THE RANGE BETWEEN PS TO NS AT A PULSE REPETITION INTERVAL OF BETWEEN SEVERAL HUNDRED MICROSECONDS TO ONE MICROSECOND DEPENDING ON THE SYSTEM DESIGN 4HE IMPULSE GENERATOR IS GENERALLY BASED ON THE TECHNIQUE OF RAPID DISCHARGE OF THE STORED ENERGY IN A SHORT TRANSMISSION LINE 4HE MOST COMMON METHOD OF ACHIEVING THIS IS BY MEANS OF A TRANSISTOR OPERATED IN AVALANCHE BREAKDOWN MODE USED AS THE FAST SWITCH AND A VERY SHORT LENGTH OF TRANSMISSION LINE )T IS QUITE FEASIBLE TO GENERATE PULSES OF SEVERAL HUNDRED K6 ALBEIT AT LONG REPETITION INTERVALS 4HE OUTPUT FROM THE RECEIVE ANTENNA IS APPLIED TO A FLASH !$ CONVERTER OR A SEQUENTIAL SAMPLING RECEIVER 4HE LATTER NOR MALLY CONSISTS OF AN ULTRAHIGH SPEED SAMPLE AND HOLD CIRCUIT 4HE CONTROL SIGNAL TO THE SAMPLE AND HOLD CIRCUIT WHICH DETERMINES THE INSTANT OF SAMPLE TIME IS SEQUENTIALLY INCREMENTED AT EACH PULSE REPETITION INTERVAL &OR EXAMPLE A SAMPLING INCREMENT OF T PS IS ADDED TO THE PREVIOUS PULSE REPETITION SAMPLING INTERVAL TO ENABLE SAM PLING OF THE RECEIVED SIGNAL AT REGULAR INTERVALS AS INDICATED IN &IGURE
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4HE PRINCIPLE OF THE SAMPLING RECEIVER IS THEREFORE A DOWNCONVERSION OF THE RADIO FREQUENCY SIGNAL IN THE NANOSECOND TIME REGION TO AN EQUIVALENT VERSION IN THE MICRO OR MILLISECOND TIME REGION 4HE INCREMENTATION OF THE SAMPLING INTERVAL IS TERMINATED AT A STAGE WHEN FOR EXAMPLE OR SEQUENTIAL SAMPLES HAVE BEEN GATHERED 4HE PROCESS IS THEN REPEATED 4HERE ARE SEVERAL METHODS OF AVERAGING OR hSTACKINGv THE DATA EITHER A COMPLETE SET OF SAMPLES CAN BE GATHERED AND STORED AND FURTHER SETS ADDED TO THE STORED DATA SET OR ALTERNATIVELY THE SAMPLING INTERVAL IS HELD CONSTANT FOR A PREDETERMINED TIME TO ACCUMULATE AND AVERAGE A GIVEN NUMBER OF INDIVIDUAL SAMPLES 4HE FIRST METHOD NEEDS A DIGITAL STORE BUT HAS THE ADVANTAGE THAT EACH WAVEFORM SET SUFFERS LITTLE DISTORTION IF THE RADAR IS MOVING OVER THE GROUND 4HE SECOND METHOD DOES NOT NEED A DIGITAL STORE AND A SIMPLE LOW PASS ANALOGUE FILTER CAN BE USED (OWEVER DEPENDING ON THE NUMBER OF SAMPLES THAT HAVE BEEN AVER AGED THE OVERALL WAVEFORM SET CAN RESULT IN BEING hSMEAREDv SPATIALLY IF THE RADAR IS MOVING AT ANY SPEED 4HE STABILITY OF THE TIMING INCREMENT IS VERY IMPORTANT AND GEN ERALLY THIS SHOULD BE OF THE SAMPLING INCREMENT HOWEVER PRACTICALLY A STABILITY IN THE ORDER OF PS TO PS IS ACHIEVED 4HE EFFECT OF TIMING INSTABILITY IS TO CAUSE A DISTORTION WHICH IS RELATED TO THE RATE OF CHANGE OF THE 2& WAVEFORM %VIDENTLY WHERE THE 2& WAVEFORM IS CHANGING RAPIDLY JITTER IN THE SAMPLING CIRCUITS RESULTS IN A VERY NOISY RECONSTRUCTED WAVEFORM 7HERE THE RATE OF CHANGE OF SIGNAL IS SLOW JITTER IS LESS NOTICEABLE .ORMALLY CONTROL OF THE SAMPLING CONVERTER IS DERIVED FROM A SAMPLE OF THE OUTPUT FROM THE PULSE GENERATOR TO ENSURE THAT VARIATIONS IN THE TIMING OF THE LATTER ARE COMPENSATED AUTOMATICALLY 4HE KEY ELEMENTS OF THIS TYPE OF RADAR SYSTEM ARE THE IMPULSE GENERATOR THE TIMING CONTROL CIRCUITS THE SAMPLING DETECTOR AND THE PEAK HOLD AND ANALOGUE TO DIGITAL CONVERTER &REQUENCY $OMAIN 2ADAR 4HE MAIN POTENTIAL ADVANTAGES OF THE FREQUENCY DOMAIN RADAR ARE THE WIDER DYNAMIC RANGE LOWER NOISE FIGURE AND HIGHER MEAN POWERS THAT CAN BE RADIATED 4HERE ARE TWO MAIN TYPES OF FREQUENCY DOMAIN RADAR &REQUENCY -ODULATED #ARRIER 7AVE &-#7 AND 3TEPPED &REQUENCY #ARRIER 7AVE 3 &-#7 RADAR TRANSMITS A CONTINUOUSLY CHANGING FREQUENCY OVER A CHOSEN FREQUENCY RANGE ON A REPETITIVE BASIS 4HE RECEIVED SIGNAL IS MIXED WITH A SAMPLE OF THE TRANSMIT TED WAVEFORM AND RESULTS IN A DIFFERENCE FREQUENCY WHICH ALTHOUGH FUNDAMENTALLY RELATED TO THE PHASE OF THE RECEIVED SIGNAL IS A MEASURE OF ITS TIME DELAY AND HENCE RANGE OF THE TARGET 4HE DIFFERENCE FREQUENCY OR INTERMEDIATE FREQUENCY )& MUST BE DERIVED FROM AN )1 MIXER PAIR IF THE INFORMATION EQUIVALENT TO A TIME DOMAIN REPRE SENTATION IS REQUIRED IE TO RECONSTITUTE AN IMPULSE AS A SINGLE ENDED MIXER ONLY PROVIDES THE MODULUS OF THE TIME DOMAIN WAVEFORM 4HE BASIC &-#7 RADAR SYSTEM IS PARTICULARLY SENSITIVE TO CERTAIN PARAMETERS )N PARTICULAR IT REQUIRES A HIGH DEGREE OF LINEARITY OF FREQUENCY SWEEP WITH TIME TO AVOID SPECTRAL WIDENING OF THE )& AND HENCE DEGRADATION OF SYSTEM RESOLUTION $ENNIS AND 'IBBS MADE AN ASSESSMENT OF THE SENSITIVITY OF TIME SIDELOBE LEVEL TO LINEARITY AND SHOWED THE RATIO OF SIDELOBE TO PEAK LEVEL WAS DEPENDENT ON THE SWEEP LINEARITY 0RACTICALLY THE EFFECT OF A NONLINEARITY OF A FEW PERCENT IS TO CAUSE SIGNIFICANT TIME SIDELOBES AS THIS NEEDS TO BE COMPENSATED IN THE TRANSMITTER MODULATOR DESIGN 4HE 3 RADAR TRANSMITS A SERIES OF INCREMENTAL FREQUENCIES AND STORES THE RECEIVED )& SIGNAL TO THEN CARRY OUT A &OURIER TRANSFORM RECONSTRUCTION OF THE TIME DOMAIN EQUIVALENT WAVEFORM 4HE 3 HAS FOUND MANY APPLICATIONS IN '02 BECAUSE THE REQUIREMENTS ON SCAN RATE ARE RELATIVELY MODEST 4HE IMPACT OF MOBILE COMMUNICATIONS TECHNOLOGY HAS HAD A SIGNIFICANT IMPACT ON REDUCING THE COST OF RADAR COMPONENTS FOR THIS DESIGN 4WO FORMS OF THE SYNTHESIZED RADAR CAN BE CONSIDERED
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4HE FIRST AND SIMPLEST SYSTEM IS STEPPED FREQUENCY CONTINUOUS WAVE RADAR 4HE SECOND FORM IS MORE COMPLEX IN THAT EACH INDIVIDUAL FREQUENCY IS APPROPRIATELY WEIGHTED IN AMPLITUDE AND PHASE PRIOR TO TRANSMISSION .ORMALLY THE RADAR IS CALIBRATED BOTH TO ESTABLISH A REFERENCE PLANE FOR MEASUREMENT AS WELL AS TO REDUCE THE EFFECT OF VARIATIONS IN THE FREQUENCY CHARACTERISTICS OF COMPONENTS AND ANTENNAS ! MUCH WIDER CLASS OF ANTENNA IS AVAILABLE FOR USE BY THE DESIGNER OF FREQUENCY DOMAIN RADARS 4HE NOISE FLOOR OF THE RECEIVER IS MUCH LOWER THAN THE TIME DOMAIN EQUIVALENT SIMPLY BY VIRTUE OF ITS LOWER BANDWIDTH AND HENCE LOWER THERMAL NOISE 4YPICALLY A SENSITIVITY OF n D"M IS FOUND AND A SYSTEM PEAK TRANSMITTED SIGNAL TO MEAN RECEIVER NOISE RANGE OF D" IS FEASIBLE )T SHOULD BE NOTED THAT THE )& BANDWIDTH OF THE RECEIVER IN &-#7 AND 3 SYSTEMS CAN BE MADE RELATIVELY SMALL WHEREAS THE SAMPLING RECEIVER IN THE TIME DOMAIN RECEIVER HAS A BANDWIDTH OF MANY '(Z AND HENCE A POOR NOISE PERFORMANCE 4HE MAIN POTENTIAL ADVANTAGE OF A STEPPED FREQUENCY OR &-#7 '02 IS ITS ABIL ITY TO ADJUST THE RANGE OF FREQUENCIES OF OPERATION TO SUIT THE MATERIAL AND TARGETS AND ELECTROMAGNETIC ENVIRONMENT UNDER INVESTIGATION IF THE ANTENNA HAS AN ADEQUATE PASS BAND OF FREQUENCIES )T CAN RADIATE A HIGHER MEAN POWER LEVEL PER SPECTRAL LINE THAN THE TIME DOMAIN RADAR AND ITS ABILITY TO INTEGRATE THE RECEIVED SIGNAL LEVEL IMPROVES THE SYSTEM SENSITIVITY 4HE CALIBRATION OF THE RADAR DOES OF COURSE DEPEND ON STABLE SYSTEM CHARACTERISTICS AND ANTENNA PARAMETERS THAT ARE INVARIANT WITH THE SPACING OF THE FRONT SURFACE AND THE ANTENNA !LTHOUGH ON FIRST CONSIDERATION FREQUENCY DOMAIN RADARS SHOULD OFFER A SUPERIOR SENSITIVITY TO TIME DOMAIN RADARS BECAUSE OF THEIR LOWER )& RECEIVER BANDWIDTH AND HENCE THERMAL NOISE BOTH THE TYPE OF RECEIVER AND THE RANGE SIDELOBES OF THE RADIATED SPECTRUM MAY RESULT IN AN EQUIVALENT OR WORSE SENSITIVITY IN TERMS OF RANGE RESOLUTION AS DISCUSSED ABOVE 0SEUDO RANDOM CODED 2ADAR 7ORK HAS BEEN CARRIED OUT ON PSEUDO RANDOM CODED MODULATION TECHNIQUES FOR '02 4HE MAIN ADVANTAGE OF THIS METHOD IS THAT THE ENERGY TRANSMITTED IS SPREAD MORE EVENLY OVER THE SPECTRUM THAN WITH ANY OTHER MODU LATION METHOD AND HENCE THE LIKELIHOOD OF INTERFERENCE TO OTHER USERS OF THE SPECTRUM IS MINIMIZED )N ADDITION THE CHANCES OF OTHER USERS OF SAY MOBILE PHONES INTERFERING WITH THE '02 OPERATOR ARE ALSO REDUCED 4HE MEAN POWER IS THE LOWEST OF ANY OF THE MODULATION SCHEMES AND THIS IS HELPFUL IN MEETING REGULATORY REQUIREMENTS 4HE TRANSMITTED SIGNAL HAS NOISE LIKE CHARACTERISTICS AND THE RECEIVED SIGNAL IS CROSS CORRELATED WITH A SAMPLE OF THE TRANSMITTED SIGNAL 4HE RANGE OF THE TARGET IS GIVEN BY THE TIME POSITION OF THE CROSS CORRELATED SIGNAL AND THE AMPLITUDE BY THE PEAK OF THE CROSS CORRELATED SIGNAL #ONTROL OF THE CROSS CORRELATION SIDELOBES IS VITAL TO ACHIEVE GOOD RANGE RESOLUTION AND THE SIDELOBES ARE AFFECTED BY THE ANTENNA AND SYSTEM CHARACTERISTICS AS WELL AS THE DURATION AND RANDOMNESS OF THE TRANSMITTED WAVEFORM &URTHER INFORMATION IS GIVEN BY .ARAYANAN AND 3ACHS ET AL
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)N THE ULTRAWIDEBAND CASE THE RADAR ANTENNAS ARE CONSIDERED IN TERMS OF THEIR TRANSFER FUNCTION RATHER THAN THEIR GAINS OR EFFECTIVE APERTURES )N MANY CASES A SEPARATE TRANSMIT AND RECEIVE ANTENNA IS USED HENCE THEIR TRANSFER FUNCTIONS MAY NOT BE IDENTICAL 4HE TYPE OF ANTENNA THAT IS USED WITH ULTRAWIDEBAND RADAR HAS AN IMPORTANT ROLE IN DEFINING THE PERFORMANCE OF THE RADAR
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%LEMENT ANTENNAS ARE CHARACTERIZED BY LINEAR POLARIZATION LOW DIRECTIVITY AND RELA TIVELY LIMITED BANDWIDTH UNLESS EITHER END LOADING OR DISTRIBUTED LOADING TECHNIQUES ARE EMPLOYED IN WHICH CASE BANDWIDTH IS INCREASED AT THE EXPENSE OF RADIATION EFFI CIENCY !N ELEMENTAL ANTENNA IS A DIPOLE IN CONTRAST TO APERTURE ANTENNAS SUCH AS HORNS ! NORMAL SHORT DIPOLE ANTENNA FED WITH A VERY SHORT CURRENT IMPULSE WILL RADIATE FROM THE FEED POINTS AND THE END OF THE ELEMENT BECAUSE OF THE LATTERS DISCONTINUITY AS FAR AS CURRENT FLOW IS CONCERNED 4HE CURRENT IMPULSE WILL BE REFLECTED FROM THE END OF THE DIPOLE AND TRAVEL UP AND DOWN THE DIPOLE CAUSING A SERIES OF IMPULSES OF RADIA TION 4HIS EXTENDS THE TIME SIGNATURE OF THE RADIATED WAVEFORM AND DEGRADES THE RANGE RESOLUTION OF THE SYSTEM 4HIS EFFECT IS SHOWN IN &IGURE WHERE THE RADIATION PAT TERN IS SHOWN AT A TIME SEVERAL PULSE DURATIONS AFTER APPLICATION 4HE OUTER PERIMETER REPRESENTS THE ENERGY RADIATED AT TIME ZERO FOLLOWED AT INTERVALS BY THE RADIATION FROM THE FEED POINTS AND THE END OF THE ELEMENT !S IT IS REQUIRED TO RADIATE ONLY A VERY SHORT IMPULSE IT IS IMPORTANT TO ELIMINATE THE REFLECTION DISCONTINUITIES FROM THE FEED POINTS AND ENDS OF THE ANTENNA EITHER BY END LOADING OR BY REDUCING THE AMPLITUDE OF THE CHARGE AND CURRENT REACHING THE ENDS 4HE LATTER CAN BE ACHIEVED EITHER BY RESISTIVELY COATING THE ANTENNA OR BY CONSTRUCTING THE ANTENNA FROM A MATERIAL SUCH AS .ICHROME WHICH HAS A DEFINED LOSS PER UNIT AREA )N THIS CASE THE ANTENNA RADIATES IN A COMPLETELY DIFFERENT WAY AS THE APPLIED CHARGE BECOMES SPREAD OVER THE ENTIRE ELEMENT LENGTH AND HENCE THE CENTERS OF RADIATION ARE DISTRIBUTED ALONG THE LENGTH OF THE ANTENNA 4YPICAL RADIATED FIELD PATTERNS FOR A RESIS TIVELY LOADED DIPOLE ARE SHOWN IN &IGURE (OWEVER THE REDUCTION IN IMPULSE DURATION IS ACHIEVED AT THE EXPENSE OF EFFICIENCY AND LOADED ANTENNAS MAY HAVE EFFI CIENCIES AS LOW AS 4HE TYPES OF ANTENNAS THAT ARE USEFUL TO THE DESIGNER OF ULTRAWIDEBAND RADAR FALL INTO TWO GROUPS DISPERSIVE ANTENNAS AND NONDISPERSIVE ANTENNAS $ISPERSIVE ANTENNAS HAVE A NONLINEAR PHASEFREQUENCY RESPONSE WHEREAS NONDISPERSIVE ANTENNAS HAVE A SUBSTANTIALLY LINEAR PHASEFREQUENCY RESPONSE %XAMPLES OF DISPERSIVE ANTENNAS THAT HAVE BEEN USED IN ULTRAWIDEBAND RADAR ARE THE EXPONENTIAL SPIRAL THE !RCHIMEDEAN
&)'52% 2ADIATED FIELD PATTERN FROM A CONDUCTING DIPOLE ELEMENT DUE TO AN APPLIED IMPULSE #OURTESY )%%
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SPIRAL THE LOGARITHMIC PLANAR ANTENNA THE 6IVALDI ANTENNA SLOT ANTENNAS AND THE EXPO NENTIAL HORN 4HE IMPULSE RESPONSE OF THIS CLASS OF ANTENNAS GENERALLY RESULTS IN A WAVEFORM WHOSE TIME FREQUENCY RESPONSE IS EXTENDED AND IS SIMILAR TO A CHIRP ALBEIT WITH AN INCONSTANT AMPLITUDE IF THE INPUT IS AN IMPULSE %XAMPLES OF NONDISPERSIVE ANTENNAS ARE THE 4%- HORN THE BICONE THE BOW TIE THE RESISTIVE LUMPED ELEMENT LOADED ANTENNA AND THE CONTINUOUSLY RESISTIVELY LOADED ANTENNA 4HE INPUT VOLTAGE DRIVING FUNCTION TO THE TERMINALS OF THE ANTENNA IN IMPULSE RADAR IS TYPICALLY A NARROW GAUSSIAN PULSE OF PS AND THIS REQUIRES THE IMPULSE RESPONSE OF THE ANTENNA TO BE EXTREMELY SHORT 4HE MAIN REASON FOR REQUIR ING THE IMPULSE RESPONSE TO BE SHORT IS THAT IT IS IMPORTANT THAT THE ANTENNA DOES NOT DISTORT THE INPUT FUNCTION AND GENERATE TIME SIDELOBES 4HESE TIME SIDELOBES WOULD OBSCURE TARGETS THAT ARE CLOSE IN RANGE TO THE TARGET OF INTEREST IN OTHER WORDS THE RESOLUTION OF THE RADAR CAN BECOME DEGRADED IF THE IMPULSE RESPONSE OF THE ANTENNA IS SIGNIFICANTLY EXTENDED (OWEVER IN PRINCIPLE ALL ANTENNAS ARE DISPERSIVE TO SOME EXTENT BUT NONDISPERSIVE ANTENNAS DO NOT NEED CORRECTION IN THE SIGNAL PROCESSING WHICH REDUCES THE OVERALL COMPLEXITY OF THE RADAR PROCESSING 4HE VERY SHORT RANGE OPERATION OF MANY '02 SYSTEMS ENABLES OPERATION OF ANTENNAS IN A WAY THAT DOES NOT CONFORM TO TRADITIONAL ANALYTIC MODELS OF ANTENNA GAIN AND APERTURE (ORN ANTENNAS HAVE FOUND MOST USE WITH &-#7 ULTRAWIDEBAND RADARS WHERE THE GENERALLY HIGHER FREQUENCY OF OPERATION AND RELAXATION OF THE REQUIREMENT FOR LINEAR PHASE RESPONSE PERMIT THE CONSIDERATION OF THIS CLASS OF ANTENNA &-#7 ULTRAWIDE BAND RADARS HAVE USED AN OFFSET PARABOLOID FED BY A RIDGED HORN 4HIS ARRANGEMENT WAS DESIGNED TO FOCUS THE RADIATION INTO THE GROUND AT A SLANT ANGLE TO REDUCE THE LEVEL OF THE REFLECTION FROM THE GROUND #ARE NEEDS TO BE TAKEN IN SUCH ARRANGEMENTS TO MINI MIZE THE EFFECT OF BACK AND SIDELOBES FROM THE FEED ANTENNA WHICH CAN EASILY GENERATE REFLECTION FROM THE GROUND SURFACE /NE METHOD OF RADIATING CIRCULAR POLARIZATION IS TO USE AN EQUI ANGULAR SPIRAL ANTENNA 4HE DISPERSIVE NATURE OF THIS TYPE OF ANTENNA CAUSES AN INCREASE IN THE DURA TION OF THE TRANSMITTED WAVEFORMS AND THE RADIATED PULSE TAKES THE FORM OF A hCHIRPv
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IN WHICH HIGH FREQUENCIES ARE RADIATED FIRST FOLLOWED BY THE LOW FREQUENCIES ! hSPIK INGv FILTER WHICH MAY TAKE THE FORM OF A CONVENTIONAL MATCHED FILTER HOWEVER MAY COMPENSATE FOR THIS EFFECT OR A MORE SOPHISTICATED FILTER SUCH AS 7IENER FILTER WHICH RECOVERS THE ORIGINAL SHAPE OF THE WAVEFORM APPLIED TO THE ANTENNA )T IS IMPORTANT TO APPRECIATE THE EFFECT OF THE MATERIAL IN CLOSE PROXIMITY TO THE ANTENNA )N GENERAL THIS MATERIAL WHICH IN MOST CASES WILL BE SOIL OR ROCKS OR INDEED ICE CAN BE REGARDED AS A LOSSY DIELECTRIC AND BY ITS CONSEQUENT LOADING EFFECT CAN PLAY A SIGNIFICANT ROLE IN DETERMINING THE LOW FREQUENCY PERFORMANCE OF THE ANTENNA AND HENCE '02 4HE BEHAVIOR OF THE ANTENNA IS INTIMATELY LINKED WITH THE MATERIAL AND IN THE CASE OF BOREHOLE RADARS THE ANTENNA ACTUALLY RADIATES WITHIN A LOSSY DIELECTRIC WHEREAS IN THE CASE OF THE '02 WORKING ABOVE THE SURFACE THE ANTENNA WILL RADIATE FROM AIR INTO A VERY SMALL SECTION OF AIR AND THEN INTO A LOSSY HALF SPACE FORMED BY THE MATERIAL 4HE BEHAVIOR OF ANTENNAS BOTH WITHIN LOSSY DIELECTRICS AND OVER LOSSY DIELECTRICS IS WELL REPORTED 4HE PROPAGATION OF ELECTROMAGNETIC PULSES IN A HOMOGE NEOUS CONDUCTING EARTH HAS BEEN MODELED BY 7AIT AND +ING AND THE DISPERSION OF RECTANGULAR SOURCE PULSES SUGGESTS THAT THE TIME DOMAIN CHARACTERISTICS OF THE RECEIVED PULSE COULD BE USED AS AN INDICATION OF DISTANCE 4HE INTERACTION BETWEEN THE ANTENNA AND THE LOSSY DIELECTRIC HALF SPACE IS ALSO SIG NIFICANT AS THIS MAY CAUSE MODIFICATION OF THE ANTENNA RADIATION CHARACTERISTICS BOTH SPATIALLY AND TEMPORALLY AND SHOULD ALSO BE TAKEN INTO ACCOUNT IN THE SYSTEM DESIGN )N THE CASE OF AN ANTENNA PLACED ON AN INTERFACE THE TWO MOST IMPORTANT PARAMETERS ARE THE CURRENT DISTRIBUTION AND THE RADIATION PATTERN !T THE INTERFACE CURRENTS ON THE ANTENNA PROPAGATE AT A VELOCITY WHICH IS INTERMEDIATE BETWEEN THAT IN FREE SPACE AND THAT IN THE DIELECTRIC )N GENERAL THE VELOCITY IS RETARDED BY THE E R 4HE NET RESULT IS THAT EVANESCENT WAVES ARE EXCITED IN AIR WHEREAS IN THE DIELECTRIC THE ENERGY IS CONCENTRATED AND PREFERENTIALLY INDUCED BY A FACTOR OF N 4HE RESPECTIVE CALCULATED FAR FIELD POWER DENSITY PATTERNS IN BOTH AIR AND DIELECTRIC ARE GIVEN BY 2UTLEDGE SEE 4ABLE AND THESE ARE PLOTTED FOR A RELATIVE DIELECTRIC CONSTANT OF IN &IGURE AND &IGURE &OR COMPARISON THE FAR FIELD PATTERN OF A DIPOLE RADIATING INTO FREE SPACE IS SHOWN IN &IGURE 4HE ABOVE EXPRESSIONS IN 4ABLE ASSUME THAT THE CURRENT SOURCE CONTACTS THE DIELECTRIC WHEREAS A MORE GENERAL CONDITION IS WHEN THE ANTENNA IS JUST ABOVE THE DIELECTRIC ! SIGNIFICANT PRACTICAL PROBLEM FOR MANY APPLICATIONS IS THE NEED TO MAIN TAIN SUFFICIENT SPACING TO AVOID MECHANICAL DAMAGE TO THE ANTENNA )T CAN THEREFORE BE APPRECIATED THAT THE EFFECT OF CHANGES IN DISTANCE BETWEEN THE ANTENNA AND HALF SPACE IS TO CAUSE SIGNIFICANT VARIATION IN THE RESULTANT RADIATION PATTERNS IN THE DIELECTRIC ! PARTICULARLY USEFUL ANTENNA CAPABLE OF SUPPORTING A FORWARD TRAVELING 4%- WAVE IS THE 4%- HORN )N GENERAL SUCH ANTENNAS CONSIST OF A PAIR OF CONDUCTORS EITHER 4!",% 0OWER $ENSITY 0ATTERNS IN !IR AND $IELECTRIC
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&)'52% % PLANE PLOT OF FAR FIELD POWER DENSITY OF A CURRENT ELEMENT RADIATING INTO A LOSSLESS MATERIAL OF DIELECTRIC CONSTANT OF
FLAT CYLINDRICAL OR CONICAL IN CROSS SECTION FORMING A 6 STRUCTURE IN WHICH RADIATION PROPAGATES ALONG THE AXIS OF THE 6 STRUCTURE !LTHOUGH RESISTIVE TERMINATION IS USED THIS TYPE OF ANTENNA HAS A DIRECTIVITY ON THE ORDER OF n D" DEPENDING ON SIZE HENCE USEFUL GAIN CAN STILL BE OBTAINED EVEN WITH A TERMINATING LOSS ON THE ORDER OF
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D" TO D" ! FURTHER DEVELOPMENT OF THE 4%- HORN IS GIVEN BY -ARTEL IN WHICH THE ANTENNA IS COMPOSED OF A SET OF SPREAD hFINGERSv FORMING THE SHAPE OF A HORN AS SHOWN IN &IGURE %ACH FINGER IS A WIRE WITH A DIAMETER OF MM AND IS RESIS TIVELY LOADED AT DIFFERENT LOCATIONS ALONG THE LENGTH OF THE ANTENNA 4HE FEED COMPO NENT FOR THE ANTENNA IS COMPRISED OF A /HM COAX FEEDING A TAPERED PARALLEL PLATE WAVEGUIDE WITH A WIDTH OF MM AND A HEIGHT OF MM ! TAPER ALONG THE WIDTH OF THE TOP PARALLEL PLATE IS USED AS A TRANSITION TO TRANSFORM A /HM UNBALANCED LINE INTO A OHM BALANCED LINE
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4HE PREDICTED AND ACTUAL TIME DOMAIN PULSE OF THE OPTIMUM DESIGN IS SHOWN IN &IGURE 4HE SHAPE OF THE TIME DOMAIN ANTENNA RESPONSE IS SIMILAR TO A SECOND DERIVATIVE GAUSSIAN SIGNAL )T CAN BE SEEN THAT MOST OF THE INTERNAL REFLECTIONS HAVE BEEN SUPPRESSED 4HE RATE OF DECREASE FOR THE UNWANTED RINGING IS BETTER THAN D"NS 4HE 6372 WAS BETTER THAN FROM -(Z TO '(Z 4HERE ARE MANY CONFIGURATIONS OF ANTENNA THAT CAN BE USED CROSSED DIPOLES AND PARALLEL DIPOLES ARE THE MOST POPULAR 4HE MAIN REASON FOR THE USE OF TWO ANTENNAS IS THAT 42 SWITCHES THAT ARE FAST ENOUGH FOR '02 ARE NOT YET AVAILABLE
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-- 4HE THREE BASIC PERMUTATIONS OF '02 DATA PRESENTATION ARE SHOWN IN &IGURE 4HE MOST BASIC '02 DATA RECORD IS AN ! SCAN !N ! SCAN PROVIDES AMPLITUDE TIME RECORD OF A SINGLE MEASUREMENT OVER A TARGET /NLY AMPLITUDE RANGE INFORMATION IS PLOTTED '02 IS GENERALLY USED IN SUCH A WAY AS TO GENERATE A SEQUENCE OF ! SCANS RELATED TO THE SURVEY POSITION ON THE GROUND SURFACE 4HIS SEQUENCE CAN BE TERMED A " SCAN AND AN EXAMPLE IS SHOWN IN &IGURE 4HIS EFFECTIVELY REPRESENTS ONE AXIS Z DEPTH AND THE ORTHOGONAL AXIS X OR Y LINEAR POSITION 4HE AMPLITUDE OF THE SIGNAL MAY BE SHOWN AS A SERIES OF OVERLAPPING SIGNALS OR ALTERNATIVELY A hWIGGLE PLOTv BORROWED FROM SEISMIC TERMINOLOGY OR A GRAYSCALE CODED INTENSITY PLOT OR A PSEUDO COLOR IMAGE )N THE MODELED EXAMPLE SHOWN THE HYPERBOLIC SPREADING OF THE TARGET SPATIAL RESPONSE CAN BE SEEN !S SHOWN IN &IGURE A # SCAN CONSISTS OF A PLAN VIEW X Y PLANE OVER A DEFINED RANGE OF DEPTH Z .OTE THAT THESE TERMS ARE NOT THE SAME AS USED IN CONVENTIONAL RADAR DISPLAY 4HE RECEIVED TIME WAVEFORM CAN BE DESCRIBED AS THE CONVOLUTION OF A NUMBER OF TIME FUNCTIONS EACH REPRESENTING THE IMPULSE RESPONSE OF SOME COMPONENT OF THE RADAR SYSTEM IN ADDITION TO NOISE CONTRIBUTIONS FROM VARIOUS SOURCES .OTE THAT TWO ANTENNAS ARE USED ONE TRANSMITS AND ONE RECEIVES
SR T SS T SAF T SC T SGF T ST T SGR T SAR T NT
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SST SIGNAL APPLIED TO THE ANTENNA SADT ANTENNA IMPULSE RESPONSE SCT ANTENNA CROSS COUPLING RESPONSE
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SGDT GROUND IMPULSE RESPONSE STT IMPULSE RESPONSE OF TARGET NT NOISE
D DENOTES DIRECTIONF BEING FORWARD AND R REVERSE DIRECTION %ACH CONTRIBUTION HAS ITS OWN PARTICULAR CHARACTERISTICS THAT NEED TO BE CONSID ERED CAREFULLY BEFORE APPLICATION OF A PARTICULAR PROCESSING SCHEME )DEALLY THE SIGNAL APPLIED TO THE ANTENNA SHOULD BE A $IRAC FUNCTION BUT PRACTICALLY IT IS MORE LIKE A SKEWED GAUSSIAN IMPULSE OF DEFINED TIME DURATION -OST ANTENNAS USED IN SURFACE PENETRATING APPLICATIONS HAVE A LIMITED LOW FREQUENCY RESPONSE AND TEND TO ACT AS HIGH PASS FILTERS EFFECTIVELY DIFFERENTIATING THE APPLIED IMPULSE AND HENCE CREATING A TIME LIMITED FUNCTION )N MOST CASES NEAR IDENTICAL ANTENNA ARE USED AND IF THESE ARE SPACED SUFFICIENTLY FAR FROM THE GROUND SURFACE THEN SAFT SART )N THE CASE OF ANTEN NAS OPERATED IN CLOSE PROXIMITY TO THE GROUND THEN BOTH SAFT AND SART ARE VARIANT WITH
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CHANGES IN THE GROUND SURFACE ELECTRICAL PARAMETERS %SSENTIALLY THE IMPEDANCE OF THE ANTENNA IS CHANGED BY ITS PROXIMITY TO THE GROUND HENCE IT CANNOT BE CONSIDERED TO HAVE A STABLE IMPULSE RESPONSE !NY PROCESSING SCHEME THAT RELIES ON INVARIANT ANTENNA PARAMETERS SHOULD TAKE INTO ACCOUNT THE MODE OF OPERATION OF THE ANTENNAS AND THE DEGREE OF STABILITY THAT IS PRAC TICALLY REALIZABLE 4HE ANTENNA CROSS COUPLING RESPONSE SC T IS COMPOSED OF A FIXED CONTRIBUTION S`CT DUE TO ANTENNA CROSS COUPLING IN AIR AND A VARIABLE CONTRIBUTION SpCT DUE TO THE EFFECT OF THE GROUND OR NEARBY OBJECTS (ENCE SCT S`CT SpCT )T HAS BEEN FOUND POSSIBLE TO REDUCE THE AMPLITUDE OF SCT TO VERY LOW LEVELS IN THE CASE OF CROSSED DIPOLE ANTENNAS TO BELOW n D" SIMPLY BY ATTENTION TO THE PRECISION OF CONSTRUCTION AND IN THE CASE OF PARALLEL DIPOLE ANTENNAS TO BELOW n D" BY THE INTERPOSING BETWEEN THE ANTENNAS OF SUITABLE ABSORBING MATERIAL (OWEVER SpCT CAN BE SIGNIFICANTLY LARGER AND DEGRADES THE OVERALL VALUE OF SCT TO n D" 4HE VALUE OF SAT IS DETERMINED BY ANY LOCAL INHOMOGENEITIES IN THE SOIL OR BY ANY COVERING MATERIAL WHETHER OF MINERAL OR VEGETABLE ORIGIN 4HERE IS UNFORTUNATELY LITTLE THAT CAN BE DONE TO PREDICT VARIATIONS IN SpCT AND IT IS NOT AMENABLE TO TREATMENT BY MANY PROCESSING ALGORITHMS 4HE VARIATION IN SpCT IS MUCH GREATER WITH THE CROSSED DIPOLE ANTENNA THAN THE PARALLEL DIPOLE 4HE GROUND IMPULSE RESPONSE SGT CAN BE DETERMINED FROM ITS ATTENUATION AND DIELECTRIC CONSTANT ACROSS THE FREQUENCY RANGE OF INTEREST 4HE TARGET IMPULSE RESPONSE CAN BE COMPOSED OF THE CONVOLUTION OF THE WANTED TARGET RESPONSE TOGETHER WITH MANY OTHER REFLECTORS WHICH MAY NOT BE WANTED BY THE USER BUT WHICH ARE VALID REFLECTING TARGETS AS FAR AS ELECTROMAGNETIC WAVES ARE CON CERNED 4HE TIME SEPARATION OF THE TARGETS IS RELATED TO THEIR PHYSICAL SPACING AS WELL AS THE VELOCITY OF PROPAGATION WHICH CAN VARY DEPENDING ON THE MATERIAL PROPERTIES 7HERE THE TARGETS ARE WELL SEPARATED IN RANGE IT IS RELATIVELY STRAIGHTFORWARD TO SEPARATE THE RADAR REFLECTIONS BUT THIS BECOMES PROGRESSIVELY MORE DIFFICULT AS TARGETS BECOME CLOSER TOGETHER AS INSTEAD OF SEPARABLE TIME DOMAIN SIGNATURES THE REFLECTIONS WILL MERGE TOGETHER !S THE ANTENNAS GENERALLY USED FOR '02 HAVE POOR DIRECTIVITY THE PATTERN OF THE REFLECTED WAVEFORM IN THE " SCAN REPRESENTED THE SPATIAL CONVOLUTION OF THE ANTENNA PATTERN WITH THE TARGET 4HE READER IS REFERRED TO &IGURE SHOWN PREVIOUSLY WHICH ILLUSTRATES THIS EFFECT 4HIS SPATIAL PATTERN DOES NOT REPRESENT AN IMAGE OF THE OBJECT OF INTEREST AND MUCH EFFORT HAS BEEN MADE TO DEVELOP METHODS TO RECONSTRUCT THE TARGET IMAGE FROM '02 DATA
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&)'52% " SCAN UNPROCESSED DATA #OURTESY )%%
$ECONVOLVING THE IMAGE USING ANY OF THE FOLLOWING PROCESSES CAN DO THIS SYN THETIC APERTURE PROCESSING CONJUGATE GRADIENT METHODS AND REVERSE TIME MIGRATION ARE EXTENSIVELY REPORTED IN THE LITERATURE -ANY OF THESE TECHNIQUES WORK WELL ON ISOLATED TARGETS SUCH AS PIPES WHICH HAVE WELL DEFINED GEOMETRICAL BOUNDARIES 4HE SITUATION IS MORE DIFFICULT WITH STRATIFIED LAYERS AND OF COURSE ANISOTROPIC MATERIALS 7HEN A RECONSTRUCTED IMAGE OF THE BURIED OBJECT IS CREATED WHETHER AS A " SCAN OR # SCAN AREA AT A PARTICULAR RANGE OF DEPTHS IT IS NECESSARY TO INTERPRET THE RADAR IMAGE AS BEING GENERATED BY A PHYSICAL STRUCTURE 4HIS IS NOT ALWAYS EASY IN THE CASE OF A CLUTTERED IMAGE AND A GREAT DEAL STILL DEPENDS ON THE FIELD EXPERIENCE OF THE OPERATOR %XAMPLES OF UNPROCESSED " SCAN DATA AND THE SAME CORRECTED FOR SPREADING LOSS AND ATTENUATION ARE SHOWN IN &IGURE AND &IGURE !LTHOUGH A # SCAN IS ESSENTIALLY AN X Y PLANE AT A SELECTED VALUE OF : OR RANGE OF VALUES OF : MANY OF THE PROCESSES DESCRIBED IN THE PREVIOUS SECTION CAN BE APPLIED
&)'52% " SCAN DATA CORRECTED FOR SPREADING LOSS AND ATTENUATION #OURTESY )%%
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2EMEMBERING THAT A '02 " SCAN RESULTS IN A HYPERBOLIC CROSS SECTION FROM A TARGET THEN AN AREA SCAN # SCAN WILL RESULT IN A HYPERBOLOID OF REVOLUTION WHOSE VERTICAL AXIS RUNS THROUGH THE TARGET ! PLANE ORTHOGONAL TO THE VERTICAL AXIS WILL GENER ATE A CIRCULAR FEATURE WHOSE RADIUS INCREASES WITH DEPTH ! TYPICAL EXAMPLE IS GIVEN IN &IGURE WHICH SHOWS THE # SCANS FROM AN ANTI TANK MINE BURIED AT DIFFERENT DEPTHS WITH THE CENTER OF THE MINE SHOWN AS AN OVERLAY 4HESE IMAGES REPRESENT AN UNFOCUSSED REPRESENTATION OF THE TARGET AS A RESULT OF THE $ SPATIAL CONVOLUTION OF THE ANTENNA PATTERN WITH THE TARGET 4HE VARIABILITY OF GROUND CONDITIONS AS WELL AS THE PHYSICS OF %- WAVE PROPA GATION AND REFLECTION MUST BE CAREFULLY TAKEN INTO ACCOUNT IN ATTEMPTING TO CLASSIFY TARGETS EVEN AFTER IMAGE PROCESSING &OR EXAMPLE THE DEPTH IMAGE OF A VOID IS ALWAYS APPARENTLY SMALLER THAN ITS PHYSICAL SIZE CORNER REFLECTORS OF ANY REASONABLE SIZE GEN ERATE LARGE APPARENTLY DISCONTINUOUS REFLECTION IMAGES AND CONDUCTIVE TARGETS WHICH REVERBERATE BY MEANS OF STORED ENERGY CREATE EXTENDED DEPTH IMAGES 4HE IMAGE OF A BURIED TARGET GENERATED BY A '02 WILL NOT OF COURSE CORRESPOND TO ITS GEOMETRICAL REPRESENTATION 4HE FUNDAMENTAL REASONS FOR THIS ARE RELATED TO THE RATIO OF THE WAVE LENGTH OF THE RADIATION AND THE PHYSICAL DIMENSIONS OF THE TARGET )N MOST CASES FOR '02 THE RATIO IS CLOSE TO UNITY 4HIS COMPARES VERY DIFFERENTLY WITH AN OPTICAL IMAGE WHICH IS OBTAINED WITH WAVELENGTHS SUCH THAT THE RATIO IS CONSIDERABLY GREATER THAN UNITY TYPICALLY )N '02 APPLICATIONS THE EFFECT OF COMBINATIONS OF SCAT TERING PLANES FOR EXAMPLE THE CORNER REFLECTOR CAN CAUSE hBRIGHT SPOTSv IN THE IMAGE AND VARIATIONS IN THE VELOCITY OF PROPAGATION CAN CAUSE DILATION OF THE ASPECT RATIO OF THE IMAGE !LTHOUGH MANY IMAGES CAN BE FOCUSED TO REDUCE THE EFFECT OF ANTENNA BEAM SPREADING REGENERATION OF A GEOMETRIC MODEL IS A MUCH MORE COMPLEX PROCEDURE AND IS NOT USUALLY ATTEMPTED 4HE GENERAL OBJECTIVE OF SIGNAL PROCESSING AS APPLIED TO '02 IS TO PRESENT EITHER AN IMAGE THAT CAN READILY BE INTERPRETED BY THE OPERATOR OR TO CLASSIFY THE TARGET RETURN WITH RESPECT TO A KNOWN TEST PROCEDURE OR TEMPLATE 4HE GENERAL PROCESSING PROBLEM ENCOUNTERED IN DEALING WITH '02 DATA IS IN THE WIDEST SENSE THE EXTRACTION OF A LOCALIZED WAVELET FUNCTION FROM A TIME SERIES WHICH DISPLAYS VERY SIMILAR TIME DOMAIN CHARACTERISTICS TO THE WAVELET 4HIS TIME SERIES IS GENERATED BY SIGNALS FROM THE GROUND AND OTHER REFLECTING SURFACE AS WELL AS INTERNALLY FROM THE RADAR SYSTEM 5NLIKE CONVENTIONAL RADAR SYSTEMS IN WHICH THE TARGET CAN GEN ERALLY BE REGARDED AS BEING IN MOTION COMPARED WITH THE CLUTTER IN THE '02 CASE THE TARGET AND THE CLUTTER ARE SPATIALLY FIXED AND THE RADAR ANTENNA IS MOVED WITH RESPECT TO THE ENVIRONMENT )T IS ASSUMED THAT DATA ARE RECORDED TO AN ADEQUATE RESOLUTION -OST ANTENNAS USED IN SURFACE PENETRATING APPLICATIONS HAVE A LIMITED LOW FREQUENCY RESPONSE AND TEND TO ACT AS HIGH PASS FILTERS EFFECTIVELY DIFFERENTIATING THE APPLIED IMPULSE !S THE GROUND ACTS AS A LOW PASS FILTER THE GROUND LARGELY DEFINES THE BANDWIDTH OF REFLECTED SIGNAL
&)'52% 3EQUENCE OF UNFOCUSSED # SCANS OF A SET OF A BURIED !4 MINE TARGETS AT DEPTH INCREMENTS OF MM #OURTESY )%%
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)N THE CASE OF ANTENNAS OPERATED IN CLOSE PROXIMITY TO THE GROUND THE ANTENNA CHARAC TERISTICS MAY VARY AS A RESULT OF CHANGES IN THE GROUND SURFACE ELECTRICAL PARAMETERS !NY PROCESSING SCHEME THAT ASSUMES THE ANTENNA PARAMETERS REMAIN CONSTANT NEEDS TO ACCOUNT FOR THE MODE OF OPERATION OF THE ANTENNAS AND THE DEGREE OF STABILITY THAT IS PRACTICALLY REALIZABLE 4HIS IS A PARTICULAR ISSUE FOR '02 AND NEEDS CAREFUL ATTENTION TO REDUCE THE EFFECT OF ANTENNA GROUND SURFACE INTERACTION 3OME OF THE ANCILLARY REQUIREMENTS OF AN OPERATIONAL '02 SYSTEM NEED TO BE CON SIDERED !CCURATE HIGH RESOLUTION LOW COST POSITION REFERENCING SYSTEMS FOR USE WITH RADAR FOR SUBSURFACE SURVEY TECHNIQUES ARE NOW AVAILABLE )T IS IMPORTANT THAT DATA CAN BE RELATED TO A TRUE GEOGRAPHIC REFERENCE PARTICULARLY WHEN FILED ON DIGITAL MAPPING SYSTEMS AND USED TO DEFINE AREAS OF SAFE WORKING !NOTHER CONSIDERATION IS THE PLANE OF POLARIZATION OF THE ELECTROMAGNETIC ENERGY &OR TARGETS WITH ONE LARGE AREA DIMENSION SUCH AS A PIPE THE RADAR CROSS SCATTERING SECTION WILL BE LARGER WHEN THE POLARIZATION VECTOR IS IN LINE WITH THE PIPE 4HIS MEANS THAT ANY AREA THAT IS SURVEYED WITH SAY PARALLEL DIPOLES MUST BE SURVEYED IN ORTHOGONAL DIRECTIONS TO ENSURE THAT NO TARGETS ARE MISSED 4HE SAME REQUIREMENT ALSO RELATES TO CROSSED DIPOLE ANTENNAS
Ó£°Ê ** /" )T IS ONLY POSSIBLE TO PROVIDE A BRIEF SUMMARY OF THE WIDE VARIETY OF THE APPLICATIONS FOR '02 WHICH HAS IN SOME CASES BECOME AN ESTABLISHED AND ROUTINE METHOD OF SUB SURFACE INVESTIGATION '02 IN THE HANDS OF AN EXPERT PROVIDES A SAFE AND NONINVASIVE METHOD OF CONDUCTING SPECULATIVE SEARCHES WITHOUT THE NEED FOR UNNECESSARY DISRUPTION AND EXCAVATION ! TYPICAL EXAMPLE OF A '02 IMAGE IS SHOWN IN &IGURE WITH THE VARIOUS FEATURES IDENTIFIED '02 HAS SIGNIFICANTLY IMPROVED THE EFFICIENCY OF THE EXPLORATORY WORK THAT IS FUN DAMENTAL TO THE CONSTRUCTION AND CIVIL ENGINEERING INDUSTRIES THE POLICE AND FORENSIC SECTORS SECURITYINTELLIGENCE FORCES AND ARCHAEOLOGICAL SURVEYS '02 HAS BEEN VERY SUCCESSFULLY USED IN FORENSIC INVESTIGATIONS 4HE MOST NOTORI OUS CASE BEING IN THE 5NITED +INGDOM IN WHEN THE GRAVESITES UNDER CONCRETE AND IN THE HOUSE OF &RED 7EST OF THE VICTIMS OF THE SERIAL MURDERER WERE PINPOINTED )N "ELGIUM THE GRAVESITES OF THE VICTIMS OF THE PEDOPHILE $UTEOUS WERE DETECTED IN
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!RCHAEOLOGICAL APPLICATIONS OF '02 HAVE BEEN VARIED RANGING FROM THE EXPLORA TION OF %GYPTIAN AND .ORTH !MERICAN )NDIAN SITES AS WELL AS CASTLES AND MONASTERIES IN %UROPE 4HE QUALITY OF THE RADAR IMAGE CAN BE EXCEPTIONALLY GOOD ALTHOUGH CORRECT UNDERSTANDING NORMALLY REQUIRES JOINT INTERPRETATION BY THE ARCHAEOLOGISTS AND RADAR SPECIALISTS 3INCE THE 3QUARE 'EOPHYSICAL 3URVEY 0ROJECT UNDER THE AUSPICES OF THE .ATIONAL -USEUM OF 3COTLAND AND THE 'LASGOW -USEUMS HAVE BEEN CARRYING OUT GEOPHYSICAL AND ARCHAEOLOGICAL SURVEYS AT 3QUARE IN %GYPT 3QUARE FORMS PART OF THE NECROPOLIS OF THE ANCIENT %GYPTIAN CAPITAL CITY OF -EMPHIS 4HE BURIAL GROUNDS EXTEND FROM !BU 2OASH JUST TO THE NORTH OF #AIRO SOUTHWARD THROUGH 'IZA !BUSIR 3AQQARA AND $AHSHUR TO -EIDUM APPROXIMATELY KM TO THE SOUTH 4HE FAMOUS 3TEP 0YRAMID OF THE RD $YNASTY RULER +ING :OSER DOMINATES THE SITE OF 3AQQARA 4HE MAIN MONUMENT IS KNOWN AS THE 'ISR EL -UDIR WHICH CONSISTS OF A METER EAST TO WEST BY METER NORTH TO SOUTH STONE ENCLOSURE 4HE WALLS ARE OF EXTREMELY CRUDE CONSTRUCTION BUT MAS SIVE 4HIS MONUMENT MAY CONSTITUTE ONE OF THE OLDEST STONE BUILDINGS IN %GYPT AND HENCE THE WORLD /NE OF THE MAIN GOALS OF THE PROJECT HAS BEEN TO DETERMINE WHAT IF ANYTHING LIES WITHIN THE ENCLOSURE $ESPITE MANY YEARS OF SURVEYING NOTHING HAS BEEN FOUND APART FROM A SMALL AREA OF MUD BRICK PAVEMENT ! NUMBER OF RADAR SECTIONS HAD BEEN MEASURED OVER THIS AREA PREVIOUSLY AND IN VIEW OF THE MAGNETOMETRY RESULTS THE RADAR PROFILES WERE REEXAMINED 4HE SECTIONS HAVE BEEN MEASURED ON METER CENTERS SO IT WAS PURELY BY CHANCE THAT ONE RADAR SURVEY LINE WENT STRAIGHT DOWN THE FLIGHT OF STEPS EXCAVATED SEEN IN &IGURE WITH THE RADAR IMAGE IN &IGURE
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!BANDONED ANTIPERSONNEL LAND MINES AND UNEXPLODED ORDNANCE ARE A MAJOR HIN DRANCE TO THE RECOVERY OF MANY COUNTRIES FROM WAR 4HEIR EFFECT ON THE CIVILIAN POPU LATION IS DISASTROUS AND MAJOR EFFORTS ARE BEING MADE BY THE INTERNATIONAL COMMUNITY TO CLEAR THE PROBLEM -OST DETECTION IS DONE WITH METAL DETECTORS WHICH RESPOND TO THE LARGE AMOUNT OF METALLIC DEBRIS IN ABANDONED BATTLEFIELD AREAS AND HENCE HAVE DIFFICULTY IN DETECTING THE MINIMUM METAL OR PLASTIC MINE '02 TECHNOLOGY IS BEING APPLIED TO THIS PROBLEM AS A MEANS OF REDUCING THE FALSE ALARM RATE AND PROVIDING IMPROVED DETECTION OF LOW METAL CONTENT MINES 4YPICAL EXAMPLES OF RADAR IMAGES AT VARIOUS SCALES ARE SHOWN IN &IGURE AND &IGURE '02 HAS BEEN USED FOR SURVEYING MANY DIFFERENT TYPES OF GEOLOGICAL STRATA RANG ING FROM EXPLORATION OF THE !RCTIC AND !NTARCTIC ICECAPS AND THE PERMAFROST REGIONS OF .ORTH !MERICA TO MAPPING OF GRANITE LIMESTONE MARBLE AND OTHER HARD ROCKS AS WELL AS GEOPHYSICAL STRATA 4HE RADAR DATA SHOWN IN &IGURE WERE COLLECTED AT &INSTERWALDERBREEN GLACIER 3VALBARD .ORWAY WHICH IS AN ISLAND ALMOST NORTH OF .ORWAY 4HE GLACIER IS AN KM LONG LAND TERMINATED GLACIER WITH AN AREA OF SQUARE KM 4HE GLACIER DEPTH STARTS AT METERS AND INCREASES DOWN TO METERS )N THE BEGINNING OF THE PROFILE ONLY THE BOTTOM ECHO IS SEEN !T AROUND KM HORIZONTAL DISTANCE SOME INTERNAL SCATTERING FROM THE GLACIER IS SEEN 4HIS IS SCATTERING FROM THE FREE WATER INSIDE THE GLACIER &ROM KM TO KM THE BOTTOM ECHO IS DIFFICULT TO SEE DUE TO SCATTERING 4HE THICKNESS OF THE VARIOUS LAYERS OF A ROAD CAN BE MEASURED USING '02 TECHNIQUES AS SHOWN IN &IGURE 4HE GREAT ADVANTAGE IS THAT THIS METHOD IS NONDESTRUCTIVE AND HIGH SPEED KMHR AND CAN BE APPLIED DYNAMICALLY TO ACHIEVE A CONTINUOUS PROFILE OR ROLLING MAP 4HE ACCURACY OF CALIBRATION TENDS TO REDUCE AS A FUNCTION OF
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)T HAS BEEN SHOWN THAT IT IS FEASIBLE TO DETECT !4 MINES IN DRY SOIL CONDITIONS USING AIRBORNE RADAR SYSTEMS THAT OPERATE OVER THE FREQUENCY RANGE n '(Z &IGURE SHOWS A RADAR IMAGE TAKEN FROM AN ALTITUDE OF METERS ABOVE THE 9UMA DESERT 4HE RADAR OPERATED AT A DEPRESSION ANGLE OF AND ACHIEVED A NOMINAL RESOLUTION OF CM )T WAS CAPABLE OF DETECTING METAL !4 MINES OF CM DIAMETER BURIED AT A DEPTH OF n CM IN A SOIL OF CONDUCTIVITY n MMHOSM &URTHER DETAILS CAN BE OBTAINED FROM 32) )NTERNATIONAL 53!
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- !LL COUNTRIES REQUIRE THAT '02 SYSTEMS ARE PROPERLY REGULATED AND OPERATED IN ACCOR DANCE WITH NATIONAL AND INTERNATIONAL REQUIREMENTS 5SERS SHOULD CONSULT WITH THEIR NATIONAL AUTHORITIES TO DETERMINE THE REGULATORY ENVIRONMENT 7ITHIN THE %UROPEAN 5NION %5 THERE ARE TWO MAIN CONSIDERATIONS GOVERN ING THE USE OF '02 4HESE ARE THE USE FIRST OF THE EQUIPMENT AS A DELIBERATE RADIO FREQUENCY RADIATOR AND SECOND AS AN EQUIPMENT THAT MUST SATISFY THE %-# REQUIRE MENTS OF THE %5 4HE %UROPEAN 4ELECOMMUNICATIONS 3TANDARDS )NSTITUTE %43) REGULATORY BODY IS IN THE PROCESS OF DRAFTING SPECIFICATIONS AND INFORMATION CAN BE FOUND AT HTTPWWWETSIORG THAT WILL COVER THE USE OF SUCH EQUIPMENT AS A DELIBER ATE RADIO FREQUENCY RADIATOR ,EGISLATION AND AN %43) PRODUCT SPECIFICATION MEANS THAT THIS EQUIPMENT WILL NEED TO CONFORM TO THE 2ADIO 4ELECOMMUNICATIONS 4ERMINAL %QUIPMENT 244% $IRECTIVE )N THE SHORT TERM UNTIL A NEW PROD UCT SPECIFICATION IS INTRODUCED AND FORMALLY PUBLISHED IN THE /FFICIAL *OURNAL OF THE %UROPEAN #OMMUNITIES THE %-# $IRECTIVE SHOULD BE APPLIED !LL EQUIP MENT INCLUDING ULTRAWIDEBAND RADAR OR '02 MUST BE #ONFORMIT£ %UROP£ENE #% MARKED TO DEMONSTRATE THAT IT SATISFIES THE RELEVANT DIRECTIVES OF THE %UROPEAN 5NION 4HE #% MARK MAY ONLY BE APPLIED WHEN THE REQUIREMENTS OF ALL OTHER RELEVANT %5 $IRECTIVES SUCH AS SAFETY HAVE ALSO BEEN DEMONSTRATED )N THE 53 THE &## WEB SITE PROVIDES CURRENT INFORMATION AND THE LIMITS ARE SHOWN IN &IGURE
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#HAPTER
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ÓÓ°£Ê /," 1 /" )N TERMS OF THE NUMBER OF SYSTEMS IN WORLDWIDE USE CIVIL MARINE RADAR #-2 IS THE LARGEST RADAR MARKET OF ALL TIME 4HE NUMBER OF VESSELS OF ALL TYPES CURRENTLY FITTED WITH RADAR PROBABLY AMOUNTS TO AROUND MILLION BUT THERE ARE NO OFFICIAL RECORDS TO VERIFY THIS ESTIMATE #-2 BREAKS DOWN INTO TWO MAIN APPLICATION AREAS 4HE VAST MAJORITY ARE USED AT SEA AND ON NAVIGABLE WATERWAYS BY SHIPS AND SMALLER CRAFT THE OTHERS ARE USED BY PORT AND COASTAL AUTHORITIES FOR VESSEL SURVEILLANCE FROM LAND BASED SITES 4HE LATTER GROUP ARE NORMALLY KNOWN AS VESSEL TRACKING SERVICE 643o RADARS 2ADARS ARE AVAILABLE FOR LEISURE CRAFT FISHING VESSELS AND MERCHANT SHIPS AND ALL OPERATE EITHER IN THE '(Z OR '(Z BANDS -ANY NAVIES ALSO USE STANDARD OR SPECIALLY MODIFIED #-2 FOR NAVI GATIONAL PURPOSES .OT ONLY DOES IT PROVIDE A SUITABLE NAVIGATIONAL TOOL BUT ALSO ITS TRANSMISSIONS ARE IDENTICAL TO CONVENTIONAL COMMERCIAL TRAFFIC ALLOWING SAFE NAVIGA TION WITHOUT NECESSARILY HIGHLIGHTING A VESSELS MILITARY PURPOSE 4HE BIGGEST INFLUENCE ON THE REQUIREMENTS OF SHIPBORNE #-2 COMES FROM THE )NTERNATIONAL -ARITIME /RGANIZATION )-/ ! 5NITED .ATIONS AGENCY BASED IN ,ONDON )-/ IS CONCERNED WITH INTERNATIONAL MARITIME SAFETY AND THE PROTECTION OF THE MARINE ENVIRONMENT )N PARTICULAR )-/ ISSUES REQUIREMENTS AND GUIDELINES ON THE INSTALLATION AND USE OF RADAR EQUIPMENT ON COMMERCIAL SHIPS 4HESE ARE VIGOROUSLY ENFORCED BY THE LAWS OF INDIVIDUAL MARITIME STATES 4HE PURPOSE OF SHIPBORNE RADAR AS DEFINED BY )-/ IS TO hASSIST IN SAFE NAVIGATION AND IN AVOIDING COLLISION BY PROVIDING AN INDICATION IN RELATION TO OWN SHIP OF THE POSITION OF OTHER SURFACE CRAFT OBSTRUC TIONS AND HAZARDS NAVIGATION OBJECTS AND SHORELINESv 4HE )NTERNATIONAL !SSOCIATION OF -ARINE !IDS TO .AVIGATION AND ,IGHTHOUSE !UTHORITIES )!,! RECOMMENDS OPER ATIONAL AND TECHNICAL REQUIREMENTS FOR 643 RADARS 4HIS CHAPTER EXPLAINS THE SPECIAL REQUIREMENTS OF #-2 BOTH FROM A PRACTICAL AND A REGULATORY POINT OF VIEW AND LOOKS AT THE TECHNOLOGY AND SYSTEM CONCEPTS THAT ARE BEING USED TO MEET THESE REQUIREMENTS 5NTIL THE FIRST DECADE OF THE PRESENT CENTURY #-2 SHIPBORNE TECHNOLOGY HAD BEEN SOLELY BASED ON MAGNETRONS AS THE BASIC SOURCE OF TRANSMITTED POWER 3INCE )-/ HAS ENCOURAGED THE USE OF COHERENT RADAR SOLU TIONS IN AN ATTEMPT TO IMPROVE THE DETECTION OF TARGETS IN HEAVY SEA CLUTTER CONDITIONS o ! LIST OF ALL USED MARITIME ABBREVIATIONS IS INCLUDED AT THE END OF THE CHAPTER
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)N THE MARINE WORLD THESE HAVE BEEN CALLED .EW 4ECHNOLOGY 2ADARS 4HEY ARE PER MITTED TO TRANSMIT ANY WAVEFORM AT '(Z PROVIDING THE SPECTRUM LIMITATIONS ON MARINE RADAR ARE NOT EXCEEDED 4HE LIMITS HAVE BEEN AGREED WITHIN THE )NTERNATIONAL 4ELECOMMUNICATION 5NION )45 A 5NITED .ATIONS AGENCY BASED IN 'ENEVA 4HIS CHAPTER CONCENTRATES ON THE REQUIREMENTS AND DESIGN OF RADARS FOR COMMER CIAL SHIPS NORMALLY IN EXCESS OF GT GROSS METRIC TONNAGE WHERE RADAR FITMENT IS COMPULSORY AND HIGHLY REGULATED 7ORLDWIDE THERE ARE ABOUT OF THESE VES SELS AND MANY ARE REQUIRED TO CARRY MORE THAN ONE RADAR 4HREE OR EVEN MORE RADARS ARE SOMETIMES CARRIED VOLUNTARILY BY LARGE SHIPS 2ADAR FORMS AN IMPORTANT PART OF A VESSELS TOTAL NAVIGATION EQUIPMENT FIT )NCREASINGLY THE BRIDGE OF A SHIP IS DESIGNED AS AN INTEGRATED CONCEPT COVERING NAVIGATION COMMUNICATIONS ENGINE CONTROL AND CARGO MONITORING FACILITIES &IGURE ILLUSTRATES A MODERN INTEGRATED BRIDGE SYSTEM )"3 AS FITTED ON A CRUISE SHIP 4HE RADAR DISPLAYS ARE SEEN TO FORM A PROMINENT PART OF THE SYSTEM 2ADARS FITTED ON SMALLER FISHING VESSELS AND LEISURE CRAFT SHARE MANY OF THE FEATURES OF RADARS DESIGNED FOR SHIPS BUT ARE NECESSARILY MORE COMPACT A TYPICAL SMALL BOAT RADAR IS SHOWN IN &IGURE 3PECIFIC REQUIREMENTS FOR THESE RADARS WHERE THEY DIFFER TO ANY EXTENT FROM THE DESIGN OF SHIPBORNE RADARS ARE DISCUSSED WITHIN RELEVANT PARTS OF THE CHAPTER 2ADAR FOR 643 IS SEPARATELY COVERED IN 3ECTION 4HE CHALLENGES FACING DESIGNERS OF SHIPBORNE RADAR ARE DETAILED WITHIN 3ECTION 4HESE RADARS HAVE TO MEET CERTAIN INTERNATIONAL STANDARDS WHICH ARE DISCUSSED IN 3ECTION 3ECTION CONCENTRATES ON THE TECHNOLOGY AND 3ECTION LOOKS AT TARGET TRACKING 2ADAR TARGETS ARE BEING INCREASINGLY DISPLAYED WITH ELECTRONIC CHART DATA AS AN UNDERLAY 4HIS IS OUTLINED IN 3ECTION TOGETHER WITH OTHER USER INTERFACE ISSUES 3ECTION LOOKS AT THE LINKS BETWEEN RADAR AND THE RELATIVELY NEW !UTOMATIC )DENTIFICATION 3YSTEM !)3 WHICH REPLICATES SOME FUNCTIONS PREVIOUSLY PROVIDED SOLELY BY RADAR -ARINE RADAR BEACONS INCLUDING RACONS 3EARCH AND 2ESCUE 4RANSPONDERS 3!24S AND 2ADAR 4ARGET %NHANCERS 24%S ARE DESCRIBED IN 3ECTION 4HERE IS A SHORT DISCUSSION IN 3ECTION ON SHIPBORNE RADAR PERFORMANCE VALIDATION TESTING
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3HIPBORNE RADAR HAS HAD A REMARKABLY LONG HISTORY )TS CONCEPTION IN THE PERIOD FROM TO WAS REMARKABLY PROPHETIC AND STILL REVERBERATES INTO THE PRESENT CENTURY &OR THIS REASON A SHORT !PPENDIX TO THIS CHAPTER OUTLINES THE EARLY STEPS IN THE EVOLU TION OF GLOBAL STANDARDS FOR SHIPBORNE RADAR
ÓÓ°ÓÊ / Ê %NVIRONMENTAL #IVIL MARINE RADAR PARTICULARLY SHIPBORNE NAVIGATION RADAR IS A SURPRISINGLY DEMANDING APPLICATION 4HE RADAR HEAD ON A #-2 COMPRISES THE ANTENNA AND TURNING GEAR THE RECEIVER DOWN TO )& OR TO DIGITAL FORMAT AND OFTEN THE TRANSMITTER )T HAS TO OPERATE IN EXTREME ENVIRONMENTAL CONDITIONS OVER AN EXTENDED TEMPERATURE RANGE DOWN TO # IN SOME PARTS OF THE WORLD IN HIGH LEVELS OF WIND VIBRATION AND SHOCK AND ALSO IN HEAVY PRECIPITATION AND SALT WATER SPRAY %VEN WITHIN THE NOR MALLY BENIGN CONDITIONS ON THE BRIDGE OF A LARGE MODERN SHIP THE DISPLAY AND RADAR PROCESSOR CAN BE SUBJECT TO HIGH LEVELS OF SHOCK AND VIBRATION AND MUST MEET HIGH VARIATIONS IN TEMPERATURE # TO # /N SMALL CRAFT THE DISPLAY AND RADAR PRO CESSOR ARE OFTEN FITTED IN MINIMALLY ENCLOSED AREAS AND ARE SUBJECT TO VERY DAMP AND SALTY CONDITIONS )N THESE ENVIRONMENTS THE RADAR HAS TO DETECT TARGETS THAT CAN HAVE ECHOING AREAS RANGING FROM LESS THAN ONE SQUARE METER TO MANY TENS OF THOUSANDS OF SQUARE METERS IMPORTANT TARGETS CAN HAVE RELATIVE SPEEDS RANGING FROM STATIONARY TO KNOTS OR MORE THE TARGETS CAN BE SITUATED IN EXTREME PRECIPITATION AND SEA CLUTTER CONDITIONS AND THE RADAR ANTENNA IS NOT MOUNTED ON A STATIC NOR A STABLE PLATFORM 4HE RADAR IS USED TO PREVENT COLLISIONS AND GROUNDINGS AT SEA AND IS THEREFORE AN IMPORTANT SAFETY RELATED SYSTEM REQUIRING INTEGRITY AND RELIABILITY &OR MOST COMMERCIAL SHIPS THE RADAR NEEDS TO MEET STRINGENT INTERNATIONALLY AGREED PERFORMANCE CRITERIA $ESPITE THESE REQUIREMENTS SYSTEMS ARE SOLD IN A HIGHLY COMPETITIVE MARKET AND PRICES ARE THEREFORE KEPT KEEN 0RICES RANGE FROM AROUND FOR A COMPLETE BUT BASIC '(Z SYSTEM TO AND ABOVE FOR A FULLY FEATURED '(Z SYSTEM 2ADAR SYSTEMS SUIT ABLE FOR THE LEISURE MARKET CAN SELL FOR LESS THAN
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"ECAUSE PRECIPITATION CLUTTER IS DISTRIBUTED IN A RELATIVELY UNIFORM MANNER PASSING THE RECEIVED WAVEFORM THROUGH A DIFFERENTIATOR GIVES PROMINENCE TO TARGETS EMBEDDED WITHIN THE CLUTTER BY ENSURING THAT THE AVERAGE CLUTTER LEVEL IS KEPT WELL BELOW SATURA TION 4HE DIFFERENTIATOR HAS MINIMAL EFFECT ON NORMAL TARGETS BECAUSE OF THEIR SMALL EXTENT IN THE TIME DOMAIN 4HIS MEANS THAT TARGET VISIBILITY IS IMPROVED )T SHOULD BE NOTED THAT THIS TECHNIQUE DOES NOT GIVE SUBCLUTTER VISIBILITY 4HIS PROCESS IS CONVENTION ALLY NAMED &AST 4IME #ONSTANT &4# 4HE TIME CONSTANT OF THE DIFFERENTIATOR IS OPERA TOR ADJUSTABLE WITH A SO CALLED RAIN CLUTTER CONTROL WHICH ALLOWS THE TARGET TO CLUTTER RATIO TO BE OPTIMIZED FOR THE PARTICULAR PRECIPITATION SCENARIO 4HE VERTICAL PATTERN OF A SHIPBORNE NAVIGATIONAL RADAR ANTENNA NEEDS TO BE RELA TIVELY WIDE TO COPE WITH THE SHIPS PITCH AND ROLL WHICH IS ASSUMED TO BE A MAXIMUM OF o 5SE OF A STABILIZED PLATFORM WOULD NOT MEET THE MARKETS PRICE DEMANDS 4HIS LIMITS THE VERTICAL BEAM SHAPING THAT CAN BE USED TO REDUCE BOTH PRECIPITATION CLUTTER AND VERTICAL LOBING EFFECTS (OWEVER THE RELATIVELY SHORT RANGE OF MOST TARGETS OF REAL INTEREST MEANS THAT THE VOLUME OF THE RADAR ILLUMINATED PRECIPITATION IS RELA TIVELY LOW HELPING TO MAKE THE CLUTTER REJECTION OF THE DIFFERENTIATOR ADEQUATE FOR ITS PURPOSE 3UCH CLUTTER VARIES APPROXIMATELY WITH THE FOURTH POWER OF FREQUENCY AND SO A '(Z SYSTEM INHERENTLY EXPERIENCES D" LESS CLUTTER THAN A '(Z SYSTEM ASSUMING IDENTICALLY SIZED CLUTTER CELLS &OR THIS REASON ON SHIPS FITTED WITH BOTH AND '(Z RADARS THE '(Z RADAR IS OFTEN PREFERABLE EXCEPT WHEN MANEUVERING IN CLOSE SITUATIONS FOR EXAMPLE IN HARBORS WHEN THE NORMALLY SUPERIOR AZIMUTH RESOLUTION OF A '(Z RADAR IS PREFERRED 3EA #LUTTER 4HE REDUCTION OF SEA CLUTTER TO LEVELS ACCEPTABLE TO THE USER IS A FAR MORE DIFFICULT PROBLEM AND AS YET COMMERCIAL RADARS DO NOT MEET ALL THE IDEAL DEMANDS OF USERS 3MALL CRAFT AND BUOYS CAN EASILY BE OBSCURED IN SEA CLUTTER )N THE DAYS BEFORE PRECISE 'LOBAL .AVIGATION 3ATELLITE 3YSTEMS '.33 SUCH AS '03 THE SAFE NAVIGATION OF A SHIP IN COASTAL WATERS IN POOR VISIBILITY WAS DOMINATED BY THE RADAR BEING ABLE TO DISCERN NAVIGATION MARKERS SUCH AS BUOYS 0ASSIVE MARKERS INCLUDING THOSE SUPPLEMENTED BY RADAR REFLECTORS CAN BE NOTORIOUSLY DIFFICULT TO DETECT IN HIGHER SEA STATES AND THEREFORE SOME MARKERS ARE SUPPLEMENTED BY RADAR BEACONS CALLED RACONSSEE 3ECTION 2ACONS ARE RELATIVELY EXPENSIVE AND NEED MAINTENANCE IN OFTEN DIFFICULT TO ACCESS LOCATIONS SO THEIR USE IS RESTRICTED 7HILE '.33 ENHANCED BY THE GROWING USE OF ELECTRONIC CHARTS HAS HELPED GREATLY IN INFORMING MARINERS OF THE PRECISE POSITION OF THEIR VESSEL RADAR IS STILL USED AS AN IMPORTANT SECONDARY SOURCE OF POSITION 2ELIANCE ON '.33 ALONE HAS BEEN AT THE ROOT OF MANY MARINE ACCIDENTS 4HE MAIN USE OF MARINE RADAR IS TO ASSIST COLLISION AVOIDANCE 6ISUAL OBSERVA TION AND RADAR REMAIN THE PRIMARY METHODS FOR DETERMINING THE RISK OF COLLISION WITH OTHER VESSELS AND ALSO WITH FLOATING DEBRIS AND ICE !UTOMATIC )DENTIFICATION 3YSTEMS !)3SEE 3ECTION OFFER POTENTIAL TO ASSIST WITH COLLISION AVOIDANCE OF COOPERA TIVE TARGETS BUT IT CANNOT BE ASSUMED THAT ALL VESSELS ARE FITTED WITH !)3 PARTICULARLY SMALL CRAFT OR THAT A TARGET VESSELS !)3 IS OPERATIONAL 4HE TRADITIONAL WAY FOR MARINERS TO OPTIMIZE THEIR RADAR FOR DETECTION OF TARGETS IN SEA CLUTTER IS BY CAREFUL ADJUSTMENT OF THE hGAINv AND hSEA CLUTTERv CONTROLS 4HE GAIN CON TROL EFFECTIVELY ALTERS THE DETECTION THRESHOLD /N A MODERN MARINE RADAR THE SEA CLUTTER CONTROL IS BEST DESCRIBED AS A METHOD FOR ADJUSTING THE SHAPE OF THE RADARS SENSITIVITY TIME CONTROL 34# IN ORDER TO MATCH IT WITH THE PRESENT LEVEL OF CLUTTER RETURNS 34# IS OFTEN ALSO CALLED SWEPT GAIN 4HE 34# LAW AND THE WAY IT VARIES BY USE OF THE MANUAL CONTROL CAN BE COMPLEX )T IS ATTEMPTING TO REDUCE THE DYNAMIC RANGE OF THE RECEIVED WAVEFORM AND TO PROVIDE IN ASSOCIATION WITH THE GAIN SETTINGS OPTIMIZED THRESHOLDS
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.OWADAYS IT NORMALLY INVOLVES SOPHISTICATED ADAPTIVE THRESHOLDING TECHNIQUES WHICH ARE DISCUSSED IN 3ECTION !LTHOUGH THIS HELPS TO SET THE THRESHOLD TO APPROPRIATE LEVELS IT DOES NOT REMOVE THE INTRUSIVE hSPIKYv COMPONENT OF SEA CLUTTER THAT CAN MAKE WANTED TARGETS DIFFICULT TO OBSERVE (OWEVER OVER A TYPICAL ANTENNA SCAN TIME OF A MARINE RADAR n SECONDS THE SPIKES ARE NORMALLY DECORRELATED WHEREAS RETURNS FROM TARGETS ARE GENERALLY CORRELATED THEREFORE THE APPLICATION OF SCAN TO SCAN CORRELATION CAN IMPROVE THE TARGET TO CLUTTER RATIO BUT IT WILL ALSO REMOVE WEAK AND FAST MOVING TARGETS -ANY YEARS AGO #RONEY SHOWED THAT SIGNIFICANT IMPROVEMENTS IN DETECTING SMALL TARGETS IN SEA CLUTTER COULD BE OBTAINED BY ENSURING THAT INTEGRATION WAS PERFORMED AT INTERVALS LONGER THAN THE DECOR RELATION TIME PERIOD OF THE SEA CLUTTER (E USED AN ANTENNA ROTATING AT UP TO RPM AND A 02& OF +(Z 4HIS GAVE TWO CORRELATED PULSES PER BEAMWIDTH BUT THE PULSES FROM THE NEXT SCAN S LATER WERE DECORRELATED FROM THE FORMER #RONY NOTED THAT THE RAPID SCANNING OF THE ANTENNA ALLOWED THE EYEBRAIN FUNC TIONS OF THE OPERATOR TO PERFORM SCAN TO SCAN CORRELATION !LTHOUGH IT IS EASY FOR MOD ERN SYSTEMS TO PERFORM THIS CORRELATION DIGITALLY THE DIFFICULTIES IN HAVING AN ANTENNA ROTATING AT THIS SPEED MAINLY NOW A COST ISSUE HAVE PREVENTED THIS FROM BECOMING ESTABLISHED PRACTICE (OWEVER MORE RECENT WORK IN #ANADA HAS RESURRECTED THIS IDEA FOR DETECTING FLOATING ICE HAZARDS WHERE ANTENNA ROTATION RATES OF RPM AND 02&S OF +(Z HAVE BEEN PROPOSED 4ERMA !3 A $ANISH COMPANY INVOLVED IN SUPPLYING HIGH PERFORMANCE MARINE RADARS MAINLY IN THE NONCOMMERCIAL MARKET PRODUCES THE 3CANTER4- RADAR WHICH HAS AN OPTION THAT SIMULTANEOUSLY TRANSMITS ON TWO FREQUEN CIES FROM A SQUINTING SLOTTED WAVEGUIDE ARRAY 4HIS PRODUCES TWO BEAMS SEPARATED BY A FEW DEGREES IN AZIMUTH 4HE TEMPORAL BEAM SEPARATION IS SUCH THAT SEA CLUTTER CAN BE DECORRELATED BETWEEN THE BEAMS FURTHER ENHANCING THE DETECTION OF TARGETS IN CLUTTER 4HIS TECHNIQUE COULD POTENTIALLY BE USED BY SOLID STATE #-2S 3ECTION /N A CONVENTIONAL SHIPBORNE RADAR AN EXPERIENCED OPERATOR CAN MANUALLY SET THE DETECTION THRESHOLD TO GIVE THE BEST SETTING OVER ANY GIVEN AREA BUT THIS IS OFTEN ONLY EFFECTIVE OVER A SMALL PROPORTION OF THE TOTAL RADAR IMAGE 4HE USE OF AUTOMATIC THRESH OLDING IS ABLE TO GIVE BETTER DETECTION OVER A COMPLETE SCAN BUT OFTEN CANNOT COMPETE WITH A SKILLED OPERATOR OPTIMIZING DETECTION OVER A RESTRICTED AREA )N SOME CONDITIONS NO EXISTING RADAR GIVES THE PERFORMANCE THAT A USER IDEALLY NEEDS DESPITE THE USE OF NS PULSES AND SOPHISTICATED CLUTTER PROCESSING TECHNOLOGY 3UB CLUTTER VISIBILITY IS POTENTIALLY OBTAINABLE FROM COHERENT #-2S WHICH HAVE BEEN MADE AFFORDABLE BY THE CONTINUED REDUCTION IN COST OF MICROWAVE POWER SEMICON DUCTORS FOR INSTANCE USING 'ALLIUM .ITRIDE TECHNOLOGY PRECISION DIGITALLY CONTROLLED SIGNAL GENERATORS AND FAST DIGITAL SIGNAL PROCESSORS #OHERENT #-2S ARE DISCUSSED UNDER h3OLID STATE #-2v IN 3ECTION 6ERTICAL ,OBING #LUTTER IS NOT THE ONLY CAUSE OF DETRIMENTAL PERFORMANCE OF MARINE RADAR $IRECT REFLECTIONS FROM A TARGET ARRIVE AT THE RADAR ANTENNA AND COMBINE VECTORIALLY WITH TARGET REFLECTIONS THAT HAVE ALSO BEEN REFLECTED BY THE SEAS SURFACE 4HIS EFFECT PRODUCES A SUMMED SIGNAL AT THE RADAR ANTENNA THAT IS A FUNCTION OF BOTH THE TARGET HEIGHT AND THE RADAR ANTENNA HEIGHT ABOVE THE SEA AS THESE AFFECT THE PATH LENGTH DIFFERENCE OF THE DIRECT AND REFLECTED RADIATION /BVIOUSLY THE EFFECT IS RECIPROCAL FOR BOTH TRANSMIT AND RECEIVE PATHS &OR A POINT TARGET AND A SEA OF DEFINED ROUGHNESS THE CALCULATION TO DETERMINE THE RESULTANT EFFECT IS RELATIVELY STRAIGHTFORWARD AND RESULTS IN THE CLASSIC LOBING PATTERN SEE FOR EXAMPLE "RIGGS &OR A TARGET WITH REASONABLE VERTICAL EXTENT SUCH AS A SHIP THE LOBING STRUCTURE BECOMES VERY COMPLEX AND IS LESS LIKELY TO PRODUCE TROUBLESOME NULLS (OWEVER THE DETECTION OF A SMALL TARGET SUCH AS
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A BUOY OR A PLEASURE CRAFT ENHANCED BY A RADAR REFLECTOR CAN CREATE SIGNIFICANT VERTICAL LOBING EFFECTS THAT CAN BE A PROBLEM TO THE USER )N PARTICULAR IN VERY CALM SEAS PRO NOUNCED NULLS CAN BE EXPERIENCED AND FOR USERS IT CAN BE DISCONCERTING WHEN A TARGET CLEARLY EVIDENT FROM THE BRIDGE WINDOW IS NOT VISIBLE ON THE RADAR DISPLAY DESPITE THE APPARENTLY GOOD CONDITIONS 3INCE SMOOTH SEAS CAN ALSO BE ASSOCIATED WITH MIST AND FOG VERTICAL LOBING EFFECTS CAN BECOME A SIGNIFICANT PROBLEM BECAUSE THE REDUCED VISIBILITY MEANS THAT RADAR OFTEN BECOMES THE SOLE METHOD OF DETECTING OTHER VESSELS 4HE ABSENCE OF SEA CLUTTER GIVES THE USER A FALSE SENSE OF SECURITY THAT ALL TARGETS WILL BE EASILY VISIBLE /N SHIPS FITTED WITH BOTH AND '(Z RADARS FREQUENCY DIVERSITY BECOMES VERY USEFUL AS THE SPATIAL FREQUENCIES OF THE VERTICAL LOBES FOR THE RADAR ARE DIFFERENT 3URPRISINGLY EVEN THOUGH SOME RADAR COMPANIES PROVIDE THE OPTION VERY FEW SHIPS HAVE FACILITIES THAT ALLOW THE AND '(Z SIGNALS TO BE COMBINED INTO A SINGLE RADAR DISPLAY IN AN AUTOMATIC PROCESS MAXIMIZING THE BENEFITS OF FREQUENCY DIVERSITY 3OME LARGE SHIPS HAVE AN ADDITIONAL '(Z RADAR MOUNTED ON THE BOW AT DECK LEVEL 4HIS HAS TWO ADVANTAGES &IRST THE VERTICAL LOBING WILL HAVE A DIFFERENT LOWER ANGULAR FREQUENCY TO THE MAIN HIGH MOUNTED '(Z RADAR 3ECOND ITS PERFORMANCE IN SEA CLUTTER WILL BE ENHANCED AS THE GRAZING ANGLE TO THE SEA WILL BE CLOSER TO HORIZONTAL THEREBY LESSENING THE REFLECTION COEFFICIENT OF THE CLUTTER 4HE LONG RANGE PERFORMANCE OF THE AUXILIARY SYSTEM IS OF COURSE COMPROMISED BY ITS LOW POSITION -OVING 0LATFORM ! PARTICULAR COMPLICATION OF SHIPBORNE RADAR ARISES BECAUSE THE ANTENNA IS MOUNTED ON AN UNSTABLE MOVING PLATFORM 4HIS MOVEMENT HAS SIX COMPONENTSTHREE TRANSLATIONAL AND THREE ROTATIONAL ALL OF WHICH ARE TYPICALLY VARYING 4HE MOTIONS ARE COMPLEX THE TRANSLATIONAL COMPONENTS ARE SURGE SWAY AND HEAVE AND THE ROTATIONAL ARE ROLL PITCH AND YAW #OMPONENTS CAN BE QUASI HARMONIC WHEN CAUSED BY WAVE MOTION )N PRACTICE THE SHIP IS NAVIGATED ON NOTIONS BASED ON COURSE HEADING AND SPEED IN %ARTH AND SEA FIXED COORDINATE SYSTEMS 4HE ADDITIONAL WAVE INDUCED MOTIONS CAN PRODUCE UNCOMPENSATED ERRORS IN RADAR DERIVED INFORMATION WHICH ADD TO ANY MEASUREMENT ERRORS IN THE COURSE HEADING AND SPEED OF THE VESSEL 4HIS AFFECTS THE PRECISION OBTAINED WHEN DISPLAYING RADAR DERIVED DATA WHICH CAN DIFFER WHEN SWITCHING BETWEEN THE VARIOUS RADAR STABILIZATION MODES USED ON #-2 &OR INSTANCE IN ORDER TO FACILITATE BOTH COLLISION AVOIDANCE AND POSITION FIXING ACTIVITIES SHIPBORNE RADAR DISPLAYS HAVE ALWAYS HAD TWO PARTICULAR STABILIZATION MODES (EAD UP AND .ORTH UP 4HE hUPv DIRECTION REFERS TO THE VERTICAL Y AXIS DIRECTION OF THE RADAR DISPLAY h(EADv REFERS TO THE SHIPS HEADING (EAD UP MAXIMIZES THE RELATIONSHIP TO THE VISUAL SCENE AND .ORTH UP AIDS COMPARISON WITH PAPER CHARTS .OWADAYS #OURSE UP IS ALSO PROVIDED AS THIS ELIMINATES SMALL OSCILLATIONS IN THE RADAR IMAGE DUE TO THE SHIPS YAW THAT OCCUR WHEN THE DISPLAY IS SET TO (EAD UP %ACH OF THESE DIRECTIONAL MODES CAN BE SET WITH TARGET TRACKING VECTORS SHOWN AS RELATIVE TO THE MOTION OF THE SHIP THE GROUND OR THE AVERAGE SEA MOTION
ÓÓ°ÎÊ / , /" Ê-/ , 3PECTRUM USE ASPECTS OF ALL RADARS INCLUDING FREQUENCY BAND OF USE AND 2& EMISSION CONSTRAINTS ARE CONTROLLED BY THE )45 &OLLOWING )45 REQUIREMENTS MARINE RADARS ARE PERMITTED TO OPERATE IN THE TO '(Z BAND 8 BAND AND IN THE TO '(Z BAND 3 BAND
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4HE )-/ )NTERNATIONAL #ONVENTION FOR THE 3AFETY OF ,IFE AT 3EA 3/,!3 IS AN ESTABLISHED AND ACCEPTED SET OF PRINCIPLES AND RULES AIMED AT ENSURING THAT SHIPS MEET CERTAIN REQUIREMENTS TO ENHANCE BOTH SAFETY AND PROTECTION OF THE ENVIRONMENT 4HE MEMBER GOVERNMENTS FLAG 3TATES OF )-/ HAVE AGREED THAT 3/,!3 REQUIREMENTS ARE EMBODIED WITHIN THEIR NATIONAL MARITIME LAWS AND REGULATIONS 7ITHIN #HAPTER 6 OF 3/,!3 3AFETY OF .AVIGATION THE REQUIREMENTS FOR THE CARRIAGE OF NAVIGATION EQUIPMENT ARE DEFINED 4HESE VARY ACCORDING TO THE SIZE AND PURPOSE OF A SHIP !LL PASSENGER SHIPS AND ALL SHIPS ABOVE GT NEED TO CARRY AT LEAST ONE RADAR WITH TRACKING FACILITIES &OOTNOTES WITHIN #HAPTER 6 OF 3/,!3 IDENTIFY THE RECOMMENDED )-/ PERFOR MANCE STANDARDS WITH WHICH THE EQUIPMENT SHOULD CONFORM )-/ HAS HAD RECOM MENDED RADAR PERFORMANCE STANDARDS SINCE PUBLISHED AS ANNEXES TO )-/ 2ESOLUTIONS (OWEVER BY RADAR MANUFACTURERS WERE REPORTING DIFFICULTIES BECAUSE DIFFERING INTERPRETATIONS BY NATIONAL MARITIME ADMINISTRATIONS MEANT THAT RADARS HAD TO BE SPECIFICALLY DESIGNED TO MEET INDIVIDUAL FLAG 3TATE REQUIREMENTS 4HE LEVEL OF TECHNICAL DETAIL REQUIRED TO REMEDY THIS WAS OUTSIDE THE REMIT OF )-/ AND IT WAS AGREED THAT A 4ECHNICAL #OMMITTEE 4# WITHIN THE )NTERNATIONAL %LECTROTECHNICAL #OMMISSION )%# WOULD DETERMINE TECHNICALLY BASED INTERPRETA TIONS OF )-/ RADAR PERFORMANCE STANDARDS )N ADDITION IT WAS AGREED THAT THE )%# STANDARDS WOULD INCLUDE TEST PROCEDURES WHICH COULD BE USED BY NATIONAL MARITIME ADMINISTRATIONS SUCH AS THE #OAST 'UARD IN THE 5NITED 3TATES OF !MERICA TO TEST FOR CONFORMANCE OF SPECIFIC DESIGNS BY MANUFACTURERS TO )-/ AND )45 REQUIREMENTS 4ODAY VIRTUALLY ALL NATIONAL ADMINISTRATIONS USE )%# STANDARDS TO ASSESS RADAR AND MOST OTHER )-/ DEFINED NAVIGATIONAL AND RADIOCOMMUNICATIONS EQUIPMENT )-/ PERFORMANCE STANDARDS AND THE 3/,!3 #ONVENTION ARE REGULARLY REVISED SO IT IS IMPORTANT TO CHECK THE CURRENT STATUS OF THE STANDARDS )%# DEFINES THE TECH NICAL AND TEST STANDARDS BASED ON THE )-/ RADAR PERFORMANCE STANDARDS )%# STANDARDS ALSO UNDERGO REGULAR REVISION !N AVERAGE RADAR INSTALLATION HAS A LIFE NORMALLY EXCEED ING YEARS SO RADARS DESIGNED AND APPROVED TO PREVIOUS STANDARDS WILL CONTINUE TO BE USED FOR SOME YEARS AFTER NEW STANDARDS HAVE BEEN PUT IN PLACE 2ETROFITTED EQUIPMENT MUST MEET THE LATEST STANDARDS )-/ RADAR PERFORMANCE STANDARDS PREVIOUS TO THOSE IN FORCE ON *ULY REQUIRE COMPATIBILITY WITH EXISTING RACONS RADAR BEACONS AND AT '(Z 3EARCH AND 2ESCUE 4RANSPONDERS 4HIS IMPLIES THE CONTINUED USE OF SHORT PULSE RADARS (OWEVER FOR THE STANDARDS )-/ HAS ENCOURAGED IMPROVEMENTS IN SEA CLUT TER PERFORMANCE BY DROPPING THE NEED FOR RACON COMPATIBILITY AT '(Z THEREBY ALLOWING OTHER FORMS OF MODULATION THAT WOULD ENABLE AFFORDABLE COHERENT PRO CESSING TECHNIQUES "ECAUSE ALL SHIPS ABOVE GT NEED TO CARRY AT LEAST A SINGLE '(Z RADAR IT MEANS THAT RACON AND 3!24 DETECTION CAPABILITY IS MAINTAINED 4HIS APPROACH GIVES )-/ AN INDEFINITE PERIOD TO ASSESS THE IMPACT OF THE NEW REGU LATIONS ON THE DETECTION OF TARGETS IN SEA CLUTTER BEFORE DECIDING WHAT SHOULD HAPPEN WITH RADAR RACONS AND 3!24S AT '(Z !NOTHER MAJOR CHANGE IN THE REQUIREMENTS OF OLDER STANDARDS IS THAT ALL NEW RADARS MUST INCLUDE PROVISION TO DISPLAY !UTOMATIC )DENTIFICATION 3YSTEM !)3 TARGETS AND THAT THEIR RELATED INFORMATION CAN BE ACCESSED ON THE RADAR DISPLAY 4HE REQUIREMENTS FOR TARGET TRACKING HAS ALSO HAD A MAJOR REVISION WITH AUTOMATIC TRACKING FACILITIES BEING REQUIRED FOR ALL RADARS 4HE INTEGRATION OF ELECTRONIC CHART DATA AS A BACKGROUND TO RADAR IMAGES IS ALSO EMBODIED WITHIN )-/ STANDARDS 2ADARS WITH THIS OPTIONAL FACILITY ARE KNOWN AS #HART 2ADARS
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4HE MINIMUM DETECTION PERFORMANCE REQUIRED IN CLEAR CONDITIONS IS TABULATED IN 4ABLE -EASUREMENTS OF RANGE HAVE TO BE WITHIN METERS ACCURACY OR WITHIN OF THE MAXIMUM RANGE SCALE IN USE AND WITHIN BEARING AZIMUTH ANGLE .AVIGATIONAL BUOYS WITH THE CHARACTERISTICS GIVEN IN 4ABLE HAVE TO BE DETECTABLE AT A MINIMUM RANGE OF METERS 4WO hPOINTv TARGETS ON THE SAME BEARING HAVE TO APPEAR AS TWO DISTINCT TARGETS IF THEY ARE SEPARATED BY MORE THAN METERS IN RANGE ! AZIMUTH RESOLUTION IS ALSO REQUIRED !LL THESE PERFORMANCE FIGURES ARE CONSIDERED TO BE PEAK ERRORS WHICH CAN BE ASSUMED TO MEAN VALUES MEASURED WITH STAN DARDIZED POINT TARGETS 4HE )-/ PERFORMANCE STANDARDS RECOGNIZE THAT THE DETECTION PERFORMANCE OF RADARS WORKING WITHIN CONDITIONS OF CLUTTER WILL NOT NECESSARILY GIVE THE PERFORMANCE DEFINED FOR CLEAR CONDITIONS -ANUFACTURERS ARE REQUIRED TO PROVIDE EFFECTIVE MANUAL AND AUTOMATIC ANTI CLUTTER FUNCTIONS AND MUST SPECIFY THE EXPECTED DEGRADATION IN RAIN AT MM AND MM PER HOUR AND FOR SEA STATES AND INCLUDING COMBINATIONS OF SEA AND RAIN CLUTTER 2ADARS DESIGNED FOR CONVENTIONAL VESSELS NEED TO OPERATE WITH RELATIVE SPEEDS UP TO KT &OR HIGH SPEED CRAFT SUCH AS MULTI HULL FAST FERRIES THE RADARS NEED TO OPERATE WITH RELATIVE TARGET SPEEDS UP TO KT /LDER STANDARDS REQUIRED A MINIMUM ANTENNA ROTATION RATE OF RPM BUT THIS EXPLICIT REQUIREMENT HAS BEEN OMITTED FROM THE NEW STANDARDS AS OTHER DEPENDENT REQUIREMENTS ARE ADEQUATELY SPECIFIED SUCH AS THE MAXIMUM RELATIVE SPEED OF TARGETS AND TRACKING ACCURACIES 4HE )-/ PERFOR MANCE STANDARDS SPECIFY THAT RADAR EQUIPMENT SHOULD MEET THE ENVIRONMENTAL REQUIRE MENTS AND TEST PROCEDURES DEFINED WITHIN )%# 4HIS IS A COMPREHENSIVE SET OF REQUIREMENTS THAT ARE APPLICABLE TO ALL SHIPS NAVIGATIONAL AND RADIO COMMUNICATIONS EQUIPMENT 4HEY COVER SUCH ASPECTS AS TEMPERATURE SHOCK VIBRATION CORROSION AND RESISTANCE TO WATER AND OIL INGRESS $ETAILED REQUIREMENTS ON ELECTROMAGNETIC EMIS SIONS AND IMMUNITY TO THE ELECTROMAGNETIC ENVIRONMENT ARE MANDATED )%# ALSO SPECIFIES GENERAL REQUIREMENTS ON ERGONOMICS SOFTWARE DEVELOPMENT AND SAFETY ! FURTHER SET OF )%# STANDARDS CONTAINED WITHIN THE )%# SERIES DEFINE THE MES SAGES USED FOR NAVIGATION AND RADIOCOMMUNICATIONS EQUIPMENT TO INTERCHANGE DIGITAL DATA ! SHIPBORNE RADAR IS LIKELY TO BE RECEIVING MESSAGES FROM MANY ITEMS OF NAVIGA TION EQUIPMENT SUCH AS !)3 '03 GYROCOMPASS LOG AND ECHO SOUNDER AND IS ALSO LIKELY TO BE COMMUNICATING TRACK INFORMATION TO ELECTRONIC CHART SYSTEMS AND POSSIBLY OTHER RADAR DISPLAYS ! NUMBER OF MANUFACTURERS PRODUCE RADARS SPECIFICALLY DESIGNED TO BE USED ON VESSELS USING THE WORLDS MAJOR INLAND WATERWAYS 4HESE ARE KNOWN AS RIVER RADARS 4HEY ARE EPITOMIZED BY THEIR SUPERIOR SHORT RANGE PERFORMANCE AND BY HAVING A DIS PLAY IN hPORTRAITv FORMAT IN ORDER TO GET MAXIMUM LOOK AHEAD ALONG THE WATERWAY 4HE MAXIMUM DISPLAY RANGE ON THE SHORTEST SCALE IS TYPICALLY METERS 4HESE RADARS ARE NORMALLY DESIGNED TO MEET REQUIREMENTS FOR RADARS ON VESSELS NAVIGATING THE 2IVER 2HINE 2ADARS FOR THE FISHING AND LEISURE MARKETS ARE NOT COVERED BY 3/,!3 5NTIL SUCH RADARS DID NOT HAVE AN INTERNATIONALLY RECOGNIZED STANDARD FOR MANUFACTURERS TO FOLLOW )%# IS NOW THE AGREED INTERNATIONAL RADAR STANDARD FOR hCRAFT NOT IN COMPLIANCE WITH )-/ 3/,!3 #HAPTER 6v AND WAS INITIALLY ISSUED AT THE INSTIGATION OF MANUFACTURERS .OW AN INCREASING NUMBER OF NATIONAL MARITIME ADMINISTRATIONS ARE INSISTING THAT ALL NEW SMALL CRAFT RADARS SOLD IN THEIR JURISDICTION CONFORM TO THIS STANDARD )%# RECOGNIZES THREE CLASSES OF RADAR #LASS ! IS INTENDED FOR COM MERCIAL CRAFT UNDER GT #LASS " IS FOR RECREATIONAL CRAFT AND #LASS # IS FOR SMALL RECREATIONAL CRAFT 4HE MAIN PERFORMANCE REQUIREMENTS ARE DETAILED IN 4ABLE
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ÓÓ°{Ê / " "9 !NTENNAS !NTENNA MAXIMUM SIDELOBES ARE SPECIFIED FOR 3/,!3 AND NON 3/,!3 RADARS IN )%# AND )%# RESPECTIVELY 4HESE ARE SUMMARIZED IN 4ABLE /N NON 3/,!3 RADARS THE ANTENNA ROTATION RATE IS SPECIFIED TO BE NOT LESS THAN RPM BUT IS NOT DIRECTLY SPECIFIED FOR 3/,!3 APPROVED RADARS )N PRACTICE ANTENNAS FOR EXISTING SHIPBORNE RADARS NORMALLY ROTATE AT n RPM ON HIGH SPEED CRAFT THE ROTATION RATE IS TYPICALLY n RPM &OR 3/,!3 VESSELS THE ANTENNA MUST BE ABLE TO START AND OPERATE IN RELATIVE WIND SPEEDS UP TO KT OTHER ENVIRONMENTAL REQUIREMENTS FOR THE ANTENNA SYSTEM ARE DETAILED IN )%# WHERE THERE ARE SPECIFIC TESTS FOR hEXPOSEDv EQUIPMENT 4HERE ARE NO EXPLICIT REQUIREMENTS ON OTHER ANTENNA PARAMETERS FOR 3/,!3 APPROVED SYSTEMS SUCH AS BEAMWIDTHS AND GAIN BUT THESE OBVIOUSLY NEED TO BE COM PATIBLE WITH THE TOTAL RADAR PERFORMANCE REQUIREMENT &OR INSTANCE AZIMUTH RESOLUTION HAS TO BE BETTER THAN TARGET BEARING HAS TO BE DETERMINED TO WITHIN AND THE SYSTEM MUST OPERATE IN CONDITIONS WHEN THE SHIP IS ROLLING AND PITCHING o 4YPICAL ANTENNA GAINS AND BEAMWIDTHS HAVE BEEN OUTLINED IN 3ECTION &ROM THE S ONWARDS THE USE OF A SLOTTED WAVEGUIDE LINEAR ARRAY MOUNTED IN A LINEAR FLARED HORN HAS BEEN THE MOST COMMON ANTENNA SOLUTION FOR SHIPBORNE RADARS "ECAUSE AT LEAST HORIZONTAL POLARIZATION HAS TO BE PROVIDED ON '(Z 3/,!3 RADARS SLOTTED ARRAY SOLUTIONS GENERALLY HAVE THEIR SLOTS CUT INTO THE NARROW WALL OF THE HORIZON TALLY MOUNTED WAVEGUIDE ! VERTICAL SLOT PERPENDICULAR TO THE WAVEGUIDE EDGE COUPLES NO POWER BUT AS THE SLOT IS INCREASINGLY ANGLED MORE POWER IS COUPLED OUT 4HE SLOTS ARE NORMALLY OF A RESONANT LENGTH HALF WAVELENGTH TO COUPLE OUT SUFFICIENT POWER 4HIS EXTENDS THE SLOT INTO THE BROAD WALL OF THE WAVEGUIDE BUT IT ALSO MAKES THEM EASIER TO CONSTRUCTCONCEPTUALLY BY A SAWING ACTION INTO THE NARROW WALL 2ESIDUAL POWER AT THE END OF THE ARRAY TYPICALLY LESS THAN IS DISSIPATED INTO A MATCHED LOAD #ONVENTIONALLY THE ARRAY IS END FED ALTHOUGH CENTER FED ALTERNATIVES ARE SOMETIMES USED 4!",% !NTENNA 3IDELOBE 0ERFORMANCE 2EQUIREMENTS #OURTESY OF )%#
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)F SLOTS WERE SPACED AT THE GUIDE WAVELENGTH IN AN ATTEMPT TO GET AN EQUI PHASE WAVEFRONT AT THE ANTENNA FACE THEN LARGE GRATING LOBES WOULD BE GENERATED IN THE FAR FIELD PATTERN 4HIS WOULD OCCUR BECAUSE THEY WOULD BE SPACED AT A FREE SPACE DISTANCE OF MORE THAN ONE WAVELENGTH 4O OVERCOME THIS SLOTS ARE SPACED AT NOMINALLY HALF THE GUIDE WAVELENGTH BUT ARE ANGLED ALTERNATELY TO THE VERTICAL IN ORDER TO INDUCE THE NECESSARY PHASE REVERSALS )N PRACTICE THE SLOTS ARE PLACED SLIGHTLY AWAY FROM HALF THE GUIDE WAVELENGTH SPACING TO AVOID SLOT GENERATED MISMATCHES IN THE WAVEGUIDE BECOMING RESONANT 4HIS CREATES A TILTED PHASE FRONT ACROSS THE ARRAY WHICH CAUSES THE BEAM TO SQUINT TO AN ANGLE THAT IS FREQUENCY DEPENDENT )NDIVIDUAL MANUFACTURERS PRO DUCE RADAR SYSTEMS OPERATING OVER A RESTRICTED BAND MUCH LESS THAN THE OVERALL RADAR BAND WHICH REMOVES ANY NEED FOR INDIVIDUAL SQUINT COMPENSATION WHEN MAGNETRONS ARE REPLACED 4HE REQUIRED SIDELOBE PERFORMANCE IS NOT DEMANDING 4ABLE AND SO SIMPLE APERTURE DISTRIBUTIONS SUCH AS PEDESTAL BASED COSINE SQUARED ARE COMMON 4HE SMALL VERTICALLY POLARIZED FIELDS PRODUCED BY EACH SLANTED SLOT NEED TO BE SUP PRESSED AS THEY CAN OTHERWISE LEAD TO HIGH CROSS POLARIZED SIDELOBES FROM THE ARRAY EXACERBATED BY THE PHASE REVERSAL OF THE CROSS POLAR COMPONENT FROM SLOT TO SLOT CAUS ING CROSS POLAR GRATING LOBES 4HIS CAN BE ACHIEVED WITH A PRINTED POLARIZATION FILTER IN FRONT OF THE ARRAY OR BY EFFECTIVELY CREATING AS PART OF THE STRUCTURE A SHORT LENGTH OF OPEN ENDED WAVEGUIDE IN FRONT OF EACH SLOT WITH DIMENSIONS THAT MAKE IT BELOW CUTOFF FOR VERTICAL POLARIZATION 3LOT CHARACTERIZATION IS NORMALLY PERFORMED BY MEASUREMENT RATHER THAN BY DETAILED ELECTROMAGNETIC ANALYSIS 4HIS ALLOWS ALL CONSTRUCTION DETAILS INCLUDING THOSE REQUIRED FOR POLARIZATION FILTERING TO BE INCORPORATED INTO THE SLOT CHARACTERIZATION SUFFICIENT ACCURACY IS DIFFICULT TO ACHIEVE USING NUMERICAL ANALYSIS 0ROVIDED THE CHAR ACTERIZATION IS DONE CAREFULLY AND GOOD MANUFACTURING TECHNIQUES CAN GUARANTEE TOLER ANCES IT IS REASONABLY STRAIGHTFORWARD TO PRODUCE AFFORDABLE ANTENNAS THAT MEET )-/ REQUIREMENTS 4HE REQUIRED VERTICAL BEAMWIDTH IS NORMALLY OBTAINED BY A LINEAR FLARE 4HE FLARE ANGLE IS CHOSEN SUCH THAT IT CREATES A REASONABLY PHASE CONSTANT VERTICAL DIS TRIBUTION AT ITS APERTURE 4HE VERTICAL AMPLITUDE DISTRIBUTION APPROXIMATES TO A COSINE BECAUSE OF THE HORIZONTALLY POLARIZED FIELD 6ERTICAL BEAMWIDTHS ARE TYPICALLY ABOUT WIDE AT THE D" POINTS .OT UNNATURALLY COST FOR A GIVEN PERFORMANCE IS THE PRIME DRIVER IN THE SYSTEM DESIGNERS CHOICE OF ANTENNA 7HILE THE CONVENTIONAL SLOTTED LINEAR ARRAY IS WIDELY USED THERE ARE EXAMPLES WHERE DIFFERENT COST TRADEOFFS HAVE BEEN MADE &OR INSTANCE THE USE OF A DIELECTRIC BLOCK MOUNTED DIRECTLY IN FRONT OF THE SLOTTED WAVEGUIDE ARRAY IN PLACE OF THE FLARED SECTION HAS BEEN USED AS AN ALTERNATIVE 4HE LEAKING ENERGY FROM THE TOP AND BOTTOM FACES OF THE DIELECTRIC BLOCK ADDS WITH ENERGY EMERGING FROM ITS FRONT FACE GIVING FORWARD GAIN )T IS THE DEPTH DIMENSION OF THE DIELECTRIC BLOCK THAT DETERMINES THE GAIN SOMEWHAT ANALOGOUS TO THE LENGTH OF A 9AGI ANTENNA 4HIS EFFECT REDUCES THE HEIGHT OF THE ANTENNA COMPARED TO A CONVENTIONAL DESIGN BY ABOUT A FACTOR OF THREE TYPICALLY FROM ABOUT MM TO MM AT '(Z 4HIS MEANS THAT THERE IS CONSIDERABLY LESS WIND LOADING 4HE DIELECTRIC CONSTANT OF THE BLOCK CAN BE QUITE LOW WHICH WITH THE REDUCED WIND LOADING RESULTS IN A VERY LIGHTWEIGHT STRUCTURE 4HIS SAVES COSTS IN THE ANTENNA TURNING GEAR AND MAKES THE INSTALLATION EASIER !N EXAMPLE OF THIS TYPE OF ANTENNA PRODUCED BY +ELVIN (UGHES IS ILLUSTRATED IN &IGURE 3MALL CRAFT RADARS HAVE USED PRINTED ARRAYS FOR SOME YEARS AS WELL AS SLOTTED WAVEGUIDE ARRAYS 3MALL HORN FED PARABOLIC REFLECTOR SYSTEMS HAVE ALSO BEEN USED !NTENNAS FOR SMALL CRAFT ARE NORMALLY HOUSED WITHIN A RADOME WHICH PROTECTS THE ANTENNA AND UP MAST ELECTRONICS OF THE RADAR ENVIRONMENTALLY AND PREVENTS THE ANTENNA FROM SNAGGING THE RIGGING )N PARTICULAR IT ASSURES THAT THERE IS NO DANGER TO
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&)'52% ,OW PROFILE METER 3 BAND SHIPBORNE RADAR ANTENNA #OURTESY OF +ELVIN (UGHES ,TD
USERS FROM ROTATING MECHANISMS SINCE THE RADAR HEAD CAN BE MOUNTED IN AREAS OPEN TO HUMAN ACCESS !NTENNAS USING PRINTED ARRAYS USE INTEGRAL PRINTED POWER DIVIDERS 4HE ARRAYS ARE USUALLY TWO DIMENSIONAL DISPENSING WITH THE NEED FOR A FLARED SEC TION AND NORMALLY CONSIST OF RADIATING PATCHES RATHER THAN PRINTED DIPOLES (ORIZONTAL APERTURES OF AND MM ARE COMMON 0RINTED TECHNOLOGY IS NOT GENERALLY USED FOR SHIPBORNE ANTENNAS SLOTTED WAVEGUIDE ARRAYS REMAIN THE COST EFFECTIVE SOLUTION FOR LARGER ARRAYS PARTICULARLY AS THE HIGHER POWER CREATES ADDITIONAL COMPLICATIONS FOR PRINTED POWER DIVIDERS 0OOR ANTENNA SITING IS A COMMON CAUSE OF RADAR PERFORMANCE DEGRADATION ON SHIPS AS WELL AS ON SMALLER CRAFT 0ARTICULARLY ON SHIPS IT IS SURPRISING THAT INSTALLATIONS ARE STILL BEING IMPLEMENTED THAT CREATE SIGNIFICANT BLOCKAGE TO THE RADAR "LIND ARCS ARE COMMON FROM FUNNELS AND OTHER SUPERSTRUCTURE AND THERE CAN BE SIGNIFICANT SIDELOBE DEGRADATION DUE TO SMALLER STRUCTURES SUCH AS 6(& ANTENNAS CAUSING BLOCKAGE CLOSE TO THE RADAR ANTENNA APERTURE 2& (EAD 4HE 2& HEAD NORMALLY COMPRISES THE TRANSMITTER AND THE RECEIVER DOWN TO )& OR DIGITAL BASEBAND AS WELL AS THE ANTENNA AND TURNING GEAR )TS DESIGN FOR BOTH MAGNETRON BASED 3/,!3 AND NON 3/,!3 RADARS FOLLOWS CONVENTIONAL PRIN CIPLES 4HE MAGNETRON IS CONNECTED TO THE ANTENNA VIA A DUPLEXER AND A ROTATING JOINT 4HE MAGNETRON HAS A TYPICAL OPERATIONAL LIFE OF ABOUT HOURS AND IS BY FAR THE LOWEST LIFED COMPONENT IN THE WHOLE SYSTEM 4HE DUPLEXER IS NOWADAYS A THREE OR FOUR PORT FERRITE CIRCULATOR 5SE OF A FOUR PORT DEVICE IS PREFERRED AS IT PRESENTS A BET TER MATCHED LOAD TO THE MAGNETRON AND THEREFORE GIVES A CLEANER 2& SPECTRUM 4HE LOW NOISE FRONT END ,.&% SUBSYSTEM IS CONNECTED TO THE CIRCULATOR VIA A 0). DIODE LIMITER WHICH PROTECTS THE ,.&% DURING PULSE TRANSMISSION 4HE MODULATOR TO THE MAGNETRON IS TYPICALLY A PULSE FORMING NETWORK 0&. BASI CALLY COMPRISED OF CAPACITORS AND INDUCTORS /PERATOR CONTROL OF THE PULSE LENGTH EFFEC TIVELY SWITCHES IN DIFFERENT CHOICES OF REACTIVE COMPONENTS 4HE DISCHARGE OF THE 0&. IS CONTROLLED BY A HIGH VOLTAGE SWITCH WHICH IS OFTEN A SILICON CONTROLLED RECTIFIER THYRISTORS AND &%4S ARE ALSO USED &%4 MODULATORS ARE SOMETIMES DRIVEN DIRECTLY BY A PULSE INPUT RATHER THAN A 0&. &INALLY A PULSE TRANSFORMER MATCHES THE 0&. TO THE IMPEDANCE SEEN AT THE MAGNETRON CATHODE ! PULSE OF AROUND K6 IS REQUIRED TO FIRE THE MAGNETRON )N ORDER TO GET GOOD PERFORMANCE OVER A WIDE RANGE OF PULSE LENGTHS DESIGNS UTILIZE A GREAT DEAL OF EMPIRICALLY DERIVED KNOWLEDGE AND ACTUAL CIRCUITS CAN BE SURPRISINGLY COMPLEX ! NS PULSE HARDLY ACHIEVES ANY PERIOD OF STABILITYRISE TIMES ARE NORMALLY RESTRICTED TO ABOUT NS IN ORDER TO LIMIT OUT OF BAND INTERFERENCE
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AND FALL TIMES ARE USUALLY LONGER 4HE EXTRA HIGH VOLTAGES INVOLVED CAN LEAD TO POOR RELIABILITY IF THE DESIGN DOES NOT ADEQUATELY ADDRESS THE ASSOCIATED PROBLEMS #AREFUL PHYSICAL LAYOUT IS ESSENTIAL AND CONSIDERATION MUST BE GIVEN TO THE EFFECTS OF OPERATING IN A POTENTIALLY DAMP ENVIRONMENT 0ULSE TIMING CAN BE PURPOSELY JITTERED ON A PULSE TO PULSE BASIS 0ULSE TO PULSE CORRELATION IN THE RADAR PROCESSOR THEN VERY EFFECTIVELY BLOCKS INTERFERENCE FROM OTHER RADARS ALBEIT WITH A SMALL BUT GENERALLY ACCEPTABLE DEGRADATION IN DETECTION PERFORMANCE !FTER THE LIMITER THE ,.&% IS PRECEDED BY A BANDPASS FILTER TO REDUCE THE EFFECTS OF OUT OF BAND INTERFERING SIGNALS 4HE ,.&% CONSISTS OF AN 2& AMPLIFIER TYPICALLY GIVING ABOUT D" GAIN AND A BALANCED MIXER LOCAL OSCILLATOR AND )& HEAD AMPLIFIER 4HESE ARE NORMALLY SUPPLIED TO THE RADAR MANUFACTURER BY SPECIALIST COMPANIES AS A COMPLETE SUBUNIT 4HE OVERALL SYSTEM NOISE FIGURE IS TYPICALLY TO D" BUT LOWER FIGURES ARE ACHIEVABLE 4HE FREQUENCY OF THE LOCAL OSCILLATOR IS GENERALLY DRIVEN BY A CONTROL SIGNAL DERIVED FROM WITHIN THE )& AMPLIFIER )T INCLUDES FACILITIES FOR MANUAL FREQUENCY CONTROL BY THE OPERATOR 4HE LATTER CAN BE USEFUL FOR INSTANCE WHEN LOOK ING FOR 3!24S IN HEAVY SEA CLUTTER AS IT ALLOWS RETURNS FROM OWN TRANSMISSIONS TO BE DESENSITIZED 4HE LOCAL OSCILLATOR USES A 'UNN DIODE OR AN &%4 GIVING A TYPICAL INTER MEDIATE FREQUENCY OF -(Z $ETECTION AND 0ROCESSING !FTER THE ,.&% A LOGARITHMIC AMPLIFIER REDUCES THE DYNAMIC RANGE OF THE RECEIVED SIGNAL TO PREVENT LIMITING ! DYNAMIC RANGE OF AROUND D" IS TYPICALLY ACHIEVED IN PERHAPS AN EIGHT STAGE AMPLIFIER &ILTERING CONSIS TENT WITH THE TRANSMITTED PULSE LENGTH IS APPLIED WITHIN THE )& AMPLIFIER 4HE OUTPUT FROM THE LOG AMPLIFIER ENTERS A DIODE BASED ENVELOPE DETECTOR CONVERTING THE SIGNAL TO BASEBAND FOR SUBSEQUENT THRESHOLD PROCESSING 3ETTING THE THRESHOLD HAS BECOME INTIMATELY CONNECTED WITH THE SENSITIVITY TIME CONTROL 34# OF THE RADAR 4HE FUN DAMENTAL USE OF 34# IS TO TAKE OUT THE DISTANCE RELATED DYNAMIC RANGE OF RECEIVED SIGNALS !T CLOSE RANGE 34# CLASSICALLY FOLLOWS AN INVERSE FOURTH POWER LAW MERGING TO AN INVERSE CUBIC LAW IN THE REGION WHERE SEA CLUTTER DOMINATES IN ACCORDANCE WITH BASIC THEORY "ECAUSE TRANSITION RANGE IS A FUNCTION OF ANTENNA HEIGHT A SETTING FOR THIS MAY BE NEEDED WHEN THE SYSTEM IS ORIGINALLY INSTALLED 4HE OPERATORS MANUAL SEA CLUTTER CONTROL IS USED TO ADJUST THE TRANSITION RANGE .OWADAYS THE FORM OF THE 34# CURVE AND THE EFFECTS OF THE MANUAL CONTROL ARE BASED ON THE PRACTICAL EXPERIENCE OF INDIVIDUAL MANUFACTURERS WHICH CONTRIBUTES GREATLY TO THE ACTUAL EFFECTIVENESS OF A PARTICULAR RADAR IN SEA CLUTTER %VEN UNDER MANUAL CONTROL THE DETAILED SHAPE OF THE 34# CURVE MAY HAVE A COMPLEX ADAPTIVE ELEMENT TO IT IN ORDER TO OPTIMIZE THRESHOLDS OVER A BROADER RANGE 5NDER AUTOMATIC SETTINGS THRESHOLDING BECOMES INCREASINGLY SOPHISTICATED BUT OFTEN STILL ALLOWS SOME MANUAL OPTIMIZATION 4HE CURVE MAY ADAPT TO INTERNAL CALCULA TIONS MADE ON RETURNS FROM THE LAST PULSE OR FROM A SUCCESSION OF PULSES )T MAY ALSO INCLUDE MORE COMPLEX CLUTTER MAPPING PROCESSES !LL OF THIS IS ATTEMPTING TO CREATE A CONSTANT FALSE ALARM RATE ACROSS THE RADAR DISPLAY 3INCE THE RADAR IS SITED ON A MOV ING PLATFORM SUBJECT TO COMPLEX DYNAMICS DIFFICULTIES ARISE WITH CLUTTER MAPPING (OWEVER MODERN PROCESSORS PERMIT AFFORDABLE THRESHOLDING ALGORITHMS OF CONSIDER ABLE COMPLEXITY -ANUFACTURERS KEEP THEIR OWN PROCESSES HIGHLY CONFIDENTIAL BECAUSE OF THE EFFORT THAT HAS GONE INTO THEIR EMPIRICAL OPTIMIZATION 4HEORETICAL CLUTTER MODELS HAVE BEEN GENERALLY FOUND UNSUITABLE TO BE USED FOR OPTIMIZATION %VEN OPTIMIZING FOR SEA CONDITIONS FOUND IN ONE PARTICULAR AREA CAN CREATE SUBOPTIMAL SOLUTIONS IN OTHER AREAS AND THEREFORE DATA FROM A NUMBER OF REGIONS NEED TO BE USED TO DESIGN A GLOB ALLY EFFECTIVE PRODUCT
