Radar Handbook

RADAR

HANDBOOK

Editor in Chief MERRILL I. SKOLNIK

Second Edition

Boston, Massachusetts Burr Ridge, Illinois Dubuque, Iowa Madison, Wisconsin New York, New York San Francisco, California St. Louis, Missouri

Library of Congress Cataloging-in-Publication Data Radar handbook / editor in chief, Merrill I. Skolnik. — 2nd ed. p. cm. Includes index. ISBN 0-07-057913-X 1. Radar—Handbooks, manuals, etc. I. Skolnik, Merrill I. (Merrill Ivan), date. TK6575.R262 1990 621.3848—dc20 89-35217

McGraw-Hill A Division of The McGraw-Hill Companies

Copyright © 1990 by McGraw-Hill, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States 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 data base or retrieval system, without the prior written permission of the publisher. Chapters 8, 13, and 24 were prepared by the contributors as part of their employment by the United States government and are not subject to copyright. 12 1314 15 16 17 18 19 BKM BKM

098765432

ISBN O - O T - Q S V T I B - X The editors for this book were Daniel A. Gonneau and Beatrice E. Eckes, the designer was Naomi Auerbach, and the production supervisor was Dianne Walber. It was set in Times Roman by the McGraw-Hill Publishing Company Professional & Reference Division composition unit.

Information contained in this work has been obtained by McGraw-Hill, Inc., from sources believed to be reliable. However, neither McGraw-Hill nor its authors guarantees the accuracy or completeness of any information published herein and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought.

CONTRIBUTORS

Lament V. Blake, Electronics Consultant (CHAPTER 2) Michael T. Borkowski, Raytheon Company (CHAPTER 5) Leopold J. Cantafio, Space and Technology Group TRW (CHAPTER 22) Theodore C. Cheston, Naval Research Laboratory (CHAPTER 7) L. J. Cutrona, Sarcutron, Inc. (CHAPTER 21) Daniel Davis, Electronic Systems Group, Westinghouse Electric Corporation (CHAPTER 6) Gary E. Evans, Electronic Systems Group, Westinghouse Electric Corporation (CHAPTER 6) A. Farina, Radar Department, Selenia S.p.A., Italy (CHAPTER 9) Edward C. Farnett, RCA Electronics Systems Department, GE Aerospace (CHAPTER 10) Joe Frank, Technology Service Corporation (CHAPTER 7) V. Gregers-Hansen, Equipment Division, Raytheon Company (CHAPTER 15) J. M. Headrick, Naval Research Laboratory (CHAPTER 24) Dean D. Howard, Locus, Inc., a subsidiary of Kaman Corp. (CHAPTER 18) Alex Ivanov, Missile Systems Division, Raytheon Company (CHAPTER 19) Eugene F. Knott, The Boeing Company (CHAPTER 11) William H. Long, Westinghouse Electric Corporation (CHAPTER 17) David H. Mooney, Westinghouse Electric Corporation (CHAPTER 17) Richard K. Moore, The University of Kansas (CHAPTER 12) David J. Murrow, General Electric Company (CHAPTER 20) William K. Saunders, formerly of Harry Diamond Laboratories (CHAPTER 14) Helmut E. Schrank, Electronics Systems Group, Westinghouse Electric Corporation (CHAPTER 6) Robert J. Serafin, National Center for Atmospheric Research (CHAPTER 23) William W. Shrader, Equipment Division, Raytheon Company (CHAPTER 15) William A. Skillman, Westinghouse Electric Corporation (CHAPTER 17) Merrill I. Skolnik, Naval Research Laboratory (CHAPTER 1) Fred M. Staudaher, Naval Research Laboratory (CHAPTER 16) George H. Stevens, RCA Electronics Systems Department, GE Aerospace (CHAPTER 10) John W. Taylor, Jr., Westinghouse Electric Corporation (CHAPTER 3) G. V. Trunk, Naval Research Laboratory (CHAPTER 8) T. A. Weil, Equipment Division, Raytheon Company (CHAPTER 4) Lewis B. Wetzel, Naval Research Laboratory (CHAPTER 13) Nicholas J. Willis, Technology Service Corporation (CHAPTER 25)

PREFACE

This edition has been thoroughly revised to reflect the advances made in radar over the past two decades. There are many new topics not found in the original, and over half of the 25 chapters were written by authors who did not participate in the first edition. The continued growth in radar capability and applications is reflected in much of the new material included in this second edition. The following are some of the many new radar advances that have occurred since the original edition (listed in no particular order): • The use of digital techniques that allow sophisticated signal processing in MTI and pulse doppler radars, as well as digital data processing to perform automatic detection and tracking. • The use of the doppler filter bank and the clutter map in MTI radar. • The reduced dependency on operators for extracting information from a radar and the incorporation of CFAR in automatic detection and tracking systems. • The emergence of the analog SAW dispersive delay line as the preferred technique for wideband (high-resolution) pulse compression; the use of digital processing for the pulse compression filter when the bandwidth permits; and the introduction of Stretch pulse compression, which allows high resolution, over a limited range interval with considerably reduced processing bandwidth. • The increased use of 3D radar for military applications. • The introduction of the ultralow-sidelobe antenna for airborne pulse doppler radar and, later, for ECCM. • The replacement of the parabolic reflector antenna with the planaraperture array antenna for 3D radar, ultralow-sidelobe antennas, and airborne radar. • The high-power solid-state transmitter that consists of many transistor modules distributed on the rows of a 3D radar (such as the AN/TPS-59), or employed at the elements of a phased array (as in PAVE PAWS), or configured as a transmitter for a conventional radar (as in the AN/SPS40 or the Canadian ATC radar known as RAMP). • The serial production of phased arrays for the Patriot, Aegis, PAVE PAWS, and Bl-B radar systems.

• The interest in the radar cross section of targets brought about by the attempts to reduce the cross section of military vehicles; and advances in computer methods for predicting the cross section of complex targets. • The increased capability of military airborne radar (airborne intercept, AW ACS, and AEW) due to advances in components and technology that permitted the application of AMTI and pulse doppler to the detection of aircraft in the midst of large clutter. • The use of radar in space for rendezvous and landing, remote sensing of the earth's environment, planetary exploration, and the detection of targets on the oceans of the world. • The use of semiactive radar for the guidance of military missile systems. • The extraction of the doppler frequency shift in meteorological radars that permits the recognition of hazardous weather phenomena not possible with previous weather radars. • The use of radar operating in the HF portion of the spectrum for longrange over-the-horizon detection of aircraft, ships, and missiles, as well as to provide the direction of the surface winds and the sea state over wide areas of the ocean. • The development of electronic counter-countermeasures (ECCM) in military radars to thwart attempts to negate radar capability by hostile electronic radiations. • The increased range resolution and doppler resolution in synthetic aperture radars (SAR) for the imaging of a scene, the use of inverse SAR (ISAR) for the imaging of targets, and the replacement of optical processing with digital processing for SAR imaging. • The adaptive antenna for application in sidelobe cancelers (as an ECCM) and AMTI radar. • The use of computers to reliably and quickly predict the capability and coverage of radar systems in the real environment. The purpose of the above listing is to indicate that radar is dynamic. Not all the new advances made since the first edition of this handbook are listed, nor does the list include all the new material discussed in this edition. There continue to be significant advances in the application of new technology and in the appearance of new applications. Radar grows and is viable since it satisfies important societal, economic, and military needs. It has no serious competitor for most of its many applications. The size of this edition of the handbook is smaller than the original edition. This is more an indication of the problems involved in technical book publishing rather than problems with the health of radar or the

availability of material to include. It was not an easy task to constrain the chapter authors to a limited page budget, and I am appreciative of their efforts to keep the size of their chapters within the allocated number of pages. It would have been easy to double the size of this edition even without increasing the number of chapters. The limitation on size was one of the reasons a number of chapters found in the first edition do not appear here. Some of the omitted chapters were concerned with subjects for which there is not as much interest as there had been or whose technology has not advanced as much as other areas of radar. It is with some regret that 16 of the chapters in the original could not be included in this second edition. As in the first edition, no attempt was made to utilize a standard notation throughout the book. Each particular subspecialty of radar seems to have developed its own nomenclature, and it is not appropriate in a book such as this to force authors to use notation that is foreign to their field even though it might be commonplace in some other aspect of radar. Each chapter author was instructed to assume that the average reader has a general knowledge of radar but is not necessarily an expert in the particular subject covered by the chapter. After a general introduction to radar in Chap. 1, there is a review of the methodology for predicting the range of a radar that has evolved over the years. This is followed by several chapters on the major subsystems of a radar: the receiver, transmitter, solid-state transmitters, reflector antennas, phased array antennas, data processing, ECCM, and pulse compression. Next are discussions of the target cross section and the nature of the radar echoes from the ground and the sea. The various types of radar systems are then discussed: CW and FM-CW, MTI, AMTI, pulse doppler, tracking, missile guidance, height finding and 3D, and synthetic aperture radar. This is followed by three specialized examples of radar that have their own unique character: radar in space, meteorological (weather) radar, and HE over-the horizon radar. The book closes with a treatment of the bistatic radar, which was the first type of radar explored during the onset of radar development in the 1930s. I would hope that readers who refer in their own writings to material from this book do so by chapter author and title and not by citing just the "Radar Handbook." This will give proper credit to the individual authors who created the work. It is with much pleasure that I acknowledge the contributions of the individual chapter authors. I enjoyed working with these talented radar engineers and having the opportunity to learn so much from my association with them. A handbook such as this exists only because of the dedicated efforts of the many experts who took the time and energy to

prepare the individual chapters. I appreciate their hard work in committing to writing their knowledge and experience, and I am grateful that they have shared this with us. Merrill Skolnik

ABOUT THE EDITOR IN CHIEF Merrill I. Skolnik, known worldwide for his leadership in radar research and development, has been affiliated with the Johns Hopkins Radiation Laboratory, Sylvania, MIT Lincoln Laboratory, the Research Division of Electronic Communications Inc., the Institute for Defense Analyses, and the U.S. Naval Research Laboratory. He received his doctorate in electrical engineering from Johns Hopkins University, where he also earned B.E. and M.S.E. degrees. He is the author of the leading college textbook on radar, Introduction to Radar Systems (McGraw-Hill), now in its second edition, and the editor of Radar Applications. He is a member of the National Academy of Engineering, a Fellow of the IEEE, and has served as editor of the Proceedings of the IEEE.

Contents

Contributors .....................................................................

xx

Preface ............................................................................

xxi

1. An Introduction to Radar ........................................

1.1

1.1 1.2

1.3

1.4

Description of Radar ...............................................

1.1

Radar Block Diagram .........................................

1.2

Radar Equation .......................................................

1.6

Tracking ............................................................

1.8

Volume Search ..................................................

1.8

Jamming ............................................................

1.9

Clutter ...............................................................

1.10

Information Available from the Radar Echo ............

1.10

Range ...............................................................

1.11

Radial Velocity ...................................................

1.11

Angular Direction ...............................................

1.12

Size ...................................................................

1.12

Shape ................................................................

1.12

Other Target Measurements ..............................

1.13

Radar Frequencies .................................................

1.13

HF (3 to 30 MHz) ...............................................

1.15

VHF (30 to 300 MHz) .........................................

1.15

UHF (300 to 1000 MHz) .....................................

1.16

L Band (1.0 to 2.0 GHz) .....................................

1.16

S Band (2.0 to 4.0 GHz) .....................................

1.16

This page has been reformatted by Knovel to provide easier navigation.

v

vi

Contents C Band (4.0 to 8.0 GHz) ....................................

1.17

X Band (8.0 to 12.5 GHz) ...................................

1.17

Ku, K, and Ka Bands (12.5 to 40.0 GHz) .............

1.17

Millimeter Wavelengths (above 40 GHz) ............

1.17

Laser Frequencies .............................................

1.18

Radar Nomenclature ..............................................

1.18

2. Prediction of Radar Range .....................................

2.1

1.5

2.1

2.2

2.3

Introduction .............................................................

2.1

Definitions .........................................................

2.1

Conventions ......................................................

2.2

Range Prediction Philosophy .............................

2.2

Historical Notes .................................................

2.3

Range Equations ....................................................

2.4

Radar Transmission Equation ............................

2.4

Maximum-Range Equation .................................

2.5

Pulse Radar Equation ........................................

2.6

Detectability Factor ............................................

2.6

Probabilistic Notation .........................................

2.8

Automatic Detection ...........................................

2.8

Bistatic Radar Equation .....................................

2.9

Equations in Practical Units ...............................

2.9

Definition and Evaluation of Range Factors ...........

2.10

Transmitter Power and Pulse Length .................

2.10

Antenna Gain, Efficiency, and Loss Factor .........

2.11

Antenna Bandwidth ............................................

2.12

Target Cross Section .........................................

2.12

Wavelength (Frequency) ....................................

2.13

Bandwidth and Matching Factors .......................

2.14

This page has been reformatted by Knovel to provide easier navigation.

Contents 2.4

2.5

2.6

vii

Minimum Detectable Signal-to-Noise Ratio ............

2.16

Integration of Signals .........................................

2.17

Number of Pulses Integrated .............................

2.17

Evaluation of Probabilities ..................................

2.18

Detector Laws ...................................................

2.23

Curves for Visual Detection ................................

2.24

Other Detection Methods ...................................

2.25

Predetection Integration .....................................

2.25

System Noise Temperature ....................................

2.26

Available Power, Gain, and Loss ........................

2.26

Noise Temperature ............................................

2.27

The Referral Concept ........................................

2.27

Antenna Noise Temperature ..............................

2.28

Transmission-Line Noise Temperature ...............

2.30

Receiver Noise Temperature .............................

2.31

Pattern Propagation Factor ....................................

2.31

General Discussion ............................................

2.32

Mathematical Definition ......................................

2.35

Pattern Factor ....................................................

2.35

Reflection Coefficient .........................................

2.36

Total Phase Difference ......................................

2.37

Reflection from a Rough Spherical Surface ........

2.38

Specular-Reflection Roughness Factor ..............

2.39

Spherical-Earth Reflection Geometry .................

2.41

Divergence Factor .............................................

2.42

Spherical-Earth Pattern Propagation Factor .......

2.42

The Intermediate Region ...................................

2.43

Elevation-Angle Interference-Region Calculation ......................................................

2.43

Refraction and Coverage Diagrams ...................

2.44

This page has been reformatted by Knovel to provide easier navigation.

viii

Contents 2.7

Loss Factors ...........................................................

2.46

Antenna Pattern Loss ........................................

2.46

Tropospheric-Absorption Loss ...........................

2.47

Lens-Effect Loss ................................................

2.52

Other Tropospheric Losses ................................

2.54

Procedure for Range-Dependent Losses ...........

2.54

Collapsing Loss .................................................

2.54

Signal-Processing Losses ..................................

2.55

Miscellaneous Losses ........................................

2.56

Jamming and Clutter ..............................................

2.56

Jamming ............................................................

2.56

Clutter ...............................................................

2.57

Targets in Clutter ...............................................

2.57

2.9

Cumulative Probability of Detection ........................

2.60

2.10

Accuracy of Radar Range Prediction .....................

2.60

2.11

A Systematic Procedure for Range Prediction .......

2.61

2.12

Computer Solution of the Range Equation .............

2.62

3. Receivers .................................................................

3.1

2.8

3.1

The Configuration of a Radar Receiver ..................

3.1

3.2

Noise and Dynamic-Range Considerations ............

3.3

Definitions .........................................................

3.4

Evaluation .........................................................

3.5

Bandwidth Considerations ......................................

3.5

Definition ...........................................................

3.5

Important Characteristics ...................................

3.5

Receiver Front End .................................................

3.7

Configuration .....................................................

3.7

Effect of Characteristics on Performance ...........

3.7

Spurious Distortion of Radiated Spectrum ..........

3.7

3.3

3.4

This page has been reformatted by Knovel to provide easier navigation.

Contents

3.5

3.6

3.7

3.8

3.9

3.10

ix

Spurious Responses of Mixers ...........................

3.8

Characteristics of Amplifiers and Mixers .............

3.11

Local Oscillators .....................................................

3.11

Functions of the Local Oscillator ........................

3.11

Stalo Instability ..................................................

3.12

Coho and Timing Instability ................................

3.16

Total Radar Instability ........................................

3.16

Gain-Controlled Amplifiers ......................................

3.17

Sensitivity Time Control (STC) ...........................

3.17

Clutter Map Automatic Gain Control ...................

3.18

Automatic Noise-Level Control ...........................

3.19

Filtering ...................................................................

3.19

Filtering of the Entire Radar System ...................

3.19

Definitions .........................................................

3.20

Approximations to Matched Filters .....................

3.21

Filtering Problems Associated with Mixer Spurious Responses .......................................

3.22

Logarithmic Devices ...............................................

3.25

Characteristics ...................................................

3.25

Analog Logarithmic Devices ...............................

3.27

Digital Logarithm ................................................

3.28

Digital Log Power Combiner ..............................

3.29

IF Limiters ...............................................................

3.30

Applications .......................................................

3.30

Characteristics ...................................................

3.30

Phase Detectors and Synchronous Detectors ........

3.32

Definitions and Characteristics ...........................

3.32

Applications .......................................................

3.33

Examples of Phase Detectors ............................

3.36

Analog-to-Digital Phase Detector .......................

3.37

This page has been reformatted by Knovel to provide easier navigation.

x

Contents Digital Phase Detector .......................................

3.38

Analog-to-Digital Converter ....................................

3.38

Applications .......................................................

3.38

Formats .............................................................

3.39

Synchronization .................................................

3.39

Performance Characteristics ..............................

3.40

Multiplexing .......................................................

3.41

I/Q Distortion Effects and Compensation Methods ..................................................................

3.41

Gain or Phase Unbalance ..................................

3.41

Time Delay and Pulse Shape Unbalance ...........

3.43

Nonlinearity in I and Q Channels ........................

3.45

DC Offset ..........................................................

3.46

CFAR Detection Processes ....................................

3.46

Application .........................................................

3.46

Amplitude-Discrimination CFAR (CellAveraging CFAR) ............................................

3.47

Phase-Discrimination CFAR (CPACS) ...............

3.49

Effect on Range Resolution and Azimuth Accuracy .........................................................

3.50

Clutter Map CFAR .............................................

3.53

Diplex Operation .....................................................

3.54

Benefits .............................................................

3.54

Recommended Implementation ..........................

3.54

4. Transmitters ............................................................

4.1

3.11

3.12

3.13

3.14

4.1

Introduction .............................................................

4.1

The Transmitter as Part of a Pulsed Radar System ............................................................

4.1

Why So Much Power? .......................................

4.2

Why Pulsed? .....................................................

4.3

This page has been reformatted by Knovel to provide easier navigation.

Contents 4.2

4.3

4.4

4.5

4.6

4.7

4.8

xi

Magnetron Transmitters .........................................

4.5

Limitations .........................................................

4.5

Magnetron Features ..........................................

4.6

Common Problems ............................................

4.7

Amplifier Chain Transmitters ..................................

4.9

Oscillator versus Amplifier .................................

4.9

Amplifier Chains: Special Considerations ...........

4.10

RF Amplifier Tubes .................................................

4.12

Crossed-Field Amplifiers (CFAs) ........................

4.12

Klystrons ...........................................................

4.14

Traveling-Wave Tubes (TWTs) ..........................

4.15

RF Tube Selection .............................................

4.17

RF Tube Power Capabilities ..............................

4.21

Combining and Arraying .........................................

4.22

Hybrid Combining (or Magic T) ..........................

4.22

Phased Arrays ...................................................

4.23

Transmitter Stability Requirements ........................

4.25

Pulsed MTI Systems ..........................................

4.25

Pulse Compression Systems .............................

4.27

Stability Improvement by Feedback or Feedforward ....................................................

4.30

Transmitter Spectrum Control ................................

4.31

Reduction of Spurious Outputs ..........................

4.31

Reduction of Spectrum Amplitude Exceeding (sin x)/x ...........................................................

4.31

Improvement over (sin x)/x by Means of Shaped Pulses ................................................

4.31

Pulse Modulators ....................................................

4.32

Line-Type Modulators ........................................

4.33

Active-Switch Modulators ...................................

4.35

This page has been reformatted by Knovel to provide easier navigation.

xii

Contents Grid Pulsers ......................................................

4.39

High-Voltage Crowbars, Regulators, and Power Supplies .......................................................

4.39

Crowbars ...........................................................

4.40

Regulators .........................................................

4.41

High-Voltage Power Supplies .............................

4.41

5. Solid-State Transmitters .........................................

5.1

4.9

5.1

Introduction .............................................................

5.1

5.2

Solid-State Microwave Power Generation ..............

5.4

Microwave Bipolar Power Transistors ................

5.5

Microwave Field-Effect Transistors (FETs) .........

5.9

Millimeter-Wave Solid-State Power Sources ......

5.11

Solid-State Microwave Design ................................

5.12

High-Power Amplifier Design .............................

5.13

Phased Array Transceiver Module Design ..........

5.16

Microwave Monolithic Integrated Circuits ...........

5.16

Transceiver Module Performance Characteristics ................................................

5.18

Transmitter System Design ....................................

5.21

Performance Sensitivities ..................................

5.21

Power Combining ..............................................

5.23

Solid-State Transmitter Design Examples ..........

5.23

6. Reflector Antennas .................................................

6.1

5.3

5.4

6.1

Introduction .............................................................

6.1

Role of the Antenna ...........................................

6.1

Beam Scanning and Target Tracking .................

6.1

Height Finding ...................................................

6.2

Classification of Antennas ..................................

6.2

This page has been reformatted by Knovel to provide easier navigation.

Contents 6.2

xiii

Basic Principles and Parameters ............................

6.2

Reciprocity ........................................................

6.2

Gain, Directivity, and Effective Aperture .............

6.3

Radiation Patterns .............................................

6.5

Types of Antennas ..................................................

6.10

Paraboloidal Reflector Antennas ........................

6.12

Parabolic-Cylinder Antenna ...............................

6.15

Shaped Reflectors .............................................

6.17

Multiple Beams and Extended Feeds .................

6.19

Monopulse Feeds ..............................................

6.21

Multiple-Reflector Antennas ...............................

6.23

Special-Purpose Reflectors ................................

6.26

6.4

Feeds ......................................................................

6.26

6.5

Reflector Antenna Analysis ....................................

6.27

6.6

Shaped-Beam Antennas ........................................

6.30

Gain Estimation .................................................

6.31

Shaped-Beam Antenna Design ..........................

6.32

Antenna Size .....................................................

6.33

Accuracy ...........................................................

6.34

Design Considerations ...........................................

6.34

Feed Blockage ..................................................

6.34

Feed Spillover and Diffraction ............................

6.37

Surface Leakage ...............................................

6.40

6.8

Mechanical Considerations ....................................

6.40

6.9

Radomes ................................................................

6.44

Types of Radomes and General Considerations ................................................

6.44

Environmental Effects ........................................

6.45

Airborne and Missile Radomes ..........................

6.46

Ground and Shipboard Radomes .......................

6.47

6.3

6.7

This page has been reformatted by Knovel to provide easier navigation.

xiv

Contents Other Radome Effects .......................................

6.48

Antenna Testing .....................................................

6.52

Pattern Test Ranges ..........................................

6.52

Elevated Ranges ...............................................

6.53

Ground Ranges .................................................

6.55

Compact Ranges ...............................................

6.56

Near-Field Ranges .............................................

6.57

Miscellaneous Tests ..........................................

6.59

7. Phased Array Radar Antennas ..............................

7.1

6.10

7.1

Introduction .............................................................

7.1

Phased Array Radars ........................................

7.1

Scanning of Arrays ............................................

7.7

7.2

Array Theory ...........................................................

7.10

7.3

Planar Arrays and Beam Steering ..........................

7.17

Planar Arrays .....................................................

7.17

Element-Phasing Calculations ...........................

7.21

Aperture Matching and Mutual Coupling ................

7.22

Significance of Aperture Matching ......................

7.22

Effects of Mutual Coupling .................................

7.23

Element Pattern .................................................

7.25

Thinned Arrays ..................................................

7.26

Impedance Variation of Free Space ...................

7.27

Element Impedance ...........................................

7.27

Analytical Techniques ........................................

7.29

Nonisolating Feeds ............................................

7.30

Mutual Coupling and Surface Waves .................

7.31

Array Simulators ................................................

7.32

Compensation for Scanned Impedance Variation ..........................................................

7.35

7.4

This page has been reformatted by Knovel to provide easier navigation.

Contents

xv

Small Arrays ......................................................

7.35

Low-Sidelobe Phased Arrays .................................

7.37

Illumination Functions ........................................

7.37

Effect of Errors ..................................................

7.38

Random Errors ..................................................

7.39

Quantization Effects ...............................................

7.43

Phase Quantization ...........................................

7.43

Periodic Errors ...................................................

7.45

Bandwidth of Phased Arrays ..................................

7.49

Aperture Effects .................................................

7.49

Feed Effect ........................................................

7.51

Broad Instantaneous Bandwidth .........................

7.53

Time-Delay Networks ........................................

7.56

7.8

Feed Networks (Beamformers) ..............................

7.58

7.9

Phase Shifters ........................................................

7.63

Diode Phasers ...................................................

7.63

Ferrite Phasers ..................................................

7.64

7.10

Solid-State Modules ...............................................

7.67

7.11

Phased Array Systems ...........................................

7.69

8. Automatic Detection, Tracking, and Sensor Integration ...............................................................

8.1

7.5

7.6

7.7

8.1

Introduction .............................................................

8.1

8.2

Automatic Detection ...............................................

8.1

Optimal Detector ................................................

8.2

Practical Detectors ............................................

8.3

False-Alarm Control ...........................................

8.12

Target Resolution ..............................................

8.21

Detection Summary ...........................................

8.23

This page has been reformatted by Knovel to provide easier navigation.

xvi

Contents 8.3

Automatic Tracking .................................................

8.23

Track-While-Scan Systems ................................

8.24

Maximum-Likelihood Approaches ......................

8.38

Multisensor Integration ...........................................

8.40

Colocated Radar Integration ..............................

8.42

Multisite Radar Integration .................................

8.43

Unlike-Sensor Integration ..................................

8.44

9. Electronic Counter-Countermeasures ..................

9.1

8.4

9.1

Introduction .............................................................

9.1

9.2

Terminology ............................................................

9.2

9.3

Electronic Warfare Support Measures ....................

9.2

9.4

Electronic Countermeasures ..................................

9.4

9.5

Objectives and Taxonomy of ECCM Techniques .............................................................

9.7

Antenna-Related ECCM .........................................

9.7

Sidelobe-Blanking (SLB) System .......................

9.9

Sidelobe Canceler (SLC) System .......................

9.11

Adaptive Arrays .................................................

9.14

9.7

Transmitter-Related ECCM ....................................

9.16

9.8

Receiver-Related ECCM ........................................

9.18

9.9

Signal-Processing-Related ECCM .........................

9.19

9.10

Operational-Deployment Techniques .....................

9.21

9.11

Application of ECCM Techniques ...........................

9.22

Surveillance Radars ...........................................

9.23

Tracking Radars ................................................

9.25

ECCM and ECM Efficacy .......................................

9.28

The Radar Equation in Jamming and Chaff Conditions .......................................................

9.29

9.6

9.12

This page has been reformatted by Knovel to provide easier navigation.

Contents

xvii

10. Pulse Compression Radar ..................................... 10.1 10.1

Introduction .............................................................

10.1

10.2

Factors Affecting Choice of Pulse Compression System .............................................

10.3

10.3

Linear FM ...............................................................

10.4

10.4

Nonlinear FM ..........................................................

10.4

10.5

Pulse Compression Devices ...................................

10.6

Digital Pulse Compression .................................

10.7

Surface-Wave Pulse Compression ..................... 10.10 Other Passive Linear-FM Devices ...................... 10.12 Voltage-Controlled Oscillator ............................. 10.15 10.6

Phase-Coded Waveforms ...................................... 10.15 Optimal Binary Sequences ................................. 10.17 Maximal-Length Sequences ............................... 10.19 Quadratic Residue Sequences ........................... 10.21 Complementary Sequences ............................... 10.21 Implementation of Biphase-Coded Systems ....... 10.22 Doppler Correction ............................................ 10.24 Polyphase Codes .............................................. 10.25

10.7

Time-Frequency-Coded Waveforms ...................... 10.26

10.8

Weighting and Equalization .................................... 10.27 Paired Echoes and Weighting ............................ 10.27 Comparison of Weighting Functions ................... 10.29 Taylor versus Cosine-Squared-Plus-Pedestal Weighting ........................................................ 10.31 Taylor Weighting with Linear FM ........................ 10.31 Discrete Time Weighting .................................... 10.34 Amplitude and Phase Distortion ......................... 10.34 Equalization ....................................................... 10.36

This page has been reformatted by Knovel to provide easier navigation.

xviii

Contents

11. Radar Cross Section ............................................... 11.1 11.1

Introduction .............................................................

11.1

11.2

The Concept of Echo Power ...................................

11.2

Definition of RCS ...............................................

11.2

Examples of RCS Characteristics ......................

11.4

11.3

RCS Prediction Techniques ................................... 11.18 Exact Methods ................................................... 11.20 Approximate Methods ........................................ 11.24

11.4

RCS Measurement Techniques ............................. 11.34 General Requirements ....................................... 11.35 Outdoor Test Ranges ........................................ 11.38 Indoor Test Ranges ........................................... 11.39

11.5

Echo Reduction ...................................................... 11.43 Shaping ............................................................. 11.44 Radar Absorbers ............................................... 11.46

11.6

Summary ................................................................ 11.51

12. Ground Echo ........................................................... 12.1 12.1

Introduction .............................................................

