Bistatic Radars: Emerging Technology

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Bistatic Radar: Emerging Technology Edited by Mikhail Cherniakov University of Birmingham, UK Authors: Antonio Moccia Marco D’Errico Alberto Moreira Gerhard Krieger Pascale Dubois-Fernandez Hubert Cantalloube Bernard Vaizan Mikhail Cherniakov Tao Zeng Paul Howland Hugh Griffiths Chris Baker John Sahr

Bistatic Radar

Bistatic Radar: Emerging Technology Edited by Mikhail Cherniakov University of Birmingham, UK Authors: Antonio Moccia Marco D’Errico Alberto Moreira Gerhard Krieger Pascale Dubois-Fernandez Hubert Cantalloube Bernard Vaizan Mikhail Cherniakov Tao Zeng Paul Howland Hugh Griffiths Chris Baker John Sahr

C 2008 Copyright

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777

Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1P 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, L5R 4J3 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available is electronic books. Library of Congress Cataloging-in-Publication Data Cherniakov, Mikhail. Bistatic radar : emerging technology / Mikhail Cherniakov. p. cm. Includes bibliographical references and index. ISBN 978-0-470-02631-1 (cloth) 1. Bistatic radar. I. Title. TK6592.B57C53 2008 621.3848–dc22 2007044549 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-02631-1 Typeset in 10/12pt Times by Aptara Inc., New Delhi, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

Contents List of Contributors Preface 1 Fundamentals of Bistatic Synthetic Aperture Radar Antonio Moccia 1.1 Introduction 1.2 BSAR Basic Geometry and Resolutions 1.3 Scientific Applications of the BSAR 1.3.1 Evaluation of the BRCS of Natural and Manmade Targets by Means of Multiangle Bistatic SAR Observations 1.3.2 Acquisition of Terrain Elevation and Slope by Means of Range and Bistatic Scattering Measurements 1.3.3 Acquisition of Velocity Measurements Due to the Simultaneous Measurement of Two Doppler Frequencies 1.3.4 Stereoradargrammetric Applications Due to the Large Antenna Separation Involved 1.3.5 Improvement of Image Classification and Pattern Recognition Procedures 1.3.6 High-Resolution Measurements of Components of Sea-Wave Spectra 1.3.7 Bistatic SAR Data Processing 1.3.8 Position and Velocity Measurements 1.3.9 Bistatic Stereoradargrammetry 1.4 Summary Abbreviations Variables References 2 Spaceborne Bistatic Synthetic Aperture Radar Antonio Moccia and Marco D’Errico 2.1 Introduction 2.2 Key Design Issues in Spaceborne BSAR 2.2.1 Basic Trade-offs in Spaceborne BSAR Configurations 2.2.2 Impact of Bistatic Observation on Mission and System Design

xi xiii 1 1 2 8 8 9 10 10 11 11 12 13 15 20 21 21 22 27 27 29 29 32

• vi

2.2.3 Payload–Bus Performance Trade-off 2.2.4 BSAR Missions Functional/Technological Key Issues 2.3 Mission Analysis of Spaceborne BSAR 2.3.1 BSAR Orbit Design 2.3.2 BSAR Attitude and Antenna Pointing Design 2.4 Summary Abbreviations Variables References

3 Bistatic SAR for Earth Observation A. Moccia and M. D’Errico

CONTENTS

35 40 42 42 49 60 60 60 62 67

3.1 Introduction 3.2 Bissat Scientific Rationale and Technical Approach 3.3 Bistatic Payload Main Characteristics and Architecture 3.3.1 Design Assumptions 3.3.2 System Architecture 3.3.3 Payload Operational Modes 3.3.4 Signal Synchronization 3.3.5 Science Data Handling and Telecommunication 3.3.6 Antenna Characteristics 3.3.7 Overall Budgets 3.4 Orbit Design 3.5 Attitude Design and Radar Pointing Design 3.6 Radar Performance 3.7 Summary Abbreviations Variables Acknowledgements References

67 68 70 70 70 71 72 73 75 75 76 78 86 91 91 92 92 92

4 Spaceborne Interferometric and Multistatic SAR Systems Gerhard Krieger and Alberto Moreira

95

4.1 Introduction 4.2 Spaceborne SAR Interferometry 4.3 Interferometric Mission Design 4.3.1 Satellite Formation 4.3.2 Phase and Time Synchronization 4.3.3 Operational Modes for Bi- and Multistatic SAR Systems 4.4 Mission Examples 4.4.1 TanDEM-X 4.4.2 Semi-active TerraSAR-L Cartwheel Configuration 4.5 Advanced Multistatic SAR System Concepts 4.5.1 SAR Tomography 4.5.2 Ambiguity Suppression and Resolution Enhancement 4.5.3 Multistatic SAR Imaging

95 97 101 101 106 112 115 115 128 137 137 139 142

CONTENTS

4.5.4 Along-Track Interferometry and Moving Object Indication 4.5.5 Multibaseline Change Detection 4.6 Discussion Abbreviations Variables References 5 Airborne Bistatic Synthetic Aperture Radar Pascale Dubois-Fernandez, Hubert Cantalloube, Bernard Vaizan, Gerhard Krieger and Alberto Moreira 5.1 Bistatic Airborne SAR Objectives 5.2 Airborne Bistatic SAR Configurations 5.2.1 Time-Invariant Configurations 5.2.2 General Bistatic Configurations 5.2.3 MTI Applications 5.2.4 Examples of Resolution Performances 5.3 Airborne Bistatic SAR Processing Specificity 5.3.1 Changes in the SAR Synthesis Process 5.3.2 Motion Compensation Issues 5.3.3 Geometrical Distortion Model for Airborne Bistatic SAR Images 5.3.4 Miscellaneous Processing Issues 5.4 Open-Literature BSAR Airborne Campaigns 5.4.1 Michigan BSAR Experiment 5.4.2 QinetiQ BSAR Experiment 5.4.3 FGAN BSAR Experiment 5.5 The ONERA-DLR Bistatic Airborne SAR Campaign 5.5.1 Preparing the Systems 5.5.2 The Campaign 5.5.3 Processing the Bistatic Images 5.5.4 Calibration of the Bistatic Images 5.6 A Selection of Results from the Campaign 5.6.1 Quasi-Monostatic versus Monostatic 5.7 Summary Abbreviations Variables Used in Section 5.3 References 6 Space-Surface Bistatic SAR Mikhail Cherniakov and Tao Zeng 6.1 System Overview 6.2 Spatial Resolution 6.2.1 Monostatic SAR Ambiguity Function 6.2.2 Resolution in BSAR 6.3 SS-BSAR Resolution 6.3.1 SS-BSAR Ambiguity Function 6.4 SS-BSAR Resolution Examples

• vii

143 144 145 147 148 150 159

159 160 161 162 163 163 166 166 177 185 188 197 197 198 198 198 199 205 206 207 208 208 210 210 210 211 215 215 217 218 223 228 228 237

• viii

6.5 Summary Abbreviations Variables Acknowledgement References

7 Passive Bistatic Radar Systems Paul E. Howland, Hugh D. Griffiths and Chris J. Baker 7.1 7.2

PBR Development Sensitivity and Coverage for Passive Radar Systems 7.2.1 The Bistatic Radar Equation 7.2.2 Target Bistatic Radar Cross-Section 7.2.3 Receiver Noise Figure 7.2.4 Effective Bandwidth and Integration Gain 7.2.5 Performance Prediction 7.2.6 Sensitivity Analysis Conclusions 7.3 PBR System Processing 7.3.1 Narrowband PBR Processing 7.3.2 Wideband PBR Processing 7.3.3 Multistatic PBR 7.4 Waveform Properties 7.4.1 Introduction 7.4.2 Range and Doppler Resolution – ‘Self-Ambiguity’ 7.4.3 Range and Doppler Resolution – ‘Bistatic and Multistatic Ambiguity’ 7.4.4 Influence of Waveform Properties on Design and Performance 7.4.5 Conclusions of Waveform Properties 7.5 Experiments and Results 7.5.1 Experimental Overview 7.5.2 Expected System Performance 7.5.3 Data Collection 7.5.4 Adaptive Filtering of the Signal 7.5.5 Target Detection by Cross-Correlation 7.5.6 Long-Integration Time 7.5.7 Use of Decimation to Improve Efficiency 7.5.8 An FMCW-Like Approach 7.5.9 Constant False Alarm Rate (CFAR) Detection 7.5.10 Direction Finding 7.5.11 Plot-to-Plot Association 7.5.12 Target State Estimation 7.5.13 Plot-to-Target Association (Multiple Illuminator Case) 7.5.14 Verification of System Performance 7.6 Summary and Conclusions Abbreviations Variables References

CONTENTS

243 243 243 245 245 247 248 251 251 253 254 255 256 260 260 260 268 273 274 274 275 283 285 287 288 288 288 291 292 295 296 299 301 303 304 304 306 306 308 309 309 310 311

CONTENTS

8 Ambiguity Function Correction in Passive Radar: DTV-T Signal Mikhail Cherniakov 8.1 8.2

Introduction DTV-T Signal Specification 8.2.1 Scattered Pilot Carrier 8.2.2 Continuous Pilot Carrier 8.2.3 Transport Parameter Signalling Carrier 8.2.4 Guard Intervals 8.3 DTV-T Signal Ambiguity Function 8.3.1 The DTV-T Signal Model 8.3.2 AF of DTV-T Signal Random Components 8.4 Impact of DTV-T Signal Deterministic Components on the Signal Ambiguity Function 8.4.1 Autocorrelation Function (ωd = 0) 8.4.2 Complex Envelope Spectrum (τ = 0) 8.4.3 Ambiguity Function of the DTV-T Signal 8.4.4 Experimental Confirmation of the Modelling Results 8.5 Mismatched Signal Processing 8.5.1 Receiver Stricture 8.5.2 Signal Pre-processing in the Receiver 8.5.3 Pilot Carrier Equalization 8.5.4 Pilot Carrier Filtering 8.6 Summary Abbreviations Variables References 9 Passive Bistatic SAR with GNSS Transmitters Mikhail Cherniakov and Tao Zeng 9.1 Global Navigation Satellite Systems 9.2 Power Budget Analysis 9.3 Analysis of the Signal-to-Interference Ratio 9.3.1 SIR at the Antenna Output 9.3.2 Analysis of the SIR Improvement Factor 9.3.3 Simulation Results 9.4 Results Discussion 9.5 Experimental Study of the SS-BSAR 9.6 Summary Abbreviations Variables References

• ix

315

315 317 318 318 319 320 320 321 322 322 324 324 325 325 327 327 328 330 332 335 336 336 337 339 340 343 345 345 345 351 354 354 358 359 359 360

10 Ionospheric Studies John D. Sahr

363

10.1 Introduction

363

• x

10.2 The Ionosphere and Upper Atmosphere 10.2.1 Gross Structure of the Ionosphere 10.2.2 Ionospheric Models 10.2.3 Fine Structure, Field-Aligned Density Irregularities 10.2.4 Radio Interaction with the Ionosphere 10.3 Bistatic, Passive Radar Studies 10.3.1 Bistatic Radar Observations of the Ionosphere 10.3.2 The Manastash Ridge Radar 10.4 Trends for Ionospheric Research Abbreviations Variables Acknowledgements References

Index

CONTENTS

365 366 370 370 373 378 378 378 383 383 384 385 385 389

List of Contributors Mikhail Cherniakov School of Engineering, EECE, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Email: [email protected] Phone: +44 (0) 121 4144286 Fax: +44 (0) 121 4144291 Marco D’Errico Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universit`a di Napoli Via Roma 29, 81031 Aversa (CE), Italy Email: [email protected] Phone: +39 0815010223 Fax: +39 0815010285 Gerhard Krieger Microwaves and Radar Institute (HR), German Aerospace Center (DLR), 82230 Wessling/Oberpfaffenhofen, Germany Email: [email protected] Tel: +49 8153283054 Fax: +49 8153281135 Hubert Cantalloube Onera Demr, Chemin de la Huni`ere, 91761 Palaiseau, France Email: [email protected] Phone: +33(0)69936232 Fax: +33(0)69936269

Tao Zeng Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, PR China Email: [email protected] Phone: +86 1068940193 Fax: +86 1068911962 Hugh Griffiths Defence College of Management and Technology Cranfield University, Shrivenham Swindon SN6 8LA, UK Email: [email protected] Phone: 01793 785436 Fax: 01793 782546 John Sahr Department of Electrical Engineering, University of Washington, Paul Allen Center – Room AE100R, Seattle, WA 98195-2500, USA Email: [email protected] Phone: 206 685 4816 Fax: 206 543 3842 Antonio Moccia Dipartimento di Ingegneria Aerospaziale, Universit`a degli Studi di Napoli “Federico II”, P.le Tecchio 80, 80125 Napoli, Italy Email: [email protected] Phone: +39 0817682158 Fax: +39 0817682160

• xii

Alberto Moreira Microwaves and Radar Institute (HR), German Aerospace Center (DLR), 82230 Wessling/Oberpfaffenhofen, Germany [email protected] Tel: +49 8153282305 Fax: +49 8153281135 Pascale Dubois-Fernandez Onera Demr, Salon de Provence, BA701 13661 Salon Air Cedex, France Email: [email protected] Phone: +33(0)490170127 Fax: +33(0)490170109 Bernard Vaizan Onera Demr, Chemin de la Huni`ere, 91761 Palaiseau, France

LIST OF CONTRIBUTORS

Email: [email protected] Phone: +33(0)69936242 Fax: +33(0)69936269 Paul Howland Nato C3 Agency, PO Box 174, 2501CD Den Haag, The Netherlands Email: [email protected] Phone: +31 (0) 70 374 3752 Fax: +31 (0) 70 374 3079 Chris Baker Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, UK Email: [email protected] Phone: +44 (0)2076793966 Fax: +44 (0)2073889325

Preface

BISTATIC RADAR: EMERGING TECHNOLOGY This book Bistatic Radar: Emerging Technology is dedicated to the advanced study of bistatic radar, currently the subject of intensive research activity, which as yet has not been able to be presented as recognized and established theory. Two main areas of research are discussed here: The bistatic synthetic aperture radar (BSAR) and passive bistatic radar systems (PBRS). This book is a logical continuation of the recently published book Bistatic Radar: Principles and Practice, edited by Mikhail Cherniakov,1 which is recommended reading for those who are interested in the broader aspects of bistatic radar technology. Bistatic Radar: Principles and Practice presents the established but recently developed problems of bistatic radar. It begins with a ‘tutorial style’ part dedicated to the basic principles of radar technology. The second part introduces the basics of bistatic radar and concentrates on the latest results in the area of bistatic radar reflections. The final part contains a systematic approach to the theory and practice of forward-scattering radar for the detection and tracking of air targets. This book, Bistatic Radar: Emerging Technology, comprises two subsections. The first part is dedicated to different aspects of the BSAR, currently one of the newest and fastest growing areas of bistatic radar related research. Using the IEEE Explore search engine it was found that in 1996–7 there was only one paper published that was directly related to the BSAR. In 1998–9 there were two and in 2002–3 twenty papers, but from the beginning of 2006 until March 2007, there have already been thirty-four papers published – an exponential increase in interest in this topic. This first BSAR-dedicated part is divided into three sections which reflect the main BSAR topologies: spaceborne BSAR, airborne BSAR and space-surface BSAR. The first two classes of BSAR are almost self-explanatory. Spaceborne BSAR comprises transmitters and receivers positioned on at least two spacecraft, whereas airborne BSAR has transmitters and receivers positioned on different aircraft. The majority of the existing and most likely forthcoming research on BSAR will fall into these two categories. The third class, space-surface BSAR, on the other hand, assumes an essentially asymmetric structure: transmitters are positioned on spacecraft, but the receivers could be maintained on aircraft, on ground vehicles or be stationary, i.e. fixed on the ground. Space-surface BSAR is a newly introduced BSAR class, 1

John Wiley & Sons, Ltd, Chichester, West Sussex, 2007.

• xiv

PREFACE

and its future is uncertain. Many research teams around the world are currently undertaking studies on this topic, which has been investigated to a lesser extent than the two former BSAR classes. Some may consider it premature to publish a book introducing SS-BSAR, but bis dat, qui cito dat.2 The second part of this book addresses passive bistatic radar systems. In contrast to BSAR, PBRS is an area perhaps as old as bistatic radar research itself, and has now become the renewed subject of intensive research. The reader familiar with literature on bistatic radar may have come across PBRS under other names, such as passive coherent location, bistatic radar with transmitters of opportunity, bistatic radar with non-cooperative transmitters, to name a few. There seems to be a number of reasons for this resurgence of interest. In the early days of PBRS study, only terrestrial TV and radio broadcasting systems were considered as possible noncooperative transmitters. Today, a wide selection of wireless systems are available, operating around the clock and covering the entire surface of the Earth: satellite and terrestrial digital video and audio broadcasting, satellite and terrestrial mobile communication systems, global positioning systems, spaceborne radars, wireless local area networks and many others. Another important reason for renewed interest is that through the increased introduction of wireless systems, the frequency spectrums, at least to millimetre wavelength, are overloaded and it becomes difficult to licence frequencies for new systems. For these and other reasons interest in PBRSs is widely discussed in the appropriate parts of this book. Twelve leading experts representing different research schools from the US, China and throughout Europe have taken part in the preparation of this book. I wish to thank them all for the time, energy and commitment invested into the project, for their wise advice and for the highly professional material submitted. During the preparation of the book I was involved in research organized and funded by Electro Magnetic Remote Sensing Defence Technology Centre (EMRC DTC), UK. This centre brought together top radar experts from UK industry (SELEX Sensors and Airborne Systems Ltd, THALES, DSTL, BAE Systems, etc.). I am most grateful to all these experts and would like to thank all of them for essentially inspiring me to compile this book. Mikhail Cherniakov

2

He gives twice who gives quickly or opportunely (Latin).

1 Fundamentals of Bistatic Synthetic Aperture Radar A. Moccia

1.1 INTRODUCTION Bistatic radar operates with separated transmitting and receiving antennas. Thanks to the possibility of using a passive, and hence undetectable, receiving antenna, since its early development bistatic radar has been extensively adopted for military applications [1.1]. In recent years, interest in surveillance applications of bistatic radar has further increased because, while it is relatively affordable to develop stealth capabilities against a monostatic illuminator, echoes reflected in other directions cannot easily be reduced. Referring to remote sensing applications, which are the topic of this chapter, bistatic radar configurations and performance have been studied because bistatic data acquisition provides additional qualitative and quantitative measurements of surface microwave scattering properties. Furthermore, if the transmitting antenna is monostatic, that is transmitting and receiving, it is possible to combine monostatic and bistatic data reflected by common covered areas or targets, thus achieving further applications. However, bistatic observation requires the coordinated use of two systems, with accurate time synchronization and antenna pointing between the transmitter and receiver and with accurate antenna separation measurement and control. For this reason, it has been mainly applied by using one or both Earth-fixed antennae and considering bistatic scattering properties of complex targets of limited dimensions, as reported in References [1.2] and [1.3]. With regards to extended surfaces, several investigators have proposed and, in some cases, successfully experienced bistatic radar for various applications. As an example, an increase of BRCS (bistatic radar cross-section) from −23 to +6 dB for rural land and from −32 to +10 dB for sea in the X-band has been reported, as a function of in-plane and out-of-plane scattering angles [1.1]. Bistatic radar scattering from ocean waves has been observed with the use of Loran A transmissions and a receiver located 280 km away [1.4]. In this application, Doppler frequency maps of bistatic echoes accounted for anisotropies in the ocean-wave spectra. Several authors Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

• 2

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

have also investigated the use of bistatic radar to detect atmospheric echo for meteorological applications [1.5–1.8], and the bistatic radar equation for meteorological targets, such as raindrops, refractivity perturbations, etc., has been derived in Reference [1.9]. Use of bistatic configurations for velocity measurements and identification of ground moving targets has been proposed in References [1.10] and [1.11]. Finally, it is worth mentioning the indoor bistatic radar facility developed at the University of Michigan for measuring the polarimetric response of both point and distributed targets [1.12], and the experiments carried out at the European Microwave Laboratory Facility for characterization of bistatic scattering [1.3]. In recent years, the use of bistatic radar configurations, adopting the signal of illuminators of opportunity as their input, is considered as a main trigger for a significant growth of bistatic techniques [1.13, 1.14], such as the use of existing microwave transmitters that are independently developed and operate for other applications (such as the GPS (global positioning system) or broadcasting satellites). Due to the relative diffusion of such noncooperative signal sources and their well-known and stable characteristics, which make their use quite reliable and inexpensive, deployment of adequately designed and located passive receivers is gaining great interest. However, it is worth noting that in this case the geometric and radiometric characteristics of bistatic observation are strictly dictated by illuminator configuration and operation, and, hence, gathered data would be unable to fulfil many applications. The signal synchronization and trajectory control aspects introduced above are even more demanding for the bistatic synthetic aperture radar (BSAR), due to the necessity of forming the synthetic aperture. The first documented experiment of synthetic aperture radar in bistatic geometry was conducted by using shipborne radar for observing wave conditions [1.15]. The motion of the ship was used to synthesize apertures approximately 350 m long. The first successful experiment adopting two airborne SARs flying with programmed separations showed peculiar aspects of bistatic scattering from rural and urban areas [1.16]. However, nonsystematic overland bistatic measurements from aircraft or spacecraft are reported in the literature, in particular considering the BSAR. In contrast, advantages connected to the use of synthetic apertures, as an example in terms of resolutions and image quality parameters, are well known and, consequently, there is an increasing worldwide interest in the scientific community and among remote sensing users in the development and exploitation of the bistatic SAR. After a brief description of the basic geometry of the BSAR, this chapter reports a comparison of the BSAR to a conventional monostatic SAR in terms of ground range and azimuth resolutions, considering airborne and spaceborne configurations. An analysis of potential scientific applications that could be fulfilled with bistatic data is then presented. Special emphasis will be given to techniques for extracting topographic data and for measuring target velocity.

1.2 BSAR BASIC GEOMETRY AND RESOLUTIONS The main geometric parameters characterizing bistatic observations with respect to monostatic ones are the distance between the antennae (defined by using the baseline vector from transmitting to receiving antenna) and the transmitter–target–receiver angle (the bistatic angle) and plane (the bistatic plane). Assuming operation in this plane, the bistatic isorange contour curves are ellipses [1.1, 1.17]. A comprehensive analysis of BSAR resolutions can be found in Reference [1.18], where a method is documented based on the description of the BSAR generalized ambiguity function in the delay Doppler domain and, then, on its spatial projection to derive range and azimuth

• 3

BSAR BASIC GEOMETRY AND RESOLUTIONS

T

B

R

ΘT

ΘR rT

H

β

H rR

flat terrain

Δ rb

Figure 1.1 Geometry of bistatic observation from two airborne antennae and bistatic ground range resolution (not to scale for clarity)

resolutions, along with further quantities of interest. Below a simple, introductory, geometrical approach is presented, aimed at specializing resolution expressions provided in References [1.1] and [1.19] to BSAR configurations in which the simultaneously operating antennae are carried along parallel trajectories by two aircraft or spacecraft, attaining a constant horizontal baseline. The goal of the analysis is to give a quick, but rigorous, overview of the effects of bistatic geometry on resolutions, parameters crucial for selection of BSAR mission configurations and operational intervals adequate for remote sensing applications. Starting with the straightforward airborne BSAR geometry and assuming a flat terrain, Figure 1.1 allows evaluation and comparison of ground range resolutions of monostatic and bistatic SARs: c , 2W sin Θ T

(1.1)

c . W (sin Θ T + sin Θ R )

(1.2)

rm = rb =

Assuming that the two antennae operate at the same altitude (for the sake of concreteness H = 5000 m has been selected) and observing from the same side with the Rx-only antenna closer to the target (to avoid excessive signal-to-noise ratio reductions and geometric distortions), Figure 1.2 reports the bistatic angles and Figure 1.3 the ratios between the ground range resolutions as a function of baseline, considering two constant values for the Tx/Rx antenna off-nadir angle. As expected, the effect of a smaller Rx-only antenna off-nadir angle is an increase in the ground range resolution. Moving to the case of the spaceborne BSAR under the same observation assumptions, a monostatic and bistatic ground range resolution can be derived from Figure 1.4 as follows: c 2 2 (ρ⊕ + H )2 + ρ⊕ − rT + 2W rT −1 −1 rm = ρ⊕ cos sin Θ T , (1.3) − sin 2ρ⊕ (ρ⊕ + H ) ρ⊕ rb ∼ =

c . 2W cos (β/2) cos ψ

(1.4)

• 4

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR 40 35 30

β [deg]

25 20

ΘT = 30 deg

ΘT = 45 deg

15 10 5 0

0

500

1000

1500

2000

2500

3000

3500

4000

4500

B [m]

Figure 1.2 Bistatic angle as a function of the baseline for airborne observation

1.8 1.7 1.6 1.5

ΘT = 30 deg

Δrb 1.4 Δrm 1.3

ΘT = 45 deg

1.2 1.1 1 0

500

1000

1500

2000

2500

3000

3500

4000

4500

B [m] Figure 1.3 Ratio between bistatic and monostatic ground range resolutions as a function of the baseline for airborne observation

• 5

BSAR BASIC GEOMETRY AND RESOLUTIONS

B

T

R

α ΘT H

β

ΘR

2

β

rT

rR

2

H

spherical earth

bistatic isorange ellipses Δrb

ψ ρ⊕

ρ⊕

ρ⊕

Figure 1.4 Geometry of bistatic observation from two spaceborne antennae and bistatic ground range resolution (not to scale for clarity)

Equation (1.3) can be obtained by applying the well-known Carnot and sine theorems, whereas Equation (1.4) has been derived in Reference [1.1] by restricting the analysis in the bistatic plane (which is acceptable in the BSAR, assuming that the range elevation planes of the two antennae are coincident after SAR focusing, i.e. the target has been focused at the boresight in both images). The approximation in Equation (1.4) can be related to the eccentricity of the bistatic isorange ellipses and Willis [1.1] demonstrated that for e = 0.45 the error between approximated and exact resolutions is less that 1 % up to bistatic angles of the order of 50◦ and that the error rapidly diminishes as the eccentricity decreases. In spaceborne geometry with the same side observation, the baseline is quite a lot smaller than the sum of the Tx/Rx and Rx-only slant ranges, i.e. the isorange ellipses eccentricity is relatively small. For the sake of concreteness an example with H = 620 km will be considered, which in the worst case (Θ T = 40◦ and B = 500 km) involves e = 0.33. Hence, Equation (1.4) allows a satisfactory comparison to be made between monostatic and bistatic resolutions in a spaceborne configuration; however, a fully numerical analysis of slant range resolution for a spaceborne BSAR and spherical Earth can be found in Reference [1.20]. Since the bistatic isorange ellipses certainly intersect the spherical Earth surface, with reference to Figure 1.4 the aspect and bistatic angles can be derived as follows: β ψ = + cos−1 2

β = sin−1

ρ⊕ + H sin Θ T , ρ⊕

B sin α , rR

(1.5)

(1.6)

• 6

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

40 35 30

β [deg ]

25 20

ΘT = 30 deg

ΘT = 40 deg

15 10 5 0

0

50

100

150

200

250

B [km]

300

350

400

450

500

Figure 1.5 Bistatic angle as a function of the baseline for spaceborne observation

where α = cos−1

rR =

B − ΘT , 2 (ρ⊕ + H )

rT2 + B 2 − 2rT B cos α,

rT = (ρ⊕ + H ) cos Θ T −

2 ρ⊕ − (ρ⊕ + H )2 sin2 Θ T .

(1.7)

(1.8)

(1.9)

Finally, Figure 1.5 reports the bistatic angle as a function of the baseline for two constant values of Tx/Rx off-nadir angles and Figure 1.6 puts in evidence again the resolution reduction due to the bistatic geometry. For plotting Figure 1.6 a value of W = 60 MHz has been assumed. Moving to the azimuth resolution, by applying the synthesized-aperture point of view presented in Reference [1.19], the phase difference between echoes from the same ground target, located in the off-boresight direction and received by the Tx/Rx antenna in two positions (AT and BT in Figure 1.7) along the synthetic aperture separated by a distance x, is given by ϕT =

2π 2π 2π 2 (rAT − rBT ) = 2x sin γT ∼ 2x γT , = λ λ λ

(1.10)

• 7

BSAR BASIC GEOMETRY AND RESOLUTIONS 2 1.9 1.8 1.7 1.6

ΘT = 30 deg

Δ rb 1.5 Δ rm 1.4

1.3

Θ T = 40 deg

1.2 1.1 1 0

50

100

150

200

250

300

350

400

450

500

B [km]

Figure 1.6 Ratio between bistatic and monostatic ground range resolutions as a function of the baseline for spaceborne observation

assuming small apertures with respect to the boresight direction. The monostatic azimuth resolution am = /2 is obtained when ϕ = π and γT = 12 (λ/ ), i.e. half of the antenna beamwidth in the along-track direction, assuming a unity antenna illumination taper factor for the sake of simplicity. In bistatic geometry γR ∼ = γT rrTR . Hence rT + rR 2π 2π 2π ∼ ) (γ ϕR = , + γ x xγ [(rAT + rAR ) − (rBT + rBR )] ∼ = T R = T λ λ λ rR (1.11) Tx/Rx antenna trajectory Δx

BT

rBT

AT γ T rAT

γT

Rx-only antenna trajectory

rT

Tx/Rx antenna boresight direction

BR Δx AR

rBR

γR

rAR

γR

rR

Rx-only antenna boresight direction

Figure 1.7 Observation of a target in two adjacent elements of the synthetic antenna

• 8

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

1 0.98 0.96

ΘT = 30 deg

0.94

Δ ab 0.92 Δ am

0.9

0.88

Θ T = 40 deg

0.86 0.84 0.82

0

500

1000

1500

2000

2500

3000

3500

4000

4500

B [m] Figure 1.8 Ratio between bistatic and monostatic azimuth resolutions as a function of the baseline for airborne observation

which allows the bistatic azimuth resolution to be derived as follows: ab =

rR . rT + rR

(1.12)

In conclusion, Figures 1.8 and 1.9 show the ratios between monostatic and bistatic azimuth resolutions, considering airborne and spaceborne antennae respectively, and put in evidence the improvement in azimuth resolution that can be obtained in the adopted bistatic geometry. In fact, the Rx-only antenna is closer to the target and receives within the azimuth aperture of the Tx/Rx one; thus it exhibits a larger Doppler bandwidth along the synthetic aperture. As a consequence, the effect is more relevant by increasing both the bistatic angle and the off-nadir angle.

1.3 SCIENTIFIC APPLICATIONS OF THE BSAR Several scientific activities and new applications can be foreseen by combining monostatic and bistatic data reflected by common covered areas or targets, as reported below.

1.3.1 Evaluation of the BRCS of Natural and Manmade Targets by Means of Multiangle Bistatic SAR Observations Bistatic measurements help to discriminate between the physical scattering mechanisms inherent to surface clutter, and are useful when the terrain’s monostatic radar cross-section is

• 9

SCIENTIFIC APPLICATIONS OF THE BSAR

1

ΘT = 30 deg

0.95

Δ ab Δ am 0.9

Θ T = 40 deg

0.85

0

50

100

150

200

250

300

350

400

450

500

B [ km ]

Figure 1.9 Ratio between bistatic and monostatic azimuth resolutions as a function of the baseline for spaceborne observation

not strong [1.21, 1.22]. As an example, thanks to reduced retroreflector effects in the bistatic data, a better discrimination is made between rural and urban areas, thus allowing biomass evaluation. It must be pointed out that monitoring the extent of urban areas, forest and rural land is one of the most important factors in observing global climate change. It is worth noting that a reduction of about 10–20 dB in the image dynamic range has been experienced in airborne X-band surveys at three bistatic angles, due to reduced retroreflector effects in built-up areas when observed under bistatic geometry [1.16]. Moreover, the availability of both monostatic and bistatic data with a reasonably large (about 30◦ ) bistatic angle would significantly help the retrieval of surface roughness and dielectric constant [1.23]. In fact, the difference in the scattering coefficient at two bistatic angles is small for very rough surfaces and large (several dB) for smooth surfaces. Finally, predicted BRCSs of complex objects are lower than measured for bistatic angles greater than 15◦ [1.3].

1.3.2 Acquisition of Terrain Elevation and Slope by Means of Range and Bistatic Scattering Measurements Obtaining a high-quality, high-resolution digital elevation model by means of low interaction by an operator seems feasible [1.20]. It could also be used to improve conventional geometric and radiometric correction procedures of monostatic and bistatic data. An example of the use of bistatic SAR data for target position measurement is presented in Section 1.3.8. Furthermore, bistatic reflectivity from rough surfaces can be used for slope determination. Among the various models presented to correlate rough surface scattering coefficients with the

• 10

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

observation geometry and surface statistical features and orientation, it is worth recalling the Kirchhoff model [1.24], the small-perturbation model [1.23, 1.25] and the two-scale model, the latter aimed at integrating the previous two [1.26]. In particular, in Reference [1.27] it is demonstrated that the bistatic scattering coefficient can be related to the root-mean-square surface slope within a resolution cell. For each of the above models the regions of validity are defined in terms of surface correlation length and surface height distribution. Satisfactory results are presented for sea and snow-covered areas by relating physical characteristics of the surfaces (i.e. dielectric properties), polarization-dependent coefficients and bistatic observation geometry.

1.3.3 Acquisition of Velocity Measurements Due to the Simultaneous Measurement of Two Doppler Frequencies Doppler centroid frequency in SAR imagery can be computed by means of well-assessed algorithms (see, for example, References [1.28] and [1.29]), and can be related to position and velocity vectors and to the slant range in monostatic [1.19] and bistatic [1.1] geometry. In particular, bistatic data analysis involves nonlinear phase functions that do not arise in the monostatic problem [1.22]. Of course, only slant range components of target–antenna relative velocities can affect Doppler centroid frequencies; therefore the analysis must be restricted to the bistatic plane [1.30]. An example of the use of bistatic SAR data for target velocity measurement is presented in Section 1.3.8.

1.3.4 Stereoradargrammetric Applications Due to the Large Antenna Separation Involved It is wellknown that SAR images can be used to perform three-dimensional terrain measurements by making use of radargrammetric techniques based on stereoscopic pairs obtained by means of repeat pass coverage [1.31, 1.32]. Differently from SAR interferometry, where phase differences due to antenna separation (baseline) can be related to terrain elevation [1.33], stereoradargrammetric procedures are based on radar image noncoherent processing. To avoid decorrelation a maximum baseline exists in interferometric pairs [1.34], whereas the minimum interferometric baseline is related to the possibility of discriminating terrain elevation differences as a function of signal wavelength. On the contrary, even if the stereoscopic images must be similar to allow correlation, they must be taken with different geometric projections, i.e. large baselines are required to generate parallaxes (coordinate differences) necessary for height measurements. These two aspects are crucial in radargrammetry, because of speckle and large off-nadir angles [1.35, 1.36]. In particular, time decorrelation [1.37] is a significant drawback that can be avoided in the bistatic configuration, because the two images are acquired simultaneously. Basically, stereoradargrammetry is a more robust method to compute terrain elevation with respect to interferometry, because it is less sensitive to decorrelation and phase unwrapping problems. In particular, bistatic radar can offer further improvements with respect to repeat-pass stereo pairs [1.38]. However, it must be pointed out that in high correlation areas elevation data provided by SAR interferometry are more accurate and have a finer resolution [1.39]. Simple models showing potentiality of bistatic data in stereoradargrammetric applications are reported in Section 1.3.9.

SCIENTIFIC APPLICATIONS OF THE BSAR

1.3.5 Improvement of Image Classification and Pattern Recognition Procedures

• 11

Echoes at bistatic receiving sites are spatially decorrelated, mainly due to the large antenna separation required, but they have been gathered simultaneously; therefore correlation can be used as additional information for terrain discrimination [1.40]. Furthermore, since signals of strong retroreflectors are reduced in bistatic SAR geometry, weak signals appear more prominent at a given dynamic range at the receiver. Consequently, more details can be detected in a bistatic SAR image, thus improving SAR mapping capabilities, in particular when assessment of the extent and monitoring of the growth of urban areas is achieved by means of change detection techniques. Moreover, it is worth noting that the increase of the signal-tonoise ratio (SNR), consequent to noncoherent integration of bistatic phase decorrelated signals, improves geometric and radiometric resolutions and other image quality parameters, such as the integrated-to-sidelobe ratio and the peak-to-sidelobe ratio [1.41]. Consequently, the SNR and/or resolution decay at any rate present in the bistatic image and due to, as an example, BSAR focusing errors or differences in slant ranges or in BRCS could be partially recovered. Then, it is interesting to recall that a coherent multilook of monostatic complex SAR data is commonly applied in interferometric applications. Moreover, the procedures adopted to coregister interferometric pairs, as an example based on cross-correlation of pixel amplitudes [1.42], can be satisfactorily adopted for computing the coefficients for coordinate transformation between monostatic and bistatic data, thus providing bistatic pairs ready for pattern recognition procedures. Finally, bistatic SAR mapping potentiality for several land applications can be emphasized by using polarization modes. In fact, valuable additional information is yielded by acquiring polarized data, in both monostatic and bistatic configurations, thus allowing improved detection and classification algorithms in oceanographic and terrestrial applications [1.43–1.49]. In particular, target detection in a natural media, such as the maritime environment, can be improved by using matched polarization states for which the clutter return is low [1.50]. It is worth noting that, depending on antenna relative positioning, bistatic configurations allow novel polarimetric data to be gathered simply by considering the peculiarity of bistatic geometry with respect to the monostatic radar.

1.3.6 High-Resolution Measurements of Components of Sea-Wave Spectra Real and synthetic aperture radars have been widely used to image ocean waves, proving themselves to be effective tools for the retrieval of sea state and wave spectrum. Theories and detailed models have been developed for microwave scattering from the sea surface and its imaging by radars [1.23, 1.51–1.53]. Basically, the sea surface height profile has been approximated as a sum of harmonic components in along- and cross-track directions and a twoscale discrete model of the sea surface has been considered, i.e. based on short waves (ripples or capillarity waves) and long gravity waves, forming together the sea-wave components. The ripples are of great interest because they represent the sea-wave components that can meet the Bragg resonance condition with electromagnetic waves [1.23]. Moreover, a linear relation is assumed between the amplitudes of sea surface harmonic components and their contributions to the scattering coefficient [1.51]. Overall, the classic configuration of an active monostatic radar system has been experienced in the literature, even though interest has also been shown

• 12

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

for bistatic antenna configurations [1.40], as in the collection of reflected L-band GPS signals [1.54, 1.55], or in the investigation of differences between monostatic and bistatic scattering of the sea surface driven by wind [1.47, 1.56]. In particular, bistatic geometry offers the capability of measuring the ocean wave spectra caused by the Bragg scattering mechanism, because it can be demonstrated that the Doppler shift of the radar echo is exactly equal to the wave frequency and is related to the bistatic angle [1.4]. As a consequence, identification of ocean waves of particular lengths and of their direction of travel can be carried out. Finally, an application of existing models for detection of ocean surface waves by means of real and synthetic aperture radar demonstrates that bistatic geometry offers, with respect to its monostatic counterpart [1.57]: (a) a different Bragg-resonant sea-wave cross-track component (thus providing an additional information on the sea state); (b) a wider range (up to 15–20 %) of sea-wave spectra, in which an approximately linear SAR modulation transfer function is applicable for removing the azimuth shift between a scattering element real position and its imaged position, due to the mean value of the radial component of the long-wave orbital velocity in the resolution cell (velocity bunching [1.51]); (c) a reduction (up to 20 %) in azimuth resolution degradation due to the instantaneous radial velocity of sea surface facets within a resolution cell during synthetic aperture (acceleration smearing [1.52]).

1.3.7 Bistatic SAR Data Processing It is worth noting that the signal processing aspects of bistatic SAR data analysis certainly represent an original scientific task because novel procedures must be studied and developed. As an example, the following problems must be investigated: bistatic Doppler shift and spread; bistatic imagery forming geometry; matched filtering, focusing and motion compensation; coregistration with monostatic data; the use of active and passive calibrators. Several authors have proposed tailoring or generalizing the procedures developed for monostatic radar to bistatic geometry [1.58, 1.59]. In parallel, other authors have focused their attention on novel techniques, e.g. the notion of the ambiguity function in the context of bistatic radar and its application to signal design was studied in References [1.18] and [1.60], showing the significant effects of bistatic geometry on the resolution capabilities of the transmitted waveform and the need for novel approaches. A method based on a Fourier analysis for Doppler processing of bistatic synthesized array data was developed in Reference [1.22] and a two-dimensional range–azimuth domain ambiguity function was presented in Reference [1.61]. Procedures for bistatic pulse compression were shown in References [1.62] and [1.63]. The importance of heterodyne synchronization to avoid or maximally reduce the Doppler frequency shift in a bistatic SAR has been pointed out in Reference [1.64]. A procedure for onboard matched filtering of a spaceborne bistatic SAR which accounts for linear range migration of moving targets was reported in Reference [1.65]. In Reference [1.66] a processing technique of airborne and space-based radar was presented. Development of a range–Doppler processor accounting for range migration and its validation performed by using airborne BSAR data was reported in Reference [1.67]. A procedure for attitude determination of bistatic radar based on single-look complex data processing was presented in Reference [1.68]. The BSAR point target response in space–time and frequency domains was derived in Reference [1.69], giving evidence of some peculiar aspects in bistatic imagery geometric characteristics. Finally, in Reference [1.12] development of a new bistatic calibration technique to be adopted within an experimental facility was described.

• 13

SCIENTIFIC APPLICATIONS OF THE BSAR

1.3.8 Position and Velocity Measurements

It is well known that SAR interferometry allows a digital terrain elevation model to be obtained by phase measurements [1.33] and that a maximum baseline exists as a function of wavelength to avoid decorrelation [1.34]. Since the BSAR baseline is much larger than the interferometric SAR one, when monostatic and bistatic data are compared the echoes are at least spatially decorrelated and coherent processing cannot be carried out. Below a procedure for obtaining a digital terrain elevation model from monostatic and bistatic data is presented. Among other hypotheses and quantities that will be detailed later, it requires accurate time synchronization between the transmitter and bistatic receiver, such as is obtainable by using GPS time on both platforms carrying the antennae [1.70]. Hence, it is assumed that monostatic and bistatic slant ranges are derived by measuring the time intervals between the pulse transmission and reception. With reference to Figure 1.10, T is the monostatic antenna (i.e. the Tx/Rx one), R is the bistatic antenna (i.e. the Rx-only one), P is the observed target and XYZ is the right-handed, inertial reference frame (IRF). If a spaceborne bistatic system is considered, the IRF is Earthcentred, with the X axis directed along the first point of Aries and the Z axis along the geographic north. In the case of an airborne system an Earth-fixed IRF can be easily selected, e.g. with the origin in the nadir of the Tx/Rx antenna initial position, the Z axis directed upward and the X axis directed horizontally in the same plane as the antenna velocity vector. For the sake of

Rx-only antenna orbit

Z

Tx/Rx antenna orbit

VR R

RR rR

ΘR

P

VT B

T

RT

rT

ΘT

RP G

X

Figure 1.10 Geometry of bistatic observation along parallel trajectories of a spaceborne system

Y

• 14

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

figure simplicity, it is assumed that the two antennae fly along parallel trajectories; however, the procedure is not affected by this condition. To estimate the position of the observed target in the IRF it is assumed that, after focusing, it lies in the range elevation planes of both the antennae (i.e. the effects of possible squint angles have been removed), but the two planes are not necessarily coincident. The equation of the range elevation plane of the Tx/Rx antenna in the IRF can be written as a function of antenna position and velocity vectors, attitude angles and antenna pointing angles as follows: ξ (X − X T ) + η (Y − YT ) + ζ (Z − Z T ) = 0,

(1.13)

where (X T , YT , Z T ) are the Tx/Rx antenna coordinates and ξ, η, ζ are the IRF components of the antenna longitudinal axis unit vector. Of course, the Rx-only antenna coordinates and its longitudinal axis unit vector must be used to define the corresponding range elevation plane. In the following, Ma is the transformation matrix between the antenna-fixed reference frame (ARF) (right-handed reference frame with the origin in the Tx/Rx antenna phase centre, and axes along the antenna longitudinal, lateral and normal axes, the first one directed forwards and the last one directed towards the Earth) and the body-fixed reference frame (BRF) (righthanded reference frame with the origin in the antenna phase centre, and axes parallel to the inertia principal axes of the platform), Mb is the transformation matrix between the BRF and the TRF (right-handed reference frame with the origin in the Tx/Rx antenna phase centre, third axis along −RT and second axis normal to the plane defined by −RT and V T in the spaceborne configuration, whereas the third axis is directed downwards and the second axis is normal to the plane defined by the third axis and V T in the airborne case), and Mt is the transformation matrix between the TRF and the IRF. Therefore, ξ η ζ can be computed as follows: [ξ η ζ ]T = Mt Mb Ma [1 0 0]T .

(1.14)

In Equation (1.14) the elements of Ma are computed by means of the Euler angles of the ARF with respect to the BRF, i.e. the known antenna pointing angles with respect to the platform. The platform attitude angles allow Mb to be computed, and the components of −RT and V T furnish Mt in the spaceborne configuration [1.71], whereas in the airborne case the local vertical must be selected instead of −RT . Finally, the IRF coordinates of the observed target (X P , YP , Z P ) are obtained by taking the numerical solution of the following system: ⎧ 2 2 2 2 ⎪ ⎨ (X P − X T ) + (YP − YT ) + (Z P − Z T ) = rT , (1.15) (X P − X R )2 + (YP − YR )2 + (Z P − Z R )2 = rR2 , ⎪ ⎩ ξ (X P − X T ) + η (YP − YT ) + ζ (Z P − Z T ) = 0, closest to the Earth’s centre. This method requires the knowledge of 14 scalars in all: the two slant ranges, position, velocity and attitude of the Tx/Rx antenna, and the position of the Rx-only one. If required for greater accuracy, the antennae phase centre IRF coordinates can be computed accounting for platform centre of mass and/or an onboard GPS receiver coordinates and for platform attitude angles, whereas the velocity difference between the platform centre of mass and antenna phase centre can certainly be considered to be negligible and the antenna can be assumed to be rigidly fixed to the platform, hence exhibiting the same attitude angles.

SCIENTIFIC APPLICATIONS OF THE BSAR

• 15

As an alternative solution, the rigorous radar stereo intersection problem can be solved [1.31, 1.72], which envisages the solution of the following set of four equations in the three unknowns (X P , YP , Z P ) by means of a least squares algorithm ⎧ |RP − RT | = r T , ⎪ ⎪ ⎪ ⎨ |RP − RR | = r R , ⎪ ⎪ V T · (RP − RT ) = 0, ⎪ ⎩ V R · (RP − RR ) = 0.

(1.16)

This technique requires again the knowledge of 14 scalars in all: the two slant ranges and the position and velocity components of both antennae. The first two equations in (1.16) correspond to the first two equations in (1.15), whereas the third and fourth equations require that the range elevation plane is normal to the velocity vector. However, the hypothesis can be removed if the attitude and pointing angles are known for each antenna, which allow the angle between the antenna longitudinal axis and the velocity vector to be computed. Finally, a procedure to compute the two slant range components of the target velocity will be described. The Doppler centroid frequency in SAR imagery can be computed by means of well-assessed algorithms (see, for example, References [1.28] and [1.29]) and can be related to the position and velocity vectors and to the slant range in monostatic [1.19] and bistatic [1.1] geometry as follows: f DT = −2 (V T − V P ) · (RT − RP )/(λrT ) , f DR = − [(V T − V P ) · (RT − RP )/r T + (V R − V P ) · (RR − RP )/rR ]/λ.

(1.17)

In the spaceborne case it may be interesting to obtain the target velocity with respect to the Earth, i.e. also accounting for Earth rotation, which can be computed by using the Earth angular rate vector V P = V P⊕ + Ω⊕ × rP .

(1.18)

If required, Equations (1.17) can be written considering vector components in well-known Earth-fixed reference frames (such as the universe transverse Mercator (UTM) system or latitude–longitude) by means of time-varying transformations [1.71]. Since only slant range components of target–antenna relative velocities can affect Doppler centroid frequencies, Equations (1.17) and (1.18) can be solved by assuming the two slant range components as unknowns; i.e. the analysis is restricted to the bistatic plane [1.1, 1.30]. Finally, in addition to the parameters previously required to compute target position by using the first presented procedure, the Rx-only antenna velocity and the two Doppler centroid frequencies are needed to estimate the target velocity components, and hence 19 scalars in all.

1.3.9 Bistatic Stereoradargrammetry Classic stereoradargrammetric models refer to the processing of pairs of monostatic images, taken on the same area under different viewing angles, for computing terrain elevation [1.31, 1.35, 1.72, 1.73]. In fact, points on the Earth’s surface exhibit different relief displacements

• 16

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

as a function of their elevation, their position in the range line and radar pointing angles. The relief reconstruction procedure is based on the measurement of the differences of target positions in the two images forming the stereoscopic pair and on the equations relating the positions and heights of the viewed targets. Typically, the target height is linked directly to the parallax difference between the two observations, with the parallax expressed as a function of target slant ranges or ground ranges, which are the typical across-track coordinates in radar images. When a monostatic image and a bistatic one are adopted to form the stereoscopic pair, new relations are needed to define the parallax as a function of the peculiar parameters of bistatic surveying geometry. Namely, the models of classical stereoradargrammetry must be specialized to the considered monostatic/bistatic configuration. A brief description of the adopted model will be given in the following, where the proposed approach is based only on slant range coordinates, since it can be applied without performance degradations due to the necessary slant to ground range coordinate transformation. Figure 1.11 shows the bistatic viewing geometry and the symbols adopted for the quantities of interest. Height computation by means of stereoradargrammetric techniques, such as in photogrammetry, is based on relative measurements; i.e. a datum must be defined and heights are computed with respect to the datum level. Hence, the absolute parallax is defined with

Tx/Rx radar trajectory

O

B

Rx-only radar trajectory

O '

'0 " H

r0

r

"0 H

r

datum Og

r0 Og T

h rg

Tx/Rx radar ground track

rg

Tg

Rx-only radar ground track

Figure 1.11 Viewing geometry of a bistatic stereoradargrammetric survey with coincident boresight observations, taken along parallel trajectories, and assuming a flat earth and zero-datum configuration

• 17

SCIENTIFIC APPLICATIONS OF THE BSAR

reference to the target relief displacement in the radar image, whereas parallax differences are obtained with respect to datum, which defines a reference absolute parallax that must be evaluated to derive the target relative height. Finally, accurate knowledge of the height of a limited number of ground control points allows topographic elevation to be evaluated [1.74–1.76]. The following hypotheses, partly derived from classic radargrammetric formulations, have been adopted for tailoring the stereo model to bistatic geometry:

1. Same side stereo configuration; i.e. the two antennae observe the scene from the same side to avoid bistatic slant range ambiguities. This might be considered a limiting factor in forming large bistatic stereo baselines with respect to monostatic stereo configurations, but it has been shown that opposite-side stereo radar images can exhibit severe geometric distortions, which make image matching difficult and involve less accurate elevation extraction [1.77, 1.78]. The Rx-only bistatic antenna is again considered the closest to the observed area. 2. Flat Earth; i.e. the viewed scene relief is reconstructed assuming that the zero-relief surface (datum) is flat and perpendicular to the antenna nadir. This assumption has been made for the sake of simplicity; a more sophisticated model could be developed for spaceborne systems, accounting for a spherical Earth, and a known nonzero datum can be easily selected. 3. Parallel tracks; i.e. the two antennae fly in formation along parallel trajectories, at the same height and with identical velocity (i.e. cross-track bistatic coverage). Antennae positions and velocities have been derived, as an example by processing GPS data, and the bistatic baseline can be computed. It is worth noting that accurate knowledge of orbital parameters is essential for extracting elevation data [1.20, 1.42, 1.74, 1.79] and that a small intersection angle between the radar trajectories is essential to reduce geometric distortions that avoid adequate stereo processing [1.77]. 4. Nominal antenna pointing at boresight; i.e. there are no squint angles. Hence the rangeelevation planes of the two antennae are coincident and perpendicular to the antenna velocity vector (evaluated with respect to the Earth, i.e. the velocity accounts for Earth rotation in the case of a spaceborne system). As a consequence, targets are focused in this common plane. Monostatic and bistatic slant ranges of a target, T, can be derived from focused images, and the bistatic baseline and antennae height with respect to the datum level can be obtained assuming accurate knowledge of antennae trajectories. Hence, with reference to Figure 1.11, it is possible to compute the ground range to the target and off-nadir pointing angles with respect to the target at the datum level as follows: rg2 + (H − h)2 = r 2 r 2 − r 2 + B 2 , (1.19) 2 2 2 ⇒ rg = (rg − B) + (H − h) = r 2B Θ 0 = tan−1 Θ 0 = tan−1

rg

H rg − B H

,

(1.20)

.

(1.21)

• 18

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

In monostatic geometry the parallax of the target is coincident with its slant range and can be related to the height: p = r =

H −h , cos Θ

(1.22)

whereas in bistatic geometry the following parallax can be defined: p =

r + r H −h = 2 2

1 1 + cos Θ cos Θ

.

(1.23)

The parallax difference between monostatic and bistatic observation is given by r − r H −h dp = p − p = = 2 2

1 1 − cos Θ cos Θ

(1.24)

and is positive for Θ > Θ , as in Figure 1.11, where the receiving-only antenna is assumed to be closer to the target to avoid too large off-nadir angles for the bistatic receiver, thus taking advantage of stronger echoes and reducing geometric distortions. The monostatic–bistatic parallax difference at the datum level can be computed as d p0 =

H 2

1 1 − cos Θ 0 cos Θ 0

.

(1.25)

This allows an equation to be obtained relating the parallax difference measured in the monostatic–bistatic stereo pair dp to the target height H H −h 1 1 1 1 d p − d p0 = − − − 2 cos Θ cos Θ 2 cos Θ 0 cos Θ 0

1 (H − h)2 + H 2 tan2 Θ 0 − (H − h)2 + H 2 tan2 Θ 0 = 2 1 1 −H − cos Θ 0 cos Θ 0

(1.26)

2 Assuming h H 1, which is acceptable both for spaceborne and airborne bistatic formations due to the large value of radar altitude with respect to terrain elevation, which is defined with reference to the datum level, the above equation can be written as H d p − d p0 = 2

1 h − −2 2 cos Θ 0 H

1 h − − 2 2 cos Θ 0 H

1 1 − cos Θ 0 cos Θ 0

. (1.27)

Hence, it has been obtained that the parallax difference, dp, consequent to target elevation with respect to a reference level, h, depends on its across-track position in the monostatic– bistatic pair r and r and observation geometry (namely radar altitude H and baseline B). This result is conceptually similar to the one obtained for monostatic radargrammetry [1.31],

• 19

SCIENTIFIC APPLICATIONS OF THE BSAR

although expressed with different equations. It is worth mentioning that evaluation of the slant range shift between homologous points in the monostatic and bistatic images can be carried out by applying the well-known procedures developed for interferometric image pair registration [1.42, 1.80] or specifically for stereoradargrammetric applications [1.36, 1.81– 1.83]. As an alternative solution for height computation by using as input a stereoradargrammetric pair obtained in bistatic geometry, but without measuring the parallaxes, a model has been developed that also accounts for Earth surface curvature (hence applicable also to the spaceborne BSAR) and actual orientation of the range elevation planes of the antennas, i.e. for differences in antenna attitude and pointing angles along nonparallel trajectories. Assuming a spherical Earth model, the instantaneous three-dimensional viewing geometry has been projected on to the range–elevation plane of the first antenna in order to compute in this plane the quantities of interest for relief reconstruction by means of trigonometric relations (Figure 1.12).

O′

V ⊕′

V ⊕′′

B⊥

Θ'

O ⊥′′

B O ′′

r ⊥′′

Θ"

r′

r ′′

R′

n

R ′′

T

R ⊥′′

h Zero elevation reference surface (spherical earth)

r⊕

Figure 1.12 Three-dimensional viewing geometry of the bistatic stereoradargrammetric survey (not to scale for clarity). Dashed lines are relevant to the projections on the range-elevation plane of the first antenna.

• 20

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

After constructing the unit vector n normal to the first antenna range elevation plane defined by the antenna position vector and boresight direction (assumed perpendicular to antenna velocity with respect to the Earth) and directed forwards R × V ⊕ × R , n= (1.28) R × V ⊕ × R the moduli of projected baseline and second antenna slant range and position vector are computed as follows: B⊥ =

r⊥ =

R⊥

|B|2 − (B·n)2 ,

(1.29)

|r |2 − (r ·n)2 ,

(1.30)

= |R |2 − (R ·n)2 .

(1.31)

Finally, the target elevation can be retrieved as h=

R 2 + r 2 − 2R r cos Θ − r⊕ ,

(1.32)

where the off-nadir angle of the first antenna is given by

Θ = cos

−1

2 R 2 + B⊥2 − R⊥ 2R B⊥

−1

− cos

r 2 + B⊥2 − r⊥2 2r B⊥

.

(1.33)

The above model can be extended to the simpler airborne geometry, defining positions of the antennae by means of two vectors representative of the heights with respect to the datum level and directed upward, instead of the position vectors with respect to the Earth’s centre.

1.4 SUMMARY This chapter gives an overview of the main issues of the BSAR for airborne and spaceborne remote sensing applications. A brief review of the state-of-the-art in bistatic radar is made, showing both limitations in availability of bistatic systems and data and the great interest for their potentialities, and then the BSAR geometry is presented. Ground range and azimuth resolutions are investigated, considering various antenna formations and showing their dependence on bistatic observation geometry. Finally, the main scientific applications of BSAR data are presented, considering both results reported in the literature and original techniques. Advantages of multiangle BSAR observations for rough surface characterization and discrimination are pointed out. Special emphasis is given to topographic applications, presenting techniques based on tailoring multirange measurements and stereoradargrammetric methods to bistatic geometry for obtaining terrain elevation measurements.

VARIABLES

ABBREVIATIONS ARF BRCS BRF BSAR GPS IRF Rx SAR SNR TRF Tx UTM

antenna-fixed reference frame bistatic radar cross-section body-fixed reference frame bistatic SAR Global Positioning System inertial reference frame receiving synthetic aperture radar signal-to-noise ratio Tx/Rx antenna-fixed reference frame Transmitting universe transverse Mercator reference system

VARIABLES B B c e fD h H

Ma Mb Mt n p r r rg r⊕ R V W (X, Y, Z ) α β γ a r x ϕ Θ

baseline baseline vector from the Tx/Rx antenna to the Rx-only one velocity of light isorange contour curve (ellipse) eccentricity Doppler centroid frequency target elevation with respect to datum antenna altitude with respect to datum antenna length transformation matrix between the ARF and the BRF transformation matrix between the BRF and the TRF transformation matrix between the TRF and the IRF unit vector normal to the first antenna range elevation plane parallax slant range slant range vector from the antenna to the target ground range spherical Earth’s local radius antenna position vector with respect to the centre of the Earth antenna velocity vector chirp bandwidth coordinates in the IRF Tx/Rx antenna depression angle with respect to the baseline bistatic angle along-track antenna beamwidth semi-aperture angle azimuth resolution ground range resolution along-track separation phase difference off-nadir angle

• 21

• 22

λ ξ, η, ζ ρ⊕ ψ Ω⊕

FUNDAMENTALS OF BISTATIC SYNTHETIC APERTURE RADAR

radiation wavelength IRF components of the Tx/Rx antenna longitudinal axis unit vector spherical Earth radius terrain aspect angle with respect to the bistatic angle bisector Earth angular rate vector

Subscripts/Superscripts b D g m P R T

0 ⊕ ⊥

bistatic Doppler ground range projections monostatic target Rx-only antenna Tx/Rx antenna first antenna (i.e. the Tx/Rx one) in the stereoradargrammetric pair second antenna (i.e. the Rx-only one) in the stereoradargrammetric pair evaluated with respect to a zero reference datum Earth range-elevation plane of the first antenna in the stereoradargrammetric pair

REFERENCES 1.1 Willis, N.J. (1995) Bistatic Radar, SciTech Publishing, Inc., Mendahm, New Jersey. 1.2 Glaser, J.I. (1989) Some results in the bistatic radar cross section (RCS) of complex objects, Proc. IEEE, 77 (5), 639–48. 1.3 Eigel, R.L., Collins, P.J., Terzuoli, A.J., Nesti, G. and Fortuny, J. (2000) Bistatic scattering characterization of complex objects, IEEE Trans., GRS-38 (5), 2078–92. 1.4 Peterson, A.M., Teague, C.C. and Tyler, G.L. (1970) Bistatic-radar observation of longperiod, directional ocean-wave spectra with Loran A, Science, 170, 158–61. 1.5 Atlas, D., Naito, K. and Carbone, R.E. (1968) Bistatic microwave probing of a refractively perturbed clear atmosphere, J. Atmospheric Sciences, 25, 257–68. 1.6 Doviak, R.J., Goldhirsh, J. and Miller, A.R. (1972) Bistatic radar detection of high altitude clear air atmospheric targets, Radio Science, 7, 993–1003. 1.7 Doviak, R.J. and Weil, C.M. (1972) Bistatic radar detection of the melting layer, J. Applied Meteorology, 11, 1012–16. 1.8 Wurman, J., Heckman, S. and Boccippio, D. (1993) A bistatic multiple-Doppler network, J. Applied Meteorology, 32, 1802–14. 1.9 Rogers, P.J. and Eccles, P.J. (1971) The bistatic radar equation for randomly distributed targets, Proc. IEEE, 59 (6), 1019–21. 1.10 Friedlander, B. and Porat, B. (1998) VSAR: a high resolution radar system for ocean imaging, IEEE Trans., AES-34 (3), 755–71. 1.11 Chen, P. and Beard, J.K. (2000) Bistatic GMTI experiment for airborne platforms, in The Record of the IEEE International Radar Conference, pp. 42–46.

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1.12 Hauck, B., Ulaby, F.T. and DeRoo, R.D. (1998) Polarimetric bistatic-measurement facility for point and distributed targets, IEEE Antennas and Propagation Mag., 40 (1), 31–41. 1.13 Willis, N.J. (2002) Bistatic radars and their resurgence: passive coherent location, Tutorial presented at the IEEE Radar Conference, Long Beach, California, 24 April 2002. 1.14 Griffiths, H.D. (2003) From a different prospective: principles, practice and potential of bistatic radar, in Proceedings of the 2003 IEEE Radar Conference, pp. 1–7. 1.15 Teague, C.C., Tyler, G.L. and Stewart, R.H. (1977) Studies of the sea using HF radio scatter, IEEE Trans. AP-25 (1), 12–9. 1.16 Autermann, J.L. (1984) Phase stability requirements for a bistatic SAR, in Proceedings of the IEEE National Radar Conference, pp. 48–52. 1.17 The Institution of Electrical Engineers (IEE) (1986) Communications, radar and signal processing: Special Issue on bistatic and multistatic radar, IEE Proc.-F, 133, 587–668. 1.18 Zeng, T., Cherniakov, M. and Long, T. (2005) Generalized approach to resolution analysis in BSAR, IEEE Trans., AES-41 (2), 461–74. 1.19 Ulaby, F.T., Moore, R.K. and Fung, A.K. (1982) Microwave Remote Sensing: Active and Passive, Vol. II: Radar Remote Sensing and Surface Scattering and Emission Theory, Advanced Book Program, Addison-Wesley, Reading, Massachusetts. 1.20 Moccia, A., Chiacchio, N. and Capone, A. (2000) Spaceborne bistatic synthetic aperture radar for remote sensing applications, Int. J. Remote Sensing, 21 (18), 3395–414. 1.21 Skolnik, M.I. (1980) Introduction to Radar Systems, McGraw-Hill, New York. 1.22 Soumekh, M. (1991) Bistatic synthetic aperture radar inversion with application in dynamic object imaging, IEEE Trans. Signal Processing, 39 (9), 2044–55. 1.23 Ulaby, F.T., Moore, R.K. and Fung, A.K. (1986) Microwave Remote Sensing: Active and Passive, Vol. III: Volume Scattering and Emission Theory, Advanced Systems and Applications, Artech House, Inc., Dedham, Massachusetts. 1.24 Ogilvy, J.A. (1991) Theory of Wave Scattering from Random Rough Surfaces, Hilger, Bristol. 1.25 Ulaby, F.T. and Elachi, C. (1990) Radar Polarimetry for Geoscience Applications, Artech House, Inc., Norwood, Massachusetts. 1.26 Khenchaf, A., Daout, F. and Saillard, J. (1996) The two-scale model for random rough surface scattering, OCEANS 96 MTS/IEEE Supplementary Proceedings, 2, 50–4. 1.27 Khenchaf, A. (2001) Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band, Waves in Random Media, 11, 61–89. 1.28 Li, F.K., Held, D.N., Curlander, J.C. and Wu, C. (1985) Doppler parameter estimation for spaceborne synthetic aperture radars, IEEE Trans., GRS-24, 1022–25. 1.29 Madsen, S.N. (1989) Estimating the Doppler centroid of SAR data, IEEE Trans., AES-25 (2), 134–40. 1.30 Farina, A. (1986) Tracking function in bistatic and multistatic radar systems, IEE Proc.-F, 133, 630–7. 1.31 Leberl, F. (1990) Radargrammetric Image Processing, Artech House, Boston, Massachusetts. 1.32 Madsen, S.N., Zebker, H.A. and Martin, J. (1993) Topographic mapping using radar interferometry: processing techniques, IEEE Trans., GRS-31 (1), 246–56. 1.33 Rosen, P.A., Hensley, S., Joughin, I.R., Li, F.K., Madsen, S.N., Rodriguez, E. and Goldstein, R.M. (2000) Synthetic aperture radar interferometry, Proc. IEEE, 88 (3) 333–82.

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1.34 Rodriguez, E. and Martin, J.M. (1992) Theory and design of interferometric synthetic aperture radars, IEE Proc. F, Radar and Signal Processing, 139 (2), 147–59. 1.35 Leberl, F., Domik, G., Raggam, J., Cimino, J.B. and Kobrick, M. (1986) Multiple incidence angle SIR-B experiment over Argentina: stereo-radargrammetric analysis, IEEE Trans., GRS-24 (4), 482–91. 1.36 Paillou, P. and Gelautz, M. (1998) The optimal gradient matching method: application to X-SAR and Magellan stereo images, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ‘98), Vol. 5, pp. 2357–9. 1.37 Zebker, H.A. and Villasenor, J. (1992) Decorrelation in interferometric radar echoes, IEEE Trans., GRS-30 (5), 950–9. 1.38 Marra, M., Maurice, K.E., Ghiglia, D.C. and Frick, H.G. (1998) Automated DEM extraction using RADARSAT ScanSAR stereo data, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ‘98), Vol. 5, pp. 2351–3. 1.39 Gelautz, M., Paillou, P., Chen, C.W. and Zebker, H.A. (2004) A comparative study of radar stereo and interferometry for DEM generation, in Proceedings of the Fringe 2004 Workshop, Frascati, Italy, ESA SP-550, June 2004. 1.40 Gens, R. and van Genderen, J.L. (1996) Review article SAR interferometry-issues, techniques, applications, Int. J. Remote Sensing, 17, 1803–35. 1.41 D’Addio, E. and Farina, A. (1986) Overview of detection theory in multistatic radar, IEE Proc.-F, 133, 613–23. 1.42 Rufino, G., Moccia, A. and Esposito, S. (1998) DEM generation by means of ERS tandem data, IEEE Trans., GRS-36 (6), 1905–12. 1.43 DeRoo, R.D. and Ulaby, F.T. (1994) Bistatic specular scattering from rough dielectric surfaces, IEEE Trans., AP-42 (2), 220–30. 1.44 Airiau, O. and Khenchaf, A. (1999) Simulation of a complete moving polarimetric bistatic radar: Application to the maritime environment, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’99), Vol. 5, pp. 2751–3. 1.45 Airiau, O. and Khenchaf, A. (2000) A methodology for modeling and simulating target echoes with a moving polarimetric bistatic radar, Radio Science, 35 (3), 773–82. 1.46 Thompson, D.R. and Elfouhaily, T.M. (1999) Microwave scattering from the ocean surface computed using an extended bistatic scattering model, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’99), Vol. 5, pp. 2748–50. 1.47 Zavorotny, V.U. and Voronovich, A.G. (2000) Scattering of GPS signals from the ocean with wind remote sensing applications, IEEE Trans., GRS-38 (2), 951–64. 1.48 Zavorotny, V.U. and Voronovich, A.G. (2000) Bistatic GPS signal reflections at various polarizations from rough land surface with moisture content, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’00), Vol. 7, pp. 2852–54. 1.49 Ulaby, F.T., van Deventer, T.E., East, J.R., Haddock, T.F. and Coluzzi, M.E. (1988) Millimeter-wave bistatic scattering from ground and vegetated targets, IEEE Trans., GRS-26 (3), 229–43. 1.50 Khenchaf, A. and Airiau, O. (2000) Bistatic radar moving returns from sea surface, IEICE Trans. Electronics, E83-C (12), 1827–35. 1.51 Alpers, W., Ross, D. and Rufenach, C. (1981) On the detectability of ocean surface waves by real and synthetic aperture radar, J. Geoph. Res., 86 (C7).