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34# AND THRESHOLDING IS A PROCESS THAT IS CONTROLLED IN THE DIGITAL DOMAIN BUT OFTEN APPLIES ANALOG GAIN PROCESSES AT 2& AND )& AT BOTH PRE AND POST LOG AMPLIFICATION AS WELL AS PROCESSES IN THE DIGITAL DOMAIN )NTIMATELY CONNECTED WITH THRESHOLDING STRATE GIES ARE SIGNAL PROCESSING SUCH AS &4# PULSE INTEGRATION AND CORRELATION PROCESSES BOTH PULSE TO PULSE AND SCAN TO SCAN -ODERN DIGITAL TECHNOLOGY WITH ITS PROCESSING SPEED AVAILABLE WORD LENGTH AND LARGE MEMORY CAPABILITY ALLOWS THE RADAR DESIGNER TO HAVE GREAT FLEXIBILITY IN THE STRATEGY APPLIED AND WHAT ARE ENTIRELY SEPARATE PRO CESSES IN THE ANALOG WORLD INCREASINGLY BECOME AN INTEGRATED DIGITAL PROCESS 3IMPLE THRESHOLDING IDEAS ARE BEING REPLACED BY COMPLEX LOGICAL PROCESSES MAKING A DETAILED EVALUATION OF WHETHER A POTENTIAL TARGET IS PRESENT OR NOT EVEN POTENTIALLY MERGING INTO PLOT EXTRACTION AND TRACKING PROCESSES -ORE COMPLEX PROCESSING CAN ALSO YIELD ADDITIONAL INFORMATION THAT IS USEFUL TO MARINE OPERATORS &OR INSTANCE BY APPLYING SPECTRUM ANALYSIS TECHNIQUES IT IS POS SIBLE TO EXTRACT ACCURATE SEA STATE INFORMATION INCLUDING SIGNIFICANT WAVE HEIGHT AND PERIOD DIRECTION AND SPEED 4HE -IROS !3 7AVEX4- SYSTEM DETERMINES DIRECTIONAL WAVE SPECTRA SCALED IN M(Z AND PARAMETERS SUCH AS SIGNIFICANT WAVE HEIGHT AND AVERAGE WAVE PERIOD !N &&4 IS PERFORMED ON DATA COLLECTED ON A SCAN BY SCAN BASIS SCANS OF DATA ARE TYPICALLY USED IN THE ANALYSIS 4HE RESULTANT INFORMATION CAN BE HIGHLY USEFUL FOR LARGE HIGH SPEED CRAFT PERHAPS TRAVELING AT UP TO KNOTS OR MORE )T IS ALSO POTENTIALLY USEFUL FOR VULNERABLE VESSELS SUCH AS CHEMICAL CARRIERS TO ENSURE THAT APPROPRIATE ACTION IN HEAVY WEATHER CAN BE TAKEN PARTICULARLY AT NIGHT OR IN POOR VISIBILITY /CEAN OIL RIG OPERATIONS CAN ALSO BENEFIT FROM SUCH SYSTEMS )NFORMATION CAN BE DISPLAYED TO THE USER IN THE FORM OF DIGITAL READOUTS OF THE PRIMARY PARAMETERS AS WELL AS GRAPHICALLY DISPLAYED DATA )NSTALLED SYSTEMS NORMALLY EXTRACT THE RAW DATA FROM THE EXISTING '(Z RADAR AND PERFORM WAVE PROCESSING AND DISPLAY FUNCTIONS ON A SEPARATE PROCESSORDISPLAY SYSTEM 3PECTRUM ANALYSIS OF THIS TYPE CAN ALSO DETECT OIL SLICKS BECAUSE THEY REDUCE THE AMPLITUDE OF SEA SURFACE CAPILLARY WAVES 3UCH SYS TEMS CAN BE VALUABLE ON VESSELS ASSISTING WITH CLEAN UP OPERATIONS AND ALSO FOR EARLY DETECTION OF SPILLS FROM OIL RIG OPERATIONS )T HAS BEEN PROPOSED THAT ADDITIONAL PROCESSING OF THE CROSS POLAR CONTENT OF THE RECEIVED RADAR SIGNAL MAY BE OF BENEFIT TO MARINE OPERATIONS WHERE SEA ICE IS A HAZARD $UE TO STRUCTURAL CHANGES THAT OCCUR IN OLDER ICE THAT AFFECT THE REFLECTION OF RADAR ENERGY IT IS POSSIBLE TO DIFFERENTIATE BETWEEN POTENTIALLY DANGEROUS OLD ICE INCLUDING GLACIAL ICE ICEBERGS AND SINGLE SEASON SEA ICE WHICH IS NORMALLY LESS DANGEROUS TO NAVIGATION 4HIS IS BECAUSE THE CROSS POLAR COMPONENT OF THE REFLECTION IS SIGNIFICANTLY HIGHER FOR OLD ICE COMPARED TO NEW ICE 4HE PROBLEM IS HOW TO AFFORDABLY DETERMINE THE CROSS POLAR COMPONENT )N PRACTICE IT HAS BEEN FOUND THAT EXCELLENT ICE DETECTION CAN BE MADE BY OPTIMIZED PROCESSING OF CONVENTIONAL MARINE RADAR SIGNALS "ECAUSE OF THE SLOW MOVING NATURE OF THE TARGETS OF INTEREST AVERAGING THE RADAR IMAGE OVER MANY ANTENNA SCANS USING AN OPTIMIZED INFINITE IMPULSE RESPONSE ))2 FILTER CAN GIVE A VERY DETAILED IMAGE THAT ALLOWS THE USER TO DIFFERENTIATE BETWEEN ICE AND WATER AREAS )N PARTICULAR SMALL ICE FEATURES SUCH AS BERGY BITS ICEBERGS WITH DIMENSIONS ABOVE THE WATERLINE OF LESS THAN METERS IN BREADTH AND GREATER THAN METER IN HEIGHT AND GROWLERS LESS THAN METERS IN BREADTH AND LESS THAN METER SHOWING ABOVE THE WATER LINE ARE READILY DETECTED BY SUCH SYSTEMS )NTEGRATION OVER SECONDS HAS BEEN FOUND TO BE SUITABLE WITH THE ANTENNA ROTATING AT RPM 4HE INCREASED CAPABILITY OF ICE TARGET DETECTION IN SEA CLUTTER WITH HIGHER ANTENNA ROTATION RATES HAS ALSO BEEN DEMONSTRATED $RAMATIC IMAGES OF ICE HAZARDS CAN BE PRODUCED BY SUCH RADARS SUCH AS THAT ILLUSTRATED IN &IGURE
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&)'52% )CE FEATURE DETECTION USING ))2 FILTERING ON 2UTTER 3IGMA RADAR PROCESSOR #OURTESY OF 4RANSPORT #ANADA
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3OLID STATE #-2 3EVERAL FACTORS HAVE COME TOGETHER TO PROMOTE THE INTRODUC TION OF CIVIL MARINE RADARS WITH SOLID STATE TRANSMITTERS 4HE MOST IMPORTANT OF THESE IS THAT AFFORDABLE MAGNETRON BASED RADARS DO NOT MEET USER DEMANDS WHEN OPERATING IN HEAVY SEA AND PRECIPITATION CLUTTER 3MALL CRAFT AND BUOYS BECOME INVISIBLE ON THE DISPLAY CREATING DANGER TO LIFE )-/ RECOGNIZED THIS PROBLEM AND IN ORDER NOT TO CON STRAIN OPPORTUNITIES FOR INNOVATIVE RADAR DESIGN REMOVED THE REQUIREMENT THAT '(Z RADARS BE COMPATIBLE WITH EXISTING RACONS 'ALLIUM .ITRIDE AND OTHER MICROWAVE POWER SEMICONDUCTORS DEVELOPED PRIMAR ILY FOR BROADBAND COMMUNICATIONS LINKS HAVE ENABLED #-2 MANUFACTURERS TO USE THESE IN THE RADAR TRANSMITTER TO REPLACE MAGNETRON BASED DESIGNS 0ULSE COMPRES SION TECHNIQUES ARE USED TO REDUCE THE REQUIRED PEAK POWER %VEN SINGLE 'ALLIUM .ITRIDE DEVICES CAN GENERATE HUNDREDS OF WATTS OF PEAK POWER AT MEAN POWERS EASILY SUFFICIENT FOR #-2 APPLICATIONS !LSO ADVANCES IN DIGITALLY CONTROLLED WAVEFORM GENERATORS HAVE GIVEN DESIGNERS THE ABILITY TO CREATE PULSE COMPRESSED WAVEFORMS WITH HIGH PRECISION AND AT LOW COST 4HESE WAVEFORMS ENABLE COHERENT PROCESSING OF THE RECEIVED SIGNAL GIVING ADDITIONAL DOPPLER INFORMATION THAT CAN BE USED TO HELP SEPARATE TARGETS FROM CLUTTER 4HE USE OF FREQUENCY DIVERSITY TECHNIQUES TO GIVE ADDED TARGET DETECTION POSSIBILITIES BECOMES POTENTIALLY AFFORDABLE BECAUSE OF THE FLEXIBILITY OF THE SIGNAL GENERATION TECHNOLOGY #OST HAS PRECLUDED THE USE OF DUAL MAGNETRON TRANSMITTERS FOR THIS PURPOSE $EMANDS FROM OTHER SERVICES FOR MORE BANDWIDTH PARTICULARLY FROM MOBILE COM MUNICATIONS OPERATORS CONTINUE TO PUT PRESSURE ON THE )45 DETERMINED MARINE RADAR SPECTRUM LIMITS SEE FOR EXAMPLE 7ILLIAMS 3INCE THE PEAK TRANSMITTED POWER FROM SOLID STATE #-2S IS VERY LOW COMPARED TO MAGNETRON BASED RADARS FOR EXAMPLE 7 COMPARED TO K7 THE SPECTRUM INTERFERENCE LEVELS ARE MUCH REDUCED AND THEREFORE EXTENDED USE OF THIS TECHNOLOGY COULD RESULT IN BETTER USE OF THE 2& SPECTRUM !LSO THE HIGHLY CONTROLLED WAVEFORMS ARE EXPECTED TO CREATE LESS SPECTRAL NOISE THAN TYPICAL MAGNETRON BASED #-2 TRANSMITTERS !N EXAMPLE OF A SOLID STATE COHERENT RADAR IS THE +ELVIN (UGHES 3HARP%YE4-THE FIRST INTRODUCTION OF SUCH AN )-/ COMPLIANT SYSTEM TO THE #-2 MARKET )T HAS A PEAK OUTPUT POWER OF 7 AND A DUTY CYCLE OF &IGURE SHOWS A PHOTOGRAPH OF THE TRANSMITTER ELECTRONICS )N ORDER TO OBTAIN THE REQUIRED SHORT RANGE PERFORMANCE IT TRANSMITS A FRAME OF PULSES WITH DIFFERING LENGTHS %ACH PULSE WITHIN THE FRAME IS OPTIMIZED TO COVER A SPECIFIED RANGE BRACKET /VERALL THE PULSE SEQUENCE COMPLETELY COVERS THE INSTRUMENTED RANGE AND ENSURES THAT THE )-/ SPECIFIED MINIMUM RANGE REQUIREMENT IS MET )N THE RECEIVER FRAMES ARE GROUPED INTO BLOCKS CALLED BURSTS 4HE DURATION OF A BURST IS APPROXIMATELY EQUAL TO THE TIME TAKEN FOR THE D" POINTS OF THE ANTENNA AZIMUTH BEAM TO SWEEP PAST A POINT TARGET CONSEQUENTLY THE NUMBER OF PULSES IN A BURST IS DIRECTLY RELATED TO THE INSTRUMENTED RANGE AND THE ANTENNA ROTATION RATE 4HE ECHOES RECEIVED DURING A BURST ARE PROCESSED BY A FILTER BANK TO EXTRACT THE RADIAL VELOCITIES OF TARGETS AND CLUTTER 7ITHIN THE DIGITAL SIGNAL PROCESSOR DETECTION THRESHOLDS FOR EACH OF THE FILTERS WITHIN THE BANK ARE CALCULATED ADAPTIVELY AIMING AT PROVIDING OPTIMUM CONTROL OF FALSE ALARMS WHILE MAXIMIZING CLUTTER SUPPRESSION AND TARGET DETECTION -ANUAL CONTROL OF THE THRESHOLDS IS ALSO PROVIDED TO BE COMPLIANT WITH )-/ REQUIREMENTS -ODERN FULLY SOLID STATE RADARS NEED LITTLE ANALOG CIRCUITRY WITHIN THEIR DESIGNS THEY OPERATE ON LOW VOLTAGES AND HAVE NO TIME LIFED COMPONENTS SUCH AS MAGNE TRONS 4HIS POTENTIALLY MAKES THEM EXTREMELY STABLE AND RELIABLE WITH A RESULTANT LOW COST OF OWNERSHIP THEREFORE MEETING THE INCREASING DEMANDS OF SHIP OPERATORS
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&)'52% +ELVIN (UGHES 3HARP%YE4- #-2 3 BAND SOLID STATE TRANSMITTER #OURTESY OF +ELVIN (UGHES ,TD
)N PREVIOUS YEARS SHIPS WERE REQUIRED TO HAVE A RADIO OFFICER WHO COULD CARRY OUT RADAR REPAIRS AT SEA 4HIS IS NO LONGER THE CASE 2ELIABILITY IS A PRIME CONCERN AS A NON OPERATING RADAR CAN FORCE THE DELAY OF THE SHIP IN PORT AT GREAT COST TO THE OPERATOR
ÓÓ°xÊ /, /Ê/, 4HE TARGET TRACKING FUNCTION OF A SHIPBORNE NAVIGATION RADAR HAS HISTORICALLY BEEN CALLED AN !UTOMATIC 2ADAR 0LOTTING !ID !20! 4HIS TERM IS BECOMING OBSOLETE )-/ NOW DEFINES THIS PROCESS AS 4ARGET 4RACKING 44 WHICH INCLUDES TARGET DATA OBTAINED FROM !)3 4HE BASIC REQUIREMENT CALLS FOR A MINIMUM RADAR TRACKING CAPAC ITY OF TARGETS ON SHIPS LESS THAN GT TARGETS ON SHIPS BETWEEN AND GT AND TARGETS ON SHIPS OVER GT )N ADDITION SHIPS OVER GT MUST HAVE AN AUTOMATIC TARGET ACQUISITION CAPABILITY !CTUAL SYSTEMS COMMONLY EXCEED THESE MINIMUM REQUIREMENTS 4ARGETS WITH A MAXIMUM RELATIVE SPEED OF KT MUST BE TRACKABLE THIS REQUIREMENT IS INCREASED TO KT FOR RADARS ON VESSELS CAPABLE OF MORE THAN KT /N THE BRIDGE THE NAVIGATORS REQUIREMENTS TO AID COLLI SION AVOIDANCE INCLUDE THE NEED TO KNOW A TARGETS CLOSEST POINT OF APPROACH #0! AND TIME TO CLOSEST POINT OF APPROACH 4#0! BOTH OF WHICH MUST BE AVAILABLE FOR ALL TRACKED TARGETS 4HE REQUIRED TRACKED TARGET ACCURACY AT LEVELS IS GIVEN IN 4ABLE
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4!",% 2EQUIREMENTS FOR RADAR TRACKED TARGET ACCURACY LEVELS #OURTESY OF )-/
4IME OF 3TEADY 3TATE MINUTES
2ELATIVE #OURSE DEGREES
MIN TRENDo
MIN MOTIONp
2ELATIVE 3PEED KN OR WHICHEVER IS GREATER OR WHICHEVER IS GREATER
#0! .-
4#0! MINUTES
4RUE #OURSE DEGREES
4RUE 3PEED KN
OR WHICHEVER IS GREATER
o 4REND IS AN EARLY INDICATION AFTER MINUTE OF THE TARGETS SPEED AND DIRECTION p -OTION IS THE ESTABLISHED ASSESSMENT AFTER MINUTES OF THE TARGETS SPEED AND DIRECTION
4HE TRACKING PROBLEM IS COMPLICATED BY THE FACT THAT BASIC RADAR MEASUREMENTS ARE MADE RELATIVE TO THE SHIPS MOTION BUT THE DISPLAY MAY BE SET TO RELATIVE OR TRUE MOTION )N ADDITION TRUE MOTION CAN BE GROUND OR SEA STABILIZED 4ARGET VECTORS AND ASSOCIATED DATA BOXES CAN BE SHOWN IN TRUE OR RELATIVE MOTION WHATEVER THE FRAME REFERENCE OF THE RADAR DISPLAY ! SHIPS ORIENTATION TO NORTH IS GIVEN BY A GYROCOM PASS OR hTRANSMITTINGv MAGNETIC COMPASSA COMPASS WITH A DIGITAL INTERFACE ! LOG GIVES SPEED THROUGH THE WATER 347 4HIS CAN BE EITHER A CONVENTIONAL ROTATING TRANSDUCER DRIVEN BY THE MOVEMENT THROUGH WATER OR ELSE AN ACOUSTIC TRANSDUCER MEASURING THE DOPPLER OF THE REFLECTED SIGNAL 4HE LATTER CAN BE SET TO ASSESS SPEED EITHER RELATIVE TO THE SURROUNDING WATER 347 OR RELATIVE TO THE SEABED IE SPEED OVER GROUND 3/' -ANDATORY CARRIAGE OF A DUAL AXIS LOG WHICH MEASURES SPEED IN THE FORWARD AND TRANSVERSE DIRECTIONS IS REQUIRED ON SHIPS ABOVE GT 4HIS IS TYPICALLY A DOPPLER LOG /N SMALLER SHIPS '.33 IS USED TO PROVIDE 3/' AND IS OFTEN THE USER PREFERRED GROUND STABILIZATION SOURCE FOR RADAR EVEN FOR A SHIP FITTED WITH A DOPPLER LOG $OPPLER LOGS DO NOT ALWAYS GIVE GOOD SPEED READINGS ON SOME TYPES OF SEABED FOR EXAMPLE SOFT MUD &ACILITIES MUST ALSO BE PROVIDED TO ALLOW THE USE OF STATIONARY TRACKED TARGETS SUCH AS RADAR CONSPICUOUS NAVIGATION MARKS TO PROVIDE THE GROUND REFERENCE !CCORDING TO THE DESIGN THE BASIC TRACKING FUNCTION CAN BE CARRIED OUT IN SHIP OR GROUNDSEA REFERENCED FRAMES USING CONVENTIONAL ALGORITHMS 4HE TRACKING PROCESS CAN BE INITIATED MANUALLY OR AUTOMATICALLY !UTOMATIC INITIATION IS BY A CONVENTIONAL PLOT EXTRACTION PROCESS CONFINED WITHIN A USER DEFINED AREA WHICH AT ITS SIMPLEST COULD BE A CHOSEN RANGE ENCIRCLING THE VESSEL 4HE DEFINED AREA MAY ALSO HAVE USER DEFINED EXCLUSION ZONES !LGORITHMS FOR PREVENTING PLOTS FROM BEING FORMED ON TYPI CALLY ENCOUNTERED WAVE FEATURES PERHAPS LASTING A FEW SCANS SUCH AS A TRAVELING WAVE CREST NEED TO BE EMPLOYED -ANUAL SELECTION IS EFFECTIVELY A PLOT EXTRACTION PROCESS OPERATING OVER A SMALL AREA SURROUNDING THE CURSOR !N ALPHA BETA TRACKER OR OTHER FILTERING TECHNIQUE IS USED TO SMOOTH MEASUREMENT NOISE 4HE CHARACTERISTICS OF THIS FILTER NEED TO ADAPT TO THE QUALITY OF THE RECEIVED TARGET SIGNAL )F TRACKING IS CARRIED OUT IN GROUND REFERENCED COORDINATES THE PROCESS AUTOMATICALLY TAKES INTO ACCOUNT OWN SHIP MOVEMENTS )N RELATIVE MOTION BASED TRACKING SYSTEMS THE FILTER NEEDS TO BE AIDED WITH OWN SHIP DATA $EPENDING ON THE USER SET MODE THE DATA HAS TO BE CONVERTED TO THE CORRECT REFER ENCE FRAME AND DISPLAYED APPROPRIATELY #0! AND 4#0! ARE CONTINUALLY CALCULATED FOR ALL TRACKED TARGETS SUCH THAT IF LIMITS PRESET BY THE USER ARE BREACHED AN ALARM
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CAN BE INITIATED !LL TRACKED TARGETS ARE DISPLAYED ON THE SCREEN WITH THEIR ASSOCIATED VELOCITY VECTORS 4RACKED TARGETS MAY BE SELECTED BY THE USER SUCH THAT ALL INFORMATION CONCERNING THAT TARGET INCLUDING #0! AND 4#0! IS DISPLAYED ON THE DATA PANEL OF THE RADAR SCREEN ,OST TARGETS CREATE A VISUAL AND AN AUDIBLE ALARM .ORMAL TERMINATION OF TRACKING OCCURS WHEN A TARGET LEAVES THE ACQUISITION ZONE OR WHEN MANUALLY CANCELLED ! GUARD ZONE MAY ALSO BE SET UP BY THE OPERATOR 4HIS MAY BE IDENTICAL TO THE ACQUISI TION ZONE BUT IS THERE TO PROVIDE AN ALARM IF ANY TRACKED TARGET PASSES INTO THE ZONE )N COMMON WITH OTHER RADAR TRACKERS STRATEGIES HAVE TO BE EVOLVED TO COPE WITH THE TARGET BEING POTENTIALLY INVISIBLE IN SOME SCANS )-/ REQUIRES THAT THE SPECIFIED PERFORMANCE IS MAINTAINED WHEN THE TARGET IS INVISIBLE IN UP TO OF SCANS !LSO FOR AN EFFECTIVE SYSTEM STRATEGIES HAVE TO BE EVOLVED TO REDUCE THE POSSIBILITIES OF TARGET IDENTITIES BEING SWAPPED WHICH CAN HAPPEN WHEN TARGETS MOVE CLOSE TOGETHER AND SUBSEQUENTLY DIVERGE )N PARTICULAR TRACKING ALGORITHMS HAVE TO ATTEMPT TO COPE WITH THE POTENTIALLY LARGE AND FAST CHANGE IN THE RADAR CENTROID AS A TARGET VESSEL TURNS )N THE WORST CASE THIS CAN AMOUNT TO ALMOST THE LENGTH OF THE VESSEL METERS OR SO FOR A LARGE SHIP )T IS AN ART TO GET A GOOD TRACKER OPTIMIZED FOR ALL SITUATIONS OVER A VARIETY OF VESSEL SPEEDS AND TO MAINTAIN AN APPROPRIATE INDICATION OF CHANGE IN HEADING WITHOUT EXCESS LATENCY /VER DAMPED SYSTEMS MAY GIVE AN APPARENTLY STABLE INDICATION OF THE TRACK OF A TARGET BUT CAN BE VERY INACCURATE WHEN A TARGET CHANGES HEADING &ROM THE POINT OF VIEW OF SAFETY OF NAVIGATION THE CHANGE IN HEADING IS OFTEN THE MORE IMPOR TANT PARAMETER 4ARGET TRACKERS FROM INDIVIDUAL MANUFACTURERS CAN HAVE QUITE DIFFERENT DESIGN AND OPTIMIZATION STRATEGIES AND CAN THEREFORE DIFFER IN PERFORMANCE 7ITHIN )%# THERE ARE DEFINED TEST SCENARIOS THAT ALL 3/,!3 APPROVED TRACKING SYS TEMS MUST MEET )-/ REQUIRES THAT THE TREND IN A TARGETS CHANGE OF DIRECTION IS SHOWN WITHIN ONE MINUTE AND THE PREDICTION OF THE TARGETS MOTION SHOULD BE AVAILABLE WITHIN THREE MINUTES AS GIVEN IN 4ABLE )N PRINCIPLE TARGET TRACKING COULD BE AIDED BY DATA FROM !)3 3ECTION (OWEVER !)3 DATA IS BEST LEFT OUT OF THE RADAR TRACKING PROCESS IN ORDER TO KEEP THEM ENTIRELY INDEPENDENT /NCE RADAR TRACKS HAVE BEEN FORMED THEY CAN THEN BE AUTO MATICALLY COMPARED TO !)3 DATA AND ASSOCIATED INTO A SINGLE TRACK IF DESIRED BY THE OPERATOR 4HIS GIVES COMPLETE INDEPENDENCE TO RADAR AND !)3 DERIVED DATA THEREFORE ENHANCING INTEGRITY CHECKING
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&ROM THE USERS POINT OF VIEW THE MOST VISIBLE AND IMPORTANT CHANGE IN MARINE RADAR FROM ITS EARLY DAYS HAS BEEN THE DEVELOPMENT OF PROCESSOR BASED DISPLAY TECHNOLOGY )N PARTICULAR MODERN WELL DESIGNED DISPLAYS ARE VIEWABLE OVER A WIDE VARIATION OF AMBIENT LIGHTING THEY MAKE EFFECTIVE USE OF COLOR AND GIVE EASY AND CLEAR ACCESS TO THE RADAR IMAGE AND ASSOCIATED DATA 4HE DAYS WHEN THE RADAR SCREEN WAS ONLY VIEWABLE IN DAYLIGHT ON DIM LONG PERSISTENCE MONOCHROME #24S THROUGH THE APERTURE OF A HOOD ARE LONG GONE -ORE RECENTLY HIGH BRIGHTNESS COLOR #24S ARE BEING REPLACED BY ,IQUID #RYSTAL $ISPLAY FLAT PANEL TECHNOLOGY WHICH IS HELPING TO MAKE THE DISPLAY MORE USER ACCESSIBLELARGE STAND ALONE RADAR CONSOLES ARE NO LONGER NECESSARY ALLOWING IMPROVEMENTS TO THE ERGONOMIC LAYOUT OF A SHIPS BRIDGE 5SER INPUT DEVICES VARY BY MANUFACTURER 3OME SOLUTIONS RELY ON LITTLE MORE THAN A TRACKER BALL AND THREE CONTROL BUTTONS /THERS HAVE A NUMBER OF DEDICATED SWITCHES AND ROTARY CONTROLS AS WELL AS A CURSOR CONTROL SUCH AS A TRACKER BALL OR JOYSTICK
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4OUCHSCREEN TECHNOLOGY IS SOMETIMES EMPLOYED )NCREASINGLY SYSTEMS ALSO INCLUDE A FULL ALPHANUMERIC KEYBOARD TO ALLOW EASY INPUT OF USER SUPPLIED DATA ESPECIALLY FOR CHART RADARS RADARS UTILIZING AN ELECTRONIC CHART BASED UNDERLAY AND RADARS INTEGRATED WITH !)3 2ADARS DESIGNED FOR SMALLER VESSELS TEND TO HAVE A COMPLETELY WATERPROOFED USER INTERFACE AS THEY ARE OFTEN USED IN MORE EXPOSED AREAS AND BY OPERATORS WITH WET SALTY HANDS )N GENERAL TRACKER BALLS ALTHOUGH THEY GIVE MORE PRECISE CONTROL AND ARE COMMON ON SHIPBORNE RADARS HAVE BEEN FOUND TO BE UNSATISFACTORY IN THE ENVIRONMEN TAL CONDITIONS FOUND ON SMALL CRAFT )NSTEAD MINI JOYSTICKS OR SIMPLE FOUR WAY ROCKER SWITCHES ARE TYPICALLY USED 4HE OPERATIONAL AREA OF A RADAR DISPLAY IS NORMALLY CIRCULAR ALTHOUGH THIS IS NO LONGER A MANDATORY REQUIREMENT )T ORIGINATES FROM THE HISTORICAL USE OF CONICAL DISPLAY TUBES BUT IS RETAINED BY MOST MANUFACTURERS AS IT GIVES ADDITIONAL SPACE OUTSIDE OF THE OPERATIONAL AREA FOR THE DISPLAY OF DATA AND MENUS SEE &IGURE 4HE MINIMUM OPERATIONAL DISPLAY AREA IS DEFINED AS A DIAMETER MM FOR SHIPS LESS THAN GT MM FOR SHIPS FROM TO GT AND MM FOR SHIPS ABOVE GT 4HE MINIMUM RECOMMENDED DISPLAY AREAS FOR SMALL CRAFT RADAR ARE GIVEN IN 4ABLE 4HE COLOR OF RADAR TARGETS AND BACKGROUND IS NOT MANDATED 4HE TARGET TRAILS THAT USED TO BE PROVIDED BY THE DESIGNED IN PERSISTENCE OF ORIGINAL RADAR MONOCHROME #24S HAVE TO BE PROVIDED ELECTRONICALLY 4HE TRAIL LENGTH IS REQUIRED TO BE USER SELECTABLE IN UNITS OF TIME 7HEN 4RUE -OTION IS SELECTED TRAILS CAN BE CHOSEN BY THE OPERATOR TO BE SHOWN IN EITHER TRUE OR SHIP RELATIVE REFERENCE FRAMES 4HE POSITION OF THE DISPLAY CURSOR IS ALWAYS AVAILABLE IN A DATA BOX IN TERMS OF RANGE AND BEARING FROM OWN SHIP ANDOR LATITUDE AND LONGITUDE COORDINATES )T IS THIS CURSOR THAT IS USED TO SELECT AND DE SELECT TARGETS WITHIN THE OPERATIONAL DISPLAY AREA AND TO DRAW USER DEFINED MAPS )T IS ALSO COMMONLY USED TO SET RANGE AND BEARING MARKERS ! CONSISTENT COMMON REFERENCE POINT ##20 TO WHICH ALL RADAR AND OTHER NAVIGA TIONAL DATA NEED TO BE REFERENCED IS IDENTIFIED ON THE SHIP 4HIS POINT CLEARLY BECOMES OF MAJOR IMPORTANCE WHEN CLOSE IN NAVIGATIONAL CALCULATIONS ARE BEING MADE (AVING A DEFINED ##20 ALSO ALLOWS A SCALED OWN SHIPS SYMBOL TO BE SHOWN ON THE RADAR DISPLAY WHEN APPROPRIATELY SHORT RANGE SCALES ARE SELECTED 4HE SYMBOLOGY OF THIS GRAPHIC TOGETHER WITH ALL OTHER SYMBOLS AND ABBREVIATIONS ON THE DISPLAY SHOULD MEET )-/ REQUIREMENTS 4HIS ENSURES THAT OPERATORS ARE FAMILIAR WITH THE RADAR PRESENTA TION WHEN WORKING ON DIFFERENT SHIPS 4HE RADAR DISPLAY SHOULD ALSO COMPLY WITH )-/S PERFORMANCE STANDARDS FOR NAVIGATIONAL DISPLAYS #ERTAIN RANGE SCALES MAXIMUM DISPLAYED RANGES ARE MANDATORY COVERING TO NM )N PRACTICE RANGE SCALES ABOVE NM ARE NORMALLY PROVIDED TYPICALLY UP TO NM 2ANGE RINGS MAY BE OPTIONALLY SWITCHED IN BY THE OPERATOR TO HELP ESTIMATE DIS TANCES 0RECISE RANGE MEASUREMENTS ARE MADE WITH THE USE OF A VARIABLE RANGE MARKER 62- !T LEAST TWO 62-S ARE NEEDED EACH WITH NUMERICAL READOUT IN THE DATA AREA OF THE DISPLAY !N ACCURACY OF IS REQUIRED BUT NOT BETTER THAN METERS ! BEARING SCALE AROUND THE PERIPHERY OF THE OPERATIONAL DISPLAY MUST BE VISIBLE 4HIS SCALE CAN HELP USERS DETERMINE THE SHIPS DIRECTION FROM VIEWING THE HEADING LINE (, WHICH HAS TO BE SHOWN ON THE DISPLAY ONLY TEMPORARY EXTINGUISHING OF THE (, IS PERMITTED )N ADDITION A SHIPS HEADING IS NORMALLY AVAILABLE WITHIN A DATA BOX OUTSIDE OF THE OPERATIONAL AREA 4HE RADAR ORIGIN CAN BE OFFSET FROM THE CENTER OF THE OPERATIONAL AREA BY THE USER THE BEARING SCALE ADJUSTS ACCORDINGLY 4WO OR MORE ELECTRONIC BEARING LINES %",S HAVE TO BE PROVIDED WITH CONTINUOUS NUMERICAL READOUT !LTHOUGH THESE ARE NORMALLY CENTERED ON THE SHIP AT THE ##20 THEY CAN ALSO BE OFFSET TO ANY POSITION 2EADOUTS RELATIVE TO OWN SHIPS HEADING OR TRUE NORTH CAN BE SET 4HE %", ORIGIN CAN ALSO BE SET SUCH THAT IT FOLLOWS OWN SHIP MOVEMENT OR IS
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&)'52% ! SHIPS RADAR DISPLAY #OURTESY OF .ORTHROP 'RUMMAN 3PERRY -ARINE "6
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GEOGRAPHICALLY FIXED 4HE DISTANCE AND BEARING OF ONE POINT TO ANOTHER ON THE DISPLAY CAN BE DETERMINED NORMALLY BY USE OF A SPECIFIC MENU ITEM AND APPROPRIATE CONTROL OF THE DISPLAY CURSOR 4HE ACTUAL IMPLEMENTATION OF %",S 62-S AND OFFSET MEASUREMENTS IS OFTEN EFFECTED BY A COMMON GRAPHICAL TOOL WHICH IS USED TO POSITION AND DRAG LINES AND CIRCLES ACROSS THE DISPLAY BY MEANS OF THE CURSOR -ANY MARINERS FIND THE USE OF SHIP REFERENCED PARALLEL INDEX 0) LINES TO BE HIGHLY USEFUL ! 0) IS A STRAIGHT LINE ON THE RADAR DISPLAY THAT IS USER SET TO A FIXED hCOMPASSv BEARING AND A FIXED PERPENDICULAR DISTANCE FROM THE RADAR ORIGIN !T LEAST FOUR OF THESE HAVE TO BE PROVIDED 4HESE CAN BE INDIVIDU ALLY SWITCHED INTO USE AND SET BY BEARING BEAM RANGE AND LENGTH 0)S ARE TYPICALLY USED TO ENSURE THAT A SHIP IS MAINTAINING A SAFE GROUND TRACK WITH REFERENCE TO A GROUND FIXED CONSPICUOUS RADAR TARGET #HART 2ADARS 4HE CAPABILITY AND RELATIVELY LOW COST OF MODERN PROCESSING AND DISPLAY SYSTEMS ALLOW GREAT FLEXIBILITY IN THE PRESENTATION OF INFORMATION TO USERS &OR MANY YEARS 3/,!3 COMPLIANT RADARS HAVE HAD THE CAPABILITY TO EMPLOY USER DEFINED MAPS AS AN UNDERLAY TO THE RADAR IMAGE -ANY MAPS CAN BE CREATED AND STORED FOR FUTURE USE !LTHOUGH THIS FACILITY IS STILL WIDELY USED THE USE OF VECTORIZED ELECTRONIC CHART DATA AS A RADAR UNDERLAY IS BECOMING MORE COMMON )N )-/ TERMS THEY ARE KNOWN AS CHART RADARS !LL APPROVED CHART RADARS HAVE TO BE CAPABLE OF DISPLAYING OFFICIALLY RECOGNIZED VECTOR DATA 4HIS DATA IS KNOWN AS THE %LECTRONIC .AVIGATIONAL #HART %.# )T IS ISSUED ON NATIONAL AUTHORITY AND COMPLIES WITH AN )NTERNATIONAL (YDROGRAPHIC /RGANIZATION )(/ STANDARD KNOWN AS 3 %.# DATA IS NORMALLY DISPLAYED ON APPROVED ELECTRONIC CHART SYSTEMS CALLED %LECTRONIC #HART $ISPLAY AND )NFORMATION 3YSTEMS %#$)3 AND MAY BE USED BY SHIPS IN PLACE OF PAPER CHARTS %.# DATA IS KEPT UP TO DATE BY HYDROGRAPHIC OFFICES THAT ISSUE UPDATE FILES ON A REGULAR BASIS !N )-/ APPROVED CHART RADAR MUST ALSO BE ABLE TO ACCEPT THESE UPDATES #HARTS AND THEIR UPDATES ARE LOADED BY #$ 2/- OR VIA A SATELLITE COMMUNICATIONS LINK /N SOME SYSTEMS THE CHART RADAR MAY HAVE ACCESS TO A SERVER ON THE SHIP THAT CENTRALIZES THE DISTRIBUTION OF SUCH DATA TO ALL EQUIPMENT NEEDING CHART INFORMATION 4HE USER HAS THE ABILITY TO CHOOSE THE %.# VECTOR LAYERS SHOWN ON THE DISPLAY OF A CHART RADAR &OR INSTANCE THIS MAY JUST INCLUDE THE COASTLINE NAVIGATION MARKS AND A SINGLE DEPTH CONTOUR CONSIDERED SAFE FOR THE DRAUGHT OF THE SHIP )F THE SHIP IS NAVIGATING ON %#$)3 RATHER THAN A PAPER CHART IT IS LIKELY THAT BOTH THE RADAR AND THE %#$)3 WILL BE COMMONLY SET TO #OURSE UP OR (EAD UP MODES .ORTH UP IS NO LONGER A PARTICULAR ADVANTAGE WHEN THE CHART IS NOT CONFINED TO SUCH A PRESENTATION SUCH AS PAPER CHARTS -OST %#$)3 EQUIPMENT CAN OPTIONALLY SHOW RADAR DERIVED DATA NORMALLY AS TRACKED TARGET VECTORS BUT SOMETIMES AS THE RADAR IMAGE ITSELF 4HIS DATA IS OBTAINED FROM THE RADAR PROCESSOR VIA A DIGITAL INTERFACE GIVING AN APPARENT CONVER GENCE OF %#$)3 AND RADAR DISPLAYS #ERTAINLY THIS IS TRUE AT A BASIC DESIGN LEVEL BUT )-/ IS KEEN TO DIFFERENTIATE BETWEEN THE TWO !N %#$)3 IS USED TO PLAN AND MONITOR PASSAGES A RADAR IS USED PRIMARILY AS A COLLISION AVOIDANCE TOOL BUT ALSO TO AID POSI TION FIXING PARTICULARLY BY IDENTIFYING GROUND FIXED RADAR CONSPICUOUS OBJECTS INCLUD ING COASTLINES 4HIS RESULTS IN MANY DIFFERENCES IN THE DETAILED REQUIREMENTS OF RADAR AND %#$)3 DISPLAYS (OWEVER FROM A DESIGN POINT OF VIEW THE DISPLAY PROCESSING REQUIREMENTS ARE VERY SIMILAR AND CAN THEREFORE USE VIRTUALLY IDENTICAL HARDWARE !S WELL AS SAVING DESIGN COSTS THIS ENABLES AN EASY TRANSITION TO MULTIFUNCTION DISPLAYS -&$S !N -&$ CAN BE INSTANTLY SWITCHED BETWEEN RADAR AND %#$)3 AS WELL AS OTHER FUNCTIONS ENABLING DYNAMIC RECONFIGURATION ON A SHIP TO OPTIMIZE DISPLAY USE FOR PARTICULAR CIRCUMSTANCES #LEAR INDICATION OF THE SELECTED MODE BECOMES NECESSARY FOR SAFETY AND STATUTORY REASONS
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-OST SMALL CRAFT RADARS NOW BEING SOLD INCLUDE THE OPTION OF A CHART UNDERLAY FACILITY AS A RELATIVELY LOW COST OPTION )N GENERAL THESE USE UNOFFICIAL VECTOR CHART DATA ISSUED BY SPECIALIST PRIVATE COMPANIES 4HIS DATA IS MORE AFFORDABLE THAN %.#S AND IS DIRECTED TO THIS PARTICULAR MARKET "ECAUSE OF COST AND SPACE CONSTRAINTS A SINGLE DISPLAY NOR MALLY ACTS AS BOTH RADAR AND ELECTRONIC CHART 4HESES DISPLAYS ARE ALL EFFECTIVELY -&$S AND CAN THEREFORE ALSO BE USED AS AN ELECTRONIC CHART SYSTEM WITHOUT RADAR INPUT
ÓÓ°ÇÊ / ,/" Ê7/Ê4HE MARITIME !UTOMATIC )DENTIFICATION 3YSTEM !)3 IS A TARGET INFORMATION SYSTEM THAT PERFORMS SIMILAR FUNCTIONS TO AIRBORNE 3ECONDARY 3URVEILLANCE 2ADAR 332 SUCH AS !IR 4RAFFIC #ONTROL "EACON 3YSTEM !4#2"3 AND )DENTIFICATION &RIEND OR &OE )&& (OWEVER THE VAST MAJORITY OF TRANSMISSIONS ARE NOT THE RESULT OF ANY INTERROGA TION AS IT MAINLY OPERATES AS A BROADCAST SYSTEM BASED AROUND A 3ELF /RGANIZING 4IME $OMAIN -ULTIPLE !CCESS 3/4$-! COMMUNICATIONS PROTOCOL 4HE COMMUNICATIONS LINK INCLUDING THE 3/4$-! DEFINITION IS DEFINED BY THE )45 3HIPS AUTOMATICALLY TRANSMIT CURRENT NAVIGATIONAL DATA AND OTHER INFORMATION ON 6(& MARINE BAND CHAN NELS ASSIGNED FOR !)3 USE 4HE TRANSMITTED INFORMATION IS RECEIVED BY OTHER SHIPS AND ALSO BY SHORE STATIONS SUCH AS COASTAL AUTHORITIES AND 643 FACILITIES 3HORE STATIONS AND SHIPS ALSO HAVE THE ABILITY TO SPECIFICALLY INTERROGATE SHIPBORNE !)3 TRANSPONDERS TO INITIATE THE SENDING OF PARTICULAR DATA !)3 HAS THREE MAJOR USES TO ENHANCE THE BRIDGE TEAMS SITUATIONAL AWARENESS TO AID 643 ACTIVITIES AND TO PROVIDE DATA TO ASSIST NATIONAL SECURITY 4HE INTENTION OF )-/ IS THAT SHIPS WILL NORMALLY DISPLAY !)3 DATA ON THE RADAR SCREEN AS IT COMPLEMENTS RADAR DERIVED DATA ADDING TO THE INTEGRITY OF THE PRESENCE POSITION AND VELOCITY OF TARGETS AND ALSO GIVING INCREASED TARGET INFORMATION )N PRINCIPLE A CONVENTIONAL SECONDARY RADAR SOLUTION COULD HAVE BEEN ADOPTED BUT INTERNATIONAL CONSENSUS FAVORED THE 3/4$-! APPROACH AS IT WAS CAPABLE OF PROVID ING HIGHER LEVELS OF DATA EXCHANGE PARTICULARLY TO AID 643 AND SECURITY ACTIVITIES !N IMPORTANT ADVANTAGE OF THE CHOSEN !)3 SOLUTION IS ITS RADIO FREQUENCY )T IS SUFFICIENTLY LOW SO THAT REASONABLE COMMUNICATIONS ARE MAINTAINED IN SITUATIONS WHERE THERE IS NO VISUAL OR RADAR LINE OF SIGHT 4HIS CAN BE IMPORTANT IN HARBOR RIVER ISLAND AND ESTUARY REGIONS WHERE SHIELDING BY THE TERRAIN OR BUILDINGS CAN AFFECT RADAR RANGE ! SHIPBORNE !)3 STATION BROADCASTS INFORMATION DIVIDED INTO A NUMBER OF SETS 4HESE COMPRISE STATIC DATA SUCH AS THE SHIPS NAME TYPE LENGTH AND BEAM DYNAMIC DATA INCLUDING POSITION 3/' #/' AND HEADING AND VOYAGE RELATED DATA SUCH AS DESTINATION PORT AND %4! DEPTH UNDER KEEL AND HAZARDOUS CARGO TYPE 4HE DYNAMIC DATA IS BROADCAST AT A RATE CONSISTENT WITH THE VESSELS VELOCITY AND WHETHER IT IS CHANG ING COURSE AS SHOWN IN 4ABLE 3TATIC AND VOYAGE RELATED DATA IS NORMALLY BROAD CAST EVERY MINUTES 4O PROVIDE SUFFICIENT BANDWIDTH TWO SPECIFIC 6(& +(Z CHANNELS ARE USED WITH STATIONS ALTERNATING BETWEEN CHANNELS AT EACH MESSAGE 4HERE ARE MESSAGE SLOTS PER CHANNEL EVERY MINUTE -INUTES ARE ALIGNED TO 5NIVERSAL 4IME #OORDINATED 54# WHICH IS OBTAINED FROM AN INTEGRAL '.33 RECEIVER 4HE 3/4$-! ALGORITHM EFFECTIVELY RESERVES FUTURE SLOTS FOR STATIONS THAT ARE IN RECEPTION RANGE OF EACH OTHER PREVENTING MUTUAL INTERFERENCE !)3 FOR 3/,!3 USE IS KNOWN AS !)3 #LASS ! 4HERE IS A #LASS " SYSTEM THAT IS DESIGNED FOR NON 3/,!3 USE 4HIS SYSTEM USES THE SAME 6(& CHANNELS AS #LASS ! AND THE TRANSMISSIONS ARE NECESSARILY COMPATIBLE BUT TO AVOID OVERLOADING THE 6(& DATA LINK 6$, #LASS " USES #ARRIER 3ENSING 4$-! 4HIS IS AIMED AT CONFINING
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4!",% !)3 0OSITION 2EPORTING )NTERVALS #OURTESY OF )-/
3HIP $YNAMICS !T ANCHOR OR MOORED AND NOT MOVING FASTER THAN KNOTS 7ITH A SPEED OF BETWEEN n KNOTS 7ITH A SPEED OF BETWEEN n KNOTS AND CHANGING COURSE 7ITH A SPEED OF BETWEEN n KNOTS 7ITH A SPEED OF BETWEEN n KNOTS AND CHANGING COURSE 7ITH A SPEED OF GREATER THAN KNOTS 7ITH A SPEED OF GREATER THAN KNOTS AND CHANGING COURSE
2EPORTING )NTERVAL SECONDS
#LASS " SYSTEMS TO USE ONLY SLOTS UNALLOCATED TO #LASS ! USERS #LASS " SYSTEMS WILL DELAY THEIR OWN TRANSMISSIONS IF SLOTS ARE NOT AVAILABLE 4HERE IS AN ADDITIONAL OPTION OF AN 3/4$-! BASED #LASS " SYSTEM )MPORTANTLY #LASS ! AND " SYSTEMS RECEIVE EACH OTHERS TRANSMISSIONS 4HE COMBINATION OF !)3 AND RADAR DERIVED DATA GIVES BENEFITS TO NAVIGATION BECAUSE OF THE COMPLEMENTARY NATURE OF THE TWO SYSTEMS 4HE RELATIVE RANGE AND BEARINGS OF A TARGET DERIVED FROM !)3 DATA ARE ENTIRELY INDEPENDENT OF THE RADAR MEASUREMENTS OF THESE PARAMETERS #LEARLY ANY OBSERVED DIFFERENCES IN RADAR AND !)3 POSITIONS WILL THEN INDICATE AN ERROR IN SOME PROCESS PROVIDED THE DIFFERENCES ARE OUTSIDE THE EXPECTED NOISE IN THE MEASUREMENTS 4HIS CAN BE HIGHLIGHTED FOR THE USER ! HIGH POSI TIONAL CORRELATION INCREASES THE INTEGRITY OF THE OBSERVATION PARTICULARLY AS SPEED AND COURSE MEASUREMENTS CAN ALSO BE USED IN THE COMPARISON ,ACK OF ANY CORRELATION CAN ALSO GIVE THE USER INFORMATION THAT MAY BE HELPFUL )F ONLY RADAR DATA IS RECEIVED IT MAY BE THAT THE TARGET IS NOT FITTED WITH !)3 WHICH MEANS IT COULD BE A SMALL CRAFT FLOATING DEBRIS OR ICE )T COULD ALSO MEAN THAT A VESSELS !)3 IS NOT OPERATING OR IS TRANSMITTING ERRONEOUS POSITIONAL INFORMATION )F ONLY !)3 DATA IS RECEIVED THE RADAR IMAGE MAY BE OBSCURED BY CLUTTER A HEADLAND OR EVEN A POORLY SETUP OR FAULTY RADAR INSTALLATION .ORMALLY JUST A FEW TARGETS WILL BE UNCORRELATED HIGHLIGHTING THAT THESE FEW SHOULD BE GIVEN ADDITIONAL CAUTION IF THEY ARE SIGNIFICANT TO OWN SHIP NAVIGATION AT LEAST UNTIL THEY CAN BE POSITIVELY IDENTIFIED PERHAPS VISUALLY )F NO TARGETS ARE CORRELATED IT SUG GESTS THAT OWN SHIP HAS A SIGNIFICANT PROBLEM PERHAPS WITH ITS RADAR '.33 POSITION OR MORE COMMONLY A GYROCOMPASS OFFSET )F THERE IS GOOD POSITIONAL TIE UP OR EVEN AN UNDERSTANDING OF WHY RADAR INFORMA TION MAY BE LACKING FOR EXAMPLE DUE TO HEAVY SEA CLUTTER THE ADDITIONAL INFORMATION TRANSMITTED ON !)3 CAN BE EXTREMELY USEFUL &OR INSTANCE A TARGETS HEADING IS TRANS MITTED BY !)3 4HIS INFORMATION IS NOT AVAILABLE FROM RADAR ONLY THE COURSE CAN BE DETERMINED AND YET HEADING IS USED AS THE BASIS FOR DETERMINING COLLISION AVOIDANCE ACTION 4HE !)3 TRANSMITTED HEADING SHOULD ALIGN WITH THE TARGETS VISUAL ASPECT AND THEREFORE THE NAVIGATIONAL LIGHTS ON A VESSEL 6ESSEL NAMES CAN BE ADDED AUTOMATICALLY TO TARGET TRACKS ON THE RADAR!)3 DISPLAY AND IF THERE IS A NEED TO COMMUNICATE ON 6(& WITH A PARTICULAR TARGET THE RADIO CALL SIGN IS ALSO AVAILABLE FROM THE !)3 DATA 4HE DESTINATION PORT AND %4! CAN SOMETIMES BE USEFUL IN DETERMINING THE LIKELY INTENTIONS OF TARGETS ALTHOUGH SUCH ASSUMPTIONS MUST BE TREATED WARILY ! SIGNIFICANT ADVANTAGE OF RADAR IS THAT IT DOES NOT NEED COOPERATIVE TARGETS )T ATTEMPTS TO DETECT ALL OBJECTS OF POTENTIAL INTEREST )TS INHERENT 2ELATIVE -OTION MODE OF OPERATION MAKES IT IDEALLY SUITED FOR COLLISION AVOIDANCE USEPARTICULARLY AS IN THIS MODE IT HAS NO REQUIREMENT TO NEED OWN SHIPS GEOGRAPHICAL POSITION (OWEVER RADAR IS BASICALLY CONFINED TO LINE OF SIGHT OPERATION ITS PERFORMANCE CAN BE SIGNIFICANTLY
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DEGRADED BY CLUTTER AND ITS TRACKING CAPABILITY IS COMPROMISED WHEN TARGETS ARE CHANG ING COURSE OR PASSING CLOSE TO OTHER TARGETS !)3 HAS REASONABLY GOOD CAPABILITY IN NON LINE OF SIGHT SITUATIONS BECAUSE OF ITS LOWER FREQUENCY )T QUICKLY REPORTS A TARGETS CHANGE IN HEADING OR COURSE INCLUDING RATE OF TURN DATA IF IT IS AVAILABLE ON THE TARGET VESSEL !)3 IS NOT AFFECTED BY SEA CLUTTER AND CAN REPORT ABSOLUTE POSITION ACCURATELYTO NORMALLY BETTER THAN METERS OR EVEN A METER OR TWO IF REPORTING DIFFERENTIAL '.33 DERIVED POSITIONAL DATA (OWEVER !)3 RELIES ON COOPERATIVE TARGETS IS PRONE TO GROSS ERRORS IN DATA ACCURACY MAINLY CAUSED BY SETUP ERRORS AND TOTALLY RELIES ON REASONABLY ACCURATE '.33 DATA BEING AVAILABLE ! '.33 BLACKOUT PERHAPS CAUSED BY INTENTIONAL OR UNINTENTIONAL JAMMING WOULD PREVENT !)3 FROM BEING AN EFFECTIVE SYSTEM POSSIBLY OVER A WIDE AREA AND FOR AN APPRECIABLE TIME &UTURE SYSTEMS MIGHT INCREASINGLY EXPLOIT THE COMPLEMENTARY ASPECTS OF RADAR AND !)3 4HIS COULD IMPROVE THE OVERALL TARGET TRACKING CAPABILITY AVAILABLE TO SHIPS AND WILL GIVE SUPPORT FOR DETECTING COOPERATIVE TARGETS IN CLUTTER 0OSSIBLY THE KNOWLEDGE FROM !)3 THAT A TARGET IS LIKELY TO BE AT A PARTICULAR RANGE AND AZIMUTH COULD DIRECT CONCENTRATED PROCESSING TECHNIQUES IN THAT AREA PERHAPS USING PATTERN MATCHING ALGO RITHMS AS WELL AS OPTIMIZING THE FALSE ALARM RATE IN THE IMMEDIATE AREA OF THE !)3 REPORTED TARGET )T IS IRONIC THAT THE VERY TARGETS THAT MAY BE HIDDEN IN CLUTTER ARE SMALLER VESSELS THAT DO NOT MANDATORILY CARRY !)3 !LSO A #LASS " SYSTEM ONLY TRANSMITS ONCE EVERY SECONDS AT A MAXIMUM AND SO WILL BE LESS USEFUL FOR AIDING RADAR EVEN THOUGH IT CAN USEFULLY ALERT NAVIGATORS THAT A SMALL TARGET IS PRESENT 4HE USE OF !)3 AS AN AID TO NAVIGATION !TO. HAS BEEN PUT FORWARD AS A POSSIBLE REPLACEMENT FOR RACONS WHICH ARE DESCRIBED IN THE NEXT SECTION )N PRINCIPLE !)3 !TO.S COULD REPLACE RACONS BUT IN PRACTICE IT WOULD BE A RETROGRADE STEP AS THEY CANNOT BE USED INDEPENDENTLY OF A POSITION FIX SYSTEM SUCH AS '.33 (OWEVER THEY CAN BE USEFULLY EMPLOYED TO INDICATE THE INTEGRITY OF THE ACTUAL POSITION OF THE MARK WHICH MAY HAVE DRAGGED OR BECOME UNATTACHED AND OTHER ADDITIONAL DATA SUCH AS SEA CURRENTS 4HE !)3 TRANSCEIVER DOES NOT HAVE TO BE SITUATED ON THE ACTUAL MARK AND COULD BE SHORE BASED TO EASE MAINTENANCE 5SED IN THIS WAY THEY ARE KNOWN AS 6IRTUAL !)3 !TO.S 5P TO DATE INFORMATION CONCERNING THE MARK AND ITS INTEGRITY CAN BE AUTOMATICALLY OR MANUALLY FED IN BY PORT AUTHORITIES 3UCH SYSTEMS CAN ALSO BE USED FOR ALERTING MARINERS OF THE POSITION OF RECENT WRECKS AND OTHER TEMPORARY AND PERHAPS VISUALLY UNMARKED NAVIGATION HAZARDS
ÓÓ°nÊ , ,Ê " 2ADAR BEACONS HAVE PLAYED AN IMPORTANT ROLE IN MARINE NAVIGATION EVER SINCE THE EARLY DAYS OF RADAR 4HEY BASICALLY DETECT INCIDENT PULSES FROM MARINE RADARS AND INSTAN TANEOUSLY TRANSMIT A DISTINCTIVE SIGNAL THAT IDENTIFIES THE BEACON AND ITS POSITION ON A RADAR DISPLAY 4HERE ARE THREE MAIN USES OF SUCH BEACONS 4HE FIRST OF THESE IS FOR ENHANCING VISUAL AIDS TO NAVIGATION SUCH AS BUOYS AND LANDMARKS TO ENABLE THEM TO BE PROMINENTLY IDENTIFIED ON A RADAR DISPLAY 4HESE ARE NORMALLY CALLED RACONS AS A CONTRACTION OF RADAR BEACONS 3UCH SYSTEMS FORM AN IMPORTANT NAVIGATIONAL SERVICE THAT IS WELL LIKED BY MARINERS 4HE SECOND USE IS FOR 3EARCH AND 2ESCUE 4RANSPONDERS 3!24S WHICH ARE MAINLY DESIGNED TO BE DEPLOYED FROM LIFE RAFTS AFTER A MARINE ACCI DENT 4HE THIRD CATEGORY OF USE IS FOR RADAR ENHANCEMENT OF SMALL TARGETS SUCH AS PLEA SURE CRAFT 4HESE ARE CALLED RADAR TARGET ENHANCERS 24% OR ACTIVE RADAR REFLECTORS
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2ACONS 4HE )NTERNATIONAL !SSOCIATION OF -ARINE !IDS TO .AVIGATION AND ,IGHTHOUSE !UTHORITIES )!,! SETS THE PERFORMANCE STANDARDS FOR RACONS 4HESE INCORPORATE THE TECHNICAL CHARACTERISTICS SET OUT IN A SPECIFIC )45 2 2ECOMMENDATION "ECAUSE RACONS NORMALLY FORM ONLY ONE SUBSYSTEM OF AN !TO. THEY THEREFORE NEED TO BE SMALL IN SIZE AND POWER EFFICIENT SINCE THEY ARE RARELY CONNECTED TO A MAIN POWER SUPPLY 4HEY OFTEN OPERATE IN AN EXTREME ENVIRONMENT SUCH AS ON A BUOY BUFFETED BY THE SEA 2ACONS ARE SPECIFIED TO MEET AN EXTENDED OPERATIONAL TEMPERATURE RANGE OF n TO # -ODERN RACONS OPERATE BY DETECTING AN INCIDENT PULSE AND THEN MEASUR ING ITS FREQUENCY AND RESPONDING AT THE SAME FREQUENCY THEREBY REDUCING THE INTERFER ENCE POTENTIAL WITH OTHER IN BAND RADARS 4HEY ARE OFTEN DUAL BAND AND '(Z 4HE )45 RECOMMENDS THAT FOR PULSE LENGTHS OF §S OR LONGER THE FREQUENCY ACCURACY OF THE RESPONDING SIGNAL SHOULD BE WITHIN o -(Z AND FOR PULSES OF LESS THAN §S THE FREQUENCY SHOULD BE WITHIN o -(Z 3WEPT FREQUENCY RACONS ARE EFFECTIVELY OBSOLESCENT BUT ARE STILL PERMITTED 4HESE WORK BY HAVING AN INTERNAL 2& SOURCE THAT IS SLEWING IN FREQUENCY ACROSS THE ENTIRE RADAR BAND WITH A SAW TOOTH WAVEFORM AT A RATE BETWEEN AND SECONDS PER -(Z !LL RECEIVED PULSES ARE RESPONDED TO BUT THE INTERROGATING RADAR WILL RECEIVE A RACON BURST ONLY ONCE EVERY ONE TO TWO MINUTES WHEN ITS RECEIVER IS IN BAND TO THE PARTICULAR TRANSMISSION )!,! RECOMMENDS THAT RACONS HAVE SUPPRESSION TECHNIQUES TO AVOID RESPONDING TO RADAR SIDELOBE TRANSMISSIONS 4HIS IS NOT AN EASY TASK TO IMPLEMENT AND PROBABLY IMPOSSIBLE TO MAKE INFALLIBLE "ASICALLY THE RACON NEEDS TO BUILD A TABLE OF RADAR SIG NATURES THAT IT IS CURRENTLY RECEIVING BASED ON FREQUENCY AND PULSE LENGTH )T THEN IDENTIFIES WHETHER HIGH LEVEL AND LOWER LEVEL PULSES OF THE SAME SIGNATURE ARE BEING RECEIVED AND MAKES THE ASSUMPTION THAT THESE ARE FROM THE SAME RADAR )T SETS A THRESH OLD LEVEL FOR INDIVIDUAL RADARS SUCH THAT IT ONLY RESPONDS TO HIGH POWER MAIN BEAM INTERROGATIONS 4YPICALLY PEAK TRANSMIT POWERS ARE ABOUT n WATTS !NTENNAS ARE USU ALLY OMNIDIRECTIONAL IN AZIMUTH BUT CAN HAVE A RESTRICTED ELEVATION BEAMWIDTH AND TYPICALLY HAVE AN OVERALL GAIN OF ABOUT D" 0RIME POWER CONSUMPTION IN AVERAGE TRAFFIC CAN BE LESS THAN WATT 4HE MODULATION ON THE RESPONSE SIGNAL OF A RACON PAINTS A -ORSE CODE IMAGE ON THE RADAR DISPLAY 4HE CODE IDENTIFIES A PARTICULAR !TO. AND APPEARS IN THE RADIAL DIRECTION CONVENTIONALLY COMMENCING WITH A DASH 4HIS DASH STARTS A SHORT DISTANCE BEYOND THE ACTUAL POSITION OF THE !TO. BECAUSE OF INHERENT DELAYS IN THE RESPONSE TIME OF THE RACON (OWEVER DELAYS GIVING AN ERROR OF LESS THAN METERS ARE READILY ACHIEVABLE )N GOOD CONDITIONS THE !TO. PRIMARY RADAR IMAGE WILL BE DISPLAYED ON THE RADAR SCREEN HELPED IF A PASSIVE RADAR REFLECTOR IS ALSO A PART OF THE !TO. 2ACONS HAVE TO INCLUDE MUTING PERIODS TO ALLOW SHIP RADARS TO LOOK FOR SMALL TARGETS IN THE VICINITY OF THE RACON IDENTIFIER 4HE LONG TERM FUTURE OF RACONS IS UNSURE ALTHOUGH MARITIME AUTHORITIES ARE ASSESS ING THE SITUATION -ARINERS LIKE THEM AS THEY ARE USEFUL FAMILIAR AND GIVE SHIP RELATIVE DATA (OWEVER IT IS DIFFICULT TO SEE HOW THEY WILL SURVIVE IN THEIR ORIGINAL FORM AS MARINE RADAR MOVES AWAY FROM UTILIZING MAGNETRON BASED SYSTEMS !LSO COMPARED WITH EARLIER YEARS WHEN RACONS WERE ESSENTIAL MANY MORE NAVIGATIONAL AIDS ARE BECOMING AVAILABLE THAT ASSIST POSITIONING 4HESE INCLUDE MULTIPLE '.33 SERVICES DIFFERENTIAL '.33 !)3 AND ENHANCED 643 FACILITIES 4HERE ARE ALSO GREAT IMPROVEMENTS IN ONBOARD NAVIGA TIONAL AIDS SUCH AS ELECTRONIC CHARTS AND INTEGRATED NAVIGATION SYSTEMS 4HE RELIANCE OF NAVIGATION ON A SINGLE SYSTEM SUCH AS '03 OR EVEN A SINGLE TECH NOLOGY SUCH AS '.33 IS NOT ACCEPTABLE TO THE MARITIME COMMUNITY AND NEITHER TO AVIATION &OR INSTANCE IT IS EASY TO JAM ALL '.33 USERS OVER A WIDE AREA BECAUSE OF THE SMALL AMPLITUDE OF THE RECEIVED SIGNAL 4HIS MEANS THAT RADAR AND OTHER POSITION ING SYSTEMS ARE LIKELY TO BE ALWAYS USED AS ESSENTIAL NAVIGATIONAL TOOLS 4HE OVERALL
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REQUIREMENTS FOR THE ELECTRONIC NAVIGATION OF SHIPS INCLUDING 643 REPORTING SYSTEMS ARE BEING EXAMINED BY )-/ AND )!,! WITH THE INTENTION OF DETERMINING A FUTURE E .AVIGATION CONCEPT E FOR ELECTRONICENHANCED 4HE CONTINUED NEED FOR RACONS OR A REPLACEMENT TECHNOLOGY WILL INEVITABLY FORM PART OF THIS PROGRAM )F THE CONTINUOUS AVAILABILITY OF PRECISE POSITIONAL INFORMATION CANNOT BE TOTALLY RELIED UPON THEN IT IS PROBABLY ESSENTIAL THAT SOME FORM OF SHIP RELATIVE SYSTEM TO IDENTIFY FIXED NAVIGA TIONAL MARKS IS AVAILABLE 3!24S 3EARCH AND 2ESCUE 4RANSPONDERS 3!24 FORM PART OF )-/S 'LOBAL -ARITIME $ISTRESS AND 3AFETY 3YSTEM '-$33 4HESE ARE '(Z RADAR TRANSPONDERS THAT ARE MAINLY DESIGNED TO BE USED ON SURVIVAL CRAFT SUCH AS LIFE RAFTS IN EMERGENCY CONDITIONS 4HEY ARE RELATIVELY SMALL AND AFFORDABLE /N BEING TRIGGERED BY A RADAR PULSE A 3!24 EMITS A CYCLE FREQUENCY SWEPT SAW TOOTH WAVEFORM COVERING TO '(Z 4HE EXTENSION DOWN TO '(Z COVERS THE BAND USED BY SEARCH AIRCRAFT 4HE VERY FAST UPWARD FREQUENCY SCAN IS ACCOMPLISHED IN §S THE DOWNWARD SCAN TAKES §S 4HIS FORMS THE POSSIBILITY OF A DISPLAYED TRACE ON THE RADAR SCREEN CONSISTING OF RADIAL DOTS AND DASHES AS THE UPWARD AND DOWNWARD SCANS CROSS THE PASSBAND OF THE RADAR RECEIVER WITH THE FIRST DOT AT A SLIGHTLY LONGER RANGE THAN THE 3!24 POSITION )N PRACTICE THE UPWARD SWEEP IS SO FAST THAT THE DOTS ARE NORMALLY NOT VISIBLE ON THE DISPLAY AND ONLY THE DASHES CAN BE SEEN %VEN THESE CAN BE QUITE DIFFICULT TO LOCATE IN ADVERSE SEA CLUTTER CONDITIONS 4HE FIRST DASH DISPLAYED ON THE RADAR SCREEN COULD BE UP TO NM AWAY FROM THE ACTUAL 3!24 POSITION AND SO SEARCH CRAFT HAVE TO TAKE PRECAUTIONS NOT TO RUN DOWN THE SURVIVAL CRAFT WHEN BEARING DOWN ON THE SIGNAL !T SHORT RANGES THE SWEPT GAIN OF THE RADAR MAY TRUNCATE THE NEARER DASHES !LSO AT SHORT RANGES BECAUSE THERE IS NO SIDELOBE SUPPRESSION CIRCUITRY 3!24S CAN BE TRIGGERED BY RADAR SIDELOBES 4O PREVENT ADJACENT 3!24S FROM CONTINUOUSLY TRIGGERING EACH OTHER THERE IS A SHORT DELAY AFTER A 3!24 TRANSMISSION BEFORE IT MAY BE TRIGGERED AGAIN 4O DETECT 3!24S IN HEAVY SEA CLUTTER IT IS OFTEN BEST TO DETUNE THE RADAR RECEIVER ELIMINATING ALL OTHER RETURNS 3OME RADAR MANUFACTURERS PROVIDE A 3!24 SEARCH MODE THAT SETS THE RADAR OPTIMALLY FOR THEIR DETECTION INCLUDING INHIBITING PULSE TO PULSE CORRELATION AND OPTIMIZING FILTER BANDWIDTHS !)3 BASED 3!24S HAVE NOW BEEN PROPOSED 4HESE MAY EVENTUALLY REPLACE RADAR BASED 3!24S BECAUSE THE LATTER ARE DIFFICULT TO DETECT IN ADVERSE CONDITIONS 2ADAR 4ARGET %NHANCERS 2ADAR TARGET ENHANCERS 24%S ARE USED INCREAS INGLY BY SMALL CRAFT BECAUSE FOR THEIR SIZE THEY OFFER A BETTER ENHANCEMENT IN RADAR CROSS SECTION THAN CAN BE GIVEN BY A PASSIVE REFLECTOR )N PRINCIPLE THEY ARE SIMPLE DEVICES )N BAND RECEIVED SIGNALS ARE AMPLIFIED AND RETRANSMITTED WITH MINIMUM DELAY $ELAYS CAN BE KEPT TO A FEW NANOSECONDS LESS THAN THE EQUIVALENT DIMEN SIONS OF THE CRAFT ENSURING CO LOCATED RETURNS OF THE ENHANCED SIGNAL AND NATURAL RADAR REFLECTION 4O PREVENT POSITIVE FEEDBACK BETWEEN RECEIVER AND TRANSMITTER THE TRANSMIT AND RECEIVE ANTENNAS ARE NORMALLY PHYSICALLY SEPARATE ONE ABOVE THE OTHER PROVIDING ISOLATION )SOLATION CAN ALSO BE INCREASED BY TRANSMITTING ON AN ORTHOGONAL POLARIZATION TO THAT RECEIVED 0ROVIDING THEY ARE OPERATING WITH LINEAR GAIN THERE ARE NO ADVERSE EFFECTS FROM RADAR SIDELOBE INTERROGATION (OWEVER AT CLOSE RANGES THE SIGNAL FROM THE MAIN BEAM OF THE RADAR MAY SATURATE WITHIN THE 24% EFFECTIVELY ENHANCING THE LEVELS OF THE 24% RECEIVED SIGNAL THROUGH THE RADAR SIDELOBES 4HE )45 REGULATIONS LIMIT 24%S TO AN %)20 OF WATTS WITH A MINIMUM GAIN OF D"
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ÓÓ°Ê 6 /" Ê/ -/ 4HE FACTORS AFFECTING THE RANGE PERFORMANCE OF A RADAR SYSTEM ARE WELL KNOWN AND INCREASINGLY SOPHISTICATED DESIGN METHODOLOGIES HAVE GREATLY IMPROVED THE DETECTION OF ALL FORMS OF RADAR 4HE FINAL PROOF HOWEVER IS HOW THE RADAR ACTUALLY PERFORMS AT SEA !S STATED PREVIOUSLY SHIPBORNE RADARS ARE VALIDATED AS MEETING )-/ PERFORMANCE STANDARDS BY BEING INDEPENDENTLY TYPE APPROVED TO TECHNICAL STANDARDS ISSUED BY THE )%# 4HE )%# STANDARDS INCLUDE DEFINED METHODS OF TESTING &OR A GIVEN TARGET AND RADAR ANTENNA HEIGHT IT IS RELATIVELY EASY TO DEFINE AND EXECUTE A TEST TO DETERMINE THAT A POINT SOURCE TARGET WITH A SPECIFIC ECHOING AREA IS DETECTED AT A GIVEN RANGE IN A MINIMAL CLUTTER FIELD )T IS VERY DIFFICULT TO EXTEND THIS TO DETERMINE IN A REPEATABLE AND QUANTI TATIVE MANNER THE PERFORMANCE OF THE RADAR AGAINST POINT TARGETS IN PREDEFINED CLUTTER CONDITIONS &OR THIS REASON SOME BASIC PERFORMANCE TESTS HAVE NECESSARILY BEEN LOOSELY DEFINED TO ALLOW SCOPE FOR APPROVED TEST LABORATORIES TO MAKE THEIR OWN QUALITATIVE JUDG MENTS ON BASIC RADAR PERFORMANCE NORMALLY BASED ON OPPORTUNISTICALLY TESTING THE RADAR OVER THE SEA AND IN PRECIPITATION IN A VARIETY OF SITUATIONS *UDGMENTS ON PERFORMANCE CAN THEREFORE BE QUITE SUBJECTIVE AND ARE NATURALLY AFFECTED BY THE CONDITIONS ACTUALLY ENCOUNTERED DURING THE TESTS #OST CONSIDERATIONS CAN SEVERELY LIMIT THE LENGTH OF TEST PROGRAMS AND THEREBY THE RANGE OF SCENARIOS USED 2ADARS UNDER TYPE APPROVAL ARE TYPI CALLY INSTALLED ON A TRIAL VESSEL FOR SUCH TESTS OR USE A LAND SITE OVERLOOKING THE SEA 4HIS SCENARIO IS BECOMING INCREASINGLY UNSATISFACTORY AS ADVANCES IN REQUIREMENTS FOR SAFETY AND THE PROTECTION OF THE ENVIRONMENT MEAN THAT IT IS NECESSARY TO ENSURE THAT TYPE APPROVAL IS CONSISTENTLY APPLIED AND IS THEREFORE MEASURED IN A QUANTITATIVE MAN NER )N AN ATTEMPT TO RESOLVE THIS SOME WORK HAS BEEN PERFORMED TO TRY TO BETTER FORMAL IZE MARINE RADAR CLUTTER PERFORMANCE TESTS INCLUDING SOME RESEARCH PERFORMED ON BEHALF OF THE 5+ -ARITIME AND #OASTGUARD !GENCY 4HIS APPROACH WAS AIMED TO MINIMIZE ANY SPECIAL CONFIGURATION OF THE RADAR UNDER TEST )T IS BASED ON A SYSTEM THAT GENERATES SIMULATED TARGET AND CLUTTER WAVEFORMS 4HESE ARE PICKED UP BY THE ANTENNA OF THE RADAR UNDER TEST FROM A NEARBY TRANSMITTING SOURCE TYPICALLY SITUATED ABOUT METERS FROM THE RADAR ANTENNA #O LOCATED WITH THE TRANSMITTING SOURCE IS A RECEIVER WHICH DETECTS THE TRANSMITTED RADAR SIGNAL AND CONTINUALLY ANALYSES ITS FREQUENCY PULSE LENGTH AND AMPLITUDE AS THE RADAR ANTENNA ROTATES &ROM THIS INFORMATION A SIGNAL WAVEFORM IS SYNTHESIZED ON A PULSE TO PULSE BASIS REPLICATING REFLECTED SIGNALS FROM TARGETS AND CLUT TER 4HE SYNTHESIS PROCEDURE CALCULATES APPROPRIATE FLUCTUATING TARGET AND CLUTTER RETURNS FROM ANY DESIRED THEORETICAL MODELWHICH COULD ALSO IN PRINCIPLE INCLUDE MODELS DERIVED FROM RECORDED DATA OF REAL TARGET AND CLUTTER REFLECTIONS "ECAUSE THE SIMULATED SIGNAL IS PREDOMINATELY ENTERING THE RADAR THROUGH THE SIDELOBES OF THE RADAR ANTENNA EXCEPT WHEN THE RADAR MAIN BEAM ALIGNS WITH THE SIMULATOR ANTENNATHE SYNTHESIZED SIGNAL NEEDS TO BE AUTOMATICALLY ADJUSTED IN AMPLITUDE TO COMPENSATE FOR THE ACTUAL SIDELOBE SENSITIVITY IN THE DIRECTION OF THE SIMULATOR %FFECTIVELY THE SYNTHESIZER HAS TO AMPLIFY THE TRANSMITTED SIGNAL ACCORDING TO THE INVERSE OF THE AMPLITUDE OF EACH PULSE RECEIVED FROM THE RADAR 4HE CHALLENGES IN DESIGNING AN AFFORDABLE SYSTEM INCLUDE THE LARGE DYNAMIC RANGES THAT HAVE TO BE ENCOMPASSED AND THE PROCESSING SPEED NEEDED TO DETERMINE THE CHARACTERISTICS OF THE TRANSMITTED SIGNAL )N PRINCIPLE A NUMBER OF CLUTTER AND TARGET MODELS COULD BE ESTABLISHED BY INTER NATIONAL AGREEMENT SUCH THAT THEY WERE CONSIDERED TO BE REPRESENTATIVE OF CONDITIONS AROUND THE WORLD AGREED UPON TEST CRITERIA COULD THEN BE DETERMINED AND SIMULATOR SYSTEMS COULD BE BASED AT MARINE RADARnTYPE APPROVAL LABORATORIES )T HAS BEEN FOUND
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THAT THE SYSTEM IS ADVERSELY AFFECTED IF SET UP CLOSE TO LARGE RADAR REFLECTING OBJECTS SUCH AS BUILDINGS AND SO NEEDS TO BE LOCATED IDEALLY IN RELATIVELY OPEN SPACES SIMILAR TO THAT FOUND ON AN ANTENNA FAR FIELD TEST RANGE 4O ENABLE TESTS TO BE MORE EASILY CARRIED OUT DIRECT INJECTION OF TEST TARGETS AND CLUTTER INTO THE 2& PATH IS FEASIBLE (OWEVER THIS INVOLVES A CERTAIN AMOUNT OF ADAPTATION OF THE RADAR UNDER TEST WHICH MAY BE CONSIDERED INAPPROPRIATE 4HE POTENTIAL MOVE AT '(Z TO PULSE COMPRESSED RADAR OFFERS ADDITIONAL CHAL LENGES IN THE DESIGN OF A UNIVERSAL SIMULATOR AS THE SYSTEM DESCRIBED IS BASED ON TESTING NONCOHERENT PULSED RADARS 3YSTEMS BASED ON DIGITAL 2& MEMORY MAY HAVE TO BE DEVISED STORING WAVEFORMS THAT CAN BE SUBSEQUENTLY PROCESSED 4ARGET AND CLUTTER MODELS WOULD OBVIOUSLY NEED TO APPROPRIATELY TAKE INTO ACCOUNT DOPPLER EFFECTS INTRO DUCED BY THE MOVEMENT OF THEIR EQUIVALENT SCATTERERS
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2ADAR HEADS FOR PORT CONTROL AND COASTAL SURVEILLANCE SYSTEMS HAVE SOME REQUIREMENTS IN COMMON WITH THOSE FOR SHIPBORNE RADARS 4HIS ORIGINALLY RESULTED IN MANY OF THE WELL KNOWN SUPPLIERS OF SHIPBORNE RADAR GETTING INVOLVED IN THIS AREA 4HEY COULD OFFER ATTRACTIVE PRICES AS THE SUBSYSTEMS WERE DERIVATIVES OF THE RELATIVELY HIGH VOLUME SHIPBORNE MARKET /VER TIME MUCH OF THE MARKET HAS BECOME MORE SOPHISTICATED AND BECAUSE OF THIS SPECIALIST ORGANIZATIONS NOW DOMINATE THE SUPPLY OF SYSTEMS FOR THIS APPLICATION 4HE LARGE COSTS ASSOCIATED WITH A MAJOR VESSEL TRACKING SERVICES 643 OPERATION INCLUDING MASSIVE ANTENNA SUPPORT TOWERS OPERATIONS BUILDINGS SPECIAL IZED SOFTWARE AND DISASTER PROOFED BROADBAND COMMUNICATION SYSTEMS MEAN THAT THE COSTS OF A MORE OPTIMIZED RADAR HEAD OFTEN BECOME A RELATIVELY INSIGNIFICANT ADDI TION 4HIS ALSO MEANS THAT SWITCHABLE LINEAR AND CIRCULAR POLARIZATION MODES ARE MORE COMMON ON 643 SYSTEMS (OWEVER BASIC LOW COST 643 SYSTEMS STILL COMMONLY USE SUBSYSTEMS INTENDED FOR SHIPBORNE USE GIVING GOOD COST SAVINGS COMPARED TO CUSTOM MADE SYSTEMS 4HERE ARE SIGNIFICANT DIFFERENCES HOWEVER IN THE REQUIREMENTS FOR A 643 RADAR COMPARED TO A SHIPBORNE SYSTEM 4HE 643 ANTENNA IS MOUNTED ON A STATIC PLATFORM 4HIS MEANS THAT THE VERTICAL PATTERN CAN BE MORE OPTIMALLY SHAPED !LSO SINCE THE DESIGN DOES NOT HAVE TO COPE WITH THE SHOCK VIBRATION AND INSTABILITY EXPERIENCED ON SHIPS RADAR MASTS LARGER ANTENNAS BECOME FEASIBLE 4HIS ALLOWS AZIMUTH BEAMWIDTHS TO BE NARROWER THEREFORE REDUCING THE SIZE OF CLUTTER CELLS 4HE REQUIRED COASTAL AREA TO BE COVERED CAN BE LARGE AND GETTING THE BEST RANGE OUT OF A FEW RADAR HEADS SITUATED ON TALL TOWERS IS OFTEN MORE COST EFFECTIVE THAN UTILIZING MANY SMALLER INSTALLATIONS "ECAUSE 643 OFTEN FORMS PART OF A NATIONS SECURITY NETWORK THEN A LONGER RANGE CAPABILITY THAN THAT JUST REQUIRED FOR PORT OPERATIONS MAY BE NECESSARY 4HIS IMPLIES THAT VERY HIGH ANTENNA TOWERS ARE OFTEN NEEDED IN SOME CASES UP TO METERS 4HIS EXACERBATES VERTICAL LOBING EFFECTS WHICH MAY NEED TO BE REDUCED BY THE USE OF VERTI CAL PATTERN SHAPING 4HE LONG RANGE REQUIREMENT OFTEN MEANS THAT GREATER TRANSMITTER POWER THAN THAT USED ON SHIPBORNE RADARS IS NEEDED EVEN THOUGH 643 ANTENNA GAINS CAN BE HIGHER 0ULSE LENGTHS MUST BE KEPT SHORT TO GET GOOD CLUTTER IMMUNITY BUT SIMUL TANEOUSLY LONG RANGE PERFORMANCE IS REQUIRED AGAIN INCREASING THE REQUIRED TRANSMIT TED POWER 643 RADAR HEADS ARE USUALLY NOT OPERATOR CONFIGURABLE BECAUSE A NUMBER OF OPERATORS CAN TYPICALLY BE USING DATA FROM ONE HEAD
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4HERE ARE MORE OPPORTUNITIES TO ENHANCE PERFORMANCE BECAUSE OF THE FIXED ANTENNA POSITION FOR INSTANCE SEA CLUTTER MAPPING BECOMES EASIER BECAUSE THE ANTENNA IS NOT ON A MOVING PLATFORM !LSO THE CLUTTER CONDITIONS CAN BE LESS VARIABLE BECAUSE OF THE RESTRICTED GEOGRAPHICAL AREA OF OPERATION AND THERE ARE NO DEGRADATIONS IN THE ACCU RACY OF THE DISPLAYED RADAR IMAGE IN HAVING TO COMPENSATE FOR A SHIPS HEADING WITH COMPASS INPUT )N PARTICULAR TARGET TRACKING IS PERFORMED FROM A STABLE AND STATIC PLAT FORM (OWEVER IT IS GENERALLY NECESSARY TO TRACK MANY MORE TARGETS THAN IS REQUIRED ON A SHIPBORNE RADAR AND NORMALLY 643 HAS FULLY AUTOMATIC PLOT EXTRACTION AND TRACK INITIATION !LSO MORE INFORMATION ON TRACKED TARGETS MAY NEED TO BE EASILY AVAILABLE -UCH OF THIS ADDITIONAL DATA CAN BE AUTOMATICALLY SUPPLIED BY !)3 4HE RADAR DATA OFTEN HAS TO BE RELAYED MANY MILES TO PERHAPS A NUMBER OF OPERATIONAL CENTERS )T MAY NEED TO BE COMBINED WITH DATA FROM A NUMBER OF RADAR HEADS AND THEREFORE WILL BE QUITE SYNTHETIC WHEN DISPLAYED ON OPERATORS SCREENS REDUCING THE POSSIBILITIES OF INDIVIDUAL OPERATOR ADJUSTMENT %XTENSIVE DATA COMMUNICATIONS NETWORKS BECOME A CRITICAL ASPECT IN THE PERFORMANCE OF THE 643 (IGH RELIABILITY OF THE SYSTEM IS REQUIRED BECAUSE OF SAFETY ENVIRONMENTAL PROTECTION AND SECURITY ASPECTS ! TOTAL SYSTEM AVAIL ABILITY OF IS NOT UNCOMMONLY SPECIFIED IMPLYING AN AVERAGE DOWNTIME OF LESS THAN MINUTES PER DAY !NOTHER MAJOR DIFFERENCE COMPARED TO SHIPBORNE RADAR IS THE CUSTOM NATURE OF THE INSTALLATION 2ADAR HEADS ARE FIXED AND THERE IS A SPECIFIC REQUIREMENT FOR CERTAIN PERFORMANCE PARAMETERS TO BE MET IN THE PARTICULAR LOCALIZED ENVIRONMENT 3EA CLUTTER ALTHOUGH VERY VARIABLE WILL HAVE CERTAIN LOCAL CHARACTERISTICS ENABLING MORE EFFECTIVE OPTIMIZATION OF THE PROCESSING )N PARTICULAR THE ACTUAL PERFORMANCE CAN BE MORE EAS ILY MEASURED AGAINST DESIGN REQUIREMENTS 4HE DESIGN OF HIGH PERFORMANCE ANTENNAS FOR 643 APPLICATIONS HAS A SIMILARITY TO AIR TRAFFIC CONTROL ANTENNAS IN THAT THEY BOTH IDEALLY REQUIRE A TAILORED ELEVATION PATTERN 4HE IDEAL PATTERN SHAPING FOR A HIGH MOUNTED 643 ANTENNA REQUIRES A SHARP CUT OFF ABOVE THE HORIZON AND A TAPERED PATTERN BELOW %NERGY DIRECTED ABOVE THE HORIZON INCREASES PRECIPITATION CLUTTER AND ALSO REDUCES THE ANTENNA GAIN !T ANGLES BELOW THE HORIZON THE GAIN SHOULD NOMINALLY FOLLOW A COSECANT SQUARED POWER LAW 4HIS IS AIMED AT GIVING A CONSTANT SIGNAL STRENGTH FROM A TARGET OF FIXED 2#3 INDEPENDENT OF RANGE 4HESE ARE OFTEN KNOWN AS INVERTED OR INVERSE COSEC SQUARED ANTENNAS TO DIFFERENTIATE THEM FROM AIR TRAFFIC CONTROL RADAR ANTENNAS THAT HAVE THEIR SHAPING AT ANGLES ABOVE THE HORIZON 3UCH SHAPING OPTIMIZES THE PATTERN TO THE APPLICATION GREATLY ENHANCING OVER ALL PERFORMANCE 4YPICALLY THE PATTERN SHAPING IS ENABLED BY A DOUBLY CURVED REFLECTOR FED FROM A POINT SOURCE PRIMARY FEED !N EXAMPLE FROM %ASAT !NTENNAS IS ILLUSTRATED IN &IGURE 4HIS IS A METER REFLECTOR ANTENNA WITH A DB GAIN AT '(Z )T HAS AN INVERSE COSECANT SQUARED ELEVATION PATTERN AND A AZIMUTH BEAMWIDTH )T IS REMOTELY CONTROLLED TO GIVE HORIZONTAL OR CIRCULAR POLARIZATION 4HE VERTICAL PATTERN SHAPING INTERACTS WITH THE 34# OF THE RADAR RECEIVER AND IT IS THEREFORE NECESSARY TO TAKE THIS INTO ACCOUNT IN THE SYSTEM DESIGN 4O IMPROVE DETECTION FREQUENCY DIVERSITY IS OFTEN USED ON PRIME SYSTEMS )!,! HAS ISSUED DETAILED RECOMMENDATIONS ON THE OPERATIONAL AND TECHNICAL PER FORMANCE REQUIREMENTS FOR 643 EQUIPMENT 4HERE IS MUCH USEFUL INFORMATION IN THE RECOMMENDATIONS AND THEY ARE ESSENTIAL FOR PROCURERS AND DESIGNERS OF 643 RADAR EQUIPMENT 4HEY COVER BOTH COASTAL AND WATERWAY INSTALLATIONS -ANY MAJOR RIVERS OF THE WORLD CARRY VAST AMOUNTS OF CARGO ON SHIPS THAT CAN BE SURPRISINGLY LARGE 4HE MEANDERING NATURE OF RIVERS AND RELATIVELY ABRUPT TURNS IN CANAL SYSTEMS TOGETHER WITH THE NATURAL AND MANMADE OBSTRUCTIONS TO RADAR MEAN THAT WATERWAY VESSEL TRAFFIC SYS TEMS ARE GENERALLY COVERED BY MANY LOW POWER RADAR HEADS ON RELATIVELY LOW TOWERS
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"ECAUSE OF THEIR NUMBER SUCH RADARS TEND TO BE MINIMALLY ADAPTED SHIPBORNE RADARS AS THEY OFFER ADEQUATE PERFORMANCE AT RELATIVELY LOW COST )NTERESTINGLY THE )!,! RECOMMENDATIONS ALLOW ##46 SOLUTIONS TO COMPETE WITH RADAR WHEN THERE IS VERY LOW TRAFFIC DENSITY !UTOMATIC TRACKING OF A SINGLE TARGET IS THEN REQUIRED (OWEVER ON BASIC RADAR BASED SYSTEMS )!,! EXPECTS A TARGET TRACK CAPABILITY AND A PLOT EXTRACTOR THAT CAN DEAL WITH MORE THAN PLOTS PER ROTATION /N AN ADVANCED SYSTEM MORE THAT TARGETS MAY HAVE TO BE TRACKED WITH A POSSIBILITY OF MORE THAN PLOTS PER ANTENNA REVOLUTION
** 8Ê / Ê , 9Ê 9-Ê"Ê , 4HE USE OF COMMERCIAL MARINE RADAR AROSE DIRECTLY FROM THE RAPID DEVELOPMENT OF RADAR TECHNOLOGY FOR MILITARY APPLICATIONS DURING 7ORLD 7AR )) %VEN AS EARLY AS SOME ATTENTION WAS BEING GIVEN TO THE PEACETIME ROLE OF RADAR AS A NAVIGATIONAL AID FOR COMMERCIAL SHIPPING )N AN h)NTERNATIONAL MEETING ON RADIO AIDS TO MARINE NAVIGATIONv WAS HELD IN ,ONDON AND ATTENDED BY REPRESENTATIVES FROM COUNTRIES 4HE MEETING WAS CHAIRED BY 3IR 2OBERT 7ATSON 7ATT )T WAS SEEN THAT RADAR ON COM MERCIAL VESSELS HAD AN IMPORTANT PART TO PLAY IN ANTI COLLISION COASTAL NAVIGATION AND PILOTAGE DECISIONS 0ILOTAGE IS NAVIGATING IN WATERS WHERE A QUALIFIED PILOT IS REQUIRED TO BE ONBOARD 4HE FUTURE COMPULSORY FITTING OF RADAR TO SHIPS WAS CONTEMPLATED AS WAS THE DESIRABILITY OF AN INTERNATIONALLY AGREED UPON MINIMUM PERFORMANCE STAN DARD WITH REQUIREMENTS FOR NATIONALLY ISSUED CERTIFICATES OF TYPE APPROVAL 4HE NEED TO INCLUDE THE USE OF RADAR WITHIN THE )NTERNATIONAL #OLLISION 2EGULATIONS WAS CLEARLY SEEN TOGETHER WITH THE NEED FOR CERTIFICATION OF USERS
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)N THE 5+ FAVORED OPERATION AT '(Z PRESUMABLY AS IT MORE AFFORDABLY MET THE 5+ PERCEIVED AZIMUTH REQUIREMENTS OF RESOLUTION AND ACCURACY 4HE 5NITED 3TATES IDENTIFIED OPERATIONAL PROBLEMS AT '(Z THAT COULD BE EXPERIENCED IN THE EXTREME RAINFALL CONDITIONS FOUND ON THE 53 EASTERN SEABOARD 4HESE CAUSED hBLACKOUTSv ON EARLY '(Z SYSTEMSDEFINED AS AN EFFECTIVE RANGE OF LESS THAN MILE !S A CONSEQUENCE THE 53 FAVORED OPERATION AT '(Z 4HE SHORTEST PULSE LENGTHS THEN COMMONLY AVAILABLE AROUND NS MADE THE CLUTTER CELLS LARGE RESULTING IN '(Z RADARS BEING VERY SUSCEPTIBLE TO RAIN CLUTTER PARTICULARLY AS CLUTTER PROCESSING TECHNIQUES WERE IN THEIR INFANCY )N THERE WAS NO QUESTION THAT A COMMERCIAL SHIP COULD AFFORD BOTH A AND A '(Z RADAR AS THE EXPENSE OF EVEN A SINGLE RADAR SYSTEM WAS SEEN TO BE A LIMITING ISSUE "ECAUSE OF COST IT WAS ALREADY ENVISAGED THAT FITMENT WOULD BE CONFINED MAINLY TO CERTAIN CLASSES OF PASSENGER SHIPS THAT HAD A DEFINITE NEED TO CARRY RADAR PARTICULARLY THOSE WORKING IN THE NORTH !TLANTIC IN CONGESTED AREAS OR AREAS SUBJECT TO FOG OR ICE 4HE EARLY TRIALS IN THE 5+ CONCENTRATED ON A SINGLE '(Z DEMONSTRATION SYSTEM FITTED TO A NAVAL VESSEL )T WAS BASED AROUND A K7 MAGNETRON CAPABLE OF NS PULSES AT A 02& OF (Z )T WAS INTERESTING THAT THE SPEED OF ROTATION COULD BE VAR IED BETWEEN AND RPM $ESPITE THE PERCEIVED MODERNITY OF TODAYS CHART RADARS IT WAS CONNECTED TO AN OPTIONAL #HART #OMPARISON 5NIT WHICH WAS AN OPTICAL SYSTEM ALLOWING THE RADAR IMAGE TO BE DISPLAYED IN COINCIDENCE WITH A PAPER CHART 4HE FACILITY TO ALLOW h.ORTH UPv OPERATION WAS ALWAYS SEEN TO BE A VITAL REQUIREMENT FOR MARINE NAVIGATION RADAR 0ARALLEL TRIALS IN THE 5NITED 3TATES WERE CONDUCTED ON A NUMBER OF CANDIDATE SYSTEMS USING A BROAD RANGE OF FREQUENCY BANDS 4HE INITIAL TRIALS WERE CONDUCTED IN THE 'REAT ,AKES AND WERE OVERSEEN BY THE #OAST 'UARD 4HE RADAR STANDARDS PROPOSED IN WERE NOT ADOPTED INTERNATIONALLY ALTHOUGH THE 5+ ISSUED NATIONAL PERFORMANCE STANDARDS BASED ON THEM IN 4HE 5+ STAN DARD WAS ALSO ADOPTED BY A NUMBER OF OTHER COUNTRIES )T WAS NOT UNTIL THAT INTERNATIONAL MARINE RADAR STANDARDS WERE AGREED BY THE )NTERGOVERNMENTAL -ARITIME #ONSULTATIVE /RGANIZATION )-#/ THE ORIGINAL NAME OF )-/ (OWEVER THE USE OF RADAR ON SHIPS WAS FIRST FORMALLY RECOGNIZED BY )-/ IN IN AN !NNEX TO THE )NTERNATIONAL 2EGULATIONS FOR 0REVENTING #OLLISIONS AT 3EA 4HE INFLUENCE OF THE PROPOSED INTERNATIONAL STANDARD WAS EVIDENT IN THE PERFORMANCE STANDARDS EVEN TO THE EXTENT OF USING IDENTICAL WORDING IN A NUMBER OF PLACES 4HE SIMILARITY IN PERFORMANCE REQUIREMENTS IS STILL EVIDENT IN THE LATEST REVISIONS OF THE )-/ PERFORMANCE STANDARD &OR INSTANCE THE PROPOSED PERFORMANCE SPECI FICATION INCLUDED THE NEED TO GIVE A CLEAR INDICATION OF COASTLINES RISING TO FT AT MILES OF A GROSS REGISTERED TON h)MPERIALv UNITS VESSEL AT MILES AND OF A FT FISHING VESSEL AT MILES 4HE MODERN PERFORMANCE REQUIREMENTS SUMMARIZED IN 4ABLE STILL USE THESE FIGURES BUT WITH PARAMETERS EXCEPT RANGES GIVEN IN EQUIVA LENT METRIC UNITS 4HE TECHNICAL VISION OF THE MEETING WAS REMARKABLE &OR INSTANCE IT WAS SEEN THAT IN THE FUTURE IT WOULD BE POSSIBLE TO OVERLAY RADAR DATA AUTOMATICALLY ONTO A CHART IMAGE DISPLAYED ON A hTELEVISIONv TYPE SCREEN 4HIS WAS NOT TO BE REALIZED ON COM MERCIAL SYSTEMS FOR YEARS !LSO IT WAS OBSERVED THAT SUCH DISPLAY SYSTEMS COULD ACCOMPLISH MORE THAN ONE FUNCTION AND NOT JUST BE USED FOR SHOWING RADAR ON A CHART 4HIS ANTICIPATED THE CONCEPT OF MULTIFUNCTION DISPLAYS NOW IN USE ON SOME INTEGRATED BRIDGE SYSTEMS )T IS INTERESTING TO NOTE THAT +ELVIN (UGHES AND $ECCA OBTAINED THE FIRST TYPE APPROVAL FOR COMMERCIAL MARINE RADAR IN EFFECTIVELY BOTH ARE STILL SUPPLYING
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MARINE RADAR TODAY +ELVIN (UGHES HAS RETAINED ITS NAME AND $ECCA IS INCORPORATED INTO THE 3PERRY -ARINE ORGANIZATION OF .ORTHROP 'RUMMAN #ORPORATION 4HE +ELVIN (UGHES 4YPE RADAR HAD A PEAK POWER OF K7 §S PULSE WIDTH AND A 02& OF (Z 4HE FT METER CHEESE ANTENNA HAD HORIZONTAL AND VERTICAL BEAMWIDTHS OF AND RESPECTIVELY ROTATING AT RPM 4HERE WAS AN ANTENNA HEATER TO PREVENT ICING AND THE TRANSMITTER AND THE RECEIVER TO )& WERE hUPMASTv INTEGRATED WITHIN THE ANTENNA TURNING UNIT 4HE DISPLAY WAS A IN CM CATHODE RAY TUBE PLAN POSITION INDICATOR 4HE SIMILARITIES WITH SYSTEMS BEING SOLD IN THE ST CENTURY ARE PERHAPS MORE SURPRISING THAN THE OBVIOUS DIFFERENCES
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"7 / -ATERIAL FROM )-/ PUBLICATIONS IS REPRODUCED WITH THE KIND PERMISSION OF THE )NTERNATIONAL -ARITIME /RGANIZATION )-/ WHICH DOES NOT ACCEPT RESPONSIBILITY FOR THE CORRECTNESS OF THE MATERIAL AS REPRODUCED IN CASE OF DOUBT )-/S AUTHENTIC TEXT SHALL PREVAIL 4HE AUTHOR THANKS THE )NTERNATIONAL %LECTROTECHNICAL #OMMISSION )%# FOR PER MISSION TO REPRODUCE INFORMATION FROM ITS )NTERNATIONAL 3TANDARD )%# ED !LL SUCH EXTRACTS ARE COPYRIGHT OF )%# 'ENEVA 3WITZERLAND !LL RIGHTS RESERVED &URTHER INFORMATION ON THE )%# IS AVAILABLE FROM WWWIECCH )%# HAS NO RESPONSIBILITY FOR THE PLACEMENT AND CONTEXT IN WHICH THE EXTRACTS AND CONTENTS ARE REPRODUCED BY THE AUTHOR NOR IS )%# IN ANY WAY RESPONSIBLE FOR THE OTHER CONTENT OR ACCURACY THEREIN
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)NTERNATIONAL -ARITIME /RGANIZATION WWWIMOORG h2EVISED RECOMMENDATIONS ON PERFORMANCE STANDARDS FOR RADAR EQUIPMENT v 2ESOLUTION -3# )NTERNATIONAL -ARITIME /RGANIZATION ,ONDON )NTERNATIONAL !SSOCIATION OF -ARINE !IDS TO .AVIGATION AND ,IGHTHOUSE !UTHORITIES WWW IALA AISMORG h4ECHNICAL CHARACTERISTICS OF MARITIME RADIO NAVIGATION RADARS v )45 2 2ECOMMENDATION - )NTERNATIONAL 4ELECOMMUNICATION 5NION 'ENEVA )NTERNATIONAL 4ELECOMMUNICATION 5NION WWWITUINT * #RONY h#IVIL MARINE RADAR v IN 4HE 2ADAR (ANDBOOK ST %D - ) 3KOLNIK ED .EW 9ORK -C'RAW (ILL #HAPTER * 2YAN AND # +IRBY h)CEBERG DETECTION PERFORMANCE ANALYSIS v 2EPORT 40 % 4RANSPORTATION $EVELOPMENT #ENTRE 4RANSPORT #ANADA * . "RIGGS h4ARGET DETECTION BY MARINE RADAR v )NSTITUTION OF %LECTRICAL %NGINEERS NOW THE )NSTITUTION OF %NGINEERING AND 4ECHNOLOGY ,ONDON h4HE INTERNATIONAL CONVENTION FOR THE SAFETY OF LIFE AT SEA 3/,!3 v )NTERNATIONAL -ARITIME /RGANIZATION ,ONDON AS AMENDED )NTERNATIONAL %LECTROTECHNICAL #OMMISSION WWWIECCH h-ARITIME NAVIGATION AND RADIOCOMMUNICATION EQUIPMENT AND SYSTEMS3HIPBORNE RADAR v )%# )NTERNATIONAL %LECTROTECHNICAL #OMMISSION 'ENEVA h-ARITIME NAVIGATION AND RADIOCOMMUNICATION EQUIPMENT AND SYSTEMS'ENERAL REQUIREMENTS v )%# )NTERNATIONAL %LECTROTECHNICAL #OMMISSION 'ENEVA h-ARITIME NAVIGATION AND RADIOCOMMUNICATION EQUIPMENT AND SYSTEMS$IGITAL INTERFACES v )%# SERIES )NTERNATIONAL %LECTROTECHNICAL #OMMISSION 'ENEVA h2EGULATIONS REGARDING THE MINIMUM REQUIREMENTS AND TEST CONDITIONS FOR RADAR EQUIPMENT USED FOR 2IVER 2HINE AND INLAND WATERWAYS v #ENTRAL #OMMISSION FOR THE .AVIGATION ON THE 2IVER 2HINE 3TRASBOURG h-ARITIME NAVIGATION AND RADIOCOMMUNICATION EQUIPMENT AND SYSTEMS2ADAR FOR CRAFT NOT IN COMPLIANCE WITH )-/ 3/,!3 #HAPTER 6 v )%# )NTERNATIONAL %LECTROTECHNICAL #OMMISSION 'ENEVA 2 'ANGESKAR AND 'RNLIE h7AVE HEIGHT MEASUREMENTS WITH A STANDARD NAVIGATION SHIP RADAR RESULTS FROM FIELD TRIALS v PRESENTED AT 3IXTH )NTERNATIONAL #ONFERENCE ON 2EMOTE 3ENSING FOR -ARINE AND #OASTAL %NVIRONMENTS #HARLESTON 3OUTH #AROLINA
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*/Ê Ê /" ! BISTATIC RADAR USES ANTENNAS AT SEPARATE SITES FOR TRANSMISSION AND RECEPTION 4HE TRANSMITTER AND RECEIVER CAN BE AND USUALLY ARE LOCATED AT THOSE SITES TO MINIMIZE TRANSMISSION LINE LOSSES )N NEARLY ALL CASES OF BISTATIC OPERATION ANTENNA SEPARATION IS SELECTED TO ACHIEVE SOME OPERATIONAL TECHNICAL OR COST BENEFIT AND IS USUALLY A SIGNIFICANT FRACTION OF THE TARGET RANGE "ISTATIC RADARS HAVE BEEN DESIGNED DEVEL OPED TESTED AND IN SOME CASES DEPLOYED FOR MILITARY COMMERCIAL AND SCIENTIFIC APPLICATIONS 4YPICAL MILITARY APPLICATIONS INCLUDE AIR AND SPACE SURVEILLANCE AND RANGE INSTRUMENTATION #OMMERCIAL APPLICATIONS INCLUDE WIND FIELD MEASUREMENTS AND TRAF FIC SURVEILLANCE 3CIENTIFIC APPLICATIONS INCLUDE MEASUREMENT OF PLANETARY SURFACES AND ATMOSPHERES AND STUDY OF IONOSPHERIC TURBULENCE %XAMPLES ARE GIVEN IN 3ECTION 7HILE THESE EXAMPLES ARE BOTH CREDIBLE AND USEFUL THEY ARE NICHE APPLICATIONS WHEN COMPARED TO THE UBIQUITOUS CAPABILITIES OF MONOSTATIC RADARS WHICH REMAIN THE PRIN CIPAL METHOD FOR RADIO DETECTION AND RANGING "ISTATIC RADARS CAN OPERATE WITH DEDICATED TRANSMITTERS WHICH ARE DESIGNED FOR BISTATIC OPERATION AND CONTROLLED BY THE BISTATIC RADAR OR WITH TRANSMITTERS OF OPPORTUNITY WHICH ARE DESIGNED FOR OTHER PURPOSES BUT FOUND SUITABLE FOR BISTATIC OPER ATION EVEN WHEN NOT CONTROLLED BY THE BISTATIC RADAR 7HEN THE TRANSMITTER OF OPPOR TUNITY IS FROM A MONOSTATIC RADAR THE BISTATIC RADAR IS OFTEN CALLED A HITCHHIKER 7HEN THE TRANSMITTER OF OPPORTUNITY IS FROM A BROADCAST STATION OR COMMUNICATIONS LINK SOURCES OTHER THAN A RADAR THE BISTATIC RADAR HAS BEEN CALLED MANY THINGS INCLUDING PASSIVE RADAR PASSIVE BISTATIC RADAR PASSIVE COHERENT LOCATION PARASITIC RADAR AND PIGGY BACK RADAR 4RANSMITTERS OF OPPORTUNITY IN MILITARY SCENARIOS CAN BE DESIGNATED EITHER COOPERATIVE OR NONCOOPERATIVE WHERE COOPERATIVE DENOTES AN ALLIED OR FRIENDLY TRANSMITTER AND NONCOOPERATIVE DENOTES A HOSTILE OR NEUTRAL TRANSMITTER "ISTATIC TARGET DETECTION USES A PROCESS SIMILAR TO THAT OF A MONOSTATIC RADAR WHERE THE TARGET IS ILLUMINATED BY A TRANSMITTER AND TARGET ECHOES ARE RECEIVED DETECTED AND PROCESSED BY A RECEIVER 7HEN OPERATING WITH TRANSMITTERS USING #7 OR HIGH DUTY CYCLE WAVEFORMS A BISTATIC RECEIVER MAY NEED TO AUGMENT ITS SPA TIAL ISOLATION WITH SPATIAL ANDOR SPECTRAL CANCELLATION TO REDUCE THE TRANSMITTERS DIRECT PATH FEED THROUGH TO ACCEPTABLE LEVELS 4HE BISTATIC RADAR CAN ALSO USE A PORTION OF THE RESIDUAL OR UNCANCELLED DIRECT PATH TRANSMIT SIGNAL AS A REFERENCE IN A CORRELATION RECEIVER WHICH CROSS CORRELATES THE RECEIVED AND TRANSMITTED SIGNALS EMULATING MATCHED FILTER OPERATION Óΰ£
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"ISTATIC TARGET LOCATION USES A PROCESS DIFFERENT FROM THAT OF A MONOSTATIC RADAR )N A TYPICAL IMPLEMENTATION THE BISTATIC RADAR MEASURES A THE TRANSMITTER TO TARGET TO RECEIVER PROPAGATION TIME CONVERTED TO A TRANSMITTER TO TARGET PLUS TARGET TO RECEIVER RANGE SUM B THE TARGET DIRECTION OF ARRIVAL $/! FROM THE RECEIVER AND C THE TRANSMITTER TO RECEIVER DISTANCE OR BASELINE TO SOLVE THE TRANSMITTER TARGET RECEIVER TRIANGLE CALLED THE BISTATIC TRIANGLE 4HIS TRIANGLE LOCATES THE TARGET USUALLY IN TERMS OF A RANGE AND ANGLE REFERENCED TO THE RECEIVE SITE /THER LOCATION SCHEMES ARE GIVEN IN 3ECTION 7HEN SEPARATE TRANSMIT AND RECEIVE ANTENNAS ARE AT A SINGLE SITE AS IS COMMON IN #7 RADARS THE RADAR HAS CHARACTERISTICS OF A MONOSTATIC RADAR AND THE TERM BISTATIC IS NOT USED TO DESCRIBE SUCH A SYSTEM )N SPECIAL CASES THE ANTENNAS CAN BE AT SEPA RATE SITES AND THE RADAR IS STILL CONSIDERED TO OPERATE MONOSTATICALLY &OR EXAMPLE AN OVER THE HORIZON /4( RADAR CAN HAVE A SITE SEPARATION OF KM OR MORE TO ACHIEVE ADEQUATE TRANSMIT SIGNAL ISOLATION "UT THAT SEPARATION IS SMALL COMPARED TO THE TARGET RANGE OF THOUSANDS OF KILOMETERS AND THE RADAR AGAIN OPERATES WITH MONO STATIC CHARACTERISTICS ! VARIATION OF THE BISTATIC RADAR IS THE MULTISTATIC RADAR WHICH USES MULTIPLE ANTEN NAS AT SEPARATE LOCATIONS ONE ANTENNA FOR TRANSMISSION AND MULTIPLE ANTENNASEACH AT A DIFFERENT LOCATIONFOR RECEPTION OR VICE VERSA !GAIN TRANSMITTERS OR RECEIVERS ARE USUALLY SITED WITH THE ANTENNAS 4ARGET DETECTION IS DONE BISTATICALLY WITH EACH TRANSMIT RECEIVE PAIR PERFORMING INDEPENDENT DETECTIONS WITHIN A SURVEILLANCE REGION COMMON TO ALL SUCH PAIRS 4ARGET LOCATION TYPICALLY MEASURES THE BASELINE AND TAKES SIMULTANEOUS RANGE SUM MEASUREMENTS FROM MULTIPLE TRANSMITTER RECEIVER PAIRS WHICH ARE PLOTTED AS ELLIPSES WITH A TRANSMITTER RECEIVER PAIR AT EACH ELLIPSE FOCI 4HE INTERSEC TION OF THESE ELLIPSES OR CONSTANT RANGE SUM CONTOURS LOCATE THE TARGET )T IS SIMILAR TO MULTILATERATION BECAUSE ONLY RANGE MEASUREMENTS ARE USED TO LOCATE THE TARGET
! MULTISTATIC RADAR CAN ALSO USE TRIANGULATION FOR TARGET LOCATION BY TAKING SIMUL TANEOUS TARGET $/! MEASUREMENTS FROM MULTIPLE RECEIVE SITES AT KNOWN LOCATIONS )T IS USED BY 30!352 AS A BRUTE FORCE SATELLITE LOCATION TECHNIQUE (OWEVER BECAUSE OF THE LARGE APERTURE SIZES OR ARRAY LENGTHS REQUIRED FOR SUFFICIENTLY ACCU RATE $/! MEASUREMENTS AT USEFUL RANGES TRIANGULATION IS SELDOM CONSIDERED FOR OTHER APPLICATIONS #ONCEPTS DATA AND EXPRESSIONS DEVELOPED FOR BISTATIC RADARS OFTEN APPLY TO MULTI STATIC RADARS FOR EXAMPLE THE RANGE EQUATION TARGET DOPPLER TARGET RADAR CROSS SECTION AND SURFACE CLUTTER 4HUS THE REMAINDER OF THIS CHAPTER WILL CONCENTRATE ON THE BISTATIC RADAR TOPIC DEVELOPING MULTISTATIC EXCURSIONS AND DEVIATIONS ONLY WHEN NECESSARY 0ASSIVE RECEIVING SYSTEMS OR ELECTRONIC SUPPORT MEASURE %3- SYSTEMS OFTEN USE TWO OR MORE RECEIVING SITES 4HEIR PURPOSE IS TYPICALLY TO DETECT IDENTIFY AND LOCATE TRANSMITTERS SUCH AS THOSE FROM MONOSTATIC RADARS 4HEY ARE ALSO CALLED EMITTER LOCATORS 4ARGET LOCATION IS BY MEANS OF COMBINED ANGLE MEASUREMENTS FROM EACH SITE EG TRIANGULATION OR TIME DIFFERENCE OF ARRIVAL ANDOR DIFFERENTIAL DOPPLER MEASURE MENTS BETWEEN SITES EG MULTILATERATION 4HESE SYSTEMS USUALLY ARE NOT DESIGNED TO DETECT AND PROCESS THE ECHOES FROM TARGETS ILLUMINATED BY THE TRANSMITTER 4HEY CAN HOWEVER BE USED BY A BISTATIC HITCHHIKER TO IDENTIFY AND LOCATE A SUITABLE TRANSMITTER 4HUS ALTHOUGH THEY HAVE MANY REQUIREMENTS AND CHARACTERISTICS COMMON TO MULTI STATIC RADARS THEY ARE NOT RADARS AND WILL NOT BE CONSIDERED HERE
4HE FOREGOING DESCRIBES MULTISTATIC OPERATION THAT COMBINES DATA NONCOHERENTLY #OHERENT DATA COMBINING IS ALSO POSSIBLE WHERE FOR EXAMPLE IN PHASE AND QUADRATURE DATA FROM EACH RECEIVE SITE IS COMBINED TO FORM A LARGE RECEIVE APERTURE %XAMPLES INCLUDE THINNED RANDOM DISTORTED AND DISTRIBUTED ARRAYS n INTERFEROMETRIC RADARS AND THE RADIO CAMERA 4HIS SUBJECT IS TREATED FURTHER IN 7ILLIS
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4HE FOREGOING DEFINITIONS ARE BROAD AND TRADITIONALn BUT ARE BY NO MEANS UNI FORMLY ESTABLISHED IN THE LITERATURE 4ERMS SUCH AS QUASI BISTATIC QUASI MONOSTATIC PSEUDO MONOSTATIC TRISTATIC POLYSTATIC REAL MULTISTATIC MULTI BISTATIC AND NETTED BISTATIC HAVE ALSO BEEN USEDn 4HEY ARE USUALLY SPECIAL CASES OF THE BROAD DEFINI TIONS GIVEN ABOVE 4HE TERM PSEUDO MONOSTATIC WILL BE USED TO CHARACTERIZE BISTATIC GEOMETRIES THAT APPROXIMATE MONOSTATIC OPERATION
ÓΰÓÊ "", / Ê-9-/ ! TWO DIMENSIONAL NORTH REFERENCED COORDINATE SYSTEM IS USED THROUGHOUT THIS CHAPTER &IGURE SHOWS THE COORDINATE SYSTEM AND PARAMETERS DEFINING BISTATIC RADAR OPERA TION IN THE X Y PLANE ALSO CALLED THE BISTATIC PLANE 4HE BISTATIC TRIANGLE LIES IN THE BISTATIC PLANE 4HE DISTANCE , BETWEEN THE TRANSMITTER AND THE RECEIVER IS CALLED THE BASE LINE RANGE OR SIMPLY THE BASELINE 24 IS THE RANGE BETWEEN TRANSMITTER AND TARGET AND 22 IS THE RANGE BETWEEN RECEIVER AND TARGET 4HE ANGLES P4 AND P2 ARE RESPECTIVELY THE TRANS MITTER AND RECEIVER LOOK ANGLES WHICH ARE TAKEN AS POSITIVE WHEN MEASURED CLOCKWISE FROM NORTH 4HEY ARE ALSO CALLED DIRECTION OF ARRIVAL $/! ANGLE OF ARRIVAL !/! OR LINE OF SIGHT ,/3 4HE BISTATIC ANGLE A P4 P2 IS THE ANGLE BETWEEN THE TRANSMITTER AND RECEIVER WITH THE VERTEX AT THE TARGET )T IS ALSO CALLED THE CUT ANGLE OR THE SCATTERING ANGLE )T IS CONVENIENT TO USE A IN CALCULATIONS OF TARGET RELATED PARAMETERS AND P4 AND P2 IN CALCULATIONS OF TRANSMITTER AND RECEIVER RELATED PARAMETERS 4HE TRANSMITTER TO TARGET TO RECEIVER RANGE MEASURED BY A BISTATIC RADAR IS THE RANGE SUM 24 22 -ETHODS FOR MEASURING THIS SUM ARE GIVEN IN 3ECTION 4HE RANGE SUM LOCATES THE TARGET SOMEWHERE ON THE SURFACE OF AN ELLIPSOID WHOSE FOCI ARE THE TRANSMITTER AND RECEIVER SITES 4HE INTERSECTION OF THE BISTATIC PLANE AND THIS ELLIPSOID
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PRODUCES THE FAMILIAR ELLIPSES OF CONSTANT RANGE SUM OR ISORANGE CONTOURS ! USEFUL RELATIONSHIP IS THAT THE BISECTOR OF THE BISTATIC ANGLE IS ORTHOGONAL TO THE TANGENT OF THAT ELLIPSE AT THE TARGET 4HE TANGENT IS OFTEN A GOOD APPROXIMATION TO AN ISORANGE CONTOUR WITHIN THE AREA COMMON TO THE TRANSMIT AND RECEIVE BEAMS 7HEN THE BISTATIC RADARS RECEIVING ANTENNA IS A PHASED ARRAY AND THE ARRAY NORMAL IS ALSO NORMAL TO THE BASELINE P2 IS MEASURED DIRECTLY BY THE ANTENNA IN ANY BISTATIC PLANE 4HIS FORTUITOUS SITUATION IS CAUSED BY CONIC DISTORTION WHICH IS INHERENT IN ANY PHASED ARRAY ANTENNA (OWEVER WHEN THE ARRAY NORMAL IS NOT NORMAL TO THE BASELINE OR WHEN THE RECEIVING ANTENNA IS MECHANICALLY STEERED OR SCANNED P2 IS NOT MEASURED DIRECTLY /FTEN $/! MEASUREMENTS ARE TAKEN INOR CONVERTED TOAZIMUTH AND ELEVA TION ANGLES REFERENCED TO AN X Y Z COORDINATE SYSTEM CENTERED AT THE RECEIVE SITE WHERE Z IS CO LINEAR WITH THE LOCAL VERTICAL #ONVERSION BETWEEN A NORTH COORDINATE SYSTEM AND AN X Y Z COORDINATE SYSTEM IS GIVEN IN 3ECTION OF 7ILLIS /THER COORDINATE SYSTEMS INCLUDING THREE DIMENSIONAL SYSTEMS HAVE BEEN USED TO DEFINE BISTATIC RADAR OPERATION n ! POLAR COORDINATE SYSTEM IS ALSO SHOWN IN &IGURE 4HE R P COORDINATES ARE LOCATED ON THE BISTATIC PLANE WITH ORIGIN AT THE MIDPOINT OF THE BASELINE )T IS USEFUL FOR PLOTTING OVALS OF #ASSINI SEE 3ECTION AND IS DETAILED IN 7ILLIS /N OCCASION THE INCLUDED ANGLES P4g AND P2g ARE USED TO DEFINE TRANSMITTER AND RECEIVER LOOK ANGLES IN THE BISTATIC TRIANGLE SUCH THAT P4g P2g A )N THIS CASE P4g n P4 AND P2g P2 CAN BE USED TO TRANSFORM NORTH REFERENCED EQUATIONS INTO INCLUDED ANGLE EQUATIONS 0LOTS OF BISTATIC CLUTTER DATA USE A SEPARATE AND QUITE ARCANE COORDINATE SYSTEM WHICH IS DEFINED IN 3ECTION 'EOMETRY IS A PRINCIPAL FACTOR DISTINGUISHING BISTATIC FROM MONOSTATIC RADAR OPERA TION )N EVALUATING BISTATIC RADAR OPERATION IT IS USEFUL TO START WITH A GEOMETRY INVARIANT PERFORMANCE MEASURE WHICH IS OBTAINED BY SETTING , OR 24 22 AND A 4HE RESULT IS DEFINED AS AN EQUIVALENT MONOSTATIC RANGE OR BENCHMARK RANGE AND IS DETAILED IN 3ECTION )T IS ALSO USEFUL AS A SANITY CHECK BECAUSE AT THESE LIMITS ALL BISTATIC RADAR EQUATIONS MUST REDUCE TO AN EQUIVALENT MONOSTATIC EQUATION
ÓΰÎÊ -// Ê, ,Ê +1/" "ENCHMARK 2ANGE #ONCEPT 5NLIKE A MONOSTATIC RADAR THE RANGE PERFORMANCE OF A BISTATIC RADAR IS A FUNCTION OF THE GEOMETRY SPECIFICALLY THE BASELINE RANGE , AND AN ANTENNA LOOK ANGLE EITHER P4 OR P2 7HEN FACTORS SUCH A DIFFRACTION REFRACTION MULTIPATH AND MASKING ARE ABSENT OR CAN BE IGNORED BISTATIC RANGE AS A FUNCTION OF THESE VARIABLES CAN BE PLOTTED ON THE BISTATIC PLANE USING AN OVAL OF #ASSINI !N OVAL OF #ASSINI IS THE LOCUS OF THE VERTEX OF A TRIANGLE WHEN THE PRODUCT OF THE SIDES ADJACENT TO THE VERTEX IS CONSTANT AND THE LENGTH OF THE OPPOSITE SIDE IS FIXED 7HEN APPLIED TO THE BISTATIC TRIANGLE SHOWN IN &IGURE THE VERTEX IS AT THE TARGET 24 AND 22 ARE THE SIDES ADJACENT TO THE VERTEX AND THE BASELINE , IS THE LENGTH OF THE FIXED OPPOSITE SIDE 4RADITIONALLY OVALS OF #ASSINI ARE DRAWN AS CONTOURS OF A CONSTANT RECEIVED SIGNAL POWER OR A RECEIVED SIGNAL TO NOISE RATIO AROUND A FIXED BASELINE RANGE , !LTHOUGH THESE SIGNAL DEPENDENT CONTOURS PROVIDE A SENSE OF BISTATIC RADAR PERFORMANCE THEY DO NOT SHOW MAXIMUMMINIMUM DETECTION RANGES AND COVERAGE FOR VARIABLE BASE LINES ALL PARAMETERS OF OPERATIONAL INTEREST 4O REMEDY THIS PROBLEM THE CONCEPT OF A BISTATIC BENCHMARK RANGE OR MORE SIMPLY BENCHMARK IS INTRODUCED )T IS ESTABLISHED AS FOLLOWS &IRST THE BISTATIC RADAR RANGE EQUATION IS DERIVED IN A MANNER COMPLETELY
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ANALOGOUS TO THAT FOR A MONOSTATIC RADAR 4HE EQUATION IS THEN SOLVED FOR THE BISTATIC MAXIMUM RANGE PRODUCT 24 22 MAX .EXT AN EQUIVALENT MONOSTATIC MAXIMUM RANGE 2- MAX IS DEFINED OMITTING THE MAX SUBSCRIPT FOR CONVENIENCE AS SHOWN HERE 2- 24 22
4HIS EQUIVALENT MONOSTATIC MAXIMUM RANGE ALSO KNOWN AS THE GEOMETRIC MEAN RANGE REPRESENTS PERFORMANCE OF THE BISTATIC RADAR WHEN TRANSMITTER AND RECEIVER ARE CO LOCATED IE WHEN , )T IS DEFINED AS THE BISTATIC RADARS BENCHMARK RANGE 3INCE THIS BENCHMARK IS GEOMETRY INVARIANT IT BECOMES USEFUL WHEN COMPARING BISTATIC TO MONOSTATIC RANGE PERFORMANCE &INALLY AN OVAL OF #ASSINI IS ESTABLISHED AS A FUNCTION OF THE BASELINE RANGE , NORMALIZED TO THE BENCHMARK RANGE 2- "ASED ON THIS OVAL MAXIMUM AND MINIMUM DETECTION RANGES AND THE COVERAGE AREA ARE CALCULATED ALL AS A FUNCTION OF 2- 4HIS PROCEDURE IS ALSO USED TO DEFINE BISTATIC OPERATING REGIONS 2ANGE %QUATION 4HE RADAR RANGE EQUATION FOR #7 OR COHERENT PULSE RADARS IS MODIFIED FOR BISTATIC OPERATION AND THEN SOLVED FOR THE BISTATIC MAXIMUM RANGE PRODUCT 24 22 MAX
WHERE