12.1

Relative Importance of Theory and Empiricism ......................................................

12.3

Available Scattering Information .........................

12.3

12.2

Parameters Affecting Ground Return .....................

12.4

12.3

Theoretical Models and Their Limitations ...............

12.6

Descriptions of a Surface ...................................

12.6

Simplified Models ..............................................

12.7

Physical Optics Models ......................................

12.9

Small-Perturbation and Two-Scale Models ......... 12.10 Other Models ..................................................... 12.12

This page has been reformatted by Knovel to provide easier navigation.

Contents 12.4

xix

Fading of Ground Echoes ....................................... 12.12 Fading-Rate Computations ................................ 12.13 Effect of Detection ............................................. 12.16 Moving Target Surfaces ..................................... 12.18

12.5

Measurement Techniques for Ground Return ........ 12.18 CW and FM-CW Systems .................................. 12.18 Range-Measuring Systems ................................ 12.21 CW-Doppler Scatterometers .............................. 12.22 Independent Samples Required for Measurement Accuracy ................................... 12.23 Near-Vertical Problem ....................................... 12.23 Ground and Helicopter Scatterometers and Spectrometers ................................................. 12.24 Scattering Coefficient from Images .................... 12.28 Bistatic Measurements ....................................... 12.28

12.6

General Models for Scattering Coefficient (Clutter Models) ...................................................... 12.28

12.7

Scattering Coefficient Data ..................................... 12.35 Effects of Roughness, Moisture Content, and Vegetation Cover ............................................. 12.35 Soil Moisture ...................................................... 12.39 Vegetation ......................................................... 12.41 Snow ................................................................. 12.42 Sea Ice .............................................................. 12.44

12.8

Imaging Radar Interpretation .................................. 12.45

13. Sea Clutter ............................................................... 13.1 13.1

Introduction .............................................................

13.1

13.2

Description of the Sea Surface ...............................

13.2

The Wave Spectrum ..........................................

13.3

General Sea Descriptors ....................................

13.5

This page has been reformatted by Knovel to provide easier navigation.

xx

Contents 13.3

Empirical Behavior of Sea Clutter ...........................

13.6

Dependence on Wind Speed, Grazing Angle, and Frequency ................................................

13.8

The Spectrum of Sea Clutter .............................. 13.21 Other Effects on Sea Clutter .............................. 13.23 13.4

Theories of Sea Clutter ........................................... 13.27 Theories Based on Global Boundary-Value Problems ......................................................... 13.29 The Composite-Surface Hypothesis ................... 13.32 Scattering by Surface Features .......................... 13.33

13.5

Summary and Conclusions ..................................... 13.35

14. CW and FM Radar ................................................... 14.1 14.1

Introduction and Advantages of CW .......................

14.1

14.2

Doppler Effect .........................................................

14.2

14.3

Unmodulated CW Radar ........................................

14.2

Spectral Spreading ............................................

14.2

Noise in Sources ...............................................

14.3

Noise from Clutter ..............................................

14.3

Microphonism ....................................................

14.7

Scanning and Target Properties .........................

14.7

Sources ..................................................................

14.8

Master Oscillator Power Amplifier (MOPA) Chains .............................................................

14.8

Active Stabilization ............................................

14.8

14.4

Stabilization of Power Oscillators ....................... 14.11 14.5

Noise Measurement Technique .............................. 14.11

14.6

Receivers ................................................................ 14.15 RF Amplification ................................................ 14.15 Generation of the Local-Oscillator Signal ........... 14.15

This page has been reformatted by Knovel to provide easier navigation.

Contents

xxi

IF Amplifier ........................................................ 14.16 Subcarriers ........................................................ 14.16 Amplication ........................................................ 14.18 Doppler Filter Banks .......................................... 14.18 Doppler Trackers ............................................... 14.18 Constant False-Alarm Rate (CFAR) ................... 14.19 14.7

Minimization of Feedthrough .................................. 14.19

14.8

Miscellaneous CW Radars ..................................... 14.20 CW Proximity Fuzes .......................................... 14.20 Police Radars .................................................... 14.21

14.9

FM Radar ................................................................ 14.21

14.10 Sinusoidal Modulation ............................................ 14.23 Double Sinusoidal Modulation ............................ 14.26 14.11 Triangular and Sawtooth Modulation ...................... 14.27 14.12 Noise Modulation .................................................... 14.28 14.13 Coded Modulations ................................................. 14.29 14.14 Dual Modulation ...................................................... 14.30 14.15 Leakage .................................................................. 14.30 14.16 Performance of FM-CW Systems ........................... 14.31 14.17 Short-Range Systems and Microwave Proximity Fuzes ...................................................... 14.31 14.18 Altimeters ................................................................ 14.34 14.19 Doppler Navigators ................................................. 14.37 14.20 Personnel Detection Radar and Miscellaneous FM-CW Systems .................................................... 14.39 14.21 Tailoring the Range Response of FM-CW Systems .................................................................. 14.41

This page has been reformatted by Knovel to provide easier navigation.

xxii

Contents

15. MTI Radar ................................................................. 15.1 15.1

Introduction to MTI Radar .......................................

15.1

Moving-Target Indicator (MTI) Block Diagram ..........................................................

15.3

Moving-Target Detector (MTD) Block Diagram ..........................................................

15.5

15.2

Clutter Filter Response to Moving Targets .............

15.7

15.3

Clutter Characteristics ............................................

15.8

Spectral Characteristics .....................................

15.8

Amplitude Characteristics .................................. 15.10 15.4

Definitions ............................................................... 15.11 Improvement Factors (I) ..................................... 15.11 Signal-to-Clutter Ratio Improvement (ISCR) ......... 15.11 Subclutter Visibility (SCV) .................................. 15.13 Interclutter Visibility (ICV) ................................... 15.13 Filter Mismatch Loss .......................................... 15.14 Clutter Visibility Factor (VOC) .............................. 15.14

15.5

Improvement Factor Calculations ........................... 15.14

15.6

Optimum Design of Clutter Filters ........................... 15.16

15.7

MTI Clutter Filter Design ......................................... 15.23

15.8

Clutter Filter Bank Design ....................................... 15.29 Empirical Filter Design ....................................... 15.29 Chebyshev Filter Bank ....................................... 15.31 Fast Fourier Transform Filter Bank ..................... 15.34

15.9

Staggered PRF ....................................................... 15.34 Stagger Design Procedures ............................... 15.34 Feedback and Pulse-to-Pulse Staggering .......... 15.37 Improvement Factor Limitation Caused by Staggering ....................................................... 15.39 Time-Varying Weights ........................................ 15.40

This page has been reformatted by Knovel to provide easier navigation.

Contents

xxiii

Depth of First Null in Velocity Response ............ 15.40 15.10 Improvement Factor Restriction Caused by Limiting ................................................................... 15.41 15.11 Radar System Stability and A/D Quantization Requirements ......................................................... 15.45 System Instabilities ............................................ 15.45 Effect of Quantization Noise on Improvement Factor .............................................................. 15.53 Pulse Compression Considerations .................... 15.55 15.12 Analog-to-Digital Conversion Considerations ......... 15.57 Dynamic Range ................................................. 15.58 I and Q Balance Requirements .......................... 15.59 Timing Jitter ....................................................... 15.60 Linearity ............................................................ 15.60 Accuracy ........................................................... 15.60 15.13 Adaptive MTI Implementation ................................. 15.61 15.14 Clutter Map Implementation ................................... 15.65 15.15 Considerations Applicable to MTI Radar Systems .................................................................. 15.69

16. Airborne MTI ............................................................ 16.1 16.1

Systems Using Airborne MTI Techniques ..............

16.1

16.2

Coverage Considerations .......................................

16.2

16.3

Platform Motion and Altitude Effects on MTI Performance ...........................................................

16.2

Effect of Slant Range on Doppler Effect .............

16.4

TACCAR ...........................................................

16.5

Platform-Motion Effect .......................................

16.7

Platform-Motion Compensation Abeam ..................

16.8

Physically Displaced Phase-Center Antenna ......

16.8

16.4

This page has been reformatted by Knovel to provide easier navigation.

xxiv

Contents Electronically Displaced Phase-Center Antenna .......................................................... 16.10 Power in the Antenna Sidelobes ........................ 16.13

16.5

Scanning-Motion Compensation ............................ 16.14 Compensation-Pattern Selection ........................ 16.16

16.6

Simultaneous Platform Motion and Scan Compensation ........................................................ 16.17

16.7

Platform-Motion Compensation, Forward Direction ................................................................. 16.20

16.8

Space-Time Adaptive Motion Compensation ......... 16.23 Performance Capability of Space-Time Adaptive Arrays ............................................... 16.26

16.9

Limitation of Improvement Factor Due to Pulse Envelope Shift ........................................................ 16.28

16.10 Effect of Multiple Spectra ........................................ 16.29 16.11 Detection of Ground Moving Targets ...................... 16.29

17. Pulse Doppler Radar ............................................... 17.1 17.1

17.2

Characteristics and Applications ............................

17.1

Nomenclature ....................................................

17.1

Applications .......................................................

17.1

PRFs .................................................................

17.1

Pulse Doppler Spectrum ....................................

17.2

Ambiguities and PRF Selection ..........................

17.5

Basic Configuration ............................................

17.7

Pulse Doppler Clutter .............................................

17.9

General .............................................................

17.9

Ground Clutter in a Stationary Radar .................

17.9

Ground Clutter in a Moving Radar ......................

17.9

Clutter Return: General Equations ..................... 17.10 Sidelobe Clutter ................................................. 17.11

This page has been reformatted by Knovel to provide easier navigation.

Contents

xxv

Sidelobe Discretes ............................................. 17.11 Main-Beam Clutter ............................................. 17.16 Main-Beam Clutter Filtering ............................... 17.16 Altitude-Line Clutter Filtering .............................. 17.18 17.3

Time Gating ............................................................ 17.19 Transmitted-Pulse Suppression ......................... 17.19 Range Gating .................................................... 17.19

17.4

Range-Ambiguity Resolution .................................. 17.19 High-PRF Ranging ............................................. 17.20 Medium-PRF Ranging ....................................... 17.25

17.5

Target Tracking ...................................................... 17.25 Single-Target Tracking ....................................... 17.25 Multiple-Target Tracking .................................... 17.26

17.6

Dynamic-Range and Stability Requirements .......... 17.26 Dynamic Range ................................................. 17.26 Stability Requirements ....................................... 17.28 Types of Spurious Modulation ............................ 17.29 Sinusoidal Modulations ...................................... 17.29 Pulse-to-Pulse Random Modulation ................... 17.33

17.7

Range Performance ............................................... 17.33 Range Equation ................................................. 17.33 System Losses .................................................. 17.33 Probability of False Alarm .................................. 17.35 Probability of Detection ...................................... 17.36

18. Tracking Radar ........................................................ 18.1 18.1

Introduction .............................................................

18.1

18.2

Scanning and Lobing ..............................................

18.3

18.3

Monopulse (Simultaneous Lobing) .........................

18.8

Amplitude-Comparison Monopulse .....................

18.9

This page has been reformatted by Knovel to provide easier navigation.

xxvi

Contents Phase-Comparison Monopulse .......................... 18.17 Monopulse Tracking with Phased Arrays ............ 18.19 One- and Two-Channel Monopulse .................... 18.19 Conopulse ......................................................... 18.21

18.4

Servosystems for Tracking Radar .......................... 18.22

18.5

Target Acquisition and Range Tracking ................. 18.26 Acquisition ......................................................... 18.26 Range Tracking ................................................. 18.27 nth-Time-Around Tracking ................................. 18.30

18.6

Special Monopulse Techniques .............................. 18.30 High-Range-Resolution Monopulse .................... 18.30 Dual-Band Monopulse ....................................... 18.31 Mirror Antenna (Inverse Cassegrain) .................. 18.32 On-Axis Tracking ............................................... 18.33

18.7

Sources of Error ..................................................... 18.33

18.8

Target-Caused Errors (Target Noise) ..................... 18.34 Amplitude Noise ................................................ 18.34 Angle Noise (Glint) ............................................ 18.37 Range Noise (Range Glint) ................................ 18.43 Doppler Scintillation ........................................... 18.45

18.9

Other External Causes of Error .............................. 18.46 Multipath ........................................................... 18.46 Crosstalk Caused by Cross-Polarized Energy ............................................................ 18.48 Troposphere Propagation .................................. 18.49

18.10 Internal Sources of Error ........................................ 18.50 Receiver Thermal Noise .................................... 18.50 Other Internal Sources of Error .......................... 18.52 18.11 Summary of Sources of Error ................................. 18.53 Angle Measurement Errors ................................ 18.53

This page has been reformatted by Knovel to provide easier navigation.

Contents

xxvii

Range Measurement Errors ............................... 18.54 18.12 Error Reduction Techniques ................................... 18.54 Multipath-Error Reduction .................................. 18.54 Target Angle and Range Scintillation (Glint) Reduction ........................................................ 18.57 Reduction of Internally Caused Errors ................ 18.57

19. Radar Guidance of Missiles ................................... 19.1 19.1

Introduction .............................................................

19.1

19.2

Overview of Semiactive CW Systems ....................

19.3

Doppler Frequency Relationships ......................

19.3

Clutter and Feedthrough Considerations ............

19.6

Guidance Fundamentals ....................................

19.7

Target Illumination .............................................

19.9

System Evolution ....................................................

19.9

19.3

Basic Semiactive Seeker ................................... 19.10 Unambiguous (Offset Video) Receiver ............... 19.10 Inverse Receiver ................................................ 19.12 Angle Tracking: Conical Scan to Monopulse ...... 19.14 Pulse Doppler (PD) Operation ............................ 19.15 Active Seekers .................................................. 19.15 Passive Seekers ................................................ 19.17 Other System Considerations ............................ 19.20 19.4

System Functional Operation ................................. 19.21 Reference-Channel Operation ........................... 19.21 Target Signal Detection ..................................... 19.23 Target Signal Tracking ....................................... 19.26 Performance Limitations .................................... 19.29

19.5

Subsystems and Integration ................................... 19.31 Radome ............................................................. 19.32

This page has been reformatted by Knovel to provide easier navigation.

xxviii

Contents Antenna ............................................................. 19.33 Receiver ............................................................ 19.35 Low-Noise Frequency Reference ....................... 19.37 Signal Processing .............................................. 19.37 Transmitter ........................................................ 19.38 Power ................................................................ 19.40 Integration ......................................................... 19.40

20. Height Finding and 3D Radar ................................. 20.1 20.1

20.2

Height Finding Radars and Techniques .................

20.1

Early Radar Techniques for Height Finding ........

20.1

Height Finding Techniques in 3D Radars ...........

20.6

Derivation of Height from Radar Measurements ........................................................ 20.14 Flat-Earth Approximation ................................... 20.14 Spherical Earth: Parabolic Approximation .......... 20.14 Spherical Earth: Exact Geometry ....................... 20.14 Corrections for Atmospheric Refraction .............. 20.15 Practical Corrections .......................................... 20.19

20.3

Height Accuracy Performance Limitations .............. 20.19 Fundamental Accuracy of Sequential Lobing ...... 20.20 Fundamental Accuracy of Simultaneous Lobing ............................................................. 20.25 Elevation Error Due to Surface Reflections ........ 20.33 Low-Angle Squinted-Beam Height Finding ......... 20.35

21. Synthetic Aperture Radar ....................................... 21.1 21.1

Basic Principles and Early History ..........................

21.1

21.2

Factors Affecting Resolution of a Radar System ....................................................................

21.4

Conventional Technique ....................................

21.4

This page has been reformatted by Knovel to provide easier navigation.

Contents

xxix

The Unfocused Synthetic Aperture .....................

21.5

The Focused Case ............................................

21.6

21.3

Radar System Preliminaries ...................................

21.7

21.4

Signal-Processing Theory ......................................

21.8

Detailed Resolution Analysis ..............................

21.8

Signal-to-Noise-Ratio Considerations ................. 21.15 Effect of Phase Errors ........................................ 21.17 Signal Processing .............................................. 21.17 21.5

Additional System Considerations .......................... 21.18 Antenna ............................................................. 21.18 Receiver-Transmitter ......................................... 21.19 Storage and Recording ...................................... 21.19 Motion Compensation ........................................ 21.20 Squint Mode ...................................................... 21.20 Spotlight Mode .................................................. 21.21 Effects of Motion Errors ..................................... 21.21 Multiple-Beam Radars ....................................... 21.21 ISAR ................................................................. 21.21 Three-Dimensional Spectrum ............................. 21.21

22. Space-Based Radar Systems and Technology .............................................................. 22.1 22.1

Introduction .............................................................

22.1

22.2

SBR Systems Considerations ................................

22.1

Types of SBR ....................................................

22.1

Considerations ..................................................

22.5

22.3

SBR System Descriptions ...................................... 22.14 STS Rendezvous Radar .................................... 22.14 Seasat-A Synthetic Aperture Radar ................... 22.15 Shuttle Imaging Radar ....................................... 22.15

This page has been reformatted by Knovel to provide easier navigation.

xxx

Contents GEOS-C SBR System Characteristics ................ 22.15 U.S.S.R. Cosmos 1500 Side-Looking Radar ...... 22.17 22.4

Technology ............................................................. 22.17 Antennas ........................................................... 22.18 Transmit/Receive Modules ................................. 22.23 On-Board Processors ........................................ 22.24 Prime Power ...................................................... 22.24

22.5

Critical Issues ......................................................... 22.26 SBR System Costs ............................................ 22.26 Survivability and Vulnerability ............................ 22.26

22.6

SBR Future Possibilities ......................................... 22.26 Rendezvous Radar Missions .............................. 22.26 Remote-Sensing Missions ................................. 22.29 Global Air Traffic Surveillance ............................ 22.30 Military SBR Systems ........................................ 22.31

23. Meteorological Radar .............................................. 23.1 23.1

Introduction .............................................................

23.1

23.2

The Radar Range Equation for Meteorological Targets ...................................................................

23.2

Design Considerations ...........................................

23.5

Attenuation Effects ............................................

23.5

23.3

Range and Velocity Ambiguities ......................... 23.10 Ground Clutter Effects ....................................... 23.11 Typical Weather Radar Designs ......................... 23.12 23.4

Signal Processing ................................................... 23.13 Measurement Accuracy ..................................... 23.15 Processor Implementations ................................ 23.17

23.5

Operational Applications ......................................... 23.17 Precipitation Measurement ................................ 23.18

This page has been reformatted by Knovel to provide easier navigation.

Contents

xxxi

Severe Storm Warning ....................................... 23.19 23.6

Research Applications ............................................ 23.23 Multiple-Parameter, Radar ................................. 23.23 Multiple Radars ................................................. 23.24 Rapid Scanning ................................................. 23.25 Airborne and Space-Borne Radars .................... 23.26 Clear-Air Radars ................................................ 23.27 Synthetic Aperture Radar and Pulse Compression ................................................... 23.28

24. HF Over-the-Horizon Radar .................................... 24.1 24.1

Introduction .............................................................

24.1

24.2

Radar Equation .......................................................

24.3

24.3

Transmitters ............................................................

24.4

24.4

Antennas ................................................................

24.5

24.5

Clutter: The Echo from the Earth ............................

24.6

24.6

Radar Cross Section .............................................. 24.10

24.7

Noise and Interference ........................................... 24.12

24.8

Spectrum Use ......................................................... 24.14

24.9

Sky-Wave Transmission Medium ........................... 24.15

24.10 Sky-Wave Radar Performance ............................... 24.22 24.11 Receiver-Processor ................................................ 24.36 24.12 Ground-Wave Radar Performance ......................... 24.38

25. Bistatic Radar .......................................................... 25.1 25.1

Concept and Definitions .........................................

25.1

25.2

History ....................................................................

25.2

25.3

Coordinate System .................................................

25.5

25.4

Range Relationships ..............................................

25.6

Range Equation .................................................

25.6

Ovals of Cassini .................................................

25.6

This page has been reformatted by Knovel to provide easier navigation.

xxxii

Contents

25.5

Operating Regions .............................................

25.7

Isorange Contours .............................................

25.8

Area Relationships .................................................

25.9

Location ............................................................

25.9

Coverage ........................................................... 25.10 Clutter Cell Area ................................................ 25.12 25.6

Doppler Relationships ............................................ 25.13 Target Doppler .................................................. 25.13 Isodoppler Contours .......................................... 25.14

25.7

Target Cross Section .............................................. 25.14 Pseudo-Monostatic RCS Region ........................ 25.15 Bistatic RCS Region .......................................... 25.17 Glint Reduction in the Bistatic RCS Region ........ 25.17 Forward-Scatter RCS Region ............................. 25.17

25.8

Clutter ..................................................................... 25.18 In-Plane Land Clutter Scattering Coefficient ....... 25.21 In-Plane Sea Clutter Scattering Coefficient ........ 25.24 Out-of-Plane Scattering Coefficient .................... 25.24

25.9

Special Techniques, Problems, and Requirements ......................................................... 25.24 Pulse Chasing ................................................... 25.24 Beam Scan on Scan .......................................... 25.26 Sidelobe Clutter ................................................. 25.27 Time Synchronization ........................................ 25.27 Phase Synchronization and Stability .................. 25.28

Index ...............................................................................

This page has been reformatted by Knovel to provide easier navigation.

I.1

CHAPTER 1 AN INTRODUCTION TO RADAR Merrill I. Skolnik

1.1

DESCRIPTIONOFRADAR

The basic concept of radar is relatively simple even though in many instances its practical implementation is not. A radar operates by radiating electromagnetic energy and detecting the echo returned from reflecting objects (targets). The nature of the echo signal provides information about the target. The range, or distance, to the target is found from the time it takes for the radiated energy to travel to the target and back. The angular location of the target is found with a directive antenna (one with a narrow beamwidth) to sense the angle of arrival of the echo signal. If the target is moving, a radar can derive its track, or trajectory, and predict the future location. The shift in frequency of the received echo signal due to the doppler effect caused by a moving target allows a radar to separate desired moving targets (such as aircraft) from undesired stationary targets (such as land and sea clutter) even though the stationary echo signal may be many orders of magnitude greater than the moving target. With sufficiently high resolution, a radar can discern something about the nature of a target's size and shape. Radar resolution may be obtained in range or angle, or both. Range resolution requires large bandwidth. Angle resolution requires (electrically) large antennas. Resolution in the cross-range dimension is usually not as good as the resolution that can be obtained in range. However, when there is relative motion between the individual parts of a target and the radar, it is possible to use the inherent resolution in doppler frequency to resolve in the cross-range dimension. The cross-range resolution of a synthetic aperture radar (SAR) for imaging a scene such as terrain can be explained as being due to resolution in doppler, although a SAR is usually thought of as generating a large "synthetic" antenna by storing received signals in a memory. The two views—doppler resolution and synthetic antenna—are equivalent. Resolution in the doppler domain is a natural way to envision the cross-range resolution achieved by the inverse synthetic aperture radar (ISAR) used for the imaging of a target. Radar is an active device in that it carries its own transmitter and does not depend on ambient radiation, as do most optical and infrared sensors. Radar can detect relatively small targets at near or far distances and can measure their range with precision in all weather, which is its chief advantage when compared with other sensors. The principle of radar has been applied from frequencies of a few megahertz

(HF, or high-frequency region of the electromagnetic spectrum) to well beyond the optical region (laser radar). This is a frequency extent of about 1 billion to 1. The particular techniques for implementing a radar differ greatly over this range of frequencies, but the basic principles remain the same. Radar was originally developed to satisfy the needs of the military for surveillance and weapon control. Military applications have funded much of the development of its technology. However, radar has seen significant civil applications for the safe travel of aircraft, ships, and spacecraft; the remote sensing of the environment, especially the weather; and law enforcement and many other applications. Radar Block Diagram. The basic parts of a radar system are illustrated in the simple block diagram of Fig. 1.1. (Other examples of radar block diagrams can be found throughout the handbook.) The radar signal, usually a repetitive train of short pulses, is generated by the transmitter and radiated into space by the antenna. The duplexer permits a single antenna to be time-shared for both transmission and reception. Reflecting objects (targets) intercept and reradiate a portion of the radar signal, a small amount of which is returned in the direction of the radar. The returned echo signal is collected by the radar antenna and amplified by the receiver. If the output of the radar receiver is sufficiently large, detection of a target is said to occur. A radar generally determines the location of a target in range and angle, but the echo signal also can provide information about the nature of the target. The output of the receiver may be presented on a display to an operator who makes the decision as to whether or not a target is present, or the receiver output can be processed by electronic means to automatically recognize the presence of a target and to establish a track of the target from detections made over a period of time. With automatic detection and track (ADT) the operator usually is presented with the processed target track rather than the raw radar detections. In some applications, the processed radar output might be used to directly control a system (such as a guided missile) without any operator intervention. ANTENNA DUPLEXER

POWER AMPLIFIER

WAVEFORM GENERATOR

LOW-NOISE AMPLIFIER LOCAL OSCILLATOR

MIXER

IF MATCHED AMPLIFIER FILTER

SECOND DETECTOR

VIDEO AMPLIFIER

DISPLAY

FIG. 1.1 Simple block diagram of a radar employing a power amplifier transmitter and a superheterodyne receiver.

The operation of the radar is described in more detail, starting with the transmitter.

Transmitter. The transmitter (Chap. 4) in Fig. 1.1 is shown as a power amplifier, such as a klystron, traveling-wave tube, crossed-field amplifier, or solidstate device (Chap. 5). A power oscillator such as a magnetron also can be used as the transmitter; but the magnetron usually is of limited average power compared with power amplifiers, especially the klystron, which can produce much larger average power than can a magnetron and is more stable. (It is the average power, rather than the peak power, which is the measure of the capability of a radar.) Since the basic waveform is generated at low power before being delivered to the power amplifier, it is far easier to achieve the special waveforms needed for pulse compression and for coherent systems such as moving-target indication (MTI) radar and pulse doppler radar. Although the magnetron oscillator can be used for pulse compression and for MTI, better performance can be obtained with a power amplifier configuration. The magnetron oscillator might be found in systems where simplicity and mobility are important and where high average power, good MTI performance, or pulse compression is not required. The transmitter of a typical ground-based air surveillance radar might have an average power of several kilowatts. Short-range radars might have powers measured in milliwatts. Radars for the detection of space objects (Chap. 22) and HF over-the-horizon radars (Chap. 24) might have average powers of the order of a megawatt. The radar equation (Sec. 1.2 and Chap. 2) shows that the range of a radar is proportional to the fourth root of the transmitter power. Thus, to double the range requires that the power be increased by 16. This means that there often is a practical, economical limit to the amount of power that should be employed to increase the range of a radar. Transmitters not only must be able to generate high power with stable waveforms, but they must often operate over a wide bandwidth, with high efficiency and with long, trouble-free life. Duplexer. The dupiexer acts as a rapid switch to protect the receiver from damage when the high-power transmitter is on. On reception, with the transmitter off, the dupiexer directs the weak received signal to the receiver rather than to the transmitter. Duplexers generally are some form of gas-discharge device and may be used with solid-state or gas-discharge receiver protectors. A solid-state circulator is sometimes used to provide further isolation between the transmitter and the receiver. Antenna. The transmitter power is radiated into space by a directive antenna which concentrates the energy into a narrow beam. Mechanically steered parabolic reflector antennas (Chap. 6) and planar phased arrays (Chap. 7) both find wide application in radar. Electronically steered phased array antennas (Chap. 7) are also used. The narrow, directive beam that is characteristic of most radar antennas not only concentrates the energy on target but also permits a measurement of the direction to the target. A typical antenna beamwidth for the detection or tracking of aircraft might be about 1 or 2°. A dedicated tracking radar (Chap. 18) generally has a symmetrical antenna which radiates a pencil-beam pattern. The usual ground-based air surveillance radar that provides the range and azimuth of a target generally uses a mechanically rotated reflector antenna with a fan-shaped beam, narrow in azimuth and broad in elevation. Airborne radars and surfacebased 3D air surveillance radars (those that rotate mechanically in azimuth to measure the azimuth angle but use some form of electronic steering or beamforming to obtain the elevation angle, as discussed in Chap. 20) often employ planar array apertures. Mechanical scanning of the radar antenna is usually quite acceptable for the vast majority of radar applications. When it is

necessary to scan the beam more quickly than can be achieved with mechanical scanning and when high cost can be tolerated, the electronically steered phased array antenna can be employed. (Beam steering with electronically steered phased arrays can be accomplished in microseconds or less if necessary.) The size of a radar antenna depends in part on the frequency, whether the radar is located on the ground or on a moving vehicle, and the environment in which it must operate. The lower the frequency, the easier it is to produce a physically large antenna since the mechanical (and electrical) tolerances are proportional to the wavelength. In the ultrahigh-frequency (UHF) band, a large antenna (either reflector or phased array) might have a dimension of 100 ft or more. At the upper microwave frequencies (such as X band), radar antennas greater than 10 or 20 ft in dimension can be considered large. (Larger antennas than the above examples have been built, but they are not the norm.) Although there have been microwave antennas with beamwidths as small as 0.05°, radar antennas rarely have beamwidths less than about 0.2°. This corresponds to an aperture of approximately 300 wavelengths (about 31 ft at X band and about 700 ft at UHF). Receiver. The signal collected by the antenna is sent to the receiver, which is almost always of the superheterodyne type (Chap. 3). The receiver serves to (1) separate the desired signal from the ever-present noise and other interfering signals and (2) amplify the signal sufficiently to actuate a display, such as a cathoderay tube, or to allow automatic processing by some form of digital device. At microwave frequencies, the noise at the receiver output is usually that generated by the receiver itself rather than external noise which enters via the antenna. The input stage of the receiver must not introduce excessive noise which would interfere with the signal to be detected. A transistor amplifier as the first stage offers acceptably low noise for many radar applications. A first-stage receiver noise figure (defined in Sec. 1.2) might be, typically, 1 or 2 dB. A low-noise receiver front end (the first stage) is desirable for many civil applications, but in military radars the lowest noise figure attainable might not always be appropriate. In a high-noise environment, whether due to unintentional interference or to hostile jamming, a radar with a low-noise receiver is more susceptible than one with higher noise figure. Also, a low-noise amplifier as the front end generally will result in the receiver having less dynamic range—something not desirable when faced with hostile electronic countermeasures (ECM) or when the doppler effect is used to detect small targets in the presence of large clutter. When the disadvantages of a low-noise-figure receiver are to be avoided, the RF amplifier stage is omitted and the mixer stage is employed as the receiver front end. The higher noise figure of the mixer can then be compensated by an equivalent increase in the transmitter power. The mixer of the superheterodyne receiver translates the receiver RF signal to an intermediate frequency. The gain of the intermediate-frequency (IF) amplifier results in an increase of the receiver signal level. The IF amplifier also includes the function of the matched filter: one which maximizes the output signalto-noise ratio. Maximizing the signal-to-noise ratio at the output of the IF maximizes the detectability of the signal. Almost all radars have a receiver which closely approximates the matched filter. The second detector in the receiver is an envelope detector which eliminates the IF carrier and passes the modulation envelope. When doppler processing is employed, as it is in CW (continuous-wave), MTI, and pulse doppler radars, the envelope detector is replaced by a phase detector which extracts the doppler frequency by comparison with a reference signal at the transmitted frequency.