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1.52 Hasselmann, K., Raney, R.K., Plant, W.J., Alpers, W., Shuchman, R.A., Lyzenga, D.R., Rufenach, C.L. and Tucker, M.J. (1985) Theory of synthetic aperture radar ocean imaging: a MARSEN view, J. Geophysical Research, 90 (C3), 4659–86. 1.53 Hasselmann, K. and Hasselmann, S. (1991) On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion, J. Geophysical Research, 96 (C6), 10.713–10.729. 1.54 Mart´ın-Neira, M., Caparrini, M., Font-Rossello, J., Lannelongue, S. and Serra Vallmitjana, C. (2001) The PARIS concept, an experimental demonstration of sea surface altimetry using GPS reflected signals, IEEE Trans., GRS-39 (1), 142–50. 1.55 Fung, A.K., Zuffada, C. and Hsieh, C.Y. (2001) Incoherent bistatic scattering from the sea surface at L-band, IEEE Trans., GRS-39 (5), 1006–12. 1.56 Huang, X.Z. and Jin, Y.Q. (1995) Scattering and emission from two-scale randomly rough sea surface with foam scatterers, IEE Proc.-Microwaves, Antennas and Propagation, 142 (2), 109–14. 1.57 Moccia, A., Rufino, G. and De Luca, M. (2003) Oceanographic applications of spaceborne bistatic SAR, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’03), Vol. 3, pp. 1452–4. 1.58 Lowe, M. (2002) Algorithms for high resolution bistatic SAR, in IEEE Radar Conference., pp. 512–5. 1.59 D’Aria, D., Monti Guarnieri, A. and Rocca, F. (2004) Bistatic SAR processing using standard monostatic processor, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR’04), pp. 385–8. 1.60 Tsao, T., Slamani, M., Varshney, P., Weiner, D. and Schwarzlander, H. (1997) Ambiguity function for a bistatic radar, IEEE Trans., AES-33 (3), 1041–51. 1.61 Soumekh, M. (1998) Wide-bandwidth continuous-wave monostatic/bistatic synthetic aperture radar imaging, in Proceedings of the ICIP’98, Vol. 3, pp. 361–5. 1.62 D’Aria, D., Monti Guarnieri, A. and Rocca, F. (2004) Focusing bistatic synthetic aperture radar using dip move out, IEEE Trans., GRS-42 (7), 1362–76. 1.63 Ogrodnik, R.F., Wolf, W.E., Schneible, R. and McNamara, J. (1997) Bistatic variants of spacebased radar, in Proceedings of the IEEE Aerospace Conference, Vol. 2, pp. 159–69. 1.64 Cherniakov, M., Kubik, K. and Nezlin, D. (2000) Bistatic synthetic aperture radar with non-cooperative LEOS based transmitter, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’00), Vol. 2, pp. 861–2. 1.65 DiPietro, R.C., Fante, R.L. and Perry, R.P. (1997) Space-based bistatic GMTI using low resolution SAR, in Proceedings of the IEEE Aerospace Conference, Vol. 2, pp. 181–92. 1.66 Tomlinson, P.G. (1999) Modeling and analysis of monostatic/bistatic space-time adaptive processing for airborne and space-based radar, in The Record of the 1999 IEEE Radar Conference, pp. 102–7. 1.67 Ender, J.H.G., Walterscheid, I. and Brenner, A.R. (2004) New aspects of bistatic SAR: processing and experiments, in Proceedings of the International Symposium on Geoscience and Remote Sensing Symposium (IGARSS’04), Vol. 3, pp. 1758– 62. 1.68 Rufino, G. and Moccia, A. (1997) A procedure for attitude determination of a bistatic SAR by using raw data, in 48th International Astronautical Federation Congress, paper IAF-97-B.2.04, pp. 1–8.

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1.69 Loffeld, O., Nies, H., Peters, V. and Knedlik, S. (2004) Models and useful relations for bistatic SAR processing, IEEE Trans., GRS-42 (10), 2031–8. 1.70 Lee, P.F. and James, K. (2001) The RADARSAT-2/3 Topographic mission, in Proceedings of the Geoscience and Remote Sensing Symposium (IGARSS’01), Vol. 3, pp. 1477–9. 1.71 Moccia, A. and Vetrella, S. (1986) An integrated approach to geometric precision processing of spaceborne high-resolution sensors, Int. J. Remote Sensing, 7 (3), 349–59. 1.72 Rosenfield, G. (1968) Stereo radar techniques, Photogrammetric Engineering, 34, 586– 94. 1.73 La Prade, G. (1963) An analytical and experimental study for stereo radar, Photogrammetric Engineering, 29 (2), 294–300. 1.74 Chen, P. and Dowman, I.J. (2001) A weighted least squares solution for space intersection of spaceborne stereo SAR data, IEEE Trans., GRS-39 (2), 233–40. 1.75 Toutin, T. (2000) Evaluation of radargrammetric DEM from RADARSAT images in high relief areas, IEEE Trans., GRS-38 (2), 782–9. 1.76 Sohn, H.G., Song, Y.S. and Kim, G.H. (2005) Radargrammetry for DEM generation using minimal control points, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’05), Vol. 2, pp. 1162–4. 1.77 Paillou, P. and Gelautz, M. (1999) Relief reconstruction from SAR stereo pairs: the ‘optimal gradient’ matching method, IEEE Trans., GRS-37 (4), 2099–107. 1.78 Lee, H., Morgan, J.V. and Warner, M.R. (2003) Radargrammetry of opposite-side stereo Magellan synthetic aperture radar on venus, in Proceedings of the Geoscience and Remote Sensing Symposium (IGARSS ’03), Vol. 1, pp. 182–4. 1.79 Singh, K., Lim, O.K., Kwoh, L.K. and Lim, H. (1997) Accuracy assessment of elevation data obtained from Radarsat stereo images, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’97), Vol. 1, pp. 213–5. 1.80 Moccia, A., Esposito, S. and D’Errico, M. (1994) Height measurement accuracy of ERS-1 SAR interferometry, EARSeL Adv. in Remote Sensing, 3 (1), 94–108. 1.81 Nocera, L., Dupont, S. and Berthold, M. (1996) A simulation-based validation of some improvements in automatic stereo-radargrammetry, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’96), Vol. 1, pp. 25–7. 1.82 Singh, K., Lim, O.K., Kwoh, L.K. and Lim, H. (1998) An accuracy evaluation of DEM generated using Radarsat stereo images, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’98), Vol. 2, pp. 1031–3. 1.83 Toutin, T. (2000) Error tracking of radargrammetric DEM from RADARSAT images, IEEE Trans., GRS-37 (5), 2227–38.

2 Spaceborne Bistatic Synthetic Aperture Radar Antonio Moccia and Marco D’Errico

2.1 INTRODUCTION In reviewing spaceborne bistatic radar, it must be acknowledged at the outset that most spaceborne active microwave missions have been carried out by monostatic radar. Few studies, and even less experimentations, have been conducted on space-based bistatic antenna configurations, despite their great applicative interest. In the case of single-pass interferometry the two antennas operate simultaneously. Therefore, in a bistatic configuration, the antenna physical separation must be kept within limited values, depending on the wavelength, to avoid decorrelation and phase ambiguities [2.1–2.3]. Moving to the subject of large baselines, which is the main focus of this chapter, a limited number of bistatic radar experiments have been conducted by making use of existing spaceborne systems. In particular, Reference [2.4] explored refraction, absorption and scattering mechanisms in the atmosphere by means of a transmitting antenna on board the orbital station Mir and a receiving antenna on board a geosynchronous satellite. Experiments have been conducted in planetology, by means of satellite-based transmitters and Earth-based receivers [2.5–2.9] or a planet-based transmitter and a satellite-based receiver [2.10]. As an example, topography, reflectivity, scattering and root-mean-square slope have been computed for the surface of the Moon, Mars and Venus. In these applications, bistatic radar has proven to be capable of: (a) providing information on surface texture and density at scales of a few centimetres to a few hundred metres, along with highly accurate dielectric constant measurements; (b) remote probing in regions and under conditions not obtainable with Earth-based systems. Finally, the capability of using an ERS-1 SAR (synthetic aperture radar) echo gathered by an airborne receiver for bistatic imaging of urban scenes was demonstrated in Reference [2.11], and an experiment in which Envisat ASAR (advanced SAR) data were collected by an Earthbased receiver for moving target detection is presented in Reference [2.12], in particular for

Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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air traffic control. These are very demanding experiments due to the extremely limited time available to exploit the signal transmitted from a single satellite in low Earth orbit (LEO) by means of a nonorbiting receiver. As a consequence, more recently, the use of spaceborne illuminators able to guarantee fulltime coverage is gaining momentum. For example, measurements of GPS (global positioning system) reflected signals for an estimation of the sea state and wind speed [2.13–2.15] and for remote sensing of rough surfaces [2.16, 2.17] have been conducted. The application of bistatic GPS echo to moving target detection has also been investigated, with particular reference to aircraft approaching a runway [2.18]. Regarding the future use of ‘illuminators of opportunity’, i.e. already existing, independently operated, noncooperative microwave illuminators, exploitable as sources of the signal to gather in bistatic configurations, a review of ideas, references and issues can be found in Reference [2.19] and a power budget analysis showing the feasibility of collecting global navigation satellite signals for synthetic aperture formation has been carried out in Reference [2.20]. In particular, among the examples present in the literature, it is worth mentioning a constellation of spaceborne receivers of GPS reflected signals for bistatic remote sensing applications [2.21], emphasizing sensor synchronization issues both in time and space. Furthermore, a passive geosynchronous SAR system, reusing backscattered digital audio broadcasting signals, has been proposed in Reference [2.22] for volcanoes or coseismic motions monitoring or GPS corrections. A bistatic radar based on noncooperative LEO commercial satellites for personal communications and an Earth-based receiver has recently been studied [2.23, 2.24]. The objective of the studies was the detection of vessels at sea and of air targets. Finally, the performance of a space-surface bistatic SAR (SS-BSAR), with an Earth-based receiver and utilizing noncooperative transmitters, such Globalstar, GPS and Galileo, were studied in References [2.25] and [2.26]. However, as a point of fact, no spaceborne experiments have been conducted by using bistatic radar for large-scale Earth observation under assigned and controlled space-based baselines, and fixed pointing and timing conditions. As a consequence, nonsystematic overland bistatic measurements from spacecraft have been reported in the literature [2.14, 2.27, 2.28], in particular considering synthetic aperture radar. However, a certain number of spaceborne bistatic radar experiments have been proposed. Ideas and feasibility studies of spaceborne bistatic radar aimed at worldwide surveillance was presented in Reference [2.29]. Integration of spaceborne radar illumination and bistatic reception by means of aerial vehicles for area surveillance and moving target detection was analysed in Reference [2.30] to [2.33]. In particular, the time and navigation synchronization issues for matching transmitting and receiving instantaneous fields of regard were put in evidence in Reference [2.33]. Bistatic radar altimeters for oceanographic applications have been studied in References [2.21] and [2.34] to [2.37]. A constellation of microsatellites, mainly oriented to interferometry (thus non bistatic with large baselines, but equipped with low-cost, passive receivers), has been proposed in Reference [2.38] and [2.39]. Finally, in recent years new spaceborne bistatic and interferometric missions have been proposed and studied as a complement to the already funded, large monostatic SAR missions that will be operative in the near future: the Italian COSMO-SkyMed [2.40, 2.41] and the German TerraSAR-X [2.42, 2.43]. The design and operation of a space formation aimed at simultaneous SAR observation under assigned baseline conditions, even if composed of only two satellites, require novel studies and procedures for evaluating the overall performance taking into account the system

KEY DESIGN ISSUES IN SPACEBORNE BSAR

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dynamics and sensor pointing. Basically, the mission analysis of a spaceborne bistatic SAR requires a thorough preliminary evaluation of the impact of the required observation and performance on the formation design and operation. Following this, the selection of more suitable approaches for achieving the desired baselines on assigned targets or latitude ranges must be carried out. Finally, a quantitative design of satellite formation orbit and attitude and SAR pointing geometry need to be conducted. In this framework, a first quantitative analysis of the concept of complementing an already existing, large SAR mission with a small, free-flying spacecraft (equipped with a receivingonly antenna operating in the bistatic configuration) has been carried out in Reference [2.44]. Assuming that the passive payload had no possibility of orienting the antenna beam, a need arose to develop the capability of the attitude manoeuvrings of the small spacecraft. It was shown that a mission conducted in tandem with Envisat and using the receiving part only of the ERS-1 SAR would have needed a small satellite bus with a mass of about 600 kg and an average power per orbit of approximately 1200 W. Such a bus would have permitted a nonsteerable payload to fly, thanks to its all-angle attitude manoeuvre capability for a two-year lifetime. The orbit control was found to be feasible, but demanded more in terms of manoeuvre frequency (90 per year during the solar maximum and 17 per year during the solar minimum) rather than of propellant mass, due to the need to fly in formation with a much larger bus characterized by a quite different ballistic coefficient. The attitude subsystem requirement resulted in a manoeuvre capability at an orbital frequency within [−6◦ ,+6◦ ], [−4◦ ,+2◦ ] and [−45◦ ,0◦ ] for yaw, pitch and roll angles respectively, to make the receiving-only antenna follow the Envisat radar swath width for a whole orbit, assuming that the Envisat radar is observing an off-nadir angle of 30◦ . Beginning with these experiences, this section is intended to go through the main design issues in a mission analysis of a spaceborne BSAR, along with presenting a comprehensive model for quantitatively carrying out such a study. In particular, the first part of the chapter is devoted to trade-off studies among several techniques and configurations adequate for bistatic coverage, but accounting for their impact on primary and bistatic system complexities. A review of the proposed orbital formations for bistatic and interferometric applications is presented, and it is shown how they impact on system design. As a result, strategies convenient for bistatic formations are outlined, and key ideas for the selection of the most appropriate are given, depending on the mission scenario (such as the use of two large, identical spacecraft operating in tandem, or of a small satellite operating in parasitic mode with a large main mission). The second part of the section deals with analytical studies aimed at defining satellite orbit and attitude, and SAR pointing geometry to guarantee bistatic baselines and coverage. The models are quite general, to account for all configurations detailed in preceding trade-off studies, and a quantitative application of presented procedures will be reported in Chapter 3.

2.2 KEY DESIGN ISSUES IN SPACEBORNE BSAR 2.2.1 Basic Trade-offs in Spaceborne BSAR Configurations Spaceborne BSAR data can be achieved if the Tx/Rx and the Rx radars operate simultaneously and are widely separated in space so that a common area on the ground is observed under quite different viewing angles. Therefore, Tx/Rx and Rx satellites must fly in orbits that ensure an adequate satellite separation and substantially stable relative dynamics; thus the differences between the orbital parameters of the two satellites are an unavoidable effect to be taken into

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account. Furthermore, the larger the satellite separation, the larger are the orbit parameter differences to be expected. As a consequence, the search for an adequate orbital configuration is the first step in spaceborne BSAR mission design. This is a critical step indeed, as the wrong orbit selection can dramatically impact mission effectiveness and lifetime. A number of orbit configurations have been proposed mainly for interferometric applications (parallel orbits, cartwheel, pendulum), and in principle are also applicable to spaceborne BSAR, although their advantages and limitations must be carefully analysed during mission design. In particular, the concept of simultaneously taking an interferometric pair along ‘parallel orbits’ was introduced in References [2.45] and [2.46] for cross-track SAR interferometric applications in the ambit of the study of the TOPSAT mission. Parallel orbits share the same orbital parameters apart from ascending node right ascensions and spacecraft anomalies, thus obtaining a separation that is mainly horizontal and cross-track with respect to the Tx/Rx satellite. In contrast, the cartwheel concept, introduced in References [2.38] and [2.39] for SAR interferometry, achieves satellite separation mainly in the orbit plane, along both the local vertical and the velocity direction. In fact, passive satellites in a cartwheel formation fly in elliptic orbits that share the orbital plane and the semi-major axis with the Tx/Rx radar. Thus, passive satellite orbits differ from each other not only in perigee anomaly but also in eccentricity and satellite anomaly with respect to the Tx/Rx satellite. Finally, the pendulum concept [2.42, 2.47] came up as a modification of the cartwheel to attain baselines (i.e. spacecraft separation) in the direction of normal to the orbit plane. As will be shown in further detail in Chapter 4, pendulum configurations can be achieved by means of different right ascensions of the ascending nodes, orbital plane inclinations and satellite true anomalies. Hence, the parallel orbit concept can be considered as a special case of pendulum configurations. The applicable orbit concepts will be analysed later in further detail, but they are differently affected by perturbations due to the differences in orbital parameters. Obviously, since larger baselines require larger differences in orbital parameters between the Tx/Rx and the Rx satellites, it is expected that bistatic configurations exhibit larger differences in orbit perturbations between satellites with respect to interferometric configurations. Thanks to the coincidence of orbit eccentricity, inclination, perigee anomaly and semi-major axis, parallel orbits allow the minimization of differences in secular effects of gravitational perturbations between the Rx and the Tx/Rx satellites, with respect to cartwheel and more sophisticated pendulum configurations. Thus, the orbit control efforts and the consequent propellant mass required to achieve the desired lifetime are reduced. Whatever orbit configuration is chosen for bistatic observation, the rather large relative dynamics give rise to the need to point the radar antenna beams to ensure that both systems are observing the same target. This is due to the large baseline extension with respect to radar swaths for most of the orbit. Spaceborne SAR interferometry operated by two antennas flying in tandem does not pose this problem since satellites, though separated in space, are so near each other that the same pointing for both Tx/Rx and Rx radars is usually sufficient to have an adequate swath overlap. More specifically, a variable cross-track separation of the two radar swaths can be envisaged in the spaceborne BSAR as a consequence of the out-of-plane satellite separation, i.e. in a direction perpendicular to the orbit plane, while the baseline component along the flight direction produces an along-track swath displacement. In addition, swaths also show a relative rotation since most SAR missions dynamically yaw-rotate the satellite along the orbit to reduce atmospheric drag and to achieve zero Doppler frequency at the boresight (yaw steering manoeuvre) [2.48]. This implicitly rotates the slant range direction around the local vertical.

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To nullify the effects of an evolving satellite relative geometry, it is possible to use a number of strategies, which can be classified into two basic families: satellite-based and payload-based strategies. Satellite-based strategies are basically mechanical ones and rely on the satellite bus to point the Rx beam towards the Tx/Rx radar swath by means of attitude manoeuvres (yaw, pitch and roll) of the Rx spacecraft. Actually, instead of pointing the whole spacecraft, only the radar antenna can be rotated with respect to the satellite structure. As a matter of fact this is basically a space system engineering trade-off decision, depending on the accuracy and capability of the available sensors and actuators for attitude control and of servomechanisms for enabling relative rotation between the spacecraft and antenna. This is well beyond the scope of this chapter. Hence, since a high-resolution remote sensing mission usually poses very stringent requirements on spacecraft attitude measurement and control, in the following only satellite-based strategies based on mechanical attitude steering will be discussed, as payload-based strategies build on the electronic steering of the radar beam in the elevation and azimuth directions. This is achieved thanks to the well-proven ‘tile’ structure of spaceborne radar rectangular antennas, which are larger in the azimuth direction than in the cross-track direction. In theory, roll attitude angles or antenna elevation angles of both the active and passive satellites or radars can be used to compensate for the effects related to cross-track swath separation. Moreover, pitch attitude angles or antenna azimuth angles of both the active and passive satellites or radars can be modified to account for along-track swath separation. Finally, swath relative rotation can be overcome by making use of the yaw attitude angles, again of both satellites. A ‘mission option’ can be defined as a combination of strategies adopted to guarantee successful bistatic data acquisitions. It is worth noting that a mission option integrating only satellite-based strategies is able to counteract any kind of swath displacement (both translations and rotation), whereas a mission option fully relying on payload-based strategies cannot avoid swath relative rotations. Of course, it is possible to identify a mission option that integrates both payload and satellite-based strategies. As an alternative, swath relative rotation could be accepted, provided that acceptable signal losses are generated; i.e. a reduced but adequate common swath width is still achieved. As a consequence, as will be shown below, this approach poses additional requirements on antenna dimensions. In conclusion, a mission option can use the actions of the Tx/Rx satellite only, the Tx/Rx payload only, the Rx satellite only and the Rx payload only, or a selection of actions of both the Tx/Rx and Rx satellites and payloads. Since a mission option makes use of a number of potential strategies, which have different impacts on the Tx/Rx mission and on Rx satellite and payload design, it must be compatible with the overall mission design, which could be driven by several and contrasting requirements, even conflicting with optimal conditions for bistatic radar, such as re-use of a payload or of a satellite bus, design of an ad hoc payload or satellite, no modifications of Tx/Rx mission design and operation, etc. Thus, the selected mission option is the most convenient in an environment where the bistatic mission is under design, being extremely difficult, if not impossible, to define an optimum solution of general validity. These points will be discussed in further detail later. As far as the bistatic payload is concerned, if a receiving-only (R/o) radar is assumed, it requires limited amounts of power, a condition that positively impacts on satellite electrical power subsystem sizing. Nevertheless, if the bistatic antenna can be electronically steered a certain amount of power must be budgeted. From the data rate point of view, a bistatic payload roughly doubles the main mission requirements. Hence it does not offer any benefit, unless the bistatic payload duty cycle is kept small, but this obvious strategy can be used with an active radar as well. In addition, benefits at the bus level can be obtained if the bistatic radar antenna

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is kept smaller than the primary radar one. Thanks to the reduction of an R/o payload mass and power, in principle a small satellite should be able to fly a BSAR, as demonstrated for the case studied in Reference [2.44]. This result has a positive impact on the BSAR mission cost, but also poses additional challenges to orbit maintenance. In fact, existing SARs are flown by heavy satellites that are able to face atmospheric drag. A program of orbital manoeuvres to counteract differential drag must be studied. Of course, as an alternative approach to designing a BSAR mission, it might be suggested that an SAR satellite could be simply duplicated using one of the two flying radars only as a receiver. This approach produces a highly reconfigurable BSAR mission since both radars can transmit a steerable radar signal; moreover, SAR satellites have typically good capabilities in terms of attitude and orbital manoeuvre. However, this possibility is in contrast to the history of SAR missions, where to date all have been characterized by large and high-performance satellite buses, with various remote sensing payloads and, in particular, with quite complex and expensive active radars, all developed thanks to great financial and technological efforts undertaken by national or international agencies. Nevertheless, duplication of an SAR satellite could become acceptable if the envisaged SAR constellation missions (COSMO-SkyMed in Italy and TanDEM-X and SAR-Lupe in Germany, as examples) become a reality. In this case it is due to less ambitious, but well-focused, design and realization of active microwave sensors and small satellites mostly based on proven technology. The recurrent cost of a BSAR satellite could be affordable, in particular if compared to the overall constellation mission cost, and it could be justified by a very satisfactory cost-benefit trade-off, considering both the additional applicative products and the improvement in overall mission reliability. In addition, the BSAR satellite cost could be further reduced in a number of ways: (a) utilizing a satellite already in the constellation, although slightly reducing its mission lifetime and, obviously, modifying constellation repetitivity; (b) using an in-orbit constellation spare, if available; and (c) realizing the satellite with the constellation qualification model with limited hardware investment as foreseen by the spare-qualification procedure in MIL HDBK 340A, ‘Test Requirements for Launch, Upper-Stage, and Space Vehicles’. The approach followed herein by the authors is that of a newly developed BSAR mission, i.e. without duplication of the primary SAR mission, although bus/payload can be derived by primary ones, by extensive re-use of experience, technology and hardware. Furthermore, it is assumed that the primary mission is more sophisticated and can offer larger capabilities than the bistatic one, although every effort must be taken to keep the impact of bistatic operation on the primary mission schedule low.

2.2.2 Impact of Bistatic Observation on Mission and System Design Science and application requirements clearly impact mission and system design of any space mission. This point is particularly critical for bistatic missions since not only can imposed constraints lead to an expensive system but they can also pose unacceptable requirements for the primary mission. As an example, science could require bistatic data to be gathered over test sites under different bistatic angles. Nevertheless, for any given couple of Tx/Rx and Rx orbits, which, in general, are repetitive in spaceborne remote sensing, a specified test site can be observed only under a given bistatic angle or under a limited set of bistatic angles, depending on the orbit repetition factor and on the way the ground tracks are distributed over the given latitude [2.49]. By slightly ‘tuning’ the repetition factor it is possible to attain a different ground

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track pattern, thus achieving a new limited set of bistatic angles, in some way different from the previous one. Thus, if analysis under variable angles is mandatory, system engineers must be aware that at least one satellite must perform the orbit manoeuvre and be capable of modifying beam pointing. In particular, it could be necessary for the Tx/Rx radar to perform acquisitions under off-nadir angles that could be different from the ones scheduled for the main monostatic mission. What is worse is that if parallel orbits are selected for achieving cross-track baselines, the required orbital manoeuvre needs out-of-plane velocity impulses to modify ascending node right ascension, which are typically among the most demanding ones. Therefore, bistatic angle variation is limited by orbital manoeuvring capabilities and by the off-nadir angles attainable by means of electronic steering or roll manoeuvring. An additional point worth mentioning is related to the extension of the Earth’s area where bistatic acquisitions are desired. This requirement bears similarities with the coverage requirement of remote sensing missions. As an example, global coverage means that the sensor is able to observe the whole of the Earth’s surface within an assigned time interval (repetition period). The ‘virtual’ version of global coverage is global access, which stands for the capability of steering sensors to select an observed area anywhere on the Earth. Of course, the coverage requirement depends on the sensor swath, while the access requirement depends on the accessible swath, i.e. on the swath of a virtual radar with a 3 dB elevation aperture coincident with an overall angular range where the sensor can be pointed. Furthermore, it should be emphasized that the steerable beam technique necessarily requires a definition of a priority in the accessed areas. In other words, whereas the global coverage condition guarantees that the whole accessible globe is certainly acquired within a repetition period, the global access capability could be degraded by increasing the number and location of target areas. Selection between more stringent coverage or access requirements is obviously dependent on applications and requires specific sensor performance, but orbit selection is vital and special emphasis must be given to the repetition period. In fact, the repetition factor is primarily regulated by the altitude, which is typically selected on the basis of the sensor power budget and spacecraft lifetime. Within a rough altitude requirement, it is possible to obtain different ground track patterns by slightly changing altitude and/or inclination and/or eccentricity, which changes the ground track pattern and the time period required to complete it. Specifically, the smaller the real or potential swath of the sensor, the larger is the time interval necessary to fulfil the global coverage or access requirement. It is worth mentioning that a radar remote sensing mission with a global coverage requirement still fails to observe some areas of the Earth. In fact, the effect of the side-looking geometry and of the inclination (around 96–99◦ to meet the usually adopted sun synchronicity condition at typical altitudes) limits the possibility to observe both polar caps. When a bistatic mission is designed, the coverage or access requirement must be analysed on the basis of the bistatic swath, obtained by interception of Tx/Rx and Rx swaths. As a consequence, bistatic coverage or access is influenced by both satellites. For instance, considering a bistatic constellation of two satellites flying always in the same parallel orbits, global access could be guaranteed only within a certain interval of latitudes, depending on the overall steering capability (Tx/Rx and Rx satellites and radars) and acceptable bistatic angles. Thus, bistatic coverage or access could be obtained over an Earth area smaller than the one where the monostatic coverage or access is achievable. In addition, if global bistatic coverage is to be guaranteed under different bistatic angles, the most suitable choice is likely to be the use of a number of bistatic platforms. Indeed, a single bistatic satellite would be quite massive for all the necessary propellant to be allocated to it, and would involve a long repetition period. In

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conclusion, there is evidence that adequate planning of bistatic test sites, for both scientific and applicative purposes, along with bistatic angle (or angles) requests, is vital for mission success. If the bistatic orbit is correctly designed, the Earth area under potential bistatic observation is maximized. Nevertheless, this step only guarantees the geometric conditions necessary to achieve bistatic data over the largest possible area. Functional conditions must be considered; that is to say, it must be decided where, when and how often bistatic observation must be performed. The ultimate result of this decision impacts on the duty cycle of the instrument, i.e. the fraction of the orbit period when the bistatic radar is operated. This parameter is vital to system design and it could also have an impact on the operations of the primary mission in a number of ways. First of all, a high duty cycle impacts on satellite design in terms of required energy per orbit and data production per orbit. The former parameter has a crystal clear impact on satellite design since for an assigned power level (possibly low, considering that the payload is passive), the larger the duty cycle, the larger is the average power required for the payload. Therefore, the solar array and battery increase if a large duty cycle is desired. In addition, the data produced over an orbit must be considered when the onboard mass memory is selected. The communication subsystem is also affected since in all probability an enhanced data rate is requested to provide downlink for all the gathered data. A larger solar array, battery and data storage unit definitively impact on the bus mass and volume, producing an associated increase in development and launch costs. These design effects are common to all satellites and are not particularly linked to a bistatic mission. However, what is almost unique is the effect that an enhanced instrument duty cycle has on the primary mission. If the primary mission has its own monostatic objectives and applications and the Tx/Rx satellite or radar must participate in the bistatic acquisition, e.g. pointing the illuminating beam along the desired direction, it has to dedicate part of its resources to the bistatic mission, thus reducing fulfilment of its primary goals. Furthermore, the bistatic data downlink is no trivial problem. Even if satellites are separated by hundreds of kilometres in space, a separation arc of 100 km produces a geocentric angle of only about 0.8◦ with nadir points separated by about 90 km. As a consequence, the same ground station servicing the primary mission must also support the bistatic satellite. Therefore, the bistatic data downlink must be separated in time from the primary mission downlink, unless the ground station supports two satellites contemporaneously. Of course, one suggestion could be to develope the bistatic ground segment as well, but this approach is probably only applicable if a large number of users is foreseen. Hence, the payload duty cycle, which depends on the number of bistatic acquisitions and on the frequency of their update, must be carefully determined: large enough to guarantee mission success and cost effectiveness, but small enough to keep satellite design and operation affordable and the impact on primary mission acceptable. In conclusion, high performance and operational flexibility inevitably lead to a complex, expensive, heavy mission with the additional bothersome impact on the primary mission. On the other hand, reduced performance and limited operational modes limit mission usefulness. The design driver should be the expected mission itself. A science and demonstration mission could investigate a limited number of test sites, possibly under a number of bistatic angles; thus the accessible Earth area could be kept small and orbital manoeuvring capabilities would be welcome but not mandatory. In contrast, an operational mission certainly requires large amounts of data collected over a large number of test sites and bistatic angle variation should be decided on the basis of the foreseen applications. Therefore, an operational mission in principle requires access to most of the Earth’s surface, achieving assigned bistatic angles, and orbital manoeuvre cannot be limited to maintenance unless a large number of receiving satellites can be considered.

KEY DESIGN ISSUES IN SPACEBORNE BSAR

2.2.3 Payload–Bus Performance Trade-off

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The main system trade-off to be performed when designing bistatic missions is related to the way the required pointing is achieved and, in particular, if it is obtained as a result of bus attitude or radar pointing manoeuvres (satellite-based strategy), or beam electronic steering (payload-based strategy), or a combination of both. Thus, a decision must be taken on what actions are provided by the primary mission and what others are left to the bistatic mission. It is worth being reminded here that three swath problems must be tackled when a mission option must be selected: cross-track separation (roll or elevation angles), along-track separation (pitch or azimuth angles) and rotation (yaw angles). In theory, a bistatic mission could be designed making use of a combination of strategies, or even duplicating them. As an example, swath cross-track separation can be cancelled by the Tx/Rx roll angle and by the Rx elevation angle, whereas along-track separation may be overcome by the Tx/Rx antenna azimuth and by the Rx satellite pitch and relative rotation performed by means of yaw manoeuvres of both satellites. Which actions should be selected and how they should be integrated to identify a mission option is a matter to be decided on the basis of the complexities introduced in the bistatic satellite or payload and of the capabilities offered by the primary mission (again considering that a modification of the primary mission is not an option). Assuming as a discriminating factor the impact of the bistatic operation on primary missions, it is possible to identify three general approaches to the bistatic mission design. The first design driver could be the assumption of having a ‘blind’ primary mission that in principle is not aware of the bistatic acquisition. As a consequence, the bistatic satellite, which is ‘fully independent’ of the primary mission, must be in charge of swath overlap. A second approach could be exactly the other way round, with a ‘fully dependent’ bistatic satellite and with the primary radar illuminating the bistatic swath and compensating for any geometric variation along the orbit. The fully independent approach requires a sophistication of the bistatic satellite (all-angle attitude manoeuvring capability) or payload (elevation/azimuth antenna pointing capability) design and operation, while the second requires a very simple bistatic satellite/payload (no attitude/antenna pointing capabilities). This inevitably leads to reduced mission flexibility and to primary mission operations heavily influenced by the bistatic objectives. Moving from a fully dependent to a fully independent bistatic mission, several intermediate options can be identified, all being characterized by a partial collaboration of the primary radar/satellite to data acquisition. Whatever primary mission involvement is selected, it can be practically achieved with different choices in terms of attitude and/or antenna pointing. A bistatic SAR mission in which the bistatic radar is fully independent from the primary SAR mission obviously has no impact on the primary mission schedule and operations. It is the passive receiver that is in charge of ensuring that bistatic acquisitions can be carried out on the selected targets at the specified times, which must be identified on the basis of the primary mission schedule. Since the primary mission could change its acquisition sequence, the bistatic mission must be quite flexible in order to be able to image different Earth areas under different angles or, eventually, to change its orbit. A fully independent bistatic mission can be implemented with different mission options. As an example, a satellite-based option relies on an all-angle attitude manoeuvre capability, while a payload-based option builds on azimuth and elevation steering with no compensation for rotation, which could be unacceptable, as will be shown in Chapter 3. A payload-based option can be enriched with a yaw manoeuvring capability to nullify swath relative rotation obtaining an enhanced payload-based mission option. The logic of satellite and payload-based strategies is straightforward: an existing, high-performance

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small bus developed for other applications could be re-used, thus developing a basic Rx radar with no steering capabilities. In contrast, an existing high-performance payload could be re-used, implementing only the receiving channel but taking advantage of steering capabilities, thus loosening bus requirements and performance. If swath relative rotation cannot be accepted, the enhanced payload-based option can be the solution since it complicates the payload-based option only with the yaw manoeuvring capability, which is easiest to obtain among the attitude manoeuvres and SAR satellites are usually equipped to perform it independently from bistatic coverage. It is worth mentioning that changing the bistatic antenna dimension so that its 3 dB aperture is larger than the primary radar one can lead to an active swath contained within the passive one. This nullifies the need for yaw manoeuvres, provided that antenna area reduction does not affect ambiguities and the signal-to-noise ratio. Furthermore, additional mission options can be identified with a different combination of actions. As an example, it is possible to develop a radar with only azimuth (elevation) steering capabilities, relying on the roll (pitch) manoeuvre to counteract swath cross-track (along-track) relative displacement, with or without considering the yaw manoeuvre for swath relative rotation compensation. These mixed solutions do not seem to offer particular benefits at a system level. In fact, it can be stated that azimuth displacements are more easily compensated than cross-track displacements from both bus and payload points of view. If, on the one hand, azimuth steering is generally easier to obtain, on the other hand the following paragraphs will show that the required pitch angles are much smaller than the required roll angles. Therefore, it is probably better to allocate the complex design solutions either on the bus or on the payload. In the ambit of the fully dependent approach, the literature only reports the case of re-using an existing SAR payload along with its receiving channel without the possibility of orienting the beam [2.44] and relying on attitude manoeuvres (satellite-based option). The main advantage of the reported design case is that a small satellite suffices to fly the payload. The disadvantage is the need to develop an ad hoc bus with an all-angle attitude manoeuvre capability, which is not standard for small-mass spacecrafts. Nevertheless, the required bus is much smaller than the ones required for typical Earth observation missions, which certainly has a positive impact in terms of overall cost and development time. In conclusion, the main advantage of the fully independent approach is that the primary mission is completely transparent to bistatic acquisitions, which of course also produces limitations. Targets can be bistatically observed only if illuminated by a noncollaborative radar, thus, it is quite complicated to identify an acquisition set that satisfies scientific requirements, since observations must be programmed according to the primary radar schedule. On the other hand, a fully dependent approach is the simplest way to implement a bistatic mission from the bistatic user’s point of view, since a very simple bus and an Rx payload are needed. The former can be a bus with neither attitude manoeuvre or orbit control capabilities and the latter may be an Rx antenna with no possibility of steering the beam. For the bistatic mission to be feasible, the primary SAR must be pointed towards the swath of the bistatic SAR by means of attitude manoeuvres or payload beam steering, or a mixture of both actions. Of course, only a limited number of possible mission options are viable from a system point of view. For example, one feature common to all modern active SAR systems, which can be of great advantage to a bistatic mission, is the electronic steering of the antenna beam in the elevation direction, which does not require any mechanical operation. As a consequence, active SAR elevation steering can be selected to counteract across-track swath separation, avoiding the need for roll rotation of the primary satellite. Thus, in the ambit of a fully dependent approach, the along-track relative displacement and the relative rotation of radar swaths can

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be tackled by pitch and yaw, obtaining a satellite-based option. A payload-based option uses azimuth steering without compensating for rotation, while an enhanced payload-based option integrates azimuth and yaw. The use of azimuth in lieu of pitch can be foreseen since a number of active SARs are able to perform azimuth steering as a way to improve azimuth resolution (spotlight mode). Nevertheless, when operating in this mode, the SAR azimuth angle is changed during the acquisition on the basis of active satellite dynamics. Therefore, if this capability is used for the bistatic acquisition, a change in software implementation might be necessary. From the attitude point of view, it should be borne in mind that most SAR satellites also have manoeuvring capabilities, generally used for yaw steering (to reduce atmospheric drag) and nadir pointing (both roll and pitch to align the satellite downward direction with the local geodetic vertical) [2.48]. Thus, when attitude is used, a variation of cross-sectional area and differences with respect to nominal attitude must be accepted. It is worth noting that foreseen options differ from the ones considered for the fully independent case because it is the primary radar in charge for all manoeuvres and because elevation steering is always used instead of roll. This latter aspect would not have been considered in the past, when SARs did not integrate beam steering capabilities (e.g. the ERS series). Hence, the fully dependent approach presumably produces the simplest and cheapest bistatic platform and payload, though requiring a huge effort from a heavy, high-performing primary mission. As a consequence, the overall mission cost could be far higher than the bistatic platform cost, unless one imagines a large number of bistatic platforms able to cover most parts of the Earth’s surface under different angles, depending on their position along the orbit. This approach has only been proposed for nonimaging applications [2.50]. In view of such applications, the payload-based option seems the only adequate choice since the heavy and expensive Tx/Rx satellite would work with the optimized cross-sectional area and could rapidly switch its beam to point towards the desired swath in view of one of the passive receivers. When a partially dependent approach is considered, collaboration with the primary mission must be defined and quantified. Partial collaboration makes sense at a system level only if it is restricted to those actions that do not require a substantial change in the primary mission schedule and operation in order to reduce the impact on its goals. From this point of view it can be stated that the primary satellite must not be required to modify its nominal attitude because: (a) most SAR satellites perform the yaw steering manoeuvre to reduce atmospheric drag and hence the yaw angle cannot be modified; (b) not all SAR satellites are capable of periodically changing roll and pitch attitude angles and, in any case, these manoeuvres modify the satellite cross-sectional area. Thus, partial collaboration should rely on beam steering capabilities provided that no change in hardware and/or software is needed. It is a foregone conclusion that the primary radar could be requested to point its beam in the elevation direction to counteract cross-track swath separation, since this feature is quite common. On the other hand, requesting azimuth steering could be critical because, if available, it could be used to implement the SAR spotlight mode. As a consequence, it should be assumed that along-track swath separation is overcome using either a pitch manoeuvre of the bistatic satellite (a requirement of the satellite design) or an azimuth pointing of the bistatic SAR (a requirement of the payload design). Finally, the only remaining strategy to account for swath relative rotation is a yaw attitude manoeuvre of the bistatic satellite. Thus, once the necessary steps are taken to limit the impact on the primary mission, the number of applicable strategies is reduced. They can be coupled to define a mission option that always guarantees low impact on the partially collaborating primary SAR mission. The remaining mission options differ in the requirements they pose on the development of the bistatic satellite and payload, while having an identical impact on the

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bus-based

payload-based

enhanced payload—based

fully independent

fully dependent

partially dependent

roll pitch yaw

elevation pitch yaw

elevation pitch yaw

elevation azimuth

elevation azimuth

elevation azimuth

elevation azimuth yaw

elevation azimuth yaw

elevation azimuth yaw

Figure 2.1 Selected strategies (columns) on the grounds of system considerations under different approaches, based on the impacts on the primary mission, and options (rows), building on the bus or on the payload. Actions can be performed by the primary system (white on dark grey) or by the bistatic one (black on light grey)

primary. Thus, under the assumption that across−track swath separation is avoided thanks to the electronic steering of the active SAR, three options can be envisaged for the Rx satellite or radar: bus-based (pitch and yaw), payload-based (azimuth) and enhanced payload-based (azimuth and yaw). The logic behind these options is the same as before, and the difference with respect to the fully dependent approach is that all actions apart from elevation steering are implemented in the bistatic system. In other words, the impact on the primary mission is very light, requiring only antenna elevation steering within nominal design constraints. In addition, the bistatic receiver options can be obtained, de-rating the fully independent options, with no roll manoeuvre for the satellite-based option and no elevation steering for the payload-based option. It is worth pointing out that if the bistatic radar can also be steered in the elevation direction, an increase in the bistatic access area can be achieved with an enhanced capability to observe targets at different bistatic angles. The partial collaboration approach was analysed in Reference [2.51] under the assumption of no duplication of actions (no bistatic elevation steering). All options analysed within the three approaches are shown in Figure 2.1, but only the payload-based option under the fully dependent approach will be considered in Section 2.3. In order to understand how design choices affect both the impact on the primary mission and the complexities introduced in the bistatic radar and satellite, it is useful to compare all mission options. This is because they are the outcome from the selection of all potential strategies to counteract swath relative displacement. With reference to the impact on the primary mission, elevation steering will be considered of the minimum effect since it is a widespread feature. The effects of azimuth steering have been considered to be larger since azimuth steering is generally used for the spotlight mode, but not as a nominal pointing mode to acquire images not at the boresight. Thus, it is likely that a modification of primary radar software is needed, even if the antenna tiles are already designed and programmed to generate azimuth pointable beams. Attitude manoeuvring capabilities must be considered to have an even deeper impact when taking into account SAR satellite typical configurations with antenna longitudinal axis aligned with roll axis. This is again aligned with the satellite atmosphere relative velocity by a programmed yaw manoeuvre. In addition, roll and pitch manoeuvring capabilities are not generally implemented and are typically limited to the small angles required to perform the

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nadir pointing manoeuvre. Thus, it is likely that the introduction of roll and pitch capabilities requires modification of primary mission hardware and software, due to rotations coupling. In addition, yaw and pitch rotations cause an increase in the satellite cross-sectional area with an enhanced effect of aerodynamics, which impacts the propellant budget or mission lifetime. As a consequence, factor 1 is considered as the impact coefficient for elevation steering, factor 2 for azimuth steering, and factors 3, 4 and 5 for roll, pitch and yaw rotations respectively. Complexities introduced in the bistatic radar and satellite are considered equivalent (i.e. factor 1 is considered for any antenna steering angle or attitude manoeuvre angle). For the sake of simplicity it can be assumed that the impact coefficients can be linearly added and that a resulting coefficient normalization, with respect to its maximum achievable value, can be performed. Figure 2.2 shows that, once normalized impact is allocated on the primary mission, several solutions can be obtained, which differ for the normalized complexities introduced at the bistatic bus and payload. On the other hand, once normalized complexities are allocated, different impacts can be caused. Of course, only a subset of options is considered to be logical from the system point of view (as discussed above, listed in Figure 2.1 and plotted in Figure 2.2(b)). If bistatic mission effectiveness is also taken into account, the partial collaboration approach seems more appropriate since: (a) it allows a strong reduction of the impact on the primary mission with respect to the fully dependent approach; (b) it reduces the efforts to design the bistatic satellite and payload with respect to the fully independent approach; and (c) it is possible to agree an acquisition schedule over selected test sites with the primary mission, which is impossible with the fully independent approach. Another interesting option is the payload-based option, within the fully dependent approach, if a cloud of the bistatic receiver is

1 impact on primary

impact on primary

1 0.75 0.5 0.25 0 0 0.25

0.25

0.5

0.5

0.75 1 satellite complexity

0

0.75 1 a)

payload complexity

0.75 0.5 0.25 0 0 0.25

0.25

0.5

0.5

0.75 1 satellite complexity

0

0.75 1

payload complexity

b)

Figure 2.2 Impact on the primary mission caused by design selection as a function of complexities introduced in the design of the bistatic satellite and payload for all possible options (a) for the options considered useful at the system level (b) Diamond stands for fully dependent, triangle for partially dependent and circle for fully independent, while black stands for satellite-based, grey for payload-based and light grey for enhanced payload-based options

• 40

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

considered. Finally, it is worth underlining that the introduced weights to quantify the impact and complexities are just examples to show how options may be traded one against another. A more thorough analysis could modulate the weights, considering detailed cost analysis, which must be performed locally as the same technology can be at a different level of maturity in different environments. In addition, industrial or national policies can drive more sophisticated solutions, which would be discarded from a pure engineering analysis but which could be of interest for other reasons; e.g. already developed technologies or experiences might be exploited.

2.2.4 BSAR Missions Functional/Technological Key Issues Key issues for BSAR mission success are related to the capability of flying two separate spacecrafts carrying the transmitting and the receiving sections separately. Formation flying is a critical point in terms of theoretical modelling, functionality implementation and technological assessment. First of all, although only introduced in the last decade, formation flying is considered by NASA and DOD (Department of Defense) as an enabling technology for future mission concepts that would otherwise be impossible. This is because not only can a system of platforms replace a larger single platform but it also has the capability of an increased performance that is unachievable using a single monolithic platform. Nevertheless, analytical modelling of relative dynamics has been mainly tackled for missions flying in the vicinity of Lagrangian points and exploiting astronomical objectives. More recently, analyses have been conducted for low Earth orbiting spacecrafts dedicated to Earth remote sensing, both in the visible and microwave spectral regions. Efforts undertaken in recent years, while achieving a good understanding of the relevant problems and offering a variety of solutions and analysis, have not yet produced an assessed and overall view of formation flying design techniques. From the design point of view, first a relatively simple mathematical model is required to design a formation (basically its geometry, the number of required components). Because this will lack a thorough description of the long-period system dynamics leading to the formation’s unpredictable evolution, a dynamics model is therefore required to propagate the formation in order to verify design effectiveness. How many effects, even in a simplified form, must be included in the design model rather than in the propagation model is still an open question [2.52, 2.53]. Following this, the problem of formation reconfiguration and control must be solved [2.54]. Different approaches have been introduced, depending on the logical organization of the formation. If a hierarchical approach is selected, the leader–follower philosophy [2.55, 2.56] can be implemented, whereas if all components are to be equal in the formation, the behavioural philosophy [2.56] describes the solution. In addition, a hierarchical method can be used where the leader is a theoretical model of the formation rather than a physical member of the formation, leading to the virtual-structure philosophy [2.57]. Hierarchical and nonhierarchical approaches must be exploited in detail before being implemented but, in theory, offer opposite advantages and disadvantages. More recently a novel approach (perspective frame) was proposed which may be able to guarantee contemporaneously the positive effects of both the hierarchical and nonhierarchical approaches [2.58]. Once decided upon, the formation concept and the formation identity can be described in terms of the hierarchical, nonhierarchical or perspective frame; several control strategies can be used to keep the formation within the tight requirement typical of such missions, trying to keep the propellant expense low and possibly uniform among the formation elements [2.54, 2.55, 2.59–2.61]. Technological challenges must also be taken into account: close flight and

KEY DESIGN ISSUES IN SPACEBORNE BSAR

• 41

tight control pose requirements on the guidance, navigation and control and on the propulsion subsystems [2.62]. In addition, for the mission to be feasible a high degree of autonomy is required at the system and subsystem levels [2.63], otherwise the system is not able to respond in time to unforeseen dynamical behaviours and collision risk becomes unacceptable. Finally, relative position control could ask for data exchange between satellites and, in any case, for relative position and velocity measurements or estimations in order to make the formation control possible. Thus, a new subsystem is needed in the formation mission: the metrology subsystem, possibly integrated with satellite interlink. Two main architectures have been studied to achieve metrology. The former essentially consists of reproduction of a kind of local GPS subsystem, due to transmitted microwave signals with the main limitation arising from heavy multipath. In addition, the adoption of differential GPS techniques [2.64, 2.65] offers further improvement in baseline measurement accuracy. The latter architecture is based on laser ranging systems and it has been essentially analysed for large mass astronomical missions [2.66]. Satellite interlink also builds either on microwave or laser communications. None of these technologies can really be considered as off-the-shelf or fully developed and tested. Bistatic formation flying is characterized by contrasting elements. Due to large and varying distances of primary and bistatic satellites, collision risk is not continuously present along the trajectories; rather it is confined to the two points where parallel orbits intercept, since the crosstrack and vertical separation is almost nullified and only small along-track relative distance components remain. Collision risk, sparsely present during orbit, can be practically avoided by selecting an orbital configuration that tends to increase relative distance thanks to the effects of orbital perturbations. In fact, bistatic satellites, predictably with a mass smaller than the primary one, but with an almost comparable cross-sectional area, are affected by atmospheric drag more heavily than the primary ones. Thus, the bistatic satellite is characterized by a faster orbit decay and an increase in orbital velocity. Therefore, atmospheric drag acts as a safety improver if bistatic satellites are positioned along the orbit with a positive anomaly shift with respect to the primary ones, which is possible if the primary satellites are right-looking and fly on retrograde orbits (which is usually the case). Nevertheless, flying a formation of spacecrafts widely separated in space is also a critical point, which poses both theoretical and technological issues. First of all, even if several authors have modelled relative dynamics when the spacecrafts are close to each other, a larger distance between satellites makes the analytical modelling of loose formations more complex, obviously because linearization errors increase and large separations generally involve large differences in orbital perturbation effects. In addition, exchange of navigation data between the satellites, which may be needed depending on the technique adopted to maintain required relative geometry, is complicated when distances of hundreds of kilometres must be realized. Finally, it must be considered that a bistatic mission could rely on a primary satellite that is not designed to fly in formation. Thus, it is very likely that the primary satellite has neither interlink capabilities nor a metrology subsystem. As a consequence, bistatic satellites must independently measure relative distance and cannot be aware of the possible control actions taken by the primary mission. Hence, the need for formation flying control with no collaboration at all of the transmitting spacecraft is the expected result. Once the two payloads are guaranteed to fly correctly over the prescribed design trajectory, the following point to be assessed is signal synchronization. For the receiving radar to gather the reflected echo of a chirp pulse transmitted from a radar far apart, two strategies can be adopted. The first option consists of a continuously sampling performed by bistatic radar,

• 42

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

since the passive receiver does not need transmission intervals. The second strategy is based on synchronization of the bistatic receiving window to the reflected echo, by also making use of the transmitted signal gathered by an ad hoc antenna on board the receiving-only spacecraft and pointed towards the transmitting radar in order to receive from its sidelobes. Of course a synchronization algorithm must be effective, depending on received sidelobe echo and on both radar orbits and pointing. This second option is more demanding, but it could take advantage of a common time reference, such as the GPS.

2.3 MISSION ANALYSIS OF SPACEBORNE BSAR 2.3.1 BSAR Orbit Design The first step to be undertaken in bistatic orbit design is to refer to orbits proposed for SAR interferometry to analyse whether they can be extended to a bistatic scope. From an orbit perspective, the InSAR (interferometric SAR) and BSAR only differ for satellite distance, which is small for the former and large for the latter. This section will deal with the analysis of orbits for BSAR, starting from a typical design choice of orbits for InSAR: parallel orbits, cartwheel and pendulum.

2.3.1.1 Parallel Orbits Parallel orbits [2.45, 2.46] share the same orbital parameters apart from the ascending node right ascension, achieving a cross-track separation. In addition, satellites are relatively phased by an adequate in-plane anomaly shift, which also allows an approximately constant alongtrack separation. The concept is visualized in Figure 2.3 where the results show that primary and bistatic satellite orbits are rotated around the Earth’s polar axis. Thus, both are tangent to the parallel at latitude 180◦ − i (for retrograde orbits, i.e. with inclination i larger than 90◦ as it is more frequent for remote sensing missions) or i (for prograde orbits, i<90◦ ) in the Northern hemisphere. In particular, it is assumed that the primary satellite performs the yaw steering manoeuvre (γ YS ), which rotates the satellite around the local vertical (Z axis of the orbiting reference frame defined with the origin in the satellite’s centre of mass, Z axis towards the Earth’s centre, X axis in the orbital plane and in the direction of motion, and Y axis to form a right-handed XYZ frame). The satellites are then phased with a shift between arguments of latitude (e.g. the anomaly measured from the ascending node) in order to place the bistatic satellite in the elevation plane of the primary radar when it passes over the equator. However, parallel orbit phasing is not sufficient for the bistatic acquisition to be feasible, even on the equator. In fact, although Ω is chosen to make swaths coincide, primary and bistatic elevation planes are not coincident due to orbit geometry and γ YS . Of course, the bistatic satellite can be yaw-rotated to align elevation planes or other options can be identified (Section 2.2.3), which are related to pointing and, hence, will be analysed in Section 2.3.2. Satellite horizontal separation depends on the difference between the ascending node right ascensions (Ω), which is small for the InSAR and becomes of the order of a few degrees for the BSAR. To meet the phasing conditions, argument of latitude shift (u) increases accordingly

• 43

MISSION ANALYSIS OF SPACEBORNE BSAR

parallel (latitude 180°-i) Earth rotation axis ψ

orbit intersection

intersection of orbit planes with Earth

ξ T/R projection of ascending nodes on the equator

ξ R/o intersection of bistatic elevation plane with Earth

orbit

i

ΔΩ

equator

° + γ YS

90

Δu X orbiting reference frame

BISTATIC SATELLITE

Z Y

intersection of primary elevation plane with Earth

PRIMARY SATELLITE

Figure 2.3 Geometry for parallel orbit synchronization (retrograde orbit case)

to Ω; u is ultimately related to the bistatic satellite initial condition on the orbit, i.e. on the difference between the times of passage over the ascending node (tAN ). Thus, by properly selecting Ω and tAN it is possible to achieve the desired equatorial separation, i.e. separation between the satellites when the bistatic one is on the equator. By inspecting the spherical triangle in Figure 2.3, angles can be quantitatively determined as follows: −1

Ω = sin

sin ϑ¯ g cos γYS sin i

,

⎞ cos ϑ¯ g cos Ω − sin Ωcos i sin2 ϑ¯ g − sin2 Ω sin2 i ⎠, u = cos−1 ⎝ 1 − sin2 Ω sin2 i

(2.1)

⎛

˙ tAN = MM(u),

(2.2)

(2.3)

• 44

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

with the mean anomaly (M) related to the true anomaly (ν), again related to u = ν + ω. In addition, the primary satellite yaw angle

◦ −1 sin i cos (360 − u) γYS = − tan (2.4) ˙ ⊕ − cos i M/

depends on u, which requires a trial-and-error solution of Equations (2.1)–(2.4). If it is assumed that the bistatic satellite yaw rotates to make the two radar elevation planes coincident, ϑ¯ g can be obtained as the difference between the geocentric angles subtending the primary and bistatic radar off-nadir angles: ϑ¯ g = ϑg (ϑT/R ) − ϑg (ϑR/o ). In the case of no yaw rotations, this calculation is an approximation not so far from reality because the two elevation planes are near each other (due to small Ω and γ YS ). For the sake of completeness, the bistatic satellite yaw rotation needed to overlap elevation planes can be computed as follows: sin u sin i γR/o,0 = i − 90◦ − sin−1 . (2.5) sin ϑ¯ g If Equations (2.1) to (2.5) are all applied, swath overlap is guaranteed once along the orbit. Then, satellite motion causes variation in satellite distance and loss of superimposition for the given ϑ T/R and ϑ R/o . Pointing strategies (Section 2.3.2) solve this problem provided that orbits have been properly designed. As an example, if primary radar elevation steering is assumed to counteract for cross-track relative displacement, Ω must account for the smallest possible value of ϑ T/R in order to enable the radar to increase the angle at higher latitudes. The model to fix Ω and tAN was applied [2.51] showing that a few degrees (1–5) and a few tens of seconds (5–15) suffice to fly bistatic radars in conjunction with most past, existing and programmed SAR missions. Parallel orbits offer great advantages to bistatic missions since, thanks to eccentricity, inclination and semi-major axis shared with the primary satellite, they guarantee that perturbed mean motion along with perigee and ascending node precession rates identically affect primary and bistatic orbits. Thus, differential secular oblateness effects are nullified. In addition, if the bistatic perigee is positioned at the same true anomaly from the ascending node as for the primary perigee (90◦ ), the frozen orbit condition [2.67] can be fulfilled for the bistatic satellite as well. Therefore, the remaining disturbances are related to the ascending node right ascension, which impacts the inclination variation of sun synchronous orbits. Nevertheless, this differential effect is negligible, thanks to the limited ascending node separation that is usually required. In conclusion, the main perturbation is the atmospheric drag, which affects satellites on the basis of their ballistic coefficient. Since the area to mass ratio is generally smaller for large satellites, an enhanced orbit decay must be budgeted if the bistatic missions is implemented with a small parasitic satellite. Therefore, orbit control requires a periodic manoeuvre to raise the orbit and to re-phase the bistatic satellite in the orbit plane by slowing it down ad hoc to reduce its anomaly [2.44]. Figure 2.3 shows that the satellites are closest when they are near to the orbit poles, where only an along-track safety distance remains due to u. Since with right-looking radars (and retrograde orbits) the small bistatic satellite precedes the main radar and is the first to reach the orbit intersection, atmospheric drag increases safety by accelerating the small satellite, as a consequence of altitude reduction, thus increasing alongtrack separation. With a left-looking radar the bistatic satellite would follow the transmitting one, a situation that could be more dangerous since atmospheric drag would reduce u and hence the two spacecraft would get closer, although with different altitudes.

• 45

MISSION ANALYSIS OF SPACEBORNE BSAR

2.3.1.2 Cartwheel

The cartwheel concept was introduced for SAR interferometric applications by means of the formation of passive microsatellites imaging the Earth area illuminated by the ENVISAT active SAR [2.38, 2.39]. The orbit configuration is based on the microsatellite orbits, which all share a semi-major axis, inclination and ascending node right ascension with the transmitting radar orbit. In addition, microsatellite orbits have identical eccentricity, while perigee anomalies are symmetrically displaced (n satellites differ by 360◦ /n in perigee anomaly). The initial position along the orbit is selected so that the primary radar is behind the microsatellites by hundreds of kilometres in order to achieve an adequate safety distance. Thus, interferometry cannot be achieved by comparing the radar signal received by a passive satellite with the one received by the transmitting radar due to the large baseline separation. Instead it is obtained by comparing the signals from a pair of passive radars. Baselines are achieved both in the along-track (target velocity measurements) and in the in-plane vertical direction (target topography) thanks to the elliptic relative motion established among microsatellites. In particular, a linearization of the relative motion model was presented in References [2.38] and [2.39], while later a model at third order in eccentricity was proposed [2.68]. In order to gain insights into cartwheel satellite relative motion, consider a fictitious reference satellite flying over a Keplerian circular orbit with the same semi-major axis, ascending node right ascension and inclination of the ith receiver satellite of the cartwheel in elliptical orbit, and consider an orbiting reference frame fixed to the reference satellite. The geometry in the common orbit plane is shown in Figure 2.4 with the ith cartwheel satellite true anomaly (νi ) and perigee anomaly (ωi ), and the reference satellite mean anomaly (Mref ). It is worth considering that for the fictitious satellite a linear relation stands between anomaly and time; hence a common time reference can be defined. Taking the satellite initial mean anomaly (Mi 0 ) and cartwheel orbit eccentricity (e) into ac˙ ref = μ⊕ /a 3 , common to all cartwheel satelcount, considering Keplerian mean motion ( M lites and to the reference satellite), it is possible to expand Keplerian dynamics in a Taylor series as a function of eccentricity, thus obtaining cartwheel satellite coordinates at third order in eccentricity as follows:

es

X ne

li

Z

νi

ωi

of

id ps

a

Mref line of nodes

Figure 2.4 XZ orbiting reference frame adopted to describe the relative motion of cartwheel formations and fixed to a fictitious satellite (dashed line) moving in a circular orbit

• 46

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

⎧ ˙ ref t + Mi0 cos (Mi0 + ωi ) − cos M ˙ ref t + Mi0 sin (Mi0 + ωi ) ae X i (t) = asin (Mi0 + ωi ) + 2 sin M ⎪ ⎪ ⎪ 2 ⎪ ⎪ 1 ˙ ⎪ ˙ ref t + Mi0 − 1 sin (Mi0 + ωi ) ae ⎪ sin 2 Mref t + Mi0 cos (Mi0 + ωi ) + cos 2 M + ⎪ 2 2 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ˙ ref t + Mi0 − 9sin M ˙ ref t + Mi0 cos (Mi0 + ωi ) ⎪ 7sin 3 M + ⎪ ⎪ 4 ⎪ ⎪ 3 ⎪ ⎪ 9 ˙ ⎪ ˙ ref t + Mi0 sin (Mi0 + ωi ) ae + O e4 , cos 3 Mref t + Mi0 − cos M + ⎨ 4

3!

˙ ref t + Mi0 cos (Mi0 + ωi ) + 2sin M ˙ ref t + Mi0 sin (Mi0 + ωi ) ae ⎪ Z i (t) = a [1 − cos (Mi0 + ωi )] + cos M ⎪ ⎪ ⎪ 2 ⎪ ⎪ ⎪ ˙ ref t + Mi0 sin (Mi0 + ωi ) ae ˙ ref t + Mi0 cos (Mi0 + ωi ) + 1 sin 2 M ⎪ + 1 − cos 2 M ⎪ ⎪ 2 2 ⎪ ⎪ ⎪ 9 ⎪ ⎪ ˙ ref t + Mi0 − cos 3 M ˙ ref t + Mi0 cos (Mi0 + ωi ) cos M + ⎪ ⎪ 4 ⎪ 3 ⎪ ⎪ 1 ⎪ ⎩ ˙ ref t + Mi0 − 7sin 3 M ˙ ref t + Mi0 sin (Mi0 + ωi ) ae + O e4 . − 9sin M 4

3!

(2.6) Considering up to first order terms only, Equation (2.6) becomes X i (t) sin (Mi0 + ωi ) =a Z i (t) 1 − cos (Mi0 + ωi ) + ae

cos (Mi0 + ωi ) sin (Mi0 + ωi )

−sin (Mi0 + ωi ) cos (Mi0 + ωi )

˙ ref t + Mi0 2 sin M , (2.7) ˙ ref t + Mi0 cos M

which represents an ellipse translated with respect to the orbiting reference frame and whose line of apses is rotated by −(Mi0 + ωi ) around the orbit normal. Considering all terms, but assuming that the ith satellite is on the line-of-nodes at initial time (ωi = −Mi0 ), equations can be simplified and interpreted more easily: ⎧ 2 ⎪ ˙ ref t − ωi + ae sin 2 M ˙ ref t − ωi ⎪ ⎪ X i (t) = 2ae sin M ⎪ 4 ⎪ ⎪ ⎪ 3 ⎪ ae ⎪ ⎨ ˙ ref t − ωi + O e4 , ˙ ref t − ωi − 9sin M + 7sin 3 M 24 2 ⎪ ⎪ ⎪ ˙ ref t − ωi + ae 1 − cos 2 M ˙ ref t − ωi ⎪ Z i (t) = ae cos M ⎪ ⎪ 2 ⎪ ⎪ 3 3 ˙ ⎪ ⎩ ˙ ref t − ωi + ae cos Mref t − ωi − cos 3 M + O e4 . 8

(2.8)

Finally, considering terms of first order in eccentricity and ωi = −Mi0 , gives the following equations: ˙ ref t − ωi , X i (t) = 2ae sin M (2.9) ˙ ref t − ωi . Z i (t) = ae cos M The motion of the ith cartwheel satellites with respect to the orbiting reference frame can therefore be interpreted. At first order in eccentricity, the satellite trajectory is an ellipse whose

MISSION ANALYSIS OF SPACEBORNE BSAR

• 47

centre coincides with the reference point and with axes coincident with the XZ directions. Horizontal and vertical semi-axes span 2ae and ae respectively. When e increases, the elliptic approximation is less representative of the satellite relative motion. Errors induced by such an approximation can be estimated on the basis of second- and third-order terms. The second-order term gives the greatest horizontal error (ae2 /4) when Mref − ωi = 45◦ + k90◦ , and the greatest vertical error (ae2 ) when Mref − ωi = 90◦ + k180◦ (when on the major axis of the relative ellipse). The relative ellipse is covered at a constant angular rate coincident with the satellite mean ˙ ref t − ωi )), motion and in the direction opposite to the orbital motion (X i (t)/Z i (t) = 2 tan( M thus explaining the formation naming. It is worth underlining that if n satellites are used in the cartwheel, they all follow the same ellipse provided that the condition ωi = −Mi0 is verified for any i. If ωi are then symmetrically selected, satellites are uniformly distributed over the ellipse. If a typical remote sensing Earth orbit (e = 10−3 , a = 7200 km) is analysed, the relative ellipse axes are 28.8 km × 14.4 km, while the maximum instantaneous horizontal error is 1.8 m (relative error is e/16 with respect to 4ae) and the maximum instantaneous vertical error is 7.2 m (relative error is e/2 with respect to 2ae). The terms of third order contribute with discrepancies of the order of magnitude of millimetres. Figure 2.5 shows how elliptic approximation fails to describe relative motion properly when eccentricity increases. A number of issues arise when trying to apply a cartwheel to bistatic acquisitions. First of all, a single bistatic platform does not suffice to form a cartwheel unless the primary satellite is itself used as a formation component. However, if this is the case, cartwheel eccentricity is no longer a design variable: it is that of the orbit of the primary radar, typically of the order of 10−3 , with the consequence that satellite distance cannot be designed on the basis of applications, but is of the order of a few tens of kilometres. If hundreds of kilometres are needed, eccentricity should range around 10−2 . Besides the fact that elliptic approximation starts to fail at large eccentricities, such a value is most likely to be unacceptable for the primary radar and it must be additionally considered that eccentricity is selected on the grounds of the frozen orbit condition. An option that may be explored consists in the bistatic satellite following a cartwheel centred far away along the orbit. The satellite distance shows a variation with time, as large as allowed by bistatic satellite eccentricity. However, an almost constant large baseline can be achieved by simply flying the bistatic satellite on the orbit of the primary radar with a shift in anomaly. Whatever option is selected, it should be noted that a cartwheel formation attains satellite separation in the orbit plane, thus generating alternatively ‘upward/downward’ and ‘forward/backward’ baselines. With respect to the reference antenna orbit, the bistatic radar has an azimuth separation in this latter case, which might be less interesting from the applicative point of view due to backscattered signal reduction in off-elevation directions. From the orbit perturbation point of view, it must be noted that cartwheel satellites share the same semi-major axis, inclination and eccentricity. Thus, they are characterized by identical J2 secular effects: perturbed mean motion, ascending node and perigee precessions equally affect all satellites. In the original idea [2.38, 2.39], the transmitting radar was behind the cartwheel flying in the same orbital plane (common inclination and ascending node right ascension) on an orbit with the same semi-major axis but with different eccentricity. This choice, while guaranteeing common Keplerian mean motion, causes secular and slow in-plane and outof-plane drifts between the transmitting satellite and the cartwheel formation. Therefore, a continuous orbital correction is required, either by the cartwheel satellites or by the primary one, to counteract this effect. Conversely, the approach with the primary satellite itself as part of the cartwheel formation does not necessitate continuous correction of secular drifts.