§ 0 T ' ' L R " &4 &2 ¶ 24 22 MAX ¨ AV O 4 2 · © P K 4O &N % . O ,4 ,2 ¸
24 4RANSMITTER TO TARGET RANGE M 22 2ECEIVER TO TARGET RANGE M 0AV 4RANSMITTED AVERAGE POWER 7 TO 3IGNAL OBSERVATION OR INTEGRATION TIME '4 4RANSMITTING ANTENNA POWER GAIN '2 2ECEIVING ANTENNA POWER GAIN K 7AVELENGTH M R" "ISTATIC RADAR CROSS SECTION M &4 0ATTERN PROPAGATION FACTOR FOR TRANSMITTER TO TARGET PATH &2 0ATTERN PROPAGATION FACTOR FOR RECEIVER TO TARGET PATH K "OLTZMANNS CONSTANT ; ¾ n *+= 4O 3TANDARD TEMPERATURE ; += &N 2ECEIVER NOISE FIGURE %.O 2ECEIVED ENERGY TO RECEIVER NOISE SPECTRAL DENSITY REQUIRED FOR DETECTION ,4 4RANSMITTING SYSTEM LOSSES ,2 2ECEIVING SYSTEM LOSSES
%QUATION ASSUMES THAT A MATCHED FILTER OR AN EQUIVALENT MATCHED FILTER SUCH AS A CROSS CORRELATOR IS USED ON RECEPTION %QUATION IS RELATED TO THE CORRESPONDING MONOSTATIC MAXIMUM RANGE EQUATION BY 24 22 2- AND R- R" WHERE R- IS THE MONOSTATIC RADAR CROSS SECTION &OR PULSED RADAR OPERATION TO N FP WHERE N IS THE NUMBER OF PULSES INTEGRATED AND FP IS THE PULSE REPETITION FREQUENCY !LSO THE SIGNAL TO NOISE RATIO REQUIRED FOR DETECTION 3. REQ %.O WHEN "S y WHERE " IS THE RECEIVER BANDWIDTH AND S IS THE PULSE WIDTH 4HE SIGNAL PROCESSING TIME TO IS SOMETIMES SET BY THE AMOUNT OF DOPPLER SPREAD ING OR VELOCITY WALK $FD GENERATED BY A MOVING TARGET 3PECIFICALLY $FD TO "N
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WHERE "N IS THE NOISE BANDWIDTH OF RECEIVERS PREDETECTION FILTER )N THE MONOSTATIC CASE DOPPLER SPREADING IS
$FD M ;AR K=
WHERE AR IS THE RADIAL COMPONENT OF TARGET ACCELERATION %QUATION ALSO APPLIES TO THE BISTATIC CASE AT SMALL BISTATIC ANGLES A PARTICULARLY IN AN OVER THE SHOULDER OPERATION WHERE THE TARGET LIES NEAR THE BASELINE EXTENDED BEYOND EITHER THE RECEIVER OR THE TRANSMITTER CALLED THE EXTENDED BASELINE (OWEVER FOR LARGER ATHE GENERAL CASETHE RADIAL COMPONENT WHICH IS ALIGNED WITH THE BISECTOR OF THE BISTATIC ANGLE WILL BE REDUCED ! RULE OF THUMB FOR THESE LARGE A CONDITIONS IS
$FD B ;AR K=
%QUATION IS USED TO SET TO AND HENCE THE NOISE BANDWIDTH OF RECEIVERS PREDETEC TION FILTER !N 3INCE $FD B $FD M THE CONSTRAINT ON BISTATIC SIGNAL PROCESSING TIME IS SLIGHTLY LESS THAN THE EQUIVALENT MONOSTATIC TIME !S IN THE MONOSTATIC EQUATION THE TRANSMITTING AND RECEIVING PATTERN PROPAGATION FACTORS &4 AND &2 EACH CONSIST OF TWO TERMS THE PROPAGATION FACTORS &g4 AND &g2 AND THE ANTENNA PATTERN FACTORS F4 AND F2 RESPECTIVELY 4HE ANTENNA PATTERN FACTORS ARE THE RELATIVE STRENGTH OF THE FREE SPACE FIELD RADIATED BY THE TRANSMITTING AND RECEIVING ANTENNAS AS A FUNCTION OF THEIR POINTING ANGLES 4HESE FACTORS ARE APPLIED WHENEVER THE TARGET IS NOT AT THE PEAK OF A BEAM 0ROPAGATION FACTORS CUSTOMARILY INCLUDE THE EFFECTS OF MULTIPATH DIFFRACTION AND REFRACTION WITH ATMOSPHERIC ABSORPTION EFFECTS INCLUDED IN THE LOSS TERMS !S WITH A MONOSTATIC RADAR BISTATIC RADAR PROPAGATION REQUIRES A SUITABLE PATH FROM THE TRANSMIT TER TO THE TARGET AND THE TARGET TO THE RECEIVER )N CONTRAST TO A MONOSTATIC RADAR HOWEVER PROPAGATION EFFECTS CAN BE SIGNIFICANTLY DIFFERENT OVER THE TWO BISTATIC PATHS AND MUST BE TREATED SEPARATELY -ULTIPATH IS THE PRIMARY EXAMPLE WHERE THE TARGET CAN BE IN A MULTIPATH LOBE ON ONE PATH AND A MULTIPATH NULL ON THE OTHER DEPENDING ON ANTENNA AND TARGET ALTITUDE AND TERRAIN CONDITIONS 7HEN A CORRELATION RECEIVER USES THE DEMODULATED DIRECT PATH 2& SIGNAL AS ITS REFER ENCE THAT SIGNAL IS SUBJECTED TO INTERFERENCE MULTIPATH AND 2&) WHICH IS DIFFERENT FROM INTERFERENCE AFFECTING THE TARGET ECHO PATH )F THE CORRELATOR OPERATES IN ITS LINEAR REGION THE ECHO PLUS ITS INTERFERENCE CONVOLVED WITH THE REFERENCE PLUS ITS INTERFERENCE PRODUCES THE DESIRED ECHO WITH FULL MATCHED FILTER GAIN PLUS INTERFERENCE WITH GAIN REDUCED BY MISMATCH 4HESE SIGNALS ADD VECTORIALLY TO MODIFY THE PATTERN PROPAGATION FACTOR (OWEVER IF THE CORRELATOR OPERATES IN ITS NONLINEAR REGION WHICH CAN FREQUENTLY HAPPEN CROSS PRODUCTS ARE GENERATED WHICH REDUCE THE ECHOS MATCHED FILTER GAIN 4HE AMOUNT OF LOSS DEPENDS ON THE MAGNITUDE OF THE INTERFERENCE AND IS ACCOUNTED FOR IN THE SIGNAL PROCESSING LOSS TERM /VALS OF #ASSINI 4HE FREE SPACE MAXIMUM DETECTION CONTOUR OF A BISTATIC RADARS BENCHMARK RANGE IS A CIRCLE OF RADIUS 2- JUST AS IN THE MONOSTATIC CASE 3UCH A CIRCLE ASSUMES CONSTANT RADAR CROSS SECTION AND PATTERN PROPAGATION FACTORS WHICH ARE SCENARIO AND GEOMETRY DEPENDENT &OR THE GENERAL BISTATIC CASE WHERE , THE FREE SPACE MAXIMUM DETECTION CONTOUR BECOMES THE FAMILIAR OVAL OF #ASSINI AGAIN
)N THE FIRST CASE THE TRANSMITTER ILLUMINATES THE TARGET OVER THE RECEIVERS SHOULDER IN THE SECOND CASE THE RECEIVER VIEWS THE TARGET OVER THE TRANSMITTERS SHOULDER
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&)'52% .ORMALIZED OVALS OF #ASSINI LYING IN THE BISTATIC PLANE THE PLANE CONTAINING TRANSMITTER RECEIVER AND TARGET #OURTESY 3CI4ECH )NC
WITH THE MONOSTATIC CAVEATS CITED ABOVE 4HUS THIS OVAL OR OVALS PROVIDES A CONVENIENTBUT AT TIMES OVER SIMPLIFIEDVIEW OF BISTATIC RANGE COVERAGE AND MUST BE USED WITH CARE !N ADDITIONAL BISTATIC CAVEAT IS NECESSARY 7HEN THE TARGET IS ON OR NEAR THE BASE LINE IE LOCATED BETWEEN RECEIVER AND TRANSMITTER WHERE THE BISTATIC ANGLE A l A COMPLETELY DIFFERENT ENVIRONMENT IS GENERATED FORWARD SCATTER FROM BOTH TARGET AND CLUTTER )N THIS CASE THE TARGET RADAR CROSS SECTION 2#3 AND CLUTTER SCATTERING COEF FICIENT RO ARE GREATLY ENHANCED WHEREAS RANGE AND DOPPLER MEASUREMENTS ARE GREATLY DEGRADED /FTEN NORMAL BISTATIC OPERATION EXCLUDES THIS REGION SO THAT A WEDGE WITH THE APEX AT THE RECEIVER AND DIRECTED AT THE TRANSMITTER IS EXCISED FROM THE OVAL $ETAILS ARE GIVEN IN 7ILLIS &IGURE SHOWS FOUR CASES OF OVALS OF #ASSINI NORMALIZED TO THE BENCHMARK RANGE A BENCHMARK , B ONE OVAL , 2- C LEMNISCATE , 2- AND D TWO OVALS , 2- )N ALL CASES THE TRANSMITTER IS LOCATED AT THE LEFT OVAL FOCUS 4HE RECEIVER IS LOCATED AT THE RIGHT OVAL FOCUS /THER TERMS AND SYMBOLS ARE DEFINED IN THE KEY SHOWN WITH &IGURE 4ABLE LISTS EXPRESSIONS FOR CALCULATING OVAL AREA AND MAXIMUMMINIMUM RECEIVER DETECTION RANGES FOR THESE FOUR CASES AGAIN REFERENCED TO THE BENCHMARK RANGE 2- &OR &IGURE D WHEN , 2- THE OVALS CAN CONVENIENTLY BE APPROXIMATED AS CIRCLES WITH RADIUS 22AV ^ 2-, AND CORRESPONDING AREA O 2-, %XPRESSIONS FOR
4HE ONE OVAL AREA FORMULA IS DERIVED FROM %Q $A IN 7ILLIS )T IS ALSO USED FOR CALCULATING THE LEMNISCATE AREA &ORMULAS FOR THE TWO OVAL AREA ARE DERIVED FROM %Q $A IN 7ILLIS -ORE TERMS IN THESE SERIES CAN BE USED IF GREATER ACCURACY IS REQUIRED
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RECEIVER AND TRANSMITTER RANGES ON THE OPPOSITE OVAL ARE READILY CALCULATED THROUGH MIRROR IMAGE SYMMETRY !LSO NOTE THAT THE AREA OF EVERY BISTATIC OVAL IS ALWAYS LESS THAN THE MONOSTATIC CIRCLE 4HE EXPRESSIONS IN 4ABLE CAN ALSO BE USED TO ASSESS FIRST ORDER BISTATIC RADAR LINE OF SIGHT ,/3 CONSTRAINTS WHERE THE ,/3 IS DEFINED AS A LINE BETWEEN TRANSMIT AND RECEIVE ANTENNAS TANGENT TO THE %ARTHS SURFACE 3PECIFICALLY FOR A GIVEN TARGET TRANSMITTER AND RECEIVER ALTITUDES THE TARGET MUST SIMULTANEOUSLY BE WITHIN ,/3 TO BOTH THE TRANSMITTER AND RECEIVER SITES &OR A SMOOTH %ARTH MODEL THE ,/3 RANGE R2 BETWEEN A RECEIVE ANTENNA OF ALTITUDE H2 AND TARGET OF ALTITUDE HT IS
R2 H2 HT
WHERE ALL UNITS ARE IN KILOMETERS 3IMILARLY THE ,/3 RANGE R4 BETWEEN A TRANSMIT ANTENNA OF ALTITUDE H4 AND TARGET OF ALTITUDE HT IS
R4 H4 HT
4HUS TO PREVENT ,/3 TRUNCATION OF THE OVALS R2 q 22MAX AND R4 q 24MAX 4HESE EXPRESSIONS IGNORE BOTH DIFFRACTION AND MULTIPATH WHICH CAN SIGNIFICANTLY ALTER THESE RANGES SO THEY MUST BE CONSIDERED FIRST ORDER APPROXIMATIONS ! TYPICAL TASK FOR BISTATIC AIR SURVEILLANCE IS TO SELECT A BASELINE , SO THAT A RECEIVER WITH ANTENNA ALTITUDE H2 WILL MATCH EXISTING ,/3 COVERAGE OF A TRANSMITTER WITH ANTENNA ALTITUDE H4 &OR THE WORST CASE OVER THE SHOULDER GEOMETRY THE REQUIREMENT WOULD BE TO MATCH ,/3 COVERAGE ON THE EXTENDED BASELINE R4 R2 , SO THAT
, H4 H2
&OR EXAMPLE WHEN H4 KM AND H2 KM , KM WHICH FROM %Q AND WILL PROVIDE ,/3 TO AN M ALTITUDE TARGET FLYING ABOVE THE EXTENDED BASELINE KM FROM THE RECEIVER AND KM FROM THE TRANSMITTER "ASELINES GREATER THAN KM CAN POSE SEVERE TARGET ,/3 PROBLEMS &OR EXAMPLE IF , KM AND H4 KM THEN FROM %Q THE TRANSMITTER WOULD ONLY ILLUMINATE A TARGET FLYING DIRECTLY ABOVE THE RECEIVER AT AN ALTITUDE HT KM 4HUS THE TARGET COULD READILY UNDER FLY THE ILLUMINATION AND LOW ALTITUDE AIR SURVEILLANCE CAPABILITY IS LOST !S A CONSEQUENCE THE BISTATIC RADAR MUST EITHER EMPLOY A GREATLY ELEVATED ^ KM TRANS MITTER AT THESE LONG BASELINES OR OPERATE WITH SHORTER BASELINES TO ACHIEVE ACCEPTABLE LOW ALTITUDE SURVEILLANCE COVERAGE .OTE THAT THE TWO OVAL CASE CAN ALSO REQUIRE A VERY HIGH ALTITUDE FOR THE SITE LOCATED IN THE OVAL NOT UNDER SURVEILLANCESO HIGH THAT THE SITE MUST OFTEN BECOME AIRBORNE &INALLY THE TRANSMIT ANTENNA WILL BE IN DIRECT ,/3 OF THE RECEIVE ANTENNA WHEN , a R4 R2 WITH HT SO THAT AGAIN WITH ALL UNITS IN KILOMETERS
, a H4 H2
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)F %Q IS SATISFIED EXTRAORDINARY MEASURES ARE USUALLY REQUIRED TO SUPPRESS THE DIRECT PATH SIGNAL TO A LEVEL WHERE TARGETS CAN BE DETECTED AS OUTLINED IN 3ECTION
Óΰ{Ê ** /" /VALS OF #ASSINI CAN BE USED TO DEFINE THREE OPERATING REGIONS FOR A BISTATIC RADAR CO SITE RECEIVER CENTERED AND TRANSMITTER CENTERED #O SITE CORRESPONDS TO &IGURE B RECEIVER CENTERED TO THE RIGHT OVAL IN &IGURE D AND TRANSMITTER CENTERED TO THE LEFT OVAL IN &IGURE D 4HE TYPE OF TRANSMITTERDEDICATED COOPERATIVE OR NON COOPERATIVECOMPLETES THE TAXONOMY ! DEDICATED TRANSMITTER IS DESIGNED AND CONTROLLED BY THE BISTATIC OR MULTISTATIC RADAR ANALOGOUS TO A MONOSTATIC RADAR "OTH COOPERATIVE AND NONCOOPERATIVE TRANSMITTERS ARE TRANSMITTERS OF OPPORTUNITY DESIGNED FOR OTHER FUNCTIONS INCLUDING RADAR AND COMMUNICATIONS BUT FOUND SUITABLE FOR BISTATIC OPERATION 4HE COOPERATIVE TRANSMITTER IS CONTROLLED BY ALLIED OR FRIENDLY FORCES THE NONCOOPERATIVE TRANSMITTER BY HOSTILE OR NEUTRAL FORCES 4ABLE SUM MARIZES BISTATIC RADAR APPLICATIONS IN THESE OPERATING REGIONS
%NTRIES IN THE DEDICATED TRANSMITTERCO SITE CATEGORY REPRESENT A COMPLETE BISTATIC RADAR SUITERADARS WITH ALL COMPONENTS INCLUDING THE TRANSMITTER DESIGNED FOR BISTATIC OPERATION -ANY OF THESE SYSTEMS WERE DEVELOPED TESTED OR DEPLOYED PRIOR TO %XAMPLES ARE THE &RENCH 5332 AND *APANESE FORWARD SCATTER FENCES USED IN 77)) THE !.&03 FOR AIR DEFENSE GAP FILLING 0!2!$/0 AND -)$/0 RANGE INSTRUMENTATION TRACKERS 30!352 FOR SPACE SURVEILLANCE AND 3ANCTUARY FOR AIR DEFENSE 4HE "27, FOR ARTILLERY MORTAR AND ROCKET LOCATION THE 2USSIAN 3TRUNA FORWARD SCATTER FENCE n AND THE &RENCH 'RAVES FOR SPACE SURVEILLANCE WERE LATER DEVELOPMENTS /MITTED ENTRIES IN THE DEDICATED TRANSMITTER COLUMN FOR OPERATION IN THE RECEIVER AND TRANSMITTER CENTERED OVALS AT LARGE BASELINE RANGES ARE DICTATED BY OPERATIONS AND COST BOTH COOPERATIVE AND NONCOOPERATIVE TRANSMITTERS OF OPPORTUNITY ARE OFTEN PRESENT AND CAPABLE OF SUPPORTING BISTATIC OPERATION IN THESE SMALL AREAS OF INTEREST
4!",% "ISTATIC 2ADAR !PPLICATIONS 2ECEIVER /PERATING 2EGIONS
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s !IR SURVEILLANCE s 2ANGE INSTRUMENTATION s 3ATELLITE TRACKING s )NTRUSION DETECTION
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! MULTISTATIC RADAR WITH ITS REQUIREMENT FOR COMMON SPATIAL COVERAGE NEARLY ALWAYS OPERATES IN THE CO SITE REGION
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&URTHERMORE THIS APPROACH IS LESS COSTLY AND WHEN EXPLOITING NONCOOPERATIVE TRANS MITTERS MORE COVERT AND LESS RISKY THAN USING A DEDICATED TRANSMITTER #ONSEQUENTLY DEDICATED TRANSMITTERS ARE NOT USUALLY CONSIDERED FOR THESE APPLICATIONS %NTRIES IN THE COOPERATIVE AND NONCOOPERATIVE TRANSMITTER COLUMNS ARE CALLED HITCHHIKERS WHEN THE TRANSMITTER IS A MONOSTATIC RADAR 7HEN THE TRANSMITTER IS FROM A COMMUNICATIONS OR BROADCAST SYSTEM IE NOT FROM A RADAR ENTRIES ARE CALLED A PASSIVE BISTATIC RADAR 0"2 %XAMPLES OF A HITCHHIKER OPERATING WITH A COOPERATIVE TRANSMITTER IN THE CO SITE REGION ARE THE -ULTISTATIC -EASUREMENT 3YSTEM OPERATING WITH 42!$%8 FOR INCREAS ING BALLISTIC MISSILE REENTRY MEASUREMENT ACCURACY AND THE COMMERCIAL "INET )NC BISTATIC RECEIVER OPERATING WITH MONOSTATIC DOPPLER WEATHER RADARS TO MEASURE THREE DIMENSIONAL VECTOR WIND FIELDS &IGURE IS A BLOCK DIAGRAM OF THE "INET )NC DEVELOPED PROTOTYPE %XAMPLES OF HITCHHIKERS OPERATING WITH A COOPERATIVE TRANSMITTER IN THE RECEIVER CENTERED REGION ARE THE #OVIN 2EST PROGRAM OPERATING WITH THE SPACE SHUTTLE RADAR FOR SYNTHETIC APERTURE RADAR 3!2 GROUND MAPPING THE 4")2$ PROGRAM OPERATING WITH *OINT 34!23 FOR SILENT AIR TO GROUND ATTACK VIA FORWARD LOOKING BISTATIC 3!2 AND THE "!# PROGRAM OPERATING WITH !7!#3 FOR ALERTING AND CUEING SHORT RANGE MOBILE AIR DEFENSE SYSTEMS
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(ITCHHIKERS USING COOPERATIVE MONOSTATIC RADAR TRANSMITTERS ALSO HAVE THE INHER ENT CAPABILITY TO COUNTER RETRO DIRECTIVE JAMMERS OPERATING AGAINST THEIR HOST RADAR "ECAUSE THE JAMMER USES A HIGH GAIN ANTENNA TO RETRO DIRECT THE TRANSMITTERS SIGNAL BACK TO THE TRANSMITTER AND THUS ITS MONOSTATIC RECEIVER THE SPATIALLY SEPARATED HITCH HIKER CAN BE POSITIONED IN THE SIDELOBES OF THAT ANTENNA THUS REDUCING THE EFFECTIVENESS OF THE JAMMER ! RULE OF THUMB IS TO ANTICIPATE ENHANCED HITCHHIKER PERFORMANCE WHEN EVER THE BISTATIC ANGLE IS GREATER THAN THE ESTIMATED D" WIDTH OF THE RETRO DIRECTED MAIN BEAM %XAMPLES OF 0"2S OPERATING WITH COOPERATIVE BROADCAST TRANSMITTERS IN THE CO SITE REGION ARE THE -ANASTASH 2IDGE 2ADAR OPERATING WITH AN &- BROADCAST TRANSMITTER FOR TROPOSPHERIC SOUNDINGS 3ILENT 3ENTRY OPERATING WITH &- AND 46 BROADCAST TRANS MITTERS AND THE ($46 "ASED 0ASSIVE 2ADAR OPERATING WITH A HIGH DEFINITION 46 BROADCAST TRANSMITTER THE LATTER TWO CONFIGURED FOR AIR SURVEILLANCE %XAMPLES OF 0"2S OPERATING WITH COOPERATIVE COMMUNICATIONS TRANSMITTERS IN THE RECEIVER AND TRANSMITTER CENTERED REGIONS ARE BISTATIC RADARS FOR PLANETARY EXPLORATION 4HEY USE A DATA LINK TRANSMITTER ON THE PROBE VEHICLE IN THE TRANSMITTER CENTERED REGION AND AN %ARTH BASED COMMAND TRANSMITTER IN THE RECEIVER CENTERED REGION 4HE TERM COOPERATIVE TRANSMITTER IS SOMEWHAT OF A MISNOMER &OR EXAMPLE A COOP ERATIVE 46 OR &- STATION OPERATOR WOULD NOT BE INCLINED TO hCOOPERATEv WITH A 0"2 BY ALTERING ANTENNA COVERAGE OR MODIFYING BROADCAST MATERIAL WITH SPECIAL WAVEFORMS &URTHERMORE THERE IS ALWAYS THE POSSIBILITY OF A TRANSMITTER FAILURE IN THE COURSE OF NORMAL OPERATIONS OR FROM AN ENEMY ATTACK 4HIS EVENT WILL DEGRADE PERFORMANCE OF A 0"2 THAT OPERATES WITH MULTIPLE TRANSMITTERS AND ELIMINATE PERFORMANCE OF A 0"2 THAT OPERATES ONLY WITH THAT TRANSMITTER !S A RESULT THE 0"2 IS FREE TO EXPLOIT COOPERATIVE OR NONCOOPERATIVE TRANSMISSIONS IF THEY ARE SUITABLE HOWEVER COMMERCE CONTROLS THEIR OPERATION WITH THE 0"2 REMAINING A USER OF OPPORTUNITY SPECIFICALLY SUFFERING NONOPTIMUM WAVEFORMS 3ECTION LIMITED ELEVATION COVERAGE AND OCCASIONALLY REDUCED OR DENIED PERFORMANCE #ONSTRAINTS ALSO APPLY WHEN A HITCHHIKER ATTEMPTS TO EXPLOIT A COOPERATIVE OR NON COOPERATIVE MONOSTATIC RADAR SPECIFICALLY WITH THE HITCHHIKER SUFFERING ANTENNA SCAN ON SCAN PROBLEMS 3ECTION (OWEVER THE POTENTIAL FOR ENHANCING PERFORMANCE OF A COOPERATIVE MONOSTATIC RADAR AGAINST RETRO DIRECTIVE TYPE JAMMERS WHEN USING A SUITABLY POSITIONED HITCHHIKER NECESSITATES DISTINGUISHING COOPERATIVE FROM NONCOOP ERATIVE TRANSMITTERS )N THE NONCOOPERATIVE TRANSMITTER COLUMN IF A NONCOOPERATIVE TRANSMITTER AND A HITCHHIKER WERE LOCATED IN OR NEAR A BATTLE AREA A HITCHHIKER COULD USE THAT TRANSMITTER IN THE CO SITE REGION JUST AS IT WOULD FOR A COOPERATIVE TRANSMITTER 4HE 'ERMAN +LEIN (EIDELBERG HITCHHIKING OFF THE "RITISH #HAIN (OME RADARS TO CONDUCT AIR SURVEILLANCE DURING 77)) IS AN EXAMPLE ! HITCHHIKER IMPLANTED IN OR FLYING OVER HOSTILE AREAS COULD USE ANY HIGH POWERED SATELLITE TRANSMITTER ILLUMINATING THAT AREA TO CONDUCT SHORT RANGE SURVEILLANCE IN THE RECEIVER CENTERED OVAL 4HE MOST SIGNIFICANT SYSTEM TO USE A DEDICATED TRANSMITTER IS THE 3PACE 3URVEILLANCE 30!352 -(Z MULTISTATIC RADAR FENCE )T WAS DEPLOYED STARTING IN AT SEVEN SITES SPANNING THE CONTINENTAL 5NITED 3TATES TO DETECT AND TRACK NONCOOPERATIVE SATEL LITES 4RANSMITTERS ARE LOCATED AT THREE SITES THE LARGEST OF WHICH TRANSMITS -7 #7 FROM A LINEAR ARRAY ABOUT KM LONG GENERATING A FIXED FAN BEAM 4HE SIX RECEIVE SITES CONSIST OF SEVEN OR EIGHT LINEAR ARRAYS WITH DIMENSIONS ON THE ORDER OF KM ALSO GENERATING FIXED FAN BEAMS COLLINEAR WITH THE TRANSMIT BEAM &IGURE SHOWS THE DATA FLOW IN A TYPICAL RECEIVING STATION
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&)'52% 2EAL TIME DATA FLOW IN A .!630!352 RECEIVING STATION h 4RANSMITTER ENERGY REFLECTED BY THE SATELLITE IS RECEIVED BY VARIOUS COLLINEAR ARRAYS OF DIPOLES AT THE RECEIVER STATIONx ;3IGNALS= FROM FOUR IN LINE ARRAYS FEEDS THE ALERT RECEIVER WHICH DETECTS THE PRESENCE OF RADIO ENERGY IN EXCESS OF PRESET THRESHOLD LEVELS 4HE REFLECTED ENERGY IS ALSO SIMULTANEOUSLY RECEIVED ON OTHER ARRAYS THAT ARE SEPARATED IN THE EAST WEST DIRECTION BY VARIOUS DISTANCES BASELINE 3IGNALS FROM ANY TWO CAN BE ADDED TO FORM A BASELINE PAIR 4HE BASELINE RECEIVERS EMPLOY TRIPLE FREQUENCY CONVERSION WHERE THE PHASE DIFFERENCE OF THE SIGNALS RECEIVED BY THE ANTENNA PAIR IS PRESERVED IN A HERTZ DIFFERENCE FREQUENCY ;CALLED A K(Z PHASE SIGNAL IN THE FIGURE=x 4HERE IS A RADIO RECEIVER AND CONSEQUENTLY A HERTZ PHASE ;SIGNAL= FOR EACH BASELINE PAIR EAST WEST AND NORTH SOUTH 4HIS PHASE SIGNAL IS COMPARED WITH A HERTZ REFER ENCE SIGNAL AND ENCODED DIGITIZED BY THE !$$!3 ENCODING EQUIPMENT 4HE DIGITAL COMBINER CONTAINED WITHIN THE !$$!3 ENCODER RECEIVES THE +(Z PHASE DATA AND GENERATES AN UNAMBIGUOUS ZENITH ANGLE SOLUTION 4HE COMBINER OUTPUTS ALONG WITH DIGI TIZED PHASE INFORMATION AND CONTROL BITS FOREMOST OF WHICH IS @ALERT ARE APPLIED TO THE TELEPHONE LINES VIA A DIGITAL DATA TRANSMITTERvFROM (ANDBOOK FOR .!630!352 3YSTEM /RIENTATION COURTESY 53 .AVY
4ARGET LOCATION IS ESTABLISHED BY TRIANGULATION IE THE INTERSECTION OF ZENITH ANGLE $/! MEASUREMENTS FROM TWO OR MORE RECEIVE SITES 3UBSEQUENTLY A THREE SITE FENCE IN 3OUTH 4EXAS WAS DEPLOYED TO EVALUATE THE USE OF BISTATIC RANGE MEASUREMENTS TO IMPROVE LOCATION ACCURACY BUT IT NEVER ENTERED CONTINUOUS OPERATION
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!CCORDING TO %ASTON THE 30!352 DESIGN WAS DRIVEN BY COST A NMI DETEC TION RANGE REQUIRED VERY HIGH AVERAGE POWER WHICH WAS SATISFIED BY THE LOWEST COST #7 OPERATION "UT THIS SOLUTION IN TURN REQUIRED SEPARATE SITES FOR ISOLATIONHENCE MULTISTATIC OPERATION 4HE STATIONARY BEAM LINEAR ARRAYS ALSO MINIMIZED COST WHEN COMPARED TO SCANNING ARRAYS OR REFLECTOR ANTENNAS )N SHORT FIX THE BEAMS AND LET THE SATELLITES FLY THROUGH THEM )T HAS BEEN IN CONTINUOUS USE SINCE ! HITCHHIKER USING A COOPERATIVE RADAR TRANSMITTER IN THE CO SITE REGION WAS THE -ULTISTATIC -EASUREMENT 3YSTEM --3 )T WAS INSTALLED AT THE 53 +WAJALEIN -ISSILE 2ANGE IN AS AN ADJUNCT TO THE 42!$%8 , BAND MONOSTATIC RADAR 42!$%8 OPERATED IN ITS NORMAL MONOSTATIC MODE ACQUIRING TRACKING AND ILLUMINATING BALLISTIC MISSILE REENTRY VEHICLES 26S 4WO UNMANNED SLAVED RECEIVE STATIONS LOCATED ABOUT KM FROM 42!$%8 RECEIVED ECHOES BISTATICALLY SCATTERED OFF THE 26 AND RECORDED BISTATIC RANGE DOPPLER AND SIGNATURE DATA FROM 26S 4HIS DATA WAS USED TO CALCULATE 26 POSITION AND DYNAMICS NEAR THE ATMOSPHERIC PIERCE POINT OR START OF RE ENTRY 4HE SYSTEM WAS PROJECTED TO MEASURE THREE DIMENSIONAL POSITION AND VELOCITY WITH ACCURA CIES BETTER THAN M AND MS RESPECTIVELY THROUGHOUT RE ENTRY &IELD TESTS SHOWED THAT --3 RANGE DATA COMBINED WITH 42!$%8S MONOSTATIC RANGE DATA IN A TRILATERATION NET PROVIDED THE MOST ACCURATE ESTIMATE OF EXO ATMOSPHERIC 26 POSITIONS OBTAINED BY ANY OF THE RANGE RADARS --3 OPERATIONS WERE CONCLUDED IN AFTER THE METRIC ACCURACY OF MONOSTATIC RADARS WAS IMPROVED )N THE MID S A 0"2 USING A COOPERATIVE &- BROADCAST TRANSMITTER IN THE CO SITE REGION WAS DEVELOPED BY THE 5NIVERSITY OF 7ASHINGTON #ALLED THE -ANASTASH 2IDGE 2ADAR -22 IT IS DESIGNED TO STUDY TURBULENCE IN THE IONO SPHERE SPECIFICALLY AURORAL % REGION IRREGULARITIES USING RANGE DOPPLER AND $/! VIA INTERFEROMETRY MEASUREMENTS -OTIVATION FOR -22 DEVELOPMENT INCLUDED LOWER COST INCREASED SAFETY SPECTRUM AVAILABILITY AND PEDAGOGICAL OPPORTUNITY -22 PROVIDES RANGE TIME INTENSITY AND RANGE DOPPLER PLOTS TO THE 7ORLD 7IDE 7EB EVERY HALF HOUR !LTHOUGH IT IS NOT SUBJECT TO THE STRINGENT AIR DEFENSE REQUIRE MENTS FOR ACCURATE LOCATION OF MULTIPLE TARGETS IN REAL TIME IT HAS DETECTED METEORS AND AIRCRAFT IN THE COURSE OF NORMAL OPERATIONS ! SECOND 0"2 CALLED THE ($46 "ASED 0ASSIVE 2ADAR EXPLOITS A COOPERATIVE HIGH DEFINITION 46 TRANSMITTER FOR AIR SURVEILLANCE IN THE CO SITE REGION )T USES RANGE MULTILATERATION FROM FOUR RECEIVERS LOCATED WITHIN KM OF THE TRANSMITTER TO TRACK LOW FLYING AIRCRAFT AND HELICOPTERS AS A GAP FILLER FOR MONOSTATIC AIR SURVEILLANCE RADARS 0REDICTED DETECTION AND TRACKING RANGES OF KM ON A M TARGET HAVE BEEN DEMONSTRATED IN REAL TIME WITH $ TRACKING ERRORS GENERALLY LESS THAN M #OARSE TARGET ELEVATION HAS ALSO BEEN MEASURED $OPPLER DATA HAS BEEN USED TO RESOLVE GHOSTS IE FALSE DETECTIONS THAT INEVITABLY ARISE WHEN USING MULTILATERATION ON UNAUGMENTED TARGETS 0"2S HAVE USED SATELLITE COMMUNICATION TRANSMITTERS TO MEASURE CHARACTERISTICS OF MOON AND PLANETARY SURFACES AND ATMOSPHERES IN BOTH THE TRANSMITTER AND RECEIVER CENTERED REGIONS 4HE FIRST SUCCESSFUL PIGGYBACK OPERATION IN EXPLOITED DATA LINK SIGNALS TRANSMITTED FROM THE ,UNA PROBE SCATTERED OFF THE MOONS SURFACE AND THEN RECEIVED BY AN %ARTH BASED STATION IN A DOWN LINK MODE CHARACTERIZED BY THE TRANSMITTER CENTERED OVAL OF #ASSINI 3UCH STATIONS INCLUDE THE !RECIBO /BSERVATORY AND THE .!3! $EEP 3PACE .ETWORK 3UBSEQUENT MEASUREMENTS WERE MADE USING ,UNAR /RBITER %XPLORER AND !POLLO n -ARS BISTATIC RADAR MEASUREMENTS WERE MADE USING -ARINER 6IKING -ARS 'LOBAL 3URVEYOR AND -ARS %XPRESS 6ENUS MEASUREMENTS WERE MADE BY 6ENERAS -AGELLAN AND 6ENUS %XPRESS &IGURE IS A SIMPLIFIED SCHEMATIC OF AN %ARTH BASED RECEIVER
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&)'52% "LOCK DIAGRAM OF A TYPICAL %ARTH BASED SYSTEM USED FOR DOWNLINK BISTATIC RADAR 4HE LOW NOISE AMPLIFIER ,.! IS EITHER A COOLED MASER OR A FIELD EFFECT TRANSISTOR AND MAY BE SWITCHED BETWEEN THE ANTENNA AND AN AMBIENT LOAD ALLOWING AMPLITUDE CALIBRATION OF THE INPUT $URING BISTATIC OPERATIONS A SIGNAL FROM THE LOW LEVEL NOISE DIODE PREVIOUSLY CALIBRATED AGAINST THE AMBIENT LOAD MAY BE INJECTED TO MONITOR REAL TIME PERFORMANCE OF THE SYSTEM -ICROWAVE INPUTS n '(Z ARE MIXED TO A -(Z INTERMEDIATE FREQUENCY )& FOR AMPLIFICATION ! PROGRAMMABLE OSCILLATOR WHICH CAN CORRECT FOR FIRST ORDER DOPPLER EFFECTS THEN MIXES THE )& SIGNAL TO BASEBAND AND DIGITAL SAMPLES ARE STORED FOR LATER PROCESSING !LTHOUGH AN ANALOG TO DIGITAL CONVERSION IS SHOWN AT THE OUTPUT THE !$# MAY ACTUALLY TAKE PLACE AT ANY POINT IN THE SYSTEM #OURTESY 3CI4ECH
! RECIPROCAL BUT MORE COMPLEX AND COSTLY UPLINK MODE USES A BISTATIC RECEIVER CARRIED BY THE PROBE COLLECTING HIGH POWER %ARTH TRANSMITTED COMMAND SIGNALS FIRST SCATTERED OFF THE PLANETS SURFACE AND CHARACTERIZED BY THE RECEIVER CENTERED OVAL OF #ASSINI )T HAS AN ^ D" GREATER LINK MARGIN WHICH WAS FIRST USED FOR -ARS /DYSSEY AND IS PLANNED FOR FUTURE PROBES )N BOTH CONFIGURATIONS EVEN THOUGH TWO LEGS OF THE BISTATIC TRIANGLE ARE EXTRAORDINARILY LONG MILES THE THIRD LEG IS SUFFICIENTLY SHORT ^ MILES TO PRODUCE STRONG ECHOES AT THE RECEIVER 4HESE PIGGYBACK BISTATIC RADARS HAVE PROVIDED USEFUL DATA IN SIMPLE INEXPENSIVE SURVEYS OF PLANETARY SURFACE PROPERTIES AS A PRELUDE TO ROBOTIC OR HUMAN EXPLORATION SPECIFICALLY CENTIMETER TO METER SCALE ROUGHNESS AND MATERIAL DENSITIES IN THE TOP FEW CENTIMETERS OF REGOLITH 3PECIAL GEOMETRIES SUCH AS NEAR BACKSCATTER TO IDENTIFY DEPOSITS OF CLEAN WATER ICE ARE ALSO A UNIQUE ADVANTAGE OF BISTATIC RADAR 4HE ABILITY TO OBSERVE FORWARD SCATTERING AT LATITUDES AWAY FROM PLANETARY EQUATORS IS ALSO ADVANTA GEOUS FOR PROBING SURFACE CHARACTERISTICS
ÓΰxÊ -// Ê "** , &IGURE DEFINES THE GEOMETRY FOR BISTATIC DOPPLER WHEN THE TARGET TRANSMITTER AND RECEIVER ARE MOVING 4HE TARGET HAS A VELOCITY VECTOR OF MAGNITUDE 6 AND ASPECT ANGLE C REFERENCED TO THE BISTATIC BISECTOR 4HE TRANSMITTER AND RECEIVER HAVE VELOCITY VECTORS OF MAGNITUDE 64 AND 62 AND ASPECT ANGLES C 4 AND C 2 RESPECTIVELY REFERENCED TO THE NORTH COORDINATE SYSTEM OF &IGURE !LL VECTORS ARE PROJECTIONS OF THE THREE DIMENSION VECTORS ONTO THE BISTATIC PLANE 4ARGET $OPPLER 7HEN THE TRANSMITTER AND RECEIVER ARE STATIONARY 64 62 THE TARGETS BISTATIC DOPPLER AT THE RECEIVE SITE F" IS
F" 6K COS C COS A
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&)'52% 'EOMETRY FOR BISTATIC DOPPLER IN THE BISTATIC PLANE
4HE TERM F" ALSO DEFINES THE DOPPLER BEAT FREQUENCY WHICH IS PRODUCED BY MIX ING THE TARGETS DOPPLER WITH THE DIRECT PATH SIGNAL IN THE RECEIVER 7ILLIS PROVIDES AN EXPRESSION FOR F" WHEN ALL THREE SITES ARE IN MOTION %QUATION SHOWS THAT 7HEN A n F" REDUCES TO THE MONOSTATIC CASE FOR A MONOSTATIC RADAR LOCATED ON THE BISTATIC BISECTOR 4HE MAGNITUDE OF THE BISTATIC DOPPLER IS NEVER GREATER THAN THAT OF THIS MONOSTATIC DOPPLER 7HEN A n F" FOR ANY C WHICH IS THE FORWARD SCATTER CASE 7HEN C o n THE BISTATIC DOPPLER IS ZERO 3INCE THESE VELOCITY VECTORS ARE ALSO TANGENT TO A RANGE SUM ELLIPSE AT THIS POINT ALL SUCH ELLIPSES INCLUDING THE BASELINE BECOME CONTOURS OF ZERO TARGET DOPPLER 7HEN C n THE BISTATIC DOPPLER IS A MAXIMUM 3INCE THIS VELOCITY VECTOR IS ALSO TANGENT TO A HYPERBOLA ORTHOGONAL TO THE RANGE SUM ELLIPSE AT THIS POINT ALL SUCH HYPERBOLAS BECOME CONTOURS OF MAXIMUM TARGET DOPPLER 7HEN C o A n THE VELOCITY VECTOR IS POINTED AT THE TRANSMITTER OR RECEIVER AND F" 6K COSA WHICH OCCASIONALLY APPEARS IN THE LITERATURE AS A SPECIAL CASE OF %Q
L
L
L
L
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)F A MONOSTATIC RADAR IS LOCATED AT THE TRANSMIT SITE AND A BISTATIC HITCHHIKER IS LOCATED AT THE RECEIVE SITE BOTH MEASURING TARGET DOPPLER F- AND F" RESPECTIVELY THE TWO MEASUREMENTS CAN BE COMBINED TO ESTIMATE THE TARGET VELOCITY VECTOR 6 C IN THE BISTATIC PLANE /NE SUCH ESTIMATE IS
C TAN [; F- F" SINA = COTA ]
6 K F" COSC K F- COSC A
WHERE A IS OBTAINED BY SOLVING THE BISTATIC TRIANGLE FOR EXAMPLE BY USING MONO STATIC RANGE MONOSTATIC ,/3 AND AN ESTIMATE OF THE BASELINE ! THIRD HITCHHIKING SITE ALLOWS THE TARGET VELOCITY VECTOR TO BE MEASURED IN THREE DIMENSIONS 4HIS PRO CESS IS CALLED DUAL DOPPLER FOR TWO MEASUREMENTS AND MULTIPLE DOPPLER FOR THREE OR MORE MEASUREMENTS AND HAS BEEN USED TO MEASURE THREE DIMENSIONAL VECTOR WIND FIELDS
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)SODOPPLER #ONTOURS 7HEN THE TARGET IS STATIONARY AND THE TRANSMITTER AND RECEIVER ARE MOVING EG ON AIRBORNE PLATFORMS THE BISTATIC DOPPLER SHIFT AT THE RECEIVER SITE F42 IS
F 42 64 K COS C 3 P 4 62 K COS C 2 P 2
WHERE TERMS ARE DEFINED IN &IGURE 4HE LOCUS OF POINTS FOR CONSTANT DOPPLER SHIFT ON THE %ARTHS SURFACE IS CALLED AN ISODOPPLER CONTOUR OR ISODOP #LUTTER RETURNS ARE CHARACTERIZED BY THESE ISODOPS WHICH ARE CALLED CLUTTER DOPPLER SHIFT )N THE MONOSTATIC CASE AND A FLAT %ARTH THESE ISODOPS ARE CONIC SECTIONS IN THREE DIMENSIONS AND RADIAL LINES EMANATING FROM THE RADAR IN TWO DIMENSIONS "ECAUSE THESE ISODOPS ARE ALIGNED WITH THE RADARS LOOK ANGLE THE CLUTTER IS CALLED STATIONARY )N THE BISTATIC CASE THE ISODOPS ARE SKEWED AWAY FROM THE LOOK ANGLE DEPENDING UPON THE GEOMETRY AND PLATFORM MOTION AND THE CLUTTER IS CALLED NONSTATIONARY "ISTATIC ISODOPS ARE DEVELOPED ANALYTICALLY FOR TWO DIMENSIONS AND A FLAT EARTH BY SETTING F42 CONSTANT IN %Q AND SOLVING FOR P2 OR P 4 IF APPROPRIATE &IGURE IS A PLOT OF BISTATIC ISODOPS IN A TWO DIMENSIONAL BISTATIC PLANE IE WHERE THE TRANSMITTER AND RECEIVER ARE AT ZERO OR NEAR ZERO ALTITUDE FOR THE FOLLOWING CONDITIONS 64 62 MS C 4 C 2 AND K M $IMENSION OF THE GRID ON THE BISTATIC PLANE IS ARBITRARY THAT IS THE ISODOPS ARE INVARI ANT WITH SCALE /N THE LEFT AND RIGHT SIDES OF &IGURE THE ISODOPS ARE APPROXIMATELY STATIONARY WHICH ARE PSEUDO MONOSTATIC OPERATING POINTS %LSEWHERE THE ISODOPS ARE NONSTATIONARY )N THESE NONSTATIONARY REGIONS THE QUALITY OF BISTATIC 3!2 IMAGERY IS LIMITED AND MOVING TARGET INDICATION -4) PERFORMANCE IS DEGRADED WHEN USING STAN DARD MONOSTATIC RADAR PROCESSING TECHNIQUES
&)'52% "ISTATIC ISODOPPLER CONTOURS FOR TWO DIMENSIONS AND A FLAT EARTH #OURTESY ,EE 2 -OYER 4ECHNOLOGY 3ERVICE #ORP
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2ESEARCH WAS STARTED IN THE S TO IMPROVE THE QUALITY OF BISTATIC 3!2 IMAGES WHICH WERE CONSTRAINED TO COHERENT INTEGRATION TIMES OF A FEW SECONDS AND CONSE QUENTLY WERE OF LIMITED TACTICAL INTEREST 3PECIFICALLY LOCAL OSCILLATOR PHASE INSTABILITIES WERE REDUCED AND BISTATIC AUTOMATIC FOCUSING AUTOFOCUS ALGORITHMS WERE DEVELOPED TO IMPROVE RANGE MEASUREMENT ACCURACY FROM THE ANTENNA PHASE CENTER TO THE IMAGED SCENE "ISTATIC AUTOFOCUS REQUIRES THAT THE POSITION OF BOTH TRANSMIT AND RECEIVE PLAT FORMS MUST BE TRACKED WITH SUBWAVELENGTH RELATIVE ACCURACY TO CORRECT TIME VARYING PHASE ERRORS AS PART OF THE IMAGE FORMATION PROCESS 4HE RESULT ALLOWED AN INCREASE IN COHERENT INTEGRATION TIMES COMPARABLE TO MONOSTATIC 3!2 TYPICALLY SECONDS #ONSEQUENTLY BISTATIC 3!2 IMAGE QUALITY WAS GREATLY IMPROVED AS REPORTED BY " 2IGLING IN #HAPTER OF 7ILLIS AND 'RIFFITHS "ISTATIC SPACE TIME ADAPTIVE PROCESSING 34!0 WAS ALSO DEVELOPED TO IMPROVE -4) PERFORMANCE OF SEPARATELY MOVING TRANSMIT AND RECEIVE PLATFORMS 3INCE BISTATIC CLUTTER EXHIBITS NONSTATIONARY SPACE TIME CHARACTERISTICS BISTATIC 34!0 METHODS ARE NOT SIMPLE APPLICATIONS OF MONOSTATIC APPROACHES BUT A NEW CLASS OF ALGORITHMS 3PECIFICALLY THEY APPLY A DATA DEPENDENT WEIGHTING TO VOLTAGES COLLECTED OVER MUL TIPLE RECEIVE ANTENNA CHANNELS AND PULSES 4HIS WEIGHTING DYNAMICALLY TAILORS A FILTER RESPONSE IN ANGLE AND BISTATIC DOPPLER TO SUPPRESS GROUND CLUTTER REFLECTIONS $IGITAL BEAMFORMING IS REQUIRED FOR THIS OPERATION /THER NECESSARY ELEMENTS INCLUDE A MEANS TO ESTIMATE THE SPATIO TEMPORAL CLUTTER COVARIANCE MATRIX THE DATA DEPENDENT ELEMENT OF THE FILTER WEIGHTING AND HYPOTHESIS OF THE TARGET STEERING VECTOR )N GENERAL AUXILIARY DATA TAKEN FROM RANGE BINS OTHER THAN THE CELL UNDER TEST IS USED TO ESTIMATE THE UNKNOWN BUT CRITICAL CLUTTER COVARIANCE MATRIX 7ITH COMPENSATION FOR NONSTA TIONARY BEHAVIOR BISTATIC CLUTTER SUPPRESSION HAS BEEN GREATLY IMPROVED AS REPORTED BY 7 -ELVIN IN #HAPTER OF 7ILLIS AND 'RIFFITHS
ÓΰÈÊ /, /Ê " /" "ISTATIC ,OCATION ! BISTATIC RECEIVER TYPICALLY USES RANGE SUM 24 22 FOR TAR GET LOCATION WHICH CAN BE ESTIMATED BY TWO METHODS )N THE DIRECT METHOD THE RECEIVER MEASURES THE TIME INTERVAL $4RT BETWEEN RECEPTION OF THE TRANSMITTED SIGNAL AND RECEP TION OF THE TARGET ECHO )T THEN CALCULATES THE RANGE SUM AS 24 22 C$4RT , 4HIS METHOD CAN BE USED WITH ANY SUITABLE MODULATED TRANSMISSION AND ANY TYPE OF TRANS MITTER DEDICATED COOPERATIVE OR NONCOOPERATIVE GIVEN AN ADEQUATE ,/3 BETWEEN TRANSMITTER AND RECEIVER )N THE INDIRECT METHOD PRESYNCHRONIZED STABLE CLOCKS ARE USED BY THE RECEIVER AND A DEDICATED TRANSMITTER 4HE RECEIVER MEASURES THE TIME INTER VAL $4TT BETWEEN THE TRANSMISSION OF A SIGNAL AND RECEPTION OF THE TARGET ECHO )T THEN CALCULATES THE RANGE SUM AS 24 22 C$4TT ! TRANSMITTER TO RECEIVER ,/3 IS NOT REQUIRED UNLESS PERIODIC CLOCK SYNCHRONIZATION IS IMPLEMENTED OVER THE DIRECT PATH 4HE TRADITIONAL METHOD FOR CONVERTING TARGET RANGE SUM INTO TARGET RANGE FROM THE RECEIVER 22 IS
22
24 22 , 24 22 , SINP 2
4HE BASELINE , CAN BE DETERMINED USING '03 OR OTHER METHODS SUCH AS AN EMITTER LOCA TOR FOR NONCOOPERATIVE TRANSMITTERS !S OUTLINED IN 3ECTION THE RECEIVER LOOK ANGLE P2 CAN BE MEASURED DIRECTLY WITH A PHASED ARRAY ANTENNA THAT SCANS IN TWO DIMENSIONS
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OR TARGET AZIMUTH AND ELEVATION MEASUREMENTS CAN BE CONVERTED TO P2 "EAM SPLITTING TECHNIQUES CAN BE USED TO REDUCE THE MEASUREMENT ERROR %VEN WITH BEAM SPLITTING P2 IS THE CRITICAL PARAMETER ESTABLISHING ACCURACY OF THE 22 ESTIMATE SINCE AS IN THE MONOSTATIC CASE ITS ERROR IS PROPORTIONAL TO TARGET RANGE ! FULL ERROR ANALYSIS OF %Q IS GIVEN IN 3ECTION OF 7ILLIS .O BISTATIC RADAR OPERATING AUTONOMOUSLY HAS BEEN SHOWN TO PROVIDE ADEQUATE LOCATION OF AIR OR SPACE TARGETS WITHOUT EMPLOYING RECEIVE APERTURES COMPARABLE IN SIZE TO MONOSTATIC RECEIVE APERTURES USED FOR THOSE PURPOSES )N THE SPECIAL CASE OF A BISTATIC RADAR USING THE DIRECT RANGE SUM ESTIMATION METHOD WHEN 24 22 y , %Q CAN BE APPROXIMATED AS
22
C$4RT SIN P 2
4WO EXAMPLES ARE A RECEIVER OPERATING IN AN OVER THE SHOULDER GEOMETRY AND THE TRANSMITTER OPERATING ON A SATELLITE WITH THE RECEIVER AND TARGET NEAR THE EARTH 4HE ERROR IN %Q IS LESS THAN PERCENT FOR n P2 n AND , 24 22 OR C$4RT 4HE ERROR GROWS RAPIDLY FOR P2 n /THER TARGET LOCATION TECHNIQUES ARE POSSIBLE n &OR EXAMPLE WHEN A BISTATIC HITCHHIKER EXPLOITS THE TRANSMITTER OF A MONOSTATIC RADAR THE RADARS LOOK ANGLE P4 CAN BE USED IN PLACE OF OR IN CONJUNCTION WITH P2 !N EXAMPLE OF THE LATTER IS THE THETA THETA LOCATION TECHNIQUE WHERE
22 , COSP 4 SIN P4 P2
AND P4 P2 A ! DEDICATED OR COOPERATIVE MONOSTATIC RADAR CAN PROVIDE VALUES OF P 4 DIRECTLY TO THE HITCHHIKER /THERWISE THE HITCHHIKER MUST ESTIMATE THE VALUE FOR EXAMPLE VIA AN EMITTER LOCATOR MEASURING THE RADARS ANTENNA SCAN RATE WHEN IT IS PRE DICTABLE )N THIS CASE TARGET LOCATION ACCURACY IS OFTEN SET BY THE P 4 ESTIMATION ERROR -ULTISTATIC ,OCATION -ULTISTATIC LOCATION TYPICALLY USES MULTIPLE TRANSMITTERS OPERATING WITH ONE RECEIVER OR MULTIPLE RECEIVERS OPERATING WITH ONE TRANSMITTER %LLIPSES OF CONSTANT RANGE SUM IE ISORANGE CONTOURS FROM EACH TRANSMITTER RECEIVER PAIR ARE CAL CULATED AND COMBINED AT A CENTRAL SITE TO PRODUCE INTERSECTING CONTOURS WHICH LOCATE THE TARGET -ULTISTATIC CROSS RANGE LOCATION CAN BE MORE ACCURATE THAN MONOSTATIC OR BISTATIC CROSS RANGE LOCATION SINCE ANGLE DATA WITH ITS RANGE DEPENDENT ACCURACY IS NOT USED 4HE MULTISTATIC RADAR MUST HOWEVER USE MULTIPLE PROPERLY LOCATED SITES WITH BOTH OVERLAP PING COVERAGE AND SIMULTANEOUS MEASUREMENTS WHICH IN TURN REQUIRE BROAD TRANSMIT AND RECEIVE BEAMS TO ACHIEVE THIS ACCURACY 4HESE REQUIREMENTS USUALLY COMBINE TO RESTRICT MULTISTATIC AIR SURVEILLANCE PERFORMANCE TO SHORT OR MEDIUM RANGES 'EOMETRIC DILUTION OF PRECISION '$/0 ESTABLISHES MULTISTATIC LOCATION ACCURACY AND RESOLUTION AND IS DEVELOPED BY $ "ARTON IN #HAPTER OF 7ILLIS AND 'RIFFITHS '$/0 IS A FUNCTION OF THE ANGLE OF INTERSECTION @ BETWEEN ISORANGE CONTOURS "ECAUSE THE BISECTOR OF A BISTATIC ANGLE IS ORTHOGONAL TO AN ISORANGE CONTOUR '$/0 CAN READILY BE DETERMINED BY THE ANGLE OF INTERSECTION ALSO @ OF THESE BISTATIC BISECTORS )N THE SIMPLEST CASE THE DOWN RANGE ERROR RDR IS PROPORTIONAL TO ; COS @ = AND CROSS RANGE ERROR RCR IS PROPORTIONAL TO ; SIN @ =
)SORANGE CONTOURS INTERSECT AT OTHER LOCATIONS AS WELL 4HESE NONTARGET LOCATIONS ARE CALLED GHOSTS WHICH MUST BE EXCISED 4HIS SUBJECT IS TREATED IN #HAPTER OF 7ILLIS AND 'RIFFITHS
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&OR EXAMPLE WHEN THE TARGET IS SURROUNDED ON THREE SIDES BY A RECEIVE SITE A TRANSMIT SITE AND ANOTHER RECEIVE SITE SUCH THAT @ RDR RCR 4HIS GEOMETRY REPRESENTS THE OPTIMUM CASE OF A UNITY '$/0 FACTOR YIELDING A CIRCULAR ERROR ELLIPSE WITH RADIUS EQUAL TO THE RANGE ERROR OF ONE TRANSMIT RECEIVE PAIR )N CONTRAST WHEN THE TARGET IS LOCATED SOME DISTANCE FROM THE THREE SITES @ IS REDUCED &OR EXAMPLE WHEN @ RDR AND RCR 4HUS THE DOWN RANGE ERROR IS SLIGHTLY REDUCED BUT THE CROSS RANGE ERROR IS GREATLY INCREASED NOT UNLIKE THAT OF A RADAR USING ANGLE DATA TO ESTABLISH CROSS RANGE ACCURACY 4HESE EXAMPLES ALSO APPLY WHEN GROUND BASED MULTISTATIC SITES ATTEMPT TO MEA SURE TARGET ALTITUDE 7HEN THE SITES SURROUND THE TARGET FOR EXAMPLE WHEN POSITIONED AROUND THE LAUNCH SITE OF A BALLISTIC MISSILE @ REMAINS RELATIVELY LARGE DURING THE MISSILES LAUNCH PHASE YIELDING PRECISE ALTITUDE ESTIMATES 7HEN THE SITES ARE SOME DISTANCE FROM THE TARGET FOR EXAMPLE WHEN CONDUCTING AIR OR MISSILE SURVEILLANCE @ IS SMALL YIELDING POOR ALTITUDE ESTIMATES "OTH BISTATIC AND MULTISTATIC RADARS CAN POTENTIALLY ACHIEVE EVEN BETTER LOCATION ACCURACY BY USING NARROW BAND DOPPLER TRACKING UNDER THE FOLLOWING CONDITIONS 7HEN INTEGRATING DOPPLER DATA INITIAL CONDITIONS THE PESKY CONSTANT OF INTEGRA TION CAN BE ESTABLISHED WITH SUFFICIENT ACCURACY 7HEN TAKING SEQUENTIAL DOPPLER MEASUREMENTS THE TARGETS VELOCITY VECTOR REMAINS CONSTANT OR PREDICTABLE &OR EXAMPLE MANY DOPPLER ONLY PRECISION RANGE INSTRUMENTATION SYSTEMS WERE DEVELOPED IN THE 53 AFTER 77)) "OTH BEACON AIDED AND SKIN TRACK SYSTEMS WERE DEVELOPED !LL REQUIRED INITIALIZATION OF THE TRACK DATA WHICH WAS CONVENIENTLY PROVIDED BY THE TARGETS LAUNCH COORDINATES (OWEVER IF THE TARGET RETURN MOMENTARILY FADED OR THE TRANSPONDER SIGNAL WAS INTERRUPTED DURING FLIGHT SO THAT TRACK WAS LOST THERE WAS NO WAY TO REINITIALIZE NEW TRACK DATA AND SUBSEQUENT LOCATION ESTIMATES BECAME BIASED OR WERE LOST 4HESE SYSTEMS WERE SUBSEQUENTLY REPLACED WITH PRECISION MONOSTATIC RADARS AND OPTICAL TRACKERS
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4HE BISTATIC RADAR CROSS SECTION 2#3 OF A TARGET R" IS A MEASURE AS IS THE MONOSTATIC RADAR CROSS SECTION R- OF THE ENERGY SCATTERED FROM THE TARGET IN THE DIRECTION OF THE RECEIVER "ISTATIC CROSS SECTIONS ARE MORE COMPLEX THAN MONOSTATIC CROSS SECTIONS IN THE OPTICAL REGION SINCE R" IS A FUNCTION OF ASPECT ANGLE AND BISTATIC ANGLE A 4HREE BISTATIC 2#3 REGIONS ARE OF INTEREST IN THE OPTICAL REGION PSEUDO MONOSTATIC BISTATIC AND FORWARD SCATTER %ACH REGION IS DEFINED BY THE BISTATIC ANGLE 4HE EXTENT OF EACH REGION IS SET PRIMARILY BY THE TARGETS PHYSICAL CHARACTERISTICS 0SEUDO -ONOSTATIC 2#3 2EGION 4HE #RISPIN AND 3IEGAL MONOSTATIC BISTATIC EQUIVALENCE THEOREM APPLIES IN THE PSEUDO MONOSTATIC REGION FOR VANISHINGLY SMALL WAVELENGTHS THE BISTATIC 2#3 OF A SUFFICIENTLY SMOOTH PERFECTLY CONDUCTING TARGET IS EQUAL TO THE MONOSTATIC 2#3 MEASURED ON THE BISECTOR OF THE BISTATIC ANGLE 3UFFICIENTLY SMOOTH TARGETS INCLUDE SPHERES ELLIPTIC CYLINDERS CONES AND OGIVES ALLOWING THE REGION TO EXTEND OUT TO A n AND OCCASIONALLY OUT TO A n n
(OWEVER IN THE RESONANCE REGION TYPICALLY AT 6(& AND LOW 5(& FOR MANY AIR TARGETS VARIATIONS IN A ^n HAVE LITTLE EFFECT ON R" SUCH THAT R" y R-
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&OR TARGETS OF MORE COMPLEX STRUCTURE THE EXTENT OF THE PSEUDO MONOSTATIC REGION IS REDUCED ! VARIATION OF THE EQUIVALENCE THEOREM DEVELOPED BY +ELL APPLIES TO SMALL BISTATIC ANGLES IN SOME CASES AS SMALL AS n THE BISTATIC 2#3 OF A COMPLEX TARGET IS EQUAL TO THE MONOSTATIC 2#3 MEASURED ON THE BISECTOR OF THE BISTATIC ANGLE AT A FRE QUENCY LOWER BY A FACTOR OF COS A +ELLS COMPLEX TARGETS ARE DEFINED AS AN ASSEMBLY OF DISCRETE SCATTERING CENTERS SIMPLE CENTERS SUCH AS FLAT PLATES REFLEX CENTERS SUCH AS CORNER REFLECTORS SKEWED REFLEX CENTERS SUCH AS A DIHEDRAL WITH CORNER w n AND STATIONARY PHASE REGIONS FOR CREEPING WAVES 7HEN THE WAVELENGTH IS SMALL COMPARED TO TARGET DIMENSIONS THESE COMPLEX TARGET MODELS APPROXIMATE CONVENTIONAL AIRCRAFT SHIPS GROUND VEHICLES AND SOME MISSILES 4HE TARGETS CAN BE COMPOSED OF CONDUCTING AND DIELECTRIC MATERIALS !T SMALL BISTATIC ANGLES THE COS A FREQUENCY REDUCTION TERM HAS LITTLE EFFECT IN +ELLS PSEUDO MONOSTATIC REGION &OR EXAMPLE A n BISTATIC ANGLE CORRESPONDS TO A SHIFT IN WAVELENGTH AND USUALLY CAN BE IGNORED "OTH VERSIONS OF THE EQUIVALENCE THEOREM ARE VALID WHEN THE POSITIONS OF THE TRANSMITTER AND RECEIVER ARE INTERCHANGED GIVEN THAT THE TARGET SCATTERING MEDIA ARE RECIPROCAL -OST MEDIA ARE RECIPROCAL %XCEPTIONS ARE GYROTROPIC MEDIA SUCH AS FERRITE MATERIALS AND THE IONOSPHERE "ISTATIC 2#3 2EGION 4HE BISTATIC ANGLE AT WHICH THE EQUIVALENCE THEOREM FAILS TO PREDICT THE BISTATIC 2#3 IDENTIFIES THE START OF THE SECOND BISTATIC REGION )N THIS REGION THE BISTATIC 2#3 DIVERGES FROM THE MONOSTATIC 2#3 +ELL IDENTIFIED THREE SOURCES OF THIS DIVERGENCE FOR COMPLEX TARGETS AND FOR A TARGET ASPECT ANGLE FIXED WITH RESPECT TO THE BISTATIC BISECTOR 4HESE SOURCES ARE CHANGES IN RELATIVE PHASE BETWEEN DISCRETE SCATTERING CENTERS CHANGES IN RADIATION FROM DISCRETE SCATTERING CENTERS AND CHANGES IN THE EXISTENCE OF CENTERSAPPEARANCE OF NEW CENTERS OR DISAPPEAR ANCE OF THOSE PREVIOUSLY PRESENT 4HE FIRST SOURCE IS ANALOGOUS TO FLUCTUATIONS IN MONOSTATIC 2#3 AS THE TARGET ASPECT ANGLE CHANGES BUT NOW THE EFFECT IS CAUSED BY A CHANGE IN BISTATIC ANGLE 4HE SECOND SOURCE OCCURS WHEN FOR EXAMPLE THE DISCRETE SCATTERING CENTER INCLUDING FLAT PLATES RETRO REFLECTS ENERGY TOWARD THE TRANSMITTER AND THE RECEIVER IS POSITIONED OUTSIDE THE RETRO REFLECTED BEAMWIDTH THUS THE RECEIVED ENERGY IS REDUCED 4HE THIRD SOURCE IS TYPICALLY CAUSED BY SHADOWING FOR EXAMPLE BY AN AIRCRAFT FUSELAGE BLOCKING ONE OF THE BISTATIC PATHSTRANSMITTER OR RECEIVER ,/3 TO A SCATTERING CENTER )N GENERAL THIS DIVERGENCE RESULTS IN A BISTATIC 2#3 LOWER THAN THE MONOSTATIC 2#3 FOR COMPLEX TARGETS &OR EXAMPLE %WELL AND :EHNER MEASURED THE MONOSTATIC AND BISTATIC 2#3 OF COASTAL FREIGHTERS AT 8 BAND WHEN BOTH THE TRANSMITTER AND THE RECEIVER WERE NEAR GRAZING INCIDENCE 4HE DATA WAS PLOTTED AS A RATIO OF BISTATIC TO MONOSTATIC 2#3 R"R- 4HE MEASUREMENTS GENERALLY MATCH +ELLS MODEL OF THE DATA POINTS SHOW BISTATIC 2#3 LOWER THAN MONOSTATIC 2#3 4HE REDUCTION IN BISTATIC 2#3 STARTS BETWEEN A n AND A n AND TRENDS DOWNWARD TO R"R- D" AT A n 4HIS RATHER SEVERE LOSS WAS MEASURED UNDER SPECIAL CONDITIONS LOW GRAZING ANGLES FOR TARGETS WITH VERTICAL SURFACES AND DIHEDRALS AND TRIHEDRALS WHICH GENERATE A LARGE MONOSTATIC 2#3 4HUS THE BISTATIC 2#3 BECOMES SIGNIFICANTLY LOWER AS THE BISTATIC ANGLE INCREASES DUE TO SHADOWING AND LOSS OF THESE SPECULARS AND RETRO REFLECTORS "ISTATIC LOSSES SHOULD NOT BE AS SEVERE FOR TARGETS WITH BLENDED SURFACES AND A LESS COMPLEX STRUCTURE SUCH AS COMBAT AIRCRAFT 'LINT 2EDUCTION IN THE "ISTATIC 2#3 2EGION ! SECOND EFFECT CAN OCCUR IN THE BISTATIC REGION 7HEN THE BISTATIC 2#3 REDUCTION IS CAUSED BY A LOSS OR ATTENUATION OF
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LARGE DISCRETE SCATTERING CENTERS FOR EXAMPLE THROUGH SHADOWING TARGET GLINT IS OFTEN REDUCED 4ARGET GLINT IS THE ANGULAR DISPLACEMENT IN APPARENT PHASE CENTER OF A TARGET RETURN AND IS CAUSED BY THE PHASE INTERFERENCE BETWEEN TWO OR MORE DOMINANT SCATTERS WITHIN A RADAR RESOLUTION CELL !S THE TARGET ASPECT ANGLE CHANGES THIS PHASE INTERFER ENCE CHANGES SHIFTING THE APPARENT PHASE CENTER OFTEN WITH EXCURSIONS BEYOND THE PHYSICAL EXTENT OF THE TARGET 4HESE EXCURSIONS CAN SIGNIFICANTLY INCREASE THE ERRORS IN ANGLE TRACKING OR MEASUREMENT SYSTEMS 7HEN THE RETURNS FROM DOMINANT SCATTERERS ARE REDUCED IN THE BISTATIC REGION THE SOURCE AND HENCE THE MAGNITUDE OF GLINT EXCUR SIONS IS REDUCED -EASUREMENTS WITH TACTICAL AIRCRAFT SHOWED THAT FOR A n BISTATIC ANGLE PEAK GLINT EXCURSIONS COULD BE REDUCED BY A FACTOR OF OR MORE WITH MOST OF THE EXCURSIONS CONTAINED WITHIN THE PHYSICAL EXTENT OF THE TARGET 4HIS REDUCTION CAN BE EXPLOITED IN A SEMI ACTIVE HOMING MISSILE BY MODIFYING ITS TRAJECTORY TO MAINTAIN A nn DURING ENDGAME &ORWARD 3CATTER 2#3 2EGION 4HE THIRD BISTATIC 2#3 REGION FORWARD SCATTER OCCURS WHEN THE BISTATIC ANGLE APPROACHES n 7HEN A n 3IEGEL SHOWED BASED ON PHYSICAL OPTICS THAT THE FORWARD SCATTER 2#3 R& OF A TARGET WITH SILHOUETTE OR SHADOW AREA ! IS
R& O !K
WHERE K THE WAVELENGTH IS SMALL COMPARED WITH THE TARGET DIMENSIONS 4HE TARGETS CAN BE EITHER SMOOTH OR COMPLEX STRUCTURES AND FROM THE APPLICATION OF "ABINETS PRINCIPLE CAN BE TOTALLY ABSORBING &OR A n THE FORWARD SCATTER 2#3 ROLLS OFF FROM R& 4HE ROLLOFF IS APPROXI MATED BY TREATING THE SHADOW AREA ! AS A UNIFORMLY ILLUMINATED ANTENNA APERTURE 4HE RADIATION PATTERN OF THIS SHADOW APERTURE IS EQUAL TO THE FORWARD SCATTER 2#3 ROLLOFF WHEN O A IS SUBSTITUTED FOR THE ANGLE OFF THE APERTURE NORMAL ! SPHERE OF RADIUS A WILL ROLL OFF D" AT O A y K O A WHEN AK 4HE ROLL OFF CONTINUES APPROXI MATING *X X DOWN TO A y n WHERE * IS A "ESSEL FUNCTION OF ZERO ORDER ! LINEAR APERTURE OF LENGTH $ WITH ASPECT ANGLE ORTHOGONAL TO THE TRANSMITTER ,/3 WILL ROLL OFF D" AT O A K $ WHEN $K 4HE FORWARD SCATTER 2#3 ROLLOFF CONTINUES WITH SIDELOBES APPROXIMATING SIN XX OVER THE FORWARD SCATTER QUADRANT A n &OR OTHER ASPECT ANGLES AND TARGETS WITH COMPLEX SHADOW APERTURES CALCULATION OF THE FORWARD SCATTER 2#3 ROLLOFF USUALLY REQUIRES SIMULATION 4HE FORWARD SCATTER 2#3 OF MORE COMPLEX BODIES HAS BEEN SIMULATED AND MEA SURED THE BODIES WERE BOTH REFLECTING AND ABSORBING n &IGURE SHOWS A METHOD OF MOMENTS SIMULATION OF A BY CM CYLINDER WITH FACETS AT '(Z FOR THREE FIXED TRANSMITTER TO TARGET GEOMETRIES A NEAR END ON B n ASPECT ANGLE AND C BROADSIDE !LL THREE BISTATIC REGIONS ARE SHOWN IN THE FIGURE )N THE BROADSIDE GEOMETRY THE PSEUDO MONOSTATIC REGION OCCURS AT A n BISTATIC AT n A n AND FORWARD SCATTER AT A n 4HE OTHER TWO GEOMETRIES SHOW A SIMILAR BUT BROADER FORWARD SCATTER LOBE AS IS EXPECTED SINCE THE SILHOUETTE AREA AND HENCE THE SHADOWING APERTURE ARE SMALLER 4HE n ASPECT GEOMETRY IS OF INTEREST BECAUSE THE 2#3 IN THE BISTATIC REGIONS IS LARGER THAN THE MONOSTATIC 2#3 FOR MOST BISTATIC ANGLES 4HE LARGE SPIKE AT A n IS THE BISTATIC SPECULAR LOBE ANALOGOUS TO THE MONOSTATIC SPECULAR LOBE IN THE BROADSIDE GEOMETRY 7HILE &IGURE SHOWS THE CLEAR DEPENDENCY OF BISTATIC 2#3 ON BOTH ASPECT AND BISTATIC ANGLES IT ALSO SERVES TO CAUTION AGAINST ATTEMPTS TO USE OVERSIMPLIFIED BISTATIC 2#3 MODELS ESPECIALLY IN THE BISTATIC REGION
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&)'52% 3IMULATED BISTATIC 2#3 REPLOTTED AS A FUNCTION OF BISTATIC ANGLE FOR A CONDUCTING CYLINDER BY CM AT '(Z (( POLARIZATION AFTER 2 # 0ADDISON ET AL A NEAR END ON B ASPECT ANGLE AND C BROADSIDE
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Ê 1// , 4HE BISTATIC RADAR CROSS SECTION OF SURFACE CLUTTER RC IS A MEASURE AS IS THE MONOSTATIC RADAR CLUTTER CROSS SECTION OF THE ENERGY SCATTERED FROM A CLUTTER CELL AREA !C IN THE DIREC TION OF THE RECEIVER )T IS DEFINED AS S C S " !C WHERE S " IS THE SCATTERING COEFFICIENT OR THE CLUTTER CROSS SECTION PER UNIT AREA OF THE ILLUMINATED SURFACE 4HE CLUTTER CELL AREA !C HAS BEEN DEVELOPED FOR BEAM AND RANGE LIMITED CASES AND IS REPORTED ELSEWHERE $OPPLER LIMITED CASES ARE A FUNCTION OF PLATFORM MOTION WHICH IN TURN DEPEND ON A SPECIFIC SCENARIO #ONSEQUENTLY THEY ARE MODELED ON A CASE BY CASE BASIS "ISTATIC 3CATTERING #OEFFICIENT 6ALUES OF THE SCATTERING COEFFICIENT S " VARY AS A FUNCTION OF THE SURFACE COMPOSITION FREQUENCY AND GEOMETRY AND ARE OBTAINED THROUGH FIELD MEASUREMENT PROGRAMS )N - - 7EINER DOCUMENTED AND EVALUATED ALL UNCLASSIFIED MEASUREMENTS OF S " HOWEVER ITS USE WAS RESTRICTED TO 53 GOVERNMENT AGENCIES )N 7ILLIS USED 7EINERS REFERENCES TO RECONSTRUCT AND EVALUATE TYPICAL DATA FROM 7EINERS WORK WHICH BECAME AVAILABLE FOR PUBLIC USE IN 7ILLIS )N 7EINERS WORK WAS CLEARED FOR PUBLIC RELEASE MAKING AVAILABLE IN ONE DOCUMENT ALL UNCLASSIFIED S " DATA AND ANALYSIS THROUGH 7EINER THEN UPDATED HIS WORK WITH DATA AVAILABLE THROUGH AND REPUBLISHED IT IN #HAPTER OF !DVANCES IN "ISTATIC 2ADAR 4HIS SECTION SUMMARIZES AND COMMENTS ON ESSENTIAL ELEMENTS OF 7EINERS WORK
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4HE AVAILABLE DATABASE FOR TERRAIN AND SEA CLUTTER AT MICROWAVE FREQUEN CIES CONSISTS OF NINE MEASUREMENT
PROGRAMS WHICH ARE SUMMARIZED IN 4ABLE 4HE MEASUREMENT ANGLES SHOWN IN 4ABLE ARE DEFINED IN
&IGURE WHICH IS A CLUTTER CENTERED COORDINATE SYSTEM SIMILAR TO THOSE
USED IN ALL THE MEASUREMENT PROGRAMS "ECAUSE TERRAIN AND SEA ARE RECIPROCAL MEDIA PI AND PS ARE INTERCHANGEABLE IN THE SUBSEQUENT DATA 4WO MEASUREMENT SETS ARE OF INTER EST IN PLANE WHERE E n AND OUT OF &)'52% #OORDINATE SYSTEM FOR BISTATIC CLUTTER PLANE WHERE E n 7HEN E n MEASUREMENTS PI INCIDENT ANGLE IN XZ PLANE A \PS PI\ )N THE MONOSTATIC CASE PS SCATTERING ANGLE IN PLANE CONTAINING Z AXIS AND E n A AND PS PI )N PLANE E OUT OF PLANE ANGLE IN XY PLANE DATA IS SHOWN IN BOLD TYPE ON THE TABLE /UT OF PLANE DATA IS OFTEN USED IN SCATTER JAMMING HOT CLUTTER CALCULATIONS 4HE BISTATIC ANGLE IS CALCULATED FROM THE ANGLES IN &IGURE BY THE USE OF DIRECTION COSINES
A COS COS PI COS PS SIN PI SIN PS COS E
4RENDS IN THIS BISTATIC SCATTERING COEFFICIENT DATABASE ARE SUMMARIZED FROM 7ILLIS 7EINER AND #HAPTER IN 7ILLIS AND 'RIFFITHS AS FOLLOWS L
L
L
L
L
L
-OST OF THE R" DATABASE IS AT 8 BAND WITH OUT OF DATA CURVES FOR BOTH TERRAIN AND SEA CLUTTER TAKEN BY OF THE ORGANIZATIONS 4HE REMAINING DATABASE CONSISTS OF DATA CURVES AT , BAND TERRAIN ONLY AT 3 BAND TERRAIN ONLY AT # BAND SEA ONLY AND AT +A BAND TERRAIN ONLY EACH PROVIDED BY ONE ORGANIZATION .O DATA IS AVAILABLE AT 6(& OR 5(& 4HUS ONLY 8 BAND ALLOWS CHOICES IN SELECTING DATA 4HE #OST0EAKE AND $OMVILLEn IN PLANE DATA SHOW GOOD CORRELATION !TTEMPTS TO MODEL R" DATA HAVE BEEN MADE USING GEOMETRICAL STATISTICAL AND SEMI EMPIRICAL TECHNIQUES INCLUDING VARIATIONS OF THOSE USED TO MODEL MONOSTATIC DATA -EANINGFUL RESULTS HAVE ONLY BEEN ACHIEVED OVER A NARROW RANGE OF IN PLANE DATA E n 6ALUES OF R" FOR E ^ n ARE NOT APPRECIABLY DIFFERENT WITHIN ^ D" FROM THE MONOSTATIC CASE 6ALUES OF R" IN A BROAD ANGULAR REGION CENTERED ON E n ARE SIGNIFICANTLY LOWER THAN ELSEWHERE AND TYPICALLY TO D" BELOW THE MONOSTATIC VALUE CONSE QUENTLY BISTATIC RADAR SURVEILLANCE CAN BE ENHANCED AND HOT CLUTTER CAN BE REDUCED IN THESE REGIONS 6ALUES OF R" ARE SIGNIFICANTLY LARGER NEAR THE FORWARD SCATTERED SPECULAR DIRECTION E n PI PS THAN ELSEWHERE AND MAY IN SOME CASES REDUCE ADVANTAGES OF THE ENHANCED FORWARD SCATTERED TARGET 2#3 PARTICULARLY AT FREQUENCIES -(Z 4HE BISTATIC MONOSTATIC EQUIVALENCE THEOREM USED TO MODEL THE 2#3 OF SOME TARGETS IS NOT GENERALLY USEFUL FOR CLUTTER MODELING EXCEPT TO INDICATE AN UPPER LIMIT TO R" IN SOME REGIONS
!UTHOR
2URAL LAND 5RBAN LAND &OREST 3EA 3EMI DESERT WET
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8 BAND 8 BAND 8 BAND
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4!",% 3UMMARY OF -EASUREMENT 0ROGRAMS FOR "ISTATIC 3CATTERING #OEFFICIENT S " )N PLANE DATA IS SHOWN IN BOLD TYPESEE SUBSEQUENT TEXT
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-EASUREMENT !NGLES DEGREES
4!",% 3UMMARY OF -EASUREMENT 0ROGRAMS FOR "ISTATIC 3CATTERING #OEFFICIENT S " )N PLANE DATA IS SHOWN IN BOLD TYPESEE SUBSEQUENT TEXT
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)N ADDITION TO THIS DATABASE BISTATIC REFLECTIVITY MEASUREMENTS HAVE BEEN MADE AT OPTICAL AND SONIC WAVELENGTHS AND OF BUILDINGS AIRPORT STRUCTURES AND PLAN ETARY SURFACES )N EACH OF THESE MEASUREMENTS THE REFLECTIVITY DATA IS EXPRESSED IN TERMS OF REFLECTED POWER NOT R"
ÓÎ°Ê 1 +1 Ê*," -Ê Ê, +1, /)N THE PREVIOUS EDITION OF THIS BOOK THIS SECTION COVERED SUCH HARDWARE PROBLEMS AS TIME AND PHASE SYNCHRONIZATION BETWEEN TRANSMITTER AND RECEIVER CONSTRAINED BY TECHNOLOGY AVAILABLE IN THE S 0HASE STABILITY WAS ALSO AN ISSUE 3INCE THEN MASSIVE ADVANCES IN DIGITAL SIGNAL CORRELATION AND PROCESSING COUPLED WITH GREAT REDUCTIONS IN THE COST OF HARDWARE TO EXECUTE SUCH PROCESSING HAVE MITIGATED THESE PROBLEMS -ANY RECENT BISTATIC RADAR PROGRAMS HAVE DEMONSTRATED QUITE ADEQUATE SYNCHRONIZATION AND STABILITYAS WELL AS DETECTION PERFORMANCEUSING OFF THE SHELF COMMERCIAL HARDWARE .OTABLE EXAMPLES ARE THE .!4/ AIR DEFENSE TRIALS AND THE 5NIVERSITY OF 7ASHINGTONS -ANASTASH 2IDGE 2ADAR MEASURING IONOSPHERE TURBULENCE BOTH PASSIVE BISTATIC RADARS EXPLOITING &- BROADCAST TRANSMITTERS THE ($46 "ASED 0ASSIVE 2ADAR EXPLOITING A HIGH DEFINITION 46 BROADCAST TRANSMIT TER FOR AIR SURVEILLANCE THE INEXPENSIVE COMMERCIAL BISTATIC RECEIVER HITCHHIKING OFF WEATHER RADARS TO MEASURE FULL VECTOR WIND FIELDS AND THE BISTATIC RADAR FOR WEAPONS LOCATION &URTHERMORE MAJOR PROGRESS HAS BEEN MADE IN DEVELOPING SIGNAL AND DATA PROCESS ING ALGORITHMS INCLUDING BISTATIC 3!2 AUTOFOCUS AND IMAGE FORMATION AND SPACE TIME ADAPTIVE PROCESSING FOR BISTATIC AIRBORNE -4) SEE 3ECTION (OWEVER TWO PROB LEMS CONTINUE TO PLAGUE BISTATIC AND MULTISTATIC RADARS AND HAVE BECOME THE TOPICS OF THIS SECTION BEAM SCAN ON SCAN FOR BISTATIC RADARS AND RADAR HITCHHIKERS AND NONCOOPERATIVE 2& ENVIRONMENTS FOR PASSIVE BISTATIC RADARS 4HESE PROBLEMS AND THEIR POTENTIAL REMEDIES ARE DETAILED NEXT "EAM 3CAN ON 3CAN 7HEN HIGH GAIN NARROW BEAM SCANNING ANTENNAS ARE USED BY BOTH TRANSMITTER AND RECEIVER IN A BISTATIC SURVEILLANCE RADAR INEFFICIENT USE IS MADE OF THE RADAR ENERGY BECAUSE ONLY THE VOLUME COMMON TO BOTH BEAMS CAN BE OBSERVED BY THE RECEIVER AT ANY GIVEN TIME /UTSIDE THIS COMMON BEAM VOLUME TARGETS ARE LOST TO THE RECEIVER &IGURE SHOWS THE GEOMETRY 4HIS PROBLEM COMMONLY ARISES WHEN ATTEMPTING TO HITCHHIKE OFF MONOSTATIC SURVEILLANCE RADARS &OUR REMEDIES ARE AVAILABLE TO MITIGATE THE BEAM SCAN ON SCAN PROBLEM STEP SCANNING FLOOD LIGHT BEAMS MULTIPLE BEAMS AND TIME MULTIPLEXED BEAMS WHICH IN THE LIMIT IS CALLED PULSE CHASING 3TEP 3CANNING &OR HITCHHIKING THE STEP SCANNING REMEDY CONSISTS OF FIXING THE RECEIVE BEAM AND WAITING FOR THE TRANSMIT BEAM TO SCAN THROUGH THE SURVEILLANCE SECTOR 4HE RECEIVE BEAM IS THEN STEPPED ONE BEAMWIDTH FOR THE NEXT TRANSMIT BEAM SCAN AND SO ON UNTIL THE RECEIVE BEAM HAS STEPPED ACROSS THE FULL SURVEILLANCE SEC TOR &OR A DEDICATED TRANSMITTER THE PROCESS CAN BE REVERSED FIX THE TRANSMIT BEAM AND SCAN THE RECEIVE BEAM 4HIS REMEDY INCREASES THE SURVEILLANCE FRAME TIME BY THE NUMBER OF REQUIRED BEAM STEPS AND IS USUALLY NOT ACCEPTABLE FOR LARGE AREA SURVEIL LANCE )T CAN BE CONSIDERED IN AN OVER THE SHOULDER GEOMETRY OR WHEN THE BASELINE IS SMALL )N THESE CASES TRANSMIT AND RECEIVE BEAMS BECOME MORE CLOSELY ALIGNED IN A
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&)'52% "EAM SCAN ON SCAN COVERAGE PROBLEM SHOWN IN TWO DIMENSIONS IN THE BISTATIC PLANE #OURTESY 3CI4ECH
PSEUDO MONOSTATIC GEOMETRY WHICH REDUCES THE NUMBER OF REQUIRED BEAM STEPS 4HE "ISTATIC 2ADAR FOR 7EAPONS ,OCATION TEST PROGRAM IS AN EXAMPLE &LOODLIGHT "EAMS ! FLOODLIGHT BEAM CAN BE USED WITH EITHER TRANSMITTER OR RECEIVER 4HE FLOODLIGHT TRANSMITTER REMEDY REQUIRES A DEDICATED TRANSMIT ANTENNA THAT IS DESIGNED TO FLOOD THE SURVEILLANCE SECTOR CONTINUOUSLY 4HE RECEIVER THEN SCANS THE SECTOR WITH A HIGH GAIN ANTENNA 4HIS REMEDY RESTORES THE SURVEILLANCE FRAME TIME LOST BY STEP SCANNING WHILE SIMULTANEOUSLY SERVICING MULTIPLE RECEIVERS (OWEVER IT INCURS A DETECTION RANGE PENALTY BY THE REDUCED TRANSMIT ANTENNA GAIN AND ALSO SUF FERS INCREASED SIDELOBE CLUTTER LEVELS 4HE FLOODLIGHT RECEIVER REMEDY CAN BE USED BY A HITCHHIKER TO FLOOD A SECTOR SCANNED BY THE TRANSMIT BEAM AGAIN RESTORING THE SUR VEILLANCE FRAME TIME )N ADDITION TO THE RANGE PENALTY THE RECEIVER WILL ALSO SUFFER INCREASED CLUTTER LEVELS AND ANGLE MEASUREMENT ERRORS $ESPITE THESE LIMITATIONS THE "INET FLOODLIGHT RECEIVER WAS FOUND QUITE ADEQUATE FOR MEASURING THREE DIMENSIONAL VECTOR WIND FIELDS -ULTIPLE "EAMS ! BISTATIC RECEIVER CAN USE MULTIPLE SIMULTANEOUS FIXED RECEIVE BEAMS TO COVER THE SURVEILLANCE SECTOR WHICH AGAIN RESTORES THE SURVEILLANCE FRAME TIME )F THE GAIN OF EACH RECEIVE ANTENNA IS MADE EQUAL TO THE GAIN OF THE INITIAL SINGLE RECEIVE ANTENNA RANGE PERFORMANCE IS ALSO RESTORED (OWEVER THIS REMEDY INCREASES THE COST AND COMPLEXITY OF THE RECEIVER SINCE A SPECIAL BEAMFORMING NETWORK IS REQUIRED ALONG WITH A RECEIVER AND SIGNAL PROCESSOR 230 FOR EACH BEAM 4HE MULTI BEAM RECEIVER CAN BE USED WITH ANY TYPE OF TRANSMITTER INCLUDING A FLOODLIGHT TRANSMIT TER WHERE THE LOSS IN RANGE PERFORMANCE MIGHT BE OFFSET BY AN INCREASE IN DWELL TIME ON TARGET AS DETAILED SUBSEQUENTLY 4IME MULTIPLEXING )F THE TRANSMITTERS BEAM SCANNING SCHEDULE IS KNOWN THE NUMBER OF RECEIVE BEAMS AND 230S CAN BE REDUCED IN SOME GEOMETRIES BY TIME MULTIPLEXING THEM TO COVER ONLY THE CURRENTLY ILLUMINATED SURVEILLANCE SECTOR
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&OR EXAMPLE IN AN OVER THE SHOULDER GEOMETRY THE RECEIVER MIGHT USE A SET OF BEAMS TO COVER THE NORTH SIDE OF THE BASELINE THEN AS THE TRANSMIT BEAM SCANS PAST THE RECEIVER IT SWITCHES THE SET TO THE SOUTH SIDE THUS HALVING THE TOTAL NUMBER REQUIRED 4HE "ISTATIC !LERTING AND #UEING TEST PROGRAM USED TIME MULTIPLEXED BEAMS WHEN HITCHHIKING OFF THE !7!#3 TRANSMITTER FOR SHORT RANGE AIR SURVEILLANCE 0ULSE #HASING )F THE TRANSMITTERS BEAM SCANNING AND PULSE TRANSMISSION SCHED ULE ARE KNOWN PULSE CHASING CAN BE CONSIDERED TO REDUCE THE MULTIBEAM COST PEN ALTY FURTHER n 4HIS WAS SUCCESSFULLY DEMONSTRATED IN THE "ISTATIC 2ADAR FOR 7EAPONS ,OCATION TEST PROGRAM 4HE SIMPLEST PULSE CHASING CONCEPT USES A SINGLE BEAM AND 230 THAT RAPIDLY SCANS THE VOLUME COVERED BY THE TRANSMIT BEAM CHASING THE PULSE AS IT PROPAGATES FROM THE TRANSMITTER 4HE RECEIVE BEAM SCANNING RATE MUST BE AT THE TRANSMITTERS PULSE PROPAGATION RATE MODIFIED BY THE USUAL GEOMETRIC CONDI TIONS 4HIS RATE P2 WAS INITIALLY IDENTIFIED BY *ACKSON AND SUBSEQUENTLY VERIFIED BY -OYER AND -ORGAN
P2 C TAN A 22
&OR OPERATION IN THE CO SITE REGION SEE 4ABLE P2 CAN VARY FROM nMS NEAR THE BASELINE TO nMS WHEN 24 22 , 4YPICAL P2 CONTOURS ARE SHOWN IN *ACKSON 4HESE RATES AND RATE CHANGES REQUIRE AN INERTIALESS ANTENNA FOR EXAMPLE A PHASED ARRAY WITH DIODE PHASE SHIFTERS .ORMALLY A PHASED ARRAY ANTENNA USED FOR SURVEILLANCE IS PROGRAMMED TO SWITCH BEAMS IN INCREMENTS OF A BEAMWIDTH &RACTIONAL SHIFTS OF A BEAMWIDTH CAN BE ACHIEVED BY CHANGING THE PHASE OF A FEW SYMMETRIC PAIRS OF PHASE SHIFTERS IN THE ARRAY )N THIS WAY A PSEUDO CONTINUOUS BEAM SCAN CAN BE GENERATED WITH THE REQUIRED RATES AND RATE CHANGES "ECAUSE OF PULSE PROPAGATION DELAYS FROM THE TARGET TO THE RECEIVER THE POINTING ANGLE OF THE RECEIVE BEAM P2 MUST LAG THE ACTUAL PULSE POSITION &OR AN INSTANTANEOUS PULSE POSITION THAT GENERATES A BISTATIC ANGLE A P2 P4 A )N TERMS OF THE BISTATIC TRIANGLE THE REQUIRED RECEIVE BEAM POINTING ANGLE IS
, COS P 4 ¤ ³ P 2 P 4 TAN ¥ 2 ¦ 4 22 , SIN P 4 ´µ
4HE MINIMUM RECEIVE BEAMWIDTH $P2 M REQUIRED TO CAPTURE ALL RETURNS FROM A RANGE CELL INTERSECTING THE COMMON BEAM AREA IS APPROXIMATED BY
$P 2 M y CS U TAN A $P 4 24 22
WHERE SU IS THE UNCOMPRESSED PULSE WIDTH AND $P4 IS THE TRANSMIT BEAMWIDTH 4HE APPROXIMATION ASSUMES THAT RESPECTIVE RAYS FROM THE TRANSMIT AND RECEIVE BEAMS ARE PARALLEL 4HE APPROXIMATION IS REASONABLE WHEN 24 22 , OR WHEN , CSU %QUATION SHOWS THAT $P2 M CHANGES AS THE RECEIVE BEAM SCANS OUT THE TRANSMIT BEAM 0HASED ARRAY ANTENNAS OPERATING WITH A DIGITAL BEAMFORMER CAN ACCOMMO DATE THIS CHANGE /THERWISE USE OF A FIXED BEAMWIDTH INCURS A SMALL BEAM MISMATCH LOSS !N EXAMPLE IS GIVEN IN 7ILLIS %VEN THOUGH ONE PULSE MUST BE CHASED AT A TIME A HITCHHIKER OPERATING IN THE CO SITE REGION HAS TIME TO CAPTURE ALL PULSES FROM A MONOSTATIC RADAR THAT USES RANGE UNAMBIGUOUS 02&S &URTHERMORE WHEN OPERATING IN THE TRANSMIT OR RECEIVE CENTERED OVALS REFER TO 4ABLE A HITCHHIKER CAN OPERATE WITH RANGE AMBIGUOUS 02&S FOR EXAMPLE WHEN TRANSMITTED FROM AN AIRBORNE RADAR %XAMPLES ARE GIVEN IN 7ILLIS
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/THER IMPLEMENTATIONS OF PULSE CHASING ARE POSSIBLE )N ONE CONCEPT THE FIXED MULTIBEAM RECEIVE ANTENNA IS USED AND TWO 230S ARE TIME MULTIPLEXED ACROSS THE MULTIBEAMS /NE 230 STEPS ACROSS THE EVEN NUMBERED BEAMS AND THE OTHER 230 STEPS ACROSS THE ODD NUMBERED BEAMS SO THAT RETURNS IN BEAM PAIRS ARE PROCESSED SIMULTANE OUSLY ETC 4HIS LEAPFROG SEQUENCE IS REQUIRED TO CAPTURE ALL RETURNS IN THE COMMON BEAM AREA ! SECOND CONCEPT USES TWO BEAMS AND TWO 230S STEP SCANNING OVER THE VOLUME COV ERED BY THE MULTIBEAM ANTENNA )T USES AN IDENTICAL LEAPFROG SEQUENCE "OTH CONCEPTS RELAX THE FRACTIONAL BEAM SCAN REQUIREMENTS BY EITHER SAMPLING OR STEPPING THE BEAMS IN UNITS OF A BEAMWIDTH 3INCE THEY BOTH PROCESS RETURNS ACROSS TWO BEAMWIDTHS BEFORE SWITCHING THE BEAM DWELL TIME 4B IS APPROXIMATELY $P2 M 22 C AND THE STEPPING RATE IS 4B 4HE APPROXIMATION ASSUMES NEGLIGIBLE PHASE SHIFT DELAYS AND SETTLING TIMES -OVING 4ARGET )NDICATION -4) CAN BE USED WITH ANY OF THESE PULSE CHASING IMPLE MENTATIONS AS LONG AS THE RECEIVE BEAM PRECISELY RETRACES ITS SCAN PATTERN ON SUCCES SIVE SWEEPS TO CAPTURE THE SAME CLUTTER SAMPLES OVER THE -4) PROCESSING TIME #OMBINATIONS #OMBINATIONS OF THESE REMEDIES CAN BE CONSIDERED &OR EXAM PLE A FIXED MULTIBEAM RECEIVE ANTENNA CAN BE USED WITH A FIXED FLOODLIGHT TRANSMIT ANTENNA 4HIS CONFIGURATION ALLOWS THE RECEIVER TO INTEGRATE LONGER SUBJECT TO TARGET CELL MIGRATION LIMITS WHICH IN TURN CAN RECOVER SOME OF THE LOST RANGE PERFORMANCE OF THE FLOODLIGHT ANTENNA )T ALSO HAS THE BENEFITS OF INCREASING DATA RATES AND SIMULTANE OUSLY SERVICING MULTIPLE RECEIVERS )T INCURS INCREASED SIDELOBE CLUTTER LEVELS AS WELL AS COMPLEXITY AND COST 3OME PASSIVE BISTATIC RADARS OPERATE IN THIS CONFIGURATION WHERE THE FLOODLIGHT TRANSMITTER IS PROVIDED BY A 46 OR &- BROADCAST STATION ! SINGLE RECEIVE BEAM CAN BE USED WITH A TRANSMIT ANTENNA THAT IS ADAPTIVELY TAPERED TO FLOOD ONLY THE ANGULAR REGION COVERED BY THE RECEIVE BEAM AT A GIVEN LOOK ANGLE WITH THE TAPERING SUCH THAT THE SIGNAL TO NOISE RATIO AT THE RECEIVER IS HELD CONSTANT AT ALL POSITIONS ALONG THE RECEIVE BEAM 4HIS SCHEME IS ANALOGOUS TO THE MONOSTATIC AIR SURVEILLANCE RADAR USING A COSECANT SQUARED ANTENNA PATTERN WHERE THE ECHO IS INDE PENDENT OF RANGE FOR A CONSTANT ALTITUDE TARGET )T HAS THE POTENTIAL OF RESTORING MUCH OF THE FRAME TIME AND RANGE PERFORMANCE BUT INCURS INCREASED SIDELOBE CLUTTER LEVELS AND INCREASED TRANSMITTER COST AND COMPLEXITY !N EXAMPLE IS GIVEN IN 7ILLIS .ONCOOPERATIVE 2& %NVIRONMENT -OST PASSIVE BISTATIC RADAR 0"2 CONCEPTS AND DEVELOPMENTS EXPLOIT COMMERCIAL BROADCAST TRANSMITTERS AS THEIR SOURCE OF RADAR ILLUMINATION &- AND (IGH $EFINITION ($ 46 TERRESTRIAL BROADCAST TRANSMITTERS ARE PARTICULARLY ATTRACTIVE DUE TO THEIR HIGH POWER NOISE LIKE WAVEFORMS AND RELATIVELY WIDE BANDWIDTHSn 7HEN THESE BROADCAST TRANSMITTERS ARE APPROPRIATELY SITED AND OPERATING THEY CAN SUPPORT MANY TYPES OF SURVEILLANCE PARTICULARLY AIR SURVEILLANCE WHICH IS OFTEN RESTRICTED FOR MONOSTATIC RADARS OPERATING AT 6(&5(& 4HE SURVEILLANCE CAN BE COVERT BECAUSE EVEN THE TRANSMITTER IS UNAWARE IT IS BEING EXPLOITED AND CAN BE COUNTER STEALTH DUE TO UNAVOIDABLE AIRCRAFT RESONANCES IN THE 6(&5(& REGION /THER ATTRACTIVE FEATURES ARE LOWER PRIME POWER REQUIREMENTS AND LOWER COSTS FOR THE 0"2 7HILE A 0"2 CAN EXPLOIT BOTH COOPERATIVE AND NONCOOPERATIVE BROADCAST TRANS MITTERS THE 0"2 HAS NO CONTROL OVER THEIR TRANSMISSION OR WAVEFORM PROPERTIES SPECIFICALLY THE TRANSMISSION SCHEDULE EFFECTIVE RADIATED POWER SPATIAL COVERAGE MODULATION TYPE MODULATION CONTENT AND RESULTING AUTOCORRELATION FUNCTION AS OUT LINED EARLIER &URTHERMORE INTERFERENCE FROM THE HOST EMITTER AND OTHER EMITTERS ESPE CIALLY IN URBAN AND SUBURBAN AREAS CAN SIGNIFICANTLY DEGRADE 0"2 PERFORMANCE 4HIS SECTION SUMMARIZES THE PROBLEMS AND REMEDIES ENCOUNTERED BY A 0"2 EXPLOITING THESE BROADCAST TRANSMITTERS
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7AVEFORMS 4HE EFFECTIVE RADIATED POWER %20 OF BROADCAST TRANSMITTERS CAN VARY FROM A MAXIMUM OF ^ -7 FOR 46 TRANSMITTERS TO A MINIMUM OF ^ 7 FOR CELL PHONE TOWER TRANSMITTERS 4HE FORMER CAN YIELD EQUIVALENT MONOSTATIC DETECTION RANGES OF AIR TARGETS OF n KM THE LATTER n KM WHICH IS OF THE ORDER OF THE CELL PHONE WAVE FORM RESOLUTION TYPICALLY KM #ONSEQUENTLY WHEN THESE LOW POWERED TRANSMITTERS ARE EVALUATED FOR SHORT RANGE GROUND OR AIR TARGET LOCATION ONLY DOPPLER AND COARSE $/! DATA ARE AVAILABLE WHICH SEVERELY RESTRICTS LOCATION CAPABILITY AS OUTLINED IN 3ECTION 4HUS THE LOW %20 OF THESE TRANSMITTERS CONSTRAINED BY THE AVAILABLE BANDWIDTH CONSPIRE TO SIGNIFICANTLY REDUCE THEIR UTILITY FOR 0"2 SURVEILLANCE 4HE TYPE OF MODULATION USED BY A BROADCAST TRANSMITTER IS PARTICULARLY IMPORTANT &OR EXAMPLE THE #RYSTAL 0ALACE 46 TRANSMITTER TRIALS IN ,ONDON ATTEMPTED RANGE MEASUREMENTS WITH ANALOG 46 WAVEFORMS BUT FOUND THAT THEY GENERATED HIGH RANGE SIDE LOBES ^ D" RANGE AMBIGUITIES EVERY KM AND MODEST RANGE RESOLUTION ^ KM AND CONCLUDED THAT SUCH WAVEFORMS WERE MORE SUITABLE FOR DOPPLER MEASUREMENTS 4HIS FINDING ESTABLISHED THE PRECEDENCE FOR SUBSEQUENT 0"2 DEVELOPMENTS DOPPLER EXPLOITATION OF STABLE NARROW BAND CARRIER LINES IN 46 TRANSMISSIONS AND RANGEDOPPLER EXPLOITATION OF THE WIDER BAND NOISE LIKE SPECTRUM OF &- TRANSMISSIONS 4HE MODULATION CONTENT OF MANY BROADCAST TRANSMITTERS CHANGES AS A FUNCTION OF TIME THEREBY COMPLICATING MATCHED FILTERING BY THE 0"2S RECEIVER 3PECIFICALLY THE RECEIVER MUST SAMPLE AND STORE A SEGMENT OF THE DIRECT PATH WAVEFORM AND THEN CROSS CORRELATE IT WITH THE RETURNED ECHO ALL IN REAL TIME 3INCE CROSS CORRELATION MUST BE PERFORMED OVER THE RANGE OF EXPECTED TARGET ECHO TIME DELAYS ANDOR DOPPLER SHIFTS CORRELATION RECEIVER COMPLEXITY IS INCREASED WITH RESPECT TO A MATCHED FILTER RECEIVER TYPICALLY USED BY MONOSTATIC RADAR 3UCH CROSS CORRELATION IS NOW FEASIBLE TO IMPLE MENT BUT COMPLICATES AN OTHERWISE WELL DEVELOPED OPERATION IN THE STABLE MORE PRE DICTABLE MONOSTATIC WORLD ! RELATED MODULATION CONTENT PROBLEM IS DEAD AIR WHERE NO INFORMATION IS BROAD CAST THUS THE BROADCAST TRANSMITTER MODULATION GOES TO ZERO AND RANGE MEASUREMENT ERRORS INCREASE WITHOUT LIMIT 4HIS CONDITION CAN OCCUR WHEN BROADCASTING A TALK SHOW OR CLASSICAL MUSIC BUT OCCURS LESS OFTEN WITH POPULAR OR ROCK MUSIC 4HE FREQUENCY OF THIS TYPE OF OUTAGE IS NOT INSIGNIFICANT OCCURRING ROUGHLY ONCE PER SECOND FOR TALK BROADCASTS #ONSEQUENTLY ONCE A TRACK HAS BEEN ESTABLISHED A NONLINEAR TRACKING FILTER MAY BE NEEDED TO EDIT OUT LARGE ERROR SPIKES SEE #HAPTER OF 7ILLIS AND 'RIFFITHS 2ADIO &REQUENCY )NTERFERENCE 0ASSIVE BISTATIC RADAR PERFORMANCE IS SUBJECT TO DEGRADATION BY RADIO FREQUENCY INTERFERENCE 2&) FROM BOTH THE EXPLOITED BROADCAST TRANSMITTER AND OTHER EMITTERS IN SPATIAL OR FREQUENCY PROXIMITY 4HESE EMITTERS CAN INCLUDE BROADCAST COMMUNICATIONS AND NAVIGATION TRANSMITTERS AS WELL AS POWER TOOLS FLUORESCENT LIGHTS COOLING FANS AND OLD AUTOMOBILE IGNITIONS WHICH TYPICALLY GENERATE IMPULSIVE NOISE 2&) CAN ARRIVE VIA A DIRECT PATH OR MULTIPATH AND INCLUDES SCATTERING FROM TERRAIN OR SEA SURFACES ALSO CALLED CLUTTER (OWEVER THE SIGNAL FROM AN EXPLOITED TRANSMITTER ARRIVING OVER THE DIRECT TRANSMITTER TO RECEIVER PATH CALLED THE DIRECT PATH IS NEARLY ALWAYS THE DOMINANT 2&) SOURCE -ULTIPATH SIGNALS FROM THAT TRANSMITTER ARE LESS SEVERE BUT CAN ALSO CONTRIBUTE TO 2&) 2&) OVER THE DIRECT PATH FROM THE EXPLOITED TRANSMITTER ALSO CALLED DIRECT PATH BREAKTHROUGH IS COMMON TO ALL BUT THE SIMPLEST LOW POWER #7 RADAR )T BECOMES
3KY NOISE CONSISTING OF SUN GALACTIC AND ATMOSPHERIC NOISE IS ANOTHER SOURCE OF 2&) WHICH CAN INCREASE THE RECEIVERS NOISE TEMPERATURE BY A FACTOR OF n AT FREQUENCIES BELOW ^ -(Z (OWEVER THIS INCREASE IS USUALLY ORDERS OF MAGNITUDE SMALLER THAN 2&) FROM OTHER SOURCES AND CAN BE IGNORED
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PARTICULARLY SEVERE WHEN THE RECEIVER IS LOCATED IN DIRECT ,/3 OF THE TRANSMITTER WHICH MUST OCCUR WHEN SURVEILLANCE OF LOW ALTITUDE AIR TARGETS IS REQUIRED %QS n )F THIS DIRECT PATH SIGNAL IS NOT ATTENUATED THE RECEIVED SIGNAL BECOMES MASKED IN RANGE AND OFTEN MASKED IN DOPPLER BY SIDELOBES OF THE CORRELATED DIRECT PATH SIGNAL $IRECT PATH BREAKTHROUGH EFFECTS ARE SIMILAR TO THOSE OF A SPOT NOISE JAMMER AND CAN BE CHARACTERIZED BY AN INCREASE IN THE SYSTEM NOISE TEMPERATURE 4S &N 4O WHERE &N IS THE RECEIVER NOISE FIGURE AND 4O + 3PECIFICALLY THE AMOUNT OF INCREASE IN 4S AND HENCE THE AMOUNT OF ATTENUATION #DP REQUIRED TO REDUCE THE DIRECT PATH SIGNAL TO THE LEVEL OF 4S IS
#DP 04 '4 '2 4 K O " , K4S
WHERE 04 '4 K AND K ARE DEFINED WITH %Q '2 4 IS THE RECEIVING ANTENNA POWER GAIN IN THE DIRECTION OF THE TRANSMITTER " IS THE INPUT 2& BANDWIDTH AND , IS THE BASELINE RANGE &OR EXAMPLE IF THE 0"2 EXPLOITS A TYPICAL &- BROADCAST TRANSMITTER LOCATED AT A KM ,/3 FROM THE RECEIVER 04 '4 K7 K M " K(Z AND , KM !SSUMING A FIXED RECEIVING ANTENNA BEAM TAILORED IN ELEVATION AND COVERING A WIDE AZIMUTH SECTOR WHICH INCLUDES THE TRANSMITTER SITE '2 4 MIGHT BE D"I !LSO ASSUM ING THE AMBIENT 2&) ENVIRONMENT DESCRIBED BELOW THE NOISE SPECTRAL DENSITY K4S
D"7(Z THUS #DP D" #OMBINATIONS OF EARTH MASKING ANTENNA SHIELDING SPATIAL CANCELLATION AND SPEC TRAL CANCELLATION CAN BE USED TO ACHIEVE THE REQUIRED DIRECT PATH ATTENUATION ! BRUTE FORCE REMEDY IS TO PHYSICALLY BLOCK THE TRANSMIT SIGNAL FROM THE RECEIVER WITH A SHROUD OR STRUCTURE OR IF COVERAGE ALLOWS OVER THE HORIZON SEPARATION 7HILE MANY ORDERS OF MAGNITUDE ATTENUATION ARE POSSIBLE WITH THESE MASKING AND SHIELDING TECHNIQUES ADDI TIONAL REDUCTION IS NEARLY ALWAYS NECESSARY (OWLAND REPORTED A TWO STAGE SPATIAL NOISE CANCELLER WITH AN ADAPTIVE - STAGE LATTICE PREDICTOR - AS THE FIRST STAGE AND AN ADAPTIVE TAPPED DELAY LINE AS THE SECOND STAGE WHICH ACHIEVED ^ D" CANCELLATION OF THE NARROW BAND STATIONARY DIRECT PATH SIGNAL 4HIS CANCELLATION COMBINED WITH MASKING ACHIEVED D" ATTENUATION WHICH SATISFIES THE #DP REQUIREMENT IN THE ABOVE EXAMPLE (OWLAND ALSO OBSERVED THAT RECEIVER DYNAMIC RANGE ULTIMATELY LIMITS THE AVAIL ABLE CANCELLATION WHICH IN TURN IS SET BY THE RECEIVERS ANALOG TO DIGITAL CONVERTER .EARBY EMITTERS CAN SIGNIFICANTLY RAISE THE SYSTEM NOISE LEVEL SIMPLY THROUGH SPEC TRAL SPILLOVER FROM ADJACENT OR NEARBY BANDS )N THE 53 THE &## MANDATES A GAUSS IAN SPECTRAL ROLL OFF FOR MANY BROADCAST TRANSMITTERS WHICH IS SUFFICIENT TO PREVENT INTERFERENCE IN ONE WAY HOME RECEIVERS FROM ADJACENT TRANSMISSIONS (OWEVER IT IS NOT SUFFICIENT FOR TWO WAY RADAR RECEIVERS WHICH NECESSARILY MUST WORK MUCH FARTHER INTO THE RECEIVER NOISE 4HE SEVERITY OF THIS PROBLEM WAS QUANTIFIED BY IN SITU MEASUREMENTS OF SEVERAL 6(& AND 5(& BANDS IN A DENSE URBAN ENVIRONMENT !MBIENT 6(& NOISE LEVELS WERE FOUND TO BE TYPICALLY D" GREATER THAN THERMAL NOISE AND DIRECT PATH ILLUMINATOR SIGNALS SOME D" GREATER STILL %VEN WITH ROBUST CANCELLATION TECHNIQUES THE RESIDUE OF THIS UNSUPPRESSED 2&) WILL INCREASE THE 0"2S SYSTEM NOISE FIGURE BY MANY TENS OF DECIBELS A D" NOISE FIGURE AT 6(& IN URBAN AND SEMI RURAL AREAS IS NOT UNCOM MON 4HIS VALUE TRANSLATES INTO A NOISE SPECTRAL DENSITY OF n D"7(Z 3IMILAR MEASUREMENTS HAVE BEEN MADE AT 5(& WITH n D" NOISE FIGURES BEING OBTAINED USING SPECTRAL CANCELLATION BY A LEAST SQUARES CHANNEL ESTIMATOR 4HESE NOISE FIGURES ARE SIGNIFICANTLY HIGHER THAN THOSE OBTAINED IN THE 53 RADAR DESIGNATED 6(&5(& CHANNELS AND ARE A PENALTY FOR EXPLOITING BROADCAST TRANSMITTERS OF OPPORTUNITY
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Ó{°£Ê /," 1 /" 3INCE 7ORLD 7AR )) BOTH RADAR AND ELECTRONIC WARFARE %7 HAVE ACHIEVED A VERY HIGH STATE OF PERFORMANCE -ODERN MILITARY FORCES DEPEND HEAVILY ON ELECTROMAGNETIC %- SYSTEMS FOR SURVEILLANCE WEAPON CONTROL COMMUNICATION AND NAVIGATION THUS ACCESS TO AND CONTROL OF THE %- SPECTRUM IS VITAL %LECTRONIC COUNTERMEASURES %#- ARE LIKELY TO BE TAKEN BY HOSTILE FORCES TO DEGRADE THE EFFECTIVENESS OF %- SYSTEMSn !S A DIRECT CONSEQUENCE %- SYSTEMS ARE MORE AND MORE FREQUENTLY EQUIPPED WITH SO CALLED ELECTRONIC COUNTER COUNTERMEASURES %##- TO ENSURE EFFECTIVE USE OF THE %- SPECTRUM DESPITE AN ENEMYS USE OF %7 ACTIONS 4HIS CHAPTER IS DEVOTED TO THE DESCRIPTION OF THE %##- TECHNIQUES AND DESIGN PRIN CIPLES TO BE USED IN RADAR SYSTEMS WHEN THEY ARE SUBJECT TO AN %#- THREAT 3ECTION STARTS WITH A RECALL OF THE DEFINITIONS PERTAINING TO %7 AND %##- 4HE TOPIC OF RADAR SIGNALS INTERCEPTION BY %7 DEVICES IS INTRODUCED IN 3ECTION THE FIRST STRATEGY TO BE ADOPTED BY RADAR DESIGNERS IS TO TRY TO AVOID INTERCEPTION BY THE OPPONENT ELECTRONIC DEVICES 3ECTION IS DEDICATED ENTIRELY TO THE ANALYSIS OF THE MAJOR %#- TECHNIQUES AND STRATEGIES )T IS IMPORTANT TO UNDERSTAND THE %#- THREAT TO A RADAR SYSTEM IN ORDER TO BE ABLE TO EFFICIENTLY REACT TO IT 4O FACILITATE THE DESCRIPTION OF THE CROWDED FAMILY OF %##- TECHNIQUES 3ECTIONS THROUGH A CLASSIFICATION IS ATTEMPTED IN 3ECTION 4HEN THE TECHNIQUES ARE INTRODUCED ACCORDING TO THEIR USE IN THE VARI OUS SECTIONS OF RADAR NAMELY ANTENNA TRANSMITTER RECEIVER AND SIGNAL PROCESSING ! KEY ROLE IS ALSO PLAYED BY THOSE %##- TECHNIQUES THAT CANNOT BE CLASSIFIED AS ELECTRONIC SUCH AS HUMAN FACTORS METHODS OF RADAR OPERATION AND RADAR DEPLOYMENT TACTICS 3ECTION 4HE ENSUING 3ECTION SHOWS THE APPLICATION OF THE AFOREMENTIONED TECHNIQUES TO THE MOST COMMON RADAR FAMILIES NAMELY SURVEILLANCE TRACKING MULTIFUNCTIONAL PHASED ARRAY IMAGING AND OVER THE HORIZON RADARS 4HE MAIN DESIGN PRINCIPLES EG SELECTION OF TRANSMITTER POWER FREQUENCY WAVEFORM AND ANTENNA GAIN AS DICTATED BY THE %#- THREAT ARE ALSO DISCUSSED IN SOME DETAIL
! LIST OF ACRONYMS IS AT THE END OF THE CHAPTER BEFORE THE LIST OF REFERENCES
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4HE CHAPTER ENDS WITH AN APPROACH TO THE PROBLEM OF EVALUATING THE EFFICACY OF %##- AND %#- TECHNIQUES 3ECTION 4HERE IS A LACK OF THEORY TO PROPERLY QUAN TIFY THE ENDLESS BATTLE BETWEEN %##- AND %#- TECHNIQUES .EVERTHELESS A COMMONLY ADOPTED APPROACH TO DETERMINE THE %#- EFFECT ON A RADAR SYSTEM IS BASED ON EVALUATION OF THE RADAR RANGE UNDER JAMMING CONDITIONS 4HE ADVANTAGE OF USING SPECIFIC %##- TECHNIQUES CAN BE TAKEN INTO ACCOUNT BY CALCULATING THE RADAR RANGE RECOVERY ! LIST OF ACRONYMS USED IN THE CHAPTER AND THE REFERENCES APPEAR AT THE END OF THE CHAPTER
Ó{°ÓÊ / , " "9 %7 IS DEFINED AS A MILITARY ACTION INVOLVING THE USE OF %- ENERGY TO DETERMINE EXPLOIT REDUCE OR PREVENT RADAR USE OF THE %- SPECTRUMn 4HE OPERATIONAL EMPLOY MENT OF %7 RELIES UPON THE CAPTURE OF RADAR %- EMISSIONS USING ELECTRONIC INTELLI GENCE %,).4 DEVICES COLLATING THE INFORMATION IN SUPPORT DATABASES THAT ARE THEN USED TO INTERPRET %- EMISSION DATA TO UNDERSTAND THE RADAR SYSTEM FUNCTIONS AND TO PROGRAM REACTIONS AGAINST THE RADAR %7 IS ORGANIZED INTO TWO MAJOR CATEGORIES ELECTRONIC WARFARE SUPPORT MEASURES %3- AND %#- "ASICALLY THE %7 COMMUNITY TAKES AS ITS JOB THE DEGRADATION OF RADAR CAPABILITY 4HE RADAR COMMUNITY TAKES AS ITS JOB THE SUCCESSFUL APPLICATION OF RADAR IN SPITE OF WHAT THE %7 COMMUNITY DOES THE GOAL IS PURSUED BY MEANS OF %##- TECHNIQUES 4HE DEFINITIONS OF %3- %#- AND %##- ARE LISTED BELOW o %3- IS THAT DIVISION OF %7 INVOLVING ACTIONS TAKEN TO SEARCH FOR INTERCEPT LOCATE RECORD AND ANALYZE RADIATED %- ENERGY FOR THE PURPOSE OF EXPLOITING SUCH RADIATIONS IN THE SUPPORT OF MILITARY OPERATIONS 4HUS %3- PROVIDES A SOURCE OF %7 INFORMATION REQUIRED TO CONDUCT %#- THREAT DETECTION WARNING AND AVOIDANCE %#- IS THAT DIVI SION OF %7 INVOLVING ACTIONS TAKEN TO PREVENT OR REDUCE A RADARS EFFECTIVE USE OF THE %- SPECTRUM %##- COMPRISES THOSE RADAR ACTIONS TAKEN TO ENSURE EFFECTIVE USE OF THE %- SPECTRUM DESPITE THE ENEMYS USE OF %7 4HE TOPIC OF %7 IS EXTREMELY RICH IN TERMS SOME OF WHICH ARE ALSO IN GENERAL USE IN OTHER ELECTRONIC FIELDS ! COMPLETE GLOSSARY OF TERMS IN USE IN THE %#- AND %##- FIELDS IS FOUND IN THE LITERATURE
Ó{°ÎÊ /," Ê7,, ÊÊ -1**",/Ê -1, %3- USUALLY CONSISTS OF SEVERAL DETECTION AND MEASUREMENT RECEIVERS AND REAL TIME PROCESSOR BOARDS DEDICATED TO THE INTERCEPTION OF RADAR EMISSIONS 4HE IDENTIFICATION OF SPECIFIC EMITTERS IS BASED ON COMPARISON WITH TACTICAL OR STRATEGIC %,).4 n %MITTER LOCATION CAN BE ADDITIONALLY PROVIDED THROUGH SEVERAL METHODS SUCH AS TRIANGULATION o 3INCE THE PUBLICATION OF THE SECOND EDITION OF THIS (ANDBOOK THE 53 !IR &ORCE CHANGED SOME OF THE %7 TERMS WE HAVE GOTTEN USED TO OVER THESE MANY YEARS %#- IS NOW %LECTRONIC !TTACK %! %##- IS %LECTRONIC 0ROTECTION %0 AND %3- IS %LECTRONIC 3UPPORT %3 4HESE TERMS ARE NOT USED IN THIS CHAPTER BECAUSE THEY ARE SELDOM USED BY THE RADAR COMMUNITY WHO SEEM TO PREFER RETAINING THE MORE FAMILIAR EXPRESSIONS %#- %##- AND %3-