There must also be included filters for rejecting the stationary clutter and passing the doppler-frequency-shifted signals from moving targets. The video amplifier raises the signal power to a level where it is convenient to display the information it contains. As long as the video bandwidth is not less than half of the IF bandwidth, there is no adverse effect on signal detectability. A threshold is established at the output of the video amplifier to allow the detection decision to be made. If the receiver output crosses the threshold, a target is said to be present. The decision may be made by an operator, or it might be done with an automatic detector without operator intervention. Signal Processing. There has not always been general agreement as to what constitutes the signal-processing portion of the radar, but it is usually considered to be the processing whose purpose is to reject undesired signals (such as clutter) and pass desired signals due to targets. It is performed prior to the threshold detector where the detection decision is made. Signal processing includes the matched filter and the doppler filters in MTI and pulse doppler radar. Pulse compression, which is performed before the detection decision is made, is sometimes considered to be signal processing, although it does not fit the definition precisely. Data Processing. This is the processing done after the detection decision has been made. Automatic tracking (Chap. 8) is the chief example of data processing. Target recognition is another example. It is best to use automatic tracking with a good radar that eliminates most of the unwanted signals so that the automatic tracker only has to deal with desired target detections and not undesired clutter. When a radar cannot eliminate all nuisance echoes, a means to maintain a constant false-alarm rate (CFAR) at the input to the tracker is necessary. The CFAR portion of the receiver is usually found just before the detection decision is made. It is required to maintain the false-alarm rate constant as the clutter and/or noise background varies. Its purpose is to prevent the automatic tracker from being overloaded with extraneous echoes. It senses the magnitude of the radar echoes from noise or clutter in the near vicinity of the target and uses this information to establish a threshold so that the noise or clutter echoes are rejected at the threshold and not confused as targets by the automatic tracker. Unfortunately, CFAR reduces the probability of detection. It also results in a loss in signal-to-noise ratio, and it degrades the range resolution. CFAR or its equivalent is necessary when automatic tracking computers cannot handle large numbers of echo signals, but it should be avoided if possible. When an operator is used to make the threshold decision, CFAR is not a necessity as in limitedcapacity automatic systems because the operator can usually recognize echoes due to clutter or to increased noise (such as jamming) and not confuse them with desired targets. Displays. The display for a surveillance radar is usually a cathode-ray tube with a PPI (plan position indicator) format. A PPI is an intensity-modulated, maplike presentation that provides the target's location in polar coordinates (range and angle). Older radars presented the video output of the receiver (called raw video) directly to the display, but more modern radars generally display processed video, that is, after processing by the automatic detector or the automatic detector and tracker (ADT). These are sometimes called cleaned-up displays since the noise and background clutter are removed. Radar Control. A modern radar can operate at different frequencies within its band, with different waveforms and different signal processing, and with different polarizations so as to maximize its performance under different environ-

mental conditions. These radar parameters might need to be changed according to the local weather, the clutter environment (which is seldom uniform in azimuth and range), interference to or from other electronic equipment, and (if a military radar) the nature of the hostile ECM environment. The different parameters, optimized for each particular situation, can be programmed into the radar ahead of time in anticipation of the environment, or they can be chosen by an operator in real time according to the observed environmental conditions. On the other hand, a radar control can be made to automatically recognize when environmental conditions have changed and automatically select, without the aid of an operator, the proper radar operating parameters to maximize performance. Waveform. The most common radar waveform is a repetitive train of short pulses. Other waveforms are used in radar when particular objectives need to be achieved that cannot be accomplished with a pulse train. CW (a continuous sine wave) is employed on some specialized radars for the measurement of radial velocity from the doppler frequency shift. FM/CW (frequency-modulated CW) is used when range is to be measured with a CW waveform (Chap. 14). Pulse compression waveforms (Chap. 10) are used when the resolution of a short pulse but the energy of a long pulse is desired. MTI radars (Chaps. 15 and 16) with low pulse repetition frequencies (PRFs) and pulse doppler radars (Chap. 17) with high PRFs often use waveforms with multiple pulse repetition intervals in order to avoid range and/or doppler ambiguities.

7.2

RADAREQUATION

Perhaps the single most useful description of the factors influencing radar performance is the radar equation which gives the range of a radar in terms of the radar characteristics. One form of this equation gives the received signal power Pr as

^ = £§X4^X^

(M)

The right-hand side has been written as the product of three factors to represent the physical processes taking place. The first factor is the power density at a distance R meters from a radar that radiates a power of Pt watts from an antenna of gain Gt. The numerator of the second factor is the target cross section a in square meters. The denominator accounts for the divergence on the return path of the electromagnetic radiation with range and is the same as the denominator of the first factor, which accounts for the divergence on the outward path. The product of the first two terms represents the power per square meter returned to the radar. The antenna of effective aperture area Ae intercepts a portion of this power in an amount given by the product of the three factors. If the maximum radar range /?max is defined as that which results in the received power Pr being equal to the receiver minimum detectable signal Smin, the radar equation may be written . PtGt A6(T R4m*x = ' 2 (4TT)Xn

(1-2)

When the same antenna is used for both transmitting and receiving, the transmitting gain Gt and the effective receiving aperture Ae are related by Gt = 4TrAJX2, where X is the wavelength of the radar electromagnetic energy. Substituting into Eq. (1.2) gives two other forms of the radar equation:

^* - jSrr

vfTr; ^ mm

a.3«)

Mna* = £&T 41TA. ^ min

<»- 3 «

The examples of the radar equation given above are useful for rough computations of range performance but they are overly simplified and do not give realistic results. The predicted ranges are generally overly optimistic. There are at least two major reasons why the simple form of the radar equation does not predict with any accuracy the range of actual radars. First, it does not include the various losses that can occur in a radar. Second, the target cross section and the minimum detectable signal are statistical in nature. Thus the specification of the range must be made in statistical terms. The elaboration of the simple range equation to yield meaningful range predictions is the subject of Chap. 2. Although the range enters as the fourth power in Eq. (1.3), it can appear as the cube, as the square, or as the first power in specific situations, some of which are described later in this section and in other chapters. In addition to its use for range prediction, the radar equation forms a good basis for preliminary system design by providing a guide to the possible tradeoffs among the various parameters that enter into radar performance. The minimum detectable signal 5min, which appears in the radar equation, is a statistical quantity and must be described in terms of the probability of detection and the probability of a false alarm. This is discussed in more detail in Chap. 2; for present purposes it suffices to state that for a signal to be reliably detected it must be larger than noise (generally by 10 to 20 dB) at the point in the receiver where the detection decision is made. The minimum detectable signal can be expressed as the signal-to-noise ratio (SIN) required for reliable detection times the receiver noise. The receiver noise is expressed relative to the thermal noise that would be produced by an ideal receiver. The thermal noise is equal to kTB, where k is Boltzmann's constant, T is the temperature, and B is the receiver bandwidth. The receiver noise is the thermal noise multiplied by the factor Fn, the receiver noise figure. The receiver noise figure is measured relative to a reference temperature TQ = 290 K (approximately room temperature), and the factor kT0 becomes 4 x 10~21 W/Hz. The minimum detectable signal in the radar equation can be written 5min = MoBFn^

(1.4)

Sometimes the factor T0Fn is replaced with J5, the system noise temperature. The above discussion of the radar equation was in terms of the signal power. Although power is a well-understood characteristic of the usual radar waveform consisting of a rectangular pulse, with more complicated waveforms the total sig-

nal energy is often a more convenient measure of waveform detectability. It also is more appropriate for theoretical reasons. The ratio of signal energy to noise energy, denoted EIN0, is a more fundamental parameter than the signal-to-noise (power) ratio in theoretical analyses based on statistical detection theory. No matter what the shape of the received waveform, if the receiver is designed as a matched filter the peak signal-to-noise (power) ratio at the output of the matched filter is 2EIN0. For a rectangular pulse of width T the signal power is Eh and the noise power is N0B9 where E = signal energy, N0 = noise energy, or noise power per unit bandwidth (provided the noise is uniform with frequency), and B - receiver bandwidth. With these substitutions, 5min becomes ^0Fn(E/N0)h. Substituting into Eq. (1.2) gives

E1G1 Aev

. *4max =

1

(4^kT0Fn(EIN0)

(1-5)

where Et = Pti is the energy contained in the transmitted waveform. Although Eq. (1.5) assumes a rectangular pulse, it can be applied to any waveform provided that Et is interpreted as the energy contained in the transmitted waveform and that the receiver of noise figure Fn is designed as a matched filter. Some of the published results of radar detection theory give the probability of detection and probability of false alarm in terms of S/N rather than EfN0. When these results assume optimum (matched-filter) processing, the required values of EIN0 for use in the radar equation can be obtained from the published results for SIN or the visibility factor as described in Chap. 2. The radar equation can be manipulated into various forms, depending on the particular application. Several examples are given below. Tracking. In this situation the radar is assumed to track continuously or "searchlight" a target for an interval of time tQ. Equation (1.5) applies, so that the tracking-, or searchlighting-, radar equation is 4

"

max

/V0G, Aev 4TTkT0Fn(EINo)

where Pavf0 = Et. Thus, in a tracking radar that must "see" to a long range, the average power must be high, the time on target must be long, and the antenna must be of large electrical size (G,) and large physical size (Ae). The frequency does not enter explicitly. Since it is easier mechanically to move a small antenna than a large one, tracking radars are usually found at the higher frequencies, where small apertures can have high gain and thus an adequate G, Ae product. The radar equation is based on detectability. A tracking radar must also be designed for good angular accuracy. Good angle accuracy is achieved with narrow beamwidths (large G,) and with high ElN0 (large Ae). Thus a large Gt Ae product is consistent with good tracking accuracy as well as good detectability. Volume Search. Assume that the radar must search an angular volume of H steradians in the time ts. If the antenna beam subtends an angle of £lb steradians, the antenna gain G, is approximately 4Tcl£lb. If the antenna beam dwells a time t0 in each direction subtended by the beam, the total scan time is ts = f0O/lV Substituting these expressions into Eq. (1.5) and noting that Et

=

^av^O*

^4

"

Fav Agg

max

ts

4^kToFn(EIN0)

ft

u

'"

Thus for a volume search radar the two important parameters for maximizing range are the average transmitter power and the antenna aperture. Any decrease in time to scan the volume or any increase in the volume searched must be accompanied by a corresponding increase in the product Pav Ae. Note that the frequency does not enter explicitly. Jamming. When the detection of the radar signal is limited by an external noise source, such as a deliberate noise jammer rather than by receiver noise, the parameters of importance in determining range performance are slightly different from those presented above (Chap. 9). The receiver noise power per unit bandwidth is now that determined by the jammer rather than the receiver noise figure. When a radar is performing volume search and jamming power enters from a particular direction via the sidelobes, the maximum range can be written -4

_P»v±

* max -

where gs Rj Bj Pj Gj

gs

«

R/Bj

flElN~0PjGj

U

'°;

= sidelobe level relative to main beam (number less than unity) = jammer range = jammer bandwidth = jammer power = jammer antenna gain

and EIN0 is the ratio of signal energy to noise power per unit bandwidth necessary for reliable detection. The parameter of importance is the average power. The antenna sidelobes are also important. This equation was derived by substituting for kT0Fn in Eq. (1.7) the jamming noise power per unit bandwidth that would enter the radar receiving-antenna sidelobes. It applies only when the normal receiver noise is negligible compared with the jamming noise. When the radar is searchlighting a target with a jammer, a mode of operation sometimes called burnthrough, the range becomes R2

K

_ *V(A omax ~

4^

B

J

EfN^PjGj

9) n U

*^

The important radar parameters are the average power, the time of observation, and the transmitting-antenna gain. The maximum range is squared rather than raised to the fourth power as in other forms of the radar equation. Note that in neither jamming example does the antenna aperture area enter explicitly. A large aperture collects more signal, but it also collects more jamming noise. The receiver noise figure does not enter because it is assumed that the jamming noise is considerably larger than the receiver noise. Thus in a noisy environment one might not benefit from the effort to design a receiver with the ultimate in sensitivity. The above two examples of jamming radar equations are simplifications. Other variations are possible.

Clutter. When the radar must detect a small target located on the surface of the sea or land, the interfering unwanted clutter echoes can severely limit the detectability of the target. When clutter power dominates receiver noise power, the range equation simply reduces to an expression for the signalto-clutter ratio. This ratio is equal to the ratio of the target cross section to the clutter cross section. If clutter is distributed more or less uniformly, the clutter echo will depend on the area illuminated by the radar resolution cell. Surface (ground or sea) clutter is described by the ratio of the clutter echo to the area illuminated by the radar. This normalized clutter coefficient is denoted a°. Consider a pulse radar viewing the target and the clutter at low grazing angles. If single-pulse detection is assumed, the signal-to-clutter ratio is s

a _ C a°/?6,(cT/2) sec <j>

=

(UO)

or R

where R 0fo c T <|>

= = = = =

max

=

Z (S/C)mincj\(cT/2) sec 4>

range to clutter patch azimuth beamwidth velocity of propagation pulse width grazing angle

The clutter patch is assumed to be determined in azimuth by the width of the antenna beam and in the range coordinate by the pulse width. The ratio SIC takes a role similar to the ratio ElN0 for thermal noise. It must be of sufficient magnitude to achieve reliable detection. The clutter statistics generally differ from the statistics of thermal noise but, as a first guess when no other information is available, the required values of SIC might be taken to be those of EIN0. It is significant that the range dependence enters linearly rather than as the fourth power. Thus for detection of a target in clutter the radar beam should be narrow and the pulse width should be short. With assumptions other than those above, the important radar parameters for detection of targets in clutter might be different. If n hits are received per scan and if the clutter is correlated from pulse to pulse, no improvement in SIC is obtained as it would be if thermal noise, rather than clutter, were the limitation.

1.3 INFORMATION AVAILABLE FROM THE RADAR ECHO Although the name radar is derived from radio detection and ranging, a radar is capable of providing more information about the target than is implied by its name. Detection of a target signifies the discovery of its presence. It is possible to consider detection independently of the process of information extraction, but it is not often that one is interested in knowing only that a target is

present without knowing something about its location in space and its nature. The extraction of useful target information is therefore an important part of radar operation. The ability to consider detection independent of information extraction does not mean that there is no relation between the two. The extraction of information generally requires a matched filter, or its equivalent, for optimum processing. The more information that is known about the target a priori, the more efficient will be the detection. For example, if the target location were known, the antenna could be pointed in the proper direction and energy or time need not be wasted searching empty space. Or, if the relative velocity were known, the receiver could be pretuned to the correct received frequency, negating the need to search the frequency band over which the doppler shift might occur. The usual radar provides the location of a target in range and angle. The rate of change of target location can also be measured from the change in range and angle with time, from which the track can be established. In many radar applications a detection is not said to occur until its track has been established. A radar with sufficient resolution in one or more coordinates can determine a target's size and shape. Polarization allows a measure of the symmetry of a target. In principle, a radar can also measure the surface roughness of a target and determine something about its dielectric properties. Range. The ability to determine range by measuring the time for the radar signal to propagate to the target and back is probably the distinguishing and most important characteristic of conventional radar. No other sensor can measure range to the accuracy possible with radar, at such long ranges, and under adverse weather conditions. Surface-based radars can be made to determine the range of an aircraft to an accuracy of a few tens of meters at distances limited only by the line of sight, generally 200 to 250 nmi. Radar has demonstrated its ability to measure interplanetary distances to an accuracy limited only by the accuracy to which the velocity of propagation is known. At more modest distances, the measurement of range can be made with a precision of a few centimeters. The usual radar waveform for determining range is the short pulse. The shorter the pulse, the more precise can be the range measurement. A short pulse has a wide spectral width (bandwidth). The effect of a short pulse can be obtained with a long pulse whose spectral width has been increased by phase or frequency modulation. When passed through a matched filter, the output is a compressed pulse whose duration is approximately the reciprocal of the spectral width of the modulated long pulse. This is called pulse compression and allows the resolution of a short (wide-bandwidth) pulse with the energy of a long pulse. A CW waveform with frequency or phase modulation can also provide an accurate range measurement. It is also possible to measure the range of a single target by comparing the phase difference between two or more CW frequencies. Range measurement with CW waveforms has been widely employed, as in aircraft radar altimeters and surveying instruments. Radial Velocity. From successive measurements of range the rate of change of range, or radial velocity, can be obtained. The doppler frequency shift of the echo signal from a moving target also provides a measure of radial velocity. However, the doppler frequency measurement in many pulse radars is highly ambiguous, thus reducing its utility as a direct measurement of radial velocity.

When it can be used, it is often preferred to successive range measurements since it can achieve a more accurate measurement in a shorter time. Any measurement of velocity, whether by the rate of change of range or by the doppler frequency shift, requires time. The longer the time of observation, the more accurate can be the measurement of velocity. (A longer observation time also can increase the signal-to-noise ratio, another factor that results in increased accuracy.) Although the doppler frequency shift is used in some applications to measure radial velocity (as, for example, in such diverse applications as the police speed meter and satellite surveillance radars), it is more widely employed as the basis for sorting moving targets from unwanted stationary clutter echoes, as in MTI, AMTI (airborne MTI), pulse doppler, and CW radars. Angular Direction. The direction of a target is determined by sensing the angle at which the returning wavefront arrives at the radar. This is usually accomplished with a directive antenna, i.e., one with a narrow radiation pattern. The direction in which the antenna points when the received signal is a maximum indicates the direction of the target. This, as well as other methods for measuring angle, assumes that the atmosphere does not perturb the straightline propagation of the electromagnetic waves. The direction of the incident waveform can also be determined by measuring the phase difference between two separated receiving antennas, as with an interferometer. Phase-comparison monopulse also is based on the phase measurement of signals in two separated antennas. The amplitude-comparison monopulse determines the angle of arrival by comparing the amplitudes of the signals received in two squinted beams generated by a single antenna. The accuracy of the angle of arrival depends on the extent of the antenna aperture. The wider the antenna, the narrower the beamwidth and the better the accuracy. The angle of arrival, or target direction, is not strictly a radar measurement (as are the range and radial velocity) if a radar measurement is defined as one obtained by comparing the reflected echo signal with the transmitted signal. The determination of angle basically involves only the one-way path. Nevertheless, the angle measurement is an integral part of most surveillance and tracking radars. Size. If the radar has sufficient resolution, it can provide a measurement of the target's extent, or size. Since many targets of interest have dimensions of several tens of meters, resolution must be several meters or less. Resolutions of this order can be readily obtained in the range coordinate. With conventional antennas and the usual radar ranges, the angular resolution is considerably poorer than what can be achieved in range. However, target resolution in the cross-range (angle) dimension can be obtained comparable with that obtained in range by the use of resolution in the doppler frequency domain. This requires that there be relative motion between the various parts of the target and the radar. It is the basis for the excellent cross-range resolution obtained in a SAR in which the relative motion between target and radar occurs because of the travel of the aircraft or spacecraft on which the radar is mounted. In an ISAR (inverse synthetic aperature radar) the relative motion is provided by the movement of the target. Shape. The size of a target is seldom of interest in itself, but its shape and its size are important for recognizing one type of target from another. A highresolution radar that obtains the profile of a target in both range and

cross range (as do SAR and ISAR) provides the size and shape of the target. The shape of an object can also be obtained by tomography, in which a twodimensional image of a three-dimensional object is reconstructed from the measurement of phase and amplitude, at different angles of observation. (The radar might rotate around the fixed object, or the radar can be fixed and the object rotated about its own axis.) Range resolution is not necessary with the coherent tomographic radar method. As mentioned earlier, comparison of the scattered fields for different polarizations provides a measure of target asymmetry. It should be possible to distinguish targets with different aspect ratios (shapes), as for example, rods from spheres and spheres from aircraft. The complete exploitation of polarization requires the measurement of phase, as well as amplitude of the echo signal at two orthogonal polarizations and a cross-polarization component. Such measurements (which define the polarization matrix) should allow in principle the recognition of one class of target from another, but in practice it is not easy to do. One characteristic of target shape is its surface roughness. This measurement can be of particular interest for echoes from the ground and the sea. Rough targets scatter the incident electromagnetic energy diffusely; smooth targets scatter specularly. By observing the nature of the backscatter as a function of the incident angle it should be possible to determine whether a surface is smooth or rough. Surface roughness is a relative measure and depends on the wavelength of the illuminating signal. A surface that appears rough at one wavelength might appear smooth when illuminated with longer-wavelength radiation. Thus another method for determining surface roughness is by varying the frequency of the illuminating radiation and observing the transition from specular to diffuse scatter. A direct method for determining roughness is to observe the scatter from the object with a resolution that can resolve the roughness scale. Other Target Measurements. Just as the radial velocity can be determined from the temporal doppler frequency shift, it is possible to measure the tangential (cross-range) component of velocity. This can be obtained from the analogous spatial doppler frequency shift that expands or compresses the apparent antenna radiation pattern (just as the radial component of velocity can expand or compress the time waveform of a radar signal reflected from a moving target to produce a temporal doppler frequency shift). A measurement of tangential velocity requires a wide-baseline antenna, such as an interferometer. The measurement of tangential velocity has not seen application because the required baseline is often too wide for practical purposes. It is also possible to note the change of a complex target's radial projection from the change of the received-signal amplitude with time. (A change in the radial projection of a target usually results in a change of the radar cross section.) Vibrations of the target, rotation of the propellers of an aircraft, or the rotation of a jet engine can induce distinctive modulation on the radar echo which can be detected by a spectral analysis of the radar echo signal.

7.4

RADARFREQUENCIES

There are no fundamental bounds on radar frequency. Any device that detects and locates a target by radiating electromagnetic energy and utilizes the echo scattered from a target can be classed as a radar, no matter what its frequency.

Radars have been operated at frequencies from a few megahertz to the ultraviolet region of the spectrum. The basic principles are the same at any frequency, but the practical implementation is widely different. In practice, most radars operate at microwave frequencies, but there are notable exceptions. Radar engineers use letter designations, as shown in Table 1.1, to denote the general frequency band at which a radar operates. These letter bands are universally used in radar. They have been officially accepted as a standard by the Institute of Electrical and Electronics Engineers (IEEE) and have been recognized by the U.S. Department of Defense. Attempts have been made in the past to subdivide the spectrum into other letter bands (as for waveguides and for ECM operations), but the letter bands in Table 1.1 are the only ones that should be used for radar. The original code letters (P, L, S, X, and K) were introduced during World War II for purposes of secrecy. After the need for secrecy no longer existed, these designations remained. Others were later added as new regions of the spectrum were utilized for radar application. (The nomenclature P band is no longer in use. It has been replaced with UHF.) Letter bands are a convenient way to designate the general frequency range of a radar. They serve an important purpose for military applications since they can describe the frequency band of operation without using the exact frequencies at which the radar operates. The exact frequencies over which a radar operates should be used in addition to or instead of the letter bands whenever proper to do so.

TABLE 1.1 Standard Radar-Frequency Letter-Band Nomenclature* Band designation

Nominal frequency range

HF VHF

3 MHz-30MHz 30 MHz-300MHz

UHF

300 MHz-IOOOMHz

L S

1000 MHz-2000MHz 2000 MHz-^OOOMHz

C X

4000 MHz-SOOOMHz 8000 MHz-12,000 MHz 12.0 GHz-ISGHz

K11

18 27 40 75

K Ka

V W mm

GHz-27GHz GHz-40GHz GHz-75GHz GHz-IlOGHz

110 GHz-300GHz

*From IEEE Standard 521-1984.

Specific frequency ranges for radar based on ITU assignments for Region 2 138 216 420 890 1215 2300 2700 5250 8500 13.4 15.7 24.05 33.4 59 76 92 126 144 231 238

MHz-144MHz MHz-225 MHz MHz-^SOMHz MHz-942MHz MHz-1400MHz MHz-2500MHz MHz-3700MHz MHz-5925MHz MHz-10,680 MHz GHz-14.0GHz GHz-17.7GHz GHz-24.25GHz GHz-36.0GHz GHz-64GHz GHz-Sl GHz GHz-IOOGHz GHz-142GHz GHz-149GHz GHz-235GHz GHz-248GHz