0

−100

−50

[km]

50

1000

3000

4000

5000

80

0

ΔZ

1000

0

6000

20

40

60

1000

2000

3000

4000

5000

6000

a = 7200km

Orbital period [seconds]

ΔX

e = 0.1

[km]

−1000

−500

0

500

1000

1500

2000

0

−6000

2000

ΔZ

3000

2ae X

4000

5000 6000

a = 7200km

6000 [km]

a = 7200km

3000

e = 0.5

0

Z

e = 0.5

Orbital period [seconds]

1000

ΔX

−3000

cartwheel ellipse

Figure 2.5 Upper diagrams show a comparison between actual relative trajectory (continuous line) and elliptic approximation (dashed line) for increasing values of eccentricity, for an orbit with a semi-major axis of 7200 km. In the lower diagrams the errors in the X and Z coordinates introduced by the first-order approximation are shown

Orbital period [seconds]

2000

[km]

a = 7200km

100

500

X

2500

5000

−5000 0

2ae

a = 7200km

−1000

Z

e = 0.1

−2500

−1000 −500

cartwheel ellipse

−500

0

−20

0

e = 0.01

50

X

−200

ΔZ

0

2ae

500

1000

0

ΔX

−50

Z

a = 7200km

ae

e = 0.01

ae

0

200

400

600

800

−100

cartwheel ellipse

[km] Error [km]

100

Error [metres]

[km] Error [km]

ae

MISSION ANALYSIS OF SPACEBORNE BSAR

2.3.1.3 Pendulum

• 49

The pendulum concept [2.42, 2.47] was introduced at DLR (Deutschen Zentrum f¨ur huft- und Raumfahrt) for cross-track interferometric applications. In particular, it came up as a modification of the cartwheel, which attains baselines in the plane of motion, to realize horizontal baselines in the direction perpendicular to the orbit plane. To achieve this goal, the orbits of the passive receivers differ from the active radar and from one another in ascending node right ascension and in inclination. It is worth underlining that a pendulum configuration with equal inclination but different ascending nodes coincides with the parallel orbits previously discussed. A difference in inclination is required to obtain large baselines at high latitudes, while parallel orbits achieve larger baselines near the equator. The relative dynamics of the satellites of a pendulum formation could be discussed on the basis of the Hill [2.69] or Clohessy–Wiltshire [2.70] equations, which are a linearization of the equation of motion under the assumption of close satellites, though no specific linearized model has been proposed for pendulum. Therefore, if on the one hand the required satellite separation should be accomplished by properly selecting ascending node separation and inclination differences, on the other hand no models exist to express these parameters as a function of the baseline. The main drawback of pendulum is that inclination has a strong impact on secular perturbations arising from the Earth’s oblateness. As a consequence, satellites in pendulum with different inclinations exhibit drifts in perigee and ascending nodes to be counteracted by orbital manoeuvres. It was estimated [2.42] that a 1 kg fuel consumption should be budgeted per year of operation and per kilometre of baseline in the case of a 100 kg microsatellite. From these figures it is clear that pendulum applicability to bistatic missions is unlikely, since satellite distance reaches the order of hundreds of kilometres, leading to unacceptable propellant budgets. Of course, pendulum is a good solution for bistatic mission phases exploring high latitudes, although they should be limited in time and propellant to keep constant inclination, and ascending node differences must be budgeted. In conclusion, there are grounds to consider parallel orbits (i.e. pendulum with ascending node separation only) as the best choice to implement a bistatic mission with a long lifetime. Major considerations driving towards this solution are related to the achievable orbit geometries, which allows bistatic angles in the range-elevation plane, and to the presence of practically the same orbital perturbations for all the satellites in formation.

2.3.2 BSAR Attitude and Antenna Pointing Design Pointing design, whether for attitude or antenna, is performed to let the two radar swaths coincide. Thus, algorithms must be determined in order to link swath positions on the Earth (assumed spherical) to rotation angles at satellite altitude. Since swath widths can be expressed in angular terms considering the angles subtended with respect to the Earth’s centre, equations to relate geocentric and satellite-centred angles are required. It must be considered, then, that pointing angles must account for two major effects: orbit separation and off-nadir looking of radars. Figure 2.3 allows further insights to be gained into these aspects since it shows that orbit separation produces a geocentric angle subtended by the elevation arc (intersection of the primary elevation plane with the Earth’s surface) between the two orbital arcs (intersections of orbital planes with the Earth’s surface). Since this analysis is not concerned in periodic

• 50

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

coverage and repetition features but only on geometrical problems, the Earth can be assumed as a nonrotating sphere. Another geocentric angle is then produced under the elevation arc of the bistatic radar, assumed to be in the opposite direction with respect to the primary radar position (a right-looking bistatic radar if a right-looking primary radar is considered, i.e. the same-side observation). The problem of relating geocentric and satellite-centred angles is common to all pointing actions, as well as the relations to be established for quantifying orbital arcs relative geometry, whereas angles subtended by radar elevation arcs and attitude/antenna pointing angles must be treated separately. Nonetheless, options belonging to the fully independent and partially dependent strategies (Figure 2.1) share the fact that the primary radar elevation plane is not changed with respect to nominal operation. On the other hand, the fully dependent strategy is also characterized by a modification of the primary elevation plane. To determine relations between satellite-centred and geocentric angles, the reader is referred to Figure 2.6 where the satellite (S) and its orbiting reference frame (XYZ) are shown along with satellite nadir (N). Consider an elevation angle (ϑ) with radar line-of-sight along the ST direction (where T is a generic terrain target), which gives a corresponding geocentric angle (ϑ g ) subtended by the elevation arc (NT). Relations between ϑ and ϑ g can be easily derived X Y Z

ϑ ϑ β

T N

N’ 90° -ζ

T’ ϑgβ

ϑg

grea

t cir cle

‘

S

ϑg

ϑ*g

tion

H

eleva

O⊕

tal

i orb

arc

P

arc c 2003 IEEE. This figure was Figure 2.6 Satellite-centred and corresponding geocentric angles. published in D’Ericco, M. & Moccia, A., 2001. Attitude and Antenna Pointing Design of Bistatic Radar Formations. IEEE Transactions on Aerospace and Electronic Systems, 39 (3), p. 949–960. Reproduced by permission of IEEE.

• 51

MISSION ANALYSIS OF SPACEBORNE BSAR

as follows:

sin ϑ 2 2 2 a cos ϑ − ρ⊕ − a sin ϑ , ϑg (ϑ) = sin ρ⊕ ⎧ ⎫ 2 −1/2 ⎬ ⎨ a/ρ⊕ − cos ϑg ϑ(ϑg ) = sin−1 1+ . ⎩ ⎭ sin ϑg −1

(2.10)

(2.11)

These simple relations stand only if the elevation arc is a great circle arc, i.e. the rangeelevation plane contains the Earth centre, which requires: (a) no attitude rotations (as in Figure 2.6 with the elevation arc perpendicular to the orbital arc); (b) the satellite rotated around the Z axis (yaw, γ ); (c) the satellite rotated around the X axis (roll, α). Conditions (b) and (c) can be applied simultaneously and, in the presence of a roll rotation, α + ϑ must be used instead of ϑ only in Equations (2.10) and (2.11). However, when pitch (β) rotations are established, the elevation arc (solid line through 2 N and T ), which is centred in H and has the radius (ρ⊕ − a 2 sin2 β)1/2 , is no longer a great arc, though it is still perpendicular in N to the orbital arc in the absence of yaw rotation. The distance between the satellite and H is a cos β. Considering the angle centred in H and subtending the elevation arc from N to T (solid line, ϑg∗ ), the geocentric angle corresponding to the arc of great circle through N and T (dashed line, ϑg ), and the angle between these arcs (ζ ), gives ⎡ ϑg∗ (ϑ, β) = sin−1 ⎣

sinϑ 2 ρ⊕ − a 2 sin2 β

⎤ 2 − a 2 sin2 ϑ − a 2 cos2 ϑ sin2 β ⎦ , a cos β cos ϑ − ρ⊕ (2.12) ⎡!

ϑg (ϑ, β) = 2 sin−1 ⎣ 1 − ζ (ϑ, β) = cos−1 cos

a sin β ρ⊕

ϑg∗ (ϑ, β) 2

2

sin

"

cos

ϑg∗ (ϑ, β) 2

ϑg (ϑ, β) 2

⎤

⎦,

(2.13)

.

(2.14)

2 Equation (2.11) can be further generalized using a cos β in lieu of a and ρ⊕ − a 2 sin2 β in lieu of ρ ⊕ : ⎧⎡ ⎫ ⎞2 ⎤−1/2 ⎪ ⎛ ⎪ ⎪ ⎪ 2 2 ∗ ⎨ ⎬ a cos β/ ρ⊕ − a 2 sin β − cosϑg ⎥ ∗ −1 ⎢ ⎠ ⎝ ϑ(ϑg ) = sin (2.15) ⎣1 + ⎦ ⎪ ⎪ sinϑg∗ ⎪ ⎪ ⎩ ⎭ With reference to relative orbit positions (common to all three strategies), consider the geocentric angles corresponding to the orbital arcs between ascending nodes and orbital arc intersection (Figure 2.3, ξ T/R and ξ R/o ), as well as the angle on the sphere between orbital arcs

• 52

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

in their intersection point (ψ): ψ = cos−1 sin2 i cos Ω + cos2 i , −1 sin Ω sin i ξT/R = sin , sin ψ % % ξR/o = 180◦ − %ξT/R % .

(2.16) (2.17) (2.18)

Once Equations (2.10) to (2.18) are established, common to all mission options and strategies, it is possible to analyse required pointing angles. Antenna elevation (ϑ) and azimuth (Az) angles, satellite roll (α), pitch (β), and yaw (γ ) attitude angles can be derived for the partially dependent (pd), fully independent (fi), and fully dependent (fd) strategies and for the bus-based (bus), payload-based (pay) and enhanced payload-based (enpay) mission options. No need arises to make explicit whether the angles are realized by the primary or bistatic satellite/payload, since no ambiguity exists when actions in Figure 2.1 are taken into account. When T/R and R/o subscripts are used, they refer to pointing angles not arising from their pointing manoeuvres (as an example, a predefined, constant elevation angle for the bistatic satellite is ϑ R/o , while the primary elevation angle deriving from nominal pointing is ϑ T/R ). The fully independent and partially dependent strategies share the same primary radar elevation arc (Figure 2.7), which gives some common features: (a) the geocentric angle subtended parallel (latitude 180°-i)

R/o

γ

ψ

ϑ

BISTATIC SATELLITE

NR/o °+

γ

YS

T’ ’R/o N ϑg intersection of primary elevation plane

90

PRIMARY SATELLITE

ϑ

NT/R

with Earth (elevation arc)

(1)

ϑg uT/R

projection of primary ascending node on the equator

* 90°+ γR/o

ϑg

uR/o O

equator projection of bistatic ascending node on the equator

intersection of orbit planes with Earth (orbit arcs)

Figure 2.7 Attitude/pointing approach to guarantee swath overlap along the orbit (bus-based option, partially dependent strategy)

• 53

MISSION ANALYSIS OF SPACEBORNE BSAR

by the elevation arc between the orbital arcs (ϑg(1) ); (b) the geocentric angle under the bistatic orbital arc between NR/o and NR/o (ϑgβ ), which is assumed negative when NR/o follows NR/o (as in Figure 2.7); (c) the angle in NR/o between the primary elevation arc and bistatic orbital ∗ to maintain compatibility with the definition of attitude angles (thus arc, defined as 90◦ + γR/o ∗ γR/o can be interpreted as a rotation around the direction O⊕ NR/o ). The angles ϑg(1) , ϑ gβ , and ∗ can be computed no matter which option is selected within the fully independent and γR/o partially dependent approaches as follows: tan ϑg(1)

=

% % %tan ξT/R − u T/R % sin cos (γYS + )

,

(2.19)

ϑgβ = ξR/o + f A/D δ − u R/o ,

∗ γR/o = sin−1 [sin γYS cos ψ+ cos γYS sin ψ cos ξT/R − u R/o

(2.20) ,

(2.21)

where tan = tan ψ cos ξT/R − u T/R , (2.22) & ' δ = cos−1 cos ξT/R − u R/o cos ϑg(1) + f A/D sin ξT/R − u R/o sin ϑg(1) sin γYS , (2.23) +1, ascending phase, f A/D = (2.24) −1, descending phase. When considering the mission options corresponding to the partially dependent strategy, it must be recalled that the bistatic radar elevation angle (ϑ R/o ) is constant and predefined, whereas the Tx/Rx elevation angle (ϑ) must be selected in order to obtain a corresponding geocentric angle that accounts for the length of the Tx/Rx elevation arc between the two orbital arcs (ϑg(1) ) and the geocentric angle subtended (along a great arc) by the passive radar (ϑg (ϑR/o , β), given by Equation (2.13)), which also depends on the Rx satellite pitch angle (β). On the other hand, β must be determined so that the satellite z axis intercepts the Earth in NR/o . As shown in Figure 2.7, the geocentric angle subtended by β is ϑ gβ , which is obtained from the R/o orbital arc between NR/o and NR/o . In order to make elevation swaths overlap, ∗ an R/o yaw angle (γ ) is also required to counteract the angle due to γR/o and ζ (ϑ R/o ,β) given by Equation (2.14), otherwise existing between T/R and R/o elevation arcs. On the grounds of Equations (2.19) to (2.24) and after some spherical trigonometry, the angles required for a partially dependent strategy and the bus-based option can be determined: & ( )' bus bus ϑpd = − f A/D ϑ ϑg(1) + ϑg ϑR/o , βpd , bus βpd = sign (ϑgβ )ϑ(ϑgβ ), ) ( ∗ bus + ζ ϑR/o , βpd γR/o bus γpd = * ( ) .

1−

a bus sinβpd ρ⊕

2

(2.25) (2.26)

(2.27)

• 54

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

bus It should be pointed out that the computed yaw rotation, γpd , around the spacecraft vertical ∗ axis can be quite easily performed, but it is not exactly equivalent to the rotation (γR/o + ζ) around the axis O⊕ NR/o . The former should also require a rotation around the tangent to the ∗ bus bistatic orbital arc in the point NR/o of (γR/o + ζ ) tan(βpd + ϑgβ ) to make both radars pointing in T . Therefore, some errors must be foreseen in the centre of beam localization and in the elevation directions. The pointing procedure described above refers to a bus-based option which is shown in Figure 2.7; in fact the primary radar elevation angle and the bistatic bus pitch and yaw angles have been the output of the procedure. As will be shown below, if the payload-based and enhanced payload-based options are selected, the azimuth angle of the bistatic radar must be used in lieu of pitch and, in the first case, the yaw manoeuvre of the bistatic bus can be removed. Pointing angles for the enhanced payload-based option can be rapidly derived on the basis bus of Equations (2.25) to (2.27), but replacing the angle, βpd , still used for derivations, by an adequate azimuth rotation. Assuming that the previously computed ϑ is not changed, the Rx antenna azimuth angle can be determined by considering that the satellite pitch axis and the antenna azimuth axis are relatively rotated around the flight direction by the angle ϑ R/o . Not only does this azimuth rotation remove any need for pitch rotation, but it also gives an effect on bus the yaw rotation by an amount βpd tan ϑR/o . It is worth noting that the yaw axis is not rotated by the antenna beam azimuth steering, while in the previous option the satellite pitch rotation modifies the yaw axis direction (from O⊕ NR/o to O⊕ NR/o ). Therefore, enpay

bus = ϑpd ,

enpay

=

ϑpd

Az pd

enpay γpd

=

(2.28)

bus βpd

cos ϑR/o

,

(2.29)

∗ bus γR/o + ζ ϑR/o , βpd cos ϑgβ enpay

bus + βpd tan ϑR/o .

(2.30)

Again, it is worth noting that the yaw rotation, γpd , is not exactly equivalent to the rotation ∗ ∗ (γR/o + ζ ) around O⊕ NR/o , since a residual rotation (γR/o + ζ ) tan(ϑgβ ) (smaller than in the previous option) around the tangent to the bistatic orbital arc in the point NR/o still exists. Regarding pointing angles in the case of the payload-based option, it must be noted that enpay enpay imposing γ = 0 and adopting previously computed ϑpd and Az pd produces a rotation between the two elevation arcs around the point NR/o , thus leading to the loss of swath centres superimposition. Since in this option yaw is to be avoided, swath centres must coincide so that rotation of elevation planes has the minimum impact; i.e. swaths are rotated around their common centre. To this end, the primary radar elevation angle and bistatic azimuth angles must change with respect to previous equations. For the time being, it will be assumed that the Rx satellite is pitch-rotated by an angle β , which brings the Rx radar swath centre on the Tx/Rx elevation arc. Afterwards, this pitch angle will be replaced by an azimuth antenna rotation. The primary elevation angle must then be determined so that its swath centre superimposes the bistatic one. The geometric concept is shown in Figure 2.8 where it is assumed that ϑ gβ , ∗ given by Equation (2.20), and γR/o , given by Equation (2.21) are both negative. The arc in NR/o is the R/o elevation arc when the pitch angle β is 0, while the solid arcs are the intersection of the elevation planes with the earth sphere for β > 0 and β < 0, which

• 55

MISSION ANALYSIS OF SPACEBORNE BSAR

R/o orbital arc ϑg(β ) (2)

WHENO K

‘

ϑ g 0> ϑ g0

*

ϑg(β )

ζ

90°

ϑgβ’

ϑg

ϑg0 OK

H W

NR/o 90°

OK

*

‘

‘

‘

ϑg(β )

* 90°+ γR/o

(2)

ϑg

N’R/o

T/R

ele vat io

na

rc

ϑgβ

T

ϑ g0

ζ

90°

EN

ϑg(β )

*

< ϑ g0

ϑgβ’

c 2003 IEEE. Figure 2.8 Pointing approach for the payload-based option, partially dependent strategy. This figure was published in D’Ericco, M. & Moccia, A., 2001. Attitude and Antenna Pointing Design of Bistatic Radar Formations. IEEE Transactions on Aerospace and Electronic Systems, 39 (3), p. 949–960. Reproduced by permission of IEEE.

are not great circle arcs. The dashed arcs having two points in common with the solid arcs are great circle arcs. Considering the rectangular spherical triangle (T∗ NR/o N R/o ),

OK ϑg0

⎧ , + ⎪ sin ϑgβ ⎪ ∗ ⎪ , when γR/o ϑgβ > 0, arctg ⎪ ∗ ⎪ ⎨ tan γR/o = , + ⎪ ⎪ sin ϑgβ ⎪ ∗ ◦ ⎪ , when γR/o ϑgβ < 0. ⎪ ⎩180 + arctg tan γ ∗ R/o

(2.31)

OK Then, depending on the value of ϑg0 = ϑg (ϑR/o , β = 0) and ϑg0 , three different cases arise. ∗ It is worth mentioning that the situation is similar when ϑ gβ and γR/o are both positive, while for opposite signs the angle at the interception of the Tx/Rx elevation arc and the Rx orbital arc is greater than 90◦ for any value of |β | < |β| (where β is a pitch-like angle corresponding OK > 90◦ (a solution exists also for |β |<|β| in the case to the geocentric angle ϑ gβ ) and ϑg0 ∗ of γR/o ϑgβ < 0, but if Rx looks on its left). All the possibilities are summarized in Table 2.1, showing the constraints on β . ∗ Angles ϑg ϑR/o , β , ϑg ϑR/o , β and ζ ϑR/o , β are given by Equations (2.12) to (2.14), but ϑg is also computed from spherical triangles. When the correct value of β is found, i.e. the one that gives the same ϑg with both Equation (2.13) and the following equation, it is possible to derive an expression for the geocentricangle subtended under the primary elevation

• 56

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR c 2003 IEEE. This Table 2.1 Possible cases for the unknown variable β table was published in D’Ericco, M. & Moccia, A., 2001. Attitude and Antenna Pointing Design of Bistatic Radar Formations. IEEE Transactions on Aerospace and Electronic Systems, 39 (3), p.949–960. Reproduced by permission of IEEE. ϑgβ

∗ γR/o

OK ϑg0 < ϑg0

OK ϑg0 = ϑg0

OK ϑg0 > ϑg0

<0 <0 >0 >0

<0 >0 <0 >0

βR/o < βR/o <0 βR/o < βR/o < 0 0 < βR/o < βR/o 0 < βR/o < βR/o

βR/o =0 Impossible Impossible βR/o =0

βR/o < 0 < βR/o Impossible Impossible βR/o < 0 < βR/o

arc between N R/o and the swath centre T (ϑg(2) ): ⎧ tan ϑg sin Γ ∗ ⎪ ⎪ when ϑgβ γR/o >0 ⎪ ⎪ cos (ζ − Γ) ⎪ ⎪ ⎪ ⎨ tan ϑ sin Γ g ∗ when ϑgβ γR/o >0 tan ϑg = ⎪ (ζ cos + Γ) ⎪ ⎪ ⎪ ⎪ ⎪ tan ϑg sin Γ ⎪ ∗ ⎩ < 0, when ϑgβ γR/o cos (ζ + Γ) % ⎧%% %% %% ∗ >0 ϑgβ − ϑgβ % when ϑgβ γR/o ⎪ ⎪ ⎨% % % % ∗ >0 ϑg = %ϑgβ % + %ϑgβ % when ϑgβ γR/o ⎪ ⎪ % % % % ⎩% % % ∗ ϑgβ − ϑgβ % when ϑgβ γR/o < 0,

and

OK ϑg0 < ϑg0 ,

and

OK ϑg0 > ϑg0 ,

and

OK ϑg0 < ϑg0 ,

and

OK ϑg0 > ϑg0 ,

% ∗ % % cosϑg tan Γ = cot %γR/o sinϑg ϑR/o , β cosζ ϑR/o , β (2) ϑg = arcsin ∗ cosγR/o

(2.32)

(2.33)

(2.34) (2.35)

and, finally, the required pointing angles:

( ) pay ϑpd = − f A/D ϑ ϑg(1) + f A/D ϑg(2) , pay

Az pd =

β . cosϑR/o

(2.36) (2.37)

Again, Az pd is not equivalent to β because the former also gives an equivalent yaw rotation pay Az pd sin ϑR/o which is not compensated, leading to a rotation of an Rx swath around the Rx nadir point; hence a residual swath rotation and a swath centre displacement must be envisaged. The fully independent approach can be explored by considering again Figure 2.7. Now the primary elevation angle (ϑ T/R ) is preassigned on the basis of the primary radar operation, thus either the bistatic antenna elevation angle or the bistatic satellite roll angle must account for cross-track relative displacement. If the bus-based option is analysed and a pitch–yaw–roll attitude rotation sequence is selected, the bistatic satellite must rotate around the pitch axis so that the vertical body axis points towards the intersection of the Rx orbitalarc and the pay

• 57

MISSION ANALYSIS OF SPACEBORNE BSAR

Tx/Rx elevation arc. The satellite must then be first yaw-rotated to align the elevation arcs and roll-rotated to make the swath centres coincident. Required angles can be computed by assuming a given and constant elevation angle of the bistatic antenna (ϑ R/o , which can be 0 if the antenna is mounted on the satellite bottom panel). In particular, the bistatic roll angle can be determined by considering the angle subtended by the primary elevation arc between the swath centre and point N R/o (ϑg ϑT/R , 0 − ϑg(1) ), which is then reported to an angle ϑg∗ , as in Figure 2.6, which can be computed by inverting Equation (2.13), and to the corresponding elevation angle through Equation (2.15): bus βfibus = βpd ,

γfibus =

(2.38)

bus

∗ γR/o + ζ ϑR/o + αfibus , βfi * )2 ( 1 − Ra⊕ sinβfibus

,

(2.39)

αfibus = ϑR/o − sin−1 ⎧⎡ ⎫ + ,2 ⎤−1/2 ⎪ ⎪ 2 ⎨ ⎬ − a 2 sin2 βfibus )1/2 − cos ϑg∗ (ϑR/o + αfibus , βfibus ) acosβfibus /(R⊕ ⎦ × ⎣1 + , bus bus ⎪ ⎪ sin ϑg∗ (ϑR/o + αfi , βfi ) ⎩ ⎭ (2.40) where the minus in Equation (2.40) has been introduced to account for positive roll angles and ⎤ ⎡ ϑg (ϑT/R ,0)−ϑg(1) sin 2 ⎢ ⎥ ⎥ ϑg∗ (ϑR/o + αfibus , βfibus ) = 2sin−1 ⎢ (2.41) * ⎣ ( ) ⎦. 1−

a ρ⊕

sin βfibus

2

Pointing angles for the enhanced payload-based option can be derived on the basis of Equations (2.38) to (2.40). If pitch is replaced by azimuth, it must be considered that the satellite y axis and the antenna y axis are relatively rotated around the flight direction by the angle ϑ R/o . Azimuth steering also contributes positively to elevation pointing by an amount βfibus tan ϑR/o and, contrary to the previous case, it does not modify the satellite yaw axis. Nevertheless, while in the previous case pitch and yaw rotations align the satellite roll axis with the correct direction around which roll must be applied, in this latter case the elevation direction still coincides with the flight direction. As a consequence, the elevation angle must be modified with respect to the roll angle before introduced and a residual rotation around the satellite yaw axis must be introduced: enpay

=

enpay

=

enpay

=

ϑfi

Az fi

γfi

αfibus , cos βfibus βfibus , cos ϑR/o ) ( ∗ bus + ζ ϑR/o , βpd γR/o cos ϑgβ

(2.42) (2.43)

bus + βpd tan ϑR/o + αfibus tan βfibus .

(2.44)

• 58

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

g ( R/o +

pay '' fi , )

T’

R/o orbital arc g ( R/o +

90° (

R/o

+

pay fi ,

''

pay '' fi , )

)

''

g

(1)

f ( )

g

(

T/

R

,0 )

-

NR/o

90° +

* R/o

N’R/o

T/R

ele vat i

no

arc

g

Figure 2.9 Pointing approach for the payload-based option, fully independent strategy

Then consider the payload-based option that only relies on azimuth and elevation steering of the bistatic antenna. With reference to Figure 2.9, given the swath centre (T ) on the primary elevation arc, which depends on the primary radar elevation angle (ϑ T/R ), it is first assumed that the satellite pitch rotates by an angle β (which will be replaced by azimuth pointing) so that its elevation arc crosses the primary arc in T . From the spherical triangle it is possible elevation pay ∗ to relate the known angles ϑg ϑT/R , 0 − ϑg(1) , ϑ gβ , and γR/o to ϑgβ , ζ (ϑR/o + ϑfi , β ) and pay ϑg (ϑR/o + ϑfi , β ): ' & cos ϑg ϑR/o + ϑ, β = cos ϑgβ + ϑg β cos ϑg ϑT/R − ϑg(1) & ' ∗ +sin ϑgβ + ϑg β sin ϑg ϑT/R − ϑg(1) sin γR/o , (2.45) ' & ∗ sin ϑg ϑR/o + ϑ, β = cos γR/o (2.46) sin ϑg ϑT/R − ϑg(1) /cosζ ϑR/o ϑ, β . Thus two equations in three unknowns are generated (ϑg , ϑ g , and ζ ), which can be coupled pay with Equations (2.10) and (2.12) to (2.14) to obtain the solution in terms of ϑfi and β . Then pay Az fi is derived by division of β and the cosine of the antenna mounting angle (ϑ R/o ). Finally, for the fully dependent strategy, refer to Figure 2.10. In particular, it is assumed that the bistatic radar is pointed with a constant off-nadir angle (ϑ R/o ) in the cross-track direction, perpendicular to the bistatic orbit arc. Thus, the primary radar must be pointed in azimuth and elevation in order to let the two radar swaths coincide. For the time being, it is assumed that a pitch rotation is used so that the primary radar elevation arc passes through the bistatic radar swath centre. It is to be noted that the primary elevation arc (represented as a solid

• 59

MISSION ANALYSIS OF SPACEBORNE BSAR

parallel (latitude 180°-i)

ψ ’ NT/R 90° ϑg(β′′′) PRIMARY SATELLITE

ψ’

P

ϑ’g(ϑT/R,β′′′)

ϑR/o

BISTATIC SATELLITE

T’ NR/o 90°

intersection of bistatic elevation plane with Earth (elevation arc)

ϑg(ϑR/o,0)

ϑ

primary elevation arc: ϑ*g(ϑT/R,β′′′)

NT/R

uR/o

uT/R

O⊕

projection of primary ascending node on the equator

equator

projection of bistatic ascending node on the equator

intersection of orbit planes with Earth (orbit arcs)

Figure 2.10 Pointing approach for the payload-based option, fully dependent strategy

arc through NR/o and T corresponding to a nongeocentric angle ϑg∗ ϑ, β in Figure 2.10, Equation (2.12)) is not a great circle arc. A great circle arc can then be generated through NR/o and T corresponding to a geocentric angle ϑg ϑ, β , Equation (2.13), and forming an angle ζ ϑ, β , Equation (2.14) and Figure 2.6, with the elevation arc in NR/o . The great circle arc is represented as a dashed arc in Figure 2.10. Geometry is completed by tracing the great circle arc through the orbit intersection (P) and the swath centre (T ), which forms an angle ψ with the bistatic orbit arc and whose length is referred to as ρ. Spherical trigonometry can be applied to the spherical triangle, PT NR/o , leading to the following equations: cos ρ = cos ξR/o − u R/o cosϑg ϑR/o , 0 , cos ψ = tan ξR/o − u R/o / tan ρ.

(2.47) (2.48)

Then, the spherical triangle PT NR/o implies: cos ϑg ϑ, β = cos ρ cos ξR/o − u R/o − ϑg β +sin ρ sin ξR/o − u R/o − ϑg β cos ψ + ψ , sin ϑg ϑ, β = sin ρ sin ψ + ψ /cos ζ ϑ, β .

(2.49) (2.50)

• 60

SPACEBORNE BISTATIC SYNTHETIC APERTURE RADAR

Thus two equations in three unknowns are generated (ϑg , ϑ g and ζ ), which can be coupled pay with Equations (2.10) and (2.12) to (2.14) to obtain the solution in terms of ϑ f d and β ; β pay is then replaced by Az f d by division through the cosine of the primary antenna mounting angle.

2.4 SUMMARY In order to maintain an adequate swath overlap along the orbit, BSAR missions require careful selection of orbits and pointing which must also take into account system-level issues, for instance impacts on a transmitting/receiving radar mission, requirements on a bistatic payload/bus and lifetime. This chapter presents an overview of candidate orbits for a BSAR mission and highlights orbit design in the case of parallel orbits. In addition, a comprehensive analysis of attitude and pointing geometry is presented. A model is developed that is applicable independently from the orbital configuration selected for the bistatic formation. The procedure is based on spherical trigonometry and allows the effects of large, time-variant baselines to be accounted for, when different strategies are selected to share tasks and complexities between main mission and parasitic spacecraft. Basically, the model has been realized for mission analysis and simulation, as will be shown in the next chapter. However, it can also be applied to develop onboard software for real-time modifying pointing angles, using satellites positions as input, in order to attain swath overlap with predefined bistatic baselines.

ABBREVIATIONS ASI DLR O( ) Rx Tx/Rx XYZ

Agenzia Spaziale Italiana Deutschen Zentrum f¨ur Luft- und Raumfahrt order of magnitude receiving transmitting/receiving orbiting reference frame

VARIABLES a Az e fA/D i M ˙ M u α β

semi-major axis antenna azimuth pointing angle orbit eccentricity flag identifying the ascending or descending phase of orbits orbit inclination mean anomaly mean motion argument of latitude (anomaly computed from the ascending node) roll attitude angle pitch attitude angle

VARIABLES

β β β γ ∗ γR/o tAN u Ω ζ ϑ ϑg ϑg(1) ϑg(2) ϑg∗ ϑg ϑ¯ g ϑ gβ ν ξ ρ ρ⊕ ω ψ ψ ⊕ μ⊗

61

‘virtual’ pitch (payload-based option, partially dependent strategy) ‘virtual’ pitch (payload-based option, fully independent strategy) ‘virtual’ pitch (payload-based option, fully dependent strategy) Yaw attitude angle plus 90◦ gives the angle between the primary elevation arc and the bistatic orbital arc in NR/o difference between times of passage on the ascending node difference between arguments of latitude difference between ascending node right ascensions angle between elevation and great circle arcs satellite-centred angle (typically the antenna elevation angle) Earth-centred angle corresponding to ϑ geocentric angle subtending the elevation arc between the orbital arcs geocentric angle subtending the primary elevation arc between N R/o and the swath centre angle subtending the elevation arc from the swath centre to the orbital arc angle subtending the great circle arc between the swath centre and the orbital arc geocentric angle between the primary satellite nadir and the bistatic satellite ascending node geocentric angle subtending the bistatic orbital arc between NR/o and NR/o μ⊕ Earth gravity constant true anomaly geocentric angle under the orbital arc between the ascending node and the orbital arcs at their intersection angle subtending the great circle arc between O and T Earth mean radius perigee anomaly angle between the orbital arcs at their intersection angle between the bistatic orbit arc and the great circle through P and T Earth rotation rate Earth provity constant

Subscripts/Superscripts bus pay enpay fi fd i pd ref R/o T/R YS

•

bus-based option payload-based option enhanced payload-based option fully independent strategy fully dependent strategy ith satellite in a cartwheel formation partially dependent strategy reference point in a cartwheel formation receiving only transmitting/receiving yaw steering

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Special Points N NR/o NT/R O⊕ P T

satellite nadir intersection of the primary elevation arc with the bistatic orbital arc intersection of the primary elevation arc with the primary orbital arc Earth centre orbit intersection swath centre

REFERENCES 2.1 Zebker, H. A. and Villasenor, J. (1992) Decorrelation in interferometric radar echoes, IEEE Trans., GRS-30 (5), 950–9. 2.2 Bamler, R. and Hartl, P. (1998) Synthetic aperture radar interferometry, Inverse Problems, 14, R1–R54. 2.3 Rosen, P. A., Hensley, S., Joughin, I. R., Li, F. K., Madsen, S. N., Rodriguez, E. and Goldstein, R. M. (2000) Synthetic aperture radar interferometry, Proc. IEEE, 88 (3), 333–82. 2.4 Pavelyev, A. G., Volkov, A. V., Zakharov, A. I., Krutikh, S. A. and Kucherjavenkov, A. I. (1996) Bistatic radar as a tool for earth investigation using small satellites, Acta Astronautica, 39 (9–12), 721–30. 2.5 Parker, M. N. and Tyler, G. L. (1973) Bistatic-radar estimation of surface-slope probability distributions with applications to the moon, Radio Science, 8 (3), 177–84. 2.6 Simpson, R. A. (1993) Spacecraft studies of planetary surfaces using bistatic radar, IEEE Trans., GRS-31 (2), 465–82. 2.7 Simpson, R. A. and Tyler, G. L. (1982) Radar scattering laws for the lunar surface, IEEE Trans., AP-30 (3), 438–49. 2.8 Simpson, R. A. and Tyler, G. L. (1999) Reanalysis of Clementine bistatic radar data from the lunar South Pole, J. Geophysical Research, 104 (E2), 3845–62. 2.9 Tyler, G. L. and Howard, H. T. (1973) Dual-frequency bistatic-radar investigations of the Moon with Apollos 14 and 15. J. Geophysical Research, 78 (23), 4852–74. 2.10 Tang, C. H., Boak, T. I. S. and Grossi, M. D. (1977) Bistatic radar measurement of electrical properties of the Martian surface, J. Geophysical Research, 82, 4305–15. 2.11 Martinsek D. and Goldstein, R. (1998) Bistatic radar experiment, in Proceedings of EUSAR, pp. 31–4. 2.12 Griffiths, H. D., Baker, C. J., Baubert, J., Kitchen, N. and Treagust, M. (2002) Bistatic radar using satellite-borne illuminators, in Proceedings of the IEE Radar Conference, pp. 1–5. 2.13 Zavorotny, V. U., Voronovich, A. G., Katzberg, S. J., Garrison, J. L. and Komjathy, A. (2000) Extraction of sea state and wind speed from reflected GPS signals: modeling and aircraft measurements, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,00), vol. 4, pp. 1507–9. 2.14 Fung, A. K., Zuffada, C. and Hsieh, C. Y. (2001) Incoherent bistatic scattering from the sea surface at L-band, IEEE Trans., GRS-39 (5), 1006–12. 2.15 Mart´ın-Neira, M., Caparrini, M., Font-Rossello, J., Lannelongue, S. and Serra Vallmitjana, C. (2001) The PARIS concept, an experimental demonstration of sea surface altimetry using GPS reflected signals, IEEE Trans., GRS-39 (1), 142–50.

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2.16 Zahn, D. and Sarabandi, K. (2000) Simulation of bistatic scattering for assessing the application of existing communication satellites to remote sensing of rough surfaces, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,00), vol. 4, pp. 1528–30. 2.17 Zavorotny, V. U. and Voronovich, A. G. (2000) Bistatic GPS signal reflections at various polarizations from rough land surface with moisture content, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,00), vol. 7, pp. 2852–4. 2.18 McIntosh, J. C., Clary, C. E. and Ray, L. (2001) An adaptive algorithm for enhanced target detetction for bistatic space-based radar, in Proceedings of the IEEE Radar Conference, pp. 70–74. 2.19 Griffiths, H. D. (2003) From a different prospective: principles, practice and potential of bistatic radar, in Proceedings of the IEEE Radar Conference, pp. 1–7. 2.20 He, X., Cherniakov, M. and Zeng, T. (2005) Signal detectability in SS-BSAR with GNSS non-cooperative transmitter, IEE Proc.-F, 152 (3), 124–132. 2.21 Mart´ın-Neira, M., Mavrocordatos, C. and Colzi, E. (1998) Study of a constellation of bistatic radar altimeters for mesoscale ocean applications, IEEE Trans., GRS-36 (6), 1898–904. 2.22 Prati, C., Rocca, F., Giancola, D. and Monti Guarnieri, A. (1998) Passive geosynchronous SAR system reusing backscattered digital audio broadcasting signals, IEEE Trans., GRS36 (6), 1973–6. 2.23 Cherniakov, M., Nezlin, D. and Kubik, K. (2002) Air target detection via bistatic radar based on LEOS communication signals, IEE Proc.-F, 149 (1), 33–38. 2.24 Cherniakov, M., Kubik, K. and Nezlin, D. (2000) Bistatic synthetic aperture radar with non-cooperative LEOS based transmitter, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,00), vol. 2, pp. 861–2. 2.25 Cherniakov, M. (2002) Space-surface bistatic synthetic aperture radar prospective and problems, in Proceedings of the IEE Radar Conference, vol. 490, pp. 22–5. 2.26 Cherniakov, M., Zeng, T. and Plakidis, E. (2003) Ambiguity function for bistatic SAR and its application in SS-BSAR performance analysis, in Proceedings of IEEE Radar Conference, pp. 343–8. 2.27 Ulaby, F. T., van Deventer, T. E., East, J. R., Haddock, T. F. and Coluzzi, M. E. (1988) Millimeter-wave bistatic scattering from ground and vegetated targets, IEEE Trans., GRS-26 (3), 229–43. 2.28 Hauck, B., Ulaby, F. T. and DeRoo, R. D. (1998) Polarimetric bistatic-measurement facility for point and distributed targets, IEEE Antennas and Propagation Mag., 40 (1), 31–41. 2.29 Hsu, Y. S. and Lorti, D. C. (1986) Spaceborne bistatic radar – an overview, IEE Proc.-F, 133, 642–8. 2.30 Guttrich, G. L. and Sievers, W. E. (1997) Wide area surveillance concepts based on geosynchronous illumination and bistatic UAV or satellite reception, in Proceedings of the IEEE Aerospace Conference, vol. 2, pp. 171–80. 2.31 Ogrodnik, R. F., Wolf, W. E., Schneible, R. and McNamara, J. (1997) Bistatic variants of spacebased radar, in Proceedings of the IEEE Aerospace Conference, vol. 2, pp. 159–69. 2.32 Hartnett, M. P. and Davis, M. E. (2001) Bistatic surveillance concept of operations, in Proceedings of the IEEE Radar Conference, pp. 75–80.

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2.33 Hartnett, M. P. and Davis, M. E. (2003) Operations of an airborne bistatic adjunct to space based radar, Proceedings of the IEEE Radar Conference, pp. 133–8. 2.34 Picardi, G., Seu, R., Sorge, S. G. and Martin-Neira, M. (1998) Bistatic model of ocean scattering, IEEE Trans., AP-46 (10), 1531–41. 2.35 Alberti, G. and Zelli, C. (1999) Design of bistatic altimetric mission for oceanographic applications, Space Technology, 19 (2), 83–96. 2.36 Raney, R. K. and Porter, D. L. (2001) WITTEX: an innovative three-satellite radar altimeter concept, IEEE Trans., GRS-39 (11), 2387–91. 2.37 Raney, R. K., Porter, D. L. and Monaldo, F. M. (2002) Bistatic WITTEX: an innovative constellation of radar altimeter satellites, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,02), vol. 3, pp. 1355–7. 2.38 Massonnet, D. (2001) Capabilities and limitations of the interferometric cartwheel, IEEE Trans., GRS-39 (3), 506–20. 2.39 Massonnet, D. (2001) The interferometric cartwheel: a constellation of passive satellites to produce radar images to be coherently combined, Int. J. Remote Sensing, 22 (12), 2413–30. 2.40 D’Errico, M. and Moccia, A. (2002) The BISSAT mission: a bistatic SAR operating in formation with COSMO/SkyMed X-band radar, in Proceedings of the IEEE Aerospace Conference, vol. 2, pp. 809–18. 2.41 Moccia, A. and Fasano, G. (2005) Analysis of spaceborne tandem configurations for complementing Cosmo with SAR interferometry, EURASIP J. Applied Signal Processing, 2005 (20), 3304–15. 2.42 Krieger, G., Fiedler, H., Mittermayer, J., Papathanassiou, K. and Moreira, A. (2003) Analysis of multistatic configurations for spaceborne SAR interferometry, IEE Proc.-F, 150 (3), 87–96. 2.43 Moreira, A., Krieger, G., Hajnsek, I., Hounam, D., Werner, M., Riegger, S. and Settelmeyer, E. (2004) TanDEM-X: a TerraSAR-X add-on satellite for single-pass SAR interferometry, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,04), vol. 2, 1000–3. 2.44 D’Errico, M., Grassi, M. and Vetrella, S. (1996) A bistatic SAR mission for Earth observation based on a small satellite, Acta Astronautica, 39 (9–12), 837–46. 2.45 Zebker, H. A., Farr, T. G., Salazar, R. P. and Dixon, T. H. (1994) Mapping the world’s topography using radar interferometry: the TOPSAT mission, Proc. IEEE, 82 (12), 1774– 86. 2.46 D’Errico, M., Moccia, A. and Vetrella, S. (1994) Attitude requirements of a twin satellite system for the global topography mission. In Proceedings of the 45th IAF Congress, IAF94-B.2.077, pp. 1–10. 2.47 Moreira, A., Krieger, G. and Mittermayer, J. (2001) Comparison of several bistatic SAR configurations for SAR Interferometry, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS,01). 2.48 Attema, E. P. W. (1991) The active microwave instrument on-board the ERS-1 satellite, Proc. IEEE, 79 (6), 791–9. 2.49 Duck, K. I. and King, J. C. (1983) Orbital mechanics for remote sensing, in Manual of Remote Sensing, 2nd edn (ed. R. N. Colwell), American Society of Photogrammetry, Falls Church. 2.50 Bekey, I. (2003) Advanced Space System Concepts and Technologies, 2010–2030, AIAA, Reston.

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2.51 D’Errico, M. and Moccia, A. (2003) Attitude and antenna pointing design of bistatic radar formations, IEEE Trans., AES-39 (3), 949–60. 2.52 Kong, E. M. C., Miller, D. W. and Sedwick, R. J., (1999) Exploiting orbital dynamics for aperture synthesis using distributed satellite systems: applications to a visible earth imager system, J. Astronautical Sciences, 47 (1–2), 53–75. 2.53 Sabol, C., Burns, R. and McLaughlin, C. A. (2001) Satellite formation flying design and evolution, J. Spacecraft and Rockets, 38 (2), 270–8. 2.54 Beard, R. W., McLain, T. W. and Hadaegh, F. Y. (2000) Fuel optimization for constrained rotation of spacecraft formations, J. Guidance, Control, and Dynamics, 23 (2), 339–46. 2.55 de Queiroz, M. S., Kapila, V. and Yan, Q. (2000) Adaptive nonlinear control of multiple spacecraft formation flying, J. Guidance, Control, and Dynamics, 23 (3), 385–90. 2.56 Wang, P. K. C. and Hadaegh, F. Y. (1996) Coordination and control of multiple microspacecraft moving in formation, J. Astronautical Sciences, 44 (3), 315–55. 2.57 Beard, R. W., Lawton, J. and Hadaegh, F. Y. (2001) A coordination architecture for spacecraft formation control, IEEE Trans., CST-9 (6), 777–90. 2.58 Kang, W., Sparks, A. and Banda, S. (2001) Coordinated control of multisatellite systems, J. Guidance, Control, and Dynamics, 24 (2), 360–8. 2.59 Beard, R. W. and Hadaegh, F. Y. (1999) Fuel optimization for unconstrained rotation of spacecraft formations, J. Astronautical Sciences, 47 (3–4), 259–73. 2.60 Alfriend, K. T. and Schaub, H. (2000) Dynamic and control of spacecraft formations: challenges and some solutions, J. Astronautical Sciences, 48 (2–3), 249–67. 2.61 Schaub, H. and Alfriend, K. T. (2001) Impulsive feedback control to establish specific mean orbit elements of spacecraft formations, J. Guidance, Control, and Dynamics, 24 (4), 739–45. 2.62 Burns, R., McLaughlin, C. A., Leitner, J. and Martin, M. (2000) TechSat21: formation design, control, and simulation, in Proceedings of the IEEE Aerospace Conference, pp. 19–25. 2.63 Chien, S., Sherwood, R., Burl, M., Knight, R., Rabideau, G., Engelhardt, B., Davies, A., Zetocha, P., Wainwright, R., Klupar, P., Cappelaere, P., Surka, D., Williams, B., Greeley, R. and Baker, B. (2001) The Techsat-21 autonomous sciencecraft constellation, in Proceedings of the International Symposium on Artificial Intelligence and Robotics and Automation in Space, pp. 1–8. 2.64 McDonald, K. D. (2002) The modernization of GPS: plans, new capabilities, and the future relationship to GALILEO, J. Global Positioning Systems, 1 (1), 1–17. 2.65 Kawano, I., Mokuno, M., Kasai, T. and Suzuki, T., (2002) First autonomous rendezvous using relative GPS navigation by ETS-VII, J. Institute of Navigation, 48 (1), 49–56. 2.66 Duren, R. M. and Lay, O. P. (2002) The StarLight formation-flying interferometer system architecture, in Proceedings of the IEEE Aerospace Conference, vol. 4, pp. 1703– 19. 2.67 Cutting, E., Born, G. H. and Frautnick, J. C. (1978) Orbit analysis for SEASAT-A, J. Astronautical Sciences, 26 (4), 315–42. 2.68 Miele, A. and D’Errico, M. (2003) A relative orbital motion model oriented to formation design, in Proceedings of the 3rd International Workshop on Satellite Constellations and Formation Flying, pp. 189–96. 2.69 Hill, G. W. (1878) Researches in Lunar theory, American J. Mathematics, 1, 5–26. 2.70 Clohessy, W. H. and Wiltshire, R. S. (1960) Terminal guidance system for satellite rendezvous, J. Astronautical Sciences, 27 (9), 653–78.

3 Bistatic SAR for Earth Observation A. Moccia and M. D’Errico

3.1 INTRODUCTION In 2000–2001 the Italian Space Agency (ASI) issued a competitive tender for defining and selecting a national scientific and technological experimental mission aimed at Earth observation and based on a small satellite [3.1, 3.2]. The BISSAT (bistatic SAR satellite) is one of the five selected options and the ASI has awarded the University of Naples to be the principal investigator and program manager for a phase A study. The BISSAT mission comprises a bistatic SAR orbiting on a small satellite which will be linked to COSMO-SkyMed (constellation of small satellites for Mediterranean basin observation). COSMO-SkyMed is the Italian constellation for high spatial and temporal resolution SAR imaging of the Earth [3.3–3.8]. Basically, it consists of four satellites, orbiting in the same plane (in sun-synchronous orbit at the nominal altitude of 619.6 km), phased at 90◦ , each equipped with an advanced X-band SAR (SAR2000). The program has been approved and founded by ASI and the Italian Ministry for Defence. The development of COSMO-SkyMed is carried out by Thales Alenia Space Italia, a Thales/Finmeccanica Company, as the prime contractor, under management of the ASI. The first satellite was successfully launched in June 2007, and the other three will follow at six month intervals. Therefore, the entire constellation, including its ground segment, is scheduled for completion by the beginning of 2009, after fulfilment of the fourth satellite commissioning phase. Thanks to its dual-use capabilities, COSMO-SkyMed will be applied in Italy to the protection of national territory, for strategic defence as well as for civilian tasks, namely remote sensing of Italian territory, monitoring environmental disasters (floods, landslides, volcanoes) and coastlines, seas and inland waterways, fulfilling cartographic applications using one-metre resolution single look images. The BISSAT is expected to be equipped with a receiving-only microwave system which receives the echo of the main monostatic X-band SAR. The proposed system envisages two antennas flying and operating in formation, along almost parallel orbits, for a two-year lifetime, thus achieving bistatic SAR implementation in space with two separate platforms. In principle, the BISSAT could fly in formation with any existing or scheduled spaceborne SAR, provided Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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that adequate payload customization has been conducted. COSMO-SkyMed has been selected for the main mission essentially because it allows existing ASI investments, well-established Italian industry expertise and interest of the scientific community to be fully exploited. Of course, the presented scientific ideas and analyses, along with the feasibility studies of the mission, could be easily extended to other spaceborne SAR, without involving significant differences in models, procedures and performance. The main features and advantages of the BISSAT can be summarized as follows: (a) The possibility of conducting original scientific experiments and the chance to investigate novel applications, in combination with an existing, already founded system, which can obtain an added value and several spin-offs, without requiring any design modification.

(b) The possibility of performing a technological demonstration of an original space formation, thus establishing the feasibility of a new observation technique, based on well-assessed sensor technology but operated in an innovative configuration with potential future application as an operational observing system. (c) The capability of offering to the Italian industry the chance to design and operate a formation within a mission scenario requiring both flight control and satellite inter-operation, thus achieving expertise in an internationally recognized strategic field. (d) The capability to keep overall costs within a small mission budget, thanks to the adoption of well-proven technologies and to transmitting main mission experience, hence reducing risks in bistatic mission design, realization and operation. This chapter is intended to present the BISSAT as a case study of a spaceborne BSAR. To this end several aspects related to the BISSAT study founded by the ASI will be reported. The main characteristics of the mission and of the payload and several results and expected performance will be detailed. Finally, many of the theoretical aspects developed in Chapter 2 will be recalled to carry out the BISSAT mission analysis.

3.2 BISSAT SCIENTIFIC RATIONALE AND TECHNICAL APPROACH Bistatic scattering has proved to be of fundamental importance to many branches of the Earth sciences and several investigations have been conducted. As an example, bistatic echoes allow innovative characterization of vegetated and urban surfaces for biomass evaluation, or sea surface waves and current to be mapped (Chapter 1). However, since bistatic observation requires accurate time synchronization and antenna pointing, as outlined in Chapter 2, the experiments were conducted using one or both Earth-based antennas and observing targets of limited extension. A BISSAT experiment could allow original scientific activities to be carried out from space, such as: (a) evaluation of the bistatic radar cross-section of natural and manmade targets, by means of multiangle bistatic SAR observations; (b) acquisition of the terrain elevation and slope by means of range and bistatic scattering measurements;

BISSAT SCIENTIFIC RATIONALE AND TECHNICAL APPROACH

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(c) acquisition of velocity measurements thanks to the simultaneous measurement of two Doppler frequencies; (d) stereoradargrammetric applications thanks to the large antenna separation involved; (e) improvement of image classification and pattern recognition procedures; (f) high-resolution measurements of components of sea wave spectra; (g) development of innovative procedures for processing bistatic data.

Furthermore, since two space platforms will operate simultaneously with formation flying control and SAR capabilities, short baseline across-track and along-track interferometry could be accomplished upon completion of the nominal bistatic mission and, for safety, at the end of the COSMO-SkyMed operational life. Finally, the BISSAT will add value to COSMO-SkyMed, because it will allow further and innovative scientific applications of the main mission. The proposed configuration is based on a small satellite, equipped with a receiving-only microwave system (BISSAT2000) that catches the echoes of the main orbiting SAR, without requiring its design modification or additional operating complexities. Technical feasibility of the mission is guaranteed by taking advantage of SAR2000 experience. Development of a bistatic receiver chain can be carried out with wide reuse of components and instruments already qualified within the COSMO-SkyMed project. This means that, as a general rule, no new equipment developments and no procurement difficulties are expected within the BISSAT program. According to this policy, the BISSAT payload and bus development logic foresees the direct development and qualification of a unique spacecraft, called the ProtoFlight Model, without any Engineering Model, Engineering Pre-Qualification Model (i.e. models functionally equivalent but physically different from the Flight Model and generally adopting less expensive, non-flight-qualified components) and Flight Model, as required for more complex and expensive missions [3.9]. Only limited breadboard activity will be developed for testing electrical interfacing, telemetry, etc., of the payload with bus. The light passive antenna will be largely derived from the SAR2000 antenna [3.10] by re-using its radiant panel with exclusion of the active modules, including the Tx/Rx chain. A new harness will be required, due to the expected differences in BISSAT2000 antenna dimensions. Ground segment and bistatic SAR processing require novel implementations, again based on well-assessed expertise. Regarding the spacecraft, the BISSAT payload can be satisfactorily mounted on a small platform, the object of worldwide research and development activities in aerospace industries and agencies. Moreover, considering the ASI interest in developing an Italian standard small platform, the BISSAT mission will allow novel experiences and potential to be fulfilled, integrated with main mission technological objectives. It is worth noting that formation flying is an internationally recognized important scenario, in particular for microwave remote sensing [3.11–3.15]. For the sake of completeness, the main key technological issues of the BISSAT payload affecting platform design are listed in the following: (a) synchronization of the bistatic echo receiving chain with a transmitted signal; (b) down-dusk orbit (beneficial impact on the power generation system thanks to short eclipse periods);

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(c) formation flying with one of the satellites of COSMO-SkyMed (need for precise position/baseline measurement and control and hence for autonomous propulsion capability as well);

(d) attitude aligned with ground velocity (three-axis stabilized spacecraft, fine attitude and pointing control, need for yaw steering); (e) SAR antenna dimensions (a major payload element to be accommodated towards nadir, on one of the spacecraft natural radiators, large subsystem to be stowed in launcher and to be deployed on orbit, in addition to solar arrays); (f) BISSAT SAR data rate (critical download requirements from the quantitative and ground station coverage point of view).

3.3 BISTATIC PAYLOAD MAIN CHARACTERISTICS AND ARCHITECTURE 3.3.1 Design Assumptions The preliminary design of BISSAT2000, the receiving-only radar onboard BISSAT, has been tuned to COSMO-SkyMed SAR2000, since the two spacecraft must operate in formation. As a design baseline, of course, SAR2000 functionality must be scaled as much as possible, but recovering relevant components and technologies, thus reducing the BISSAT payload risk, cost, mass and power absorption. Due to the stringent requirements dictated by the ASI of low cost of the mission and in the adoption of a small bus, no redundancy has been considered at the payload level, but open architecture has been envisaged in order to make possible partial or complete redundancy, if required in a future design.

3.3.2 System Architecture Five subsystems constitute BISSAT2000 and are listed in Table 3.1. Each one is autonomous from both a technological and functional point of view. From the mechanical point of view, the payload is composed of two electronic boxes and by the antenna, along with relevant connectors. Regarding the ICSS, RFSS and PSU, it is assumed that they constitute a unique electronic box with dimensions of the order of 250 mm × 320 mm × 210 mm, and mass of about 22 kg. Thermal control of the electronic units is in charge of the bus, within [−10 ◦ C, +45 ◦ C] during operating phases and otherwise within [−25 ◦ C, +75 ◦ C]. Two unregulated (22–37 V) main power buses are input to the above electronic boxes. The first power bus feeds the ICSS only, with 30 W, whereas the second power bus furnishes Table 3.1 BISSAT2000 subsystems ICRSR S/S (ICSS) RF S/S (RFSS) MMSU Antenna S/S (ASS) PSU

Instrument controller and radar signal receiver S/S Radio frequency S/S Mass memory storage unit X-band passive antenna S/S Power supply unit

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120 W to the other two subsystems, when the instrument is operational (i.e. during data takes). Thus, the PSU performs power conditioning functions and provides a regulated 28 V DC to the payload, starting from the input bus. From a functional point of view, the ICSS is in charge of health management and control of other subsystems and of timing and data transmission among them. It also operates as an interface between the payload and bus and hence manages state transitions among payload operational modes, which will be described in the next subsection. The radar signal receiver is in charge of generating transmitted chirp and of handling received echo, including its digitalto-analog conversion and heterodyne processing. The RFSS includes the ultra-stable oscillator (USO) and the frequency generator unit (FGU), needed for generating a reference signal.

3.3.3 Payload Operational Modes With reference to Figure 3.1, the instrument states are as follows:

r OFF. During this phase the payload is inactive (i.e. launch, nominal orbit acquisition, orbit manoeuvres, etc.) and does not require power.

r INIT, initialization mode. During this phase the ICSS is switched on from the spacecraft. Switch OFF from any state

MCM PowerOFF

OFF

Re-INIT on FATAL ERROR TLM ERROR or RUN ERROR

INIT

autonomous transition after initialisation

OPERATIONAL

CLEAN/ WAIT RECOVERABLE ERROR REFUSE

MCM INIT

MCM PRE-OPE TLM ERROR or RUN ERROR

MCM 'ANY MODE'

TLM ERROR TLM ERROR STANDBY

PRE-OPE

MCM UNLOCK HEATER

MCM PRE-OPE

MCM HEATER MCM PowerOFF

STANDBY -LOCK

MCM LOCK

MCM LOCK MCM LOCK

MCM UNLOCK

MCM UNLOCK

MCM PowerOFF

PRE-OPE -LOCK HEATER -LOCK

MCM PowerOFF

Figure 3.1 Diagram of state transitions for BISSAT2000

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r CLEAN/WAIT. This state corresponds to a local reset of the ICSS. r STANDBY. At this stage reset has been performed and the ICSS is ready to receive macrocommands from an onboard computer.

r STANDBY-LOCK. This state is similar to STANDBY but, for safety (to avoid abrupt absorption differences that could damage the spacecraft bus), the ICSS is sensitive only to the RECOVER macro-command.

r HEATER. This state is similar to STANDBY but it envisages thermal control of the unit and

is a warm reset; at this stage telemetry data include current and temperature measurements.

r HEATER-LOCK. This state is similar to HEATER but, for safety (to avoid abrupt absorption differences which could damage the spacecraft bus), the ICSS is sensitive only to the RECOVER macro-command.

r PRE-OPE. During this phase all S/S are sequentially activated by the ICSS and are able to acquire telemetry data and commands and to furnish status information.

r PRE-OPE-LOCK. This state is similar to PRE-OPE but, for safety (to avoid abrupt absorption differences which could damage the spacecraft bus), the ICSS is sensitive only to OFF, RESUME and RESET macro-commands.

r OPERATIONAL. BISSAT2000 is on and, at the end of data acquisition, goes automatically to the PRE-OPE state.

r REFUSE. This state is reached in the case of anomaly. BISSAT2000 polarization is selectable between HH and VV, and operates in tandem with SAR2000 when the latter is in its conventional strip-mapping modes, named HIMAGE and PING PONG, to simplify swath overlap and sensor synchronization.The HIMAGE mode is characterized by elevation steering of the beam, as it is required for improving bistatic coverage (Section 2.2). In HIMAGE mode SAR2000 operates the same polarization in transmission and reception, whereas BISSAT2000 can operate with the same or the normal. In this mode the swath width is of the order of 40-60 km, depending on off-nadir angle, and the nominal resolution is 5m×5m. In PING PONG mode transmitted polarization is selectable, the swath width is about 30 km, and the nominal resolution is 15 m×15 m.

3.3.4 Signal Synchronization To make BISSAT2000 design and operation easier, sensor synchronization is achieved by using a unique time reference: GPS time. To this end a GPS receiver has been included in the BISSAT payload and will generate the time reference needed for synchronizing the satellites [3.11] and for determining the spacecraft position necessary for applications and navigation. The required power is of the order of 3.5 W, with a voltage of 9–32 V DC. The operating temperature is within [−40 ◦ C,+71 ◦ C], whereas the storage temperature interval is of the order [−55 ◦ C,+85 ◦ C]. The assumed receiver dimensions are 127 mm × 207 mm × 56 mm and mass 1.3 kg. Regarding the GPS antenna, the dimensions are 96 mm × 102 mm × 19 mm and mass is 0.28 kg. Furthermore, BISSAT2000 continuously samples the received echo at the same frequency of SAR2000, on phase and quadrature channels. Hence, as a matter of fact, a real synchronization

Table 3.2 Main characteristics and requirements of the transmitted signal and received echo Central frequency Bandwidth Signal pulse length Rx signal noise figure (with an antenna loss value ≤1.2 dB) Rx signal receiving duty cycles Beam re-shaping and re-pointing time

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9.6 GHz 60 MHz 5–30 μs ≤2.5 dB 80–100 % Within a few pulses

between the signals is not achieved in real time, because it is not strictly necessary and synchronization can be accomplished by processing sampled echoes. A more effective solution for sensor synchronization might be attained by using a receiving antenna on board the BISSAT pointed towards an SAR2000 sidelobe. In this case the transmitted echo would be directly available as well. However, it would require a pointable antenna that should be steerable according to spacecraft dynamics and main SAR pointing geometry. Considering the demonstrative character of the mission and cost limitations posed from a small mission budget, the simple idea of having a common GPS time reference has been selected, which avoids problems of synchronizing the receiving window trigger and of PRI ambiguities by taking advantage of the bistatic configuration. The time reference is packed along with digitized echo by the radar signal receiver S/S. By inserting suitable calibration tones at the RF level it will be possible to perform calibration of the receiving path. Table 3.2 reports the signal main characteristics and Table 3.3 outlines the expected performance of the echo digitizer.

3.3.5 Science Data Handling and Telecommunication Considering the huge amount of data gathered by an SAR and the limitations in real-time data transmission expected for a small satellite on a parasitic mission at a small distance from the Table 3.3 Main parameters of the analog-to-digital conversion Number of channels I/Q gain unbalance I/Q phase orthogonality error Noise figure Frequency amplitude response Input saturation power level : Single channel Contemporary I and Q Number of bits in I and Q codewords Achievable sampling rate interval on each channel Sampling frequency step I/Q sample misalignment Subsampling type Decimation factor Data reduction type Data reduction algorithm Payload acquisition data rate

2 (I/Q) <0.15 dB <2◦ <26 dB +0/−0.15 dB −13 dBm −10 dBm 4+4 bit 93.75–187.50 MHz 3.75 MHz <30 ps Decimation 2–32 Codeword bit reduction Block adaptive quantizer 0.63 Gbps

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Table 3.4 Power requirements of the mass memory storage unit

Component DC/DC CONVERTER Module SUPERVISOR Module Tc/Tm Module SAR I/F Module WIDE BAND DATA HANDLER Module MEMORY Module 1 MEMORY Module 2 MEMORY Module 3 (back-up) Total

Maximum stand-by power dissipation (W)

Maximum operating power dissipation (W)

14.52 6.24 6.2 8.86 5.46

21.5 6.24 6.2 17 17

4.86 4.86 2.17 53.17

7.65 7.65 2.17 85.41

main monostatic mission, an onboard solid state MMSU has been introduced, thus avoiding the fact that the BISSAT may need to download data simultaneously to the main mission and to the same ground station. A provisional power budget is reported in Table 3.4. MMSU dimensions have been estimated on the order of 430 mm × 250 mm × 250 mm and its mass is about 16 kg. Each memory module has a capacity of 2 GB, thus allowing 4 GB as the total onboard capacity for science data. In order to evaluate the BISSAT2000 duty cycle, this 4 GB capacity must be considered as referred to compressed data. Assuming 80 MHz as the sampling frequency and 8 bits/sample (4I+4Q), an overall production of 0.625 Gbps of compressed science data is achieved. This means that the MMSU will be filled in about 50 s, the mean acquisition time per orbit of BISSAT2000. It should correspond to a coverage of two or three test sites per orbit, depending on their extension and swath width and resolution. This value is certainly adequate to achieve the scientific objectives of the mission. Download of radar data is always a key and limiting issue in spaceborne SAR missions, in particular when considering small satellites. The factor is even more limiting in the BISSAT case, due to the fact that the main mission operation cannot be affected by the parasitic appendage. Two possible options for telecommunications have been considered. The baseline option consists of a downlink payload data rate of 1.5 Mbps in the S-band (2.2 GHz) provided by the ASI standard platform, named MITA in the HypSEO Earth Observation Mission configuration [3.2], and hence considered acceptable by the Agency. The enhanced option foresees X-band (8.5 GHz) telecommunication, similar to COSMO-SkyMed but in a scaled configuration, achieved thanks to inclusion in the payload of an additional module that could allow a downlink of payload data at a rate of 150 Mbps. In the first case the nominal capacity of 4 GB of science data can be downloaded in a time span close to 6 hours,which would be fulfilled in about 2.5 days assuming one receiving station at high (or low) latitude and one receiving station in Italy. This performance would be satisfactory for an experimental, scientific mission but unacceptable for an operational one. In the latter case, the total MMSU could be downloaded in less than 4 minutes, achievable in only one passage at a high (or low) latitude station. In this case 14.8 accesses per day lasting 514.3 s (in the mean) are available, thus removing any science data download problem and allowing a larger mass memory to be embarked if further resources could be available on board. However, the second option could determine a payload mass greater than the maximum value of 100 kg, considered acceptable by the ASI for a small mission.

BISTATIC PAYLOAD MAIN CHARACTERISTICS AND ARCHITECTURE Table 3.5 Main characteristics of antenna beam Azimuth beamwidth Azimuth sidelobe level Azimuth steering angle (passive) Azimuth steering resolution (step) Elevation beamwidth Elevation sidelobe level Elevation steering angle (passive) Elevation steering resolution (step) Elevation main beam gain flatness Antenna pointing error (azimuth and elevation planes) Polarization

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0.7◦ <14 dB ± 3◦ <0.03◦ 4◦ <20 dB ± 3◦ <0.3◦ <2 dB ± 0.1◦ HH or VV

3.3.6 Antenna Characteristics Development of a light passive antenna is a key point in payload design. The main features of the antenna beam are reported in Table 3.5. Regarding azimuth and elevation steering, it must be considered an interesting, but optional, feature, which would offer increased bistatic coverage capabilities, as outlined in Section 2.2, but it is not strictly required for fulfilling scientific objectives of a small demonstrative mission. Therefore, depending on the overall cost envelope, it could be considered or not. Use of more panels constituted by 12-patch arrays, spaced 0.7λ apart, will be adopted to develop BISSAT2000 antenna. Electronic steering is achieved by means of the feeding network and can operate only in reception (passive steering); reported values are acceptable with technological and cost constraints for the tile architecture of the antenna. Its dimensions are 2.2 m as the azimuth length, 0.4 m as the elevation length and 40 mm as the overall mechanical thickness, 12 mm of which are devoted to electrical circuitry. The mass of the antenna is estimated as 31 kg. Antenna boresight direction nominally forms an angle of 4◦ with respect to the local vertical, towards the right side of the ground track. Antenna will be composed of three elements, a central one corresponding to the half-length adjacent to the spacecraft body and two wings each one-quarter-length folded during launch, and will be thermally autonomous and insulated from the satellite. It is worth noting that, besides mass reduction and before considering attitude and pointing control issues described in Sections 2.1 and 2.3, a BISSAT2000 larger aperture consequent to an antenna smaller than the SAR2000 one makes beam overlapping easier, provided that an adequate antenna gain is guaranteed. In particular, the reduction in the bistatic signal-to-noise ratio, as a consequence of the smaller antenna, is in part recovered by the smaller bistatic slant range achieved when a large baseline is accomplished, with the bistatic receiver closer than the transmitter to the swath. Furthermore, no ambiguity problems arise due to a smaller antenna area, because the duration of the echo from the swath is related to the transmitting antenna aperture in elevation, despite a larger beam of the BISSAT2000 antenna.