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FROM REMOTE SYSTEMS OR SINGLE PLATFORM SEQUENTIAL BEARING MEASUREMENTS DIFFERENCE TIME OF ARRIVAL $4O! OR HYPERBOLATION AND 0HASE $IFFERENCE 2ATE 0$2 -ODERN DIGITAL RECEIVER TECHNOLOGY COUPLED WITH STATE OF THE ART DEINTERLEAVING SIGNAL PRO CESSING TO CLEANLY ISOLATE AND IDENTIFY INDIVIDUAL %- EMITTERS WILL ENHANCE SITUATION AWARENESS 5SING TECHNIQUES SUCH AS TIME AND FREQUENCY DIFFERENCE OF ARRIVAL WILL IMPROVE SINGLE AND MULTIPLE PLATFORM SPATIAL LOCATION THIS WILL ALLOW %7 TO BE USED TO CUE TARGETING SYSTEMS 2ADAR INTERCEPTION WHICH IS OF PARTICULAR INTEREST IN THIS SECTION IS BASED ON THE RECEPTION AND MEASUREMENTS OF THE SIGNALS TRANSMITTED BY RADAR SYSTEMS WHETHER PULSE OR #ONTINUOUS 7AVE #7 4HE OPERATIONAL SCENARIO IN WHICH %3- SHOULD OPERATE IS GENERALLY CROWDED WITH PULSED RADAR SIGNALS FIGURES OF TO MILLION PULSES PER SECOND ARE FREQUENTLY QUOTED IN THE LITERATURE 4HE CENTER FREQUENCY AMPLITUDE PULSE WIDTH TIME OF ARRIVAL 4O! AND BEARING OF EACH DETECTED PULSE ARE MEASURED CON VERTED IN DIGITAL FORMAT AND PACKED INTO A PULSE DESCRIPTOR WORD 0$7 4HE TRAIN OF 0$7S ARE SENT TO A PULSE SORT PROCESSOR THAT DEINTERLEAVES THE SEQUENCES BELONGING TO DIFFERENT EMITTERS AND IDENTIFIES 0ULSE 2EPETITION )NTERVAL 02) VALUES AND MODULATION LAWS RANDOM JITTER STAGGER SWITCHING &URTHER COMPARISON AGAINST AN EMITTER DATA BASE WHICH CONTAINS THE RANGE OF CHARACTERISTIC PARAMETERS FREQUENCY PULSE WIDTH 02) THE RELATED PATTERN OF AGILITY RANDOM STAGGER ETC FOR EACH EMITTER THE TYPE OF ANTENNA SCANNING PATTERN AND PERIODS PERMITS THE GENERATION OF AN EMITTER LIST WITH AN IDENTIFICATION SCORE 4HE %3- RECEIVER IS USED TO CONTROL THE DEPLOYMENT AND OPERATION OF %#- THE LINK BETWEEN %3- AND %#- IS OFTEN AUTOMATIC ! SINGLE RECEIVED RADAR PULSE IS CHARACTERIZED BY A NUMBER OF MEASURABLE PARAME TERS 4HE AVAILABILITY RESOLUTION AND ACCURACY OF THESE MEASUREMENTS MUST ALL BE TAKEN INTO ACCOUNT WHEN DESIGNING THE DEINTERLEAVING SYSTEM BECAUSE THE APPROACH USED DEPENDS ON THE PARAMETER DATA SET AVAILABLE /BVIOUSLY THE BETTER THE RESOLUTION AND ACCURACY OF ANY PARAMETER MEASUREMENT THE MORE EFFICIENTLY THE PULSE SORT PROCES SOR CAN CARRY OUT ITS TASK (OWEVER THERE ARE LIMITATIONS ON THE MEASUREMENT PROCESS FROM OUTSIDE THE %3- SYSTEM EG MULTIPATH FROM INSIDE THE SYSTEM EG TIMING CONSTRAINTS DEAD TIME DURING RECEPTION AND FROM COST EFFECTIVENESS CONSIDERATIONS !NGLE OF ARRIVAL IS THE MOST IMPORTANT SORTING PARAMETER AVAILABLE TO THE DEINTERLEAV ING PROCESS SINCE THE TARGET BEARING DOES NOT VARY FROM PULSE TO PULSE 4HEREFORE AMPLITUDE COMPARISON MONOPULSE ANTENNAS OR MULTIPLE BASE INTERFEROMETRIC PHASE COMPARISON SYSTEMS ARE OFTEN USED IN ORDER TO WARRANT BOTH SPATIAL COVERAGE AND PULSE BASED ANGLE OF ARRIVAL MEASUREMENT -ONOPULSE ROTATING ANTENNAS CAN ALSO BE USED WHEN THE TIME TO INTERCEPT IS NOT CRITICAL THIS IS THE %,).4 CASE AND IT IS POSSIBLE TO SCAN SEQUENTIALLY THE OPERATIONAL SCENARIO 4HE CARRIER FREQUENCY IS THE NEXT MOST IMPORTANT PULSE PARAMETER FOR DEINTERLEAV ING ! COMMON METHOD OF FREQUENCY MEASUREMENT IS TO USE A SCANNING SUPERHETERO DYNE RECEIVER THAT HAS THE ADVANTAGE OF HIGH SENSITIVITY GOOD FREQUENCY RESOLUTION AND IMMUNITY WITH RESPECT TO THE INTERFERENCE OF NEARBY EMITTERS 5NFORTUNATELY THIS TYPE OF RECEIVER HAS A POOR PROBABILITY OF INTERCEPT FOR THE SAME REASONS AS THE ROTATING BEARING MEASUREMENT SYSTEM 4HE SITUATION IS MUCH WORSE IF THE EMITTER IS ALSO FREQUENCY AGILE RANDOM VARIATION OR FREQUENCY HOPPING SYSTEMATIC VARIA TION ! COMMON METHOD TO ALLOW FOR WIDEBAND FREQUENCY MEASUREMENTS IS BASED ON INTERFEROMETRIC DEVICES THAT PROVIDE INSTANTANEOUS FREQUENCY MEASUREMENT WITH GOOD ACCURACY AND ARE ABLE TO REJECT SIGNAL INTERFERENCE WITH LOWER INTENSITY 4HE HIGHER SENSITIVITY AND PROBABILITY OF INTERCEPTION ARE PROVIDED BY WIDE INSTANTANEOUS BAND SUPERHETERODYNE RECEIVERS FOLLOWED BY BANKS OF CONTIGUOUS RECEIVER CHANNELS
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2!$!2 (!.$"//+
3EVERAL TECHNOLOGIES HAVE BEEN PROPOSED IN THE PAST SUCH AS SURFACE ACOUSTIC WAVE 3!7 FILTERS AND "RAGG CELLS 4HE PREFERRED APPROACH IS BASED ON DIGITAL RECEIVERS THAT INTEGRATE WIDEBAND SPECTRAL ANALYSIS AND SEVERAL POST DETECTION FUNCTIONS SUCH AS INTRAPULSE MODULATION MEASUREMENT AND WAVEFORM CODE RECONNAISSANCE 0ULSE WIDTH IS AN UNRELIABLE SORTING PARAMETER BECAUSE OF THE HIGH DEGREE OF CORRUP TION RESULTING FROM MULTIPATH TRANSMISSION -ULTIPATH EFFECTS CAN SEVERELY DISTORT THE PULSE ENVELOPE FOR EXAMPLE BY CREATING A LONG TAIL TO THE PULSE AND EVEN DISPLACING THE POSITION OF THE PEAK 4HE 4O! OF THE PULSE CAN BE TAKEN AS THE INSTANT THAT A THRESHOLD IS CROSSED BUT IN THE PRESENCE OF NOISE AND DISTORTION THIS BECOMES A VARIABLE MEASUREMENT .EVERTHELESS THE 4O! IS USED FOR DERIVING THE 02) OF THE RADAR 4HE AMPLITUDE OF THE PULSE IS TAKEN AS THE PEAK VALUE $YNAMIC RANGE CONSIDERATIONS MUST TAKE INTO ACCOUNT AT LEAST SOME THREE ORDERS OF MAGNITUDE FOR RANGE VARIATION AND THREE ORDERS OF MAGNITUDE FOR SCAN PATTERN VARIATIONS )N PRACTICE D" INSTANTANEOUS DYNAMIC RANGE SOUNDS LIKE A MINI MUM VALUE IN MANY APPLICATIONS IT SHOULD BE LARGER 4HE AMPLITUDE MEASUREMENT IS USED ALONG WITH 4O! FOR DERIVING THE SCAN PATTERN OF THE EMITTER 4HE CLASSIFICATION OF RADAR INTERCEPTION SYSTEMS IS BASED ON THE TYPE OF REPRESEN TATION THEY PROVIDE OF THE ELECTRONIC ENVIRONMENT ! RADAR WARNING RECEIVER 272 IN AN AIRBORNE INSTALLATION PROVIDES ALERTS OF THE PRESENCE OF THREATS SUCH AS RADAR ON A MISSILE SUPPLYING THE RELATIVE BEARING ON A COCKPIT BASED DISPLAY 3EARCH RADARS ARE NOT THE PRIMARY TARGET FOR THESE SYSTEMS THOUGH RANGE ADVANTAGE DUE TO ONE WAY PROPAGATION WITH RESPECT TO TWO WAY PROPAGATION ALLOWS RADAR INTERCEPTION AT FARTHER RANGE THAN OWN PLATFORM DETECTION 2EQUIRED SENSITIVITY VALUES RANGE FROM n D"M D" MILLI7ATT WITH RESPECT TO THE ISOTROPIC TO n D"M %3- IS THE MOST COMPLEX SYSTEM AND USUALLY COMPRISES THE CAPABILITY TO PRODUCE A PICTURE OF THE COMPLETE ELECTRONIC ORDER OF BATTLE IN ITS DEPLOYMENT AREA AND ALERT FUNCTION 4HIS KIND OF SYSTEM IS ABLE TO DETECT AND ANALYZE EMITTER WAVEFORMS AND SCANNING PATTERNS 4HE REACTION TIME FOR THE RECONNAISSANCE OF THE OPERATIONAL ENVIRONMENT MAY BE LESS THAN S THOUGH DANGEROUS EMITTERS AND ALERT FUNCTIONS CALL FOR TIGHTER CONSTRAINTS 2EQUIRED SENSITIVITY RANGES FROM n D"M TO BETTER THAN n D"M %,).4 SYSTEMS ARE SIMILAR TO %3- BUT MAY NOT REQUIRE PROBABILITY OF INTERCEPT 4HE REACTION TIME MAY BE MINUTES OR HOURS 4HE PURPOSE IS NOT TO DETECT EMITTERS AS SOON AS THEY SWITCH ON IN THE OPERATIONAL ENVIRONMENT BUT TO PROVIDE DETAILED CHARACTERISTICS OF EMITTERS TO ALLOW THE GENERATION OF AN IDENTIFICATION DATABASE FOR 272 AND %3- SYSTEMS %,).4 SYSTEM SENSITIVITY MAY REACH n D"M BUT THEY DONT NEED TO PRO VIDE SURVEILLANCE AND THEY CAN REACH SUCH PERFORMANCE BY MEANS OF SEVERAL DIRECTIVE ANTENNAS 4HE RANGE AT WHICH A RADAR EMISSION IS DETECTED BY AN 272 DEPENDS PRIMARILY ON THE SENSITIVITY OF THE RECEIVER AND THE RADIATED POWER OF THE VICTIM RADAR 4HE CALCU LATION OF THE WARNING RANGE CAN BE OBTAINED BY THE BASIC ONE WAY BEACON EQUATION WHICH PROVIDES THE SIGNAL TO NOISE RATIO 3.2 AT THE 272
¤ 3³ ¤ 0 ³ ¤ 'R L ³ ¤ ³ ' ¥ ¥¦ . ´µ ¦ P 2 ´µ T ¥¦ P ´µ ¥¦ K43 "´µ , AT 272
WHERE 0 IS THE RADAR RADIATED POWER 2 IS THE RANGE FROM THE 272 TO THE RADAR 'T IS THE TRANSMITTING ANTENNA GAIN OF THE RADAR 'R IS THE RECEIVING ANTENNA GAIN OF THE 272 K IS THE RADAR WAVELENGTH THE QUANTITY K4S" IS THE TOTAL SYSTEM NOISE POWER OF THE 272 AND , IS THE LOSSES
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%QUATION IS THE BASIS OF PERFORMANCE CALCULATION FOR AN 272 )T IS NOTED THAT THE 272 DETECTION PERFORMANCE IS INVERSELY PROPORTIONAL TO 2 RATHER THAN TO 2 OF THE RADAR TARGET DETECTION EQUATION &OR THIS REASON THE 272 CAN DETECT A RADIATING RADAR AT DISTANCES FAR BEYOND THOSE OF A RADARS OWN TARGET DETECTION CAPABILITY 4HE RADAR VERSUS INTERCEPTOR PROBLEM IS A BATTLE IN WHICH THE RADARS ADVANTAGE LIES IN THE USE OF MATCHED FILTERING WHICH CANNOT BE DUPLICATED BY THE INTERCEPTOR IT DOES NOT KNOW THE EXACT RADAR WAVEFORM WHILE THE INTERCEPTORS ADVANTAGE LIES IN THE FUNDAMENTAL 2 ADVANTAGE OF ONE WAY VERSUS TWO WAY RADAR PROPAGATIONn ,OW PROBABILITY OF INTERCEPT ,0) TECHNIQUES ARE APPLIED TO RADAR TO WIN THE BATTLE OF hTO SEE AND NOT TO BE SEENv SEE 3CHLEHER AND REFERENCES THEREIN
Ó{°{Ê /," Ê "1 / , -1, 4HE OBJECTIVES OF AN %#- SYSTEM ARE TO DENY INFORMATION DETECTION POSITION TRACK INITIATION TRACK UPDATE AND CLASSIFICATION OF ONE OR MORE TARGETS THAT THE RADAR SEEKS OR TO SURROUND DESIRED RADAR ECHOES WITH SO MANY FALSE TARGETS THAT THE TRUE INFORMATION CANNOT BE EXTRACTEDn %#- TACTICS AND TECHNIQUES MAY BE CLASSIFIED IN A NUMBER OF WAYS IE BY MAIN PURPOSE WHETHER ACTIVE OR PASSIVE BY DEPLOYMENT BY PLATFORM BY VICTIM RADAR OR BY A COMBINATION OF THESEn !N ENCYCLOPEDIA OF %#- TACTICS AND TECHNIQUES CAN BE FOUND IN THE LITERATURE (ERE DESCRIPTION IS LIMITED TO THE MOST COMMON TYPES OF %#- %#- INCLUDES BOTH JAMMING AND DECEPTION *AMMING IS THE INTENTIONAL AND DELIB ERATE TRANSMISSION OR RETRANSMISSION OF AMPLITUDE FREQUENCY PHASE OR OTHERWISE MODULATED INTERMITTENT #7 OR NOISE LIKE SIGNALS FOR THE PURPOSE OF INTERFERING WITH DISTURBING EXPLOITING DECEIVING MASKING OR OTHERWISE DEGRADING THE RECEPTION OF OTHER SIGNALS THAT ARE USED BY RADAR SYSTEMSn ! JAMMER IS ANY %#- DEVICE THAT TRANSMITS A SIGNAL OF ANY DUTY CYCLE FOR THE SOLE OR PARTIAL PURPOSE OF JAMMING A RADAR SYSTEMn 2ADIO SIGNALS BY SPECIAL TRANSMITTERS INTENDED FOR INTERFERING WITH OR PRECLUDING THE NORMAL OPERATION OF A VICTIM RADAR SYSTEM ARE CALLED ACTIVE JAMMING 4HEY PRODUCE AT THE INPUT OF A VICTIM SYSTEM A BACKGROUND THAT IMPEDES THE DETECTION AND RECOGNITION OF USEFUL SIGNALS AND DETERMINATION OF THEIR PARAMETERS 4HE MOST COMMON FORMS OF ACTIVE NOISE JAMMING ARE SPOT SWEPT AND BARRAGE NOISES 3POT NOISE IS USED WHEN THE CENTER FREQUENCY AND BANDWIDTH OF THE VICTIM SYSTEM TO BE JAMMED ARE KNOWN AND CONFINED TO A NARROW BAND (OWEVER MANY RADARS ARE FREQUENCY AGILE OVER A WIDEBAND AS AN %##- AGAINST SPOT JAMMING )F THE RATE OF FREQUENCY AGILITY IS SLOW ENOUGH THE JAMMER CAN FOLLOW THE FREQUENCY CHANGES AND MAINTAIN THE EFFECT OF SPOT JAMMING "ARRAGE OR BROAD BAND JAMMING IS SIMULTANEOUSLY RADIATED ACROSS THE ENTIRE BAND OF THE RADAR SPECTRUM OF INTEREST 4HIS METHOD IS USED AGAINST FREQUENCY AGILE SYSTEMS WHOSE RATES ARE TOO FAST TO FOLLOW OR WHEN THE VICTIMS FREQUENCY PARAMETERS ARE IMPRECISELY KNOWN *AMMER SIZE IS CHARACTERIZED BY THE EFFECTIVE RADIATED POWER %20 'J0J WHERE 'J IS THE TRANSMIT ANTENNA GAIN OF THE JAMMER AND 0J IS THE JAMMER POWER 0ASSIVE %#- IS SYNONYMOUS WITH CHAFF DECOYS AND OTHER REFLECTORS THAT REQUIRE NO PRIME POWER 4HE CHAFF IS MADE OF ELEMENTAL PASSIVE REFLECTORS THAT CAN BE FLOATED OR OTHERWISE SUSPENDED IN THE ATMOSPHERE OR EXOATMOSPHERE FOR THE PURPOSE OF CONFUSING SCREENING OR OTHERWISE ADVERSELY AFFECTING THE VICTIM ELECTRONIC SYSTEM %XAMPLES ARE METAL FOILS METAL COATED DIELECTRICS ALUMINUM SILVER OR ZINC OVER FIBERGLASS OR NYLON
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2!$!2 (!.$"//+
BEING THE MOST COMMON STRING BALLS ROPE AND SEMICONDUCTORS #HAFF CONSISTS OF DIPOLES CUT TO APPROXIMATELY A HALF WAVELENGTH OF THE RADAR FREQUENCY )T IS SUITABLY PACKAGED TO CONTAIN A BROAD RANGE OF DIPOLE LENGTHS DESIGNED TO BE EFFECTIVE OVER A WIDE FREQUENCY BAND 4HE BASIC PROPERTIES OF CHAFF ARE EFFECTIVE SCATTER AREA THE CHARACTER AND TIME OF DEVELOPMENT OF A CHAFF CLOUD THE SPECTRA OF THE SIGNALS REFLECTED BY THE CLOUD AND THE WIDTH OF THE BAND THAT CONCEALS THE TARGET &ROM A RADAR VIEWPOINT THE PROPERTIES OF CHAFF ARE VERY SIMILAR TO THOSE OF WEATHER CLUTTER EXCEPT THAT ITS BROADBAND IN FREQUENCY CAN EXTEND DOWN TO 6(& 4HE MEAN DOPPLER FREQUENCY OF THE CHAFF SPECTRUM IS DETERMINED BY THE MEAN WIND VELOCITY WHILE THE SPECTRUM SPREAD IS DETERMINED BY WIND TURBULENCE AND A SHEARING EFFECT DUE TO DIFFERENT WIND VELOCITIES AS A FUNCTION OF ALTITUDE $ECOYS WHICH ARE ANOTHER TYPE OF PASSIVE %#- ARE A CLASS OF PHYSICALLY SMALL RADAR TARGETS WHOSE RADAR CROSS SECTIONS 2#3 ARE GENERALLY ENHANCED BY USING REFLEC TORS OR A ,UNEBURG LENS TO SIMULATE FIGHTER OR BOMBER AIRCRAFT 4HE OBJECTIVE OF DECOYS IS TO CAUSE A DILUTION OF THE ASSETS OF THE DEFENSIVE SYSTEM THEREBY INCREASING THE SUR VIVABILITY OF THE PENETRATING AIRCRAFT (OWEVER WHEN THE DECOYS GROW TOO LARGE THEY HAVE TO BE ENGAGED IF THEY ARE THOUGHT LARGE ENOUGH TO CARRY A WEAPON 0ENETRATION !ID 0ENAIDS COULD BE USED BY INCOMING BALLISTIC MISSILES "-S 0ENAID DECOYS ARE ONLY ONE OF SEVERAL POSSIBLE PENAIDS ! DECOY PROVIDES ANOTHER TARGET THAT THE DEFENSE HAS TO HANDLE IF THE DEFENSE CANNOT DISTINGUISH A DECOY FROM A RE ENTRY VEHICLE 4HE OTHER MAJOR TYPE OF ACTIVE JAMMER IS DECEPTIVE %#- $%#- $ECEPTION IS THE INTENTIONAL AND DELIBERATE TRANSMISSION OR RETRANSMISSION OF AMPLITUDE FREQUENCY PHASE OR OTHERWISE MODULATED INTERMITTENT OR #7 SIGNALS FOR THE PURPOSE OF MISLEAD ING IN THE INTERPRETATION OR USE OF INFORMATION BY ELECTRONIC SYSTEMS 4HE CATEGORIES OF DECEPTION ARE MANIPULATIVE AND IMITATIVE -ANIPULATIVE IMPLIES THE ALTERATION OF FRIENDLY %- SIGNALS TO ACCOMPLISH DECEPTION WHEREAS IMITATIVE CONSISTS OF INTRODUCING RADIATION INTO RADAR CHANNELS THAT IMITATES A HOSTILE EMISSION $%#- IS ALSO DIVIDED INTO TRANSPONDERS AND REPEATERS 4RANSPONDERS GENERATE NONCOHERENT SIGNALS THAT EMU LATE THE TEMPORAL CHARACTERISTICS OF THE ACTUAL RADAR RETURN 2EPEATERS GENERATE COHERENT RETURNS THAT ATTEMPT TO EMULATE THE AMPLITUDE FREQUENCY AND TEMPORAL CHARACTERISTICS OF THE ACTUAL RADAR RETURN 2EPEATERS USUALLY REQUIRE SOME FORM OF MEMORY FOR MICROWAVE SIGNALS TO ALLOW ANTICIPATORY RETURNS TO BE GENERATED THIS IS USUALLY IMPLEMENTED BY USING A MICROWAVE ACOUSTIC MEMORY OR A DIGITAL 2& MEMORY $2&- )N A $2&- SYSTEM THE INPUT 2& SIGNAL IS GENERALLY FIRST DOWN SHIFTED IN FREQUENCY AND THEN SAMPLED WITH A HIGH SPEED ANALOGUE TO DIGITAL CONVERTER !$# 4HE SAMPLES STORED IN MEMORY CAN BE MANIPULATED IN AMPLITUDE FREQUENCY AND PHASE TO GENERATE A WIDE RANGE OF JAMMING SIGNALS 4HE STORED SAMPLES ARE LATER RECALLED PROCESSED BY THE DIGITAL TO ANALOGUE CONVERTER $!# UP CONVERTED AND TRANSMITTED BACK TO THE VICTIM RADAR 4HE INFORMATION CONTENT OF AN INTERCEPTED RADAR SIGNAL IS MAINLY CARRIED IN THE PHASE OF THE SIGNAL AND THEN THE AMPLITUDE IS USUALLY DISCARDED AND ONLY THE PHASE CONTRIBUTION IS QUANTIZED AND PROCESSED 4HE PHASE QUANTIZATION IS PERFORMED BY THE $2&- BY MEANS OF - BITS INTO . - LEVELS !FTER THE PHASE QUANTIZATION INTRODUCED ON THE SIGNAL BY THE $2&- THE JAMMING SIGNAL IS TRANSMITTED BACK TO THE VICTIM RADAR WITH AN INCREASING DELAY WITH RESPECT TO THE RECEIVED RADAR SIGNAL 4HIS DELAY IS QUANTIZED BY A RANGE GATE PULL OFF 2'0/ DEVICE ! RANGE GATE STEALER SYSTEM LINEARLY DELAYS THE QUANTIZED SIGNAL IN ORDER TO GENERATE A CONSTANT RANGE RATE FALSE TARGET 4HE JOINT EFFECT OF PHASE AND DELAY QUANTIZATION IN $2&- CAN BE ANALYZED AS REPORTED IN 'RECO 'INI AND &ARINA /THER ARTIFACTS IN THE DECEPTION SIGNALS CAN BE INTRODUCED BY IMPERFECTIONS IN THE DOWN UP CONVERSION AND DEMODULATIONMODULATION OF THE SIGNAL PERFORMED IN THE $2&- DEVICE ! DETAILED ANALYSIS OF THIS KIND OF ERRORS IS IN "ERGER
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4HE $2&- IS THE PRINCIPAL MEANS TO IMPLEMENT A DECEPTION JAMMER THE RANGE GATE STEALER PULLS THE RADAR TRACKING GATE FROM THE TARGET POSITION THROUGH THE INTRODUCTION OF A FALSE TARGET INTO THE RADARS RANGE TRACKING CIRCUITS ! REPEATER JAMMER SENDS BACK AN AMPLIFIED VERSION OF THE SIGNAL RECEIVED FROM THE RADAR 4HE DECEPTION SIGNAL BEING STRONGER THAN THE RADARS RETURN SIGNAL CAPTURES THE RANGE TRACKING CIRCUITS 4HE DECEP TION SIGNAL IS THEN PROGRESSIVELY DELAYED BY USING THE $2&- THEREBY hWALKINGv THE RANGE GATE OFF THE ACTUAL TARGET 2'0/ TECHNIQUE 7HEN THE RANGE GATE IS SUFFICIENTLY REMOVED FROM THE ACTUAL TARGET THE DECEPTION JAMMER IS TURNED OFF FORCING THE TRACK ING RADAR INTO A TARGET REACQUISITION MODE !NOTHER FORM OF DECEPTION IS THE VELOCITY GATE PULL OFF 6'0/ A COMBINATION OF 2'0/ AND 6'0/ IS ALSO POSSIBLE !NOTHER $%#- TECHNIQUE IS CALLED INVERSE GAIN JAMMING IT IS USED TO CAPTURE THE ANGLE TRACKING CIRCUITS OF A CONICAL SCAN TRACKING RADAR 4HIS TECHNIQUE REPEATS A REPLICA OF THE RECEIVED SIGNAL WITH AN INDUCED AMPLITUDE MODULATION THAT IS THE INVERSE OF THE VICTIM RADARS COMBINED TRANSMITTING AND RECEIVING ANTENNA SCAN PATTERNS !GAINST A CONICALLY SCANNING TRACKING RADAR AN INVERSE GAIN REPEATER JAMMER HAS THE EFFECT OF CAUSING POSITIVE FEEDBACK WHICH PUSHES THE TRACKING RADAR ANTENNA AWAY FROM THE TARGET RATHER THAN TOWARD THE TARGET )NVERSE GAIN JAMMING AND 2'0/ ARE COMBINED IN MANY CASES TO COUNTER CONICAL SCAN TRACKING RADARS 4HE VULNERABILITY OF CONICAL SCAN TO SUCH COUNTERMEASURES MOTIVATES THE USE OF MONOPULSE TRACKERS THAT ARE ALMOST ALWAYS USED IN MILITARY TRACKING RADARS ! DIFFERENT FORM OF $%#- USED AGAINST THE MAIN BEAM OF SURVEILLANCE RADAR ATTEMPTS TO COVER THE TARGETS SKIN RETURN WITH A WIDE PULSE IN ORDER TO CONFUSE THE RADARS SIGNAL PROCESSING CIRCUITRY INTO SUPPRESSING THE ACTUAL TARGET RETURN 7HAT THE RADAR CAN DO AGAINST $%#- IS DISCUSSED LATER SEE 3ECTION )N THE DEPLOYMENT OF %#- SEVERAL CLASSES CAN BE SINGLED OUT )N THE STAND OFF JAMMER 3/* CASE THE JAMMING PLATFORM REMAINS CLOSE TO BUT OUTSIDE THE LETHAL RANGE OF ENEMY WEAPON SYSTEMS AND JAMS THESE SYSTEMS TO PROTECT THE ATTACKING VEHICLES 3TAND OFF %#- SYSTEMS EMPLOY HIGH POWER NOISE JAMMING THAT MUST PENETRATE THROUGH THE RADAR ANTENNA RECEIVING SIDELOBES AT LONG RANGES %SCORT JAMMING IS ANOTHER %#- TACTIC IN WHICH THE JAMMING PLATFORM ACCOMPANIES THE STRIKE VEHICLES AND JAMS RADARS TO PROTECT THE STRIKE VEHICLES -UTUAL SUPPORT OR COOPERATIVE %#- INVOLVES THE COORDINATED CONDUCT OF %#- BY COMBAT ELEMENTS AGAINST ACQUISITION AND WEAPON CONTROL RADARS /NE ADVANTAGE OF MUTUAL SUPPORT JAMMING IS THE GREATER %20 AVAILABLE FROM A COLLECTION OF PLATFORMS IN CONTRAST WITH A SINGLE PLATFORM (OWEVER THE REAL VALUE OF MUTUAL SUPPORT JAMMING IS IN THE COORDINATED TACTICS THAT CAN BE EMPLOYED ! FAVORITE TACTIC EMPLOYED AGAINST TRACKING RADARS FOR EXAMPLE IS TO SWITCH BETWEEN JAMMERS LOCATED ON SEPARATE AIRCRAFT WITHIN THE RADARS BEAMWIDTH 4HIS BLINKING HAS THE EFFECT OF INTRODUCING ARTIFICIAL GLINT INTO THE RADAR TRACKING CIRCUITS WHICH IF INTRODUCED AT THE PROPER RATE TYPICALLY TO (Z CAN CAUSE THE RADAR TO BREAK ANGLE TRACK )N ADDITION BLINKING HAS THE DESIRABLE EFFECT OF CONFUSING RADIATION HOMING MISSILES THAT MIGHT BE DIRECTED AGAINST THE JAMMER RADIATIONS 3TAND FORWARD JAMMING IS AN %#- TACTIC IN WHICH THE JAMMING PLATFORM IS LOCATED BETWEEN THE WEAPON SYSTEMS AND THE STRIKE VEHICLES AND JAMS THE RADARS TO PROTECT THE STRIKE VEHICLES 4HE STAND FORWARD JAMMER IS USUALLY WITHIN THE LETHAL RANGE OF DEFEN SIVE WEAPON SYSTEMS FOR A CONSIDERABLE TIME 4HEREFORE ONLY THE USE OF RELATIVELY LOW COST REMOTELY PILOTED VEHICLES MIGHT BE PRACTICAL THEY CAN ASSIST STRIKE AIRCRAFT OR MISSILES IN PENETRATING RADAR DEFENDED AREAS BY JAMMING EJECTING CHAFF DROPPING EXPENDABLE JAMMERS OR DECOYS ACTING AS DECOYS THEMSELVES AND PERFORMING OTHER RELATED %#- TASKS
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2!$!2 (!.$"//+
! SELF SCREENING JAMMER 33* IS USED TO PROTECT THE CARRYING VEHICLE 4HIS SITUATION STRESSES THE CAPABILITY OF AN %#- SYSTEM RELATING TO ITS POWER SIGNAL PROCESSING AND %3- CAPABILITIES 3ELF PROTECTION 30 DECOY JAMMING IS AN OFF BOARD TECHNIQUE INTENDED TO CREATE ANGLE DECEPTION BY CAUSING A MISSILE SEEKER TO TRANSFER ANGLE TRACK FROM THE TARGET TO A DECOY #ONSEQUENTLY THE MISSILE GUIDES TOWARD THE DECOY AND AWAY FROM THE TARGET ! SELF PROTECTION DECOY IS MOST LIKELY TO BE USED BY LARGE FIGHTERATTACK AND BOMBER AIRCRAFT 4HE 30 DECOYS ARE EXPENDABLE OR TOWED %XPENDABLE DECOYS ARE EJECTED OR DROPPED FROM THE AIRCRAFT WHEREAS TOWED DECOYS ARE TETHERED BEHIND THE AIRCRAFT %XPENDABLE DECOYS CONTAIN MINIATURE JAMMING SYSTEMS THAT ARE SMALL ENOUGH TO FIT INTO A STANDARD CHAFFFLARE DISPENSER 4HE DECOY ORIENTS ITSELF TO THE AIR STREAM BY DEPLOYING LOW DRAG AERODYNAMIC FINS SUFFICIENT TO MAINTAIN STABLE FLIGHT 4HE DECOY DIVERGES FROM THE VELOCITY VECTOR OF THE LAUNCH AIRCRAFT BY NATURAL DECELERATION AS A RESULT OF AIR STREAM AND FALLING DUE TO GRAVITY 4HE DECOY TYPICALLY STARTS RADIATING JAMMING SIGNALS TOWARD THE MISSILE SEEKER IMMEDIATELY AFTER EJECTION FROM THE AIRCRAFT AND CONTINUES RADIATION THROUGHOUT ITS FLIGHT $ECOY EJECTION IS TYPICALLY COMMENCED WHEN THE 272 DETECTS INCOMING RADAR GUIDED MISSILES -ULTIPLE DECOYS ARE SOMETIMES DISPENSED AT PREDETER MINED RATES IN ORDER TO IMPROVE THE CUMULATIVE PROBABILITY OF AIRCRAFT SURVIVAL ! TOWED DECOY IS A SMALL AERODYNAMICALLY STABLE BODY THAT HOUSES A MINIATURE JAM MER 4HE DECOY IS DEPLOYED BY REELING IT OUT ON A CABLE BEHIND THE AIRCRAFT TO A FIXED DISTANCE OR OFFSET 4HIS OFFSET IS CHOSEN SUCH THAT EVEN IF A MISSILE HITS THE DECOY THE AIRCRAFT WILL NOT BE DAMAGED 4HE DECOY CAN EITHER BE POWERED BY THE AIRCRAFT VIA THE CABLE OR BE SELF POWERED "ESIDES PROVIDING POWER TO THE DECOY THE CABLE CAN ALSO BE USED AS A DATA LINK TO CONTROL JAMMER OPERATION /NCE DEPLOYED THE TOWED DECOY CAN BEGIN RADIATING JAMMING SIGNALS TOWARD THE MISSILE SEEKER 7HEN THE TOWED DECOY IS NO LONGER NEEDED IT IS EITHER REELED IN OR JETTISONED 4HE MAJOR DRAWBACK WITH TOWED DECOYS IS THAT THEY MIGHT SEVERELY DEGRADE AIRCRAFT MANEUVERABILITY !CCORDING TO THE PLATFORM THE JAMMER CAN BE CLASSIFIED AS AIRBORNE MISSILE BORNE NAVAL BASED OR GROUND BASED ! SPECIAL CLASS OF MISSILE BORNE THREAT IS THE ANTI RADIATION MISSILE !2- HAVING THE OBJECTIVE OF HOMING ON AND DESTROYING THE VICTIM RADAR 4HE SORTING AND ACQUISITION OF RADAR SIGNALS IS PRELIMINARILY MADE BY AN %3- SYSTEM AFTERWARD IT CUES THE !2- WHICH CONTINUES HOMING ON THE VICTIM RADAR BY MEANS OF ITS OWN ANTENNA RECEIVER AND SIGNAL PROCESSOR !CQUISITION DEPENDS ON THE DIRECTION OF ARRIVAL $O! OPERATING BAND CARRIER FREQUENCY PULSE WIDTH 02) SCAN RATE AND OTHER PARAMETERS OF THE VICTIM RADAR !N !2- HOMES ON THE CONTINUOUS RADIATION FROM THE RADAR SIDELOBES OR ON THE FLASH OF ENERGY FROM THE MAIN BEAM !2- BENEFITS FROM THE ONE WAY ONLY RADAR SIGNAL ATTENUA TION (OWEVER !2- RECEIVER SENSITIVITY IS AFFECTED BY MISMATCHING LOSSES ACCURACY IN LOCATING THE VICTIM RADAR IS AFFECTED BY THE LIMITED DIMENSION OF THE !2- ANTENNA
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Ê/ +1 4HE PRIMARY OBJECTIVE OF %##- TECHNIQUES WHEN APPLIED TO A RADAR SYSTEM IS TO ALLOW THE ACCOMPLISHMENT OF THE RADAR INTENDED MISSION WHILE COUNTERING THE EFFECTS OF THE ENEMYS %#- )N GREATER DETAIL THE BENEFITS OF USING %##- TECHNIQUES MAY BE SUMMARIZED AS FOLLOWS PREVENTION OF RADAR SATURATION ENHANCEMENT OF THE SIGNAL TO JAMMING RATIO DISCRIMINATION OF DIRECTIONAL INTERFERENCE REJECTION OF
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FALSE TARGETS MAINTENANCE OF TARGET TRACKS COUNTERACTION OF %3- AND RADAR SYSTEM SURVIVABILITY 4HERE ARE TWO BROAD CLASSES OF %##- ELECTRONIC TECHNIQUES 3ECTION n AND OPERATIONAL DOCTRINES 3ECTION 3PECIFIC ELECTRONIC TECHNIQUES TAKE PLACE IN THE MAIN RADAR SUBSYSTEMS NAMELY THE ANTENNA TRANSMITTER RECEIVER AND SIG NAL PROCESSOR 4ABLE SHOWS A CATEGORIZATION OF SOME %##- TECHNIQUES ALONG WITH THE %#- TECHNIQUES THAT ARE USED TO COUNTER 3UITABLE BLENDING OF THESE %##- TECHNIQUES CAN BE IMPLEMENTED IN THE VARIOUS TYPES OF RADARS AS DISCUSSED IN 3ECTION 4HE ENSUING DESCRIPTION IS LIMITED TO THE MAJOR %##- TECHNIQUES THE READER SHOULD BE AWARE THAT AN ALPHABETICALLY LISTED COLLECTION OF %##- TECHNIQUES AND AN ENCY CLOPEDIA OF %##- TACTICS AND TECHNIQUES CAN BE FOUND IN THE LITERATURE -ANY OTHER REFERENCES DESCRIBE THE %##- PROBLEM AMONG WHICH 3LOCUMB AND 7EST -AKSIMOV ET AL 'ROS ET AL AND *OHNSON AND 3TONER ARE WORTH NOTING 4!",% %##- 4ECHNIQUES 6ERSUS %#- 4ECHNIQUE #OUNTERED 2EPRODUCED WITH PERMISSION
FROM 3LOCUMB AND 7EST Ú !RTECH (OUSE AND ' 6 -ORRIS %#- 4ECHNIQUE #ATEGORY #OUNTERED 2ADAR 3UBSYSTEM
!NTENNA RELATED
%##- 4ECHNIQUE ,OW OR ULTRA LOW SIDELOBES -ONOPULSE ANGLE TRACKING ,OW CROSS POLARIZED RESPONSE 3," SIDELOBE BLANKING 3,# SIDELOBE CANCELER %LECTRONIC SCAN !DAPTIVE RECEIVE POLARIZATION #ROSS POLARIZATION CANCELLATION
,OW CROSS POLARIZED ANTENNA (IGH POWER 4RANSMITTER 0ULSE COMPRESSION &REQUENCY DIVERSITY RELATED &REQUENCY AGILITY 02& JITTER
2ECEIVER RELATED
3IGNAL PROCESSING RELATED
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"ECAUSE THE ANTENNA REPRESENTS THE TRANSDUCER BETWEEN THE RADAR AND THE ENVIRON MENT IT IS THE FIRST LINE OF DEFENSE AGAINST JAMMING 4HE DIRECTIVITY OF THE ANTENNA IN THE TRANSMISSION AND RECEPTION PHASES ALLOWS SPACE DISCRIMINATION TO BE USED AS AN %##- STRATEGY 4ECHNIQUES FOR SPACE DISCRIMINATION INCLUDE ANTENNA COVERAGE AND SCAN CONTROL REDUCTION OF MAIN BEAM WIDTH LOW SIDELOBES SIDELOBE BLANKING SIDE LOBE CANCELERS AND ADAPTIVE ARRAY SYSTEMS 3OME OF THESE TECHNIQUES ARE USEFUL DUR ING TRANSMISSION WHEREAS OTHERS OPERATE IN THE RECEPTION PHASE !DDITIONALLY SOME ARE ACTIVE AGAINST MAIN BEAM JAMMERS AND OTHERS PROVIDE BENEFITS AGAINST SIDELOBE JAMMERS "LANKING OR TURNING OFF THE RECEIVER WHILE THE RADAR IS SCANNING ACROSS THE AZI MUTH SECTOR CONTAINING THE JAMMER OR REDUCING THE SCAN SECTOR COVERED ARE MEANS TO PREVENT THE RADAR FROM LOOKING AT THE JAMMER #ERTAIN DECEPTION JAMMERS DEPEND ON ANTICIPATION OF THE BEAM SCAN OR ON KNOWLEDGE OR MEASUREMENT OF THE ANTENNA SCAN RATE 2ANDOM ELECTRONIC SCANNING EFFECTIVELY PREVENTS THESE DECEPTION JAMMERS FROM SYNCHRONIZING TO THE ANTENNA SCAN RATE THUS DEFEATING THIS TYPE OF JAMMER ! HIGH GAIN ANTENNA CAN BE EMPLOYED TO SPOTLIGHT A TARGET AND BURN THROUGH THE JAMMERS !N ANTENNA HAVING MULTIPLE BEAMS CAN ALSO BE USED TO ALLOW DELETION OF THE BEAM CON TAINING THE JAMMER AND STILL MAINTAIN DETECTION CAPABILITIES WITH THE REMAINING BEAMS !LTHOUGH THEY ADD COMPLEXITY COST AND POSSIBLY WEIGHT TO THE ANTENNA REDUCTION OF MAIN BEAM WIDTH AND CONTROL OF COVERAGE AND SCAN ARE VALUABLE AND WORTHWHILE %##- FEATURES OF ALL RADARS )F AN AIR DEFENSE RADAR OPERATES IN A SEVERE %#- ENVIRONMENT THE DETECTION RANGE CAN BE DEGRADED BECAUSE OF JAMMING ENTERING THE SIDELOBES /N TRANSMIT THE ENERGY RADIATED INTO SPATIAL REGIONS OUTSIDE OF THE MAIN BEAM IS SUBJECT TO BEING RECEIVED BY ENEMY 272S OR !2-S &OR THESE REASONS LOW SIDELOBES ARE DESIRABLE ON BOTH RECEIVE AND TRANSMIT SEE 3CHRANK 0ATTON AND #HAPTER IN &ARINA 3OMETIMES THE INCREASE IN MAIN BEAM WIDTH THAT RESULTS FROM LOW SIDELOBES WORSENS THE PROBLEM OF MAIN BEAM JAMMING THIS CONSEQUENCE SHOULD BE CAREFULLY CONSIDERED IN SPECIFYING THE ANTENNA RADIATION PATTERN 5SUALLY SPECIFICATION OF THE SIDELOBES AS A SINGLE NUMBER EG D" MEANS THAT THE PEAK OF THE HIGHEST SIDELOBE IS D" BELOW THE PEAK OF THE MAIN BEAM 4HE AVERAGE OR ROOT MEAN SQUARE RMS SIDELOBE LEVEL IS OFTEN MORE IMPORTANT &OR EXAMPLE IF OF THE RADIATED POWER IS IN THE SIDELOBES THE AVERAGE SIDELOBE LEVEL IS D" WHERE D" REFERS TO THE NUMBER OF DECIBELS BY WHICH THE AVERAGE SIDELOBE LEVEL IS BELOW THE GAIN OF AN ISOTROPIC IDEAL RADIATOR )N THEORY EXTREMELY LOW SIDELOBES CAN BE ACHIEVED WITH APERTURE ILLUMINATION FUNCTIONS THAT ARE APPRO PRIATELY TAPERED 4HIS LEADS TO THE WELL KNOWN TRADEOFFS AMONG GAIN BEAMWIDTH AND SIDELOBE LEVEL )N ORDER TO KEEP THE BEAMWIDTH SMALL WITH LOW SIDELOBES A LARGER AND COSTLY THE COST COULD NOT BE THAT LARGE UNLESS THE RADAR USES AN ACTIVE APERTURE ANTENNA IS NEEDED 4HE CHIEF PROBLEM WITH THE LOW SIDELOBE ANTENNA IN ITS EARLY DAYS WAS THAT IT HAD MORE MECHANICAL PROBLEMS BECAUSE IT WAS A WAVEGUIDE ARRAY AND NOT A REFLECTOR /THER DESIGN PRINCIPLES INVOLVED IN LOW ANTENNA SIDELOBES ARE THE USE OF RADAR ABSORBENT MATERIAL ABOUT THE ANTENNA STRUCTURE THE USE OF A FENCE ON GROUND INSTALLATIONS AND THE USE OF POLARIZATION SCREENS AND REFLECTORS 4HIS MEANS THAT VERY LOW SIDELOBE ANTENNAS ARE COSTLY IN TERMS OF SIZE AND COMPLEXITY WHEN COMPARED WITH CONVENTIONAL ANTENNAS OF SIMILAR GAIN AND BEAMWIDTH CHARACTERISTICS 3ECOND AS THE DESIGN SIDELOBES ARE PUSHED LOWER AND LOWER A POINT IS REACHED WHERE
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MINOR ERROR CONTRIBUTIONS TO SCATTERED ENERGY RANDOM ERRORS OR MISDIRECTED RADIA TION SYSTEMATIC ERRORS BECOME SIGNIFICANT )N PRACTICE PEAK SIDELOBE LEVELS AS LOW AS TO D" AVERAGE LEVEL TO D" CAN BE READILY REALIZED WITH PHASED ARRAY ANTENNAS THAT ELECTRONICALLY SCAN 4O OBTAIN SIDELOBES AT LEVELS D" DOWN FROM THE MAIN BEAM AVERAGE LEVEL BELOW D" THE TOTAL PHASE ERROR BUDGET IS REQUIRED TO BE IN THE ORDER OF n RMS OR LESS 4HIS IS DIFFICULT IN ARRAYS THAT ELEC TRONICALLY SCAN THE ERRORS INDUCED BY PHASE SHIFTERS ACTIVE COMPONENTS AND FEED ELEMENTS MUST BE INCLUDED IN THIS BUDGET !RRAYS HAVE BEEN REALIZED IN PRACTICE THAT HAVE PEAK SIDELOBES IN THE VICINITY OF THE D" LEVEL HOWEVER THESE ARE GENERALLY MECHANICALLY SCANNED AND THE LOW ERROR BUDGETS ARE ACHIEVED BY USING ALL PASSIVE FEED COMPONENTS 0HASED ARRAY DEVELOPMENTS WHICH DO SCAN ELECTRONICALLY ALSO FORESEE FAIRLY GOOD SIDELOBE PERFORMANCE SEE THE FOLLOWING REFERENCESn FOR A VIEW OF RELEVANT DEVELOPMENTS 4WO ADDITIONAL TECHNIQUES TO PREVENT JAMMING FROM ENTERING THROUGH THE RADARS SIDELOBES ARE THE SO CALLED SIDELOBE BLANKING 3," AND SIDELOBE CANCELER 3,# !N EXAMPLE OF THE PRACTICAL EFFECTIVENESS OF THE 3," AND 3,# DEVICES IS PRESENTED IN THE LITERATURE WHERE THE PLAN POSITION INDICATOR 00) DISPLAY IS SHOWN FOR A RADAR SUBJECT TO AN %#- EQUIPPED WITH AND WITHOUT THE 3," AND 3,# SYSTEMS /THER DISCRIMINATION MEANS ARE BASED ON POLARIZATION 4HE POLARIZATION CHARACTER ISTICS OF A RADAR CAN BE EXPLOITED AS %##- TECHNIQUES IN TWO WAYS &IRST THE CROSS POLARIZED PATTERN IE THE ORTHOGONAL POLARIZATION TO THE MAIN PLANE OF POLARIZATION OF A RADAR ANTENNA SHOULD BE KEPT AS LOW AS POSSIBLE CONSISTENT WITH RADAR SYSTEM COST 2ATIOS OF COPOLARIZED MAIN BEAM PEAK GAIN TO CROSS POLARIZED GAIN ANYWHERE IN THE ANTENNA PATTERN SHOULD BE GREATER THAN D" TO PROVIDE PROTECTION AGAINST COMMON CROSS POLARIZED JAMMING 4HIS IS THOUGHT OF AS AN %##- TECHNIQUE BUT IT IS REALLY NO MORE THAN GOOD ANTENNA DESIGN 4HE CROSS POLARIZED JAMMING IN THIS CASE ATTACKS A DESIGN DEFICIENCY IN THE RADAR 4HE REQUIREMENT FOR GOOD CROSS POLARIZATION DESIGN PRACTICE IN A RADAR ANTENNA SYSTEM EXTENDS TO ANY AUXILIARY %##- ANTENNAS AS WELL )F THEIR CROSS POLARIZED GAINS ARE HIGH %##- TECHNIQUES SUCH AS 3,# AND 3," MAY NOT BE EFFECTIVE AGAINST CROSS POLARIZED NOISE OR REPEATER JAMMERS )N THE SECOND USE OF POLARIZATION THE RADAR ANTENNA SYSTEM PURPOSELY RECEIVES THE CROSS POLARIZATION COMPONENT OF THE RADAR WAVE IN ADDITION TO THE COPOLARIZED COMPONENT 4HE TWO ORTHOGONALLY POLARIZED COMPONENTS CAN BE USED TO DISCRIMINATE THE USEFUL TARGET FROM CHAFF AND JAMMER ON THE BASIS OF THEIR DIFFERENT POLARIZATIONS (OWEVER LIMITED BENEFITS A FEW DECIBELS OF CANCELLATION RATIO CAN BE OBTAINED AT THE EXPENSE OF A MORE COMPLEX ANTENNA SYSTEM CONSIDER FOR EXAMPLE A PHASED ARRAY WITH RADIATING ELEMENTS ABLE TO SEPARATELY RECEIVE AND POSSIBLY TRANSMIT THE TWO ORTHOGONAL COMPONENTS OF A RADAR WAVE AND OF A DUPLICATION OF THE RECEIVER AND SIGNAL PROCESSING 3IDELOBE "LANKING 3," 3YSTEM 4HE PURPOSE OF AN 3," SYSTEM IS TO PREVENT THE DETECTION OF STRONG TARGETS AND INTERFERENCE PULSES AS THEY MIGHT APPEAR AFTER PULSE COMPRESSION ENTERING THE RADAR RECEIVER VIA THE ANTENNA SIDELOBES 4HUS 3," IS MAINLY USED TO ELIMINATE INTERFERENCE FROM OTHER PULSE TRANSMISSIONS AND DELIBER ATE PULSE LIKE JAMMING !LSO 3," IS EFFECTIVE AGAINST COHERENT REPEATER INTERFERENCE #2) HERE hCOHERENTv MEANS THAT THE INTERFERENCE TRIES TO MIMIC THE CODED WAVEFORM RADIATED BY THE RADAR APPEARING AS A SPIKE SIGNAL AFTER PULSE COMPRESSIONn ! METHOD OF ACHIEVING THIS IS TO EMPLOY AN AUXILIARY ANTENNA COUPLED TO A PARALLEL RECEIV ING CHANNEL SO THAT TWO SIGNALS FROM A SINGLE SOURCE ARE AVAILABLE FOR COMPARISON
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&)'52% A -AIN AND AUXILIARY ANTENNA PATTERNS FOR THE 3," AFTER , -AISEL Ú )%%%
"Y SUITABLE CHOICE OF THE ANTENNA GAINS ONE MAY DISTINGUISH SIGNALS ENTERING THE SIDELOBES FROM THOSE ENTERING THE MAIN BEAM AND THE FORMER MAY BE SUPPRESSED &IGURE A ILLUSTRATES THE RADIATION PATTERN OF THE MAIN ANTENNA TOGETHER WITH A LOW GAIN AUXILIARY ANTENNA !N IMPLEMENTATION OF THE 3," PROCESSOR IS SHOWN IN &IGURE B WHERE THE SQUARE LAW DETECTED OUTPUTS OF THE TWO CHANNELS IDEALLY IDENTICAL EXCEPT FOR THE ANTENNA PATTERNS ARE COMPARED 4HE COMPARISON IS MADE AT EACH RANGE BIN FOR EACH PULSE RECEIVED AND PROCESSED BY THE TWO PARALLEL CHANNELS 4HUS THE 3," DECIDES WHETHER OR NOT TO BLANK THE MAIN CHANNEL ON A SINGLE SWEEP BASIS AND FOR EACH RANGE BIN ! TARGET ! IN THE MAIN BEAM WILL RESULT IN A LARGE SIGNAL IN THE MAIN RECEIVING CHANNEL AND A SMALL SIGNAL IN THE AUXILIARY RECEIVING CHANNEL ! PROPER BLANKING LOGIC ALLOWS THIS SIGNAL TO PASS 4ARGETS ANDOR JAMMERS * SITUATED IN THE SIDELOBES GIVE SMALL MAIN BUT LARGE AUXILIARY SIGNALS SO THAT THESE TARGETS ARE SUP PRESSED BY THE BLANKING LOGIC )T IS ASSUMED THAT THE GAIN '! OF THE AUXILIARY ANTENNA IS HIGHER THAN THE MAXIMUM GAIN 'SL OF THE SIDELOBES OF THE RADAR ANTENNA 4HE PERFORMANCE OF THE 3," MAY BE ANALYZED BY LOOKING AT THE DIFFERENT OUTCOMES OBTAINED AS A CONSEQUENCE OF THE PAIR U V OF THE PROCESSED SIGNALS SEE &IGURE B
&)'52% B 3CHEME OF SIDELOBE BLANKING SYSTEM AFTER , -AISEL Ú )%%%
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4HREE HYPOTHESES HAVE TO BE TESTED THE NULL HYPOTHESIS ( CORRESPONDING TO THE PRESENCE OF NOISE IN THE TWO CHANNELS THE ( HYPOTHESIS PERTAINING TO THE TARGET IN THE MAIN BEAM AND THE ( HYPOTHESIS CORRESPONDING TO TARGET OR INTERFERENCE SIGNAL IN THE SIDELOBE REGION 4HE NULL AND ( HYPOTHESES CORRESPOND TO THE USUAL DECI SIONS OF hNO DETECTIONv AND hTARGET DETECTION v RESPECTIVELY 4HE BLANKING COMMAND IS DELIVERED WHEN ( IS DETECTED 3," PERFORMANCE CAN BE EXPRESSED IN TERMS OF THE FOLLOWING PROBABILITIES I 4HE PROBABILITY 0" OF BLANKING A JAMMER IN THE RADAR SIDELOBES WHICH IS THE PROBABILITY OF ASSOCIATING THE RECEIVED SIGNALS U V WITH ( WHEN THE SAME HYPOTHESIS IS TRUE 0" IS A FUNCTION OF THE JAMMER TO NOISE RATIO *.2 VALUE THE BLANKING THRESHOLD & AND THE GAIN MARGIN A '!'SL OF THE AUXILIARY ANTENNA WITH RESPECT TO THE RADAR ANTENNA SIDELOBES II 4HE PROBABILITY 0&! OF FALSE ALARM WHICH IS THE PROBABILITY OF ASSOCIAT ING THE RECEIVED SIGNALS U V WITH THE HYPOTHESIS ( WHEN THE TRUE HYPOTHESIS IS ( 0&! IS A FUNCTION OF THE DETECTION THRESHOLD @ NORMALIZED TO THE NOISE POWER LEVEL AND OF THE BLANKING THRESHOLD & III 4HE PROBABILITY 0$ OF DETECTING A TARGET IN THE MAIN BEAM WHICH IS THE PROBABILITY OF ASSOCIATING THE RECEIVED SIGNAL U V WITH ( WHEN THE SAME HYPOTHESIS IS TRUE 0$ DEPENDS AMONG OTHER THINGS ON THE SIGNAL TO NOISE POWER RATIO 3.2 0&! AND THE BLANKING THRESHOLD & IV 4HE PROBABILITY 0&4 OF DETECT ING A FALSE TARGET PRODUCED BY A JAMMER ENTERING THROUGH THE RADAR SIDELOBES 0&4 IS THE PROBABILITY OF ASSOCIATING U V WITH ( WHEN ( IS TRUE IT IS A FUNCTION OF *.2 THE THRESHOLDS @ AND & AND THE GAIN MARGIN A V 4HE PROBABILITY 04" OF BLANKING A TARGET RECEIVED IN THE MAIN BEAM 4HIS IS THE PROBABILITY OF ASSOCIATING U V WITH ( WHEN ( IS THE TRUE HYPOTHESIS 04" IS RELATED TO 3.2 & AND THE AUXILIARY GAIN W '!'T NORMALIZED TO THE GAIN 'T OF THE MAIN BEAM 4O COMPLETE THE LIST OF PARAM ETERS NEEDED TO DESCRIBE THE 3," PERFORMANCE THE LAST FIGURE TO CONSIDER IS THE DETEC TION LOSS , ON THE MAIN BEAM TARGET 4HIS CAN BE FOUND BY COMPARING THE 3.2 VALUES REQUIRED TO ACHIEVE A SPECIFIED 0$ VALUE FOR THE RADAR SYSTEM WITH AND WITHOUT THE 3," , IS A FUNCTION OF MANY PARAMETERS SUCH AS 0$ 0&! & '! *.2 AND A ! NUMERICAL EVALUATION OF THESE PERFORMANCE PARAMETERS CAN BE FOUND IN THE LITERATURE SPECIFICALLY #HAPTER OF &ARINA AMONG OTHERSn 4HE 3," DESIGN REQUIRES THE SELECTION OF SUITABLE VALUES FOR THE FOLLOWING PARAME TERS #HAPTER OF &ARINA I THE GAIN MARGIN A AND THEN THE GAIN '! OF THE AUXILIARY ANTENNA II THE BLANKING THRESHOLD & AND THE NORMALIZED DETECTION THRESHOLD @ 4HE A PRIORI KNOWN PARAMETERS ARE HYPOTHESIZED TO BE THE RADAR SIDELOBE LEVEL 'SL AND THE VAL UES OF 3.2 AND *.2 4HE DESIGN PARAMETERS CAN BE SELECTED BY TRYING TO MAXIMIZE THE DETECTION PROBABILITY 0$ WHILE KEEPING AT PRESCRIBED VALUES THE PROBABILITIES 0" AND 0&! AND TRYING TO MINIMIZE 0&4 04" AND , 4HE CHOICE OF THE POSITION OF THE AUXILIARY ANTENNA HAS AN IMPACT ON 3," PERFORMANCE IN PRESENCE FOR INSTANCE OF MULTIPATH TO AVOID ITS EFFECT THE PHASE CENTERS OF MAIN AND AUXILIARY ANTENNAS SHOULD BE POSITIONED AT THE SAME HEIGHT WITH RESPECT TO THE TERRAIN SURFACE )N MODERN RADAR THE BLANKING OF SIDELOBE IMPULSIVE INTERFERENCE MAY BE ACHIEVED BY THE COMPARISON OF SIGNALS PERTAINING TO THE SAME CELLS OF THE RANGE FILTER MAP 2&- OF MAIN BEAM AND 3," CHANNELS 4HE 2&- IS A TWO DIMENSIONAL MAP COL LECTING THE RADAR ECHOES OF ALL RANGE CELLS AFTER PULSE COMPRESSION AND ALL DOPPLER FILTERS OF A RADAR BURST 4HE TWO 2&-S ARE INDEPENDENTLY GENERATED FOR THE MAIN AND AUXILIARY SIGNALS AND THE TESTING OF THE MAIN AND AUXILIARY RECEIVED POWER VALUES IS PERFORMED FOR ALL RANGE CELLS AND ALL DOPPLER FILTERS 4HIS IS DIFFERENT FROM A CONVEN TIONAL 3," APPROACH SUCH AS THE ONE ILLUSTRATED IN &IGURE OPERATING SO THAT IF INTERFERINGREPEATER JAMMER POWER IS DETECTED AT A PARTICULAR RANGE CELL THEN THAT RANGE CELL HAS TO BE EFFECTIVELY BLANKED 4HE 2&- BASED 3," LOGIC GREATLY REDUCES
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THE RISK OF SUCCESSFULLY EMULATING A USEFUL TARGET BECAUSE A REPEATER HAS TO APPEAR IN THE SAME TARGET RANGE CELL AND HAS TO EMULATE THE SAME TARGET DOPPLER 3IDELOBE #ANCELER 3,# 3YSTEM 4HE OBJECTIVE OF THE 3,# IS TO SUPPRESS HIGH DUTY CYCLE OR EVEN CONTINUOUS NOISE LIKE INTERFERENCES .,) EG 3/* RECEIVED THROUGH THE SIDELOBES OF THE RADAR 4HIS IS ACCOMPLISHED BY EQUIPPING THE RADAR WITH AN ARRAY OF AUXILIARY ANTENNAS USED TO ADAPTIVELY ESTIMATE THE $O! AND THE POWER OF THE JAMMERS AND SUBSEQUENTLY TO MODIFY THE RECEIVING PATTERN OF THE RADAR ANTENNA TO PLACE NULLS IN THE JAMMERS DIRECTIONS 4HE 3,# WAS INVENTED BY 0 (OWELLS AND 3 !PPLEBAUMn ! SAMPLE OF SUBSEQUENT REFERENCES ON 3,# ARE ALSO IN THE LITERATURE n 4HE CONCEPTUAL SCHEME OF AN 3,# SYSTEM IS SHOWN IN &IGURE 4HE AUXILIARY ANTENNAS PROVIDE REPLICAS OF THE JAMMING SIGNALS IN THE RADAR ANTENNA SIDELOBES 4O THIS END THE AUXILIARY PATTERNS APPROXIMATE THE AVERAGE SIDELOBE LEVEL OF THE RADAR RECEIVING PATTERN )N ADDITION THE AUXILIARIES ARE PLACED SUFFICIENTLY CLOSE TO THE PHASE CENTER OF THE RADAR ANTENNA TO ENSURE THAT THE SAMPLES OF THE INTERFERENCE THAT THEY OBTAIN ARE STATISTICALLY CORRELATED WITH THE RADAR JAMMING SIGNAL )T IS ALSO NOTED THAT AS MANY AUXILIARY ANTENNAS ARE NEEDED AS THERE ARE JAMMING SIGNALS TO BE SUPPRESSED )N FACT AT LEAST . AUXILIARY PATTERNS PROPERLY CONTROLLED IN AMPLITUDE
&)'52% 0RINCIPLE OF 3,# OPERATION CONNECTION A ONLY IN THE CLOSED LOOP IMPLEMENTATION TECHNIQUES 28 RECEIVER
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AND PHASE ARE NEEDED TO FORCE TO ZERO THE MAIN ANTENNA RECEIVING PATTERN IN . GIVEN DIRECTIONS 4HE AUXILIARIES MAY BE INDIVIDUAL ANTENNAS OR GROUPS OF RECEIVING ELE MENTS OF A PHASED ARRAY ANTENNA 4HE AMPLITUDE AND PHASE OF THE SIGNALS DELIVERED BY THE . AUXILIARIES ARE CONTROLLED BY A SET OF SUITABLE WEIGHTS DENOTE THE SET WITH THE . DIMENSIONAL VECTOR 7 7 7 x 7. 4HE JAMMING SIGNAL IS CANCELED BY A LINEAR COMBINATION OF THE SIGNALS FROM THE AUXILIARIES AND THE MAIN ANTENNA 4HE PROBLEM IS TO FIND A SUITABLE MEANS OF CONTROLLING THE WEIGHTS 7 OF THE LINEAR COMBINATION SO THAT THE MAXIMUM POSSIBLE CANCELLATION IS ACHIEVED /WING TO THE STOCHASTIC NATURE OF THE JAMMING SIGNALS IN THE RADAR AND IN THE AUXILIARY CHANNELS AND TO THE HYPOTHESIZED LINEAR COMBINATION OF SIGNALS IT IS ADVIS ABLE TO RESORT TO THE TECHNIQUES OF LINEAR PREDICTION THEORY FOR STOCHASTIC PROCESSES $ENOTE WITH 6- THE RADAR SIGNAL AT A CERTAIN RANGE BIN AND WITH 6 6 6 x 6. THE . DIMENSIONAL VECTOR CONTAINING THE SET OF SIGNALS AT THE SAME RANGE BIN FROM THE . AUXILIARY ANTENNAS )T IS ASSUMED THAT ALL THE SIGNALS HAVE BANDPASS FREQUENCY SPEC TRA THEREFORE THE SIGNALS CAN BE REPRESENTED BY THEIR COMPLEX ENVELOPES WHICH MODU LATE A COMMON CARRIER FREQUENCY THAT DOES NOT APPEAR EXPLICITLY 4HE JAMMING SIGNALS IN THE CHANNELS MAY BE REGARDED AS SAMPLES OF A STOCHASTIC PROCESS HAVING ZERO MEAN VALUE AND A CERTAIN TIME AUTOCORRELATION FUNCTION &OR LINEAR PREDICTION PROBLEMS THE SET OF SAMPLES 6 IS COMPLETELY DESCRIBED BY ITS . DIMENSIONAL COVARIANCE MATRIX - %6 64 WHERE % DENOTES THE STATISTICAL EXPECTATION THE ASTERISK INDICATES THE COMPLEX CONJUGATE AND 64 IS THE TRANSPOSE VECTOR OF 6 4HE STATISTICAL RELATIONSHIP BETWEEN 6- AND 6 IS MATHEMATICALLY REPRESENTED BY THE . DIMENSIONAL COVARIANCE } IS DETERMINED BY MINIMIZING THE VECTOR 2 %6-6 4HE OPTIMUM WEIGHT VECTOR 7 MEAN SQUARE PREDICTION ERROR WHICH EQUALS THE OUTPUT RESIDUAL POWER } 4 6 \] 0: %[\ : \] %[\ 6- 7
WHERE : IS THE SYSTEM OUTPUT )T IS FOUND THAT THE FOLLOWING FUNDAMENTAL EQUATION APPLIES } L- 2 7
WHERE L IS AN ARBITRARY CONSTANT VALUE 4HE BENEFIT OF USING THE 3,# CAN BE MEASURED BY INTRODUCING THE JAMMER CANCELLATION RATIO *#2 DEFINED AS THE RATIO OF THE OUTPUT NOISE POWER WITHOUT AND WITH THE 3,#
*#2
%[\ 6- \] %[\ 6- \] 4
4 } %[\ 6- 7 6 \ ] %[\ 6- \ ] 2 - 2
"Y APPLYING %QS AND TO THE SIMPLE CASE OF ONE AUXILIARY ANTENNA AND ONE JAMMER THE FOLLOWING RESULTS ARE FOUND
} %[6- 6! ] $ R 7 %[\ 6! \ ]
*#2
\ R \
)T IS NOTED THAT THE OPTIMUM WEIGHT IS RELATED TO THE CORRELATION COEFFICIENT Q BETWEEN THE MAIN SIGNAL 6- AND THE AUXILIARY SIGNAL 6! HIGH VALUES OF THE CORRELATION COEF FICIENT PROVIDE HIGH VALUES OF *#2 4HE PROBLEM OF IMPLEMENTING THE OPTIMUM WEIGHT SET %Q IS ESSENTIALLY RELATED TO THE REAL TIME ESTIMATION OF - AND 2 AND TO THE INVERSION OF - 3EVERAL PROCESSING
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SCHEMES HAVE BEEN CONCEIVED THAT MAY BE CLASSIFIED IN TWO MAIN CATEGORIES CLOSED LOOP TECHNIQUES IN WHICH THE OUTPUT RESIDUE CONNECTION A IN &IGURE IS FED BACK INTO THE ADAPTIVE SYSTEM AND DIRECT SOLUTION METHODS OFTEN REFERRED TO AS OPEN LOOP WHICH OPERATE JUST ON THE INCOMING SIGNALS 6- AND 6 "ROADLY SPEAKING CLOSED LOOP METHODS ARE CHEAPER AND SIMPLER TO IMPLEMENT THAN DIRECT SOLUTION METHODS ONE OF SEVERAL PRACTICAL IMPLEMENTATIONS IS DESCRIBED IN 'RIFFITHS "Y VIRTUE OF THEIR SELF CORRECTING NATURE THEY DO NOT REQUIRE COMPONENTS THAT HAVE A WIDE DYNAMIC RANGE OR A HIGH DEGREE OF LINEARITY AND SO THEY ARE WELL SUITED TO ANALOGUE IMPLEMENTATION (OWEVER CLOSED LOOP METHODS SUFFER FROM THE FUNDAMENTAL LIMITATION THAT THEIR SPEED OF RESPONSE MUST BE RESTRICTED IN ORDER TO ACHIEVE A STABLE AND NOT NOISY STEADY STATE $IRECT SOLUTION METHODS ON THE OTHER HAND DO NOT SUFFER FROM PROBLEMS OF SLOW CONVERGENCE BUT IN GENERAL REQUIRE COMPONENTS OF SUCH HIGH ACCURACY AND WIDE DYNAMIC RANGE THAT THEY CAN ONLY BE REALIZED BY DIGITAL MEANS /F COURSE CLOSED LOOP METHODS CAN ALSO BE IMPLEMENTED BY USING DIGITAL CIRCUITRY IN WHICH CASE THE CONSTRAINTS ON NUMERICAL ACCURACY ARE GREATLY RELAXED AND THE TOTAL NUMBER OF ARITHMETIC OPERATIONS IS MUCH REDUCED BY COMPARISON WITH DIRECT SOLUTION METHODS 4HE MAJORITY OF IMPLEMENTATIONS HAS BECOME OPEN LOOP WITH DIGITAL TECHNOLOGY 0RACTICAL CONSIDERATIONS SEE #HAPTER OF &ARINA FOR A DETAILED ANALYSIS OFTEN LIMIT THE 3,# NULLING CAPABILITIES TO A *#2 OF ABOUT TO D" BUT THEIR THEORETI CAL PERFORMANCE IS POTENTIALLY MUCH HIGHER !DEQUATE CANCELLATION OF THE DIRECTIONAL INTERFERENCE IS OBTAINED IF THE RECEIVING CHANNELS ARE PROPERLY MATCHED IN AMPLITUDE AND PHASE ACROSS THE RADAR RECEIVING BANDWIDTH 4HIS CONDITION IS NECESSARY TO ATTRI BUTE THE AMPLITUDE AND PHASE DIFFERENCES MEASURED ACROSS THE CHANNELS ONLY TO THE NATURE POWER AND $O! OF THE IMPINGING INTERFERENCE 4HERE ARE SEVERAL SOURCES OF MISMATCHING THE IMPERFECT MATCHING OF THE ANALOGUE RECEIVING CHANNELS IS ONE OF THE MAIN LIMITATIONS TO THE INTERFERENCE CANCELLATION 4HE EFFECT OF THIS MISMATCH ON THE *#2 HAS BEEN STUDIED IN THE LITERATURE SEE &ARINA AND REFERENCES THEREIN &OR CONTEMPORARY PRESENCE OF AMPLITUDE AND PHASE MISMATCHES THE *#2 HAS AN EXPRESSION THAT IS DERIVED IN !PPENDIX ! NUMERICAL APPLICATION OF THIS EQUATION IS SHOWN IN &IGURE THE PARAMETER VALUES OF THE STUDY CASE ARE QUOTED IN &ARINA &IGURE SHOWS THE *#2 CONTOUR CURVES VERSUS THE NORMALIZED AMPLITUDE AN AND THE PHASE B DEGREES MISMATCHES OF THE ANALOGUE RECEIVING CHANNELS SEE &ARINA FOR THE PRECISE DEFINITION OF THESE PARAMETERS )T IS SEEN THAT TO HAVE D" OF *#2 ONE NEEDS TO SPECIFY TIGHT REQUIREMENTS FOR BOTH AMPLITUDE BELOW AND PHASE BELOW MISMATCHES 4HIS FIGURE MOTIVATES THE NEED TO RESORT TO EQUALIZATION DIGITAL FILTERS TO COMPENSATE FOR THE MISMATCHES OF THE AUXILIARY CHANNELS IN THEIR ANALOGUE PART WITH RESPECT TO THE MAIN CHANNEL 4HIS SUBJECT IS COVERED IN &ARINA AND REFERENCES THEREIN %XAMPLES OF OTHER POSSIBLE LIMI TATIONS TO CANCELLATION ARE LISTED BELOW -ISMATCH BETWEEN THE MAIN AND AUXILIARY SIGNALS INCLUDING THE PROPAGATION PATHS THE PATTERNS OF THE MAIN AND AUXILIARY ANTENNAS THE PATHS INTERNAL TO THE SYSTEM UP TO THE CANCELLATION POINT AND THE CROSSTALK BETWEEN THE CHANNELSn 4HE LIMITED NUMBER OF AUXILIARY CHANNELS ADOPTED IN A PRACTICAL SYSTEM AS COM PARED WITH THE NUMBER OF JAMMING SIGNALS !PERTURE FREQUENCY DISPERSION OFTEN EXPRESSED IN TERMS OF APERTURE BANDWIDTH PRODUCT 4HE LIMITED BANDWIDTH OF THE MAJORITY OF THE SCHEMES IMPLEMENTING %Q AS COMPARED WITH THE WIDEBAND OF A BARRAGE JAMMER THAT CAN BE REGARDED AS A CLUSTER SPREAD IN ANGLE OF NARROWBAND JAMMERS 1UADRATURE ERRORS IN SYNCHRONOUS IE ) 1 DETECTORSn
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&)'52% #ONTOUR CURVE OF *#2 D" VERSUS THE AMPLITUDE IN NATURAL NUMBER ALONG THE HORIZONTAL AXIS AND PHASE IN DEGREES ALONG THE VERTICAL AXIS MISMATCHES OF THE ANALOGUE RECEIVING CHANNELS
$IGITAL RECEIVER CHANNEL ERRORS SUCH AS !$# QUANTIZATION SAMPLEHOLD JITTER AND DIGITAL CONVERTER OFFSET 4HE PULSE WIDTH THAT LIMITS THE REACTION TIME OF THE ADAPTIVE SYSTEM IN ORDER TO AVOID THE CANCELLATION OF TARGET SIGNAL 4HE TARGET SIGNAL IN THE AUXILIARY ARRAY THAT MAY RESULT IN NONNEGLIGIBLE STEERING OF THE AUXILIARIES TOWARD THE MAIN BEAM DIRECTION -ULTIPATH DELAY OFTEN EXPRESSED IN TERMS OF DELAY BANDWIDTH PRODUCTn 4HE PRESENCE OF CLUTTER THAT IF NOT PROPERLY REMOVED MAY CAPTURE THE ADAPTIVE SYS TEM GIVING RISE TO NULLS ALONG DIRECTIONS DIFFERENT FROM THOSE OF THE JAMMERS 4HE TRADEOFF THAT HAS TO BE SOUGHT BETWEEN THE ACCURACY OF WEIGHTS ESTIMATION AND THE REACTION TIME OF THE ADAPTIVE SYSTEM 4HE LIMITED NUMBER OF TIME SAMPLES AVAILABLE TO ESTIMATE THE JAMMER COVARIANCE MATRIX USUALLY . SAMPLE SHOULD BE AVAILABLE IF . IS THE NUMBER OF ADAPTIVE CHANNELS 4HE ANTENNA ROTATION RATE THAT MIGHT PRODUCE A FAST TIME VARYING POWER AND JAMMER $O! *OINT 3," AND 3,# 3," IS EFFECTIVE AGAINST SPIKY SIGNAL AFTER PULSE COMPRES SION LIKE #2) WHEREAS 3,# COMBATS THE CONTINUOUS .,) !S PREVIOUSLY STATED BOTH TECHNIQUES COMBAT THE INTERFERENCES IMPINGING ON THE MAIN ANTENNA SIDELOBES 4HE TWO TECHNIQUES CAN BE JOINTLY USED AGAINST THE SIMULTANEOUS PRESENCE OF #2) AND .,) !N APPROACH IS TO CASCADE THE 3,# AND 3," TECHNIQUES AS SHOWN IN &IGURE 4HE SCHEME DEPICTS THREE RECEIVING CHANNELS EACH ONE HAVING AN ANTENNA A RECEIVER AND AN !$# THEY PROVIDE THREE SIGNALS LABELED RESPECTIVELY AS 3,# -!). AND 3," 4HE LEFT HAND SIDE ANTENNA IS A LOW GAIN AUXILIARY PERFORMING THE 3,# PROCESSING IN
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&)'52% ! PROCESSING SCHEME INCORPORATING 3,# AND 3," DEVICES
THE MAIN AND SIDELOBE BLANKING CHANNELS 4HE CENTER ANTENNA IS THE HIGH GAIN RADAR ANTENNA TO DETECT TARGETS NOTWITHSTANDING IMPULSIVE AND NOISE LIKE INTERFERENCES 4HE RIGHT HAND SIDE ANTENNA IS A LOW GAIN AUXILIARY THAT IS USED FOR 3," PROCESSING IN THE MAIN CHANNEL 4HE ADAPTIVE CANCELLATION OF .,) RECEIVED BY THE MAIN ANTENNA IS ACHIEVED BY THE LINEAR COMBINATION OF THE 3,# AND -!). SIGNALS WITH THE ADAPTIVE WEIGHTS 7 AND RESPECTIVELY THE RESULTING ADAPTED SIGNAL -!).g DOESNT CONTAIN THE .,) 3IMILARLY THE ADAPTIVE CANCELLATION OF .,) RECEIVED BY THE RHS AUXILIARY ANTENNA IS REACHED BY THE LINEAR COMBINATION OF THE 3,# AND 3," SIGNALS WITH THE ADAPTIVE WEIGHTS 7 AND RESPECTIVELY THE ADAPTED SIGNAL 3,"g DOESNT CONTAIN THE .,) /NCE THE .,) IS REMOVED FROM THE TWO CHANNELS THEN THE CLASSIC 3," LOGIC CAN BE APPLIED AGAINST THE #2) BY COMPARING THE AMPLITUDE \-!).g\ OF THE MAIN CHANNEL WITH THAT \3,"g\ OF THE BLANKING CHANNEL WHICH ARE BOTH .,) FREE "ECAUSE THE PHASE CENTERS OF THE THREE ANTENNAS THE MAIN AND THE TWO AUXILIARIES ARE SPACED IN GENERAL MORE THAN K WHERE K IS THE LENGTH OF THE RADIATED %- WAVE THE ADAPTED PATTERNS OF THE MAIN AND 3," CHANNELS FLUCTUATE AROUND AVERAGE CURVES DUE TO THE PRESENCE OF GRATING LOBES .EVERTHELESS A REASONABLE GAIN MARGIN IS PRESENT BETWEEN THE PATTERN OF THE ADAPTED 3," AND THE SIDELOBES OF THE ADAPTED MAIN ANTENNA THUS AN ADEQUATE PROBABILITY OF BLANKING THE #2) IN THE PRESENCE OF ADAPTIVELY NULLED .,) SHOULD BE EXPECTED )N ORDER TO IMPROVE THE ABOVE GAIN MARGIN AND CONSEQUENTLY THE BLANKING PROBABILITY OF #2) THE FOLLOWING PROCESSING STRATEGIES ARE SUGGESTED SPATIAL AND FREQUENCY DIVERSITY 3PATIAL $IVERSITY 4HE RATIONALE IS TO USE TWO LOW GAIN AUXILIARIES INSTEAD OF ONE AS SHOWN IN &IGURE FOR THE 3," BECAUSE THEIR PHASE CENTERS WILL BE DIFFERENT THE GRATING LOBES AFFECTING THE ADAPTED PATTERNS OF THE TWO 3," ANTENNAS WILL BE DIFFERENT TOO 4AKING THE GREATER OF THE TWO ADAPTED 3," SIGNALS THE GAIN MARGIN BETWEEN THE 3," AND THE MAIN ANTENNA SIDELOBES WILL INCREASE WITH A CONSEQUENT IMPROVEMENT OF THE PERFORMANCE OF THE BLANKING LOGIC
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&REQUENCY $IVERSITY !NOTHER TECHNIQUE TO IMPROVE THE BLANKING PERFORMANCE IS TO RESORT TO THE DIVERSITY OF THE RADAR CARRIER FREQUENCY IN THIS CASE WE NEED JUST ONE LOW GAIN ANTENNA AS SHOWN IN &IGURE FOR THE 3," 4HE RADAR OPERATES IN FREQUENCY DIVERSITY MODE IE IT RADIATES A BURST OF , PULSES 4 SECONDS APART WITH SLIGHTLY DIFFERENT CARRIER FREQUENCIES 4HE GRATING LOBES IN THE ADAPTED MAIN AND THE , 3," PATTERNS WILL CHANGE AS A FUNCTION OF THE CARRIER FREQUENCY 4AKING THE MAX OF THE OUTPUT OF THE , 3," SIGNALS IS EQUIVALENT TO A SMOOTHING OF THE GRAT ING LOBES )N A SPECIFIC EXAMPLE PRESENTED IN &ARINA AND 4IMMONERI TWO CARRIER FREQUENCIES ARE USED AND THE VALUES OF DK WHERE hDv IS THE INTER ELEMENT DISTANCE FOR THE ARRAY OF RECEIVING ELEMENTS ARE RESPECTIVELY AND 4HE BLANKING IS SEPARATELY APPLIED ON THE RECEIVED DATA AT THE TWO CARRIER FREQUENCIES SUBSEQUENTLY THE SEPARATE BLANKING BITS ARE PROCESSED BY A LOGIC /2 THE GLOBAL BLANKING LOGIC 4HE ENSUING &IGURE DISPLAYS THE BLANKING CURVES FOR THE TWO SEPARATE CARRIER FREQUENCIES AND FOR THE LOGIC /2 )T IS NOTED THAT THE FREQUENCY DIVERSITY AND THE LOGIC /2 PROVIDE AN IMPROVEMENT OF THE BLANKING PROBABILITY THIS IS DUE TO THE DIFFERENT SHAPES OF THE ANTENNA PATTERNS AT THE TWO SLIGHTLY DIFFERENT CARRIER FREQUEN CIES &IGURE ALSO PRESENTS THE PROBABILITY OF BLANKING A USEFUL TARGET 04" RECEIVED BY THE MAIN ANTENNA BEAM 4HE PROBABILITIES ARE ESTIMATED VIA INDE PENDENT -ONTE #ARLO SIMULATIONS 4HE TARGET 3.2 IS D" THE *.2 IS D" THE TARGET $O! IS ASSUMED TO BE EVENLY DISTRIBUTED IN THE MAIN BEAM ANGULAR INTERVAL ;n = DETAILS ON THE NUMERICAL PARAMETERS USED IN THE STUDY CASE ARE IN THE REFERENCE )T IS NOTED THAT 04" IS NEGLIGIBLE FOR & D" WHILE 0" q !FTER A CAREFUL PERFORMANCE EVALUATION OF THE SYSTEM DEPICTED IN &IGURE IT MIGHT BE NECESSARY TO ALWAYS RESORT TO EITHER SPATIAL OR FREQUENCY DIVERSITY TO IMPROVE THE 3," PERFORMANCE 4HE SELECTION OF ONE OF THE TWO DIVERSITY TECHNIQUES DEPENDS ON OVERALL SYSTEM CONSIDERATIONS RELATED TO THE IMPACT OF ADDING MORE AUXILIARIES AND OR RADIATING WITH THE RADAR PROPER CARRIER FREQUENCIES &URTHERMORE IF COMPACT AND HIGH SPEED PROCESSING ARE REQUESTED SPATIAL AND FREQUENCY DIVERSITY TECHNIQUES CAN BE FRUITFULLY IMPLEMENTED RESORTING TO SYSTOLIC SCHEMES
&)'52% "LANKING PROBABILITY 0" AND TARGET BLANKING PROBABILITY 04" VERSUS THE BLANKING THRESHOLD & IN D" FOR THE FREQUENCY DIVERSITY SCHEME
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3YSTOLIC 3CHEMES FOR 3," AND 3,# )N THE QUEST FOR EFFICIENT PARALLEL PROCESSING THE SYSTOLIC SCHEMES COME INTO THE SCENE THEIR USE HAS BEEN DESCRIBED FOR THE IMPLE MENTATION OF 3,# AND MORE GENERAL ADAPTIVE ARRAY PROBLEMS IN THE LITERATURE 4HE RATIONALE AND THE USE OF A SYSTOLIC ARRAY THAT PROCESSES THE SIGNALS RECEIVED BY 3,# AND MAIN CHANNEL IS REPORTED ON PAGES n OF &ARINA AND IN &ARINA AND 4IMMONERI &IGURES TO DEPICT THE USE OF A SYSTOLIC PROCESSING SCHEME THAT INCORPORATES THE 3," AND 3,# 4HE ADVANTAGE OF THESE SCHEMES RESIDES IN THE DECOMPOSITION OF THE COMPLEX PROCESSING FOR ADAPTIVE CANCELLATION OF THE .,) INTO A NETWORK OF SIMPLE PROCESSING ELEMENTS THAT CAN BE CONVENIENTLY MAPPED ONTO A PARALLEL PROCESSING ARCHI TECTURE BASED EITHER ON #OMMERCIAL OFF THE 3HELF #/43 TECHNOLOGY OR CUSTOM 6ERY ,ARGE 3CALE )NTEGRATION 6,3) DEVICES )N THE LITERATUREn IT HAS BEEN SHOWN THAT A WIDE SPECTRUM OF TECHNOLOGIES CAN BE USED LIKE &IELD 0ROGRAMMABLE 'ATE !RRAYS &0'! #OORDINATE 2OTATION $IGITAL #OMPUTER #/2$)# IMPLEMENTED WITH 6,3) AND OPTICAL COMPUTERS 0IONEERING WORK ON THE USE OF #/2$)# FOR ADAPTIVE NULL ING DATES BACK TO # 2ADER AT -)4 ,INCOLN ,ABORATORY 4HE ADVANTAGE OF SYSTOLIC IMPLEMENTATION IS HIGH PROCESSING SPEED AND COMPACT LOW WEIGHT LOW POWER CON SUMPTION HARDWARE !DAPTIVE !RRAYS !N ADAPTIVE ARRAY &IGURE IS A COLLECTION OF . ANTENNAS WITH THEIR OWN RECEIVERS 28 AND !$# FEEDING A WEIGHTING AND SUMMING NETWORK WITH AUTOMATIC SIGNAL DEPENDENT WEIGHT ADJUSTMENT TO REDUCE THE EFFECT OF UNWANTED
&)'52% 4HE ADAPTIVE ARRAY SCHEME
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SIGNALS ANDOR TO EMPHASIZE THE DESIRED SIGNAL OR SIGNALS IN THE SUMMING NETWORK OUTPUT /UTPUT SIGNAL : IS ENVELOPE DETECTED AND COMPARED WITH A SUITABLE THRESH OLD @ TO DETECT THE PRESENCE OF A USEFUL TARGET SEE #HAPTER IN &ARINA AND OTHER SOURCESn 4HE ADAPTIVE ARRAY IS A GENERALIZATION OF THE 3,# DESCRIBED IN THE PRECEDING SUBSECTION 4HE BASIC THEORY OF JAMMER CANCELLATION AND TARGET ENHANCE MENT IS CONSIDERED FIRST ATTENTION IS THEN FOCUSED ON THE FOLLOWING TOPICS MAIN BEAM JAMMER CANCELLATION TARGET $O! ESTIMATION IN PRESENCE OF JAMMER TWO DIMENSIONAL ADAPTIVE PROCESSING FOR JOINT CLUTTER AND JAMMER CANCELLATION ADAPTIVITY AT THE SUBAR RAY LEVEL AND SUPERRESOLUTION 4HE IMPLEMENTATION OF THE ADAPTIVE ARRAY CONCEPT IS MORE AND MORE RELATED TO DIGITAL BEAMFORMINGn AND TO DIGITAL ARRAY RADAR $!2 TECHNOLOGIES *AMMER #ANCELLATION AND 4ARGET 3IGNAL %NHANCEMENT !DAPTIVE ARRAY PRIN CIPLES HAVE FOUND A THOROUGH MATHEMATICAL TREATMENT SINCE THE LATE S FOR A BRIEF HISTORY OF ADAPTIVE ARRAYS SEE 2EED FOR AN OVERVIEW OF LEAST SQUARES ADAP TIVE PROCESSING IN MILITARY APPLICATIONS WITH CELEBRATION OF " &RANKLIN MEDAL TO " 7IDROW FOR PIONEERING WORK ON ADAPTIVE SIGNAL PROCESSING SEE %TTER ET AL 4HE THEORY AND APPLICATION OF ADAPTIVE ARRAY PRINCIPLES TO RADAR IS WELL ESTABLISHED FOR A LOOK TO POPULAR PUBLICATIONS SEE FOR INSTANCE (AYKIN AND 3TEINHARDT 3MITH AND &ARINA ET AL 4HE BASIC RESULT IS GIVEN BY THE EXPRESSION OF THE OPTIMUM SET OF WEIGHTS
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WHERE - %6 64 IS THE . DIMENSIONAL COVARIANCE MATRIX OF THE OVERALL DISTURBANCE NOISE AND JAMMER 6 RECEIVED BY THE ARRAY AND 3 IS THE . DIMENSIONAL VECTOR CON TAINING THE EXPECTED SIGNAL SAMPLES IN THE ARRAY FROM A TARGET ALONG A CERTAIN DIRECTION OF ARRIVAL 4HE SIMILARITY OF %Q TO %Q GOVERNING THE 3,# IS IMMEDIATELY RECOGNIZED 7ITH RESPECT TO 3,# ADAPTIVE ARRAY TECHNIQUES OFFER THE CAPABILITY OF ENHANCING THE TARGET SIGNAL WHILE CANCELING THE DISTURBANCE 4HE ADAPTIVE SYSTEM ALLOCATES IN AN OPTIMUM FASHION ITS DEGREES OF FREEDOM TO THE ENHANCEMENT OF THE TARGET SIGNAL AND TO THE CANCELLATION OF JAMMER 3EVERAL GENERALIZATIONS OF THE BASIC THEORY HAVE BEEN CONSIDERED INCLUDING I THE TARGET MODEL 3 IS NOT KNOWN A PRIORI AS IT IS ASSUMED IN DERIVING %Q II IN ADDITION TO SPATIAL FILTERING DOPPLER FILTERING IS PERFORMED TO CANCEL CLUTTER AND CHAFF AND III THE RADAR PLATFORM IS MOVING AS IN SHIPBORNE AIRBORNE OR EVEN SPACEBORNE APPLICATIONS ! RELEVANT ADVANCEMENT OF THE ADAPTIVE ARRAY CONCEPT IS SPACE TIME ADAP TIVE PROCESSING 34!0 n 34!0 MAY BE THOUGHT OF AS A TWO DIMENSIONAL ADAPTIVE FILTER THAT COMBINES RECEIVE BEAMFORMING AND DOPPLER FILTERING ! BASIC ILLUSTRATION OF 34!0 IS GIVEN IN &IGURE OF 7ARD WHERE A PICTORIAL VIEW OF THE INTERFERENCE ENVIRONMENT SEEN BY AN AIRBORNE RADAR AND THE CORRESPONDING ADAPTED TWO DIMENSIONAL FILTER RESPONSE ARE SHOWN 4HE POWER SPECTRAL DENSITY RESULTING FROM JAMMER AND CLUTTER IS DEPICTED AS A FUNCTION OF THE SPATIAL IE THE SINANGLE AND THE TEMPORAL IE DOPPLER FREQUENCIES "ARRAGE NOISE JAMMING APPEARS AS A WALL LOCALIZED IN ANGLE AND DISTRIBUTED ALL OVER DOPPLER FREQUENCIES 4HE CLUTTER ECHO FROM A SINGLE GROUND PATCH HAS A DOPPLER FREQUENCY THAT DEPENDS ON THE ANGLE BETWEEN THE CLUTTER PATCH AND THE PLATFORM FLIGHT DIRECTION CLUTTER FROM ALL ANGLES LIES ON A DIAGONAL RIDGE ACROSS THE SPACE TIME FREQUENCY PLANE ! MAIN BEAM TARGET COMPETES WITH BOTH MAIN BEAM AND SIDELOBE CLUTTER AS WELL AS JAMMING
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4HE 34!0 GENERATES A SPACE TIME FILTERING RESPONSE WITH A MAIN BEAM ALONG THE EXPECTED DOPPLER FREQUENCY AND ANGLE OF ARRIVAL OF TARGET AND DEEP NULLS ALONG THE JAMMER WALL AND THE CLUTTER RIDGE 4O PERFORM 34!0 THE RADAR SHOULD HAVE AN ARRAY OF . ANTENNAS EACH WITH THEIR OWN RECEIVING CHANNEL AND !$# %ACH CHANNEL RECEIVES - ECHOES FROM A TRANSMITTED TRAIN OF - COHERENT PULSES !DAPTIVITY INVOLVES THE .- ECHOES 4HE DETECTION PROBABILITY 0$ FOR THE OPTIMUM FILTER OF %Q IS FOR A CONSTANT CROSS SECTION TARGET MODEL
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WHERE 1 IS THE -ARCUM 1 FUNCTIONp AND 0&! IS THE PRESCRIBED PROBABILITY OF FALSE ALARM )T IS ALSO SHOWN THAT THE SET OF WEIGHTS OF %Q PROVIDES THE MAXIMUM VALUE OF THE IMPROVEMENT FACTOR )F WHICH IS DEFINED AS FOLLOWS
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SIGNALnTOnINTERFERENCE PLUS NOISE POWER RATIO AT THE OUTPUT SIGNALnTOnINTERFERENCE PLUS NOISE POWER RATIO AT THE INPUT
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4HE SIGNAL TO INTERFERENCE PLUS NOISE POWER RATIO 3).2 ) IS MEASURED AT THE INPUT OF A RECEIVING ELEMENT OF THE ARRAY AND REFERS TO ONE ECHO PULSE 4HE )F REPRESENTS THE PERFORMANCE OF THE ADAPTIVE ARRAY IT ACCOUNTS FOR THE TARGET SIGNAL INTEGRATION AND THE INTERFERENCE CANCELLATION 0RACTICAL APPLICATIONS OF THE EQUATION ABOVE ARE FOR INSTANCE IN #HAPTER OF &ARINA #RUCIAL FOR THE UNDERSTANDING OF THE ADAPTED ARRAY PATTERN IS THE CONCEPT OF EIGENVALUE EIGENVECTOR DECOMPOSITION OF THE INTERFERENCE COVARIANCE MATRIX - SEE AGAIN #HAPTER OF &ARINA AND 4ESTA AND 6ANNICOLA !N IMPORTANT TECHNIQUE THAT MITIGATES THE DELETERIOUS EFFECTS OF THE NOISE EIGENVECTORS THUS CONTINUING TO MAINTAIN A PRESCRIBED LEVEL OF LOW SIDELOBES IN THE ADAPTED ARRAY PATTERN IS THE SO CALLED DIAGONAL LOADING !DAPTIVE ARRAYS CAME ABOUT AFTER THE SUCCESSFUL APPLICATION OF 3,# THE APPLICA TION OF %Q AND OF MORE GENERAL AND POWERFUL ADAPTIVE ARRAY CONCEPTS EG '3,# GENERALIZED 3,# #LEARLY THE EFFICIENCY OF THE ADAPTIVE ARRAY DEPENDS ON THE NUMBER OF DEGREES OF FREEDOM DOF AND THE ACCURACY OF RECEIVING CHAN NELS EG DEGREES OF MATCHING 4HERE IS SOME TRADE OFF BETWEEN ACCURACY AND NUMBER OF CHANNELS A SYSTEM WITH ONE DOF IS LESS EFFICIENT AND REQUIRES MAXIMUM ACCURACY THAN A SYSTEM WITH SAY FOUR DOF !N ADAPTIVE SYSTEM WITH . DOF CAN THEORETICALLY SUPPRESS . n JAMMERS REALISTICALLYAS A RULE OF THUMB. OR . )F THE NUMBER OF JAMMERS IS HIGHER THE ADAPTIVE ARRAY IS STILL USEFUL BECAUSE SOME JAMMER SUPPRESSION IS ACHIEVED WITH AN ACCORDINGLY REDUCED DETECTION RANGE p 4HE -ARCUM 1 FUNCTION IS DEFINED AS
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#ONCERNING THE COMPARISON BETWEEN ADAPTIVE BEAMFORMING AND A VERY LOW SID ELOBE ANTENNA IT IS IN THE IMPORTANT CASE OF CLOSE TO MAIN BEAM JAMMING WHERE ADAPTIVE BEAMFORMING IS SUPERIOR /N THE OTHER HAND THE ADAPTIVE ARRAY ALLOWS ONE TO OBTAIN CERTAIN LOWERED SIDELOBES SIMULTANEOUSLY TO JAMMING NULLING #ONCERNING THE PRACTICAL APPLICABILITY OF ADAPTIVE ARRAYS SOME CONSIDERATIONS FOLLOW ! NUM BER OF OPERATIONAL RADAR SYSTEMS ARE ADAPTIVE THEY ARE DESCRIBED IN THE TECHNICAL LITERATUREn ! MODERN RADAR WITH DIGITAL PROCESSING ALREADY HAS AT LEAST FOUR DIGITAL CHANNELS SUM DIFFERENCE IN AZIMUTH DIFFERENCE IN ELEVATION AND GUARD )N GENERAL THE NUMBER OF IMPLEMENTED RECEIVING CHANNELS IS MAINLY A MATTER OF COST )T HAS BEEN ARGUED THAT RADAR SYSTEMS WITH A NUMBER OF ADAPTIVE DOF OF A FEW TENS ARE ALREADY IN OPERATION IN THE MICROWAVE BAND THE NUMBER OF ADAPTIVE DOF MAY BE MORE IN THE OVER THE HORIZON /4( RADAR &OR THE FORESEEABLE FUTURE THE FULLY ADAPTIVE ARRAY IE WITH ADAPTIVITY AT RECEIVING ELEMENT LEVEL HAS ONLY THEORETICAL VALUE FOR ANTENNAS WITH A THOUSAND ELEMENTS 4HERE ARE RADARS THAT ARE FULLY ADAPTIVE BUT THEY HAVE ONLY A LIMITED NUMBER OF ELEMENTS THAT CAN BE ECONOMICALLY HANDLED IN AN ADAPTIVE ARRAY !RRAYS WITH A LARGE NUMBER OF RECEIVING ELEMENTS NEED SOME FORM OF PROCESSING REDUCTION /NE METHOD OF PARTIAL ADAPTIVITY IS TO ARRANGE THE ARRAY ELEMENTS IN SUBGROUPS THAT FORM THE INPUTS OF THE ADAPTIVE PROCESSOR #AREFUL SELECTION OF THE SUBGROUP ELEMENTS IS NECESSARY TO AVOID GRATING LOBES THIS TOPIC IS DISCUSSED IN A FOLLOWING SECTION !NOTHER SIMPLIFICATION OF THE FULLY ADAPTIVE ARRAY IS THE DETERMINISTIC SPATIAL FILTERING WHERE A FIXED REDUCTION OF THE SIDELOBES IS OPERATED IN THOSE DIRECTIONS OR SOLID ANGLES FROM WHICH THE INTERFER ENCES ARE EXPECTED TO COME !S AN EXAMPLE A PROBABLE REGION WITH INTERFERENCES IS THE HORIZON OR PART OF IT BECAUSE JAMMERS ARE MOSTLY GROUND BASED OR AT LONG RANGE 4HE WEIGHTS ARE COMPUTED OFFLINE BY ASSUMING AN A PRIORI KNOWN COVARIANCE MATRIX - AND STORED IN A MEMORY WHERE A hMENUv OF WEIGHTS IS AVAILABLE TO AN OPERATOR OR AN AUTOMATIC DECISION SYSTEM PP n OF &ARINA -AIN "EAM #ANCELLATION -"# 3YSTEMS 4HE OBJECTIVE OF THE -"# IS TO SUP PRESS HIGH DUTY CYCLE AND .,) RECEIVED THROUGH THE MAIN BEAM OF THE RADAR 4HE CONCEPTUAL SCHEME OF -"# IS ANALOGOUS TO THE SCHEME OF 3,# HOWEVER HIGH GAIN BEAMS ARE EMPLOYED IN LIEU OF LOW GAIN AUXILIARY ANTENNAS *AMMING IS CANCELLED BY A LINEAR COMBINATION OF THE SIGNALS FROM THE HIGH GAIN BEAMS AND THE MAIN ANTENNA 4HE WEIGHTS TO BE APPLIED CAN BE COMPUTED BY %Q 4HE CAPABILITY TO CANCEL A CERTAIN NUMBER OF MAIN BEAM INTERFERENCES DEPENDS ON THE AVAILABLE NUMBER OF HIGH GAIN BEAMS ! SO CALLED FOUR LOBED PATTERN CAN BE USED FOR MAIN BEAM INTERFERENCE CANCEL LATION 4HE USE OF LOW GAIN AUXILIARY ANTENNAS JOINED TO HIGH GAIN BEAMS ALLOWS THE CONTEMPORANEOUS CANCELLATION OF SIDELOBE AND MAIN BEAM INTERFERENCES 4ARGET $O! %STIMATION IN 0RESENCE OF 3IDELOBE AND -AIN "EAM )NTERFERENCES 0HASED ARRAY RADARS ARE REQUIRED TO DETECT LOCATE AND TRACK TARGETS IN THE PRESENCE OF NATURAL INTERFERENCE AND JAMMING -ONOPULSE IS THE TECHNIQUE OF CHOICE TO DETERMINE THE TARGET ANGULAR COORDINATES WHEN %#- IS ENCOUNTERED SINCE IT IS MUCH HARDER TO DECEIVE THAN A CONICAL SCAN (OWEVER THE APPLICATION OF ADAPTIVE BEAMFORMING TO BET TER MITIGATE THE PRESENCE OF AN INTENSE JAMMER WITH THE RELATED DISTORTION OF SUM AND DIFFERENCE BEAM SHAPES MAY INTRODUCE ERRORS IN THE CONVENTIONAL MONOPULSE TECHNIQUE IN PARTICULAR IF THE JAMMER IS CLOSE TO THE MAIN BEAM THUS THE CONVENTIONAL MONO PULSE TECHNIQUE CANNOT BE APPLIED ! -AXIMUM ,IKELIHOOD -, APPROACH FOR TARGET $O! ESTIMATION IS CONSIDERED WHICH GENERALIZES THE MONOPULSE CONCEPTn
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4HE TARGET ANGULAR COORDINATESAZIMUTH AND ELEVATION P E CAN BE ESTIMATED BY -, ALSO IN THE PRESENCE OF MAIN BEAM AND SIDELOBE JAMMING BY PROCESSING THE DATA RECEIVED BY A SET OF LOW AND HIGH GAIN BEAMS 4HE SET OF RECEIVED RADAR ECHOES 6 x B3P4 E4 D DEPENDS ON THE ANGULAR COORDINATES OF THE TARGET P4 E4 THE COMPLEX TARGET AMPLITUDE B AND WHITE GAUSSIAN ZERO MEAN NOISE PLUS JAMMING DISTURBANCE D 3 IS A VECTOR CONTAINING THE VALUES OF THE PATTERNS OF HIGH AND LOW GAIN ANTENNAS IN A CERTAIN DIRECTION P E 4HE DATA 6 ARE CHARACTERIZED BY A GAUSSIAN PROBABILITY DENSITY FUNCTION CONDITIONED TO THE TARGET UNKNOWN PARAMETERS IE PV6B P4 E4 4HE -, ESTIMATION OF THE TARGETS UNKNOWN PARAMETERS IS OBTAINED AS FOLLOWS
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B} Q}4 F}4 ARG MIN B Q F ;6 B3Q F = - D ;6 B3Q F = ARG MIN B Q F [& B Q F ] (
WHERE -D IS THE DISTURBANCE COVARIANCE MATRIX -D S N ;) *.2 s 3P* E* s 3P* E* (= DEPENDING ON THE ANGULAR COORDINATES OF THE JAMMING P* E* e AND ON THE JAMMING TO NOISE POWER RATIO *.2 0* S N IN %Q ( STANDS FOR THE COM PLEX CONJUGATE TRANSPOSE OPERATION 4HE AMPLITUDE B CAN BE SEPARATELY ESTIMATED BY NULLING THE FIRST DERIVATIVE OF THE FUNCTION TO BE MINIMIZED "Y REPLACING THE AMPLI TUDE ESTIMATION B} INTO THE FUNCTION TO BE MINIMIZED THE FOLLOWING $O! ESTIMATOR IS OBTAINED ª 3( Q F ; - ; 6 ¹ D Q}4 F}4 ARGMAXQ F [5 Q F ] ARGMAXQ F « ( º
Q F Q F 3 ; ; 3 D » ¬
)T CAN BE NOTED THAT THE NUMERATOR OF THE FUNCTIONAL 5P E IS THE SQUARED ADAPTED OUTPUT \ 3 ( Q F ; - D ; 6 \ OF A GENERALIZED ARRAY OF HIGH AND LOW GAIN ANTENNA PATTERNS THE DENOMINATOR ;3 ( Q F ; - D ; 3 Q F = IS A NORMALIZING TERM THAT AS WE WILL SEE IN A MOMENT PLAYS A KEY ROLE 4HE 5 FUNCTION FOR A CERTAIN PAIR OF ANGLES P E DETERMINES AFTER COMPARISON WITH A SUITABLE THRESHOLD IF A TARGET IS DETECTED 4HE SAME 5 FUNCTIONAL WHEN SCANNED ACROSS A SUITABLE SET OF P E ANGLE VALUES PROVIDES BY MEANS OF %Q THE TARGET $O! ESTIMATE 7E REFER TO %Q AND ITS PRACTICAL IMPLEMENTATION AS THE GENERALIZED MONOPULSE TECHNIQUE 4HE ALGORITHM NEEDS THE ESTIMATION OF THE DISTURBANCE COVARIANCE MATRIX -D WHICH IS OBTAINED BY THE RADAR ECHOES CORRESPONDING TO RANGE CELLS ADJACENT TO THE CELL UNDER TEST WHERE A POTENTIAL TARGET IS SOUGHT 4HE MAXIMUM OF THE 5 FUNCTIONAL CAN BE ESTIMATED BY AN EXHAUSTIVE SEARCH IN THE RANGE OF VALUES OF INTEREST OF P E OR BY USING A FAST RECURSIVE ALGORITHM 4HE RECURSION CAN BE INITIALIZED WITH THE ANGULAR COORDINATES OF THE MAIN BEAM POINTING "Y REPLACING THE ESTIMATED DISTUR BANCE COVARIANCE MATRIX INTO THE 5 FUNCTIONAL A #ONSTANT &ALSE !LARM 2ATE #&!2 DETECTOR IS OBTAINED 4HUS THE COMPARISON OF THE 5 FUNCTIONAL WITH A SUITABLE THRESHOLD PERMITS THE TARGET DETECTION MAINTAINING THE PRESCRIBED #&!2 /NLY FOR THE RANGE CELL IN WHICH THE DETECTION OCCURRED THE RADAR SIGNALS ARE TAKEN AND FURTHER PROCESSED BY THE -, ALGORITHM TO PRODUCE THE TARGET $O! ESTIMATE 4HE PERFORMANCE OF THE -, ESTIMATION ALGORITHM OF TARGET $O! CAN BE STUDIED BY RESORTING TO THE #RAMER 2AO ,OWER "OUND #2," ANALYSIS AND -ONTE #ARLO SIMULATIONS n )N THESE STUDIES IT IS SHOWN THAT THE SHAPE OF THE 5 FUNCTIONAL e (ERE JUST ONE JAMMER IS CONSIDERED BUT THE MATHEMATICAL APPROACH IS EASILY EXTENDED TO MORE THAN ONE JAMMER
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DEPICTS THE PRESENCE OF THE TARGET AS WELL AS OF THE JAMMING )T HAS BEEN DEMONSTRATED THAT -ONTE #ARLO SIMULATION IS IN CLOSE AGREEMENT WITH #2," ANALYSIS )T HAS BEEN FOUND THAT THE USE OF THE FOUR LOBED ANTENNA PATTERN IN ADDITION TO THE CONVENTIONAL MONOPULSE BEAMS SUM DIFFERENCE IN AZIMUTH AND ELEVATION CAN IMPROVE THE ESTIMA TION OF THE TARGET $O! IN PRESENCE OF A JAMMER *OINT !DAPTIVE *AMMER AND #LUTTER #ANCELLATION #LUTTER ALWAYS PRESENT IN A RADAR NEGATIVELY AFFECTS THE PERFORMANCE OF THE ADAPTIVE JAMMER CANCELLATION THEREFORE MEANS HAVE TO BE ADOPTED TO EFFECTIVELY CONTRAST THE CONTEMPORANEOUS PRESENCE OF CLUTTER AND JAMMER 7HEN HEAVY CLUTTER IS PRESENT THE 3,# AND ADAPTIVE ARRAY WILL ATTEMPT TO MINIMIZE THE POWER IN THE ADAPTED OUTPUT WITHOUT DIFFERENTIAT ING BETWEEN CLUTTER AND OTHER FORMS OF INTERFERENCE )N OTHER WORDS THE ADAPTED PAT TERN WILL CONTAIN NULLS STEERED IN THE DIRECTION OF THE MAIN BEAM ANTENNA ! NUMBER OF TECHNIQUES MAY BE USED TO AVOID THE PROBLEMS RAISED BY THE PRESENCE OF CLUT TER ! TECHNIQUE PARTICULARLY SUITABLE FOR LOW 02& 0ULSE 2EPETITION &REQUENCY RADAR AVOIDS THE INFLUENCE OF CLOSE IN CLUTTER RETURNS ON ADAPTIVE WEIGHTS BY SIMPLY SELECTING FOR ADAPTATION THE CLUTTER FREE RANGES AT THE END OF EACH 02) 4HIS TECH NIQUE DOES NOT APPLY TO RADARS OPERATING IN HIGH 02& RANGE AMBIGUOUS MODES WITH SIGNIFICANT CLUTTER IN ALL RANGE CELLS )F THE CLUTTER AND JAMMER CANNOT BE SEPARATED EITHER IN RANGE OR DOPPLER DOMAINS THEN A TWO DIMENSIONAL IN DOPPLER FREQUENCY AND ANGLE ADAPTIVE FILTER MIGHT BE REQUIRED THIS IS PARTICULARLY TRUE WHEN THE STATIS TICAL FEATURES OF CLUTTER AND JAMMER ARE NOT KNOWN A PRIORI )N FACT WHEN EITHER THE JAMMING OR CLUTTER STATISTICS CANNOT BE ESTIMATED INDEPENDENTLY OF ONE ANOTHER IT BECOMES DIFFICULT TO DESIGN AN EFFECTIVE SPATIAL ADAPTIVE FILTER FOR JAMMING REJECTION OR A TEMPORAL ADAPTIVE FILTER FOR CLUTTER MITIGATION SINCE THE PRESENCE OF ONE CON TAMINATES THE ESTIMATION PROCESS FOR THE OTHER 4HIS PROBLEM IS MOST ACCENTUATED WHEN THE CLUTTER TO JAMMING RATIO APPROACHES UNITY IN WHICH CASE THE CASCADE OF A SPATIAL AND A TEMPORAL ADAPTIVE PROCESSORS MAY PERFORM POORLY )N SUCH SITUATIONS A JOINT TWO DIMENSIONAL ADAPTIVE FILTERING IN DOPPLER AND ANGLE DOMAINS REPRESENTS A MEANS TO CANCEL THE COMPOSITE DISTURBANCE IE THE SUPERPOSITION OF JAMMING AND CLUTTER JOINTLY RATHER THAN SEQUENTIALLY 4HE PERFORMANCE ADVANTAGES OF TWO DIMENSIONAL ADAPTIVITY SHALL BE TRADED OFF WITH THE COMPUTATIONAL COST 4O REDUCE THE COMPUTATIONAL LOAD DIFFERENT COMPUTATIONAL STRATEGIES MAY BE DEVISED FOR EXAMPLE BY CALCULATING THE ADAPTED TWO DIMENSIONAL WEIGHTS AT A RATE LOWER THAN THE INPUT DATA AND APPLYING THEM TO THE RADAR SNAPSHOTS AT THEIR NATURAL RATE !N EFFI CIENT ALGORITHMIC PROCEDURE TO EXTRACT THE WEIGHTS NAMED )NVERSE 12 IS DETAILED IN "OLLINI ET AL /THER POSSIBILITIES ARE TO USE MODERN COMPUTING TECHNOLOGIES LIKE THE &0'! 0OWER 0# OR HIGH SPEED OPTICAL PROCESSOR TO SUPPORT THE TWO DIMENSIONAL ADAPTIVE PROCESSING !DAPTIVITY AT THE 3UB !RRAY ,EVEL &OR AN OPERATIONAL PHASED ARRAY RADAR 0!2 WITH THOUSANDS OF ELEMENTS IT IS NOT POSSIBLE TO ADAPT DIRECTLY THE SIGNALS FROM EACH RADIATING ELEMENT )T IS NECESSARY TO REDUCE THE SYSTEM COMPLEXITY BY USING SUB ARRAYS ! SUB ARRAY IS AN AGGREGATION OF ANTENNA ELEMENTARY RADIATORS THE WHOLE ANTENNA CAN BE CONSIDERED AS AN ARRAY OF THESE SUPER ELEMENTS !DAPTIVE PROCESS ING CAN BE APPLIED AT THE OUTPUT SIGNALS OF EACH SUB ARRAY THUS REDUCING THE SYSTEM COMPLEXITY 0ROVIDED THAT THE SUB ARRAYS ARE CONFIGURED REASONABLY THE NUMBER OF SUB ARRAYS AND THE RECEIVING CHANNEL ERRORS EG CHANNEL MISMATCHING DETERMINE THE CANCELLATION PERFORMANCE 4HUS THE NUMBER OF SUB ARRAYS IS A TRADE OFF BETWEEN HARDWARE COMPLEXITY COST AND ACHIEVABLE PERFORMANCE
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)T IS HIGHLY DESIRABLE IN 0!2 TO HAVE LOW SIDELOBES THIS IS OBTAINED BY I FIXED WEIGHT ING LAYER WITH ANALOGUE TECHNOLOGY IE AT THE MICROWAVE ELEMENT STAGE TO REDUCE THE SIDELOBE LEVEL EVERYWHERE II FIXED WEIGHTS AT THE DIGITAL SUB ARRAY LEVEL TO REACH A PRESCRIBED PEAK TO SIDELOBE RATIO 03,2 AND III AN ADAPTIVE WEIGHTING LAYER WITH DIGITAL TECHNOLOGY TO PUT NULLS ALONG THE JAMMER $O! OF HIGH DIRECTIONAL BEAMS SUM DIFFERENCE CLUSTER OF HIGH GAIN PATTERNS AND LOW GAIN POSSIBLY OMNIDIRECTIONAL BEAMS EG GUARD CHANNEL 7 &IGURE PRESENTS A SIMPLIFIED SCHEME OF A MODERN 0!2 &ORMATION OF 3UM AND $IFFERENCE 0ATTERNS #ONSIDER THE PROBLEM OF HOW TO FORM SUM AND DIFFERENCE BEAMS WITH PRESCRIBED LOW SIDELOBES IN A 0!2 WITH SUB ARRAYS ! STRATEGY IS TO APPLY A TAPERING AT ELEMENT LEVEL IE IN THE ANALOGUE RECEIVING SEC TION WHERE ONE ATTENUATOR IS GENERALLY AVAILABLE PER ELEMENT THUS ONE TAPER FUNCTION IS AVAILABLE TO ACHIEVE REASONABLE LOW SIDELOBES FOR BOTH SUM AND DIFFERENCE BEAMS 3UBSEQUENTLY A FIXED DIGITAL TAPER AFTER THE FORMATION OF SUB ARRAYS IS APPLIED WITH A SET OF WEIGHTS FOR THE SUM AND A DIFFERENT SET OF WEIGHTS FOR EACH DIFFERENCE CHANNEL 4HIS IS SCHEMATICALLY ILLUSTRATED IN &IGURE FOR A UNIFORM LINEAR ARRAY 5,! THAT GENERATES A SUM AND A DIFFERENCE CHANNEL 4HE FIGURE DEPICTS A 5,! WITH RECEIVING ELEMENTS CLUSTERED INTO FOUR NOT OVERLAPPING AND NOT REGULAR SUB ARRAYS 4HE CALCULATION OF ANALOGUE TAPER IS MADE BY RESORTING TO THE NULLING OF FICTITIOUS WIDE ANGLE JAMMING WHICH OCCUPIES THE WHOLE ANGULAR SECTOR WHERE SIDELOBES OF SUM AND DIFFERENCE BEAMS HAVE TO BE KEPT LOW )N &ARINA ET AL IT WAS FOUND THAT THE ANALOGUE TAPERING IS A COMPROMISE BETWEEN THE 4AYLOR WHICH IS THE BEST TAPER FOR THE SUM BEAM AND THE "AYLISS WHICH IS THE BEST TAPER FOR THE DIFFERENCE BEAM THE DEGREE OF COMPROMISE BEING REGULATED BY AMOUNT OF FICTITIOUS *.2 SELECTED FOR THE SUM AND DIFFERENCE BEAMS ! NUMERICAL EXAMPLE REPORTED IN &ARINA ET AL FOR A 5,! OF . ELEMENTS AND A UNIFORM DISTRIBUTION OF THE FICTITIOUS JAMMER OUT OF THE MAIN BEAMS OF THE SUM AND DIFFERENCE BEAMS GIVES A 03,2 OF D" AND D" FOR THE SUM AND DIFFERENCE BEAMS RESPECTIVELY 4HE NEXT STEP IS TO DERIVE THE FIXED TAPERS AT A DIGITAL LEVEL FOR SUM AND DIFFERENCE BEAMS A SUITABLE TECHNIQUE IS DESCRIBED IN .ICKEL 4HE RATIONALE OF THE APPROACH
&)'52% 3CHEME OF A 0!2
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# $ "
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&)'52% %XAMPLE OF A 5,! WITH SUB ARRAYS THAT GENERATE SUM AND DIFFERENCE CHANNELS
IS TO OBTAIN THE SUM BEAM BY COMPENSATING AT THE SUB ARRAY LEVEL THE ANALOGUE TAPER AT THE ELEMENT LEVEL TO ACHIEVE AN OVERALL TAPER MORE SIMILAR TO THE 4AYLOR ONE THIS IS OBTAINED BY INCREASING THE CONTRIBUTION OF CENTRAL SUB ARRAY WEIGHTS IE THE SUB ARRAYS AND SHOWN IN &IGURE WITH RESPECT TO THE WEIGHTS OF THE SIDE SUB ARRAYS AND 4O OBTAIN THE DIFFERENCE BEAM THE ANALOGUE TAPERING AT THE ELEMENT LEVEL IS COMPENSATED AT THE SUB ARRAY LEVEL TO ACHIEVE AN OVERALL TAPER FUNCTION MORE SIMILAR TO THE "AYLISS ONE THIS IS OBTAINED BY DECREASING THE CONTRIBUTION OF THE CENTRAL SUB ARRAYS AND ! NUMERICAL EXAMPLE IS REPORTED IN &ARINA ET AL WITH AN 5,! OF . ELEMENTS AND - SUB ARRAYS 4HE CHOSEN WEIGHT IS A 4AYLOR TAPERING WITH D" OF 03,2 4HERE ARE ONLY DIGITAL DEGREES OF FREEDOM THIS MEANS THAT MARGINAL IMPROVEMENT OF PERFORMANCE IN TERMS OF 03,2 CAN BE ACHIEVED .EVERTHELESS A 03,2 OF D" WAS OBTAINED FOR THE COMBINATION OF ANALOGUE WEIGHTS AND DIGITAL WEIGHTS &OR THE SAME 5,! ABOUT D" OF 03,2 WAS OBTAINED FOR THE DIFFERENCE CHANNEL #ONSIDERATIONS 2ELATED TO 3UB ARRAY !DAPTIVITY 4APERING AT THE ARRAY ELEMENT LEVEL PRODUCES UNEQUAL NOISE POWER AT SUB ARRAY OUTPUTS BECAUSE OF THE DIFFERENT NUMBER OF ELEMENTS IN EACH SUB ARRAY !DAPTIVITY WOULD TRY TO EQUALIZE THE NOISE BETWEEN CHAN NELS THUS NEGATING THE TAPERING EFFECT 4HE TRANSFORMATION 4 THAT ENCODES THE SUB ARRAY ARCHITECTURE SHOULD BE SUCH THAT 4(4 ) )N THIS WAY THE NOISE POWER AT SUB ARRAY OUTPUTS IS EQUAL SUBSEQUENTLY THE MISSING TAPER WEIGHTS ARE APPLIED DIGITALLY AT SUB ARRAY OUTPUTS WEIGHT RESCALING !S AN EXAMPLE CONSIDER A LINEAR ARRAY OF ELEMENTS AND RAISED COSINE TAPERING &IGURE DEPICTS THE FOLLOWING #ONTINUOUS CURVE PATTERN OF ARRAY
4HE SUB ARRAYS ARCHITECTURE CAN BE REPRESENTED BY A MATRIX 4 HAVING A NUMBER - OF COLUMNS EQUAL TO THE NUMBER OF SUB ARRAYS AND A NUMBER . OF ROWS EQUAL TO THE NUMBER OF ELEMENTARY RADIATORS 4HE ELEMENT TIJ OF THE MATRIX IS DEFINED EITHER AS WI IF THE I TH ELEMENTARY RADIATOR BELONGS TO THE J TH SUB ARRAY OR AS IF THE I TH ELEMENTARY RADIATOR DOES NOT BELONG TO THE J TH SUB ARRAY WHERE WI IS THE TAPERING WEIGHT IN THE ANALOGUE LAYER OF &IGURE
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2!$!2 (!.$"//+
&)'52% %XAMPLES OF THE ANTENNA PATTERNS ACHIEVED IN SEVERAL CASES
OF SUB ARRAYS WITHOUT NOISE NORMALIZATION AT THE OUTPUT OF SUB ARRAYS IT APPROXIMATELY FOLLOWS THE UNIFORM TAPERING DASHED LINE $OTTED LINE PATTERN OF ARRAY OF ELEMENTS AND OF ARRAY OF SUB ARRAYS AFTER NOISE NORMALIZATION AND WEIGHT RESCALING 4HE NUMERICAL EXAMPLE FOLLOWS WITH &IGURE WHICH PORTRAYS THE CANCELLATION OF A JAMMER WITH THE $O! n AND A *.2 OF D" 4HE CONTINUOUS LINE REFERS TO AN UNADAPTED PATTERN TAPERED AT THE ELEMENT LEVEL WHEREAS THE DOTTED LINE PERTAINS TO THE ADAPTED PATTERN AT THE SUB ARRAY LEVEL 3UB ARRAYS ARE IN GENERAL CHOSEN TO BE IRREGULAR IN THEIR SHAPE AND POSITION TO AVOID GRATING LOBES )F A JAMMER IMPINGES ON A GRATING LOBE THE JAMMER WILL BE NULLED BY DISTORTING THE GRATING LOBE AND AS A CONSEQUENCE THE ARRAY MAIN BEAM GRATING NOTCH &OR EXAMPLE CONSIDER A 5,! WITH . ELEMENTS THEN FORM TWO TYPES OF NOT OVERLAPPING SUB ARRAY CONFIGURATIONS BOTH HAVING - SUB ARRAYS
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&)'52% *AMMER CANCELLATION AT SUB ARRAY LEVEL
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&)'52% 3).2 VERSUS THE JAMMER $O! *$O!