The International Telecommunications Union (ITU) assigns specific frequency bands for radiolocation (radar) use. These are listed in the third column of Table 1.1. They apply to ITU Region 2, which encompasses North and South America. Slight differences exist in the other two ITU regions. Although L band, for example, is shown in the second column of the table as extending from 1000 to 2000 MHz, in practice an L-band radar would be expected to be found somewhere between 1215 and 1400 MHz, the frequency band actually assigned by the ITU. Each frequency band has its own particular characteristics that make it better for certain applications than for others. In the following, the characteristics of the various portions of the electromagnetic spectrum at which radars have been or could be operated are described. The divisions between the frequency regions are not as sharp in practice as the precise nature of the nomenclature. HF (3 to 30 MHz). Although the first operational radars installed by the British just prior to World War II were in this frequency band, it has many disadvantages for radar applications. Large antennas are required to achieve narrow beam widths, the natural ambient noise level is high, the available bandwidths are narrow, and this portion of the electromagnetic spectrum is widely used and restrictively narrow. In addition, the long wavelength means that many targets of interest might be in the Rayleigh region, where the dimensions of the target are small compared with the wavelength; hence, the radar cross section of targets small in size compared with the (HF) wavelength might be lower than the cross section at microwave frequencies. The British used this frequency band, even though it had disadvantages, because it was the highest frequency at which reliable, readily available high-power components were then available. Ranges of 200 mi were obtained against aircraft. These were the radars that provided detection of hostile aircraft during the battle of Britain and were credited with allowing the limited British fighter resources to be effectively used against the attacking bomber aircraft. They did the job that was required. Electromagnetic waves at HF have the important property of being refracted by the ionosphere so as to return to the earth at ranges from about 500 to 2000 nmi, depending on the actual condition of the ionosphere. This allows the overthe-horizon detection of aircraft and other targets. The long over-the-horizon ranges that are possible make the HF region of the spectrum quite attractive for the radar observation of areas (such as the ocean) not practical with conventional microwave radar. VHF (30 to 300 MHz). Most of the early radars developed in the 1930s were in this frequency band. Radar technology at these frequencies represented a daring venture that pushed to the edge of technology known in the thirties. These early radars served quite well the needs of the time and firmly established the utility of radar. Like the HF region, the VHF (very high frequency) region is crowded, bandwidths are narrow, external noise can be high, and beamwidths are broad. However, the necessary technology is easier and cheaper to achieve than at microwave frequencies. High power and large antennas are readily practical. The stable transmitters and oscillators required for good MTI are easier to achieve than at higher frequencies, and there is relative freedom from the blind speeds that limit the effectiveness of MTI as the frequency is increased. Reflections from rain are not a problem. With horizontal polarization over a good reflecting sur-

face (such as the sea), the constructive interference between the direct wave and the wave reflected from the surface can result in a substantial increase in the maximum range against aircraft (almost twice the free-space range). However, a consequence of this increase in range due to constructive interference is that the accompanying destructive interference results in nulls in the coverage at other elevation angles and less energy at low angles. It is a good frequency for lowercost radars and for long-range radars such as those for the detection of satellites. It is also the frequency region where it is theoretically difficult to reduce the radar cross section of most types of airborne targets. In spite of its many attractive features, there have not been many applications of radar in this frequency range because its limitations do not always counterbalance its advantages. UHF (300 to 1000 MHz). Much of what has been said regarding VHF applies to UHF. However, natural external noise is much less of a problem, and beamwidths are narrower than at VHF. Weather effects usually are not a bother. With a suitably large antenna, it is a good frequency for reliable longrange surveillance radar, especially for extraterrestrial targets such as spacecraft and ballistic missiles. It is well suited for AEW (airborne early warning), e.g., airborne radar that uses AMTI for the detection of aircraft. Solid-state transmitters can generate high power at UHF as well as offer the advantages of maintainability and wide bandwidth. L Band (1.0 to 2.0 GHz). This is the preferred frequency band for landbased long-range air surveillance radars, such as the 200-nmi radars used for en route air traffic control [designated ARSR by the U.S. Federal Aviation Administration (FAA)]. It is possible to achieve good MTI performance at these frequencies and to obtain high power with narrow-beamwidth antennas. External noise is low. Military 3D radars can be found at L band, but they also are at S band. L band is also suitable for large radars that must detect extraterrestrial targets at long range. S Band (2.0 to 4.0 GHz). Air surveillance radars can be of long range at S band, but long range usually is more difficult to achieve than at lower frequencies. The blind speeds that occur with MTI radar are more numerous as the frequency increases, thus making MTI less capable. The echo from rain can significantly reduce the range of S-band radars. However, it is the preferred frequency band for long-range weather radars that must make accurate estimates of rainfall rate. It is also a good frequency for medium-range air surveillance applications such as the airport surveillance radar (ASR) found at air terminals. The narrower beamwidths at this frequency can provide good angular accuracy and resolution and make it easier to reduce the effects of hostile main-beam jamming that might be encountered by military radars. Military 3D radars and height finding radars are also found at this frequency because of the narrower elevation beamwidths that can be obtained at the higher frequencies. Long-range airborne air surveillance pulse doppler radars, such as AWACS (Airborne Warning and Control System) also operate in this band. Generally, frequencies lower than S band are well suited for air surveillance (detection and low-data-rate tracking of many aircraft within a large volume). Frequencies above S band are better for information gathering, such as high-datarate precision tracking and the recognition of individual targets. If a single fre-

quency must be used for both air surveillance and precision tracking, as in military air defense systems based on phased array multifunction radar, a suitable compromise might be S band. C Band (4.0 to 8.0 GHz). This band lies between the S and X bands and can be described as a compromise between the two. It is difficult, however, to achieve long-range air surveillance radars at this or higher frequencies. It is the frequency where one can find long-range precision instrumentation radars used for the accurate tracking of missiles. This frequency band has also been used for multifunction phased array air defense radars and for medium-range weather radars. X Band (8 to 12.5 GHz). This is a popular frequency band for military weapon control (tracking) radar and for civil applications. Shipboard navigation and piloting, weather avoidance, doppler navigation, and the police speed meter are all found at X band. Radars at this frequency are generally of convenient size and are thus of interest for applications where mobility and light weight are important and long range is not. It is advantageous for information gathering as in high-resolution radar because of the wide bandwidth that makes it possible to generate short pulses (or wideband pulse compression) and the narrow beam widths that can be obtained with relatively small-size antennas. An X-band radar may be small enough to hold in one's hand or as large as the MIT Lincoln Laboratory Haystack Hill radar with its 120-ft-diameter antenna and average radiated power of about 500 kW. Rain, however, can be debilitating to X-band radar. Ku, K, and Ka Bands (12.5 to 40 GHz). The original K-band radars developed during World War II were centered at a wavelength of 1.25 cm (24 GHz). This proved to be a poor choice since it is too close to the resonance wavelength of water vapor (22.2 GHz), where absorption can reduce the range of a radar. Later this band was subdivided into two bands on either side of the water-vapor absorption frequency. The lower frequency band was designated K11, and the upper band was designated Ka. These frequencies are of interest because of the wide bandwidths and the narrow beam widths that can be achieved with small apertures. However, it is difficult to generate and radiate high power. Limitations due to rain clutter and attenuation are increasingly difficult at the higher frequencies. Thus not many radar applications are found at these frequencies. However, the airport surface detection radar for the location and control of ground traffic at airports is at Ku band because of the need for high resolution. The disadvantages that characterize this band are not important in this particular application because of the short range. Millimeter Wavelengths (above 40 GHz). Although the wavelength of Ka band is about 8.5 millimeters (a frequency of 35 GHz), the technology of Kaband radar is more like that of microwaves than that of millimeter waves and is seldom considered to be representative of the millimeter-wave region. Millimeter-wave radar, therefore, is taken to be the frequency region from 40 to 300 GHz. The exceptionally high attenuation caused by the atmospheric oxygen absorption line at 60 GHz precludes serious applications in the vicinity of this frequency within the atmosphere. Therefore, the 94-GHz-frequency region (3mm wavelength) is generally what is thought of as a "typical" frequency representative of millimeter radar. The millimeter-wave region above 40 GHz has been further subdivided into

letter bands in the IEEE Standard, as shown in Table 1.1. Although there has been much interest in the millimeter portion of the electromagnetic spectrum, there have been no operational radars above Ka band. High-power sensitive receivers and low-loss transmission lines are difficult to obtain at millimeter wavelengths, but such problems are not basic. The major reason for the limited utility of this frequency region is the high attenuation that occurs even in the "clear" atmosphere. The so-called propagation window at 94 GHz is actually of greater attenuation than the attenuation at the water-vapor absorption line at 22.2 GHz. The millimeter-wave region is more likely to be of interest for operation in space, where there is no atmospheric attenuation. It might also be considered for shortrange applications within the atmosphere where the total attenuation is not large and can be tolerated. Laser Frequencies. Coherent power of reasonable magnitude and efficiency, along with narrow directive beams, can be obtained from lasers in the infrared, optical, and ultraviolet region of the spectrum. The good angular resolution and range resolution possible with lasers make them attractive for target information-gathering applications, such as precision ranging and imaging. They have had application in military range finders and in distance measurement for surveying. They have been considered for use from space for measuring profiles of atmospheric temperature, water vapor, and ozone, as well as measuring cloud height and tropospheric winds. Lasers are not suitable for wide-area surveillance because of their relatively small physical aperture area. A serious limitation of the laser is its inability to operate effectively in rain, clouds, or fog.

1.5

RADARNOMENCLATURE

Military electronic equipment, including radar, is designated by the Joint Electronics Type Designation System (JETDS), formerly known as the Joint ArmyNavy Nomenclature System (AN System), as described in Military Standard MIL-STD-196D. The letter portion of the designation consists of the letters AN, a slant bar, and three additional letters appropriately selected to indicate where the equipment is installed, the type of equipment, and the purpose of the equipment. Table 1.2 lists the equipment indicator letters. Following the three letters are a dash and a numeral. The numeral is assigned in sequence for that particular combination of letters. Thus the designation AN/SPS-49 is for a shipboard surveillance radar. The number 49 identifies the particular equipment and indicates it is the forty-ninth in the SPS category to which a JETDS designation has been assigned. A suffix letter (A, B, C, etc.) follows the original designation for each modification where interchangeability has been maintained. A change in the power input voltage, phase, or frequency is identified by the addition of the letters X, Y, or Z to the basic nomenclature. When the designation is followed by a dash, the letter T, and a number, the equipment is designed for training. The letter V in parentheses 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). Experimental and developmental systems sometimes are assigned special indicators enclosed in parentheses, immediately following the regular designation, to identify the development organization; for example, (XB) indicates the Naval Research Laboratory, and (XW) indicates the

Rome Air Development Center. Empty parentheses, commonly called ''bowlegs," are used for a developmental or series "generic" assignment. TABLE 1.2 JETDS Equipment Indicators* Installation (first letter)

Type of equipment (second letter)

Purpose (third letter)

A Piloted aircraft B Underwater mobile, submarine D Pilotless carrier F Fixed ground G General ground use K Amphibious M Ground, mobile P Portable S Water T Ground, transportable U General utility V Ground, vehicular W Water surface and underwater combination Z Piloted and pilotless airborne vehicle combination

A Invisible light, heat radiation C Carrier D Radiac (radioactive detection, indication, and computation devices) E Laser G Telegraph or teletype I Interphone and public address J Electromechanical or inertial wire-covered K Telemetering L Countermeasures M Meteorological N Sound in air P Radar Q Sonar and underwater sound R Radio S Special types, magnetic, etc., or combinations of types T Telephone (wire) V Visual and visible light W Armament (peculiar to armament, not otherwise covered) X Facsimile or television Y Data processing

A Auxiliary assembly B Bombing C Communications (receiving and transmitting) D Direction finder reconnaissance and/or surveillance E Ejection and/or release G Fire control or searchlight directing H Recording and/or reproducing (graphic meteorological) K Computing M Maintenance and/or test assemblies (including tools) N Navigational aids (including altimeters, beacons, compasses, racons, depth sounding, approach and landing) Q Special or combination of purposes R Receiving, passive detecting S Detecting and/or range and bearing, search T Transmitting W Automatic flight or remote control X Identification and recognition Y Surveillance (search, detect, and multipletarget tracking) and control (both fire control and air control)

*From Military Standard Joint Electronics Type Designation System, MIL-STD-196D, Jan. 19, 1985.

In the first column of Table 1.2, the installation letter M is used for equipment installed and operated from a vehicle whose sole function is to house and transport the equipment. The letter T is used for ground equipment that is normally moved from place to place and is not capable of operation while being trans-

ported. The letter V is used for equipment installed in a vehicle designed for functions other than carrying electronic equipment (such as a tank). The letter G is used for equipment capable of being used in two or more different types of ground installations. Equipment specifically designed to operate while being carried by a person is designated by the installation letter P. The letter U implies use in a combination of two or more general installation classes, such as ground, aircraft, and ship. The letter Z is for equipment in a combination of airborne installations, such as aircraft, drones, and guided missiles. The equipment indicator letter (second column of Table 1.2) that designates radar is the letter P; but it is also used for beacons which function with a radar, electronic recognition and identification systems, and pulse-type navigation equipment. Canadian, Australian, New Zealand, and United Kingdom electronic equipment can also be covered by the JETDS designations. For example, a block of numbers from 500 to 599 and 2500 to 2599 is reserved for Canadian use. The radars used in the air traffic control system of the FAA utilize the following nomenclature: ASR ARSR ASDE TDWR

airport surveillance radar air route surveillance radar airport surface detection equipment terminal doppler weather radar

The numeral following the letter designation indicates the particular radar model of that type. Weather radars in use by the U.S. National Weather Service employ the designation WSR, which is not associated with the JETDS nomenclature. The number following the designation indicates the year in which the radar was put into service. When a letter follows the number, it indicates the letter-band designation. Thus, the WSR-74C is a C-band weather radar introduced in 1974.

GENERAL BOOKS ON RADAR 1. Skolnik, M. L: "Introduction to Radar Systems," 2d ed., McGraw-Hill Book Co., New York, 1980. 2. Skolnik, M. L: "Radar Applications," IEEE Press, New York, 1988. 3. Barton, D. K.: "Modern Radar System Analysis," Artech House, Norwood, Mass., 1988. 4. Barton, D. K.: "Radar System Analysis," originally published by Prentice-Hall in 1964 and republished by Artech House, Norwood, Mass., in 1977. 5. Nathanson, F.: "Radar Signal Processing and the Environment," McGraw-Hill Book Co., New York, 1969. 6. Brookner, E.: "Aspects of Modern Radar," Artech House, Norwood, Mass., 1988. 7. Brookner, E.: "Radar Technology," Artech House, Norwood, Mass., 1977. 8. Levanon, N.: "Radar Principles," John Wiley & Sons, New York, 1988. 9. Eaves, J. L., and E. K. Reedy: "Principles of Modern Radar," Van Nostrand Reinhold Company, 1987.

10. Berkowitz, R.: "Modern Radar," John Wiley & Sons, New York, 1965. 11. Reintjes, J. F., and G. T. Coate: "Principles of Radar," McGraw-Hill Book Co., New York, 1952. 12. Ridenour, L. N.: "Radar System Engineering," McGraw-Hill Book Co., New York, 1947.

CHAPTER 2 PREDICTION OF RADAR RANGE Lamont V. Blake Electronics Consultant

2.1

INTRODUCTION

The basic physics governing the prediction of radar maximum detection range, for a specified target under free-space conditions with detection limited by thermal noise, has been well understood since the earliest days of radar. The term free space implies (in the present context) that a spherical region of space, centered at the radar and extending to considerably beyond the target, is empty except for the radar and the target. (Considerably as used here can be precisely defined for specific radars, but a general definition would be lengthy and not very useful.) It also implies that the only radar-frequency electromagnetic waves detectable within this region, other than those emanating from the radar itself, are from natural thermal and quasi-thermal noise sources, as described in Sec. 2.5. Although this condition is never fully realized, it is approximated for some radar situations. Under many non-free-space conditions and with radically nonthermal forms of background noise, the prediction problem is considerably more complicated. Complications not considered in early analyses also result from modification of the signal and noise relationship by the receiving-system circuitry (signal processing). In this chapter the free-space equation will be presented, basic signal processing will be discussed, and some of the most important non-free-space environments will be considered. The effect of some common nonthermal types of noise will be considered. Although it will not be feasible to consider all the possible types of radar situations, the methods to be described will indicate the general nature of the necessary procedures for environments and conditions not specifically treated here. Some of the specialized types of radar, for which special analyses are required, are described in later chapters of this handbook. Definitions. The radar range equation contains many parameters of the radar system and its environment, and some of them have definitions that are interdependent. As will be discussed in Sec. 2.3, some definitions contain an element of arbitrariness, and it is common for different authors to employ different definitions of some of the range-equation factors. Of course, when

generally accepted definitions do exist, they should be observed. But even more important, although some arbitrariness may be permissible for individual definitions, once a particular definition has been adopted for one of the rangeequation factors, it will be found that definition of one or more of the other factors is no longer arbitrary. As an example, for pulsed radar the definitions of pulse power and pulse length are highly arbitrary individually, but once a definition for either one of them has been adopted, the definition of the other is determined by the constraint that their product must equal the pulse energy. In this chapter, a set of definitions that are believed to conform to such rules of consistency, as well as to definitions adopted by standards organizations, will be presented. Conventions. Because of the wide variability of propagation-path and other range-equation factors, certain conventions are necessary for predicting range under standard conditions when specific values of those factors are not known. A convention is a generally accepted standard assumption, which may never be encountered exactly in practice but which falls within the range of conditions that will be encountered, preferably somewhere near the middle of the range. An example is the conventional geophysical assumption, for calculating certain earth environment effects that depend on the earth's curvature, that the earth is a perfect sphere of radius 6370 km. The importance of conventions is that they provide a common basis for comparison of competing radar systems. To the extent that they are fairly representative of typical conditions, they also allow prediction of a realistic detection range. Commonly accepted conventions will be used in this chapter, and where needed conventions do not exist, appropriate ones will be suggested. Range Prediction Philosophy. It is apparent from the foregoing discussion that a range prediction based on conventional assumptions will not necessarily be confirmed exactly by experimental results. This conclusion is further warranted by the statistical nature of the "noise" which is usually the limiting factor in the signal detection process. In other words, even if all the environmental factors were precisely known, a range prediction would not be likely to be verified exactly by the result of a single experiment. A statistical prediction refers to the average result of many trials. Therefore, radar range prediction is not an exact science. (In fact, the lesson of quantum mechanics seems to be that there is no such thing as an exact science in the strict sense.) Nevertheless, calculations to predict radar range are useful. However inexact they may be on an absolute basis, they permit meaningful comparisons of the expected relative performance of competing system designs, and they indicate the relative range performance change to be expected if the radar parameters or environmental conditions are changed. They are therefore a powerful tool for the system designer. The predicted range is a figure of merit for a proposed radar system. It is not necessarily a complete one, since other factors such as targetposition-measurement accuracy, data rate, reliability, serviceability, size, weight, and cost may also be important. Despite the inexactness of range predictions in the absolute sense, the error can be made small enough that the calculated range is a good indication of the performance to be expected under average environmental conditions. Section 2.10 is a more detailed discussion of prediction accuracy. Attempts to evaluate range prediction factors accurately, to better than perhaps 1 dB, are sometimes disparaged on the grounds that some factors are un-

likely to be known with accuracy in operational situations and that hence it is useless to seek better accuracy for any factor. Although there is some basis for this viewpoint, the overall accuracy will be unnecessarily degraded if the accuracy of all the factors in the equation is deliberately reduced. Therefore it is recommended that range predictions be based on as careful an evaluation of all the factors as is possible. A goal of 0.1 dB accuracy is perhaps reasonable, although admittedly it may be impossible to evaluate all the factors in the equation with that degree of precision. Historical Notes. Possibly the first comprehensive treatise on radar maximum-range prediction was that of Omberg and Norton,1 published first as a U.S. Army Signal Corps report in 1943. It presents a fairly detailed range equation and contains information on evaluating some of the more problematical factors, such as multipath interference and minimum detectable signal, within the limitations of the then-available knowledge. The signal detection process was assumed to be based on visual observation of a cathoderay-tube display. The antenna was assumed to "searchlight" the target. Statistical aspects of signal detection were not considered. D. O. North,2 in a classical report published with a military security classification in 1943, outlined the basic theory of a statistical treatment of signal detection. (This report was republished in Proceedings of the IEEE, but not until 1963.) He introduced the concepts that are now called probability of detection and false-alarm probability, and he clearly delineated the role of integration in the detection of pulse signals. This report also introduced the concept of the matched filter, a contribution for which it had achieved some recognition prior to 1963. But except for the matched-filter concept, its contributions to signal detection theory were virtually unrecognized by radar engineers generally until the report was republished 20 years after its first appearance. In a famous report3 first published in 1948 and republished in IRE Transactions on Information Theory in 1960, J. I. Marcum extensively developed the statistical theory of detection with the aid of machine computation, referencing North's report. He computed probabilities of detection as a function of a range parameter related to signal-to-noise ratio, for various numbers of pulses integrated and for various values of a false-alarm parameter which he designated false-alarm number. He employed this type of computation to study the effects of various amounts and kinds of integration, different detector (demodulator) types, losses incurred by "collapsing" one spatial coordinate on the radar display, and various other effects. His results are presented as curves for probability of detection as a function of the ratio of the actual range to that at which the signalto-noise ratio is unity, on the assumption that the received-signal power is inversely proportional to the fourth power of the range. Since this proportionality holds only for a target in free space, application of Marcum's results is sometimes complicated by this mode of presentation. Marcum considered only steady signals (target cross section not varying during the period of observation), and most of his results assume the use of a squarelaw detector. Robertson4 has published exceptionally detailed and useful steadysignal results applicable to the linear-rectifier detector, which is the type of detector almost universally used. (The square-law-detector results are also useful because they differ very little from the linear-detector results.) Swerling extended Marcum's work to include the case of fluctuating signals.5 His report was republished in IRE Transactions on Information Theory in 1960. Fehlner6 recomputed Marcum's and Swerling's results and presented them in the more useful form of

curves with the signal-to-noise power ratio as the abscissa. The fluctuating-signal problem has subsequently been further treated by Kaplan, 7 Schwartz,8 Heidbreder and Mitchell, 9 Bates,10 and others. Hall 11 published in 1956 a comprehensive paper on radar range prediction in which the concepts of probability of detection, false-alarm probability, the relative effects of predetection and postdetection integration, and the effects of scanning the antenna beam were considered. The range equation was formulated in terms of an ideal (matched-filter) utilization of the available received-signal power, with loss factors to account for departures from the ideal. Blake 12 published an updating of the subject in 1961, applying recent advances in system-noisc-tcmperature calculation, atmospheric absorption, plotting of coverage diagrams based on a realistic atmospheric refractive-index model, and multipath-interference calculation. This work was followed by Naval Research Laboratory (NRL) reports 13 and a book 14 in which further details were presented. Contributions to the subject of range prediction have also been made by many others, far too numerous to mention by name. Only the major contributions can be recognized in this brief history. Special mention should be made, however, of the many contributions in two volumes (13 and 24) of the MIT Radiation Laboratory Series, edited by Kerr15 and by Lawson and Uhlenbeck. 16 Much use is made in this chapter of results originally published in those volumes.

2.2

RANGEEQUATIONS

Radar Transmission Equation. The following equation, in the form given in Kerr,15 is called the transmission equation for monostatic radar (one in which the transmitter and receiver are colocated): P1.

-P, = where Pr Pt Gt Gr a X Ff Fr R

G1G^K2F2F2

(4^)3*4

W

= received-signal power (at antenna terminals) = transmitted-signal power (at antenna terminals) = transmitting-antenna power gain = receiving-antenna power gain = radar target cross section = wavelength = pattern propagation factor for transmitting-antenna-to-target path = pattern propagation factor for target-to-receiving-antenna path - radar-to-target distance (range)

This equation is not identical to Kerr's; he assumes that the same antenna is used for transmission and reception, so that GfGr becomes G2 and Ft2Fr2 becomes F4. The only factors in the equation that require explanation are the pattern propagation factors F1 and F1.. The factor Ft is defined as the ratio, at the target position, of the field strength E to that which would exist at the same distance from the radar in free space and in the antenna beam maximum-gain direction, E0. The factor F1. is analogously defined. These factors account for the possibility that the target is not in the beam maxima (G, and Gr are the gains in the

maxima) and for any propagation gain or loss that would not occur in free space. The most common of these effects are absorption, diffraction and shadowing, certain types of refraction effects, and multipath interference. For a target in free space and in the maxima of both the transmit and receive antenna patterns, Ft = Fr = 1. Detailed definitions of these and other rangeequation factors are given in Sees. 2.3 to 2.7. Maximum-Range Equation. Equation (2.1) is not a range equation as it stands, although it can be rewritten in the form

\w*wr L

(47T)3 Pr

\

This equation states that R is the range at which the received-echo power will be Pr if the transmitted power is Pt, target size a, and so forth. It becomes a maximum-range equation by the simple expedient of attaching subscripts to Pr and R so that they become Pr>min and /?max- That is, when the value of Pr in Eq. (2.2) is the minimum detectable value, the corresponding range is the maximum range of the radar. However, this is a very rudimentary maximum-range equation, of limited usefulness. A first step toward a more useful equation is replacement of Pr by a more readily evaluated expression. This is done by first defining the signal-to-noise power ratio: SIN = P1IPn

(2.3)

where Pn is the power level of the noise in the receiving system, which determines the minimum value of Pr that can be detected. This noise power, in turn, can be expressed in terms of a receiving-system noise temperature Ts\ Pn = kTsBn

(2.4)

where k is Boltzmann's constant (1.38 x 10~23 Ws/K) and Bn is the noise bandwidth of the receiver predetection filter, hertz. (These quantities are defined more completely in Sees. 2.3 and 2.5.17) Therefore, Pr = (SIN) KT8Bn

(2.5)

This expression can now be substituted for Pr in Eq. (2.2). A further convenient modification is to redefine Pt as the transmitter power at the terminals of the transmitter, rather than [as in Eq. (2.1)] the usually somewhat smaller power that is actually delivered to the antenna terminals because of loss in the transmission line. This redefinition is desirable because when radar system designers or manufacturers specify a transmitter power, the actual transmitter output power is usually meant. With this changed definition, Pt must be replaced by /VL,, where Lt is a loss factor defined as the ratio of the transmitter output power to the power actually delivered to the antenna. (Therefore, Lt ^ 1.) It will later prove convenient to introduce additional loss factors similarly related to other factors in the range equation. These loss factors are multiplicative;

that is, if there are, for example, three loss factors L1, L2, and L3, they can be represented by a single system loss factor L = L7L2L3. The resulting maximumrange equation is

max

*

. r pfifirfFW

r

[(410'(5/AOn^WJ

u>6;

The quantities (S/N)min and J5 as here defined are to be evaluated at the antenna terminals, and that fact detracts from the utility of this form of the equation. As thus defined, (S/N)min is not independent of Bn, and the dependence is difficult to take into account in this formulation. If that dependence were ignored, this equation would imply that /?max is an inverse function of Bn, i.e., if all the other range-equation factors were held constant, RmSLX could be made as large as desired simply by making Bn sufficiently small. This is well known to be untrue. To remedy this difficulty, several factors must be considered. It is convenient to do this in terms of a particular transmitted waveform. Pulse Radar Equation. Equation (2.6) does not specify the nature of the transmitted signal; it can be CW (continuous-wave), amplitude- or frequency-modulated, or pulsed. It is advantageous to modify this equation for the specific case of pulse radars and in so doing to remove the "bandwidth" difficulty encountered in using Eq. (2.6). Pulse radars are of course the most common type. As will be shown, although the equation thus modified will ostensibly be restricted to pulse radars, it can in fact be applied to other types of radar by appropriate reinterpretation of certain parameters. D. O. North 2 demonstrated that the detectable signal-to-noise ratio (Sl A0min will have its smallest possible value when the receiver bandwidth Bn has a particular (optimum) value and that this optimum value of Bn is inversely proportional to the pulse length T. This implies that an equation can be written with pulse length in the numerator rather than with bandwidth in the denominator. North also showed that signal detectability is improved by integrating successive signal and noise samples in the receiver and that the detectability is a function of the total integrated signal energy. (The integration process is discussed in Sec. 2.4.) Finally, he showed that when the receiver filter is matched to the pulse waveform, the ratio of the received-pulse energy to the noise power spectral density at the output of the receiver filter is maximized and is equal to the signal-to-noise power ratio at the antenna terminals. The term matched in this context means, partially, that the filter bandwidth is optimum. The full meaning is that the filter transfer function is equal to the complex conjugate of the pulse spectrum. Detectability Factor. An equation based on these facts can be derived by utilizing a parameter called detectability factor, defined by the Institute of Electrical and Electronics Engineers (IEEE)18 as follows: 44 In pulsed radar, the ratio of single-pulse signal energy to noise power per unit bandwidth that provides stated probabilities of detection and false alarm, measured in the intermediate-frequency amplifier and using an intermediate-frequency filter matched to the single pulse, followed by optimum video integration." Deferring

for the moment discussion of the meaning of some aspects of this definition, it can be expressed mathematically as follows:* D0 = EJN* = PtT/kTs

(2.7)

where D0 is the detectability factor, Er is the received-pulse energy, and N0 is the noise power per unit bandwidth, both measured at the output of the receiver filter (i.e., at the demodulator input terminals). The next step in this reformulation of the range equation is to define a bandwidth correction factor CB, to allow for the possibility that the receiver filter bandwidth Bn may not be optimum. This factor is defined by the following relationship: (5/AOmuA. =tf/AOminCoA,optQ = AA., optQ

(2.8)

where Bn^opt is the optimum value of Bn. The factor CB has been named the bandwidth correction factor because it was originally defined in terms of bandwidth optimization, but in actuality it is a filter mismatch factor, in the North matched-filter sense. As Eq. (2.8) implies, CB^\. Evaluation of CB is discussed in Sec. 2.3. The quantity (S/N)min(0) in Eq. (2.8) is the optimum-bandwidth (matched-filter) value of (S/N)min, which North showed to be equal to D0. It is this fact that allows the range equation to be written, as desired, in terms of the signal-to-noise ratio at the detector input terminals (filter output) rather than the ratio at the antenna terminals. North deduced that Bnopi = I/T exactly. As will be discussed later, some radar detection experiments with human observers have subsequently suggested that the constant of proportionality may not be exactly unity. However, North's analysis is theoretically correct for pulses of rectangular shape and for the definition to be given in Sec. 2.3 for the noise bandwidth Bn. For pulses of other shapes the pulse-length-bandwidth relationship is subject to the particular definition used for the pulse length. That definition is not an issue, of course, when the pulse shape is rectangular. Based on that result, the range equation can be written with pulse length in the numerator by means of the following equivalence, in terms of the parameters of Eq. (2.8): (SIN)n^nBn = AAA

(2.9)

The expression of the left-hand side of Eq. (2.9), where it occurs in the denominator of Eq. (2.6), can now be replaced by the expression of the right-hand side. The result is the desired pulse radar form of the range equation: D ™

R

=

IP/rGfiptfFfF*}™ _£ i L i L_ [ (4^kT1D0C8L \

n 1 (Yl '

(2 10)

*In some of the literature it is stated that the matched-filter output signal-to-noise ratio is 2EJN0. That statement is based on defining peak signal power as the instantaneous value occurring not only at the peak of the output-pulse waveform but also at the peak of an RF cycle, where the instantaneous power is theoretically twice the average power. North's definition, based on the signal power averaged over an RF cycle, is consistent with the definition of noise power as the average over both the RF cycles and the random noise fluctuations.