3.3.7 Overall Budgets In conclusion, Table 3.6 reports the estimated mass and power budget, assuming the baseline S-band option for telecommunication.

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Table 3.6 Mass and power budget for BISSAT2000 Component

Mass (kg)

Power (average) (W)

Power (peak) (W)

Antenna S/S (ASS) ICSS, RFSS and PSU MMSU

31 22 16

— 30 55

GPS

2

5

— 150 (during data takes) 90 (during data takes and telecommunications) 5

Total

71

90

245 (during data takes) 125 (during telecommunications)

3.4 ORBIT DESIGN Parallel orbits are selected for the BISSAT mission to take advantage of equivalent J2 secular perturbations. In addition, since SAR2000 radar is right looking, BISSAT must pass through its ascending node before the COSMO-SkyMed satellite. Therefore, considering that the BISSAT is a small satellite, which generally gives a larger ballistic coefficient, aerodynamic drag behaves as a safety enhancer, pulling the satellites downward and forward with respect to the Tx/Rx satellite. Bearing in mind that all orbit parameters of the Rx satellite must coincide with those of the Tx/Rx satellite, apart from ascending node right ascension and the time of the passage on the ascending node, and considering COSMO-SkyMed elevation steering capabilities (from 23.3◦ to 43.7◦ towards the right side of the ground track and (hence a negative clockwise rotation around the spacecraft longitudinal axis) and that the BISSAT2000 antenna is mounted with a −4◦ elevation angle pointing, the parallel orbit model (Section 2.3.1 [3.16]) can be applied (Table 3.7) under the assumption that a bistatic observation is realized when the BISSAT satellite is on the equator with SAR2000 operating at its maximum off-nadir angle. Recalling the definitions given in Figure 2.3, it is also possible to compute ψ (∼5.2◦ ), ξ T/R (∼89.6◦ ) and ξ R/o (∼90.4◦ ). Moreover, it is emphasized that if parallel orbits allow nodal passage of the Rx satellite to be placed in the Tx/Rx elevation plane, they do not produce swath superimposition since the Rx elevation plane does not coincide with the Tx/Rx one. Swath superimposition must be guaranteed by adequate attitude/radar pointing. As an example, it can be decided to yaw-rotate the Rx satellite by an angle γ R/o,0 (∼−3.84◦ for the BISSAT) to let the two centres of swath coincide and to align the elevation directions. This effect can be visualized by plotting the two radar swaths. To this end, each swath will be approximated Table 3.7 BISSAT orbit parameters. This table was published in D’Ericco, M. & Moccia, A., 2001. Remote sensing satellite formation for bistatic synthetic aperture radar observation. Proceedings of SPIE, 4540, p. 240. Reproduced by permission of SPIE. Semimajor axis Inclination Eccentricity Argument of perigee Ascending node separation (Ω) Anomaly separation (M) Time separation (tAN )

6997.9 km 97.870◦ 1.18·10−3 90◦ −5.2470◦ 1.0663◦ 17.255 s

5

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ORBIT DESIGN

–20

–15

–10

–5

0

5

10

15

20

15

20

without yaw angle

0

Azimuth direction (km)

Primary Radar Swath Passive Radar Swath

–5

–10

Elevation direction (km) 5

with yaw angle r Swath

0

–5

e Rada Passiv

–20

–15

–10

Primar y Radar Swath

–5

0

5

10

Figure 3.2 Effects of the yaw angle on the relative swath position

by five intersections of the antenna beam with the Earth, along the directions: centre of beam, 3 dB azimuth, 3 dB elevation. Then project the five points on the plane tangent to the Earth in the centre of the swath of the Tx/Rx radar and there approximate the swath with an ellipse. The usefulness of BISSAT yaw rotation arises from Figure 3.2, where the primary radar swath has been computed assuming 1.1◦ and 0.28◦ as the elevation and azimuth antenna 3 dB apertures; the BISSAT2000 ones are given in Table 3.5. In Figure 3.2 and in the successive figures relevant to swath overlaps (Figures 3.7 and 3.12), the five points previously introduced for limiting the swath are represented with circles for the primary radar and with asterisks for the receiving-only bistatic one. Of course, yaw rotation is but an option among a wider number of pointing strategies. In addition, swath superimposition must be guaranteed along the orbit by modifying pointing. In fact, as anticipated in preceding sections, satellites show a periodic relative dynamics with an inherent (in the ambit of a secular-J2 schematization of relative dynamics) stable oscillation of the satellite distance (baseline). To show this effect, COSMO-SkyMed and BISSAT orbits have been simulated and baseline components have been derived in the right-handed orbiting reference frame (origin in the centre of mass, y axis perpendicular to the orbital plane, z axis directed along the local vertical towards the Earth’s centre) centred in the Tx/Rx satellite. Figure 3.3 shows that: (a) the Bx component ranges from 27.9 to 56.7 km; (b) the absolute value of the B y component ranges from 0 to 633.9 km; (c) Bz ranges from 130 m to 28.9 km. Furthermore, the baseline is greater on the equator, where the satellites are at their maximum distance, whereas it attains its minimum value near the poles, where the two orbits intersect. Since B y is almost null near the poles, where Bz is also very small, the Bx component represents the residual safety distance, as demonstrated by the fact that the minimum distance is about 42.67 km, which is almost completely an along-orbit component (42.56 km out of 42.67 km). This distance corresponds to a time shift at the passage of the orbit crossing point of about 5.7 s.

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Bz (km)

30 20 10 0

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270

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600 By (km)

300 0 −300 −600

Bx (km)

60 50 40 30

B (km)

600 400 200 0

Figure 3.3 BISSAT position with respect to COSMO-SkyMed (baseline) in the orbiting reference frame. This figure was published in D’Ericco, M. & Moccia, A., 2001. Remote sensing satellite formation for bistatic synthetic aperture radar observation. Proceedings of SPIE, 4540, p. 243. Reproduced by permission of SPIE.

3.5 ATTITUDE DESIGN AND RADAR POINTING DESIGN Figure 3.3 clearly demonstrates the need for pointing laws to be implemented along the orbit in order to account for baseline variation and to guarantee an adequate overlap between the Tx/Rx and the Rx swaths. If, on the one hand, COSMO-SkyMed radar offers an elevation steering capability, on the other hand, azimuth steering, though implemented, is only foreseen when the radar operates in the spotlight mode (azimuth resolution enhancement), not as a SAR pointing mode. As already noted, it is unacceptable to introduce any change in the primary mission

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40 30

elevation angle (°)

20 10 0 −10 −20 −30 −40 0

30

60

90

120

150 180 210 240 Mean anomaly (°)

270

300

330

360

bus Figure 3.4 Required elevation angle (ϑpd ) of COSMO-SkyMed (partial collaboration, bus-based option) and limits of the SAR2000 elevation steering capability (bold lines)

at any level. As a consequence, taking COSMO-SkyMed mission objectives and constraints into account, elevation steering is the only help that can be expected from the main mission, discarding both azimuth steering and attitude pointing. Thus, a fully dependent strategy cannot be considered for the mission under design. A fully independent strategy can also be excluded when considering the complexity of the Rx system, bistatic mission objectives and the need to prepare bistatic test sites on the ground, which implies collaboration from the primary mission to schedule and perform data acquisitions. The bistatic mission is then developed under the assumption of partial collaboration. In this ambit, all three possible options can be considered: bus-based, payload-based and enhanced payload-based options. In particular, mathematical models proposed in Chapter 2 have been applied for the busbased option, and the required elevation steering angle for the primary radar has been computed and plotted in Figure 3.4. The elevation angle theoretically needed to guarantee swath superimposition has been determined, but SAR2000 limitations have also been shown in the figure by horizontal solid lines to account for minimum (−23.3◦ ) and maximum (−43.7◦ ) practical angles. Thus, the foreseen outcome is that it is possible to carry out the mission only during the ascending phase of the orbit, in the ranges of COSMO-SkyMed mean anomaly [0◦ , 66.7◦ ] and [292.5◦ , 360◦ ], corresponding to latitudes of the observed target ranging between −65.2◦ and 66.2◦ . With reference to the BISSAT attitude, the required pitch and yaw angles are shown in Figure 3.5. In addition, the yaw angle is compared with the one that would be required in the case of implementation of the yaw steering manoeuvre for drag reduction. Results show that the required pitch is negative almost everywhere since it ranges between a maximum value of about 0.35◦ to a minimum of about −3.94◦ , thus showing an oscillation around −1.80◦

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pitch angle (°)

1 0 −1 −2 −3 −4

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pitch angle (°)

0 3 −0 −3 −6 mean anomaly (°) bus bus Figure 3.5 Pitch (βpd ) and yaw (γpd ) attitude angles of the BISSAT (partial collaboration, bus-based option). Yaw angle in the case of the yaw steering manoeuvre for drag reduction (dashed curve)

with an amplitude of about 2.14◦ . If only the range of latitude is considered where the bistatic experiment is feasible (BISSAT anomaly between 0◦ and 67.7◦ and between 293.3◦ and 360◦ ), the pitch angle varies between –2.21◦ and –3.89◦ , reaching the positive value of 0.35◦ before becoming negative again. Therefore, restricting the analysis to the exploitable range does not substantially change the foreseen pitch variation. Analysis of yaw angles allows the statement to be made that the angle required for swath overlap and the angle required for drag reduction are similar. Thus, attitude control can in principle apply the manoeuvre for drag reduction switching to the manoeuvre for swath overlap only where and when bistatic data are under acquisition. Furthermore, it is useful to note that, despite the observing geometry with the active radar always looking at a larger off-nadir angle, the passive radar swath is always greater than the active one (Figure 3.6), thanks to the reduced dimensions of the receiving-only antenna. In addition, the overlap area always coincides with the active swath area. In conclusion, it should be pointed out that the effect of the attitude and antenna rotations allows the active radar swaths always to be kept inside the passive radar swaths, resulting from the plot of Tx/Rx and Rx swaths at different latitudes (Figure 3.7). It is worth pointing out that care must be taken in reducing the area of the Rx antenna to avoid ambiguities and a decrease in the signal-to-noise ratio. However, although smaller, the Rx antenna is closer to the viewed area and, due to accurate pointing, the echo from the Tx/Rx radar can be received within a high-gain region of the receiving lobe. enpay Considering the enhanced payload-based option, the required elevation angle (ϑpd ) cobus incides with the previous case (ϑpd ). As a consequence, no change can be envisaged with

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ATTITUDE DESIGN AND RADAR POINTING DESIGN

263

area (km2)

BISSAT2000 swath 262

261

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360

100 SAR2000 swath swath overlap

area (km2)

80 60 40 20 0

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mean anomaly (°)

Figure 3.6 Swath areas for the partially dependent, bus-based option

reference to the interval of latitudes where a bistatic acquisition is feasible. As far as the BISSAT is concerned, the satellite has to perform a yaw manoeuvre, which exhibits practically the same values of the previous case. The difference with respect to a manoeuvre for drag reduction is small as well (Figure 3.8). Thus, switching from one to another depending on payload activity can also be envisaged in this case. As for BISSAT2000 antenna angles, it is worth recalling that elevation is constant at 4◦ and corresponds to a fixed mechanical mounting angle of the antenna panel under the satellite bottom panel towards the right side of the ground track; hence the angle can be expressed as a negative roll rotation with respect to the spacecraft longitudinal axis. The azimuth angle, varying between 0.35◦ and −3.9◦ , exceeds the minimum allowable by the BISSAT2000 capability (−3◦ ). Nevertheless, the total variation is about 4.3◦ , well below the maximum allowed capability (6◦ , Table 3.5). Therefore, provided that the antenna is mounted with a fixed mechanical azimuth angle of −1.8◦ , the azimuth variation is limited within the range ±2.1◦ (Figure 3.9). With reference to the swath area overlap and swath relative position, results similar to the previous case have been derived. pay Considering the payload-based option, the required elevation angle (ϑpd ) is different from enpay bus the previous cases (ϑpd = ϑpd ). Nonetheless, numerical differences are so small that they could not be appreciated on a plot. Thus, Figure 3.4 can also be considered as representative of this case. As a consequence, no substantial change can be envisaged with reference to the interval of latitudes where bistatic acquisition is feasible.

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Elevation direction (km)

5

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15

20

maximum achievable latitude 0

5

maximum “bistatic” latitude 0

−5 5

equator

Azimuth direction (km)

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0

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−5

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0

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active radar swath passive radar swath

−5

20

Figure 3.7 Swath relative position for the partially dependent, bus-based option

To guarantee swath overlap, in addition to the −4◦ constant mounting elevation angle, azimuth steering must be implemented (Figure 3.10). Considering the range of latitude where SAR2000 is able to steer the beam for swath superimposition and the relative range of the BISSAT mean anomaly [0◦ , 67.7◦ ] and [293.3◦ , 360◦ ], the azimuth varies within [0.25◦ , −4.13◦ ] and [−1.76◦ , 0.25◦ ] (going through the maximum value of 0.71◦ ), which seems beyond the capability of the BISSAT2000 antenna (±3◦ ). Again the problem can be overcome by mounting the BISSAT2000 antenna with a fixed azimuth angle of –1.7◦ , which produces a variation of the azimuth angle of ±2.4◦ , which is acceptable. Such an option does not foresee alignment of the elevation direction of radar swaths, which, as a consequence, exhibit a relative rotation, as shown in Figure 3.11. Nevertheless, overlap is fully maintained in high-gain sections of

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ATTITUDE DESIGN AND RADAR POINTING DESIGN

6

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enpay

Figure 3.8 Yaw (γpd ) attitude angle of BISSAT (partial collaboration, enhanced payload-based option). Yaw angle in the case of the yaw steering manoeuvre for drag reduction (dashed curve)

elevation angle (°)

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Figure 3.9 Constant elevation mounting angle and azimuth (Az pd ) angle of the BISSAT2000 antenna for partial collaboration, enhanced payload-based option

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elevation angle (°)

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Figure 3.10 Constant elevation mounting angle and azimuth (Az pd ) angle of the BISSAT2000 antenna for partial collaboration, payload-based option

elevation direction relative misalignment (°)

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Figure 3.11 Relative rotation between elevation directions of SAR2000 and BISSAT2000 swaths

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Elevation direction (km) 5

−20

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−5 5

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c 2003 IEEE. Figure 3.12 Swath relative position for the partially dependent, payload-based option. This figure was published in D’Ericco, M. & Moccia, A., 2001. Attitude and Antenna Pointing Design of Bistatic Radar Formations. IEEE Transactions on Aerospace and Electronic Systems, 39 (3), p. 949–960. Reproduced by permission of IEEE.

antenna lobes. Results are in fact similar to the ones obtained for the bus-based option, with the BISSAT2000 swath always larger than the SAR2000 one and with the latter always included within the former; i.e. the effect of a smaller receiving-only antenna predominates over the effect of a larger off-nadir angle of the transmitting/receiving antenna. Figure 3.12 [3.17] clarifies the effect of the payload-based pointing option by plotting swaths for various latitudes, which result in common centres but slightly rotated elevation directions. In particular, bistatic observation is possible only when the Tx /Rx off-nadir angle is within its allowable limits [−43.7◦ , −23.3◦ ]. Hence it is possible to determine a latitude interval within which it is possible to gather bistatic data by means of the proposed COSMO-SkyMed/BISSAT formation. Finally, as far as the SAR2000 elevation angle is concerned, bus-based and enhanced payload-based options give the same angle, while the angle for the payload-based option does

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not differ significantly from the previous values. Since SAR2000 is steerable within [−43.7◦ , −23.3◦ ], bistatic acquisition can be obtained in the ranges of the COSMO-SkyMed mean anomalies [0◦ , 66.7◦ ] and [292.5◦ , 360◦ ], which correspond to BISSAT anomalies within [0◦ , 67.7◦ ] and [293.3◦ , 360◦ ] and to latitudes of the observed target ranging from [−65.2◦ , 66.2◦ ] (coverage obtained during ascending phases). It is worth noting that extension of latitude intervals where bistatic observation is feasible is strongly dependent on the primary radar elevation steering capability. Along-track swath displacement can be avoided either by pitch angles or azimuth angles. In particular, the pitch for the bus-based option and the azimuth for the enhanced payload-based option have very close values all along the orbit, while the azimuth range for the enhanced payload-based option is slightly larger. If the pitch is almost negative everywhere and ranges between 0.3◦ and −3.9◦ (0.7◦ and −4.1◦ ) the azimuth varies between ±2.1◦ (±2.4◦ ) if the antenna is mechanically mounted with an azimuth angle of −1.8◦ (−1.7◦ ) for the enhanced payload-based (payload-based) option. Swath relative rotation is avoided by means of yaw rotations for both bus-based and enhanced payload-based options. For both cases yaw is found to vary between approximately ±6.5◦ over the orbit. Such oscillation is similar to the one required by the yaw steering manoeuvre for drag reduction (about ±4.5◦ ). Since the difference between the ‘swath-driven’ yaw angles and the ‘minimum drag-driven’ ones basically involves different satellite cross-sections, the BISSAT could implement ‘swath-driven’ yaw only when acquiring bistatic data, switching to the minimum drag rotations when not operating the payload. In the case of the payload-based option, elevation directions show a misalignment varying within about ±6.5◦ along the orbit because no yaw correcting manoeuvre is implemented. To verify manoeuvre effectiveness, swath superimposition can be evaluated and results show a 100 % overlap for all three considered options. Therefore, the yaw manoeuvre is not strictly necessary for the BISSAT mission, provided that an antenna of reduced dimensions can operate satisfactorily. A smaller antenna also produces advantages in satellite stowing in the launcher and a smaller satellite cross-section with a positive impact on orbit decay and lifetime. In conclusion, the analysis has shown that the bistatic requirement can be met by any of the identified options. As a consequence, a decision can be been made on the basis of upgrade costs. The result is that, considering the design environment, a pitch manoeuvring capability would impact on mission cost much more than an antenna azimuth pointing capability because it is expected that industries involved in SAR2000 development can also be involved in BISSAT2000 design, thus allowing wide re-use of existing hardware and expertise.

3.6 RADAR PERFORMANCE For the sake of completeness a computer simulation has been carried out to put in evidence BISSAT performance along the orbit, adopting BISSAT and COSMO-SkyMed parameters previously reported in Section 3.1 and Table 3.7, and considering the three available options for the partial collaboration strategy. First of all, Figures 3.13 and 3.14 represent essential parameters to investigate the relative motion of bistatic spacecraft-targets, i.e. the modulus of relative velocity accounting for orbital motion and earth rotation, and the modulus of beam velocity with respect to the Earth’s surface. The corresponding COSMO-SkyMed values are plotted as terms of reference.

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RADAR PERFORMANCE

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Figure 3.13 Spacecraft-target relative velocity modulus as a function of mean anomaly for the main monostatic mission and the three bistatic options

6.95 6.945 6.94

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Figure 3.14 Beam velocity modulus as a function of mean anomaly for the main monostatic mission and the three bistatic options

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2000 0

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−2000 −4000 −6000 −8000 −10000 −12000 −14000 −16000

bus-based enhanced payload-based payload-based

−18000

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Figure 3.15 Doppler centroid frequency as a function of mean anomaly for the main monostatic mission and the three bistatic options

Basic Doppler parameters along the BISSAT orbit are plotted in Figures 3.15 and 3.16. The Doppler centroid frequency has been computed as follows: f DR = −[(V T − V P ) · (RT − RP )/rT + (V R − V P )·(RR − RP )/rR ]/λ

(3.1)

and varies from −8000 to −18 000 Hz in the range of BISSAT mean anomalies where bistatic acquisitions are feasible [-67.7◦ , 67.7◦ ], going through zero Doppler on the equator, as expected considering selected initial conditions. It is worth noting the effect of COSMO-SkyMed yaw steering which allows zero Doppler frequency to be achieved along the whole orbit of the Tx/Rx antenna. The Doppler frequency bandwidth (Figure 3.16) and the integration time (Figure 3.17) have been estimated by considering the space and time interval within which a target is inside the 3 dB aperture of the Tx/Rx antenna pattern at mid-range, i.e. at antenna boresight, and the Tx/Rx swath is fully included in the Rx one. In particular, Figure 3.17 demonstrates that monostatic and bistatic integration times are practically coincident, with slight differences only at the equator. As shown in Section 1.2, due to the bistatic geometry, the BISSAT exhibits a larger Doppler bandwidth when operating with large baselines, approaching the SAR2000 bandwidth at poles. Finally, Figure 3.18 reports ratios between the bistatic and monostatic ground range and azimuth resolutions during the ascending phase of the orbit, when the Rx antenna is closer than the main Tx/Rx one to the observed area, which is the orbital configuration selected for bistatic observation. Furthermore, the corresponding elevation angle of the Tx/Rx antenna, the

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Figure 3.16 Doppler bandwidth as a function of mean anomaly for the main monostatic mission and the three bistatic options

0.64

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Figure 3.17 Integration time as a function of mean anomaly for the main monostatic mission and the three bistatic options

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Resolution ratio (°)

1.9 1.7

Azimuth

1.5

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Figure 3.18 Ratio between bistatic and monostatic resolutions as a function of mean anomaly, and the corresponding Tx/Rx elevation angle, bistatic angle and horizontal baseline component

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ABBREVIATIONS

bistatic angle and the baseline component perpendicular to the orbit plane in the [−67.7◦ , 67.7◦ ] true anomaly interval are plotted in Figure 3.18. Results are in excellent agreement with the analysis presented in Section 1.2. As a concluding remark, it is worth noting that all presented quantities are practically coincident for the three studied options, thus demonstrating again the wide applicability of the proposed models, which allow selection of the more convenient strategy for bistatic data gathering from the system design, development and operation point of view, thus always guaranteeing the expected radar performance. In particular, the resolution ratio curves are equivalent for all three considered options.

3.7 SUMMARY This chapter presents a case study of a spaceborne BSAR based on a small satellite equipped with a receiving-only antenna flying in formation along parallel orbits with a main monostatic mission. First of all, payload aspects are dealt with, focusing in particular on the overall BSAR architecture and performance, and presenting solutions for key technical issues of the bistatic mission. The models presented in Chapter 2 are then applied to perform a bistatic mission analysis, and the results and performance are reported in detail. After a definition of the orbital configuration of the formation, time histories of essential parameters for swath overlap during bistatic observation are derived, showing the possibility of carrying out a bistatic mission with a low cost satellite, exploiting expected attitude and pointing capabilities of the main mission, but without posing any constraint on its design. Finally, Doppler and resolution characteristics of bistatic and monostatic SAR data are compared.

ABBREVIATIONS ASI ASS BISSAT COSMO-SkyMed DC FGU GPS ICSS I/F I/Q MCM MMSU PRI PSU RF RFSS Rx SAR S/S Tc/Tm

Italian Space Agency antenna subsystem bistatic SAR satellite constellation of small satellites for Mediterranean basin observation direct current frequency generator unit Global Positioning System instrument controller and radar signal receiver S/S interface phase and quadrature channels macro-command mass memory storage unit pulse repetition interval power supply unit radio frequency radio frequency S/S receiving synthetic aperture radar subsystem telecommand/telemetry

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transmitting/receiving telemetry ultra stable oscillator

VARIABLES Az fD r R V β γ ϑ λ

antenna azimuth pointing angle Doppler centroid frequency slant range antenna position vector with respect to the centre of the Earth antenna velocity vector pitch attitude angle yaw attitude angle satellite-centred angle (typically antenna elevation angle) radiation wavelength

Subscripts/Superscripts bus bus-based option pay payload-based option enpay enhanced payload-based option pd partially dependent strategy P target R Rx antenna T Tx/Rx antenna

ACKNOWLEDGEMENTS The study presented in this chapter has been carried out under a research contract of the Italian Space Agency (I/R/213/00, Science Small Missions Program). The authors acknowledge the former Alenia Spazio (today Thales Alenia Space Italia SpA, a Thales/Finmeccanica Company), prime contractor of the ASI for the COSMO-SkyMed mission and subcontractor of the University of Naples for the BISSAT study, for its support in the bistatic payload preliminary definition.

REFERENCES 3.1 Zoffoli, S., Crisconio, M., Musso, C. and Bignami, G.F. (2001) A small glance to Earth from space, in Proceedings of the 3rd International Symposium of the IAA on Small Satellites for Earth Observation, pp. 99–103. 3.2 Aceti, R., Annoni, G., Dalla Vedova, F., Lupi, T., Morea, G.D., Sabatini, P., De Cosmo, V. and Viola, F. (2003) MITA: in orbit results of the Italian small platform and the first Earth observation mission, Hypseo, Acta Astronautica, 52 (9–12), 727–32.

REFERENCES

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3.3 Impagnatiello, F., Bertoni, R. and Caltagirone, F. (1998) The SkyMed/COSMO system: SAR payload characteristics, in Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS, 98, vol 2, pp. 689–91. 3.4 Caltagirone, F., Mariani, A., Impagnatiello, F., Bertoni, R., Oricchio, D., and Preti, G. (1999) The SkyMed/COSMO mission payload characteristics, Space Technology, 19 (5–6), 259–66. 3.5 Caltagirone, F., Spera, P., Gallon, A., Manoni, G., and Bianchi, L. (2001) COSMOSkyMed: a dual use earth observation constellation, in Proceedings of the Second International Workshop on Satellite Constellations and Formation Flying, Israel, pp. 87–94. 3.6 Verdone, G. R., Viggiano, R., Lopinto, E., Milillo, G., Candela, L., Lombardi, N., and Giannini, V. (2002) Processing algorithms for COSMO-SkyMed SAR sensor, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS ’02), vol. 2, pp. 2771–4. 3.7 Albanese, A., Mazzini, L., Galeazzi, C., and Scorzafava, R. (2003) COSMO-SkyMed constellation maintenance using POD and COD on-board functions, in Proceedings of the Third International Workshop on Satellite Constellations and Formation Flying, Pisa, Italy, pp. 167–71. 3.8 Caltagirone, F., Angino, G., Coletta, A., Impagnatiello, F., and Gallon, A. (2003) COSMO-SkyMed Program: status and perspectives, in Proceedings of the Third International Workshop on Satellite Constellations and Formation Flying, Pisa, Italy, pp. 11–16. 3.9 Pisacane, V. L., and Moore, R. C. (1994) Fundamentals of Space Systems, Oxford University Press, New York. 3.10 Capece, P., Sirocchi, G., Santachiara, V., Trento, R., Capuzi, A., and Stopponi, E. (2002) X-band active SAR antenna architecture for COSMO-SkyMed mission, in 25th ESA Antenna Workshop on Satellite Antenna Technology, ESTEC. 3.11 Mart´ın-Neira, M., Mavrocordatos, C., and Colzi, E. (1998) Study of a constellation of bistatic radar altimeters for mesoscale ocean applications, IEEE Trans. Geoscience and Remote Sensing, 36 (6), 1898–904. 3.12 Raney, R. K., and Porter, D.L. (2001) WITTEX: an innovative three-satellite radar altimeter concept, IEEE Trans. Geoscience and Remote Sensing, 39 (11), 2387–91. 3.13 Massonnet, D. (2001) Capabilities and limitations of the interferometric cartwheel, IEEE Trans. Geoscience and Remote Sensing, 39 (3), 506–20. 3.14 Massonnet, D. (2001) The interferometric cartwheel: a constellation of passive satellites to produce radar images to be coherently combined, Int. J. Remote Sensing, 22 (12), 2413–30. 3.15 Raney, R. K., Porter, D.L., and Monaldo, F.M. (2002) Bistatic WITTEX: an innovative constellation of radar altimeter satellites, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’02), vol. 3, pp. 1355–7. 3.16 D’Errico, M., and Moccia, A. (2001) A remote sensing satellite formation for bistatic synthetic aperture radar observations, Proc. SPIE, 4540, 237–45. 3.17 D’Errico, M., and Moccia, A. (2003) Attitude and antenna pointing design of bistatic radar formations, IEEE Trans., AES-39 (3), 949–60.

4 Spaceborne Interferometric and Multistatic SAR Systems Gerhard Krieger and Alberto Moreira

4.1 INTRODUCTION The previous chapters have extensively discussed the potentials and challenges of the bistatic synthetic aperture radar (SAR). This chapter extends this discussion and investigates spaceborne bistatic imaging radar systems employing two or more receiver antennas on different platforms. Such radar systems are commonly denoted as multistatic [4.1, 4.2]. The simultaneous data reception by multiple receivers enables a wealth of new SAR imaging modes, which evaluate the scattering signals from multiple view angles in combination. Potential application areas of multistatic SAR systems include, but are not limited to, single-pass cross-track and along-track interferometry, spaceborne tomography, wide-swath SAR imaging, resolution enhancement, interference suppression, ground moving target indication (GMTI) and multistatic SAR imaging [4.3]. Some of these applications can also be realized via multiple data acquisitions from repeat satellite passes. However, the simultaneous data acquisition with multiple satellites in a multistatic configuration avoids temporal decorrelation and atmospheric disturbances, improves the performance and enables the detection of fast changes. Multistatic SAR systems may be divided into semi-active and fully active configurations (Figure 4.1). Semi-active configurations combine multiple passive receivers with one active radar illuminator. The signal reception by multiple receivers enlarges the overall receptive antenna aperture and enables a simultaneous SAR imaging from different view angles, thereby making multiple use of the signal energy provided by the transmitter. The separation of the transmitter from the receiver hardware also simplifies the design of the radar payloads. For example, the low power demands and the use of deployable antennas allows for the accommodation of the receiver payload on lightweight microsatellites, which reduces the costs for the satellite-bus and launch. The economic advantage is especially pronounced if the constellation of passive receivers is combined with a conventional SAR mission. This combination allows Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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Figure 4.1 Semi-active (left) and fully active (right) multistatic SAR systems

not only for the efficient derivation of new data products, but it may also improve the data quality of the products provided by the master mission. Examples for such a synergy are more accurate geocoding and backscattering evaluation via a simultaneously acquired Digital Elevation Model (DEM). The use of passive receivers will, moreover, in the long term, support an integration of the complete receiver hardware into the antenna, thereby enhancing the sensitivity and enabling new imaging modes, like digital beam-forming on receive [4.3]. First suggestions for complementing conventional SAR missions with additional receiveonly satellites have been made in Reference [4.4]. These concepts have then been extended to interferometric applications by using close formations of multiple microsatellites [4.5, 4.6]. Future semi-active SAR systems may in principle also combine multiple satellites in different orbital altitudes, like, for example, a transmitter in a geostationary or geosynchronous orbit with multiple passive receivers in low earth orbit [4.7, 4.8]. Such systems would be well suited for interferometric or even tomographic applications, which require a short re-visit time for regions of special interest on the Earth’s surface. Fully active SAR constellations use two or more conventional radar satellites flying in close formation to acquire multistatic radar data during a single pass. Each of the satellites has a fully equipped radar payload with transmit and receive capabilities, which offers a number of advantages as compared to a semi-active constellation. Examples are the increased redundancy, the higher flexibility and easy reconfigurability, the less demanding orbit keeping in the case of using spacecraft with similar ballistic coefficients and the opportunity for phase synchronisation, e.g. by using the alternating bistatic or the simultaneous transmit mode (cf. Section 4.3.3). Multistatic satellite formations have in addition the potential to provide more observables and interferometric baselines for a given number of satellites, since it now becomes possible to gain bistatic images from each satellite pair within the multistatic configuration. The information space is further enhanced by multiple monostatic images. However, a fully active SAR is also associated with higher costs for each satellite if compared with a semi-active SAR. Hence, any decision between a fully and semi-active SAR constellation also has to trade off the benefits mentioned above to the benefits that may be gained from an increased number of passive receivers affordable for the same financial budget.

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SPACEBORNE SAR INTERFEROMETRY Table 4.1 Comparison of DTED/HRTI standards for Digital Elevation Models (DEMs) Requirement

Specification

DTED-2

HRTI-3

HRTI-4

Relative vertical accuracy

90 % linear point-to-point error over a 1◦ cell 90 % linear error

12 m (slope < 20 %) 15 m (slope > 20 %) 18 m

2 m (slope < 20 %) 4 m (slope > 20 %) 10 m

0.8 m (slope < 20 %) 1 m (slope > 20 %) 5m

90 % circular error Independent pixels

23 m 30 m (1 arc s)

10 m 12 m (0.4 arc s)

10 m 6 m (0.2 arc s)

Absolute vertical accuracy Horizontal accuracy Spatial resolution

Examples for fully active SAR constellations are twin satellite formations like the Radarsat2/3 tandem [4.9] or TanDEM-X [4.10], as well as multisatellite constellations like the Technology Satellite of the twenty-first century (TechSAT 21, [4.11]). The primary goal of the Radarsat-2/3 tandem and the TanDEM-X mission is cross-track interferometry, which will allow for the derivation of a global digital elevation model (DEM) with unprecedented height accuracy, in accordance with the emerging HRTI-3 standard (cf. Table 4.1). TechSAT 21 is intended as a reconfigurable multipurpose technology demonstrator for a broad range of applications and measurement modes, including cross-track interferometry, sparse aperture sensing, ground moving target indication (GMTI) and geolocation. TanDEM-X has been approved for realization and has a planned launch date in 2009, while Radarsat-2/3 and TechSAT 21 have undergone a study and technology demonstration phase. The following sections provide a comprehensive overview of the potentials and challenges of semi-active and fully active multistatic SAR systems. For this, Section 4.2 starts with a short introduction to SAR interferometry, which represents from a historical point of view the major motivation for the deployment of multistatic radar missions in space. The design of such missions will be discussed in Section 4.3, while Section 4.4 illustrates the achievable performance for two mission examples. Section 4.5 introduces advanced multistatic SAR system concepts, which are likely to gain more importance for future applications. The chapter is concluded with a discussion of the main challenges for the successful deployment and operation of multistatic radar systems in space.

4.2 SPACEBORNE SAR INTERFEROMETRY SAR interferometry is a powerful and well-established remote sensing technique for the quantitative measurement of important bio- and geophysical parameters of the Earth’s surface [4.12–4.15]. By exploiting the phase difference between pairs of coherent radar signals, SAR interferometry enables relative range measurements with subwavelength accuracy. Numerous terrestrial applications have been demonstrated with airborne experiments [4.16–4.21] and during spaceborne SAR missions [4.22–4.32]. The presumably most prominent application is topographic mapping, which enables the generation of DEMs with high accuracy. Accurate DEMs are of fundamental importance for a wide range of scientific and commercial applications ranging from a mere cartographic mapping to sophisticated ecologic studies [4.33, 4.34]. Precise knowledge about topography is furthermore required for orthorectification of optical images or during radiometric calibration and geocoding of conventional SAR images. Other

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outstanding applications emerge from along-track interferometry, which evaluates the phase difference of two radar images acquired at different times. This phase comparison enables a precise estimation of radial displacements with millimetric accuracy, and by varying the temporal baseline between the interferometric acquisitions, velocities ranging from several metres per second down to a few millimetres per year can be accurately measured. Important applications covering the whole range of potential timescales are the detection of moving objects like cars or ships [4.32, 4.35], the observation of ocean surface currents [4.18, 4.36], the measurement of sea ice drift and glacier flow [4.29], the study of seismic deformations and volcanic activities [4.24, 4.28], as well as the monitoring of land subsidence [4.31]. Further potential arises from a comparison of the coherence between several data acquisitions, which can be used for land classification and change detection [4.26, 4.37, 4.38]. The capability of radar interferometers can even be enhanced with additional radar observables. An example is polarimetric SAR interferometry (PolInSAR), which combines the capabilities of radar polarimetry for the separation of different scattering mechanisms with the vertical resolution capabilities of cross-track interferometry [4.30, 4.39]. This combination enables accurate measurements of vegetation height and its underlying topography and has the potential to provide global biomass estimates as required for climate studies and the verification of the Kyoto Protocol. Many of these interferometric applications have successfully been demonstrated in a singlepass configuration on airborne platforms or by evaluating the radar data from multiple satellite passes. However, airborne sensors have the disadvantage of limited coverage which restricts their application to local areas. On the other hand, spaceborne repeat-pass interferometry suffers from the long time lag between the individual data takes. As a result, the achievable accuracy of many interferometric applications is severely limited by temporal decorrelation resulting from relative scatterer movements and changes in their dielectric properties [4.40]. Additional errors are atmospheric disturbances like variations of the tropospheric water vapour or ionospheric propagation delays, which lead to spatially correlated phase shifts in the final interferogram [4.15]. Further common problems in repeat-pass interferometry arise from insufficient a posteriori baseline knowledge as well as the limited opportunities for precise a priori orbit tuning. A first step to overcome such limitations was the Shuttle Radar Topography Mission (SRTM) which used a deployable mast to acquire interferometric data in a spaceborne single-pass configuration [4.14, 4.41]. This challenging mission was flown in February 2000 and acquired a DEM of the Earth’s landmass between −56◦ and +60◦ latitudes. The interferometric performance was essentially determined by the fixed mast length of 60 m, which limited the achievable DEM accuracy to approximately the DTED-2 standard (cf. third column in Table 4.1). A further opportunity arose in SRTM due to an additional along-track antenna separation of 7 m, which resulted in an effective time lag of about 0.5 ms between the two image acquisitions. This temporal baseline has been used to demonstrate for the first time the feasibility of spaceborne along-track interferometry for applications like traffic monitoring [4.32] and the measurement of ocean currents [4.36]. However, the performance was again limited by the short length of the along-track baseline. To overcome such fundamental limitations, several suggestions have been made to acquire interferometric data in a single pass by using two or more independent radar satellites operating in either a fully or a semi-active SAR mode [4.5, 4.11, 4.33]. A multistatic satellite formation offers a natural way to implement single-pass SAR interferometry in space and enables a flexible imaging geometry with large and reconfigurable baselines, thereby increasing significantly the interferometric performance for applications like DEM generation or the extraction of

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Figure 4.2 Across-track SAR interferometry

vegetation parameters by polarimetric SAR interferometry. Further potentials arise from a systematic evaluation of the interferometric coherence which directly reflects spatial variations of the volumetric scattering coefficient. Such information is well suited for improved scene classification and to gain new radar parameters for enhanced image understanding. Even more opportunities arise from a combination of multiple single-pass SAR interferograms acquired at different instances of time. Such observations enable, for example, the unambiguous measurement of slight height changes, the determination of three-dimensional scatterer movements, as well as the observation of variations in dielectric constant and vertical scatterer structure, all without the limitations imposed by temporal decorrelation. A multistatic SAR is furthermore well suited for the implementation of along-track interferometry in space, which can be used for applications like ground moving target indication, the measurement of ocean currents or the monitoring of sea ice drift. An essential prerequisite for high precision cross-track and along-track interferometry is the provision of suitable baselines. For this, the example of DEM generation by cross-track interferometry is considered, where the range of suitable baselines is limited by several factors. The imaging geometry of a single-pass cross-track interferometer with two receivers is illustrated in Figure 4.2. It becomes apparent from Figure 4.2 that for large satellite distances r0 (if compared to h) and short baselines B⊥ (if compared to r0 ) the measured range difference r will be proportional to the height difference h. This proportionality can be expressed as r =

B⊥ h, r0 sin(θi )

(4.1)

where r0 is the slant range, θi is the local incident angle and B⊥ is the baseline perpendicular to the line of sight. Since the phase difference ϕ is given by ϕ =

2π r, λ

(4.2)

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Equation (4.1) can be rewritten as ϕ 2πB⊥ = . h λr0 sin(θi )

(4.3)

This equation describes the sensitivity of the radar interferometer to small height differences h. It is obvious that the sensitivity can be increased by increasing the length of the perpendicular baseline B⊥ . However, the maximum useful baseline length is constrained by two factors. A first limitation is baseline decorrelation. To understand this limitation, imagine the recorded SAR signal from a single resolution cell as being composed of the echoes from a large number of elementary point-like scatterers. Each of these scatterers contributes to the overall radar signal with a phase shift that is proportional to its distance from the receiving antenna. If now such a scatterer ensemble is considered and the view angle varied, it becomes clear that the relative phase contributions from the individual scatterers change. This results in a fluctuation of the recorded signal, which is also known as the speckle effect. Regarding now interferometry, this has the major consequence that with increasing baseline length the phase contributions from each resolution cell become more and more different between the two SAR images. As a result, the correlation between the two complex SAR images decreases systematically with increasing baseline length until it completely vanishes. The baseline length for which the two SAR images become completely decorrelated is known as the critical baseline B⊥,crit . For flat surfaces, this can be expressed mathematically as [4.40, 4.42] B⊥,crit =

λr0 tan(θi ) , δr

(4.4)

100

18

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16 Ambiguous Height [m]

Critical Baseline [km]

where δr is the slant range resolution, which is usually approximated by δr = c0 /(2Brg ), c0 being the velocity of light and Brg the range or system bandwidth. The left hand-side of Figure 4.3 shows the critical baselines B⊥,crit for the L-, C- and X-band SAR satellites TerraSAR-L [4.43], Radarsat-2 [4.44] and TerraSAR-X [4.45] as a function of the incident angle assuming a semi-active single-pass radar interferometer with receivers at the same altitude

60 40 20 0 20

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50

Figure 4.3 Critical baseline B⊥,crit (left) and ambiguous height (right) for TerraSAR-L (solid), Radarsat2 (dotted) and TerraSAR-X (dashed)

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as the transmitter. The critical baseline varies between several kilometres for TerraSAR-X and several tenths of kilometres for TerraSAR-L. A second and, from a practical point of view, often more restrictive limitation for the maximum baseline length results from ambiguities in the phase-to-height conversion. For this, consider again Equation (4.3) and recall that the interferometric measurement provides only phase values that are ambiguous by integer multiples of 2π. As a result, the height measurements are also ambiguous by multiples of h amb =

λr0 sin(θi ) . B⊥

(4.5)

Such ambiguities are usually resolved during phase unwrapping which exploits spatial correlations between the height values of natural topography [4.12, 4.14, 4.22]. The accuracy of this absolute phase (or height) reconstruction process depends on several factors, like the signal-to-noise ratio, the surface and volume decorrelation, the ground resolution and, most important, the actual terrain itself. The latter may strongly limit the useful baseline length for rough terrain like deep valleys, isolated peaks, tall forests or mountains with steep slopes. On the other hand, large baselines are desired to achieve a sensitive radar interferometer with a good phase-to-height scaling. This dilemma becomes especially pronounced for future radar sensors which will provide a high range bandwidth and hence enable coherent data acquisitions with long interferometric baselines. To illustrate this problem, for the aforementioned satellites just 10 % of the critical baseline is chosen. The corresponding baseline lengths vary between several hundred metres for TerraSAR-X and several kilometres for TerraSAR-L. The spatial decorrelation will be small in this case and can be removed by range filtering [4.46]. The corresponding heights of ambiguity are shown in Figure 4.3 on the right. It becomes clear that the ambiguous heights are rather low in this case, which may cause irresolvable height errors in areas with rough terrain. It is hence in general not possible to take full advantage of the opportunity for large baseline acquisitions in these high-bandwidth radar systems. A solution to this dilemma is an interferometric system with flexible baseline lengths. This enables an adaptation of the baseline to the actual terrain and offers furthermore the possibility to image one and the same area with multiple baselines of different lengths. The latter can be used for an unambiguous reconstruction of the terrain height (cf. Section 4.4.2.3). A natural way to implement such a system is a multistatic radar with multiple spacecraft flying in close formation. Such systems enable adjustable baselines ranging from a few hundred metres up to several kilometres. It allows also an optimization of the baseline to estimate the height of volume scatterers. The design of such systems will be discussed in the next section.

4.3 INTERFEROMETRIC MISSION DESIGN 4.3.1 Satellite Formation The relative movement between free-flying satellites in a close formation can be described by using a co-moving and rotating reference frame [4.47–4.49]. As the origin of this reference frame one can chose, for example, one of the satellites or their common centre of mass. Assuming now a close formation with satellites following a nearly circular orbit with equal

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x z

xi yi

zi

y

Figure 4.4 Definition of coordinates in Hill’s equations [4.47]

orbital periods T0 , the relative satellite movement can be approximated as1 2π xi (t) = Ai sin t + αi T0 2π yi (t) = 2Ai cos t + αi + yi T0 2π z i (t) = Bi sin t + βi T0

(4.6)

where the x axis describes the relative displacement along the radius vector, the y axis points in the direction of motion and the z axis is perpendicular to the orbital reference plane (cf. Figure 4.4). A constant along-track displacement of satellite i with respect to the reference frame is given by yi . From these equations it becomes clear that the out-of-plane relative motion along the z axis is a harmonic oscillation with amplitude Bi , which is completely decoupled from the motion in the x–y plane. The relative motion in the x–y plane follows an ellipse with semi-major axis Ai and an aspect ratio of 2; i.e. the periodic variation in the along-track direction y is twice as large as the oscillation in the radial direction x. Several examples for spaceborne bistatic radar systems in co- and crossing-orbit configurations have been suggested in Reference [4.8]. The following sections discuss these formations in more detail and extend the results to configurations with multiple receivers.

4.3.1.1 Twin Satellite Formations One of the first suggestions to use a close satellite formation for interferometric DEM generation was a twin satellite formation employing a small difference in the right ascensions of the ascending nodes [4.33, 4.50]. The baseline evolution in such a formation can be described 1

Note that this approximation is only used to illustrate the principal characteristics of baseline evolution for interferometric applications during one orbit. An actual implementation must of course also consider the orbital dynamics of the formation’s long-term evolution, which is affected by several perturbation sources like irregularities in the gravitational geopotential, atmospheric drag, solar radiation pressure, etc. The compensation of such disturbances requires periodic orbit manoeuvres that control the formation within predefined limitations [4.52].

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horizontal baseline

0

45

5 360 70 31 225 2 0 8 1 ion 35 90 1 Orbit Posit

Figure 4.5 Twin satellite formation with different ascending nodes. The right-hand side illustrates the evolution of the interferometric baseline as a function of the orbit position

by setting in Equations (4.6) Ai = 0, βi = 90◦ and (B2 − B1 ) ≈ a sin i, where a is the orbits’ semi-major axis, the difference in the right ascensions of the ascending nodes and i the inclination, which is the same for both spacecraft. This selection results in a sinusoidal variation of the horizontal cross-track baseline with a maximum spacecraft separation at the equator as illustrated in Figure 4.5. A drawback of the formation in Figure 4.5 is the vanishing cross-track baseline at the northern and southern turns. This has two major consequences: first, accurate DEM generation will become impossible at higher latitudes and, second, a sufficient along-track separation y has to be ensured to avoid a satellite collision risk at the two orbit intersections. The impact of reduced baseline length at higher latitudes can be somewhat mitigated by increasing the equatorial orbit separation, but a significant performance gap will always remain for polar regions. An alternative is a modification of the orbit formation such that the orbits have an additional vertical separation at the intersection of the orbital planes [4.51]. Such a separation can be achieved with slightly elliptical orbits by a relative shift of the two eccentricity vectors e1 , e2 which has the primary effect of setting in Equations (4.6) the coefficients |A2 − A1 | = a ||e||, where e = e2 − e1 is the offset between the two eccentricity vectors. The phase difference βi − αi is usually kept in the vicinity of 90◦ , but its natural longterm drift due to secular disturbances can also be used for a fine tuning of the cross-track baselines [4.52]. This can be performed by adjusting the temporal schedule and the v of the orbital manoeuvres that are required to compensate the natural phase drifts due to deviations from frozen eccentricity [4.53]. Figure 4.6 illustrates the orbits and the resulting cross-track baselines. The latter can be regarded as forming a satellite helix, and such a formation will be used in the TanDEMX mission [4.10]. The additional vertical (radial) separation between the satellites can be chosen rather small (e.g., 300 m) since a high momentum would be required to compensate this eccentricity-induced vertical offset within a reasonable time-span. The helix concept will hence enable a safe operation of the satellite formation without autonomous control, which is

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SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS

vertical baseline horizontal baseline

0

45

0 25 27 180 2 5 3 90 1 osition Orbit P

60 315 3

Figure 4.6 Helix satellite formation. Left: orbital arrangement. Right: cross-track baselines as a function of the orbit position. The shown positions correspond to one complete orbit cycle

also of special interest in the case of contingency conditions. Since there is no crossing of the satellite orbits in the helix configuration, the satellites may now be shifted arbitrarily along their individual orbits. This is of great advantage, since it enables almost vanishing along-track baselines for predefined latitudes. Short along-track baselines are, for example, desired in case of DEM generation to minimize the relative Doppler shift between the interferometric images (cf. Section 4.4.1.2) and to avoid residual temporal decorrelation due to wind for some types of vegetation [4.54]. Another opportunity is the mapping of ocean surface currents, which will also require rather short along-track baselines to avoid temporal decorrelation and ambiguities in the derivation of the velocity vector field [4.55, 4.56]. Very short along-track baselines are furthermore required for at least some orbital positions if it is planned to use the ocean surface for DEM calibration purposes. The accurate control of the along-track displacement requires precise actuation thrusters with fine quantization. An alternative is a controlled increase in the ballistic coefficient, e.g. by appropriate satellite canting. 4.3.1.2 Multi-Satellite Formations Up to now only twin satellite formations have been considered. An alternative is the use of more than two satellites. A prominent example for such a configuration is the interferometric cartwheel, which has been suggested in 1998 [4.5, 4.57]. The interferometric cartwheel is a semi-active system that combines a conventional monostatic synthetic aperture radar with a set of passive low-cost receivers on board a constellation of microsatellites. The use of satellites with different ballistic coefficients for transmission and reception requires a sufficient separation of several tens of kilometres between the master satellite and the receiver formation to ensure safe operation. This may in turn have some consequences for the timing if it is desired to receive simultaneously the scattered radar data by the master satellite and the passive

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INTERFEROMETRIC MISSION DESIGN

0

45

5 360 70 31 225 2 0 8 1 35 90 1 rbit Position O

Figure 4.7 Orbits and interferometric baselines for the cartwheel formation

receivers [4.58]. The original cartwheel formation itself consists of three microsatellites on slightly elliptical orbits with equal eccentricity. All orbits share the same orbital plane and the arguments of perigee are uniformly distributed. The relative movement can be expressed by setting in Equation (4.6) Bi = 0 and Ai ≈ a ||e|| where ||e||, is the eccentricity of the orbits. The relative phase shifts are α2 − α1 = 120◦ and α3 − α1 = 240◦ . As can be seen in Figure 4.7, this choice provides a very stable envelope of the vertical baselines, if for each orbital position the satellite pair with maximum vertical separation is considered. The residual baseline variation is of the order of ± 7 %. An inherent property of the interferometric cartwheel is the close coupling between the vertical cross-track separation x(t) and the along-track displacement y(t). The relative satellite movement within the orbital plane can be approximated by an ellipse with an aspect ratio of two. This coupling prevents, however, an independent optimization of the along-track baselines for applications like ocean current mapping and it may furthermore reduce the common Doppler bandwidth in the case of large interferometric baselines. A similar choice has been suggested for TechSAT 21 [4.59], where the satellite orbits are not only offset in their eccentricity vectors but also differ in their inclinations and right ascensions of the ascending nodes. By this, an inclined ellipse may be obtained which is no longer restricted to the orbital plane of the reference orbit. For example, setting in Equations (4.6) Bi = 2Ai and βi = αi slants the ellipse by 63◦ , which leads to a circular movement if projected on the horizontal y–z plane of the Hill frame. The angular positions αi of the N satellites may then be chosen as αi+1 − αi = 360◦ /N , which results in a uniform distribution of the satellites along the ellipse. Such a formation with constant horizontal baselines is of high interest for GMTI and geolocation applications. Further configurations providing approximately constant cross-track baselines have been analysed in Reference [4.6]. An alternative orbit formation is given by constellations that provide multiple baselines at a fixed baseline ratio along the whole orbit cycle [4.52, 4.60]. Large baselines increase the sensitivity of the cross-track interferometer in the case of DEM generation, while short baselines are required to assist phase unwrapping, especially in mountainous terrain. The simultaneous data acquisition with multiple baselines at a fixed baseline ratio is hence well suited to push the interferometric performance up to the limits of the critical baseline, but a latitude-based acquisition strategy has to be applied to achieve global coverage. While it is

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SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS

0

60 315 3 5 270 2 2 0 18 0 135 it Position 45 9 Orb

Figure 4.8 Orbits and interferometric baselines for the Trinodal Pendulum

in principle also possible to fuse multiple single-baseline acquisitions, this approach has the advantage that it reduces significantly the data acquisition time and minimizes possible error sources due to temporal changes between subsequent scene acquisitions. One example for such a formation is the Trinodal Pendulum, which is shown in Figure 4.8. This formation consists of three receiver satellites with the same inclination but different ascending nodes. Safe operation in such a formation can again be achieved by adding slight offsets to the eccentricity vectors of the satellite orbits [4.52]. As in the helix formation, this enables a vertical separation at the northern and southern turns (cf. Figure 4.8, right). The radial separation can furthermore be used to acquire cross-track interferograms in the polar regions, but the additional fuel demands to compensate the natural rotation of the eccentricity vectors increases with increasing vertical separation. An alternative for polar mapping is a temporary transition to orbits with different inclinations. This has the side effect of causing a relative drift of the ascending nodes, which can be exploited for a fuel saving adjustment of the horizontal cross-track baselines. Such an adjustment enables an almost constant interferometric performance for all latitudes in the case of global DEM generation. The along-track baselines in the Trinodal Pendulum, which can be selected independently and almost arbitrarily by shifting the satellites along their orbits, are also well suited for applications like GMTI or ocean current mapping. Here, the simultaneous availability of multiple along-track baselines helps again to resolve ambiguities and to improve the performance.

4.3.2 Phase and Time Synchronization Oscillator stability deserves special attention in the design of bi- and multistatic SAR systems, since there is no cancellation of low-frequency phase errors as in a monostatic SAR, where the same oscillator signal is used for modulation and demodulation. The following subsections discuss the resulting errors in the bistatic SAR image and show potential solutions to avoid such disturbances.

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exp jm 2 fT t

exp j 2 fT t

T

(t)

m

exp j 2 f R t

R

(t)

m

(t)

Tx

Tx

exp jm 2 f R t

Bistatic SAR Signal s(t)

T

R

Rx

(t)

* X

Rx

Figure 4.9 Derivation of baseband bistatic phase errors after demodulation. fT and fR denote the transmit and receive oscillator frequencies, ϕT (t) and ϕR (t) are the corresponding phase errors and τ is the travelling time of the radar pulse

4.3.2.1 Modelling Oscillator Phase Noise in Bi- and Multistatic SAR Figure 4.9 shows a block diagram of a bistatic SAR that uses separate oscillators for transmission and reception. The frequencies of the transmitter and receiver oscillators are denoted as f T and f R (t) respectively. The corresponding phase noise is referred to as ϕT (t) and ϕR (t). The round trip delay of the radar pulse, which is responsible for the azimuth modulation, is indicated by τ = τTx + τRx and m = f 0 / f osc is the frequency up-conversion factor which transforms the oscillator frequency f osc to the radar carrier frequency f 0 . The demodulated bistatic SAR signal in the receiver is then given by s(t) = exp { jm [−2π f T τ + 2π ( f T − f R ) t + ϕT (t − τ ) − ϕR (t)]} .

(4.7)

The recorded signal s(t) will be distorted by two phase terms. The first distortion is due to an initial frequency offset f = f T − f R between the two oscillators. This results in a linear modulation 2πm f t of the recorded bistatic SAR signal. The second distortion is due to random phase noise ϕ{T,R} (t) from the two oscillators. This noise is often modelled by a second-order stationary stochastic process, which is conveniently characterized in the Fourier frequency domain by its power spectral density Sϕ ( f ), where Sϕ ( f ) describes the one-sided spectral density of phase fluctuations in units of radians squared per hertz bandwidth at Fourier frequency f from the carrier [4.61, 4.62]. The phase spectrum Sϕ ( f ) is often expressed by a composite power law model Sϕ ( f ) = a f −4 + b f −3 + c f −2 + d f −1 + e,

(4.8)

where the coefficients a to e describe the contributions from (a) random walk frequency noise, (b) frequency flicker noise, (c) white frequency noise, (d) flicker phase noise and (e) white phase noise, respectively. The middle row of Table 4.2 shows exemplary coefficients of a typical 10 MHz USO which can be taken as representative for current spaceborne SAR systems. The coefficients yield Allan standard deviations of σa (1 s) ≈ 1 × 10−11 , σa (10 s) ≈ 3 × 10−11 and σa (100 s) ≈ 8 × 10−11 . The oscillator with the improved phase spectrum Sϕb in the lower row of Table 4.2 will be discussed in Section 4.3.2.4.

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SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS Table 4.2 Coefficients of two exemplary 10 MHz oscillators

Sϕa Sϕb

a

b

c

d

e

−90 dB

−90 dB

−180 dB

−130 dB

− 150 dB

−130 dB

−130 dB

−180 dB

−130 dB

−150 dB

4.3.2.2 Disturbances of the Azimuth Impulse Response After bistatic SAR processing, oscillator phase errors manifest themselves as a deterioration of the impulse response function (IRF). Typical disturbances are a time-variant shift of the mainlobe, spurious sidelobes and a broadening of the impulse response, as well as phase errors in the focused SAR signal. Plate 1 (in the colour section) shows an example for the potential impact of oscillator noise on azimuth focusing in the X-band for a coherent integration time of 2 seconds. It becomes evident that the oscillator phase noise may not only defocus the SAR image in azimuth, but it will also introduce significant positioning and phase errors along the scene extension. The following subsections discuss the individual errors in more detail (cf. Reference [4.63]). Spurious sidelobes in azimuth High-frequency phase noise will cause spurious sidelobes in the impulse response function. This deterioration can be characterized by an increase of the integrated sidelobe ratio (ISLR), which measures the energy in the impulse response sidelobes relative to the energy in the mainlobe [4.64]. For an azimuth integration time Ta , the deterioration of the ISLR may be approximated from the phase spectrum as [4.1, 4.65] ISLR ≈

2 σϕ,HF

1 f > Ta

=2

f0

2

f osc

∞

Sϕ ( f ) d f.

(4.9)

1/Ta

The factor 2 is due to the use of two independent oscillators with equal phase noise spectrum Sϕ ( f ) and the scaling factor in the parentheses is due to the multiplication of the oscillator frequency fosc by m = f 0 / f osc to obtain the radar signal with centre (carrier) frequency f0 . The upper integration limit may be substituted by the inverse of the transmit pulse duration, since higher frequency phase errors are averaged during range compression. The left diagram of Figure 4.10 shows estimates of the ISLR in the X-band and L-band for the oscillator phase spectrum Sϕa given in the middle row of Table 4.2. A typical requirement for the maximum tolerable ISLR increase is −25 dB which would enable for this oscillator a maximum coherent integration time Ta of approximately 1 s in the X-band and 6 s in the L-band. Mainlobe dispersion Quadratic phase errors cause a broadening of the azimuth response. An approximation of these errors may be derived by expanding the phase for each frequency component of the stochastic process in a second-order Taylor series [4.66]: σQ2 = 2

f0 f osc

2

(πTa )4 4

0

1/Ta

f 4 Sϕ ( f ) d f.

(4.10)

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Figure 4.10 Predicted disturbances of the azimuth impulse response for the L-band (solid) and X-band (dashed). Left: integrated sidelobe ratio. Middle: quadratic phase errors. Right: azimuth displacement Interferometric Phase Error

Phase Error [deg]

100.00

10.00

1.00

0.10

0.01 0.1

1.0 10.0 Reference Point Distance [s]

100.0

Figure 4.11 Predicted interferometric phase error for a multistatic L-band system with a coherent integration time of Ta = 2 s. The solid and dashed lines show the phase errors for Sϕa and Sϕb , respectively. The dotted line is for periodic synchronization via a direct path link

A typical requirement for quadratic phase errors is σQ < π/4, which leads to a resolution loss of approximately 3 % in the case of unweighted azimuth processing [4.67].2 The middle plot of Figure 4.10 shows estimates of the quadratic phase errors in the X-band and L-band for the phase spectrum Sϕa of Table 4.2. In this example, a coherent integration time up to 2 s would still be tolerable in the X-band, ensuring good bistatic focusing of the impulse response. Azimuth displacement Any difference between the oscillator frequencies will cause a shift of the bistatic impulse response in the azimuth direction. Assuming a nonsquinted quasi-monostaticimaging geometry, 2

This requirement becomes much more severe for interferometric applications (cf. Section 4.3.2.4.).

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the azimuth shift is given by az =

c0 r 0 f , 2v f osc

(4.11)

where v is the platform velocity, r0 is the slant range and ( f / f osc ) is the relative frequency deviation between the two USOs. Note that a frequency deviation of only 1 Hz between two 10 MHz oscillators (corresponding to a relative frequency deviation of 10−7 ) causes a constant azimuth shift of az ≈ 1.7 km for v = 7 km/s and r0 = 800 km. A coarse estimate of f can be obtained from a spectral analysis of the demodulated azimuth signal (assuming a known Doppler centroid). A precise measurement of the azimuth displacement requires ground control points or an appropriate phase referencing system (cf. Section 4.3.2.4). A further opportunity arises in fully active systems with simultaneous mono- and bistatic SAR data acquisition, where it is possible to estimate f via co-registration between the monostatic and bistatic SAR images. The variance of the remaining azimuth shift may then be derived from the spectral representation of the Allan variance with non-adjacent samples [4.61, 4.62] as [4.63]

c r 2 ∞ f 2 sin(2π f t) 2 sin(πTa f ) 2 0 0 2 σaz (t) = 2 1− d f, (4.12) Sϕ ( f ) 2 v f osc πTa f 2 sin(π f t) 0 where t is the time interval elapsed from the last reference point. The sin c(πTa f ) function is due to averaging over the coherent azimuth integration time Ta and the sin(2π f t)/sin(π f t) function is due to the temporal difference between the Doppler frequency ‘measurements’ during the last reference and the actual satellite position. The right diagram of Figure 4.10 shows the standard deviation of the predicted azimuth shift for the phase spectrum Sϕa as a function of t (r0 = 800 km and v = 7 km/s). Note that the azimuth shift is independent of the wavelength, but depends slightly on the coherent integration time.

4.3.2.3 Range Displacement and Time Synchronization The range shift will be dominated by deviations between the pulse repetition frequencies (PRFs) of the transmitter and receiver. Since the PRF is usually derived from the local oscillator by appropriate frequency division, the shift in slant range may be expressed as r (t) = c0 f t/(2 f osc ), where again a quasi-monostatic imaging geometry is assumed. A frequency deviation of f = 1 Hz between two 10 MHz oscillators will hence cause a linear range drift of 15 m/s. From this it becomes clear that already small frequency deviations between the two oscillators may cause rather large range shifts for long data acquisitions. As a first consequence, this will require an adaptation of the recording window to the transmit event. This may be achieved by periodic PRF synchronization using a communication link [4.65], an evaluation of the directly received radar signal [4.68], or a reference to a common time standard as provided by, for example, GPS signals [4.69]. An alternative is continuous recording [4.5]. Precise range measurements will furthermore require an accurate time referencing between the transmitter and receiver. Several solutions for precise time synchronization on a nanoseconds level are discussed in References [4.1] and [4.70] to [4.72]. Such techniques allow for bistatic range measurements with accuracies in the metre range. The achievable accuracy with these ‘conventional’ methods is in general not sufficient for the requirements originating from high resolution SAR interferometry.

INTERFEROMETRIC MISSION DESIGN

4.3.2.4 Phase Synchronization

• 111

The most demanding requirements for phase stability arise from multistatic interferometry. For example, the generation of a high-resolution DEM will require precise relative phase knowledge in the order of a few degrees between the involved bistatic SAR images in order to avoid a low-frequency modulation of the DEM in the azimuth direction. For an estimation of the bistatic phase error ϕ it is assumed, first, that the relative phase is known for two reference points separated by a (temporal) distance Tc . Such references could, for example, be provided by two ground control (or tie) points, which can be used to eliminate a linear phase ramp resulting from a frequency offset between the two oscillators. The variance of the remaining phase error can then be derived from the oscillator phase noise spectrum Sϕ ( f ) as [4.63] 2 σϕ =2

f0 f osc

2 0

∞

6 + 2 f 2 π2 Tc2 sin(πTa f ) 2 2 Sϕ ( f ) 2 − sin (πT f ) d f. (4.13) c 3 f 2 π2 Tc2 πTa f

The solid curve in Figure 4.11 shows an example of the resulting phase error for an L-band system with a coherent integration time of Ta = 2 seconds. It can be seen that a rather dense net of ground control points (with spatial separations in the order of 10 to 50 km) would be required to achieve low interferometric phase errors. An alternative is the use of oscillators with significantly improved longterm frequency stability. For example, the space qualified 5 MHz oscillators in Reference [4.73] have a typical short-term stability of σa (τ = 10 s) = 10−13 , which would decrease the interferometric phase errors by two orders of magnitude. This is illustrated in Figure 4.11 by the dashed line. The required distance between the ground control points is then relaxed to several hundred kilometres. An alternative is a time and phase synchronization between the transmitter and receiver satellites via a direct path link, as suggested in Reference [4.8]. This link employs separate synchronization antennas to exchange relative time and phase information between the two satellites. A bidirectional version of such a synchronization technique will be used for the fully active TanDEM-X SAR interferometer (Section 4.4.1). For this, the usual transmit sequence of radar pulses will shortly be interrupted and a radar pulse will be redirected from the main RF antenna to the synchronization antenna [4.74]. The pulse is then recorded by the other satellite, which in turn transmits a radar pulse to the first satellite. Such a bidirectional phase referencing has the advantage of eliminating potential errors from varying intersatellite distance and internal delays [4.75, 4.76]. The periodic synchronization provides a regular grid of phase references separated by Tc . By this, it becomes possible to correct for low-frequency phase errors between the references via sin(x)/x interpolation. The variance of the residual bistatic phase errors between the phase references can then be derived as [4.63] ∞ f0 2 sin(πTa f ) 2 2 σϕ = 2 Sϕ ( f ) df f osc πTa f 1/(2Tc )

∞ 1/2Tc i sin(πTa f ) 2 2 + Sϕ f + d f + σϕ,link , (4.14) Tc πTa f i=1 −1/2Tc where the first integral describes the residual high-frequency phase errors between the phase references and the second integral corresponds to residual low-frequency phase errors caused 2 by aliasing artefacts. The last term, σϕ,link , describes additional errors due to an imperfect

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synchronization link, as discussed in Reference [4.77]. The dotted line in Figure 4.11 illustrates the resulting phase error for a periodic two-way synchronization assuming a random phase error of 1◦ for each synchronization pulse (corresponding to a single-pulse SNR of approximately 30 dB). It becomes clear that for equal Tc the sin(x)/x interpolation from the periodic synchronization link yields slightly better results than the linear interpolation from the (nonperiodic) ground control points. The residual (uncompensated) oscillator errors will become small for synchronization frequencies above 1 Hz (i.e. Tc < 1 s), and the performance is mainly determined by the SNR of the synchronization link. The same is true for a continuous, bidirectional synchronization, as suggested for semi-active SAR configurations [4.75, 4.77]. Further options to synchronize multistatic SAR systems will be discussed later on.