4HE FIRST CONFIGURATION IS REGULAR WITH TWO ELEMENTS FOR EACH SUB ARRAY 4HE SECOND CONFIGURATION IS IRREGULAR WITH AND ELEMENTS RESPECTIVELY &IGURE SHOWS THE 3).2 AT THE OUTPUT OF THE ARRAY VERSUS THE JAMMER $O! 4HE TARGET $O! IS AT THE 3.2 IS D" THE *.2 IS D" 4HREE CURVES SUMMARIZE THE SYSTEM PERFORMANCE 4HE DASHED LINE IS THE ARRAY PATTERN WITH RAISED COSINE TAPER THIS IS SHOWN FOR THE SAKE OF COMPARISON WITH THE OTHER TWO CURVES OF THE 3).2 4HE DOT TED LINE IS THE 3).2 FOR THE QUIESCENT ABSENCE OF ADAPTIVITY PATTERN IT MIMICS THE RECIPROCAL OF THE SIDELOBE AND MAIN BEAM PATTERN 4HE CONTINUOUS LINE IS THE 3).2 FOR THE ADAPTIVE IRREGULAR SUB ARRAY ARCHITECTURE THE MAXIMUM VALUE OF THE 3).2 IS LOG n TAPERING LOSSES &IGURE DEPICTS THE 3).2 FOR THE REGULAR ARRAY CONFIGURATION AND ABSENCE OF TAPERING )T IS NOTED THAT WHEN THE JAMMER $O! IS AROUND THE 3).2 DECREASES THIS IS BECAUSE OF THE GRATING LOBE 4HE MAXIMUM VALUE OF 3).2 IS D" LOG BECAUSE THERE ARE NO TAPERING LOSSES
&)'52% 3).2 VERSUS THE *$O! FOR A REGULAR SUB ARRAY ARCHITECTURE AND NO TAPERING
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3UPERRESOLUTION 4HE RESOLUTION OF A CONVENTIONAL ANTENNA IS LIMITED BY THE WELL KNOWN 2AYLEIGH CRITERION WHICH STATES THAT TWO EQUAL AMPLITUDE NOISE SOURCES CAN BE RESOLVED IF THEY ARE SEPARATED IN ANGLE BY K, IN RADIANS WHERE K IS THE WAVELENGTH AND , IS THE APERTURE LENGTH 7HEN THE INCIDENT WAVE IS RECEIVED WITH A HIGH *.2 AN ADAPTIVE ARRAY ANTENNA MAYIN PRINCIPLEACHIEVE A NARROWER ADAPTIVE BEAMWIDTH GIVING A SHARPER BEARING ESTIMATION OF THE INCIDENT WAVE )F ACCURATE STROBES OF THE JAM MERS CAN BE OBTAINED THESE CAN BE EXPLOITED TO FORM BEAMS IN THE JAMMER DIRECTIONS WHICH ARE USED AS AUXILIARY CHANNELS FOR ADAPTIVE INTERFERENCE SUPPRESSION 4HE INTERFERENCE DIRECTIONS CAN ALSO BE USED FOR DETERMINISTIC NULLING WHICH IS OF INTEREST FOR MAIN BEAM NULLING )N ADDITION TO THE INTERFERENCE SOURCE DIRECTIONS AND SOURCE STRENGTHS THIS TECHNIQUE CAN PROVIDE OTHER INFORMATION AS TO THE NUMBER OF SOURCES AND ANY CROSS CORRELATIONS COHERENCE BETWEEN THE SOURCES 3UCH INFORMATION CAN BE USED TO TRACK AND CATALOGUE THE INTERFERENCE SOURCES IN ORDER TO PROPERLY REACT TO THEM THE JAMMER MAPPINGA FUNCTION RUNNING IN THE BACKGROUNDIS USEFUL TO SELECT THE MODES EG ADMISSIBLE POINTING DIRECTIONS AND WAVEFORMS OF MULTIFUNCTION RADAR AND FOR GENERAL SITUATION AWARENESS 3UPERRESOLUTION MIGHT BE ABLE TO RESOLVE MULTIPLE INDEPENDENT SOURCES DUE TO SIDELOBE SUPERPOSITION AND MASKING PROBLEMS SUPERRESO LUTION MIGHT BE VITAL FOR JAMMER MAPPING IN CASE OF MULTIPLE JAMMERS 3UPERRESOLUTION IS ALSO OF INTEREST AS AN %##- TO COUNTER CROSS EYE JAMMING IN SEEKER HEAD APPLICA TIONS SEE 3ECTION OF 7IRTH 4HE SUPERRESOLUTION CONCEPT WAS MAINLY DEVELOPED AND ANALYZED BY 7 & 'ABRIEL AT THE .AVAL 2ESEARCH ,ABORATORY 53 $IFFERENT METHODS FOR BEARING ESTIMATION WERE DESCRIBED BY 'ABRIEL AND SUBSEQUENTLY BY OTHER AUTHORS n /NE IS THE MAXI MUM ENTROPY METHOD -%- INVENTED BY * 0 "URG )T WORKS WELL WITH A (OWELLS !PPLEBAUM ADAPTIVE BEAMFORMER WHICH HAS AN OMNIDIRECTIONAL RECEIVING PATTERN EXCEPT WHERE JAMMERS ARE PRESENT 4HE PRESENCE OF JAMMERS IS INDICATED BY NULLS IN THE RECEIVING PATTERN "ECAUSE NULLS ARE ALWAYS SHARPER THAN ANTENNA LOBES JAMMER BEARINGS CAN BE OBTAINED MORE ACCURATELY FROM THE ADAPTIVE BEAM PATTERN AND SUPER RESOLUTION IS THE RESULT 4HE DESIRED SPATIAL SPECTRUM PATTERN IS OBTAINED AS SIMPLY THE INVERSE OF THE ADAPTED PATTERN !S 'ABRIEL POINTED OUT THERE IS NOT A TRUE ANTENNA PATTERN BECAUSE THERE IS NO LINEAR COMBINATION OF THE SIGNALS FROM AN ARRAY THAT COULD PRODUCE SUCH A PEAKED SPATIAL PATTERN )T IS SIMPLY A FUNCTION COMPUTED FROM THE RECIPROCAL OF A TRUE ADAPTED ANTENNA PATTERN 3UPERRESOLUTION AND ADAPTIVE ANTENNAS FOR JAMMER CAN CELLATION ARE INTIMATELY RELATED 2OUGHLY SPEAKING THE DIFFERENCE IS THAT ONE PRODUCES A PATTERN WITH THE NULLS DOWN ADAPTIVE ANTENNA FOR JAMMER CANCELLATION AND THE OTHER WITH THE NULLS UP IE PEAKS SUPERRESOLUTION OF JAMMERS /NE LIMITING FACTOR OF SUPERRESOLUTION TECHNIQUES IS THAT THEY OFTEN REQUIRE THE RECEIVED SIGNALS TO OBEY ACCURATE MODELS OF THE ARRAY MANIFOLD 4HIS CAN BE VIOLATED DUE TO PROPAGATION EFFECTS EG SPATIAL SPREADING AND NONSTATIONARITY AS WELL AS INSTRU MENTAL EFFECTS EG CHANNEL MISMATCH 4HESE FACTORS ALSO AFFECT THE PERFORMANCE OF ADAPTIVE ANTENNAS FOR JAMMER CANCELLATION BUT MODEL MISMATCHES CAN DEGRADE THE PERFORMANCE OF SUPERRESOLUTION TECHNIQUES MORE SEVERELY 4HE HIGHER PERFORMANCE OF THE SUPERRESOLUTION TECHNIQUES IS OFTEN OBTAINED AT THE EXPENSE OF REQUIRING A STRICTER ADHERENCE TO THE ASSUMED MODEL IF THE MODEL IS INACCURATE THESE TECHNIQUESWHICH RELY ON ITS HEAVY EXPLOITATIONSUBSEQUENTLY BECOME THE MOST SENSITIVE AND MORE PRONE TO PERFORM BADLY &OR EFFICIENT SUPERRESOLUTION AN ARRAY WITH A REASONABLE NUMBER OF SUB ARRAYS IS REQUIRED THIS MAY BE THE REASON FOR THE LACK OF APPLICATION OF THIS TECHNIQUE TO PRACTI CAL RADAR SYSTEMS EXCEPT FOR EXPERIMENTAL PURPOSES 3UPERRESOLUTION BASED ON A SMALL
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3,# CONFIGURATION IS NOT EFFICIENT BECAUSE THIS LEADS TO THE MAXIMUM ENTROPY OR AUTOREGRESSIVE METHODS THAT BEING NONLINEAR PROCESSING HAVE A HIGH PROBABILITY OF SPURIOUS PEAKS 0RACTICAL EXPERIENCES INDICATE THAT THE RESOLUTION LIMIT IS DETERMINED RATHER MORE BY IMPLEMENTATION AND ENVIRONMENTAL FACTORS THAN BY THE PURE *.2 CONSIDERATIONS
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4HE DIFFERENT TYPES OF %##- ARE RELATED TO THE PROPER USE AND CONTROL OF THE POWER FREQUENCY AND WAVEFORM OF THE RADIATED SIGNAL /NE BRUTE FORCE APPROACH TO DEFEAT NOISE JAMMING IS TO INCREASE THE RADARS TRANSMITTER POWER 4HIS TECHNIQUE WHEN COU PLED WITH hSPOTLIGHTINGv THE RADAR ANTENNA ON THE TARGET RESULTS IN AN INCREASE OF THE RADARS DETECTION RANGE 3POTLIGHTING OR BURNTHROUGH MODES MIGHT BE EFFECTIVE BUT A PRICE MUST BE PAID !S THE RADAR DWELLS IN A PARTICULAR DIRECTION IT IS NOT LOOKING ELSEWHEREWHERE IT IS SUPPOSED TO LOOK )N ADDITION THE BURNTHROUGH MODE IS NOT EFFECTIVE AGAINST CHAFF DECOYS REPEATERS SPOOFERS AND SO ON -ORE EFFECTIVE IS THE USE OF COMPLEX VARIABLE AND DISSIMILAR TRANSMITTED SIGNALS THAT PLACE A MAXIMUM BURDEN ON %3- AND %#- $IFFERENT WAYS OF OPERATION REFER TO THE CHANGE OF THE TRANSMITTED FREQUENCY IN FREQUENCY AGILITY OR FREQUENCY DIVERSITY MODES OR TO THE USE OF WIDE INSTANTANEOUS BANDWIDTHn &REQUENCY AGILITY USUALLY REFERS TO THE RADARS ABILITY TO CHANGE THE TRANSMITTER FREQUENCY ON A PULSE TO PULSE OR A BATCH TO BATCH BASIS 4HE BATCH TO BATCH APPROACH ALLOWS DOPPLER PROCESSING WHICH IS NOT COMPATIBLE WITH FREQUENCY AGILITY ON A PULSE TO PULSE BASIS )N A WAVEFORM WITH PULSE TO PULSE FREQUENCY AGILITY THE CENTER FREQUENCY OF EACH TRANSMITTED PULSE IS MOVED IN EITHER A RANDOM OR A PROGRAMMED SCHEDULE BETWEEN A LARGE NUMBER OF CENTER FREQUEN CIES 4HE FREQUENCY OF THE NEXT PULSE CANNOT GENERALLY BE PREDICTED FROM THE FREQUENCY OF THE CURRENT PULSE &REQUENCY DIVERSITY REFERS TO THE USE OF SEVERAL COMPLEMENTARY RADAR TRANSMISSIONS AT DIFFERENT FREQUENCIES EITHER FROM A SINGLE RADAR EG A RADAR HAV ING STACKED BEAMS IN ELEVATION BY EMPLOYING DIFFERENT FREQUENCIES ON EACH ELEVATION BEAM OR FROM SEVERAL RADARS 4HE OBJECTIVE OF FREQUENCY AGILITY AND DIVERSITY IS TO FORCE THE JAMMER TO SPREAD ITS ENERGY OVER THE ENTIRE AGILE BANDWIDTH OF THE RADAR THIS CORRESPONDS TO A REDUCTION OF THE JAMMER DENSITY AND RESULTING %#- EFFECTIVENESS ! GOOD EXAMPLE OF THE USE OF THE FREQUENCY DOMAIN FOR PURPOSE OF %##- IS THE 3ENRAD AN EXPERIMENTAL LONG RANGE AIR SURVEILLANCE RADAR BUILT AND TESTED AT THE .AVAL 2ESEARCH ,ABORATORY 53 3ENRAD WAS AN EXAMPLE OF HOW TO BUILD A RADAR SO AS TO FORCE THE JAMMER TO DILUTE ITS RADIATED ENERGY PER UNIT BANDWIDTH IT INCLUDES BOTH FREQUENCY AGILITY AND FREQUENCY DIVERSITY 4HIS RADAR SHOWS THAT ITS UNUSUALLY WIDE BANDWIDTH ALLOWS A REDUCTION OF THE EFFECTIVENESS OF THE NOISE JAMMER THAT CAN SERI OUSLY DEGRADE MORE NARROWBAND RADARS &REQUENCY AGILITY DIVERSITY AND INSTANTANEOUS WIDEBAND TECHNIQUES REPRESENT A FORM OF %##- IN WHICH THE INFORMATION CARRYING SIGNAL IS SPREAD OVER AS WIDE A FREQUENCY OR SPACE OR TIME REGION AS POSSIBLE TO REDUCE DETECTABILITY BY %3- ANDOR !2- AND MAKE JAMMING MORE DIFFICULT 4HIS %##- TECHNIQUE PERTAINS TO THE REALM OF WAVEFORM CODING n 4HE AMBIGUITY FUNCTION !& IS THE TOOL TO CHARACTERIZE WAVEFORM CODING IN TERMS OF RESOLUTION SIDELOBE LEVEL AND AMBIGUITY )N SELECTING A WAVEFORM FOR A GIVEN RADAR APPLICATION THE !& SHOULD BE TESTED AGAINST THE ENVIRONMENT IN WHICH THE RADAR
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WILL BE EXPECTED TO OPERATE 4HE SO CALLED ENVIRONMENTAL DIAGRAM DEPICTS SPECTRAL SPATIAL AND AMPLITUDE CHARACTERISTICS OF THE RADAR ENVIRONMENT CLUTTER %#- SUCH AS CHAFF INTENTIONAL INTERFERENCES ANDPERHAPSINTERFERENCES FROM NEIGHBORING %- APPARATUSES AND IS USED TO ASSIST THE RADAR WAVEFORM DESIGN !N EXAMPLE OF AN ENVI RONMENTAL DIAGRAM IS ON P OF ,EVANON AND -OZESON ON THE RANGE DOPPLER PLANE ARE SHOWN THE REGIONS IN WHICH SEVERAL TYPES OF CLUTTER AND HIGH ALTITUDE CHAFF ARE EXPECTED /N THE SAME DIAGRAM ARE SUPERIMPOSED THE EXPECTED TARGET TRAJECTORIES AND THE !& CONTOUR OF A SAY PULSE BURST WAVEFORM !S THE TARGET FOLLOWS A PARTICULAR TRA JECTORY THE !& WILL MOVE ACCORDINGLY AND THE SPURIOUS !& PEAKS WILL SLIDE ACROSS THE CLUTTER AND CHAFF REGIONS DETERMINING THE INTENSITY AND FEATURES OF THE RADAR ECHOES 7AVEFORM CODING INCLUDES 02& JITTER AND 02& STAGGER WHICH ARE HELPFUL FOR SOME DECEPTION JAMMER BUT DONT HELP AGAINST NOISE JAMMER 7AVEFORM CODING MAKES DECEP TION JAMMING OR SPOOFING OF THE RADAR DIFFICULT SINCE THE ENEMY SHOULD NOT KNOW OR ANTICIPATE THE FINE STRUCTURE OF THE TRANSMITTED WAVEFORM AS A CONSEQUENCE IT GIVES ASSURANCE OF MAXIMUM RANGE PERFORMANCE AGAINST SUCH TYPES OF JAMMING )NTRAPULSE CODING TO ACHIEVE PULSE COMPRESSION MAY BE PARTICULARLY EFFECTIVE IN IMPROVING TARGET DETECTION CAPABILITY BY RADIATION OF ENOUGH AVERAGE RADAR POWER WITHOUT EXCEEDING PEAK POWER LIMITATIONS WITHIN THE RADAR AND BY IMPROVING RANGE RESOLUTION LARGER BAND WIDTH WHICH IN TURN REDUCES CHAFF RETURNS AND RESOLVES TARGETS TO A HIGHER DEGREE 3OME ADVANTAGE CAN BE GAINED BY INCLUDING THE CAPABILITY TO EXAMINE THE JAMMER SIGNALS FIND HOLES IN THEIR TRANSMITTED SPECTRA AND SELECT THE RADAR FREQUENCY WITH THE LOWEST LEVEL OF JAMMING 4HIS APPROACH IS PARTICULARLY USEFUL AGAINST PULSED %#- SPOT NOISE AND NONUNIFORM BARRAGE NOISE ITS EFFECTIVENESS DEPENDS PRIMARILY ON THE EXTENT OF THE RADAR AGILE BANDWIDTH AND THE ACQUISITION SPEED AND FREQUENCY TRACKING OF AN hINTELLIGENTv JAMMER ! TECHNIQUE SUITED TO THIS PURPOSE IS REFERRED TO AS AUTOMATIC FREQUENCY SELECTION !&3 !NOTHER METHOD TO REDUCE THE EFFECT OF MAIN BEAM NOISE JAMMING IS TO INCREASE THE TRANSMITTER FREQUENCY AS AN ALTERNATIVE MEANS TO THE USE OF A LARGER ANTENNA IN ORDER TO NARROW THE ANTENNAS BEAMWIDTH 4HIS RESTRICTS THE SECTOR THAT IS BLANKED BY MAIN BEAM JAMMING AND ALSO PROVIDES A STROBE IN THE DIRECTION OF THE JAMMER 3TROBES FROM A FEW SPATIALLY SEPARATED RADARS ALLOW THE JAMMER TO BE LOCATED 4HE AVAILABILITY OF SOLID STATE TRANSMITTER TECHNOLOGYn ALLOWS THE GENERATION OF HIGH DUTY CYCLE WAVEFORMS WHICH MAY BE OF SOME HELP TO REALIZE ,0) RADAR !S A GENERAL REMARK ONE OF THE FACTORS PREVENTING GOOD %##- IS THE REDUCTION OF %- SPECTRUM ALLOCATED TO RADAR !S DISCUSSED OPERATING OVER A WIDE SPECTRAL RANGE HAS IMPORTANT ADVANTAGES FOR %##- BUT THE CIVILIAN AND COMMERCIAL TELECOMMUNICA TION SYSTEMS ERODE MORE AND MORE PORTIONS OF THE SPECTRUM AT THE EXPENSE OF MILITARY %##- CAPABILITY
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*AMMING SIGNALS THAT SURVIVE THE ANTENNA %##- EXPEDIENTS CAN IF LARGE ENOUGH SATURATE THE RADAR PROCESSING CHAIN 7IDE DYNAMIC RANGE RECEIVERS NEED TO BE USED TO AVOID SATURATION ! LOGARITHMIC LOG RECEIVER MIGHT HELP AGAINST NOISE JAMMING BUT IT HAS DETRIMEN TAL EFFECTS AGAINST CLUTTER WHEN DOPPLER PROCESSING IS USED ! LOG RECEIVER IS A DEVICE WHOSE VIDEO OUTPUT IS PROPORTIONAL TO THE LOGARITHM OF THE ENVELOPE OF THE 2& INPUT SIGNAL OVER A SPECIFIED RANGE )T MIGHT BE USEFUL IN PREVENTING RECEIVER SATURATION IN
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THE PRESENCE OF VARIABLE INTENSITIES OF JAMMING NOISE "Y COMPARISON WITH A LINEAR RECEIVER OF LOW DYNAMIC RANGE MODERATE JAMMING NOISE LEVELS WILL NORMALLY CAUSE THE COMPUTER TO SATURATE SO THAT THE TARGET SIGNAL WILL NOT BE DETECTED 4HE MAIN DISAD VANTAGE IS THAT A LOG CHARACTERISTIC CAUSES SPECTRAL SPREADING OF THE RECEIVED ECHOES )T WOULD NOT BE POSSIBLE TO MAINTAIN CLUTTER REJECTION IN AN -4) OR PULSE DOPPLER RADAR IF THE SPECTRUM OF CLUTTER ECHOES WERE TO SPREAD INTO THE SPECTRAL REGION IN WHICH TARGET RETURNS WERE EXPECTED 4HE MAIN MESSAGE IS THAT THE DYNAMIC RANGE PROBLEM IS IMPORTANT FOR THE REJECTION OF JAMMER AS WELL AS CLUTTER THE LATTER ALWAYS PRESENT IN A RADAR 4HUS THE RECOM MENDATION IS TO IMPLEMENT IN A MODERN RADAR A RECEIVER WITH A WIDE LINEAR DYNAMIC RANGE EG D" 4HIS WIDE DYNAMIC RANGE NEEDS TO BE MAINTAINED ALSO IN THE !$# DEVICES WITH A SUITABLE NUMBER OF BITS AS A RULE OF THUMB EACH BIT ADDS D" TO THE DYNAMIC RANGE COUNT (ARD OR SOFT LIMITERS CAN ALSO BE USED TO COUNTER JAMMING SIGNALS 4HEY ARE NONLINEAR MEMORYLESS DEVICES THAT CUT JAMMING SIGNALS HAVING WIDE AMPLITUDES 4HE $ICKE &IX RECEIVER COUNTERS HIGH RATES OF SWEPT FREQUENCY #7 JAMMING AND SWEPT SPOT NOISE JAM MERS )N A RADAR RECEIVER THE $ICKE &IX USES A WIDEBAND INTERMEDIATE FREQUENCY )& AMPLIFIER AND A LIMITER AHEAD OF THE NARROW BANDWIDTH )& AMPLIFIER 4HE WIDEBAND AMPLIFIER ALLOWS A RAPID RECOVERY TIME FROM THE EFFECTS OF THE SWEPT JAMMER AND THE LIMITER CUTS THE JAMMING SIGNAL 4HE NARROWBAND TARGET SIGNAL AFTER TRANSIT THROUGH THE WIDEBAND AMPLIFIER AND THE LIMITER WITHOUT REMARKABLE DEGRADATION IS INTEGRATED BY THE NARROWBAND FILTER MATCHED TO THE SIGNAL 4HE WORD &IX IN THE $ICKE &IX WAS PUT THERE MANY YEARS AGO TO INDICATE IT WAS A hFIXv FOR A PROBLEM THAT OCCURRED AT THE TIME AND WAS TO BE REPLACED BY SOMETHING BETTER )T WAS USUALLY INSTALLED WITH A SWITCH TO TURN IT OFF IF NECESSARY 4ODAY $ICKE &IX IS NOT USED IN A MODERN RADAR ESPECIALLY ONE THAT EMPLOYS DOPPLER PROCESSING THUS IT IS NO LONGER OF INTEREST IN MANY RADAR APPLICATIONS /THER SPECIAL PROCESSING CIRCUITS CAN BE USED IN THE RADAR TO AVOID SATURATION IE FAST TIME CONSTANT &4# DEVICES PERHAPS OF LITTLE USE IN MODERN RADAR AUTOMATIC GAIN CONTROL !'# AND #&!2 (OWEVER THEY CANNOT BE SAID TO BE %##- TECH NIQUES &OR EXAMPLE &4# ALLOWS THE DETECTION OF SIGNALS THAT ARE GREATER THAN CLUTTER BY PREVENTING THE CLUTTER FROM SATURATING THE COMPUTER &4# DOES NOT PROVIDE SUB CLUTTER VISIBILITY !'# KEEPS THE RADAR RECEIVER OPERATING WITHIN ITS DYNAMIC RANGE PREVENTING SYSTEM OVERLOAD AND PROVIDING PROPER NORMALIZATION SO AS TO FURNISH SIG NALS OF STANDARDIZED AMPLITUDE TO RADAR RANGE VELOCITY AND ANGLE PROCESSING TRACKING CIRCUITS )N CONCLUSION THESE DEVICES HAVE A PLACE IN THE RADAR BUT NOT AS MEANS FOR FIGHTING THE %#- BATTLE )N SUMMARY THERE ISNT MUCH THAT HAS BEEN DONE IN THE RECEIVER TO COMBAT %#- OTHER THAN TO INSURE THERE IS A GOOD RECEIVER THAT DOES ITS JOB 4ODAY MODERN PHASED ARRAY MULTI CHANNEL RADAR ARE GOING TO ADOPT FULLY DIGITAL SOFTWARE CONTROLLED RECEIVERS AS IN THE $!2 CASE HERE THE EXPECTED ADVANTAGES ARE THE WIDER LINEAR DYNAMIC RANGE AND THE WITHIN BAND CALIBRATION OF THE RECEIVERS THAT WILL SUPPORT THE ADAPTIVITY ON SEV ERAL TENS OF CHANNELS A DISTINCTIVE ADVANTAGE AGAINST DIRECTIONAL NOISE JAMMERS
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$IGITAL COHERENT SIGNAL PROCESSING GREATLY ALLEVIATES THE EFFECTS OF CLUTTER AND CHAFF 4HIS IS MOTIVATED BY THE USE OF COHERENT DOPPLER PROCESSING TECHNIQUES SUCH AS FIXED ADAPTIVE -4) OR OPTIMUM PULSE DOPPLER PROCESSING .ONCOHERENT DEVICES ARE ALSO
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REQUIRED BECAUSE OF THE LIMITED DEGREE OF CLUTTER CHAFF AND JAMMER SUPPRESSION PRACTI CALLY ACHIEVED BY COHERENT DEVICES SO THAT THE CANCELLATION RESIDUE MAY STILL BE A SIG NIFICANT SOURCE OF FALSE ALARM !MONG THE NONCOHERENT DEVICES IT IS WORTH MENTIONING THE #&!2 DETECTORn AND THE PULSE WIDTH DISCRIMINATOR THIS LATTER BEING EFFECTIVE AGAINST PULSED JAMMERS 4HE PULSE WIDTH DISCRIMINATION CIRCUIT MEASURES THE WIDTH OF EACH RECEIVED PULSE )F THE RECEIVED PULSE IS NOT OF APPROXIMATELY THE SAME WIDTH AS THE TRANSMITTED PULSE IT IS REJECTED ! PULSE WIDTH DISCRIMINATION TECHNIQUE CAN HELP IN REJECTING CHAFF IN FACT ECHO RETURNS FROM CHAFF CORRIDORS ARE MUCH WIDER THAN THE TRANSMITTED PULSE (OWEVER IF A TARGET IS WITHIN THE CHAFF CORRIDOR THE PULSE WIDTH DISCRIMINATOR MIGHT ALSO ELIMINATE THE TARGET #OHERENT 0ROCESSING 4HE MOST EFFECTIVE ANTI CHAFF TECHNIQUE AVAILABLE TO RADAR IS THE USE OF DOPPLER FILTERING WHICH EXPLOITS THE DIFFERENT MOTION CHARACTERISTICS OF THE TARGET AND THE CHAFF 4HE CHARACTERISTICS OF CHAFF ARE SIMILAR TO THOSE OF WEATHER CLUTTER EXCEPT THAT THE CHAFF SCATTERING ELEMENTS ARE CUT TO RESPOND TO A BROAD SPECTRUM OF RADAR FREQUENCIES 7EATHER CLUTTER AND CHAFF DIFFER FROM GROUND CLUTTER IN THAT BOTH THE MEAN DOPPLER SHIFT AND THE SPREAD ARE DETERMINED BY WIND VELOCITY AND WIND SHEAR THE LAT TER ARISING FROM THE VARIATION OF WIND VELOCITY WITH HEIGHT #HAFF MOVES WITH THE LOCAL WIND AND THERE ARE WAYS ADAPTIVE -4) AND OPTIMUM DOPPLER PROCESSINGo TO MAKE AN -4) NULL OUT BOTH MOVING AND STATIONARY UNWANTED ECHOES 4HERE ARE TWO BASIC DOPPLER FILTERING TECHNIQUES THAT ARE USED 4HE FIRST IS THE -4) WHICH EMPLOYS A 02& THAT PROVIDES UNAMBIGUOUS RANGE COVERAGE WHILE USING A COMB DOPPLER FILTER WHOSE NULLS ARE TUNED TO THE AVERAGE RADIAL SPEED OF CHAFF 4HE SECOND IS THE PULSE DOPPLER WHICH CAN USE A HIGH 02& TO PROVIDE UNAMBIGUOUS DOPPLER COVERAGE IN CONJUNCTION WITH A DOPPLER FILTER BANK ALLOWING SEPARATION OF TARGET FROM THE CHAFF ! PROBLEM WITH CHAFF MIGHT BE WHEN THERE IS A SIGNIFICANT WIND SHEAR IN THE ATMOSPHERE 7ITH WIND SHEAR THE DOPPLER SPECTRUM FROM CHAFF CAN HAVE A WIDE SPECTRAL WIDTH UNLESS THE ELEVA TION BEAMWIDTH IS VERY NARROW AS MIGHT OCCUR WITH TRI DIMENSIONAL RADAR WITH STACKED BEAMS IN ELEVATION SO THAT IT IS DIFFICULT TO CANCEL MOVING CHAFF ECHOES ! PULSE DOP PLER RADAR HAS A BETTER CHANCE BUT IT HAS PROBLEMS OF ITS OWN BECAUSE OF THE FOLDOVER OF THE CLUTTER THAT MIGHT OCCUPY A LARGE RANGE EXTENT #OHERENT DOPPLER PROCESSORS MIGHT REQUIRE RELATIVELY LARGE AMOUNTS OF PULSES EG MORE THAN WHICH MUST BE TRANSMITTED AT A STABLE FREQUENCY AND 02& ! RESPONSIVE JAMMER COULD MEASURE THE FREQUENCY OF THE FIRST TRANSMITTED PULSE AND THEN CENTER THE JAMMER TO SPOT JAM THE FOLLOWING PULSES !LSO THE REQUIREMENT FOR A STABLE 02& PRE CLUDES THE USE OF PULSE TO PULSE JITTER WHICH IS ONE OF THE MOST EFFECTIVE TECHNIQUES AGAINST DECEPTION JAMMERS THAT RELY ON ANTICIPATING THE RADAR TRANSMITTER PULSE #OHERENT DOPPLER PROCESSORS ARE ALSO GENERALLY VULNERABLE TO IMPULSIVE RADIO FREQUENCY INTERFER ENCE ESPECIALLY IN RADARS WITH A LIMITED NUMBER OF COHERENT BURSTS ON TARGET !NOTHER %##- TECHNIQUE TO BE CONSIDERED IS PULSE COMPRESSION BY MATCHED FILTERING IT IS INTIMATELY RELATED TO THE WAVEFORM CODING DISCUSSED IN 3ECTION 0ULSE COMPRESSION IS A PULSE RADAR TECHNIQUE IN WHICH LONG PULSES ARE TRANS MITTED TO INCREASE THE ENERGY ON THE TARGET WHILE STILL RETAINING THE TARGET RANGE RESO LUTION OF A SHORT PULSE TRANSMISSION )T IS ALMOST ALWAYS USED IN RADAR FOR ACHIEVING o 4HE ADAPTIVE -4) ESTIMATES THE MEAN DOPPLER FREQUENCY OF A MOVING CLUTTER SOURCE AND PLACES THE NULL OF SAY A BINOMIAL -4) /PTIMUM DOPPLER PROCESSING ESTIMATES THE WHOLE SPECTRUM OF CLUTTER AND SHAPES BY MEANS OF THE INVERSE OF THE CLUTTER COVARIANCE MATRIX THE CANCELLATION FILTER ACCORDINGLY FURTHERMORE WITH A DOPPLER FILTER BANK IT INTEGRATES THE ECHO SIGNAL FROM MOVING TARGETS 4HE OPTIMUM FILTER WEIGHTS ARE CALCULATED BY AN EQUATION SIMILAR TO %Q APPLIED TO THE RADAR ECHOES RECEIVED BY A COHERENT PULSE TRAIN TRANSMITTED BY THE RADAR
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HIGH RANGE RESOLUTION OR REDUCING THE PEAK POWER 0ULSE COMPRESSION OFFERS SOME %##- ADVANTAGE THAT IS DISCUSSED HEREAFTER 7HEN THE PULSE COMPRESSION SEARCH RADAR IS COMPARED FROM AN %3- STANDPOINT WITH A CONVENTIONAL SEARCH RADAR WITH THE SAME WIDE PULSE THE ENEMY RECEIVER ON A JAMMING PLATFORM WILL NOT KNOW IN THE GENERAL CASE THE PULSE COMPRESSION REFERENCE CODE AND WILL BE AT A DISADVANTAGE #OMPARED WITH A RADAR THAT USES AN UNCOMPRESSED WIDE PULSE THE PULSE COMPRESSION TECHNIQUE INCREASES THE RADARS CAPABILITY AGAINST EXTENDED SIGNAL RETURNS LIKE CHAFF AND CLUTTER )N ADDITION NOISE FROM A JAMMER DOES NOT PULSE COMPRESS %XTENDED CLUTTER TENDS TO BE NOISE LIKE AND WILL NOT PULSE COMPRESS WHICH KEEPS DOWN INTER FERENCE DISPLAYED TO OPERATORS 4HE DISADVANTAGES OF PULSE COMPRESSION ARE RELATED TO THE LONG DURATION OF THE CODED PULSE WHICH GIVES MORE TIME FOR THE %#- EQUIP MENT TO PROCESS THE PULSE )N MANY CASES PULSE COMPRESSION CAN PROVIDE THE MEANS FOR EASY RADAR JAMMING FOR THE ENEMY %#- OPERATOR 0ULSE COMPRESSION IS ALSO VULNERABLE TO COVER PULSE JAMMING IN WHICH THE %#- PULSE IS RETURNED TO THE RADAR WITH A HIGH *.2 SUCH THAT THE NORMAL TARGET RETURN IS COVERED BY THE JAMMING PULSE 4HE WIDTH OF THE %#- PULSE IS NORMALLY WIDER THAN THE RADAR SKIN RETURN 4HIS TYPE OF DECEPTION CAN BE COUNTERACTED BY AN %##- TECHNIQUE SUCH AS THE COVER PULSE CHANNEL WHERE THE TRACKING IS ON THE %#- TRANSMISSION RATHER THAN ON THE SKIN RETURN FROM THE TARGET 4HE DIGITAL COHERENT IMPLEMENTATION OF THE $ICKE &IX RECEIVER CONCEPT REQUIRES THE USE OF A COHERENT HARD LIMITER THAT PRESERVES THE PHASE OF THE SIGNAL WHILE KEEPING THE AMPLITUDE AT A CONSTANT VALUEp 4HE COHERENT LIMITER IS INSERTED UPSTREAM OF THE PULSE COMPRESSION FILTER IN A RADAR THAT USES PHASE CODED SIGNALS )N RECEPTION THE JAMMER AND TARGET SIGNALS ARE CUT IN AMPLITUDE 4HE PRESERVATION OF THE TARGET SIGNAL PHASE CODING ALLOWS THE INTEGRATION OF TARGET ENERGY BY MEANS OF THE PULSE COMPRESSION FILTER MATCHED TO THE PHASE CODE 4HE $ICKE &IX PROCESSING SCHEME SUFFERS FROM THREE LIMITATIONS 4HE FIRST IS RELATED TO THE DETECTION LOSS EXPERIENCED WHEN THE TARGET DOES NOT COMPETE WITH THE JAMMER 4HE SECOND DISADVANTAGE REFERS TO THE MASKING EFFECT OF A WEAK TARGET SIGNAL SUFFICIENTLY CLOSE IN RANGE COMPARED WITH THE SPATIAL EXTEN SION OF THE CODE TO A STRONG TARGET &URTHERMORE IT CANNOT BE USED IN CONJUNCTION WITH DOPPLER PROCESSING #&!2 #&!2 IS A TECHNIQUE MADE NECESSARY TO PREVENT THE COMPUTER FROM BEING OVERLOADED BY FALSE ALARMS WHICH REDUCE THE CAPABILITY OF THE RADAR TO DETECT DESIRED TARGETS 4HIS PROCESSING ALSO PLAYS A ROLE AS %##- THERE ARE THREE MOTIVA TIONS FOR THIS &IRST THE SCOPE OF %#- TECHNIQUES IN A BROAD SENSE IS TO IMPAIR THE TARGET DETEC TION AND TRACKING PERFORMANCE OF A RADAR SYSTEM $ETECTION PERFORMANCE IS MEASURED BY THE PROBABILITY OF DETECTION TRACKING PERFORMANCE IS DETERMINED BY THE PROBABILITY OF DETECTION AND THE PROBABILITY OF FALSE ALARM AS WELL #ONVENTIONAL CELL AVERAGING #&!2 RAISES THE THRESHOLD IN THE PRESENCE OF NOISE JAMMING AND REDUCES THE NUMBER OF TARGETS DETECTED (OWEVER THE TARGETS THAT SURVIVE CAN BE EFFECTIVELY TRACKED BECAUSE THE PROBABILITY OF FALSE ALARM HAS BEEN MAINTAINED AT SUFFICIENTLY LOW LEVELS 7ITHOUT #&!2 AND APPROPRIATE THRESHOLD ADJUSTMENTS PERHAPS NO TARGETS WILL BE TRACKED DUE TO THE VERY LARGE NUMBER OF FALSE PEAKS DETECTIONS ON THE JAMMER MAKING IT THROUGH TO SATURATE THE TRACKER #ONVENTIONAL #&!2 IS NOT REALLY REMOVING THE INTERFERENCE IT IS JUST hHIDINGv IT FROM THE RADAR OPERATOR (OWEVER IT IS ALLOWING THE TRACKER TO OPERATE p 4HIS IS USED WITH "ARKER CODES FOR INSTANCE WHERE THE AMPLITUDE LIMITATION DOESNT IMPAIR THE PHASE CODE
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EFFECTIVELY FOR THE TARGETS THAT SURVIVE AND SO IN THIS WAY IT CAN PREVENT THE OVERALL FAILURE OF THE RADAR )N THE LIMIT OF NO TARGETS BEING DETECTED IE A VERY POWERFUL JAM MER THEN IT COULD STILL BE ARGUED THAT NO TRACKS ARE BETTER THAN MANY FALSE TRACKS 3ECOND NOT ALL JAMMERS ARE NOISE JAMMERS 3OME INDEED HAVE A STRUCTURE IN RANGE DOPPLER SPACE AND #&!2 TECHNIQUES CAN POTENTIALLY BE USED TO LOWER THESE UNWANTED SIGNALS BENEATH THE DETECTION THRESHOLD ONCE AGAIN PREVENTING THE DETEC TION OF FALSE TRACKS WHICHFROM A TACTICAL PERSPECTIVECAN CAUSE SERIOUS DILEMMAS FOR A RADAR OPERATOR 4HIRD THERE ARE THE ADAPTIVE #&!2 DETECTORS !-& OR ADAPTIVE MATCHED FILTER FOR EXAMPLE THAT REALLY ARE %##- TECHNIQUES IN THE SENSE THAT THEY ENHANCE THE PROBABILITY OF DETECTION AGAINST STRUCTURED INTERFERENCES IN SPACE ANDOR TIME WHILE MAINTAINING THE CONSTANT FALSE ALARM RATE PROPERTY THAT ALLOWS THESE DETECTED TARGETS TO BE EFFECTIVELY TRACKED RATHER THAN BEING SEDUCED BY A HIGH NUMBER OF FALSE DETECTIONS 4HIS TYPE OF PROCESSINGOR SIMILARLY DERIVED FROM THE GENERALIZED LIKELIHOOD RATIO TEST ',24 HAS BEEN USED IN SOME PRACTICAL RADAR &URTHERMORE ANY SELF RESPECTING RADAR SYSTEM SHOULD MAKE THE OPERATOR AWARE OF HIGHER NOISE LEVELS DUE TO JAMMING EVEN THOUGH THEY MAY NOT BE VISIBLE ON THE #&!2 DISPLAY THE ACT OF PERFORMING #&!2 SHOULD NOT EXCLUDE THE OPERATOR FROM KNOWING THAT JAMMING IS PRESENT AND THAT THE DETECTION THRESHOLD HAS BEEN RAISED
Ó{°£äÊ "* ,/" * "9 /Ê / +1 4O THIS POINT IN THE CHAPTER ONLY ELECTRONIC %##- TECHNIQUES HAVE BEEN CONSIDERED (OWEVER RADAR OPERATIONAL PHILOSOPHY AND DEPLOYMENT TACTICS MAY ALSO HAVE A SIG NIFICANT EFFECT ON THE RADARS RESISTANCE TO %#- %3- AND !2- 4HIS GROUP OF TECH NIQUES CAN BE SUBDIVIDED INTO THOSE INVOLVING THE OPERATOR THE METHODS OF OPERATION THE RADAR DEPLOYMENT TACTICS AND THE FRIEND %3- IN SUPPORT TO %##- !N OPERATIONAL TECHNIQUE AGAINST %#- IS TO USE MISSILES WITH HOME ON JAM (/* GUIDANCE TO INTER CEPT NOISE JAMMERS (/* IS A MEANS WHEREBY A MISSILE GUIDANCE RECEIVER UTILIZES THE SELF SCREENING TARGET JAMMING SIGNAL TO DEVELOP ANGULAR STEERING INFORMATION SO THE MISSILE CAN HOME ON THAT TARGET 4HE ROLE OF THE OPERATOR IN THE %##- CHAIN PERTAINS TO THE MORE GENERAL TOPIC OF HUMAN FACTOR %##- 4HIS IS A GENERIC %##- TECHNIQUE THAT COVERS THE ABILITY OF AN AIR DEFENSE OFFICER A RADAR OPERATOR A COMMANDING OFFICER ANDOR ANY OTHER AIR DEFENSE ASSOCIATED PERSONNEL TO RECOGNIZE THE VARIOUS KINDS OF %#- TO ANALYZE THE EFFECT OF THE %#- TO DECIDE WHAT THE APPROPRIATE %##- SHOULD BE ANDOR TO TAKE THE NECESSARY %##- ACTION WITHIN THE FRAMEWORK OF THE PERSONS COMMAND STRUCTURE (OWEVER THE HUMAN OPERATOR IS LESS EFFECTIVE AGAINST A SIMULTANEOUS ATTACK OF MANY ENEMY VEHICLES SUPPORTED BY A STRONG %#- FORCE !N OPERATOR CONFRONTED WITH A LARGE MIX OF %#- TYPES AND A LARGE NUMBER OF %##- TECHNIQUES IS LIKELY TO DO THE WRONG THING ANDOR REACT TOO SLOWLY )N THIS SITUATION IT MIGHT BE PROPER TO RESORT TO AUTO MATICALLY APPLIED %##- TECHNIQUES THIS IS THE TENDENCY TODAY (OWEVER A POSSIBLE CONCERN IS THAT THIS COULD SOMETIMES HURT THE %##- CAPABILITY OF THE RADAR SINCE A WELL TRAINED OPERATOR CAN OFTEN FIGURE OUT WHAT IS HAPPENING BUT THE AUTOMATIC PROCES SOR CAN ONLY MAKE DECISIONS BASED ON PREPROGRAMMED LOGICS INSTALLED IN ITS COMPUTER AND MIGHT NOT RECOGNIZE WHEN SOMETHING UNUSUAL AS IN JAMMING OCCURS 4HIS IS A POSSIBLE ADVERSE EFFECT OF THE ABSENCE OF A DECISION MAKING OPERATOR
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4HE OPERATIONAL METHODS INCLUDE EMISSION CONTROL %-#/. THE APPROPRIATE ASSIGNMENT OF OPERATING FREQUENCIES TO VARIOUS RADARS THE USE OF COMBINED %##-S TO MEET COMBINED %#-S THE USE OF DUMMY TRANSMITTERS TO DRAW %#- TO OTHER FRE QUENCIES AND SO ON %-#/. IS A TECHNIQUE FOR THE MANAGEMENT OF ALL %- RADIA TIONS OF A FRIENDLY SYSTEM FORCE OR COMPLEX TO OBTAIN MAXIMUM ADVANTAGES IN THE AREAS OF INTELLIGENCE DATA RECEPTION DETECTION IDENTIFICATION NAVIGATION MISSILE GUID ANCE ETC OVER THE ENEMY IN A GIVEN SITUATION %-#/. PERMITS ESSENTIAL OPERATIONS WHILE MINIMIZING THE DISCLOSURE OF LOCATION IDENTIFICATION FORCE LEVEL OR OPERATIONAL INTENTIONS TO ENEMY INTELLIGENCE RECEPTORS )T INCLUDES THE AUTHORIZATION TO RADIATE THE CONTROL OF RADIATION PARAMETERS SUCH AS AMPLITUDE FREQUENCY PHASE DIRECTION AND TIME THE PROHIBITION OF RADIATION AND THE SCHEDULING OF SUCH ACTIONS FOR ALL UNITS AND EQUIPMENT OF A COMPLEX 4HE ON OFF SCHEDULING OF THE RADARS OPERATION TO INCLUDE ONLY THOSE TIME INTERVALS WHEN SURVEILLANCE IS REQUIRED CAN REDUCE THE PROBABILITY OF THE RADAR LOCATION BEING FOUND BY DIRECTION FINDING $& EQUIPMENT OR RADAR HOMING AND WARNING RECEIVERS 2ADAR BLINKING USING MULTIPLE RADARS WITH COORDINATED ON OFF TIMES CAN CONFUSE AN !2- SEEKER AND GUIDANCE OR A $& RECEIVER $ECOY TRANSMITTERS RADIATING FROM ANTENNAS NOT LOCATED AT THE RADAR MAY ALSO BE EMPLOYED TO CONFUSE $& RECEIVERS AND !2-S THESE DECOYS CAN ALSO OPERATE IN CONJUNCTION WITH THE RADARS IN A BLINKING MODE 0ROPER SITE SELECTION FOR GROUND BASED RADARS IN FIXED INSTALLATIONS CAN PROVIDE A DEGREE OF NATURAL SIGNAL MASKING TO PREVENT FOR EXAMPLE DETECTION BY GROUND BASED %3- EQUIPMENT ! HIGH DEGREE OF MOBILITY FOR TACTICAL SYSTEMS ALLOWS hRADIATE AND RUNv OPERATIONS WHICH ARE DESIGNED TO PREVENT THE RADAR FROM BEING ENGAGED BY $& LOCATION TECHNIQUES AND ASSOCIATED WEAPONS 4HE DEPLOYMENT OF A RADAR NETWORK WITH OVERLAP PING COVERAGE COULD PROVIDE SOME %##- BENEFITS )N THE NETTED MONOSTATIC CASE THE RADARS HAVE DIFFERENT FREQUENCIES FOR INTERFERENCE REDUCTION PURPOSES CONSEQUENTLY THE %#- HAS TO CONSIDER JAMMING ALL RADARS IN THE OVERLAPPING ZONE THUS REDUCING ITS EFFICACY 4HIS IS THE KIND OF FREQUENCY DIVERSITY DISCUSSED IN 3ECTION &INALLY IT IS WORTH NOTING THAT FRIENDLY %3- CAN SUPPORT %##- ACTION BY WARN ING OF POSSIBLE HOSTILE ACTIVITY PROVIDING ANGULAR LOCATIONS OF HOSTILE JAMMERS AND INFORMATION CHARACTERISTICS OF JAMMERS 4HIS INFORMATION IS HELPFUL IN THE SELECTION OF A SUITABLE %##- ACTION
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Ê/ +1 4HIS SECTION SHOWS THE APPLICATION OF THE PREVIOUSLY DESCRIBED %##- TECHNIQUES TO SURVEILLANCE TRACKING PHASED ARRAY IMAGING AND OVER THE HORIZON RADARS 4HE USE OF %##- TECHNIQUES IN OTHER TYPES OF RADARS SUCH AS MORTAR LOCATION RADARS MISSILE GUIDANCE RADARS AND NAVIGATION RADARS IS CONSIDERED IN THE LITERATURE 3URVEILLANCE 2ADARS 4HE FUNCTION OF A SURVEILLANCE RADAR IS TO SEARCH A LARGE VOLUME OF SPACE AND LOCATE THE POSITION OF TARGETS WITHIN THE SEARCH COVERAGE 4HE RADAR RANGE AND THE AZIMUTH ELEVATION COVERAGE DEPEND ON THE SPECIFIC RADAR APPLICA TIONS 4HE TARGET REPORTS GENERATED BY A SURVEILLANCE RADAR ARE PROCESSED TO FORM TARGET TRACKS 4HE KEY FEATURES OF A SURVEILLANCE RADAR ARE THE DETECTION RANGE IN CLEAR CLUTTER AND JAMMING ENVIRONMENTS THE ACCURACY AND RATE OF THE EXTRACTED DATA AND THE FALSE ALARM RATE )N THE ENSUING DISCUSSION THE DESIGN PRINCIPLES DRIVEN BY THE REQUIREMENTS FORCED BY THE THREAT ARE MAINLY ADDRESSED
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$ETECTION IN A CLEAR ENVIRONMENT IS A FEATURE OF EARLY WARNING RADARS e WHICH LOOK PRIMARILY FOR HIGH ALTITUDE TARGETS AT LONG RANGES BEYOND THE SURFACE HORIZON WHERE THE EFFECTS OF CLUTTER CAN BE IGNORED 5NDER THESE CONDITIONS A SIMPLIFIED ANALYSIS STATES THAT RADAR PERFORMANCE IS RELATIVELY INSENSITIVE TO TRANSMITTER FREQUENCY AND WAVEFORM SHAPE IN PRACTICE THE LOWER MICROWAVE FREQUENCIES ARE PREFERRED BECAUSE IT IS EASIER TO OBTAIN LARGE ANTENNA AND HIGH AVERAGE POWER AT LOWER FREQUENCIES AND RAIN CLUTTER IS NOT IMPORTANT 4HE MAXIMUM DETECTION RANGE ON A TARGET WITH A CERTAIN 2#3 R IN FREE SPACE FOR A SURVEILLANCE RADAR THAT MUST UNIFORMLY SEARCH A SPECIFIED VOLUME IN A GIVEN TIME PERIOD DEPENDS ON THE PRODUCT OF THE AVERAGE TRANSMITTER POWER 0 AND THE EFFECTIVE ANTENNA APERTURE !R )T ALSO DEPENDS ON THE INVERSE OF THE SYSTEM NOISE TEMPERATURE BUT THIS IS OF LITTLE CONSEQUENCE SINCE THE NOISE TEMPERATURE IS NOT A MAJOR DESIGN ISSUE ANYMORE 4HE SITUATION IS MORE COMPLEX WHEN THE TARGET TO BE DETECTED IS OF THE STEALTH TYPE 7AVEFORM DESIGN AND OPERATING FREQUENCY ARE RELEVANT PARAMETERS IN TACTICAL AND VOLUME SURVEILLANCE RADARS WHICH MUST BE ABLE TO DETECT LOW FLYING PENETRATING TAR GETS THAT ATTEMPT TO USE TERRAIN SHIELDING EFFECTS TO ESCAPE RADAR DETECTION )N THIS CASE THE SELECTION OF WAVEFORM AND FREQUENCY IS MADE TO TACKLE THE PROBLEMS OF MASKING MULTIPATH CHAFF CLUTTER AND %#- 4HE MAJOR %7 THREATS TO A SURVEILLANCE RADAR ARE I NOISE JAMMING II CHAFF III DECEPTION JAMMING IV DECOYS AND EXPENDABLES AND V !2- #OMMON TYPES OF JAMMING ARE MAIN BEAM NOISE JAMMING AND SIDELOBE NOISE JAMMING !GAINST THIS THREAT GOOD RADAR %##- PERFORMANCE IS ACHIEVED BY INCREAS ING THE PRODUCT 0!R OF AVERAGE TRANSMITTER POWER BY THE EFFECTIVE ANTENNA APERTURE ! MILITARY RADAR SHOULD ALWAYS HAVE D" MORE POWER APERTURE PRODUCT THAN GIVEN BY STANDARD DESIGNS YET THIS IS SELDOM ALLOWED 4HE REQUEST FOR A LOW SIDELOBE LEVEL HAS TO BE TRADED OFF WITH THE CORRESPONDING DEGRADATION OF THE MAIN BEAM WIDTH THE WIDENING OF THE MAIN BEAM WIDTH MAY MAKE THE RADAR MORE VULNERABLE TO MAIN BEAM JAMMING 4HE NOISE JAMMER SITUATION IS BASICALLY AN ENERGY BATTLE BETWEEN THE RADAR AND THE JAMMER )N THE MAIN BEAM NOISE JAMMING SITUATION THE ADVANTAGE IS WITH THE JAMMER BECAUSE THE RADAR EXPERIENCES A TWO WAY PROPAGATION LOSS OF ITS ENERGY AS CONTRASTED WITH THE ONE WAY PROPAGATION LOSS BETWEEN THE JAMMER AND THE RADAR 7ITH SIDELOBE JAMMING THE RADAR DESIGNER CAN REDUCE THE JAMMER ADVANTAGE BY LOW SIDELOBE DESIGN COUPLED WITH THE USE OF SIDELOBE CANCELLATION TECHNIQUES 7ITH MAIN BEAM NOISE JAM MING THE RADAR CAN MAXIMIZE THE RECEIVED TARGET ENERGY BY TRANSMITTING MORE AVERAGE POWER DWELLING LONGER ON THE TARGET OR INCREASING THE ANTENNA GAIN )F THE RADARS DATA RATE IS FIXED AND A UNIFORM ANGULAR SEARCH RATE IS DICTATED BY MECHANICAL OR SEARCH STRATEGY THEN THE ONLY OPTION FOR THE RADAR IS TO INCREASE ITS AVERAGE TRANSMITTER POWER 4HE NEXT OPTION IS TO MANAGE THE DATA RATE THEREBY ALLOWING A LONGER DWELL TIME ON THE TARGET BURNTHROUGH MODE ALONG SPECIFIC SPATIAL SECTORS WHERE NEEDED 4HE ABILITY TO VARY THE DATA RATE IN AN OPTIMAL MANNER IS ONE OF THE PRINCIPAL ADVANTAGES OF PHASED ARRAY RADARS !NOTHER PRINCIPLE OF %##- DESIGN AGAINST MAIN BEAM NOISE JAMMING IS TO MINI MIZE THE AMOUNT OF JAMMING ENERGY ACCEPTED BY THE RADAR 4HIS IS ACCOMPLISHED BY SPREADING THE TRANSMITTED FREQUENCY RANGE OF THE RADAR OVER AS WIDE A BAND AS POS SIBLE THUS FORCING THE JAMMER INTO A BARRAGE JAMMING MODE 4HIS CAN BE OBTAINED BY e /F COURSE SUCH RADARS HAVE TO SEE ALSO TARGETS AT SHORTER RANGES WHERE CLUTTER ECHOES CAN MASK THE TARGETS ECHO FOR THIS REASON ALL LONG RANGE CIVIL AIR TRAFFIC CONTROL RADAR EMPLOY DOPPLER PROCESSING
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RESORTING TO FREQUENCY AGILITY ANDOR FREQUENCY DIVERSITY 3OME RADARS INCORPORATE AN !&3 DEVICE THAT ALLOWS THE RADAR FREQUENCY TO BE TUNED TO THAT PART OF THE SPECTRUM CONTAINING THE MINIMUM JAMMING ENERGY )N ACCORDANCE WITH THE SEARCH RADAR EQUATION SEE 3ECTION %##- PERFOR MANCE APPEARS EXPLICITLY TO BE INSENSITIVE TO FREQUENCY )NCREASING THE RADAR FRE QUENCY DOES NOT AFFECT THE SIGNAL TO INTERFERENCE ENERGY RATIO WITHIN A RADAR RESOLUTION CELL WHEN THE ANTENNA APERTURE AND THE RADAR DATA RATE ARE HELD CONSTANT 4HE INCREASED FREQUENCY INCREASES BOTH THE ANTENNA GAIN AND THE NUMBER OF RADAR RESOLUTION CELLS THAT MUST BE SEARCHED BY EQUIVALENT AMOUNTS THE NET EFFECT IS THAT THE TARGET RETURN POWER IS INCREASED BY THE SAME AMOUNT BY WHICH THE TARGET DWELL TIME IS DECREASED THEREBY HOLDING THE TARGET TO JAMMING ENERGY RATIO CONSTANT .EVERTHELESS IN PRACTICE THE EFFECT OF MAIN BEAM NOISE JAMMING CAN BE REDUCED WITH HIGH RADAR FREQUENCY (IGHER FREQUENCY RADARS TEND TO HAVE NARROWER ANTENNA BEAMWIDTHS AND LARGER OPERATING FRE QUENCY BANDWIDTHS TO PERCENT OF RADAR CENTER FREQUENCY THAN LOWER FREQUENCY RADARS 4HUS MAIN BEAM JAMMERS WILL BLANK SMALLER SECTORS OF HIGH FREQUENCY RADARS THAN OF LOW FREQUENCY RADARS )N ADDITION MAIN BEAM JAMMING OF A NARROW BEAM RADAR TENDS TO PROVIDE A STROBE IN THE DIRECTION OF THE JAMMER WHICH CAN BE USED TO TRIANGULATE AND REVEAL THE JAMMER LOCATION 7IDER RADAR BANDWIDTH WITH APPROPRIATE CODING FORCES THE JAMMER TO SPREAD ITS ENERGY OVER A WIDER BAND THEREBY DILUTING THE EFFECTIVE JAMMING ENERGY %##- DESIGN PRINCIPLES FOR MAIN BEAM NOISE JAMMING ALSO APPLY TO SIDELOBE NOISE JAMMING WITH THE ADDITION THAT THE SIDELOBE RESPONSE IN THE DIRECTION OF THE JAMMER MUST BE MINIMIZED 5LTRALOW SIDELOBES IN THE ORDER OF SAY D" BELOW THE ANTENNAS MAIN BEAM PEAK RESPONSE ARE FEASIBLE BY USING ADVANCED TECHNOLOGY 3OMETIMES THE CONTROL OF SIDELOBE NOISE JAMMING BY USING ULTRALOW SIDELOBE ANTEN NAS IS NOT PROPER THIS IS TRUE BECAUSE THE MAIN BEAM WIDTH MIGHT BE INCREASED TWO TO THREE TIMES )N ADDITION MOST OPERATIONAL RADARS DO NOT USE ULTRALOW LESS THAN
D" OR LOW TO D" SIDELOBE ANTENNAS AND HAVE ANTENNA SIDELOBES IN THE
TO D" REGION WITH AVERAGE SIDELOBES OF TO D" BELOW ISOTROPIC 3,# HAS THE POTENTIAL OF REDUCING NOISE JAMMING THROUGH THE ANTENNA SIDELOBES AND IT IS USED FOR THIS PURPOSE IN OPERATIONAL RADARS !S EXPLAINED IN 3ECTION %##- TECHNIQUES AGAINST CHAFF ARE MAINLY THOSE BASED ON COHERENT DOPPLER PROCESSING )N PARTICULAR THE REFERENCE DESCRIBES A COMPARISON OF FIXED AND ADAPTIVE DOPPLER CANCELERS APPLIED TO CHAFF DATA RECORDED BY A MULTIFUNCTIONAL PHASED ARRAY RADAR OPERATING AT 3 BAND "OTH CANCELERS PROCESS AN PULSE COHERENT BURST 4HE FIXED IE NONADAPTIVE PROCESSING IS A $OLPH #HEBYSHEV FILTER WITH D" OF SIDELOBE ATTENUATION WITH RESPECT TO PEAK 4HE ADAPTIVE FILTER BASED ON THE OPTIMUM DOPPLER FILTERING SEE 3ECTION AND THE LITERATURE HAS THE WEIGHTS BUILT AROUND THE ESTIMATION AND INVERSION OF THE DISTURBANCE CHAFF AND NOISE COVARIANCE MATRIX 4HE TARGET DETECTABILITY IS EVALUATED AGAINST A DENSE CHAFF CLOUD &OR THE PARTICULAR SET OF RECORDED MEASUREMENTS IT HAS BEEN SHOWN A SUBSTANTIALLY ENHANCED PERFORMANCE OF THE ADAPTIVE FILTER OVER THE NONADAPTIVE FILTER
!S MENTIONED PREVIOUSLY THE LOWER FREQUENCIES MIGHT BE PREFERRED FOR LONG RANGE SURVEILLANCE BECAUSE THE USUAL RADAR EQUATION DOES NOT INCLUDE ALL THE PERTINENT FACTORS )N THE JAMMING CASE ONE SHOULD TAKE ACCOUNT THAT THE JAMMING ANTENNA ON AN AIRCRAFT HAS A LOWER GAIN AT LOWER FREQUENCIES SO THE JAMMING POWER DENSITY MIGHT BE LESS AT THE LOWER FREQUENCIES !LSO WHEN MULTIPATH IS IMPORTANT BY SELECTING THE RADAR FREQUENCY PROPERLY ONE MIGHT REDUCE THE JAMMING POWER RECEIVED BY BEING IN A NULL OF THE JAMMER TRANSMITTING ANTENNA #HAFF MIGHT NOT BE AS EASY TO DEPLOY AT THE LOWER FREQUENCIES )N CONCLUSION THE LOWER RADAR FREQUENCIES MIGHT NOT BE AS VULNERABLE AS ONE MIGHT THINK BY EXAMINING THE TRADITIONAL RADAR EQUATION
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2!$!2 (!.$"//+
!NOTHER CLASS OF %##- TECHNIQUES IS AIMED TO CONTRAST THE DECEPTIVE %#- $ECEPTION JAMMERS HAVE A NUMBER OF SPECIFIC CHARACTERISTICS THAT CAN BE USED BY RADARS TO IDENTIFY THEIR PRESENCE 4HE MOST PROMINENT IS THAT FALSE TARGET RETURNS MUST USUALLY FOLLOW THE RETURN FROM THE JAMMER CARRYING TARGET AND MUST ALL LIE IN THE SAME DIRECTION WITHIN A RADAR 02) )F THE DECEPTION JAMMER USES A DELAY THAT IS GREATER THAN A 02) PERIOD TO GENERATE AN ANTICIPATORY FALSE TARGET RETURN THEN PULSE TO PULSE 02) JITTER IDENTIFIES THE FALSE TARGET RETURNS 4HE GENERATION OF FALSE TARGETS IN DIRECTIONS DIFFERENT FROM THAT OF THE JAMMER CARRYING AIRCRAFT REQUIRES INJECTING PULSE JAMMING SIGNALS INTO THE RADARS SIDELOBES -ANY RADARS EMPLOY THE 3," SEE 3ECTION TO DEFEAT THIS TYPE OF %#- 4RUE TARGET RETURNS TEND TO FLUCTUATE FROM SCAN TO SCAN WITH FIXED FREQUENCY RADARS AND FROM PULSE TO PULSE WITH FREQUENCY AGILITY RADARS 4RANSPONDER JAMMERS GENER ALLY SEND THE SAME AMPLITUDE REPLY TO ALL SIGNALS THEY RECEIVE ABOVE A THRESHOLD AND THEREFORE DO NOT SIMULATE ACTUAL TARGET FLUCTUATION RESPONSES )N ADDITION THEY USUALLY APPEAR WIDER IN AZIMUTH THAN REAL TARGETS OWING TO THE MODULATION EFFECT OF THE RADAR SCANNING ANTENNAS RESPONSE ON THE REAL TARGET 2EPEATER JAMMERS CAN BE MADE TO SIMU LATE THE ACTUAL AMPLITUDE RESPONSE OF REAL TARGETS AND HENCE ARE MORE EFFECTIVE OVER TRANSPONDER TYPE JAMMERS FROM AN %#- VIEWPOINT !N OPERATING MODE TO BE INCLUDED IN A RADAR TO DISTINGUISH USEFUL TARGETS FROM TRANSPONDER AND REPEATER JAMMERS IS BASED ON A DOPPLER SPECTRUM ANALYSIS PROVIDED ENOUGH TIME ON TARGET IS AVAILABLE !DDITIONAL EXPENSIVE TECHNIQUES AGAINST DECEPTIVE JAMMING CAN BE BASED ON THE MEASUREMENT AND ANALYSIS OF THE ANGULAR AND POLARIZATION SIGNATURES OF THE ECHO SIGNALS 4HE SAME %##- CONSIDERATIONS APPLY WITH DECOY TARGETS THAT HAVE THE GENERAL ATTRIBUTES OF REAL TARGETS AND ARE VERY DIFFICULT TO IDENTIFY AS FALSE TARGETS ! METHOD SOMETIMES EMPLOYED IS TO TEST THE SCINTILLATION CHARACTERISTICS OF THE DETECTED TARGETS TO DETERMINE WHETHER OR NOT THEY FOLLOW THOSE OF REAL TARGETS %XPENDABLES THAT TEND TO BE DESIGNED UNDER STRINGENT ECONOMIC CONSTRAINTS OFTEN RETURN ONLY A STEADY SIGNAL TO THE RADAR 7ITH DOPPLER SPECTRUM ANALYSIS IT IS POSSIBLE TO LOOK FOR RETURNS FROM ROTATING COMPONENTS OF THE TARGET THAT ANY FORM OF POWERED TARGET MUST POSSESS %XAMPLES ARE JET ENGINE OR PROPELLER MODULATION RETURNS ASSOCIATED WITH AIRCRAFT TARGETS !2-S POSE A SERIOUS THREAT TO A SURVEILLANCE RADAR 4HE SURVIVABILITY OF A SURVEIL LANCE RADAR TO AN !2- ATTACK RELIES UPON WAVEFORM CODING TO DILUTE THE ENERGY IN THE FREQUENCY RANGE THE MANAGEMENT OF RADIATED ENERGY IN TIME AND ALONG THE ANGULAR SECTORS AND THE ADOPTION OF LOW SIDELOBES IN TRANSMISSION 4HESE ACTIONS MAKE IT MORE DIFFICULT FOR AN !2- TO HOME ON RADAR 7HEN AN !2- ATTACK IS DETECTED IT MAY BE USEFUL TO TURN ON SPATIALLY REMOTE DECOY TRANSMITTERS TO DRAW THE !2- AWAY FROM THE RADAR SITE "LINKING WITH A NETWORK OF RADARS ACHIEVES BETTER RESULTS 4HE !2- TRAJECTORY IS USUALLY SELECTED TO ATTACK THE RADAR THROUGH THE ZENITH HOLE REGION ABOVE THE RADAR WHERE ITS DETECTION CAPABILITY IS MINIMAL 4HUS A SUPPLEMENTAL RADAR THAT PROVIDES A HIGH PROBABILITY OF DETECTION IN THE ZENITH HOLE REGION IS REQUIRED 4HERE ARE CERTAIN ADVANTAGES IN CHOOSING A LOW TRANSMITTING FREQUENCY 5(& OR 6(& FOR THE SUPPLEMENTAL RADAR 4HE 2#3 OF THE !2- BECOMES GREATER AS THE WAVELENGTH OF THE RADAR APPROACHES THE MISSILE DIMENSIONS CAUSING A RESONANCE EFFECT ! LOW FREQUENCY RADAR IS SOMEWHAT LESS VULNERABLE TO AN !2- ATTACK OWING TO THE DIFFICULTY OF IMPLE MENTING A LOW FREQUENCY ANTENNA WITH THE LIMITED APERTURE AVAILABLE IN THE MISSILE (OWEVER LOW FREQUENCY RADAR HAS POOR ANGULAR RESOLUTION 4RACKING 2ADARS 4RACKING RADARS PROVIDE GOOD RESOLUTION AND PRECISE MEASURE MENT OF THE KINEMATIC PARAMETERS POSITION VELOCITY AND ACCELERATION OF TARGETS 4HE ESTIMATION UPDATED WITH MEASUREMENTS AND PREDICTION OF THE KINEMATIC PARAMETERS
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AS THE TIME RUNS ARE THE PROCESSING STEPS USED TO BUILD UP THE TRACKS OF TARGETS 4RACKS ALLOW GUIDANCE AND CONTROL OF FRIENDLY FORCES THREAT ASSESSMENT AND ENEMY TARGET ENGAGEMENT BY WEAPONS 4RACKING CAN BE ACCOMPLISHED IN FOUR WAYS I 4HE DEDICATED RADAR TRACKER SOMETIMES CALLED A SINGLE TARGET TRACKER AND DENOTED 344 CONTINUOUSLY POINTS ITS ANTENNA AT A SINGLE TARGET BY SENSING ERRORS FROM THE TRUE TARGET POSITION AND CORRECTING THESE ERRORS BY A SERVO CONTROL SYSTEM 4HEN THERE ARE TWO DIFFERENT TYPES OF RADARS CALLED IN THE PAST TRACK WHILE SCAN II /NE IS A LIMITED ANGLE SCAN AS IN SOME AIR DEFENSE RADARS AND AIRCRAFT LANDING RADARS WHICH SEARCH A LIMITED ANGULAR SECTOR AT A RAPID RATE EG OR TIMES A SECOND III 4HE OTHER TYPE OF TRACK WHILE SCAN 473 WAS WHAT IS NOW CALLED AUTOMATIC DETECTION AND TRACKING !$4 4HE !$4 SYSTEM GENERATES TRACKS OF MORE THAN ONE TARGET BY USING A SERIES OF SCAN TO SCAN TARGET MEASUREMENTS TAKEN AS THE ANTENNA SAMPLES THE TARGET PATHS IV 4HE MULTIFUNCTIONAL PHASED ARRAY RADAR TRACKS MULTIPLE TARGETS BY MULTIPLE INDEPENDENT BEAMS FORMED BY THE SAME ARRAY APERTURE THAT ARE ALLOTTED TO DIFFERENT TARGETS 4HIS SUBSECTION IS LIM ITED TO THE DESIGN PRINCIPLES DRIVEN BY THE THREAT REQUIREMENTS OF THE DEDICATED RADAR TRACKER 4HE ENSUING SUBSECTION WILL REFER TO MULTIFUNCTIONAL PHASED ARRAY RADAR 'OOD %##- PERFORMANCE IS ACHIEVED BY RADIATING AS LARGE AN AVERAGE TRANSMITTER POWER AT THE HIGHEST TRANSMITTER FREQUENCY PRACTICABLE COUPLED WITH AS LOW A SIDELOBE LEVEL AS ACHIEVABLE )NCREASING THE TRANSMITTER FREQUENCY FOR A FIXED ANTENNA SIZE INCREASES THE ANTENNA GAIN 'T WHICH IN TURN INCREASES THE RECEIVED TARGET POWER AS 'T &OR MAIN BEAM NOISE JAMMING THE RECEIVED JAMMING POWER INCREASES DIRECTLY AS 'T RESULTING IN A NET INCREASE IN SIGNAL TO JAMMING POWER BY A FACTOR PROPORTIONAL TO THE ANTENNA GAIN 'T (ERE IT IS NOTED A BASIC DIFFERENCE BETWEEN SURVEILLANCE AND TRACKING RADAR THE DETECTION RANGE OF A TRACKING RADAR IMPROVES AS THE FREQUENCY IS INCREASED FOR A FIXED SIZE ANTENNA 4HE REASON FOR THIS IMPROVEMENT IS THAT THE ANTENNA GAIN IS DIRECTLY INCREASED WITH FREQUENCY THEREBY FOCUSING MORE POWER ON THE TARGET 4HIS INCREASED POWER IS INTEGRATED FOR A TIME WHICH IS INVERSELY PROPORTIONAL TO THE BANDWIDTH OF THE SERVO CONTROL LOOP &OR A SURVEILLANCE RADAR THIS INCREASED POWER IS COLLECTED FOR A PROPORTIONALLY SHORTER TIME SINCE THE RADAR MUST SEARCH MORE CELLS IN THE SAME TIME BECAUSE OF THE NARROWER ANTENNA BEAMWIDTH 7ITH SIDELOBE JAMMING THE RECEIVED JAMMING POWER IS PROPORTIONAL TO THE SIDELOBE ANTENNA GAIN 'SL RESULTING IN A NET INCREASE IN SIGNAL TO JAMMING POWER RATIO BY THE FACTOR 'T'SL !S WITH SURVEILLANCE RADARS SIDELOBE NOISE JAMMING AND DECEPTION CAN BE FURTHER ATTENUATED BY THE USE OF 3,# IN CONJUNCTION WITH 3," AS DESCRIBED IN 3ECTION 4HE USE OF HIGHER TRANSMISSION FREQUENCIES FOR TRACKING RADARS GENERALLY MAKE THEM LESS SUSCEPTIBLE TO NOISE JAMMING THAN SURVEILLANCE RADARS )N ADDITION TACTICAL TRACK ING RADARS MAY TRACK THE NOISE JAMMER IN ANGLE 4RACKING A NOISE JAMMER IN ANGLE FROM TWO SPATIALLY SEPARATED RADARS PROVIDES ENOUGH INFORMATION TO LOCATE A JAMMER WITH SUFFICIENT ACCURACY ! MORE THREATENING %#- AGAINST TRACKING RADARS IS $%#- 4HESE THREATS REQUIRE CONSIDERABLY LESS ENERGY THAN NOISE JAMMING A FEATURE PARTICULARLY IMPORTANT ON TACTI CAL AIRCRAFT WHERE AVAILABLE SPACE IS LIMITED .EVERTHELESS THEY ARE VERY EFFECTIVE IN CAPTURING AND DECEIVING THE RANGE GATE WITH THE 2'0/ TECHNIQUE THE VELOCITY GATE WITH THE 6'0/ TECHNIQUE AND THE ANGLE TRACKING CIRCUITS ! PRIMARY %##- DEFENSE AGAINST 2'0/ IS THE USE OF A LEADING EDGE RANGE TRACKER 4HE ASSUMPTION IS THAT THE DECEPTION JAMMER NEEDS TIME TO REACT AND THAT THE LEADING EDGE OF THE RETURN PULSE WILL NOT BE COVERED BY THE JAMMER 02) JITTER AND FREQUENCY AGILITY BOTH HELP TO ENSURE THAT THE JAMMER WILL NOT BE ABLE TO ANTICIPATE THE RADAR PULSE AND LEAD THE ACTUAL SKIN INTERVAL !LTERNATIVELY THE TRACKING RADAR MIGHT EMPLOY A MULTIGATE RANGE TRACKING
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2!$!2 (!.$"//+
SYSTEM TO SIMULTANEOUSLY TRACK BOTH THE SKIN AND FALSE TARGET RETURNS 4HIS APPROACH UTILIZES THE FACT THAT BOTH THE JAMMING SIGNALS AND THE TARGET RETURN COME FROM THE SAME ANGULAR DIRECTION SO THAT THE RADARS ANGLE TRACKING CIRCUITS ARE ALWAYS LOCKED ONTO THE REAL TARGET 4HE METHODOLOGY OF INTRODUCING 6'0/ INTO THE RADARS TRACKING CIRCUITS IS ANALOGOUS TO THE METHOD USED WITH 2'0/ 4HE FREQUENCY SHIFT IS INITIALLY PROGRAMMED SO THAT THE REPEATED SIGNAL IS WITHIN THE PASSBAND OF THE DOPPLER FILTER CONTAINING THE TARGET RETURN 4HIS IS NEEDED TO CAPTURE THE DOPPLER FILTER CONTAINING THE TARGET THROUGH THE RADARS !'# ACTION 4HE REPEATER JAMMER SIGNAL IS THEN FURTHER SHIFTED IN FREQUENCY TO THE MAXIMUM EXPECTED DOPPLER FREQUENCY OF THE RADAR 4HE REPEATED SIGNAL IS THEN SWITCHED OFF FORCING THE VICTIM RADAR TO REACQUIRE THE TARGET #OHERENT TRACKING RADARS CAN CHECK THE RADIAL VELOCITY DERIVED FROM DOPPLER MEASUREMENTS WITH THAT DERIVED FROM DIFFERENTIATED RANGE DATA !NOMALOUS DIFFERENCES PROVIDE A WARNING OF THE PROBABLE PRESENCE OF A DECEPTION JAMMER 7HEN 2'0/ AND 6'0/ OPERATE SIMULTANEOUSLY THE BEST DEFENSE IS THE CONTEM PORARY TRACKING OF TRUE AND FALSE TARGETS IN BOTH RANGE AND DOPPLER DIMENSIONS 4HE USE OF MULTIMODE HIGH LOW AND MEDIUM 02& RADARS CAN ALSO BE AN EFFECTIVE %##- MEASURE HELPING TO COUNTER RANGE GATE AND VELOCITY GATE STEALERS BY SWITCHING RADAR MODES !NGLE GATE STEALING IS PARTICULARLY EFFECTIVE AGAINST CONICAL SCANNING OR SEQUEN TIAL LOBING TRACKING RADARS )T IS FOR THIS REASON THAT SUCH TRACKERS CANNOT BE USED IN MILITARY APPLICATIONS 4HE FUNDAMENTAL PROBLEM WITH THESE RADARS IS THAT ANGLE TRACKING IS ACCOMPLISHED BY DEMODULATING THE AMPLITUDE MODULATION IMPOSED ON THE TARGET RETURN PULSES OVER A COMPLETE SCANNING OR LOBING CYCLE 4O JAM THIS TYPE OF RADAR EFFECTIVELY THE RADARS ANGLE TRACKING ERROR SENSING CIRCUITS MUST BE CAPTURED WITH A FALSE AMPLITUDE MODULATED SIGNAL AT THE SCANNING OR LOBING RATE WHICH IS SIGNIFICANTLY OUT OF PHASE WITH THAT FROM THE TARGET RETURN 7HEN THE CONICAL SCAN OR LOBING MODULATION IS IMPOSED ON BOTH THE TRANSMITTER AND THE RECEIVER BEAMS IT IS RELATIVELY SIMPLE FOR A JAMMER TO SYNTHESIZE THE APPROPRIATE JAMMING SIGNAL BY INVERTING AND REPEATING THE TRANSMITTER MODULATION INVERSE GAIN REPEATER 4HIS CAN BE PARTIALLY OVERCOME BY A CONICAL SCAN ON RECEIVER ONLY #/32/ SYSTEM WHERE THE TRACKING RADAR RADIATES A NONSCANNING TRANSMITTING BEAM BUT RECEIVES WITH A CONICAL SCAN BEAM 4HE JAMMER THEN HAS NO KNOWLEDGE OF THE PHASE OF THE CONI CALLY SCANNED RECEIVING BEAM AND MUST ADOPT A TRIAL AND ERROR METHOD OF SCANNING THE JAMMING MODULATION UNTIL A NOTICEABLE REACTION OCCURS IN THE TRACKING RADAR BEAM 4HIS JAMMING TECHNIQUE IS CALLED JOG DETECTION ! SEQUENTIAL LOBING ON RECEIVE ONLY ,/2/ SYSTEM CONCEALS THE LOBING RATE FROM A POTENTIAL JAMMER #ONICAL SCAN AND SEQUENTIAL LOBING ARE GOING TO BE REPLACED BY THE MONOPULSE TECH NIQUE THUS #/32/ AND ,/2/ ARE BECOMING OBSOLETE -ONOPULSE TRACKING IS INHERENTLY INSENSITIVE TO ANGLE DECEPTIVE JAMMING FROM A SINGLE POINT SOURCE 4HIS IS A RESULT OF THE MONOPULSE ANGLE ERROR SENSING MECHANISM THAT FORMS AN ERROR PROPORTIONAL TO THE ANGLE BETWEEN THE TARGET AND THE ANTENNAS BORESIGHT ON EACH RETURN PULSE 4HIS IS ACCOMPLISHED BY COMPARING SIGNALS RECEIVED SIMULTANEOUSLY IN TWO OR MORE ANTENNA BEAMS AS DISTINGUISHED FROM TECHNIQUES SUCH AS LOBE SWITCHING OR CONICAL SCANNING IN WHICH ANGLE INFORMATION REQUIRES MULTIPLE PULSES %FFECTIVE MONOPULSE JAMMING TECHNIQUES GENERALLY ATTEMPT TO EXPLOIT THE MON OPULSE RADARS SUSCEPTIBILITY TO TARGET GLINT OR MULTIPATH SIGNALS /NE JAMMING APPROACH KNOWN AS CROSS EYE USED AGAINST MONOPULSE RADARS GENER ATES ARTIFICIAL GLINT INTO THE MONOPULSE TRACKING LOOP 4HE INVENTORS OF THE CROSS EYE TECHNIQUE ARE " ,EWIS .2, 53! AND $ (OWARD SEE THEIR PATENT ORIGINALLY FILED THE #ROSS EYE IS BASICALLY A TWO SOURCE INTERFEROMETER WHOSE ANTENNAS USUALLY ARE
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MOUNTED ON THE AIRCRAFTS WINGTIP AS FAR APART AS POSSIBLE 4HE SIGNALS RECEIVED IN EACH WINGTIP ANTENNA ARE REPEATED IN THE OPPOSITE WINGTIP ANTENNA EXCEPT FOR A n PHASE SHIFT WHICH IS INSERTED IN ONE LINE TO DIRECT AN INTERFEROMETRIC NULL TOWARD THE VICTIM RADAR )N EFFECT THIS CREATES AN APPARENT CHANGE OF TARGET DIRECTION AS VIEWED FROM THE RADAR ! LARGE REPEATER GAIN IS REQUIRED TO GENERATE A HIGH JAMMER TO SIGNAL RATIO OTH ERWISE THE SKIN ECHO WILL OVERWHELM THE JAMMING SIGNALS IN THE INTERFEROMETER PATTERN NULLS 4HE MAXIMUM EFFECTIVENESS OF THE TECHNIQUE IMPLIES A CONSIDERABLE DELAY ON THE ORDER OF NS IN THE REPEATED SIGNAL OWING TO THE TRANSMISSION LINE AND AMPLIFIER BETWEEN THE RECEIVER AND TRANSMITTER ANTENNAS 4HUS LEADING EDGE OR MULTIGATE RANGE TRACKING SHOULD BE AN EFFECTIVE %##- TECHNIQUE AGAINST CROSS EYE JAMMING 4ERRAIN BOUNCE JAMMING OR TERRAIN SCATTERED INTERFERENCE 43) OR HOT CLUTTER IS ANOTHER MONOPULSE JAMMING TECHNIQUE THAT IS USED AGAINST SEMIACTIVE MISSILE SEEKERS AND AIRBORNE TRACKING RADARS 7ITH THIS TECHNIQUE THE JAMMER AIRCRAFT ILLUMINATES THE %ARTHS SURFACE IN FRONT OF AND BELOW IT SO THAT THE SEMIACTIVE MISSILE HOMES ON THE ILLUMINATED GROUND SPOT AND NOT ON THE JAMMER AIRCRAFT 4HE UNCERTAINTY OF THE TERRAIN SCATTERING PARAMETERS AND THE POSSIBLE DEPOLARIZING EFFECTS OF SURFACE REFLECTION ARE SOME OF THE PROBLEMS ASSOCIATED WITH THIS TECHNIQUE 4HE 43) AGAINST AIRBORNE RADAR AND THE CORRESPONDING MITIGATION TECHNIQUES ARE DESCRIBED IN DETAIL IN THE LITERATUREn 43) IS A SIGNIFICANT PROBLEM TO MILITARY AIR BORNE RADAR IN FACT AN OFTEN WEAK TARGET SIGNAL IN THE MAIN BEAM HAS TO COMPETE WITH JAMMER THAT PROPAGATES NOT ONLY VIA DIRECT PATH BUT ALSO VIA MULTIPATH FROM THE UNDERLYING TERRAIN -ITIGATION TECHNIQUES HAVE BEEN FOCUSED ON ESTIMATING THE DIRECT JAMMER SIGNAL ESTIMATING THE LINEAR SYSTEM CREATED BY THE MULTIPATH AND REMOVING AN ESTIMATE OF THE REFLECTED JAMMER SIGNAL FROM THE MAIN RECEIVED RADAR SIGNAL THIS IS ALSO ALLOWED BY USING REFERENCE BEAMS POINTED AT HOT CLUTTER !DAPTIVE CANCELLA TION TECHNIQUES HAVE TO BE ABLE TO ACCOUNT FOR THE DOPPLER INDUCED BY RELATIVE MOTION BETWEEN AIRBORNE RADAR AND JAMMER PLATFORMS AND THE JAMMER SIGNAL NONSTATIONARITY THAT IS PRODUCED FROM SUCH A BISTATIC GEOMETRY 43) MITIGATION FOR OVER THE HORIZON /4( RADAR IS DESCRIBED IN !BRAMOVICH ET AL -ONOPULSE RADARS THAT USE PARABOLIC REFLECTOR ANTENNAS ARE SUSCEPTIBLE TO JAMMING THROUGH CROSS POLARIZATION LOBES GENERATED BY THE REFLECTOR SURFACE 4HIS OCCURS BECAUSE THE ANGLE ERROR SENSING DISCRIMINATOR HAS AN INVERSE SLOPE FOR A CROSS POLARIZED SIGNAL WHICH CAUSES THE ANGLE TRACKING SERVO TO HAVE POSITIVE FEEDBACK INSTEAD OF THE NEGATIVE FEEDBACK REQUIRED FOR TRACKING -ONOPULSE ESTIMATES WITH PLANAR ARRAY ANTEN NAS USUALLY HAVE A HIGH RESISTANCE TO CROSS POLARIZATION JAMMING SEE 3ECTION OF 7IRTH 7ITH ARRAY ANTENNASIN CONTRAST TO REFLECTOR ANTENNASALL THE SINGLE ANTENNA ELEMENTS HAVE THE SAME POLARIZATION DEPENDENT PATTERN 4HIS IS MULTIPLIED WITH THE ARRAY FACTOR AND ALSO APPLIES FOR THE SUM AND DIFFERENCE PATTERNS 4HE RESULTANT FORM OF THE BEAM PATTERN WILL THUS BE INDEPENDENT OF POLARIZATION 4HEREFORE THE MONOPULSE OPERA TION WILL ALSO NOT BE DISTURBED 0HASED !RRAY 2ADARS )N THIS SUBSECTION WE ILLUSTRATE BY A NUMERICAL EXAM PLE THE ROLE PLAYED BY THE SCHEDULER IN A MULTIFUNCTIONAL 0!2 TO COMBAT %#- 4O THIS END WE RESORT TO A BENCHMARK STUDY DESCRIBED IN THE LITERATURE WHICH DEFINES TYPICAL %#- THREATS OPERATIONAL SCENARIOS AND PHASED ARRAY PERFORMANCE MAINLY IN TERMS OF TARGET TRACKING UNDER %#- 4HE SIMULATION BENCHMARK INCLUDES TWO TYPES OF %#- NAMELY 3/* AND 2'0/ 4HE 3/* MOUNTED ON AN AIRCRAFT TRANSMITS BROADBAND NOISE TOWARD THE RADAR 4HE 3/* FLIES AN OVAL RACE COURSE HOLDING PATTERN IN A CLOCK WISE DIRECTION AT AN ALTITUDE OF M AND A SPEED OF MS IT IS APPROXIMATELY
Ó{°{{
2!$!2 (!.$"//+
KM FROM THE RADAR 4HE TWO CIRCULAR TURNS ARE PERFORMED AT AN ACCELERATION OF G 4HE TRANSMITTED 3/* NOISE IMPACTS THE RADAR WITH POWER F NOT EXCEEDING EIGHT TIMES THE RECEIVER NOISE POWER 4HUS A 3/* WILL NOT COMPLETELY HIDE A TARGET AND IT CAN BE DEFEATED WITH A HIGHER ENERGY WAVEFORM )N 2'0/ THE TARGET UNDER TRACK REPEATS WITH DELAY AND AMPLIFICATION THE RADAR PULSE SO AS TO PULL THE RADAR RANGE GATE OFF THE TARGET 4HE TIME DELAY IS CONTROLLED SO THE FALSE TARGET IS SEPARATED FROM THE TRUE ONE WITH EITHER LINEAR OR QUADRATIC MOTION &OR THE LINEAR CASE THE RANGE OF THE FALSE TARGET 2KFT IS RELATED TO THE RANGE OF THE TRUE TARGET 2KT VIA
2KFT 2KT VPO TK T
WHERE VPO IS THE PULL OFF RATE TK IS THE TIME AT WHICH THE TARGET IS BEING OBSERVED AND T IS THE INITIAL REFERENCE TIME OF THE 2'0/ FALSE TARGET !LTERNATIVELY FOR THE QUADRATIC CASE
2KFT 2KT
A T T PO K
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
&)'52% )NTERACTION OF RADAR SCHEDULER AND TRACKING FILTER
%,%#42/.)# #/5.4%2 #/5.4%2-%!352%3
Ó{°{x
4HE SCHEME IS BUILT AROUND TWO CLOSED LOOPS I THE LOOP ENCOMPASSING THE RADAR MODEL THE TRACKING FILTER AND THE SCHEDULER AND II THE TRACKING FILTER LOOP 4HE SCE NARIO IS OBSERVED BY THE RADAR AT TIME TK THE RADAR MODEL PROVIDES THE MEASUREMENTS RK BK EK AND 3.2K 4HE TRACKING FILTER UPDATES THE PREVIOUS TARGET STATE ESTIMATE 8K \K AND ITS COVARIANCE MATRIX 0K \K AT TIME TK PROVIDING THE NEW ESTIMATES 8K\K AND 0K\K AND THE VALUES RK \K BK \K AND EK \K AT THE NEXT TIME INSTANT TK 4HE SCHEDULER PROVIDES THE WAVEFORM TO RADIATE 7K AND THE THRESHOLD AK TO APPLY FOR TARGET DETECTION AT TK 3ELECTION OF THE 3AMPLING 0ERIOD 4HE SAMPLING PERIOD IS CHOSEN AMONG A FINITE NUMBER OF POSSIBLE DIFFERENT VALUES BASED ON KINEMATIC CONSIDERATIONS ON THE TARGET ESTIMATED SPEED AS WELL AS ON WHETHER MISSED DETECTIONS HAVE OCCURRED )F THERE IS NO MEASUREMENT TO BE ASSOCIATED TO THE TARGET THE SAMPLING PERIOD IS SET EQUAL TO 4S S AND THE WAVEFORM OF HIGHEST ENERGY IS SELECTED SO AS TO POSSIBLY AVOID A SECOND MISSED DETECTION DUE TO THE POSSIBLY LOW TARGET 2#3 #ONVERSELY THE SAM PLING PERIOD IS SELECTED AS FOLLOWS
4S S FOR TARGETS WITH ESTIMATED SPEED GREATER THAN MS
4S S FOR TARGETS WITH ESTIMATED SPEED BETWEEN AND MS
4S S FOR TARGETS WITH ESTIMATED SPEED LESS THAN MS %VEN THOUGH THE TARGET MAY ACCELERATE OR MANEUVER FOR THE SAKE OF SIMPLICITY THE SAMPLING PERIOD IS SELECTED ONLY ON THE BASIS OF THE TARGET ESTIMATED SPEED 3ELECTION OF THE $ETECTION 4HRESHOLD 4HE PRESENCE OF A JAMMING SIGNAL CAN INCREASE THE NUMBER OF FALSE ALARMS AND WRONG PLOT TRACK ASSOCIATIONS UP TO AN UNAC CEPTABLE LEVEL THUS INCREASING SIGNIFICANTLY THE PROBABILITY OF LOOSING A TARGET UNDER TRACK )T IS THEREFORE IMPORTANT THAT THE RADAR RECEIVER BE EQUIPPED WITH A #&!2 3INCE THE FALSE ALARM PROBABILITY IS RELATED TO THE DETECTION THRESHOLD THE LATTER SHOULD BE ADAPTED ONLINE BASED ON THE INTENSITY OF DISTURBANCES 3ELECTION OF THE 7AVEFORM 4HE BENCHMARK INCLUDES WAVEFORMS INDEXED BY I AND CHARACTERIZED BY A DIFFERENT PULSE WIDTH SEI SO THAT THE WAVEFORM CAN BE SELECTED IN ORDER TO PROVIDE A 3.2 GREATER THAN THE DETECTION THRESHOLD AND THUS MAINTAIN AN ASSIGNED PROBABILITY OF TARGET DETECTION 4HIS CAN BE ACCOMPLISHED BY FIRST ESTIMATING THE AVERAGE TARGET 2#3Ko AT TIME TK AND THEN COMPUTING FOR EACH WAVEFORM I THE PRE DICTED 3.2KI AND FINALLY SELECTING THE WAVEFORM INDEX I SUCH THAT THE CORRESPONDING 3.2KI IS JUST GREATER THAN THE DESIRED DETECTION THRESHOLD PLUS A GIVEN TOLERANCE %##- ! 3/* AND ! 2'0/ (EREAFTER SPECIFIC ANTI 3/* ! 3/* AND ANTI 2'0/ ! 2'0/ TECHNIQUES WILL BE DESCRIBED ! 3/* IS BASED ON ESTIMATING THE JAMMER POSITION AND POWER LEVEL AND THEN USING SUCH ESTIMATES TO ADAPT THE RADAR DETECTION THRESHOLD ONLINE u *AMMER STATE ESTIMATION 7HENEVER THE RADAR OPERATES IN THE PASSIVE MODE IE WITH OUT EMITTING PULSES BEARING BKJ AND ELEVATION EKJ OF THE JAMMER AS WELL AS THE RELATIVE STANDARD DEVIATIONS RKJB AND RKJE AND THE JAMMER TO NOISE RATIO QKJ IN THE FOLLOWING o 4HE 2#3 IS CERTAINLY A FLUCTUATING QUANTITY VERSUS TIME IT ALSO DEPENDS UPON THE TARGET ASPECT ANGLE (OWEVER IF ENOUGH TIME ON TARGET IS AVAILABLE THE 2#3 ESTIMATE CAN BE SUFFICIENTLY ACCURATE
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2!$!2 (!.$"//+
EXPRESSED IN D" ARE MEASURED 4HIS ALLOWS THE TRACKING FILTER TO ESTIMATE THE JAMMER STATE MADE UP OF FOUR STATE COMPONENTS THE TWO ANGULAR POSITIONS BEARING AND ELEVA TION AND THE RELATIVE ANGULAR SPEEDS 4HE JAMMER TRACK IS INITIALIZED BY USING THE FIRST TWO MEASUREMENTS PROVIDED BY THE RADAR u *AMMER POWER LEVEL ESTIMATION !N ESTIMATE OF THE POWER LEVEL CAN BE OBTAINED BY THE FIRST ORDER LINEAR FILTER INITIALIZED FROM FTJ FOR A SUITABLE FILTER COEFFICIENT @J
J
G O TKJ A J G O TKJ A J RK
u !DAPTATION OF THE DETECTION THRESHOLD &OR A GIVEN DETECTION THRESHOLD A IN D" THE PROBABILITY OF FALSE ALARM TURNS OUT TO BE ¤ ³ B 0FA EXP ¥ ´ J ¦ G 'STC 2 3 K µ
(ENCE THE DETECTION THRESHOLD CAN BE SELECTED AT EACH TIME INSTANT TK IN THE FOLLOW ING WAY
[
]
BK MAX LOG § G TKJ 'STC RK K 3 KJ ¶ LN 0FA © ¸
J IS THE MOST RECENT AVAILABLE ESTIMATE OF THE JAMMER POWER LEVEL THE WHERE FT K VALUE AK D" IS THE ONE WHICH ALLOWS IN THE ABSENCE OF JAMMERS THE DESIRED FALSE ALARM PROBABILITY 0FA RK\K IS THE FILTERED ESTIMATE OF THE TARGET RANGE 'STC IS THE SENSITIVITY TIME CONTROL GAIN AND 3KJ IS THE NORMALIZED ANTENNA GAIN FOR THE RECEIVED SIGNAL COMPUTED IN THE RADAR ACTIVE MODE
"ECAUSE THE PHASED ARRAY RADAR CONSIDERED HERE IS A MULTIFUNCTIONAL ONE IT HAS ALSO A TRACKING MODE THAT MIGHT BE AFFECTED BY THE 2'0/ FOR THIS REASON AN ! 2'0/ IS CONSIDERED AN %##- TECHNIQUE 7HENEVER 2'0/ IS ACTIVE TWO HIGH AMPLITUDE SIGNALS ARE RECEIVED FROM THE RADAR THE TRUE TARGETS ECHO AND AN 2'0/ INDUCED SIGNAL 3INCE THE TIME AT WHICH THE TARGET UNDER TRACK ACTIVATES 2'0/ IS UNKNOWN TO THE TRACKING ALGORITHM THE LATTER MUST FIRST RECOGNIZE THAT 2'0/ IS ACTIVE AND THEN IMPLEMENT AN APPROPRIATE ! 2'0/ TECHNIQUE )N ORDER TO ESTABLISH WHETHER 2'0/ IS ACTIVE THE FOL LOWING TEST CAN BE ADOPTED ,ET . BE THE NUMBER OF MEASUREMENTS EXCEEDING THE DETEC TION THRESHOLD OF MORE THAN D" 4HEN IF . IT IS DECIDED THAT 2'0/ IS NOT ACTIVE AND NO ! 2'0/ ACTION IS UNDERTAKEN OTHERWISE IF . THE ! 2'0/ %##-S DESCRIBED BELOW ARE APPLIED .OTICE THAT THE TEST ALSO AIMS AT DISCRIMINATING THE TYPE OF %#- BEING ACTIVE IE 3/* OR 2'0/ )N FACT WHENEVER THE NOISE JAMMER IS IN THE ANTENNA MAIN BEAM MANY FALSE MEASUREMENTS WITH HIGH JAMMER TO NOISE RATIO ARE INDUCED IN THIS CASE IT TURNS OUT THAT . AND 2'0/ IS DECLARED INACTIVE 7HENEVER THE JAMMER IS NO LONGER IN THE TARGETS LINE OF SIGHT IT MAY HAPPEN THAT MULTIPLE MEASUREMENTS EXCEED THE DETECTION THRESHOLD BUT THE CONDITION THAT THE EXCESS IS GREATER THAN D" WILL BE VERY UNLIKELY TO BE FULFILLED IN PRACTICE /NCE IT HAS BEEN ESTABLISHED THAT 2'0/ IS ACTIVE SEVERAL DEVICES CAN BE ADOPTED IN ORDER TO PREVENT THE LOSS OF THE TARGET UNDER TRACK ! FIRST APPROACH CONSISTS OF MAINTAINING TWO TRACKS UNTIL THE 2'0/ IS DEACTIVATED ! SECOND APPROACH CONSISTS OF PENALIZING IN THE DATA ASSOCIATION THE MEASURE MENTS WHOSE RANGE IS GREATER THAN THE AVERAGE RANGE OF MEASUREMENTS WITH 3.2 HIGHER THAN THE DETECTION THRESHOLD
%,%#42/.)# #/5.4%2 #/5.4%2-%!352%3
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! THIRD MORE DRASTIC APPROACH CONSISTS OF DISCARDING THE MEASUREMENT WITH HIGHER RANGE AMONG THE TWO MEASUREMENTS THAT HAVE EXCEEDED THE DETECTION THRESHOLD OF MORE THAN D" )T IS IMPORTANT TO GUARANTEE UNDER 2'0/ A VERY HIGH 3.2 FOR THE TARGET )N FACT IT MIGHT HAPPEN THAT THE SIGNAL PRODUCED BY THE FALSE TARGET OVERCOMES THE DETECTION THRESHOLD WHEREAS THE ONE FROM THE TRUE TARGET DOES NOT THUS CAUSING AN ASSOCIATION ERROR WITH POSSIBLE SERIOUS CONSEQUENCES IN THE TARGETS TRACKING (ENCE WHENEVER 2'0/ IS ACTIVE A HIGH ENERGY WAVEFORM MUST BE SELECTED ! FURTHER PRECAUTION IS THE FOLLOWING IF THERE ARE MISSED DETECTIONS FOR AT LEAST TWO OUT OF THE LAST THREE SCANS AN IMMEDIATE REVISIT WITH SAMPLING INTERVAL 4S S IN SEARCH DWELL MODE IS PERFORMED )N SEARCH MODE THE RANGE GATE IS KM INSTEAD OF KM SO IN THIS WAY IT IS POSSIBLE TO OBTAIN A NEW TARGET MEASUREMENT FOR UPDATING THE TRACKING FILTER AND THUS AVOID THE TARGETS LOSS 3IMULATION 2ESULTS -ONTE #ARLO SIMULATION EXPERIMENTS USING THE BENCHMARK HAVE BEEN CARRIED OUT IN ORDER TO ASSESS THE BENEFITS OF THE ABOVE DESCRIBED %##-S -ORE SPECIFICALLY THE ADAPTATION OF THE DETECTION THRESHOLD HAS BEEN USED AS ! 3/* WHEREAS THE TECHNIQUE BASED ON DISCARDING THE MEASUREMENTS WITH HIGHER RANGE HAS BEEN ADOPTED AS ! 2'0/ 4HREE TYPES OF TARGETS NUMBERED AND HAVE BEEN CONSIDERED TARGET REPRESENTS A CARGO AIRCRAFT WHILE TARGETS AND REPRESENT FIGHTER ATTACK AIRCRAFTS WITH A MUCH HIGHER DEGREE OF MANEUVERABILITY &OR EACH EXPERIMENT THE FOLLOWING RESULTS ARE DISPLAYED NUMBER OF LOST TARGETS OVER -ONTE #ARLO TRIALS 4S RADAR SAMPLING TIME 4AVE AVERAGE FRACTION OF TIME REQUIRED BY THE RADAR FOR TARGET TRACKING 0- AVERAGE POWER POSITION ERROR AND VELOCITY ERROR 4ABLE SHOWS SIMULATION RESULTS FOR THE )NTERACTING -ULTIPLE -ODEL )-- TRACKING ALGORITHM IN THE ABSENCE OF %#-S 4ABLES AND REPORT THE RESULTS IN THE PRESENCE OF 3/* WITHOUT AND RESPECTIVELY WITH ! 3/* 3IMILARLY 4ABLES AND REPORT THE RESULTS IN THE PRESENCE OF 2'0/ WITHOUT AND RESPECTIVELY WITH ! 2'0/ 4HE EXAMINATION OF THESE TABLES REVEALS THAT THE PRESENCE OF %#-S CONSIDERABLY DETERIORATES THE TRACKING PERFORMANCE IF NO APPROPRIATE %##-S ARE UNDERTAKEN #ONVERSELY THE ADOPTION OF THE ABOVE DESCRIBED ! 3/* AND ! 2'0/ TECHNIQUES ALLOWS THE PERFORMANCE THAT WOULD BE ATTAINED IN THE ABSENCE OF THE CORRESPONDING %#-S TO BE RESTORED 4!",% 3IMULATION 2ESULTS 7ITHOUT %#-
4!2'%4 ./
,/34 4!2'%43
4S S
4AVE S
0- 7
0/3 %22 M
6%, %22 MS
n n n
4!",% 3IMULATION 2ESULTS 7ITH 3/* AND 7ITHOUT ! 3/*
4!2'%4 ./
,/34 4!2'%43
4S S
4AVE S
0- 7
0/3 %22 M
6%, %22 MS
n n
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2!$!2 (!.$"//+
4!",% 3IMULATION 2ESULTS 7ITH 3/* AND ! 3/*
4!2'%4 ./
,/34 4!2'%43
4S S
4AVE S
0- 7
0/3 %22 M
6%, %22 MS
n n n
4!",% 3IMULATION 2ESULTS 7ITH 2'0/ AND 7ITHOUT ! 2'0/
4!2'%4 ./
,/34 4!2'%43
4S S
4AVE S
0- 7
0/3 %22 M
6%, %22 MS
n
4!",% 3IMULATION 2ESULTS 7ITH 2'0/ AND ! 2'0/
4!2'%4 ./
,/34 4!2'%43
4S S
4AVE S
0- 7
0/3 %22 M
6%, %22 MS
n n n
)MAGING 2ADAR 4HERE ARE TWO TYPES OF IMAGING RADAR THAT WILL BE DISCUSSED SYNTHETIC APERTURE RADAR 3!2 AND INVERSE 3!2 )3!2 3!2 3!2 ALLOWS US TO HAVE A HIGH RESOLUTION MAPPING OF THE %- BACKSCATTER FROM AN OBSERVED SCENE -ORE PRECISELY THE RADAR DATA IS OBTAINED IN POLAR COORDI NATES IE SLANT RANGE AND AZIMUTH WHILE A TWO DIMENSIONAL IMAGE IN THE RECTANGULAR COORDINATES X Y IS PROVIDED (IGH RESOLUTION IN SLANT RANGE IS OBTAINED BY TRANS MITTING A CODED WAVEFORM WITH A LARGE VALUE OF THE TIME BANDWIDTH PRODUCT AND COHERENTLY PROCESSINGIN A FILTER MATCHED TO THE WAVEFORMTHE ECHO SIGNALS (IGH RESOLUTION ALONG THE TRANSVERSAL DIRECTION IS ACHIEVED BY FORMING A SYNTHETIC APERTURE 4HIS REQUIRES I TO PUT THE RADAR ONBOARD A MOVING PLATFORM EG AN AIRCRAFT OR A SATELLITE II TO RECORD THE %- SIGNALS FROM EACH SCATTERER THAT IS ILLUMINATED BY THE MOVING ANTENNA BEAM IN SUCCESSIVE INSTANTS OF TIME AND III TO COHERENTLY COMBINE THE SIGNALSVIA A SUITABLE AZIMUTHAL MATCHED FILTERTHUS FOCUSING THE SLIDING ANTENNA PATTERN IN A NARROWER SYNTHETIC BEAM 2ADIOMETRIC RESOLUTION ANOTHER KEY PARAMETER IS RELATED TO THE CAPABILITY OF 3!2 OF DISTINGUISHING DIFFERENT OBJECTS IN THE SCENE ON THE BASIS OF THEIR %- REFLECTIVITY 2ADIOMETRIC RESOLUTION DETERMINES HOW FINE A SENSOR CAN DISTINGUISH BETWEEN OBJECTS WITH SIMILAR %- REFLECTION PROPERTIES )T IS A PARAMETER OF GREAT IMPORTANCE ESPECIALLY FOR THOSE APPLICATIONS ORIENTED TO EXTENDED TARGET EXPLOITATION LIKE POLARIMETRY AND CLASSIFICATION 4HUS THE RADIOMETRIC RESOLU TION SHOULD BE OPTIMIZED MAINLY FOR GOOD EXTENDED TARGET INTERPRETATION ACCOUNTING FOR ALL KIND OF BACK SCATTERERS -ULTILOOK PROCESSING IS COMMONLY USED IN 3!2 IMAGE
%,%#42/.)# #/5.4%2 #/5.4%2-%!352%3
Ó{°{
FORMATION IN ORDER TO REDUCE THE SPECKLE NOISE 4RADITIONAL DIGITAL MULTILOOK PROCESSING CONSISTS OF AN INCOHERENT ADDITION OF INDEPENDENT IMAGES LOOKS OF THE SAME SCENE 4HE LOOKS CAN BE OBTAINED BY PARTITIONING THE AVAILABLE SIGNAL BANDWIDTH RANGE AND OR AZIMUTH AND PROCESSING EACH LOOK INDEPENDENTLY 4HE FINAL IMAGE IS PRODUCED BY ADDING THE LOOKS INCOHERENTLY PIXEL BY PIXEL 4HE DIRECT TRADE OFF BETWEEN GEOMETRIC AND RADIOMETRIC RESOLUTION MUST BE CONSIDERED WHEN CHOOSING THE NUMBER OF LOOKS FOR PROCESSING /NE LOOK PROCESSING MEANS A FULLY COHERENT USE OF THE BANDWIDTH BEST GEOMETRIC RESOLUTION AND IN THIS CASE THE SPECKLE NOISE WILL OBEY AN EXPONENTIAL DIS TRIBUTION WHERE THE STANDARD DEVIATION IS EQUAL TO THE MEAN VALUE IN THE INTENSITY IMAGE MULTIPLICATIVE CHARACTERISTIC &OR MULTILOOK PROCESSING THE GEOMETRIC RESOLUTION WILL DEGRADE AS THE NUMBER OF LOOKS INCREASES AND THE SPECKLE STATISTICS OF THE INTENSITY IMAGE OBEY A GAMMA DISTRIBUTION WHERE THE STANDARD DEVIATION DECREASES WITH THE SQUARE ROOT OF THE NUMBER OF INDEPENDENT LOOKS 3!2 IMAGES ARE USEFUL FOR SURVEILLANCE AND RECONNAISSANCE APPLICATIONS (OWEVER JAMMING COULD MAKE 3!2 IMAGES UNUSABLE 4HE USE OF %##- IS THEREFORE ESSEN TIAL TO REDUCING THE VULNERABILITY OF 3!2 TO JAMMERS 4HE SUSCEPTIBILITY TO INTERCEPT SIGNALS FROM 3!2 AND VULNERABILITY TO JAMMING ARE DESCRIBED IN 'OJ ! SIMULATED NOISE JAMMING PRODUCES STRIPES ON THE 3!2 IMAGES THAT DEMONSTRATE THE EFFECTIVE NESS OF JAMMING AGAINST TARGETS LIKE STRONG POINT SCATTERERS SUCH AS ELECTRIC POWER LINE TOWERS AS WELL AS LOW REFLECTIVITY AGRICULTURAL PATTERNS AND DESERT LAND 4HE REFER ENCES DISCUSS THE SIGNIFICANT VULNERABILITY TO %#- OF SPACEBORNE 3!2 DUR ING MARITIME RECONNAISSANCE MISSIONS )N TYPICAL IMAGERY FROM 3EASAT 3!2 SHOWED SEVERAL FEATURES THAT MADE THE 3!2 A POWERFUL MARITIME SURVEILLANCE SENSOR 4HE SHIPS AND THE WAKES PRODUCED BY THE SHIP MOTION WERE IMAGED 4HE SHIP IMAGE A BLOB APPEARED DISPLACED FROM ITS WAKE DUE TO THE DOPPLER SHIFT CAUSED BY THE SHIPS MOTION RELATIVE TO THE SPACECRAFT (OWEVER THE SHIPS POSITION AT THE TIME OF IMAGING AND ITS COURSE COULD BE DETERMINED FROM THE WAKE 4HE SHIP SPEED CAN BE CALCULATED TOO BY THE DISPLACEMENT OF THE SHIP FROM ITS WAKE !LL THIS INFORMATION IS OBTAINABLE ONLY IF ENOUGH 3.2 IS AVAILABLE FOR THE IDENTIFICATION OF THESE IMAGE FEATURES EITHER BY A HUMAN OPERATOR OR AN AUTOMATIC PROCESSOR 4HERE EXISTS THEREFORE A POTENTIAL VULNERABILITY TO 3!2 IN THE MARITIME SURVEILLANCE APPLICATION IF A HIGH LEVEL OF BACK GROUND NOISE CAUSES DEGRADATIONS OF THE 3!2 IMAGE TO AN EXTENT WHERE SHIP AND WAKE CAN NO LONGER BE IDENTIFIED IN THE IMAGE )N THE LITERATURE SOME CRITICAL ASPECTS IN TERMS OF JAMMER RECEIVER SENSITIVITY AND TRANSMITTED POWER FOR SPOT NOISE JAMMING ARE CONSIDERED AND THE SYSTEM REQUIREMENTS ARE DERIVED TO DETERMINE THE FEASIBILITY AND PRACTICALITY OF SUCH JAMMER 2ESULTS OF A COMPUTER SIMULATION OF AN ENGAGEMENT BETWEEN 3!2 AND REPRESENTATIVE JAMMING SYSTEM ARE GIVEN TO ENABLE THE EFFECTIVE NESS OF %#- TO BE ASSESSED 4HE THREATS TO A 3!2 ARE BARRAGE JAMMING SPOT JAMMING RANDOM PULSE JAMMING AND REPEATER JAMMING 2EPEATERDECEPTION JAMMING IS A MAJOR THREAT BECAUSE IT MIGHT NOT BE RECOGNIZABLE WHEREAS THE OTHERS ARE AT LEAST IN PRINCIPLE RECOGNIZABLE 4HE IMPACT OF EACH THREAT AND THE POSSIBLE COUNTERMEASURES ARE DESCRIBED IN THE REMAINING PART OF THIS SECTION u "ARRAGE JAMMER 4HE DISTURBANCE NOISE EXTENDS OVER THE ENTIRE SWATH OF THE 3!2 IMAGE AND IT SHOWS GENERALLY A UNIFORM INTENSITY 4HE RADAR IMAGE OF BARRAGE JAM MER NOISE WILL EXHIBIT SPECKLE IE A BRIGHTNESS VARIATION FROM ONE RESOLUTION CELL TO ANOTHER )N ADDITION BECAUSE A LARGE NUMBER OF NOISE SAMPLES ARE ADDED NONCOHER ENTLY THE MULTIPLE LOOKS OF JAMMER NOISE TEND TO SMOOTH OUT THE INTENSITY VARIATION FROM PIXEL TO PIXEL JUST AS IN THE CASE OF THERMAL NOISE
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u 3POT JAMMER )T ALSO COVERS THE ENTIRE SWATH AND WITH UNIFORM INTENSITY DISTURBING NOISE AS FOR THE BARRAGE JAMMER HOWEVER ITS IMAGE WILL DIFFER FROM THE BARRAGE NOISE BECAUSE THE &OURIER TRANSFORM OF NARROWER BAND JAMMER NOISE WILL RESULT IN SPECKLE SIZE IN THE RANGE DIMENSION THAT IS LARGER THAN THAT OF THERMAL NOISE OR CLUTTER 4HE PROCESSED CROSS RANGE DIMENSION IS AGAIN EQUAL TO THAT OF CLUTTER OR THERMAL NOISE 3POT JAMMER NOISE WILL APPEAR TO BE STRETCHED IN RANGE u 2ANDOM PULSE JAMMING 4HE JAMMER PULSES MAY ALSO BE TRANSMITTED AT RANDOM INTER VALS SO THAT SUCH NOISE PULSES CAN APPEAR IN ANY PART OF THE RANGE SWATH 7HEN OBSERVED OVER A SUFFICIENT NUMBER OF SAMPLES THE NOISE PULSES WILL OCCUPY ALL PARTS OF THE RANGE SWATH IN ONE SAMPLE OR ANOTHER 4HE AZIMUTH PROCESSOR FORMS THE SUM OF THE NOISE POWER FROM ALL SAMPLES WITHIN ONE SYNTHETIC APERTURE LENGTH 4HAT SUM WILL BE EQUAL TO THE TOTAL NOISE POWER IN THE APERTURE WHICH IS PROPORTIONAL TO THE AVERAGE JAMMER NOISE POWER !LSO IN THIS CASE THE SPECKLE DIMENSION WILL APPEAR STRETCHED IN RANGE JUST AS IN THE SPOT JAMMER CASE (OWEVER THE RANDOM PULSE JAM MER SPECKLE WILL EXHIBIT MORE PRONOUNCED BRIGHTNESS VARIATIONS THAN THAT FROM SPOT OR BARRAGE JAMMING BECAUSE FEWER NOISE SAMPLES ARE ADDED NONCOHERENTLY THEREBY REDUCING THE SMOOTHING EFFECT OF MULTIPLE LOOKS u 2EPEATER JAMMING 4HE ENEMY MAY UTILIZE THE TRANSMITTING RADAR TO SEND OUT A SIGNAL WITHIN THE BAND OF THE 3!2 TO CONFUSE THE 3!2 SYSTEM RECEIVER 4HE JAMMING SIGNAL CAUSES THE 3!2 TO RECEIVE AND PROCESS ERRONEOUS INFORMATION THAT RESULTS IN SEVERE DEGRADATIONS IN THE 3!2 IMAGES ANDOR FORMATION OF THE IMAGE OF NONEXISTENT TARGETS ! DECEPTION JAMMING COULD BE COMPOSED OF MANIPULATED REPLICAS OF THE TRANSMITTED RADAR SIGNALS VIA $2&- )N (YBERG THE POSSIBILITY OF PREVENTING 3!2 MAPPING THROUGH COHERENT $2&- JAMMING HAS BEEN INVESTIGATED ! SOFTWARE MODEL HAS BEEN DEVELOPED AND VERIFIED IN SEVERAL FLIGHT TRIALS IN THE CASE OF A GROUND BASED $2&- JAMMER %##- TECHNIQUES FOR 3!2 CAN BE DIVIDED INTO I ANTENNA BASED TECHNIQUES LOW SIDELOBES ADAPTIVE ARRAYS AND II TRANSMITTERRECEIVERPROCESSINGnBASED TECHNIQUES FREQUENCY AGILITY PULSE CODING u ,OW SIDELOBES 3!2 ANTENNAS WITH LOW SIDELOBES REDUCE THE LEVEL OF JAMMING POWER RECEIVED AND IN ADDITION REDUCE THE PROBABILITY OF BEING INTERCEPTED BY %#- STATIONS IN THE SIDELOBE REGION )N RELATION TO LOW SIDELOBES THE FOLLOWING COMMENT IS IN ORDER )N A CONVENTIONAL RADAR THE EFFECT OF LOW SIDELOBES IS CLEAR BUT THERE IS A DIFFERENCE IN 3!2 BECAUSE THE BEAMWIDTH IS MUCH WIDER THAN IN OTHER RADAR APPLICATIONS )N PRINCIPLE THE FINER THE RESOLUTION THE SMALLER THE 3!2 PHYSICAL ANTENNA AND THE WIDER IS ITS BEAMWIDTH 4HUS JAMMING IN THE MAIN BEAM IS MORE LIKELY IN A 3!2 THAN IN OTHER RADARS BECAUSE OF THE WIDE MAIN BEAM 4O GET FALSE TARGETS INTO THE 3!2 IT WOULD HAVE TO COME FROM THE MAIN BEAM SO LOW SIDELOBES MIGHT NOT BE MUCH INVOLVED IN DECEPTION JAMMER ,IKEWISE MAIN BEAM JAMMING MAY BE MORE OF A THREAT TO 3!2 THAN SIDELOBE JAMMING u !DAPTIVE ARRAYS 4HE REFERENCESn DEAL WITH THE REJECTION OF A BARRAGE NOISE JAMMING USING AN ADAPTIVE SPATIAL NULLING %QUIPPING THE 3!2 SYSTEM WITH AN ANTENNA PARTITIONED INTO SEVERAL SUB APERTURES CONNECTED TO PARALLEL CHANNELS IE MULTICHANNEL 3!2 ALLOWS SPATIAL ADAPTIVE PROCESSING TO SUPPRESS THE INTERFERING SIGNAL )N &ARINA AND ,OMBARDO THE PERFORMANCE OF SUCH A TECH NIQUE IS EVALUATED IN TERMS OF 3!2 IMPULSE RESPONSE DETECTION PERFORMANCE OF POINT TARGET AND RADIOMETRIC RESOLUTION OF AN EXTENDED SCENE )N %NDER A 3!2 IMAGE TAKEN WITH AN EXPERIMENTAL FOUR CHANNEL 3!2 JAMMED BY A SMALL WATT
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NOISE JAMMER LEADING TO A *.2 IN THE RAW DATA OF ABOUT D" WHEN THE JAMMER PASSES THE CENTER OF THE MAIN BEAM IS DEPICTED 4HE DE JAMMED IMAGE BY ADAP TIVE SPATIAL SUPPRESSION IS ALSO SHOWN DEMONSTRATING THE GOOD PERFORMANCE OF ADAPTIVE SPATIAL CANCELLATION 4HE REFERENCE PROVIDES A COMPREHENSIVE STUDY OF ANTI JAMMING SPATIAL ADAPTIVE TECHNIQUES INCLUDING ALSO THE SPACESLOW TIME ANTI JAMMING FILTER WITH SUITABLE IMAGE RECONSTRUCTION ALGORITHM 2ESULTS INDI CATE THAT THE SLOW TIME 34!0 PROVIDES SUPERIOR INTERFERENCE CANCELLATION THAN SPATIAL ONLY FILTERING 3!2 USUALLY INVOLVES WIDEBAND PROCESSING REQUIRING FOR ADAPTIVE NULLING TECHNIQUES PECULIAR ALGORITHMS %FFICIENT BROADBAND JAMMER NULLING HAS TO BE COUNTERED WITH SPACEFAST TIME IE RANGE CELL PROCESSING 4HE EXPECTED NUMBER OF SPATIAL DOF IS NOT HIGHER WE HAVE ONLY TO ADD THE DOF IN TIME 4HE ADAPTIVE BEAMFORMING ALGORITHMS HAVE TO BE IMPLEMENTED INTO THE 3!2 PROCESSING WHICH IS ALWAYS SPACE TIME PROCESSING TYPICALLY POST DOPPLER 2OSENBERG AND 'RAY TACKLE THE PROBLEM OF MITIGATING THE EFFECTS OF AN AIRBORNE BROADBAND JAMMER PRESENT IN THE MAIN BEAM OF A 3!2 )N ADDITION TO THIS MUL TIPATH REFLECTIONS FROM THE GROUND KNOWN AS HOT CLUTTER WILL ADD A NONSTATIONARY INTERFERENCE COMPONENT TO THE IMAGE 4HE AUTHORS SHOW THE IMAGE DEGRADATION FROM HOT CLUTTER THE LIMITED RESTORATION THAT MULTI CHANNEL SPATIAL IMAGING AND SLOW TIME 34!0 CAN PROVIDE AND HOW FAST TIME 34!0 CAN IMPROVE THE FINAL IMAGE QUALITY u &REQUENCY AGILITY 3!2 PROCESSING NEEDS PHASE COHERENCE FOR OBTAINING THE SYN THETIC APERTURE THUS FREQUENCY AGILITY HAS TO BE USED WITH CARE &REQUENCY CHANG ING DURING A SYNTHETIC APERTURE LENGTH TIME RESULTS IN A CHANGE OF FOCAL LENGTH DIFFERENT COEFFICIENT OF THE QUADRATIC PHASE TERM OF THE PHASE HISTORY OF THE ILLU MINATED TARGETS THAT DEGRADES THE CROSS RANGE RESOLUTION 3!2 OPERATING IN BURST MODE CAN CHANGE ITS CENTRAL FREQUENCY FROM ONE LOOK TO ANOTHER WITHOUT ANY DEGRADATION IN IMAGE QUALITY 'IVEN THE EFFICIENCY OF SIMPLE BROADBAND JAMMING AND MODERN %3- WE NEED TO CONCLUDE THAT FREQUENCY AGILITY IS NOT OF GREAT HELP IN 3!2 %##- u 0ULSE CODING !N EFFECTIVE %##- AGAINST A $2&- REPEAT JAMMER IS TO CHANGE THE RADAR TRANSMITTED PULSE CODE FROM ONE 02) TO ANOTHER 4HE RADAR MAINTAINS THE SAME CARRIER AND BANDWIDTH HOWEVER THE PULSES ARE CODED TO BE APPROXI MATELY ORTHOGONAL TO EACH OTHER IE THEIR CROSS CORRELATION IS APPROXIMATELY EQUAL TO ZERO 3UCH A RADAR IS LESS SUSCEPTIBLE TO A $2&- REPEATER BECAUSE I THE JAMMER CANNOT ADAPT EASILY SINCE THE RADAR SIGNAL IS VARYING IN THE 02) DOMAIN AND II THE SIGNAL TRANSMITTED BY A $2&- REPEATER JAMMER AT A GIVEN 02) IE THE RADAR SIGNAL THAT IS USED BY THE 3!2 AT THE PREVIOUS 02) IS APPROXI MATELY ORTHOGONAL TO THE RADAR SIGNAL THAT THE 3!2 IS UTILIZING AT THE CURRENT 02) AND THUS A MATCHED FILTERING WITH THE CURRENT 02) RADAR SIGNAL WOULD WEAKEN THE $2&- REPEATER JAMMER SIGNAL )N 3OUMEKH A NOVEL METHOD IS OUTLINED THAT COMBINES THE ABOVE MENTIONED PULSE DIVERSITY RADAR SIGNALING WITH A NEW COHER ENT TWO DIMENSIONAL PROCESSING OF THE MEASURED DATA TO EFFECTIVELY SUPPRESS A $2&- REPEATER JAMMER )3!2 4HE INVERSE 3!2 IS A METHOD OF RECONSTRUCTING A HIGH RESOLUTION TWO DIMENSIONAL %- INTENSITY IMAGE OF MOVING TARGETS EG SHIPS AIRCRAFT IN THE RANGE AND CROSS RANGE DOPPLER DOMAINS )3!2 IMAGING IS IMPORTANT IN MILITARY APPLICATIONS SUCH AS TARGET RECOGNITION AND CLASSIFICATION SINCE IT CAN USUALLY RECOGNIZE THE CLASS OF TARGET THAT CAN ALSO BE USED TO CUE WEAPON SYSTEMS 4HE NEED FOR COHERENT COUNTERING OF THESE IMAGING SENSORS IS A HIGH PRIORITY FOR %7 4HE REFERENCES PRESENT THE
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DESIGN OF A PIPELINED ALL DIGITAL IMAGE SYNTHESIZER CAPABLE OF GENERATING FALSE TARGET IMAGES FROM A SERIES OF INTERCEPTED )3!2 CHIRP PULSES THUS PROVIDING 2& IMAGING DECOY CAPABILITY 4HE IMAGE SYNTHESIZER MODULATES THE PHASE SAMPLES FROM A PHASE SAMPLING $2&- THAT STORES INTERCEPTED )3!2 PULSES 4HE IMAGE SYNTHESIZER MUST ALSO SYNTHESIZE THE TEMPORAL LENGTHENING AND AMPLITUDE MODULATION CAUSED BY THE MANY REFLECTIVE SURFACES OF A TARGET AND MUST GENERATE A REALISTIC DOPPLER PROFILE FOR EACH SUR FACE 4HE POSITION OF A FALSE TARGET IMAGE IN RANGE CAN BE CONTROLLED BY DELAYING IN TIME THE READ OUT SAMPLES GOING TO THE IMAGE SYNTHESIZER 4HE RANGE DOPPLER IMAGE OF A SHIP WITH RANGE BINS IS SYNTHESIZED AS AN EXAMPLE IN 0ACE ET AL %##- TECHNIQUES TO DEFEAT THIS TYPE OF JAMMING SIGNALS ARE SIMILAR TO THOSE PROPOSED FOR 3!2 /VER THE (ORIZON 2ADAR !N IMPORTANT DEFENSE RELATED ROLE OF HIGH FREQUENCY (& OVER THE HORIZON /4( RADAR IS TO PROVIDE A CAPABILITY FOR EARLY WARNING DETEC TION AND TRACKING OF AIR AND SHIP TARGETS "Y USING THE IONOSPHERE AS A PROPAGATION MEDIUM SKYWAVE /4( RADARS CAN OPERATE AT VERY LONG DISTANCES TO ACHIEVE DETECTION AND TRACKING AT RANGES OF n KM /N THE OTHER HAND SURFACE WAVE /4( RADARS EXPLOIT VERTICALLY POLARIZED (& SIGNALS n -(Z AND THE CONDUCTIVE PROPERTIES OF SEA WATER TO DETECT TARGETS AT RANGES LIMITED TO ABOUT KM 4HIS UPPER LIMIT GENERALLY APPLIES TO LARGE SHIPS AND FREQUENCIES IN THE LOWER (& BAND %#- TO /4( 2ADAR &OR BOTH SKYWAVE AND SURFACE WAVE /4( RADAR SYSTEMS THE IONOSPHERE ALSO PROPAGATES UNWANTED INTERFERENCE SIGNALS TO THE RADAR SITE PAR TICULARLY AT NIGHT WHEN THE IONOSPHERE IS PRONE TO PROPAGATING RADIO FREQUENCY INTER FERENCE 2&) SOURCES FROM VERY LONG DISTANCES 2&) CAN ARISE FROM UNINTENTIONAL AND INTENTIONAL ANTHROPOGENIC EMITTERS IN THE USER CONGESTED (& BAND AS WELL AS JAMMING SOURCES *AMMING SOURCES MAY BE LOCATED ON THE TARGET PLATFORM ITSELF SELF SCREENING AND RECEIVED BY THE MAIN ANTENNA BEAM OR RADIATE FROM A SEPARATE LOCATION STAND OFF AND BE RECEIVED MAINLY THROUGH THE ANTENNA BEAMPATTERN SIDELOBES 4HE JAMMING SIG NAL MAY BE INCOHERENT WITH THE RADAR WAVEFORM AND OPERATE IN A hSPOTv OR hBARRAGEv FASHION TO RAISE THE NOISE FLOOR IN BOTH RANGE AND DOPPLER SEARCH SPACES TO POTENTIALLY IMPAIR DETECTION PERFORMANCE OR IT CAN BE COHERENT WITH THE RADAR WAVEFORM AS IN THE CASE OF DECEPTION JAMMING WHICH MAY GENERATE FALSE TARGETS AND POTENTIALLY IMPAIR THE TRACKING SYSTEM FROM FOLLOWING THE TRUE TARGET )MPACT OF )ONOSPHERE !N IMPORTANT ASPECT THAT DISTINGUISHES /4( RADAR FROM LINE OF SIGHT SYSTEMS IS THE IMPACT OF THE IONOSPHERIC PROPAGATION MEDIUM ON THE CHARACTERISTICS OF THE RECEIVED INTERFERENCE 4HE IONOSPHERE IS STRATIFIED WITH DIFFER ENT REFLECTING LAYERS SO A SINGLE INTERFERENCE SOURCE IS OFTEN RECEIVED AS A NUMBER OF MULTIPATH COMPONENTS WITH DIFFERENT $O!S BOTH IN ELEVATION DUE TO THE DIFFERENT HEIGHTS OF REFLECTION POINTS AND IN AZIMUTH DUE TO LAYER DEPENDENT IONOSPHERIC TILTS OR GRADIENTS )N ADDITION TO MULTIPATH EACH INTERFERENCE COMPONENT IS SUBJECTED TO TEMPORAL AND SPATIAL DISTORTIONS CAUSED BY THE DYNAMIC BEHAVIOR OF ELECTRON DENSITY IRREGULARITIES PRESENT IN THE INDIVIDUAL REFLECTING LAYERS 4HIS PHYSICAL PHENOMENON IS KNOWN NOT ONLY TO DEFORM THE INTERFERENCE WAVEFRONTS RELATIVE TO THE ANTICIPATED PLANE WAVEFRONT BUT ALSO TO INDUCE A SIGNIFICANT LEVEL OF SPATIAL NONSTATIONARITY ON THE VARIOUS INTERFERENCE COMPONENTS OVER TIME INTERVALS COMMENSURATE WITH THE COHERENT PROCESSING INTERVAL OF /4( RADARS IN THE ORDER OF A FEW TO TENS OF SECONDS 2ELEVANCE TO )NTERFERING 3IGNALS 3OURCES OF INTERFERENCE WITHIN THE RADAR COVERAGE EG ON AN AIRBORNE PLATFORM CAN POTENTIALLY SCREEN THE PLATFORM IN RANGE AND IMPAIR THE DETECTION OF OTHER TARGETS WITH SIMILAR AZIMUTH BUT POSSIBLY AT DIFFERENT RANGES