A primary advantage of this formulation of the equation is that standard curves for the parameter D0, as a function of the number of pulses integrated, are available, with the probabilities of detection and false alarm as parameters (Sec. 2.4). Calculation of these curves is necessarily done in terms of D0, the signalto-noise ratio at the demodulator input terminals. The emphasis of this equation on the significance of the pulse energy (the product PtT in the numerator) is valuable to the system designer. It also provides a simple answer to the question of which pulse length to use in the range equation when the radar employs pulse compression, in which a coded pulse waveform of relatively long duration is transmitted and then "compressed" to a short pulse upon reception. The correct answer is deduced from the fact that the product P,T must equal the transmitted pulse energy. Therefore if the pulse power Pt is the power of the long (uncompressed) transmitted pulse, then T must be the duration of that pulse. A further advantage of this form of the equation, or more specifically of the definition of the detectability factor, is the indicated dependence of the radar detection range on the integration of successive pulses, if any, that takes place in the receiving system. Integration is discussed in Sec. 2.4. Finally, as was mentioned earlier, this formulation of the range equation, although derived specifically in terms of pulse radar parameters, can be applied to CW radars and to radars that utilize forms of signal modulation other than pulses. Its application to these other radar types is accomplished by redefining the parameters T and D0. Details of this procedure are presented in Ref. 14, Chaps. 2 and 9. Probabilistic Notation. It has been mentioned (Sec. 2.1) that the radar signal detection process is basically probabilistic or statistical in nature. This results from the nature of the noise voltage that is always present in the receiver circuits. This voltage is randomly varying or fluctuating, and when it is intermixed with a radar echo signal, it becomes impossible to tell with certainty whether a momentary increase of the receiver output is due to a signal or to a chance noise fluctuation. However, it is possible to define probabilities for these two possibilities and to discuss the detection process in terms of them in a quantitative manner. The probability that the signal, when present, will be detected is called the probability of detection, Pd, and the probability that a noise fluctuation will be mistaken for a signal is called the false-alarm probability, Pfa. The notations /?max, Pr,min> and (S/N)min can then be replaced by more precise notation, using subscripts to denote the applicable values of Pd and Pfa. However, the/a subscript is ordinarily suppressed, though implied. Thus R5Q can denote the range for 0.5 (i.e., 50 percent) probability of detection and some separately specified false-alarm probability. If the target cross section a fluctuates, this fluctuation will alter the signalplus-noise statistics. As mentioned in Sec. 2.1, this problem has been analyzed by Swerling5 and others.6"10 Curves have been calculated that allow determining the appropriate value OfD 0 for the fluctuating-signal case, for various probabilities of detection and false alarm (Sec. 2.4). Automatic Detection. Detection* is said to be automatic if the decision concerning the presence or absence of a received signal is made by a purely *A note on various meanings of the words detect, detector, and detection is desirable here. In radio usage, a detector has come to mean either a frequency converter (e.g., a superheterodyne first detector) or a demodulator (often the "second detector" of a superheterodyne receiver, which is usually a linear rectifier). Then, detection means the waveform modification produced by such a device. An automatic

physical device, without direct human intervention. Such a device, described by North,2 establishes a threshold voltage level (for example, by means of a biased diode). If the processed (e.g., integrated) receiver output exceeds the threshold (as evidenced by diode current flow), some mechanism is actuated to indicate this fact in an unequivocal fashion. The mechanism could be the lighting of a light, the ringing of a bell, or more generally the setting of a bit to 1 in a binary data channel wherein a O corresponds to no signal. Various additional consequences may then automatically ensue. The analysis of radar detection can thus be regarded as a problem in statistical decision theory. Bistatic Radar Equation. The foregoing equations assume that the transmitting and receiving antennas are at the same location (monostatic radar). A bistatic radar (Chap. 25) is one for which the two antennas are widely separated, so that the distance and/or the direction from the transmitting antenna to the target are not necessarily the same as the distance and/or direction from the receiving antenna to the target. Moreover, since the signal reflected from the target to the receiving antenna is not directly backscattered, as it is for monostatic radar, the target cross section is not usually the same (for a given target viewed in a given aspect by the transmitting antenna). A bistatic radar cross section ab is defined to apply for this situation. The symbol a in the preceding equations implies a monostatic cross section. Range equations for bistatic radar are obtained from the foregoing monostatic equations by replacing the range R and the target cross section a by the corresponding bistatic quantities. The bistatic equivalent of R is\/RtRn where Rt is the distance from the transmitting antenna to the target and Rr is the distance from the target to the receiving antenna. Equations in Practical Units. The equations that have been given are valid when a consistent system of units is used, such as the rationalized meterkilogram-second (mks) system. In many applications, however, it is convenient or necessary to employ "mixed" units. Moreover, it is usually more convenient to express the wavelength X in terms of the equivalent frequency in megahertz. It is also desirable to combine all the numerical factors and the various unit-conversion factors into a single numerical constant. For a particular system of mixed units, the following equation is obtained from Eq. (2.10): P - 1?0 ?[/>/(kW)TM<sfi^r^/2^r211/4 *--129'2[ /MHz2W,L J

r? - n (2J1)

The subscript notation Rm&x is now meant to imply the range corresponding to specified detection and false-alarm probabilities. For this equation, the range is given in international nautical miles. (One international nautical mile is exactly 1852 m.) The target cross section a is in square meters, transmitter power Pt in kilowatts, pulse length T in microseconds, frequency/in megahertz, and system noise temperature T5 in kelvins. (All other quantities are dimensionless.) If the range is desired in units other than nautical miles (all other units remaining the same), in place of the factor 129.2 the following numerical constants should be used in Eq. (2.11): detector, however, is a decision-making device—for example, a device that replaces the human observer of a cathode-ray-tube display—and in that context detection is the making of a positive decision. In this chapter the meaning will ordinarily be evident from the context. Where confusion might otherwise result, the term detection-decision device may be used to denote an automatic detector.

Range units

Constant, Eq. (2.11)

148.7 239.3 261.7 785.0

Statute miles Kilometers Thousands of yards Thousands of feet

A decibel-logarithmic form of the range equation is sometimes useful. An equation of that type, corresponding to Eq. (2.11), is readily obtained as the algebraic sum of the logarithms of the terms of that equation (with appropriate multipliers for the decibel format and for exponents), since it involves only multiplication, division, and exponentiation.

2.3 DEFINITION AND EVALUATION OF RANGE FACTORS There is an element of arbitrariness in the definition of most of the factors of the radar range equation, and for some of them more than one definition is in common use. Since the definitions in these cases are arbitrary, one definition is in principle as good as another. However, once a definition has been chosen for one factor, there is no longer freedom of choice for one or more of the others. The factors are interdependent, and mutual compatibility is essential. A set of definitions that are believed to be mutually compatible will be given here. Also, information needed for evaluating these factors will be given insofar as is practicable. Certain range-equation factors that present special problems will be considered at greater length in subsequent sections of the chapter. Transmitter Power and Pulse Length. The radar transmission equation, from which all the subsequent range equations are derived, is an equation for the dimensionless ratio Pt/Pr. Consequently, the most basic requirement on the definition of Pt is that it agree with the definition of Pr. For a CW radar, the power (averaged over an RF cycle) is constant, and there is no definition problem. For a pulse radar, both Pt and Pr are usually defined as the pulse power, which is the average power during the pulse. More precisely, -T 12

Pt = \fw(t)dt

(2.12)

where W(t) is the instantaneous power (a function of time, t). The definition of W(O, however, excludes "spikes," "tails," and any other transients that are not useful for radar detection. The time interval T is the pulse period (= 1/PRF, where PRF is the pulse repetition frequency in pulses per second). Because of the exclusion of nonuseful portions of the waveform (as it exists at the transmitter output terminals), Pt as thus defined may be called the effective pulse power. It is often referred to as the peak power. However, peak power more properly signifies the power level at the peak of the pulse waveform (averaged over an RF cycle), and pulse power is more appropriate.

In the transmission equation, Eq. (2.1), Pt and Pr are the transmitted and received powers at the antenna terminals. As was mentioned in Sec. 2.2, Pt is now defined at the transmitter output terminals, and any loss between these terminals and the antenna input terminals must be expressed as a loss factor Lt. The pulse power P1 and the pulse length T must be defined so that their product is the pulse energy. Any definition of T will produce this result if the same definition is used in Eq. (2.12). The customary definition, and the one recommended here, is the time duration between the half-power points of the envelope of the RF pulse (0.707-V points). For some purposes, such as analyzing the range resolution or accuracy, this arbitrary definition of the pulse length is not permissible. But the half-power definition is customary and acceptable for use in the range equation. The range equation can be written with the product P/r replaced by the pulse energy Ef. The more detailed notation is used here because, for ordinary pulse radars, Pt and T are usually given explicitly and Et is not. However, the use of E1 in the equation does have the advantage of avoiding the problems of defining P1 and T, and it is especially useful when complicated waveforms are transmitted. If coherent integration for a fixed integration time is assumed, the equation can also be written with the transmitted average power in the numerator. For simple pulse radars, the average power is the product of pulse power, pulse length, and pulse repetition frequency. In this average-power formulation, the average power Pt is multiplied by the integration time tf (assumed to be long compared with the interpulse period) to obtain the transmitted energy. Then the value of D0 used is that which would apply if detection were based on observation of a single pulse. (See Sec. 2.4, Fig. 2.3.) The average-power formulation is especially useful for CW or pulse doppler radars. Antenna Gain, Efficiency, and Loss Factor. The gains Gt and Gr are defined as the power gains of the antennas in the maximum-gain direction. If a target of interest is at an elevation angle not in the beam maxima, that fact is accounted for by the pattern propagation factors Ft and Fr, discussed in Sec. 2.6. The maximum power gain of an antenna is equal to its directivity (maximum directive gain) multiplied by its radiation efficiency.19 The directivity D is defined in terms of the electric-field-strength pattern £(6,4>) by the expression 4

D = 2, ,

^"""

(2.13)

2

J j£ (6,<|>) sin 6 d9 d$ o o where 6 and are the angles of a spherical-coordinate system whose origin is at the antenna and £ max is the value of £(0,4>) in the maximum-gain direction. The radiation efficiency of the transmitting antenna is the ratio of the power input at the antenna terminals to the power actually radiated (including minorlobe radiation). In terms of the receiving antenna, the equivalent quantity is the ratio of the total signal power extracted from the incident field by the antenna, with a matched-load impedance, to the signal power actually delivered to a matched load. The reciprocal of the radiation efficiency is the antenna loss factor L,,, which plays a part in the calculation of antenna noise temperature (Sec. 2.5). Measured antenna gains are usually power gains, whereas gains calculated

from pattern measurements or theory are directive gains. If the antenna gain figures supplied for use in the range equations of this chapter are of the latter type, they must be converted to power gains by dividing them by the appropriate loss factor. For many simple antennas the ohmic losses are negligible, and in those cases the power gain and the directive gain are virtually equal. However, this is by no means a safe assumption in the absence of specific knowledge. Array antennas in particular are likely to have significant ohmic losses in waveguides or coaxial lines used to distribute the power among the radiating elements. If separate transmitting and receiving antennas are used and if their maximum gains occur at different elevation angles (this is a possible though not a common situation), appropriate correction can be made by means of the pattern factors /,(8) and/r(6), contained in the pattern propagation factors Ft and Fr (Sec. 2.6). Antenna Beamwidth. This property of the antenna does not appear explicitly in the range equations, but it affects the range calculation through its effect on the number of pulses integrated when the antenna scans. The conventional definition is the angular width of the beam between the halfpower points of the pattern. Pattern is used here in the usual antenna sense, for one-way transmission. It is not the two-way pattern of the radar echo signal from a stationary target as the antenna scans past it. If a radar target, as viewed from the radar antenna, has an angular dimension that is appreciable compared with the beamwidth, the target cross section becomes a function of the beamwidth (see Sec. 2.8). For computing an effective value of a in this case, in principle a special definition of beamwidth is needed (Ref. 15, p. 483). For practical work, however, the error that results from using the half-power beamwidth in this application is usually acceptable. Target Cross Section. The definition of radar target cross section that applies for use in the foregoing radar range equations is given in Chap. 11, and the reader is referred to that chapter for a detailed discussion of the subject. Here mention will be made of a few aspects of the definitions that are of particular significance to the range prediction problem. Targets can be classified as either point targets or distributed targets. A point target is one for which (1) the maximum transverse separation of significant scattering elements is small compared with the length of the arc intercepted by the antenna beam at the target range and (2) the maximum radial separation of scattering elements is small compared with the range extent of the pulse. At distance R from the antenna, the transverse dimension of the antenna beam is R times the angular beamwidth in radians. The range extent of the pulse is cr/2, where c is the speed of wave propagation in free space, 3 x 105 km/s, and T is the pulse duration in seconds. Most of the targets for which range prediction is ordinarily of interest are point targets, e.g., aircraft at appreciable distances from the radar. However, range predictions for distributed targets are sometimes wanted. The moon, for example, is a distributed target if the radar beamwidth is comparable to or less than 0.5° or if the pulse length is less than about 11.6 ms. A rainstorm is another example of a distributed target. Often, distributed targets are of interest because echoes from them (called radar clutter) tend to mask the echoes from the point targets whose detection is desired (see Sec. 2.8). Echoes from rain may be regarded as clutter when they interfere with detection of aircraft or other point targets, but they are themselves the signals of prime interest for weather radar.

The radar range equation is derived initially for a point target, and when that equation or the subsequent equations derived from it are used to predict the detection range for distributed targets, complications arise. In many cases, however, the point-target equation can be used for distributed targets by employing a suitable "effective" value of a (Sec. 2.8). The cross section of any nonspherical target is a function of the aspect angle from which it is viewed by the radar. It may also be a function of the polarization of the radar electromagnetic field. Therefore, in order to be wholly meaningful, a radar range prediction for a specific target, such as an aircraft, must stipulate the target aspect angle assumed and the polarization employed. Ordinarily, the nose aspect of an aircraft (approaching target) is of principal interest. The commonly used polarizations are horizontal, vertical, and circular. Tabulations of radar cross-section measurements of aircraft sometimes give nose, tail, and broadside values. If the values are obtained from dynamic (moving-target) measurements, they are usually time averages of fluctuating values; otherwise they are static values for a particular aspect. Since the instantaneous cross section of a target is a function of the aspect angle, targets that are in motion involving random changes of aspect have cross sections that fluctuate randomly with time, as was mentioned in Sec. 2.2. This fluctuation must be taken into account in the calculation of probability of detection, as will be discussed in Sec. 2.4. When a fluctuates, the value to be used in the range equation as formulated here is the time average. Because of the wide variation of cross-section values of real targets, the range performance of a radar system is often stated for a particular target-cross-section assumption. A favorite value for many applications is 1 m2. This represents the approximate cross section of a small aircraft, nose aspect, although the range for different "small" aircraft may be from less than 0.1 m2 to more than 10 m2. Radars are often performance-tested by using a metallic sphere, sometimes carried aloft by a free balloon, as the target because the cross section of a sphere can be accurately calculated and it does not vary with the aspect angle or the polarization. A special definition problem arises when the target is large enough to be nonuniformly illuminated by the radar. A ship, for example, may be tall enough so that the pattern propagation factor F has different values from the waterline to the top of the mast. This matter is discussed in Ref. 15, p. 472 ff. Wavelength (Frequency). There is ordinarily no problem in definition or evaluation (measurement) of the frequency to be used in the radar range equation. However, some radars may use a very large transmission bandwidth, or they may change frequency on a pulse-to-pulse basis, so that a question can exist as to the frequency value to be used for predicting range. Also, the presence of/(or X) in the range equations makes it clear that the range can be frequency-dependent, but the exact nature of the frequency dependence is not always obvious because other factors in the range equation are sometimes implicitly frequency-dependent. Therefore an analysis of how the range depends on frequency can be rather complicated, and the answer depends partly on what factors are regarded as frequency-dependent and which ones are held constant as the frequency is changed. For example, most antennas have gain that is strongly frequency-dependent, but some antenna types are virtually frequency-independent over a fairly wide frequency band.

Bandwidth and Matching Factors. The frequency-response width (bandwidth) of the receiver selective circuits appears explicitly in Eqs. (2.4) to (2.6), but it is an implicit factor in the other range equations as well, through the factor CB. From Eq. (2.4) it is clear that Bn directly affects the noise level in the receiver output. In general it also affects the signal, but not necessarily in the same manner as the noise is affected, because the signal spectrum is not usually uniform. There is a value of Bn that optimizes the output signal-to-noise ratio, as indicated by Eq. (2.8), and this optimum bandwidth is inversely proportional to the pulse length T. (This statement applies to pulse compression radars as well as to others if T is, in this context, the compressed pulse length, since it is the compressed pulse that is amplified in the receiver. However, as has been emphasized in Sec. 2.2, in the numerator of the range equation the uncompressed pulse length must be used along with the actual radiated pulse power, P1.) Since the range equation (2.6) and those subsequently derived from it incorporate the assumption of Eq. (2.4) (namely, that the noise output power of the receiver is equal to /CT^nG0), the definition of Bn—the noise bandwidth—must conform to that assumption. The resulting correct definition, due to North,20 is

X B

» = (k!G(fW

<2-14)

where G0 is the gain at the nominal radar frequency and G(/) is the frequency-power gain characteristic of the receiver predetection circuits, from antenna to detector. The definition specifies G(/) to be the response characteristic of the predetection circuits only. That is because for maximum postdetection signal-tonoise ratio the video bandwidth should be equal to at least half of the predetection bandwidth; and if it is of this width or wider, its exact width has little or no effect on signal detectability (Ref. 16, p. 211 ff.). It is common practice to describe receiver bandwidth as the value between half-power points of the frequency-response curve. Fortunately, this value is usually very close to the true noise bandwidth, although the exact relationship of the two bandwidths depends on the particular shape of the frequency-response curve (Ref. 16, p. 177). The bandwidth correction factor C3 in Eqs. (2.10) and (2.11) accounts for the fact that if Bn is not the optimum value, a value of signal-to-noise ratio larger than the optimum-bandwidth value D0 is required. Therefore CB ^ 1. From data obtained in signal detection experiments during World War II at the Naval Research Laboratory, Haeff 21 devised the following empirical expression:

c

"£['*£r

where Bn is the noise bandwidth, T is the pulse length, and a is the product of T and Bn>opl (optimum bandwidth). Figure 2.1 is a plot of Haeff s equation. Actually, Haeff deduced from his experiments, as did North from theoretical analysis, that Bnj0pl = I/T; that is, a = 1, for rectangular-shaped pulses. How-

C 8 (DECIBELS)

B/B0pt FIG. 2.1 Bandwidth correction factor CB as a function of bandwidth Bn relative to optimum bandwidth £opt; plotted from Haeffs empirical formula, Eq. (2.15).

ever, on the basis of experiments at the Massachusetts Institute of Technology (MIT) Radiation Laboratory conducted somewhat later (also with rectangular pulses), it was concluded (Ref. 16, p. 202) that a = 1.2 for detection of signals by visual observation of cathode-ray-tube displays. Figure 2.2 is a plot of the Radiation Laboratory experimental results. The value 1.2 has subsequently been widely used for determining #n,opt m radar design and for computing CB in radar range prediction.11'12 However, North* has suggested that the a = 1.2 figure may be based on a misinterpretation of the Radiation Laboratory data. Also, it has been notedt that the number of actual data points in Fig. 2.2 may be too few on which to base a good estimate of the optimum. Consequently, it is possible that the value of a for human observation of visual displays is much closer to 1 than was deduced by Lawson and Uhlenbeck. Fortunately, the minima of the curves (Fig. 2.2) are very broad and flat, and therefore the exact value of a does not make much difference for the usual range of values of .BnT. The interpretation of CB as a factor that accounts only for nonoptimum width of the predetection filter is permissible for simple pulse shapes and approximate results, but in principle it must also account for the complete amplitude-phase characteristic of the filter: its departure from a matched-filter characteristic. The *In a private communication to the author in 1963. tBy M. I. Skolnik, editor of this handbook, in his review of this chapter.

DETECTABILITY FACTOR DQOO) (DECIBELS)

BT FIG. 2.2 Experimental results showing the effect of bandwidth (parameter BT) on 90 percent probability detectability factor D^90), with pulse repetition frequency (PRF) as a parameter. The experiments were performed during World War II at the MIT Radiation Laboratory. (From Ref. 15, Fig. 8.7.)

matched-filter condition as stated by North2 is that the receiver transfer characteristic must be the complex conjugate of the spectrum of the echo at the receiving-antenna terminals.

2.4 MINIMUM DETECTABLE SIGNAL-TO-NOISE RATIO In Sec. 2.3, factors in the range equations were defined, and some information on how to evaluate them in typical cases was given. However, several very important factors were not covered because they are of sufficient importance to warrant more extensive treatment in separate sections. In this section and in Sees. 2.5 to 2.7, these additional factors will be discussed. The quantities Pr,min, (S/N)min9 and D0 are all related, as indicated in the development of Eqs. (2.3) to (2.9). Determination of the appropriate numbers to use for these quantities in their respective equations is a basic problem of radar range prediction. As will be seen, one of the problems is to define the meaning of detectable.

Integration of Signals. Detection of radar echo signals is usually (with some exceptions) accomplished by first integrating (e.g., adding) a sequence of received pulses and basing the detection decision on the resultant integrated signal voltage. Integrators that perform this operation will of course necessarily add noise as well as signals, but it is demonstrable that the ratio of the added signal voltages to the added noise voltages will be greater than the preintegration signal-to-noise ratio. Stated otherwise, the detectable signal-to-noise ratio evaluated ahead of an integrator will be smaller than when detection is performed by using single pulses. There are many different methods of accomplishing integration. One method is the use of a feedback-loop delay line with a delay time equal to the interpulse period, so that signals (and noise) separated by exactly one pulse period will be directly added. Integration also occurs for visual detection by human radar operators if the phosphor of the cathode-ray-tube radar display (such as a PPI) has sufficient luminous persistence. In recent years, integration methods based on digital circuitry have become practical and are now perhaps the method of choice in many if not most cases. The benefit of integration is a function of the number of pulses integrated. If integration is performed in the predetection stages of a receiver, ideally the addition of M equal-amplitude phase-coherent signal pulses will result in an output (integrated) pulse of voltage M times the single-pulse voltage. Adding M noise pulses, however, will result in an integrated noise pulse whose rms voltage is only VM times as great as that of a single noise pulse if (as is true of ordinary receiver noise and many other types of noise) the added noise pulses are not phase-coherent. Therefore the signal-to-noise voltage-ratio improvement is, ideally, MIvM = VM. Consequently the signal-to-noise power-ratio improvement, and the reduction of the single-pulse minimum-detectable signal-to-noise power ratio, is equal to M. Integration can also be performed after detection. In fact postdetection integration is used more commonly than is predetection integration, for reasons that will be explained, but the analysis of the resulting improvement is then much more complicated. After detection, the signals and the noise cannot be regarded as totally separate entities; the nonlinear process of detection produces an inseparable combination of signal and noise, so that one must then consider the comparison of signal-plus-noise to noise. As will be shown, the improvement that results from this type of integration is usually not as great as with ideal predetection integration of the same number of pulses. Nevertheless, postdetection integration produces worthwhile improvement. Moreover, "ideal" predetection integration is virtually unachievable because the echo fluctuation from most moving targets severely reduces the degree of phase coherence of successive received pulses. With rapidly fluctuating signals, in fact, postdetection integration will provide greater detectability improvement than does predetection integration, as discussed later in this section under the heading "Predetection Integration." Number of Pulses Integrated. The number of pulses integrated is usually determined by the scanning speed of the antenna beam in conjunction with the antenna beamwidth in the plane of the scanning. The following equation can be used for calculating the number of pulses received between half-power-beamwidth points for an azimuth-scanning radar: M=

_^ 6 RPM cos 6e

(2.16)

where (fr is the azimuth beam width, PRF is the radar pulse repetition frequency in hertz, RPM is the azimuthal scan rate in revolutions per minute, and Qe is the target elevation angle. This formula strictly applies only if <j>/cos Qe, the "effective" azimuth beamwidth, is less than 360°. (At values of 6e for which <|>/cos 6e is greater than 360°, the number of pulses computed from this formula will obviously be meaningless. Practically, it is suggested that it be applied only for elevation angles such that <|>/cos Qe is less than about 90°.) This formula is based on the properties of spherical geometry. The formula also assumes that the beam maximum is tilted upward at the angle 6e, but it can be applied with negligible error if Qe is only approximately equal to the beam tilt angle. The formula for the number of pulses within the half-power beamwidth for an azimuth- and elevation-scanning radar (which can be applied with minor modification to a radar scanning simultaneously in any two orthogonal angular directions) is M=

*JP 6OVyRPM cos O6

(2.17)

where <j> and B are the azimuth (horizontal-plane) and elevation (vertical-plane) beam widths in degrees, Qe is the target elevation angle, o>v is the vertical scanning speed in degrees per second, and tv is the vertical-scan period in seconds (including dead time if any). This formula should also be restricted to elevation angles for which <|>/cos Qe is less than about 90°. Here M is a function of the target elevation angle not only explicitly but also implicitly in that o>v may be a function of 6e. Some modern radars, especially those capable of scanning by electronic means— i.e., without mechanical motion of the antenna—employ step scanning. In this method, the antenna beam is pointed in a fixed direction while a programmed number of pulses is radiated in that direction. Then the beam is shifted to a new direction, and the process is repeated. The number of pulses integrated in this scanning method is thus determined by the programming and not by the beamwidth. Also, the integrated pulses are then all of the same amplitude (except for the effect of target fluctuation), and so there is no pattern loss of the type described in Sec. 2.7. There is, however, a statistical loss if the target direction and the antenna beam maximum do not always coincide when the pulses are radiated. Evaluation of Probabilities. As was mentioned in Sec. 2.2, if a threshold device is employed to make a decision as to the presence or absence of a signal in a background of noise, its performance can be described in terms of two probabilities: (1) the probability of detection, Pd9 and (2) the false-alarm probability, Pfa. The threshold device is characterized by a value of receiver output voltage Vt (the threshold, equivalent to Marcum's3 bias level), which, if exceeded, results in the decision report that a signal is present. If the threshold voltage is not exceeded at a particular instant, the detector reports "no signal." There is always a definite probability that the threshold voltage will be exceeded when in fact no signal is present. The statistics of thermal random-noise voltage are such that there is a usually small but nonzero probability that it can attain a value at least equal to the saturation level of the receiver. (In the mathematical theory of thermal noise, there is a nonzero probability that it can attain any finite value, however large.) The probability that Vt is exceeded when no signal is present is the false-alarm probability. It is calculated from the equation

Pfa = fPnMdV

(2.18)

Vt

where pn(v) is the probability density function of the noise. The probability of detection is given by the same expression, with the probability density function that of the signal-noise combination (usually called signal-plus-noise, but the 4 'addition" is not necessarily linear):

OC Pd = J Psn(v)dv

(2.19)

The signal-plus-noise probability density function psn(v) depends on the signalto-noise ratio as well as on the signal and noise statistics. Also, both pn and psn are functions of the rectification law of the receiver detector and of any postdetection processing or circuit nonlinearities. Primarily, however, psn and therefore the probability of detection are functions of the signal-to*noise ratio. From Eq. (2.19), the variation of Pd with SIN can be determined. As would logically be assumed, it is a monotonic-increasing function of SIN for a given value of Vt. Similarly, the variation of Pfa as a function of V1 can be found from Eq. (2.18); it is a monotonic-decreasing function. The method of applying these concepts to the prediction of radar range consists of four steps: (1) decide on a value of false-alarm probability that is acceptable (the typical procedure for making this decision will be described); (2) for this value of Pf09 find the required value of threshold voltage Vn through Eq. (2.18); (3) decide on a desired value of Pd (in different circumstances, values ranging from below 0.5 up to as high as perhaps 0.99 may be selected); and (4) for this value of Pd and for the value of Vt found in step 2 find the required signal-to-noise ratio through Eq, (2.19). This requires evaluating the function p5n(v), taking into account the number of pulses integrated. Iteration is required, in this procedure, to find the value of D0 corresponding to a specified probability of detection and number of pulses integrated. The value of Z)0 thus found is the value to be used in the range equation [e.g., Eqs. (2.10) and (2.11)]. The process of finding the required value of D0 for use in the range equation is greatly facilitated by curves that relate the number of pulses integrated to D0 with Pfa and Pd as parameters. Many such curves have been published, and some representative ones are given as Figs. 2.3 through 2.7. The principal difficulty in computing them is determination of the probability density functions pn(v) and psn(v) and in performing the requisite integrations. North2 gives the exact functions that apply for single-pulse detection with a linear rectifier as detector and the approximations that apply when many pulses are integrated. The density functions appropriate to other situations, e.g., square-law detection and fluctuation of signals, are given by various authors.3"10 The decision as to the acceptable level of false-alarm probability is usually made in terms of a concept called false-alarm time, which will here be defined as the average time between false alarms. Other definitions are possible; Marcum3 defines it as the time for which the probability of at least one false alarm is 0.5. However, the average time between false alarms seems a more practically useful concept. With it, for example, one can compute the average number of false alarms that will occur per hour, day, year, etc. With this definition, the falsealarm time is given by

DETECTABILITY FACTOR D0 (DECIBELS)

PROBABILITY OF DETECTION FIG. 2.3 Required signal-to-noise ratio (detectability factor) for a singlepulse, linear-detector, nonfluctuating target as a function of probability of detection with false-alarm probability (Pfa) as a parameter. (From Ref. 13.)

MT tfa = -p1 fa

(2.20)

where M is the number of pulses integrated and T is the pulse duration. This formula assumes that the integrator output is sampled at time intervals equal to T. If range gates are employed and M pulses are integrated, if the ON time of the gate tg is equal to or greater than the pulse length T, and if there is some fraction of the time 8 when no gates are open (dead time, e.g., just before, during, and after the occurrence of the transmitter pulse), then the formula is

*f"

=

Mtg Pfa(l - 5)

(2 21)

'

These false-alarm-time formulas assume that the receiver predetection noise bandwidth Bn is equal to or greater than the reciprocal of the pulse length and that the postdetection (video) bandwidth is equal to or greater than 0.5 Bn (as it usually is). These assumptions, usually met, amount to assuming that values of the noise voltage separated by the pulse duration are statistically independent; this independence occurs for times separated by 1/Bn, sometimes called the Nyquist interval. Since ordinarily Bn = I/T and tg = T, 1/Bn is sometimes used in place of T or t in the false-alarm-time equations. Marcum's false-alarm number ri is related to the false-alarm probability by the equation

DETECTABILITY FACTOR D0 (DECIBELS)

NUMBER OF PULSES FIG. 2.4 Required signal-to-noise ratio (detectability factor) as a function of number of pulses noncoherently integrated, linear detector, nonfluctuating target, and 0.5 probability of detection. (From Ref. 13.)

I-(I- Pfaf = 0.5 (2.22«) For the usual large values of n' that are of interest, a highly accurate approximate solution of this equation for Pfa is

^.!e^.o^l

C.22H

Fluctuating Target Cross Section. In general, the effect of fluctuation is to require higher signal-to-noise ratios for high probability of detection and lower values for low probability of detection than those required with nonfluctuating signals. Swerling has considered four cases, which differ in the assumed rate of fluctuation and the assumed statistical distribution of the cross section. The two assumed rates are (1) a relatively slow fluctuation, such that the values of a for successive scans of the radar beam past the target are statistically independent but remain virtually constant from one pulse to the next, and (2) a relatively fast fluctuation, such that the values of cr are independent from pulse to pulse within one beamwidth of the scan (i.e., during the integration time). The first of the two assumed distributions for the received-signal voltage is of the Rayleigh form,* which means that the target cross section cr has a probability density function given by *The Rayleigh density function for a voltage v is 2V

/ x p(v) =-^e -

V2Ir2

where r is the rms value of v.