4.3.3 Operational Modes for Bi- and Multistatic SAR Systems Interferometric data acquisitions in fully active satellite formations can in principle be performed in multiple operational modes. Examples are (a) the pursuit monostatic mode where the satellites are operated independently from each other, (b) the bistatic mode where one satellite serves as a transmitter and all other satellites record the scattered signal simultaneously, (c) the alternating bistatic mode where the transmitter changes from pulse to pulse and (d) the simultaneous transmit mode where multiple satellites transmit at the same time. The operation of a semi-active system is restricted to the bistatic mode. 4.3.3.1 Pursuit Monostatic Mode The pursuit monostatic mode illustrated in Figure 4.12 assumes for each satellite an independent radar signal transmission and reception. The independent operation of the radar instruments avoids the need for phase and PRF synchronization, but the along-track displacement between the satellites should be large enough to avoid any RF interference. As a result, temporal

Figure 4.12 Pursuit monostatic mode

INTERFEROMETRIC MISSION DESIGN

• 113

decorrelation may become significant for some terrain types like water surfaces or vegetation at moderate to high wind speeds. The pursuit monostatic mode also makes rather inefficient use of the available RF energy since the scattered signal from each transmit pulse is only seen by a single antenna as opposed to a mode where multiple receiver antennas collect the scattered echoes simultaneously. A further issue to be considered is that the interferometric height sensitivity is doubled with respect to bistatic operation, meaning that the baseline determination has to be more accurate. The pursuit monostatic mode may, on the other hand, provide a natural fallback solution in case of problems with instrument synchronization or close formation control. It may also be used for calibration purposes during a limited mission period. The design of formations using the pursuit monostatic mode has to take Earth rotation into account, which leads to a latitude dependent additional cross-track baseline between the two monostatic data acquisitions imaging a given point on the Earth’s surface with equal Doppler frequencies. 4.3.3.2 Bistatic Mode The bistatic mode uses one dedicated transmitter to illuminate a common radar footprint on the Earth’s surface. As shown in Figure 4.13, the scattered signal is then recorded simultaneously by all receiver satellites. The simultaneous data acquisition with multiple antennas makes efficient use of the available RF signal energy and minimizes errors from atmospheric disturbances and temporal decorrelation. Essential requirements for DEM generation in the bistatic mode are relative phase referencing and PRF synchronization as discussed in Section 4.3.2. A further requirement for interferometric applications with natural surfaces is a sufficient overlap of the recorded Doppler spectra. In the bistatic mode, the Doppler spectra are mutually shifted with respect to each other and the amount of this shift is linearly related to the along-track displacement between the individual receiver satellites. This results in an upper limit of the maximum tolerable along-track displacement between the receiver satellites, which is for satellites in a low Earth orbit (LEO) configuration typically in the order of one to ten kilometres.

Figure 4.13 Bistatic mode

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Figure 4.14 Alternating transmit mode

4.3.3.3 Alternating Transmit Mode A third operational mode for a fully active satellite configuration is the alternating transmit mode, where the transmitter is switched from pulse to pulse [4.9]. The scattered signal from the ground is then simultaneously recorded by all receivers, as illustrated in Figure 4.14 for a twin satellite formation. In this dual satellite case, the alternating transmit mode acquires two monostatic and two bistatic SAR images during a single pass. Assuming an ideal system and scatterer reciprocity, the two bistatic SAR images should become identical. Systematic lowfrequency phase deviations between the two bistatic SAR images in a real-world system will be mainly due to unsynchronized radar instruments, while deviations from scatterer reciprocity can be neglected in the case of interferometric acquisitions with small bistatic angles. An evaluation of the phase difference between the two bistatic data sets is hence well suited for the identification and measurement of oscillator-induced phase errors, thereby enabling a calibration of the bistatic SAR interferometer. The simultaneous availability of mono- and bistatic SAR interferograms may, moreover, support the process of phase unwrapping. For example, the twin satellite configuration in Figure 4.14 provides interferograms with single and double phase-to-height sensitivity:

r The combination of one monostatic and one bistatic image yields a cross-track interferogram with a height of ambiguity of h amb = (λr0 sin θi )/B⊥ . Each combination between mono- and bistatic images can be selected and a combination of the four possible interferograms is of great advantage for relative phase calibration and to improve the performance.

r The combination of the two monostatic SAR images yields an interferogram with double

phase-to-height sensitivity, resulting in a height of ambiguity of h amb = (λr0 sin θi )/(2 B⊥ ). Low-frequency phase noise from the oscillators is suppressed due to the exclusive use of monostatic data.

MISSION EXAMPLES

• 115

The combination of the mono- and bistatic SAR interferograms is hence well suited to alleviate the problem of phase synchronization and height ambiguities. A major drawback of the alternating bistatic mode is its increased susceptibility to range and/or azimuth ambiguities. Such ambiguities can in principle be reduced by combining the redundant information from the two monostatic and the two bistatic images. For example, a bistatic SAR image with double PRF can be obtained from a coherent combination of the two bistatic SAR images, while an equivalent combination of the two monostatic SAR images requires a compensation of the topographic phase in, for instance, an iterative process [4.3, 4.78]. 4.3.3.4 Simultaneous Transmit Mode

A fully active satellite configuration may also be operated in a synchronized transmit mode where some (or all) spacecraft transmit their radar pulses at the same time. Potential interferences can be mitigated by an appropriate waveform design. Each receiver then records a linear superposition of all transmitted and scattered radar signals. This enables not only an efficient share of the transmit energy between the spacecraft but also allows the acquisition of unambiguous mono- and bistatic SAR images from all satellites within the multistatic configuration. One simple example is a splitting of the total frequency spectrum into multiple sub-bands. Each radar transmits in one of these sub-bands and records the full spectrum of scattered signals comprising its own bandwidth and that of all other illuminators. In this way multiple unambiguous bistatic interferograms can be formed between each satellite pair. The coherent combination of bistatic and monostatic interferograms enables furthermore the identification and suppression of system-induced phase errors. This can be achieved by exploiting the wavenumber shift in the monostatic interferograms which allows for coherent interferometric data acquisitions without overlapping frequency bands. By comparing the redundant information in the (spectrally filtered) low-resolution monostatic interferograms with their bistatic counterparts, low-frequency phase errors may be extracted, resulting from instrument and oscillator phase drifts. The simultaneous transmit mode with split frequency bands therefore enables a phase synchronization without the susceptibility to ambiguities if compared with the alternating transmit mode. The price to be paid is a lower range resolution for each individual SAR image and the loss of coherence between the monostatic images for a significant part of the frequency spectrum. In the case of high bandwidth interferometric systems employing multilooking in range, the resolution loss is more than compensated by the higher SNR in each sub-band. A simultaneous transmit mode has also been suggested in Reference [4.59] to improve the GMTI performance. A further performance gain can be obtained by digital beam-forming in each receiver, which allows, in combination with an appropriate Tx waveform design, for a reliable separation of the signals from the individual transmitters [4.79].

4.4 MISSION EXAMPLES 4.4.1 TanDEM-X 4.4.1.1 Mission Overview A representative example for a fully active twin satellite configuration is the TanDEM-X mission [4.10]. The mission concept is based on two TerraSAR-X radar satellites [4.80] flying in close formation to achieve the desired interferometric baselines in a highly reconfigurable

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Table 4.3 TanDEM-X system parameters Parameter

Value

Parameter

Value

Satellite height (nominal) Nominal swath width Swath overlap Centre frequency Chirp bandwidth (variable) Peak transmit power Duty cycle

514 km 30 km 6 km 9.65 GHz < 150 MHz 2260 W 18 %

4.8 m 0.7 m 32 × 12 Linear phase 33.8◦ 4 bits/sample 2266 Hz

Noise figure (TRM) Losses (processing, atmosphere, taper, degradtion, etc.) Independent post-spacing

4.3 dB 4.1 dB

Antenna length Antenna height Antenna elements Antenna tapering Antenna mounting Quantization Processed azimuth bandwidth Misregistration Sigma nought model (Ulaby, 90 %, X-band) Along-track baseline

12 m × 12 m

0.1 pixel Soil and rock VV < 1 km

configuration. The major goal of the TanDEM-X mission is the generation of a worldwide, consistent, timely and high-precision digital elevation model (DEM) according to the emerging HRTI-3 standard (cf. Table 4.1). The TanDEM-X DEM is of great importance for a wide range of scientific applications as well as for operational and commercial DEM production. Besides the primary goal of the mission, several secondary mission objectives based on along-track interferometry as well as new techniques with bistatic SAR have been defined which represent an important asset of the mission. The TanDEM-X operational scenario requires a coordinated operation of two satellites flying in close formation. Several options have been investigated and the helix satellite formation introduced in Section 4.3.1.1 has finally been selected for operational DEM generation. The helix formation enables a complete coverage of the Earth with a stable height of ambiguity of approximately 35 m by using a small number of formation reconfigurations (e.g. a ∈ {300 m, 400 m, 500 m} and a e ∈ {300 m, 500 m}, [4.81]). Baseline fine tuning is achieved by taking advantage of the natural rotation of the eccentricity vectors due to secular disturbances and fixating the eccentricity vectors at different relative phasings. An appropriate reference scenario has been derived which enables one complete coverage of the Earth within somewhat more than 1 year, assuming a bistatic acquisition in stripmap mode with an average acquisition time of 140 s per orbit [4.81]. In the following, the interferometric performance of TanDEM-X will be analysed. The performance estimation can be regarded as representative for fully active twin satellite configurations. Aspects that are characteristic for semi-active and multibaseline acquisitions will be treated in Section 4.4.2. The major system and instrument parameters of TanDEM-X are summarized in Table 4.3. 4.4.1.2 Coherence Estimation A key quantity in estimating the performance of any interferometric SAR system is the coherence. For a pair of random complex signals u 1 and u 2 , the coherence is defined as [4.40]

E u 1 u ∗2 γ= (4.15)

, E u 1 u ∗1 E u 2 u ∗2

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MISSION EXAMPLES

where E[..] denotes ensemble averaging (which is often replaced by a spatial average). The interferometric coherence can be regarded as a measure for the mutual phase information between two complex signals, and high coherence values are desired for good performance. Major factors that affect the coherence of a single-pass SAR interferometer are the radiometric sensitivity of each SAR instrument, range and azimuth ambiguities, quantization noise, processing and co-registration errors as well as surface and volume decorrelation. Temporal decorrelation, which is a major source for coherence loss in repeat-pass systems, can often – but not always – be neglected. Assuming additive and statistically independent error sources, the total coherence γ˜tot including both the interferometric correlation coefficient and the interferometric phase is then given by the product γ˜ tot = γSNR γQuant γAmb γCoreg γGeo γAz γ˜Vol γ˜Temp ,

(4.16)

where the right-hand side describes the individual error contributions: γSNR γQuant γAmb γCoreg γGeo γAz γ˜Vol γ˜Temp

finite SNR due to thermal noise quantization errors range and azimuth ambiguities co-registration and processing errors baseline decorrelation decorrelation due to relative Doppler shift volume decorrelation temporal decorrelation

The first six terms are decorrelation contributions due to system, processing and acquisition geometry effects. They are scalar quantities as they contribute only to the overall interferometric correlation coefficient. The last two terms are introduced by the scatterer and reflect its structural and temporal stability properties. They are complex contributions as they also affect the measured interferometric phase. In the following, each contribution will be discussed in more detail. Thermal noise The finite radiometric sensitivity of the multistatic radar will cause a coherence loss γSNR which is given by [4.40] γSNR =

1+

1

SNR−1 1

1 + SNR−1 2

,

(4.17)

where SNR1,2 is the signal-to-noise ratio for each interferometric channel. The SNR is given by SNR =

σ0 (θi − α) , NESZ(θi − α)

(4.18)

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SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS

where σ0 is the normalized backscattering coefficient. NESZ is the noise equivalent sigma zero level of the system, which can be derived as [4.82] NESZ =

44 π3r03 v sin(θi − α)kTBrg FL PTx G Tx G Rx λ3 c0 τp PRF

(4.19)

with transmit and receive range r0 , satellite velocity v, incident angle θi , local slope angle α, Boltzmann constant k, receiver temperature T, bandwidth of the radar pulse Brg , noise figure F, losses L, transmit power PTx , gain of the transmit and receive antennas GTx and GRx , wavelength λ, velocity of light c0 , pulse duration τ p and pulse repetition frequency PRF. The maximum gain of the antennas can often be approximated by G {Tx,Rx} =

4π A{Tx,Rx} , λ2

(4.20)

where ATx and ARx are the effective antenna areas of the transmitter and receiver, respectively. Figure 4.15 shows the predicted NESZ in the stripmap mode for 30 km swaths as defined for the acquisition of the standard TerraSAR-X data products in Reference [4.83]. The chirp bandwidth has been selected to yield a constant ground range resolution of 3 m and no antenna tapering is used to compensate for the steep sensitivity decay at the swath borders. A potential system optimization could of course include an appropriate Rx elevation tapering as well as a complete redefinition of the beams to improve both the sensitivity and the coverage by using optimized beams with less than 6 km overlap. For reference, Figure 4.15 also shows the scattering coefficients for rock and soil surfaces at VV polarization for occurrence levels of 50 % (dashed) and 90 % (dotted) as provided in Reference [4.84].

Figure 4.15 NESZ for the untapered stripmap mode with 30 km swaths (solid) and scattering coefficients for 50 % (dashed) and 90 % (dotted) occurrence levels

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MISSION EXAMPLES

Quantization

Another potential error source is due to the quantization of the recorded raw data signals [4.85]. The investigation of quantization errors is an important aspect, since the number of bits used for the digital representation of the recorded radar signals directly impacts on the data rate to be transmitted to the ground. In a strict sense, quantization errors have to be regarded as a nonlinear and signal-dependent distortion, but for the current investigation it is reasonable to approximate them as additive white Gaussian noise. This is justified by comparing the phase error estimates computed from the signal-to-quantization noise ratio (SQNR) to the phase errors obtained from a simulation of the complete quantizer (cf. Table 4.4). For this simulation, a nonuniform Lloyd–Max quantizer [4.86] has been used, which will minimize the distortion for a given bit rate in the case of a Gaussian signal (assuming independent Cartesian quantization of I and Q channels; see also Reference [4.87]). It becomes clear that quantization could affect the interferometric performance in the case of a low bit rate. Hence, a quantization with 4+4 bits/sample will be assumed in the following. This will lead to an SQNR of approximately 20 dB and a coherence of γQuant ≈ 0.99. Lower bit rates could be used in case of onboard memory and downlink bottlenecks (from a pure performance point of view it would even be better to have two 2+2 bit acquisitions with different interferometric baselines than a single data acquisition with 4+4 bit quantization). Co-registration errors Processing and co-registration errors can be modelled as phase aberrations in the transfer functions of the SAR processor. With az and rg being the relative azimuth and range shift between the two interferometric images in fractions of a resolution cell, the coherence loss due to misregistration is given by [4.88] sin(π rg) sin(π az) γCoreg = . (4.21) π rg π az A co-registration accuracy better than one-tenth of an image pixel can be expected in both the azimuth and range. This will yield a coherence of γCoreg ≥ 0.97. Ambiguities The coherence loss due to range and azimuth ambiguities can be approximated by 1 1 γAmb = , 1 + RASR 1 + AASR

(4.22)

Table 4.4 Signal-to-quantization noise and estimated standard deviation of phase errors for a BAQ with nonuniform Lloyd–Max quantization

Bits

SQNR (Lloyd-Max quantization) dB

Coherence (theoretic)

Interferometric phase error (from coherence) (deg)

2+2 3+3 4+4 5+5

9.3 14.6 20.2 26.0

0.895 0.966 0.991 0.997

40.3 23.9 13.9 7.8

Simulation for optimum Lloyd-Max quantization (deg) 1 channel

2 channels

30.7 18.8 10.5 6.1

43.4 26.6 14.8 8.6

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where RASR and AASR are the range and azimuth ambiguity-to-signal ratios, respectively. For TanDEM-X, the predicted RASR and AASR will be below −20 dB [4.89], which leads to a coherence of γ Amb > 0.98. The impact of ambiguities will be more severe for semi-active systems with small receiver antennas; a detailed discussion is therefore postponed to Section 4.4.2.2. Baseline and Doppler decorrelation The along-track and cross-track displacement between the receiving satellites causes a relative shift of the Doppler and ground range spectra between the two interferometric channels. As a result, the signals will become more and more decorrelated for increasing baseline length. This coherence loss can be compensated by range and azimuth spectral filtering to a common frequency band (γGeo = γAz = 1.0) [4.46]. The reduced bandwidth will imply a reduced number of looks for a given independent post-spacing, which will be taken into account in the computation of the final height errors (cf. Section 4.4.1.3). Volume decorrelation Volume scattering in vegetated areas can have a significant impact on the coherence of the interferometric signal and the achievable height accuracy. The increased ‘phase noise’ in the case of large baselines and high volumes may also cause problems with phase unwrapping. To model the coherence loss, it is noted first that for vegetated areas the effective scattering cross-section will be a function of the penetration into the vegetation layer. Taking into account extinction in a homogeneous medium, a vertical scattering profile (weighting) is assumed: σ 0 (z) = exp[−2β(h v − z)],

0 ≤ z < hv,

(4.23)

where h v is the vegetation height and β the one-way amplitude extinction coefficient in nepers per metre. The coherence of a random volume with vertical scatterer distribution defined by Equation (4.23) is then given by [4.39, 4.90]

γ˜vol

2πh v B⊥ 2βh v −1 +j exp cos θ i λ sin θi r0 = B⊥ 2βh v π exp −1 1+j cos θi βλ tan θi r0

(4.24)

Figure 4.16 shows two examples of the coherence loss from volume decorrelation for the X-band and L-band with extinction coefficients of 1.0 and 0.2 dB/m, respectively. For TanDEMX, which will use interferometric baselines in the order of 300 m at an incident angle of 35◦ , in this (low-extinction) example a coherence loss of up to 0.85 is observed for tall vegetation. The potential impact of volume decorrelation on the TanDEM-X performance has been investigated in more detail in Reference [4.89], where it is shown that volume decorrelation may cause a notable increase in the height errors in light vegetation with low extinction. The potential impact of volume decorrelation on the TanDEM-X performance can be mitigated by increasing the bandwidth and/or the independent post-spacing in vegetated areas, which both increase the number of independent looks (cf. Section 4.4.1.3).A systematic evaluation of the coherence is

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MISSION EXAMPLES

1.0 0.9

0.8

0.8

0.7

0.7

0.6 0.5 0.4 0.3

Coherence [ ]

Coherence [ ]

Volume Decorrelation 1.0 0.9

Volume Decorrelation

0.6 0.5 0.4 0.3

0.2

0.2

0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Effective Baseline [km]

0.1 0.0 0

1

2

3 4 5 6 7 8 Effective Baseline [km]

9

10

Figure 4.16 Coherence loss from volume decorrelation for the X-band (left) and L-band (right). The volume heights are 5 m (solid), 10 m (dashed–dotted), 20 m (dashed) and 40 m (dotted). The incident angle is 35◦ and the assumed slant range is 615 km in both cases

furthermore an indicator for the presence of vegetation and may assist phase unwrapping at the border of tall forests. Temporal decorrelation Any change of the scatterer structure between an acquisition of the two interferometric channels with equal Doppler frequencies may cause a loss of coherence. In the following any coherence loss due to temporal decorrelation will be neglected. While such an assumption seems to be justified for most types of land cover, it might cause problems, e.g. in dynamic oceanographic mapping if the along-track distance between the receiver satellites exceeds a few hundred metres. Temporal decorrelation of ocean surfaces may also limit their usability for height calibration if the along-track baseline exceeds a few hundred metres. Rather short decorrelation times in the order of 50 ms have furthermore been observed for some types of vegetation imaged in the X-band at moderate to high wind speeds [4.54]. It is hence of great importance to keep the along-track baseline of the single-pass SAR interferometer in such areas as short as possible. Figure 4.17 shows the total coherence γ tot for TanDEM-X operating in the standard stripmap mode. The dotted curves show the estimated coherence for the scattering coefficients with an occurrence level of 50 %. The coherence is in the order of 0.9. The solid lines are for scattering coefficients corresponding to an occurrence level of 90 %. The lower scattering reduces the coherence, especially at higher incident angles, where the limited SNR becomes the dominant error source.

4.4.1.3 Interferometric Phase Errors Knowledge of the total coherence γ tot allows for the derivation of the interferometric phase error. The probability density function (PDF) of the phase difference pϕ (ϕ) between the two

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Total Coherence (soil & rock, W) 1.0

Gamma [ ]

0.9

0.8

0.7

0.6 150

200 20

250 25

300 350 400 Ground Range [km] 30

35 40 Incident Angle [deg]

450 45

500

550 50

Figure 4.17 Total coherence γtot in the stripmap mode. Solid and dashed curves are for scattering coefficients with occurrence levels of 50 % and 90 %, respectively

interferometric SAR channels is given by [4.91] 2 n 2 n

n + 12 1 − γtot γtot cos ϕ 1 − γtot 2 pϕ (ϕ) = √ cos2 ϕ , F n, 1; 12 ; γtot n+1/2 + 2 2π 2 π (n) 1 − γtot cos2 ϕ

(4.25)

where n is the number of independent looks, F the Gauss hypergeometric function and the gamma function [4.92]. The standard deviation of the interferometric phase error is then given by σϕ =

π

−π

ϕ 2 pϕ (ϕ) dϕ

(4.26)

The left-hand side of Figure 4.18 illustrates the dependency of σϕ on the coherence γ for different look numbers n. An estimation of the 90 % point-to-point height errors as required by the emerging HRTI3 standard requires the computation of the difference between two random variables where each describes the fluctuation of the interferometric phase at one location. This difference corresponds to a convolution between the two probability density functions pϕ (ϕ) [4.93]. The 90 % point-to-point phase error ϕ90 % is then obtained from ϕ90 %

pϕ (ϕ) ⊗ pϕ (ϕ) dϕ = 0.9, (4.27) −ϕ90 %

where ⊗ denotes convolution and pϕ (ϕ) is the PDF given in Equation (4.25). The right-hand side of Figure 4.19 shows the multi-look phase error ϕ90 % as a function of the coherence for different look numbers. To compute the number of independent looks for TanDEM-X, recall first that range and azimuth filtering has been assumed for an optimization of the interferometric coherence. As a result, the bandwidth in each channel will be reduced, thereby affecting the geometric resolution

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MISSION EXAMPLES

90 80 70 60 50 40 30 20 10 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 gamma

Interferometric Phase Error (90%) [deg]

Interferometric Phase Error (stdv) [deg]

Phase Error from Gamma (stdv) 110 100

Phase Error from Gamma (90%) 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 gamma

Figure 4.18 Standard deviation (left) and 90 % point-to-point errors (right) of the interferometric phase. The look numbers are indicated above each curve

Figure 4.19 Relative height accuracy for an effective baseline of 500 m in the stripmap mode. Solid: 90 % point-to-point height errors. Dotted: standard deviation

and decreasing the number of independent looks for a given post-spacing. The number of independent looks is given by n=

δx δy δrg δaz

(4.28)

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SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS

where δx and δy is the assumed post-spacing of the final product in range and azimuth, respectively. The ground range resolution δrg may be computed from δrg =

c0 cos(α) B⊥,crit , 2Brg sin(θinc − α) B⊥,crit − B⊥

(4.29)

where B⊥ is the interferometric baseline perpendicular to the line of sight and B⊥,crit is the critical baseline as defined in Equation (4.4). As mentioned above, azimuth filtering of the two channels prior to forming the interferogram is also assumed in order to prevent any decorrelation due to different Doppler centroids. In the case of a single-pass scenario, the azimuth filtering will lead to a degraded azimuth resolution δaz =

vgrd , Bproc − f

(4.30)

where Bproc is the processed Doppler bandwidth (2266 Hz for TerraSAR-X) and f the relative shift between the monostatic and bistatic Doppler centroids. The Doppler shift can be approximated as 1 vRx,1 ◦ pRx,1 vRx,2 ◦ pRx,2 vsat dalong ≈ f = ( f Tx + f Rx,1 ) − ( f Tx + f Rx,2 ) = , − λ pRx,1 pRx,2 λr0 (4.31) where ◦ denotes the scalar product, vRx,1 and vRx,2 are the velocity vectors for the two satellites and the vectors pRx,1 and pRx,2 point from the corresponding satellites to the centre of the illuminated scene. The variation of the Doppler centroid across the imaged swath and differential effects from Earth rotation can be neglected for the current analysis. It is clear that the relative frequency shift f depends strongly on the along-track distance dalong between the two receivers. For the helix configuration as used for TanDEM-X a maximum along-track displacement of 1 km is assumed, which leads to a relative shift of the mono- and bistatic Doppler spectra in the order of 350–400 Hz. Such a shift corresponds to an azimuth resolution loss of approximately 15 %. An independent posting of 12 m by 12 m then yields 10 to 12 looks and the resulting phase errors range from 4 to 8◦ for σϕ and 10 to 20◦ for ϕ90 % .

4.4.1.4 Relative Height Accuracy The relative height errors may now be derived from Equation (4.3), where ϕ is given by either σϕ or ϕ90% . Figure 4.19 shows the predicted height accuracy for an effective baseline B⊥ = 500 m assuming an operation of TanDEM-X in the bistatic stripmap mode. The solid lines indicate the 90 % point-to-point height errors, and the dotted lines indicate the corresponding standard deviation. The height errors in Figure 4.19 show a significant increase from near range-to-far range swaths. One reason for this increase is the systematic decrease in the phase-to-height scaling corresponding to a systematic increase in the height of ambiguity with increasing incident angles. As TanDEM-X enables a flexible selection of the interferometric baseline, it is hence advisable to adapt the length of the baselines to a fixed height of ambiguity. Figure 4.20 shows the point-to-point height errors for the 90 % confidence interval assuming fixed heights of

• 125

MISSION EXAMPLES Relative Height Accuracy (90% Point-to-Point) 4

Height Error [m]

3

2

1

0 150

200 20

250 25

300 350 400 Ground Range [km] 30

35 40 Incident Angle [deg]

450 45

500

550 50

Figure 4.20 Height accuracy for fixed heights of ambiguity of 50 m (top), 35 m (middle) and 20 m (bottom) in the stripmap mode after combination of adjacent swaths. All errors are point-to-point height errors for a 90 % confidence interval

ambiguity of 50 m (top), 35 m (middle), and 20 m (bottom). The derivation of the height accuracies in this figure assumes a weighted combination of the interferometric data from overlapping swath segments. The impacts of slopes, volume decorrelation, etc., have been analysed in Reference [4.89], where it is shown that, for example, a variation of the slopes by ±20 % may cause an increase in the height errors by a factor of <1.1 for medium incident angles and 1.2 for either very steep or very shallow incident angles. It becomes apparent from Figure 4.20 that the acquisition of DEMs with 2 m relative height accuracy (point-to-point errors at 90 % occurrence level according to HRTI-3 standard) will require a height of ambiguity in the order of 35 m. This height of ambiguity corresponds to perpendicular baselines of B⊥ = 260 m and B⊥ = 439 m at incident angles of 30◦ and 45◦ , respectively. It is clear that unambiguous DEM generation in mountainous areas will require additional data takes with different baselines to support phase unwrapping (cf. Section 4.4.2.3). The current TanDEM-X data acquisition plan assumes one or two additional data takes for areas with moderate slopes and tall vegetation and three or four additional data takes for mountainous terrain with steep slopes. This plan also includes an imaging from ascending and descending orbits, which improves the performance for terrain with different slopes and provides additional incident angles in the case of shadow and layover. Difficult terrain can furthermore be imaged in the alternating bistatic mode, which enables the acquisition of two interferograms with an effective baseline ratio of two in one single pass.

4.4.1.5 Absolute Height Accuracy Up to now, errors due to the finite accuracy of relative baseline estimation and relative RF phase knowledge have been neglected. Such errors will mainly cause a low-frequency modulation of

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the DEM, thereby contributing simultaneously to relative and absolute height errors. For the latter, the HRTI-3 standard is much less stringent and requires an accuracy of only 10 m at a 90 % confidence level. Baseline estimation errors Baseline estimation errors can be divided into along-track, cross-track and radial errors. Alongtrack errors will be sufficiently resolved during the co-registration and are hence regarded as uncritical. Cross-track and radial errors may cause errors in both the line of sight (B ) and perpendicular (B⊥ ) to the line of sight. Baseline errors perpendicular to the line of sight will cause a bias in the phase-to-height scaling. The resulting height error is given by h =

h B⊥ , B⊥

(4.32)

where h is the topographic height, B⊥ is the error of the baseline estimate perpendicular to the line of sight and B⊥ is the length of the perpendicular baseline. Assuming a maximum topographic height of h = 9000 m and baselines corresponding to a height of ambiguity of hamb = 35 m (i.e. B⊥ = 260 m for θi = 30◦ and B⊥ = 439 m for θi = 45◦ ), a baseline estimation error of B⊥ = ±1 mm will result in height errors of ±3.5 and ±2.1 cm for incident angles of θi = 30◦ and θi = 45◦ , respectively. Errors in the relative position estimates of the antenna phase centres parallel to the line of sight (B ) will primarily cause a rotation of the reconstructed DEM about the (master) satellite position. As a result, the DEM will be vertically displaced by h =

B r sin θi B h amb = , B⊥ λ

(4.33)

where r and θi are the slant range distance and the incident angle of an appropriately selected reference point (e.g. at mid-swath). This vertical displacement will be h = ±1.1 m for B = ±1 mm and h amb = 35 m. A parallel baseline error will furthermore cause a tilt of the DEM, which is given by E tilt =

B h = , s B⊥

(4.34)

where s is the ground range distance from the selected reference point. The resulting tilt will be 3.8 and 2.3 mm/km for incident angles of θi = 30◦ and θi = 45◦ , respectively (B = 1 mm and hamb = 35 m). Table 4.5 summarizes the predicted height errors resulting from B = 1 mm and B ⊥ = 1 mm. The TanDEM-X mission concept assumes precise baseline determination by a double differential evaluation of GPS carrier phase measurements. Current analyses indicate an achievable accuracy for the estimation of relative satellite positions in the order of 1–2 mm [4.94]. Additional errors may arise from satellite attitude errors and uncertainties in both the GPS and the RF antenna phase centre positions. Note in this context that both satellites experience almost the same gravity field and are exposed to highly correlated orbit perturbations. Residual

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MISSION EXAMPLES Table 4.5 Height errors for 1 mm baseline uncertainty Height errors (for h amb = 35 m) Incident angle (deg)

B = 1 mm

B⊥ = 1 mm

Normal baseline (hamb = 35 m) (m)

h(m)

h/s (tilt) (mm/km)

h (h = 9 km) (cm)

260 439

1.1 1.1

3.8 2.3

3.5 2.1

30 45

(i.e. unmodelled) variations of the baseline vector will hence show a high degree of temporal correlation. Even in case of a large differential acceleration of ¨x = 100 × 10−9 m/s2 (e.g. due to unmodelled differential drag between the two satellites, etc.), the resulting differential error after a 100 km data take will be in the order of only 10 μm. Noting, furthermore, that such an acceleration will mainly affect estimates of the along-track baseline (which are uncritical for cross-track interferometry), it might be concluded that residual orbit fluctuations can be neglected in the computation of relative height errors (the area for relative point-to-point height errors in HRTI-3 is approximately 100 km × 100 km). A factor not to be ignored is the initial uncertainty in the relative RF phase centre positions which may result in a tilt of the acquired DEM swath. For example, an initial error in the estimate of the RF relative phase centre position of B = ±1 cm can in the worst case result in a relative height error of ±3.8 m for s = 100 km (assuming an ideal mosaic of equally tilted swaths). Such a tilt can be reduced by additional calibration data takes from crossing orbits by applying an appropriate bundle block adjustment in either radar or DEM geometry. Calibration data takes could also profit from larger baselines and/or different interferometric (e.g. pursuit monostatic or alternating bistatic) and/or different SAR (e.g. ScanSAR) modes. HRTI-3 DEM calibration requires a final absolute height accuracy of 10 m and will be based on a combination of (a) a sparse net of calibration targets, (b) altimetry data, (c) GPS tracks and (d) ocean data takes with short along-track baselines. Further calibration strategies are currently under investigation.

Oscillator phase noise The impact of oscillator phase noise in the bistatic mode has been analysed in Section 4.3.2, where it is shown that oscillator noise may cause errors in both the interferometric phase and SAR focusing. The stringent requirements for interferometric phase stability in the bistatic mode will require an appropriate relative phase referencing. Direct transmission and reception of radar pulses via dedicated synchronization horn antennas is foreseen on both the TerraSARX and the TanDEM-X satellites [4.10, 4.74]. Assuming a height of ambiguity of 35 m, the sensitivity to residual phase errors will be hamb /360◦ = 0.097 m/deg. The maximum allowed phase error for a height error of ±1 m is hence ±10.3◦ . The required synchronization frequency is in the order of 1–10 Hz depending on (a) the tolerable height errors, (b) the exact specification of the phase spectra of the two local oscillators and (c) the phase noise on the ‘synchronization’ link. Alternative solutions are an operation in the alternating bistatic mode or the simultaneous transmit mode (cf. Section 4.3.3).

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Table 4.6 System and instrument parameters for a TerraSAR-L cartwheel configuration

Frequency Chirp bandwidth Tx power Losses (Tx) Losses (Atm) Losses (Rx) Noise figure

1.2575 GHz 80 MHz 6400 W 1.3 dB 1.0 dB 1.5 dB 2.5 dB

Swath width Antenna look angle Incident angles (deg) PRF (Hz) Ground range (km) Antenna tapering Processed bandwidth (Hz)

75 km 25.2 24.6–30.6 2950 259–334 None 1200

System parameters Duty cycle Posting Sigma nought Tx antenna Rx antenna Co-registration Quantization Swath selection 70 km 29.2 30.3–35.5 2190 330–400 Taylor 1200

60 km 33.7 35.2–39.3 2490 396–456 None 1000

7% 12 m × 12 m Shrubs, L-band, HH 11 m × 2.86 m 3 m ring focus 1/10 pixel 4 bits/sample (BAQ) 50 km 36.6 39.0–42.2 2200 452–502 Taylor 1200

50 km 38.8 42.0–44.9 1950 498–548 Taylor 1200

4.4.2 Semi-active TerraSAR-L Cartwheel Configuration 4.4.2.1 Mission Overview The European Space Agency (ESA) has initiated and supported an investigation to analyse the option of adding an interferometric constellation of passive receiver satellites to an L-band SAR mission [4.60]. The mission proposal TerraSAR-L [4.43] was selected as a reference for this investigation. The primary objective is again the generation of a global DEM of HRTI level-3 quality. Ocean current monitoring is another important application facilitated by such a single-pass InSAR configuration [4.95]. In the following, the constellation will be regarded as an integral element of TerraSAR-L, i.e. special modes exploiting the full capabilities of the main spacecraft will allow for an improved performance. Furthermore, intersatellite links can be used to synchronize the data recording and provide a TT&C communication and science data downlink via TerraSAR-L and hence simplify the microsatellite architecture. Table 4.6 summarizes the main mission and instrument parameters. Using the swath partitioning shown in the lower part of Table 4.6 it has been shown in Reference [4.60] that a global DEM according to the HRTI-3 standard could be derived with the Trinodal Pendulum and TerraSAR-L in less than 1 12 years. This calculation assumes dual mapping with ascending and descending orbits and a mean monitoring time of 180 seconds per orbit. The combination of interferograms from ascending and descending orbits is well suited to solve residual problems in DEM generation arising, for example from shadow in an alpine terrain [4.96]. The following sections highlight important aspects for such a semi-active satellite constellation if compared to a fully active tandem configuration as analysed in the previous section. 4.4.2.2 Ambiguity Analysis Range and azimuth ambiguities deserve special attention in the case of semi-active SAR systems. For example, the antennas of the passive receivers in the TerraSAR-L cartwheel

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MISSION EXAMPLES

constellation will be substantially smaller than the 11 m by 2.86 m transmit aperture (cf. Table 4.6). Small antennas are a prerequisite for an accommodation of all satellites in a common launcher. The allowed antenna size and its shape is further limited by the maximum momentum and weight that can be handled by a microsatellite. In consequence, the small aperture of the receiver antennas may raise the ambiguity level. Hence, a detailed ambiguity analysis has to be conducted. Range ambiguities Range ambiguities are caused by an overlap of the desired swath echo with signal returns from succeeding and preceding radar pulses. As range ambiguities become more prominent with decreasing interpulse periods, they lead to an upper bound of the PRF. Major factors that affect the range ambiguities besides the PRF are the transmit and receive antenna patterns, the incident angle and the scattering coefficients for ambiguous and unambiguous signal returns. The range ambiguity-to-signal ratio (RASR) can been computed as [4.82]

σ0 (θi ) G Tx (θi ) G Rx (θi ) ri3 sin(θi ) RASR(θi ) =

i=0

3

, r0 sin(θ0 )

σ0 (θ0 ) G Tx (θ0 ) G Rx (θ0 )

(4.35)

where G Tx and G Rx are the transmit and receive antenna patterns in elevation. In this equation, the incident angle and slant range are denoted by θi and ri , respectively. The index i is equal to zero for the swath echo and different from zero for the ambiguous returns. A spherical Earth model has been assumed for computing the incident angles from the slant ranges:

(1 + h sat /re )2 − 1 − (ri /re )2 θi = ±acos 2ri /re

with ri = r0 + i

c0 2 PRF

(4.36)

In the following, the same scattering model as indicated in Table 4.6 will be used for both the ambiguous and unambiguous signal returns. Figure 4.21 shows the results of a parametric analysis of the range ambiguity to signal ratio for the TerraSAR-L cartwheel configuration as a function of the ground range position relative to the swath centre and the pulse repetition frequency (PRF) for incident angles of 30◦ (upper left), 35◦ (upper right) 40◦ (lower left) and 45◦ (lower right). The arrows indicate the maximum PRF for a range ambiguity-to-signal ratio of −20 dB and swath widths of 40 and 70 km, respectively. It becomes clear from the upper left part of Figure 4.21 that the PRF must stay below 3.1 kHz for an incident angle of 30◦ to ensure a range ambiguity ratio below −20 dB within a 70 km swath. A reduction of the swath width to, for example, 40 km allows for an increased PRF of up to 3.9 kHz. Such an increased PRF may also be of interest for a polarimetric mode, where the transmitter switches the polarization plane from pulse to pulse to acquire dual or fully polarimetric data in a single pass (cf. Section 4.4.2.5). As can be seen from Figure 4.21, the range ambiguity-to-signal ratios increase quickly with increasing incident angles, thereby restricting the range of possible PRFs to lower frequencies at higher incident angles. At an incident angle of 45◦ , the maximum tolerable PRF is only 1.8 kHz for an RASR of −20 dB and a swath width of 70 km (cf. Figure 4.22, bottom right). By limiting the swath to 40 km, the PRF may be increased to 2.1 kHz. A reduction of the required range ambiguity-to-signal ratio

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Figure 4.21 Range ambiguity-to-signal ratio (RASR) as a function of swath position and PRF for incident angles of 30◦ (upper left), 35◦ (upper right), 40◦ (lower left) and 45◦ (lower right)

to, for example, −16 dB will admit increased PRFs, but this effect is not very pronounced due to the steep gradient of the RASR at the swath border. Azimuth ambiguities Azimuth ambiguities arise from a sampling of the azimuth signal with a PRF that is below the Nyquist frequency of the Doppler spectrum recorded by the receiver antenna. Azimuth ambiguities will be of special concern for the TerraSAR-L cartwheel constellation due to the

Azimuth Ambiguity-to-Signal Ratio –5

AASR [dB]

–10 –15 –20 –25 –30 –35 1500

1750

2000

2250 2500 PRF [Hz]

2750

3000

Figure 4.22 Azimuth ambiguities as a function of the PRF for constant (solid), Taylor (dashed–dotted), Hamming (dashed) and Dolph–Tschebyscheff (dotted) tapering

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MISSION EXAMPLES

small receiver antennas. The azimuth ambiguity-to-signal ratio (AASR) can be computed by [4.82] Bproc/2 AASR ≈

i=0

−Bproc/2

A GA Tx ( f + i PRF) G Rx ( f + i PRF) d f

Bproc/2

−Bproc/2

A GA Tx ( f ) G Rx ( f ) d f

,

(4.37)

A where f denotes the Doppler frequency, G A Tx and G Rx are the directional patterns of the transmit and receive antennas in the azimuth direction Bproc is the processed Doppler bandwidth. This simplified analysis does not take into account yaw (and pitch) steering, which is necessary to compensate a latitude dependent Doppler shift due to Earth rotation. Furthermore, the additional azimuth steering required to provide an overlap between the Tx and Rx antenna footprints has been neglected. This additional azimuth steering is typically below 10◦ ; the exact values depend on the selected bistatic Doppler centroid as well as on the along-track displacement between the transmitter and the receiver satellites. The solid curve in Figure 4.22 shows the predicted AASR as a function of the PRF. The short antenna length of the passive receiver satellites will cause an azimuth antenna pattern with a broad mainlobe. Hence, the level of the azimuth sidelobes in the joint antenna pattern will be substantially increased. To alleviate this effect, advantage may be taken of the long transmit antenna, which allows for a reduction of the sidelobe levels by appropriate antenna tapering. Three different tapering functions have been investigated for TerraSAR-L: (a) Taylor, (b) Hamming and (c) Dolph–Tschebyscheff tapering. The tapering coefficients for the different weighting functions are provided in Table 4.7. Figure 4.22 shows the reduction of the AASR for Taylor (dashed–dotted), Hamming (dashed) and Dolph–Tschebyscheff (dotted) tapering at a processed bandwidth of 1.2 kHz. It is clear, that an appropriate tapering of the TerraSAR-L antenna pattern has a great potential for a reduction of the azimuth ambiguities. For example, Hamming weighting is an efficient means of reducing azimuth ambiguities by ca. –5 dB to a level of –19 dB for the interesting PRF range between 2 and 2.7 kHz. The reduced effect of Dolph–Tschebyscheff tapering at low PRFs is due to the increased width of the antenna mainlobe. A final assessment of the optimum tapering function and the processing bandwidth must be based on a trade-off between the gain loss due to tapering and a loss of interferometric accuracy due to a reduced number of looks. A detailed optimization is beyond the scope of this investigation, but the exemplary results show the potentials of such an optimization for ambiguity reduction in a semi-active multistatic SAR system.

Table 4.7 Azimuth tapering coefficients for TerraSAR-L

No tapering Taylor Hamming Dolph–Tschebyscheff

a1 = a10

a2 = a9

a3 = a8

a4 = a7

a5 = a6

1.0 1.0 0.54 0.357

1.0 0.7 0.7 0.485

1.0 0.83 0.84 0.705

1.0 0.93 0.94 0.892

1.0 1.0 1.0 1.0

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Figure 4.23 Predicted DEM performance for a semi-active TerraSAR-L cartwheel configuration. The estimated height accuracy (standard deviation) is shown for two baselines corresponding to a height of ambiguity of 100 m (dashed) and 10 m (solid)

4.4.2.3 Multibaseline Processing Figure 4.23 shows the predicted height accuracy of the TerraSAR-L cartwheel constellation for a height of ambiguity of 100 m (dashed, corresponding to an effective interferometric baseline of B⊥ ∼ 1 km) and 10 m (solid, corresponding to B⊥ ∼ 10 km) assuming an independent post-spacing of 12 m × 12 m. It is obvious that the height accuracy increases with a decreasing height of ambiguity. On the other hand, a small height of ambiguity is likely to cause phase wrapping problems, especially in mountainous areas. The baseline ratio of the example in Figure 4.23 has been chosen such that the height errors from the DEM acquisition with the small baseline stay below the height of ambiguity for the large baseline. It would hence be possible to use the interferometric data from the small baseline acquisition to resolve phase ambiguities in the highly sensitive large baseline interferogram. Several techniques have been suggested to resolve phase ambiguities by a combination of multiple SAR images acquired with different baselines [4.96–4.101]. Some of these techniques evaluate the phase increments between adjacent pixels in multiple co-registered interferograms, thereby taking advantage of the deterministic relation between the baseline length and the phase gradient [4.97]. Other techniques resolve height ambiguities independently for each pixel [4.98], e.g. in an Earth-based coordinate system by using a maximum likelihood approach [4.96]. This offers the opportunity to fuse multiple height estimates acquired in completely different imaging geometries, but requires also a precise knowledge of the remainder phase (more precisely, remainder topographic height) for each interferometric image pair. Still other techniques regard height determination as a direction of arrival (DOA) estimation in a sparse array and apply, for example, model-based spectral estimation techniques to fuse the

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Relative Height Accuracy (Stdv)

Height Error [m]

100.0

10.0

1.0

0.1 250

300

350

400

450

500

550

Ground Range [km] 25

30

35 40 Incident Angle [deg]

45

Figure 4.24 Predicted DEM performance for a semi-active TerraSAR-L cartwheel configuration in combination with absolute ranging. The solid and dashed lines show the interferometric height accuracy for a height of ambiguity of 10 and 100 m, respectively. The dotted line shows the height accuracy obtained from differential ranging

information from multiple SAR images in an unambiguous height estimate [4.99]. Interferometric acquisitions with large baselines may also use a joint multichannel processing to minimize deteriorations from slope-dependent baseline decorrelation [4.100]. These multibaseline techniques can also be combined with differential ranging, which estimates the mutual range shift between corresponding pixels of two complex SAR images [4.102, 4.103]. The height accuracy from such an absolute phase estimation is usually not sufficient for the generation of high-resolution DEMs, but it can be used to resolve residual phase ambiguities in a multibaseline SAR interferometer [4.104]. This is illustrated in Figure 4.24 for the semi-active TerraSAR-L formation with two interferometric baselines. The performance example shows that the height of ambiguity of the small baseline interferogram (hamb = 100 m) remains well below the height estimate obtained by differential ranging with the large baseline. The combination of the two interferograms with differential ranging is hence sufficient to recover the height without phase unwrapping. In this way, it becomes possible to push the DEM performance up to the limits of the critical baseline, which enables powerful SAR interferometers for the acquisition of high-resolution DEMs with a vertical accuracy below 1 m. A suitable satellite formation for such a multibaseline SAR interferometer is the Trinodal Pendulum of Figure 4.8, which acquires all interferometric data in a single pass using the same imaging geometry, thereby enabling an efficient fusion of the SAR image stack in radar slant range geometry. Multiple baseline interferometry has furthermore the potential to resolve phase ambiguities in areas with high vegetation and to solve problems from foreshortening and layover. Further opportunities arise from a joint evaluation of multibaseline coherence, which reflects important characteristica of both volume and surface scatterers. These aspects will be discussed in more detail in Section 4.5.

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Relative Height Accuracy (Stdv) 6

5

5 Height Error [m]

Height Error [m]

Relative Height Accuracy (Stdv) 6

4 3 2

4 3 2 1

1 0 250 25

300

350 400 450 Ground Range [km] 30

35 40 Incident Angle [deg]

500

550 45

0 250 25

300

350 400 450 Ground Range [km] 30

35 40 Incident Angle [deg]

500

550 45

Figure 4.25 Impact of volume scattering on the achievable height accuracy for an effective baseline of 1.2 km (left) and an effective baseline of 6 km (right). The extinction coefficient is 0.2 dB/m and the volume heights are 0 m (solid), 5 m (dashed), 10 m (dashed–dotted) and 20 m (dotted)

4.4.2.4 Volume Decorrelation Figure 4.25 shows an estimate of the impact of volume decorrelation on the relative height error for a typical extinction coefficient of 0.2 dB/m and volume heights of 5 m (dashed), 10 m (dashed–dotted) and 20 m (dotted). The left plot is for an effective baseline of 1.2 km and the right plot is for an effective baseline of 6 km. It is clear that the additional ‘noise’ contribution due to volume scattering depends strongly on the length of the interferometric baseline. While the additional noise contribution is quite small for the 1.2 km baseline, it may almost completely destroy the signal in the case of the 6 km baseline as soon as the volume height exceeds a value of 10 m. The deteriorating effect of volume decorrelation can be substantially reduced by selecting smaller baselines, as provided in the Trinodal Pendulum. Hence, the simultaneous interferometric data acquisition with large and small baselines will help to acquire valuable data over both bare and vegetated areas. It is expected that further information can be gained from a joint evaluation of the interferometric data acquired with different baselines, but this topic clearly deserves further investigation. In homogeneous areas, the impact of volume decorrelation can also be reduced by increasing the size of the independent post-spacing.

4.4.2.5 Polarimetric SAR Interferometry The previous section revealed that volume decorrelation may limit the usefulness of large baseline acquisitions in the case of strong wave penetration into the volume. Polarimetric SAR interferometry (PolInSAR) provides a solution to this problem. It enables a measurement of the ground topography as well as a quantitative retrieval of important biophysical parameters like vegetation height and density [4.21, 4.30, 4.39]. For this, the radar is operated in a fully polarized mode, where the polarization of the transmitted wave is altered between vertical and horizontal polarization from pulse to pulse. The scattered signal is then recorded by all

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MISSION EXAMPLES

Figure 4.26 Single-pass polarimetric SAR interferometry with a microsatellite array

receivers in both polarizations simultaneously, as illustrated in Figure 4.26. The additional use of polarization enables a separation of the effective phase centres from different scattering mechanisms. This is exploited to separate random volume scattering, which has a coherence that is invariant to changes of the wave polarization, from contributions of the underlying ground that have a strong polarimetric signature. PolInSAR is hence well suited for DEM generation since it enables a clear distinction between the Digital Terrain Model (DTM) and Digital Surface Model (DSM), which are both of high interest for a broad spectrum of scientific and commercial applications. Further very promising applications are the detection of buried objects beneath foliage and global biomass estimation [4.105, 4.106]. Figure 4.27 illustrates the achievable performance of a fully polarimetric TerraSAR-L cartwheel configuration (cf. Reference [4.107]). The diagram shows the interferometric height errors as a function of the ground-to-volume scattering ratio corresponding to different polarizations. In this simulation, vegetation scattering has been approximated by the random volume over ground (RVoG) model, which combines the contributions from surface and volume scattering in a coherent scattering model comprising two vertical layers [4.21, 4.30, 4.39]. The dashed line in Figure 4.27 illustrates the variation of the vertical phase centre as a function of the ground-to-volume scattering ratio μ for a vegetation layer with a height of hv = 20 m and an extinction coefficient of β = 0.3 dB/m. It has been computed from [4.21] γ˜vol (w) = exp( jφ0 )

γ˜v + μ(w) 1 + μ(w)

(4.38)

where φ0 is the ground topography phase, μ(w) is the effective ground-to-volume scattering ratio for polarization w and γ˜v denotes the coherence for the volume alone (cf. Section 4.4.1.2). The inner (light grey) tube shows the height errors due to volume decorrelation for an effective baseline B⊥ of 1200 m and 42 independent looks, which corresponds to an independent postspacing of 30 m × 30 m in this example. The middle (dark grey) tube shows additional height errors due to the limited system accuracy of the multistatic SAR polarimeter assuming an illumination by TerraSAR-L. All errors are indicated as ±σ h (standard deviation of the height

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Height Error and Height Bias Lambda: 23.8 cm Baseline: 1200.0 m H_SAT: 629.0 km Theta Inc.: 35.0° NESZ (HH): –23.4 dB Bandwidth: 80. MHz Rg Res: 30.0 m Az Res: 30.0 m Looks: 42.2

15

Δϕ

Height [m]

10

5

0

Δμ

sig0: mu_max: mu_min: Extinction: Vegetation: Kappa_z:

–30

–11.0 dB –2.0 dB –26.0 dB 0.3 dB/m 20.0 m 0.073 rad/m

–20

–10

0

10

20

Ground/Volume Ratio [dB]

Figure 4.27 Vertical separation of interferometric phase centres (ϕ) in a TerraSAR-L single-pass interferometer as a function of the ground-to-volume scattering ratio μ

errors) relative to the vertical phase centre. The darker area of each tube marks the expected range of ground-to-volume ratios μ resulting from mapping a Scots Pine forest scenario with different polarizations at an incident angle of 35◦ [4.105]. The performance analysis predicts a sufficient separation ϕ of the vertical phase centres to enable a successful retrieval of the ground topography and important vegetation parameters like volume height, extinction, etc. For comparison, the outer (dotted) tube shows the expected height errors for a TerraSAR-L repeat-pass mission scenario with a temporal decorrelation of γtemp = 0.5. In this case, there will be a significant overlap of the probability density functions at the left and right borders of the addressable ground-to-volume scattering range. Hence, a substantial performance gain can be expected by using a multistatic single pass SAR interferometer instead of the conventional repeat-pass technique. Multistatic configurations with multiple independent baselines are also of great advantage for polarimetric SAR interferometry. For example, the more detailed analysis in References [4.107] and [4.108] demonstrates the intricate connection of the PolInSAR performance with radar instrument settings, baseline length and volume height. The availability of multiple baselines would hence allow a space-variant selection of those baselines that provide an optimum separation between the vertical phase centres, thereby improving the PolInSAR performance and avoiding phase ambiguities. Further improvements are expected by a joint evaluation of all multibaseline SAR signals, which allows for a more accurate inversion of scattering models where the extinction coefficient varies as a function of volume height [4.90].

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4.5 ADVANCED MULTISTATIC SAR SYSTEM CONCEPTS 4.5.1 SAR Tomography

A constellation of multiple radar satellites recording the scattered signals from a common illuminated footprint can be regarded as a large aperture system with sparsely distributed subaperture elements. The combination of multiple receiver signals can hence be treated in the framework of array processing. A prominent example is SAR tomography, which combines the signals from several receivers to form a sparse aperture perpendicular to the flight direction (e.g. in the elevation plane, cf. Figure 4.28) [4.109–4.113]. This enables a real three-dimensional imaging of semi-transparent volume scatterers such as vegetation, dry soil, sand or ice. SAR tomography has furthermore the potential to resolve SAR image distortions due to layover and foreshortening [4.111, 4.113]. Besides some laboratory experiments, SAR tomography has up to now only been demonstrated by using multiple passes either in an airborne [4.110] or a spaceborne configuration [4.112]. In these examples, major problems arise from temporal decorrelation and unevenly spaced passes, which both limit the achievable performance and require a sophisticated processing to avoid high sidelobes in the tomographic response. Pendulum-like satellite formations, as shown in Figure 4.8, are well suited to overcome such limitations by providing multiple baselines with a precisely adjustable baseline ratio in a single pass. Further advantages of single-pass multistatic data acquisitions are improved baseline knowledge, no distortions due to scatterer movements, the cancellation of atmospheric disturbances and better predictability of the noise level within each channel, thereby improving the inversion performance significantly. The minimization of such disturbances becomes even more important, as advanced SAR tomography techniques try to incorporate more and more a priori information in the multibaseline inversion process in order to increase, for example,

1 2 .. N-1 N

z

n L

r

x y

Figure 4.28 Flight geometry for SAR tomography. A multistatic configuration consisting of several microsatellites flying in formation can be used in the case of a spaceborne system realization.

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the resolution beyond the Rayleigh limit given by the maximum baseline length (an extreme example is conventional DEM generation, which assumes exactly one vertical layer within each resolution cell). For generating a tomographic image, first the individual SAR images acquired in a multipass or single-pass geometry need to be processed. The co-registration of the images must be performed with subpixel accuracy and precise phase preservation is required, including the accurate correction of possible motion errors. In a second step the tomographic processing is performed by a coherent combination of the images in order to form a synthetic aperture in the elevation plane. The synthetic aperture consists of N points and has a total extension of L (cf. Figure 4.28). While the synthetic aperture length defines the tomographic resolution, the distance between the individual passes determines the unambiguous volume height to be imaged [4.110]. Typical numbers for N range between 6 and 15. Due to the low number of points, time-domain processing can be adopted for the tomographic processing. Alternatively, the SPECAN (spectral analysis) approach can also be used if an interpolation to equalize the distance between the passes has been performed prior to the deramping and fast Fourier transform (FFT) operations. A tomographic experiment has been performed in 1998 using fully polarimetric L-band data of the airborne E-SAR system of DLR [4.110]: 14 tracks were flown by the E-SAR system with a nominal spacing of 20 m, which is required for an unambiguous tomographic imaging up to ca. 35 metres. The tomographic synthetic aperture was ca. 240 metres, leading to a height resolution of ca. 3 metres. The temporal decorrelation between the images was very small, showing a coherence higher than 0.9, even over forested areas. Investigations of a spruce forest area reveal the potential of SAR tomography, especially in combination with polarimetry. As shown in Figure 4.29, the following contributions can easily be distinguished: (a) dihedral scattering with a phase centre at a height of ca. 5 metres due to the ground and stem interaction (clearly seen in the HH-VV channel of the Pauli decomposition) and (b) random volume scattering in the crowns (dominant in HV polarization). The separation

HV 40

30

30 Height [m]

Height [m]

HH-VV 40

20 10 0 –10 –8

20 10

–6

–4

–2

0

Backscattering [dB]

2

4

0 –12 –10

–8

–6

–4

–2

0

2

Backscattering [dB]

Figure 4.29 Distribution of backscatter intensity versus height for a spruce forest in different polarizations (HH-VV and HV). The plot on the left shows the strong reflection at ca. 5 m height caused by the double bounce scattering due to the interaction between the tree trunk and ground (observed in the HH-VV channel of the Pauli representation). On the right the dominant reflection of the canopy observed in the cross-polarization channel (HV+VH) is recognized

ADVANCED MULTISTATIC SAR SYSTEM CONCEPTS

• 139

of the scattering centres in height between the ground and canopy also gives a good indication of forest height (ca. 20 m) and the height of the crown above ground, and indicates no presence of understory for this forest type. Several other tomographic plots of deciduous and mixed forests have shown that the canopy can generally be assumed to be a random volume at the L-band, confirming the model used for height retrieval with the polarimetric SAR interferometric technique in Section 4.4.2.5. Today’s research work concentrates on the reduction of the number of acquisitions, e.g. by means of spectral estimation techniques [4.114–4.116]. Further research is being performed towards the spaceborne implementation of tomography, e.g. in connection with the interferometric cartwheel or Trinodal Pendulum. With the selection of proper orbit configurations, three or four microsatellites in a repeat-pass scenario can acquire suitable tomographic data after two or three revisit cycles of the satellites. The effect of the temporal decorrelation in this acquisition scenario related to the selection of the optimal baselines is also a research topic. Tomographic techniques can moreover be combined with applications from cross-track interferometry. One example is layover resolution in conjunction with multibaseline DEM generation. This enables data takes with steep incident angles, thereby increasing the SNR and avoiding DEM voids due to shadows. Steep incident angle imaging is also of high interest for urban environments and deep valleys. The first steps in this direction have already been made in Reference [4.113], but further work is required to apply such techniques to a realworld environment with, for example, multipass effects in urban areas, uneven satellite orbit spacing, unknown number of layover layers, etc. Additional baselines for the layover solution can also be acquired with multiple passes, but the spatiotemporal processing should then clearly differentiate between the errors from the highly coherent single-pass acquisitions and the less-coherent repeat-pass acquisitions to optimize the performance.

4.5.2 Ambiguity Suppression and Resolution Enhancement Another opportunity of a sparse satellite array is the formation of very narrow antenna beams to enhance the geometrical resolution and to suppress range and azimuth ambiguities during the SAR image generation [4.78, 4.117–4.120]. This will in turn lead to a reduction in the required antenna size for each receiver, thereby enabling cost-effective and powerful SAR missions with wide coverage and high resolution. The opportunity for high-resolution wide-swath SAR imaging avoids conflicts from operating SAR systems in mutually exclusive imaging modes like ScanSAR, Stripmap and Spotlight. This enables in turn regular observations of large areas, satisfies a wider user community and facilitates mission planning. A further potential is efficient interference suppression, which will become more and more important as the congestion of the frequency spectrum by an ever-rising number of different users increases continuously. Sparse array beam-forming in a multistatic configuration could moreover be combined with digital beam-forming within each receiver. This combination of small and large array beam-forming is well suited to improve the performance further [4.3, 4.118]. An additional performance gain can be achieved by using nonseparable and/or orthogonal waveforms on transmit in combination with digital beam-forming on receive [4.79]. One example for a multistatic sparse aperture system is shown in Figure 4.30 on the upper left, where a single transmitter (Tx) illuminates a wide image swath and n passive receivers (Rx) record simultaneously the scattered signal from the illuminated footprint. Such a system

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Rx 2

Rx 1

Tx

0

v

Amplitude [dB]

Rx 3

–10 –20 –30 –40 –50

PRF

0 50 Along Track Position [km]

h1(t; Δ x1) h2(t; Δ x2) h3(t; Δ x3)

Reconstruction & SAR Processing

Amplitude [dB]

0 –10 –20 –30 –40 –50

0 50 Along Track Position [km]

Figure 4.30 Azimuth ambiguity suppression with multistatic SAR. Upper left: satellite configuration with along-track displacement between the receivers. Lower left: multichannel model of the data acquisition by multiple receivers. Upper right: azimuth response for one receiver. Lower right: azimuth response after the coherent combination of all receiver responses

is well suited to overcome the fundamental ambiguity limitation of conventional monostatic SAR systems where the unambiguous swath width and the achievable azimuth resolution pose contradicting requirements in the system design process. This becomes possible by a coherent combination of the individual receiver signals, which allows for a reduction of the PRF by a factor of n without raising azimuth ambiguities [4.78]. The reduced azimuth sampling rate will then enable the mapping of a wide image swath with high azimuth resolution. For optimum performance, the along-track displacement of the passive receivers i = {2, . . ., n} relative to the first receiver (i = 1) should be chosen as 2v i −1 xi − x1 ≈ (4.39) + ki , ki ∈ Z , PRF n where PRF is the pulse repetition frequency of the transmitter and v is the velocity of the SAR carrier. Note that the use of different ki for each satellite gives a great flexibility in selecting the along-track distance between the receivers. The data acquisition in such a multiple-aperture SAR can be modelled by a linear system with multiple receiver channels (cf. Figure 4.30, lower left). Each channel corresponds to a linear filter hi (t) which can be derived from the bistatic azimuth impulse response of a point target: 2π h i (t; xi ) = ATx (vt) ARx,i (vt) exp −j r02 + (vt)2 + r02 + (vt − xi )2 , (4.40) λ

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where λ denotes the wavelength, r0 is the slant range and xi corresponds to the along-track displacement between receiver i and the transmitter. The functions ATx and ARx define the envelope of the azimuth signal arising from the projection of the transmit and receive antenna patterns on the ground. For such a multichannel system a lot of powerful theorems exist in linear systems theory. Of special importance for the present context is a generalization of the sampling theorem according to which a band-limited signal u(t) is uniquely determined in terms of the samples hi (nT) of the responses hi (t) of n linear systems with input u(t) sampled at 1/n of the Nyquist frequency [4.121]. In order to be valid, the transfer functions of the linear filters may be selected in a quite general sense, but not arbitrarily (for details, see Reference [4.121]). The reconstruction consists essentially of n linear filters Pi (f) which are individually applied to the subsampled signals of the receiver channels and then superimposed. Each of the reconstruction filters Pi (f) can again be regarded as a composition of n bandpass filters Pi j (f), where 1 ≤ j ≤ n. As shown in Equation 4.42, the reconstruction filters can be derived from a matrix H(f) consisting of the n transfer functions Hi (f), which have to be shifted by integer multiples of the PRF in the frequency domain: ⎡ ⎢ ⎢ H( f ) = ⎢ ⎢ ⎣

H1 ( f )

...

Hn ( f )

H1 ( f + PRF) .. .

... .. .

Hn ( f + PRF) .. .

H1 ( f + (n − 1) PRF) . . .

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

(4.41)

Hn ( f + (n − 1) PRF)

The reconstruction filters Pi j (f) are then derived from an inversion of the matrix H(f) as ⎡

P11 ( f )

⎢P ( f ) ⎢ 21 H (f) = ⎢ ⎢ .. ⎣ . Pn1 ( f ) −1

P12 ( f + PRF) P22 ( f + PRF) .. .

... ... .. .

⎤ P1n ( f + (n − 1) PRF) P2n ( f + (n − 1) PRF)⎥ ⎥ ⎥ .. ⎥ ⎦ .

Pn2 ( f + PRF)

...

Pnn ( f + (n − 1) PRF)

(4.42)

As an example, consider an L-band system with three passive receivers (cf. Table 4.8). Note that the short antennas will enable an azimuth resolution in the order of 3 m while the low PRF allows for the unambiguous mapping of a wide image swath with a lateral extension of more than 100 km. The upper right-hand side of Figure 4.30 shows the processed azimuth response of a single receiver to a point scatterer located at an along-track position of 0 km. The response is highly ambiguous in azimuth with strong spurious responses at x = k PRF r0 λ/(2v) = {−37.0 km, −18.5 km, 18.5 km, 37.0 km}, which result from the short antenna length in combination with the low PRF. The lower right-hand side of Figure 4.30 shows the azimuth response after a coherent combination of the three receiver signals. Note that, in this simulation, the three receivers have a nonoptimum along-track displacement with slightly different Doppler centroids. Furthermore, independent white noise has been added to each receiver channel in order to simulate a more realistic scenario. It becomes clear that all ambiguities are now well suppressed to a level below −20 dB, which corresponds to the ambiguity level of a single satellite with a threefold PRF value (cf. the third ambiguity in the upper right plot of Figure 4.30). The previous simulation illustrated the potentials of a sparse satellite array for the unambiguous mapping of a wide image swath with high azimuth resolution. Note that the reconstruction

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SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS Table 4.8 System parameters of a distributed SAR for high-resolution wide-swath imaging Wavelength Antenna length (Tx) Antenna length (Rx) PRF Displacement (Rx 1) Displacement (Rx 2) Displacement (Rx 3) Slant range Satellite velocity Processed bandwidth SNR

24 cm 5m 5m 1350 Hz 400 m 800 m 1200 m 800 km 7 km/s 3750 Hz 20 dB

algorithm also includes the case of super-resolution in azimuth where multiple receivers record the scattered SAR signal with different Doppler centroids. This can be regarded as a bandpass decomposition of the SAR signal where each branch in the system model of Figure 4.30 contains a narrow-band filter with no (or only partial) spectral overlap between adjacent channels. The achievable resolution is then given by the combined Doppler bandwidth from all receivers. The small Doppler bandwidth for each individual receiver requires, of course, more extended antennas than is required in the ambiguity suppression case. Both techniques can jointly be treated in the framework of multichannel signal processing where they mark the extremes of a continuous range of potential multistatic system configurations for high-resolution, wide-swath SAR imaging. A coherent combination of multiple SAR images acquired from different incident angles can also enhance the geometric resolution in range [4.5, 4.122]. This super-resolution technique may be regarded as the formation of narrow beams in elevation which divide each resolution cell into multiple sub cells. The accurate combination of the individual receiver signals requires topography information that could, in principle, be acquired during the same pass in a multisatellite configuration. Multiple SAR images with sufficient view angle separation can furthermore be combined incoherently to reduce speckle and to improve thereby the radiometric resolution without any loss of spatial resolution. Such techniques are of high interest to alleviate the bandwidth limitations for spaceborne SAR sensors posed by international frequency regulations. Range and azimuth ambiguity suppression can moreover be combined with multibaseline SAR interferometry or tomography [4.3]. This enables compact and highly reconfigurable multistatic SAR systems for a wide range of remote sensing applications. For this, it becomes necessary to consider the complete three-dimensional signal focusing from raw data, and not, as usually done in SAR interferometry and tomography, only the one-dimensional operator applied to the stack of range and azimuth focused SAR images. Further investigations are required to exploit fully the potentials of such distributed SAR systems based on small antennas.

4.5.3 Multistatic SAR Imaging A multistatic SAR is an efficient means of acquiring multiple SAR images with different viewing geometries in a single pass, thereby increasing the observation space considerably (Figure 4.31). The combined information from multistatic SAR data takes facilitates the

ADVANCED MULTISTATIC SAR SYSTEM CONCEPTS

Tx

• 143

Rx

φ

Figure 4.31 Extended observation space in multistatic SAR

detection, classification and recognition of both natural and artificial objects [4.123, 4.124]. Multistatic SAR observations are furthermore of great interest for measurements of surface and vegetation parameters [4.125, 4.126]. The ONERA-DLR bistatic SAR experiment (cf. Chapter 5) revealed that even small bistatic angles may already cause a notable change in the scattering behaviour in both natural and artificial environments [4.69]. A joint evaluation of mono- and bistatic SAR images could also be used to isolate different scattering mechanisms, such as a distinction between highly directive dihedral returns from more isotropic volume scattering. Such bi- and multistatic scattering profiles could further be augmented with interferometric information. The evaluation of multistatic SAR data can moreover use indirect information, e.g. systematic variations of the shadow pairs seen by each bistatic receiver [4.69, 4.72]. Additional potentials arise for and from radargrammetry [4.127]. Radargrammetric measurements can even be used in combination with interferometric data, e.g. for calibration purposes. Multistatic SAR data acquisitions are also well suited to localize and track small objects in three-dimensional space [4.128]. A further potential arises from the fact that the bistatic imaging geometry allows for the acquisition of high-resolution SAR images with nadir-looking receivers. This enables a simultaneous data acquisition of the same area with other remote sensing instruments like altimeters, lidars or optical/hyperspectral sensors. The data from the various sensors can then be combined for such different purposes as DEM calibration, orthorectification or multisensor object and scene classification.