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3UCH SOURCES CAN EXPECT GOOD PROPAGATION TO THE RADAR RECEIVER BECAUSE THE CHOICE OF OPERATING FREQUENCY IS USUALLY OPTIMIZED FOR THE COVERAGE AREA )N THE CASE OF STAND OFF INTERFERENCE SOURCES WHICH ARE LOCATED ARBITRARILY WITH RESPECT TO THE SURVEILLANCE REGION EG A GROUND BASED EMITTER PROPAGATION CONDITIONS WILL GENERALLY BE SUB OPTIMUM (OWEVER SUCH SOURCES MAY HAVE GREATER POWER AND ANTENNA GAIN AT THEIR DISPOSAL ALLOWING THE SIGNALS TO REACH THE RADAR RECEIVER WITH APPRECIABLE STRENGTH SOMETIMES AFTER PROPAGATION VIA HIGHLY DISTURBED AND NONSTATIONARY IONOSPHERIC PATHS AS COMMONLY OCCURS IN THE EQUATORIAL AND POLAR REGIONS 5NDER NORMAL CIRCUMSTANCES /4( RADARS SEEK TO FIND RELATIVELY CLEAR FREQUENCY CHANNELS IN THE USER CONGESTED (& SPECTRUM SO THE PRESENCE OF INTERFERENCE FROM OTHER MANMADE SOURCES IS EFFECTIVELY DIMINISHED BY SUITABLE FREQUENCY SELECTION 7HEN JAMMING IS PRESENT THE RADAR MAY NEED TO OPERATE WITH MUCH HIGHER THAN USUAL LEVELS OF INTERFERENCE THAT CAN DEGRADE PERFORMANCE &OR THIS REASON PROTECTION IN THE FORM OF %##- TECHNIQUES BECOMES NECESSARY %##- 4ECHNIQUES %LECTRONIC PROTECTION FOR /4( RADAR ANTENNA ARRAYS CAN BE PROVIDED IN THE FORM OF ADAPTIVE SIGNAL PROCESSING IN SPACE AND TIME 4HE STOCHASTIC CONSTRAINTS ADAPTIVE BEAMFORMING AND 34!0 METHODSn WERE DEVELOPED SPECIFI CALLY FOR THE (& ENVIRONMENT TO ADDRESS THE REJECTION OF NONSTATIONARY INTERFERENCE WHILE PROTECTING THE CLUTTER DOPPLER SPECTRUM PROPERTIES ! METHOD FOR TIME VARYING SPATIAL ADAPTIVE PROCESSING 46 3!0 THAT ADDRESSES THE SAME PROBLEM WAS FOUND TO BE MORE ATTRACTIVE FOR PRACTICAL IMPLEMENTATION DUE TO THE MUCH LOWER COMPUTATIONAL COST IN REAL TIME APPLICATIONS AS WELL AS GREATER ROBUSTNESS IN PROTECTING SUB CLUTTER VISIBILITY AFTER DOPPLER PROCESSING 4HE PROBLEM OF REDUCING FALSE ALARMS CAUSED BY STRONG SIDELOBE TARGETS AND SPATIALLY STRUCTURED NON GAUSSIAN DISTRIBUTED 2&) WAS TREATED IN &ABRIZIO ET AL WHERE THE ADVANTAGES OF ADAPTIVE SUBSPACE DETECTORS RELA TIVE TO CONVENTIONAL APPROACHES WERE SHOWN 34!0 TECHNIQUES WITH TEMPORAL DEGREES OF FREEDOM SPACED AT THE 02) IE SLOW TIME HAVE BEEN PROPOSED IN &ARINA ET AL TO JOINTLY CANCEL 2&) AND CLUTTER WHEN BOTH ARE OF SIMILAR STRENGTH BUT NEITHER CAN BE ISOLATED FOR ESTIMATION WHEREAS AN ALTERNATIVE LOW DIMENSION 34!0 FORMULATION WITH TEMPORAL TAPS SPACED AT THE RANGE CELL INTERVAL IE FAST TIME HAS BEEN PROPOSED IN &ABRIZIO ET AL TO JOINTLY CANCEL SIDELOBE AND MAIN BEAM 2&) THAT EXHIBITS CORRELA TION IN THE RANGE DIMENSION 4HE 34!0 METHODS USED IN /4( RADAR ARE VERY SIMILAR CONCEPTUALLY TO THOSE ADOPTED FOR AIRBORNE RADAR ESPECIALLY THE FORMER TAP ARCHITEC TURE 4HE CHIEF DIFFERENCE IS THAT IN BENIGN CONDITIONS FREE OF SIGNIFICANT CO CHANNEL INTERFERENCEp 34!0 IS NOT INDICATED FOR /4( RADAR BECAUSE THE SIDELOBE CLUTTER DOES NOT TYPICALLY MASK DOPPLER SHIFTED TARGETS ANY MORE THAN THE MAIN BEAM CLUTTERe ! POSSIBLE EXCEPTION TO THIS IS SHIPBORNE (& SURFACE WAVE RADAR ALTHOUGH SUCH SYS TEMS HAVE BEEN PROPOSED THEY HAVE NOT YET DEMONSTRATED THEIR PRACTICAL UTILITY p #O CHANNEL INTERFERENCE FOR /4( RADAR REFERS MAINLY TO OTHER TRANSMISSIONS IN THE (& SPECTRUM THAT EITHER FULLY OR PARTIALLY OVERLAP THE RADAR BANDWIDTH e 4HE MAIN BEAM AND SIDELOBE CLUTTER RECEIVED BY AIRBORNE RADARS CAN HAVE QUITE DIFFERENT DOPPLER SHIFTS DUE TO THE MOVEMENT OF THE PLATFORM WITH RESPECT TO THE GROUND RESULTING IN THE ANGLE DOPPLER COUPLING OF THE CLUTTER (OWEVER IN /4( RADAR MAIN BEAM AND SIDELOBE CLUTTER FROM A SINGLE IONOSPHERIC MODE TYPICALLY HAVE SIMI LAR DOPPLER SPECTRUM CHARACTERISTICS BECAUSE THE RADAR IS STATIONARY 4HIS MEANS THAT SIDELOBE CLUTTER APPEARS AT ROUGHLY THE SAME DOPPLER SHIFT AS MAIN BEAM CLUTTER AND DOPPLER FILTERING CAN BE USED EFFECTIVELY FOR DETECTING TARGETS USUALLY WITHOUT SPECIAL NEED TO REJECT THE SIDELOBE CLUTTER SPATIALLY
/BVIOUSLY THE SITUATION MAY CHANGE IN SHIPBORNE (& SURFACE WAVE RADAR BECAUSE THE PLATFORM IS MOVING WITH RESPECT TO THE SEA SURFACE AND HENCE A CONCEPTUALLY SIMILAR SITUATION ARISES FOR THE CLUTTER AS ENCOUNTERED IN AIRBORNE RADAR
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Ê Ê Ê 9 4HERE IS A NEED FOR A QUANTITATIVE MEASUREMENT OF THE EFFICACY OF ONE OR MORE %##- ELECTRONIC TECHNIQUES WHEN A RADAR EQUIPPED WITH THESE DEVICES IS SUBJECT TO AN %#- THREAT /NE PERFORMANCE MEASURE GENERALLY USED FOR AN UNJAMMED SEARCH RADAR IS THE DETECTION RANGE OF A CERTAIN TARGET AGAINST A SYSTEM NOISE BACKGROUND THIS SITUATION IS REFERRED TO AS DETECTION IN CLEAR ENVIRONMENT 7HEN THE RADAR IS JAMMED IT IS OF INTER EST TO CALCULATE THE DEGRADATION OF THE DETECTION RANGE WITH RESPECT TO SELF SCREENING STANDOFF AND ESCORT JAMMERS 4HESE CALCULATIONS APPLY TO BOTH SEARCH AND TRACKING RADARS &OR TRACKING RADARS IT IS ALSO WORTHWHILE TO CONSIDER THE DEGRADATION OF MEA SUREMENT ACCURACY AND RESOLUTION 4HE BENEFITS OF USING %##- TECHNIQUES SUCH AS FREQUENCY AGILITY COHERENT DOPPLER PROCESSING VERY LOW SIDELOBE ANTENNAS AND 3,# CAN BE EASILY ASSESSED AT A FIRST APPROXIMATION BY PROPERLY MODIFYING THE PARAMETERS INVOLVED IN THE RADAR EQUATION )F FOR INSTANCE AN 3,# IS ADOPTED AGAINST AN 3/* ITS NET EFFECT IS TO REDUCE JAMMING POWER BY THE AMOUNT OF JAMMER CANCELLATION RATIO THAT THE 3,# CAN OFFER 4HE PREDICTION OF RADAR RANGE IS DIFFICULT BECAUSE OF THE MANY FACTORS THAT ARE HARD TO REPRESENT WITH MODELS OF THE REQUIRED ACCURACY 4HE FACTORS INVOLVE THE TARGET TO BE DETECTED TARGET RETURNS OF AN UNKNOWN STATISTICAL NATURE THE NATURAL ENVIRON MENT IN WHICH THE TARGET IS EMBEDDED EG CLUTTER RETURNS UNINTENTIONAL INTERFERENCE UNCONTROLLABLE ENVIRONMENTAL REFRACTION AND ABSORPTION THE RANDOM NATURE OF THE INTERFERENCE AND THE RADAR ITSELF SYSTEM NOISE TEMPERATURE SIGNAL DISTORTIONS ETC .EVERTHELESS RADAR RANGE PREDICTION MADE UNDER AVERAGE CONDITIONS PROVIDES A PRE LIMINARY AND USEFUL INDICATION OF PERFORMANCE UNDER %#- THREAT AND %##- DESIGN EFFECTIVENESS THAT PRODUCES BASELINE VALUES PRIOR TO SIMULATION AND OPERATIONAL TESTS ! CLASSICAL BOOK PRESENTS ACCURATE DETECTION RANGE EQUATIONS IN A VARIETY OF PRACTICAL SITUATIONS )N THE SECOND PART OF THIS SECTION A REVIEW OF SOFTWARE TOOLS AVAILABLE FOR THE PREDICTION OF RANGE EQUATION IN JAMMING AND CHAFF CONDITIONS IS GIVEN /F COURSE THE RADAR EQUATION IS A SIMPLIFICATION IN ASSESSING %#- %##- INTERAC TIONS A MEASURE OF %##- EFFECTIVENESS SHOULD INVOLVE THE WHOLE WEAPON SYSTEM IN WHICH THE RADAR OPERATES 4HE MEASURE OF EFFECTIVENESS SHOULD BE EXPRESSED IN TERMS OF THE NUMBER OF ATTACKERS DESTROYED OR THE PROBABILITY OF RADAR SURVIVAL 2EFERENCES IN THE LITERATURE ATTEMPT TO ASSESS THE %##- EFFICACYn 3IMULATION IS ANOTHER MEANS TO ASSESS THE %##- BENEFITS IN RADAR AND WEAPON SYSTEMS !N ADVANTAGE OF THIS APPROACH RESIDES IN THE CAPABILITY TO ARTIFICIALLY GENERATE DIFFERENT TYPES OF THREATS AND TO LOOK AT THE RADAR AND WEAPON SYSTEM REACTIONS (OWEVER THE SIMULATION OF SUCH A COMPLEX SYSTEM IS A DIFFICULT TIME CONSUMING TASK THAT SOMETIMES INVOLVES THE USE OF AD HOC PROGRAMMING LANGUAGES SUITABLE FOR SIMULATION 3IMULATION OF A COMPLEX SYSTEM ON A DIGITAL COMPUTER IS A TECHNIQUE USED FOR THE ANALYSIS DESIGN AND TESTING OF A SYSTEM WHOSE BEHAVIOR CANNOT BE EASILY EVALUATED BY MEANS OF ANALYSIS OR COMPUTATION 4HE PROCEDURE ESSENTIALLY CONSISTS OF REPRODUC ING THE ALGORITHMS OF A SUITABLE MODEL OF THE EXAMINED SYSTEM BY MEANS OF COMPUTER PROGRAMS 0ROPER INPUTS TO THE MODEL CORRESPONDING TO THE MOST RELEVANT OPERATIONAL CONDITIONS FOR THE REAL SYSTEM CAN BE GENERATED BY THE SAME COMPUTER PROGRAMS 4HE OUTPUTS OBTAINED ARE COMPARED WITH SOME REFERENCE VALUES EXPECTED OR THEORETICAL TO ASSESS SYSTEM PERFORMANCE 7HEN RANDOM INPUTS ARE PROVIDED A NUMBER OF STATISTI CALLY INDEPENDENT TRIALS ARE PERFORMED TO ACHIEVE A SIGNIFICANT SAMPLE OF THE OUTPUT VALUES FROM WHICH RELIABLE STATISTICS CAN BE ESTIMATED
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4HE ACCURACY AND DETAIL OF THE MODEL MAY VARY FROM A COARSE FUNCTIONAL DESCRIPTION OF THE SYSTEM TO A VERY ACCURATE ONE ACCORDING TO THE PURPOSE OF THE SIMULATION AND THE REQUIRED ACCURACY OF THE RESULTS (OWEVER IT IS DESIRABLE TO LIMIT THE COMPLEXITY OF THE SIMULATION TOOLS IN ORDER TO HAVE MANAGEABLE PROGRAMS GIVING RESULTS THAT ARE EASILY INTERPRETED 4HE ACCURACY IN REPRESENTING EACH SYSTEM FUNCTION DEPENDS UPON ITS RELEVANCE WITH RESPECT TO SYSTEM PERFORMANCE 7HEN A VERY COMPLEX SYSTEM IS TO BE SIMULATED IT IS GENERALLY PREFERRED TO RESORT TO SEVERAL PROGRAMS OF LIMITED COM PLEXITY IN LIEU OF A SINGLE BULKY SIMULATION 4HIS APPROACH CORRESPONDS TO PARTITIONING THE WHOLE SYSTEM INTO SUBSYSTEMS SEPARATELY MODELED IN DETAIL &ROM EACH PARTIAL SIMULATION A LIMITED NUMBER OF RELEVANT FEATURES ARE EXTRACTED AND EMPLOYED TO BUILD A SIMPLIFIED MODEL OF THE OVERALL SYSTEM 3IMULATION IS PARTICULARLY IMPORTANT TO ACCOUNT FOR THE ADAPTIVE NATURE EG #&!2 ADAPTIVE BEAMFORMING AUTOMATIC RADAR MANAGEMENT ADAPTIVE TRACKING ADAPTIVE CLUT TER CANCELLATION OF MODERN RADAR SYSTEMS )N THIS CASE TRADITIONAL STATIC MEASURES SUCH AS DETECTION RANGE AGAINST A GIVEN TARGET WILL NO LONGER ADEQUATELY DEFINE THE CAPABILITIES OF RADAR SYSTEMS -EASURES OF RADAR DYNAMIC CHARACTERISTICS SUCH AS THE SUSCEPTIBILITY TO PROCESSOR OVERLOAD OR THE TIME TO ADAPT IN CHANGING CONDITIONS ARE MORE IMPORTANT -ODELING AND SIMULATIONS TO EVALUATE THE RADAR RESPONSE TO STANDARD IZED CHANGING SCENARIOS REPRESENT AN ATTRACTIVE TECHNICAL SOLUTION 3IMULATION IS ALWAYS OF VALUE HOWEVER THE EFFECTIVENESS OF %#- AND %##- IS ULTIMATELY DONE WHEN POSSIBLE WITH TESTS OF REAL %7 CAPABILITIES AGAINST REAL RADAR SYSTEMS UNDER REAL WORLD CONDITIONS 4HIS IS ESPECIALLY IMPORTANT FOR RADAR EQUIPPED WITH ADAPTIVE TECHNIQUES SINCE THEY MIGHT NOT BE ALWAYS FULLY MODELED IN A SIMULATION AS THEY ARE IN THE REAL WORLD ENVIRONMENT IN WHICH THEY MUST OPERATE 4HE 2ADAR %QUATION IN *AMMING AND #HAFF #ONDITIONS !N EXAMPLE OF RADAR RANGE PERFORMANCE UNDER NOISE JAMMING IS REPORTED ON PP n OF &ARINA WHERE THE IMPORTANT ROLE PLAYED BY A RADAR WITH LOW SIDELOBE ANTENNAS IS ALSO NOTED 4ODAY THE USE OF COMPUTER PROGRAMS FOR PREDICTING RADAR PERFORMANCE UNDER JAMMING CLUT TER AND CHAFF AND IN THE PRESENCE OF VARIOUS REFINED PROPAGATION MODELS IS WELL ESTAB LISHED THERE ARE PROGRAMS DEVELOPED IN HOUSE BY INDIVIDUAL RADAR COMPANIES OR AVAILABLE ON THE MARKET 4HE 2ADAR 7ORK 3TATION 273 IS AN EXAMPLE OF A DEVELOPED IN HOUSE PROGRAM 273 ORIGINATES FROM THE MODELING AND SIMULATION ACTIVITIES CARRIED OUT FOR PREDICTION OF RADAR PERFORMANCE IN SEVERAL SCENARIOS /NE MAIN OBJECTIVE OF 273 IS TO PROVIDE THE RADAR ANALYST OR SYSTEM DESIGNER WITH A FRIENDLY BUT COMPREHENSIVE TOOLKIT FOR PREDICTION OF RADAR PERFORMANCE BASED ON WELL RECOGNIZED FLEXIBLE AND DOCUMENTED MATHEMATICAL MODELS ! BROAD RANGE OF RADAR TYPES BI DIMENSIONAL MULTI BEAM THREE DIMENSIONAL PHASED ARRAY COMPOSITE CLUTTER %#- AND PROPAGATION SCENARIOS AND A TARGETS KINEMATICS AND 2#3 FEATURES ARE COVERED )NPUT AND OUTPUT DATA CAN BE SAVED LOADED AND EXPORTED TO OTHER SIMILAR APPLICATIONS OR FOR GENERAL USE IE -3 /FFICE TOOLS FOR DATA ANALYSIS ! SECOND PURPOSE IS TO PROVIDE A HANDY AND RELIABLE TOOL FOR TECHNICIANS AND ENGINEERS PERFORMING SYSTEM SETUP AT THE SITE OR ACCEPTANCE TESTS BY MEANS OF FIELD TRIALS BY PROVIDING NOT ONLY THE SOFTWARE TOOLS AND MODELS BUT ALSO WHERE REQUIRED A DATABASE OF PREDICTION RESULTS AND ALLOWING SIMPLE PARAMETRIC EXCURSIONS THEREOF WITHOUT THE NEED TO CONSULT A BULKY REFERENCE DOCUMENTATION )N BRIEF THE MOST VALUABLE OUTCOMES THAT CAN BE OBTAINED WITH THE 273 ARE RADAR RANGE CALCULATION RADAR ELEVATION COVERAGE DIAGRAMS IN CLEAR %#- AND MULTI PROPAGATION BOTH FOR COHERENT AND NONCOHERENT RADARS RANGE AND VELOCITY RESPONSES IN COMPLEX
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SCENARIOS MULTIPLE CLUTTER SOURCES USER DEFINED TRAJECTORY IN TERMS OF SIGNAL TO DIS TURBANCE POWER RATIO AND DETECTION PROBABILITY AND RADAR RANGE AND HEIGHT ACCURACY CALCULATION RADAR RESOLUTION EVALUATIONS EMPLOYING SUITABLE DATA EXTRACTING LOGICS 4HE 273 SUITE CONSISTS OF THE FOLLOWING MAIN MODULES #<# AND &ORTRAN TO CALCU LATE SPECIAL FUNCTIONS LIKE 'AMMA AND "ESSEL + CODED LIBRARIES A STANDARD LIBRARY OF 7INDOWS !0)S !PPLICATION 0ROGRAMMING )NTERFACES TO DRAW THE COVERAGE DIAGRAMS A TEMPLATE LIBRARY TO IMPLEMENT THE MATRIX ALGEBRA AN APPLICATION BASED ON -3 /FFICE %XCEL TO CODE THE "LAKE #HARTo A SET OF 6ISUAL "ASIC TOOLS TO EVALUATE SOME ASPECTS OF RADAR PERFORMANCE EG !$# JITTER ATMOSPHERIC LOSS TAPERING LOSS ETC AND AN UNFORMATTED ARCHIVE OF RADAR DATA AS SIMPLE !3#)) FILES PERTINENT TO PERFORMANCE ENVIRONMENT TRAJECTORIES TERRAIN HEIGHT AND WAVEFORM 5SER FRIENDLY INTERFACES RUN ON LOW COST PLATFORMS 0# AND POPULAR ENVIRONMENTS 7IN 7IN.4 7IN 7INDOWS 80 6ISTA FOR USERS AND DEVELOPERS )N THE 273 THE CHAFF VOLUME CLUTTER MODEL IS CHARACTERIZED IN TERMS OF VOLUME EXTENT %- REFLECTIVITY AND DOPPLER SPECTRUM 4HE SIGNAL TO NOISE PLUS CHAFF RATIO IS DETERMINED ON THE BASIS OF THE CHAFF LOCATION IN THE SPACE THE ANTENNA RECEIVING PATTERN AND THE RADIATED RADAR WAVEFORM 4HE RADAR EQUATION CAN BE APPLIED AND THE SIGNAL PROCESSING SCHEME CAN BE EMULATED TO DETERMINE THE AMOUNT OF CHAFF MITIGA TION ! BARRAGE NOISE JAMMER IS MODELED IN TERMS OF EFFECTIVE RADIATED POWER %20 AND FREQUENCY BAND OF OPERATION 4HE SIGNAL TO NOISE PLUS JAMMER RATIO IS DETERMINED ON THE BASIS OF THE *$O! AND THE ANTENNA RECEIVING PATTERNS THE RADAR EQUATION IS THEN APPLIED AND SUITABLE %##- SIGNAL PROCESSING SCHEMES CAN BE EMULATED TO DETERMINE TO WHICH EXTENT THE JAMMER IS ATTENUATED #OMPUTER !IDED 2ADAR 0ERFORMANCE %VALUATION 4OOL #!20%4 IS AN EXAMPLE OF AVAILABLE SOFTWARE ON THE MARKET )N THE #!20%4 MANUAL THE EQUATIONS FOR CALCULATING THE CONTRIBUTIONS FROM CHAFF VOLUME CLUTTER IN THE SIGNAL TO INTERFERENCE RATIO ARE DESCRIBED ON PP AND AND THE EQUATIONS FOR CALCULATING THE CONTRIBUTION FROM NOISE JAMMING BARRAGE OR RESPONSIVE ARE DESCRIBED ON P #!20%4 IS PROGRAMMED IN # AND HAS A 7INDOWS 80 COMPATIBLE USER FRIENDLY GRAPHICAL INTERFACE
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o !CTUALLY IT IS A GENERALIZED "LAKE CHART THAT IMPROVES ON THE ORIGINAL "LAKE CHART WHICH INCLUDES DETAILS SUCH AS ANTENNA PATTERNS PROCESSING SYSTEM LOSSES ETC IN A SUITABLE ELECTRONIC FORMAT
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"ALLISTIC -ISSILE #OMPUTER !IDED 2ADAR 0ERFORMANCE %VALUATION 4OOL #ONSTANT &ALSE !LARM 2ATE #/ORDINATE 2OTATION $IGITAL #OMPUTER #ONICAL 3CAN ON 2ECEIVER /NLY #OMMERCIAL /FF 4HE 3HELF #OHERENT 2EPEATER )NTERFERENCE #RAMER 2AO ,OWER "OUND #ELL 5NDER 4EST #ONTINUOUS 7AVE $IGITAL TO !NALOGUE #ONVERTER $IGITAL !RRAY 2ADAR $ECEPTIVE %#$IRECTION &INDING $IRECTION OF !RRIVAL $EGREE OF FREEDOM $IGITAL 2ADIO &REQUENCY -EMORY $IFFERENCE 4IME OF !RRIVAL %LECTROMAGNETIC %LECTRONIC !TTACK %LECTRONIC #OUNTER #OUNTER -EASURE %LECTRONIC #OUNTER -EASURE %,ECTRONIC ).4ELLIGENCE %-ISSION #/.TROL %LECTRONIC 0ROTECTION %FFECTIVE 2ADIATED 0OWER %LECTRONIC 3UPPORT %LECTRONIC WARFARE 3UPPORT -EASURE %LECTRONIC 7ARFARE &AST &OURIER 4RANSFORM &IELD 0ROGRAMMABLE 'ATE !RRAYS &AST 4IME #ONSTANT 'ENETIC !LGORITHM 'ENERALIZED 3IDE ,OBE #ANCELER (OME /N *AM (IGH &REQUENCY )NTERMEDIATE &REQUENCY )NTERACTING -ULTIPLE -ODEL )NVERSE 3YNTHETIC !PERTURE 2ADAR *AMMER #ANCELLATION 2ATIO *AMMER $IRECTION OF !RRIVAL *AMMER TO .OISE 2ATIO ,OBING /N 2ECEIVE /NLY ,OW 0ROBABILITY OF )NTERCEPT -AIN "EAM #ANCELER -AXIMUM %NTROPY -ETHOD -AXIMUM ,IKELIHOOD -OVING 4ARGET $ETECTOR -OVING 4ARGET )NDICATOR
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.OISE ,IKE )NTERFERENCE /VER 4HE (ORIZON 0HASED !RRAY 2ADAR 0HASE $IFFERENCE 2ATE 0ULSE $ESCRIPTION 7ORD 0ENETRATION !ID $ECOY 0LAN 0OSITION )NDICATOR 0ULSE 2EPETITION &REQUENCY 0ULSE 2EPETITION )NTERVAL 0EAK TO 3IDE ,OBE 2ATIO 2ADAR #ROSS 3ECTION 2ADIO &REQUENCY 2ADIO &REQUENCY )NTERFERENCE 2ANGE &ILTER -AP 2ANGE 'ATE 0ULL /FF 2ADAR 7ARNING 2ECEIVER 2OOT -EAN 3QUARE 2ADAR 7ORK 3TATION 2ECEIVER 3YNTHETIC !PERTURE 2ADAR 3URFACE !COUSTIC 7AVE 3IGNAL TO )NTERFERENCE PLUS .OISE 2ATIO 3IDE,OBE "LANKING 3IDE,OBE #ANCELER 3IGNAL TO .OISE 2ATIO 3TAND /FF *AMMER 3ELF 0ROTECTION 3ELF 3CREENING *AMMER 3PACE 4IME !DAPTIVE 0ROCESSING 3INGLE 4ARGET 4RACKER 4IME OF !RRIVAL 4ERRAIN 3CATTERED )NTERFERENCE 4IME 6ARYING 3PATIAL !DAPTIVE 0ROCESSING 4RACK 7HILE 3CAN 5LTRA (IGH &REQUENCY 5NIFORM ,INEAR !RRAY 6ELOCITY 'ATE 0ULL /FF 6ERY (IGH &REQUENCY 6ERY ,ARGE 3CALE )NTEGRATION
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3 , *OHNSTON h7ORLD 7AR )) %##- HISTORY v SUPPL TO )%%% )NT 2ADAR #ONF 2EC -AY n PP n ! % (OFFMANN (EIDEN h!NTI JAMMING TECHNIQUES AT THE 'ERMAN !!! RADARS IN 7ORLD 7AR )) v SUPPL TO )%%% )NT 2ADAR #ONF 2EC PP n -AY n $ # 3CHLEHER )NTRODUCTION TO %LECTRONIC 7ARFARE .ORWOOD -! !RTECH (OUSE )NC $ # 3CHLEHER %LECTRONIC 7ARFARE IN THE )NFORMATION !GE .ORWOOD -! !RTECH (OUSE )NC " * 3LOCUMB AND 0 $ 7EST h%#- MODELING FOR MULTITARGET TRACKING AND DATA ASSOCIATION v IN -ULTITARGET -ULTISENSOR 4RACKING !PPLICATIONS AND !DVANCES VOL ))) 9 "AR 3HALOM AND 7 $ "LAIR EDS .ORWOOD -! !RTECH (OUSE )NC PP n & .ERI )NTRODUCTION TO %LECTRONIC $EFENSE ND %D .ORWOOD -! !RTECH (OUSE )NC , .ENGJING AND : 9I 4ING h! SURVEY OF RADAR %#- %##- v )%%% 4RANS VOL !%3n NO PP n *ULY 3 , *OHNSTON ED 2ADAR %LECTRONIC #OUNTER #OUNTERMEASURES .ORWOOD -! !RTECH (OUSE )NC 3PECIAL )SSUE ON ELECTRONIC WARFARE )%% 0ROC VOL PT & NO PP n *UNE 7 ! $AVIS h0RINCIPLES OF ELECTRONIC WARFARE 2ADAR AND %7 v -ICROWAVE * VOL PP n n &EBRUARY , " 6AN "RUNT 4HE 'LOSSARY OF %LECTRONIC 7ARFARE $UNN ,ORING 6! %7 %NGINEERING )NC $EPARTMENT OF $EFENSE *OINT #HIEFS OF 3TAFF $ICTIONARY OF -ILITARY AND !SSOCIATED 4ERMS *#3 0UB 3EPTEMBER , " 6AN "RUNT !PPLIED %#- VOL $UNN ,ORING 6! %7 %NGINEERING )NC 2 ' 7ILEY %LECTRONIC )NTELLIGENCE 4HE !NALYSIS OF 2ADAR 3IGNALS .ORWOOD -! !RTECH (OUSE )NC 2 ' 7ILEY %LECTRONIC )NTELLIGENCE 4HE )NTERCEPTION OF 2ADAR 3IGNALS .ORWOOD -! !RTECH (OUSE )NC 2 ' 7ILEY %,).4 4HE )NTERCEPTION AND !NALYSIS OF 2ADAR 3IGNALS .ORWOOD -! !RTECH (OUSE )NC 2 ! 0OISEL %LECTRONIC 7ARFARE 4ARGET ,OCATION -ETHODS .ORWOOD -! !RTECH (OUSE )NC % 0 0ACE $ETECTING AND #LASSIFYING ,OW 0ROBABILITY OF )NTERCEPT 2ADAR .ORWOOD -! !RTECH (OUSE )NC $ # 3CHLEHER h,0) RADAR &ACT OR FICTION v )%%% !%3 -AGAZINE VOL NO PP n -AY 3 , *OHNSTON h0HILOSOPHY OF %##- UTILIZATION v %LECTRON 7ARFARE VOL PP n -AYn*UNE - 6 -AKSIMOV ET AL 2ADAR !NTI *AMMING 4ECHNIQUES .ORWOOD -! !RTECH (OUSE )NC 4RANSLATED FROM 2USSIAN :ASCHITA AT 2ADIOPOMEKH 3OVIET 2ADIO $ #LIFFORD "ELL h2ADAR COUNTERMEASURES AND COUNTER COUNTERMEASURES v -IL 4ECHNOL PP n -AY * ! !DAM AND - ! &ISCHETTI h3TAR 7ARS 3$) 4HE GRAND EXPERIMENT v )%%% 3PECTRUM VOL NO PP n 3EPTEMBER 3 * 2OOME h$IGITAL RADIO FREQUENCY MEMORY v %LECTRONIC #OMMUNICATION %NGINEERING *OURNAL PP n !UGUST * 7 'OODMAN AND - 3ILVESTRI h3OME EFFECTS OF &OURIER $OMAIN 0HASE 1UANTIZATION v )"- * 2ES $EVELOP PP n 3EPTEMBER - 'RECO & 'INI AND ! &ARINA h#OMBINED EFFECT OF PHASE AND 2'0/ DELAY QUANTIZATION ON JAMMING SIGNAL SPECTRUM v 0ROC OF )%%% )NT #ONF ON 2ADAR 2ADAR 7ASHINGTON $# 53! -AY n PP n 3 $ "ERGER h$IGITAL RADIO FREQUENCY MEMORY LINEAR GATE STEALER SPECTRUM v )%%% 4RANS VOL !%3n NO PP n !PRIL
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' 6 -ORRIS ET AL h0RINCIPLES OF ELECTRONIC COUNTER COUNTERMEASURES v SHORT LECTURE NOTES 'EORGIA )NSTITUTE OF 4ECHNOLOGY , " 6AN "RUNT !PPLIED %#- VOL $UNN ,ORING 6! %7 %NGINEERING )NC 0 * 'ROS $ # 3AMMONS AND ! # #RUCE h%##- !DVANCED 2ADAR 4EST "ED %!24" SYSTEMS DEFINITION v )%%% .AT !EROSP %LECTRON #ONF .!%#/. -AY n PP n - ! *OHNSON AND $ # 3TONER h%##- FROM THE RADAR DESIGNERS VIEW POINT v -ICROWAVE * VOL PP n -ARCH ( % 3CHRANK h,OW SIDELOBES PHASED ARRAY AND REFLECTORS ANTENNAS v IN !SPECTS OF -ODERN 2ADAR % "ROOKNER ED .ORWOOD -! !RTECH (OUSE )NC 7 4 0ATTON h,OW 3IDELOBE !NTENNAS FOR 4ACTICAL 2ADARS v )%%% )NT 2ADAR #ONF 2EC !PRIL n PP n ! &ARINA !NTENNA "ASED 3IGNAL 0ROCESSING 4ECHNIQUES FOR 2ADAR 3YSTEMS .ORWOOD -! !RTECH (OUSE )NC & * (ARRYS h/N THE USE OF WINDOWS FOR HARMONIC ANALYSIS WITH THE $ISCRETE &OURIER 4RANSFORM v 0ROC )%%% VOL PP n *ANUARY % "ROOKNER h4RENDS IN RADAR SYSTEMS AND TECHNOLOGY TO THE YEAR AND BEYOND v IN !SPECTS OF -ODERN 2ADAR % "ROOKNER ED !RTECH (OUSE )NC .ORWOOD -! % "ROOKNER h0HASED ARRAY AROUND THE WORLD 0ROGRESS AND FUTURE TRENDS v )%%% )NT 3YMP ON 0HASED !RRAY 3YSTEMS AND 4ECHNOLOGY "OSTON 53! /CTOBER n PP n - #ICOLANI ! &ARINA % 'IACCARI & -ADIA 2 2ONCONI AND 3 3ABATINI h3OME PHASED ARRAY SYSTEMS AND TECHNOLOGIES IN !-3 v )%%% )NT 3YMP ON 0HASED !RRAY 3YSTEMS AND 4ECHNOLOGY "OSTON 53! /CTOBER n PP n 7 +UHN 7 3IEPRATH , 4IMMONERI AND ! &ARINA h0HASED ARRAY RADAR SYSTEMS IN SUPPORT OF THE -EDIUM %XTENDED !IR $EFENSE 3YSTEM -%!$3 v )%%% )NT 3YMP ON 0HASED !RRAY 3YSTEMS AND 4ECHNOLOGY "OSTON 53! /CTOBER n PP n ! 2 -OORE $ - 3ALTER AND 7 + 3TAFFORD h-%3!2 -ULTI &UNCTION %LECTRONICALLY 3CANNED !DAPTIVE 2ADAR v 0ROC OF )NT #ONF 2ADAR %DINBURGH /CTOBER n 0UBLICATION NO ,ONDON 5+ )%% PP n $ 'IULI h0OLARIZATION DIVERSITY IN RADARS v 0ROC )%%% VOL PP n &EBRUARY , -AISEL h0ERFORMANCE OF SIDELOBE BLANKING SYSTEMS v )%%% 4RANS VOL !%3n NO PP n -ARCH 0 / !RANCIBIA h! SIDELOBE BLANKING SYSTEM DESIGN AND DEMONSTRATION v -ICROWAVE * VOL PP n -ARCH REPRINTED IN 2EF $ ( (ARVEY AND 4 , 7OOD h$ESIGNS FOR SIDELOBE BLANKING SYSTEMS v )%%% )NT 2ADAR #ONF 2EC !PRIL PP n - /3ULLIVAN h! COMPARISON OF SIDELOBE BLANKING SYSTEMS )%% )NT #ONF 2ADARn #ONF 0UB ,ONDON 5+ /CTOBER n PP n ! &ARINA AND & 'INI h#ALCULATION OF BLANKING PROBABILITY FOR THE SIDELOBE BLANKING 3," FOR TWO INTERFERENCE STATISTICAL MODELS v )%%% 3IGNAL 0ROCESSING ,ETTERS VOL NO PP n !PRIL ! &ARINA AND & 'INI h"LANKING PROBABILITIES FOR 3," SYSTEM IN CORRELATED CLUTTER PLUS THERMAL NOISE v )%%% 4RANS VOL 30n NO PP n -AY ! &ARINA AND & 'INI h$ESIGN OF 3," SYSTEMS IN PRESENCE OF CORRELATED GROUND CLUTTER v )%% 0ROC VOL PT & NO PP n ! $E -AIO ! &ARINA AND & 'INI h0ERFORMANCE ANALYSIS OF THE SIDELOBE BLANKING SYSTEM FOR TWO FLUCTUATING JAMMER MODELS v )%%% 4RANS VOL !%3n NO PP n *ULY $ ! 3HNIDMAN AND 3 3 4OUMODGE h3IDELOBE BLANKING WITH INTEGRATION AND TARGET FLUCTUATION v )%%% 4RANS VOL !%3n NO PP n *ULY 0 7 (OWELLS h)NTERMEDIATE &REQUENCY 3IDELOBE #ANCELER v 53 0ATENT !UGUST 3 0 !PPLEBAUM 0 7 (OWELLS AND # +OVARIK h-ULTIPLE )NTERMEDIATE &REQUENCY 3IDE ,OBE #ANCELER v 53 0ATENT !UGUST
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2 ! -ONZINGO AND 47 -ILLER )NTRODUCTION TO !DAPTIVE !RRAYS .EW 9ORK *OHN 7ILEY 3ONS * (UDSON !DAPTIVE !RRAY 0RINCIPLES ,ONDON 0ETER 0EREGRINUS ,TD 2 .ITZBERG !DAPTIVE 3IGNAL 0ROCESSING FOR 2ADAR .ORWOOD -! !RTECH (OUSE )NC ( $ 'RIFFITHS h! FOUR ELEMENT 6(& ADAPTIVE ARRAY PROCESSOR v 0ROC ND )%% )NT #ONF ON !NTENNAS AND 0ROPAGATION )%% #ONF 0UB NO PT 9ORK 5+ !PRIL n PP n ! &ARINA h$IGITAL EQUALISATION IN ADAPTIVE SPATIAL FILTERING A SURVEY v 3IGNAL 0ROCESSING %LSEVIER VOL NO PP n *ANUARY " $ #ARLSON , - 'OODMAN * !USTIN - 7 'ANZ AND , / 5PTON h!N ULTRALOW SIDELOBE ADAPTIVE ARRAY ANTENNA v 4HE ,INCOLN ,ABORATORY *OURNAL VOL NO PP n 7 & 'ABRIEL h!DAPTIVE DIGITAL PROCESSING INVESTIGATION OF $&4 SUB BANDING VS TRANSVERSAL FILTER CANCELER v .AVAL 2ESEARCH ,ABORATORY .2, 2EPORT *ULY 7ASHINGTON $# 53! ! &ARINA AND 2 3ANZULLO h0ERFORMANCE LIMITATIONS IN ADAPTIVE SPATIAL FILTERING v 3IGNAL 0ROCESSING %LSEVIER VOL NO PP n /CTOBER + 'ERLACH h4HE EFFECTS OF )& BANDPASS MISMATCH ERRORS ON ADAPTIVE CANCELLATION v )%%% 4RANS VOL !%3n NO PP n -AY ! &ARINA ' 'OLINO , 4IMMONERI AND ' 4ONELLI h$IGITAL EQUALISATION IN ADAPTIVE SPATIAL FILTERING FOR RADAR SYSTEMS !PPLICATION TO LIVE DATA ACQUIRED WITH A GROUND BASED PHASED ARRAY RADAR v 2ADAR 4OULOUSE &RANCE /CTOBER n 2 &ANTE 2 $AVIS AND 4 'UELLA h7IDEBAND CANCELLATION OF MULTIPLE MAINBEAM JAMMERS v )%%% 4RANS VOL !0n NO PP n /CTOBER & % #HURCHILL ' 7 /GAR AND " * 4HOMPSON h4HE CORRECTION OF ) AND 1 ERRORS IN A COHERENT PROCESSOR v )%%% 4RANS VOL !%3n NO PP n *ANUARY + 'ERLACH h4HE EFFECT OF ) 1 MISMATCHING ERRORS ON ADAPTIVE CANCELLATION v )%%% 4RANS VOL !%3n NO PP n *ULY + 'ERLACH AND - * 3TEINER h!N ADAPTIVE MATCHED FILTER THAT COMPENSATES FOR ) 1 MISMATCH ERRORS v )%%% 4RANS VOL 30n NO PPn $ECEMBER ! &ARINA AND , /RTENZI h%FFECT OF !$# AND RECEIVER SATURATION ON ADAPTIVE SPATIAL FILTERING OF DIRECTIONAL INTERFERENCE v 3IGNAL 0ROCESSING %LSEVIER VOL NO PP n ! &ARINA 2 3ANZULLO AND , 4IMMONERI h0ERFORMANCE LIMITATIONS AND REMEDIES IN ADAPTIVE SPATIAL FILTERING WITH TIMING ERRORS v 3IGNAL 0ROCESSING %LSEVIER VOL NO PP n &EBRUARY $ 2 -ORGAN AND ! !RIDGIDES h!DAPTIVE SIDELOBES CANCELLATION OF WIDE BAND MULTIPATH INTERFERENCE v )%%% 4RANS VOL !0n NO PP n !UGUST 2 , &ANTE h#ANCELLATION OF SPECULAR AND DIFFUSE JAMMER MULTIPATH USING A HYBRID ADAPTIVE ARRAY v )%%% 4RANS VOL !%3n NO PP n 3EPTEMBER ! &ARINA AND , 4IMMONERI h#ANCELLATION OF CLUTTER AND EM INTERFERENCE WITH 34!0 ALGORITHMS !PPLICATION TO LIVE DATA ACQUIRED WITH A GROUND BASED PHASED ARRAY RADAR DEMONSTRATOR v 0ROC OF )%%% 2ADAR #ONF 0HILADELPHIA 53! !PRIL n PP n ! &ARINA , 4IMMONERI AND 2 4OSINI h#ASCADING 3," AND 3,# DEVICES v 3IGNAL 0ROCESSING %LSEVIER VOL NO PP n ! &ARINA AND , 4IMMONERI h3YSTOLIC SCHEMES FOR *OINT 3," 3,# AND ADAPTIVE PHASED ARRAY v 0ROC OF )NT #ONF ON 2ADAR 2ADAR 7ASHINGTON $# 53! -AY n PP n , 4IMMONERI ) + 0ROUDLER ! &ARINA AND * ' -C7HIRTER h12$ "ASED -6$2 ALGORITHM FOR ADAPTIVE MULTIPULSE ANTENNA ARRAY SIGNAL PROCESSING v )%% 0ROC VOL PT & NO PP n !PRIL 0 "OLLINI , #HISCI ! &ARINA - 'IANNELLI , 4IMMONERI AND ' :APPA h12 VERSUS )12 ALGORITHMS FOR ADAPTIVE SIGNAL PROCESSING PERFORMANCE EVALUATION FOR RADAR APPLICATIONS v )%% 0ROC VOL PT & NO PP n /CTOBER ! &ARINA AND , 4IMMONERI h2EAL TIME 34!0 TECHNIQUES v %LECTRONICS #OMMUNICATIONS %NGINEERING *OURNAL 3PECIAL )SSUE ON 34!0 VOL NO PP n &EBRUARY
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0 +APTEIJIN % $EPRETTERE , 4IMMONERI AND ! &ARINA h)MPLEMENTATION OF THE RECURSIVE 12 ALGORITHM ON A #/2$)# TEST BOARD A CASE STUDY FOR RADAR APPLICATION v 0ROC OF THE TH %UROPEAN -ICROWAVE #ONF "OLOGNA )TALY 3EPTEMBER n PP n ! $!CIERNO - #ECCARELLI ! &ARINA ! 0ETROSINO AND , 4IMMONERI h-APPING 12 DECOMPOSITION ON PARALLEL COMPUTERS A STUDY CASE FOR RADAR APPLICATIONS v )%)#% 4RANS ON #OMMUNICATIONS VOL %n" NO PP n /CTOBER ! &ARINA AND , 4IMMONERI h0ARALLEL PROCESSING ARCHITECTURES FOR 34!0 v IN !PPLICATIONS OF 3PACE 4IME !DAPTIVE 0ROCESSING 2 +LEMM ED ,ONDON 5+ )%% 2ADAR 3ONAR AND .AVIGATION 3ERIES PP n ! &ARINA ! !VERBOUCH $ 'IBOR , ,ESCARINI 3 ,EVIT 3 3TEFANINI AND , 4IMMONERI h-ULTI CHANNEL RADAR !DVANCED IMPLEMENTATION TECHNOLOGY AND EXPERIMENTAL RESULTS v 0ROC OF )NT 2ADAR 3YMP )23 "ERLIN 'ERMANY 3EPTEMBER n PP n # - 2ADER h7AFER SCALE INTEGRATION OF A LARGE SCALE SYSTOLIC ARRAY FOR ADAPTIVE NULLING v 4HE ,INCOLN ,ABORATORY *OURNAL VOL NO PP n # - 2ADER h6,3) SYSTOLIC ARRAY FOR ADAPTIVE NULLING v )%%% 3IGNAL 0ROCESSING -AGAZINE VOL NO PP n *ULY 3 0 !PPLEBAUM h!DAPTIVE ARRAYS v 3YRACUSE 5NIVERSITY 2ESEARCH #ORPORATION 2EPT 30, 42 n 4HIS REPORT IS REPRODUCED IN )%%% 4RANS VOL !0n PP n 3EPTEMBER , % "RENNAN AND ) 3 2EED h4HEORY OF ADAPTIVE RADAR v )%%% 4RANS VOL !%3 NO PP n -ARCH " 7ARDROP h4HE ROLE OF DIGITAL PROCESSING IN RADAR BEAMFORMING v '%# * 2ES VOL NO PP n 0 6ALENTINO h$IGITAL BEAMFORMING NEW TECHNOLOGY FOR TOMORROWS RADARS v $EF %LECTRON PP n /CTOBER ( 3TEYSKAL h$IGITAL BEAMFORMING ANTENNAS AN INTRODUCTION v -ICROWAVE * PP n *ANUARY " #ANTRELL * DE 'RAAF , ,EIBOWITZ % 7ILLWERTH ' -EURER # 0ARRIS AND 2 3TAPLETON h$EVELOPMENT OF A $IGITAL !RRAY 2ADAR $!2 v 0ROC OF )%%% 2ADAR #ONF !TLANTA 'EORGIA -AY n PP n - :ATMAN h$IGITIZATION REQUIREMENTS FOR DIGITAL RADAR ARRAYS v )%%% 2ADAR #ONF !TLANTA 'EORGIA -AY n PP n ) 3 2EED h! BRIEF HISTORY OF ADAPTIVE ARRAYS v 3UBDURY7AYLAND ,ECTURE 3ERIES 2AYTHEON $IV %DUCATION NOTES /CTOBER $ %TTER ! 3TEINHARDT AND 3 3TONER h,EAST SQUARES ADAPTIVE PROCESSING IN MILITARY APPLICA TIONS v )%%% 3IGNAL 0ROCESSING -AGAZINE VOL NO PP n -AY /N OCCASION OF THE " &RANKLIN -EDAL AWARDED TO " 7IDROW FOR PIONEERING WORK ON ADAPTIVE SIGNAL PROCESSING 3 (AYKIN AND ! 3TEINHARDT !DAPTIVE 2ADAR $ETECTION AND %STIMATION .EW 9ORK *OHN 7ILEY 3ONS )NC 3 4 3MITH h!DAPTIVE 2ADAR v IN 7ILEY %NCYCLOPEDIA OF %LECTRICAL AND %LECTRONIC %NGINEERING * ' 7EBSTER ED VOL .EW 9ORK 7ILEY UPDATED *ULY PP n ! &ARINA # ( 'IERULL & 'INI AND 5 .ICKEL EDS 3PECIAL )SSUE h.EW TRENDS AND FIND INGS IN ANTENNA ARRAY PROCESSING v 3IGNAL 0ROCESSING %LSEVIER VOL NO PP n 3EPTEMBER * 7ARD h3PACE TIME ADAPTIVE PROCESSING FOR AIRBORNE RADAR v -)4 ,INCOLN ,ABORATORY 4ECHNICAL 2EPORT 42n $ECEMBER 2 +LEMM 0RINCIPLES OF 3PACE 4IME !DAPTIVE 0ROCESSING RD %D ,ONDON 5+ )%4 2ADAR 3ONAR AND .AVIGATION 3ERIES 2 +LEMM ED !PPLICATIONS OF 3PACE 4IME !DAPTIVE 0ROCESSING ,ONDON 5+ )%% 2ADAR 3ONAR AND .AVIGATION 3ERIES * 2 'UERCI 3PACE 4IME !DAPTIVE 0ROCESSING FOR 2ADAR .ORWOOD -! !RTECH (OUSE )NC " 4ESTA AND 6 6ANNICOLA h4HE PHYSICAL SIGNIFICANCE OF THE EIGENVALUES IN ADAPTIVE ARRAYS v $IGITAL 3IGNAL 0ROCESSING VOL PP n
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! &ARINA ED /PTIMISED 2ADAR 0ROCESSORS ,ONDON 0ETER 0EREGRINUS ,TD % &ONG * ! 7ALKER AND 7 ' "ATH h-OVING TARGET INDICATION IN THE PRESENCE OF RADIO FRE QUENCY INTERFERENCE v 0ROC )%%% )NT 2ADAR #ONF !RLINGTON 6! 53! -AY n PP n , "6AN "RUNT h0ULSE COMPRESSION RADAR %#- AND %##- v $EF %LECTRON VOL PP n /CTOBER ( +USHEL h6(&5(& 0ART CHARACTERISTICS v %LECTRONICS #OMMUNICATIONS %NGINEERING *OURNAL VOL NO PP n !PRIL 2 * 'ALEJS h6OLUME SURVEILLANCE RADAR FREQUENCY SELECTION v 0ROC OF )%%% )NT 2ADAR #ONF !LEXANDRIA 6! 53! -AY n PP n ( +USHEL h6(&5(& 0ART OPERATIONAL ASPECTS AND APPLICATIONS v %LECTRONICS #OMMUNICATIONS %NGINEERING *OURNAL VOL NO PP n *UNE 7 . $AWBER AND . - (ARWOOD h#OMPARISON OF DOPPLER CLUTTER CANCELLATION TECHNIQUES FOR NAVAL MULTI FUNCTION RADARS v )%% )NT #ONF 2ADAR #ONF 0UB .O %DINBURGH 5+ /CTOBER PP ! ) ,EONOV AND + * &OMICHEV -ONOPULSE 2ADAR .ORWOOD -! !RTECH (OUSE )NC 3 , *OHNSTON h4RACKING RADAR ELECTRONIC COUNTER COUNTERMEASURES AGAINST INVERSE GAIN JAM MERS v )%% )NT #ONF 2ADARn #ONF 0UB ,ONDON /CTOBER PP n " , ,EWIS AND $ ( (OWARD h3ECURITY $EVICE v 53 0ATENT &EBRUARY FILED !UGUST 2 , &ANTE AND * ! 4ORRES h#ANCELLATION OF DIFFUSE JAMMER MULTIPATH BY AN AIRBORNE ADAPTIVE RADAR v )%%% 4RANS VOL !%3n NO PP n !PRIL 3 +OGON h!LGORITHMS FOR MITIGATING TERRAIN SCATTERED INTERFERENCE v %LECTRONICS #OMMUNICATIONS %NGINEERING *OURNAL VOL NO PP n &EBRUARY 3 "JORKLUND AND ! .ELANDER h4HEORETICAL ASPECTS ON A METHOD FOR TERRAIN SCATTERED INTER FERENCE MITIGATION IN RADAR v 0ROC OF )%%% )NT 2ADAR #ONF !LEXANDRIA 6! 53! -AY n PP n 9 !BRAMOVICH 3 * !NDERSON AND ! 9 'OROKOV h3TOCHASTICALLY CONSTRAINED SPATIAL AND SPATIO TEMPORAL ADAPTIVE PROCESSING FOR NON STATIONARY HOT CLUTTER CANCELLATION v #HAPTER IN !PPLICATIONS OF 3PACE 4IME !DAPTIVE 0ROCESSING 2 +LEMM ED ,ONDON )%% 2ADAR 3ONAR AND .AVIGATION 3ERIES PP n 7 $ "LAIR ' ! 7ATSON 4 +IRUBARAJAN AND 9 "AR 3HALOM h"ENCHMARK FOR RADAR ALLOCATION AND TRACKING IN %#- v )%%% 4RANS VOL !%3n NO PPn 4 +IRUBARAJAN 9 "AR 3HALOM 7 $ "LAIR AND ' ! 7ATSON h)--0$!& FOR RADAR MANAGEMENT AND TRACKING BENCHMARK WITH %#- v )%%% 4RANS VOL !%3n NO PPn ( "LOM AND 9 "AR 3HALOM h4HE INTERACTING MULTIPLE MODEL ALGORITHM FOR SYSTEMS WITH -ARKOVIAN SWITCHING COEFFICIENTS v )%%% 4RANS VOL !#n NO PP n !UGUST ! -OREIRA h)MPROVED MULTILOOK TECHNIQUES APPLIED TO 3!2 AND 3#!.3!2 IMAGERY v )%%% 4RANS ON 'EOSCIENCE AND 2EMOTE 3ENSING VOL NO PP n *ULY 7 'OJ 3YNTHETIC !PERTURE 2ADAR AND %LECTRONIC 7ARFARE $EDHAM -! !RTECH (OUSE )NC # * #ONDLEY h4HE POTENTIAL VULNERABILITY TO INCREASED BACKGROUND NOISE OF SYNTHETIC APER TURE RADAR IN THE MARITIME ENVIRONMENT v )%% #OLLOQUIUM ON 3YNTHETIC !PERTURE 2ADAR .OVEMBER PP n # * #ONDLEY h3OME SYSTEM CONSIDERATIONS FOR ELECTRONIC COUNTERMEASURES TO SYNTHETIC APERTURE RADAR v )%% #OLLOQUIUM ON %LECTRONIC 7ARFARE 3YSTEMS *ANUARY PP n - 3OUMEKH h3!2 %##- USING PHASED PERTURBED ,&- CHIRP SIGNALS AND $2&- REPEAT JAMMER PENALIZER v )%%% 4RANS VOL !%3n NO PP n *ANUARY 0 (YBERG h!SSESSMENT OF MODERN COHERENT JAMMING METHODS AGAINST SYNTHETIC APERTURE RADAR 3!2 v 0ROC OF %53!2 %UROPEAN #ONF ON 3YNTHETIC !PERTURE 2ADAR &RIEDRICHSHAFEN 'ERMANY -AY n PP n # "OESSWETTER h%##- EFFECTIVENESS OF A LOW SIDELOBE ANTENNA FOR 3!2 GROUND MAPPING v !'!2$ !60 3YMP h-ULTIFUNCTION 2ADAR FOR !IRBORNE !PPLICATIONS v 4OULOUSE
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Óx°£Ê /," 1 /" 4HE EXPONENTIAL GROWTH IN DIGITAL TECHNOLOGY SINCE THE S ALONG WITH THE COR RESPONDING DECREASE IN ITS COST HAS HAD A PROFOUND IMPACT ON THE WAY RADAR SYSTEMS ARE DESIGNED -ORE AND MORE FUNCTIONS THAT HISTORICALLY WERE IMPLEMENTED IN ANALOG HARDWARE ARE NOW BEING PERFORMED DIGITALLY RESULTING IN INCREASED PERFORMANCE AND FLEXIBILITY AND REDUCED SIZE AND COST !DVANCES IN ANALOG TO DIGITAL CONVERTER !$# AND DIGITAL TO ANALOG CONVERTER $!# TECHNOLOGIES ARE PUSHING THE BORDER BETWEEN ANALOG AND DIGITAL PROCESSING CLOSER AND CLOSER TO THE ANTENNA &OR EXAMPLE &IGURE SHOWS A SIMPLIFIED BLOCK DIAGRAM OF THE RECEIVER FRONT END OF A TYPICAL RADAR SYSTEM THAT WOULD HAVE BEEN DESIGNED AROUND .OTE THAT THIS SYSTEM INCORPORATED ANALOG PULSE COMPRESSION 0# )T ALSO INCLUDED SEVERAL STAGES OF ANALOG DOWNCONVERSION IN ORDER TO GENERATE BASEBAND IN PHASE ) AND QUADRATURE 1 SIGNALS WITH A SMALL ENOUGH BANDWIDTH THAT THE !$#S OF THE DAY COULD SAMPLE THEM 4HE DIGITIZED SIGNALS WERE THEN FED INTO DIGITAL DOPPLER-4) AND DETECTION PROCESSORS "Y CONTRAST &IGURE DEPICTS A TYPICAL DIGITAL RECEIVER FOR A RADAR FRONT END 4HE 2& INPUT USUALLY PASSES THROUGH ONE OR TWO STAGES OF ANALOG DOWNCONVERSION TO GENERATE AN )NTERMEDIATE &REQUENCY )& SIGNAL THAT IS SAMPLED DIRECTLY BY THE !$# ! DIGITAL DOWNCONVERTER $$# CONVERTS THE DIGITIZED SIGNAL SAMPLES TO COMPLEX FORM AT A LOWER RATE FOR PASSING THROUGH A DIGITAL PULSE COMPRESSOR TO BACKEND PROCESSING .OTE THAT THE OUTPUT OF THE !$# HAS A SLASH THROUGH THE DIGITAL SIGNAL LINE WITH A LETTER ABOVE 4HE LETTER DEPICTS THE NUMBER OF BITS IN THE DIGITIZED INPUT SIGNAL AND REPRESENTS THE MAXIMUM POSSIBLE DYNAMIC RANGE OF THE !$# !S WILL BE DESCRIBED LATER THE USE OF DIGITAL SIGNAL PROCESSING $30 CAN OFTEN IMPROVE THE DYNAMIC RANGE STABILITY AND OVERALL PERFORMANCE OF THE SYSTEM WHILE REDUCING SIZE AND COST COMPARED TO THE ANALOG APPROACH 4HIS CHAPTER WILL PROVIDE A HIGH LEVEL OUTLINE OF SOME OF THE MAJOR DIGITAL PRO CESSING TECHNIQUES FOR RADAR SYSTEMS THAT HAVE BECOME PRACTICAL SINCE THE 3ECOND %DITION OF THIS (ANDBOOK WAS PUBLISHED AS WELL AS SOME DESIGN TRADEOFFS THAT NEED TO BE CONSIDERED Óx°£
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-AJOR ADVANCES IN ANALOG TO DIGITAL CONVERTER AND DIGITAL COMPONENT TECHNOLOGY HAVE TRANSFORMED THE RECEIVER FRONT ENDS OF RADAR SYSTEMS PROVIDING HIGHER PERFORMANCE AT LOWER COST 4HIS SECTION WILL DESCRIBE HOW THESE NEW TECHNOLOGIES ARE BEING APPLIED TO RADAR SYSTEMS AND THE BENEFITS THEY BRING TO SYSTEM PERFORMANCE 3IGNAL 3AMPLING "ASICS $IGITAL SIGNAL PROCESSORS ARE SAMPLED SIGNAL SYSTEMS 3AMPLING IS THE PROCESS BY WHICH A CONTINUOUS ANALOG SIGNAL IS MEASURED AT REGULAR INTERVALS OF TIME THE SAMPLING INTERVAL PRODUCING A SEQUENCE OF DISCRETE NUMBERS SAMPLES THAT REPRESENTS THE VALUES OF THE SIGNAL AT THE SAMPLING INSTANTS 4HE SAM PLING FREQUENCY IS THE INVERSE OF THE SAMPLING INTERVAL AND IS TYPICALLY DESIGNATED FS 3AMPLED SYSTEMS ARE SUBJECT TO THE .YQUIST LIMIT WHICH LOWER BOUNDS THE SAMPLING RATE AT WHICH RECONSTRUCTION OF THE UNSAMPLED SIGNAL FROM ITS SAMPLES IS POSSIBLE WITH OUT CORRUPTION BY ALIASING THE OVERLAPPING OF SPECTRAL COMPONENTS 4HE BOUND TERMED THE .YQUIST FREQUENCY OR .YQUIST RATE IS EQUAL TO THE TWO SIDED SIGNAL BANDWIDTH " THE BANDWIDTH CONSIDERING COMPONENTS AT BOTH POSITIVE AND NEGATIVE FREQUENCIES 3AMPLING BELOW THE .YQUIST RATE ALWAYS RESULTS IN ALIASING BUT SAMPLING ABOVE IT DOES NOT GUARANTEE ALIAS FREE OPERATION 7E WILL SEE THAT FOR BANDPASS SIGNALS A SAMPLING RATE HIGHER THAN .YQUIST MAY BE REQUIRED TO AVOID ALIASING IN SOME SITUATIONS 4HE .YQUIST RATE IS OFTEN SAID TO BE TWICE THE SIGNAL BANDWIDTH BUT THAT REFERS TO A ONE SIDED BANDWIDTH POSITIVE FREQUENCIES ONLY OF A REAL SIGNAL /UR DEFINITION REFERS TO THE TWO SIDED BANDWIDTH BOTH POSITIVE AND NEGATIVE FREQUENCIES OF A SIGNAL THAT IN GENERAL IS COMPLEX WITH A REAL SIGNAL AS A SPECIAL CASE )S THE TWO SIDED BANDWIDTH ALWAYS TWICE THE ONE SIDED BANDWIDTH &OR COMPLEX SIGNALS IN GENERAL NO BUT FOR REAL SIGNALS IN PARTICULAR YES (ERES WHY ANY SIGNAL REAL OR COMPLEX WHEN EXPRESSED AS A &OURIER INTEGRAL INVERSE &OURIER TRANSFORM IS
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SEEN TO BE A COMBINATION OF SPECTRAL COMPONENTS OF THE FORM ! E JO FT 3AMPLED SIGNALS HAVE T N4 WITH 4 A SAMPLING INTERVAL AND N AN INTEGER TIME BUT SAMPLED OR NOT THE BASIC COMPONENT FORM IS THE SAME !ND EITHER WAY COMPLEX AMPLITUDE ! IS A FUNCTION OF FREQUENCY F BUT LETS WRITE ! INSTEAD OF ! F FOR SIMPLICITY )N THESE TERMS THEN WHATS SPECIAL ABOUT REAL SIGNALS IS THAT AN EASILY DERIVED &OURIER TRANSFORM PROPERTY REQUIRES THEIR &OURIER COMPONENTS TO OCCUR IN CONJUGATE PAIRS SO THAT IF THERE IS A COMPONENT ! E JO FT AT FREQUENCY F WITH COMPLEX AMPLITUDE ! THERE IS ALSO A COMPONENT ! E JO FT AT FREQUENCY F WITH THE COMPLEX CONJUGATE ! OF THAT COMPLEX AMPLITUDE )F A BAND OF POSITIVE FREQUENCIES FROM F TO F IS OCCUPIED BY SPECTRAL COMPONENTS THE CORRESPONDING BAND OF NEGATIVE FREQUENCIES FROM F TO
F WILL BE OCCUPIED BY SPECTRAL COMPONENTS ALSO SO THE TWO SIDED BANDWIDTH MUST BE TWICE THE ONE SIDED BANDWIDTH 2EAL SIGNALS HAVE SPECTRAL COMPONENTS IN CONJUGATE PAIRS BECAUSE BY USING COM PLEX AMPLITUDE EXPRESSED IN POLAR FORM AS ! R EJP ! E JO FT ! E JO FT 2E[!E JO FT] 2E[R E JP E JO FT] R 2E[E JO FT P ] R COSO FT P 4HE IMAGINARY PARTS OF THE CONJUGATE SPECTRAL COMPONENTS HAVE CANCELED TO REVEAL THAT THOSE COMPONENTS TOGETHER INDEED REPRESENT A REAL SIGNAL A SINUSOID WITH AMPLI TUDE AND PHASE SPECIFIED BY THE MAGNITUDE AND ANGLE OF THE COMPLEX AMPLITUDE 4HE LATTER RELATIONSHIP IS SO MUCH A PART OF THE ENGINEERING CULTURE THAT THE TERMS AMPLITUDE AND PHASE ARE COMMONLY IF IMPRECISELY USED TO REFER TO THE MAGNITUDE AND ANGLE OF A COMPLEX SIGNAL AT AN INSTANT IN TIME 4HE FOLLOWING FIGURES ILLUSTRATE THE ORIGIN OF THE .YQUIST RATE )MAGINE THAT A REAL SIGNAL WITH A LOWPASS SIGNAL SPECTRUM OF TWO SIDED BANDWIDTH " IS PLOTTED ON A LONG PIECE OF PAPER AS SHOWN IN &IGURE A )N THE FIGURE THE POSITIVE FREQUENCY SPECTRAL COMPONENTS OF THE SIGNAL ARE DARKLY SHADED AND THE NEGATIVE FREQUENCY COMPONENTS ARE LIGHTLY SHADED 4O SEE THE EFFECT OF SAMPLING THIS SIGNAL AT .YQUIST RATE " THE LONG SHEET IS CUT INTO SMALLER SHEETS WITH THE FIRST CUT AT ZERO FREQUENCY AND SUBSEQUENT CUTS AT SAMPLE RATE " IN THIS CASE INTERVALS IN POSITIVE AND NEGATIVE FREQUENCY 4HE SHEETS ARE STACKED ONE ON TOP OF THE OTHER AS SHOWN ON THE LEFT SIDE OF &IGURE B AND THE RESULTING PORTION OF THE SAMPLED SIGNAL SPECTRUM FROM TO THE SAMPLING RATE OF " IS GENERATED BY ADDING THE SPECTRA OF THE STACKED PAGES TOGETHER AS SHOWN ON THE RIGHT
&)'52% A "ANDLIMITED REAL SIGNAL SPECTRUM BEFORE SAMPLING B PORTION OF SAMPLED SPECTRUM FROM TO " AND C FULL SAMPLED SIGNAL SPECTRUM
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&)'52% A "ANDLIMITED LOWPASS SIGNAL SPECTRUM BEFORE SAMPLING B ALIASED LOWPASS SIGNAL SPECTRUM AFTER SAMPLING AT RATE FS " AND C ALIASED SAMPLED SIGNAL SPECTRUM
.OTE THAT THE LIGHTLY SHADED NEGATIVE FREQUENCY PORTION OF THE SPECTRUM NOW APPEARS ON THE RIGHT OF THE SAMPLED SPECTRUM AND DOESNT OVERLAP THE DARKER POSITIVE FREQUENCY PORTION !S LONG AS THE TWO PORTIONS OF THE SAMPLED SIGNAL DONT OVERLAP THE SIGNAL IS NOT ALIASED 4HE FULL SAMPLED SIGNAL SPECTRUM IS OBTAINED BY LAYING COPIES OF THIS PAGE END TO END AS SHOWN IN &IGURE C PRODUCING COPIES OF THE TO " PORTION OF THE SAMPLED SIGNAL SPECTRUM AT " INTERVALS &IGURE SHOWS THE RESULT OF SAMPLING BELOW THE .YQUIST RATE &IGURE A SHOWS THE SAME BANDLIMITED SIGNAL AS THE PREVIOUS EXAMPLE BUT THIS TIME IT IS SAMPLED AT SOME RATE THAT IS LESS THAN .YQUIST RATE " 4HE RESULTING SAMPLED SPECTRUM SHOWN IN &IGURE B AND C CONTAINS OVERLAPPED OR ALIASED SPECTRAL COMPONENTS THAT ADD AND REPRESENT CORRUPTION OF THE SIGNAL &IGURE REPEATS THIS .YQUIST ANALYSIS FOR A BANDPASS SIGNALA SIGNAL NOT CONTAINING SPECTRAL COMPONENTS AT OR NEAR (Z &IGURE A SHOWS A REAL BANDPASS SIGNAL WITH TWO SIDED BANDWIDTH " AND COMPOSED OF POSITIVE FREQUENCY AND NEGATIVE FREQUENCY SPECTRAL COMPONENTS EACH OF BANDWIDTH " THAT ARE COMPLEX CONJUGATED MIRROR IMAGES 4HE .YQUIST RATE IS THE SIGNALS TWO SIDED BANDWIDTH IRRESPECTIVE OF THE PARTICULAR PORTION OF THE SPECTRUM IN WHICH THE SIGNAL RESIDES 4HEREFORE FOR THIS SIGNAL THE .YQUIST FREQUENCY IS " EVEN THOUGH THE SIGNAL CONTAINS COMPONENTS AT ACTUAL FREQUENCIES GREATER THAN " &IGURE B SHOWS THE RESULT OF SAMPLING THIS SIGNAL AT
&)'52% A "ANDLIMITED REAL PASSBAND SIGNAL SPECTRUM BEFORE SAMPLING AND B SIGNAL SPECTRUM AFTER SAMPLING
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&)'52% A .ON REAL SIGNAL SPECTRUM BEFORE SAMPLING BY .YQUIST FREQUENCY " AND B SIGNAL SPECTRUM AFTER SAMPLING
THE .YQUIST BOUND 4HE SAMPLED SPECTRA OF THE TWO PORTIONS OF THE SIGNAL DO NOT OVER LAP THE SAMPLED SIGNAL IS NOT ALIASED !S WILL BE DESCRIBED IN MORE DETAIL LATER IN THE CHAPTER THIS TECHNIQUE BANDPASS SAMPLING IS A POWERFUL TOOL THAT ALLOWS A RELATIVELY HIGH FREQUENCY SIGNAL TO BE SAMPLED BY A RELATIVELY LOW PERFORMANCE DIGITIZER WHICH CAN RESULT IN CONSIDERABLE COST SAVINGS &IGURE A SHOWS THE SPECTRUM OF A MORE GENERAL COMPLEX SIGNAL OF BANDWIDTH " BEFORE SAMPLING .OTE THAT THIS SIGNAL DOES NOT POSSESS COMPLEX CONJUGATE SPECTRAL SYMMETRY 4HE SIGNAL SPECTRUM AFTER SAMPLING BY ITS .YQUIST FREQUENCY " IS SHOWN IN &IGURE B 4HERE IS NO ALIASING 4HE .YQUIST RATE IS A MINIMUM SAMPLING FREQUENCY FOR A SIGNAL A BOUND AND MEETING THE BOUND IS NECESSARY BUT NOT SUFFICIENT TO ENSURE THAT NO ALIASING OCCURS #ONSIDER THE CASE PRESENTED IN &IGURE A WHICH IS THE SAME BANDLIMITED BANDPASS SIGNAL SHOWN IN &IGURE BUT SHIFTED IN FREQUENCY SO THAT IT DOESNT BEGIN EXACTLY AT " 4HE SAMPLED SIGNAL SPECTRUM IN &IGURE B SHOWS THAT ALTHOUGH THE SAMPLING RATE SATISFIES THE .YQUIST BOUND THE SAMPLED SIGNAL IS STILL ALIASED 4O SOLVE THIS PROB LEM THE SIGNAL COULD BE MOVED TO A DIFFERENT CENTER FREQUENCY BEFORE SAMPLING OR THE SAMPLING RATE COULD BE INCREASED 4HE SYSTEM DESIGNER MUST ALWAYS DEVELOP THE FREQUENCY PLAN OF A SAMPLING SYSTEM CAREFULLY TO DETERMINE AN APPROPRIATE SAMPLING FREQUENCY AND TO ENSURE THAT ALIASING DOES NOT OCCUR ! FULL TREATMENT OF THIS SUBJECT IS PRESENTED BY ,YONS )N AN ACTUAL SYSTEM BEFORE SAMPLING THE SIGNAL IS TYPICALLY PASSED THROUGH AN ANTI ALIASING FILTER WHICH IS AN ANALOG LOWPASS OR BANDPASS FILTER THAT PLACES AN UPPER LIMIT ON THE SIGNAL BANDWIDTH 4HE FILTER NEEDS TO PROVIDE ENOUGH STOPBAND REJECTION THAT ANY ALIASED COMPONENTS ARE INSIGNIFICANT /F COURSE PRACTICAL FILTERS DO NOT HAVE
&)'52% A "ANDLIMITED REAL PASSBAND SIGNAL SPECTRUM BEFORE SAMPLING AND B SIGNAL SPECTRUM AFTER SAMPLING
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PASSBANDS EXTENDING RIGHT UP TO THEIR STOPBAND EDGES SO THE WIDTHS OF INTERVENING TRANSITION BANDS MUST BE COUNTED AS PART OF TWO SIDED SIGNAL BANDWIDTH " FOR PURPOSES OF DETERMINING THE .YQUIST RATE AS THE FILTER OUTPUT MAY CONTAIN COMPONENTS IN THESE TRANSITIONS BANDS THAT COULD OTHERWISE RESULT IN SIGNIFICANT ALIASING $IGITAL $OWNCONVERSION $$# 4HE APPLICATION OF DIGITAL TECHNOLOGY TO )1 DEMODULATION WHICH IS JUST DOWNCONVERSION OF AN )& SIGNAL TO A COMPLEX BASEBAND HAS GREATLY IMPROVED THE PERFORMANCE OF COHERENT SYSTEMS (ERE WE EXPLORE TWO FORMS OF SUCH DIGITAL DOWNCONVERSION A GENERAL FORM THAT IS STRUCTURALLY PARALLEL TO TRADITIONAL ANALOG DOWNCONVERSION AND A RESTRICTED FORM DIRECT DIGITAL DOWNCONVER SION WHICH IS MORE ECONOMICAL WHEN IT IS APPLICABLE !NALOG $OWNCONVERSION AND 3AMPLING 4HE GENERAL APPROACH TO DIGITAL DOWN CONVERSION DERIVES FROM ANALOG DOWNCONVERSION AND SAMPLING AS ILLUSTRATED IN THE FREQUENCY DOMAIN IN &IGURE 4HE SPECTRA ON THE FIRST AND LINES REPRESENT SIGNALS AT VARIOUS POINTS IN THE SYSTEM AND THE SPECTRA ON THE AND r LINES RESPECTIVELY REP RESENT SPECTRAL CONVOLUTION AND POINT BY POINT SPECTRAL MULTIPLICATION OPERATIONS THAT RELATE THOSE SIGNALS 4HE FIRST LINE IN THE FIGURE DEPICTS SCHEMATICALLY A REAL )& SIGNAL WITH ONE AND TWO SIDED BANDWIDTHS OF -(Z AND -(Z RESPECTIVELY AND WITH POSITIVE AND NEGATIVE FREQUENCY COMPONENTS RESPECTIVELY CENTERED AT -(Z AND -(Z 4HE SECOND LINE OF &IGURE SHIFTS THE )& SIGNAL BY ,/ FREQUENCY -(Z USING SPEC TRAL CONVOLUTION 7ELL SEE SHORTLY HOW THIS IS DONE IN HARDWARE 4HE RESULT ON THE THIRD LINE HAS SPECTRAL COMPONENTS CENTERED AT -(Z AND -(Z -ULTIPLICATION BY THE LOWPASS FILTER FREQUENCY RESPONSE IN LINE THEN REMOVES THE LATTER COMPONENT LEAVING ONLY THE COMPLEX BASEBAND SIGNAL OF LINE WHICH HAS A TWO SIDED BANDWIDTH AND A .YQUIST FREQUENCY OF -(Z 4HE SPECTRAL CONVOLUTION ON LINE CORRESPONDS
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TO TIME DOMAIN MULTIPLICATION OF A UNIFORM IMPULSE TRAIN AT THE -(Z SAMPLING FREQUENCY WITH THE SIGNAL REPRESENTED BY LINE )N THE TIME DOMAIN THE RESULT IS A -(Z TRAIN OF SAMPLING IMPULSES WITH AREAS THAT ARE GIVE OR TAKE A SCALE FACTOR THAT WE ARE IGNORING SAMPLES OF THE LINE SIGNAL AT THE SAMPLING INSTANTS /F COURSE WE WILL NOT CREATE THE LINE IMPULSES IN HARDWARE BUT WILL INSTEAD REALIZE THE IMPULSE AREAS DIGITALLY AS NUMBERS IN REGISTERS ! BLOCK DIAGRAM SHOWING HOW THIS PROCESS MIGHT BE IMPLEMENTED IN HARDWARE IS SHOWN IN &IGURE 4HE )& SIGNAL IS SENT TO TWO MIXERS )N ONE MIXER THE )& SIGNAL IS BEAT WITH THE -(Z ,/ WITH COSINE PHASING AND IN THE OTHER MIXER THE )& IS BEAT WITH THE SAME ,/ BUT WITH NEGATIVE SINE PHASING SO THAT THE MIXERS ARE OPERATED IN QUADRATURE O APART 4HE MIXER OUTPUTS TAKEN TOGETHER AS A COMPLEX PAIR FORM A COMPLEX SIGNAL WITH THE SPECTRUM SHOWN IN LINE OF THE PREVIOUS FIGURE 4HESE SIG NALS ARE THEN PASSED THROUGH LOWPASS FILTERS ,0& TO REMOVE THE SPECTRAL COMPONENT CENTERED AT -(Z THAT WOULD OTHERWISE HAVE RESULTED IN ALIASING IN THE SAMPLING STEP TO FOLLOW ,ABELS ) IN PHASE AND 1 QUADRATURE ARE TRADITIONALLY USED TO INDICATE THE REAL AND IMAGINARY PARTS OF COMPLEX TIME DOMAIN SIGNALS LIKE THOSE HERE THAT ARE REALIZED AS PAIRS OF REAL SIGNALS 7HEN A VERTICAL CUT THROUGH A DIAGRAM SUCH AS IN &IGURE PICKS UP ONE ) SIGNAL AND ONE 1 SIGNAL THE REPRESENTED COMPLEX SIGNAL CROSSING THAT CUT IS ) J1 )N THE DIAGRAM CUTS JUST BEFORE AND AFTER THE ,0& BLOCKS PICK UP COMPLEX SIGNALS WITH THE SPECTRA SHOWN ON LINES AND OF &IGURE RESPECTIVELY 4HE LINE SIGNAL IS CREATED IN THE TIME DOMAIN AS ;LINE = ;LINE = E JO F,/T
;LINE = COSO F,/T nJ;LINE = SINO F,/T
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&)'52% 4YPICAL ANALOG DOWNCONVERSION TO BASEBAND AND DIGITIZER
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WHERE F,/ -(Z 3IMILARLY USING FOR TIME DOMAIN CONVOLUTION FILTERING WITH AN IMPULSE RESPONSE
;LINE = ;LINE = HT ;) J1= HT ) HT J1 HT ) J1
7HEN THE FILTER OUTPUTS ARE VIEWED AS COMPLEX SIGNAL ;LINE = ) J1 !EJP THE COMPLEX MAGNITUDE ! AND ANGLE P GIVE THE AMPLITUDE GIVE OR TAKE A SCALE FACTOR AND PHASE OF THE )& SIGNAL BECAUSE THE ORIGINAL )& SIGNAL COULD BE RE CREATED FROM THE LINE SIGNAL IN THE TIME DOMAIN AGAIN GIVE OR TAKE A SCALE FACTOR AS ;LINE = 2E[;LINE = EJO F,/T] FROM WHICH IT FOLLOWS THAT ;LINE = 2E[! EJP E JO F,/T] ! 2E[EJO F,/T P ] ! COSO F,/T P !S A FINAL STEP THE BASEBAND ) AND 1 SIGNALS AFTER THE FILTERS ARE DIGITIZED BY !$#S AT A -(Z SAMPLING RATE PRODUCING ) AND 1 OUTPUT SAMPLES OR EQUIVALENTLY COMPLEX OUTPUT SAMPLES ) J1 4HE SLASH THROUGH THE OUTPUT OF THE !$# WITH A hv ABOVE IT IN &IGURE INDI CATES THAT OUR !$# PRODUCES BITS OF DIGITAL OUTPUT !$#S PROVIDE APPROXIMATELY D" OF DYNAMIC RANGE PER BIT SO OUR BIT !$# PROVIDES ABOUT D" OF DYNAMIC RANGE ASSUMING !$# NONLINEARITIES ARE NEGLIGIBLE ! 'ENERAL !PPROACH TO $IGITAL $OWNCONVERSION )N DIGITAL DOWNCONVERSION THE ANALOG )& SIGNAL IS FIRST SAMPLED BY AN !$# AND ALL OF THE SUBSEQUENT PROCESSING IS THEN DONE DIGITALLY &IGURE DEPICTS THE DIGITAL DOWNCONVERSION PROCESS FOR OUR PREVIOUS EXAMPLE AGAIN IN THE FREQUENCY DOMAIN 4HE TOP LINE SCHEMATICALLY REPRE SENTS THE REAL )& SIGNAL WITH PARAMETERS AS BEFORE 0ERFORMING THE SAMPLING ANALYSIS DESCRIBED PREVIOUSLY WE DISCOVER THAT SETTING THE SAMPLE RATE TO THE TWO SIDED SIGNAL BANDWIDTH OF -(Z WOULD PRODUCE ALIASING (OWEVER A -(Z SAMPLE RATE DOES NOT CAUSE ALIASING AND IS USED ON THE SECOND LINE OF THE FIGURE 3AMPLING THE INPUT SIGNAL AT -(Z REPLICATES THE SIGNAL SPECTRUM AT -(Z INTERVALS AS SHOWN ON LINE &REQUENCY SHIFTING IS ACCOMPLISHED BY SPECTRALLY CONVOLVING THIS SIGNAL WITH THE COMPLEX n -(Z ,/ TONE SHOWN IN LINE PRODUCING THE FREQUENCY SHIFTED SIG NAL ON LINE 4HE LATTER SIGNAL IS SPECTRALLY MULTIPLIED BY THE FILTER RESPONSE SHOWN ON LINE TO REMOVE THE COPIES OF THE NEGATIVE FREQUENCY SIGNAL COMPONENT PRODUCING THE COMPLEX BASEBAND SIGNAL SHOWN ON LINE 4HIS SIGNAL WHICH NOW HAS A TWO SIDED BANDWIDTH AND .YQUIST FREQUENCY OF -(Z IS SPECTRALLY CONVOLVED IN LINE WITH IMPULSES AT THE SPECTRAL ORIGIN AND AT -(Z TO EFFECTIVELY DECIMATE THE SIGNAL BY A FACTOR OF TWO 4HE FINAL BASEBAND SIGNAL ON LINE HAS A SAMPLE RATE OF -(Z &IGURE DEPICTS THE HARDWARE IMPLEMENTATION OF THIS $$# ARCHITECTURE 4HE )& SIGNAL CENTERED AT -(Z IS DIGITIZED DIRECTLY BY AN !$# !FTER THE !$# THE ARCHITECTURE IS VERY SIMILAR TO ANALOG DOWNCONVERSION EXCEPT THAT THE PROCESSING IS PERFORMED DIGITALLY )N OUR EXAMPLE WE ELECT TO SAMPLE THE )& SIGNAL AT A RATE OF -(Z WITH A BIT !$# 4HIS ARCHITECTURE REALIZES THE ,/ WITH A NUMERICALLY CONTROLLED OSCILLATOR .#/ THAT GENERATES DIGITAL WORDS TO REPRESENT THE COSINE AND NEGATIVE SINE SIGNALS AT THE ,/ FREQUENCY HERE -(Z AND SAMPLED AT THE !$#
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SAMPLE RATE 4HE SINE AND COSINE SIGNALS FROM THE .#/ ARE THEN DIGITALLY MULTIPLIED BY THE DIGITIZED )& SIGNAL )N THIS PARTICULAR EXAMPLE THE RELATIONSHIP BETWEEN THE ,/ FREQUENCY AND THE SAMPLING RATE WILL MAKE THE REQUIRED .#/ AND THE MULTIPLIERS BOTH RATHER TRIVIAL BECAUSE EACH REQUIRED .#/ OUTPUT VALUE IS ZERO OR o AND THAT SPECIAL CASE WILL BE ADDRESSED SHORTLY &OR NOW THIS ARCHITECTURE SUPPOSES THAT NO SUCH SPECIAL SITUATION EXISTS AND THAT A GENERAL .#/MULTIPLIER STRUCTURE IS NEEDED 4HE DESIGN OF
&)'52% $IGITAL DOWNCONVERSION ARCHITECTURE
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A GENERAL .#/ WILL BE IN 3ECTION &OLLOWING THE MULTIPLICATIONS DIGITAL LOWPASS FILTERS PREVENT ALIASING WHEN THEIR OUTPUTS ARE DECIMATED BY A FACTOR OF TWO TO PRODUCE COMPLEX OUTPUT SAMPLES AT A -(Z RATE )N THE FIGURE -#303 STANDS FOR MILLION COMPLEX SAMPLES PER SECOND 4HE LOWPASS FILTER ALSO REDUCES OUT OF BAND NOISE AND THUS INCREASES SIGNAL TO NOISE RATIO 3.2 )N ORDER TO PRESERVE THIS 3.2 GROWTH THE NUMBER OF BITS USED TO REPRESENT THE FILTER OUTPUT MIGHT NEED TO INCREASE )F THE FILTER REDUCES THE BAND WIDTH OF THE DATA BY A FACTOR 2 WITHOUT AFFECTING THE SIGNAL OF INTEREST THEN THE 3.2 INCREASE IN D" IS GIVEN BY LOG2 )N OUR EXAMPLE A ¾ REDUCTION IN BANDWIDTH RESULTS IN APPROXIMATELY A D" INCREASE IN 3.2 7ITH EACH BIT REPRESENTING ABOUT D" OF 3.2 THE MINIMUM NUMBER OF BITS REQUIRED TO REPRESENT THE FILTERED SIGNAL COULD GROW FROM TO )N AN ACTUAL APPLICATION THE SYSTEM DESIGNER NEEDS TO ANALYZE THE EFFECTS OF SAM PLING AND DIGITAL PROCESSING AND DETERMINE HOW MANY BITS NEED TO BE CARRIED THROUGH THE CALCULATIONS IN ORDER TO PRESERVE 3.2 AND PREVENT OVERFLOW #ONSIDERATIONS INCLUDE FRONT END SYSTEM NOISE WHICH IS TYPICALLY ALLOWED TO TOGGLE TWO OR MORE BITS FOUR OR MORE QUANTIZATION LEVELS OF THE !$# OUTPUT !LSO AN ACTUAL . BIT !$# NEVER PROVIDES EXACTLY . D" OF 3.2 DUE TO !$# INDUCED ERRORS &OR EXAMPLE A TYPICAL BIT !$# GENERALLY PROVIDES ABOUT BITS OR ABOUT D" OF 3.2 #ARRYING BITS THROUGH THE SIGNAL PROCESSING PROVIDES ABOUT D" OF DYNAMIC RANGE )N THIS CASE THE DESIGNER MAY ELECT TO ALLOW THE DATAPATH THROUGH THE LOWPASS FILTER TO REMAIN AT BITS REALIZING THAT THE FILTERING PROCESS HAS SIMPLY INCREASED THE 3.2 OF THE SIGNAL TO D" WHICH COULD STILL BE ACCOMMODATED BY THE BIT DATAPATH ! $$# PROVIDES SEVERAL BENEFITS COMPARED TO ANALOG DOWNCONVERSION 4HE ANA LOG APPROACH IS SUBJECT TO VARIOUS HARDWARE ERRORS INCLUDING MISMATCH OF THE MIX ERS ,/ SIGNALS NOT EXACTLY O APART AND MISMATCHES IN THE GAINS $# OFFSETS OR FREQUENCY RESPONSES OF THE ) AND 1 SIGNAL PATHS ! $$# AVOIDS THESE PROBLEMS THOUGH IT IS VULNERABLE TO THE PHASE NOISE OF THE !$# SAMPLE CLOCK !$# NONLIN EARITIES AND ARITHMETIC ROUND OFF NOISE 2EALIZING MAXIMUM PERFORMANCE REQUIRES CAREFUL ATTENTION TO DESIGN DETAILS $IRECT $IGITAL $OWNCONVERSION )F THE DESIGNER HAS SOME FLEXIBILITY IN EITHER THE )& CENTER FREQUENCY OR !$# SAMPLE RATE A SIMPLIFIED $$# ARCHITECTURE DIRECT DIGITAL DOWNCONVERSION CAN BE CONSIDERED )F THE !$# SAMPLE RATE IS FOUR TIMES THE CENTER OF THE )& BAND THEN THE SAMPLING PROCESS CAN ALSO SHIFT THE SPECTRUM TO BASEBAND AND THE .#/ AND ASSOCIATED MULTIPLIERS OF THE GENERAL $$# ARE NOT NEEDED )N GENERAL DIRECT CONVERSION TO BASEBAND IS A SIMPLE AND COST EFFECTIVE $$# METHOD THAT CAN BE USED WHEN THE SIGNAL BEING SAMPLED IS ALWAYS CENTERED AT A SINGLE FREQUENCY 4HE STANDARD $$# ARCHITECTURE MIGHT NEED TO BE USED WHEN THE CENTER FREQUENCY OF THE SIGNAL BEING SAMPLED DYNAMICALLY CHANGES WHICH FORCES THE $$#S ,/ TO CHANGE ACCORDINGLY ,ETS LOOK AT THE DIRECT $$# IN THE TIME DOMAIN FIRST FOR INTUITION AND THEN WE CAN CAREFULLY DERIVE THE ARCHITECTURE IN THE FREQUENCY DOMAIN 3UPPOSE THE $$# ARCHI TECTURE IS AS SKETCHED IN &IGURE WITH AN )& CENTERED AT -(Z AND A -(Z ,/ AND SUPPOSE THE .#/ IS SET TO -(Z SO THAT IT PRODUCES THE SAMPLED SINES AND COSINES SHOWN IN &IGURE A WHERE VERTICAL LINES AND DOTS INDICATE SAMPLE TIMES AND VALUES RESPECTIVELY "ECAUSE THE SAMPLE RATE IS FOUR TIMES THE ,/ FREQUENCY THE COS SIN ,/ SAMPLE PAIRS CYCLE REPEATEDLY THROUGH n n AND .EXT SUPPOSE THE )& SIGNAL IS A -(Z SINUSOID OF ARBITRARY PHASE AS IN LINE B 4HE $$#S MIXER OUTPUTS ) AND 1 THE PRODUCTS OF THE LINE B )& SIGNAL WITH THE TWO
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&)'52% 6ARIOUS SIGNALS SAMPLED AT -(Z A -(Z COSINE AND nSINE ,/ SIGNALS B -(Z )& TONE AND C RESULT OF MULTIPLYING A SAMPLES BY B SAMPLES
LINE A ,/ SIGNALS ARE THEN AS IN LINE C "ECAUSE OUR HYPOTHETICAL )& SIGNAL ON LINE B WAS EXACTLY AT ONE QUARTER OF THE SAMPLE RATE BOTH ) AND 1 ARE CONSTANTS THE SINE AND COSINE OF THE )& SIGNALS PHASE ANGLE &IGURE SHOWS THE SAME -(Z )& TONE BUT SAMPLED AT -(Z AND -(Z WHICH ARE ODD INTEGER SUBMULTIPLES AND OF THE ORIGINAL SAMPLE RATE OF ¾ THE )& CENTER FREQUENCY -(Z .OTE THAT ODD SAMPLES STILL CYCLE BETWEEN ) AND ) AND THE EVEN SAMPLES SWITCH BETWEEN 1 AND 1 /DD INTEGER SUBMULTIPLES OF ¾ THE )& CENTER FREQUENCY CAN THEREFORE BE VIABLE ALTERNATIVE SAMPLE RATES ! .YQUIST BOUND APPLIES AND REQUIRES THE TWO SIDED )& BANDWIDTH TO BE LESS THAN THE SAMPLING RATE .OW LETS DERIVE THE DIRECT $$# ARCHITECTURE CAREFULLY IN THE FREQUENCY DOMAIN 3UPPOSE A REAL )& SIGNAL IS ONCE AGAIN CENTERED AT -(Z AND SAMPLED AT -(Z AS IN LINE A OF &IGURE 4HE FIRST THREE LINES OF &IGURE ILLUSTRATE THIS IN THE FREQUENCY DOMAIN WITH LINE SHOWING THE SAMPLED )& SIGNAL 4HE BANDPASS FILTER RESPONSE ON LINE REMOVES THE UNWANTED SPECTRAL COMPONENTS TO PRODUCE THE COMPLEX PASSBAND SIGNAL OF LINE 4HIS SIGNAL IS THEN DECIMATED BY AND SHIFTED BY n -(Z TO PRODUCE AT A -(Z SAMPLING RATE THE DESIRED COMPLEX BASEBAND SIGNAL SHOWN ON LINE &IGURE SHOWS THE CORRESPONDING BLOCK DIAGRAM 4HE MAGNITUDE OF THE FRE QUENCY RESPONSE ON LINE OF &IGURE IS NEITHER AN EVEN NOR AN ODD FUNCTION SO THE CORRESPONDING IMPULSE RESPONSE IS NEITHER PURELY REAL NOR PURELY IMAGINARY
&)'52% -(Z TONE SAMPLED AT A -(Z r )& AND B -(Z r )&
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7RITING THAT IMPULSE RESPONSE AS HN H)N JH1N USING REAL FUNCTIONS H)N AND H1N THE LINE OPERATION BECOMES
;LINE = ;LINE = HN
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&)'52% 4IME DOMAIN IMPLEMENTATION OF A DIRECT DIGITAL DOWNCONVERTER
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&)'52% A (ALFBAND BANDPASS FILTER COEFFICIENTS FOR A DIRECT DIGITAL DOWNCONVERTER B REAL ODD AND C IMAGINARY EVEN PARTS OF THE COMPLEX IMPULSE RESPONSE
&)2 FILTERS ARE DESCRIBED IN 3ECTION WHERE THE TOP AND BOTTOM FILTERS APPLY THE REAL AND IMAGINARY PARTS OF THE COEFFICIENTS RESPECTIVELY 4HE EQUIVALENT COMPLEX IMPULSE RESPONSE FILTER WITH THE FREQUENCY RESPONSE SHOWN IN LINE OF &IGURE IS A HALFBAND FILTER BECAUSE THAT FREQUENCY RESPONSE AND A VERSION SHIFTED IN FREQUENCY BY HALF A PERIOD SUM TO A CONSTANT 4HIS PROPERTY CAUSES ALMOST HALF OF ITS IMPULSE RESPONSE COEFFICIENTS TO BE ZERO &IGURE A ILLUSTRATES THE COEFFICIENTS OF A TYPICAL FILTER FOR THIS APPLICATION !LL OF THE ODD NUMBERED COEFFICIENTS EXCEPT FOR THE ONE IN THE CENTER ARE ZERO SO THE FILTER IS VERY EFFICIENT TO IMPLEMENT AS THE ZERO COEFFI CIENTS DONT REQUIRE MULTIPLIERS 4HE FREQUENCY RESPONSES SYMMETRY ABOUT OF THE SAMPLING RATE CAUSES THE EVEN AND ODD NUMBERED COEFFICIENTS TO BE PURELY REAL AND PURELY IMAGINARY RESPECTIVELY SO THE EVEN AND ODD NUMBERED COEFFICIENTS ARE USED TO RESPECTIVELY CREATE ) AND 1 AS SHOWN IN &IGURE B AND C !FTER THE FILTERS THE COMPLEX SIGNAL IS DECIMATED BY TO PRODUCE A -(Z OUTPUT SAMPLE RATE 4HE FINAL SPECTRAL CONVOLUTION BY A n -(Z TONE IS ACCOMPLISHED BY NEGATING EVERY OTHER SAMPLE )N &IGURE WE TRANSFORM THE SYSTEM OF &IGURE TO MAKE IT MORE COMPUTA TIONALLY EFFICIENT 7E BEGIN WITH THE STRUCTURE IN &IGURE A WHICH SHOWS THE FILTERING IN DETAIL USING S TO INDICATE EACH CLOCK INTERVAL DELAY 4HE LOCATION OF THE ONE NONZERO COEFFICIENT IN THE REAL PART H)N OF THE &IGURE IMPULSE RESPONSE CORRESPONDS TO AN ODD NUMBERED DELAY SO H)N IS REALIZED USING A SINGLE DELAY AND SOME NUMBER OF DOUBLE DELAYS 4HE IMAGINARY PART H1N OF THE IMPULSE RESPONSE IN CONTRAST HAS NONZERO COEF FICIENTS ONLY AT EVEN NUMBERS OF DELAYS SO IT IS REALIZED WITH DOUBLE DELAYS ONLY 4HE ARCHITECTURE CAN THEN BE FURTHER SIMPLIFIED BY MOVING THE DECIMATION AHEAD OF THE S DELAYS AS SHOWN IN &IGURE B 4HIS CHANGES EACH DOUBLE DELAY TO A SINGLE DELAY AT THE LOWER CLOCK RATE AT WHICH THE FILTER COMPUTATIONS ARE NOW MORE EFFICIENTLY CLOCKED /PTIONALLY THE NEGATION OF ALTERNATE SAMPLES AT THE OUTPUT CAN NOW BE RELO CATED TO THE DECIMATIONS OUTPUT %ACH DELAY THAT THE NEGATION CROSSES AS IT MOVES IN THIS TRANSFORMATION CAUSES A NET SIGN CHANGE IN THE SIGNAL SO EACH SIGNAL PATH BETWEEN THE OLD LOCATION AND THE NEW THAT CONTAINS ODD NUMBERS OF DELAYS REQUIRES COEFFICIENT NEGATION TO COMPENSATE 4HE RESULT IN THE DESIGN OF &IGURE C IS NEGATION OF ALTER NATE COEFFICIENTS IN THE 1 FILTER AS SHOWN IN &IGURE C 4HE OPTIONAL NEGATION MOVING TRANSFORMATION JUST DESCRIBED YIELDS A SIMPLE INTER PRETATION OF SYSTEM OPERATION &IGURE SHOWS THAT THE LEADING S DELAY DECIMA TION AND SIGN NEGATION OPERATIONS OF &IGURE C WORK TOGETHER TO STEER ) AND 1 SAMPLES INTO THE UPPER AND LOWER FILTER PATHS RESPECTIVELY BUT THE SAMPLES THAT ARE
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&)'52% $IRECT DIGITAL DOWNCONVERTER A BASELINE IMPLEMENTATION B DECIMATING BEFORE FILTERS AND C INVERTING EVERY OTHER SAMPLE AFTER DECIMATION
NOW ALIGNED IN TIME AS THEY PASS THROUGH THE REMAINING PROCESSING DO NOT ACTUALLY COR RESPOND TO THE SAME POINTS ON THE )& SIGNAL INPUTS TIME LINE SINCE THE ) AND 1 SAMPLES WERE DERIVED FROM ALTERNATE !$# SAMPLES (OWEVER THE 1 FILTER WITH ALTERNATE COEF FICIENTS NEGATED SHOWN IN &IGURE ACTUALLY APPROXIMATES THE HALF SAMPLE DELAY
&)'52% .EGATED ALTERNATE SIGNS VERSION OF 1 FILTER COEFFICIENTS
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REQUIRED TO REALIGN THE DATA IN THE TWO PATHS AND THIS CAUSES THE ) AND 1 OUTPUT VALUES TO BE EFFECTIVELY SAMPLED AT THE SAME INSTANTS 3IGNAL 3AMPLING #ONSIDERATIONS !CTUAL DEVICES AND SIGNALS INTRODUCE ERRORS &OR EXAMPLE CLOCK JITTER RESULTS IN ERRORS IN THE SAMPLED OUTPUT OF AN !$# AS SHOWN IN &IGURE )N ADDITION REAL !$#S ALSO ADD INTERNAL JITTER OR APERTURE UNCERTAINTY WHICH MUST BE TAKEN INTO ACCOUNT )F THE ERRORS IN THE EFFECTIVE SAMPLING INSTANT INTRO DUCED BY THESE JITTERS ARE UNCORRELATED A REASONABLE APPROXIMATION THE 2-3 SAMPLE TIME JITTER THEY INTRODUCE T* IS T * §©T * !$# T * #,/#+ ¶¸
WHERE T*!$# AND T*#,/#+ ARE THE 2-3 SAMPLE TIME JITTERS INTRODUCED BY THE !$# AND THE CLOCK RESPECTIVELY ! SINUSOIDAL INPUT SIGNAL OF AMPLITUDE ! AND FREQUENCY F IS EXPRESSED AS
VT !SINO FT
WHICH HAS DERIVATIVE
DVT DT !O FCOSO FT
4HE MAXIMUM ERROR DUE TO JITTER OCCURS AT T WHEN THE DERIVATIVE OF THE SIGNAL IS AT ITS PEAK OR
DV DT !O F 4HE 2-3 ERROR VOLTAGE 6E PRODUCED BY AN 2-3 SAMPLE TIME JITTER T* IS GIVEN BY 6E !O F T*
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4HIS ERROR VOLTAGE LIMITS THE THEORETICAL MAXIMUM 3.2 OF AN !$# BY 3.2MAX LOG!6E nLOG;O F T*=
4HIS RELATIONSHIP IS PRESENTED IN &IGURE WHICH PLOTS ON THE LEFT AND RIGHT AXES RESPECTIVELY THE 3.2 AND THE EQUIVALENT !$# EFFECTIVE NUMBER OF BITS OR %./" y 3.2 D" BOTH VERSUS ANALOG FREQUENCY AND FOR DIFFERENT VALUES OF 2-3 SAMPLE JITTER $UE TO A VARIETY OF ERROR SOURCES INTERNAL TO AN !$# APERTURE UNCERTAINTY NON LINEARITIES ADDED NOISE ETC THE SPECIFIED %./" OF AN !$# IS ALWAYS LESS THAN THE NUMBER OF BITS IT PROVIDES &OR EXAMPLE A BIT !$# TYPICALLY HAS AN %./" OF 7ITH THE BANDPASS SAMPLING TECHNIQUE DESCRIBED EARLIER WHERE THE !$# CAN SAM PLE AT A RATE THAT IS CONSIDERABLY LOWER THAN THE ANALOG FREQUENCIES BEING SAMPLED IT MIGHT SEEM ATTRACTIVE TO DO AWAY WITH THE RECEIVER ALTOGETHER AND SAMPLE THE 2& SIGNAL DIRECTLY !LTHOUGH THIS IS POSSIBLE !$# LIMITATIONS RESTRICT THE PERFORMANCE OF SUCH ARCHITECTURES &IRST THE ANALOG FRONT END OF AN !$# HAS A LOWPASS D" CUTOFF FREQUENCY SPECIFIED BY THE MANUFACTURER !$# INPUT FREQUENCIES SHOULD BE KEPT WELL BELOW THIS CUTOFF 3ECOND AS SHOWN PREVIOUSLY IN &IGURE SAMPLING THE 2& SIGNAL DIRECTLY WILL DRAMATICALLY INCREASE THE SLEW RATE OF THE SIGNAL PRESENTED TO THE !$# THUS REQUIRING VERY LOW LEVELS OF 2-3 CLOCK JITTER !LSO THE !$# HAS INHERENT NONLINEARITIES THAT PRODUCE SPURS IN THE !$# OUTPUT A PROBLEM WHICH TYPICALLY WORS ENS WITH INCREASING INPUT FREQUENCY !$# DATASHEETS SPECIFY THE SPUR FREE DYNAMIC RANGE 3&$2 OF THE DEVICE WHICH IS TYPICALLY DEFINED AS THE D" DIFFERENCE IN SIGNAL LEVEL BETWEEN THE DESIRED SIGNAL AND THE LARGEST SPUR MEASURED AT THE !$# OUTPUT WITH A SINGLE TONE APPLIED TO THE INPUT 4HE 3&$2 OF A TYPICAL !$# IS HIGHER THAN ITS SPECIFIED 3.2 5NFORTUNATELY THERE ARE MANY DEFINITIONS OF 3&$2 SO THE DESIGNER IS ADVISED TO READ MANUFACTURERS DATASHEETS CAREFULLY IN THIS REGARD !S MENTIONED EARLIER THE 3.2 OF A SAMPLED SIGNAL CAN BE INCREASED BY FILTERING TO ELIMINATE NOISE IN PARTS OF THE SPECTRUM THAT ARE OTHERWISE UNUSED (OWEVER THE SPURS GENERATED BY AN !$# MAY LIE IN THE BAND OF INTEREST WHERE FILTERING WOULD BE INAPPROPRIATE 4HEREFORE SPURS LOWER THAN THE UNFILTERED NOISE LEVEL CAN BECOME RELATIVELY SIGNIFI CANT AFTER !$# NOISE IS REDUCED THROUGH FILTERING (% &' (%&'
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-ULTI "EAM $IGITAL "EAMFORMING !N IMPORTANT APPLICATION OF DIGITAL TECHNOL OGY IS FOR THE BEAMFORMING FUNCTION IN A PHASED ARRAY ANTENNA SYSTEM &IGURE A DEPICTS AN ANALOG BEAMFORMING SYSTEM 4HE WAVEFRONT SHOWN CAN BE THOUGHT OF AS THE RETURN FROM A TARGET OF INTEREST .OTE THAT THE WAVEFRONT WILL HIT EACH ELEMENT OF THE ARRAY AT DIFFERENT TIMES )N ORDER TO FORM A BEAM IN THAT PARTICULAR DIRECTION EACH ELEMENT OF THE ARRAY NEEDS TO BE FOLLOWED BY A TIME DELAY UNIT THAT DELAYS THE SIGNAL RECEIVED AT EACH ELEMENT BY THE APPROPRIATE AMOUNT SUCH THAT WHEN ALL OF THE OUTPUTS OF THE TIME DELAYS ARE SUMMED THEY ADD UP COHERENTLY TO FORM A BEAM IN THE DESIRED DIRECTION )F THE SYSTEM HAS A NARROW BANDWIDTH BANDWIDTH ^ OF 2& FREQUENCY AND THE ANTENNA BEAMWIDTH IS NOT TOO NARROW SO THAT THE D" BEAMWIDTH IN DEGREES IS GREATER THAN THE PERCENT BANDWIDTH THE TIME DELAY CAN BE APPROXIMATED USING PHASE SHIFTERS 7IDE BANDWIDTH SYSTEMS REQUIRE hTRUEv TIME DELAYS IN ORDER TO FORM THE BEAMS AND PRESERVE THE BANDWIDTH 4HE RECEIVER WOULD FOLLOW THE ANALOG BEAMFORMER AS SHOWN IN THE FIGURE &IGURE B SHOWS AN EXTREME APPLICATION OF DIGITAL BEAMFORMING WHERE
&)'52% A !NALOG BEAMFORMER B EVERY ELEMENT DIGITAL BEAMFORMER AND C SUBARRAY DIGITAL BEAMFORMER
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A RECEIVER AND !$# ARE BEHIND EVERY ELEMENT )N THIS SYSTEM THE TIME DELAY IS IMPLE MENTED EITHER AS A DIGITAL PHASE SHIFT OR DIGITAL TIME DELAY FOLLOWED BY A DIGITAL SUMMER 4HIS CONFIGURATION ALLOWS BEAMS TO BE FORMED IN ANY DIRECTION AND MULTIPLE BEAMS CAN BE FORMED SIMULTANEOUSLY IF DESIRED BY USING THE SAME SAMPLE DATA AND IMPLEMENTING DIFFERENT TIME DELAYS TO FORM THE DIFFERENT BEAMS (OWEVER AT THIS WRITING PUTTING A DIGITAL RECEIVER BEHIND EVERY ELEMENT IS EXPENSIVE AND IS USUALLY NOT FEASIBLE FOR MOST LARGE ANTENNA APPLICATIONS IE FOR SYSTEMS WITH THOUSANDS OF ELEMENTS /NE COMPRO MISE SOLUTION IS SHOWN IN &IGURE C WHERE ANALOG BEAMFORMING IS USED TO IMPLE MENT SUBARRAYS WHICH ARE FOLLOWED BY DIGITAL RECEIVERS AND DIGITAL TIME DELAYS $IGITAL BEAMFORMING OFFERS SEVERAL ADVANTAGES OVER ANALOG BEAMFORMING 7ITH AN ANALOG BEAMFORMER USUALLY ONLY ONE BEAM IS FORMED AT A TIME 2ADARS ARE TYPICALLY REQUIRED TO PERFORM MULTIPLE FUNCTIONS SUCH AS VOLUME SURVEILLANCE TARGET CONFIR MATION TRACKING ETC 7ITH ONLY ONE BEAM AT A TIME THERE MAY NOT BE ENOUGH TIME AVAILABLE TO PERFORM ALL OF THE REQUIRED FUNCTIONS ! DIGITAL BEAMFORMER ALLOWS THE FORMATION OF MULTIPLE SIMULTANEOUS BEAMS ALLOWING THE VOLUME SURVEILLANCE FUNC TION TO BE PERFORMED MUCH MORE QUICKLY ALLOWING MORE TIME TO DO OTHER THINGS /F COURSE IN ORDER TO FORM MULTIPLE SIMULTANEOUS RECEIVE BEAMS THE TRANSMITTED BEAM MUST BE MADE BROADER TO ENCOMPASS THE RECEIVE BEAMS WHICH MIGHT REQUIRE A MORE POWERFUL TRANSMITTER OR MORE INTEGRATION ON RECEIVE TO PROVIDE THE SAME PERFORMANCE AS A SINGLE BEAM SYSTEM !NOTHER ADVANTAGE HAS TO DO WITH DYNAMIC RANGE )N AN ANALOG BEAMFORMING SYS TEM THERE IS ONLY ONE RECEIVER AND !$# AND THE DYNAMIC RANGE PERFORMANCE IS LIM ITED TO THE CAPABILITY OF A SINGLE CHANNEL )N A DIGITAL BEAMFORMING SYSTEM THERE ARE MULTIPLE RECEIVERS AND !$#S AND THE NUMBER OF !$#S THAT ARE COMBINED DETERMINES THE SYSTEM DYNAMIC RANGE &OR EXAMPLE IF THE OUTPUTS OF !$#S WERE COMBINED TO FORM A BEAM ASSUMING THAT EACH !$# INDUCES NOISE THAT IS OF EQUAL AMPLITUDE AND UNCORRELATED WITH THE OTHERS THERE WOULD BE A D" INCREASE IN SYSTEM DYNAMIC RANGE COMPARED TO A SINGLE RECEIVER SYSTEM USING THE SAME !$# &IGURE SHOWS A BLOCK DIAGRAM OF A TYPICAL DIGITAL BEAMFORMING SYSTEM %ACH ANTENNA OUTPUT PORT BE IT FROM AN ELEMENT OR A SUBARRAY IS FOLLOWED BY A DIGITAL
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DOWNCONVERTER AND AN EQUALIZATION FILTER %15 &)2 4HE EQUALIZATION FILTER IS TYPI CALLY A COMPLEX FINITE IMPULSE RESPONSE &)2 FILTER DESCRIBED LATER THAT ADJUSTS THE FREQUENCY RESPONSE OF EACH CHANNEL SO THAT ITS PASSBAND MATCHES THE OTHER CHANNELS IN PHASE AND AMPLITUDE BEFORE IT IS SUMMED WITH THE OTHER CHANNELS IN THE BEAMFORMER 4HE COEFFICIENTS OF THIS FILTER ARE DETERMINED THROUGH A CALIBRATION PROCESS $URING CALIBRATION A TEST SIGNAL IS PRESENTED TO THE 2& INPUT OF ALL CHANNELS 4HIS SIGNAL IS TYPI CALLY A SWEPT FREQUENCY TONE OR A NOISE INPUT THAT COVERS THE CHANNEL BANDWIDTH 4HE !$# SAMPLES OF ALL CHANNELS ARE COLLECTED SIMULTANEOUSLY AND COMPLEX WEIGHTS ARE CALCULATED FOR THE EQUALIZATION FILTERS THAT FORCE THE FREQUENCY RESPONSE OF EACH CHANNEL TO BE MATCHED /NCE THE CHANNEL IS EQUALIZED A UNIQUE TIME DELAY IS IMPLEMENTED FOR EACH BEAM TO BE FORMED !S MENTIONED EARLIER THIS TIME DELAY CAN BE REALIZED EITHER AS A PHASE SHIFT FOR A NARROWBAND SYSTEM OR AS A TIME DELAY FOR A WIDEBAND SYSTEM ! PHASE SHIFT CAN BE IMPLEMENTED WITH A COMPLEX MULTIPLY OR A #/2$)# OPERATION BOTH OF WHICH WILL BE DESCRIBED LATER ! TIME DELAY CAN BE IMPLEMENTED WITH A &)2 FILTER THAT IMPOSES A LINEARLY CHANGING PHASE SHIFT OVER FREQUENCY ON THE SIGNAL /NCE THE TIME DELAY IS REALIZED IN EACH CHANNEL THE APPROPRIATE COMPLEX TIME DELAYED SIGNALS FROM ALL OF THE CHANNELS ARE SUMMED TO FORM A BEAM - COMPLEX SUMMERS ARE REQUIRED TO FORM - BEAMS $IGITAL 0ULSE #OMPRESSION 0ULSE COMPRESSION IS ANOTHER SIGNAL PROCESSING FUNCTION THAT IS PREDOMINANTLY BEING PERFORMED DIGITALLY IN RADAR SYSTEMS (OWEVER AT THIS WRITING MANY SYSTEMS STILL EXIST WITH ANALOG DELAY LINE PULSE COMPRESSORS )N THESE SYSTEMS ANALOG PULSE COMPRESSION IS PERFORMED AT AN )& FOLLOWED BY THE !$# IN THE PROCESSING CHAIN "ECAUSE PULSE COMPRESSION INCREASES THE 3.2 OF THE SIGNAL PERFORMING IT BEFORE SAMPLING INCREASES THE DYNAMIC RANGE REQUIREMENT OF THE !$# )N A DIGITAL PULSE COMPRESSION SYSTEM THE !$# PRECEDES THE PULSE COMPRESSOR AND ONLY HAS TO ACCOMMODATE THE PRECOMPRESSION DYNAMIC RANGE OF THE SIGNAL WHICH CAN BE A SIGNIFICANTLY LOWER REQUIREMENT 4HE DIGITIZED SIGNAL IS CONVERTED TO BASEBAND AND PASSED TO THE DIGITAL PULSE COMPRESSOR 4HE INCREASED DYNAMIC RANGE DUE TO THE PULSE COMPRESSION GAIN IS ACCOMMODATED BY INCREASING THE NUMBER OF BITS IN THE DIGITAL COMPUTATION #HAPTER IS DEVOTED TOTALLY TO PULSE COMPRESSION RADAR )N SUMMARY THERE ARE TWO BASIC APPROACHES TO IMPLEMENTING DIGITAL PULSE COMPRESSION TIME DOMAIN AND FREQUENCY DOMAIN CONVOLUTION ! GENERIC TIME DOMAIN CONVOLVER CONSISTS OF A COM PLEX &)2 FILTER WHERE THE COEFFICIENTS ARE THE COMPLEX CONJUGATE OF THE TRANSMITTED BASEBAND WAVEFORM SAMPLES IN TIME REVERSED ORDER WHICH IS ALSO THE DEFINITION OF THE MATCHED FILTER FOR THE TRANSMITTED SIGNAL 4HIS ARCHITECTURE CAN COMPRESS ANY ARBITRARY WAVEFORM ! SIMPLIFIED VERSION OF THE ARCHITECTURE RESULTS WHEN THE MODU LATION IS A BINARY PHASE CODE )N THIS CASE THE COEFFICIENTS ARE EITHER OR n SO THE ARITHMETIC PERFORMED FOR EACH SAMPLE IS A COMPLEX SUM OR SUBTRACTION INSTEAD OF A FULL COMPLEX MULTIPLICATION 0ULSE COMPRESSION MAY ALSO BE ACCOMPLISHED BY OPERATING IN THE FREQUENCY DOMAIN WHERE IT IS REFERRED TO AS FAST CONVOLUTION )N THIS CASE THE BASEBAND SAMPLES OF THE RECEIVE DATA AND THE REFERENCE TRANSMIT WAVEFORM ARE PASSED THROUGH FAST &OURIER TRANSFORMS &&4S THE DATA &&4 OUTPUTS ARE MULTIPLIED POINT BY POINT BY THE COMPLEX CONJUGATE OF THE REFERENCE &&4 OUTPUTS AND THEN THE RESULT IS CONVERTED BACK TO THE TIME DOMAIN BY AN INVERSE &&4 )N GENERAL IT IS MORE HARDWARE EFFICIENT TO PERFORM TIME DOMAIN CONVOLUTION FOR A SMALL NUMBER OF COEFFICIENTS AND FREQUENCY DOMAIN CONVOLUTION FOR A LARGE NUMBER MORE THAN OR COEFFICIENTS
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"EFORE DIGITAL TECHNOLOGY BECAME WIDELY AVAILABLE ANALOG TECHNIQUES WERE EMPLOYED TO GENERATE RADAR TRANSMIT WAVEFORMS 3IMPLE PULSED SYSTEMS USED ANALOG 2& SWITCHES TO GATE THE ,/ ON AND OFF &REQUENCY MODULATED SIGNALS WERE GENERATED BY SURFACE ACOUSTIC WAVE 3!7 DEVICES 3IMPLE BINARY PHASE MODULATION SCHEMES LIKE PSEUDO RANDOM NOISE WAVEFORMS WERE ALSO POSSIBLE $IGITAL TECHNOLOGY HOW EVER PRESENTS THE RADAR SYSTEM DESIGNER WITH MANY MORE OPTIONS AND ALLOWS ARBI TRARILY MODULATED TRANSMIT WAVEFORMS TO BE MODIFIED PULSE TO PULSE IF DESIRED 4HIS SECTION DESCRIBES SEVERAL OF THE TECHNIQUES COMMONLY USED TO GENERATE THE RADAR TRANSMIT SIGNAL DIGITALLY $IRECT $IGITAL 3YNTHESIZER $$3 &IGURE SHOWS A BLOCK DIAGRAM OF THIS TECHNIQUE IN WHICH A NUMERICALLY CONTROLLED OSCILLATOR .#/ GENERATES A DIGITIZED SINUSOID THAT IS CONVERTED TO AN ANALOG SIGNAL BY A DIGITAL TO ANALOG CONVERTER $!# &IGURE DEMONSTRATES HOW AN .#/ OPERATES TO PRODUCE A SINE WAVE 4HE N BIT TUNING WORD IS ACTUALLY A PHASE INCREMENT THAT DETERMINES THE FREQUENCY OF THE SINE WAVE OUTPUT 4HE PHASE INCREMENT IS EXPRESSED IN A FORMAT CALLED "INARY !NGLE -EASUREMENT "!- IN WHICH THE MOST SIGNIFICANT BIT -3" OF THE WORD REPRE SENTS O THE NEXT BIT REPRESENTS O AND SO ON )N THE PHASE ACCUMULATOR THE TUN ING WORD IS ADDED TO THE OUTPUT OF A RUNNING SUM IMPLEMENTED AS AN ADDER FOLLOWED BY A REGISTER 2%' 4HIS PRODUCES A UNIFORMLY INCREASING PHASE INCREMENTED AT THE SYSTEM CLOCK RATE 4HE M -3"S OF THE RUNNING SUM ARE SENT TO A PHASE TO AMPLITUDE CONVERTER WHICH IS A LOOKUP TABLE THAT PRODUCES A K BIT VALUE THAT REPRESENTS THE AMPLITUDE OF THE SINE WAVE AT THE INPUT PHASE )F WE REPRESENT THE TUNING WORD BY - THE SAMPLE FREQUENCY BY FS AND THE NUMBER OF BITS IN THE PHASE ACCUMULATOR BY N THEN THE FREQUENCY OF THE OUTPUT SINE WAVE CAN BE EXPRESSED AS -FSN )N THIS SCHEME THE PHASE REPRESENTED BY THE RUNNING SUM WILL OVERFLOW WHEN IT CROSSES OVER O 4HE ADVANTAGE OF EXPRESSING THE PHASE IN "!- NOTATION IS THAT IT ALLOWS MODULO O ARITHMETIC AND OVERFLOWS ARE AUTOMATICALLY TAKEN CARE OF SINCE A O PHASE SHIFT IS THE SAME AS O &OR EXAMPLE ASSUME WE HAVE A BIT "!- NOTA TION WHICH MEANS THAT THE LEAST SIGNIFICANT BIT ,3" REPRESENTS A PHASE SHIFT OF O ,ETS ALSO ASSUME THAT THE TUNING WORD IS REPRESENTED BY FOR A PHASE INCREMENT OF O EVERY CLOCK 4HE RUNNING SUM PHASE WOULD STEADILY INCREASE ON EVERY CLOCK EDGE BECOMING O O x O AND O /N THE NEXT CLOCK EDGE THE PHASE SHOULD BE REPRESENTED BY FOR O (OWEVER WE ARE ONLY PRO VIDED A BIT ADDER SO THE -3" IS SIMPLY LOST LEAVING US WITH A PHASE CODE OF O WHICH IS THE SAME AS O 4HEREFORE THE RESULTING PHASE WAVEFORM TAKES ON A SAWTOOTH PATTERN LINEARLY RAMPING FROM O TO NOT QUITE O AND THEN RESETTING TO O AND RAMPING AGAIN !N IMPORTANT FEATURE OF AN .#/ FOR A RADAR APPLICATION IS THE #,%!2 SIGNAL SHOWN GOING TO THE PHASE ACCUMULATOR REGISTER &OR A COHERENT RADAR EXCITER IMPLEMENTA TION THE TRANSMIT SIGNAL MUST START AT THE SAME PHASE ON EVERY PULSE /THERWISE THE
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TRANSMITTED SIGNAL WILL HAVE ARBITRARY PHASE FROM PULSE TO PULSE MAKING DOPPLER PROCESSING DIFFICULT IF NOT IMPOSSIBLE 4HE #,%!2 CONTROL PROVIDES THE MEANS TO DO THIS )N SOME APPLICATIONS LIKE FOR A TRANSMIT BEAMFORMER THE STARTING PHASE IN EACH CHANNEL MAY NEED TO BE DIFFERENT IN ORDER TO STEER THE BEAM )N THIS CASE WE COULD PROVIDE A MECHANISM TO SET THE PHASE TO THE DESIRED VALUE AT THE BEGINNING OF A PULSE INSTEAD OF SIMPLY CLEARING IT 4HE $$3 CAN ALSO BE USED TO GENERATE LINEAR AND NONLINEAR &- hCHIRPv WAVEFORMS 4HIS IS ACCOMPLISHED BY PROVIDING CIRCUITRY THAT CHANGES THE TUNING WORD FROM SAMPLE TO SAMPLE IN ORDER TO PROVIDE THE DESIRED FREQUENCY OR PHASE MODULATION &OR EXAM PLE A LINEAR &- CHIRP WAVEFORM REQUIRES A PHASE THAT CHANGES IN A SQUARE LAW FASHION WITH TIME 4HIS CAN BE ACCOMPLISHED BY CHANGING THE TUNING WORD OR PHASE STEP SIZE IN A LINEARLY INCREASING OR DECREASING WAY ON EVERY SAMPLE $IGITAL 5PCONVERTER $5# !NOTHER POPULAR METHOD TO IMPLEMENT A TRANSMIT WAVEFORM IS THROUGH DIGITAL UPCONVERSION ALSO REFERRED TO AS ARBITRARY WAVEFORM GEN ERATION )N THIS TECHNIQUE A DIGITAL COMPLEX BASEBAND WAVEFORM USUALLY READ FROM A MEMORY IS FIRST INTERPOLATED TO A HIGHER SAMPLE RATE AND THEN MODULATED WITH DIGITIZED SINE AND COSINE SIGNALS TO PRODUCE A MODULATED CARRIER &IGURE PROVIDES A BLOCK DIAGRAM OF A $5# THAT TRANSLATES A COMPLEX BASEBAND SIGNAL UP TO A -(Z )& 4HE BASEBAND ) AND 1 SIGNALS ENTER THE $5# AT A RATE OF -#303 AND ARE FIRST UP SAMPLED BY A FACTOR OF 4HIS IS ACCOMPLISHED BY INSERTING ZEROES BETWEEN EACH INPUT SAMPLE AND INCREASING THE CLOCK RATE TO -(Z 4HIS SIGNAL IS THEN PASSED THROUGH A DIGITAL LOWPASS FILTER THAT PERFORMS THE INTERPOLATION 4HESE SIGNALS ARE THEN MULTIPLIED
&)'52% $IGITAL UPCONVERTER $5#
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BY DIGITIZED SINE AND COSINE WAVEFORMS FOR THE MODULATION CARRIER FREQUENCY PRODUC ING A COMPLEX MODULATED )& AS AN OUTPUT 4HESE SIGNALS ARE DIGITALLY SUMMED CON VERTED TO ANALOG THROUGH A $!# AND PASSED THROUGH A BANDPASS FILTER TO PRODUCE AN )& OUTPUT &OR LARGE UPSAMPLING RATIOS A CASCADED INTEGRATOR COMB #)# INTERPOLATOR DESCRIBED IN THE NEXT SECTION PROVIDES AN EFFICIENT IMPLEMENTATION
Óx°{Ê -*Ê/"" 4HIS SECTION WILL DESCRIBE VARIOUS PROCESSING ARCHITECTURES AND TECHNIQUES THAT ARE AVAILABLE TO $30 ENGINEERS 0HASE 3HIFT 4HE PHASE SHIFT IS A CORE ELEMENT IN $30 DESIGN AND THERE ARE SEV ERAL TECHNIQUES AVAILABLE TO IMPLEMENT ONE 4HE MOST STRAIGHTFORWARD APPROACH IS TO SIMPLY PERFORM A COMPLEX MULTIPLY AS SHOWN IN &IGURE )N THIS EXAMPLE THE COMPLEX INPUT SAMPLE IS DENOTED AS ! J" WHICH IS MULTIPLIED BY THE COMPLEX COEF FICIENT # J$ TO PRODUCE !# n "$ J!$ "# IN ORDER TO EFFECT THE PHASE SHIFT 4HIS OPERATION REQUIRES FOUR MULTIPLIERS AND TWO ADDERS !FTER SOME MANIPULATION THE FOLLOWING CAN BE SHOWN
) !# n "$ $! n " !# n $
1 !$ "# #! " n !# n $
.OTING THAT THE FINAL TERM IS THE SAME IN BOTH EQUATIONS WE SEE THAT THIS COMPLEX MULTIPLIER CAN BE IMPLEMENTED WITH ONLY THREE REAL MULTIPLIERS AND FIVE REAL ADDS 4HIS CAN BE IMPORTANT IF REAL MULTIPLIERS ARE AT A PREMIUM &IGURE SHOWS A BLOCK DIAGRAM OF THIS ARCHITECTURE #/2$)# 0ROCESSOR !N EFFICIENT AND VERSATILE ALGORITHM THAT CAN IMPLEMENT A PHASE SHIFT WITHOUT USING MULTIPLIERS IS THE #/ORDINATE 2OTATION $)GITAL #OMPUTER #/2$)# FUNCTION FIRST DESCRIBED BY 6OLDER IN 4HE #/2$)# CAN IMPLEMENT
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A VARIETY OF FUNCTIONS INCLUDING SINE COSINE VECTOR ROTATION PHASE SHIFT POLAR TO RECTANGULAR AND RECTANGULAR TO POLAR CONVERSIONS ARCTANGENT ARCSINE ARCCOSINE AND VECTOR MAGNITUDE THROUGH AN ITERATIVE PROCESS THAT JUST USES BIT SHIFTS AND ADDS 4HE FOLLOWING DISCUSSION DESCRIBES THE #/2$)# ALGORITHM 4HE EQUATIONS THAT SHIFT THE PHASE OF COMPLEX NUMBER ) J1 BY AN ANGLE P TO PRODUCE ) J1 ARE AS FOLLOWS
) )COSP 1SINP
1 )SINP 1COSP 4HESE EQUATIONS CAN BE MANIPULATED TO PROVIDE
) COSP ;) 1TANP =
1 COSP ;1 )TANP =
4HE #/2$)# ALGORITHM TAKES ADVANTAGE OF THIS RELATIONSHIP TO APPROXIMATE AN ARBI TRARY PHASE SHIFT BY IMPLEMENTING MULTIPLE STAGES OF PHASE SHIFTS WHERE THE TANGENT OF THE PHASE SHIFT IN EACH SUCCESSIVE STAGE IS THE NEXT SMALLER FRACTIONAL POWER OF AND MULTIPLICATION BY THIS NUMBER CAN BE IMPLEMENTED BY SHIFTING THE INPUT DATA BITS AN INTEGER NUMBER OF PLACES 4HE FIRST FEW STAGES ARE AS FOLLOWS
) COSP ;) n 1TANP = COSP ;) n 1 =
1 COSP ;1 )TANP = COSP ;1 ) =
) COSP ;) n 1TANP = COSP ;) 1 = 1 COSP ;1 )TANP = COSP ;1 ) =
4ABLE SHOWS THESE PARAMETERS FOR AN EIGHT STAGE #/2$)# PROCESSOR %ACH ROW OF THE TABLE REPRESENTS SUCCESSIVE ITERATIONS OF THE ALGORITHM 4HE TANP I COLUMN SHOWS THE FACTOR BY WHICH THE ) AND 1 VALUES ARE MULTIPLIED FOR EACH ITERATION .OTE THAT THESE VALUES ARE FRACTIONAL POWERS OF SO THE MULTIPLICATION CAN BE REALIZED BY SHIFTING THE BINARY ) AND 1 VALUES RIGHT BY I PLACES 4HE P I COLUMN SHOWS THE ARCTANGENT OF THIS FACTOR WHICH CAN ALSO BE THOUGHT OF AS THE PHASE SHIFT APPLIED DURING EACH ITERATION
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2!$!2 (!.$"//+
4!",% #/2$)# 0ARAMETERS FOR &IRST %IGHT 3TAGES
I
TANP I
P I DEG
COSP I
0 ;COSP I =
4HE COSP I COLUMN SHOWS THE COSINE OF THIS ANGLE WHICH SHOULD BE MULTIPLIED BY THE RESULT OF EACH ITERATION AS SHOWN IN THE EQUATIONS ABOVE )N ACTUAL APPLICATIONS HOWEVER THIS COSINE MULTIPLICATION IS NOT PERFORMED AT EVERY ITERATION !T EACH STAGE THE IMPLIED FACTOR THAT NEEDS TO BE MULTIPLIED BY THE )1 OUTPUTS OF THE STAGE IN ORDER TO PROVIDE THE CORRECT ANSWER IS THE PRODUCT OF ALL OF THE COSINES UP TO THAT POINT AS SHOWN IN THE 0;COSP I = COLUMN &OR A LARGE NUMBER OF ITERATIONS THIS PRODUCT OF COSINES CONVERGES TO A VALUE OF )N MOST CASES THIS SCALING CAN BE COMPEN SATED FOR IN LATER STAGES OF PROCESSING 4HE INVERSE OF THIS FACTOR FOR A LARGE NUMBER OF ITERATIONS IS THE PRO CESSING GAIN IMPOSED ON THE )1 RESULTS
OF THE #/2$)# )F INTEGER ARITHMETIC IS PERFORMED AN EXTRA BIT SHOULD BE PRO VIDED AT THE MOST SIGNIFICANT END OF THE ADDERS IN ORDER TO ACCOMMODATE THIS INCREASED SIGNAL LEVEL &IGURE IS A FLOW CHART THAT REPRESENTS THE #/2$)# ALGORITHM TO IMPLEMENT A PHASE SHIFT 4HE INPUTS TO THE ALGORITHM ARE THE )IN 1IN AND EIN
THE DESIRED PHASE SHIFT 4HE VARIABLE I WILL KEEP TRACK OF THE PROCESSING STAGE BEING PERFORMED AND IS INITIALIZED TO ZERO 4HE BASIC ALGORITHM CAN PERFORM A PHASE SHIFT BETWEEN oO )F THE DESIRED PHASE SHIFT IS OUTSIDE OF THAT RANGE THE INPUT ) AND 1 VALUES ARE FIRST NEGATED IMPOSING A O PHASE SHIFT AND O IS SUBTRACTED FROM THE DESIRED PHASE SHIFT 4HE NEW PHASE SHIFT IS NOW WITHIN oO AND THE ALGORITHM PROCEEDS NORMALLY .EXT THE ALGORITHM LOOPS THROUGH . ITERATIONS WITH THE GOAL OF DRIVING
THE RESIDUAL PHASE ERROR E TO ZERO )N EACH ITERATION A NEW E IS CALCULATED BY SUBTRACTING OR ADDING THE PHASE SHIFT FOR &)'52% #/2$)# ALGORITHM FLOW CHART
2!$!2 $)')4!, 3)'.!, 02/#%33).'