DETECTABILITY FACTOR D0 (DECIBELS)

NUMBER OF PULSES FIG. 2.5 Required signal-to-noise ratio (detectability factor) as a function of number of pulses noncoherently integrated, linear detector, nonfluctuating target, and 0.9 probability of detection. (From Ref. 13.)

p(
(2.23)

where a is the average cross section. (This is a negative-exponential density function, but a target having this distribution is called a Rayleigh target because this distribution of a produces a received signal voltage which is Rayleighdistributed.) The second assumed cross-section density function is P(a) = ^ e~2^

(2.24)

The first distribution, Eq. (2.23), is observed when the target consists of many independent scattering elements of which no single one or few predominate. Many aircraft have approximately this characteristic at microwave frequencies, and large complicated targets are usually of this nature. (This result is predicted, for such targets, by the central limit theorem of probability theory.) The second distribution, Eq. (2.24), corresponds to that of a target having one main scattering element that predominates together with many smaller independent scattering elements. In summary, the cases considered by Swerling are as follows: Case Case Case Case

1 2 3 4

Eq. Eq. Eq. Eq.

(2.23), slow fluctuation (2.23), fast fluctuation (2.24), slow fluctuation (2.24), fast fluctuation

DETECTABILITY FACTOR D0 (DECIBELS)

NUMBER OF PULSES FIG. 2.6 Required signal-to-noise ratio (detectability factor) as a function of number of pulses noncoherently integrated, square-law detector, Swerling Case 1 fluctuating target, and 0.5 probability of detection. (From Ref. 13.)

The distribution of Eq. (2.24) is sometimes assumed for a small, rigid streamlined aircraft at the lower radar frequencies (e.g., below 1 GHz). Subsequent to Swerling's work, it has been found that many targets of the non-Rayleigh type are better represented by the so-called log-normal distribution, and analyses have been made for this case.9 Swerling's Case 1 is the one most often assumed when range prediction is to be made for a nonspecific fluctuating target. Results for this case are presented in Figs. 2.6 and 2.7. Curves for the other fluctuation cases and for additional values of detection probability are given in Refs. 13 and 14. Detector Laws. A linear detector is a rectifier which has the rectification characteristic

',:'-?' B? 8}

**>

where I0 is the instantaneous output current, V1- is the instantaneous input voltage, and a is a positive constant. Typical diodes approximate this law if V1 is larger than some very small value (e.g., a few millivolts). Such a diode is ordinarily used as the second detector of a superheterodyne radar receiver. Also, appreciable RF and IF gain usually precedes the second detector, so that the voltage applied to it is usually large enough (typically, an appreciable fraction of a volt) to ensure this "linear" type of operation. A square-law detector is one that has the nonlinear characteristic /O = CtV;2

(2.26)

DETECTABILITY FACTOR D0 (DECIBELS)

NUMBER OF PULSES FIG. 2.7 Required signal-to-noise ratio (detectability factor) as a function of number of pulses noncoherently integrated, square-law detector, Swerling Case 1 fluctuating target, and 0.9 probability of detection. (From Ref. 13.)

Marcum3 showed that a square-law detector is very slightly superior to a linear detector when many pulses are integrated, by about 0.2 dB. For a few pulses integrated, 10 or less, a linear detector is slightly superior—again, by about 0.2 dB or less. The mathematical analysis of probability of detection is somewhat more tractable when a square-law detector is assumed; this is probably its principal advantage. The complexity of this matter is further compounded by the fact that, because of the statistics of the signal-noise superposition, in a linear rectifier there is a square-law relationship between the signal input voltage and the signal-plus-noise output voltage for small signal-to-noise ratios. This relationship becomes linear for large signal-to-noise ratios, as shown by Bennett,22 North, and Rice.23 Because of this effect, it is sometimes erroneously thought that such a detector becomes square-law for small signal-to-noise ratios. But it is the input signal-plusnoise voltage V1, and not the signal-to-noise ratio, that determines whether a diode rectifier is a linear or a square-law detector. Curves for Visual Detection. The curves of Figs. 2.3 to 2.7 apply when the detection decision is based on an automatic threshold device as described. It is reasonable to suppose, however, that a human observer of a cathode-ray-tube display makes decisions in an analogous manner. That is, the equivalent of a threshold voltage (which would be a luminosity level for the PPI-scope type of display and a "pip-height" level for the A-scope display) exists somewhere in the observer's eye-brain system. This threshold, resulting in a particular falsealarm probability, is probably related to the observer's experience and personality: his or her innate cautiousness or daring. The probability of detection probably depends not only on the signal-to-noise ratio in relation to the threshold but on the observer's visual-mental acuity, alertness or fatigue,

and experience. Consequently, curves calculated for an automatic threshold decision device cannot be assumed to apply accurately to the performance of a human observer of a cathode-ray-tube display. But such an assumption does not give grossly erroneous results, and it is justifiable when experimental humanobserver data are not available or are of questionable accuracy. Curves based on actual experiments with human observers, analogous to those of Figs. 2.4 through 2.7, are given in Ref. 14, Chap. 2, along with further discussion of visual detection. Other Detection Methods. The discussion and results that have been presented have assumed perfect postdetection (video) integration of pulses prior to decision by an automatic threshold device. The noise statistics have been implicitly assumed to be those of ordinary receiver noise of quasi-uniform spectral density and (before detection) of gaussian probability density. A great many other detection procedures and signal-noise statistics are possible. Some of them are discussed in Ref. 14, Chap. 2.* Predetection Integration. The results depicted in Figs. 2.3 through 2.7 apply for perfect postdetection (video) integration of a specified number of pulses. It was shown by North2 that under ideal conditions predetection integration results in the smallest possible detectability factor and that for ideal predetection integration of M pulses the following relation holds: D0(M) = D^l)IM

(2.27)

That is, the minimum detectable signal-to-noise power ratio at the demodulator input terminals is improved, relative to single-pulse detection, by a factor exactly equal to the number of pulses integrated, M. For perfect postdetection integration, the improvement factor is generally less than M, asymptotically approaching M as M becomes indefinitely large. An exception occurs in the M < 10 region for fast-fluctuating targets and high probabilities of detection. For those circumstances the postdetection integration improvement factor can actually exceed M, and under the same circumstances predetection integration yields little or no improvement. The result of adding successive fast-fluctuating signals before detection, with virtually uncorrelated phases, is practically the same as that of adding noise voltages. Therefore there is virtually no integration improvement. Predetection integration is also called coherent integration, because of its dependence on phase coherence of the integrated pulses, and postdetection integration is called noncoherent integration. When integration is not perfect, as is always the case practically, if the value of D0 used in the range equation is based on perfect integration, an imperfectintegration loss factor or factors must be included in the system loss factor L, as discussed in Sec. 2.7. Although the full benefits of predetection integration are realizable only for nonfluctuating targets, some benefit can be achieved by predetection integration of a moderate number of slowly fluctuating targets. For such targets, the phase fluctuation from pulse to pulse is small. This type of integration is being employed to an increasing extent in modern systems when the utmost sensitivity is important and when fast fluctuation is not expected. *Chapter written by Lowell W. Brooks, Technology Service Corporation, Salida, Colo.

Since radial target motion produces a frequency shift of the received-echo signal (doppler effect) which is proportional to the target's radial velocity, this shift must be taken into account if predetection integration is used. This is done in pulse doppler radar (Chap. 17). Some radar systems that integrate many pulses utilize a combination of coherent and noncoherent integration when the phase stability of the received pulses is sufficient for some coherent integration but not great enough to allow coherent integration of the entire pulse train during the antenna on-target dwell time. If the total number of received pulses is Af and M of them (with M < N) are coherently integrated and if the coherent integrator is followed by a noncoherent integrator, then (assuming an appropriate implementation and ideal integrations) the detectability factor will be %M,N) = Dv(NIAf)IM

(2.28)

where D0(M,AO means the detectability factor for the assumed combination of coherent and noncoherent integration and D0(NIM) is the detectability factor for noncoherent integration of NIM pulses with no coherent integration (e.g., a value read from curves such as those of Figs. 2.4 through 2.7). As an example, if a train of N = 24 pulses is received and each set of M = 8 pulses is predetection- (coherently) integrated and if the predetection integrator is followed by a postdetection (noncoherent) integrator, the integration process produces at best a combined detectability-factor improvement corresponding to that of coherent integration of 8 pulses and noncoherent integration of 3 pulses.

2.5

SYSTEMNOISETEMPERATURE

The concept of a noise temperature is derived from Nyquist's theorem,24 which states that if a resistive circuit element is at temperature T (kelvins) there will be generated in it an open-circuit thermal-noise voltage given by Vn = VJkTRB

volts

(2.29)

where k is Boltzmann's constant (1.38054 x 10~23 Ws/K), R is the resistance in ohms, and B is the bandwidth, in hertz, within which the voltage is measured (that is, the passband of an infinite-impedance voltmeter). The absence of the frequency in this expression implies that the noise is white—that the spectrum is uniform and extends to infinitely high frequency. But this also implies infinite energy, an obvious impossibility, indicating that Eq. (2.29) is an approximation. A more exact expression, which has frequency dependence, must be used if the ratio flT exceeds about 108, where/is the frequency in hertz and T is the kelvin temperature of the resistor. Thus Eq. (2.29) is sufficiently accurate at a frequency of 30 GHz if the temperature is at least 300 K. The more accurate equations are given in Ref. 14 and in radio astronomy texts. Available Power, Gain, and Loss. As thus defined, Vn is the open-circuit voltage at the resistor terminals. If an external impedance-matched load of resistance RL = R is connected, the noise power delivered to it will be Pn = kTBn

(2.30)

which does not depend on the value of R. This is of course also an approximation, but it is quite accurate at ordinary radar frequencies and temperatures. This matched-load power is called the available power.17 The concepts of available power, available gain, and its reciprocal, available loss, are assumed in all noise-temperature and noise-factor equations. These and other noise-temperature concepts are explained fully in Refs. 14, 17, and 25. Briefly, available power at an output port is that which would be delivered to a load that matches (in the complex-conjugate sense) the impedance of the source. Available gain of a two-port transducer or cascade of transducers is the ratio of the available power at the output port to that available from the source connected to the input port, with the stipulation that the available output power be measured with the actual input source (not necessarily impedance-matched) connected. Noise Temperature. The usual noise that exists in a radar receiving system is partly of thermal origin and partly from other noise-generating processes. Most of these other processes produce noise which, within typical receiver bandwidths, has the same spectral and probabilistic nature as does thermal noise. Therefore it can all be lumped together and regarded as thermal noise. This is done, and the available-power level Pn is described by assigning to the noise a semifictitious "noise temperature" Tn, which is Tn = PnKkBn)

(2.31)

This is of course simply an inversion of Eq. (2.30), except that T in Eq. (2.30) refers to an actual (thermodynamic) temperature. The temperature defined by Eq. (2.31) is semifictitious because of the nonthermal origin of some of the noise. When this temperature represents the available-noise-power output of the entire receiving system, it is commonly called the system noise temperature or operating noise temperature,17 and it is then used to calculate the system noise power and signal-to-noise ratio, as in Eqs. (2.4) to (2.6). The Referral Concept. A receiving system can be represented as a cascade of two-port transducers, preceded by a source (the antenna) and terminated by a load. [However, in the discussion of system noise temperature, only those parts of the receiver that precede the detector (demodulator) are of significance, for the noise level at that point determines the signal-to-noise ratio for signal-detection-calculation purposes.] Noise may arise at any and all points in this cascade, so that the noise level changes from point to point. The important quantity is the output noise power Pno. For purposes of signal-to-noise calculation, however, it is convenient to refer this output noise to the system input terminals. This is done by defining the system noise temperature Ts so that it satisfies the relation kTsBn = PJG0

(2.32)

where G0 is the overall-system available gain and Bn is the noise bandwidth of the system [Eq. (2.14)]. The output power Pno is thus "referred" to the system input (the antenna terminals), and Ts is actually the system input noise temperature. The product W8Bn is thus the system output noise power referred to the antenna terminals. Each two-port transducer of the receiving-system cascade can be regarded as

having its own effective input noise temperature Te, representing its intrinsic available output noise power referred to its own input terminals. Here intrinsic means the power that the transducer would generate with a noise-free input termination of the same impedance as the actual input termination. Transducer output power is referred to the input terminals by dividing the output power by the available gain of the transducer. For an TV-transducer cascade, the system input noise temperature (with the antenna terminals considered to be the system input terminals) is then given by T.-T. + Z

-£

.2.33,

Here T0 is the antenna noise temperature, representing the available noise power at the antenna terminals, and G, is the available gain of the system between its input terminals and the input terminals of the /th cascaded component. (By this definition G1 = 1 always.) To illustrate these principles concretely, this formula will here be applied to a two-transducer cascade representing a typical receiving system (Fig. 2.8). The first transducer is the transmission line that connects the antenna to the receiver input terminals, and the second transducer is the predetection portion of the receiver itself. (As mentioned above, for purposes of signal-noise analysis subsequent portions of the receiver are not considered.) If desired, a many-transducer receiving system could be further broken down, with a preamplifier and possibly other units considered as separate elements of the cascade. For this system, if the receiving-transmission-line noise temperature is represented by Tr and its loss factor is Lr (=1/G2) and if the receiver effective input noise temperature is Te, Eq. (2.33) becomes T5 = Ta + TV + LrTe

(2.34)

It now remains to discuss evaluation of T0, Tr, Lr, and Te. Antenna Noise Temperature. Antenna noise is the result of (1) noise in the form of electromagnetic waves received by the antenna from external radiating sources and (2) thermal noise generated in the ohmic components (resistive conductors and imperfect insulators) of the antenna structure. The product kT0Bn is the noise power available at the antenna terminals within the receiver bandwidth. This noise temperature is dependent in a somewhat complicated way on the noise temperatures of various radiating sources within the receiving-antenna pattern, including its sidelobes and backlobes. The concept of noise temperature of a radiating source is based on Planck's law or on the Rayleigh-Jeans approximation to it, analogous to the relationship of resistor noise temperature to Nyquist's theorem. SOURCE (ANTENNA) T0

PASSIVE TRANSDUCER A (TRANS. LINE) L r , Tr

B

ACTIVE TRANSDUCER (RECEIVER) T 6 ,G

FIG. 2.8 Block diagram of a cascade receiving system.

OUTPUT

NOISE TEMPERATURE (K)

The antenna noise temperature is not dependent on the antenna gain and beam width when a uniform-temperature source fills the beam. If the noise sources within the beam are of different temperatures, the resulting antenna temperature will be a solid-angle-weighted average of the source temperatures. The noise temperatures of most of the radiating sources that an antenna "sees" are frequency-dependent; therefore antenna temperature is a function of frequency. That is, antenna noise is not truly "white," but within any typical receiver passband it is virtually white. In the microwave region, it is also a function of the antenna beam elevation angle, because in this region most of the "sky noise" is the result of atmospheric radiation. This radiation is related to atmospheric absorption, which is greater at low angles where the antenna beam sees a thicker slice of the lossy atmosphere than it does at higher angles. Curves of antenna temperature for a lossless antenna are shown in Fig. 2.9, calculated for typical conditions.14'25

FREQUENCY (MHz) FIG. 2.9 Noise temperature of an idealized antenna (lossless, no earth-directed sidelobes) located at the earth's surface, as a function of frequency, for a number of beam elevation angles. Solid curves are for geometric-mean galactic temperature, sun noise 10 times quiet level, sun in unity-gain sidelobe, cool temperate-zone troposphere, 2.7 K cosmic blackbody radiation, and zero ground noise. The upper dashed curve is for maximum galactic noise (center of galaxy, narrow-beam antenna), sun noise 100 times quiet level, and zero elevation angle; other factors are the same as for the solid curves. The lower dashed curve is for minimum galactic noise, zero sun noise, 90° elevation angle. (The bump in the curves at about 500 MHz is due to the sun-noise characteristic. The curves for low elevation angles lie below those for high angles at frequencies below 400 MHz because of reduction of galactic noise by atmospheric absorption. The maxima at 22.2 and 60 GHz are due to water-vapor and oxygen absorption resonances; see Fig. 2.19.) (From Ref. 13.)

The curves of Fig. 2.9 apply to a lossless antenna that has no part of its pattern directed toward a warm earth. The lossless condition means that the curves represent only the noise received from external radiating sources. Therefore any thermal noise generated in the antenna must be added to the noise represented by these curves. In most practical cases, a ground noise-temperature component must also be added because part of the total antenna pattern is directed toward the ground. (This will be true because of sidelobes and backlobes even if the main beam is pointed upward.) But then also the sky-noise component given by Fig. 2.9 must be reduced somewhat because part of the total antenna pattern is not then directed at the sky. The reduction factor is (1 - TagITtg), where Tag is the ground noise-temperature contribution to the total antenna temperature and Ttg is the effective noise temperature of the ground. If a is the fraction of the solid-angle antenna power pattern subtended by the earth, then Tag = a.Ttg. If the earth is perfectly absorptive (a thermodynamic blackbody), its effective noise temperature may be assumed to be approximately 290 K. A suggested conventional value for Tag is 36 K, which would result if a 290 K earth were viewed over a ir-steradian solid angle by sidelobes and backlobes averaging 0.5 gain (-3 dB). These sidelobes are typical of a "good" radar antenna but not one of the ultralow-noise variety. Moreover, some practical antennas have appreciable ohmic loss, expressed by the loss factor La (Sec. 2.3). An additional thermal-noise contribution of amount Tta(\ - l/La) then results, where Tta is the thermal temperature of the lossy material of the antenna. However, the noise from external sources is then also reduced by the factor I/1La. The total correction to the temperature values given by Fig. 2.9, to account for both ground-noise contribution and antenna loss, is then given by the following formula: Ta =

Tatt - TaglTtg) + Tag

?*-£ La

^ + Tta(l - 1/LJ

(2.35«)

where Tar is the temperature given by Fig. 2.9. For Tag = 36 K and Ttg = Tta = 290 K, this becomes Ta =

0.876 Ti - 254

+ 290

(2.35«

La

and if L0 = 1 (lossless antenna), it further simplifies to Ta = 0.876 JJ + 36

(2.35c)

26

Transmission-Line Noise Temperature. Dicke has shown that if a passive transducer of noise bandwidth Bn connected in a cascade system is at a thermal temperature Tt and if its available loss factor is L, the thermal-noise power available at its output terminals is Pno = kTfln(\ - UL)

(2.36)

A transmission line is a passive transducer. From Eq. (2.36) together with Eq. (2.31) and the definition of input temperature, it is deduced that the input noise temperature of a receiving transmission line of thermal temperature Ttr and loss factor Lr is

Tr = Ttr(Lr - 1)

(2.37)

(In this referral operation, multiplication by loss factor is equivalent to division by gain.) The receiving-transmission-line loss factor Lr is defined in terms of a CW signal received at the nominal radar frequency by the antenna. It is the ratio of the signal power available at the antenna terminals to that available at the receiver input terminals (points A and B, Fig. 2.8). A suggested conventional value for Ttr is 290 K. Receiver Noise Temperature. The effective input noise temperature of the receiver Te may sometimes be given directly by the manufacturer or the designer. In other cases, the noise figure Fn may be given. The relationship between the noise figure and the effective input noise temperature of the receiver or, in fact, of any transducer is given by17 Te = T0(Fn - 1)

(2.38)

where T0 is, by convention, 290 K. In this formula Fn is a power ratio, not the decibel value that is usually given. This formula is applicable to a single-response receiver (one for which a single RF input frequency corresponds to only one output or IF frequency and vice versa). Methods of computing noise temperatures when a double- or multipleresponse receiver is used (e.g., for a superheterodyne receiver without preselection) are described in Refs. 17 and 25. Single-response receivers are ordinarily used in radar systems. It is worth mentioning a point that has been well emphasized in the specialized literature of radio noise but is nevertheless easily overlooked. A receiver noisetemperature or noise-figure rating applies when a particular terminating impedance is connected at the receiver input. If this impedance changes, the noise temperature changes. Therefore, in principle, when a noise-temperature rating is quoted for a receiver, the source impedance should be specified, especially since the optimum (lowest) noise temperature does not necessarily occur when impedances are matched. However, when a receiver noise temperature is quoted without this impedance specification, it is presumable that the optimum source impedance is implied.

2.6

PATTERNPROPAGATIONFACTOR

The pattern propagation factors Ft and Fr in the range equation account for the facts that (1) the target may not be in the beam maximum of the vertical-plane antenna pattern and (2) non-free-space wave propagation may occur. This single factor, rather than two separate factors, is designed to account for both of those effects. This is necessary because they become inextricably intertwined in the calculation of multipath interference, which is the most important non-free-space effect. As will be seen, this effect can result in very considerable increase or decrease of the radar detection range compared with the free-space range. In this chapter, the basic ideas of pattern-propagation-factor calculation and some typical multipath-interference results will be presented. Additional details are given in Ref. 14, Chap. 6, and in Ref. 15.

CHAPTER 3 RECEIVERS John W. Taylor, Jr. Westinghouse Electric Corporation

3.1 THE CONHGURA TION OF A RADAR RECEIVER The function of a radar receiver is to amplify the echoes of the radar transmission and to filter them in a manner that will provide the maximum discrimination between desired echoes and undesired interference. The interference comprises not only the noise generated in the radar receiver but also energy received from galactic sources, neighboring radars and communication equipment, and possibly jammers. The portion of the radar's own radiated energy that is scattered by undesired targets (such as rain, snow, birds, insects, atmospheric perturbations, and chaff) may also be classed as interference. Where airborne radars are used for altimeters or mapping, other aircraft are undesired targets, and the ground is the desired target. More commonly, radars are intended for detection of aircraft, ships, surface vehicles, or personnel, and the reflection from sea or ground is classified as clutter interference. The boundaries of the radar receiver must be defined arbitrarily. This chapter will consider those elements shown in Fig. 3.1 as the receiver. The input signal is derived from the duplexer, which permits a single antenna to be shared between transmitter and receiver. Some radar antennas include low-noise amplifiers prior to forming the receive beams; although these are generally considered to be antenna rather than receiver elements, they will be discussed in this chapter. The receiver filters the signal to separate desired echoes from interference in many ways, but some elements of such processing are covered by other chapters because of the depth of treatment required: Chapter 14 describes continuous-wave (CW) and FM-CW radars; the discussion here will be confined to receivers for pulse radars, the dominant form. Lowpulse-repetition-frequency (PRF) pulse radars transmit a burst of energy and listen for echoes between transmissions. Their outstanding advantage is that neither leakage from the transmitter nor the very strong echoes from close-range clutter occur at the same instant as reception of weak echoes from long-range targets. The delay of the pulsed echo also provides an instantaneous measurement of range. Chapters 15 to 17 relate to discrimination of desired targets from interference on the basis of velocity or the change in phase from one pulse to the next; the

ECHOES FROM DUPLEXER RF AMPLIFIER STCATTENTION CONTROL

MIXER

AGC

STALO

IF AMPLIFIER IF FILTER

COHO

IF LIMITER

APC

SYNCHRONOUS DETECTOR ANALOG RECEIVER DIGITAL SIGNAL PROCESSOR

90°

ANALOG TO DIGITAL CONVERTER

PHASE DETECTOR

DECODER

PHASE DETECTOR

LOG DETECTOR

DECODER

LOG POWER COMBINER

CELL-AVERAGING CFAR DETECTED TARGET DATA TO PROCESSOR

RMSCOMBINER

CLUTTER MAP CFAR

INTEGRATOR

INTEGRATOR

DETECTION DECISIONS TO DISPLAY AND DATA PROCESSOR

FIG. 3.1 General configuration of a radar receiver.

CPACS DECODER

DOPPLER FILTER OR FILTERS

receiver discussed here serves only to provide the individual pulse signals in proper form for such doppler filtering. Section 3.12 will discuss data distortions in the synchronous detector or analog-to-digital (A/D) converter which affect these doppler filters. Chapter 10 deals with pulse compression, and only brief mention of its ability to aid in the discrimination process will be included here. Physically, decoding such echoes may occur as part of the intermediate-frequency (IF) filter, typically with surface acoustic-wave (SAW) devices or with digital correlators, either preceding or following doppler filtering. In Fig. 3.1, pulse compression is provided by the cascade combination of IF filter and digital decoders (correlators) after doppler filtering. Similarly, Chaps. 18 and 20 describe tracking radars and height finding radars, but the peculiarities of the receivers required to perform these functions will be mentioned briefly. The purpose of Fig. 3.1 is to illustrate the usual sequence of processing functions that may occur in any radar receiver and the variety of possible outputs, although no radar receiver will include all these functions or provide all these outputs. Virtually all radar receivers operate on the superheterodyne principle shown in Fig. 3.1. The echo, after modest amplification, is shifted to an intermediate frequency by mixing with a local-oscillator (LO) frequency. More than one conversion step may be necessary to reach the final IF, generally between 0.1 and 100 MHz, without encountering serious image- or spurious-frequency problems in the mixing process. Not only is amplification at IF less costly and more stable than at microwave frequency, but the wider percentage bandwidth occupied by the desired echo simplifies the filtering operation. In addition, the superheterodyne receiver can vary the LO frequency to follow any desired tuning variation of the transmitter without disturbing the filtering at IF. These advantages have been sufficiently powerful that competitive forms of receivers have virtually disappeared; only the superheterodyne receiver will be discussed in any detail. Other receiver types include the superregenerative, crystal video, and tuned radio frequency (TRF). The superregenerative receiver is sometimes employed in radar-beacon applications because a single tube may function as both transmitter and receiver and because simplicity and compactness are more important than superior sensitivity. The crystal video receiver also is simple but of poor sensitivity. The TRF receiver uses only RF and video amplification; although its noise temperature may be low, its sensitivity is poor because optimum-bandwidth filtering of the usual radar echo spectrum is generally impractical to achieve. Only for radars that radiate a relatively wide-percentage-bandwidth signal is filtering practical.

3.2 NOISE ANDDYNAMIC-RANGE CONSIDERATIONS Receivers generate internal noise which masks weak echoes being received from the radar transmissions. This noise is one of the fundamental limitations on the radar range, and for this reason the subject has been treated in Sec. 2.5. The analysis of radar sensitivity is facilitated if the noise contribution of each element of

the system is expressed as a noise temperature rather than as a noise factor or noise figure', these terms are defined and interrelated in Sec. 2.5. The noise temperature of the radar receiver has been reduced to the point that it no longer represents a dominant influence in choosing between available alternatives. It is a paradox that a noise parameter is usually the first characteristic specified for a radar receiver, yet few radars employ the lowest-noise receiver available because such a choice represents too great a sacrifice in some other characteristic. Cost is rarely a consideration in rejecting a lower-noise alternative. A reduction of requirements for antenna gain or transmitter power invariably produces cost savings far in excess of any added cost of a lower-noise receiver. More vital performance characteristics generally dictate the choice of receiver front end: 1. 2. 3. 4.

Dynamic range and susceptibility to overload Instantaneous bandwidth and tuning range Phase and amplitude stability Cooling requirements

A direct compromise must be made between the noise temperature and the dynamic range of a receiver. The introduction of an RF 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. Even if the RF amplifier itself has more than adequate dynamic range, the mixer dynamic range has been compromised, as indicated below: Ratio of front-end noise to mixer noise Sacrifice in mixer dynamic range Degradation of system noise temperature by mixer noise

6 dB 7 dB 1 dB

1OdB 10.4 dB 0.4 dB

13.3 dB 13.5 dB 0.2 dB

Definitions. Section 2.5 defined the noise parameters of a receiver in simple terms. Dynamic range, which represents the range of signal strength over which the receiver will perform as expected, is more difficult to define. It requires the specification of three parameters: 1. Minimum signal of interest: This is usually defined as the input signal that produces unity signal-to-noise ratio (SNR) at the receiver output. Occasionally, a minimum-detectable-signal definition is employed. 2. Allowable deviation from expected characteristic: The maximum signal is one that will cause some deviation from expected performance. Linear receivers usually specify a 1 dB decrease in incremental gain (the slope of the outputversus-input curve). Limiting or logarithmic receivers must define an allowable error in their outputs. Gain-controlled receivers must distinguish between instantaneous dynamic range and that achieved partly as a result of programmed gain variation. 3. Type of signal: Three types of signals are of general interest in determining dynamic-range requirements: distributed targets, point targets, and widebandnoise jamming. If 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 distributed clutter; the bandwidth-time product of the coded pulse indicates the added dynamic range that the decoder will extract from point targets. Conversely, if the radar incorporates an excessively wide-

bandwidth RF amplifier, its dynamic range to wideband-noise interference may be severely restricted. When low-noise amplifiers (LNAs) are included in the antenna, prior to forming the receive beams, the sidelobe levels achieved are dependent upon the degree to which gain and phase characteristics are similar in all LNAs. Dynamic range has an exaggerated importance in such configurations because matching nonlinear characteristics is impractical. The effect of strong interference [mountain clutter, other radar pulses, or electronic countermeasures (ECM)], entering through the sidelobes, will be exaggerated if it exceeds the dynamic range of the LNAs because sidelobes will be degraded. The LNAs 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 echoes in the LNA to be distorted, degrading the effectiveness of doppler filtering and creating false alarms. This phenomenon is difficult to isolate as the cause of false alarms in such radars owing to the nonrepetitive character of many sources of interference. Evaluation. A thorough evaluation of all elements of the receiver is necessary to prevent unanticipated degradation of noise temperature or dynamic range. Inadequate dynamic range makes the radar receiver vulnerable to interference, which can cause saturation or overload, masking or hiding the desired echoes. A tabular format for such a computation (a typical example of which is shown as Table 3.1) will permit those components that contribute significant noise or restrict the dynamic range to be quickly identified. 'Typical" values are included in the table for purposes of illustration. One caution is required in using Table 3.1. The dynamic range of each component is computed by comparing the maximum signal and system noise levels at the output of each component. The assumption inherent in this method is that all filtering (bandwidth reduction and decoding) by this component is accomplished prior to any saturation. It is important to treat those stages of the receiver that provide significant filtering as separate elements; if multiple stages are lumped into a single filter, this assumption may be grossly in error.