4.5.4 Along-Track Interferometry and Moving Object Indication Multistatic SAR satellite formations are predestinated for large baseline along-track interferometry (ATI), which compares the phase of two or more complex SAR images acquired in identical geometries but separated by short time intervals [4.18, 4.55, 4.56, 4.129–4.131]. This technique is well suited for monitoring dynamic processes. A prominent ATI application is the measurement of ocean and tidal currents. Large along-track baselines are required for accurate measurements of slow movements, while short baselines are required to avoid temporal decorrelation and ambiguities in the case of higher velocities. Hence, an acquisition with multiple along-track baselines would be of great help to resolve ambiguities, thereby enabling improved and more accurate measurements over a wide spectrum of potential scatterer velocities [4.129, 4.131]. Additional along-track baselines may be provided by multiple antennas on each receiver (cf. Figure 4.32) or by increasing the number of satellites. Multistatic formations with

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short baseline ( t ≈ 0.2 ms)

long baseline ( t ≈ 10-200 ms)

split antenna

HELIX

sensitive to fast movements

sensitive to slow movements

Figure 4.32 Along-track interferometry with TanDEM-X. The helix orbit concept allows a flexible adjustment of the desired along-track separation between the satellites. In addition, a short along-track baseline is provided by each satellite

three or more satellites are also well suited for the reliable detection, localization and velocity estimation of slowly moving objects on the ground [4.132–4.135]. Due to the large and potentially nonuniform separation between the individual receiver satellites, efficient clutter suppression may be achieved, which allows for the detection and localization of even weak scatterers with a low signal-to-clutter ratio. The large receiver separation enables highly accurate velocity estimates and mitigates the problem of blindness against certain directions of scatterer movement. This is of high importance for future spaceborne traffic monitoring systems [4.136, 4.137].

4.5.5 Multibaseline Change Detection Further opportunities arise from a comparison of several multistatic data sets acquired during different passes of the satellite formation. For example, the combination of single-pass and repeat-pass interferograms will have great potential for such different applications as the detection of the grounding line that separates the shelf from the inland ice, monitoring of vegetation growth, mapping of atmospheric water vapour with high spatial resolution, measurement of snow accumulation or detection of anthropogenic changes of the environment, e.g. due to deforestation. Note that most of these combinations rely on a comparison of two or more single-pass (large baseline) cross-track interferograms and therefore do not necessarily require coherence between the different passes (cf. Figure 4.33). Further information may be gained from an evaluation of coherence changes between different passes, potentially augmented by polarimetric information. This may, for instance, reveal even slight changes in the soil and vegetation structure, reflecting vegetation growth and loss, freezing and thawing, fire destruction, human activities and so on. Note again that such measurements do not necessarily require temporal coherence between the interferometric data takes. The information space of a multipass sparse aperture SAR may further be increased by varying some system and/or instrument parameters between the different passes. One example is a PolInSAR system which acquires the interferometric data in a single pass and the different polarizations in subsequent passes. This ensures high coherence within the interferometric channels while simplifying the mission design [4.107]. Another example is a systematic change

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DISCUSSION

Relative Height Accuracy (Stdv)

Height Error [m]

ϕ1

ϕ2

h < 10 cm

Ground Range [km]

Δ h ~ ϕ2 – ϕ1

Incident Angle [deg]

Figure 4.33 Performance example for double differential SAR interferometry with TanDEM-X (crosstrack baseline = 3000 m, posting = 12 m)

of the viewing geometry between different passes. This is well suited to resolve errors during DEM generation in mountainous terrain where steep slopes cause foreshortening, layover and shadows [4.138]. SAR interferograms from different passes can furthermore be used to calibrate interferometric data acquisitions, e.g. by block adjustment from crossing orbits. Bi- and multistatic data acquisitions are also well suited to separate the topographic (and in some cases also the atmospheric) phase from scatterer movements between different passes, thereby facilitating highly accurate measurements of even small terrain and object displacements [4.13, 4.23, 4.31]. Single-pass acquisitions with large cross-track baselines could moreover help to resolve ambiguities from nonlinear scatterer displacements and have the potential to reveal movement vectors in three dimensions. Further potentials arise from differential tomography, which combines differential interferometry with multibaseline SAR tomography [4.139].

4.6 DISCUSSION The previous sections revealed the great potential of multistatic SAR satellite formations for a wealth of powerful remote sensing applications. Most of these applications require close satellite formations. Hence, orbit selection and collision avoidance becomes an important design driver. Safe operation may be achieved by autonomous control [4.56]. An alternative is a slight modification of the satellite formation such that the orbits have a small vertical separation at the intersection of the orbital planes. As discussed in Section 4.3.1.1, this results in a helix-like movement without orbit crossing and the satellites may now be shifted arbitrarily along their individual orbits. This enables the adjustment of very short along-track baselines which are, for example, desired in the case of DEM generation to avoid residual temporal decorrelation for some types of vegetation, or for interferometric data acquisitions of the ocean surface. The opportunity for safe satellite operation in close formations allows, moreover, for

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a closer distance between the transmitter and the passive receivers in a semi-active cartwheellike constellation, thereby increasing in the coherent data space with monostatic SAR images from the transmitter. Besides the provision of additional cross-track baselines, this may also be exploited for large baseline along-track interferometry, which has a high potential for the observation of large-scale dynamic processes like sea ice drift. Ambiguities can then be resolved by the additional short along-track baselines within the receiver formation. Many applications demand very precise relative position sensing of the satellites. An example is cross-track interferometry where a relative three-dimensional position sensing error of 1 cm may cause (in the worst case) an interferometric phase error of up to 116◦ in the X-band and up to 15◦ in the L-band. Close satellite formations enable a highly accurate measurement of the relative satellite positions by evaluating GPS differential carrier phase signals [4.94]. This improves the baseline knowledge by at least one order of magnitude if compared with the difference of independently estimated orbit state vectors used in conventional repeat-pass interferometry. Since formation flying satellites are moreover exposed to highly correlated orbit perturbations, it becomes possible to reduce further the impact of residual baseline estimation errors [4.140]. Close formations also allow a precise adjustment of the intersatellite baselines as required by many interferometric and tomographic applications. Such a baseline adjustment is orders of magnitude less sensitive to slight changes in gravitational forces than the fuel consuming baseline control in repeat orbits. A further challenge is phase and time synchronization. As discussed in Section 4.3.2, phase errors may cause a time-variant shift, spurious sidelobes and a broadening of the bistatic SAR impulse response, as well as phase errors in the focused signal. Hence, appropriate calibration strategies are required to avoid such errors, especially in the case of interferometric data acquisitions. One solution is a bidirectional phase synchronization link between each receiver pair, e.g. by radiating the USO signal [4.75] or by transmitting dedicated RF pulses as implemented in the TanDEM-X mission [4.10]. The use of higher synchronization frequencies has the advantage of minimizing potential errors from the ionosphere. Fully active systems may also evaluate the scattered signals from the common illuminated footprint, either by switching the transmitter from pulse to pulse (cf. Section 4.3.3.3) or by a simultaneous transmission of orthogonal waveforms (e.g. different RF sub-bands, cf. Section 4.3.3.4), thereby avoiding the necessity of dedicated antennas for phase referencing. An alternative is the use of oscillators with significantly improved longterm stability [4.73] in combination with a sparse net of calibration targets. Phase errors in multistatic SAR can be further reduced by comparing the signals from multiple baselines, analyzing multiple azimuth looks, comparing the azimuth shift between monostatic and bistatic SAR images, and evaluating the signals from multiple passes. Absolute DEM calibration could furthermore take advantage of large baseline stereogrammetric radar data acquired in repeat passes (e.g. by evaluating monostatic data with large incident angle differences). Such data are then well suited to eliminate low-frequency height errors caused by both insufficient oscillator synchronization and limited baseline estimation accuracy. The focusing of bi- and multistatic SAR data with large bistatic angles requires new processing algorithms. The first promising steps in this direction have already been achieved (see, for example, References [4.141] to [4.146] and chapters). Note that nonparallel satellite trajectories and/or different velocities may cause different range–Doppler histories for each point on the ground, thereby leading to a nonstationary translationally variant data acquisition in the along-track direction (cf. taxonomy in Reference [4.147]). New processing algorithms are also required to take full advantage of the multiple monostatic and bistatic SAR data sets

ABBREVIATIONS

• 147

acquired in multistatic satellite configurations. The combination of the recorded signals may be either linear, as in three-dimensional imaging tomography, ambiguity suppression or superresolution, which are (essentially) based on a weighted superposition of the signals from the individual array elements or nonlinear as in the various interferometric modes that evaluate the conjugate product of two or more SAR images. In order to take full advantage of the recorded data from multiple satellites it would be highly desirable to develop a generalized processing scheme that combines the various interferometric and array processing techniques in a unified framework. As an example, consider the multistatic sparse aperture SAR for high-resolution wide-swath imaging in Section 4.5.2 where any cross-track separation of the receivers introduces topography-dependent phase offsets between the received signals. Successful ambiguity suppression will then require a compensation of these phase offsets, e.g. via the simultaneous acquisition of a DEM. This approach leads to a combination of linear along-track ambiguity suppression with second-order cross-track interferometry, thereby enabling the use of smaller satellites with reduced antenna size without increasing the ambiguity level [4.3, 4.78]. A further challenge arises from the huge amount of data collected by multiple independent apertures. This will require broadband data links and/or appropriate data reduction strategies, e.g. by onboard preprocessing that exploits redundancies between the different channels. The redundancies can, for example, be reduced by an appropriate bit-allocation in a threedimensional ‘information cube’, where the three axes correspond to range time, azimuth frequency and spatial direction of the recorded signals. Optimized data compression algorithms may be derived from information theory by applying the general concept of rate distortion analysis to multichannel SAR systems [4.148]. Another possibility is the direct and selective parameter retrieval. This immediate and nonreversible data reduction would facilitate a data distribution directly to the users. One remaining factor for the successful implementation of multistatic SAR configuration in space is the associated system costs. The opportunity to distribute the required functionality on multiple satellites will have several advantages, like low-cost mass production due to the minimization of recurrent costs, greater system reliability due to graceful degradation and lower launch and manufacturing costs by taking advantage of microsatellite technology. A further aspect is the scalability by a phased deployment of the spacecraft. This allows for a distribution of the costs over a longer period of time, reduces the risk of a total mission failure and increases the flexibility by enabling a fast adaptation to changing threats or user requirements. A cost–benefit analysis has to take into account all these aspects when comparing single-satellite SAR missions with multifunctional satellite formations. The new techniques and concepts summarized in this chapter may be regarded as a first step in a paradigm shift from traditional monostatic SAR systems towards highly reconfigurable satellite constellations for a broad range of powerful remote sensing applications.

ABBREVIATIONS ATI BAQ DEM DLR DSM DTED

along-track interferometry block adaptive quantizer Digital elevation model Deutsches Zentrum f¨ur Luft- und Raumfahrt (German Aerospace Centre) Digital surface model digital terrain elevation data

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DTM ESA GMTI HH HRTI HRWS InSAR IRF LEO NIMA ONERA PolInSAR PRF RF SAR SRTM TanDEM-X TechSAT21 TRM USO VV XTI

SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS

digital terrain model european space agency ground moving target indication polarization with horizontal transmission and horizontal reception high-resolution terrain information high-resolution wide-swath interferometric SAR impulse response function low Earth orbit National Imagery and Mapping Agency, USA ´ Office National d’Etudes et de Recherches A´erospatiales polarimetric SAR interferometry pulse repetition frequency radio frequency synthetic aperture radar shuttle radar topography mission TerraSAR-X add-on for digital elevation measurements technology satellite of the twenty-first century transmit receive module ultra-stable oscillator polarization with vertical transmission and vertical reception cross-track interferometry

Variables a AASR Ai , Bi , αi , βi ATx , ARx Bproc Brg B⊥ B⊥,crit c0 dalong e E[] f osc fT, fR f0 F F G Tx , G Rx h amb h sat hv

semi-major axis of the elliptical orbit (m) azimuth ambiguity-to-signal ratio amplitude and phase of relative satellite movement in Hill’s frame effective area of transmit and receive antennas (m2 ) processed azimuth bandwidth (Hz) bandwidth of the chirp signal in range (Hz) baseline perpendicular to the line of sight (m) critical baseline (m) velocity of light (2.998 × 108 m/s) along-track displacement between receiver satellites (m) eccentricity vector expectation operator nominal oscillator frequency (Hz) frequencies of transmit and receive oscillators (Hz) radar carrier frequency (Hz) system noise figure Gauss hypergeometric function gain of transmit and receive antennas height of the ambiguity (m) satellite height (m) volume height (m)

ABBREVIATIONS

ISLR i k L m n NESZ PTx PRF re r0 RASR Sϕ , Sϕa , Sϕb SNR SQNR Ta Tc Tsys T0 vgrd vsat xi , yi , z i α β γAmb γAz γCoreg γGeo γQuant γSNR γtot γ˜Temp γ˜vol

δr δrg δaz δx δy f h r rg , az s ϕ θi λ μ σa

integrated sidelobe ratio inclination (rad) Boltzman constant (1.38 × 10−23 J/K) system losses frequency up-conversion factor number of looks noise equivalent sigma zero peak transmit power (W) pulse repetition frequency (Hz) Earth radius (m) slant range (m) range ambiguity-to-signal ratio one-sided power spectral density of oscillator noise (rad2 /Hz) signal-to-noise ratio signal-to-quantization noise ratio azimuth integration time (s) temporal distance between control points for phase synchronization (s) system temperature (K) orbital period (s) beam velocity on the ground (m/s) satellite velocity (m/s) coordinates in Hill’s frame (radial, along-track, cross-track) (m) local slope angle (rad) extinction coefficient (neper/m) coherence from ambiguities coherence from the relative Doppler shift coherence from co-registration coherence from baseline decorrelation coherence from quantization coherence from the signal-to-noise ratio total coherence coherence from temporal decorrelation coherence from volume decorrelation gamma function range resolution (m) ground range and azimuth resolution (m) independent post-spacing in the ground range and azimuth (m) difference between the transmit and receive oscillator frequencies (Hz) DEM height difference (m) range difference (m) displacement in the range and azimuth (m) swath width (m) interferometric phase difference (rad) incident angle (rad) wavelength (m) ground-to-volume scattering ratio Allan standard deviation

• 149

• 150

σQ σx σ0 τ τp ϕT (t), ϕR (t) ϕ90 %

SPACEBORNE INTERFEROMETRIC AND MULTISTATIC SAR SYSTEMS

standard deviation of the quadratic phase error (rad) standard deviation of the azimuth displacement (m) normalized scattering coefficient radar signal delay time (s) pulse duration (s) phase noise of transmit and receive oscillators (rad) 90 % confidence interval for the phase error (rad) right ascension of the ascending node (rad)

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5 Airborne Bistatic Synthetic Aperture Radar Pascale Dubois-Fernandez, Hubert Cantalloube, Bernard Vaizan, Gerhard Krieger and Alberto Moreira

5.1 BISTATIC AIRBORNE SAR: OBJECTIVES The bistatic SAR imaging configuration is characterized by an increased technological complexity compared to the more straightforward monostatic case. Nevertheless, the resulting enhanced imaging capabilities may well be worth this additional complexity. The bistatic configuration can be an attractive alternative considering the following civilian and military applications:

r For providing more diversity in the analysis of the radar cross-section and Doppler characteristics of a target. Bistatic geometry is characterized by an extra degree of freedom in remote sensing observation of natural and man-made targets and is also essential to counter stealth target design associated with low monostatic radar cross-section (RCS).

r For providing a lower detectability of the receiving platform as it transmits no power while the active part may be placed in a stand-off position.

r For cost purposes, by sharing the expensive transmitter part of the system among several receivers. The bistatic synthetic aperture radar can be an efficient design when simultaneous imaging of the same scene with different geometries is required. The active part of the system, which is in general the most expensive one, is then concentrated on one platform and the geometry diversity is reached by distributing the multiple receiver systems. As an illustration, a series of applications can be listed where a bistatic configuration could prove to be useful: cross-track interferometry for DEM generation or three-dimensional imaging, along-track interferometry for seacurrent mapping and, bistatic radar cross-section analysis for surface characterization [5.1–5.3]. Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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Among the potential applications, the global Digital Elevation Model (DEM) generation based on cross-track interferometry was extensively demonstrated with ERS-1 and ERS-2 data [5.4–5.6]. Two images acquired at different times and with slightly different geometry are used to create an interferogram, the phase of which is related to the pixel elevation and the temporal changes in the scene. If the temporal changes are significant, the elevation information is perturbed. Simultaneous acquisitions of the two images will then guarantee that the true pixel elevation can be retrieved [5.7–5.11] as in the SIR-C/X-SAR SRTM mission [5.12], which provided a global Earth DEM by using two antennas. However, the distance between the two antennas needs to be sufficient to provide a satisfactory height resolution in the case of DEM generation. The SIR-C/X-SAR SRTM mission on board the space shuttle Endeavour had a 60 m long mast to provide for this antenna separation. This option is not realistic for the typical spaceborne SAR altitude, where an equivalent mast (for the same height resolution) would have to be more than twice as long. Putting two radar systems in orbit on two different platforms is then the only option. To avoid interference problems and as a less costly alternative to two fully active radar systems, only one may be active, the other one being in a passive configuration, thus concentrating the active part on one platform as it is the major cost contributor [5.13]. An airborne bistatic constellation can be attractive as well as it provides opportunity for observation diversity, for improved stealth target detection and for imaging capacity involving a forward-looking radar on one platform. Innovative concepts have been proposed where radars in space illuminate a large portion of the Earth and the receiving radars are either on airplanes or on low orbiting satellites, acquiring images on demand [5.13]. The costly part of the radar is then shared among many users. A bistatic imaging SAR constellation (airborne, spaceborne or dual) is promising but raises a complete range of new technological challenges. In order to apprehend these challenges and test the potential of the bistatic configuration in the wide range of possible applications, airborne experiments are an essential step as they provide a unique opportunity to evaluate technical solutions or choices before the final design of the operational mission. Such experiments are nevertheless complex as they require two compatible radar systems and two airplanes. Airborne bistatic SAR experiments can also be needed as a demonstrator to an operational airborne system, a spaceborne system or a dual system (space- and airborne). The goals are then to identify and solve some of the challenges associated with the bistatic mode of operation.

5.2 AIRBORNE BISTATIC SAR CONFIGURATIONS The geometry of monostatic SAR configurations can be derived in a rather straightforward way: most often, a side-looking observation is considered, as this leads to optimal synthetic antenna generation, but on some occasions a squinted pointing may also be needed. This could be driven by coverage aspects or because a SAR mode has to be operated from a nose implemented forward-looking radar. Also, it is well known that no SAR effect may be generated when looking in the direction of the platform velocity vector. Now, with two cooperative platforms in a bistatic configuration, the potential combination of geometrical arrangements is much wider. In fact, both the platform initial positions and their velocity vectors may be selected independently. Of course, not all of these configurations are of equal interest, the associated SAR performance, especially resolution and SNR, being highly variable.

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Flexibility in the choice of bistatic SAR configurations is also constrained by visibility considerations: first, the area of interest must be within the visibility of the two platforms. This has to be carefully considered, especially in the case of large bistatic angles. Second, the antenna footprints of both platforms must provide sufficient overlap during the data take over a period corresponding to at least the requested integration time. Third, the bistatic configuration should also take into account the reduced visibility arising from two shadows as opposed to one shadow in a monostatic configuration. It is obvious that time-invariant configurations, i.e. configurations where both platforms have the same constant velocity vectors, greatly mitigate the beam constraints, but more complex trajectories may be needed resulting from operational considerations. In Section 5.2.4, some of these configurations will be qualitatively illustrated to give an insight of the expected performance. No mathematical development, such as resolution formulae, will be inserted here since this may be found with a lot of detail in other chapters of this book.

5.2.1 Time-Invariant Configurations Time-invariant configurations are configurations where both platforms have the same constant velocity vectors. This implies that the platforms fly on parallel tracks with the same constant speed during the whole data take. A further implicit assumption is that the antenna beams are not changing during the data take. As a result, the imaging geometry is translationally invariant along the velocity vector, which allows for the application of efficient processing algorithms. In the following, two examples for such configurations will be considered in more detail. 5.2.1.1 Along-Track Time-Invariant Configuration As a first example a configuration is considered where the two platforms fly one behind the other on the same track, imaging the scene in the stripmap mode. Some freedom is given to the pointing direction of the two antennas, which has a direct impact on the Doppler centroid. For example, a symmetric pointing geometry may be used where the antenna footprints overlap over the median of the two aircrafts. This results in a zero Doppler centroid. Another possibility is to use a perpendicular illumination from the transmitter and to steer the receiving antenna to this footprint. Such a squinted geometry may cause high Doppler centroids for large alongtrack displacements between the aircraft. An investigation of the latter configuration is also of high interest for spaceborne applications. For example, the cartwheel concept (cf. Chapter 4) augments a conventional SAR mission by additional receive-only satellites flying in close formation. This enables, besides other powerful applications, the generation of accurate digital elevation models. For safety reasons, an along-track separation of several tens of kilometres will be required between the transmitter and the passive receivers. Since the transmitter is usually operated in a boresight illumination mode, this results in rather high Doppler centroids of several thousand hertz. The potential impact of such an additional Doppler centroid on bistatic and interferometric SAR processing can then be investigated by an airborne experiment with a time-invariant along-track configuration. Additional satellite movements within the receiver formations like the interferometric cartwheel [5.14] or the cross-track pendulum [5.11] can usually be neglected, since their evolution is slow with respect to the typical SAR integration time. In the above cases, the along-track separation between the main platform and the receiver satellites is mainly required for safety reasons and is not exploited as such. However, it is also

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of interest to adjust the along-track baseline for interferometric processing. In particular, alongtrack interferometry (ATI) SAR modes may be optimized. In such modes, two SAR images are formed from the two antenna phase centres and the interferometric phase is computed. Any moving element in the scene (such as sea currents) in the time interval for the two phase centres virtually to coincide will generate a phase difference proportional to the radial velocity component. Such ATI configurations may also be available from a single platform, e.g. through antenna partitioning, but then the phase centre separation is at best a few metres, which may be insufficient for accurate measurements. Maximum separation constraints also exist, induced by the need to preserve both angular coherency (the so-called critical baseline constraint, similar to that of the cross-track interferometry case for height estimation) and temporal coherency due to scatterer internal motion [5.15, 5.16].

5.2.1.2 Across-Track Time-Invariant Configuration In this case, the two platforms fly along two parallel tracks (the same or different altitudes) at the same speed. The simplest configuration is a side-looking implementation for the two radars, and the bistatic angle is obtained in the vertical plane through a difference between the respective local incidence angles. Such a configuration might be motivated by the need to put a vulnerable and easily detectable emitting platform in a safe stand-off position, while the passive platform is placed at a closer range of the imaged area. Such a configuration is well suited for strip mapping. However, maintaining equal platform velocities may be an unachievable constraint, depending on the respective type of platforms (e.g. a large body aircraft combined with a UAV). Possible advantages are also related to the bistatic radar equation, due to the combined dependence on R1 and R2, the respective emitter-to-target and target-to-receiver ranges. For example, the emitter can be placed at a longer range than would be allowed from SNR monostatic performance consideration, provided the receiver is at a sufficiently short range from the imaged area. On the other hand, the range resolution is degraded as the bistatic angle is increased [5.1]. This will be illustrated later. Most often, the two flight tracks are located on the same side from the area to be imaged and so the bistatic angle will be less than 90◦ . Very large bistatic angles might also be considered, with relation to specific forward-scattering properties of objects, but then the range resolution is drastically degraded, as it will be seen later on.

5.2.2 General Bistatic Configurations General bistatic configurations offer maximum flexibility from an operational point of view, such as the possibility for one of the platforms to operate in a forward-looking direction or at a different velocity. This is obviously at the expense of increased constraints: e.g. beam-pointing agility is required and large-area stripmap imaging becomes quite challenging. Configurations with nonparallel trajectories and/or different platform velocities are also a challenge with respect to SAR processing, due to the fact that the data collection space for the raw data varies with time for nonparallel trajectories (see Section 5.3). In Section 5.2.4, some typical configurations will be illustrated and discussed.

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5.2.3 MTI Applications

Up to now, only bistatic SAR configurations have been considered; nevertheless, in many concepts, related to ground surveillance, for example, multimode radars are considered, combining SAR modes with ground moving target indication (GMTI). In order to improve performance in terms of minimum detectable velocity, antennas with multiple receive channels are often needed in order to implement processing techniques known as DPCA or STAP [5.17]. This leads to more complex systems, and it would be possible to take advantage of specific bistatic geometries that minimize clutter Doppler spread to get good MTI detection performance with single-channel antennas (an accurate azimuth location would imply monopulse-like techniques). Another interesting point is that combining monostatic and bi(multi)static systems can increase moving target visibility, due to the fact that in a bistatic configuration the optimum direction of motion for detecting a vehicle is given by the bisector of the bistatic angle (for which the vertex is located on the target and pointing to the emitter and to the receiver respectively).

5.2.4 Examples of Resolution Performances This section illustrates the expected resolution performances for various bistatic SAR configurations. A two-dimensional horizontal view of the investigated configurations is shown on the left-hand side of Figures 5.1 to 5.5. The platform velocity vectors are indicated by arrows, and the observed area is shown as a rectangle at x = 0 and y = 0. The right drawings show the iso-range, iso-Doppler network within this observed area, which spans a fixed size of 1 km width by 2 km depth. It is assumed that the antenna beams fully cover the scene. The ground resolution may be inferred from the overall Doppler spread and the bistatic range spread values and the potential benefit of such a configuration may then be assessed. The first example (Figure 5.1) corresponds to the case of two platforms on parallel tracks with different ranges, altitudes and velocities, in a side-looking configuration. The corresponding bistatic angle is 10◦ . Let S be the ‘depth’ of the ground swath (here 2000 m), δ R the ‘monostatic’ waveform range resolution, R the bistatic range defined as the average of the two target-to-sensor distances and R the bistatic range spread within the scene. The bistatic ground range resolution δ Rb is then approximately given by δ Rb = δ R

S · R

Assume that δ R is equal to 1 m; then the bistatic range resolution is degraded to 1.18 m. Regarding the azimuth resolution, consider a coherent integration time Tint , a scene width W (here 1000 m), and a bistatic Doppler spread DS within the scene indicated in Figure 5.1 on the right. The bistatic azimuth resolution δ A z is then approximately given by δ Az =

W · DS Tint

Assuming Tint equal to one second results in a 0.95 m azimuth resolution.

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In the second example (Figure 5.2), the two trajectories are orthogonal. The shape of the resolution cells appears on the right drawing, showing up as a slight distortion. Note the 74◦ resulting bistatic angle. The typical resolutions, based on the same assumptions as before, become 1.7 m in range and 1.33 m in azimuth.

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2D view of bistatic geometry; True Bistatic Angle: 10° Platforms Ranges: 4000 and 12000 m Platforms heights: 3000 and 6000 m Platforms velocities: 80 and 240 m/s 0 −2000 −4000 −6000 −8000 −10000 −12000 −6000 −4000 −2000

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The third case (Figure 5.3) illustrates the combination of side-looking and forward-looking platforms. The resolution cells are significantly distorted. Even though they no longer appear with a rectangular shape, the resolution values along the scene main axis are given, keeping the same assumptions on radial resolution and integration time: they result in about 1.2 m in range and 1.8 m in azimuth. It is not surprising to obtain a degradation factor of about two in the azimuth resolution since the synthetic aperture is only generated by one of the two platforms. The fourth example considered is with parallel tracks again, but located on each side of the scene. Note that the bistatic angle is now 117◦ . While the Doppler spread is maintained when compared to the first example (and so is the azimuth resolution), the resolution in range is drastically degraded. As the bistatic range interval is only about 100 m, the average range resolution is considerably degraded, around 20 m in this case (Figure 5.4). 2D view of bistatic geometry; True Bistatic Angle: 117° Platforms Ranges: 4000 and 12000 m Platforms heights: 3000 and 6000 m Platforms velocities: 80 and 240 m/s

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Figure 5.5 Case 5: orthogonal ground tracks, opposite angular rotation

The last example refers to a GMTI oriented configuration. This is the same geometrical configuration as the second example but now the two platforms are counterrotating. This is illustrated in Figure 5.5. Now it can be seen that the range resolution remains unchanged while the Doppler spread in the scene has been considerably reduced to only about 40 Hz. In view of SAR imaging, this would be an unacceptable degradation, but if GMTI applications are the point of interest, then vehicles with velocities as low as 1 m/s may be detected out of clutter in the X-band by a mere lowpass notch filter.

5.3 AIRBORNE BISTATIC SAR PROCESSING SPECIFICITY Bistatism changes the SAR processing in three critical steps. First, the kernel of the SAR image synthesis must be changed and provision has to be made for near-range (blind distance) drift due to the build-up of the clock drift between transmitter and receiver master oscillators. Second, the motion compensation process must be adapted to dual trajectories. Third, the image geometrical distortion model must be adapted to dual trajectories and extraneous near-range drift input.

5.3.1 Changes in the SAR Synthesis Process On most SAR systems, the raw signal is uncompressed both in range and Doppler; namely the pulse synthesis is done by the processing computer after signal digitization. Range compression does not present any specific difficulty due to the bistatic aspect of the acquisition, with one design issue excepted: deramp on receive (demodulation by a linear ramp, the replica, similar to the one transmitted) may not be practicable. This technique allows a sampling rate reduction

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Figure 5.6 Principle of deramp on receive. Demodulation of the received signal with a replica of the same slope allows, provided the swath is narrowed, a digitizing bandwidth Bdig much lower than the received demodulated bandwidth Bres , which sets the resolution. In this example, Bdig is centred on the zero frequency.

below the signal bandwidth (which limits range resolution) at the cost of a significant narrowing of the swath (see Figure 5.6). In the bistatic case, even a small drift in the timing of the replica may cause a shift of the useful swath out of the digitizer bandwidth thereby deteriorating the imaging process, as illustrated in Figure 5.7. 5.3.1.1 The Image Geometry Issue The first question that arises when a bistatic SAR processor is built is, ‘What is the geometry of the final image?’ Indeed, for the monostatic case, the answer to this question is quite natural: assuming that the trajectory is perfectly linear, the range history of any point in space is invariant if the trajectory is rotated along its axis. Therefore all the points of a circle perpendicular to the trajectory line with the centre on the line have the same range (hence phase) history and are processed identically. It is then quite natural to build the SAR image in cylindrical (the

Figure 5.7 Effect of a clock drift. The drifted swath echoes are demodulated to a shifted effective bandwidth Beff that may fall outside the digitizer’s bandwidth Bdig .

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Figure 5.8 Definition of the slant-range coordinates in the monostatic case. The δ angle is the squint of the coordinate system (generally π/2 or the squint angle of the look, z is the azimuth (along-track) coordinate and r is the range coordinate.

so-called ‘zero Doppler slant-range’ coordinate system) or in conical (or squinted slant-range coordinates) form, depending on the squint angle and designer preferences, as illustrated in Figure 5.8. The along-track coordinate in the slant-range system is generally taken as a distance along the trajectory. This is especially sound in the airborne case, since the aircraft velocity fluctuates around an average value (there is a kind of natural oscillation between velocity and altitude due to the pitch axis stability of the aircraft). Using a straight line along the trajectory axis makes the image coordinates truly spatial while keeping with the time coordinates shows local contractions and dilations of lines. In fact, a SAR processor often resamples the signal in time as a first stage in order to make along-track velocity uniform. Note that this rotation invariance has one important consequence: in this ideal case (perfectly linear trajectory) image focusing does not depend on the terrain elevation. Not only are elevated features correctly focused but their position in the final image is that of the ground level points on the same perpendicular circle regardless of the squint angle. This also means that multilooking of an elevated object is not a problem (the overlay direction is as just shown towards the trajectory axis and not, as sometimes incorrectly believed, in the range or looking direction). The case of bistatic SAR processing is not as straightforward because the rotational invariance does hold (except for the very specific case of colinear trajectories, i.e. no larger platforms flying on the same linear track, with possibly different velocities). First, the image

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Figure 5.9 Image geometry convention used for ‘slant-range’ coordinates in the bistatic case. Note that the range r differs significantly from half the bistatic propagation length.

‘along-track’ coordinate now requires apparent velocities of both aircrafts (addressing the most difficult airborne case) to be uniform, which of course is not possible with a simple resampling in time, as the velocity fluctuations of both aircrafts are not identical. Hence, all that can be done is to make the average velocity uniform, which is defined as the velocity of the mid-point between the transmitter and receiver. Thus the ‘along-track’ coordinate becomes the length along the middle (transmitter–receiver) trajectory. For the ‘range’ coordinate, either the range to the middle trajectory or the bistatic range (i.e. the sum of the transmitter to the point and the point to the receiver distances) computed for the nominal transmitter and receiver trajectories may be used. Because readers are certainly more familiar with the slant-range monostatic image, the images of this chapter use the ‘range to middle trajectory’ convention (Figure 5.9). Note that ‘natural’ coordinates could be used similar to the monostatic ones, such as the bistatic range and the time the point Doppler (equivalently the rate of change of the bistatic range) reaches a given value that would play the role of the squint angle. In the following sections on the frequency-domain processing it will be seen that this is not a convenient coordinate system for the processor, and that even in the constant geometry cases (parallel trajectories, equal velocities) the ‘squint’ defined in that way is not coherent with the squint angle of the transmitter and receiver antennas, which define the direction in which the antenna patterns overlap (hence the imaging is possible). 5.3.1.2 Time-Domain Processing Issues The synthetic aperture synthesis can be done either in the temporal domain, leading to slow, but easy to compensate, algorithms, or in the frequency domain, leading to fast, but more difficult to compensate, algorithms. The basic principle of time-domain processing is to correlate the

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Figure 5.10 Example of the bistatic image computed with a time-domain processor. X-band image of the Nˆımes airport illuminated by the RAMSES (ONERA) radar and received by the E-SAR (DLR) radar.

range-compressed signal (in the range × along-track domain) with the predicted point echo response of each pixel centre of the image to be constructed. Though simple, such a direct approach is generally not used since it is extremely inefficient. For covering a given constant area, the computation time grows as the third power of the resolution (the number of pixels grows as the square of the resolution and integration time grows proportionally). Hence, time processing is done in successive stages, leading to the fast back-projection algorithm [5.18]. The idea is to compute small pre-integrations, yielding a lower angular resolution than the final one, but focused for a set of squint angles covering the full integration angle. The second stage uses these pre-integrated signals (the PRF of which has been significantly reduced) to make longer integrations and so on, up to the final integration. Theoretically, the computation time for a given area grows with the resolution as the square times the logarithm (the base 2 logarithm if successive integrations are made to grow as the power of two in length). Time-domain processing is illustrated through an example in Figure 5.10. Such a computing scheme creates a specific problem for bistatic processing. For monostatic SAR synthesis, the Doppler frequency is proportional to the sine of the squint angle; hence the (complex) weight factors of the sample during the early stages of the time-domain processing are constant across the swath (the so-called ‘depth of field’ of the focusing decreases as the square of integration time and hence it can be assumed that it is wider than the swath but for the last stage). On the contrary, for truly bistatic configurations (i.e. excepted the quasimonostatic case when two platforms are separated by a constantly small distance compared to the swath range), the Doppler varies along the swath and hence the weight factors of the preintegration phases are range-dependent. This dependence precludes pre-summing of the raw data for bistatic configurations. This has a strong impact on data flow and data computation as pulse compression for range processing needs to be performed on the full raw data, as opposed to the monostatic case, where the pre-summing can occur before any pulse compression. 5.3.1.3 Frequency-Domain Processing Paradigm (Monostatic) Knowing the time-domain monostatic processing principle, it can be observed that the integration corresponds to a convolution with a kernel varying along the range; hence the use of the convolution theorem might be tempting. Instead of a computation time proportional to the third power of the resolution (integration length times the number of pixels) the processing by Fourier transform multiplication by the kernel spectrum and inverse Fourier transform would yield a computation time proportional to the second power times the logarithm of the resolution. Indeed such a direct approach is limited in range since the convolution kernel should depend

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on the range (its support is a hyperbola with the same asymptotic slope and with the summit corresponding to the nearest distance of the image pixel). However, such a processing scheme is possible provided the spectrum is mapped before the inverse Fourier transform. The reason is that a given frequency on the two-dimensional input signal, which corresponds to a pure frequency in the radar bandwidth with a given fixed frequency along track modulation, corresponds in space to a conical set of fringes in the final image. The simplest way to find that is to replace two-way propagation at light speed by oneway propagation at half the light speed. Triangle proportionality shows that all radiated ‘waves’ have conical caustics, with the important consequence that in the slant-range coordinates this is a pure spatial frequency. Thus a given point in the signal two-dimensional spectrum yields (up to a complex factor) some point of the slant-range image spectrum. The mapping between the two spectra (well known as ‘Stolt mapping’) can be derived from a simple geometrical construct, as illustrated in Figures 5.11 and 5.12. Indeed, the along-track component is unchanged, since it is forced by the along-track component of the signal frequency at zero range, where the propagation factor (inverse square distance) becomes infinite. The across-track component is given by Pythagoras’s theorem because the caustic lines are perpendicular to the circles corresponding to the propagation of a single sample, as illustrated in Figure 5.13.

Figure 5.11 Geometrical explanation of the Stolt mapping. A pure frequency (single k, ku point) of the signal spectrum corresponds to a plane sine wave in the r, z (range × along-track) space. Top: particular case of a zero along-track (Doppler) frequency. Bottom: generic case with a non-zero Doppler component.

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wavefront

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Figure 5.12 Geometrical explanation of the Stolt mapping. Assuming one-way propagation at half-light speed (instead of the two-way propagation at light speed), a single signal frequency yields a single image frequency in slant-range coordinates. The propagation from each radar pulse is a sphere; the constant Doppler frequency corresponds to a uniform rate of change in the sphere radii. The resulting wave front is conical in the generic case (bottom) and cylindrical in the particular zero-Doppler case (top).

The spectrum mapping is not the only geometrical transformation described above, because the relative phase and amplitude of the spectrum points also need to be matched. This is simply the multiplication of each sample by a complex number depending on the (k, ku ) or (k x , k y ) position of the sample. This step, arguably called ‘nominal processing’ can be performed either before or after the geometrical mapping. Given the nominal range R0 (reference distance for the phases) and squint angle δ0 of the view, the phase of the nominal processing factor is 2π R0 [k y sin(δ0 ) + k x cos(δ0 )] − 4πk R 0 . This can easily be derived graphically (see Figure 5.14). Considering a generic squint angle δ, the corresponding ku (Doppler) is given by ku = 2k cos(δ) (keep in mind the half light speed velocity due to the two-way propagation). The difference in range of the wave front of squint δ is R = R0 [cos(δ − δ0 ) − 1] according to the figure. The corresponding phase correction is 4πkR, which with a few basic algebra steps yields the above formula. The amplitude of the nominal processing factor is noncritical for focusing and requires knowledge of the antenna pattern and terrain elevation (DEM). It cannot be exactly compensated in the (k, ku ) nor the (k x ,k y ) spaces. Indeed, compensation is made for it in two stages;

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Figure 5.13 The mapping of the signal spectrum coordinates k, ku to the image spectrum coordinates kx , k y (the Stolt transform) can be geometrically derived from the tangency of the wave front spheres transmitted from two positions separated by the Doppler wavelength λu . Clearly the along-track coordinate is unchanged and the across-track component is given by a Pythagoras rule (note that the across-track wavelengths are half the real signal and image wavelengths because of the half light speed velocity in this representation; therefore the Stolt transform formulae are 4k x2 = 4k 2 − ku2 and k y = ku ).

first, before the range Fourier transform (thus in the (t, ku ) or range-Doppler space), compensation is made for propagation (R factor), any additional range filters (deramp case) and range variation of the antenna pattern, computed for the average squint angle δ (of each subaperture) using the DEM for computing the elevation and azimuth angle from the antenna. Later, while in the (k, ku ) space, the variation is modelled for the squint angle δ of the antenna pattern

Figure 5.14 Graphical representation of the nominal processing phase factor. Fat solid grey lines represent the wave front surface for two squint angle values. R yields the phase difference at the nominal point R0 , δ0 of the conical wave for δ, while k and ku are figured for information only.

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Figure 5.15 Synoptic of an –k frequency-domain SAR processor. This is a simplified view without the motion compensation detailed in Section 5.3.2.1.

for the average range and terrain elevation and is corrected for each (k, ku ) point knowing (δ = arccos(2k/ku ). The above described amplitude compensation is sufficient for yielding a correct pulse response shape, but it introduces radiometric errors in the final SAR image. Radiometry is therefore corrected after synthesis by estimating the true illumination along the integration interval (by numerical integration of the antenna pattern in the sensor to ground point direction) and removal of the modelled (squint angle × range) illumination pattern used during the synthesis. Due to the slow variation of aircraft attitude and the slow drift of the ground within the antenna pattern, this numerical integration can be accurately performed on a small number of points (typically five to nine) and thus does not represent a significant computation overload. This principle is generally used for wide-swath large-bandwidth SAR image synthesis. This is the algorithm known as ‘–k’ or the ‘range migration algorithm’, for which the main algorithm steps are illustrated in Figure 5.15 on monostatic airborne X-band data. Indeed, narrow bandwidth radar signals are often computed using approximate algorithms such as ‘range doppler’ or ‘chirp scaling’ algorithms, but the following dissertation will be restricted to the exact algorithm. 5.3.1.4 Bistatic Frequency-Domain Processing In order to adapt the above design to bistatic SAR imaging, the image coordinates will be found in which a pure signal frequency yields a pure image frequency. In the monostatic case the obvious slant-range coordinate system is adequate. For bistatic configuration such an coordinate system does not exist. Having this objective in mind, it is possible to build an ad hoc coordinate system. Due to the loss of elevation invariance from the monostatic

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case, the computation must involve a ground plane or an elevation model (DEM) for the focusing. Given the imaged area, the first coordinate a axis (corresponding to the range axis in the monostatic case) can be found by unwrapping the phase of the caustic fringes obtained for the mid-bandwidth frequency and Doppler frequency estimated at the mid-swath distance and the desired squint angle. Indeed, such a coordinate axis is valid for the full bandwidth line in the signal spectrum for proportional Doppler frequency, because the pattern does not change when the phases are multiplied by a constant. In order to derive the second dimension b of the coordinate system, a derivative of the unwrapped phase is found with respect to the Doppler frequency (note that uniformity of the midpoint velocity is assumed prior to this construct, which means that Doppler frequency is ‘frequency versus run length of the middle of the transmitter to the receiver segment along the nominal midpoint trajectory’). This is illustrated in Figure 5.16. Equivalently (the zeroDoppler case excepted), the second coordinate b can be obtained by integrating the rate of change of the bistatic distance along the lines of constant a. The numerical computation of the Z , R to a, b mapping is detailed in Figure 5.17. Given a processing bloc centre M0 (the middle between transmit T0 and receive R0 antennae positions) the middle swath target point P0 is determined (as in monostatic case) and the local slope of the intersection of the isobistatic distance ellipsoid with the ground is computed (using the implicit function theorem). Integration of this vector field (computed for the generic point P) yields iso-a lines of the coordinate system. The a value for the line is the difference of bistatic distance (i.e. T0 P + P R0 ) from that of the midswath bistatic distance, the point P being a point on

δ0 middle trajectory

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Figure 5.16 Analogue of Figure 5.12 (bottom) for a two-dimensional bistatic configuration. The wave front propagates as ellipsoids of focal points on the transmitter and receiver trajectories. The mapping of the a, b coordinate system in the final Z,R slant-range coordinate system is obtained by integration along the ellipsoid tangents (in fact the intersection of the ellipsoid and the (ground) surface of focusing).

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Figure 5.17 Construction of the a, b coordinate system (image synthesis coordinates)

the cone of angle δ from the point M0 for a generic range value. Along the iso-a lines b is obtained by integrating the difference between the bistatic distance T P + P R and that of P0 . Since the aim is eventually to map the constructed image to the bistatic coordinate system of Figure 5.9, the above a, b coordinate system obtained through integration is sheared to get rid of the nominal wave front slope. Namely, the sheared a, b coordinate is given from the unsheared aint , bint one by a = sin(δ)aint − sin(δ)bint and b = cos(δ)aint + sin(δ)tg(δ)bint (where the zero-Doppler case is excluded, but in this case no shear is needed). By construction, in a narrow Doppler band around the bandwidth line of the desired squint angle, a pure signal frequency is mapped to a pure image frequency; hence the –k type of processing is possible. Unlike the monostatic case, however, the fringes corresponding to Doppler frequency outside the immediate neighbourhood of the b = 0 line are not parallel equidistant straight lines. This means that the –k algorithm is not exact for long integration times (high along-track resolution). This does not disqualify this type of algorithm in practice because there is not an ideal world: aircraft definitively do not fly along straight lines at uniform velocity and the algorithms (even in monostatic cases) are adapted to nonlinearities in trajectory. The so-called ‘motion compensation’ modifications can encompass the ‘algorithmic systematic error compensation’. Indeed, what is required for motion compensation, namely the range error as a function of the squint angle (or equivalently of the Doppler frequency), can also be derived for the algorithmic error. In fact, as seen in the derivation of the bistatic motion compensation below, the algorithmic systematic error is implicitly compensated for, which means that unlike the monostatic case, even if the transmitter and receiver trajectories were perfectly uniform linear motion, compensation would be necessary.

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This section will describe motion compensation (mocomp) for frequency domain processing only. Indeed, time-domain mocomp is trivial, simply using instead of the distances between nominal trajectories and the point integrated as range history, the distances between the actual trajectories and the current point. The motion compensation for bistatic SAR is very similar in principle, though it requires numerical computation instead of the formal calculation possible in the monostatic case. Before introducing bistatic motion compensation, a brief description of the monostatic –k mocomp is useful.

5.3.2.1 Monostatic Frequency-Domain mocomp The motion compensation strategy for the monostatic –k algorithm is based on separation of the compensations into high-frequency errors and low-frequency errors. The first stage is a uniformization of the along-track velocity and an offset from the actual range to the range from the nominal trajectory. This uniformization yields an even sampling of the slow-time along the nominal trajectory (i.e. the orthogonal projection of the antenna position at the sample times are uniformly spaced on the nominal, straight line, trajectory). It will be seen later that this resampling is somehow redundant, together with the next along-track resampling, but this first step also reduces the pulse repetition frequency and makes the squint/Doppler relationship simpler. The pre-summing uses weights to focus the beam onto the middle of the swath at an effective squint value. The effective squint value is close but not exactly the nominal squint of the look (or of the sublook in the case of subaperture processing). The difference is due to the z-migration (along-track migration) described in Figure 5.18. The pre-integrated new sample at N (tnew ) will in fact be used at a different time N (teff (t, r )) depending on the range r, the effective squint being the angle α between the nominal trajectory and the direction of the point P seen from the true acquisition time point N (tnew ). The squint of the point P from the nominal point N (teff (t, r0 )) is the nominal squint angle δ (r0 is the mid-swath range). The computation of α is performed adaptively by a simple control loop (called the ‘α–δ loop’) using the fact that the α–δ deviation evolves slowly with time. During the pre-integration, the range profiles are also resampled in range at the nominal range bin positions from the nominal point N (tnew ). Thus, after pre-integration, the signal is resampled evenly, as seen from the nominal trajectory. Note that this resampling is valid for the squint angle α only and this is far from sufficient to insure a correctly focused image. Indeed, a given sample of the (range-compressed) signal is used in the computation of several points of the final image. These points are at the intersection of the ground surface and a sphere centred at the true antenna position T and span an angular sector roughly equal to that of the synthetic antenna aperture (if the ground is a plane, the points form a circular arc). As seen in Figure 5.19, the distances for these points seen from the nominal trajectory point N are different from the true ones, the central one excepted. It can also be seen in Figure 5.19 that the first order of the range error versus squint angle is nonzero. The aim of the above-mentioned z-migration is to cancel the first-order terms. This is simply done by sliding the N (teff (t, r )) along the nominal trajectory up to the point where the two arcs are tangent; hence the range error with squint cancels at first order, as illustrated in

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Figure 5.18 Definition of the pre-integration actual squint angle α and its relation to the nominal squint angle δ. The pre-integration focus point P is determined as being visible under the nominal squint δ after the azimuth migration (from tnew to teff ).

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Figure 5.19 Remaining range error before z-migration. If range migration is compensated for the nominal (effective) squint, there is an uncompensated range error for the other squint values within the synthetic antenna aperture. This error has a nonzero first order in the squint angle because the sphere’s intersections with the ground (assumed plane for clarity) are not tangential.

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ctory

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P P'

Figure 5.20 Cancellation of the first order of range error for nonnominal squints by z-migration (alongtrack migration) in the flat ground case. The signal sample at time t is used at the nominal point N at some different time instead of the nominal point Nt at time t.

Figure 5.20. It is to be emphasized that the along-track resampling (note its range dependency) being performed in the time-domain is wide-band compatible. Provided either the ground is flat or it is modelled by a digital terrain elevation model (DEM) to be sufficiently smooth (in particular it should be free of sampling artefacts that ruin the continuity of the DEM normal), the migration can be computed geometrically by using the terrain normal. Indeed, the tangency of the circle arcs, as illustrated in Figure 5.20, is granted when, from the P point position, the terrain normal, the nominal trajectory point N and the true trajectory point Tt are coplanar. Hence in the flat ground on the smooth DEM cases the z-migration is computed as follows. For any given teff time and range r, the nominal point P is computed on the ground – the point at squint δ and range r on the imaging side of N (teff ). Next the normal z to the ground at P is evaluated. The point P, the point N (teff ) and the vector z define a plane and the intersection T (tnew ) of the true trajectory with this plane is found. This yields N (tnew ) − N (teff ), the z-migration that will cancel the range error to the first order. In the case of a rough terrain or a poorly quantified DEM, the normal will not provide the best first-order cancellation of the range error. The z-migration is in this case computed numerically by minimizing the distance between the two ‘arcs’ measured on a set of test points when the z-migration is adjusted. The computation of the test points (for the given teff time and range r) is required for the higher-order term cancellation as described below. Hence, the computation added by this method is very limited. At this point first-order errors have been cancelled by resampling in the time domain, but a higher-order range error remains that cannot be processed in the time domain (because, for the same time samples, it depends on the squint and hence on the Doppler frequency in which

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Δz trajectory

N δ0 T

α

R

R0

) nt(δ 0

efro wav

Figure 5.21 Slant-range plane representation of the z-migration –z and its relation to the α–δ control loop. The thick line is the nominal trajectory and the dashed sphere is the nominal wave surface corresponding to the nominal point N. Point T is the true sensor position and the thin oval is the slant-range projection of the intersection with the terrain surface of the spherical true wave surface.

the sample will be used). These errors are due to the difference of curvature radii of the two arcs. In the case of flat ground, this curvature difference is related to the distance of the nadir points of the nominal and true trajectories. Since this distance varies slowly with time, the higher-order error (what is called ‘quadratic phase correction’ even if it is not purely second order, because the second-order term is predominant) is processed by along-track sub-blocks in the range-Doppler space under the narrow bandwidth hypothesis. The principle is to process a sub-block (overlapping sub-blocks weighted by a triangular window are generally taken) in the range-Doppler domain by adding to each range line a polynomial phase computed from the residual range errors of a set of test points spanning the used squint sector of the nominal arc. In order to explain the computation principle for this ‘quadratic phase component’ consider the two ‘circles’ in Figure 5.20 in the slant-range plane. This is illustrated in Figure 5.21. Note that on this drawing the deviation to the nominal trajectory of the true trajectory point has been extremely exaggerated in order to make the drawing legible. The α and δ angles of Figure 5.17 are shown with their relation to the nominal wave front (i.e. the wave front for the nominal squint angle δ0 ). If a wave front for a generic squint angle δ (within the angular integration interval) is drawn (the overall set-up is that of Figure 5.14) it can be seen in Figure 5.22 that the nominal processing phase factor (proportional to R) needs to be altered by a minor amount (details of the construct are given in Figure 5.23), denoted dR on the drawing. In order to model the quadratic phase component as a polynomial, dR is computed for 2n points evenly spaced in sin(δ) and spanning the angular integration interval. Since the correspondence between δ and the Doppler (i.e. along the ku axis) frequency is altered by the z-migration, the apparent Doppler is computed for 2n + 1 points, where the extra one is the nominal (δ0 squinted) focus point P, and a polynomial is fitted to dR as a function of the apparent Doppler.

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Δz N

trajectory δ0 δ

T

R0

R

ΔR

α

dΔR

) wavefront(δ

) (δ 0

ont

r vef wa

Figure 5.22 Alteration (denoted dR) of the ‘nominal processing’ phase R (see Figure 5.14) due to the displacement from the nominal trajectory point N to the effective trajectory point T

This correction is narrow band, since range error is transformed as phase error, which is, strictly speaking, valid only for the centre frequency. The maximum contribution of the quadratic phase is monitored during the image synthesis and violations of the narrow-band hypothesis are signalled (as a rule of thumb, the acceptable maximum phase correction is in the order of 2π F0 /B, where B/F0 is the relative bandwidth). If the narrow-band assumption is invalid there are two possible corrective actions. One solution is to reduce the Doppler width of the processed data. This amounts to processing separately (but with a lower PRF) the signal for several nominal squints spanning the full angular aperture up to the quadratic phase compensation where the spectra are seamed (generally triangular weighting windows are used, thus linearly interpolating the correction). After the merging, the algorithm proceeds with Stolt interpolation. Because of the quadratic aspect of the higher-order corrections, if the angular aperture is divided by two the maximum compensation is reduced fourfold.

δ0 δ

T

R0

R

α

dΔR

) t(δ 0

n fro e v wa

Figure 5.23 Detail of Figure 5.22 where dR is the distance between the cones of angle δ and axed on the nominal trajectory respectively tangent to the nominal wave surface (dashed sphere) and to the intersection of the ground with the true spherical wave surface (solid oval)

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The alternative solution is to reduce the bandwidth. This amounts to processing subbandwidths separately. Unlike the previous approach, the maximum compensation is only reduced to half when two sub-bandwidths are processed. However, a sub-bandwidth might be preferred for two reasons. In the first case frequency agility is used to increase the bandwidth beyond that of a single chirp, because processing each agile bandwidth separately (with intermediate true trajectory points) and adding the final SAR images elegantly solves the Doppler/agility coupling difficulty in the range compression (pulse synthesis). Second, instead of merging the subprocessings before the Stolt interpolation, it is advisable to proceed up to the final image output at a lower range resolution (thus reducing proportionally the memory requirement) only interpolating in the range before summing together the subprocessed outputs. Because of the structure of modern computers, such a processing scheme is more efficient (even without narrow bandwidth violation) because manipulation of smaller memory blocks is more efficient and multiprocessing capability is more and more common, even on small laptop computers). Frequency agility Frequency agility is a technique for increasing the total signal bandwidth, and hence the range resolution, above the capability of the chirp (linear ramp) generator. The principle is to interleave the transmission of chirps spanning consecutive sub-bands which are subsequently received and demodulated with offset frequencies. It is possible to reassemble the spectra of a sequence of chirps to form a full-resolution range profile, and then process the SAR signal as normal. However, the spectrum reassembly is only valid for a given squint angle (the time delay between the sub-band transmission induces a small displacement that depends on the direction of observation). When the integration angle is wide, the high-resolution profile reconstruction is incorrect for the extremities of the integration angle and this results in periodic discontinuities in the range spectrum, thus increasing the spurious sidelobe level. This effect is called ‘Doppler agility coupling’. 5.3.2.2 Bistatic Frequency Domain mocomp In the bistatic case, the above-described motion compensation techniques applies with some minor changes discussed in the following in the same order as the previous development for the monostatic case. Bistatic Stolt transform The mapping of the signal spectrum coordinates k, ku to the image spectrum coordinates ka , kb (the bistatic analogue to the Stolt transform) is numerically derived from a geometrical principle very similar to the monostatic case. Unlike the monostatic case, the formula is not in a convenient closed form because the circles of Figure 5.13 are now the oval intersection of the ground and an elongated ellipsoid with foci at the nominal transmitter and receiver positions. Furthermore, in the generic nonstationnary case (i.e. in the case where the transmitter and receiver craft have different nominal velocity vectors) the oval shape varies with time (see Figure 5.24 in which the effect is emphasized). This has the immediate consequence that λb = λu ; i.e. the bistatic Stolt transform is an uneven mapping in both dimensions in space. Nevertheless, the numerical value of k, ku as a function of ka , kb can be derived from the tangency of the

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λa λ λb

δ0 λu

Figure 5.24 The mapping of the signal spectrum coordinates k, ku to the image spectrum coordinates ka , kb (the bistatic analogue to the Stolt transform) is numerically derived from the tangency of the wave front ovals transmitted from two positions separated by the Doppler wavelength (in fact by an infinitesimal fraction of it through a differentiation). Note that unlike Figure 5.13 λb = λu since the ovals are not of the same shape (in the non-stationary generic bistatic case). Even the interfringe λ must be measured in the nominal squint direction δ0 .

wave front ovals transmitted from two positions separated by the Doppler wavelength (in fact, the limit is taken at a vanishing fraction of it). Note also that in the a, b space the interfringe λ (the half wave length) is the distance between the successive fringes from the same position only in the nominal squint direction δ0 due to the construction of the a, b coordinate system by unwrapping the Fresnel wavelets in this direction from the median trajectory. Nominal processing The nominal processing phase is in fact computed numerically together with the quadratic phase component. Therefore Figure 5.14 will be skipped, proceeding directly to z-migration and the α–δ control loop. Z-migration and α–δ control loop For these points of the algorithm, consider Figure 5.21 on which N is the middle between the transmitter N T and receiver N R positions (instead of the mere sensor position in the monostatic case). Similarly, T becomes a couple of points instead. Besides that, the only change in the figure is that the dashed sphere needs to be replaced by an oval shape (the intersection of the ground with the elongated ellipsoid of range 2R0 to the two foci N T and N R ), which will further be denoted ζ N . In the implementation of the computation, the terrain normal at P cannot be used any more for deriving position N as the intersection of the plane defined by P, T and the normal. Indeed, this is due to the fact that the ellipse defined as the intersection of a plane is not orthogonal at a generic point P to the vector joining this point to the ellipsoid centre (replace ‘ellipse’ and ‘ellipsoid’ by ‘circle’ and ‘sphere’ respectively and that property becomes true). The consequence is that the numerical approach sketched for rough terrain in the monostatic case becomes compulsory in bistatic cases even if the terrain is perfectly flat.

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Hence in practice, for a nominal ‘position’ (point couple) N and nominal ‘range’ R0 the point P of tangency to ζ N to the nominal wave front in the (a, b) coordinate space is, by construct of the coordinate system, the point of ‘bistatic squint’ δ0 . Iteratively starting from the previous extrapolated value of the z-migration Z , the true position T is sought for which the intersection ζT of the ellipsoid of foci T through point P of the slope is tangent to ζ N . (This can be efficiently asserted by the implicit derivation formula.) From T both the migration z (directly used for resampling) and angle α used in the pre-integration phase can be deduced. Note that unlike the simpler ‘soft terrain’ computation using the terrain normal, which provides Z as a function of T, here Z is derived as a function of N, which is more convenient for z-migration resampling. Indeed, ‘soft terrain’ compensation is required to tabulate Z values and solve in z T the equation z T + Z (T ) = z N for finding the interpolating point giving the sample signal at z N .

Quadratic phase component The principle is the same as in the monostatic case of Figures 5.22 and 5.23, but in the (a, b) space. On the ζT curve, a search is made for 2n points (n for each side) around point P of the nominal δ0 squint. These test points are chosen in order for their tangent to have the slope of a δ squinted wave front for δ spanning more or less evenly the integration angular interval. (In the monostatic case, these points were taken to be evenly spaced in sin(δ) from point N, but here they are approximately so in order to reduce the computational effort of spreading them using a precise law.) As in Figures 5.22 and 5.23, from the measure of cumulated distance between the test point and the true position couple T, the equivalent of R + dR (bi R is denoted as the bistatic range difference) is measured directly and the apparent Doppler (or kb ) is evaluated after z-migration. From the 2n + 1 Doppler and bi R values at the middle of the band and processing block, a degree 2n polynomial is fitted (note that, by construct, its constant term is zero and its first degree term is small). This polynomial plays here the role of the nominal processing phase R in the monostatic case. Note that in the monostatic case, this value was derived explicitly and was a first-degree polynomial in x (slant range) and y (azimuth) coordinates. The difference between this bistatic nominal processing term R and bi R for a generic a ‘range’ or kb ‘Doppler’ is fitted as a polynomial of degree 2n and used in a similar fashion to the monostatic quadratic phase component in the monostatic case. It is worth emphasizing at this point that, unlike the monostatic case, the quadratic phase component needs to be compensated for even in case of perfectly linear uniform trajectories (i.e. –k algorithmic errors are also corrected and not only motion disturbances). There are two strategies for bistatic motion compensation. The first one is to define the (a, b) coordinate system from the nominal linear uniform transmitter and receiver trajectories, and correct for the deviations of both the true transmitter and receiver positions with respect to these linear uniform trajectories (the preintegration phase uniformises the middle point velocity only). The second one [5.19] is to fit both transmitter and receiver trajectories to polynomials, construct the (a, b) coordinate system with respect to these nominal trajectories and correct for the deviations of the true transmitter and receiver positions with respect to these polynomial trajectories. Whether the complication of the coordinate system integration is traded-off with an increased validity range of the quadratic phase correction is still controversial.

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5.3.3 Geometrical Distortion Model for Airborne Bistatic SAR Images

Synthesizing a SAR image is only the first step in the use of a SAR system data, and several applications require accurate positioning of the image pixels in geographical coordinates. Mapping of a two-dimensional image to/from geographical coordinates depends of a third dimension, generally taken as the elevation to the Geoid (the zero-level surface of the geodetic system called ‘sea level’). Because the SAR image is the result of a deterministic computation, this mapping could be easily computed from the radar characteristics (waveform), the carrier trajectory and the SAR image squint angle. However, the latter excepted (it is a computation parameter), all result from measurements (therefore affected by system biases like electronic delays or limited accuracy for GPS measurements). Hence there is a need to evaluate these parameters from tie points. For example, stereo-radargrammetry uses two images acquired from two different trajectories to derive terrain elevation from homologous points in both images and by adjusting the elevation parameter under the constraint that the geographical coordinates of the two homologous pixels are equal. Another example is the calibration of the electronic delay associated with a radar system relying on the geographical position of a known corner reflector. More difficult is the ‘frame-drift autofocus’ technique, which matches SAR images from the same signal acquisition computed for several different squint angles for deriving carrier trajectory updating. This is a very useful operation for airborne SAR because the trajectory is more perturbed than that of a spacecraft and inertial and/or GPS navigation units are generally not accurate enough for image synthesis with full resolution. In the bistatic case, there is the extra complication of the clock drift, which is unpredictable and can really ruin geometry and even resolution of the bistatic image in a few minutes.

5.3.3.1 Monostatic SAR Geometrical Distortion Model In the monostatic case the geometrical distortion model must contain the direct mapping (Z , R, H, θ) → (L , G) and inverse mapping (L , G, H, θ ) → (Z , R) between the image azimuth (the along-track distance on the nominal trajectory) Z and range (along the squint angle distance to the nominal trajectory) R coordinates and the geographic latitude L and longitude G coordinates, given the elevation H and radar θ parameters. The parameters θ are transmitreceive delay error, frequency bias, sampling frequency bias and trajectory measurement errors. Some uses of the SAR images also require (or at least are made easier by) knowledge of the derivatives of the mappings with respect to their variables or parameters. Hence the geometrical model package (associated with a given SAR processor) also contains the derivative of the maps as well as some auxiliary functions: illumination compensation models needed to adjust or correct antenna patterns, the frequency centroid computation function used for phasepreserving image resampling and observer position determination (used for phase-to-elevation translation in SAR interferometry). All the computations involve two main subproblems. The first (trivial) is ‘given a point N and a direction vector (trajectory direction) in space, what is the distance r of another given point P and what is the angle δ at N between the vector and P?’ The second (slightly less trivial) subproblem is ‘Given a point N and a direction vector (trajectory direction) in space, where is the point P on the horizontal plane of given elevation H that is at distance r of N and

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ctor

N

d

traje

y

δ r

H d1

d2

P

Figure 5.25 Elementary computation involved in the monostatic geometrical distortion model. Given a trajectory point N, a (local) route and a (local) slope, an elevation H and range r (for a squint angle δ), the target point P can be derived from d = r sin(δ) and hence d1 = d cos(slope), d22 = r 2 − H 2 − d12 .

such that the angle at N between the vector and P is δ?’ Resolution of this latter subproblem is only a matter of a few floating point operations. Inverse transform (mapping from the image coordinates to the geographical coordinates) is the easiest to program (it corresponds to the second subproblem above). Note that there are in fact two solutions for the second subproblem (Figure 5.25) since the sign of d2 is arbitrary in this derivation. This is the well-known ‘left-right ambiguity’ of the SAR geometry. In practice, this ambiguity is solved due to the directivity of the radar antenna pattern (i.e. the radar system is either ‘looking to the left’ or ‘looking to the right’). Direct transform (mapping from the geographical coordinates to the image coordinates), however, is less straightforward, since it is made by iterative search of the nominal point N for which the squint angle to the point P (known from its geographical coordinates L, G, H) is the squint angle δ of the SAR image. The range coordinate r is then the distance NP. It could be thought that determination of N can be done immediately by projecting the point P on the nominal trajectory line. Indeed, this would work, but only for θ = 0 and H being exactly equal to the terrain elevation used for focusing the image (as already mentioned, the focusing is elevation-dependent in airborne cases because the trajectory is nonlinear). This statement needs some explanation. Given a point P, for which the corresponding points on the nominal and effective trajectories are respectively N and T, it should be noted that the effective squint angle (hence Doppler frequency) and range of the point P differ from the nominal values (see Figure 5.26). Thus alteration of the Doppler frequency and the range is a consequence of the motion compensation step. The true direct mapping process is therefore the following. Given an hypothesis on the Z coordinate (the along-track coordinate, hence the point N) the apparent range r is computed, and knowing the focusing elevation of this (Z, r) cell the effective range and squint angle used for computing this (Z, r) cell is found and the effective (seen from T) squint angle of point P is checked. If it is bigger (respectively smaller) than δeff , the estimation of Z is late (respectively early). The direct transform iterative computation can converge rapidly when an appropriate estimation of the Z coordinate is given as an input. This is often the case in the most common systematic use of this function, which is the geocoding of a SAR image. Once the inverse transform is used to delineate the area covered by the image (the footprint), each pixel of it (of which geographical coordinates correspond to the pixel position, and elevation given by a digital elevation model) is computed by interpolating the source SAR image (in its native slant-range coordinates). The image coordinates of a point are linearly extrapolated

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nal omi

n

N

δ r

ctor

traje

ry

cto

aje

e tr ctiv

y

effe

δeff

T

reff P

Figure 5.26 Basics of the monostatic geometrical distortion model. A point P of nominal squint angle δ and nominal range r from the nominal trajectory point N is in fact at an effective squint angle δeff and range reff of the effective trajectory point T.

from the neighbouring already computed pixels and the iterative solving converges very rapidly. The introduction of parametric errors is relatively straightforward in this scheme; trajectory errors amount to a different effective T point and velocity vector than the ones used for image synthesis. Hence the localization problem is the first to compute the effective range and radial velocity by assuming the trajectory used for focusing. Then, using the updated trajectory, the point at the corresponding range and radial velocity is retrieved from the updated trajectory point. Radar parameters amount to an offset, or a scaling on the effective range, or an offset on the radial velocity in the middle of this process. Due to the iterative form of the direct transform, its derivatives are computed by inversion of the derivatives of the inverse transform (an application of the ‘implicit function theorem’). The derivatives of the inverse transform are efficiently computed by formal derivation of the formulae given in Figure 5.25. 5.3.3.2 Bistatic SAR Geometrical Distortion Model The bistatic case is more difficult because, unlike the monostatic case, the basic subcomputations are not given by trivial formulae. Although the first subproblem is easily transposed in bistatic as ‘Given two points T and R and two vectors VT and VR , what is the average distance between a point P and the two points and what is the mean of the projections of the vectors VT and VR on the vectors TP and RP respectively?’ Unlike the monostatic case, the radial velocity is not univocally linked to the squint angle δ because of the possibly different modulus of the two vectors – the velocity of the two carriers may not be the same and what is significant is the bistatic radial velocity, i.e. the rate of change of 12 (rR + rT ) and hence 1 [VT sin(δT ) + VR sin(δ R )] (see Figure 5.27). 2

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ectory y er traj rajector receiv ry dle t VR d i cto m aje R r tr e V t t δR N i T sm T δ tran δT r rT rR

P

Figure 5.27 Bistatic geometry basics. T and R are the phase centres of the transmitting (respectively receiving) antennae and V T and V R are their respective velocities.