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THAT STAGE P I FROM THE TABLE TO THE PREVIOUS VALUE OF E )F E P I IS ADDED TO E /THERWISE P I IS SUBTRACTED FROM E )N EACH STAGE THE 1 OR ) INPUT IS DIVIDED BY A FAC TOR OF I BY SHIFTING THE NUMBER TO THE RIGHT BY I BITS AND THEN ADDED TO OR SUBTRACTED FROM THE ) OR 1 INPUT DEPENDING ON THE SIGN OF E 4HE VARIABLE I IS INCREMENTED AND THE PROCESS REPEATS UNTIL I . AT WHICH POINT THE PHASE SHIFTED RESULTS ARE AVAILABLE &IGURE IS A BLOCK DIAGRAM OF AN EIGHT STAGE #/2$)# PROCESSOR THAT IMPLE MENTS A PHASE SHIFT WHERE EACH STAGE REPRESENTS AN ITERATION IN THE FLOW CHART !N . STAGE PROCESSOR PROVIDES A PHASE SHIFT THAT IS ACCURATE TO WITHIN oP . DEGREES FROM THE TABLE SO THE MORE STAGES IN THE PROCESSOR THE MORE ACCURATE THE ANSWER 4HE INPUT ) AND 1 VALUES CHANGE ON THE RISING EDGE OF AN ASSUMED SAMPLE CLOCK )N THE FIRST STAGE THE ) VALUE IS EITHER ADDED TO OR SUBTRACTED FROM THE 1 VALUE IN THE !$$35" BLOCK 4HE CONTROL BLOCK ON THE BOTTOM OF THE FIGURE DETERMINES WHETHER ADDITIONS OR SUBTRACTIONS ARE PERFORMED AT EACH STAGE BASED ON THE ALGORITHM DESCRIBED PREVIOUSLY )F THE !$$35" BLOCK IN THE 1 CHANNEL PERFORMS AN ADDITION THE SAME BLOCK IN THE ) CHANNEL WILL PERFORM A SUBTRACTION AND VICE VERSA 4HE RESULT OF THE !$$35" BLOCKS IS STORED IN A REGISTER 2%' ON THE NEXT CLOCK EDGE AND PASSED TO THE NEXT STAGE OF PROCESSING )N THIS IMPLEMENTATION THE LAST BLOCK LABELED 0!33).6 PERFORMS THE REQUIRED INVERSION OF ) AND 1 IF THE DESIRED PHASE SHIFT IS BEYOND THE oO RANGE OF THE ALGORITHM 4HE FINAL MULTIPLICATION BY A CONSTANT IS OPTIONAL AS DESCRIBED EARLIER 4HE ARCHITECTURE SHOWN IN &IGURE IS A GOOD EXAMPLE OF A PIPELINED PROCESSOR IN WHICH A PORTION OF THE COMPUTATION IS PERFORMED AND THE RESULT IS STORED IN A REGISTER ON EACH RISING EDGE OF THE SAMPLE CLOCK AND PASSED TO THE NEXT STAGE OF PROCESSING 4HE PROCESSOR WOULD STILL FUNCTION IF THE REGISTERS WERE REMOVED (OWEVER IN THAT CASE WHEN THE INPUT ) AND 1 VALUES CHANGED THE FINAL OUTPUT WOULD NOT BE USEABLE UNTIL THE RESULTS OF THE NEW INPUT VALUES RIPPLED THROUGH ALL OF THE STAGES OF PROCESSING WHICH WOULD GENERALLY BE AN UNACCEPTABLY LONG PERIOD OF TIME )N A PIPELINED PROCESSOR A SMALL PORTION OF THE TOTAL CALCULATIONS IS PERFORMED AT A TIME AND THE RESULT IS STORED IN A REGISTER AND PASSED TO THE NEXT PROCESSING STAGE 4HIS ARCHITECTURE PROVIDES A HIGHER THROUGHPUT THAN THE NONPIPELINED VERSION WHICH MEANS THAT THE FINAL RESULT CAN BE PRODUCED AT A MUCH HIGHER SAMPLE RATE WHICH IS INVERSELY PROPORTIONAL TO THE DELAY OF A SINGLE STAGE 4HE LATENCY OF A PIPELINED PROCESSOR REFERS TO THE DELAY EXPERIENCED BETWEEN THE TIME A NEW DATA SAMPLE IS ENTERED INTO THE PROCESSOR AND THE TIME THAT THE RESULT BASED ON THAT INPUT IS AVAILABLE ON THE OUTPUT 4HE EIGHT STAGE PIPELINED #/2$)# PROCESSOR SHOWN IN THE FIGURE WOULD HAVE A LATENCY EQUIVALENT TO EIGHT CLOCK PERIODS AND A THROUGHPUT EQUIVALENT TO THE CLOCK RATE IE ONCE THE PIPELINE IS FILLED AND THE FIRST RESULT IS AVAILABLE ON THE OUTPUT SUCCESSIVE CLOCKS WILL PRODUCE NEW OUT PUTS AT THE CLOCK RATE
!
&)'52% %IGHT STAGE #/2$)# PROCESSOR
!
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2!$!2 (!.$"//+
$IGITAL &ILTERS AND !PPLICATIONS 4HIS SECTION DESCRIBES SEVERAL OF THE MAJOR FORMS OF DIGITAL FILTERS AND HOW THEY ARE USED IN RADAR SIGNAL PROCESSING
&INITE )MPULSE 2ESPONSE &)2 AND )NFINITE )MPULSE 2ESPONSE ))2 &ILTERS &IGURE SHOWS A BLOCK DIAGRAM OF A DIRECT FORM DIGITAL &)2 FILTER 4HE INPUT SAMPLE FEEDS A SHIFT REGISTER WHERE EACH BLOCK LABELED S INDICATES A ONE SAMPLE DELAY IN THE SHIFT REGISTER 4HE INPUT SAMPLE AND THE OUTPUT OF EACH STAGE OF THE SHIFT REGISTER ARE MULTIPLIED BY UNIQUE COEFFICIENTS AND THE MULTIPLIER OUTPUTS ARE SUMMED TO PRODUCE THE FILTERED OUTPUT 3OFTWARE TOOLS EXIST THAT GENERATE THESE COEFFICIENTS AND THE NUMBER REQUIRED WHEN THE USER PROVIDES THE DESIRED FILTER CHARACTERISTICS SUCH AS FILTER TYPE LOWPASS &)'52% 'ENERAL DIRECT FORM HIGHPASS BANDPASS ETC SAMPLE RATE CUTOFF AND &)2 FILTER BLOCK DIAGRAM STOPBAND FREQUENCY DESIRED PASSBAND RIPPLE AND STOPBAND ATTENUATION 4HE FILTER SHOWN IS REFERRED TO AS A REAL &)2 FILTER SINCE THE INPUT DATA AND COEFFICIENTS ARE REAL VALUES AND REAL MATHEMATICAL OPERATIONS ARE PERFORMED )N A COMPLEX &)2 FILTER THE DATA SAMPLES COEFFICIENTS AND MATH ARE COMPLEX 4HIS TYPE OF FILTER IS TERMED FINITE IMPULSE RESPONSE BECAUSE AN IMPULSE PRESENTED AT THE INPUT A SINGLE SAMPLE OF hv SURROUNDED BY SAMPLES OF ZEROES WOULD PRODUCE A FINITE LENGTH OUTPUT CONSISTING OF THE COEFFICIENTS OF THE FILTER OUTPUT IN ORDER AS THE hv PROPAGATES DOWN THE SHIFT REGISTER AS SHOWN IN &IGURE FOR A &)2 FILTER WITH SEVEN COEFFICIENTS COMMONLY REFERRED TO AS A TAP &)2 FILTER )N THIS EXAMPLE ZERO VALUED SAMPLES ARE FIRST CLOCKED INTO THE &)2 FILTER SHIFT REGISTER FILLING THE SHIFT REGISTER WITH ZEROES AND FORCING THE FILTER OUTPUT TO BE ZERO 7HEN THE SAMPLE WITH A VALUE OF hv IS CLOCKED INTO THE FILTER THE FILTER OUTPUT PRODUCES THE FIRST COEFFICIENT A SINCE THE OTHER SAMPLES IN THE FILTER ARE STILL ZERO /N THE NEXT CLOCK THE hv MOVES TO THE SECOND TAP OF THE SHIFT REGISTER AND A hv IS CLOCKED INTO THE FIRST TAP FORCING THE FILTER OUTPUT TO PRODUCE THE SECOND FILTER COEFFICIENT A /N SUCCESSIVE CLOCKS THE hv PROPAGATES THROUGH THE SHIFT REGISTER WHILE ZEROES ARE CLOCKED INTO THE SHIFT REGISTER INPUT PRODUCING ALL OF THE FILTER COEFFICIENTS ON THE OUTPUT IN SEQUENCE 4HE &)2 FILTER USES FEED FORWARD TERMS ONLY MEANING THAT THE OUTPUT VALUES ONLY DEPEND ON THE INPUT VALUES WITH NO FEEDBACK TERMS &IGURE DEPICTS THE GENERAL FORM FOR AN INFINITE IMPULSE RESPONSE ))2 FILTER ))2 FILTERS MAKE USE OF FEED FORWARD AND FEEDBACK TERMS 4HEY ARE REFERRED TO AS INFINITE IMPULSE RESPONSE BECAUSE AN IMPULSE PRESENTED AT THE INPUT TO THE FILTER WILL PRODUCE AN INFINITE STRING OF NONZERO OUTPUTS IN AN IDEAL SITUATION
&)'52% )MPULSE RESPONSE OF TAP &)2 FILTER
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&)'52% 'ENERAL ))2 FILTER BLOCK DIAGRAM
#OMPARED TO &)2 FILTERS ))2 FILTERS OFFER SEVERAL ADVANTAGES )N GENERAL THEY REQUIRE LESS PROCESSING AND MEMORY TO IMPLEMENT SIMILAR FUNCTIONS )T IS ALSO EASIER TO IMPLE MENT SOME FILTER RESPONSES AS ))2 RATHER THAN &)2 FILTERS (OWEVER WITHOUT CAREFUL DESIGN ))2 FILTER RESPONSES CAN BE VERY SENSITIVE TO COEFFICIENT QUANTIZATION LIMITATIONS AND COULD EXHIBIT A TENDENCY TO OVERFLOW IE PRODUCE AN OUTPUT THAT EXCEEDS THE PROCES SOR DYNAMIC RANGE DETERMINED BY THE NUMBER OF BITS IN THE DATAPATH !LTHOUGH ))2 FIL TERS ARE ALMOST NEVER USED IN RADAR SYSTEMS FOR THESE AND A VARIETY OF HISTORICAL REASONS A CAUTIOUS DESIGNER MIGHT FIND AN APPLICATION WHERE THEY CAN BE USED TO GOOD ADVANTAGE "Y CONTRAST &)2 FILTERS ARE INHERENTLY STABLE 2EAL &)2 FILTERS WITH SYMMETRIC COEF FICIENTS AUTOMATICALLY PROVIDE A LINEAR PHASE SHIFT OVER FREQUENCY INTRODUCING LITTLE OR NO PHASE DISTORTION TO THE FILTERED SIGNAL WHICH IS HIGHLY DESIRABLE IN MANY APPLICA TIONS "ECAUSE &)2 FILTERS REQUIRE NO FEEDBACK THEY ARE EASIER TO USE IN VERY HIGH SPEED APPLICATIONS THAN ))2 FILTERS WHICH TYPICALLY REQUIRE THE COMPU TATION OF AN OUTPUT SAMPLE BEFORE THE NEXT OUTPUT SAMPLE CAN BE FORMED #OMPLEX &)2 FILTERS WHERE A COMPLEX MULTIPLICATION IS PERFORMED AT EACH TAP CAN BE USED TO IMPLEMENT EQUALIZATION FILTERS TIME DELAYS AND PULSE COMPRESSION FILTERS &IGURE SHOWS AN ALTERNATIVE FORM FOR A &)2 FILTER CALLED A TRANSPOSED FORM &)2 FILTER )N THIS CONFIGURATION EACH INPUT SAMPLE IS MULTIPLIED BY ALL OF THE COEFFICIENTS AT ONCE WITH THE SAMPLE DELAYS BETWEEN THE SUMMER OUTPUTS )F THE COEFFICIENTS OF A &)2 FILTER ARE SYMMETRIC SO THAT THE COEFFICIENTS ON EITHER SIDE OF THE CENTER OF THE FILTER ARE MIRROR IMAGES OF EACH OTHER AS IS THE CASE WITH LINEAR PHASE FILTERS MULTIPLIERS CAN BE SAVED BY ADDING THE SAMPLES THAT GET MULTIPLIED BY THE SAME COEFFICIENT FIRST THEREBY REQUIRING ABOUT HALF AS MANY MULTIPLIERS AS SHOWN IN &IGURE &)'52% 4RANSPOSED FORM FOR A TAP EXAMPLE &)2 FILTER
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2!$!2 (!.$"//+
&)'52% TAP &)2 FILTER WITH SYMMETRIC COEFFICIENTS
$ECIMATION &ILTERS !S MENTIONED PREVIOUSLY THE COMPLEXITY AND COST OF A SIGNAL PROCESSOR IN TERMS OF THE AMOUNT OF SYSTEM RESOURCES REQUIRED TO IMPLEMENT IT GENER ALLY VARIES LINEARLY WITH THE DATA SAMPLE RATE &OR THIS REASON IN MOST SYSTEM APPLICA TIONS IT IS COST EFFECTIVE TO REDUCE THE DATA SAMPLE RATE TO A VALUE THAT IS JUST ADEQUATE TO SUPPORT THE BANDWIDTH OF THE SYSTEM )N APPLICATIONS WHERE THE SAMPLE RATE OF A SIGNAL IS TO BE DECREASED DECIMATED THE FREQUENCY CONTENT OF THE SIGNAL MUST FIRST BE REDUCED SO THAT THE .YQUIST CRITERION IS SATISFIED FOR THE NEW SAMPLE RATE 4HIS CAN BE ACCOMPLISHED BY FIRST PASSING THE SIGNAL THROUGH A DIGITAL &)2 FILTER TO RESTRICT THE BANDWIDTH OF THE SIGNAL TO LESS THAN HALF OF THE DECIMATED SAMPLE RATE AND THEN REDUCING THE SAMPLE RATE OF THE FILTERED SIGNAL BY A FACTOR OF 2 BY SELECTING EVERY 2TH SAMPLE AS DESCRIBED IN THE PREVIOUS DISCUSSION OF DECIMATION ! DESIGNER CAN TAKE ADVANTAGE OF DECIMATION BY REALIZING THAT ONLY THE FILTER OUTPUTS THAT ARE USED NEED TO BE COMPUTED &OR EXAMPLE IF THE OUTPUT OF A &)2 FILTER IS TO BE DECIMATED BY A FACTOR OF ONLY EVERY FOURTH FILTER OUTPUT NEEDS TO BE COMPUTED WHICH REDUCES THE REQUIRED PROCESSING BY A FACTOR OF )NTERPOLATION &ILTERS )NTERPOLATION IS THE PROCESS BY WHICH THE SAMPLE RATE OF A SIGNAL IS INCREASED FOR EXAMPLE IN PREPARING THE SIGNAL TO BE UPCONVERTED TO AN )& AS SHOWN IN &IGURE )NTERPOLATORS ARE TYPICALLY &)2 FILTERS WITH A LOWPASS FILTER RESPONSE 4O INCREASE THE SAMPLE RATE BY A FACTOR 2 2 n ZEROES ARE FIRST INSERTED BETWEEN THE LOW RATE DATA SAMPLES CREATING A DATA STREAM AT A SAMPLE RATE 2 TIMES FASTER THAN THE INPUT RATE UPSAMPLING 4HIS DATA STREAM IS THEN PASSED THROUGH THE LOWPASS &)2 FILTER TO PRODUCE THE INTERPOLATED HIGH SAMPLE RATE OUTPUT /F COURSE THE &)2 FILTER MUST BE CLOCKED AT THE HIGHER DATA RATE 4HIS PROCESS IS ILLUSTRATED IN &IGURE FOR A FOUR TIMES INCREASE IN SAMPLE RATE
&)'52% )LLUSTRATION OF INTERPOLATION FILTERING
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#ASCADED )NTEGRATOR #OMB #)# &ILTERS )N DECIMATION OR INTERPOLATION APPLI CATIONS WHERE THE RATE CHANGE FACTOR IS LARGE TYPICALLY OR GREATER A &)2 FILTER IMPLEMENTATION MIGHT BE PROHIBITIVELY COSTLY DUE TO THE LARGE NUMBER OF FILTER TAPS THAT WOULD BE REQUIRED #)# FILTERS ARE A CLASS OF FILTERS INTRODUCED BY (OGENAUER THAT PROVIDE A VERY EFFICIENT MEANS OF IMPLEMENTING THESE FILTER FUNCTIONS THAT DO NOT REQUIRE MULTIPLIERS %XCELLENT DESCRIPTIONS OF THIS CLASS OF FILTER ARE PROVIDED BY ,YONS AND (ARRIS WHICH FORM THE BASIS FOR THE FOLLOWING DISCUSSION &IGURE A SHOWS A SINGLE STAGE #)# DECIMATOR 4HE FILTER CONTAINS AN INTEGRATOR STAGE CONSISTING OF A SINGLE SAMPLE DELAY AND AN ADDER FOLLOWED BY A COMB STAGE WITH A $ STAGE SHIFT REGISTER DENOTED BY THE $S BLOCK AND A SUBTRACTOR 4HE COMB FILTER GETS ITS NAME BECAUSE ITS FREQUENCY RESPONSE LOOKS LIKE A RECTIFIED SINE WAVE AND RESEMBLES THE TEETH OF A COMB !FTER THE COMB STAGE THE SIGNAL IS DECIMATED BY A FACTOR 2 DENOTED BY THE m2 BLOCK BY ONLY PASSING EVERY 2TH SAMPLE )N MOST APPLICATIONS THE NUMBER OF STAGES IN THE SHIFT REGISTER $ IS EQUAL TO THE RATE CHANGE FACTOR 2 &IGURE B DEPICTS A #)# INTERPOLATOR WHERE UPSAMPLING BY A FACTOR OF 2 DENOTED BY THE k2 BLOCK IS FOLLOWED BY A COMB SECTION AND AN INTEGRATOR 4HE UPSAMPLING IS ACCOMPLISHED BY ZERO INSERTION AS DESCRIBED IN THE PREVIOUS SECTION h)NTERPOLATION &ILTERSv .OTE THAT THE PROCESSING ONLY CONSISTS OF DELAYS AND ADDS &IGURE A SHOWS THE SINX X FREQUENCY RESPONSE OF A SINGLE STAGE #)# DECI MATOR WHERE 2 $ 4HE DESIRED PASSBAND IS THE LIGHTLY SHADED AREA CENTERED AT (Z WITH BANDWIDTH "7 4HE DARKER SHADED AREAS WITH BANDWIDTH "7 IN &IGURE A INDICATE SIGNALS THAT WILL ALIAS INTO THE BASEBAND SIGNAL AFTER DECIMATION BY AS SHOWN IN &IGURE B AFTER ,YONS .OTE THAT UNLESS "7 IS VERY SMALL A SIGNIFICANT PORTION OF OUT OF BAND SIGNALS WOULD GET FOLDED INTO THE DECIMATED BASEBAND SIGNAL 4HE TYPI CAL METHOD USED TO IMPROVE THIS FILTER RESPONSE IS TO INCREASE THE FILTER ORDER BY ADDING MORE STAGES &IGURE SHOWS A THREE STAGE #)# DECIMATION FILTER AND ITS FREQUENCY RESPONSE BEFORE AND AFTER DECIMATION BY IS SHOWN IN &IGURE A AND B RESPECTIVELY .OTE THAT THE ALIASED COMPONENTS ARE SIGNIFICANTLY REDUCED IN AMPLITUDE COMPARED TO THE SINGLE STAGE #)# FILTER RESPONSE AND THE MAIN PASSBAND HAS MORE ATTENUATION TOWARD THE EDGES )N TYPICAL APPLICATIONS A #)# DECIMATOR IS FOLLOWED BY A &)2 LOWPASS FILTER AND A FINAL DECIMATION BY 4HAT IS A DECIMATE BY FILTER WOULD BE COMPOSED OF A DECIMATE BY #)# FILTER FOLLOWED BY A DECIMATE BY &)2 FILTER 4HE &)2 FILTER CAN BE TAILORED TO REMOVE THE UNDESIRED RESIDUAL COMPONENTS BEFORE THE FINAL DECIMATION 4HE &)2 FILTER CAN ALSO BE CONFIGURED TO COMPENSATE FOR THE DROOP IN THE PASSBAND RESPONSE &IGURE SHOWS AN EQUIVALENT FORM FOR A #)# DECIMATION FILTER WHERE THE DECI MATION OCCURS RIGHT AFTER THE INTEGRATOR SECTION AND BEFORE THE COMB SECTION 4HE DELAY IN THE COMB FILTER BECOMES A VALUE .S WHERE . IS EQUAL TO $2 4HIS ALLOWS THE COMB SECTION TO OPERATE AT THE DECIMATED SAMPLE RATE WHICH MAKES IT SIMPLER TO IMPLEMENT $UE TO THIS SIMPLIFICATION #)# DECIMATORS ARE GENERALLY IMPLEMENTED IN THIS FORM
&)'52% A #)# DECIMATION FILTER AND B #)# INTERPOLATION FILTER
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2!$!2 (!.$"//+
&)'52% &REQUENCY RESPONSE OF SINGLE STAGE #)# DECIMATION FILTER A BEFORE DECIMATION AND B AFTER DECIMATION
&)'52% 4HREE STAGE #)# DECIMATION FILTER
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&)'52% &REQUENCY RESPONSE OF THIRD ORDER #)# DECIMATION FILTER A BEFORE DECIMATION AND B AFTER DECIMATION
&)'52% #)# FILTER WITH DECIMATION AFTER INTEGRATOR
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2!$!2 (!.$"//+
#AREFUL INSPECTION OF THE DECIMATOR ARCHITECTURE REVEALS A POTENTIAL PROBLEM WITH THE INTEGRATOR 4HE INPUT SAMPLES CONTINUALLY GET ADDED TO THE RUNNING SUM PRODUCING A DEFINITE OVERFLOW CONDITION 4HE BEAUTY OF THE ARCHITECTURE IS THAT OVERFLOWS ARE ALLOWED AND COMPENSATED FOR BY THE COMB SECTION AS LONG AS THERE ARE ENOUGH BITS IN THE ADDERS TO REPRESENT THE MAXIMUM EXPECTED OUTPUT VALUE AND THE FILTER IS IMPLEMENTED USING TWOS COMPLEMENT ARITHMETIC !S DESCRIBED BY (ARRIS THE NUMBER OF BITS REQUIRED IN THE ADDERS B!$$%2 IS GIVEN BY
B!$$%2 B$!4! #%),;LOG'!). =
WHERE B$!4! IS THE NUMBER OF BITS IN THE INPUT DATA AND #%),; = INDICATES ROUNDING THE NUMBER IN THE BRACKETS TO THE NEXT HIGHEST INTEGER '!). IS GIVEN BY
'!). 2+
WHERE 2 IS THE DECIMATION FACTOR AND + IS THE NUMBER OF STAGES IN THE FILTER RESULTING IN
B!$$%2 B$!4! #%),;LOG2+ =
&OR EXAMPLE ASSUME WE HAVE BIT INPUT DATA B$!4! AND A STAGE #)# FILTER + THAT DECIMATES THE SAMPLE RATE BY A FACTOR OF 2 3UBSTITUTING INTO THIS EQUATION PRODUCES
B!$$%2 #%),;LOG = #%),;=
)N PRACTICE ALTHOUGH THE FIRST ADDER STAGE MUST SUPPORT THIS NUMBER OF BITS LOWER ORDER BITS MAY BE PRUNED FROM THE ADDERS IN SUCCESSIVE STAGES AS DESCRIBED BY (ARRIS ! #)# INTERPOLATING FILTER WOULD BE PRECEDED BY A &)2 FILTER BASED INTERPOLATOR #)# INTERPOLATORS ARE DESCRIBED IN DETAIL IN THE REFERENCED LITERATURE 4HE $ISCRETE &OURIER 4RANSFORM $&4 )N MANY SAMPLED DATA SYSTEMS SPEC TRAL ANALYSIS IS IMPLEMENTED BY PERFORMING THE DISCRETE &OURIER TRANSFORM $&4 4HE $&4 FORMS THE BASIS FOR MANY RADAR SIGNAL PROCESSING ALGORITHMS SUCH AS DOPPLER PROCESSING AND FAST CONVOLUTION PULSE COMPRESSION DESCRIBED IN #HAPTER AS WELL AS RADAR FUNCTIONS SUCH AS SYNTHETIC APERTURE RADAR 3!2 AND INVERSE SYNTHETIC APERTURE RADAR )3!2 4HE $&4 TAKES . DATA SAMPLES REAL OR COMPLEX AS INPUT AND GENER ATES . COMPLEX NUMBERS AS OUTPUT WHERE THE OUTPUT SAMPLES REPRESENT THE FREQUENCY CONTENT OF THE INPUT DATA SEQUENCE &OR A SAMPLE RATE FS EACH OUTPUT FREQUENCY SAMPLE BIN HAS A WIDTH OF FS. 4HE MTH OUTPUT SAMPLE 8M REPRESENTS THE AMPLITUDE AND PHASE OF THE FREQUENCY CONTENT OF THE FINITE LENGTH INPUT SEQUENCE CENTERED AT THE FREQUENCY MFS. )F AN INPUT SIGNAL IS EXACTLY CENTERED IN ONE OF THE $&4 FREQUENCY BINS THE OUTPUT WILL HAVE A MAXIMUM VALUE FOR THAT BIN AND NULLS FOR ALL OTHER BINS (OWEVER ANY FRE QUENCY OTHER THAN ONE CENTERED IN A BIN WILL BLEED INTO THE OTHER BINS 4HE BASIC $&4 BIN HAS A FREQUENCY RESPONSE SIMILAR TO SINX X WHICH MEANS THAT A SIGNAL IN ANOTHER BIN MIGHT BLEED INTO A $&4 FREQUENCY BIN WITH AN ATTENUATION AS SMALL AS D" 4O COMPENSATE FOR THIS THE INPUT SAMPLES CAN BE WEIGHTED IN AMPLITUDE WITH A WIDE SELEC TION OF WEIGHTS SUCH AS (ANNING AND (AMMING WEIGHTS WHICH BROADEN THE MAIN LOBE RESPONSE OF THE $&4 OUTPUT BUT REDUCE THE AMPLITUDE OF THE SIDE LOBES ! THOROUGH TREATMENT OF $&4 WEIGHTING FUNCTIONS AND THEIR EFFECTS IS GIVEN BY (ARRIS
2!$!2 $)')4!, 3)'.!, 02/#%33).'
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&)'52% 2ADIX BUTTERFLY
4HE &AST &OURIER 4RANSFORM &&4 4HE IMPLEMENTATION OF A $&4 IS COMPUTA TIONALLY INTENSIVE REQUIRING . COMPLEX MULTIPLIES 4HE FAST &OURIER TRANSFORM &&4 IS A VERY EFFICIENT TECHNIQUE TO IMPLEMENT THE $&4 IF . IS A POWER OF WHICH REQUIRES ONLY . LOG. COMPLEX MULTIPLIES 4HE BASIC COMPUTATIONAL ELEMENT IN AN &&4 IS THE BUTTERFLY SHOWN IN &IGURE )N THE BUTTERFLY OPERATION ONE INPUT IS PHASE SHIFTED AND THEN ADDED TO AND SUBTRACTED FROM A SECOND INPUT TO FORM TWO OUTPUTS 4HIS STRUCTURE IS REFERRED TO AS A RADIX BUT TERFLY BECAUSE IT HAS TWO INPUTS &OR CERTAIN &&4 CONFIGURATIONS RADIX AND HIGHER RADIX BUTTERFLIES PROVIDE SOME COMPUTATIONAL SAVINGS &IGURE SHOWS A RADIX POINT &&4 4HE PHASE SHIFTS ARE REPRESENTED AS COMPLEX WEIGHTS 7.K WHERE . IS THE NUMBER OF POINTS IN THE &&4 AND K INDICATES THE PARTICULAR PHASE SHIFT APPLIED 7.K DENOTES A PHASE SHIFT OF KP. 4HESE WEIGHTS ARE OFTEN REFERRED TO AS TWIDDLE FACTORS &IGURE SHOWS THE PHASE SHIFTS ASSOCIATED WITH VARIOUS TWIDDLE FACTORS .OTE THAT THE POINT &&4 CONSISTS OF THREE STAGES !LL OF THE COMPUTATIONS IN EACH STAGE ARE EXECUTED BEFORE PROCEEDING TO THE NEXT STAGE !LSO NOTE THAT THE PHASE SHIFT IN THE FIRST STAGE 7 IS ZERO WHICH REQUIRES NO COMPUTATION AT ALL
&)'52% %IGHT POINT 2ADIX &&4
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2!$!2 (!.$"//+
&)'52% 0HASE SHIFTS INFERRED BY VARIOUS TWIDDLE FACTORS
3INCE ADDITIONS ARE PERFORMED IN EACH STAGE THE MAGNITUDE OF EACH OUTPUT STAGE SAMPLE COULD BE A FACTOR OF TWO OR MORE GREATER THAN THE INPUT SAMPLES )F FIXED POINT COMPUTATIONS ARE USED THEN THIS INCREASED DYNAMIC RANGE RESULTS IN A GROWTH IN THE NUMBER OF BITS REQUIRED TO REPRESENT THE VALUES AND THERE NEEDS TO BE A STRATEGY TO ACCOMMODATE IT 4HERE ARE SEVERAL TECHNIQUES GENERALLY USED TO HANDLE THIS INCREASED DYNAMIC RANGE IN FIXED POINT &&4S /NE SCHEME WOULD BE TO ENSURE THAT THE COMPUTATION STAGES CARRY ENOUGH BITS TO ACCOMMODATE THE BIT GROWTH &OR EXAMPLE IN OUR POINT &&4 EXAMPLE IF WE ASSUME THAT THE INPUT SAMPLES ARE BIT COMPLEX NUMBERS AND IF WE ASSUME THAT THE MAGNITUDES OF THE COMPLEX NUMBERS DO NOT EXCEED BITS THEN THE FINAL &&4 OUTPUTS COULD GROW BITS COMPARED TO THE INPUTS SO THE &&4 COMPUTATIONS COULD BE PERFORMED WITH BIT OR LARGER ADDERS 4HIS ALSO MEANS THAT THE MULTIPLIERS WOULD HAVE TO HANDLE THE LARGER NUMBER OF BITS ON THE INPUTS 4HIS METHOD COULD GET UNWIELDY FOR LARGE &&4S !NOTHER TECHNIQUE IS TO AUTOMATICALLY SCALE THE OUTPUTS OF EACH STAGE BY A FACTOR OF WHICH WOULD NOT ALLOW THE OUTPUTS TO GROW 5NFORTUNATELY THIS WOULD ALSO LIMIT ANY PROCESSING GAIN THAT THE &&4 MIGHT OFFER ! THIRD METHOD CALLED BLOCK FLOATING POINT CHECKS THE MAGNITUDES OF ALL THE OUT PUTS AFTER EACH STAGE IS COMPUTED AND PROVIDES A SINGLE EXPONENT FOR ALL OUTPUT VALUES )F ANY OF THE OUTPUTS HAVE OVERFLOWED OR COME NEAR TO OVERFLOWING THEN ALL OF THE OUTPUTS ARE SCALED BY A FACTOR OF AND THE COMMON EXPONENT IS INCREMENTED BY %NOUGH BITS HAVE TO BE PROVIDED IN THE FINAL MANTISSA TO ACCOMMODATE THE DYNAMIC RANGE GROWTH 4HIS TECHNIQUE IS POPULAR BECAUSE IT ONLY SCALES THE OUTPUT VALUES WHEN ABSOLUTELY NECESSARY
Óx°xÊ - Ê " - ,/" 4HIS SECTION ADDRESSES TOPICS THAT NEED TO BE CONSIDERED IN THE DESIGN OF RADAR $30 SYSTEMS AS WELL AS IMPLEMENTATION ALTERNATIVES 4IMING $EPENDENCIES )N COHERENT RADAR SYSTEMS ALL LOCAL OSCILLATORS ,/S AND CLOCKS THAT GENERATE SYSTEM TIMING ARE DERIVED FROM A SINGLE REFERENCE OSCILLA TOR (OWEVER THIS FACT ALONE DOES NOT ENSURE THAT THE TRANSMITTED WAVEFORM STARTS AT THE SAME 2& PHASE ON EVERY PULSE WHICH IS A REQUIREMENT FOR COHERENT SYSTEMS
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#ONSIDER A SYSTEM WITH A -(Z REFERENCE OSCILLATOR FROM WHICH IS DERIVED A -(Z )& CENTER FREQUENCY ON TRANSMIT AND RECEIVE AND A COMPLEX SAMPLE RATE OF -(Z ! RULE OF THUMB IS THAT THE CLOCK USED TO PRODUCE THE PULSE REPETITION INTERVAL 02) NEEDS TO BE A COMMON DENOMINATOR OF THE )& CENTER FREQUENCIES ON TRANSMIT AND RECEIVE AND THE COMPLEX SAMPLE FREQUENCY IN ORDER TO ASSURE PULSE TO PULSE PHASE COHERENCY &OR THIS EXAMPLE WITH AN )& CENTER FREQUENCY OF -(Z AND A COMPLEX SAMPLE RATE OF -(Z ALLOWABLE 02) CLOCK FREQUENCIES WOULD INCLUDE -(Z AND -(Z (ARDWARE )MPLEMENTATION 4ECHNOLOGY )N THE PAST IMPLEMENTING A REAL TIME RADAR DIGITAL SIGNAL PROCESSOR TYPICALLY REQUIRED THE DESIGN OF A CUSTOM COMPUT ING MACHINE USING THOUSANDS OF HIGH PERFORMANCE INTEGRATED CIRCUITS )#S 4HESE MACHINES WERE VERY DIFFICULT TO DESIGN DEVELOP AND MODIFY $IGITAL TECHNOLOGY HAS ADVANCED TO THE POINT WHERE SEVERAL IMPLEMENTATION ALTERNATIVES EXIST THAT MAKE THE PROCESSOR MORE PROGRAMMABLE AND HENCE EASIER TO DESIGN AND CHANGE 0ARALLEL 'ENERAL PURPOSE #OMPUTERS 4HIS ARCHITECTURE EMPLOYS MULTIPLE GEN ERAL PURPOSE PROCESSORS THAT ARE CONNECTED VIA HIGH SPEED COMMUNICATION NETWORKS )NCLUDED IN THIS CLASS ARE HIGH END SERVERS AND EMBEDDED PROCESSOR ARCHITECTURES 3ERVERS ARE TYPICALLY HOMOGENEOUS PROCESSORS WHERE ALL OF THE PROCESSING NODES ARE IDENTICAL AND ARE CONNECTED BY A VERY HIGH PERFORMANCE DATA BUS ARCHITECTURE %MBEDDED PROCESSOR ARCHITECTURES ARE TYPICALLY COMPOSED OF SINGLE BOARD COMPUTERS BLADES THAT CONTAIN MULTIPLE GENERAL PURPOSE PROCESSORS AND PLUG INTO A STANDARD BACKPLANE ARCHITECTURE SUCH AS 6-% 4HIS CONFIGURATION OFFERS THE FLEXIBILITY OF SUP PORTING A HETEROGENEOUS ARCHITECTURE WHERE A VARIETY OF DIFFERENT PROCESSING BLADES OR INTERFACE BOARDS CAN BE PLUGGED INTO THE STANDARD BACKPLANE TO CONFIGURE A TOTAL SYSTEM !T THIS WRITING BACKPLANES ARE MIGRATING FROM PARALLEL ARCHITECTURES WHERE DATA IS TYPICALLY PASSED AS OR BIT WORDS TO SERIAL DATA LINKS WHICH PASS SINGLE BITS AT VERY HIGH CLOCK RATES CURRENTLY IN EXCESS OF GIGABITS PER SECOND 'BPS 4HESE SERIAL DATA LINKS ARE TYPICALLY POINT TO POINT CONNECTIONS )N ORDER TO COMMUNI CATE WITH MULTIPLE BOARDS THE SERIAL LINKS FROM EACH BOARD GO TO A HIGH SPEED SWITCH BOARD THAT CONNECTS THE APPROPRIATE SOURCE AND DESTINATION SERIAL LINKS TOGETHER TO FORM A SERIAL FABRIC %XAMPLES OF POPULAR SERIAL FABRIC BACKPLANES AT THIS WRITING INCLUDE 683 608 AND !4#! )T IS APPARENT THAT HIGH SPEED SERIAL LINKS WILL BE THE PRIMARY COMMUNICATION MECHANISM FOR MULTIPROCESSOR MACHINES INTO THE FUTURE WITH EVER INCREASING DATA BANDWIDTHS 4HESE PARALLEL PROCESSOR ARCHITECTURES OFFER THE BENEFIT OF BEING PROGRAMMABLE USING HIGH LEVEL LANGUAGES SUCH AS # AND # ! RELATED ADVANTAGE IS THAT PROGRAM MERS CAN DESIGN THE SYSTEM WITHOUT KNOWING THE INTIMATE DETAILS OF THE HARDWARE !LSO THE SOFTWARE DEVELOPED TO IMPLEMENT THE SYSTEM CAN TYPICALLY BE MOVED RELA TIVELY EASILY TO A NEW HARDWARE ARCHITECTURE AS PART OF A TECHNOLOGY REFRESH CYCLE /N THE NEGATIVE SIDE THESE SYSTEMS CAN BE DIFFICULT TO PROGRAM TO SUPPORT REAL TIME SIGNAL PROCESSING 4HE REQUIRED OPERATIONS NEED TO BE SPLIT UP APPROPRIATELY AMONG THE AVAILABLE PROCESSORS AND THE RESULTS NEED TO BE PROPERLY MERGED TO FORM THE FINAL RESULT ! MAJOR CHALLENGE IN THESE APPLICATIONS IS TO SUPPORT THE PROCESSING LATENCY REQUIREMENTS OF THE SYSTEM WHICH DEFINES THE MAXIMUM LENGTH OF TIME ALLOWED TO PRODUCE A RESULT 4HE LATENCY OF A PROCESSOR IS DEFINED AS THE AMOUNT OF TIME REQUIRED TO OBSERVE THE EFFECT OF A CHANGE AT A PROCESSORS INPUT ON ITS OUTPUT !CHIEVING LATENCY GOALS OFTEN REQUIRES ASSIGNING SMALLER PIECES OF THE WORKLOAD TO INDIVIDUAL PROCESSORS LEADING TO MORE PROCESSORS AND A MORE EXPENSIVE SYSTEM !NOTHER CHALLENGE FACING
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THESE SYSTEMS IN A RADAR APPLICATION IS RESET TIME )N A MILITARY APPLICATION WHEN A SYSTEM NEEDS TO BE RESET IN ORDER TO FIX A PROBLEM THE SYSTEM NEEDS TO COME BACK TO FULL OPERATION IN A VERY SHORT PERIOD OF TIME 4HESE MULTIPROCESSOR SYSTEMS TYPICALLY TAKE A LONG TIME TO REBOOT FROM A CENTRAL PROGRAM STORE AND HENCE HAVE DIFFICULTY MEETING RESET REQUIREMENTS $EVELOPING TECHNIQUES TO ADDRESS THESE DEFICIENCIES IS AN ACTIVE AREA OF RESEARCH &INALLY THESE PROCESSORS ARE GENERALLY USED FOR NON REAL TIME OR NEAR REAL TIME DATA PROCESSING AS IN TARGET TRACKING AND DISPLAY PROCESSING 3INCE THE S THEY HAVE STARTED TO BE APPLIED TO REAL TIME SIGNAL PROCESSING APPLICATIONS !LTHOUGH THEY MIGHT BE COST EFFECTIVE FOR RELATIVELY NARROWBAND SYSTEMS THEIR USE IN WIDEBAND $30 SYSTEMS IN THE EARLY ST CENTURY IS TYPICALLY PROHIBITIVELY EXPENSIVE DUE TO THE LARGE NUMBER OF PROCESSORS REQUIRED 4HIS SITUATION SHOULD IMPROVE OVER TIME AS FASTER AND FASTER PROCESSORS BECOME AVAILABLE #USTOM DESIGNED (ARDWARE 4HROUGH THE S REAL TIME RADAR $30 SYSTEMS WERE BUILT USING DISCRETE LOGIC 4HESE SYSTEMS WERE VERY DIFFICULT TO DEVELOP AND MOD IFY BUT IN ORDER TO ACHIEVE THE REQUIRED SYSTEM PERFORMANCE IT WAS THE ONLY OPTION AVAILABLE -ANY SYSTEMS WERE BUILT USING !PPLICATION 3PECIFIC )NTEGRATED #IRCUITS !3)#S WHICH ARE CUSTOM DEVICES DESIGNED TO PERFORM A PARTICULAR FUNCTION 4HE USE OF !3)#S ALLOWED $30 SYSTEMS TO BECOME VERY SMALL WITH HIGH PERFORMANCE (OWEVER THEY WERE AND STILL ARE DIFFICULT AND EXPENSIVE TO DEVELOP OFTEN REQUIRING SEVERAL DESIGN ITERATIONS BEFORE THE DEVICE WAS FULLY OPERATIONAL )F AN !3)# BASED SYSTEM NEEDS TO BE MODIFIED THE !3)#S NEED TO BE REDESIGNED INCURRING SIGNIFICANT EXPENSE 4YPICALLY THE USE OF !3)#S MAKES SENSE IF TENS OR HUNDREDS OF THOUSANDS OF UNITS ARE TO BE SOLD SO THAT THE DEVELOPMENT COSTS CAN BE AMORTIZED OVER THE LIFE OF THE UNIT 4HIS IS RARELY THE CASE FOR RADAR SYSTEMS (OWEVER MANY !3)#S HAVE BEEN DEVEL OPED TO SUPPORT THE COMMUNICATION INDUSTRY SUCH AS DIGITAL UP AND DOWNCONVERTERS WHICH CAN BE UTILIZED IN RADAR SYSTEMS 4HE INTRODUCTION OF THE &IELD 0ROGRAMMABLE 'ATE !RRAY &0'! IN THE S HERALDED A REVOLUTION IN THE WAY REAL TIME $30 SYSTEMS WERE DESIGNED &0'!S ARE INTEGRATED CIRCUITS THAT CONSIST OF A LARGE ARRAY OF CONFIGURABLE LOGIC ELEMENTS THAT ARE CONNECTED BY A PROGRAMMABLE INTERCONNECT STRUCTURE !T THE TIME OF THIS WRITING &0'!S CAN ALSO INCORPORATE HUNDREDS OF MULTIPLIERS THAT CAN BE CLOCKED AT RATES UP TO A HALF BILLION OPERATIONS PER SECOND AND MEMORY BLOCKS MICROPROCESSORS AND SERIAL COMMUNICATION LINKS THAT CAN SUPPORT MULTIGIGABIT PER SECOND DATA TRANSFERS #IRCUITS ARE TYPICALLY DESIGNED USING A HARDWARE DESCRIPTION LANGUAGE ($, SUCH AS 6($, 6(3)# (ARDWARE $ESCRIPTION ,ANGUAGE OR 6ERILOG 3OFTWARE TOOLS CON VERT THIS HIGH LEVEL DESCRIPTION OF THE PROCESSOR TO A FILE THAT IS SENT TO THE DEVICE TO TELL IT HOW TO CONFIGURE ITSELF (IGH PERFORMANCE &0'!S STORE THEIR CONFIGURATION IN VOLATILE MEMORY WHICH LOSES ITS CONTENTS WHEN POWERED DOWN MAKING THE DEVICES INFINITELY REPROGRAMMABLE &0'!S ALLOW THE DESIGNER TO FABRICATE COMPLEX SIGNAL PROCESSING ARCHITECTURES VERY EFFICIENTLY )N TYPICAL LARGE APPLICATIONS &0'! BASED PROCESSORS CAN BE A FACTOR OF TEN OR MORE SMALLER AND LESS COSTLY THAN SYSTEMS BASED ON GENERAL PURPOSE PROCESSORS 4HIS IS DUE TO THE FACT THAT MOST MICROPROCESSORS ONLY HAVE ONE OR VERY FEW PROCESSING ELEMENTS WHEREAS &0'!S HAVE AN ENORMOUS NUMBER OF PROGRAMMABLE LOGIC ELEMENTS AND MULTIPLIERS &OR EXAMPLE TO IMPLEMENT A TAP &)2 FILTER IN A MICROPROCESSOR WITH A SINGLE MULTIPLIER AND ACCUMULATOR IT WOULD TAKE CLOCK CYCLES TO PERFORM THE MULTIPLICATIONS )N AN &0'! WE COULD ASSIGN MULTIPLIERS AND ACCUMULATORS TO THE TASK AND THE FILTER COULD BE PERFORMED IN ONE CLOCK CYCLE
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)N ORDER TO USE AN &0'! MOST EFFICIENTLY WE HAVE TO TAKE ADVANTAGE OF ALL OF THE RESOURCES IT OFFERS 4HESE INCLUDE NOT ONLY THE LARGE NUMBERS OF LOGIC ELEMENTS MULTIPLIERS AND MEMORY BLOCKS BUT ALSO THE RATE AT WHICH THE COMPONENTS CAN BE CLOCKED )N THE PREVIOUS EXAMPLE ASSUME THAT THE DATA SAMPLE RATE IS -(Z AND ALSO ASSUME THAT THE MULTIPLIERS AND LOGIC CAN BE CLOCKED AT -(Z )F WE SIMPLY ASSIGN ONE MULTIPLIER TO EACH COEFFICIENT WE WOULD USE MULTIPLIERS CLOCKING AT -(Z 3INCE THE DATA RATE IS ONLY -(Z EACH MULTIPLIER WOULD ONLY PERFORM ONE SIGNIFICANT MULTIPLICATION EVERY MICROSECOND AND THEN BE IDLE FOR THE OTHER CLOCKS IN THE MICROSECOND WHICH IS VERY INEFFICIENT )T WOULD BE MUCH MORE EFFICIENT IN THIS CASE TO USE ONE MULTIPLIER TO PERFORM AS MANY PRODUCTS AS POSSIBLE 4HIS TECHNIQUE CALLED TIME DOMAIN MULTIPLEXING REQUIRES ADDITIONAL LOGIC TO CONTROL THE SYSTEM AND PROVIDE THE CORRECT OPERANDS TO THE MULTIPLIER AT THE RIGHT TIME 3INCE AN &0'! CAN INCORPORATE HUNDREDS OF MULTIPLIERS ONE CAN APPRECIATE THE POWER OF THIS TECHNIQUE /N THE NEGATIVE SIDE UTILIZING AN &0'! TO ITS BEST ADVANTAGE TYPICALLY REQUIRES THE DESIGNER TO HAVE A THOROUGH UNDERSTANDING OF THE RESOURCES AVAILABLE IN THE DEVICE 4HIS TYPICALLY MAKES EFFICIENT &0'! BASED SYSTEMS HARDER TO DESIGN THAN SYSTEMS BASED ON GENERAL PURPOSE PROCESSORS WHERE A DETAILED UNDERSTANDING OF THE PROCES SOR ARCHITECTURE IS NOT NECESSARILY REQUIRED !LSO &0'! DESIGNS TEND TO BE AIMED AT A PARTICULAR FAMILY OF DEVICES AND TAKE FULL ADVANTAGE OF THE RESOURCES PROVIDED BY THAT FAMILY (ARDWARE VENDORS ARE CONSTANTLY INTRODUCING NEW PRODUCTS INVARIABLY INCORPORATING NEW AND IMPROVED CAPABILITIES /VER TIME THE OLDER DEVICES BECOME OBSOLETE AND NEED TO BE REPLACED DURING A TECHNOLOGY REFRESH CYCLE 7HEN A TECHNOL OGY REFRESH OCCURS SEVERAL YEARS DOWN THE ROAD TYPICALLY THE AVAILABLE RESOURCES IN THE LATEST &0'!S HAVE CHANGED OR A TOTALLY DIFFERENT DEVICE FAMILY IS USED WHICH PROBABLY REQUIRES A REDESIGN /N THE OTHER HAND SOFTWARE DEVELOPED FOR GENERAL PURPOSE PRO CESSORS MAY ONLY NEED TO BE RECOMPILED IN ORDER TO MOVE IT TO A NEW PROCESSOR 4OOLS CURRENTLY EXIST THAT SYNTHESIZE # OR -ATLAB CODE INTO AN &0'! DESIGN BUT THESE TOOLS ARE TYPICALLY NOT VERY EFFICIENT 4HE EVOLUTION OF DESIGN TOOLS FOR &0'!S TO ADDRESS THESE PROBLEMS IS AN AREA OF MUCH RESEARCH AND DEVELOPMENT (YBRID 0ROCESSORS !LTHOUGH IT WOULD BE VERY DESIRABLE TO SIMPLY WRITE # CODE TO IMPLEMENT A COMPLEX RADAR SIGNAL PROCESSOR THE REALITY IN THE EARLY ST CENTURY IS THAT FOR MANY SYSTEMS IMPLEMENTING SUCH A SYSTEM WOULD BE PROHIBITIVELY EXPENSIVE OR INFLICT MAJOR PERFORMANCE DEGRADATION !LTHOUGH THE STEADY INCREASE IN PROCESSOR THROUGHPUT MAY SOMEDAY COME TO THE RESCUE THE REALITY AT THIS WRITING IS THAT HIGH PERFORMANCE RADAR SIGNAL PROCESSORS ARE USUALLY A HYBRID OF APPLICATION SPECIFIC AND PROGRAMMABLE PROCESSORS $EDICATED PROCESSORS SUCH AS &0'!S OR !3)#S ARE TYPI CALLY USED IN THE HIGH SPEED FRONT END OF RADAR SIGNAL PROCESSORS PERFORMING DEMAND ING FUNCTIONS SUCH AS DIGITAL DOWNCONVERSION AND PULSE COMPRESSION FOLLOWED BY PROGRAMMABLE PROCESSORS IN THE REAR PERFORMING THE LOWER SPEED TASKS SUCH AS DETEC TION PROCESSING 4HE LOCATION OF THE LINE THAT SEPARATES THE TWO DOMAINS IS APPLICATION DEPENDENT BUT OVER TIME IT IS CONSTANTLY MOVING TOWARD THE FRONT END OF THE SYSTEM
Óx°ÈÊ -1 ,9 4HE PURPOSE OF THIS CHAPTER WAS TO PROVIDE AN OVERVIEW OF HOW DIGITAL SIGNAL PROCESS ING HAS TRANSFORMED RADAR SYSTEM DESIGN AND TO GIVE SOME INSIGHT INTO THE TECHNIQUES AND TRADEOFFS THAT A DESIGNER HAS TO CONSIDER 7ITH MANUFACTURERS CONTINUALLY PRODUCING
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&)'52% $IRECT SAMPLING RADAR DIGITAL RECEIVER
FASTER AND MORE POWERFUL !$#S $30 DEVICES AND GENERAL PURPOSE PROCESSORS MORE AND MORE OF THE RADAR SYSTEM FRONT END WILL MOVE FROM ANALOG TO DIGITAL DESIGNS &OR EXAMPLE &IGURE SHOWS A TYPICAL DIGITAL RECEIVER FOR A RADAR FRONT END WHICH REQUIRES TWO STAGES OF ANALOG DOWNCONVERSION TO BRING THE 2& SIGNAL DOWN TO AN )& THAT CAN BE SAMPLED BY AN !$# 4HIS IS REQUIRED BECAUSE OF THE CHARACTERISTICS OF THE !$# WHICH TYPICALLY HAS POORER SIGNAL TO NOISE RATIO 3.2 AND SPUR FREE DYNAMIC RANGE 3&$2 WHEN THE INPUT ANALOG SIGNAL IS TOO HIGH AS WOULD BE THE CASE IF IT WERE PRESENTED WITH THE 2& OR HIGH )& SIGNAL DIRECTLY (OWEVER WHEN FASTER !$#S BECOME AVAILABLE WHICH CAN ACCOMMODATE HIGHER ANALOG INPUT FREQUENCIES WHILE PROVIDING ADEQUATE 3.2 AND 3&$2 SYSTEMS WILL BE DESIGNED THAT SAMPLE THE 2& DIRECTLY AS SHOWN IN &IGURE !T THIS WRITING !$# TECHNOLOGY ALLOWS DIRECT SAMPLING SYSTEMS WITH RESPECTABLE PERFOR MANCE TO BE DESIGNED FOR RADARS IN THE (& AND 6(& BANDS $OUBTLESS FUTURE COMPONENTS WILL EXTEND THIS PERFORMANCE TO HIGHER 2& FREQUENCIES
"7 /4HE AUTHORS WOULD LIKE TO ACKNOWLEDGE THE EFFORTS OF AND EXTEND THEIR SINCERE GRATI TUDE TO SEVERAL INDIVIDUALS WHO HELPED THEM IMMENSELY IN THE PREPARATION OF THIS CHAPTER &IRST TO -R 'REGORY 4AVIK OF .2, FOR HIS THOROUGH REVIEW OF THIS CHAPTER AND THE MANY EXCELLENT COMMENTS HE MADE .EXT TO $R &RED (ARRIS OF 3AN $IEGO 3TATE 5NIVERSITY AND -R 2ICHARD ,YONS WHO GRACIOUSLY REVIEWED SECTIONS OF THE CHAPTER AND OFFERED SEVERAL SUGGESTIONS ALL OF WHICH WERE INCORPORATED
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! 6 /PPENHEIM AND 2 7 3CHAFER $IGITAL 3IGNAL 0ROCESSING ND %D %NGLEWOOD #LIFFS .* 0RENTICE (ALL 2 ' ,YONS 5NDERSTANDING $IGITAL 3IGNAL 0ROCESSING ND %D 5PPER 3ADDLE 2IVER .* 0RENTICE (ALL * / #OLEMAN h-ULTI RATE $30 BEFORE DISCRETE TIME SIGNALS AND SYSTEMS v PRESENTED AT &IRST )%%% 7ORKSHOP ON 3IGNAL 0ROCESSING %DUCATION 30% (UNT 48 /CTOBER 7 - 7ATERS AND " 2 *ARRETT h"ANDPASS SIGNAL SAMPLING AND COHERENT DETECTION v )%%% 4RANS /N !EROSPACE %LECTRONIC 3YSTEMS VOL !%3 NO PP n .OVEMBER $ 0 3CHOLNIK AND * / #OLEMAN h)NTEGRATED ) 1 DEMODULATION MATCHED FILTERING AND SYMBOL RATE SAMPLING USING MINIMUM RATE )& SAMPLING v IN 0ROC OF THE 3YMPOSIUM ON 7IRELESS 0ERSONAL #OMMUNICATION "LACKSBURG 6! *UNE
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#HAPTER
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iÊ,>`>ÀÊ µÕ>Ì 7>ÞiÊ °Ê*>ÌÌiÀÃ 3PACE AND .AVAL 7ARFARE 3YSTEMS #ENTER !TMOSPHERIC 0ROPAGATION "RANCH
ÓÈ°£Ê /," 1 /" 0ARALLELING THE DEVELOPMENT OF RADAR TECHNOLOGY IS THE DEVELOPMENT OF THE RADAR EQUA TION !S ENGINEERING CONSIDERATIONS SUCH AS THE PROBABILITY OF DETECTION PROBABILITY OF FALSE ALARM SIGNAL LOSS FACTORS AND SIGNAL TO NOISE RATIO ALLOWED THE RADAR RANGE EQUATION TO DEVELOP SUFFICIENTLY TO BE USEFUL IN RADAR PERFORMANCE ANALYSIS DEVELOPING COMPUTER TECHNOLOGIES ALLOWED FOR MORE SOPHISTICATED RADAR RANGE EQUATION SOLUTION TECHNIQUES 4HUS SOLUTION TECHNIQUES TO THE RADAR RANGE EQUATION MIGRATED FROM PENCIL AND PAPER hWORKSHEETSv TO SIMPLE COMPUTER PROGRAMS AUTOMATING THE hWORKSHEETv TO HIGHLY SOPHISTICATED COMPUTER PROGRAMS ACCOUNTING FOR TECHNOLOGY ADVANCES IN SIGNAL PROCESSING AND ENVIRONMENTAL MODELING 4HE INTENT OF THIS CHAPTER IS TWOFOLD 4HE FIRST IS TO FOCUS ON ONE PARTICULAR TERM OF THE RADAR RANGE EQUATION THE PROPAGATION FACTOR &0 DEFINED IN 3ECTION %NCOMPASSED WITHIN THE PROPAGATION FACTOR ARE ALL THE EFFECTS UPON PROPAGATION ATTRIB UTABLE TO THE NATURAL ENVIRONMENT 4HESE EFFECTS ARE ENERGY ABSORPTION FROM GASSES AND LIQUID WATER DIFFRACTION REFRACTION MULTIPATH INTERFERENCE EARTH SURFACE DIELECTRICS TERRAIN INTERFERENCE AND A NUMBER OF OTHER NATURAL ENVIRONMENTAL CONSIDERATIONS 4HE SECOND FOCUS OF THIS CHAPTER IS TO DESCRIBE THE COMPUTER MODELING OF THE PROPA GATION FACTOR &OR EASE OF COMPUTATIONS IN EARLY SOLUTION TECHNIQUES THE PROPAGATION FACTOR WAS OFTEN TAKEN AS UNITY A CONDITION REPRESENTING FREE SPACE 7ITH COMPUTER IMPLEMENTED PROPAGATION MODELS HOWEVER THE ASSUMPTION OF FREE SPACE NEED NO LONGER BE A LIMITING FACTOR /NE SUCH PROPAGATION MODEL THE !DVANCED 0ROPAGATION -ODEL !0- AND ITS GRAPHICAL USER INTERFACE PROGRAM THE !DVANCED 2EFRACTIVE %FFECTS 0REDICTION 3YSTEM !2%03 ARE FEATURED HERE 7HILE THE FOCUS UPON !2%03 WITHIN THIS CHAPTER IS FOR THE UNDERSTANDING OF HOW IMPORTANT THE PROPAGATION FACTOR IS WITHIN THE RADAR EQUATION !2%03 IS MUCH MORE THAN A PROPAGATION FACTOR TOOL !2%03 PROVIDES THE RADAR ENGINEER AND THE OPERATIONAL RADAR OPERATOR WITH AN EASY TO USE BUT EXTREMELY POWERFUL METHOD TO DEFINE THE NATURAL ATMOSPHERIC ENVIRONMENT USING DATA FROM A WIDE RANGE OF SOURCES TO MANAGE CREATE AND DEFINE VARIOUS ELEMENTS OF TER RAIN DATA TO EXECUTE THE APPROPRIATE PROPAGATION MODEL FOR THE TASK AT HAND AND THEN TO PRESENT THE RESULTS IN A NUMBER OF DIFFERENT AND HIGHLY CONFIGURABLE GRAPHIC AND ÓÈ°£
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TEXT DISPLAYS INCLUDING EXPORTING COMPUTED DATA IN SEVERAL FORMATS FOR IMPORT INTO OTHER APPLICATIONS !2%03 IS NOT LIMITED TO JUST RADAR APPLICATIONS HOWEVER !2%03 TOGETHER WITH !0- AND ITS OTHER EMBEDDED PROPAGATION MODELS CAN PROVIDE ASSESS MENTS FOR ,& TO %(& COMMUNICATIONS GROUND AND SKY WAVE STRIKE AND ELECTRONIC COUNTERMEASURES %LECTRONIC 3UPPORT -EASURES %3- VULNERABILITIES AND MANY OTHER APPLICATIONS !2%03 AND !0- ARE PRODUCTS OF THE ATMOSPHERIC PROPAGATION BRANCH OF THE 3PACE AND .AVAL 7ARFARE 3YSTEMS #ENTER 30!7!2393#%. 3AN $IEGO !2%03 WILL EXECUTE ON A PERSONAL COMPUTER DESKTOP OR LAPTOP USING A -ICROSOFT 7INDOWS OPERATING SYSTEM SUCH AS .4 80 OR 6ISTA AND REQUIRES NO ADDITIONAL SPECIAL HARDWARE !2%03 MAY BE FREELY OBTAINED AT THE 52, LISTED IN THE FIRST REFERENCE "EFORE CONTINUING WITH THE DISCUSSION OF ELECTROMAGNETIC %- PROPAGATION MOD ELS AND ASSESSMENT SYSTEMS IT IS APPROPRIATE TO DISCUSS THE NATURAL ENVIRONMENT AND ITS INFLUENCE UPON %- SYSTEM PERFORMANCE
ÓÈ°ÓÊ / Ê ,/½-Ê/ "-* , £ 3TRUCTURE AND #HARACTERISTICS 4HE %ARTHS ATMOSPHERE IS A COLLECTION OF MANY GASES TOGETHER WITH SUSPENDED PARTICLES OF LIQUIDS AND SOLIDS %XCLUDING VARIABLE COMPONENTS SUCH AS WATER VAPOR OZONE SULFUR DIOXIDE AND DUST THE GASES OF NITROGEN AND OXYGEN OCCUPY ABOUT OF THE VOLUME WITH ARGON AND CARBON DIOXIDE BEING THE NEXT TWO MOST ABUNDANT GASES &ROM THE %ARTHS SURFACE TO AN ALTITUDE OF APPROXIMATELY KILOMETERS MECHANICAL MIXING OF THE ATMOSPHERE BY HEAT DRIVEN AIR CURRENTS EVENLY DISTRIBUTES THE COMPONENTS OF THE ATMOSPHERE !T ABOUT KILOMETERS THE MIXING DECREASES TO THE POINT WHERE THE GASES TEND TO STRATIFY IN ACCORDANCE WITH THEIR WEIGHTS 4HE LOWER WELL MIXED PORTION OF THE ATMOSPHERE IS CALLED THE HOMOSPHERE WHILE THE HIGHER STRATIFIED PORTION IS CALLED THE HETEROSPHERE 7ITHIN THE HETEROSPHERE LIES THE IONOSPHERE 4HE BOTTOM PORTION OF THE HOMOSPHERE IS CALLED THE TROPOSPHERE 4ROPOSPHERE 4HE TROPOSPHERE EXTENDS FROM THE %ARTHS SURFACE TO AN ALTITUDE OF TO KILOMETERS AT POLAR LATITUDES TO KILOMETERS AT MIDDLE LATITUDES AND UP TO KILOMETERS AT THE EQUATOR )T IS CHARACTERIZED BY A TEMPERATURE DECREASE WITH HEIGHT 4HE POINT AT WHICH THE TEMPERATURE CEASES TO DECREASE WITH HEIGHT IS KNOWN AS THE TROPOPAUSE 4HE AVERAGE VERTICAL TEMPERATURE GRADIENT OF THE TROPOSPHERE VARIES BETWEEN AND #ELSIUS PER KILOMETER 4HE CONCENTRATIONS OF GAS COMPONENTS OF THE TROPOSPHERE VARY LITTLE WITH HEIGHT EXCEPT FOR WATER VAPOR 4HE WATER VAPOR CONTENT OF THE TROPOSPHERE COMES FROM EVAP ORATION OF WATER FROM OCEANS LAKES RIVERS AND OTHER WATER RESERVOIRS $IFFERENTIAL HEATING OF LAND AND OCEAN SURFACES PRODUCES VERTICAL AND HORIZONTAL WIND CIRCULATIONS THAT DISTRIBUTE THE WATER VAPOR THROUGHOUT THE TROPOSPHERE 4HE WATER VAPOR CONTENT OF THE TROPOSPHERE RAPIDLY DECREASES WITH HEIGHT !T AN ALTITUDE OF KILOMETERS THE WATER VAPOR CONTENT IS APPROXIMATELY HALF OF THE SURFACE CONTENT !T THE TROPOPAUSE THE CONTENT IS ONLY A FEW THOUSANDTHS OF WHAT IT IS AT THE SURFACE )N THE 7EATHER "UREAU AT THE REQUEST OF THE .ATIONAL !DVISORY #OMMITTEE FOR !ERONAUTICS .!#! PREPARED A STANDARD ATMOSPHERE FOR SCIENTIFIC AND ENGINEERING USE BASED PRIMARILY ON THE AVERAGE CONDITIONS OVER THE 5NITED 3TATES AT LATITUDE )N THE COMPUTATIONS WERE EXTENDED TO METERS USING CONSTANTS ADOPTED BY THE .!#! !N EXTENSION OF THE STANDARD ATMOSPHERE TO METERS WAS PREPARED IN
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4HE STANDARD ATMOSPHERE IS BASED PRIMARILY ON THE ASSUMPTION OF A LINEAR DECREASE IN TEMPERATURE WITH HEIGHT UP TO THE TROPOPAUSE AND AN ISOTHERMAL LAYER ABOVE )N ADDI TION CERTAIN OTHER ASSUMPTIONS ARE A 4HE AIR IS DRY B 4HE AIR IS A PERFECT GAS OBEYING THE ,AWS OF #HARLES AND "OYLE C 'RAVITY IS CONSTANT AT ALL ALTITUDES D 4HE TEMPERATURE OF THE ISOTHERMAL ATMOSPHERE IS # E 4HE LINEAR DECREASE OF TEMPERATURE WITH HEIGHT IS # PER KILOMETER 4HE )NTERNATIONAL #OMMISSION FOR !IR .AVIGATION )#!. USES THE .!#! STANDARD ATMOSPHERE WITH MINOR MODIFICATIONS PRIMARILY IN THE VALUE OF GRAVITY AND THE TEMPERATURE OF THE ISOTHERMAL REGION &OR GENERIC RADAR STUDIES AND OTHER RADAR APPLICATIONS SUCH AS TARGET HEIGHT CALCULATIONS FOR HEIGHT FINDING RADARS IT IS THE PROP AGATION THROUGH THIS STANDARD ATMOSPHERE THAT IS CONSIDERED
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)NDEX OF 2EFRACTION 4HE TERM REFRACTION REFERS TO THE PROPERTY OF A MEDIUM TO BEND AN ELECTROMAGNETIC WAVE AS IT PASSES THROUGH THE MEDIUM ! MEASURE OF THE AMOUNT OF REFRACTION IS THE INDEX OF REFRACTION N DEFINED AS THE VELOCITY C OF PROPAGA TION IN FREE SPACE AWAY FROM THE INFLUENCE OF THE %ARTH OR OTHER OBJECTS TO THE VELOC ITY V IN THE MEDIUM 4HIS IS
N
C V
2EFRACTIVITY AND -ODIFIED 2EFRACTIVITY IN THE 4ROPOSPHERE 4HE NORMAL VALUE OF THE REFRACTIVE INDEX N FOR THE ATMOSPHERE NEAR THE %ARTHS SURFACE VARIES BETWEEN AND &OR STUDIES OF PROPAGATION THE INDEX OF REFRACTION IS NOT A VERY CONVENIENT NUMBER THEREFORE A SCALED INDEX OF REFRACTION . CALLED REFRACTIVITY HAS BEEN DEFINED !T MICROWAVE FREQUENCIES AND BELOW THE RELATIONSHIP BETWEEN THE INDEX OF REFRACTION N AND REFRACTIVITY . FOR AIR THAT CONTAINS WATER VAPOR IS GIVEN AS
. N
P ES r 4 4
WHERE ES IS THE PARTIAL PRESSURE OF WATER VAPOR IN MILLIBARS OR
ES X
RH E X
4 ¤ 4 ³
LOG E ¥ 4 ¦ ´µ
P ATMOSPHERES BAROMETRIC PRESSURE IN MILLIBARS 4 ATMOSPHERES ABSOLUTE TEMPERATURE IN +ELVIN RH ATMOSPHERES RELATIVE HUMIDITY IN PERCENT
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4HUS THE ATMOSPHERIC REFRACTIVITY NEAR THE %ARTHS SURFACE WOULD NORMALLY VARY BETWEEN AND . UNITS "ECAUSE THE BAROMETRIC PRESSURE AND WATER VAPOR CONTENT OF THE ATMOSPHERE DECREASE RAPIDLY WITH HEIGHT WHILE THE TEMPERATURE DECREASES SLOWLY WITH HEIGHT THE INDEX OF REFRACTION AND THEREFORE REFRACTIVITY NORMALLY DECREASES WITH INCREASING ALTITUDE 7HILE A RADAR ENGINEER MAY LIKE TO CONSIDER REFRACTION IN TERMS OF . UNITS BECAUSE IT PROVIDES A BETTER PHYSICAL POINT OF VIEW AN !2%03 USER MAY NOT BE A RADAR ENGINEER BUT A TACTICAL OPERATOR SUCH AS A COMBAT PILOT )N GRAPHICALLY EXAMINING REFRACTIVE GRA DIENTS AND THEIR EFFECT UPON PROPAGATION SUCH AS DUCTING DESCRIBED IN 3ECTION A MODIFIED REFRACTIVITY DEFINED AS
- . H FOR ALTITUDE H IN METERS AN
- . H FOR ALTITUDE H IN FEET
IS USED IN PLACE OF THE REFRACTIVITY 7HILE A GRAPHICAL . UNIT VERSUS HEIGHT DISPLAY WILL SHOW A NEGATIVE SLOPE DECREASING . UNITS WITH HEIGHT A GRAPHICAL - UNIT VERSUS HEIGHT DISPLAY WILL SHOW A CHANGE IN SLOPE FROM POSITIVE INCREASING - UNITS UNDER STANDARD ATMOSPHERIC CONDITIONS TO A NEGATIVE SLOPE DECREASING - UNITS UNDER DUCTING ATMOSPHERIC CONDITIONS 4HEREFORE A - UNIT TYPE DISPLAY IS MORE READILY UNDERSTOOD BY THE TACTICAL RADAR OPERATOR LOOKING FOR AN OPTIMUM FLIGHT ALTITUDE FOR HIS ATTACK
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3TANDARD PROPAGATION MECHANISMS ARE THOSE MECHANISMS AND PROCESSES THAT OCCUR IN THE PRESENCE OF A STANDARD ATMOSPHERE 4HESE PROPAGATION MECHANISMS ARE STANDARD REFRACTION FREE SPACE PROPAGATION MULTIPATH INTERFERENCE OR SURFACE REFLECTION DIFFRACTION AND TROPOSPHERIC SCATTER .ORMAL3TANDARD 2EFRACTION 4HE REFRACTIVITY DISTRIBUTION WITHIN THE ATMO SPHERE IS NEARLY AN EXPONENTIAL FUNCTION OF HEIGHT 4HE DECREASE OF . WITH HEIGHT CLOSE TO THE %ARTHS SURFACE WITHIN KILOMETER IS SUFFICIENTLY SMOOTH HOWEVER TO ALLOW AN APPROXIMATION OF THE EXPONENTIAL FUNCTION BY A LINEAR FUNCTION 4HIS LINEAR FUNC TION IS KNOWN AS A STANDARD GRADIENT AND IS CHARACTERIZED BY A DECREASE OF . UNITS PER KILOMETER OR AN INCREASE OF - UNITS PER KILOMETER ! STANDARD GRADIENT WILL CAUSE TRAVELING %- WAVES TO BEND DOWNWARD FROM A STRAIGHT LINE 'RADIENTS THAT CAUSE EFFECTS SIMILAR TO A STANDARD GRADIENT BUT VARY BETWEEN AND . UNITS PER KILOMETER OR BETWEEN AND - UNITS PER KILOMETER ARE KNOWN AS NORMAL GRADIENTS &REE SPACE 0ROPAGATION 4HE SIMPLEST CASE OF ELECTROMAGNETIC WAVE PROPAGA TION IS THE TRANSMISSION OF A WAVE BETWEEN A TRANSMITTER AND A RECEIVER IN FREE SPACE &REE SPACE IS DEFINED AS A REGION WHOSE PROPERTIES ARE ISOTROPIC HOMOGENEOUS AND LOSS FREE IE AWAY FROM THE INFLUENCES OF THE %ARTHS ATMOSPHERE AND SURFACE )N FREE SPACE THE ELECTROMAGNETIC WAVEFRONT FROM AN ISOTROPIC RADIATOR SPREADS UNIFORMLY IN ALL DIRECTIONS FROM THE TRANSMITTER -ULTIPATH )NTERFERENCE AND 3URFACE 2EFLECTION 7HEN AN ELECTROMAGNETIC WAVE STRIKES A NEARLY SMOOTH LARGE SURFACE SUCH AS THE OCEAN A PORTION OF THE ENERGY IS REFLECTED FROM THE SURFACE AND CONTINUES PROPAGATING ALONG A PATH THAT MAKES AN
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ANGLE WITH THE SURFACE EQUAL TO THAT OF THE INCIDENT WAVE AS SHOWN IN &IGURE
4HE STRENGTH OF THE REFLECTED WAVE IS DETERMINED BY THE REFLECTION COEFFICIENT A VALUE THAT DEPENDS UPON THE FREQUENCY AND POLARIZATION OF RADIATION THE ANGLE OF INCIDENCE AND THE ROUGHNESS OF THE REFLECTING SURFACE &)'52% 3URFACE REFLECTION &OR SHALLOW INCIDENCE ANGLES AND SMOOTH SEAS TYPI CAL VALUES OF THE REFLECTION COEFFICIENT ARE NEAR UNITY IE THE REFLECTED WAVE IS ALMOST AS STRONG AS THE INCIDENCE WAVE !S THE WIND SPEED INCREASES THE OCEAN SURFACE GROWS ROUGHER AND THE REFLECTION COEFFICIENT DECREASES &OR A TRANSMITTER NEAR THE SURFACE THE REFLECTION PROCESS RESULTS IN TWO PATHS TO A RECEIVER WITHIN THE LINE OF SIGHT !S STATED ABOVE UPON REFLECTION A PORTION OF THE ENERGY IS PROPAGATED IN THE DIREC TION OF INITIAL WAVE MOTION ! PORTION OF ENERGY IS ALSO REFLECTED BACKWARD TOWARD THE TRANSMITTER 4HIS BACKWARD REFLECTED ENERGY IS ALSO RECEIVED BY THE RADAR AND MAY INTER FERE WITH THE RADARS ABILITY TO DISTINGUISH A DESIRED TARGET 4HIS BACKWARD REFLECTED ENERGY IS CALLED CLUTTER .OT ONLY IS THE MAGNITUDE OF THE REFLECTED WAVE REDUCED BUT ALSO THE PHASE OF THE WAVE IS ALTERED &OR HORIZONTALLY OR VERTICALLY POLARIZED WAVES AT LOW GRAZING ANGLES THE PHASE CHANGE UPON REFLECTION IS APPROXIMATELY 7HENEVER TWO OR MORE WAVE TRAINS TRAVELING OVER DIFFERENT PATHS INTERSECT AT A POINT IN SPACE THEY ARE SAID TO INTER FERE MULTIPATH INTERFERENCE )F TWO WAVES ARRIVE AT THE SAME POINT IN PHASE THEY CONSTRUCTIVELY INTERFERE AND THE ELECTRIC FIELD STRENGTH IS GREATER THAN EITHER OF THE TWO COMPONENT WAVES TAKEN ALONE )F THE TWO WAVES ARRIVE TOGETHER OUT OF PHASE THEY DESTRUCTIVELY INTERFERE AND THE RESULTANT FIELD STRENGTH IS WEAKENED !S THE GEOMETRY OF THE TRANSMITTER AND RECEIVER CHANGE THE RELATIVE LENGTHS OF THE DIRECT PATH AND REFLECTED PATH ALSO CHANGE WHICH RESULTS IN THE DIRECT AND REFLECTED WAVE ARRIVING AT THE RECEIVER IN VARYING AMOUNTS OF PHASE DIFFERENCE 4HE RECEIVED SIG NAL STRENGTH WHICH IS THE VECTOR SUM OF THE SIGNAL STRENGTHS OF THE DIRECT AND REFLECTED WAVE MAY VARY UP TO D" ABOVE AND D" OR MORE BELOW THE FREE SPACE VALUE $IFFRACTION %NERGY TENDS TO FOLLOW ALONG THE CURVED SURFACE OF AN OBJECT 4HE DEGREE OF REFRACTION IS DEPENDENT UPON THE POLARIZATION OF THE PROPAGATING WAVE AND THE SIZE OF THE DIFFRACTING OBJECT RELATIVE TO THE WAVELENGTH $IFFRACTION IS THE PROCESS BY WHICH THE DIRECTION OF PROPAGATING RADIATION IS CHANGED SO THAT IT SPREADS INTO THE GEOMETRIC SHADOW REGION OF AN OPAQUE OBJECT THAT LIES IN THE RADIATION FIELD )N THE EARTH ATMOSPHERE SYSTEM DIFFRACTION OCCURS WHERE THE STRAIGHT LINE DISTANCE BETWEEN THE TRANSMITTER AND RECEIVER IS JUST TANGENT TO THE %ARTHS SURFACE &OR A HOMOGENEOUS ATMOSPHERE THIS POINT OF TANGENCY WITH THE %ARTH IS REFERRED TO AS THE GEOMETRICAL HORIZON &OR AN INHOMOGENEOUS ATMOSPHERE USING AN EFFECTIVE EARTH RADIUS AND AT RADAR AND OPTICAL FREQUENCIES THIS POINT OF TANGENCY IS REFERRED TO AS THE RADAR AND OPTICAL HORIZON RESPECTIVELY 4HE ABILITY OF THE ELECTROMAGNETIC WAVE TO PROPAGATE BEYOND THE HORIZON BY DIFFRAC TION IS HIGHLY DEPENDENT UPON FREQUENCY 4HE LOWER THE FREQUENCY THE MORE THE WAVE IS DIFFRACTED !T MICROWAVE RADAR FREQUENCIES THE WAVELENGTH IS SMALL WHEN COMPARED
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TO THE %ARTHS DIMENSIONS AND LITTLE ENERGY IS DIFFRACTED !T OPTICAL FREQUENCIES OR VERY SHORT RADAR WAVELENGTHS THE OPTICAL HORIZON REPRESENTS THE APPROXIMATE BOUNDARY BETWEEN REGIONS OF PROPAGATION AND NO PROPAGATION 4ROPOSPHERIC 3CATTER !T RANGES FAR BEYOND THE HORIZON THE PROPAGATION LOSS IS DOMINATED BY TROPOSCATTER 0ROPAGATION IN THE TROPOSCATTER REGION IS THE RESULT OF SCATTERING BY SMALL INHOMOGENEITIES WITHIN THE ATMOSPHERES REFRACTIVE STRUCTURE !T RADAR FREQUENCIES TROPOSCATTER IS GENERALLY NOT CONSIDERED FOR RADAR RANGE PERFOR MANCE (OWEVER TROPOSCATTER SCATTERING COULD BE AN IMPORTANT CONSIDERATION IN TARGET DETECTION BY A RECEIVER NOT CO LOCATED WITH THE RADAR ITSELF OR DETECTION OF THE RADARS EMISSIONS BY AN %LECTRONIC 3UPPORT -EASURES %3- SYSTEM
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!NOMALOUS OR NONSTANDARD WAVE PROPAGATION USUALLY REFERS TO THE CONSIDERATION OF NONSTANDARD REFRACTION VERSUS STANDARD REFRACTION 4HESE NONSTANDARD REFRACTIVE CONDI TIONS LEAD TO TRANS HORIZON PATHS DECREASED HORIZON PATHS AND DISTORTIONS IN SIMPLE SURFACE REFECTION AND MULTIPATH INTERFERENCE 3UBREFRACTION )F THE MOTIONS OF THE ATMOSPHERE PRODUCE A SITUATION WHERE THE TEMPERATURE AND HUMIDITY DISTRIBUTION CREATE AN INCREASING VALUE OF . WITH HEIGHT THE WAVE PATH WOULD ACTUALLY BEND UPWARD AND THE ENERGY WOULD TRAVEL AWAY FROM THE %ARTH 4HIS IS TERMED SUBREFRACTION !LTHOUGH THIS SITUATION OCCURS INFREQUENTLY IN NATURE IT STILL MUST BE CONSIDERED WHEN ASSESSING ELECTROMAGNETIC SYSTEMS PER FORMANCE &OR EXAMPLE AN !TLANTIC COAST VESSEL TRAFFIC CONTROL RADAR LOCATED NEAR THE ENTRANCE TO THE $ELAWARE "AY OBSERVED A REDUCTION IN DETECTION RANGE FROM TO KM 3OMETIMES SHIPS CAN BE SEEN VISUALLY FROM THE RADAR TOWER BEFORE THEY CAN BE OBSERVED ON THE RADAR SCREEN 4HE REDUCTION IN THE RADAR DETECTION RANGE USUALLY LASTS SEVERAL HOURS AND OCCURS OFTEN WHEN FOG IS PRESENT ! SUBREFRACTIVE LAYER OF THE TROPOSPHERE WOULD CAUSE THE PROPAGATING ENERGY TO BEND UPWARD OR AWAY FROM THE %ARTHS SURFACE THEREBY LEADING TO DECREASED DETECTION RANGES AND SHORTENED RADIO HORIZONS 3UBREFRACTIVE LAYERS MAY BE FOUND AT THE %ARTHS SURFACE OR ALOFT )N AREAS WHERE THE SURFACE TEMPERATURE IS GREATER THAN #ELSIUS AND RELATIVE HUMIDITIES ARE LESS THAN IE LARGE DESERT AND STEPPE REGIONS SOLAR HEATING WILL PRODUCE A VERY NEARLY HOMOGENEOUS SURFACE LAYER OFTEN SEVERAL HUNDREDS OF METERS THICK "ECAUSE THIS LAYER IS UNSTABLE THE RESULTANT CONVECTIVE PROCESSES TEND TO CONCENTRATE ANY AVAIL ABLE MOISTURE NEAR THE TOP OF THE LAYER 4HIS IN TURN CREATES A POSITIVE . GRADIENT OR SUBREFRACTIVE STRATUM ALOFT 4HIS LAYER MAY RETAIN ITS SUBREFRACTIVE NATURE INTO THE EARLY EVENING HOURS ESPECIALLY IF A RADIATION INVERSION DEVELOPS TRAPPING THE WATER VAPOR BETWEEN TWO STABLE LAYERS &OR AREAS WITH SURFACE TEMPERATURES BETWEEN AND #ELSIUS AND RELATIVE HUMIDITIES ABOVE IE THE WESTERN -EDITERRANEAN 2ED 3EA )NDONESIAN 3OUTHWEST 0ACIFIC SURFACE BASED SUBREFRACTIVE LAYERS MAY DEVELOP DURING THE NIGHT AND EARLY MORNING HOURS 4HESE LAYERS ARE CHARACTERISTICALLY CAUSED BY ADVECTION OF WARM MOIST AIR OVER A RELATIVELY COOLER AND DRIER SURFACE 7HILE THE . GRADIENT IS GENERALLY MORE INTENSE THAN THAT DESCRIBED ABOVE THE LAYER IS OFTEN NOT AS THICK 3IMILAR CONDITIONS MAY ALSO BE FOUND IN REGIONS OF WARM FRONTAL ACTIVITY
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3UPERREFRACTION )F THE TROPOSPHERES TEMPERATURE INCREASES WITH HEIGHT TEM PERATURE INVERSION ANDOR THE WATER VAPOR CONTENT DECREASES RAPIDLY WITH HEIGHT THE REFRACTIVITY GRADIENT WILL DECREASE FROM THE STANDARD 4HE PROPAGATING WAVE WILL BE BENT DOWNWARD FROM A STRAIGHT LINE MORE THAN NORMAL !S THE REFRACTIVITY GRADIENT CONTINUES TO DECREASE THE RADIUS OF CURVATURE FOR THE WAVE PATH WILL APPROACH THE RADIUS OF CUR VATURE FOR THE %ARTH 4HE REFRACTIVITY GRADIENT FOR WHICH THE TWO RADII OF CURVATURE ARE EQUAL IS REFERRED TO AS THE CRITICAL GRADIENT !T THE CRITICAL GRADIENT THE WAVE WILL PROPA GATE AT A FIXED HEIGHT ABOVE THE GROUND AND WILL TRAVEL PARALLEL TO THE %ARTHS SURFACE 2EFRACTION BETWEEN THE NORMAL AND CRITICAL GRADIENTS IS KNOWN AS SUPERREFRACTION 3UPERREFRACTIVE CONDITIONS ARE LARGELY ASSOCIATED WITH TEMPERATURE AND HUMIDITY VARIATIONS NEAR THE %ARTHS SURFACE )NVERSIONS ALOFT DUE TO LARGE SCALE SUBSIDENCE WILL LEAD TO SUPERREFRACTIVE LAYERS ALOFT 3UPERREFRACTIVE LAYERS WILL LEAD TO AN INCREASE OF RADAR DETECTION RANGES AND EXTENSIONS OF THE RADIO HORIZON 4HE EFFECTS OF A SUPERREFRACTIVE LAYER UPON A SURFACE BASED SYSTEM ARE DIRECTLY RELATED TO ITS HEIGHT ABOVE THE %ARTHS SURFACE &OR AIRBORNE SYSTEMS THE EFFECTS OF A SUPERREFRACTIVE LAYER DEPEND UPON THE POSITION OF THE TRANSMITTER AND RECEIVER RELATIVE TO THE LAYER "OTH OF THESE FACTORS ARE RELATED TO THE ELECTROMAGNETIC WAVES ANGLE OF LAYER PENETRATION 4HE STEEPER THE PENETRATION ANGLE THE LESS OF AN EFFECT THE LAYER WILL HAVE UPON PROPAGATION 4RAPPING 4RAPPING IS AN EXTENSION OF SUPERREFRACTION BECAUSE THE METEOROLOGICAL CONDITIONS FOR BOTH ARE THE SAME 3HOULD THE REFRACTIVITY GRADIENT DECREASE BEYOND THE CRITICAL GRADIENT THE RADIUS OF CURVATURE FOR THE WAVE WILL BECOME SMALLER THAN THE %ARTHS CURVATURE 4HE WAVE WILL EITHER STRIKE THE %ARTH AND UNDERGO SURFACE REFLECTION OR ENTER A REGION OF STANDARD REFRACTION AND BE REFRACTED BACK UPWARD ONLY TO REENTER THE AREA OF REFRACTIVITY GRADIENT THAT CAUSES DOWNWARD REFRACTION 4HIS REFRACTIVE CONDITION IS CALLED TRAPPING BECAUSE THE WAVE IS CONFINED TO A NARROW REGION OF THE TROPOSPHERE 4HE COMMON TERM FOR THIS CONFINEMENT REGION IS A TROPOSPHERIC DUCT OR A TROPOSPHERIC WAVEGUIDE )T SHOULD BE NOTED THAT A TROPOSPHERIC WAVEGUIDE IS NOT A WAVEGUIDE IN THE TRUE SENSE OF THE WORD BECAUSE THERE ARE NO RIGID WALLS THAT PREVENT THE ESCAPE OF ENERGY FROM THE GUIDE 4HE REFRACTIVITY GRADIENTS AND THEIR ASSOCIATED REFRACTIVE CONDITIONS ARE SUMMA RIZED IN 4ABLE !TMOSPHERIC $UCTS ! DUCT IS A CHANNEL IN WHICH ELECTROMAGNETIC ENERGY CAN PROPAGATE OVER GREAT RANGES 4O PROPAGATE ENERGY WITHIN A DUCT THE ANGLE MADE BY THE ELECTROMAGNETIC SYSTEMS ENERGY WITH THE DUCT MUST BE SMALL USUALLY LESS THAN 4HICKER DUCTS IN GENERAL CAN SUPPORT TRAPPING FOR LOWER FREQUENCIES 4HE VERTICAL DISTRIBUTION OF REFRACTIVITY FOR A GIVEN SITUATION MUST BE CONSIDERED AS WELL AS THE GEO METRICAL RELATIONSHIP OF TRANSMITTER AND RECEIVER TO THE DUCT IN ORDER TO ASSESS THE DUCTS EFFECT AT ANY PARTICULAR FREQUENCY 4!",% 2EFRACTIVE 'RADIENTS AND #ONDITIONS
#ONDITION 4RAPPING 3UPERREFRACTION .ORMAL 3TANDARD 3UBREFRACTION
. 'RADIENT
- 'RADIENT
.KM OR .KFT
TO .KM OR TO .KFT
TO .KM OR TO .KFT
.KM .KM OR .KFT
-KM OR -KFT TO -KM OR TO -KFT TO -KM OR TO -KFT -KM -KM OR -KFT
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! SIMPLE RELATIONSHIP BETWEEN A DUCTS THICKNESS AND ITS ABILITY TO TRAP A PARTICULAR FREQUENCY IS GIVEN BY ¤C . ³ KMAX r ¥
´ ¦ T µ
T
WHERE KMAX IS THE MAXIMUM FREQUENCY TRAPPED C . IS THE REFRACTIVE INDEX CHANGE ACROSS THE DUCT AND T IS THE DUCT THICKNESS )N ADDITION TO EXTENDED RADAR RANGES ATMOSPHERIC DUCTS AND OTHER PROPAGATION EFFECTS SUCH AS MULTIPATH INTERFERENCE HAVE OTHER SIGNIFICANT IMPACTS UPON RADAR PER FORMANCE 4HESE EFFECTS MAY BE VISUALIZED WITH THE AID OF A HEIGHT VERSUS RANGE GRAPHIC AVAILABLE FROM AN ASSESSMENT SYSTEM SUCH AS !2%03 3UCH A GRAPHIC IS SHOWN IN &IGURE )N THIS FIGURE THE DIFFERENT SHADINGS CORRESPOND TO DIFFERENT PROPAGATION LOSS VALUES DEFINED LATER AS COMPUTED BY THE PROPAGATION MODEL 4HE ACTUAL VALUES ARE IMMATERIAL TO THIS ILLUSTRATION AS THE IMPORTANT FEATURES TO NOTE ARE THE CONSEQUENCES OF DUCTING )N THIS FIGURE ONE CAN CLEARLY SEE THE NULL AND LOBE STRUCTURE RESULTING FROM MULTIPATH INTERFERENCE 7HILE A DISCUSSION OF DUCTING CONDITIONS UPON %- WAVE PROPAGATION IS USUALLY CONCERNED WITH PROPAGATION BEYOND THE NORMAL HORIZON DUCT ING CAN HAVE AN EFFECT WITHIN THE HORIZON $UCTING CAN ALTER THE NORMAL LOBE PATTERN CAUSED BY THE INTERFERENCE OF THE DIRECT RAY AND THE SURFACE REFLECTED RAY 4HE RELATIVE PHASE BETWEEN THE DIRECT AND REFLECTED PATH MAY BE CHANGED AS WELL AS THE RELATIVE AMPLITUDES OF THE TWO RAYS 4HE EFFECT OF THE DUCT ON THE LINE OF SIGHT PROPAGATION IS TO REDUCE THE ANGLE OF THE LOWEST LOBE BRINGING IT CLOSER TO THE SURFACE
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$UCTS NOT ONLY GIVE EXTENDED RADAR DETECTION RANGES FOR SYSTEMS WITHIN THE DUCT BUT THEY MAY ALSO HAVE A DRAMATIC EFFECT UPON TRANSMITTERRECEIVER SYSTEMS THAT TRAN SCEND DUCT BOUNDARIES &OR EXAMPLE AN AIR TARGET THAT WOULD NORMALLY BE DETECTED MAY BE MISSED IF THE RADAR IS WITHIN OR JUST ABOVE THE DUCT AND THE TARGET IS JUST ABOVE THE DUCT 4HIS AREA OF REDUCED COVERAGE IS KNOWN AS A RADAR HOLE OR SHADOW ZONE !NOTHER INTERESTING FEATURE OF SURFACE BASED DUCTS IS THE SKIP ZONE NEAR THE NORMAL HORIZON IN WHICH THE DUCT HAS NO INFLUENCE )T SHOULD BE NOTED THAT THE SURFACE DUCT CRE ATED FROM A SURFACE BASED TRAPPING LAYER DOES NOT HAVE THIS SKIP ZONE PHENOMENON (EIGHT FINDING RADARS USUALLY DETERMINE HEIGHT FROM ENERGY PATH ASSUMPTIONS WITHIN A NORMAL ENVIRONMENT .ONSTANDARD REFRACTIVE CONDITIONS AS DISCUSSED EARLIER WILL CAUSE THE ENERGYS PATH TO DEVIATE FROM THESE ASSUMPTIONS RESULTING IN ERRORS IN ALTITUDE CALCULATIONS &IGURE SHOWS THE DOWNWARD DEVIATED PATH ASSOCIATED WITH A SURFACE DUCTING CONDITION COMPARED TO THE PATH UNDER NORMAL CONDITIONS )T CAN BE SEEN THAT ACTUAL ALTITUDE OF THE RADAR TARGET IS LOWER THAN CALCULATED BY THE HEIGHT FINDING RADAR 4HIS ERROR COULD LEAD TO SIGNIFICANT TACTICAL CONSEQUENCES IN A SHIPS SELF DEFENSE SCENARIO &OR A PRACTICAL EXAMPLE OF DUCTING EFFECTS ONE CAN READ ABOUT THE h"ATTLE OF THE 0IPSv $URING THE SUMMER OF TWO 53 .AVY TASK GROUPS WERE DEPLOYED TO REMOVE THE *APANESE OCCUPATION OF !TTU !LASKA /N THE NIGHT OF *ULY TH THE 533 -ISSISSIPPI GAINED RADAR CONTACT WITH WHAT WAS BELIEVED TO BE *APANESE FLEET UNITS MOV ING TOWARD !TTU IN ORDER TO WITHDRAW TROOPS 2ADARS ONBOARD THE 533 .EW -EXICO THE 533 0ORTLAND AND THE 533 7ICHITA CONFIRMED THE RADAR CONTACTS /N THE ORDERS OF !DMIRAL 'IFFEN THE 53 .AVY SHIPS OPENED FIRE 4HE FIRING CONTINUED FOR ABOUT HALF AN HOUR DURING WHICH TIME INCH SHELLS AND INCH SHELLS WERE EXPENDED 'UN FLASHES WERE REPORTEDLY SEEN BY THE *APANESE ON +ISKA MILES AWAY 4WO OTHER SHIPS THE DESTROYERS 533 3AN &RANCISCO AND 533 3ANTA &E COULD NOT GAIN RADAR CON TACT BUT THEY DID DETECT THE SPLASHES MADE BY SHELLS HITTING THE WATER .OTHING WAS EVER FOUND 7HEN 53 AND #ANADIAN FORCES LANDED AT !TTU ON !UGUST TH THEY FOUND THE ISLAND ABANDONED 4HE *APANESE TROOPS HAD BEEN EVACUATED UNDER COVER OF FOG AND RAIN ON *ULY TH ,ATER INVESTIGATION DETERMINED THAT THE *APANESE EVACUATION
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SHIPS WERE NAUTICAL MILES 37 OF +ISKA DURING THE FIRING 4HE RADAR CONTACTS WERE ACTUALLY RETURNS FROM LAND THAT HAD BEEN DUCTED OVER THE HORIZON 3EVERAL METEOROLOGICAL CONDITIONS WILL LEAD TO THE CREATION OF DUCTS 7HERE THESE CON DITIONS EXIST AND WHAT THESE CONDITIONS ARE DETERMINES THE NAME AND NATURE OF THE DUCT 3URFACE $UCTS )F THE METEOROLOGICAL CONDITIONS CAUSE A TRAPPING LAYER TO OCCUR SUCH THAT THE BASE OF THE RESULTANT DUCT IS AT THE %ARTHS SURFACE A SURFACE DUCT IS FORMED 4HERE ARE THREE TYPES OF SURFACE DUCTS BASED ON THE TRAPPING LAYERS RELATION SHIP TO THE %ARTHS SURFACE 4HE TRAPPING LAYER IS INDICATED GRAPHICALLY BY THE SOLID BLACK - UNIT VERSUS HEIGHT LINE WHERE THE SLOPE OF THE LINE IS NEGATIVE - UNIT DECREASE WITH HEIGHT 4HE FIRST TYPE OF DUCT IS A SURFACE DUCT CREATED FROM A SURFACE BASED TRAPPING LAYER 4HIS DUCT IS REFERRED TO AS A SURFACE DUCT AND IS ILLUSTRATED IN &IGURE 4HE DOTTED LINE IN THE FIGURE SHOWS THE VERTICAL DIMENSION OF THE DUCT FROM BOTTOM TO TOP 4HE SECOND TYPE OF SURFACE DUCT IS CREATED FROM AN ELEVATED TRAPPING LAYER 4HIS DUCT IS COMMONLY REFERRED TO AS A SURFACE BASED DUCT AND IS ILLUSTRATED IN &IGURE .OTE THE DUCT IDENTIFIED BY THE DASHED LINE CONTAINS THE TRAPPING LAYER AND hNORMALv GRADIENT LAYER BELOW 4HE THIRD TYPE OF SURFACE DUCT IS ONE CREATED BY A RAPID DECREASE OF RELATIVE HUMIDITY IMMEDIATELY ADJACENT TO THE AIR SEA INTERFACE 4HIS DUCT IS REFERRED TO AS AN EVAPORATION DUCT "ECAUSE THE EVAPORATION DUCT IS OF GREAT IMPORTANCE FOR OVER WATER %- PROPAGATION IT WARRANTS A DETAILED DISCUSSION 4HIS DISCUSSION APPEARS IN ITS OWN SECTION BELOW 3URFACE BASED DUCTS OCCUR WHEN THE AIR ALOFT IS EXCEPTIONALLY WARM AND DRY COM PARED WITH THE AIR AT THE %ARTHS SURFACE 3EVERAL METEOROLOGICAL CONDITIONS MAY LEAD TO THE FORMATION OF SURFACE BASED DUCTS /VER THE OCEAN AND NEAR LAND MASSES WARM DRY CONTINENTAL AIR MAY BE ADVECTED OVER THE COOLER WATER SURFACE %XAMPLES OF THIS TYPE OF ADVECTION ARE THE 3ANTA !NA OF SOUTHERN #ALIFORNIA THE 3IROCCO OF THE SOUTHERN -EDITERRANEAN AND THE 3HAMAL OF THE 0ERSIAN 'ULF 4HIS ADVECTION WILL LEAD TO A TEMPERATURE INVERSION AT THE SURFACE )N ADDITION MOISTURE IS ADDED TO THE AIR BY EVAPORATION PRODUCING A MOISTURE GRADIENT TO STRENGTHEN THE TRAPPING GRADIENT 4HIS TYPE OF METEOROLOGICAL CONDITION ROUTINELY LEADS TO A SURFACE DUCT CREATED BY A SURFACE BASED TRAPPING CONDITION (OWEVER AS YOU TRAVEL FROM THE COASTAL ENVIRONMENT INTO THE OPEN OCEAN THIS TRAPPING LAYER MAY WELL RISE FROM THE SURFACE THEREBY CREATING THE SURFACE BASED DUCT 3URFACE BASED DUCTS TEND
&)'52% 3URFACE DUCT
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TO BE ON THE LEEWARD SIDE OF LAND MASSES AND MAY OCCUR BOTH DURING THE DAY AND AT NIGHT )N ADDITION SURFACE BASED DUCTS MAY EXTEND OVER THE OCEAN FOR SEVERAL HUNDRED KILOMETERS AND MAY BE VERY PERSISTENT LASTING FOR DAYS !NOTHER METHOD OF PRODUCING SURFACE BASED DUCTING CONDITIONS IS BY DIVERGENCE SPREADING OUT OF RELATIVELY COOL AIR UNDER A THUNDERSTORM 7HILE THIS METHOD MAY NOT BE AS FREQUENT AS THE OTHER METHODS IT MAY STILL ENHANCE SURFACE PROPAGATION DURING THE THUNDERSTORM ACTIVITY USUALLY ON THE ORDER OF A FEW HOURS 7ITH THE EXCEPTION OF THUNDERSTORM CONDITIONS SURFACE BASED DUCTING IS ASSOCI ATED WITH FAIR WEATHER AND WITH INCREASED OCCURRENCE OF SURFACE BASED DUCTS DURING THE WARMER MONTHS AND IN MORE EQUATORIAL LATITUDES !NY TIME THE TROPOSPHERE IS WELL MIXED SUCH AS WITH FRONTAL ACTIVITY OR WITH HIGH WIND CONDITIONS SURFACE BASED DUCT ING IS DECREASED %VAPORATION $UCTS ! CHANGE IN THE MOISTURE DISTRIBUTION WITHOUT AN ACCOM PANYING TEMPERATURE CHANGE CAN ALSO LEAD TO A TRAPPING REFRACTIVITY GRADIENT 4HE AIR IN CONTACT WITH THE OCEANS SURFACE IS SATURATED WITH WATER VAPOR ! FEW METERS ABOVE THE SURFACE THE AIR IS NOT USUALLY SATURATED SO THERE IS A DECREASE OF WATER VAPOR PRES SURE FROM THE SURFACE TO SOME VALUE WELL ABOVE THE SURFACE 4HE RAPID DECREASE OF WATER VAPOR INITIALLY CAUSES THE MODIFIED REFRACTIVITY - TO DECREASE WITH HEIGHT BUT AT GREATER HEIGHTS THE WATER VAPOR DISTRIBUTION WILL CAUSE - TO REACH A MINIMUM AND THEREAFTER INCREASE WITH HEIGHT 4HE HEIGHT AT WHICH - REACHES A MINIMUM IS CALLED THE EVAPORATION DUCT HEIGHT AS ILLUSTRATED IN &IGURE %VAPORATION DUCTS EXIST OVER THE OCEAN TO SOME DEGREE ALMOST ALL THE TIME 4HE DUCT HEIGHT VARIES FROM A METER OR TWO IN NORTHERN LATITUDES DURING WINTER NIGHTS TO AS MUCH AS METERS IN EQUATORIAL LATITUDES DURING SUMMER DAYS /N A WORLD AVERAGE THE EVAPORATION DUCT HEIGHT IS APPROXIMATELY METERS )T SHOULD BE EMPHASIZED THAT THE EVAPORATION DUCT hHEIGHTv IS NOT A HEIGHT BELOW WHICH AN ANTENNA MUST BE LOCATED IN ORDER TO HAVE EXTENDED PROPAGATION BUT A VALUE THAT RELATES TO THE DUCTS STRENGTH OR ITS ABILITY TO TRAP RADIATION 4HE DUCT STRENGTH IS ALSO A FUNCTION OF WIND VELOCITY &OR UNSTABLE ATMOSPHERIC CONDITIONS CONDITIONS WHERE A COOLER LAYER OF AIR OVERLIES A WARMER LAYER OF AIR STRONGER WINDS GENERALLY RESULT IN STRONGER SIGNAL STRENGTHS OR LESS PROPAGATION LOSS THAN DO WEAKER WINDS
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&)'52% %VAPORATION DUCT
"ECAUSE THE EVAPORATION DUCT IS MUCH WEAKER THAN THE SURFACE BASED DUCT ITS ABIL ITY TO TRAP ENERGY IS HIGHLY DEPENDENT ON FREQUENCY 'ENERALLY THE EVAPORATION DUCT IS ONLY STRONG ENOUGH TO AFFECT ELECTROMAGNETIC SYSTEMS ABOVE -(Z &OR SURFACE DUCTING CONDITIONS THE VERTICAL EXTENT OF THE DUCT IS SUFFICIENT TO ALLOW FOR ITS MEASUREMENT USING AN ASCENDING RADIOSONDE A DESCENDING ROCKETSONDE OR A MICRO WAVE REFRACTOMETER ONBOARD SOME SORT OF AIR VEHICLE (OWEVER FOR AN EVAPORATION DUCT IT IS NOT THE VERTICAL EXTENT OF THE DUCT THAT IS IMPORTANT BUT THE REFRACTIVE GRADIENT WITHIN THE DUCT #HANGES OF REFRACTIVE GRADIENTS OVER VERTICAL HEIGHTS LESS THAN A FEW MILLIMETERS MAY HAVE A SIGNIFICANT IMPACT UPON THE DUCTS TRAPPING ABILITY 4HUS ASSESSMENT OF THE EVAPORATION DUCT IS BEST PERFORMED BY MAKING SURFACE METEOROLOGICAL MEASUREMENTS AND INFERRING THE DUCT HEIGHT FROM THE METEOROLOGICAL PROCESSES OCCURRING AT THE AIRSEA INTER FACE AND NOT FROM DIRECT MEASUREMENTS USING THE TRADITIONAL RADIOSONDE ROCKETSONDE OR MICROWAVE REFRACTOMETER 7ITH THE ADVENT OF NEWER HIGH RESOLUTION SONDES THAT MAY BE LOWERED TO THE SURFACE FROM A SHIP THE IMPRESSION IS GIVEN THAT THE EVAPORATION DUCT MAY BE MEASURED DIRECTLY &OR PRACTICAL APPLICATIONS HOWEVER THIS IMPRESSION IS FALSE AND A DIRECT MEASUREMENT SHOULD NOT BE ATTEMPTED $UE TO THE TURBULENT NATURE OF THE TROPO SPHERE AT THE OCEAN SURFACE A REFRACTIVITY PROFILE MEASURED AT ONE TIME WOULD MOST LIKELY NOT BE THE SAME AS ONE MEASURED AT ANOTHER TIME EVEN WHEN THE TWO MEASUREMENTS ARE SECONDS APART 4HEREFORE ANY MEASURED PROFILE WOULD NOT BE REPRESENTATIVE OF THE AVERAGE EVAPORATION DUCTING CONDITIONS THE CONDITIONS THAT AN ASSESSMENT SYSTEM MUST CONSIDER %LEVATED $UCTS )F METEOROLOGICAL CONDITIONS CAUSE A TRAPPING LAYER TO OCCUR ALOFT SUCH THAT THE BASE OF THE DUCT OCCURS ABOVE THE %ARTHS SURFACE THE DUCT IS REFERRED TO AS AN ELEVATED DUCT AS ILLUSTRATED IN &IGURE .OTE AGAIN THE ADVANTAGE OF SHOWING - UNIT GRADIENTS VERSUS . UNIT GRADIENTS &ROM &IGURE IT CAN BE SEEN THAT THE DUCT EXTENDS FROM THE TOP OF THE TRAPPING LAYER DOWNWARD UNTIL IT INTERSECTS WITH THE - UNIT LINE WHERE THE - UNIT AT THE TOP OF THE DUCT IS THE SAME AS THE - UNIT AT THE BOTTOM OF THE DUCT ILLUSTRATED BY THE DASHED LINE 'REAT SEMIPERMANENT SURFACE HIGH PRESSURE SYSTEMS CENTERED AT APPROXIMATELY NORTH AND SOUTH LATITUDE COVER THE OCEAN AREAS OF THE WORLD 0OLEWARD OF THESE SYSTEMS LAY THE MID LATITUDE WESTERLY WINDS AND EQUATORWARD LAY THE TROPICAL EASTERLIES OR THE TRADE WINDS 7ITHIN THESE HIGH PRESSURE SYSTEMS LARGE SCALE SUBSIDENCE OF AIR CAUSES HEATING AS THE AIR UNDERGOES COMPRESSION 4HIS LEADS TO A LAYER OF WARM DRY AIR OVERLAY ING A COOL MOIST LAYER OF AIR OFTEN CALLED THE MARINE BOUNDARY LAYER
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&)'52% %LEVATED DUCT
4HE RESULTANT INVERSION IS REFERRED TO AS THE TRADEWIND INVERSION AND MAY CREATE A STRONG DUCTING CONDITION AT THE TOP OF THE MARINE BOUNDARY LAYER %LEVATED DUCTS MAY VARY FROM A FEW HUNDRED METERS ABOVE THE SURFACE AT THE EASTERN PART OF THE TROPICAL OCEANS TO SEVERAL THOUSAND METERS AT THE WESTERN PART &OR EXAMPLE ALONG THE SOUTHERN #ALIFORNIA COAST ELEVATED DUCTS OCCUR AN AVERAGE OF OF THE TIME WITH AN AVERAGE TOP ELEVATION OF METERS !LONG THE COAST OF *APAN ELEVATED DUCTS OCCUR AN AVERAGE OF OF THE TIME WITH AN AVERAGE TOP ELEVATION OF METERS )T SHOULD BE NOTED THAT THE METEOROLOGICAL CONDITIONS NECESSARY FOR A SURFACE BASED DUCT ARE THE SAME AS THOSE FOR AN ELEVATED DUCT )N FACT A SURFACE BASED DUCT MAY SLOPE UPWARD TO BECOME AN ELEVATED DUCT AS WARM DRY CONTINENTAL AIR GLIDES OVER COOL MOIST MARINE AIR 4HE TRADEWIND INVERSION MAY ALSO INTENSIFY THEREBY TURNING AN ELEVATED DUCT INTO A SURFACE BASED DUCT
ÓÈ°ÈÊ *,"*/" Ê " Ó]Ç 2ADIO WAVE MODELING IS IMPORTANT FOR A NUMBER OF REASONS ALL OF WHICH COULD BE SUMMARIZED INTO TWO LARGE CATEGORIES OF ENGINEERING STUDIES AND OPERATIONAL PERFOR MANCE &OR ENGINEERING STUDIES THE EFFECTS OF PROPAGATION MAY BE CONSIDERED IN NEW SYSTEM DESIGN OR IN THE EVALUATION OF LONG TERM PERFORMANCE OF EXISTING SYSTEMS &OR OPERATIONAL PERFORMANCE CONSIDERATION OF PROPAGATION EFFECTS IS USUALLY BASED UPON A SINGLE MEASURED OR FORECASTED ATMOSPHERE SUCH THAT THESE EFFECTS CAN BE EXPLOITED OR MITIGATED BY ALTERING THE SYSTEMS USE TACTICS /VER THE YEARS MANY PROPAGATION MODELS HAVE BEEN DEVELOPED TO ACCOUNT FOR THE EFFECTS IMPORTANT TO A PARTICULAR APPLI CATION 4HESE MODELS SPAN THE SPECTRUM OF VERY FAST EXECUTING BUT WITH LOW FIDELITY SIMPLIFIED MODELING OF OR THE COMPLETE IGNORING OF CERTAIN PROPAGATION MECHANISMS TO RELATIVELY SLOW EXECUTING BUT WITH HIGH FIDELITY PHYSICALLY RIGOROUS MODELING OF AND FULL INCLUSION OF ALL PROPAGATION MECHANISMS 3PHERICAL 3PREADING OR &REE SPACE 0ROPAGATION -ODEL 4HE SIMPLEST PROPAGA TION MODEL IS SPHERICAL SPREADING WHERE THE TRANSMITTER AND RECEIVER ARE FAR REMOVED
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FROM THE %ARTHS SURFACE AND THE ATMOSPHERE IE FREE SPACE &REE SPACE IS DEFINED AS A REGION WHOSE PROPERTIES ARE ISOTROPIC HOMOGENEOUS AND LOSS FREE 3PHERICAL SPREADING MODELS ONLY CONSIDER THE INCREASING SURFACE AREA OF A SPHERE CENTERED ON THE TRANSMITTER AND RADIATING OUT UNIFORMLY IN ALL DIRECTIONS 4HE FIELD STRENGTH AT ANY POINT IS INVERSELY PROPORTIONAL TO THE SQUARE OF THE RANGE BETWEEN TRANSMITTER AND THE POINT 4HIS IS CALLED FREE SPACE PATH LOSS 4HE POWER DENSITY 0A OVER A SPHERE AT ANY POINT IN FREE SPACE IS
¤ 0' ³ 0A ¥ T T ´ 7 M ¦ O R µ
WHERE 0T IS THE POWER RADIATED BY THE TRANSMITTER R IS THE RADIUS OF THE SPHERE AND 'T IS THE TRANSMITTING ANTENNAS GAIN &OR A LOSS FREE ISOTROPIC ANTENNA THE GAIN IS UNITY )N FREE SPACE THE POWER DENSITY AT A LOSS FREE ISOTROPIC RECEIVING ANTENNA IS THE POWER DENSITY OVER THE ENTIRE SPHERES SURFACE TIMES THE AREA OF THE SPHERE COVERED BY THE RECEIVER ANTENNA ALSO CALLED THE ANTENNAS EFFECTIVE APERTURE !E 4HE EFFECTIVE APERTURE IS RELATED TO THE WAVELENGTH K OF RADIATION BY
!E
'K O
4HUS THE POWER AT THE RECEIVER 0R FOR ISOTROPIC RADIATING AND RECEIVING ANTENNAS 'T 'R IS
0R 0A !E
0T K O R
4HE FREE SPACE PATH LOSS ,FS EXPRESSED IN TERMS OF THE SPHERES RADIUS R AND WAVE LENGTH K WHERE R AND K ARE IN THE SAME UNITS IS
§ O R ¶ ¤0³ ,FS LOG ¥ T ´ LOG ¨ · ¦ 0R µ © K ¸
&REE SPACE PATH LOSS ,FS EXPRESSED IN TERMS OF RANGE AND FREQUENCY IN DECIBELS IS GIVEN BY
,FS LOG F LOGR