3.3 BANDWIDTHCONSIDERATIONS Definitions. The instantaneous bandwidth of a component is the frequency band over which the component can simultaneously amplify two or more signals to within a specified gain (and sometimes phase) tolerance. The tuning range is the frequency band over which the component may operate without degrading the specified performance if suitable electrical or mechanical controls are adjusted. Important Characteristics. The environment in which a radar must operate includes many sources of electromagnetic radiation, which can mask the relatively weak echoes from its own transmission. The 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. One must be concerned with the response of the receiver in both frequency and time domains. Generally, the critical response is determined in the IF portion of the receiver; this will be discussed in Sec. 3.7. However, one cannot ignore the RF portion of the receiver merely by making it have wide bandwidth. Section 3.2 discussed

Gain of component*

dB

Total gain to input

dB System 838 K

Noise- temperature contribution referred to antenna

-1.0

Log detector

520 1300

300

24K

RF amplifier

Filter

K

Mixer

Noise temperature of component

Trans-line

Noise and Dynamic-Range Characteristics

Antenna

TABLE 3.1

25

-6

15

-1,0

24

18

33

5

12

80

75

660

6

-106

-107

-82

-88

73 (-73)

29.3 dB K

Overall RX bandwidth

63.0 dBHz 92.3

Boltzmann's constant

-198.6

Narrowband noise level *

-106.3 dBm

Maximum signal capability

dBm

-5

-16

+5

(+7)

Dynamic range to distributed targets"^

dB

77

72

78

(80)

Bandwidth x time of point targef T

dB

11

11

O

O

Dynamic range fo point target "*"

dB

88

83

78

(80)

MHz

200

100

2

2

100

50

1

1

Bandwidth of receiver 1 " Ratio to overall receiver bandwidth 1

r

11

11

Wideband- noise vulnerability "

dB

20

17

O

O

Dynamic range to wideband noise "I"

dB

57

55

78

(80)

* CW output-CW input on the center frequency, not coded pulse. At the output terminal of the designated component except where indicated by parentheses (at the input terminal of a nonlinear device). how excessively wide bandwidth can penalize dynamic range if the interference is wideband noise. Even more likely is an out-of-band source of strong interference (TV station or microwave communication link) which, if allowed to reach this point, can either overload the mixer or be converted to IF by one of the spurious responses of the mixer. Ideal mixers in a superheterodyne receiver act as multipliers, producing an output proportional to the product of the two input signals. Except for the effect of nonlinearities and unbalance, these mixers produce only two output frequencies, equal to the sum and the difference of the two input frequencies. Product mixers, although common at intermediate frequencies, are not generally available for RF

conversion down to IF, and diode mixers are most commonly employed. The frequency-conversion properties of the diode are produced by its nonlinear characteristics. If its characteristic is defined by a power series, only the square-law term produces the desired conversion. The other terms produce spurious products, which represent an unwanted ability to convert off-frequency signals to the IF of the receiver. The efficiency of conversion of these unwanted frequencies, except for the image frequency, is sufficiently poor that the system noise temperature is not significantly degraded, but the mixer is vulnerable to strong out-of-band interference. The best radar receiver is one with the narrowest RF instantaneous bandwidth commensurate with the radiated spectrum and hardware limitations, and with good frequency and impulse responses. A wide tuning range provides a flexibility to escape interference, but if the interference is intentional (jamming), change in frequency on a pulse-to-pulse basis may be required. Such frequency agility can be achieved by using switchable microwave filters or electronically tuned yttrium iron garnet (YIG) filters to restrict the instantaneous bandwidth. Each involves some insertion loss, another sacrifice in noise temperature to achieve more vital objectives.

3.4

RECEIVERFRONTEND

Configuration. The radar front end consists of a bandpass filter or bandpass amplifier followed by a downconverter. The radar frequency is downconverted to an intermediate frequency, where filters with suitable bandpass characteristics are physically realizable. The mixer itself and the preceding circuits are generally relatively broadband. Tuning of the receiver, between the limits set by the preselector or mixer bandwidth, is accomplished by changing the LO frequency. Effect of Characteristics on Performance. Noncoherent pulse radar performance is affected by front-end characteristics in three ways. Noise introduced by the front end restricts the maximum range. Front-end saturation on strong signals may limit the minimum range of the system or the ability to handle strong interference. Finally, the front-end spurious characteristic affects the susceptibility of off-frequency interference. Coherent radar performance is even more affected by spurious mixer characteristics. Range and velocity accuracy is degraded in the pulse doppler radar; stationary-target cancellation is impaired in MTI (moving-target indication) radar; and range sidelobes are raised in high-resolution pulse compression systems. Spurious Distortion of Radiated Spectrum. It is a surprise to many radar engineers that components of the radar receiver can cause degradation of the radiated transmitter spectrum, generating harmonics of the carrier frequency or spurious doppler spectra, both of which are often required to be 50 dB or more below the carrier. Harmonics can create interference in other electronic equipment, and their maximum levels are specified by the National Telecommunications and Information Administration (NTIA) and MILSTD-469. Spurious doppler spectra levels are dictated by requirements to suppress clutter interference through doppler filtering. Harmonics are generated by any component which is nonlinear at the power level created by the transmitter and which passes those harmonics to the an-

tenna. Gaseous or diode receiver-protectors are designed to be nonlinear during the transmitted pulse and reflect the incident energy back toward the antenna. Isolators or circulators are often employed to absorb most of the reflected fundamental, but they are generally much less effective at the harmonics. Moreover, these ferrite devices are nonlinear in themselves and can generate harmonics. Harmonic filters are included in most radars but often are improperly located to perform adequately. It is useless to locate the harmonic filter between the transmitter and the duplexer if the latter generates unacceptable harmonic levels itself; the filter must be located between the antenna and the duplexer. Spurious doppler spectra are created by any process which does not reoccur precisely on each transmitted pulse. Gaseous receiver-protectors ionize under transmitter power levels, but there is some small statistical variation in the initiation of ionization on the leading edge of the pulse and in its subsequent development. In radars demanding high clutter suppression (in excess of 50 dB), 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. Spurious Responses of Mixers

Mathematical Mixer Model. The power-series representation of the mixer is perhaps the most useful in predicting the various spurious effects that are often noted. The current / flowing in a nonlinear resistance may be represented by a power series in the voltage V across the resistor terminals: i = OQ + a}V + a2V2 + ^ 3 V 3 + • • • + anVn

(3.1)

The voltage applied to the mixer is the sum of the LO voltage V}eJ<*lt and the signal voltage V2ej(*2t: V = V,£>i' + v2ej"2t

(3.2)

When V from Eq. (3.2) is substituted into Eq. (3.1) and the indicated operations performed, the spectral characteristics are predicted. Mixer Spurious-Effects Chart. The results of these calculations have been tabulated in several forms to show the system designer at a glance which combinations of input frequencies and bandwidths are free of strong low-order spurious components. The most useful form of the mixer chart1 is shown in Fig. 3.2. The heavy line shows the variation of normalized output frequency (H - L)IH with normalized input frequency LIH. This response is caused by the first-order mixer product H-L, which originates mainly from the square-law term in the powerseries representation. All other lines on the chart define spurious effects arising from the cubic and higher-order terms in the power series. To simplify use of the chart, the higher input frequency is designated by H and the lower input frequency by L. Seven particularly useful regions have been outlined on the chart. Use of the chart is illustrated by means of the region marked A, which represents the widest available spurious-free bandwidth centered at LIH = 0.63. The available RF passband is from 0.61 to 0.65, and the corresponding IF passband is from 0.35 to 0.39. However, spurious IF frequencies of 0.34 (4H - 6L) and 0.4 (37/ - 4L) are generated at the extremes of the RF passband. Any extension of the instantaneous RF bandwidth will produce overlapping IF frequencies, a condition that is not corrected by IF filtering. The 4H - 6L and 3// - 4L spurious frequencies,

H-L H

L/H FIG. 3.2 Downconverter spurious-effects chart. H = high input frequency; L = low input frequency.

like all spurious IF frequencies, arise from cubic or higher-order terms in the power-series model of the mixer. The available spurious-free bandwidth in any of the designated regions is roughly 10 percent of the center frequency or (H - L)IlQH. Thus receivers requiring a wide bandwidth should use a high IF frequency centered in one of these regions. For IF frequencies below (H - L)IH = 0.14 the spurious frequencies originate from extremely high-order terms in the power-series model and are consequently so low in amplitude that they can usually be ignored. For this reason, single-conversion receivers generally provide better suppression of spurious responses than double-conversion receivers. The rationale for a choice of double conversion should always be validated. The spurious-effects chart also demonstrates spurious input responses. One of the stronger of these occurs at point B, where the 2H - 2L product causes a mixer output in the IF passband with an input frequency at 0.815. All the products of the form N(H - L) produce potentially troublesome spurious responses. These frequencies must be filtered at RF to prevent their reaching the mixer.

A spurious input response not predicted by the chart occurs when two or more off-frequency input signals produce by intermodulation a third frequency that lies within the RF passband. This effect is caused by quartic and higher-order even terms in the series. Its effect will be noted, for example, when Vt^2 __ ^ Intermodulation is reduced in some mixer designs by forward-biasing the mixer diodes to reduce the higher-order curvature. The Balanced Mixer. The mixer model and the spurious-effects chart predict the spectral characteristics of a single-ended mixer. In the balanced-mixer configuration these characteristics are modified by symmetry. The two most common forms of balanced-mixer configuration are shown by Fig. 3.30 and b. The configuration of Fig. 3.3a suppresses all spurious IF frequencies and spurious RF responses derived from even harmonics of the signal frequency. For the case where the subtraction is not obtained by a time delay, the LO frequency and all its harmonics are suppressed at the signal input port. Also of importance, noise sidebands of the LO which are converted to IF frequency are suppressed at the mixer IF port. The configuration of Fig. 3.3£ suppresses all spurious IF frequencies and spurious responses derived from even harmonics of the LO frequency. For the case where the RF phase shift is not obtained by a time delay, the LO frequency and RF SIGNAL

LOCAL OSCILLATOR

IF SIGNAL (Q)

LOCAL EL OSCILLATOR IF SIGNAL

RF SIGNAL (b)

LOCAL RF OSCILLATOR SIGNAL

HIGH SIDEBAND LOW SIDEBAND (c)

FIG. 3.3 (a) Balanced mixer with an inverted signal, (b) Balanced mixer with an inverted LO. (c) Image-reject mixer.

its odd harmonics are suppressed at the signal input port. Noise sidebands of the LO converted to IF are not rejected by this configuration, however. Image-Reject Mixer. The single-ended mixer has two input responses which are derived from the square-law term in the power series. The responses occur at points above and below the LO frequency where the frequency separation equals the IF. The unused response, known as the image, is suppressed by the imagereject or single-sideband mixer shown in Fig. 3.3c. The RF hybrid produces a 90° phase differential between the LO inputs to the two mixers (which may be balanced mixers). The effect of this phase differential on the IF outputs of the mixers is a +90° shift in one sideband and a -90° shift in the other. The IF hybrid, adding or subtracting another 90° differential, causes the high-sideband signals to add at one output port and to subtract at the other. Where wide bandwidths are involved, the IF hybrid is of the all-pass type. Characteristics of Amplifiers and Mixers Noise Temperature. The most frequently cited figure of merit for a mixer or amplifier is its noise figure. However, the concept of noise temperature has proved more useful. Chapter 2 defines the usage of these parameters in determining the detectability of signals in a noise background. Dynamic Range. A second useful figure of merit of the front-end device is the dynamic range from rms noise to the signal level that causes 1 dB compression in dynamic gain. Since the rms noise is dependent on the IF bandwidth, the effective dynamic range decreases with increasing IF bandwidth. The balanced-diode mixer exhibits the largest dynamic range for a given IF bandwidth. However, the dynamic range of the mixer preceded by a low-noise amplifier will be reduced in proportion to the gain of the amplifier. Thus noise performance and dynamic range cannot be simultaneously optimized. A solution to this problem may come in the form of an active converter.23

3.5

LOCALOSCILLATORS

Functions of the Local Oscillator. The superheterodyne receiver utilizes one or more local oscillators and mixers to convert the echo to an intermediate frequency that is convenient for filtering and processing operations. The receiver can be tuned by changing the first LO frequency without disturbing the IF section of the receiver. Subsequent shifts in intermediate frequency are often accomplished within the receiver by additional LOs, generally of fixed frequency. Pulse-amplifier transmitters also use these same LOs to generate the radar carrier with the required offset from the first local oscillator. Pulsed oscillator transmitters, with their independent "carrier" frequency, use automatic frequency control (AFC) to maintain the correct frequency separation between the carrier and first LO frequencies. In many early radars, the only function of the local oscillators was conversion of the echo frequency to the correct intermediate frequency. The majority of modern radar systems, however, coherently process a series of echoes from a target. The local oscillators act essentially as a timing standard by which the echo delay is measured to extract range information, accurate to within a small fraction of a wavelength. The processing demands a high degree of phase stability

throughout the radar. Although these processing techniques are described elsewhere (Chaps. 15 to 17 and 21), they determine the basic stability requirements of the receiver. The first local oscillator, generally referred to as a stable local oscillator (stalo), has a greater effect on processing performance than the transmitter. The final local oscillator, generally referred to as a coherent local oscillator (coho), is often utilized for introducing phase corrections which compensate for radar platform motion or transmitter phase variations. Stalo Instability. The stability requirements of the stalo are generally defined in terms of a tolerable phase-modulation spectrum. Sources of unwanted modulation are mechanical or acoustic vibration from fans and motors, power supply ripple, and spurious frequencies and noise generated in the stalo. In general, the tolerable phase deviation decreases with increasing modulation frequency because the doppler filter is less efficient in suppressing the effects. In a radar having two-pulse MTI, there is a linear relationship between the tolerable phase deviation and the period of the modulation. Their ratio is the allowable FM (frequency modulation) or short-term frequency stability sometimes encountered in the literature. This parameter does not adequately define the phase-stability requirements for pulse doppler or MTI radars where more than two pulses are coherently processed. The phase-modulation spectrum of the stalo may be measured and converted into the MTI improvement factor limitation, which is dependent on range to the clutter and the characteristics of the two cascaded filters in the radar receiver. This conversion process involves three steps, described below. It should be noted that some spectrum analyzers do not distinguish between frequencies below the desired stalo frequency and those above; their response is the sum of the power in the two sidebands at each designated modulation frequency. This is of no consequence in MTI radars which have equal response to positive and negative doppler frequencies. In radars using doppler filters unsymmetrical about zero doppler, it is necessary to assume that the stalo spectrum measured is symmetrical, generally a valid assumption. The examples shown subsequently employ measured data from this type of double-sideband (DSB) spectrum analyzer. If a single-sideband (SSB) spectrum analyzer is available, positive and negative modulation-frequency components can be measured separately and analyzed without any assumption of symmetry. It is essential that the measured data be defined as SSB or DSB, since there is a 3 dB difference in the two forms of data. Range Dependence. Most modern radars use the stalo to generate the transmitted pulse as well as to shift the frequency of the received echoes. The transmitters are power amplifiers (traveling-wave tubes, klystrons, twystrons, crossed-field amplifiers, solid-state amplifiers, etc.) rather than oscillators (magnetron, etc.). It is this double use of the stalo that introduces a dependence on range of the clutter and exaggerates the effect of certain unintentional phasemodulation components by 6 dB, the critical frequencies being those which change phase by odd multiples of 180° during the time period between transmission and reception of the clutter echo from a specified range. At these critical frequencies, a maximum positive phase deviation on transmission changes to a maximum negative deviation at the time of reception, doubling the undesired phase modulation of the echo at IF. Figure 3.4 shows this range-dependent filter characteristic, which may be expressed mathematically as

dB = 10 log 4 sin2 (2vfmR/c) = 10 log 4 sin2 (ir/ m f) where fm R c t

(3.4)

= modulation frequency, Hz = range, m = propagation velocity, 3 x 108 m/s = time delay = 2RIc

RANGE FACTOR (dB)

A short time delay can tolerate much higher disturbance at low modulation frequencies, as illustrated by the two cases in Fig. 3.4. Consequently, stalo stability needs to be computed for several time delays.

CURVE DELAY (us)

FREQUENCY (kHz) FIG. 3.4 Ei'lcct ot range delay on clutter cancellation.

For example, stalo phase modulation caused by power supply ripple at 120 Hz creates nearly equivalent phase modulation of a clutter echo from nearly 100-nmi range (delay of 1200 JJLS resulting in O dB range factor). Phase modulation of a clutter echo with a range delay of 15 JJLS is about 38 dB less than the stalo phase modulation because the stalo phase has changed only slightly in this short time interval; the phase added by the stalo to the transmitted pulse is nearly the same as the phase subtracted from the received echo in the mixer. Adding the decibel values of the measured stalo spectrum and the rangedependent effect at each modulation frequency provides the spectrum of undesired doppler modulation at the output of the mixer. Receiver Filtering. Subsequent stages of the radar receiver have responses which are functions of the doppler modulation frequency; so the output residue spectrum can be obtained by adding the decibel responses of these filters to the preceding spectrum at the mixer. The receiver contains two cascaded filters: an optimum-bandwidth filter at IF and a doppler filter, generally implemented digitally in modern radars. The example illustrated in Fig. 3.5 includes a gaussian filter at IF with a 3 dB bandwidth of 1.6 MHz and a four-pulse MTI with variable interpulse periods and time-

IF FILTER RESPONSE (dB)

RELATIVE RESPONSE (dB)

CURVE 1 MTIVELOCITYRESPONSE 2 IF FILTER RESPONSE

IF BANDWIDTH = 1.6 MHz F R E Q U E N C Y (kHz) FIG. 3.5 Frequency responses of radar receiver.

varying weights. This MTI exaggerates certain stalo modulation frequencies by as much as 5 dB more than average. Note that for this analysis to be correct the MTI velocity response must be scaled to have O dB gain to noise, not to an optimum doppler frequency. Integration of Residue Power. The MTI improvement factor limitation of the stalo may be expressed as the ratio of the stalo power to the total power of the echo modulation spectrum it creates at the output of the cascaded filters (Figs. 3.4 and 3.5). Figure 3.6 shows an example of the measured modulation spectrum of a stalo (curve 1) and the effect of 15-|jis delay on the clutter residue (curve 2). A computer program can be utilized to alter the measured spectral data, using the filters of Fig. 3.4 and 3.5, and to integrate the total power in the doppler residue spectrum, with the exception of modulation frequencies below 100 Hz, which cannot be measured. The result (51.8 dB) is the MTI improvement factor limitation due to stalo instability. Figure 3.7 shows the same measured stalo modulation spectrum, subjected to a range delay of 1200 jxs. The clutter residue spectrum contains more power at the lower modulation frequencies than Fig. 3.6, but the MTI residue is increased by only 1 dB. Long-range clutter is suppressed to nearly the same degree as short-range clutter. If the radar utilizes more than one doppler filter, the effect of stalo instability should be calculated for each individually. If an individual filter's doppler response is unsymmetrical, residues from positive and negative doppler bands must be computed separately and added in power. It should be noted that many textbooks analyze only a simple two-pulse MTI, and the resulting equations for the limitation on MTI improvement factor cannot be employed for more sophisticated doppler filters. This important fact is generally overlooked by the casual reader.

CURVE 1

NOISE LEVEL (dBc/Hz)

2

SINGLE-SIDEBAND SPECTRUM

INTEGRATED DOUBLESIDEBAND NOISE (dBc)

STALO (COMBINATION P c ) -53.4 NOISE MTI RESIDUE -51.8 AT 15^5 PRF (av.) = 275Hz IF BANDWIDTH= 1.6MHz

FREQUENCY (kHz) FIG. 3.6 Effect of 15-jxs range delay on stalo MTI limitation.

CURVE 1

NOISE LEVEL (dBc/Hz)

2

SINGLE-SIDEBAND SPECTRUM

INTEGRATED DOUBLESIDEBAND NOISE (dBc)

STALO(COMBINATION Pc) -53.4 NOISE MTI RESIDUE -50.8 AT 1200/is PRF (av.) = 275 Hz IF BANDWIDTH = 1.6 MHz

FREQUENCY (kHz) FIG. 3.7 Effect of 1200-^s range delay on stalo MTI limitation.

It should be noted that most textbook analyses assume that the stalo instability is due either to a single modulation frequency or to a combination of white gaussian-noise modulations. Rarely are these assumptions valid for real stales; so a different method of analysis must be employed.

The computer analysis described measures the colored modulation spectrum of the stalo, modifies it in conformance with the range-dependent effect and receiver filters of the radar, and integrates the output residue power. It is a valid procedure for determining stalo stability that requires no assumptions, but the resulting value must be considered merely a figure of merit to compare different stales for a given application. The same stalo would have a different stability value in another application with different receiver filters. Coho and Timing Instability. In modern radars using pulsed amplifier transmitters, the coho is rarely a significant contributor to receiver instability. However, in older radars using pulsed oscillator transmitters, the coho must compensate for the random phase of each individual transmitter pulse, and imperfect compensation results in clutter residue at the output of the doppler filters. Compensation is possible only for echoes from the most recent transmission; echoes from prior transmissions (multiple-time-around clutter) cannot be suppressed by doppler filtering in pulsed oscillator radars, and for this reason alone such radars are no longer popular. Those readers interested in the methods employed to compensate the coho in these older radars are referred to Sec. 5.5 of the 1970 edition of this handbook. When the radar is on a moving platform or when the clutter is moving rain or sea, the frequency of the coho is sometimes varied to try to compensate for this motion, shifting the clutter spectrum back to zero doppler. The servo which accomplishes this task, if properly designed, will introduce insignificant instability under ideal environmental conditions (solely clutter echoes and receiver noise typical of laboratory tests), but the effect of strong moving targets and pulsed interference from other radars can sometimes be serious, shifting the coho frequency from the proper compensation value. Timing signals for the transmitter and A/D converter are usually generated from the coho, and timing jitter can cause clutter attenuation to be degraded. However, the effect of timing jitter is too complex to predict accurately; so it is rarely measured separately. Total Radar Instability. The primary sources of radar instability are usually the stalo and the transmitter. If the doppler spectra of these two components are available, either through measurements or through predictions based on similar devices, the convolution of the two-way stalo spectrum (modified by the range-dependent effect) and the transmitter doppler spectrum provides an estimate of the spectrum of echoes from stable clutter, which is then modified by the two receiver filters and integrated to obtain the residue power caused by these two contributors. This power can be larger than the sum of the residues created by each contributor alone. These 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. Measurement of total radar instability can be conducted with the radar antenna searchlighting a stable point clutter reflector which produces an echo close to (but below) the dynamic-range limit of the receiver and doppler filter. Suitable clutter sources are difficult to find at many radar sites, and interruption of rotation of the antenna to conduct 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. All sources of instability are included in this single measurement except for any contributors outside the delay-line loop. It is important to recognize that timing jitter does not produce equal impact on all

parts of the echo 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 echo, including leading and trailing edges. The 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. Stability is the inverse of this ratio; both are generally expressed in decibels. In 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. Measurement of stability of such radars must employ a very large number of data points to obtain an answer valid for clutter distributed in range. Radar instability produces predominantly phase modulation of the echoes, and the scanning antenna produces predominantly amplitude modulation; so the combined effect is the sum of the residue powers produced by each individually.

3.6

GAIN-CONTROLLED AMPLIFIERS

Sensitivity Time Control (STC). The search radar detects echoes of widely differing amplitudes, typically so great that the dynamic range of any fixed-gain receiver will be exceeded. Differences in echo strength are caused by differences in radar cross sections, in meteorological conditions, and in range. The effect of range on radar echo strength overshadows the other causes, however. The radar echo power received from a reflective object varies inversely with the fourth power of the range or propagation time of the radar energy. The effect of range on signal strength impairs the measurement of target size. Yet determination of target size is needed to discriminate against radar echoes from insects, atmospheric anomalies, or birds (which in some cases have radar cross sections only slightly less than that of a jet fighter). Also, many radar receivers exhibit objectionable characteristics when signals exceed the available dynamic range. These effects are prevented 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 echo strength is independent of range. Search radars often employ a cosecant-squared antenna pattern whose gain diminishes with increasing elevation angle. The pattern restricts the power at high elevation angles, since an aircraft at a high elevation angle is necessarily at close range and little power is required for detection. At the high elevation angles, however, the echo power becomes independent of range and varies instead with the inverse fourth power of the altitude. An STC characteristic that is correct for the low-angle radar echoes restricts high-angle coverage. This incompatibility of the STC requirements at the elevation extremes severely limits the usefulness of STC. The restriction on STC imposed by the cosecant-squared antenna pattern can be reduced by a more realistic radar design philosophy. It is recognized that the antenna must radiate more energy at the high angles than is provided by the cosecant-squared pattern. There are two reasons for this. First, high-angle coverage is limited by clutter from the stronger low-altitude section of the beam rather than from system noise. Second, ECM reduces both the maximum range

and the altitude coverage of the radar. Of these, the loss of altitude coverage is the more serious. Both factors have caused the cosecant-squared pattern to be abandoned in favor of one that directs more energy upward. The advent of stacked-beam radars, which achieve their coverage pattern by use of multiple beams, has liberated STC from the restrictions of the antenna pattern. In these systems, there is one receiver channel for each beam, and STC may be applied to the receiver channels independently. Consequently, the upperbeam receivers may be allowed to reach maximum sensitivity at short ranges, whereas the lower-beam receiver reaches maximum sensitivity only at long range. Most modern radars generate STC waveforms digitally. The digital commands may be used directly by digital attenuators or converted to voltage or current for control of diode attenuators or variable-gain amplifiers. Digital control permits calibration of each attenuation to determine the difference between the actual attenuation and the command, by injecting a test pulse during dead time. This is essential in monopulse receivers which compare the echo amplitudes received in two or more beams simultaneously to accurately determine the target's position in azimuth or elevation. Accurate measurements depend on compensation for any difference in gains of the monopulse receivers. Readers interested in the methods of generating the analog STC waveforms used in older radars may find descriptions of various methods in Sec. 5.6 of the 1970 edition of this handbook. Clutter Map Automatic Gain Control. In some radars, mountain clutter can create echoes which would exceed the dynamic range of the subsequent stages of the receiver (A/D converter, etc.) if the STC attenuation at that range allows detection of small aircraft. The spatial area occupied by such clutter is typically a very small fraction of the radar coverage; so AGC is sometimes considered as an alternative to either boosting the STC curve (a performance penalty affecting detectability of small aircraft in areas of weaker clutter or no clutter) or increasing the number of bits of the A/D converter and subsequent processing (an economic penalty). Clutter map AGC is controlled by a digital map which measures the mean amplitude of the strongest clutter in each map cell of many scans and adds attenuation where necessary to keep the mean amplitude well below saturation. One disadvantage of clutter map AGC is that it degrades detectability of small aircraft over clutter which, in the absence of AGC, would be well below saturation. The scan-to-scan fluctuation of clutter requires a 6 to 10 dB safety margin between the maximum mean level controlled and saturation. Another problem is the vulnerability of the map to pulsed interference from other radars. Clutter map AGC can serious degrade other critical signal-processing functions, and the following fundamental incompatibilities prevent its successful application to many types of radars: • Suppression of clutter by doppler filtering is degraded by change of attenuation from one interpulse period to the next. • Control of false alarms in distributed clutter (rain, sea) can be degraded by change of attenuation from one range sample to the next (see Sec. 3.13). • Time sidelobes of compressed pulses in radars which transmit coded waveforms are degraded by attenuation variation in range prior to compression. Gradual STC variations can be tolerated, but not large step changes.

Automatic Noise-level Control. AGC is widely employed to maintain a desired level of receiver noise at the A/D converter. As will be described in Sec. 3.11, too little noise relative to the quantization increment of the A/D converter causes a loss in sensitivity; too much noise means a sacrifice of dynamic range. Samples of noise are taken at long range, often beyond the instrumented range of the radar (in dead time), to control the gain by means of a slow-reaction servo. If the radar has RF STC prior to any amplification, it can achieve meaningful dead time by switching in full attenuation; this minimizes external interference with minimal (and predictable) effect on system noise temperature. Most radars employ amplifiers prior to STC; so they cannot attenuate external interference without affecting the noise level which they desire to sense, and the servo must be designed to tolerate pulses from other radars and echoes from rainstorms or mountains at extreme range. This interference occasionally can be of high amplitude but generally has a low duty cycle during a 360° scan; so the preferred servo is one which increments a counter when any sample is below the desired median noise level and decrements the counter when the sample is above that level, independently of how great the deviation is. The most significant bits of the counter control the gain, and the number of bits of lesser significance in the counter dictates the sluggishness of the servo.