The second subproblem becomes much harder: ‘Given two points T and R and two vectors VT and VR where is the point P on the horizontal plane of given elevation H that is at an average distance 12 (rR + rT ) = r and a radial velocity of 12 [VT sin(δT ) + VR sin(δR )] = v?’ Note that this subproblem may have up to four solutions depending on the bistatic configuration. The direct transform is not significantly different from the monostatic case (except that two square root evaluations are needed per iteration), but the computation of the inverse transform now becomes an iterative solving of the second subproblem. Namely, given a position Z, R in the image and an elevation H, first the nominal position in space Pref is found at range r and squint δ and altitude Href given by the focusing DEM. From the point the bistatic range 12 (rR + rT ) and radial velocity 12 [VT sin(δT ) + VR sin(δR )] used for the focusing are deduced. These values and the trajectories points and velocities (T, VT , R and VR ) are possibly altered according to radar parameter errors θ and the new point P is searched that has the values of bistatic range and radial velocity for the new trajectory points and velocities. The last system of equations is solved iteratively starting from the monostatic approximation (from the middle point 12 (R + T ) and velocity 12 (VR + VT ) taking the bistatic range and velocity as monostatic ones) using a Newton scheme.

5.3.4 Miscellaneous Processing Issues This section presents the above-described processing applied to real data acquired in February 2003 during two flights of the German E-SAR system (from the DLR) and the French RAMSES system (from the ONERA) operating at X-band (100 MHz bandwidth around 9.6 GHz). The example is the same acquisition as in Figure 5.10 (seventh acquisition of the second flight) in which the two aircrafts were following the same track with a small separation (Figure 5.28 taken from a video taping of the experiment is illustrative of this configuration). The average separation during this acquisition is 50 m along-track and 9 m vertically. Figures 5.29 and 5.30 show respectively the monostatic (RAMSES) and the bistatic (RAMSES transmit, E-SAR receive) images. There is some saturation at the airport on the monostatic image and on a large tin-roofed barn at the right edge on both images. At first

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Figure 5.28 Bistatic acquisition along parallel tracks for the cross-platform interferometry. E-SAR system of the German DLR flies in front and slightly above the RAMSES system of the French ONERA (for minimizing wake perturbation on the trailing aircraft).

glance the images seem to have the same geometry, but subtracting the second from the first reveals a spatial displacement around 120 m (Figure 5.31). This mismatch is measured by correlating small square windows (typically 256 × 256) of the two images. On the small square window, once the (nominal) geometry is matched by a linear transformation of one of the windows, the distortion can be assumed to be a simple translation; hence the correlation peak measures the local displacement between the images. This peak is

Figure 5.29 Monostatic RAMSES image. Illumination is from the top edge, acquisition from left to right.

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Figure 5.30 Corresponding bistatic (RAMSES transmit/E-SAR receive) image before compensation of the clock drift

modelled as a quadratic function in order to allow for one-dimensional fitting in case there is only a linear feature in this part of the image and lower or stronger fitting according to the sharpness of the peak. This results in a displacement field of the type shown in Figure 5.32. Note that there are many erroneous measures, principally in featureless uniform areas and dense urban areas where the correlation has several local maxima. The parameter fitting process (based on a downhill simplex on the above-mentioned quadratic error) is, however, tolerant to local isolated errors. Note also that Figure 5.32 illustrates only the estimated motion, and not its quality expressed as a 2 × 2 quadratic cost matrix. Apparently wrong matching may also correspond to correct one-dimensional matching. In the process of optimizing, the matches that differ too strongly to the current model (i.e. whose cost exceeds a given tolerance) are discarded. Thus from this matching process, a time-varying near-range error, and hence a clock drift, is estimated (Figure 5.33). The bistatic view is resynthesized with this time-varying near-range, and the same squint angle as the monostatic one. The new view is coherent with respect to the monostatic view. It is worth emphasizing that the mere geometrical rectification of the genuine image is not

Figure 5.31 Difference between the two preceding images, illustrating the effect of the clock drift. As time increases, from left to right, range (vertical) error builds up. However, the error at the beginning of acquisition is not zero because the rate of clock drift induces an offset Doppler frequency that causes an along-track (horizontal) misalignment

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Figure 5.32 Distortion field measured by local correlation between the bistatic and monostatic image. There are a significant number of correlation errors (missing vectors are points where the correlation peak is discarded by the algorithm). Wrong pairings are globally filtered out because the distortion model searches for parameters matching the distortion field.

sufficient to make an interferometric pair. Indeed, the clock drift rate of change (seen by the processor as a time varying Doppler frequency offset) has as a consequence the fact that the effective squint of the view is different from the one assumed during the first synthesis. This difference in squint causes the Doppler spectra of the two images to drift apart, thus ruining the coherency of the interferogram. Figures 5.34 and 5.35 show the newly synthesized image and its subtraction from the monostatic one. This figure has several interesting features. If the radar saturations and the slight remains of antenna pattern miscorrections are neglected, there are three types of differences. The easiest to understand are the pairs of white and black spots around the motorway; these are the moving vehicles that have an along-track velocity component (the bistatic image is taken one-third of a second earlier than the monostatic one because of the along-track separation of the aircrafts). The second striking feature is the numerous black spots in the urban areas. These are strong echoes in the monostatic image that disappear in the bistatic image (the overall effect

0.600 μs 0.500 μs 0.400 μs 0.300 μs 0.200 μs 0.100 μs 0.000 μs 0.100 μs 0.200 μs

Figure 5.33 Clock drift retrieved by matching the monostatic and bistatic images. It appears as linear, though there is significant undulation (five cosine terms are modelled but these are not visible at this scale).

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Figure 5.34 Bistatic image resynthesized with compensation of the clock drift estimated

is that urban areas appear clearly as much dimmer in the bistatic image than in the monostatic image). These should be triple reflection echoes, very common in urban areas, which have a high directivity – higher than the minute (0.5◦ ) angle of bistatism. This should imply that the dimensions of the corresponding facets are larger than 2 m and their orthogonality is accurate to less than half a degree. The last and more obscure features appear on Figure 5.35 as isolated white spots. The physical nature of these objects characterised by a stronger bistatic RCS than the monostatic one is still unknown. Since these white spots are blurred compared to a typical point scatterer, a motion induced effect has been considered and rejected for the following reason. The bistatic antenna pattern is narrower than the monostatic one as the antenna pattern on receive is narrower for the passive system than for the active one. The radial motion of vehicles induces an off-axis migration in the antenna pattern (vehicles are imaged while their Doppler matches that of the motionless landscape), and as a consequence the resulting effect associated with motion should be a more important decrease in the vehicle RCS for the bistatic case than for the monostatic case. A moving object should appear as a dark spot and not a white spot. Now that the first estimation of the clock drift has been compensated for, it is possible to make a second pass of local correlation. This time, because of coherency conditions, the correlation works even on the uniform area (i.e. the speckle correlate) and the peak width collapses to one-half as the noncoherent (amplitude only) one. Alternatively, it is possible to proceed with computing of an interferogram between the monostatic and the bistatic images

Figure 5.35 Difference between the two monostatic and bistatic images after clock drift compensation

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Figure 5.36 Raw bistatic cross-platform (bistatic versus monostatic) interferogram. The strong alongtrack fringes are due to the remaining clock drift.

such as the ones presented in Figures 5.36 (phase) and 5.37 (coherency). The aspect of the fringe pattern is unusual compared with that of a classical monostatic or repeat-pass interferogram in that there are along-track fringes due to remaining clock drift. The average along-track gradient of the interferometric phase is then integrated as a secondary clock drift estimation (Figure 5.38) and subtracted from the interferometric phase (Figure 5.39) before phase unwrapping. Though this increases the robustness of the phase unwrapping, it is not completely legitimate to consider that the along-track component of the phase gradient is only due to clock drift (there is also an ‘orbital fringe’ or trajectory error part). This is why a third estimation (jointly with a trajectory update estimation) is needed. The next step common to classical repeat-pass interferometry (with the extra trick that some along-track part of the phase gradient should be taken back from the clock drift estimation) is the orbital fringe removal. This consists in estimating a trajectory (in fact baseline) error that explains the overall slope of the phase in range. Since, unlike the spaceborne case, the trajectory error is time-varying, the estimation of trajectory error from the ground control point would require hundreds of such points on the area, which is not practically feasible. Therefore the assumption is used that average interferometric elevation is zero across-track. Since all images involved in the processes were focused on a prior

Figure 5.37 Coherency (linear scale from black = 0 to white = 1) of the above raw bistatic crossplatform interferogram.

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0.000 µs

−0.001 µs −0.002 µs −0.003 µs −0.004 µs −0.005 µs −0.006 µs

Figure 5.38 Second estimation (updating) of the clock drift from the average along-track phase gradient of the interferogram. Beware that vertical graduations are only 1 ns here compared to the 100 ns of vertical graduations in Figure 5.33.

DEM, the interferograms built are differential interferograms and hence it may be assumed that this assumption is globally true (there is no overall terrain slope that was not detected by the prior DEM) and that an infrastructure elevation model can be constructed. For that purpose, the average quadratic across-track phase slope is minimized by adjusting the trajectory and clock drift parameters. These parameters are, for example, either a discrete cosine transform type of coefficient or a local spline coefficient (the latter being apparently more numerically stable for the third modelling). This yields a trajectory and a final clock drift update (Figure 5.40) that can be either compensated for in the interferogram or in a third bistatic image synthesis. The squint angle error induced by the second and third clock drift corrections is not critical for Doppler spectra overlap as the first one was; hence both approaches are acceptable.

Figure 5.39 Interferogram after compensating for the second estimation of the clock drift, where all the along-track component of the phase is cancelled out (though real orbital fringes have some along-track components).

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Figure 5.40 Third updating, horizontal passive receiver trajectory update (top), vertical passive receiver trajectory update (middle) and clock drift updating (bottom)

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Figure 5.41 Cross-platform (bistatic versus monostatic) interferogram after the third compensation (applied on the interferometric phase)

Phases in the interferograms of Figures 5.41 and 5.42 correspond to an oblique baseline. The along-track displacement is compensated for by the along-track sampling: Basically the bistatic image is in fact acquired 0.3 second earlier, the time for the middle of the two aircrafts (centre of phase of the bistatic antenna) to be reached by the trailing one (the monostatic operating aircraft). Thus, the phase on the interferogram is proportional to the elevation of the infrastructures (see, for example, the motorway trench and the bridges crossing it, the hedges, the urban area buildings or the aircrafts on the airport parking area). The along-track baseline correction, however, is not valid for moving objects such as vehicles. Hence moving targets should be visible on such an interferogram. Their detectability is nevertheless strongly obscured by the infrastructure elevation-induced phase. Were the vertical aircraft separation exactly zero (i.e. the trailing aircraft follow exactly the same track) the cross-platform interferogram would be of uniform grey with a few isolated darker and lighter spots – the moving targets. This is the principle of the along-track interferometry for moving target indication (MTI). What is new with bistatism is that elevation of

Figure 5.42 Cross-platform (bistatic versus monostatic) interferogram after re-synthesis of the bistatic SAR image with the new receiver aircraft trajectory and clock drift. The interferogram is has an improved quality since a slightly better Doppler spectra match increases the coherency (this is most noticeable in the low signal-to-noise area at the extremities of the swath)

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OPEN-LITERATURE BSAR AIRBORNE CAMPAIGNS Table 5.1 Comparison of MTI requirements for monostatic and multistatic systems Pure along-track baselines (monostatic)

Oblique baselines (multistatic)

Requirement for detection of moving targets

2 channels

Requirement for localization of moving targets

3 channels Spinoff: target and clutter RCS

3 channels Spinoff: infrastructure elevation 4 channels Spinoff: target and clutter RCS and elevation

Configuration

the infrastructure must be evaluated together with moving target detection and localization. More generally, it is the case for any configuration with an oblique baseline. Indeed, in any multiplatform multistatic system, even in space, an exact along-track baseline is almost impossible to attain. This results in an increase in the number of channels required for detection and localization of moving targets (see Table 5.1).

5.4 OPEN-LITERATURE BSAR AIRBORNE CAMPAIGNS Over the last years several bistatic airborne SAR experiments have been conducted in the United States and, more recently, also in Europe. Major objectives of these experiments were (a) to demonstrate the feasibility of bistatic SAR imaging, (b) to explore potential specificities in bistatic and multistatic SAR imagery and (c) to derive in more detail the technical challenges for future fully operational bistatic SAR systems. All bistatic SAR demonstrations have up to now been conducted in the X-band reusing essentially two conventional monostatic radar systems with a minimum amount of modification. This section provides a short summary of these experiments with the exception of the DLR-ONERA bistatic SAR campaign, which will be explained in more detail later on.

5.4.1 Michigan BSAR Experiment The first publicly available results of an airborne bistatic SAR experiment were published in 1984 by James Auterman [5.20]. The experiment took place in Michigan, USA, in 1983 and involved two Convair CV-580 aircraft flying with a nominal velocity of 180 kt (∼333 km/h). Three flight configurations were flown using either a vertical separation of 1000 ft (∼300 m) or horizontal along-track separations of several km, resulting in bistatic angles of 2◦ , 40◦ and 80◦ at a nominal range of approximately 10 km. Time synchronization to a few microseconds was achieved by observing the direct radar signal in combination with a transponder measurement of the distance between the two aircraft. The transponder ranging also assisted an accurate antenna pointing to ensure sufficient overlap of the antenna footprints. No explicit phase synchronization has been used, but the selection of appropriate quartz crystal master oscillators allowed for coherent integration times in the order of 2/3 seconds in the X-band and reduced the frequency offset to a few hertz. The final images were focused with a monostatic SAR processor to resolutions of 12.5 ft (∼3.8 m) in the slant range and 7 ft (∼2.1 m) in the azimuth, although that level of resolution was not completely achieved for all configurations due to

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the bistatic imaging geometry. A reproduction of the processed images can also be found in Reference [5.1] together with a detailed discussion of the experimental results.

5.4.2 QinetiQ BSAR Experiment Another airborne bistatic SAR experiment has been conducted by QinetiQ Malvern under the UK MoD Corporate Research Programme in September 2002. Results of this experiment were first published at the European Conference on Synthetic Aperture Radar in 2004 [5.21]. The bistatic configuration combined QinetiQ’s enhanced surveillance radar (ESR) on board a BAC1-11 airplane as the transmitter with the Thales/QinetiQ airborne data acquisition system (ADAS) on board a helicopter as the passive receiver. A distinctive feature of this experiment was the use of nonparallel trajectories with a Spotlight mode of operation where both radar beams were steered onto a pre-agreed spot on the ground [5.22]. The aircraft were tens of kilometres apart and imaged an urban environment surrounded by natural clutter regions. Synchronization was achieved by a pair of caesium atomic clocks which were connected with the monostatic radar hardware. A series of ground experiments had been conducted to verify this synchronization approach and it was shown that the range pulses with a resolution of 1–2 m remained in the same range gate of the receiving window. The final SAR focusing was based on a bistatic adaptation of the polar format algorithm [5.22]. In addition, autofocusing techniques had to be applied to mitigate image distortions due to residual motion and phase synchronization errors. No explicit values have been provided for the finally achieved range and azimuth resolution, but the experimental results from the ground experiment indicate resolutions in the order of 1–2 m.

5.4.3 FGAN BSAR Experiment Another bistatic SAR experiment has been conducted in November 2003 by FGAN using its two SAR sensors PAMIR and AER-II [5.23, 5.24]. The transmitter (AER-II) was placed on a Dornier Do-228 and the receiver (PAMIR) on a Transall C-160. The experiments used a rather large bandwidth of 300 MHz and consisted of several flight configurations with bistatic angles ranging from 13◦ up to 76◦ . All bistatic configurations used parallel tracks in a translationally invariant configuration where both aircraft had the same velocity vector. The distance and altitude of the aircraft were adjusted in such a way that bistatic angles of 13◦ , 29◦ , 51◦ and 76◦ resulted. Neither time nor phase synchronization has been performed thanks to the availability of a large receiving window. The experimental results show images with a ground range and azimuth resolution below 1 m [5.23].

5.5 THE ONERA-DLR BISTATIC AIRBORNE SAR CAMPAIGN The purpose of the following paragraphs is to present in detail the example of a bistatic airborne SAR campaign from design to acquisition [5.25] and data analysis, thereby highlighting the different steps of a full bistatic operation. Compromises had to be made in the design process, taking into account the specific objectives of the project, the limited budget, the short timeframe and the technical constraints driven by the inherited design of the two radar systems RAMSES and E-SAR.

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In the following paragraphs, the pre-flight engineering phase is described. First a short summary is given of the RAMSES and E-SAR radar systems. Then, the selection of the bistatic configurations and their instrument settings are explained in detail. Special emphasis is put on critical issues like PRF synchronization and relative platform navigation. A summary of the data acquisition plan concludes this section.

5.5.1 Preparing the Systems When the bistatic SAR campaign was first decided by DLR and ONERA in 2001, it was understood that it had to be conducted without major system upgrades and at minimum cost. A first step was hence an evaluation of the compatibility of the two radar systems. The following paragraphs summarize their main characteristics. 5.5.1.1 The RAMSES System RAMSES is a radar imaging system flown on board a Transall C-160 aircraft operated by the French CEV (Centre d’Essais en Vol). It can be best described as an experimental test bench for radar imaging with a high modularity and flexibility [5.26, 5.27]. For each acquisition campaign, it can be configured with three bands picked among eight possible choices ranging from the P-band to the W-band. Two selected frequencies can then be operated simultaneously. Once the system is mounted on the aircraft, the radar acquisition configuration can be varied from pass to pass. Six of the bands (all except Ka and W) can be operated from a single polarization mode to a fully polarimetric mode. The associated bandwidth and waveforms can be adjusted to meet the data acquisition objectives (optimizing the swath width versus the range resolution for example) and the antenna boresight incidence angle can be set from 30◦ to 85◦ . Several bands are available with the 1.2 GHz bandwidth corresponding to a 10 cm achievable range resolution. The X-band and the Ku-band systems have interferometric capabilities and can be flown in a ‘polarimetric interferometry’ mode. Table 5.2 describes the system. RAMSES is right-looking. In the table, PolInSAR indicates that the system can be operated in a single-pass polarimetric interferometric mode and Multi-B stands for single-pass multibaseline (at least three antennas). The letters in the polarization column indicate the polarization of the transmit antenna (first letter) and of the receive antenna (second letter) with V for vertical, H for horizontal, L for left circular and R for right circular. Table 5.2 Main characteristics of the RAMSES system Band P L S C X Ku Ka W

Centre frequency (GHz)

Bandwidth (MHz)

0.43 1.3 3.2 5.3 9.5 14.3 35 95

75 200 300 300 1200 1200 1200 500

Antenna

Polar

Array Array Array Array Both Horn Horn Horn

Full Full Full Full Full Full VV, HH LR, LL

Mode

PolInSAR, Multi-B PolInSAR, Multi-B

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Table 5.3 Main characteristics of the E-SAR system. The letters in the polarization column indicate the polarization of the transmit antenna (first letter) and of the receive antenna (second letter), with V for vertical and H for horizontal Centre frequency (GHz)

Bandwidth (MHz)

P L C

0.35 1.3 5.3

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9.6

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100 100 100

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100

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Full Full H and V, VH/VV or HV/HH VV or HH single polarization VV

Array

Look direction Left looking Left looking Left looking Left looking XTI or ATI Right looking

5.5.1.2 The E-SAR System E-SAR, the airborne experimental SAR system of DLR, was designed originally as a test bed for new radar technologies and processing algorithms and has been upgraded and expanded over the years to a multichannel SAR system with high flexibility and innovative operating modes [5.28]. The radar is operational in the P-, L-, C- and X-bands with selectable vertical or horizontal antenna polarizations (see Table 5.3). In the P- and L-bands the system can be operated fully polarimetric. Interferometric data acquisition is possible in the X-band in the singlepass mode and in the L- and P-bands in the repeat-pass mode. The resolution of the E-SAR image products is up to 1.5 m in the slant range and 0.5 m in the azimuth (single look). Typical swath widths are 3 to 5 km and the scene length is not limited in general. The precision navigation system on board the Dornier 228-212 aircraft ensures the measurement of the platform position with an accuracy of 0.1 m absolute and of its attitude by 0.01◦ for pitch and roll and 0.1◦ for yaw angle. The system also gives the pilot an online control about the actual flight path to help keep the nominal track with accuracy better than 3 m. 5.5.1.3 Selection of the Frequency As a first experiment, in order to answer the scientific and technical objectives highlighted above, it was decided to start the investigation with the bistatic configurations where both radars are looking in the same direction (the bistatic angle in the vertical plane lower than 90◦ ). The X-band with the interferometric antenna for E-SAR was then the only possibility. RAMSES has three different X-band antennas with different beam shapes adapted to different applications. A horn antenna, characterized by the widest beam width, was selected as a conservative choice in order to simplify the requirements on relative position and attitude accuracy between the airplanes, as required for an overlap of the RAMSES and E-SAR antenna beam patterns. The centre frequencies of the two X-band systems (RAMSES and E-SAR) are offset by 140 MHz. RAMSES was able to shift its frequency slightly to adapt to the E-SAR one. The E-SAR maximum chirp bandwidth is 100 MHz, and it was decided to use the 100 MHz but also a 50 MHz mode allowing a lower sampling frequency and, as a direct consequence, a longer recording window as both systems are data rate constrained. The longer recording window

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THE ONERA-DLR BISTATIC AIRBORNE SAR CAMPAIGN Table 5.4 RAMSES and E-SAR X-band systems

Centre frequency (GHz) Maximum chirp bandwidth Polarization Azimuth beamwidth Elevation beamwidth Boresight incidence angle Antenna look direction Bits per sample Peak transmit power (W)

RAMSES

E-SAR

9.46 600 Quad polarization 16◦ 16◦ [30◦ –75◦ ] Right 8 300

9.6 100 VV 8◦ 35◦ 55◦ Right 6 1000

enabled a recording of the direct air-to-air transmit pulses if desired and provides a useful margin in case the two pulse repetition frequencies (PRF) become desynchronized. In Table 5.4, a more detailed description of both X-band systems is given. Note the higher transmit power associated with E-SAR, resulting from a higher operational altitude. E-SAR has, furthermore, a fixed boresight incidence angle of 55◦ , which is optimized for wide-swath monostatic data acquisitions over a large range of incidence angles. RAMSES can vary its boresight incidence angle from 30◦ to 85◦ . All these characteristics have a definite impact on the definition of the bistatic configuration and a careful analysis of the different potential configurations had to be conducted.

5.5.1.4 Defining the Configurations During the ONERA-DLR campaign, two main geometrical configurations were flown to explore specific scientific and technical objectives:

r In the first geometrical configuration, the quasi-monostatic mode, also referred to as the ‘DLR configuration’, the two planes were flying close together, one following the other, to investigate phase synchronization and to simulate single-pass cross-platform interferometry from space with a large baseline. The across-track distance was selected such that it was well below the critical baseline in order to ensure sufficient coherence between the monostatic and bistatic data sets.

r The second geometrical configuration, referred to as the ‘ONERA configuration’ was de-

signed to acquire images with a large bistatic angle. The two planes were flying on parallel tracks around 2 km apart, at similar altitudes, with the antennas pointing to the same side at an area on the ground. These configurations are shown in Figure 5.43. In the DLR configurations, the two planes were flown on almost the same track, RAMSES following closely E-SAR, at a slightly lower altitude. The distance between the two planes was less than 100 m in along-track and less than 20 m in altitude. In the ‘ONERA’ configurations, the two planes were flying on parallel tracks offset by about 2 km across-track. In the ONERA-grazing configuration, the E-SAR boresight incidence angle (BIA) was 55◦ and the RAMSES BIA was 75◦ , creating a bistatic

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(a)

(c)

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Figure 5.43 Bistatic configuration: (a) quasi-monostatic case (BIA E-SAR 55◦ , RAMSES 45◦ ), (b) grazing angle configuration (BIA E-SAR 55◦ , RAMSES 75◦ ), (c) steep angle configuration (BIA E-SAR 55◦ , RAMSES 30◦ )

angle of around 20◦ . In the other ONERA configuration, RAMSES was flying on the right side of E-SAR with a BIA of 30◦ . The geometry associated with each configuration was fine-tuned to optimize the SAR performance, like the signal-to-noise ratio (SNR), range resolution or timing issues [5.29–5.31]. In the timing analysis, there was a requirement that both the direct path (from one plane to the other) and the specular path (plane 1–ground forward scattering–plane 2) did not interfere with

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the useful data, as illustrated in Figure 5.44. In Figure 5.45, the variation of the signal-to-noise ratio is presented for the DLR configuration. It can be observed that the two antenna footprint centres are not co-located. This is a deliberate choice to provide the best possible composite bistatic (round-trip) ‘antenna pattern’, shown as a dotted line in the figure. One peculiar characteristic of the bistatic configurations is clearly illustrated in Figure 5.45. In monostatic processing, the area within the 3 dB antenna pattern is used. These zones are indicated as solid lines. The antenna pattern is usually very well known in these areas. However, as outlined by the dotted line, the corresponding 3 dB pattern in the bistatic mode includes zones outside the 3 dB pattern of either E-SAR or RAMSES. The pattern is not as well-characterized there and this creates difficulties in the calibration process. In the ONERA bistatic configurations, the two aircraft altitudes could have been adjusted such that the intersection of the antenna boresight and the ground would match. However, this option was not taken for three reasons:

r SNR issues; r the RAMSES flight altitude is limited to 12 000 feet because it is operated with an open door;

r a specific request from the pilots to fly the two systems at a similar altitude in order to facilitate the control of the relative positions of the two airplanes. The final selected geometrical configurations have the characteristics given in Table 5.5.

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Table 5.5 Geometry of flight configurations

Configuration ID DLR IF 1 DLR IF 3 ONERA 1 ONERA 2

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Transall altitude (ft)

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< 20 < 20 150 150

< 100 < 100 0 0

45 45 30 75

Several technological challenges had to be overcome for the acquisition. The main one was the synchronization between the two radar systems. The second issue concerned the relative geometry control strategy.

5.5.1.5 The Pre-flight Testing The two radar systems have their own stable oscillators and while the short time phase stability of the clock between the transmission and reception of a radar pulse is of major concern in a monostatic SAR operation, the exact central frequency of this clock is not essential: a shift of a few hertz will not affect the data quality as the same clock is used in the transmit and receive channels. However, in bistatic operation, this becomes a major issue [5.32, 5.33]. This is especially the case for the present experiment where the two radars had no communication link to exchange timing information. Two major difficulties can be identified: a slightly different central frequency for the transmit signal or for the sampling frequency and the positioning of the receiving window on the passive system. Both points are developed in the following paragraphs. The acquisition systems of E-SAR and RAMSES cannot operate in a continuous sampling and recording mode. Therefore, for each pulse, there is only a limited window during which the signal is digitized and recorded. This window has to be positioned properly and in the monostatic case it is done with respect to the PRF (pulse repetition frequency) signal as this signal also triggers the transmit pulse. In the bistatic case, the PRF signal on the passive system (triggering the receiving window) may occur at a different time from the PRF signal on the active system. Both RAMSES and E-SAR operate with a 10 MHz STALO (stable local oscillator) frequency. Based on the configurations proposed earlier and a pulse length of around 5 μs, a useful recording window of the order of 16 μs is typical. For a PRF of 1 kHz and a sampling rate of 100 MHz, the maximum recording window size that E-SAR can manage in this mode is of the order of 25 μs, allowing a 4.5 μs time margin at the beginning and end of the recording window. Both systems use the same type of STALO. These STALOs are extremely stable but the inherent relative drift, even if very small, can create an unacceptable shift in the recording window. The flights were planned to last for around 3 hours. For a 3 hour flight, this translates into a relative maximum shift between the two STALO frequencies ( f / f ≤ 10−9 ). The resulting frequency stability requires a STALO of the class of a rubidium clock, known however to be sensitive to vibration and to have poor phase noise characteristics. Such an upgrade was too costly and another solution had to be found.

THE ONERA-DLR BISTATIC AIRBORNE SAR CAMPAIGN

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The two systems include a GPS receiver with a 10 MHz internal clock, controlled by the standard pulse per second (PPS) signal. These clocks are therefore available on both radars. Characterization of the associated performances of a SAR system mastered by such a clock was done in the laboratory. Because these clocks are constantly adjusted to match the PPS signal information, their actual frequencies are also constantly changing, creating an unacceptable phase noise in the radar signal if used as a STALO. An intermediate solution was engineered: both radars are controlled by their own internal STALO, avoiding the excessive phase noise effect. Before take-off, the two STALOs are connected and their frequencies matched as precisely as possible. Once disconnected, the two STALOs are left undisturbed. Then, just before each acquisition, the two PRF signals are synchronized to the PPS coming from the GPS system. This ensures that the recording window on the passive system is set properly in order to record useful data even if the frequencies of the two STALOs are not exactly matched or are slowly drifting during the acquisition. In this way, the tolerable frequency deviation between the oscillators is increased by two orders of magnitude. The residual discrepancy between the two STALOs (shift and/or drift) can be observed in the resulting data and has to be corrected in the data processing chain.

5.5.1.6 Navigation Issues The overlapping of the two antenna footprints on the ground is an essential condition for data quality. As a consequence, the two planes have to be flown precisely together in order to maintain the proper relative geometry during each data acquisition. This constraint is driven by the fixed beam configuration. The two types of configurations are quite different. In the DLR case, where the two planes are flying one behind the other in a very compact formation, the Transall pilot was simply following the Dornier plane. The ONERA configuration is more challenging as the two planes were about 2.5 km apart. An analysis of the relative shift of the antenna footprints due to positioning and attitude errors between the two planes indicated that a maximum along-track displacement of 100 m is allowed. A similar analysis was done on the roll, squint and pitch angles. A 100 m positioning requirement over a 2.5 km distance cannot be met with visual means only. An alignment procedure was defined involving two predefined sets of ground control points, one for each aircraft. The corresponding points had to be overflown simultaneously. The pilots adjusted their speed to a known airspeed velocity and had six nautical miles before acquisition to line up the two planes using the ground points and communicating through VHF channels. Flight test centre air controllers also provided a helpful guidance to achieve the correct configuration. This alignment phase was also used to synchronize both PRF signals by resetting the internal PRF counter in each radar system to the GPS PPS signal as described in the previous section.

5.5.2 The Campaign In all acquisitions, both systems are receiving simultaneously so that a monostatic image is always acquired along with the bistatic image. For each geometrical configuration, several data takes were acquired with varying system parameters (a bandwidth of 50 or 100 MHz,

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Figure 5.46 Calibration devices, trihedral corner reflector, Lunneberg sphere and transponder

RAMSES or E-SAR transmitting). The campaign consisted of two flights. During the second flight, RAMSES was receiving on two interferometric antennas. During the experiment, two trihedral corner reflectors and one Luneberg sphere were deployed to calibrate the monostatic images. The calibration targets are presented in Figure 5.46. The DLR configuration is referred to as a quasi-monostatic mode as the bistatic angle is smaller than 0.1◦ . Both monostatic and quasi-monostatic images can be radiometrically calibrated using the passive targets. The ONERA configurations, however, correspond to a large bistatic angle and this calibration option is not possible. For the calibration of the corresponding bistatic images, a transponder that was originally designed to calibrate X-SAR, the German radar on board the shuttle mission, was deployed. The quasi-monostatic configurations were flown at two different altitudes, in order to study the effect of different signal-to-noise ratios and to have different interferometric baseline angles. Furthermore, the low-altitude configurations also allowed for a recording of the air-to-air direct path radar signal, which may be used for phase synchronization [5.33].

5.5.3 Processing the Bistatic Images The processing of bistatic images was first done with the regular monostatic RAMSES SAR processor by using the average trajectory of the two planes as the ‘monostatic’ equivalent. This provided nice-looking images with good impulse responses for all configurations. However, the resulting image geometry was severely distorted for the ONERA configurations as the monostatic approximation is clearly not appropriate in this case. In order to analyse the influence of bistatic angle on scattering, it was necessary to develop a more complex processing that took into account the bistatic geometry and allowed a proper projection of the data into a common cartographic system. This processing is done according to the description provided in Section 5.3. Clock drift between the radars must be evaluated and compensated for. Typical drifts observed during a one minute acquisition are a few μs, with a 1 μs drift resulting in a 150 m slant range error. Estimation of this clock drift is performed by comparing the bistatic and the monostatic image geometry as illustrated in Plate 2 (in the colour section). A bistatic image distortion model was developed which provides a library of functions (and their derivatives) for mapping image coordinates to geographical coordinates (and conversely) depending on trajectories, system parameters and clock drift. Based on these functions, the observed distortion between the bistatic image (including drift effect) and the monostatic image (driftless) obtained through local image correlation can be translated into an estimated clock drift. Once the clock drift is known, the bistatic image can be reprocessed.

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The bistatic and monostatic images are now superposed with an accuracy of better than 1 pixel. This is adequate for most applications. However, for cross-platform interferometry, the superposition accuracy must be of the order of one-tenth of a pixel. In order to meet this requirement, another step in the processing has to be performed. A map of subpixel shifts and an interferogram are computed based on local maximization of interferometric coherence. The interferometric phase behaviour, the residual fringes and the variation of subpixel shifts in the image are used as an input to fine-tune the clock drift (of the order of a few ns) and the bistatic trajectory using the distortion model described earlier. The output of this process is a better knowledge of the relative trajectory of the two planes. This step has been detailed in Section 5.3. The images are then reprocessed and the antenna patterns removed.

5.5.4 Calibration of the Bistatic Images

σ [dBsm]

The calibration steps described in the following apply to processed images for which both the receive and transmit antenna patterns have been removed. Calibration of the quasi-monostatic bistatic images was simply done by using the passive calibration targets (trihedral reflectors and a Luneberg sphere deployed on the scene). Calibration of the ONERA configuration bistatic images is more of a challenge as the passive targets can no longer be used as the bistatic angle is of the order of 20◦ . Figure 5.47 provides the bistatic behaviour of a trihedral corner reflector for two different sizes. As can be seen in this figure, the width of the trihedral pattern is extremely narrow (a few degrees) and therefore cannot be used for bistatic angles of the order of 20◦ . 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 0.0°

3dB Bistatic Angle

ϑH ≈

IF 3: −1dB

14.5° a[m]⋅f [GHz]

(H.H. Meinke and F.W. Gundlach, “Taschenbuch der Hochfrequenztechnik”, Springer, 1986)

IF 1: −4dB

Side Size 800 mm Side Size 500 mm

0.5°

1.0°

1.5°

2.0°

2.5°

3.0°

3.5°

4.0°

4.5°

Bistatic Angle β

Figure 5.47 Bistatic patterns of two trihedral corner reflectors

5.0°

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AIRBORNE BISTATIC SYNTHETIC APERTURE RADAR

Monostatic image

Calibrated monostatic images

Transponder gain

Corner reflector

Bistatic images

Calibrated bistatic images Figure 5.48 Synoptic of the calibration procedure for the bistatic images

The calibration of the bistatic images was performed following the synoptic presented in Figure 5.48:

r The corresponding monostatic image is calibrated using the trihedral corner reflector response. Note that a monostatic image is always acquired at the same time as a bistatic image (both systems were receiving). From this calibrated monostatic image, the gain of the transponder was determined (taking into account the off-boresight angle). This is essential as the transponder was originally designed for X-SAR and therefore had a very high gain, potentially saturating the airborne data. In order to avoid this problem, its gain was lowered using a noncalibrated built-in attenuator resulting in an unknown gain.

r The expected level of the transponder in the bistatic image is then computed, taking into account both off-boresight angles, and an overall calibration factor for the bistatic image is then obtained.

The calibration procedure is validated over the quasi-monostatic images where either the transponder or the trihedral methods can be used.

5.6 A SELECTION OF RESULTS FROM THE CAMPAIGN 5.6.1 Quasi-Monostatic versus Monostatic It is interesting to note that a comparison of the quasi-monostatic and the monostatic images reveals noticeable differences. As expected, these differences are observed in the urban areas, where scattering is dominated by dihedral effects known to be extremely sensitive to aspect angle, especially when the dihedral facets are large. In addition, significant changes are also visible over agricultural fields. This is rather unexpected since natural surfaces are supposed

A SELECTION OF RESULTS FROM THE CAMPAIGN

• 209

to have a slowly varying scattering pattern for which a 0.1◦ change should have no effect. In Plate 3, a colour composite of a monostatic and quasi-monostatic image is presented. The differences in shades between different fields are clearly visible. 5.6.1.1 Bistatic Angle Effect on the Scattering The colour composite image in Plate 4 shows the superposition of three bistatic images acquired with different bistatic angles. It illustrates the effect of the bistatic angle on scattering. The blue colour corresponds to a quasi-monostatic image acquired in the DLR configuration. In this case, the double-bounce reflection is still very strong in the village. The green colour corresponds to a bistatic angle further away from the specular direction and the denser vegetation is green, indicating that for vegetation the scattering is very homogeneously distributed over all bistatic directions. The stereoscopic effect that can be observed along the tree edges in Figure 5.51 is linked to the different shadowing effects from the tree edges associated with the different observation geometries. As expected, the shadow increases with incidence angle, as can be observed when comparing the quasi-monostatic image and the grazing bistatic image. However, the shadows seem better defined and wider in the steep configuration than in the quasi-monostatic case. This is linked to the overlay phenomena. In ground geometry, the distance between the top of the tree edge and the shadow limit is larger for the steep configuration case:

r The shadow limit is at the same ground position for both images as it is determined by the larger incidence angle (which is 55◦ in both cases).

r The hedge top position is distorted due to an overlay phenomenon. Its position, as projected on the ground, will be further away from the real position in the bistatic case as the isodistance surface (an ellipsoid) for the bistatic case has a smaller slope than the corresponding isodistance sphere associated with the quasi-monostatic case. The comparison between the quasi-monostatic image and the steep configuration image shows that the bistatic angle helps to differentiate natural surfaces and to discriminate between different types of land cover (vineyard, orchard, wheat, bare fields, etc.). 5.6.1.2 Bistatic Interferometric Images In this example, illustrated in Plate 5, E-SAR is transmitting and RAMSES receiving on two distinct antennas separated by 80 cm in the cross-track direction, allowing interferometric processing. The bistatic configuration is the grazing one. Here the relative geometry of the two images is intrinsically robust to trajectory or clock drift errors as they have almost the same effect on both images. The hilly nature of the terrain is visible, with one of the villages, Garons, being set on a small hill. 5.6.1.3 Cross-Platform Bistatic Interferometric Images In the previous case, each image is a bistatic image. In the quasi-monostatic configuration, it is also possible to perform interferometry between a monostatic image and a bistatic image. In Plate 6, E-SAR is transmitting and receiving, thus forming the master image, while in the

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AIRBORNE BISTATIC SYNTHETIC APERTURE RADAR

so-called slave image E-SAR is transmitting and RAMSES receiving. During the interferometric processing, the matching of the geometry of the two images is critical and a careful adjustment of the trajectory as detailed in Section 5.3 was necessary. Furthermore, the underlying topography is interpreted as motion or a timing error and is removed at the same time as the clockdrift effect. The resulting product is a differential digital elevation model where the average topography has been flattened. The manmade constructions are then clearly visible in the pink colour, while the large freeway crossing the image appears to be below the average ground level.

5.7 SUMMARY The first results from the ONERA/DLR bistatic SAR campaign have already proved the great potential of bistatic SAR imaging for signature analysis, urban area remote sensing (less saturation due to the absence of strong dihedral reflections) and natural surface characterization. Furthermore, the cross-platform interferometry, illustrated above, clearly demonstrates that this technique can be used for terrain elevation retrieval from only one transmitting and two receiving radars. This supports the setup of spaceborne multistatic SAR systems such as the interferometric cartwheel, pendulum or tandem missions. Note that the orbital fringe removal is expected to be much simpler than in the above described airborne experiment since the typical satellite trajectories are usually orders of magnitude smoother than the aircraft ones. A follow-on DLR/ONERA bistatic compaign is planned in 2008, for which more sophisticated flight geometries are being considered.

ABBREVIATIONS DEM Digital Elevation Model DLR German Aerospace Center ONERA Office National d’ Etudes et de Recherche Aerospatiales PRF Pulse Repetition Frequency RCS Radar Cross-Section STALO Stable Local Oscillator

VARIABLES USED IN SECTION 5.3 a aint , bint b B dR F0 G H k ka , kb ku kx

‘across-track’ coordinate for bistatic image synthesis intermediate coordinates (linear transformed to a, b) ‘along-track’ coordinate for bistatic image synthesis radar bandwidth δ-dependent alteration of the range migration R due to motion compensation middle frequency of the radar transmitted wave longitude elevation of a generic ground point fast time (signal) wavenumber bistatic image wavenumbers slow time (signal) wavenumber across-track (image) wavenumber

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ky along-track (image) wavenumber L latitude N(u) point on the nominal trajectory at position u from start PRF pulse repetition frequency (slow time u sampling rate) R range to the nominal trajectory measured along the cone of angle δ0 R true receiver position (bistatic case) R0 nominal range (reference distance for the phases, focus point for processing) t fast (signal) time during the recording of one single pulse teff (t,r) slow time at which the sample acquired at slow time t is effectively used (along-track or z-migration) T true trajectory position (of sensor if monostatic, of transmitter if bistatic) u slow (signal) time, measures the succession of radar pulses VR receiver velocity vector VT transmitter velocity vector x orthogonal range to the nominal trajectory, (monostatic image) column coordinate y distance to the start point along the nominal trajectory, (monostatic image) line coordinate Z position along the nominal trajectory of the cone tip α effective squint angle from the real trajectory point T corresponding to a δ squint for the matched nominal point N δ instantaneous squint angle (varying during integration) δ0 squint angle of the image R range migration (as a function squint angle δ) bi R bistatic range migration (nominal + mocomp + algorithmic aberration compensation) Z along-track migration ζN oval shape intersection of the ground with the ellipsoid of foci N (pair of transmitter/receiver position) θ error parameter vector λ fast time (signal) wavelength λa , λb bistatic image wavelengths slow time (signal) wavelength λu λx across-track (image) wavelength along-track (image) wavelength λy

REFERENCES 5.1 Willis, N. J. (1991) Bistatic Radar, Artech House, Norwood, Massachusetts. 5.2 Moccia, A., Chiacchio, N. and Capone, A. (2000) Spaceborne bistatic synthetic aperture radar for remote sensing applications, Int. J. Remote Sensing, 21 (18), 3395–414. 5.3 Krieger, G., Fiedler, H. and Moreira, A. (2004) Bi- and multi-static SAR: potential and challenges, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2004), 25–27 May 2004, Ulm, Germany. 5.4 Zebker, H., Werner, C. L., Rosen, P. A. and Hensley, S. (1994) Accuracy of topographic maps derived from ERS-1 interferometric radar, IEEE Trans. Geoscience and Remote Sensing, 32 (4), 823–36.

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5.5 Rosen, P. A., Hensley, S., Joughin, I. R., Li, F. K., et al. (2000) Synthetic aperture radar interferometry, Invited Paper, Proc. IEEE, 88 (3), 333–82. 5.6 Zebker, H. (2000) Studying the Earth with interferometric radar, Computing in Science and Engineering, 2 (3), 52–60. 5.7 Zebker, H., Farr, T., Salazar, R. and Dixon, T. (1994) Mapping the World’s topography using radar interferometry: the TOPSAT Mission, Proc. IEEE, 82 (12), 1774–86. 5.8 Hanssen, R. (2001) Radar Interferometry: Data Interpretation and Error Analysis, Kluwer Academic Publishers, Dordrecht. 5.9 Evans, N. B., Lee, P. and Girard, R. (2002) The RADARSAT-2/3 Topographic Mission, in Proceedings of the European conference on Synthetic Aperture Radar (EUSAR 2002), Cologne, pp. 37–39. 5.10 Massonnet, D. (2001) The interferometric cartwheel, a constellation of low cost receiving satellites to produce radar images that can be coherently combined, Int. J. Remote Sensing, 22 (12), 2413–30. 5.11 Krieger, G., Fiedler, H., Mittermayer, J., Papathanassiou, K. and Moreira, A. (2003) Analysis of multistatic configurations for spaceborne SAR interferometry, IEE Proc.Radar, Sonar and Navigation, 150 (3), 87–96. 5.12 Farr, T. and Kobrick, M. (2004) The Shuttle Radar Topography Mission, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2004), 25–27 May 2004, Ulm, Germany. 5.13 Hartl, P. and Braun, H. M. (1989) Bistatic radar in space, in Space Based Radar Handbook, Artech House, Norwood, Massachusetts. 5.14 Massonnet, D. (2001) Capabilities and limitations of the interferometric cartwheel, IEEE Trans. Geoscience and Remote Sensing, 39 (3), 506–20. 5.15 Zebker, H. A. and Villasenor, J. (1992) Decorrelation in interferometric radar echoes, IEEE Trans. Geoscience and Remote Sensing, 30 (5), 950–59. 5.16 Romeiser, R., Schw¨abisch, M., Schulz-Stellenfleth, J., Thompson, D., Siegmund, R., Niedermeier, A., Alpers, W. and Lehner, S. (2002) Study of concepts for radar interferometry from satellites for ocean (and land) applications, Koriolis Report PDF file www.ifm.zmaw.de. 5.17 Klemm, R. (2002) Principles of Space-Time Adaptive Processing, Institution of Electrical Engineers (IEE), London. 5.18 Ulander, L., Hellsten, H. and Stenstrom, G. (2000) Synthetic aperture radar processing using fast factorised back projection, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2000), pp. 753–6. 5.19 Giroux, V. (2008) M´ethodes de formation d’image pour radars SAR bistatiques, PhD Thesis Dissertation, University of Nanterre-France (to be submitted). 5.20 Auterman, J. L. (1984) Phase stability requirements for a bistatic SAR, in IEEE National Radar Conference, Atlanta, Georgia. 5.21 Yates, G., Horne, M., Blake, A., Middleton, R. and Andre, D. B. (2004) Bistatic image formation, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2004), 25–27 May 2004, Ulm, Germany. 5.22 Yates, G., Horne, A. M., Blake, A. P., Middleton, R. and Andre, D. B. (2006) Bistatic SAR image formation, IEE Proc. Radar, Sonar and Navigation, 153 (3), 208–13, June 2006, DOI: 10.1049/ip-rsn:20045091. 5.23 Walterscheid, I., Brenner, A. R. and Ender, J. H. G. (2004) Results on bistatic synthetic aperture radar, Electronics Letters, 40 (19), 1224–5.

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5.24 Ender, J. H. G., Walterscheid, I. and Brenner, A. R. (2004) New aspects of bistatic SAR: processing and experiments, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS’04), Anchorage, Alaska. 5.25 Dubois-Fernandez, P., Cantalloube, H., Vaizan, B., Krieger, G., Horn, R., Wendler, M. and Giroux, V. (2006) ONERA-DLR SAR bistatic campaign: planning, data acquisition, and first analysis of bistatic behavior of natural and urban targets, IEE Proc. Radar, Sonar and Navigation, 153 (3), 214–23, June 2006, DOI: 10.1049/ip-rsn:20045117. 5.26 Dubois-Fernandez, P., Ruault du Plessis, O., et al. (2002), The RAMSES experimental SAR system, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS’02), Toronto, Canada. 5.27 Dubois-Fernandez, P., Ruault du Plessis, O., et al. (2004) The ONERA RAMSES SAR: status in 2004, in Proceedings of the International Radar Symposium 2004, Toulouse, France. 5.28 Horn, R., Moreira, A., Buckreuss, S. and Scheiber, R. (2000) Recent developments of the airborne SAR system E-SAR of DLR, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2000), Munich, Germany. 5.29 Krieger, G., Wendler, M., Fiedler, H. and Werner, M. (2002) The preparation of a bistatic airborne SAR experiment DLR/ONERA: interferometric X-band configurations with along-track separation, DLR Technical Note, February 2002. 5.30 Dubois-Fernandez, P., Cantalloube, H., Ruault du Plessis, O., Wendler, M., Horn, R., Vaizan, B., Boumahmoud, A., Coulombeix, C., Heuz´e, D., Krieger, G. and Gabler, B. (2003) ONERA-DLR bistatic SAR experiment: design of the experiment and preliminary results, in Proceedings of the ASAR Workshop 2003, CEOS WGCV SAR, 25–27 June 2003, Montr´eal, Canada. 5.31 Wendler, M., Krieger, G., Horn, R., et al. (2003) Results of a bistatic airborne SAR experiment, in Proceedings of the International Radar Symposium 2003, DGON, pp. 247–53, Dresden, Germany. 5.32 Cantalloube, H., Dubois-Fernandez, P. and Giroux, V. (2004) Challenges in SAR processing for airborne bistatic acquisitions, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2004), 25–27 May 2004, Ulm, Germany . 5.33 Weiss, M. (2004) Time and frequency synchronization aspects for bistatic SAR systems, in Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR 2004), 25–27 May 2004, Ulm, Germany.

6 Space-Surface Bistatic SAR Mikhail Cherniakov and Tao Zeng

6.1 SYSTEM OVERVIEW Various aspects of bistatic synthetic aperture radar (BSAR) were discussed in Chapters 1 to 5. Two major BSAR classes were considered: spaceborne and airborne systems. From their names it can easily be recognized that, in the first case, transmitters and receivers are based on two or more satellites, whereas for airborne systems transmitters and receivers are situated on different aircrafts. These two classes are the focus of a number of prospective researches. Here, BSAR systems are introduced that are essentially asymmetric, the illumination path being much longer than the echo propagation path. The basic operation of such systems is much the same as the operation of other BSAR systems, as previously discussed, the differences being introduced mainly as a consequence of the geometry employed. The discussion that follows is focused on systems using a satellite to carry the transmitter and locating the receiver on, or near, the Earth’s surface; the receiver may, or may not, be stationary (Figure 6.1). Such systems are identified as space-surface bistatic synthetic aperture radars (SS-BSAR) and are a newly introduced subclass of BSAR1 [6.1–6.4]. Thus, when the transmitter is spaceborne the receivers could be airborne, ground vehicle or shipboard mounted, or even stationary positioned on the ground. For the latter case, nongeostationary satellites should be used to provide the aperture synthesis. From this inherent peculiarity follows most of their unique properties and potentials, which are yet to be investigated on a full scale. This chapter is the first attempt to introduce systematically the main peculiarities of this BSAR subclass. In addition to the transmitting waveform and power the satellite trajectory parameters have an essential influence on the system configuration and performance. Artificial Earth satellites (typically used for broadcasting, navigation, communication and remote sensing of the Earth’s surface) can move in very different types of orbit depending on their application. These orbits 1

BSARs with high-orbited and low-orbited satellites also introduce a high level of asymmetry in their topology but will not be specifically considered in this chapter.

Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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Synchronisation

Synchronisation

SS-BSAR with an airborne receiver

Synchronisation Echo Echo

Echo

SS-BSAR with a vehicle based receiver

SS-BSAR with a stationary receiver

Figure 6.1 A simplified SS-BSAR topology

can be variously classified according to inclination with respect to the equator, altitude and eccentricity. Satellite altitude rorb may be low (1000 km or less), medium (10 000 km or more) or high (around 36 000 km).2 From the antenna synthesis point of view, the period of satellite rotation around the Earth is specifically important as it specifies the rotation angle over a given antenna synthesis time. For a circular orbit this time can be evaluated as Torb ≈

π 3/2 r . 107 orb

(6.1)

Satellites in geostationary Earth orbits (GEOs) follow an approximately circular path (above the equator) with a radius about 5.6 times the Earth’s radius. They can provide reliable, constantly available, global coverage of the Earth’s surface from the equator to moderate latitudes. Most broadcasting and communication satellites use this orbit. They exhibit little apparent movement, when viewed from Earth, and aperture synthesis relies on receiver movement. Depending on the antennas used, the nominal coverage of a GEO satellite may be close to hemispherical for ∼17◦ satellite’s antenna beamwidth, i.e. the Earth’s angular visibility from the satellite position, or the antenna beams may cover particular regions. Under other equal conditions for a regional coverage a bigger power spectral density near the Earth’s surface could be achieved due to a bigger satellite antenna gain. Wide nominal coverage does not ensure good local coverage in hilly or urban areas within the nominal coverage area because of shadowing. This is an important point to be taken into account when a GEO satellite transmitter is used. For terrain-mapping radar, clear lines-ofsight from the target to both the transmitter and receiver are required and the real coverage area is likely to be patchy. Another important issue is that GEO satellites are above the equator and consequently the system topology is essentially predefined. Satellites in medium and low earth orbits (MEO and LEO) move relatively quickly relevant to the Earth’s surface. They may potentially have any orbit inclination, but the orbits are not 2

The Earth’s mean radius is approximately 6378 km.

SPATIAL RESOLUTION

• 217

necessarily circular. The radius of an MEO is about 2.5 or more and an LEO has a radius around 1.1–1.2 times the Earth’s radius. As an example of an MEO, a GPS system could be considered. The satellites use circular orbits with an inclination of ∼55◦ and an altitude of ∼20 200 km above the Earth’s surface, which corresponds to Torb 12 h or approximately 0.008◦ per second. An LEO example would be the mobile satellite communication system Iridium. The satellites use circular orbits with an inclination of ∼86.4◦ , an altitude of ∼780 km and Torb ∼ 100 minutes or approximately 0.06◦ per second. These satellites offer global coverage as the satellite moves and the Earth rotates; if appropriate, a number of similar satellites may be deployed in a constellation. The availability of target illumination at a particular time and place depends on the number of orbits populated by satellites and on the number of satellites in each orbit. If images of a particular target need not be collected frequently, or at arbitrary times, a single satellite may be adequate, but for more demanding applications, more satellites would be required. Highly elliptical orbits allow coverage of areas at high latitudes for a large fraction of the orbital period. Satellite orbits are affected by the gravitational pull of nearby objects and the asymmetrical pull caused by the Earth’s equatorial bulge may be used to provide sun-synchronous orbits in which a satellite passes over a particular point on the Earth’s surface at approximately the same time every day. A well-known synthetic aperture radar (SAR) system, Radarsat, utilizes this orbit (∼98.6◦ inclination, ∼800 km altitude with the orbit period ∼100 minutes). Most satellites using transmitters operate in the microwave frequency region, the power density per unit area of the Earth’s surface and the usable signal bandwidth depending, of course, on the satellite’s orbit and the characteristics of the transmitter. A purpose-designed space segment can be expected to provide adequate power density and bandwidth, but care is needed in the choice of a noncooperative transmitter since broadcast and communication satellites provide signals that are not designed for radar applications but are intended for reception over a line-of-sight (LOS) link (see Chapter 7). Assuming sufficient echo signal power, the main characteristic of radar is its target resolution capability. This commonly depends on the characteristics of the radiated signal and the antenna, but in the case of BSAR and specifically SS-BSAR it also depends on system geometry (the relative positions of the transmitter, target and receiver). Target resolution is the subject of the following discussion.

6.2 SPATIAL RESOLUTION Understanding that SS-BSAR is a subclass of BSAR a start is made with a generic BSAR configuration consideration. Any BSAR employs a separately located receiver and transmitter and the motion of both of these locations forms an appropriate synthetic array. In general, the transmitter and the receiver movement may be independent, the trajectories and speeds being essentially different. Such a general topology presented in Cartesian coordinates is illustrated in Figure 6.2, where Rx and Tx are the transmitter and the receiver, Rt and Rr are the receiver and the transmitter target range corresponding and β is the bistatic angle. As in the monostatic SAR, synthetic arrays are formed by processing the phase history of echoes integrated over the period of target observation. However, in the bistatic case this phase history will in general depend on the trajectories and mutual position of the transmitter, receiver and targets. A rather general remark could be made here that is relevant to the aggregate aperture synthesis. When the GEO satellite transmitter is used, the receiver motion entirely

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Rx synthetic array Tx synthetic array

ρRx

Rr Rt ρTx

β

Observation area Figure 6.2 Array synthesis in BSAR

forms the aperture. For the MEO case and airborne or vehicle mounted receiver the aperture synthesis is specified mainly by the receiver motion. However, the satellite position variation must be taken into account during the signal and image processing stage and specifically for the high-resolution mapping. Finally, for the LEO case, the satellite motion over the aperture synthesis time can essentially influence the aggregate aperture characteristic and in many cases is as important as the receiver platform motion. The general benefits and drawbacks of the bistatic geometry are, of course, applicable to SS-BSAR, but the solutions of synchronization, baseline measurement and antenna pointing problems may be essentially more complex. Position measurement errors can introduce image smearing in azimuth, degraded image contrast and possibly higher sidelobe levels. Fortunately, the latest progress in satellite navigation systems makes accurate measurements at least feasible [6.5–6.10]. These estimates can be performed by differential GPS and inertial navigation systems (INSs) with further application of autofocus techniques (which are well established for a monostatic SAR but not for bistatic systems [6.11–6.14]). To study the resolution problems in radar an appropriate ambiguity function (AF) analysis could be applied [6.15]. Although this approach is widely used in conventional radars analysis it is not so popular for SAR investigation. Consequently, the first step for the SS-BSAR resolution analysis is the introduction of the monostatic SAR ambiguity function.

6.2.1 Monostatic SAR Ambiguity Function The cross-range resolution of radar systems employing real antennas is largely determined by the width of the antenna’s beam although, in the case of antenna arrays, processing techniques for obtaining improved resolution [6.16–6.18] exist. Radiated contributions from the elements of a real array are added at the target, the magnitude and phase of the sum depending on the

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magnitudes and phases of the individual contributions; if the array elements radiate identical signals, the phases of contributions at the target will be determined by the lengths of the paths travelled. A beam is formed if contributions add in phase in one particular direction (typically the broadside direction, along the perpendicular bisector of the array) but not in others. At short ranges in this direction, contributions do not add in phase but radiation can be focused on the target by suitable adjustment of the phase of the signal emanating from each element. If the range of the target is greater than about L2 /λ (L being the aperture length), then the path lengths can be taken to be approximately the same so the contributions are essentially in phase. In this (far-field) region, a beam of width (λ/L) is formed, the direction of which can be changed by changing the phase gradient across the array. The radiation pattern in the far field is approximately the product of two factors, one being the radiation pattern of an element and the other being an array factor. The array factor (field intensity) for an array of N elements, separation d, radiating in-phase signals is given by [6.19] sin[N π(d/λ) sin θ ] . |E a (θ )| = [sin π(d/λ) sin θ ]

(6.2)

Ambiguities (grating lobes) may arise depending on the value of d/λ; grating lobes can be avoided by placing array elements sufficiently close together. Systems employing synthetic apertures seek to overcome the constraints of real antenna arrays by moving a single antenna to different positions in an array, collecting and storing echo signals in each position. In this way very long arrays can be formed and, if the array is sufficiently long, its effective length when observing a target will depend on the beamwidth of the physical antenna (array element) and the range of the target. The array length is the lateral width of the physical beam at the range of interest. Monostatic synthetic aperture radar systems typically radiate chirp or phase coded pulses, the echoes of which are compressed on reception to provide improved range resolution. The echoes collected from a target in the near field of the synthesized array exhibit phases that depend on the positions in the array at which they were collected. This results in the formation of a spatial chirp signal in the cross-range direction. This chirp signal is compressed to give an improved cross-range resolution. Assuming unlimited data collection in the cross-range direction, the length of the synthesized array is proportional to the target range and the cross-range resolution is independent of range. It is noteworthy that the cross-range chirp is a sampled signal and that this may result in repeated peaks (grating lobes) in the compressed signal if the elements of the synthetic array are not positioned sufficiently close together. An AF can be used to study spatial resolution performance, the AF here being the twodimensional response of the radar to a point target (the point spread function, PSF); it is defined in terms of the echo from the target compared with the echo, which would be obtained from a specified reference point [6.19]. The transmitted signal is taken to be f (t) = s(t) exp(jω0 t),

(6.3)

in which s(t) is the complex envelope. A typical monostatic SAR geometry is shown in Figure 6.3.

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SPACE-SURFACE BISTATIC SAR

Aircraft velocity v z

x x

R0

h

R

x, R

x

,

( x,, y0, 0)

(0, y0, 0) Target Location y

Reference Point Figure 6.3 Typical SAR geometry

Any reflectors within the resolution cell will, of course, contribute to a composite target echo, but if a single point target is considered, the target echo can be written, apart from a complex weighting factor, as f (t − 2R/c).

(6.4)

f (t − 2R /c),

(6.5)

The reference signal is, similarly,

where R is the current distance from the transceiver to the target position and R is a distance to the reference point. The correlation function for these signals (changing relative position) is χss (x, y, z; x , y , z ) =

f (t − 2R c) f ∗ (t − 2R c)dt.

(6.6)

In terms of complex envelopes,

χss (x, y, z; x , y , z ) =

s(t − 2R/c)s ∗ (t − 2R /c) exp[−jω0 (2R/c − 2R /c)]dt.

(6.7)

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During one pulse repetition interval the ranges to the target and reference positions change very little. The correlation function for one pulse can therefore be written as χss (x, y, z; x , y , z ) = exp[−j2ω0 (R − R ) c] s(t − 2R c)s ∗ (t − 2R c)dt. (6.8) and the autocorrelation of the complex envelope as φss (R; R ) = s(t − 2R/c)s ∗ (t − 2R /c)dt.

(6.9)

During the time of aperture synthesis, it is assumed that echoes are collected from a number of array locations xn (see Figure 6.3). The single pulse autocorrelation functions are then summed over the length of the array to obtain the autocorrelation function of the aperture, it being assumed that R and R are constant at each array point and the φss (R; R ) is almost not changed for all array points during the aperture synthesis χ (x, y, z; x , y , z ) = φss (R; R )

exp[−j2ω0 (Rn − Rn )/c].

(6.10)

n

The functionχ is a product of two factors. The first factor in Equation (6.10) is F1 ≡ φss (R; R ) = s(t − 2R/c)s ∗ (t − 2R /c)dt. Taking the transmitted waveform to be chirp pulses, of duration T, so that s(t) = rect(t/T ) exp(jαt 2 ), this factor is F1 ≡ φss (R; R ) = T

sin{πB[2(R − R )/c]} . πB[2(R − R )/c]

(6.11)

The second factor, F2 ≡ n exp[−j2ω0 (Rn − Rn )/c], is a summation over the N elements in the synthetic array. For an even number of elements the limits will be ± N/2 and for an odd number, ±(N − 1)/2, i.e. F2 =

(N −1)/2

exp[−j2ω0 (Rn − Rn )/c],

(6.12)

n=−(N −1)/2

where Rn and Rn are target and reference ranges from the element at xn = n x = nvTPR and v is the aircraft velocity and TPR is the pulse repetition period. This notations is used to derive the next equations:

1 xn 2 2 2 2 Rn = h + y0 + (n x) ≈ R0 1 + , (6.13) 2 R0

1 xn − x 2 2 2 2 Rn = h + y0 + (n x − x ) ≈ R0 1 + (6.14) 2 R0 and Rn − Rn ≈ (2x xn − x 2 )/2R0 ,

• 222

SPACE-SURFACE BISTATIC SAR

whence F2 =

(N −1)/2

exp[−j2ω0 (Rn − Rn )/c] = exp[j2πx 2 /(λR0 )]

n=−(N −1)/2

exp[−j4πx n x/(λR0 )]

n

2π vTPR N x λ R 0 ,

= exp[j2πx 2 /(λR0 )] 2π vTPR sin x λ R0 sin

(6.15)

where R0 is the closest slant range between the transceiver and the target. Note that function Sa(N θ ) = sin N θ/ sin θ is repetitive, with peaks occurring when θ = mπ, m = 0, 1, 2, 3, . . . , indicating that peaks in the cross-range direction occur at D/(2 x) times L the synthetic aperture length (D being the effective length of the physical antenna and x the element spacing). To avoid repetitions within the length of the synthetic aperture (defined by the beamwidth of the physical antenna) x ≤ D/2.

(6.16)

For large N, the function close to the origin is approximately

sin(N θ) Sa(N θ ) ≈ N . Nθ

(6.17)

Note also that sin θ/θ ≈ 0.7 when θ ≈ 1.4 radians. The range (δr) and cross-range (δa) −3 dB resolution can be obtained from the SAR ambiguity function |χ | as δr ≈

1.4c , π F

(6.18)

δa =

1.4λR0 1.4λR0 . = πL πN vTPR

(6.19)

The system example with parameters described in Table 6.1 has been simulated to provide an example. The range and cross-range profiles and ambiguity function are plotted in Figure 6.4a–c. Cuts through the range and cross-range profiles at the −3 dB level give the Table 6.1 Sample system parameters Parameter

Value

Wavelength Bandwidth Pulse duration Sampling rate Synthetic aperture length Platform velocity Pulse repetition frequency

0.03 m 50 MHz 10−5 s 100 MHz 200 m 100 m/s 300 Hz

• 223

SPATIAL RESOLUTION

4

x 10

180

8

160

7

140

6

120

5

100

4

80

3

60

2

40

1

20

–4

–2

0 m

2

4

1.014

1.0145

1.015

1.0155 4

x 10

m

(b) Cross range profile

(a) Range profile x 105 6 magnitude

5 4 3 2 1 0 100 50

50 0

–50 –100 –50 (range coordinate)m

0 (azimuth coordinate)m

(c) Ambiguity function

Figure 6.4 SAR ambiguity function example

respective resolutions as being 3 and 0.75 m. Figure 6.4 shows |χ | as being separable sin θ/θ functions in the range and cross-range directions, within the range plotted.

6.2.2 Resolution in BSAR The analysis regarding the resolution of the bistatic radar can be found in different materials [6.20–6.22]. However, these results cannot be used in the BSAR system because of the significant difference between the geometry of the ground-based bistatic radar and that of the BSAR. The resolution and ambiguity properties of the BSAR are introduced via the AF [6.23]. The characteristics of this function for bistatic operation are different in comparison with its monostatic counterpart. Mapping from the measured range and range-rate coordinates in the BSAR into Cartesian spatial coordinates requires a nontrivial transformation. In the general case, the azimuth direction is not the cross-range direction; range resolution and azimuth resolution directions are not mutually orthogonal.

• 224

SPACE-SURFACE BISTATIC SAR

B

rt

rs ut A

Tx

rr

ur

Rx

Rt

Rr

Figure 6.5 Relative geometry of two point targets (A, B)

Briefly consider the resolution for two points, A and B, separated by a space distance rs , shown in Figure 6.5. The analysis proceeds by taking the spatial gradient of the range [6.24], at some target position A, to indicate the range resolution direction and the temporal gradient (time derivative) to give the range rate, the spatial gradient of which indicates the direction of range-rate resolution that is the Doppler resolution. The analysis uses a Cartesian image coordinate system centred on A. As shown in the figure, the range from transmitter Tx to a scatterer at A is Rt and the range from the scatterer to the receiver is Rr . The total range is a scalar function of position R(r) which relates the range measured by the time delay to the target separation distance, where r is the target position vector in the defined coordinate system. For some scatterer at B in the neighbourhood of A, displaced by a separation vector r s , the total range to point B is given by RB ≈ Rt + Rr + r t + r r ,

(6.20)

where rt and rr are shown in Figure 6.5. Assuming that ut and ur are unit vectors in the transmitter and the receiver directions respectively, then for a vicinity of point A, rt ≈ ut • r s ;

rr = ur • r s ,

(6.21)

where notation (•) is a scalar vector product and the relative total range from A to B is r = (ut − ur ) • r s .

(6.22)

The distance from A to B is |r s |, which can be found using the spatial gradient of r in the direction of rs . The steepest gradient is given by grad(r) and the direction of this vector is taken as the range direction, i.e. the direction of range resolution (see Figure 6.6). The change of the scalar point function r(r) associated with a change in position rs in the direction of range resolution is rs • grad(r). Comparison with the expression given above indicates that the gradient of the relative total range at point A is the vector (ut − ur ), whose direction coincides with the bisector of the bistatic angle and its magnitude is 2 cos(β/2). If ub is a unit vector in this direction, so that ub =

grad(r ) |grad(r )|

and

grad(r ) = ut − ur = 2 ub cos(β/2).