WHERE F IS FREQUENCY IN -(Z AND R IS THE DISTANCE BETWEEN THE TRANSMITTER AND RECEIVER IN KILOMETERS &REE SPACE IS INCLUDED IN MANY MODELING APPLICATIONS AS A REFERENCE FOR OTHER PROPAGATION EFFECTS )F NONISOTROPIC ANTENNA RADIATIONAL PATTERNS ARE CONSIDERED WITHIN THE LOSS CALCULA TIONS THE LOSS IS REFERRED TO AS A PROPAGATION LOSS RATHER THAN A PATH LOSS 4HE PROPAGA TION LOSS CAN BE DESCRIBED WITH THE AID OF THE PROPAGATION FACTOR & WHICH IS DEFINED AS THE RATIO OF THE ACTUAL FIELD STRENGTH AT A POINT IN SPACE TO THE FIELD STRENGTH THAT WOULD EXIST AT THE SAME RANGE UNDER FREE SPACE CONDITIONS WITH THE BEAM OF THE TRANSMITTER DIRECTED TOWARD THE POINT IN QUESTION 3YMBOLICALLY THIS IS
&
\%\ \ %O \
WHERE %O IS THE MAGNITUDE OF THE ELECTRIC FIELD UNDER FREE SPACE CONDITIONS AND % IS THE MAGNITUDE OF THE FIELD TO BE INVESTIGATED AT THE SAME POINT
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4HE PROPAGATION FACTOR IS A DESIRABLE QUANTITY SINCE IT IS AN IDENTIFIABLE PARAMETER IN MOST RADAR EQUATIONS !S STATED EARLIER IT ALSO CONTAINS ALL THE INFORMATION NECESSARY TO ACCOUNT FOR NATURAL ENVIRONMENTAL EFFECTS 4HUS IF THE FUNCTIONAL FORM OF & IS KNOWN THEN THE PROPAGATION LOSS AT ANY POINT CAN BE DETERMINED BECAUSE THE CALCULATION OF THE FREE SPACE FIELD IS QUITE SIMPLE 4HE PROPAGATION LOSS INCLUDING ANTENNA PARAMETERS IS EQUIVALENT TO
, ,FS LOG &
%FFECTIVE EARTH RADIUS -ODEL 3INCE THE MAJORITY OF HUMAN ACTIVITY TAKES PLACE WITHIN THE %ARTHS ATMOSPHERE THE FREE SPACE PROPAGATION MODEL IS USUALLY INADEQUATE FOR PROPAGATION ASSESSMENT APPLICATIONS AND OTHER PROPAGATION MECHANISMS NEED CON SIDERATION 5NDER STANDARD OR NORMAL ATMOSPHERIC CONDITIONS THE RADIO RAY CURVES DOWNWARD WITH A CURVATURE LESS THAN THE %ARTHS SURFACE 4HE EFFECTIVE EARTH RADIUS CONCEPT REPLACES THE %ARTHS TRUE RADIUS WITH A LARGER RADIUS SUCH THAT THE RELATIVE CURVATURE BETWEEN THE RAY AND THE %ARTHS SURFACE IS MAINTAINED AND THE RAY BECOMES A STRAIGHT LINE 4HE EFFECTIVE EARTH RADIUS AE AND THE ACTUAL EARTH RADIUS A ARE RELATED BY AN EFFECTIVE EARTH RADIUS FACTOR K SUCH THAT AE KA
K MAY BE COMPUTED USING
K
; A DN DH =
WHERE DNDH IS THE VERTICAL REFRACTIVE INDEX GRADIENT 5SING THE MEAN EARTH RADIUS OF KILOMETERS AND A REFRACTIVITY GRADIENT OF n .KM GIVES A K OF OR ABOUT )N ADDITION TO THE CONSIDERATION OF REFRACTION OTHER STANDARD PROPAGATION MECH ANISMS SUCH AS MULTIPATH INTERFERENCE DIFFRACTION TROPOSCATTER AND TERRAIN MAY BE INCLUDED !MONG THE GENERAL CLASS OF EFFECTIVE EARTH RADIUS MODELS ARE THE 3TANDARD 0ROPAGATION -ODEL & &ACTOR THE 4ERRAIN )NTEGRATED 2OUGH %ARTH -ODEL 4)2%- THE )RREGULAR 4ERRAIN -ODEL )4- ALSO KNOWN AS ,ONGLEY 2ICE AND THE 3PHERICAL %ARTH +NIFE %DGE 3%+% 7HILE THESE EFFECTIVE EARTH RADIUS MODELS ARE OF THE SAME NATURE THEY DO NOT IMPLEMENT THE VARIOUS PROPAGATION MECHANISMS EQUALLY &OR EXAMPLE THE & FACTOR MODEL PROPERLY IMPLEMENTS MULTIPATH PROPAGATION FOR OVER WATER SURFACES WHEREAS THE 4)2%- MODEL IS BASED UPON KNIFE EDGE DIFFRACTION TECHNIQUES MAKING THE 4)2%- MODEL INAPPROPRIATE FOR OVER WATER APPLICATIONS !GAIN WHILE TROPOSCATTER MAY BE UNIMPORTANT FOR ACTIVE RADAR APPLICATIONS ITS EFFECTS NEED TO BE INCLUDED FOR APPLICA TIONS OF RADAR INTERCEPT BY OTHER SENSORS 7AVEGUIDE -ODELS !S ENGINEERING REQUIREMENTS DEMANDED GREATER AND GREATER FIDELITY OTHER MODELING TECHNIQUES WERE DEVELOPED /NE SUCH MODELING TECHNIQUE IS USING NORMAL MODE THEORY TO COMPUTE FIELD STRENGTH UNDER STANDARD OR NONSTANDARD REFRACTIVE CONDITIONS 4HIS CLASS OF MODELS IS REFERRED TO AS WAVEGUIDE MODELS 4HE USE OF WAVEGUIDE MODELS DATES BACK TO THE EARLY S WHEN THEY WERE USED TO EXPLAIN THE PROPAGATION OF LONG WAVELENGTH RADIO WAVES AROUND THE SURFACE OF THE %ARTH IN A WAVE GUIDE FORMED BY THE %ARTH AND THE IONOSPHERE ! DESCRIPTION OF WAVEGUIDE MODELS IS BEYOND THE SCOPE OF THIS CHAPTER BUT MAY BE FOUND IN A PUBLICATION BY "UDDEN
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7HILE WAVEGUIDE MODELS ARE MOST USEFUL FOR CONDITIONS WHERE THE VERTICAL REFRACTIV ITY PROFILE DOES NOT CHANGE ALONG THE PROPAGATION PATH HOMOGENEOUS ENVIRONMENTS THEY CAN BE APPLIED TO INHOMOGENEOUS ENVIRONMENTS BY BREAKING THE WAVEGUIDE UP INTO SLABS IN A TECHNIQUE KNOWN AS MODE CONVERSION 7HILE SUCCESSFUL THIS TECHNIQUE IS LESS COMPUTATIONALLY EFFICIENT THAN OTHER MODELING TECHNIQUES AND HENCE WAVE GUIDE MODELS ARE NOT GENERALLY USED FOR ASSESSMENT SYSTEMS REQUIRING RAPID EXECUTION TIMES 7AVEGUIDE MODELS SERVE AS hLABORATORY BENCHMARKv MODELS AGAINST WHICH THE RESULTS OF OTHER MODELING TECHNIQUES CAN BE COMPARED /NE SUCH WAVEGUIDE MODEL IS THE -,!9%2 DERIVED FROM THE ORIGINAL WORKS OF "AUMGARTNER 0ARABOLIC %QUATION -ODELS )N &OCK USED THE PARABOLIC EQUATION 0% METHOD TO DESCRIBE ELECTROMAGNETIC PROPAGATION IN A VERTICALLY STRATIFIED TROPOSPHERE )N (ARDIN AND 4APPERT DEVELOPED AN EFFICIENT PRACTICAL SOLUTION CALLED THE SPLIT STEP &OURIER METHOD BASED UPON FAST &OURIER TRANSFORMS &&4S THAT HAS BEEN WIDELY APPLIED TO OCEAN ACOUSTIC PROPAGATION PROBLEMS 4HE 0% METHOD AND ITS SOLUTION BY THE SPLIT STEP &OURIER TECHNIQUE PROVIDES A VERY ROBUST MODEL FOR COMPLICATED REFRACTIVITY STRUCTURES FOR WITHIN NEAR AND BEYOND THE HORIZON EFFECTS AND IS PARTICULARLY GOOD FOR PROPAGATION OVER IRREGULAR TERRAIN 4HUS 0% MODELS ALLOW FOR A SINGLE MODEL ASSESS MENT IN MANY IMPORTANT APPLICATIONS 4HREE SUCH 0% MODELS ARE THE 4ERRAIN 0ARABOLIC %QUATION -ODEL 40%- THE 4ROPOSPHERIC %LECTROMAGNETIC 0ARABOLIC %QUATION 2OUTINE 4%-0%2 AND THE 6ARIABLE 4ERRAIN 2ADIO 0ARABOLIC %QUATION 6420% (YBRID -ODELS 7HILE 0% MODELS ARE VERY ATTRACTIVE THEY ALSO HAVE THEIR DISAD VANTAGES 0ROBABLY THE BIGGEST DISADVANTAGE IS THAT THEY REQUIRE VERY LARGE COMPUTER RESOURCES BOTH IN TERMS OF MEMORY AND EXECUTION TIMES PARTICULARLY FOR APPLICATIONS INVOLVING COMBINATIONS OF HIGH FREQUENCIES HIGH ELEVATION ANGLES HIGH TERMINALS AND LONG RANGES )N SOME CASES THIS COMPUTATIONAL BURDEN CAN BE REDUCED BY COMBIN ING THE BEST FEATURES OF THE VARIOUS OTHER MODELS IN A HYBRID MODEL /NCE SUCH MODEL IS THE !DVANCED 0ROPAGATION -ODEL !0- DESCRIBED BY "ARRIOS )N !0- THE 0% MODEL IS COMBINED WITH VARIOUS RAY OPTICS AND OTHER PHENOMENA MODELS TO CREATE A HYBRID MODEL THAT CAN BE UP TO TIMES FASTER THAN A 0% MODEL FOR STRESSFUL CASES 4HREE OTHER HYBRID MODELS ARE 2ADIO 0HYSICAL /PTICS 20/ 4%20%- AUTHORED BY 3IGNAL 3CIENCE ,IMITED AND A HYBRID METHOD FOR COMPUTING TRANSMISSION LOSSES IN AN INHOMOGENEOUS ATMOSPHERE OVER IRREGULAR TERRAIN BY -ARCUS 7ITHIN !0- THE ASSESSMENT SPACE IS DIVIDED INTO FOUR REGIONS OR SUBMODELS AS ILLUSTRATED IN &IGURE !T RANGES LESS THAN M AND FOR ALL ELEVATION ANGLES ABOVE !0- USES A FLAT EARTH &% MODEL THAT IGNORES REFRACTION AND EARTH CURVATURE EFFECTS &OR RANGES BEYOND THE &% REGION WHERE THE GRAZING ANGLES OF REFLECTED RAYS FROM THE TRANSMITTER EXCEED A SMALL LIMITING VALUE A FULL RAY OPTIC 2/ MODEL IS USED THAT ACCOUNTS FOR THE EFFECTS OF REFRACTION AND EARTH CURVATURE 4HE 0% MODEL IS USED FOR RANGES BEYOND THE 2/ REGION BUT ONLY FOR ALTITUDES BELOW A MAXIMUM 0% ALTI TUDE DETERMINED BY A MAXIMUM FAST &OURIER TRANSFORM &&4 SIZE ALLOWED &OR RANGES BEYOND THE 2/ REGION AND ABOVE THE 0% REGION AN EXTENDED OPTICS 8/ METHOD IS USED THAT IS INITIALIZED BY THE 0% MODEL AT THE MAXIMUM 0% ALTITUDE AND USES RAY OPTICS METHODS TO PROPAGATE THE SIGNAL TO HIGHER ALTITUDES #ONTINUITY OF THE SOLUTIONS ACROSS EACH REGIONS BOUNDARIES IS KEPT LESS THAN D" BY CAREFUL SELECTION OF THE LIMITING 2/ GRAZING ANGLE AND THE MAXIMUM 0% PROPAGATION ANGLE 4HE PROPAGATION MODELS WITHIN !0- HAVE ALSO BEEN COMBINED WITH OTHER ENVI RONMENTAL EFFECTS MODELS SUCH AS GASEOUS ABSORPTION AND SURFACE CLUTTER TO FORM A COMPLETE PROPAGATION PACKAGE 4HE PHYSICAL PROPAGATION PHENOMENA CONSIDERED BY !0- VERSION ARE ILLUSTRATED IN 4ABLE !S CAN BE SEEN FROM THE TABLE
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4!",% 0ROPAGATION %FFECTS -ODELED BY !0-
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!0- CONSIDERS ALMOST EVERY ENVIRONMENTAL EFFECT MAKING IT A HIGHLY DESIRABLE MODEL FOR USE IN COMPLEX ASSESSMENT SYSTEMS
&)'52% !0- SUBMODEL REGIONS
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ÓÈ°ÇÊ Ê-9-/ Ê-- -- /Ê*,", 5SING THE POWER OF THE PERSONAL COMPUTER IN CONJUNCTION WITH THE MATURITY OF %- SYSTEM AND ENVIRONMENTAL PROPAGATION MODELING ASSESSMENT PROGRAMS AND ASSOCIATED SOFTWARE ALLOW A USER TO DEFINE AND MANIPULATE REFRACTIVITY AND OTHER NATURAL ENVIRONMENT DATA RUN PROPAGATION MODELS ON THAT DATA AND DISPLAY THE RESULTS IN TERMS OF EXPECTED PERFORMANCE ON ACTUAL OR PROPOSED ELECTROMAGNETIC SYSTEMS 7HILE THERE ARE SEVERAL ASSESSMENT SYSTEMS IN USE WITHIN THE 53 AND IN VARIOUS OTHER COUNTRIES THE FOLLOWING DISCUSSION IS LIMITED TO !2%03 )T IS USED EXTENSIVELY THROUGHOUT THE 53 $EPARTMENT OF $EFENSE $O$ AND OTHER FEDERAL GOVERNMENT AGENCIES 53 PRIVATE INDUSTRY THEIR FOREIGN COUNTERPARTS AND BY PRIVATE INDIVIDUALS !2%03 GREW OUT OF AN URGENT MILITARY OPERATIONAL REQUIREMENT FOR RADAR PERFOR MANCE AND PROPAGATION MODELING WITHIN A TERRAIN EFFECTS DOMINATED ENVIRONMENT 4HE ASSESSMENT SYSTEM REQUIREMENTS INCLUDED MODELING ALL NATURAL ENVIRONMENTAL EFFECTS BEING QUICKLY EXECUTABLE AND EXECUTING ON A -ICROSOFT 7INDOWS OPERATING SYSTEM PERSONAL COMPUTER !N EVALUATION OF THE VARIOUS PROPAGATION MODELS FOR THEIR STRENGTHS AND WEAKNESSES QUICKLY SHOWED THAT A HYBRID MODEL WAS THE ONLY ACCEPT ABLE SOLUTION 4HE !2%03 GRAPHICAL USER INTERFACE WAS CREATED AND INTERFACED TO THE !0- TO PROVIDE THE USER AN END TO END RADAR PROPAGATION ASSESSMENT TOOL "ECAUSE %- PROPAGATION EFFECTS ARE NOT JUST LIMITED TO RADAR FREQUENCIES OVER TIME THE INITIAL RADAR REQUIREMENTS FOR !2%03 WERE EXPANDED BEYOND SIMPLE RADAR DETECTION APPLI CATIONS TO INCLUDE APPLICATIONS IN COMMUNICATIONS AND ELECTRONIC WARFARE !2%03 IS THE ONLY APPROVED %- SYSTEM ASSESSMENT APPLICATION WITHIN THE $EPARTMENT OF THE .AVY #HIEF )NFORMATION /FFICER $/. !PPLICATIONS $ATABASE -ANAGEMENT 3YSTEM $!$-3 !0- IS THE ONLY ACCREDITED BY THE #HIEF OF .AVAL /PERATIONS %- PROPA GATION -(Z TO '(Z MODEL FOR USE IN .AVY SYSTEMS "OTH !2%03 AND !0- ARE ACCREDITED WITHIN THE .AVY -ODELING AND 3IMULATION /FFICE .-3/ !2%03 IS ALSO A .ORTH !TLANTIC 4REATY /RGANIZATION .!4/ APPLICATION APPROVED BY THE -ILITARY #OMMITTEE -ETEOROLOGICAL 'ROUP7ORKING 'ROUP "ATTLE !REA -ETEOROLOGICAL 3YSTEMS AND 3UPPORT PLUS WITH 0ARTNERS !2%03 VERSION CONTAINS SEVERAL %- PROPAGATION MODELS FOR APPLICATIONS AT VARIOUS FREQUENCIES &OR FREQUENCIES OF -(Z TO '(Z !2%03 USES THE !0- &OR (& SKY WAVE COMMUNICATIONS !2%03 USES AN (& MODELING SUITE CONSISTING OF A FULLY $ IONOSPHERE RAY TRACE MODEL AN (& FIELD STRENGTH MODEL AND AN (& NOISE MODEL )N ADDITION TO THESE %- PROPAGATION MODELS !2%03 MAY OPTIONALLY USE TWO INTERNATIONALLY RECOGNIZED IONOSPHERE MODELS THE 0ARAMETERIZED )ONOSPHERIC -ODEL 0)- AND THE )NTERNATIONAL 2EFERENCE )ONOSPHERE )2) )N ADDITION TO THE PROPAGA TION MODELS !2%03 CONTAINS A SYSTEM PERFORMANCE RADAR MODEL WHICH IS DISCUSSED IN THE NEXT SECTION !2%03 CONSIDERS RANGE AND AZIMUTH ANGLEnDEPENDENT INFLUENCES FROM SURFACE FEATURES TO INCLUDE TERRAIN ELEVATION FINITE CONDUCTIVITY DIELECTRIC GROUND CONSTANTS AND SCATTERING EFFECTIVENESS FACTORS 4HE TERRAIN ELEVATION DATA MAY BE OBTAINED FROM THE .ATIONAL 'EOSPATIAL )NTELLIGENCE !GENCYS .'! $IGITAL 4ERRAIN %LEVATION $ATA $4%$ OR FROM ANY OTHER SUITABLE SOURCE 4HE FINITE CONDUCTIVITY AND DIELEC TRIC GROUND CONSTANTS MAY BE SELECTED FROM THOSE DEFINED BY THE )NTERNATIONAL 4ELECOMMUNICATION 5NION )NTERNATIONAL 2ADIO #ONSULTATIVE #OMMITTEE ##)2 OR FROM ANY OTHER SUITABLE SOURCE
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!2%03 CONSIDERS RANGE AND AZIMUTH ANGLEnDEPENDENT ATMOSPHERIC REFRACTIVITY DATA DERIVED FROM THE UPPER AIR OBSERVATIONS OF RADIOSONDES OTHER SENSORS OR MESO SCALE METEOROLOGICAL MODELS SUCH AS THE 53 .AVY #OUPLED /CEAN!TMOSPHERE -ESOSCALE 0REDICTION 3YSTEM #/!-03 2ADIOSONDE DATA MAY BE MANUALLY ENTERED OR AUTOMATICALLY DECODED FROM EITHER THE 7ORLD -ETEOROLOGICAL /RGANIZATION 7-/ OBSERVATIONAL MESSAGE FORMAT OR A FREE FORM COLUMN FORMAT OBTAINED FROM A NUMBER OF DIFFERENT DATA SOURCES )N ADDITION CLIMATOLOGICAL REFRACTIVE CONDI TIONS MAY BE SELECTED FROM A 7-/ STATION WORLDWIDE REPORTING DATABASE &OR OCEAN REPORTING STATIONS OR NUMERICAL WEATHER PREDICTION GRID POINTS OVER THE OCEAN !2%03 AUTOMATICALLY CALCULATES AN EVAPORATION DUCT REFRACTIVE PROFILE AND APPENDS IT TO THE BOTTOM OF THE UPPER AIR OBSERVATION FOR A COMPLETE DESCRIPTION OF THE PROPA GATION ENVIRONMENT !2%03 COMPUTES AND DISPLAYS A NUMBER OF %- SYSTEM PERFORMANCE ASSESSMENT TACTICAL DECISION AIDS 4HESE ARE RADAR PROBABILITY OF DETECTION %3- VULNERABILITY ,& TO %(& COMMUNICATIONS SIMULTANEOUS RADAR DETECTION AND %3- VULNERABILITY AND SURFACE SEARCH DETECTION RANGES !LL DECISION AIDS ARE DISPLAYED AS FUNCTIONS OF RANGE AZIMUTH ANGLE ANDOR HEIGHT $ETECTION PROBABILITY %3- VULNERABILITY AND COMMUNI CATIONS ASSESSMENTS ARE BASED ON %- SYSTEM PARAMETERS STORED IN A USER DEFINED AND CHANGEABLE DATABASE )N ADDITION TO NORMAL RADAR PARAMETERS A USER MAY COMPLETELY DEFINE THE ANTENNA RADIATION PATTERN TO ACCOUNT FOR SIDELOBE CONSIDERATIONS 4HE DATA BASE ALSO INCLUDES RADAR TARGET DESCRIPTIONS AND PLATFORMS %- EMITTER SUITES &IGURE IS AN ILLUSTRATION OF AN !2%03 FOUR PANEL DISPLAY 4HIS DISPLAY WAS CREATED IN SUPPORT OF 53 HOMELAND DEFENSE FOR THE &EBRUARY 3UPER "OWL 8, 4HE 3UPER "OWL 8, 2OMAN NUMERAL FOR IS A CHAMPIONSHIP FOOTBALL GAME
&)'52% !2%03 HOMELAND DEFENSE APPLICATION
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PLAYED IN THE 5NITED 3TATES )T WAS ATTENDED BY OVER PEOPLE ALL CONFINED IN ONE SPORTING EVENT STADIUM WHICH PRESENTED A SIGNIFICANT TARGET FOR A TERRORISM ATTACK 4HE DISPLAY SHOWS A RADAR PROBABILITY OF DETECTION IN A RANGE VERSUS HEIGHT DEPICTION RADAR PROBABILITY OF DETECTION VERSUS RANGE AT A CONSTANT ALTITUDE DEPICTION AND RADAR PROBABILITY OF DETECTION VERSUS HEIGHT AT A CONSTANT RANGE DEPICTION 4HIS DISPLAY IS COURTESY OF THE TH 2ADAR %VALUATION 3QUADRON (ILL !IR &ORCE "ASE 5TAH 4HE RADAR DEPICTED IS THE !232 % 53 !IR 2OUTE 3URVEILLANCE 2ADAR LOCATED AT #ANTON -ICHIGAN 4HE TARGET OF INTEREST IS A SMALL PRIVATE AIRCRAFT !S THE PERSONAL COMPUTER VERSION OF !2%03 DEVELOPED IT ALSO TRANSITIONED INTO AN APPLICATION CALLED THE .AVAL )NTEGRATED 4ACTICAL %NVIRONMENTAL 3UBSYSTEM .)4%3 A SEGMENT OF THE 'LOBAL #OMMAND AND #ONTROL 3YSTEM -ARITIME '##3 - )N .)4%3 THE !2%03 FUNCTIONALITY OF THE PERSONAL COMPUTER WAS CODED IN *AVA AND INTERFACED TO THE #OMMON /PERATING 0ICTURE #/0 4HE #/0 IS A REAL TIME DISPLAY OF TACTICAL INFORMATION AND CURRENT FORCE POSITIONING 4HUS A RADAR ASSESSMENT PROVIDED BY !2%03 MAY BE DISPLAYED AS A TACTICAL OVERLAY UPON THE OPERATING PICTURE &IGURE IS AN ILLUSTRATION OF SUCH A #/0 DISPLAY )N THIS ILLUSTRATION THE RADAR COVERAGE OF THREE COASTAL SURVEILLANCE RADARS IS SHOWN ALONG WITH THE TRADITIONAL HEIGHT VERSUS RANGE COVERAGE DISPLAY TYPICAL OF THE PERSONAL COMPUTER VERSION OF !2%03 !S THE .AVY PROGRESSED INTO WEB BASED APPLICATIONS THE DISPLAY OF !2%03 TACTICAL DECISION AIDS FOLLOWED SUIT /NE SUCH WEB BASED APPLICATION IS THE .AVYS #OMPOSABLE &ORCE.ET AN APPLICATION SIMILAR IN NATURE TO THE '##3 - &IGURE IS AN ILLUSTRATION OF THE #OMPOSABLE &ORCE.ET APPLICATION &OR THIS ILLUSTRATION THE BACKGROUND FOR THE #OMPOSABLE &ORCE.ET #/0 IS A HYPOTHETICAL OCEAN AND ISLAND OPERATION AREA 4HE SYMBOLOGY SUCH AS THE SMALL CIRCLES SQUARES AND HALF CIRCLES REPRESENT THE DISPOSITION OF VARIOUS FORCES SUCH AS SHIPS AND AIRCRAFT 4HE MULTIPLE ELLIPTICAL AND FAN SHAPED SHADED AREAS CORRESPOND TO A CERTAIN RADAR PROBABILITY OF DETECTION OF VARIOUS TARGETS BY VARIOUS OPERATIONAL RADARS &OR EXAMPLE THE SMALL FAN SHAPED SHADED AREA IN THE UPPER RIGHT CORNER OF THE DISPLAY REPRESENTS THE AREA WHERE A GROUND BASED RADAR WOULD BE ABLE TO DETECT WITH A CERTAIN PROBABILITY OF DETECTION A PARTICULAR AIRCRAFT TARGET !N OPTIONAL CAPABILITY OF !2%03 IS TO PROVIDE TO AN EXTERNAL APPLICATION THE COM PUTED RADAR PROBABILITY OF DETECTION PROPAGATION LOSS OR PROPAGATION FACTOR TO AN EXTER NAL APPLICATION 4HUS A TACTICAL APPLICATION DEVELOPER NEED NOT HAVE KNOWLEDGE OF THE UNDERLYING RADAR PROPAGATION MODELING TECHNIQUES OR OTHER ENVIRONMENTAL CONSIDER ATIONS BUT CAN RELY UPON !2%03 TO hSERVE UPv DATA FOR DISPLAY WITHIN HIS OR HER OWN APPLICATION 3UCH AN APPLICATION IS THE 3IMULATION AND $ISPLAY 3YSTEM 3)-$)3 AUTHORED BY THE .AVAL 2ESEARCH ,ABORATORY 7ASHINGTON $# &IGURE IS AN ILLUS TRATION OF !2%03 COMPUTED DATA DISPLAYED THREE DIMENSIONALLY WITHIN 3)-$)3 )N THIS FIGURE THE VIEW IS LOOKING NORTHWARD WITHIN THE BYTE OF 3OUTHERN #ALIFORNIA 4HE EASTERN TERRAIN OF 3AN #LEMENTE )SLAND SHOWS IN THE MIDDLE LEFT OF THE FIGURE &ROM THIS CURRENT VIEW A SHIP WITH A PARTICULAR AIR SEARCH RADAR IS LOCATED BEYOND NORTH OF THE ISLAND 4HE DARKENED FAN SHAPED AREA EXTENDING UPWARD OVER THE ISLAND REPRESENTS THE RADARS PROBABILITY OF DETECTION OF A CERTAIN TARGET AS THE RADAR SWEEPS SOUTHWARD OVER THE ISLAND &OR A TARGET LOCATED IN THE FOREFRONT OF THE ISLAND AND AT A SUFFICIENTLY LOW ALTITUDE THE DISPLAY SHOWS THE TARGET IS NOT DETECTABLE BY THE RADAR AS THE TARGET IS MASKED BY THE INTERVENING TERRAIN
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&)'52% !2%03 COMPUTATIONS DISPLAY WITHIN 3)-$)3 SHOWING RADAR PROBABILITY OF DETECTION OF A SMALL TARGET UNDER THE INFLUENCE OF TERRAIN MASKING EFFECTS
ÓÈ°nÊ , *-Ê, ,Ê-9-/ ÊÊ -- -- /Ê " 4HE MAIN PURPOSE OF !2%03 IS TO OFFER RADAR OPERATORS THE ABILITY TO VISUALIZE THEIR RADARS DETECTION OF THREAT TARGETS OR THEIR OWN PLATFORMS DETECTION BY THREAT RADARS UNDER VARIOUS NATURAL ENVIRONMENTAL CONDITIONS 4HE PRIMARY VISUALIZATION IS A HEIGHT VERSUS RANGE DISPLAY OF RADAR PROBABILITY OF DETECTION WHERE THE RADAR PROBABILITY OF DETECTION EXPRESSED IN PERCENT CORRESPONDS TO CERTAIN ENERGY LEVELS IN HEIGHT AND RANGE FROM THE RADAR !0- COMPUTES PROPAGATION LOSS IN D" 4O MAKE A DETERMINATION OF RADAR PERFORMANCE !2%03 NEEDS TO MAKE A COMPARISON OF FREE SPACE PROPAGATION LOSS AND PROPAGATION LOSS WITHIN THE %ARTHS ENVIRONMENT AS COMPUTED BY !0- 4HUS !2%03 CONTAINS A FAIRLY SIMPLISTIC PULSED RADAR MODEL TO CALCULATE FREE SPACE PROPAGA TION LOSS FROM RADAR SYSTEM PARAMETERS SUCH AS FREQUENCY PULSE LENGTH ETC 4HE MODELS TO DO THIS CALCULATION ARE TAKEN FROM "LAKE AND ARE FULLY DESCRIBED WITHIN THE !2%03 ONLINE HELP AND THE !2%03 OPERATORS MANUAL 4HUS !2%03 RADAR SYSTEM ASSESSMENT MODEL WILL NOT BE REPEATED HERE 4HE INTENT OF THIS SECTION IS TO SHOW THE NECESSARY RADAR SYSTEM AND RADAR TARGET INPUTS NEEDED BY THE !2%03 PROGRAM 4HESE INPUTS ARE SHOWN IN &IGURES AND &OR A COMPLETE DESCRIPTION OF EACH INPUT PARAMETER YOU MAY REFER TO THE !2%03 ONLINE HELP OR THE !2%03 OPERATORS MANUAL
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4O ASSIST THE !2%03 USER THESE AND OTHER INPUT WINDOWS HAVE MANY hCANNEDv DEFAULT VALUES COMBINED WITH MANY UNIT OPTIONS /NE EXAMPLE IS THE TRANSMITTING ANTENNA PATTERN !0- WILL CONSIDER THE FULL ANTENNA PATTERN OF THE TRANSMITTING ANTENNA
&)'52% !2%03 TARGET WINDOW
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!2%03 PROVIDES SOME BASIC hCANNEDv ANTENNA PATTERNS SUCH AS OMNI 3IN88 COSE CANT SQUARED AND A GENERIC HEIGHT FINDER 7ITH A USER SPECIFIED ANTENNA TYPE THE OPERA TOR MAY ENTER THE PATTERN ANGLE AND FACTOR DIRECTLY )N ADDITION TO ENTERING THE ANTENNA PATTERN DIRECTLY FROM THE KEYBOARD !2%03 ALSO PROVIDES THE CAPABILITY OF IMPORTING AN ANTENNA PATTERN FROM AN !3#)) TEXT FILE THAT YOU MAY HAVE CREATED FROM ANOTHER APPLICATION !N EXAMPLE OF MULTIPLE UNITS IS THE TRANSMITTERS PEAK POWER 4HE DEFAULT UNIT FOR PEAK POWER IS +ILOWATTS "Y RIGHT CLICKING ON THE LABEL ASSOCIATED WITH PEAK POWER YOU MAY SELECT OTHER UNITS OF INPUT !2%03 WILL EVEN CONVERT THE INPUT NUMBER AUTOMATICALLY FROM ONE UNIT TO THE OTHER UNIT
ÓÈ°Ê , *-Ê, ,Ê -* 9"Y DEFAULT THE RESULTS OF THE PROPAGATION MODEL CALCULATIONS ARE SHOWN IN TERMS APPRO PRIATE FOR A TACTICAL RADAR OPERATOR IE A HEIGHT VERSUS RANGE DISPLAY OF RADAR PROBABILITY OF DETECTION AS A PERCENTAGE AS ILLUSTRATED IN &IGURE 4HIS DISPLAY IS REFERRED TO AS A TACTICAL DECISION AID BECAUSE IT WILL ALLOW THE RADAR OPERATOR TO MAKE SOME SORT OF TACTICAL DECISION &OR EXAMPLE SUPERIMPOSED ON THIS TACTICAL DECISION AID IS THE FLIGHT PROFILE OF A TARGET MISSILE THE SOLID LINE SLOPING DOWNWARD TO THE ORIGIN FROM RIGHT TO LEFT 4HE ATMOSPHERIC ENVIRONMENT IS SURFACE BASED DUCTING 4HE NONDETECTION SKIP ZONE IS CLEARLY SEEN IN ADDITION TO THE TARGETS FLIGHT PATTERN ALLOWING THE OPERATOR TO SEE HOW THE PROBABILITY OF DETECTION OF THE TARGET WILL VARY WITH RANGE AND HEIGHT 7ITH THIS KNOWLEDGE A DECISION ABOUT WHEN TO ATTEMPT AN ATTACK ON THE MISSILE CAN BE MADE
&)'52% !2%03 HEIGHT VERSUS RANGE COVERAGE FOR SURFACE SEARCH RADAR AND SMALL MISSILE TARGET PROBABILITY OF DETECTION
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WHERE ,FS IS THE FREE SPACE PROPAGATION LOSS GIVEN BY %Q AND ,D" IS THE PROPAGA TION LOSS IN D" AS COMPUTED BY !0- !S A CONVENIENCE FOR THE RADAR ENGINEER !2%03 WILL ALSO DISPLAY THE !0- OUTPUT IN TERMS OF PROPAGATION FACTOR 4HUS &IGURE DISPLAYED IN TERMS OF RADAR PROBABILITY OF DETECTION AS A PERCENTAGE WILL APPEAR AS SHOWN IN &IGURE WHEN DISPLAYED IN TERMS OF PROPAGATION FACTOR )N ADDITION TO THE DEFAULT HEIGHT VERSUS RANGE DISPLAY !2%03 CONTAINS MANY OTHER DISPLAY AND DATA OUTPUT OPTIONS &OR EXAMPLE &IGURE SHOWS FOR THE SAME MISSILE DETECTION EXAMPLE A SIGNAL TO NOISE RATIO VERSUS RANGE DISPLAY SUPERIMPOSED WITH A CLUTTER TO NOISE RATIO COMPUTED FROM AN METER PER SECOND WIND SPEED 4HE DISPLAY ALTITUDE IS FEET ABOVE SEA LEVEL /NE CAN SEE THE EFFECTS OF MULTIPATH INTERFERENCE BETWEEN A RANGE OF AND ABOUT NAUTICAL MILES "EYOND THE MULTIPATH INTERFERENCE REGION ONE CAN SEE A MAJOR FALL OFF OF SIGNAL TO NOISE AND CLUTTER TO NOISE RATIO COMES WITHIN THE SURFACE BASED DUCT SKIP ZONE BETWEEN ABOUT NAUTICAL MILES AND NAUTICAL MILES .OTE HOWEVER THE INCREASE IN RATIOS FOR RANGES BEYOND THE SKIP ZONE )N FACT IT IS EVEN SEEN THAT FOR RANGES BETWEEN AND NAUTICAL MILES THE CLUTTER TO NOISE RATIO EXCEEDS THE SIGNAL TO NOISE RATIO 4HUS FOR THESE RANGES THE RADAR RETURN IS OVERWHELMED WITH CLUTTER
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I_1
INDEX
A A-12 low cross section aircraft, 14.40 Absorbers, 14.32, 14.36 to 14.38 Active aperture, 13.53 to 13.55 Active Electronically Scanned Array (AESA), 5.1, 5.8 to 5.10, 10.28 compared to mechanical scan, 5.9 to 5.10 timing structure, 5.15 to 5.16 typical waveform parameters, 5.13, 5.15 waveform variations for air-to-surface mode, 5.12 to 5.13 Active jamming, 24.5 Active-switch modulator, 10.24 A/D converter and MTI dynamic range, 2.78 to 2.80 Adaptive arrays (ECCM), 24.20 to 24.30 Adaptive jammer and clutter cancellation, 24.25 Adaptive MTI, 2.80 to 2.83 Adaptive thresholding, 7.11 to 7.19 Advanced Propagation Model (APM), 26.16 to 26.17 Advanced Refractive Effects Prediction System (AREPS), 26.1 to 26.2, 26.18 to 26.27 Aid to Navigation (AtoN), 22.25 to 22.26 Air-to-air ground ranging, 5.33 Air-to-air mission profile, 5.12 to 5.14 Air-to-air modes, 5.14, 5.16 to 5.28 medium PRF, 5.16 to 5.20 Air-to-surface mission profile, 5.10 Air-to-surface mode suite, 5.11 to 5.12 Air-to-surface radar modes, 5.28 to 5.42 Air-traffic control (ATC) radar, 1.21 to 1.22 Air Traffic Control Radar Beacon System (ATCRBS), 7.49 Airborne Early Warning, 3.1. See also Airborne Moving Target Indication antenna sidelobes, 3.13 to 3.14 coverage, 3.2 to 3.3 platform motion, 3.3 to 3.14 TACCAR, 3.4 to 3.9 Airborne Moving Target Indication (AMTI) example of, 3.32 to 3.33 improvement factor, 3.8 multiple spectra, 3.31 to 3.32 scanning motion compensation, 3.14 to 3.17 and STAP, 3.23 to 3.31 Aircraft radar cross section, 14.13 to 14.14 Alpha-beta (-) filter, 7.26 to 7.27, 7.30 Altimeters, from space, 18.33 to 18.57 Altitude line, 4.4 to 4.5 Ambiguity function, 8.40 Ambiguity resolution, in MTI, 2.89 to 2.91 Amplitude-comparison monopulse, 9.3 to 9.11 Amplitude noise, in tracking, 9.27 to 9.30 AN/APG-76, 17.25 AN/APY-9, 3.32 to 3.33 AN/FPQ-6, 9.2, 9.9, 9.18, 9.21, 9.44 AN/FPS-23, 23.7 AN/EPS-117, 8.30, 13.63 to 13.64 AN/MPS-39, 9.2, 9.26 AN/SPS-40, 10.27, 11.32 to 11.33 AN/SPY-1, 13.62
AN/SPY-3, 13.69 AN/TPS-59, 8.30, 13.63 to 13.64 AN/TPS-63, 12.18 AN/TPS-77, 13.63 to 13.64 AN/TPS-78, 13.65 to 13.66 Analog-to-digital (A/D) converters, 6.35 to 6.40
I_2
Anechoic chamber, 14.32 Angle accuracy, by beam splitting, 7.5 to 7.7 Angle measurement errors, 9.43 to 9.44 Angle noise, 9.30 to 9.35 Angle scintillation (glint), 9.30 to 9.35, 9.47 Angular direction, 1.8 Anomalous propagation, 26.6 to 26.13 Antenna-related ECCM, 24.10 to 24.31 Antennas, 1.2, 1.4 to 1.5. See also phased arrays, reflector antennas basic principles, 12.3 to 12.15 for civil marine radar, 22.10 to 22.12 for ground penetrating radar, 21.24 to 21.30 phased array, 13.2 to 13.3 for pulse doppler, 4.12 to 4.13 reflector antennas, role of, 12.1 reflector antennas, types of, 12.7 Anti-radiation missile (ARM), 24.40 Anti-range-gate pull-off (A-RGPO), 24.46 Aperture gain, of antennas, 12.4 to 12.5 Apollo Lunar Sounder, 18.60 to 18.61 Aquarius scatterometer, 18.58 Area MTI, 2.84 Array feeds, for reflector antennas, 12.28 to 12.30 ARSR-4, 12.30 ASR-9, 10.27 to 10.28, 12.20 to 12.21 ASR-11 MTI filter design, 2.50 to 2.51 ASR-12, 8.30, 10.27 to 10.28 Atmosphere, of the Earth, 26.2 Atmospheric ducts, 26.7 to 26.10 Attenuation, by clouds, 19.7 to 19.8 by fog, 19.12 by hail, 19.11 to 19.12 by rain, 19.8 to 19.11 Automatic detection, 7.1 to 7.2, 7.20 to 7.22 Automatic gain control (AGC), in monopulse tracker, 9.5, 9.10 to 9.11 Automatic Identification System (AIS) in civil marine radar, 22.23 to 22.25 in search and rescue, 22.27 Automatic noise-level control, 6.23 to 6.24 Automatic Radar Plotting Aid (ARPA), 22.17 Automatic tracking, 7.22 to 7.46 alpha-beta (-) filter, 7.26 to 7.27, 7.30 detection acceptance, 7.25 to 7.26 Interacting Multiple Model (IMM), 7.35 to 7.37 Kalman filter, 7.28 to 7.35 new track formation, 7.41 to 7.46 retrospective processing, 7.42 to 7.43 scheduling and control, 7.46 track association, 7.38 to 7.41 track file, 7.23 to 7.25 updating tracks, 7.26 to 7.30 AWACS, 13.65
B B-2 low cross section aircraft, 14.18, 14.42 Ballistic missile defense, 13.54 Bandwidth importance of, 1.8 to 1.9 of phased arrays, 13.38 to 13.45 receiver, 6.9 Bar, in airborne radar, 5.15 to 5.16 Barker codes, 8.17
Batch processor, 7.8 to 7.11 Battle of the Pips, ducting effects, 26.9 Beacon equation, 24.4 Beacon rendezvous, 5.27 Beam-shape factor, 7.3 Beam-shape loss, 4.40 Beam-splitting angle accuracy, 7.5 to 7.7 Beam steering, 13.15 to 13.19 Beam steering control, 5.10 Binary integrator, 7.7 to 7.8, 7.12 to 7.13 Birds, and MTI, 2.96 to 2.98 Bistatic plane, 23.3 Bistatic radar applications, 23.9 to 23.14 benchmark range, 23.4 to 23.5 concept of, 23.1 to 23.3 coordinate system, 23.3 to 23.4 doppler in, 23.14 to 23.17 floodlight beams, 23.27 forward scatter, 23.21 glint in, 23.20 to 23.21 ground echo, 16.29 hitchhiker, 23.10 with noncooperative transmitter, 23.29 to 23.31 ovals of Cassini, 23.6 to 23.8 passive, 23.10 pseudo-monostatic region, 23.19 to 23.20 pulse chasing, 23.28 to 23.29
I_3
range equation, 23.5 to 23.6 SAR, 23.17 scattering coefficient, 23.22 to 23.25 surface clutter in, 23.22 to 23.26 target cross section, 23.19 to 23.21 target location, 23.17 to 23.19 with TV transmitter, 23.29 to 23.31 Blind speeds, 2.9 to 2.10 Block diagram digital receiver, 25.2 medium PRF air-to-air pulse doppler, 5.17 monopulse tracking radar, 9.4 to 9.5 Moving Target Detection, 2.6 to 2.7 multifunctional fighter aircraft radar, 5.3 pulse compression, 8.1 to 8.2 pulse doppler, 4.11 radar, 1.3 SBR altimeter, 18.40 Bodies of revolution radar cross section, 14.39 to 14.40 Bragg scatter, 15.2, 15.28 to 15.32, 15.38, and ground echo, 16.11 to 16.12 Burst mode, in SBR SAR, 18.23 to 18.24
C C band, 1.16 Calibrate and self-test, 5.42 Calibration of meteorological radar, 19.18 to 19.19 Cascaded Integrator-Comb (CIC) Filters, 25.29 to 25.32 Cassegrain antenna, 12.21 to 12.23, 12.25, 14.34 Cassini, 18.46 Cathode pulser, 10.23 Cell-averaging CFAR, 7.11 to 7.12, 7.17 CFAR, 7.11 to 7.18 and ECCM, 24.35 to 24.36 loss, 4.44 probability of detection, 7.15 target suppression in, 7.16 to 7.17 Chaff, 24.5 to 24.6 Chaff and ECCM, 24.19, 24.34 Chart radars, 22.22 to 22.23 Chebyshev filter bank, 2.54 to 2.55 Civil Marine Radar (CMR), 22.33 and aids to navigation (AtoN), 22.25, 22.26 antennas, 22.10 to 22.12 Automatic Identification System (AIS), 22.2, 22.8 integration with, 22.23 to 22.25 cost of, 22.3 detection performance, 22.4 to 22.6 detection and processing, 22.13 to 22.15 display, 22.21 early days of, 22.31 to 22.33 environmental conditions, 22.3 international standards for, 22.7 to 22.10 magnetrons for, 10.16 precipitation and sea clutter, 22.5 racons and, 22.26 radar beacons and, 22.25 radar target enhancers (RTEs), 22.27 RF head (transmitter and receiver), 22.12 to 22.13 search and rescue transponders, 22.27 solid-state, 22.16 to 22.17 target tracking, 22.17 to 22.19 user interface, 22.19 to 22.22
validation testing of, 22.28 to 22.29 vertical lobing in, 22.6 to 22.7 Class of (amplifier) operation, 11.18 to 11.20 Clouds, attenuation in, 19.7 to 19.8 CloudSat, 18.63, 19.39 Clustered-cavity klystron, 10.12 to 10.13 Clutter amplitude characteristics, 2.17 attenuation, in MTI, 2.20 to 2.21 characteristics for MTI, 2.10 to 2.19 exponential model, 2.12 to 2.16 in ground penetrating radar, 21.5, 21.10 maps, 2.83 to 2.87, 6.23, 7.19 models, for ground echo, 16.29 to 16.34 MTI filter design, 2.33 to 2.46 optimum filter design, 2.25 to 2.33 point scatterers, 2.18 to 2.19 in pulse doppler radar, 4.14 to 4.24 reflectivity, 2.17 to 2.18 Clutter-limited detection in pulse doppler, 4.48 Coaxial magnetron, 10.14 to 10.15 Coaxitron, 10.21 Cobra Dane radar, 8.36 Coherent processing, and ECCM, 24.34 to 24.35 Coherent Processing Interval (CPI), 2.7 Coherent on receive, 10.14
I_4
COHO, 6.3, 6.20 Collapsing loss, 7.3 Compact range, 14.32 to 14.33 Complementary pulse compression waveforms, 8.19 Complex envelope representation, 8.38 to 8.39 Computer codes for reflector design, 12.33 to 12.35 Conformal arrays, 13.3 Conical-scan tracking, 9.16 to 9.17 Conopulse, 9.15 Constant false alarm rate. See CFAR Continuous wave (CW) radar, 1.5 Constant Efficiency Amplifier (CEA), 10.21 to 10.22, 10.26 Cooperative target identification, 5.22 to 5.23 CORDIC processor, 25.22 to 25.25 Corner reflector, radar cross section, 14.9 to 14.11 Corporate feed monopulse phased array, 9.14 Co secant-squared antenna, and STC, 2.98 COSMO-SkyMed SAR, 18.12 Costas codes, 8.25 to 8.26 Counter Battery Radar (COBRA), 13.62 Creeping waves, 14.3, 14.5 Critical frequency, in HE OTH, 20.3 Crossed-field amplifier (CFA), 10.3, 10.16 to 10.17 Crossed-field tubes, 10.2 Cross-eye ECM, 24.42 to 24.43 Cross-polarization jamming, 24.43 Cross-polarization tracking, 9.40 to 9.41 Crossrange resolution, 17.1 Cross section. See radar cross section Crosstalk, in tracking, 9.40 to 9.41 Crowbar, in transmitters, 10.24 CryoSat altimeter, 18.42 to 18.43
D D region, 20.14 Dällenbach layer, 14.37 to 14.38 Data link, missile, 5.26 Data links, in MFAR, 5.24 to 5.27 Data processing, 1.3 dBZ, 19.5 to 19.6 DC operation of CFA, 10.17, 10.24 Deceptive ECM (DECM), and ECCM, 24.6 to 24.7, 24.40 and tracking radar, 24.41 to 24.42 Decimation, 6.41 to 6.42 Decimation filters, 25.28 to 25.32 Decoys, 24.6, 24.8 Delta-Sigma converters, 6.36 Depressed collector, 10.10 Detection acceptance, 7.25 to 7.26 Detectors batch processor, 7.8 to 7.11 binary integrator, 7.7 to 7.8, 7.12 to 7.13 M-out-of-N, 7.7 to 7.8 moving window, 7.4 to 7.7 nonparametric, 7.17 to 7.18 optimal, 7.2 to 7.4 practical, 7.4 to 7.11 rank, 7.17 to 7.18 Dicke fix, 24.33, 24.35 Differential reflectivity, 19.18 Diffraction, 26.5 Digital beamforming, 13.8, 13.56 to 13.57 multiple beams, 25.17 to 25.19
Digital downconversion (DDC), 6.41 to 6.42, 6.44 to 6.45, 25.6 to 25.15 Digital filters, 25.26 to 25.32 Digital pulse compression, 25.19 generation of, 8.28 to 8.30 Digital receiver, 6.40 to 6.46 block diagram, 25.2 direct sampling, 25.38 Digital RF memory (DREM), 24.6 to 24.7 Digital signal processing hardware implementation, 25.35 to 25.37 timing dependence, 25.34 to 25.35 tools, 25.22 to 25.34 Digital upconverter (DUC), 25.21 to 25.22 Diode phase shifter, 13.51 to 13.52 Dipole antenna, 21.25 to 21.26 Direct digital downconversion, 25.10 to 25.15 Direct digital synthesizer (DDS), 6.22, 6.48 to 6.49, 25.20 to 25.21 Direct sampling digital receiver. 25.38 Direction finding (DF) and radar, 7.50 to 7.54 Directive gain, of an antenna, 12.5 Discrete Fourier transform (DFT), 25.32 to 25.34 Displaced Phase Center Antenna (DPCA), 3.10 to 3.13, 3.19 to 3.21, 5.2 to 5.3 Distortion, in receiver, 6.6 to 6.7 Doppler ambiguity resolution, 4.33 to 4.34
I_5
Doppler beam sharpening (DBS), 5.34 to 5.36, 5.37, 17.2, 17.3 Doppler, in bistatic radar, 23.14 to 23.17 Doppler filter bank, 2.7 to 2.9 Doppler filter straddle loss, 4.43 Doppler filter weighting loss, 4.43 Doppler radars, 4.1 Doppler scintillation, in tracking radars, 9.36 to 9.37 Doppler shift, 1.10 Doppler spectra, spurious, 6.11 Doppler spectrum of ground echo, 16.16 to 16.19 of HF sea echo, 20.49 to 20.52, 20.75 Doppler weather radar, 1.7 Ducts atmospheric, 26.7 to 26.10 elevated, 26.12 to 26.13 evaporation, 26.11 to 26.12 surface, 26.10 to 26.11 Duplexer, 1.2, 6.2 Dynamic range, 1.3, 6.4 to 6.8 of A/D converters, 6.38 to 6.39 and ECCM, 24.32 to 24.33 in pulse doppler radar, 24.32 to 24.33
E E-2C, 3.3 E-2D, 3.1 to 3.3 E region, 20.14 Early-late gate range tracking, 9.21 to 9.22 Eclipsing loss, 4.40 to 4.43, 5.18 Effective-earth-radius model, 26.15 Eldora radar, 19.37 to 19.38 EM system assessment, 26.18 to 16.23 Electronic Attack, 24.2 Electronic counter-countermeasures (ECCM) antenna-related, 24.10 to 24.31 decoys, 24.8 efficiency, 24.54 to 24.56 and imaging radar, 24.48 to 24.52 and ISAR, 24.51 to 24.52 operational-deployment techniques, 24.36 to 24.37 and over-the-horizon radar, 24.52 to 24.53 and phased array radar, 24.43 to 24.48 and radar equation, 24.55 to 24.56 receiver related, 24.32 to 24.33 role of the operator with, 24.36 SLB and SLC, 24.17 to 24.20 sidelobe canceler, 24.14 to 24.20 signal-processing related, 24.33 to 24.36 STAP, 24.21 to 24.22 and subarrays, 24.25 to 24.29 and surveillance radars, 24.37 to 24.40 and SAR, 24.48 to 24.51 techniques, 24.8 to 24.9, 24.37 to 24.53 terminology, 24.2 and tracking radars, 24.40 to 24.43 transmitter related, 24.31 to 24.32 Electronic countermeasures (ECM), 24.5 to 24.8 Electronic Protection (EP), 24.2 Electronic-scan monopulse, 9.12 to 9.13 Electronic Support (ES), 24.2 Electronic Warfare Support Measures (ESM), 24.2 to 24.5 Elevated ducts, 26.12 to 26.13
Elint, 24.2, 24.3, 24.4 Emission Control (EMCON), 24.37 ENVIS AT, 18.11 Errors in tracking radar external causes of, 9.37 to 9.43 internal sources of, 9.42 to 9.43, 9.47 reduction techniques, 9.46 to 9.47 sources of, 9.26 target caused, 9.26 to 9.37 ERS SAR, 18.8 to 18.9 Evaporation ducts, 26.11 to 26.12 Exponential model of land clutter, 2.12 to 2.16 Extended Interaction Klystron (EIK), 10.11 External noise at HF, 20.43 to 20.45
F F-117 low cross section aircraft, 14.40 to 14.42 F region, 20.14 to 20.15 Fading, 16.12 False-alarm control, 7.11 to 7.19 Far field, 14.4 Far-field criterion, 14.27 to 14.28 Fast Fourier transform (FFT), 25.33 to 25.34 filter bank, 2.55 to 2.56 Fast Time Constant (FTC), in CMR, 22.5 Fast-wave tube, 10.3 Ferrite phase shifters, 13.52 to 13.53 Fighter aircraft missions, 5.10 to 5.16
I_6
Filter-bank design, 2.52 to 2.59 Filter mismatch loss, in MTI, 2.22 to 2.23 Filters, in radar, 6.24 to 6.29 Finite impulse response (FIR) filters, 2.33, 25.26 to 25.28 FM-CW radar, 1.5, 9.20 Focused SAR, 17.2 Foliage-penetration (FOPEN) SAR, 17.33 to 17.34 Fog, attenuation in, 19.12 Forward scatter, in bistatic radar, 23.21 Fourier transform, 8.38 Frank codes, 8.19 to 8.20 Free-space propagation, 26.13 to 26.15 Frequency agility, 1.9, 24.31 Frequency diversity, 1.9, 24.31 Frequency, effect on radar, 1.14 to 1.18 Frequency multipliers, 6.49 to 6.50 Frequency synthesis, 6.21 to 6.22 Front end, of receiver, 6.10 to 6.14
G GaAs PHEMT FET, 11.12 to 11.16 Geometrical optics, 14.20 to 14.21 and ground echo, 16.8 reflector analysis, 12.33 Geometric theory of diffraction, 14.24 to 14.25 Geosat, 18.41 to 18.42 Ghosts, 2.88, 4.33, 14.35 Glint in bistatic radar, 23.20 to 23.21 in tracking radar, 9.30 to 9.35 Global Nearest Neighbor (GNN), 7.39 to 7.40 Graceful degradation, 13.4 Graded absorber, 14.37 Grating lobes, 13.10 to 13.12 Gregorian antenna, 12.21, 12.25 Gregorian system, 14.33 to 14.34 Grid-controlled vacuum tubes, 10.21 to 10.23, 10.25 Grid locking, 7.49 Ground echo available information from, 16.4 bistatic, 16.29 fading of, 16.12 to 16.19 at HF, 20.29 to 20.30 imaging radar interpretation, 16.55 to 16.56 at low grazing angle, 16.52 to 16.55 measurement techniques for, 16.19 to 16.29 in meteorological radar, 19.13 to 19.14 models for scattering coefficient, 16.29 to 16.34 near-grazing angle, 16.52 to 16.55 near-vertical, 16.25 number of independent samples, 16.24 parameters affecting, 16.4 to 16.7 polarimetry, 16.46 to 16.52 scattering coefficient data, 16.35 to 16.46 scattering coefficients from radar images, 16.28 to 16.29 sea ice, 16.44 to 16.46 snow, 16.42 to 16.44 soil moisture, 16.40 to 16.41 speckle, 16.55 theoretical models, 16.7 to 16.12 vegetation, 16.41 Ground moving target indication (GMTI), 5.38 to 5.42, 17.25 Ground moving target thresholding, 5.39 to 5.40
Ground moving target track (GMTT), 5.38 Ground moving target weapon delivery, 5.40 to 5.41 Ground penetrating radar (GPR) antennas, 21.24 to 21.30 applications of, 21.3, 21.35 to 21.40 archeological applications, 21.36 and land mines, 21.37 AT mines, 21.34, 21.39 attenuation with, 21.7 to 21.9 bandwidth, 21.1 characteristics of, 21.4 clutter in, 21.5, 21.10 comparison with optical image, 21.4 depth resolution, 21.11 description of, 21.1 to 21.6 dispersion in, 21.11 earth material properties, 21.18 to 21.19 example of, 21.2 forensic investigations, 21.35 and frequency domain, 21.23 and glacier, 21.37 image processing, 21.30 to 21.35 licensing of, 21.39 to 21.40 modeling of, 21.13 to 21.18 modulation techniques, 21.21 to 21.24
I_7
polarization, 21.10 to 21.11 propagation, 21.6 to 21.13 reflections in, 21.9 to 21.10 resolution, 21.13 road thickness measurement, 21.37 to 21.38 and SAR, 21.13 signal processing, 21.30 to 21.35 soil suitability map, 21.20 from space, 18.59 to 18.62 systems, 21.20 to 21.21 velocity of propagation, 21.11 Ground plane, 14.31 Guard blanking loss, 4.44 Guard channel, in pulse doppler, 4.19 to 4.22 Gyrotrons, 10.3, 10.17 to 10.19, 10.26
H Hail, attenuation in, 19.11 to 19.12 Hail, detection of, 19.31 Height measurement, with InSAR, 17.30 to 17.33 Height measurement, with SAR, 17.27 to 17.33 HF, 1.15 HF over-the-horizon radar. See over-the-horizon radar High-medium PRF, 4.7 High-PRF pulse doppler, 4.7 to 4.8 High-PRF range-while-search, 4.36 High-PRF ranging, in pulse doppler, 4.34 to 4.35 High-resolution radar, 1.5 Hilbert transform, 6.43 to 6.44 HJ-1-C SAR, 18.13 Hot clutter, 24.43 Hybrid models for propagation, 26.16 to 26.17 Hybrid processors, 25.37
I Identification friend or foe (IFF), integration with radar, 7.50 I/Q channels, 6.31 to 6.35 Image-reject mixer, 6.13 Imaging radar ground echo, 16.55 to 16.56 Improvement factor, for AMTI, 3.8 Improvement factor limitations caused by staggering, 2.42 to 2.44 Improvement factor, for MTI, 2.19 to 2.20, 2.23 to 2.25, 6.17 to 6.18 Inductive output tube, 10.22 Infinite impulse response (IIR) filters, 2.33, 25.26 to 25.27 Insets, radar cross section of, 14.11 to 14.12 Instabilities in MTI, 2.65, 2.73 Instability limitations in MTI, 2.72 Instantaneous bandwidth, 6.9 Interclutter visibility in MTI, 2.22 Interacting multiple model (IMM) in ADT, 7.35 to 7.37 Interferometric SAR (InSAR), 17.5, 17.23 to 17.24 target height measurement, 17.30 to 17.33 International Maritime Organization (IMO), 22.1, 22.4, 22.8, 22.27, 22.28, 22.32 Interpolation filters, 25.28 Inverse Cassegrain, 9.25 Inverse SAR (ISAR), 5.23 to 5.24, 5.31 to 5.33, 9.37, 17.5 and ECCM, 24.51 to 24.52 Ionogram, 20.16 to 20.17 Ionosphere, 20.13 to 20.21 Ionospheric models, 20.19 to 20.20 Isodoppler contours in bistatic radar, 23.16
J Jamming, 5.27, 24.5 Jaumann absorber, 14.36 to 14.37 J-ERS SAR, 18.9 Jet-engine modulation, 5.23 JianBing-5 SAR, 18.12 Jindalee OTH radar, 20.3, 20.22 performance model, 20.67 to 20.70 Joint STARS, 13.66 to 13.67, 17.23 to 17.24 JORN OTH, 20.12, 20.19
K K band, 1.17 Kalman filter, 7.28 to 7.35 Klystrode, 10.22 Klystron, 10.5 to 10.8, 10.26 origin of, 10.2 to 10.3
L L band, 1.16 Land clutter. See ground echo Laser radar, 1.18
I_8
Letter-band nomenclature, 1.13 to 1.14 Lewis and Kretschmer codes, 8.20 to 8.22 Limiters, 6.29 to 6.31 Line-type modulator, 10.23 Linear array antenna, 13.11 to 13.13 Linear-beam vacuum tube, 10.3 Linear-beam amplifier, 10.4 to 10.13 Linear FM pulse compression, 8.3 to 8.11 Liquid crystal display, for CMR, 22.19 Lobing, in elevation, 22.6 to 22.7 Local oscillator, 6.14 to 6.22 Low-earth orbit, 18.2 Low grazing-angle clutter measurements, 16.52 to 16.55 Low-noise amplifier, 6.10 Low radar cross section ships 14.42 to 14.43 vehicles, 14.39 to 14.43 Low-sidelobe antenna, 24.10 to 14.11
M Madre HF OTH radar, 20.24 to 20.45 Magellan Venus mapper, 18.48 to 18.52 Magnetron, 10.2, 10.14 to 10.16, 10.26 for civil marine radar, 10.16, 22.12 Main-beam cancellation, 24.33 MAPSAR, 18.14 to 18.15 Marcum Q-function, 24.22 Marine boundary layer, 26.12 Matched filter, 1.3, 6.25, 8.39 to 8.40 loss in pulse doppler, 4.40 Maximal-length sequences, 8.18 Maxwell’s equations, 14.17 Mechanical design of antenna, 12.35 to 12.41 Medium PRF for air-to-air mode, 5.16 to 5.20 Medium PRF for pulse doppler, 4.8 Medium PRF for range while search, 4.37 to 4.38 Medium PRF selection algorithms, 5.18 to 5.20 Metal plate, radar cross section of, 14.8 to 14.9 Meteor trails, and HF OTH radar, 20.38 to 20.40 Meteorological radar airborne, 19.37 to 19.38 attenuation effects, 19.7 to 19.12 calibration, 19.18 to 19.19 design considerations, 19.6 to 19.19 ground clutter effects, 19.13 to 19.14 measurement accuracy, 19.22 to 19.23 microbursts, 19.29 to 19.31 MTI filter design for, 2.46 to 2.51 multiple radars, 19.33 to 19.35 operational applications, 19.25 to 19.33 phased array, 19.35 to 19.37 polarization, 19.18, 19.27 to 19.28, 19.33 precipitation measurement, 19.26 to 19.28 processor implementation. 19.24 to 19.25 pulse compression, 19.23 to 19.24 pulse-pair algorithm, 19.21 range and velocity ambiguities, 19.12 to 19.13 research applications, 19.33 to 19.40 severe storm warning, 19.28 to 19.33 signal processing, 19.19 to 19.25 spaceborne, 19.38 to 19.39 spaced antenna techniques, 19.40 spectrum moment estimation, 19.20 to 19.21
typical designs, 19.14 to 19.18 whitening filter, 19.24 wind profiler, 19.39 to 19.40 Method of moments, 14.1, 14.18 to 14.19 MFAR. See Multifunctional Fighter Aircraft Radar Microbursts, 19.29 to 19.31 Microwaves, 1.1, 1.14 Microwave monolithic integrated circuits (MMIC) characteristics of, 11.24 to 11.29 power amplifiers, 11.26 low-noise amplifiers, 11.26 phase shifters, 11.27 to 11.29 transmit/receive switching, 11.27 Microwave power module (MPM), 10.13 Military radar, 1.20 Millimeter waves, 1.14, 1.17 to 1.18 Mirror-scanned antenna, 9.25 Missile guidance performance assessment, 5.42 Missile-range instrumentation radar, 9.2 Mixer, image-reject, 6.13 Mixers, performance parameters, 6.14 Mixers, spurious response of, 6.11 to 6.13 MMIC. See Microwave monolithic integrated circuits
I_9
Modeling, of propagation, 26.13 to 26.17 Modified generalized sign test processor, 7.17 to 7.19 Modulators, 10.23 to 10.25 Monopulse-antenna feed techniques, 9.6 to 9.10 Monopulse antenna feeds, 12.26 to 12.28 Monopulse, dual band, 9.24 to 9.25 Monopulse, and ECM, 24.23 to 24.24, 24.42 to 24.43 Monopulse, phased arrays, 13.4 Monopulse tracking, 9.3 to 9.16 Moving Target Indication (MTI), 1.5, 4.2 A/D converter effect on dynamic range, 2.78 to 2.80 adaptive, 2.80 to 2.83 binomial weight cancelers, 2.35 and birds as clutter, 2.85, 2.87 to 2.88, 2.96 to 2.98 blind speeds, 2.9 to 2.10 block diagram, 2.4 to 2.7 canonical filter design, 2.34 clutter attenuation (CA), 2.20 to 2.21 clutter characteristics, 2.10 to 2.19 clutter filter-bank design, 2.52 to 2.59 clutter filter response, 2.9 to 2.10 clutter maps, 2.83 to 2.87 clutter visibility factor (Voc), 2.23 definitions, 2.19 to 2.23 dynamic range, 2.78 to 2.80 environmental considerations, 2.94 to 2.100 feedforward canceler, 2.39 filter design, 2.25 to 2.46 filter design for weather radar, 2.46 to 2.51 filter mismatch loss, 2.22 to 2.23 hardware considerations, 2.92 to 2.94 improvement factor, 2.19 to 2.20, 2.23 to 2.25, 6.17 to 6.18 interclutter visibility (ICV), 2.22 limitation due to scanning, 2.23, 2.38 limiting in receiver, 2.59 to 2.65 one-delay canceler, 2.35 optimum clutter filter design, 2.25 to 2.33 performance degradation due to limiting, 2.59 to 2.65 pulse compression considerations, 2.75 to 2.78 purpose of, 2.2 radial velocity ambiguity resolution, 2.89 to 2.91 range ambiguity resolution, 2.89 to 2.91 rules for, 2.92 to 2.94 in SAR, 17.23 and STC, 2.96 to 2.98 sensitivity velocity control (SVC), 2.87 to 2.91, 2.99 to 2.100 signal-to-clutter ratio improvement (ISCR), 2.21 to 2.22 stability requirements, 2.65 to 2.78 staggered PRF design, 2.39 to 2.46 subclutter visibility (SCV), 2.6, 2.22 superclutter visibility, 2.84 three-delay canceler, 2.37 two-delay canceler, 2.36 unwanted targets, removal of, 2.96 to 2.100 Moving targets, in SAR, 17.23 to 17.27 Moving Target Detection (MTD), 2.6 to 2.9 block diagram, 2.6 to 2.7 ducted propagation, effect of, 2.95 Moving-window detector, 7.4 to 7.7 MTBF, of klystrons, 10.6 to 10.7 Multi-beam digital beamforming, 25.17 to 25.19 Multifunction radar, 1.7, 13.1 Multifunctional Fighter Aircraft Radar (MFAR), 5.2 to 5.7 processing, 5.5 range-doppler situation in, 5.7 to 5.8
software structure, 5.6 to 5.7 Multipath, 26.4 to 26.5 in tracking radar, 9.37 to 9.40, 9.46 to 9.47 Multiple-beam klystron, 10.7 to 10.8 Multiple hypothesis algorithm in track association, 7.40 to 7.41 Multiple Object Tracking Radar (MOTR), 9.2, 9.26 Multiple reflector antenna, 12.21 to 12.24 Multiple scattering in target recognition, 14.35 Multiplicative noise, 4.28, 18.18 in SAR, 17.17 to 17.18
N NCAR dual band radar, 19.17 Networked radar, 7.46 to 7.49
I_10
Nexrad (WSR-88D) weather radar, 19.1, 19.16 to 19.17 automated weather products, 19.25 Noise, in receiver, 6.4 to 6.5 Noise, in tracking, 9.27 to 9.30 Noncooperative air target recognition, 5.22 to 5.24 Nonlinear FM pulse compression, 8.12 to 8.16 Nonparametric detectors, 7.17 to 7.18 Nonspecular absorbers, 14.38 nth-time-around tracking, 9.24 Nyquist, 25.2, 25.4 to 25.6
O Ogive, radar cross section of, 14.7 to 14.8 On-axis tracking 9.25 to 9.26 Operating bandwidth, 6.9 Optics region, 14.5 to 14.6 Optimal detection, 7.2 to 7.4 Orographic rain, 19.26 Oscillator vs. amplifier transmitter, 10.4 Ovals of Cassini, 23.6 to 23.8 Over-the-horizon radar antennas for, 20.24 to 20.26, 20.45 to 20.46 calibration, 20.48 to 20.49 clutter, 20.29 to 20.33 coherent processing for, 20.6 compared to microwave radar, 20.7 to 20.10 doppler spectrum of the sea, 20.49 to 20.52 and ECCM, 24.52 to 24.53 examples of, 20.11 to 20.12 external noise in, 20.40 and meteor trails, 20.38 to 20.40 noise models, 20.43 to 20.45 oceanography, 20.33 to 20.38 performance modeling, 20.55 to 20.70 propagation factor, 20.6 to 20.7 radar cross section, 20.26 to 20.29 radar equation, 20.5 to 20.7 receiving system, 20.45 to 20.49 resource management, 20.54 to 20.55 revisit times, 20.4 to 20.5 signal processing, 20.49 to 20.54 sky wave radar design, 20.8 to 20.13 spectrum occupancy, 20.40 to 20.45 surface-wave radar, 20.70 to 20.76 tracking, 20.53 to 20.54 transmitters, 20.23 to 20.26 waveforms, 20.21 to 20.23
P PALSAR, 18.11, 18.15 to 18.16 Parabolic cylinder antenna, 12.18 to 12.19 Parabolic equation methods, for propagation, 26.16 Parabolic reflector antenna, 12.17 to 12.18 Passive bistatic radar, 23.29 Passive ECM, 24.5 to 24.6 Passive listening, 5.34 Patriot radar, 13.66 to 13.67 Pave Paws radar, 11.31 to 11.32 Penetration aids accompanying ballistic missiles, 24.6 Phase-comparison monopulse, 9.11 to 9.12 Phase instabilities, 2.66 to 2.70
Phase noise in pulse doppler, 4.28 to 4.30 Phase shifters, 13.51 to 13.53 Phased array radar active aperture, 13.53 to 13.55 antennas, 13.2 to 13.3 AN/SPY-1, 13.62 AN/SPY-3, 13.69 aperture matching, 13.20 array simulator for, 13.25 to 13.26 bandwidth of, 13.38 to 13.45 beam switching, 13.8 calibration of active arrays, 13.60 to 13.62 circular polarization, 13.6 constrained feed, 13.46 Counter Battery Radar (COBRA), 13.62 digital beamforming, 13.56 to 13.57 diode phase shifters, 13.51 to 13.52 and ECM, 24.43 to 24.48 element pattern, 13.22 to 13.23 errors in, 13.30 to 13.38 feed networks, 13.46 to 13.50 ferrite phase shifters, 13.52 to 13.53 frequency scan, 13.7 to 13.8 gain, 13.13 to 13.15 grating lobes, 13.10 to 13.12, 13.17 to 13.19 ground-based, 13.63 to 13.65 illumination functions, 13.28 to 13.29 instantaneous bandwidth, 13.42 to 13.45 limited scan, 13.6 to 13.7
I_11
linear array, 13.11 to 13.13 low sidelobes, 13.28 to 13.33 meteorological, 19.35 to 19.37 monitoring of, 13.4 to 13.5 monopulse tracking, 9.12 to 9.13, 13.4 multifunction, 13.1 mutual coupling, 13.20 to 13.22 optical feed, 13.46 parallel feed, 13.48 to 13.49 periodic errors in, 13.35 to 13.38 phase-only control, 13.58 phase quantization, 13.34 phase shifters, 13.51 to 13.53 planar array, 13.15 to 13.19 radiation pattern nulling, 13.57 to 13.60 scanning, 13.7 to 13.9 series feed, 13.47 to 13.48 simultaneous receive beams, 13.54 to 13.56 small arrays, 13.27 solid-state modules for, 13.53 to 13.54 solid-state transmitter for, 11.24 to 11.31 subarrays, 13.43 to 13.44, 13.49 to 13.50 surface waves and mutual coupling, 13.24 to 13.45 Taylor illumination, 13.29 thinned arrays, 13.23 to 13.24 3D search, 13.4 theory, 13.9 to 13.15 time-delay networks, 13.44 to 13.45 time-delay scanning, 13.7 tracking with, 7.46 Volume Search Radar (VSR), 13.62 to 13.63 wide bandwidth operation, 13.6 Phase shift in DSP, 25.22 to 25.25 Physical optics, 14.21 to 14.24 and ground echo, 16.9 to 16.10 reflector analysis, 12.31 to 12.33 Physical theory of diffraction, 14.25 to 14.26 Pilotage and CMR, 27.31 Pioneer Venus, 18.44 Planar array, 13.15 to 13.19 Planetary radars, 18.43 to 18.53 atmospheric sounding, 18.62 to 18.63 Cassini, 18.46 Clementine, 18.46 to 18.47 cloud profiling, 18.63 flight systems, 18.43, 18.56 to 18.58 ice exploration, 18.47 to 18.48 ionospheric sounding, 18.62 Magellan, 18.45 to 18.46, 18.48 to 18.52 polarization, 18.52 rainfall measurement, 18.62 scatterometers, 18.53 to 18.58 sounders, 18.59 to 18.63 table of, 18.44 Venera, 18.43 to 18.45 Plasma frequency, 20.2 Platform motion, in AMTI, 3.3 to 3.14 compensation abeam, 3.10 to 3.14 forward direction, 3.21 to 3.23 and scan compensation, 3.18 to 3.21 P(n,k) polyphase codes, 8.22 to 8.24 Point-clutter scatterers, 2.18 to 2.19 Polarimetric SAR, 17.22 Polarization and ground echo, 16.46 to 16.52
in ground penetrating radar, 21.10 to 21.11 in meteorological radar, 19.18 for planetary radar, 18.52 Polarization-twist reflector, 12.23 Polyphase codes, 8.19 to 8.24 Power-aperture product, 10.1 Power supply, for AESA, 5.10 Practical detectors, 7.4 to 7.11 Precipitation measurement, 19.26 to 19.28 Precision velocity update, 5.33 to 5.34 Probabilistic data association, 7.39 to 7.40 Probability of detection, in pulse doppler, 4.46 to 4.48 Probability of false alarm, in pulse doppler, 4.44 to 4.46 Propagation, anomalous, 26.6 to 26.13 Propagation factor, 26.1 Propagation, in free space, 26.13 to 26.15 Propagation loss, 4.40 Propagation modeling, 26.13 to 26.17 Propagation, standard, 26.4 to 26.6 Pseudo coherent radar, 6.20 Pulse chasing in bistatic radar, 23.28 to 23.29 Pulse compression block diagram, 8.1 to 8.2 comparison of various waveforms, 8.27 digital, 25.19 and ECCM, 24.34 to 24.35 examples of, 8.30 to 8.36 factors affecting choice of, 8.26 to 8.27
I_12
Pulse compression (cont.) implementation of, 8.28 to 8.30 linear FM, 8.3 to 8.11 in meteorological radar, 19.23 to 19.24 and MTI, 2.75 to 2.78 nonlinear FM, 8.12 to 8.16 phase coded, 8.16 to 8.24 radar, 1.5 range sidelobes, 6.29 SAW devices for, 8.10 to 8.11 signal analysis definitions, 8.36 to 8.37 stretch, 8.31 to 8.36 time-frequency coded, 8.25 to 8.26 waveforms, 8.2 to 8.26 Pulse doppler antenna, 4.12 to 4.13 applications, 4.2 to 4.3 basic configuration, 4.10 to 4.14 block diagram, 4.11 clutter, 4.14 to 4.24 clutter-limited detection, 4.48 doppler ambiguity resolution, 4.33 to 4.34 dynamic range, 4.24 to 4.27 high-PRF ranging, 4.34 to 4.35 losses in, 4.39 nomenclature, 4.1 to 4.2 probability of detection, 4.46 to 4.48 probability of false alarm, 4.44 to 4.46 range ambiguity resolution, 4.31 to 4.33 range performance, 4.39 to 4.48 search mode, 4.36 to 4.38 spectrum, 4.4 to 4.6 stability requirements, 4.27 to 4.31 timeline definitions, 4.9 to 4.10 track mode, 4.38 to 4.39 Pulse-pair algorithm for meteorological radar, 19.21 Pulse repetition frequency and ambiguities in pulse doppler, 4.6 to 4.10 and doppler, 4.2 to 4.4 for SAR, 17.13 to 17.15 Pyramidal absorber, 14.37 to 14.38
Q Quadraphase codes, 8.24 Quantization noise, affect on MTI, 2.73 to 2.74
R Racons, and CMR, 22.26 to 22.27 Radar applications of, 1.20 to 1.22 bandwidth in, 1.8 to 1.9 basic parts of, 1.2 beacons, in CMR, 22.25 blinking for ECCM, 24.37 block diagram, 1.3 in brief, 1.1 conceptual system design, 1.22 to 1.23 cross section of aircraft, 14.13 to 14.14 approximate methods, 14.19 to 14.27 approximations for simple scatterers, 14.10
basic echo mechanisms, 14.2 to 14.4 of birds, 14.11 bistatic, 23.19 to 23.21 of bodies of revolution, 14.39 to 14.40 characteristics, 14.5 to 14.16 of complex objects, 14.11 to 14.16 of a corner reflector, 14.9 to 14.11 definition of, 14.4 to 14.5 exact methods, 14.16 to 14.19 at HF, 20.26 to 20.29 general, for various target types, 14.16 of insects, 14.11 to 14.12 of a man, 14.11 to 14.12 measurement ranges, 14.30 to 14.35 measurement techniques, 14.27 to 14.35 of a metal plate, 14.8 to 14.9 of an ogive, 14.7 to 14.8 prediction techniques, 14.16 to 14.27 of ships, 14.13 to 14.15 of a short wire dipole, 14.7 of a sphere, 14.5 to 14.6 of string, 14.6, 14.7, 14.29 and surface traveling waves, 14.7 of target support, 14.29 to 14.30 doppler shift in, 1.10 echo suppression, 14.36 to 14.43 in A-12, 14.40 in B-2, 14.42 in F-117, 14.40 to 14.42 in SR-71, 14.39 to 14.41 in X-45C, 14.42 to 14.43 by absorbers, 14.36 to 14.38
I_13
by shaping, 14.36, 14.38 to 14.39 in ships, 14.42 to 14.43 equation, 1.10 to 1.13 bistatic, 23.4 to 23.6 and chaff, 24.55 to 24.56 in conceptual design, 1.23 ground penetrating radar, 21.8 to 21.9 HF over-the-horizon, 20.5 to 20.7 and jamming, 24.55 for meteorological targets, 19.3 to 19.6 surveillance, 3.1 frequency bands, 1.13 to 1.14 hole, in propagation, 26.9 information from, 1.7 to 1.10 letter-band nomenclature, 1.13 to 1.14 multifunction, for fighter aircraft, 5.1 to 5.10 networked, 7.46 to 7.49 nomenclature, 1.18 to 1.19 oceanography at HF, 20.30 to 20.38 past advances in, 1.19 to 1.20 reflectivity, 19.3 reflectivity factor, Z, 19.4 scheduling and control, 7.46 types of, 1.5 to 1.7 warning receiver (RWR), 24.4 to 24.5 work station, 24.55 to 24.56 RADARS AT, 18.9 to 18.10 Radial velocity, 1.7 Radiating elements, 13.5 to 13.6 Radomes, 12.39 to 12.41 Radome loss, 4.40 Rain, attenuation by, 19.8 to 19.11 Rain, detection of, 19.3 to 19.6 RAMP air traffic control radar, 11.33 to 11.34 Range, as used in radar, 1.2, 1.7 Range ambiguities, in meteorological radar, 19.12 to 19.13 ambiguity resolution in pulse doppler, 4.31 to 4.33 and doppler, in MFAR, 5.7 to 5.8 error, in tracking radar, 9.43 to 9.44 filter map in sidelobe blanking, 24.13 to 24.14 -gate pull-off, 24.6, 24.44 -gate straddle loss, 4.40 to 4.43 -gated high PRF (RGHPRF), 5.20 to 5.22 gates, 4.2 gating in pulse doppler, 4.9 glint, 9.35 to 9.36, 9.47 noise, 9.35 to 9.36 sidelobes, 6.29 tracking, 9.21 to 9.24 Rank detector, 7.17 Rapid Doppler on Wheels (Rapid-DOW) 19.36 to 19.37 Ratio detector, 7.13 to 7.14 Rayleigh region, 14.5, 19.3 to 19.4 Rayleigh scattering, 14.19 to 14.20 Ray tracing, 20.20 to 20.21 Receiver, 1.3 analog-to-digital converter, 6.35 to 6.40 bandwidth, 6.9 channel matching, 6.29 COHO, 6.20 configuration of, 6.1 to 6.4 digital, 6.40 to 6.46 diplex operation, 6.46 to 6.47 dynamic range, 6.4 to 6.8
effect on radiated signal, 6.11 exciter, 6.47 filtering, 6.24 to 6.29 front end, 6.10 to 6.14 gain control of, 6.22 to 6.24 instability, 6.20 to 6.21 I/Q channels, 6.31 to 6.35 limiter, 6.29 to 6.31 local oscillator, 6.14 to 6.22 multi-channel, 6.45 to 6.46 noise, 6.4 to 6.5 and tracking accuracy, 9.42 spurious response, 6.11 to 6.12 STALO, 6.14 to 6.20 upconversion, 6.47 to 6.50 waveform generation, 6.47 to 6.50 Receiver-related ECCM, 24.32 to 24.33 Reentrant structures and cross section, 14.3 Reflectivity, 19.3 Reflectivity factor, Z, 19.4 Reflector antenna analysis, 12.31 to 12.35 applications of, 12.1 to 12.2 architecture, 12.16 to 12.25 array feeds for, 12.28 to 12.30 basic principles of, 12.3 to 12.15 environmental factors, 12.39 feed blockage, 12.6 to 12.8
I_14
Reflector antenna (cont.) feed displacement, 12.14 feeds for, 12.25 to 12.30 gain optimization, 12.8 to 12.10 mechanical design, 12.35 to 12.41 radomes for, 12.39 to 12.41 role in radar, 12.1 spillover loss, 12.6 strut blockage, 12.14 to 12.15 surface ace of, 12.10 to 12.14 surface roughness loss, 12.12 to 12.14 types of, 12.2 Refraction, 14.20, 26.3 to 26.4 Refractivity, 26.3 to 26.4 Refractivity measurements, 19.32 to 19.33 Region of uncertainty (ROU) in target tracking, 7.47 to 7.48 Remote sensing of the environment, 1.21 Remote sensing, with SBR, 18.11 Repeater jammer, 24.6 Resolution, in GPR, 21.11 to 21.13 Resonance region, 14.5 RF receive loss, 4.40 RF transmit loss, 4.40 RGHPRF (Range Gated High PRF) algorithm, 5.22 Ricker wavelet, 21.11, 21.21 RIS AT SAR, 18.14 River radar, 22.9 ROTHR, 20.3
S S-193 altimeter, 18.33 S band, 1.16 Salisbury screen, 14.36 Sampled signal spectrum, 25.3 to 25.5 Sampling period in phased arrays, 24.45 Sampling receiver, 21.23 SAR-Lupe radar, 18.13 to 18.14 SARTs (Search and Rescue Transponders), 22.27 SAW delay line for pulse compression, 8.10 to 8.11 Scan compensation, and platform motion, 3.18 to 3.21 Scan SAR, 18.12 to 18.13, 18.24 Scatterer, 14.4 Scatterometers, 16.19 to 16.24, 16.26 to 16.28 space based, 18.53 to 18.58 table of, 18.56 wind measurement, 18.54 to 18.55 Sea clutter Bragg scatter, 15.28 to 15.32, 15.38 breaking waves, 15.6 to 15.7 composite-surf ace model, 15.30 to 15.32 contaminants, effect of, 15.26 to 15.27 and ducting, 15.24 to 15.25 empirical behavior of, 15.7 to 15.27 as a global boundary-value problem, 15.27 to 15.32 at HF, 15.19, 20.30 to 20.33 at high grazing angles, 15.16 at low grazing angles, 15.16 to 15.18 at millimeter waves, 15.20 numerical methods for, 15.36 rain, effect of, 15.23 to 15.24 sea spikes, 15.2, 15.16 to 15.17, 15.35 shadowing, effect of, 15.25 sigma zero definition, 15.7
spectrum, 15.20 to 15.23 statistics, 15.8 to 15.9 surface currents, effect of, 15.25 to 15.26 surface features, 15.33 to 15.34 theories of, 15.27 to 15.37 wind speed and direction, 15.12 to 15.16 Sea descriptors, general, 15.5 to 15.6 Sea echo. See sea clutter Sea ice, 16.44 to 16.46, 16.48, 22.14 Sea spikes, 15.2, 15.16 to 15.17, 15.35 Sea state, 15.6, 22.14 Sea surface, 15.3 Sea surface search, 5.30 to 5.31 Seawinds scatterometer, 18.58 Sensitivity time control (STC), 2.96 to 2.98, 6.22 to 6.24, 19.6 in CMR, 22.5, 22.13 and cosecant-squared antenna, 2.98 in pulse doppler, 4.22 Sensitivity velocity control (SVC), 2.87 to 2.91, 2.99 to 2.100 Sensor integration, other than radar, 7.49 to 7.54 Senrad broadband radar, 24.31 Sequential lobing, 9.16 to 9.17 Servosystems, for tracking radar, 9.17 to 9.19 Shaped pulses for transmitter, 10.19 to 10.20 Shaped reflector antennas, 12.19 to 12.20
I_15
Shaping, for radar cross-section reduction, 14.38 to 14.39 Ship, radar cross section, 14.13 to 14.15 Ships, low cross section, 14.42 to 14.43 Sidelooking airborne radar (SLAR), 1.6 17.3 Sidelobe blanking (SLB), 24.11 to 24.14 Sidelobe canceler, 24.14 to 24.20 Sigma zero (for clutter echo), 15.7, 16.1 to 16.3 Signal-to-clutter ratio improvement, 2.21 to 2.22 Signal-to-noise ratio, 1.9 in SAR, 17.16 to 17.17 Signal processing, and ECCM, 24.33 to 24.36 Signal processing, for meteorological radar, 19.19 to 19.25 Signal processor, 1.3 Signal sampling, 25.15 to 25.16 Silicon bipolar junction transistor, 11.10 to 11.11 Silicon LDMOS FET, 11.11 to 11.12 Silicon transistor capabilities, 11.13 Simultaneous lobing, 9.3 SIR-C, 16.46 SIR (spaceborne) SARs, 18.8 Skin depth, 21.8 Skip zone, 20.3 Sky wave OTH radar, 20.8 to 20.13 Slip-SAR, 18.14 Slow-wave tubes, 10.3 Sniff (or passive listening), 5.34 Snow, echo from, 16.42 to 16.44 Software structure, in MFAR, 5.6 to 5.7 Soil, dielectric properties of, 21.19 Soil moisture, effect on radar echo, 16.38, 16.40 to 16.41 Solar calibration of radar, 19.19 SOLAS (Safety of Life at Sea), 22.8 Solid-state advantages of, 11.1 to 11.5 amplifier, 10.4, 10.26 to 10.28 amplitude and phase sensitivities, 11.22 to 11.23 AN/SPS-40 transmitter, 11.32 to 11.33 class of (amplifier) operation, 11.18 to 11.20 devices, 11.5 to 11.17 examples of, 11.31 to 11.34 MMIC, 11.24 to 11.29 modulator, 11.24 to 11.25 modules, 13.53 to 13.54 Pave Paws radar, 11.31 to 11.32 performance capability, 11.2 phased array transmitter, 11.24 to 11.31 power combining, 11.20 to 11.22 power limitations, 11.8 to 11.10 RAMP radar, 11.33 to 11.34 spectral emissions, 11.23 transmit/receive modules, 11.29 to 11.31 Sounders, 18.59 to 18.63 Space-based radars (SBR) altimeters, 18.29 to 18.43 block diagram, 18.40 CryoSat, 18.42 to 18.43 flight systems, 18.33 to 18.37 Geosat, 18.41 to 18.42 orbit considerations, 18.37 to 18.38 overview, 18.30 to 18.31 precision, 18.31 theoretical foundations, 18.38 to 18.41 hardware, 18.4 to 18.5 meteorological, 19.38 to 19.39 planetary. See planetary radars
synthetic aperture radars (SAR), 18.5 to 18.29 ambiguities, 18.17 to 18.18 ambiguity limits, 18.22 to 18.24 antennas, 18.19 applications, 18.29 data products, 18.21 to 18.22 data rate, 18.20 design issues, 18.16 to 18.24 interferometry, 18.24 to 18.27 Kosmos, 18.8 list of, 18.6 to 18.7 multiple channels, 18.24 to 18.29 nadir, return from, 18.18 orbit characteristics, 18.2 to 18.4 polarimetry, 18.27 to 18.29 PRF constraints, 18.16 to 18.17 processing, 18.20 to 18.21 Quill (first space-based SAR), 18.6 ScanSAR, 18.12 to 18.13, 18.24 Seasat, 18.7 to 18.8 Shuttle Imaging Radar (SIR), 18.8 spotSAR 18.23 strip map, 18.23 transmitters, 18.19
I_16
Space-time adaptive processing (STAP), 3.23 to 3.31, 3.33, 5.2 to 5.3, 5.17, 24.21 to 24.22 in HF OTH radar, 20.53, 24.52 Spark-gap transmitter, 10.2 SPASUR, 23.2, 23.9, 23.11 to 23.13 Speckle, 16.55 Spectral characteristics of clutter, 2.11 to 2.16 Spectral noise in doppler radars, 10.20 to 10.21 Spectrometers, 16.20, 16.26 to 16.28 Spectrum, of pulse doppler radar, 4.4 to 4.6 Specular point, 14.20 to 14.21 Specular scatterers, 14.3 Sphere, radar cross section of, 14.5 to 14.6 Spherical reflector antenna, 12.24 to 12.25 Spotlight SAR, 17.4 to 17.5 SpotSAR, 18.12, 18.23 Spread-F region, 20.19 Spurious output, in transmitters, 10.19 Spurious response of mixers, 6.11 to 6.13 SR-71 low cross section aircraft, 14.39 to 14.41 Stability requirements in pulse doppler, 4.27 to 4.31 Stagger PRF design for MTI, 2.39 to 2.46 STALO, 6.3, 6.14 to 6.20 Standard atmosphere, 26.3 Stand-off jamming (SOJ), 24.43 to 24.44 Station keeping, airborne, 5.27 Stealth, 14.2, 14.36, 24.38 Stratiform rain, 19.26 Stretch pulse compression, 6.10, 6.22, 8.31 to 8.36 in SBR altimeter, 18.40 to 18.41 String, radar cross section of, 14.6 to 14.7 Strip map, 18.23 Stripmap SAR (or “strip” SAR), 17.3 to 17.4 Subarray adaptivity to ECM, 24.25 to 24.27 Subarrays, 13.43 to 13.44, 13.49 to 13.50 Subclutter visibility, in MTI, 2.22 Subrefraction, 26.6 Sudden ionospheric disturbance, 20.18 Sunspot number, 20.17 Superclutter visibility, 2.84 Superheterodyne, 6.1 Superrefraction, 26.7 Superresolution, 24.30 to 24.31 Surface discontinuities, and radar cross section, 14.3 Surface ducts, 26.10 to 26.11 Surface traveling-wave echoes, 14.36, 14.38 Surface ace-wave absorbers, 14.38 Surface winds, and HF radar, 20.37 to 20.38 Surveillance radar, 1.5 Surveillance radar equation, 1.12 Synthesizer, digital, 25.20 to 25.22 Synthetic aperture radar (SAR) autofocus, 17.15 basic principle of 17.1 burst mode, 18.23 to 18.24 clutterlock, 17.15 comparison with optical imaging, 17.18 to 17.21 comparison with real-aperture radar, 17.9 to 17.10 crossrange resolution, 17.7 to 17.8 design issues for SBR, 18.16 to 18.24 doppler beam sharpening, 5.34 to 5.36, 5.37, 17.2, 17.3 early history of, 17.2 and ECCM, 24.48 to 24.51 fast-time processing, 17.6 focused, 17.3 to 17.5 foliage penetration, 17.33 to 17.34
and ground penetrating radar, 21.4, 21.13 height measurement with, 17.27 to 17.23 image quality, 17.16 to 17.21 interferometric (InSAR), 17.5, 17.23 to 17.24, 17.30 to 17.33 inverse (ISAR), 5.23 to 5.24, 5.31 to 5.33, 9.37, 17.5, 24.51 to 24.52 Joint STARS, 17.23 to 17.24 key aspects of, 17.10 to 17.15 key equations, 17.21 to 17.22 motion compensation in, 17.12 moving targets in, 17.23 to 17.27 multiplicative noise ratio, 17.17 to 17.18 point-spread function, 17.16 polarimetric, 17.22 pulse repetition frequency requirements for, 17.13 to 17.15 range migration, 17.15 range resolution, 17.6 to 17.7 range and velocity contours, 17.10 to 17.12
I_17
resolution, 17.5 to 17.10 resolution (crossrange) examples, 17.5 to 17.6 shadows in, 17.28 signal-to-noise ratio, 17.16 to 17.17 slow-time processing, 17.6 for space applications, 18.5 to 18.29 specific aspects of, 17.22 to 17.34 spotlight, 17.4 to 17.5 squinted stripmap, 17.4 stereo, 17.29 to 17.30 stripmap, 17.3 to 17.4, 17.14 to 17.15 types of, 17.2 to 17.6 vibrating targets in, 17.25 to 17.27 unfocused, 17.3 Washington monument image, 17.18 to 17.21 System instabilities and MTI, 2.65 to 2.73 System noise, 6.5
T TACCAR, 3.4 to 3.9, 3.33 Target acquisition, in tracking radar, 9.20 to 9.21 Target caused errors in tracking, 9.26 to 9.37 Target cross section. See radar cross section Target noise, in tracking radar, 9.26 to 9.37 Target recognition, 1.7 cooperative, 5.22 to 5.23 noncooperative 5.22 to 5.24 Target resolution, in automatic detection, 7.19 to 7.20 Taylor weighting or illumination, 8.7 to 8.9, 13.29 TecSAR, 18.12 TEM horn, 21.27 to 21.30 Terminal Doppler Weather Radar (TDWR), 19.1, 19.30 to 19.31 MTI filter design for, 2.47 to 2.50 Terrain avoidance, 5.28 to 5.29 Terrain-bounce jamming, 24.43 Terrain database and radar, 5.30 Terrain following, 5.28 to 5.29 Terrain height estimation, 5.29 to 5.30 Terrain scattered interference, 24.43 TerraS AR-X, 18.12 Test ranges, indoor, 14.32 to 14.35 Test ranges, outdoor, 14.30 to 14.32 THAAD radar, 13.68 Thunderstorm prediction, 19.32 Time-delay scanning, 13.7 Time-frequency coded waveforms, 8.25 to 8.26 Topex altimeter parameters, 18.35 Tornado detection, 19.28 to 19.29 Towed decoy, 24.8 T/R module, 10.28 Track association, 7.38 to 7.41 Track file, 7.23 to 7.25 Tracking, automatic, 7.22 to 7.46 Tracking radar, 1.6 acquisition with, 9.20 to 9.21 automatic gain control (AGC), 9.33 to 9.35 conical scan, 9.16 to 9.17 dual band, 9.24 to 9.25 and ECCM, 24.43 error reduction techniques, 9.46 to 9.47 errors in, 9.26 to 9.46 external causes of error, 9.37 to 9.42 glint in, 9.30 to 9.35, 9.47
limitations in performance, 9.44 to 9.45 monopulse, 9.3 to 9.16 two-channel, 9.14 to 9.15 multipath error reduction, 9.46 to 9.47 nth-time-around tracking, 9.24 on-axis tracking, 9.25 to 9.26 range tracking in, 9.21 to 9.24 sequential lobing, 9.16 to 9.17 servosystems for, 9.17 to 9.19 sources of error in, 9.26 updating tracks, 7.26 to 7.30 TRAKX, dual band monopulse radar, 9.24 Transmit/receive module characteristics, 11.29 to 11.31 Transmit signal digital processing, 25.20 to 25.22 Transmitter-related ECCM, 24.31 to 23.32 Transmitters, 1.2, 1.4 clustered-cavity klystrons, 10.12 to 10.13 constant efficiency amplifier, 10.21 to 10.22, 10.26 crossed-field amplifiers (CFA), 10.16 to 10.17 extended interaction klystron (EIK), 10.11 grid-controlled tubes, 10.21 to 10.23, 10.25 gyrotrons, 10.17 to 10.19, 10.26 for HF OTH radar, 20.23 to 20.26 linear-beam amplifiers, 10.4 to 10.13
I_18
Transmitters (cont.) klystrons, 10.5 to 10.8, 10.26 multiple-beam, 10.7 to 10.8 magnetrons, 10.14 to 10.16, 10.26 microwave power module (MPM), 10.13 modulators for, 10.23 to 10.24 MTBF of tubes, 10.6 to 10.7, 10.10, 10.15, 10.16 oscillator vs. amplifier, 10.4 role in radar, 10.1 to 10.2 solid-state, 10.26 to 10.28. See also solid-state spectrum control, 10.19 to 10.21 traveling wave tube, 10.3, 10.8 to 10.10, 10.26 Twystron, 10.11 types of, 10.2 to 10.4 variants of klystrons and TWTs, 10.11 to 10.13 which type to use, 10.25 to 10.28 Transponder, 24.6 Trapping, in ducting, 26.7 Tropical Rainfall Measurement Mission (TRMM) SBR, 18.62, 19.39 Troposphere, 26.2 effect on tracking accuracy, 9.41 to 9.42
U UHF, 1.15 Ultralow sidelobes, 24.37 Ultrawideband (UWB), 21.1 Updating tracks, 7.26 to 7.30
V Velocity ambiguities, in meteorological radar, 19.12 to 19.13 Velocity-Azimuth-Display (VAD), 19.31 to 19.32 Velocity estimation, 19.22 Velocity of propagation, in GPR, 21.11 Velocity search, in pulse doppler, 4.36 Venera, 18.43 to 18.45 Vessel tracking service (VTS) radars, 22.1 Vessel tracking services, 22.29 to 22.31 VHF, 1.15 Vibrating targets, in SAR, 17.25 to 17.27 Volume Search Radar (VSR), 13.62 to 13.63
W Wake detection, 5.31 Warloc millimeter-weave radar, 10.18 Washington Monument SAR image, 17.18 to 17.21 Water vapor, attenuation in, 19.7 Water vapor measurement with radar, 19.32 to 19.33 Wave spectrum, of the ocean, 15.3 to 15.5 Waveform upconversion, 6.50 Waveguide models, for propagation, 26.15 to 26.26 Weather avoidance, with fighter radar, 5.24 Weather radar. See meteorological radar Wedgetail AEW radar, 3.3 Wide bandgap semiconductors, 11.15 to 11.17 Wind measurement, 19.31 to 19.32 Wind profiler, 19.39 to 19.40 WSR-88D (Nexrad), 19.1, 19.16 to 19.17
X X-45C low cross section unmanned combat aircraft, 14.42 to 14.43 X band, 1.17 X-Band Radar (XBR), 13.68 to 13.69
Z Z (radar reflectivity factor), 19.4 Ze (effective reflectivity factor), 19.6