3.7

FILTERING

Filtering of the Entire Radar System. The filter provides the principal means by which the receiver discriminates between desired echoes and interference of many types. It may approximate either of two forms: a matched filter, which is a passive network whose frequency response is the complex conjugate of the transmitted spectrum, or a correlation mixer, an active device which compares the received signals with a delayed replica of the transmitted signal. Receiver filters are assumed to have no memory from one transmission to the next; their response is to a single transmission. Actually, most radars direct a multiplicity of pulse transmissions at a target before the antenna beam is moved to a different direction, and the multiplicity of echoes received is combined in some fashion. The echoes may be processed by an integrator, which is analogous to a matched filter in that ideally its impulse response should match the echo modulation produced by the scanning antenna. The echoes may be applied directly to a PPI, with the viewer visually integrating the dots in an arc which he or she associates with the antenna beam width. Various doppler processes (including MTI) may be applied to separate desired from undesired targets. From the radar system standpoint, these are all filtering functions, but they are treated in other chapters of this handbook. The receiver filtering to be discussed here is that associated with separating a single pulse from interference, although the subsequent problem of filtering the train of echoes from a single target dictates the stability of the receiver filter. At some point in the radar receiver, a detector produces an output voltage which is some function of the envelope of the IF signal. If it provides a linear function, it is termed an envelope detector; logarithmic detectors will be described in Sec. 3.8. The response of a linear detector to weak signals which do not greatly exceed noise level has been extensively analyzed.4 Various pairs of frequency components of input noise, which may be far removed from the spec-

trum of the desired echo, can intermodulate to produce a beat-frequency component at the detector output that is within the desired band. Similarly, the noise intermodulation smears some of the signal energy outside the desired band. As a consequence, filtering after envelope detection is less efficient than filtering prior to detection. All postdetection circuitry should have several times the bandwidth of the echo, and predetection filtering should be optimized, as will be described. Definitions. The reader is cautioned that there are no universally accepted definitions of the terms pulse duration and spectral bandwidth of the transmitted signal, impulse response and bandwidth of filters, or the equivalent antenna parameters, beamwidth and spectral bandwidth caused by scanning. These terms should always be used with clarifying adjectives to define their meaning. Energy Definitions. For detection of radar echoes against a noise background, the only fundamental parameters are the energy content of the transmitted signal, of the receiver noise, and of the echoes received as the antenna scans past the target. These energy parameters define the width of a rectangular function that has the same peak response and same energy content as the real function. Their only purpose is to relate the peak value of the function to the more vital energy content. Of these parameters, only the energy of the pulse is easy to measure (average power/PRF), and this may be employed in the radar range equation directly, without distinguishing peak power and "energy" pulse width. The noise or energy bandwidth of a receiver is often employed in theoretical analyses but rarely stated in the tabulation of radar parameters; bandwidth need not even be included in the radar range equation if the receiver approximates a matched filter. 3 dB Definitions. In the interest of making possible direct measurement of parameters from oscilloscope waveforms or pen recordings of these functions, it has been customary to utilize widths measured either at half-power (3 dB) or halfvoltage (6 dB) points. For functions that resemble a gaussian pattern, the 3 dB width is a close approximation to the energy width; the receiver bandpass generally fulfills this condition sufficiently to make the 3 dB bandwidth meaningful. Transmitter pulse shapes and spectra generally deviate significantly from gaussian. 6 dB Definitions. Although antenna beamwidths (and number of echoes received) are often specified between the 3 dB points, this actually represents a 6 dB definition of the echo response as the radar antenna scans past the target; in those radars whose transmitting and receiving beams are not identical, the 6 dB points of the two-way pattern are usually specified. Most definitions of pulse shapes include voltage parameters, with rise and fall times being represented by 10 and 90 percent points and pulse duration by 50 percent (6 dB) points. Likewise, filter bandpass characteristics are often defined by their widths at the 6 and 60 dB points. The 6 dB definitions will be the dominant definitions employed in this chapter. Entirely aside from custom, there are several valid arguments favoring the use of 6 dB parameters. As indicated in Table 3.2, the optimum bandwidth-time product for detection of a pulse in white gaussian noise, with each defined at the 6 dB points, does not deviate significantly from unity for most practical functions. The 3 dB or energy definitions yield widely variable optimum bandwidths, dependent upon the shape of the pulse and the bandpass of the filter; there can be no quick estimation of optimum bandwidth if these parameters are utilized.

Distributed clutter, rain or chaff, is often a more serious interference with target detection than noise. In passing through an optimum-bandwidth filter and optimum-bandwidth integrator, the echo is stretched in both range and angle; the clutter spectrum, being the product of the transmitted spectrum and the bandpass of the receiver, is narrower than either. As a result, the 6 dB two-way beamwidth and the 6 dB pulse width closely approximate the extent of the radar cell from which the "optimum" receiver accumulates clutter energy. To summarize the general utility of 6 dB definitions: (1) The range equation for detection in noise need not include peak power, pulse width, or receiver bandwidth; only the efficiency of the integrator requires a definition of the number of pulses being received, and a 6 dB echo definition is universally employed. (2) The optimum bandwidth is close to the inverse of the echo duration if both are 6 dB definitions; this applies to both the receiver filter and the integrator. (3) The energy of the interference from clutter, rain or chaff, that is accepted by an approximately matched receiver is well defined by the 6 dB pulse duration and 6 dB two-way beamwidth. Approximations to Matched Filters. The most efficient filter for discriminating between white gaussian noise and the desired echoes is a matched filter, a passive network whose frequency response is the complex conjugate of the transmitted spectrum. It can process echoes from all ranges. The correlation mixer, an active device which compares the received signals with a delayed replica of the transmitted signal, is mathematically equivalent to a matched filter, but it is responsive only to echoes from one specific range; consequently its use in radar systems is more limited. Table 3.2 illustrates the degree of sacrifice in detectability that results in approximating a matched filter, either to simplify the hardware or to achieve better filtering of other forms of interference. The optimum bandwidths of these filters TABLE 3.2

Approximations to Matched Filters

Transmitted pulse shape Gaussian Gaussian Rectangular Rectangular Rectangular Rectangular Rectangular Phase-coded Biphase Quadriphase

Optimum bandwidthtime product

Mismatch loss, dB

Receiver filter

6dB

3dB

Energy

Gaussian bandpass Rectangular bandpass Gaussian bandpass 5 synchronously tuned stages 2 synchronously tuned stages Single-pole filter Rectangular bandpass

0.88

0.44

0.50

O

1.05

0.74

0.79

0.51

1.05

0.74

0.7

0.51

0.97

0.67

0.76

0.51

0.95

0.61

0.75

0.56

0.70 1.37

0.40 1.37

0.63 1.37

0.88 0.85

1.05 1.01

0.74 0.53

0.79 0.5

0.51 0.09

Gaussian Gaussian

also are tabulated in terms of product of the filter bandwidth and pulse duration. Typically, the bandwidth may deviate 30 to 50 percent from the optimum value before the detectability is degraded by an additional 0.5 dB. This rather broad 4 'optimum" region is centered near unity bandwidth-time product for virtually all practical filters if one uses the 6 dB definitions. Sometimes the bandwidth of a radar receiver is in excess of the optimum to allow for some offset between the echo spectrum and the filter bandpass, caused by target velocity and receiver tuning tolerances. Although this makes the radar more susceptible to off-frequency narrowband interference (Fig. 3.8), it reduces the time required to recover from impulse interference (Fig. 3.9). These figures also illustrate that, to provide good suppression of both forms of interference, the shape of the filter bandpass characteristic is even more important than its bandwidth. Rectangular bandpass or impulse responses should be avoided; the closer one approximates a gaussian filter, the better the skirts in both frequency and time domains. In the case of phase-coded transmissions, the duration of the subpulses is the time parameter. This is equivalent to the spacing of the subpulses with one exception: the quadriphase code5'6 employs half-cosine subpulses with 6 dB width equal to fourthirds of subpulse spacing. One of the virtues of the quadriphase code is the unusually low mismatch loss, owing to the fact that the impulse response of the gaussian filter is an excellent approximation to the subpulse shape. A digital correlator in a later stage of the receiver completes the matched filter.

dB BELOW OUTPUT AT CENTER FREQUENCY

Filtering Problems Associated with Mixer Spurious Responses. The approximation of a matched filter is generally most easily accomplished at some

RECTANGULAR

GAUSSIAN FILTER BANDWIDTH RATIOS TYPE 3dB/6dB [NOISE/3dB RECTANGULAR I 1-000 1000 ONESINGLE-TUNEDSTAGE 0.577 1.570 TWO SYNCHRONOUS STAGES 0.645 1.220 FIVESYNCHRONOUSSTAGES 0.683 1.114 FIVE-POLE GAUSSIAN 0.707 1.077 NINE-POLE GAUSSIAN 0.707 1.066 INFINITE-POLE GAUSSIAN 0.707 1.065

DEVIATION FROM CENTER FREQUENCY PER 6 dB BANDWIDTH (AfXB 6 ) FIG. 3.8 Bandpass characteristics of filters.

NINE-POLE GAUSSIAN INFINITE-POLE GAUSSIAN FIVE-POLE GAUSSIAN ONESINGLE-TUNED STAGE FIVE TUNED STAGES

RELATIVE VOLTAGE

dB BELOW OUTPUT AT CENTER OF PULSE

RECTANGULAR

TWO TUNED STAGES

TIME DEVIATION FROM PEAK OF OUTPUT PULSE x 6 dB BANDWIDTH(B 6 At) FIG. 3.9 Impulse characteristics of filters. frequency other than that radiated by the radar. The optimum filtering frequency is a function of the bandwidth of the echo and the characteristics of the filter components. Consequently, it is necessary for the radar receiver to translate the frequency of the echo to that of the filter, in one or more steps, using local oscillators and mixers. Section 3.4 described how spurious responses are generated in the mixing process. Unwanted interference signals can be translated to the desired intermediate frequency even though they are well separated from the echo frequency at the input to the mixer. The 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. The image frequency is the most serious of the spurious-response bands, but an image-rejection mixer can readily suppress these signals by 20 dB. A filter can further attenuate image-frequency signals before they reach the mixer unless the ratio of input to output frequencies of the mixer exceeds the loaded Q of the available filters. This image-suppression problem is the reason why some receivers do not translate from the echo frequency directly to the final intermediate frequency in a single step. The other spurious products of a mixer generally become more serious if the ratio of input to output frequencies of the downconverter is less than 10. The spurious-effects chart (Fig. 3.2) shows that there are certain choices of frequency ratio that provide spurious-free frequency bands, approximately 10 percent of the intermediate frequency in width. By the use of a high first IF, one can eliminate the image problem and provide a wide tuning band free of spurious effects. Filtering prior to the mixer remains important, however, because the neighboring spurious responses are of relatively low order and may produce strong outputs from the mixer. In addition to external sources of interference, the radar designer must be concerned with internal signal sources. MTI and pulse doppler radars are particularly

susceptible to any such internal oscillators that are not coherent, i.e., that do not have the same phase for each pulse transmission. The effect of the spurious signal then is different for each echo, and the ability to reject clutter is degraded. A truly coherent radar generates all frequencies, including its interpulse periods, from a single stable oscillator. Not only all the desired frequencies but also all the internally generated spurious signals are coherent, and they do not affect the clutter rejection. More commonly, MTI and pulse doppler radars are pseudo-coherent, as illustrated in Fig. 3.10. The coho is the master reference for the phase detector and may be the clock from which the interpulse periods are determined. The coho also is employed in generating the transmitter frequency, offset from a noncoherent local oscillator. Neither the local oscillator nor the transmitter is CO-

PULSEDAMPLIFIER TRANSMITTER

ANTENNA DUPLEXER

RF AMPLIFIER

MIXER

STALO

MIXER

IF AMPLIFIER SYNCHRONOUS DETECTOR

TO MTI CANCELER

decibels

COHO

STALO

ECHOw 3

RADIO-FREQUENCY SPECTRUM (b)

decibels

^a = DESIRED SIGNAL L* = SPURIOUS SIGNAL

MATCHED-FILTER BANDPASS

INTERMEDIATE-FREQUENCY SPECTRUM (c) FIG. 3.10 Pseudo-coherent radar, (a) Block diagram, (b) RF spectrum of the echo, (c) IF spectrum of the echo.

herent; their phases are different for each pulse transmitted. Only in the IF portion of the receiver is the desired echo from a stationary target coherent (a = constant, where a is the phase of the echo when the transmitter is turned on); virtually all the spurious outputs of the mixer are noncoherent and produce a fluctuating signal at IF. The only spurious component that may be coherent in the pseudo-coherent radar is the image frequency. As illustrated in Fig. 3.10, a pulsed spectrum can have fairly wide skirts and can overlap into the image band. The folded spectrum at intermediate frequency has two components within the bandpass of the matched filter, and if the percentage bandwidth at IF is large, the undesired image component can be significant. Only when it is coherent is a degradation of clutter cancellation impossible. Consider a pseudo-coherent radar in which the interpulse periods are generated from an independent source. Now the phase of the coho (a) changes from pulse to pulse, and although the phase of the desired echo from a stationary target changes equally, the phase of the spurious image echo changes oppositely. The cancellation of the stationary-target echo is limited to the level of the spurious echo. It is clear that the overall filtering capability of the radar, its ability to enhance the desired echoes and suppress undesired interference, may be degraded by the spurious responses of the various mixing stages. Particularly susceptible to degradation are MTI and pulse doppler radars, which may not provide the expected improvement in the rejection of clutter if the coho is not at the same phase condition each time that the transmitter pulses. All radars are susceptible to offfrequency interference, which, unless it is filtered before reaching the mixer, may create a detectable output in the desired IF band. The ability of MTI or pulse doppler processing to suppress clutter may be degraded if the receiver filter is not perfectly stable. The receiver's transfer characteristic (gain, time delay, and bandpass or impulse response) must be constant so that its effect on each echo pulse is identical. The mixer spurious responses just discussed and the stalo and coho problems of Sec. 3.5 represent only the most likely sources of instability to be encountered. Other elements of the receiver require attention to avoid instability problems. Vibration or power supply ripple can cause gain and phase modulation, particularly in RF amplifiers. Such modulation will degrade clutter attenuation unless the ripple frequency is a harmonic of the PRF.

3.8

LOGARITHMICDEVICES

Characteristics

Accuracy. Logarithmic devices and IF amplifiers are devices whose output is proportional to the logarithm of the envelope of the IF input. They often approximate the logarithmic characteristic by multiplicity of linear segments. Normally linear segments of equal length ratio and varying slope are joined to give a best fit to a logarithmic curve. Each segment will be correct at two points and will have a maximum error at the ends and center. The magnitude of the error7 increases with the length ratio of the segment. Figure 3.11 shows how this error changes with segment length ratio (also called gain per segment). In practice, the joints between the "linear" segments are not abrupt, and the best fit to the logarithmic curve may have less than the theoretical error.

Logarithmic detectors and amplifiers are frequently designed with adjustments in each stage. This allows for adjustment of the slope and/or length of the segment for a better fit. A precision exponentially decaying IF waveform from a test set is applied to the unit under test. The unit is adjusted for a linearly decaying output, which indicates the correct adjustment. Dynamic Range. The dynamic range of a logarithmic detector or amplifier is dependent on the number of linear segments N and on the length ratio G of the segments: Dynamic range = 2QN log G (3.5)

RESPONSE AT CENTER FREQUENCY

PERFORMANCE OF PRACTICAL LOGARITHMIC DETECTORS

GAIN PER SEGMENT (dB) FIG. 3.11 Error in the approximation of a logarithmic curve by linear approximation.

OUTPUT VOLTAGE

MAXIMUM ERROR (dB)

A well-designed logarithmic detector may have a dynamic range of 80 dB derived from nine stages with an error as low as ±0.2 dB. Bandwidth. The bandwidth of a logarithmic detector or amplifier generally varies with signal level. For this reason the logarithmic device is usually designed with excess bandwidth and is preceded by filters which establish the receiver bandwidth. However, the large signal bandwidth of the logarithmic device itself may be measured by using the method indicated in Fig. 3.12. The input voltage is increased from V1 to V1 + 3 or 6 dB, changing the operating point from A to B. The frequency is now changed in both directions to find those two frequencies that place the operating point at C. The same result also may be obtained by changing the frequency until the output is reduced by 35 or 65, where S is the volts-per-decibel characteristic. This places the operating point at C, which lies on the same curve as C. Because of the dependence of bandwidth on signal level, if possible the logarithmic amplifier should be aligned with signals below the threshold and its pulse response used as a criterion of performance. The pulse response is measured with a pulsed IF signal having much faster rise and fall times than those of the logarithmic device being tested. The rise time is the time required for the output to rise from the -205 to the -S point, and the fall time is the time required for the output to fall from the -S point to the -205 point. Because of the logarithmic characteristic, the fall time tends to be a straight line and to exceed the rise time.

FREQUENCY DEVIATION

Vj V1-I-SdB INPUT VOLTS (dB) 3.12 Method of measuring amplifier bandwidth.

logarithmic-

Analog Logarithmic Devices Logarithmic Detector. A well-known form of the logarithmic detector uses successive detection,6 wherein the detected outputs of Af similar limiter stages are summed as shown by Fig. 3.13. If each stage has a small signal gain G and a limited output level E, the intersections of the approximating segments fall on a curve described by [ 1OgEXM)G^+1 / i I l\] E0(M) = n\E / ^ + E I—J+ - • - + —72 + M l L log G \G ~ G G/J

(3.6)

where n is the detector efficiency and E1(M) represents the particular input levels that correspond to the intersections of the line segments, E1(M] = ^M

(3.7)

G

STAGE 1

LIMITING AMPLIFIERS

STAGE N

E1

DET.

DET.

DET.

DET.

AMPL. Z

(a)

EO

(b)

FIG. 3.13 («) Logarithmic detector, (b) Nine-stage logarithmic detector. Gain adjustment for each stage is shown below the transistor.

The independent variable M is the order of the stage at incipient saturation and will take on only integer values from 1 to N. A nonlogarithmic term in the form of a power series in 1/G has only a minor effect on logarithmic accuracy. The successive difference in this term as M is varied from 2 to N is ElGM~l. The overall tendency of this term, therefore, is to produce an offset in the output with only a minor loss in logarithmic accuracy at the highest signal levels. A typical logarithmic detector may have an accuracy of ±4 dB, a dynamic range of 80 dB, and a bandwidth of 5 to 10 MHz at 30 MHz, derived from nine stages (Fig. 3.136). However, Rubin9 describes a four-stage successive detection design having a bandwidth of 640 MHz centered at 800 MHz. Pulse response time of 2.5 ns is claimed. Logarithmic Amplifier. A logarithmic IF amplifier may be implemented with N identical cascaded dual-gain stages. In this case a precise logarithmic response results if each amplifier has a threshold ET below which the gain is a fixed value G and above which the incremental gain is unity. The intersections of the approximating segments fall on a curve described by log Ei(M}GN E0(M) = ET G -i— log G

(3.8)

where E1(M) represents the input levels corresponding to the intersection of the line segments: E1(M) = ETGl~M

(3.9)

The independent variable M is the order of the stage that is at incipient saturation; M will have integer values between 1 and N. In the case of the dual-gain logarithmic amplifier, all intersections of the line segments fall on a logarithmic curve. A typical logarithmic amplifier may have a dynamic range of 80 dB, derived from nine stages, with an overall bandwidth of 5 MHz or more. Typical accuracy is ±!/4 dB over 70 dB dynamic range and ±1 dB over the full dynamic range. Details of a typical stage are shown in Fig. 3.14, and the voltage characteristics in Fig. 3.15. The stage consists of an attenuator bridged by a series-diode limiter and followed by an amplifier. In the absence of an input voltage, the current divides equally between the limiter diodes. The thresholds are reached when diode D2 carries either all or none of the current. If the voltage drops across the diodes are neglected, this occurs when

* ' - * ' = * KaT*;)

(3 10)

'

Signals above the threshold in magnitude are attenuated by a factor RI(R + /?f), the reciprocal of the amplifier gain. The incremental gain in this region is therefore unity. The blocking capacitors are used because of the dc offset voltage that is characteristic of this form of limiter. Digital Logarithm. The trend toward digital processing requires mention of a piecewise linear digital approximation which may be accomplished after analog-to-digital conversion and digital doppler filtering to suppress clutter

FIG. 3.15 Dual-gain-stage voltage characteristic.

FIG. 3.14 Dual-gain IF stage.

interference prior to any nonlinear operation. A digital word in the power-of-2 binary format may be written £

= 2»-(»N+1_M + ^ + ^ + . . . + ^ )

(3,1)

where M is the place beyond which all coefficients to the left are zero. Note that M has essentially the same significance as in previous sections. The logarithm of E to the base 2 is

( ( _^ 1+

\ Jb\f—M | M + ^ b\]—\—\j l _ L J l + . . . + _ Jbf\L j

UKJ-. fut

UKj_\-.\A

+

Uf)

\

^_LJ£+...+_JLj

(312)

(3 . 13)

The whole number (N-M) becomes the characteristic, and the series, a fractional number, is a line approximation of the mantissa. The approximation is accurate to ±0.25 dB if the mantissa contains at least 4 bits. The accuracy may be improved to any desired degree by use of a programmable read-only memory (PROM) to convert the linear approximation to the true mantissa. Digital Log Power Combiner. In log format fewer bits of data need to be stored or manipulated, and many arithmetic computations are simplified. For example, the rms combination of the voltages (/ and Q) is complicated in linear format, and approximations are generally employed which introduce some error. In log format the process is simple and more accurate: Iog2 /2 = 2 Iog2 I/I

Iog2 Q2 = 2 log IgI

(3.14)

Iog2 (I2 + Q2) = Iog2 /2 + Iog2 (1 + Q2II2)

(3.15)

The latter term of Eq. (3.15) is the output of a PROM, using Iog2 /2 - Iog2 Q2 as the address.

The size of the PROM can be substantially reduced by comparing the two variables to determine the larger (L) and smaller (S): Iog2 (I2 + Q2) = Iog2 L + Iog2 (1 + S2IL2)

(3.16)

The latter term of Eq. (3.16) requires fewer bits than that of Eq. (3.15) because its maximum value is 3 dB. The PROM address also is unipolar and may be limited at a ratio where the PROM output drops to zero. The log power combiner makes power (square-law) integration feasible. A number of variables may be weighted by addition of logarithmic scaling factors and successively accumulated, using the log power combiner to combine each with the prior partial power summation. Square-law integration of multiple echoes from a target provides better sensitivity than prior methods, but this was impossible with analog signal processing and costly when using conventional digital processing.

3.9

IFLIMITERS

Applications. When signals are received that saturate some stage of the radar receiver which is not expressly designed to cope with such a situation, the distortions of operating conditions can persist for some time after the signal disappears. Video stages are most vulnerable and take longer to recover than IF stages; so it is customary to include a limiter in the last IF stage, designed to quickly regain normal operating conditions immediately following the disappearance of a limiting signal. The limiter may be set either to prevent saturation of any subsequent stage or to allow saturation of the A/D converter, a device which is usually designed to cope with modest overload conditions. The IF phase detector described in Sec. 3.10 requires a limiter to create an output dependent on phase and independent of amplitude. It is employed in phase-lock servos and phase-monopulse receivers. An IF limiter is sometimes employed prior to doppler filtering to control the false-alarm rate when the clutter echo is stronger than the filter can suppress below noise level. This was widely used in early two-pulse MTI, but it has drastic impact on the performance of the more complex doppler filters of modern radars. It is only compatible with phase-discrimination constant false-alarm rate (CFAR; Sec. 3.13), but it serves a useful purpose in radars utilizing this CFAR process after doppler filtering. Characteristics. The limiter is a cjrcuit or combination of like circuits whose output is constant over a wide range of input signal amplitudes. The output waveform from a bandpass limiter is sinusoidal, whereas the output waveform from a broadband limiter approaches a square wave. There are three basic characteristics of limiters whose relative importance depends upon the application. They are performance in the presence of noise, amplitude uniformity, and phase uniformity. When the input signal varies over a sufficiently wide range, all these characteristics become significant. Amplitude uniformity and phase uniformity are dependent largely on the design of the limiter and are a direct measure of its quality. Noise. Limiter performance in the presence of noise is characterized by a failure to limit signals buried in noise and by an output signal-to-noise ratio that

CHAPTER 4 TRANSMITTERS T. A. Weil Equipment Division Raytheon Company

4.1

INTRODUCTION

The Transmitter as Part of a Pulsed Radar System. Figure 4.1 shows a block diagram of a typical pulsed radar system. Of these dozen blocks, the public news media generally show only the antenna and displays. The rest of the blocks are ''unsung heroes," but they are equally important to the system and can be equally interesting from a design standpoint. ANTENNA DUPLEXER

EXCITER

SYNCHRONIZER

SIGNAL PROCESSOR

POWER SUPPLIES

COOLING

RADAR SET CONTROL

DISPLAY

FIG. 4.1 Block diagram of a typical radar system.

The transmitter is usually a large fraction of radar system cost, size, weight, and design effort, and it typically requires a major share of system prime power and maintenance. It generally ends up being a big box that sits in the corner of the radar equipment room, hums to itself, and has a big sign on it that says, "Danger, High Voltage"; so most people prefer to keep away from it. Its insides tend to look peculiar, more like a brewery than a TV set or a computer. This chapter will try to explain why transmitters have to be what they are and hopefully will make them appear a little less peculiar to the reader.

Why So Much Power? Transmitters are big, heavy, and costly and draw so much prime power because they are required to generate so much RF power output; and that requirement, in turn, comes from the radar system design tradeoffs. The useful range of a search radar varies as the fourth root of the product of average RF power, antenna aperture area (which determines antenna gain), and the time allowed to scan the required solid angle of coverage (which limits how long the signal in each direction can be collected and integrated to improve signal-to-noise ratio): R4 * P x A x T

(4.1)

The range varies as the fourth root of power because both the outgoing transmitted power density and the returning echo energy density from the target become diluted as the square of the distance traveled. Trying to increase range by increasing transmitter power is costly: a 16-fold increase in power is needed to double the range. Conversely, negotiating a reduced range requirement can produce remarkable savings in system cost. Power-aperture product as a measure of radar performance is fundamental. It is so fundamental that it was explicitly mentioned in the SALT-I Treaty as the basis for limiting the capabilities of antiballistic missile (ABM) radars. Receiver sensitivity is not shown as a factor in Eq. (4.1) because thermal noise sets a definite limit on receiver sensitivity, and this simplified range equation merely assumes that the receiver is always made as sensitive as possible. Since average transmitter power is only one of the factors in the range equation and is so costly, why does power usually end up being so high? Wouldn't it be better to use less power and to make up for it with more aperture or more scan time? The flaw in this argument is that increasing the antenna aperture increases its cost quickly because its weight, structural complexity, dimensional tolerance problems, and pedestal requirements grow rapidly with antenna size. The only other factor, scan time, is usually set by some definite system operational requirement: to look at all aircraft within 100 mi every 4 s, for example, to permit prompt recognition of changes in aircraft direction of travel; so scan time is usually not flexible (which probably explains why everyone talks about the "poweraperture product" of a radar rather than its "power-aperture-scan-time product"). It obviously would not make sense for a radar to have a huge, costly antenna and a tiny, inexpensive transmitter, or vice versa, because doubling the tiny part would allow cutting the huge part in half, which would clearly reduce total system cost. Thus, minimizing total system cost requires a reasonable balance between the costs of these two subsystems. The result, for any nontrivial radar task, is that significant transmitter power is always demanded by the system designers. The same result occurs when the system design is based on a required range coverage in the presence of standoff jammers (rather than just thermal noise). For detection of a target carrying a self-screening jammer, the range equation becomes R2 a (Pr x Ar) I (Pj x Aj)

(4.2)

where P1. and Ar are the power and aperture of the radar and Pj and Aj are those of the jammer. The result is very similar: power and aperture are still the driving

factors, and a balanced system design again results in significant transmitter power. The inescapable conclusion is that "It's watts up front that count." The desire to attain maximum radar performance capability thus means, more often than not, that both the antenna size and the transmitter power are pushed to the maximum affordable. Pushing the transmitter design to the maximum affordable power is not without its problems, however. Historically, this pressure has often led to problems in development time, unexpected costs, and other risks, especially when a new RF tube had to be developed for the application. The AN/FPN-10 L-band beacon radar system development, for example, was never completed because the tube vendor was unable to make the magnetron stable enough over the wide range of duty cycle. The ballistic missile early-warning system (BMEWS) radar development was in similar danger until a second (backup) tube development contract was placed that used integral vacuum cavities rather than external cavities for the high-average-power klystron development.1 Even a "successful" RF tube development may end up with a design that is marginal in arcing rate and/or in cooling design, leading to reliability problems, excessive maintenance and logistics costs, and an unhappy customer. As a result of the risks of pushing RF tube developments to (or unwittingly beyond) the state of the art, and especially if the desired power is known to be beyond the capabilities of a single tube, it becomes attractive to use more than a single RF tube and to combine their RF outputs; this turns out to be a very practical approach, as will be discussed later (Sec. 4.5). This ability to combine, readily and reliably, is also what makes solid-state transmitters practical, since individual solid-state RF devices have much lower power-handling capability than single RF tubes. Combining a few RF tubes to obtain a needed high-power level adds complexity to a transmitter, of course; but, on the other hand, combining a large number of RF devices, as must typically be done for solid-state transmitters, leads to certain advantages, such as graceful degradation and improved reliability, as described in Chap. 5. Why Pulsed? Radar transmitters would be much less complex and costly if they could simply operate CW (continuous-wave) like broadcast stations. Having to generate very high pulsed RF power leads to much higher operating voltages (both dc and RF), energy storage problems, and the necessity for highpower switching devices. Some RF devices, like Class C amplifiers (tube or solid-state), are self-pulsing and draw current only when RF drive is applied, but most microwave tubes require some type of pulse modulator (Sec. 4.8) so they won't waste power and so they won't generate interfering noise during the receiving