(6.23)

• 225

SPATIAL RESOLUTION

Range resolution direction Iso-range contour

ut ub

β/2

–ur

Grad (r)

Figure 6.6 Isoranges and range resolution direction

The bistatic range rate, which is associated with the Doppler frequency shift, can be found by differentiation, with respect to time, of the relative total range. If A–B separation is fixed, then a nonzero derivative depends on there being changes in the line-of-sight direction vectors ut and ur . r˙ = d/dt[(ut − ur ) • r s ] = d/dt[2 cos(β/2)ub • r s ].

(6.24)

This is also a scalar function of position, having a spatial gradient that is a function of position. A comparison with the general expression given previously indicates that the spatial gradient of the range rate is the vector d[2 cos(β/2)ub ]/dt, the direction of which is the direction of the steepest change of the measured range rate with changing spatial position; it is taken as the range-rate resolution direction and grad(˙r ) =

d {2 cos[β(t)/2]ub } . dt

(6.25)

Now differentiation of any unit vector ub multiplied by some scalar v(t) gives d dv(t) dv(t) dub [v(t)ub ] = ub + v(t) = ub + ω × ub v(t), dt dt dt dt

(6.26)

in which ω is a vector having a magnitude equal to the angular rate of turn of ub , and directed along the axis about which ub is turning. Thus ˙ sin[β(t)/2]ub + 2ω × ub {cos[β(t)/2]} . grad(˙r ) = −β(t)

(6.27)

The first term above vanishes if β(t) or dβ(t)/dt is zero. The second term is zero if the angular speed of rotation is zero or if β(t) = π ; otherwise it is orthogonal to grad(r). It seems then that the direction of range-rate resolution is perpendicular to the range resolution direction only if the bistatic angle is zero or, at least, constant. In the monostatic SAR, β is zero so the two resolution directions are orthogonal but, in the bistatic SAR, the expectation

• 226

SPACE-SURFACE BISTATIC SAR

is that these two directions will not be mutually orthogonal. A unit vector (ua ) in the direction of range-rate resolution is given by ua =

grad(˙r ) . |grad(˙r )|

(6.28)

Resolution in the measured range, r , and measured range rate, r˙ , can (see Figure 6.7) be plotted (in the range and range-rate directions) after division, as appropriate, by grad(r ) or grad |˙r |. The direction of range resolution is the direction of ub . The direction of range-rate resolution depends on the angular velocity of ub , which can be related to the radar system geometry by expressing ub in terms of its components. The range-rate gradient is grad(˙r ) =

d (ut − ur ) = (ω t × ut ) − (ω r × ur ), dt

(6.29)

where each cross product results in a vector, orthogonal to the relevant line-of-sight and to its axis of rotation, the magnitudes being proportional to the angular velocities. Unit vectors in the directions of these cross products are here denoted by Γt (for the transmitter component) and −Γr (for the receiver component) and will be used later in the text. The range-rate resolution direction is the direction of the sum of the weighted vectors (positioned at the target, of course). The resolution cell, i.e. the area restricted by range and range-rate resolution boundaries, is shown in Figure 6.7. The relevant vectors in various system geometries are shown below. For example, if both transmitter and receiver are stationary, translational movement of a target may give rise to rotational movement of the lines-of-sight, as shown in Figure 6.8. If the transmitter and the target are stationary, the array synthesis depends on movement of the receiver and the range-rate Range resolution direction: grad (r)

Resolution cell

Iso-range

δr Iso-range rate

α

Range-rate resolution direction •

grad (r)

δa δr •

δa =

•

grad (r)

Figure 6.7 Resolution direction

• 227

SPATIAL RESOLUTION

vt

v

vr

ur

ω t x ut

ω r x ur

ut

ωt

ωr Rx

Tx

Figure 6.8 Stationary transmitter and receiver, moving target Rx

ωr

Tx

ur

ωr x ur Figure 6.9 Stationary transmitter and target, moving receiver

resolution direction is taken as the direction of Γr =

ω r × (−ur ) , |ω r × (−ur )|

(6.30)

giving a vector aligned with the direction of rotation (Figure 6.9). Contours of the AF function for such a system (with the major parameters given in Table 6.2) are plotted in Figure 6.10. The contour plots at relatively high levels are, approximately, ellipses fitted inside the resolution cell parallelogram shown in Figure 6.10. Table 6.2 System parameters Parameter

Value

Wavelength Signal bandwidth Pulse duration Transmitter velocity Receiver velocity PRF Synthetic aperture time Bistatic angle Transmitter centre position Receiver centre position

0.03 m 100 MHz 4 × 10−6 s 0 −100 m/s 200 Hz 1.06 s 90◦ (x, y) = (0, −5000 m) (x, y) = (5000 m, 0)

• 228

SPACE-SURFACE BISTATIC SAR

10 8 iso-range line

6

y coordinate(m)

4 2

iso-doppler line

0 −2 range resolution direction

−4

azimuth resolution direction

−6 −8 −10 −10

−8

−6

−4

−2 0 2 x coordinate(m)

4

6

8

10

Figure 6.10 Example of BSAR AF contour plots

Therefore, for a general BSAR configuration the traditional definition of ‘range’ and ‘crossrange’ resolutions cannot be used as they are at least not orthogonal. In the next section, using ambiguity function analysis compact equations will be derived that could be used for the resolution analysis in SS-SAR.

6.3 SS-BSAR RESOLUTION 6.3.1 SS-BSAR Ambiguity Function Space-surface bistatic synthetic aperture radar systems observing stationary targets are considered in this section [6.25, 6.26]. They differ from monostatic systems in that the transmitter and the receiver are in different locations, moving along different trajectories at different speeds. As was discussed above, if both the transmitter and receiver move significantly during the time of target observation, two synthetic arrays are involved; if either one is stationary (or nearly so), only one synthetic aperture needs to be considered. Consider the general topology of such systems presented in Figure 6.11, which is a modification of Figure 6.2. In Figure 6.11, W T and W R are position vectors of the transmitter and receiver, V T and VR being the associated velocity vectors. The vector A specifies an arbitrary target position in the observation area and the vectors (W T −A) and (W R − A) are the respective lines of sight from this position, having magnitudes (ranges) of RTA and RTR , their sum being RA . Even though the transmitter and the receiver may move continuously, it is assumed for the purpose of analysis that signals are transmitted and received at discrete points along the trajectories of motion, corresponding to common discrete intervals of time; these points are the positions of synthetic array elements. The received signal is modelled as a function of two variables: t (fast time), which is used in the description of the range measurement at each point in the

• 229

SS-BSAR RESOLUTION

Tx Trajectory VT VR

Rx Trajectory z

WT WR Transmitter LOS distance R t Receiver LOS distance R r

x

A y

Figure 6.11 SS-BSAR topology

receiver’s array, and u (slow time), which is used to identify array elements in the description of the cross-range measurement. At time u the positions of the transmitter and the receiver are W T (u) = W T (0) + uV T , . W R (u) = W R (0) + uV R .

(6.31)

Let the transmitted signal be ST r = s(t) exp(j2π f 0 t). For a target located at point A, the time delay between the signal transmission and the receipt of an echo is τA (u) = RA /c = (RTA + RRA )/c = (|A − W T (u)| + |A − W R (u)|)/c.

(6.32)

Using the traditional radar equation [6.19], the power of the received echo is PR (u) =

PT G T (A, u)G R (A, u)λ2 , (4π)3 Rt2 Rr2

(6.33)

where PT is the transmitted signal power, GT (A,u) and GR (A,u) are the gains (at slow time u) of the physical antennas along the lines of sight to point A. The ratio of received to transmitted power is therefore MA (u) =

λ2 G T (A, u)G R (A, u) 2 2 (4π)3 RTA RRA

and the received echo can be described as h A (t, u) = MA (u)s(t − τA (u)) exp {j2π f 0 [t − τA (u)]} .

(6.34)

(6.35)

To formulate the generalized ambiguity function for the bistatic SAR, as in the case of monostatic SAR the normalized correlation between the echo from the target is taken at point A and

• 230

SPACE-SURFACE BISTATIC SAR

the echo which would be received from a reference target at some point B: h A (t, u)h ∗B (t, u)dt du χ(A, B) = |h A (t, u)|2 dt du |h B (t, u)2 |dt du √ √ MA (u) MB (u)s(t − τA (u))s ∗ (t − τB (u)) exp{j2π f 0 [τB (u) − τA (u)]}dt du = MA (u)|s(t − τA (u))|2 dt du MB (u)|s(t − τB (u)|2 dt du (6.36) It is useful for subsequent analysis to reformulate χ (A, B) in the frequency domain using Parseval’s theorem [6.27, 6.28], i.e. ∞ ∞ ∞ ∞ |s(t)|2 dt = |S( f )|2 d f . (6.37) s1 (t)s2∗ (t) dt = S1 ( f )S2∗ ( f ) d f and −∞

−∞

−∞

−∞

Then

√ P( f ) exp{j2π f [τB (u)−τA (u)]}d f MA (u)MB (u) exp{j2π f 0 [τB (u) − τA (u)]}du χ (A, B)= . P( f ) d f MA (u) du P( f ) d f MB (u) du (6.38) In order to simplify these expressions, the following assumptions are made:

r Since both targets are considered to have unit echoing area and are located close together (antenna gains in the directions of both therefore being approximately the same), the powers of the echoes from both are approximately equal, i.e. MA (u) ≈ MB (u).

r It is assumed that the length of each synthetic array is much smaller than the ranges to the target area, which means that the difference between the total propagation path lengths (via points A and B) will not change much as the receiver’s beam sweeps past the targets. Using the first-order Taylor expansion of delay difference about u A , the exponential in the outer integral above can be expressed as 2π f 0 τB (u) − 2π f 0 τA (u) = 2π f 0 [τB (u A ) + (u − u A )τ˙B (u A )] − 2π f 0 [τA (u A ) + (u − u A )τ˙A (u A )].

(6.39) The rates of change of the delays, associated with rates of change of path lengths, imply rates of change of the signal phase (Doppler shifts). For the target at point A, ˙ A )/c = 2π f dA (u A ). 2π f 0 τ˙ (u A ) = 2π f 0 R(u

(6.40)

Similarly for position B, so that 2π f 0 τB (u) − 2π f 0 τA (u) ≈ 2π f 0 [τB (u A ) − τA (u A )] + (u − u A )2π[ f dB (u A ) − f dA (u A )] (6.41)

• 231

SS-BSAR RESOLUTION

and 2π f 0 [τB (u) − τA (u)] ≈ 2π f 0 τ (u A ) + (u − u A )2π f d (u A ).

(6.42)

In this equation, τ (uA ) and fd (uA ) are the differences in delay and Doppler at uA .

r P(f) and its associated exponential factor, in the inner integral, arise from the transformation to the frequency domain of the integral s(t − τA (u))s ∗ (t − τB (u)) dt,

(6.43)

which has an associated time resolution δ τ . If (for any location B in the neighbourhood of A) the change in delay difference (as u varies during target observation) is small, say | τ (u) − τ (u A )| < δτ 2, then the phase factor associated with P( f ) can be written using τ (u) ≈ τ (uA ) as: P( f ) exp {j2π f [τB (u) − τA (u)]} ≈ P( f ) exp {j2π f [τB (u A ) − τA (u A )]} . On the basis of these assumptions, χ(A, B) can be rewritten as follows: P( f ) exp j2π f τ (u A ) d f χ(A, B) = exp[j2π f 0 τ (u A )] P( f ) d f MA (u) exp [2π (u − u A ) f d (u A )] du × . MA (u) du

(6.44)

(6.45)

Then, changing the variable u and putting ¯ f ) = P( f ) , P( P( f ) d f

(6.46)

¯ A (u) = MA (u + u A ) , M MA (u + u A ) du

(6.47)

the correlation function (6.38) can be presented as ∞ ¯ f ) exp[2π f τ (u A )] d f χ(A, B) = exp[j2π f 0 τ (u A )] P( −∞

∞

−∞

¯ A (u) exp(j2π f d u) du. M (6.48)

¯ f ) and M ¯ A (u): Transforming P( χ (A, B) = exp(j2π f 0 τ ) p( τ )m A ( f d ) ¯ f ) and mA ( fd ) is the transform of M ¯ A (u). where p( τ ) is the transform of P(

(6.49)

• 232

SPACE-SURFACE BISTATIC SAR Γ TA

Tx dp

B A cos θ (B A) T ΦTA

VTE dθ

Φ TB

−Φ TA

A

A

B

B

θ

(a)

(b)

(c)

Figure 6.12 Vector positions

This analysis shows that χ (A, B) and hence |χ(A,B)| are the product of two functions, one being the inverse transform of the signal power spectrum (specifying range resolution) and the other being the inverse transform of the normalized signal magnitude pattern across the receiving array (specifying resolution based on Doppler difference). It is of interest that the latter contains information about antenna radiation patterns and the system geometry, whereas the original Woodward’s ambiguity function is fully determined by the signal transmitted. Now to the ambiguity function should be expressed as a function of coordinate vectors and the spatial resolution obtained directly. The delay and Doppler differences are expressed in spatial terms and suitable approximations are made. The delay difference at time uA is a function of target separation. If the target separation is much smaller than the line-of-sight distances, an approximation for the delay difference can be obtained by projecting the separation on to the lines-of-sight at point A. The illumination path length difference is approximately (B − A)T ΦTA , where ΦTA is a unit vector along the line-of-sight from the target’s position at point A to the transmitter (see Figure 6.12(a) for an illustration). The approximate total delay difference is 1 (6.50) (B − A)T [ΦTA + ΦRA ]. c The Doppler difference at time uA depends on the difference between rates of change of path lengths, and this difference depends on the target separation as well as platform velocity. The rate of change in the length of the illumination path to the target at point A is the projection of the transmitter platform velocity on to the line-of-sight between A and the transmitter (see Figure 6.12(b) for an illustration). The rate of change of path length (range rate) to point A and the difference between the range rates to locations A and B are τ (u A ) ≈

R˙ TA = V TT ΦTA

and

R˙ TB − R˙ TA = V TT [ΦTB − ΦTA ].

(6.51)

The difference between the range rates is obtained by projecting the transmitter platform velocity in a direction perpendicular to a line bisecting the angle between the two lines-ofsight. This velocity component, VTE , is confined to the plane spanned by ΦTA and ΦTB (which includes the transmitter’s position and the locations points A and B); it is the velocity component

• 233

SS-BSAR RESOLUTION

useful for resolving targets at points A and B using Doppler history. For a small separation between A and B the approximate direction of this velocity component is along a unit vector ΓTA perpendicular to ΦTA (see Figure 6.12(c) for an illustration). As shown above, the path length difference is approximately |B − A| cos θ . If the effective velocity of the transmitter causes a small change in its position dp, the angle between the line-of-sight and the target separation vector changes by dθ and the new path difference is |B − A| cos(θ + dθ ). The change in path difference is therefore |B − A| (cos θ cos dθ − sin θ sin dθ − cos θ ) ,

(6.52)

and for the small dθ a replacement cos dθ ≈ 1 and sin dθ ≈ dθ can be made. Therefore the change in path difference is approximately − |B − A| sin θ dθ, which can be written as (B − A)T ΓTA dθ, in which ΓTA is a unit vector perpendicular to the transmitter’s line-of-sight to point A. The rate of change of path difference is (B − A)T ΓTA dθ/dt = (B − A)T ΓTA ωTA ,

(6.53)

where ω TA is rotation rate of the transmitter about A. A similar argument can be applied to the paths from A and B to the receiver. Combining the results leads to f d (u A ) ≈

1 [ω TA ΓTA + ω RA ΓRA ]T (B − A). λ

(6.54)

Now, substituting the expressions for τ and fd into the equation for χ(A, B), [ΦTA + ΦRA ]T (B − A) χ (A, B) ≈ exp j2π λ [ΦTA + ΦRA ]T (B − A) [ω TA ΓTA + ω RA ΓRA ]T (B − A) p mA . (6.55) c λ Positions and directions of the main vectors under consideration are shown in Figure 6.13. Tx Basic Plane

Rx Θ

η x

y

Nb Ξ

Figure 6.13 Vector positions and directions

• 234

SPACE-SURFACE BISTATIC SAR

The sum of ΦRA and ΦTA is a vector in the direction of the bisector of the bistatic angle, β. Therefore, if Θ is a unit vector in this direction, ΦTA + ΦRA = 2 cos(β/2)Θ.

(6.56)

The sum of ω TA ΓTA and ω RA ΓRA is a vector in a direction depending on the angle between the rotation direction vectors and the angular speeds of the transmitter and the receiver. If Ξ is a unit vector in this direction and if the modulus of the resultant is written as 2ω E , then ωTA ΓTA + ωRA ΓRA = 2ωE Ξ.

(6.57)

This result is supportive of intuition. If, say, the transmitter is stationary (or nearly so) it makes little or no contribution and the direction of its movement (if any) is irrelevant. In this case, the best azimuth resolution is obtained in a direction that is a projection of the receiver’s trajectory and it depends on the receiver’s angular speed. Similar remarks apply in the case of a stationary receiver. It is noted, in passing, that a monostatic SAR moving in the direction Ξ with angular speed ω E would exhibit similar Doppler-based resolution characteristics and that, for this reason, Ξ and ω E are sometimes referred to as the ‘equivalent’ direction and angular speed. Consider some illustrations to Equation (6.57). Assume that an SS-BSAR receiver is on an airplane moving at a speed of 200 m/s relevant to the observation area, which is at a distance 10 km from the plane. An evaluation is made that ω RA ∼1◦ per second. Above, it was considered that the maximal angular speed of satellites corresponds to a low orbit and is equal to ∼0.06◦ per second. It can be seen that the main input for the synthetic aperture forming will be from the receiver motion. Of course, the satellite motion should be taken into account when BSAR algorithms are considered. On the other hand, if the receiver is on a small unmanned aerial vehicle (UAV), which usually has a low speed, say 25 m/s or ∼0.1◦ per second angular speed relevant to the considered target, about equal input to the aperture synthesis can be expected from both the satellite and airplane motions. The two vectors Ξ and Θ span a plane referred to as the basic plane, which is different from the bistatic plane determined by the positions of the transmitter, the receiver and the target. The unit vector normal to the basic plane is here identified as Nb and the angle between the basic and terrain (x, y) planes as η. The vectors and Θ are not necessarily mutually orthogonal (see Figure 6.14). It has been established that the ambiguity function comprises, approximately, the product of two separable functions, the argument of one being derived from the difference in propagation

β Ξ

Θ

ηΘ A

B

A

Figure 6.14 Mutual vector positions

B

ηΞ

SS-BSAR RESOLUTION

• 235

delay while that of the other is based on the Doppler difference. The complete function describes a surface over the basic plane and determination of the resolution performance in an arbitrary direction involves taking a slice through the AF in the required direction:

2 cos(β/2) T 2ωE T |χ (A, B)| ≈ p (6.58) Θ (B − A) m A Ξ (B − A) . c λ

The first of the two factors above has an argument involving β, Θ and the target separation vector, all of which could, in principle, vary during the target observation interval, but for a short observation time or slow angular speeds the magnitude of β and the direction of Θ might be regarded as constant. In this case, this factor can be explored as the target separation vector varies in magnitude and direction. For any specified direction of separation, the argument is the scaled target separation distance and the scaling factor depends on the angle between Θ and the target separation vector, which is zero when targets are positioned along the line of Θ. The projection on the x, y plane of the resolution measured along Θ is obtained by division by cos η Θ , where η Θ is the angle between Θ and the x, y plane. If the target separation vector is normal to the line of Θ (the direction of range resolution) then it lies along an iso-range contour and (since ΘT (B − A) = 0) the modulus of the ambiguity function involves only the second factor given above. The second of the two factors of |χ| has an argument involving ωE Ξ and the target separation vector. Remarks similar to those made above are applicable, the argument again being the scaled magnitude of the target separation distance. Resolution along Ξ is the azimuth resolution on the basic plane and its projection on the x, y plane can be found by division by cos η Ξ . If the target separation vector is chosen to be normal to Ξ, then it lies along an iso-Doppler contour and (since ΞT (B − A) = 0) the modulus of the ambiguity function involves only the first of the two factors given above. Nominal resolution is determined by the width of a slice through |χ| at the −3 dB level. If the relevant inverse functions are known, the nominal range and azimuth resolution can be calculated easily, but the resolution capabilities offered by specific systems are generally to be found by numerical computation. However, an analytic description may aid understanding and assist in the formulation of such computation. The area of a resolution cell is given by the area of a section of |χ(∗ )|, parallel to the basic plane, again at the −3 dB level. This area can be represented by a vector normal to its surface (i.e., normal to the basic plane), its length being equal to the area in question; the area projected on to the terrain plane can be represented similarly. If the basic plane area is Sb , the terrain plane area is given by Sb /cosη. The area of a resolution cell cannot be estimated using the product of the range and azimuth resolutions because these, in general, refer to nonorthogonal directions. The area is given by ∞ ∞ ∞ √ T Sb = u χ A, [x, y, z]T − 1/ 2 δ [x, y, z]T − A Nb dxdydz,

(6.59)

−∞ −∞ −∞

in which u(∗ ) and δ(∗ ) are the step and impulse functions respectively. The meaning of this integral may not be obvious. If the area under consideration were parallel to the x, y plane it could be described by a double integral with appropriate limits. However, here an area parallel to the basic plane should be described where the limits depend

• 236

SPACE-SURFACE BISTATIC SAR

z’ Nb z

H

Ξ

A

y’ α x’

Θ y

x

Figure 6.15 Coordinate transformations

on the form of the AF. Clearly the integral must involve all three (x, y, z) coordinates but it is not intended to describe a volume; the purpose of the impulse function in the integral is to provide an appropriate reduction to two dimensions, confining the integration to the basic plane (over which its argument is zero). The step function has the magnitude-shifted ambiguity function as its argument, the argument being positive only when the ambiguity function is above its 3 dB level. The step function is nonzero (having value unity) only over the area of interest and it can therefore provide appropriate limits on the integration. Clarification is obtained by coordinate transformation, first to an orthogonal system set in (and normal to) the basic plane, and then (by rotation of one axis) to the directions of Θ, Ξ and Nb (see Figure 6.15). The transformation involves an initial shift of the origin to the target position (point A), giving new coordinates xA , yA , zA . Then xA is moved to the Θ direction and zA to the Nb direction, bringing yA to an orientation (orthogonal to the other two axes) identified by a unit vector H. This axis is then rotated to the Ξ direction and, finally, the axes in the Θ and Ξ directions are scaled as required by the arguments of p(∗ ) and mA (∗ ). The steps in the transformation are ⎡

⎤ ⎡ x [2 cos(β/2)]/c ⎢ ⎥ ⎢ 0 ⎣y ⎦=⎣ 0 z

⎤ ⎡ ⎤ ⎤⎡ ⎤⎡ 0 0 xA 1 0 0

x y z ⎥ ⎢ ⎥ ⎥⎢ ⎥⎢ 2ωE /λ 0⎦ ⎣ cos α sin α 0 ⎦ ⎣ Hx Hy Hz ⎦ . ⎣ yA ⎦ . 0 1 0 0 1 Nbx Nby Nbz zA (6.60)

The integral is now to be expressed with reference to dx dy dz , which requires the inclusion of the appropriate Jacobian determinant (which is not affected by the initial shift of the origin) −1 so that dxdydz = |J | dx dx dz . Writing the transformation as X = TXA or X A = T X , the required Jacobian is det ∂ xA.i /∂ x j . Differentiation of XA with respect to X gives T−1 , so |J | = det T −1 =

1 , det [T ]

(6.61)

and for [T ] = [T1 ] [T2 ] [T3 ] , |J | =

1 . det[T3 ] det[T2 ] det[T1 ]

(6.62)

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Now the matrix describing the first step (T1 ) is an orthogonal matrix describing a rotation, so det [T1 ] = 1. The determinant of the matrix (T2 ) describing the second step, the rotation of H, is det[T2 ] = sin α. The determinant of the scaling matrix (T3 ) is det [T3 ] = 4ωE cos(β/2)/cλ. Hence |J | =

λc , 4ωE cos(β/2) sin α

(6.63)

and in terms of the new variables ∞ ∞ ∞ √ Sb = u p(x )m A (y ) − 1/ 2 δ[z ]|J |dx dy dz −∞ −∞ −∞

∞ ∞ √ = |J | u p(x )m A (y ) − 1/ 2 dx dy .

(6.64)

−∞ −∞

6.4 SS-BSAR RESOLUTION EXAMPLES This section reports on the analysis of a specific SS-BSAR system. The system under consideration employs a moving transmitter Tx, carried by a satellite, and a stationary receiver Rx situated (as is the target Tgt) on the terrain x–y plane. The geometry of the system is as shown in Figure 6.16. The transmitter’s trajectory is parallel to the x axis and the grazing angle of the radiation in the vicinity of the receiver is ε. The power spectrum and received signal pattern are as shown below.

1 1 f2 u2 ¯P( f ) = √ ¯ (6.65) and M(u) = √ exp − 2 . exp − 2 2σu 2σ f σ f 2π σu 2π Now the system’s resolution in the x and y directions should be found. VT Tx ΓT ( Ξ ) z

Θ Tgt

ε

Rx y

x

Figure 6.16 SS-BSAR with stationary receiver and moving transmitter

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z Θ

Ξ

θ ax

y x

θ rx

Figure 6.17 Local coordinate system

The ambiguity function is described by (6.58). To support the analysis Figure 6.17 shows a local coordinate system centred on the target (as is the ambiguity function). The resolution distance along any direction line through the origin is similarly centred. If points A and B are positioned on the x axis, respectively at x = 0 and x = δx/2, then ΘT (B − A) =

δx cos θr x , 2

(6.66)

in which θ r x is the angle between Θ and the x axis. If θ ax is the angle between Ξ and the x axis, then ΞT (B − A) =

δx cos θax . 2

(6.67)

Resolution (−3 dB level) in the x direction can then be found by solving the following equation:

2 cos(β/2) δx 1 ωTA δx p cos θr x m A cos θax = √ . (6.68) c 2 λ 2 2 Similarly, resolution in the y direction is given by

2 cos(β/2) δ y ωTA δ y 1 p cos θr y m A cos θay = √ . c 2 λ 2 2

(6.69)

The transforms of the power spectrum and the received signal pattern are p( τ ) = exp −2π2 σ 2f τ 2 and

m A ( f d ) = exp −2π2 σu2 f d2 .

(6.70)

Therefore δx can be obtained from !

2 "

2 1 2 2 2 cos(β/2) δx 2 2 ωTA δx exp −2π σ f exp −2π σu =√ , cos θr x cos θax c 2 λ 2 2 (6.71)

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which, for σ f ≈ δ f and σu ≈ δu , leads to √

1 ln 2 # π 4 cos2 (β/2) cos2 (θr x )δ 2f

δx ≈

≈ #

c2 0.26

+

2 cos2 (θax )δu2 ωTA λ2

2 4 cos2 (β/2) cos2 (θr x ) ωTA cos2 (θax ) + (cδτ )2 (λδD )2

(6.72)

.

Resolution in the y direction, δy, can be obtained from !

2 "

2 1 2 2 2 cos(β/2) δ y 2 2 ωTA δ y exp −2π σ f exp −2π σu =√ , cos θr y cos θay c 2 λ 2 2 (6.73) which leads to √ δy ≈

ln 2 1 # π 4 cos2 (β/2) cos2 (θr y )δ 2f c2

ω2 cos2 (θay )δu2 + TA λ2

.

(6.74)

In order to find the area of a resolution cell it is first noted that, for the assumed model of the AF, the −3 dB contour of the cell (on the basic plane) is approximately an ellipse. As the intercept on the Θ axis is δr/2 and that on the Ξ axis is δa/2, these axes are not necessarily orthogonal. The equation of an ellipse with intercepts kx and k y on the orthogonal x and y axes is as given below, with that of its area (Se ) also given: x2 y2 + 2 = 1, 2 kx ky

Se = πk x k y .

(6.75)

Recalling that the angle between Θ and Ξ is α, the area of the resolution cell can be written approximately as Sb ≈ π

δr δa 1 . 2 2 sin α

(6.76)

The area on the terrain x–y plane is Sg =

1 Sb cδτ λδD πcλ δ τ δD . =π = cos η 4 cos(β/2) 2ωTA sin α cos η 8 cos(β/2)ωTA

(6.77)

The radar’s resolution capability depends on target coordinates, as illustrated below. The various resolution measures discussed above have been evaluated for radar having the parameter values shown in the Table 6.3. For this purpose the earth’s rotation and the curvature of the earth (the observation area being small) have been ignored.

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SPACE-SURFACE BISTATIC SAR Table 6.3 System parameters Satellite altitude Satellite speed Satellite motion direction Wavelength Delay resolution Doppler resolution Grazing angle ε

20 381 km 3870 m/s Parallel with the x axis 0.2 m 33 ns 1/200 Hz 30◦

As previously noted, range resolution depends on the bistatic angle (see Figure 6.18). For targets close to the negative half of the y axis, the bistatic angle is (at least approximately) ε, but for targets close to the positive half of the y axis the bistatic angle is around 180 − ε. For targets close to the x axis, in the vicinity of the receiver, the bistatic angle is about 90◦ . It is therefore to be expected that range resolution improves as y becomes negative. Range resolution is poorest at x = 0 with y positive; resolution will not be lost completely though unless ε is zero, in which case the target is positioned on the baseline. The azimuth resolution plot shows no spatial variation (see Figure 6.19). This is also to be expected since azimuth resolution in this system is determined completely by the motion of the satellite. Variation in target position implies a slight change in the slant range, and consequently in the satellite’s angular speed, but this is so small as to be negligible. The satellite’s trajectory is parallel to the x axis and, consequently, the resolution in the x direction is determined mainly by the azimuth resolution (see Figure 6.20); the resolution in the y direction is determined mainly by the range resolution (see Figure 6.21). As a result, δx varies little but δy varies considerably, being worse for y positive and x approaching zero when δy becomes much larger than δr. Contours of the ground projection of the area resolution variation are plotted in Figure 6.22. km

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c 2005 IEEE. This figure was published in Figure 6.19 Contours of azimuth resolution (m) [6.26] Zeng, T., Cherniakov, M & Long, T., 2005. Generalized approach to resolution analysis in BSAR. IEEE Transactions on Aerospace and Electronic Systems, 41(2), p. 461–474. Reproduced by permission of IEEE. km

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c 2005 IEEE. This figure was published Figure 6.21 Contours of resolution in the y direction (m) [6.26] in Zeng, T., Cherniakov, M & Long, T., 2005. Generalized approach to resolution analysis in BSAR. IEEE Transactions on Aerospace and Electronic Systems, 41(2), p. 461–474. Reproduced by permission of IEEE. km 50 40

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c 2005 IEEE. This figure was Figure 6.22 Contours of the ground resolution area (Sg ) (m2 ) [6.26] published in Zeng, T., Cherniakov, M & Long, T., 2005. Generalized approach to resolution analysis in BSAR. IEEE Transactions on Aerospace and Electronic Systems, 41(2), p. 461–474. Reproduced by permission of IEEE.

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VARIABLES

6.5 SUMMARY

The space-surface BSAR is a new class of radar and a lot of research is yet to be done to understand and evaluate the system’s performance, as well as its practicality. The problem of resolution analysis is the focus of the chapter. There are a lot of other extremely important problems behind the SS-BSAR study. Nevertheless, deformation, or more precisely, degradation of the system space resolution is the inherent problem that specifies the system topology. For example, if only transmitters on the geostationary orbit are considered the region of the system’s applicability is immediately reduced. Moreover, to still obtain reasonable resolution degradation an aircraft should provide a special manoeuvre and have its trajectory within a relatively narrow corridor to acquire an SAR image. On the other hand, using transmitters on medium or low orbits, similar, for example, to GPS satellites, nearly monostatic resolution can be achieved across the entire Earth’s surface. Unfortunately, this approach makes the SS-BSAR design with dedicated transmitters a very expensive enterprise. Therefore, the problem of system topology specification versus spatial resolution degradation is perhaps the most important and awkward problem of SS-BSAR design. The chapter material here could help to estimate the SS-BSAR resolution for the common case, and a particular topology resolution could easily be derived from this general consideration.

ABBREVIATIONS AF BSAR GEO GPS INS LEO LOS MEO PSF Rx SAR SS-BSAR Tgt Tx UAV

ambiguity function bistatic synthetic aperture radar geostationary Earth orbit global positioning system inertial navigation systems low Earth orbit line-of-sight medium Earth orbit point spread function receiver synthetic aperture radar space-surface bistatic synthetic aperture radar target transmitter unmanned aerial vehicle

VARIABLES A arbitrary target position B neighbourhood of A c speed of light d separation between array antenna elements

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D physical antenna aperture effective length E a (θ) array factor central frequency f0 G R (A, u) receiving antenna gain G T (A, u) transmitting antenna gain h transmitter (receiver) altitude L aperture length m A (u) ratio of transmit to receive power Nb normal vector of the bistatic basic plane receiver power PR PT transmitted signal power P(f) transmitting signal power spectrum density rorb satellite altitude rs space distance R current distance from the transceiver to the target position R current distance from the transceiver to the reference point Rr receiver target range receiver target at the position A range RRA Rt transmitter target range RTA transmitter target at the position A range s(t) complex envelope s ∗ (t) complex conjugate to s(t) Sb resolution cell area in the bistatic plane Sg resolution cell area in the ground plane t fast (real) time T duration of chirp Torb period of satellite rotation TPR pulse repetition period u slow time in SAR u(∗ ) step function ua unit vector in the direction of range-rate resolution unit vector in the direction of the bistatic angle bisector ub ur unit vector in the receiver direction unit vector in the transmitter direction ut v velocity component VR receiver velocity vector transmitter velocity vector VT WR position vectors of the receiver WT position vectors of the transmitter xn array locations β bistatic angle Γr receiver tangent speed direction with respect to the target transmitter tangent speed direction with respect to the target Γt δ(∗ ) impulse function δτ time resolution δa cross-range resolution δr range resolution

REFERENCES

δx δy F x η λ φss (.) |χ| χ ss ω0 ωE

resolution in the x axis direction resolution in the y axis direction signal bandwidth element spacing in the synthetic array angle between the basic and terrain planes wavelength equivalent speed direction autocorrelation function of a complex envelope ambiguity function single pulse ambiguity function central angular frequency equivalent rotation angle speed

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ACKNOWLEDGEMENT The authors would like to thank Dr J. Edwards for his valuable contribution to the preparation of this chapter.

REFERENCES 6.1 Cherniakov, M. (2002) Space-surface bistatic synthetic aperture radar – prospective and problems, in International Radar Conference, Edinburgh, pp. 22–6. 6.2 Cherniakov, M., Zeng, T. and Plakidis, E. (2003) GALILEO signal based bistatic system for avalanche prediction, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’03), Toulouse, France. 6.3 Cherniakov, M., Kubik, K. and Nezlin, D. (2000) Bistatic synthetic aperture radar with non-cooperative LEOS based transmitter, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’00), Hawaii, pp. 834–7. 6.4 Cherniakov, M., Kubik, K. and Nezlin, D. (2000) Radar sensors based on communication LEOS microwave emission, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’00), Hawaii, pp. 1007–8. 6.5 Weib, M. (2004) Synchronisation of bistatic radar systems, in IEEE Proceedings of the International Geoscience and Remote Sensing Symposium (IGRSS’04), Vol. 3, pp. 1750–3. 6.6 Horne, A.M. and Yates, G. (2002) Bistatic synthetic aperture radar, in International Radar Conference, Edinburgh, Scotland, 6–10 October 2002. 6.7 Yates, G., Horne, A. M., Blake, A.P., Middleton, R. and Andre, D.B. (2004) Bistatic SAR image formation, in European Coference on Synthetic Aperture Radar (EUSAR), Germany. 6.8 Davis, J. A., Lewandowski, W., Young, J.A., Kirchner, D., Hetzel, D., Parker, P., Klepczynski, W., Jong, G., Soring, A., Baumont, F., Bartle, K. A., Ressler, H., Robnik, R. and Veenstra, L. (1996) Comparison of two-way satellite time and frequency transfer and GPS common-view time transfer during the INTELSTAT field trial, in IEE Conference Publication of European Frequency and Time Forum (EFTF96), pp. 382–7.

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6.9 Powell, N.E. et al. (1986) Autonomous synchronization of a bistatic synthetic aperture radar addition holograghy for imaging, US Patent 4602257. 6.10 Auterman, J. L. (1984) Phase stability requirements for bistatic SAR, in IEEE National Radar Conference, Atlanta, Georgia, pp. 48–52. 6.11 Daniel, F.L., Held, N., Curlander, J.C. and Chialin, W. (1985) Doppler parameter estimation for spaceborne synthetic-aperture radars, IEEE Trans., GRS-23 (1), 47–56. 6.12 Moreira, J.R. (1990) Estimating the residual error of the reflectivity displacement method for aircraft motion error extraction from SAR raw data, in IEEE International Radar Conference, pp. 70–75. 6.13 Wahl, D.E., Eichel, P.H., Ghiglia, D.C. and Jakowatz, C.V. (1994) Phase gradient autofocus–a robust tool for high resolution SAR phase correction, IEEE Trans., AES-30, 827–35. 6.14 Walter, G. C., Goodman, R. S. and Majewski, R.M. (1995) Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House, Norwood Massachusetts. 6.15 Woodward, P.M. (1980) Probability and Information Theory, with Applications to Radar, Artech House, Norwood, Massachusetts. 6.16 Krim, H. and Viberg, M. (1996) Two decades of array signal processing research: the parametric approach, IEEE Trans., SP-13 (4), 67–94. 6.17 Capon, J. (1969) High-resolution frequency-wavenumber spectrum analysis, IEEE Proc., 57(8), 1408–18. 6.18 Schmidt, R. (1986) Multiple emitter location and signal parameter estimation, IEEE Trans., AP-35 (7), 276–80. 6.19 Skolnik, M. (1990) Radar Handbook, McGraw-Hill, New York. 6.20 Tsao, T., Slamani, M., Varshney, P., Weiner, D. and Schwarzlander, H. (1997) Ambiguity function for a bistatic radar. IEEE Trans., AES-33 (3), 1041–51. 6.21 Moyer, L.R., Morgan, C.J. and Rugger, D.A. (1989) An exact expression for resolution cell area in special case of bistatic radar systems. IEEE Trans., AES-25 (4), 584–7. 6.22 Willis, N. (1991) Bistatic Radar, Artech House, Norwood, Massachusetts. 6.23 Soumekh, M. (1999) Synthetic Aperture Radar Signal Processing, John Wiley & Sons Inc., New York. 6.24 Cardillo, G.P. (1990) On the use of the gradient to determine bistatic SAR resolution, in AP-S International Symposium, Vol. 2, pp. 1032–5. 6.25 Cherniakov, M., Zeng, T. and Plakidis, E. (2003) Ambiguity function for bistatic SAR and its application in SS-BSAR performance analysis, in International Radar Conference, Adelaide, Australia. 6.26 Tao, Z., Cherniakov, M. and Teng, L. (2005) Generalized approach to resolution analysis in BSAR, IEEE Trans., AES-41 (2), 461–74. 6.27 Van, T. and Harry, L. (1971) Detection, Estimation, and Modulation Theory, John Wiley & Sons Inc., New York. 6.28 Oppenheim, A.V., Willsky, A.S. and Young, I.T. (1983) Signal and System, Prentice-Hall, London.

7 Passive Bistatic Radar Systems Paul E. Howland, Hugh D. Griffiths and Chris J. Baker

In this chapter attention is turned to a class of radar systems termed ‘passive bistatic radar’. Passive bistatic radar (PBR) systems are a variant of bistatic radar that exploit ‘illuminators of opportunity’ as their sources of radar transmission. Dispensing with the need for a dedicated transmitter makes PBR inherently low cost and hence attractive for a broad range of applications. This chapter begins by reviewing the development of PBR systems. This is followed by an examination of system coverage and sensitivity via a PBR specific form of the bistatic radar range equation. This is used to simulate realistic scenarios to examine and compare variations in sensitivity and coverage for three candidate transmitters of opportunity. These examples show that a wide and extremely useful set of detection ranges are achievable but also highlights some of the key issues underpinning more detailed aspects of predicting detection performance. The key elements that constitute the essential building blocks of three approaches to PBR radar system design are then introduced, namely narrowband, wideband and multistatic. The narrowband approach adopted for signals with a poor ambiguity function and a significant continuous wave component (such as a carrier tone) is to sample the signal in a bandwidth small enough to capture the expected range of Doppler shifts of target echoes and then to attempt to estimate the aircraft’s location from the time history of the aircraft’s Doppler shift. Particularly in the late 1980s and early 1990s, when analogue-to-digital conversion (ADC) systems were limited to a few thousand samples per second, this approach was popular. Because the sampled bandwidth is much narrower than the original signal bandwidth, these techniques are often referred to as ‘narrowband’. The wideband approach, adopted more recently as ADC technology improved and increased computational power became available, samples the full signal bandwidth and attempts to perform more classical matched filtering approaches to the detection and tracking of aircraft. To contrast this with the early approach, this is sometimes referred to as ‘wideband’, although it would perhaps be better described as ‘fullband’ as the bandwidth is not wide in the classical sense of being large compared to the carrier frequency. Multistatic PBR exploits the fact that usually a number of transmitters are able to contribute directly and indirectly as received signals and are thus available for radar use. These can fall into both narrowband and wideband categories. Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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Subsequently it is shown that the performance of PBR systems is additionally determined by the transmitted waveform, the location of the transmitter, the location of the receiver and the location and velocity of the target. Consequently, the scope for radar design and optimization would seem to be severely restricted as many factors are not within the control of the radar designer. To investigate this further the ‘self-ambiguity function’ is introduced, which enables the limits on range and Doppler resolution to be established. The bistatic form of the ambiguity function may then be used to illustrate how these best-case parameters vary as a function of transmitter, receiver and target locations. Understanding the forms that these functions can take and subsequently the implications for system performance is most important if this type of radar is to be used effectively. This analysis can subsequently be used to show that the radar designer does in fact have a number of freedoms to improve system performance. Finally, practical aspects of system design for aircraft detection are examined using an experimental PBR radar system demonstrating the degree of performance that can be achieved.

7.1 PBR DEVELOPMENT The very earliest radar systems were bistatic, with the transmitter and receiver at separate locations [7.1]. The advent of the duplexer, which permitted simplicity of operation as well as cost and space savings, has meant that transmitting and receiving through the same antenna (i.e. monostatic radar) has since dominated radar design. However, the bistatic radar has a number of advantages that have continued to make it of interest, and now practical and capable systems are beginning to emerge. Indeed, there has been something of a resurgence of interest in bistatic radar systems that exploit transmitters of opportunity, partly because they do not require fielding of expensive transmitters and partly fuelled by technology developments in digital signal processors and processing. The most appropriate name for this set of techniques has been discussed by Willis and Griffiths [7.2]: PBR is but one of many names used for this subset of bistatic radars. Other names include passive coherent location (PCL), passive radar, passive and covert radar (PCR), covert radar, noncooperative radar, broadcast radar, parasitic radar, and opportunistic radar. PCL has been subdivided into narrowband PCL and wideband PCL, where narrowband characterizes the video or audio carrier of a TV signal and wideband characterizes the full modulation spectrum of an FM signal. The term passive is somewhat of a misnomer since all radars, including bistatic, require an active transmitter. Thus, only in the sense that the PBR’s transmitter is unaware it is being used for another purpose is there anything passive about the operation. The term covert is too restrictive. It suggests that since the receiver has no radio frequency (RF) signature it is difficult to detect and locate. However, some PBRs are used for scientific experiments and have no need or interest in being covert. The term noncooperative is also too restrictive in that cooperative, that is, friendly, transmitters have often been used for radar illumination. The term broadcast suffers the same restriction since it covers only one type of transmitter. The term parasitic is rather pejorative, suggesting an organism living in or on another organism, which it usually injures. A second definition, one frequenting the tables of the rich and earning welcome by flattery, is hardly better. The term

PBR DEVELOPMENT

opportunistic has the same problem: taking advantage of opportunities with little regard for principles or consequences. Thus, no term fully captures this type of bistatic radar operation. PCL has been favored in the United States, parasitic radar in the GDR, and passive radar in the United Kingdom. One selection criterion could be based on the amount of country interest, as evidenced by its publications. Since a full IEE Proc. Radar, Sonar and Navigation was devoted to passive radar in the United Kingdom, passive radar would be favoured. A second criterion could be based on the opinion of radar lexical experts. One such expert expressed serious reservations about the term passive radar, along with the other candidate terms. After much dialogue, some of which is reflected in the preceding paragraphs, he suggested what appears to be a reasonable compromise: PBR (Merrill I. Skolnik, private communication, October 2005).

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In general the principal advantages of the bistatic radar are (a) the fact that the receiver is passive, making it far less vulnerable to electronic countermeasures (ECM) and (b) a counter to stealth technology that is primarily designed to defeat monostatic radar. In addition multiple receivers can be employed, each one forming a bistatic radar with a single transmitter. This offers the potential for tailored coverage and a richer information source to enable more accurate location, high-resolution imaging and target reconstruction. The price to be paid for these advantages is an increase in system complexity and processing. In particular time and space (transmit and receive beam) synchronization is more difficult to implement and has probably held back the take-up of bistatic radar and exploitation of free-to-air transmissions in particular. With the onset of affordable digital signal processing in the mid-1980s, the concept of exploiting high-power analogue television signals for the purposes of detecting and tracking aircraft began to attract significant interest. The basic phenomenon of aircraft reflections from analogue television signals can be readily observed even on a domestic television set, by tuning to a weak station and observing ghost images as an aircraft passes nearby. In the laboratory, the effect can be better observed by downconverting the television signal to baseband and then passing it into a digital spectrum analyser, on which the target returns can then be clearly observed on a waterfall display as Doppler-shifted echoes of the strong vision carrier signal. Such experiments clearly demonstrate the potential for exploiting television signals for radar use, but determining the location of the aircraft remains a far greater challenge. The first mention in the open literature of work on the exploitation of analogue television signals was by Griffiths and Long [7.3, 7.4] of University College London (UCL). This work addressed the exploitation of the pulse-like nature of parts of the UK phase alternate line (PAL) television signal for bistatic radar use. They investigated the use of a ‘sync-pluswhite’ waveform, in which the broadcaster cooperatively transmitted an all-white picture, so that the synchronization pulse and pedestal are the only features in the waveform. Using this, they demonstrated the reception of clutter from local buildings. Using offline processing, they implemented a simple two-pulse moving target indicator (MTI) canceller and were able to resolve moving targets. The system was impractical, however, as it required the transmission of a special waveform and, even then, had a range resolution of only 1800 m and was ambiguous every 9600 m. To try to improve the performance, they then investigated the use of the multiburst test pattern, which is a black-and-white video signal containing a number of 6 μs black-to-white bursts at frequencies of 0.5, 1, 2, 3, 4 and 5 MHz. Although they could once again detect local clutter sources, it was not possible to detect moving targets reliably,

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possibly due to the lower energy of the multiburst pattern compared with the sync-plus-white waveform. Subsequently, further improvements in technology have continued to take place that are of immediate use to PBR. These include high-speed digital signal processors (DSP), phased array antennas and the deployment of a GPS satellite navigation system, which can be used for synchronization. These have provided motivation for an upsurge of interest in bistatic radar systems that exploit illuminators of opportunity. The rapid growth in the number of RF emissions for TV and radio broadcasts as well as terrestrial and space-based communications has resulted in a wide range of signal types available for exploitation by passive radar. Further, many such transmissions are at VHF and UHF frequencies, which allows these parts of the spectrum not normally available for radar use, and at which stealth treatment of targets may be less effective, to be used. However, in the PBR, the location of the transmitter and the form of the transmission to be exploited is no longer under the control of the radar designer. The multiplicity of transmissions from both terrestrial [7.5] and space-based sources [7.6, 7.7] provide spatial and frequency diversity and can be exploited to improve detection performance further. Examples of reported operational systems include the Lockheed Martin ‘Silent Sentry’ system for air and space surveillance [7.5], the Roke Manor Research CELLDAR system for air target detection [7.8] and the Manastash Ridge radar for atmospheric and ionospheric studies [7.9]. Other reported experimental systems include those proposed by Dynetics [7.10], NATO C3 Agency [7.11] and UCL [7.3, 7.12, 7.13]. Applications include air-space surveillance [7.2, 7.5], maritime surveillance [7.14], atmospheric studies [7.9], ionospheric studies [7.9], oceanography [7.15], mapping lightning channels in thunderstorms [7.16] and monitoring radioactive pollution [7.17]. There have also been recent reports of algorithm development for interferometry [7.18], target tracking [7.19] and target classification [7.20, 7.21]. This range and diversity of systems and applications is indicative of the increasing importance of this form of sensor system. There have been relatively few publications (e.g. References [7.22] and [7.23]) describing detailed aspects of system performance such as waveform properties [7.25] and real geometrical factors and almost nothing on the impact these features may have on the overall system capability. In this chapter, all these factors that affect the achievable detection performance of passive coherent location radar systems are examined. One of the primary motivations for investigating passive coherent location (PBR) techniques is the detection and tracking of aircraft. In an era of falling budgets and increasing demands on the electromagnetic spectrum, PBR promises the potential of both low-cost surveillance and operation without the need for frequency allocation. In a military context, the technology promises covert operation, frequency diversity and some advantages against the countermeasures to conventional radars. Inevitably, however, these advantages come at a price – and for the PBR this is the difficulty of detecting and tracking aircraft using signals that have been designed for some other purpose. Indeed, for many years these problems meant that the PBR was impractical for any form of real-time surveillance. Continuing improvements in digital receiver technology and the power of computing equipment has brought the technology within the grasp of even the smallest of budgets. The majority of researchers have concentrated on the exploitation of commercial broadcast transmitters due to their high powers, attractive locations and density of deployment. Analogue television (TV) stations offer some of the highest equivalent radiated powers – sometimes as high as 1 MW – and so are one of the most attractive illuminators purely from the perspective of detection. However, target location and tracking is difficult. As a consequence, the most successful systems fielded to date primarily exploit frequency modulated (FM) radio stations

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SENSITIVITY AND COVERAGE FOR PASSIVE RADAR SYSTEMS Table 7.1 Signal parameters for typical passive radar illumination sources

Transmission

Frequency

Modulation, bandwidth

Pt G t

HF broadcast

10–30 MHz

DSB AM, 9 kHz

50 MW

VHF FM (analogue)

∼100 MHz

FM, 50 kHz

250 kW

UHF TV (analogue)

∼550 MHz

1 MW

Digital audio broadcast Digital TV

∼220 MHz

Vestigial sideband AM (vision); FM (sound), 5.5 MHz digital, OFDM, 220 kHz

10 kW

∼750 MHz

digital, 6 MHz

8 kW

Cellphone basestation (GSM) Cellphone basestation (3G)

900 MHz, 1.8 GHz

GMSK, FDM/TDMA/FDD, 200 kHz CDMA, 5 MHz

10 W

2 GHz

10 W

Power density (W/m2 ) Pt G t = 4πr1 2 67 to 53 dB W/m2 at r1 = 1000 km 57 dB W/m2 at r1 = 100 km 51 dB W/m2 at r1 = 100 km 71 dB W/m2 at r1 = 100 km 72 dB W/m2 at r1 = 100 km 81 dB W/m2 at r1 = 10 km 81 dB W/m2 at r1 = 10 km

which, although typically only one-tenth of the power of analogue TV, have a far more suitable waveform for radar purposes. Table 7.1 shows the signal parameters for a variety of PBR illumination sources. Most recently, research has begun to focus on the exploitation of digital transmissions in anticipation of the eventual withdrawal of the analogue broadcast services. Digital signals generally offer a close-to-ideal ambiguity function for target detection, but present their own problems, with typically much greater numbers of low-power transmitters, forcing the radar designer to cope with the problems of increased interference and shorter inherent detection ranges. Here both analogue and digital transmissions will be considered.

7.2 SENSITIVITY AND COVERAGE FOR PASSIVE RADAR SYSTEMS 7.2.1 The Bistatic Radar Equation The starting point for an analysis of the performance of a passive radar system is the well-known bistatic radar equation: Pr 1 G r λ2 1 Pt G t L, = σb 2 Pn 4πr1 4πr22 4π kT0 BF where Pr = received signal power, Pn = receiver noise power, Pt = transmit power,

(7.1)

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G t = transmit antenna gain, r1 = transmitter-to-target range, σb = target bistatic radar cross-section, r2 = target-to-receiver range,

G r = receive antenna gain, λ = signal wavelength, k = Boltzmann’s constant, T0 = noise reference temperature, 290 K, B = receiver effective bandwidth, F = receiver effective noise figure, L (≤ 1) = system losses. In using this equation to predict the performance of a passive radar system it is critical to understand the correct value of each of the parameters that is to be used. The transmit power Pt is substantial for many passive radar sources, since broadcast and communications receivers often have inefficient antennas and poor noise figures and the transmission paths are often far from line-of-sight; thus the transmit powers have to be significantly higher to overcome the inefficiencies and losses. In the United Kingdom, the highest power FM radio transmissions are 250 kW (ERP) per channel, with many more of lower power [7.25]. The highest power analogue TV transmissions are 1 MW (ERP) per channel [7.25]. These are omnidirectional in the azimuth, and are sited on tall masts on high locations to give good coverage. The verticalplane radiation patterns are tailored to avoid wasting too much power above the horizontal. GSM cellphone transmissions in the United Kingdom are in the 900 MHz and 1.8 GHz bands. The modulation format is such that the downlink and uplink bands are each of 25 MHz bandwidth, split into 125 FDMA channels each of 200 kHz bandwidth, and a given basestation will only use a small number of these channels. Each channel carries eight signals via TDMA, using GMSK modulation. Third-generation (3G) transmissions are in the 2 GHz band, using CDMA modulation over a 5 MHz bandwidth. The radiation patterns of cellphone basestation antennas are typically arranged in 120◦ azimuth sectors, and shaped in the vertical plane again to avoid wasting power. The pattern of frequency re-use means that there will be cells using the same frequencies within quite short ranges. Licensed ERPs are typically in the region of 400 W, although in many cases the actual transmit powers are lower. The OFCOM sitefinder website [7.26] gives details of the location and operating parameters of each basestation throughout the United Kingdom, and an example of the information provided by this website is shown in Table 7.2. In all cases it is necessary to consider the power in the portion of the signal spectrum used for passive radar purposes, which may not be the same as the power of the total signal spectrum. For example, the ambiguity properties of the full signal may not be as favourable as those of a portion of the signal. This is the case for an analogue television transmission; the full signal has pronounced ambiguities associated with the 64 μs line repetition rate, but a better ambiguity performance may be realized by taking just a portion of the signal spectrum at the expense of reduced signal power.

SENSITIVITY AND COVERAGE FOR PASSIVE RADAR SYSTEMS Table 7.2 Example attributes of a mobile phone basestation located to the northern end of Gower Street in London, UK Name of operator Operator site reference Height of antenna Frequency range Transmitter power Maximum licensed power Type of transmission

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T-MOBILE 98463 35.8 m 1800 MHz 26 dB W 32 dB W GSM

7.2.2 Target Bistatic Radar Cross-Section In the PBR, target detection and location are a function of the spatially dependent bistatic RCS and target dynamics, as well as the radar design parameters. Targets can be detected in range, Doppler and angle using conventional processing approaches. The target bistatic radar cross-section σb will not in general be the same as the monostatic cross-section, though for nonstealthy targets the range of values may be comparable [7.27, 7.28]. However, rather little has appeared in the open literature as to the bistatic radar cross-section of targets and this remains an area for future research. In additional there have been only a few published reports of bistatic clutter measurements (e.g. References [7.29] to [7.31]) and a much more complete treatment is required to enable more realistic calculations of the PBR performance. As the bistatic angle is increased to 180◦ the forward scatter region is encountered. In this region target cross-sections can be considerably enhanced. This is explained by Babinet’s principle, which says that the forward scatter from a perfectly absorbing target is the same (apart from a 180◦ phase shift) as that from a target-shaped aperture in a perfectly conducting sheet, which for a target of physical cross-sectional area A gives a radar cross-section of σb =

4πA2 . λ2

(7.2)

The angular width of the scattered signal in the horizontal or vertical plane is given by θb =

λ , d

(7.3)

where d is the target linear dimension in the appropriate plane. Figure 7.1 plots the dependence of σb and θb on frequency, for a target with A = 10 m2 and d = 20 m, showing that σb increases with frequency as the forward scatter is concentrated into an increasingly narrow beam. This implies that low frequencies are more favourable for the exploitation of forward scatter, so that target detection may be achieved over an adequately wide angular range. Forward scatter does not enable the range to be measured directly; however, the target location can be estimated using a combination of Doppler and bearing, as explained in Reference [7.19]. Another mechanism for enhancement of bistatic RCS of aircraft targets is specular reflection from the underside of the aircraft. However, this would depend on the specular condition being met and would therefore be ephemeral in nature. This may improve the sensitivity to elevated targets, given that most transmitters direct their signals towards the Earth’s surface.

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PASSIVE BISTATIC RADAR SYSTEMS

σ b (dBm 2)

θb

+60

20º

+50 10º

+40

+30

log10f

0º 10 MHz

30 MHz

100 MHz

300 MHz

1 GHz

3 GHz

10 GHz

Figure 7.1 Variation of RCS σb and angular width θb of forward scatter of a target of physical area 10 m2 and linear dimension 20 m, as a function of frequency

7.2.3 Receiver Noise Figure The noise and interference level against which the wanted signal must compete for detection is made up of several components. These may be visualized in the form of a two dimensional function Pi (θ, f ) of direction and frequency. These components are as follows: 1. The basic noise figure of the receiver, which at VHF or UHF will be of the order of a few dBs at most. The noise power will be uniformly distributed over θ and f . 2. The direct signal from the bistatic transmitter. This will be the dominant component, and will occur at the appropriate incidence angle and occupy the appropriate bandwidth. 3. Multipath versions of the direct signal, each of a particular signal level and at a particular incidence angle, and possibly time-varying and Doppler-shifted. 4. Direct and multipath versions of other co-channel transmissions. 5. Other signals due to (for example) radiation from computers, impulsive or spurious signals. Unless steps are taken to suppress these components the sensitivity and dynamic range of the system will be severely limited. Measurements were made of the signal and noise environment in the VHF broadcast band around 100 MHz in central London, using a vertically polarized dipole antenna outside the tenth floor of the University College London Engineering Sciences Faculty building. A typical spectrum is provided in Figure 7.2, which shows direct signal levels of the order of −45 dBm and a noise level (in between the broadcast signals) of the order of −90 dBm in 30 kHz, which is some 40 dB above thermal noise in this bandwidth. This result is important, because it shows that the signal and noise environment can be severe. In the example of Figure 7.2 the noise level is some 40 dB greater than thermal noise, and the direct signals are some 45 dB greater still. The effective value of noise figure to be used

SENSITIVITY AND COVERAGE FOR PASSIVE RADAR SYSTEMS

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Figure 7.2 Noise levels in a passive radar receiver: (a) thermal noise in a 30 kHz bandwidth corresponding to a 5 dB receiver noise figure; (b) signal and noise levels measured from tenth floor of UCL in Central London. Horizontal scale 95–100 MHz; vertical scale 10 dB/division; top of screen = 40 dBm

in Equation (7.1) will depend on the particular signal and noise environment and on the degree of suppression that can be obtained. While the example of Figure 7.2 is severe, lower noise levels might be expected in suburban and rural environments, and at the higher frequencies used by television and cellphone transmission; nevertheless, an effective noise figure of 25 dB is not pessimistic.

7.2.4 Effective Bandwidth and Integration Gain In a PBR system the direct signal is used as a reference against which the indirect or reflected signal can be correlated to provide processing gain for sensitivity and bandwidth for resolution via its modulation content. The effective receiver bandwidth B is that of the directly received signal. This bandwidth is subject to the processing gain due to coherent integration, which in turn depends on the time for which the target echoes remain coherent. A rule of thumb for the maximum value of the coherent processing integration interval is TMAX =

λ AR

1/2

,

(7.4)

where AR is the radial component of target acceleration. Hence the maximum processing gain is G p = TMAX B.

(7.5)

For example, with a VHF FM radio waveform with an effective bandwidth of 50 kHz and an integration time of 1 second, the processing gain will be 47 dB. From this, the bistatic radar equation can be re-cast in the following form: (r2 )max =

σb G r λ2 LG p (4π)2 (S/N )min kT0 BF

1/2 (7.6)

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This predicts the coverage around the transmitter and receiver in the form of the well-known ovals of Cassini (loci corresponding to r1r2 = constant). This is the form of the bistatic radar equation that will be used to predict the performance for differing illuminators of opportunity in the next section.

7.2.5 Performance Prediction All of the foregoing has shown that some care must be taken in using the bistatic radar equation to predict the performance of passive radar systems. Performance predictions are now presented for three ‘straw man’ systems, attempting to show the likely achievable performance and to identify critical factors. The systems considered are: (a) FM radio, (b) cellphone basestations and (c) digital radio. In each case an omnidirectional receive antenna, a noise figure of 25 dB, losses of 5 dB and full suppression of direct signal leakage are assumed. FM radio transmissions have the inherently attractive properties of very broad coverage and relatively high transmitter powers. In this example the transmitter is taken as that located at Wrotham in the South-East of England and a receiver sited at the Roberts building of UCL. The transmitted power is 250 kW and broadcasts are made in the frequency range 89.1–93.5 MHz. Figure 7.3 shows a plot of the detection range assuming a target cross-section of 1 m2 , an integration time of 1 second and a modulation bandwidth of 55 kHz. The results can readily be scaled for other values of the target radar cross-section. The commencement of the white region represents a contour with a signal-to-noise ratio of 15 dB (and this value of signal-to-noise ratio is used for all subsequent figures of this type). Note that the modulation bandwidth is considerably less than that specified for the transmissions. As will be demonstrated in Section 7.4, the modulation bandwidth is a function of programme content and therefore varies with time, 55 kHz representing a typical value. A signal-to-noise ratio of 15 dB or greater is maintained out to a range of nearly 30 km. This performance is constrained by the effective

range (m)

4

× 104

Oval of Cassini W.PIUCL in FM Pt=250KW

3

80

2

70

1

60

0

50

−1

40

−2 30 −3 20 −4 −4

−3

−2

−1

0 1 range (m)

2

3

4 × 104

Figure 7.3 Detection range for a transmitter at Wrotham in South-East England and a receiver at UCL

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SENSITIVITY AND COVERAGE FOR PASSIVE RADAR SYSTEMS

1.5

× 104 Oval of Cassini Cr.PIUCL in FM Pt=4KW 80

1

range (m)

70 60

0

50 −0.5 40 −1

30 20

−1.5 −1.5

−1

−0.5

0 range (m)

0.5

1

1.5 × 104

Figure 7.4 Detection range with a transmitter at Crystal Palace and the receiver at UCL

noise figure of the receiver, and better performance would be obtained with better suppression of direct signals and noise. It should be noted that the power emitted by transmitters across the UK varies from as little as 4 W to a maximum of 250 kW, and of course this variation has to be carefully factored in to performance predictions. Figure 7.4 shows how the detection range varies when a second transmitter is exploited. Here the transmitter at Crystal Palace, which has a transmit power of 4 kW, is exploited. The range of coverage is proportionally less as there is approximately 18 dB less transmitted power and the signal-to-noise ratio of 15 dB is limited to around a little over 10 km. Figure 7.5 illustrates how the coverage changes when the two transmitters are exploited together using noncoherent integration. Now the detection range is extended to over 30 km. However, an alternative is to process the detections from each transmitter independently and then combine them, as this is simpler. Coherent combination is unlikely as the transmissions will probably be at differing frequencies and not synchronized. Overall the high transmit powers and good coverage make FM radio transmissions particularly well suited to air target detection for both civil and military applications. Equally they could be used for marine navigation in coastal waters although clutter may be a more significant problem. The second system uses a cellphone basestation transmitter with the parameters listed in Table 7.2. This particular transmitter has an operating frequency of 1800 MHz and is located towards the northern end of Gower Street approximately 200 m from the Roberts building of UCL where the receiver is again placed. The other parameters are maintained constant, as with the first case. A plot of the detection range is shown in Figure 7.6, which suggests a maximum range of around 1.2 km, although this is probably pessimistic since the actual interference environment may not be quite as severe as assumed here. Clearly this is much less than for the first example, and would therefore seem to have more limited application. However, as there is such an extensive and diverse network of basestations, targets could be tracked though such a network and hence the coverage may be extended, greatly encompassing the area covered

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3

× 104 Oval of Cassini for SNR FM Cristal (Pt=4KW)-UCL-Wrotham(Pt=250KW)

80 2 70 1 range (m)

60 0

50

−1

40 30

−2

20 −3 −3

−2

−1

0 range (m)

1

2

3 × 104

Figure 7.5 Detection range for transmitters at Wrotham and Crystal Palace and a receiver at UCL

by the network itself. This extends the range of application to include counting of vehicles for traffic flow management and remote monitoring of movement around buildings as a security device, possibly acting as a cue for a camera system. The third example uses a digital audio broadcast (DAB) transmission from Crystal Palace in South London. This has a transmit power of 10 kW. Figure 7.7 shows the detection range.

1.5

× 104

Oval of Cassini Green pl UCL in GSM 100 90

1

80

range (m)

0.5

70 60

0

50 −0.5 40 −1

30 20

−1.5 −1.5

−1

−0.5

0 range (m)

0.5

1

1.5

× 104

Figure 7.6 Detection range for a mobile phone basestation located at the northern end of Gower Street in Central London and the receiver at UCL

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1

× 104 Oval of Cassini Crystal. pl-UCL in DAB Pt=10KW

0.8

90

0.6

80

range (m)

0.4

70

0.2 60

0 −0.2

50

−0.4

40

−0.6

30

−0.8 −1 −1

20 −0.5

0 range (m)

0.5

1 × 104

Figure 7.7 Detection range for a DAB transmitter at Crystal Palace and a receiver at UCL

As might be expected for a high-power transmitter of this type, the coverage is out to a range of around 9 km. Thus, despite the higher transmit power than for the FM transmission, the maximum detection range is shorter. This is due to the higher frequency offsetting the lower transmit power. Again it should be noted that output powers of transmissions of this kind vary between 500 W and 10 kW. Additionally coverage is not currently as universal as is the case for FM transmissions although new transmitters are constantly being added. One of the strengths of the PBR is that several different types of emission of opportunity could be exploited at a single receiver site. This has the advantage of providing frequency diversity and spatial diversity and as such makes the PBR somewhat equivalent to a multisite or netted radar system (i.e. multiple transmitter locations and a single receiver). There are also a number of aspects of performance that have not yet been considered. For example, FM transmissions have been used to probe the ionosphere and therefore might be expected to have useful height coverage, but mobile phone basestations deliberately concentrate their emissions towards the ground and may not necessarily have such good coverage of higher altitude aircraft. Another factor that has to be carefully considered is integration time. It has been assumed that the integration time is 1 second and that the integration is 100 % efficient. In practice, targets will decorrelate and the integration efficiency will be less. A reasonable assumption might be for a reduction in the signal-to-noise ratio of 3 dB. Implementation of a Doppler tracking filter could improve upon this. In estimating the performance potential it is advisable to adopt a slightly conservative approach when choosing values for the parameters comprising the system. Indeed, performance calculations of this type are only indicative, especially as they do not include a full treatment of losses, the environment and clutter properties. Ultimately these and other aspects of performance do not lend themselves well to modelling and real systems will have to be constructed and tested.

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7.2.6 Sensitivity Analysis Conclusions In this section the bistatic radar equation has been re-cast into a form that readily reflects the design features of a PBR system. This highlights the importance of the bistatic geometry and the key dependence on the nature of the illuminating waveform. The form and nature of bistatic target and clutter reflections are not well known and require extensive further research. It has been shown that the noise and signal environment for a PBR receiver can be severe and that appropriate suppression of direct signals and noise will be necessary. Even then, the radar equation should use an appropriate value of noise figure to predict detection performance. A ‘rule of thumb’ expression has been presented that indicates the high levels of direct signal suppression that are required to ensure that maximum detection ranges can be achieved. The prediction of detection range and coverage for a variety of illuminators of opportunity shows that detection ranges of several tens of km are readily achievable. This is again, however, highly dependent on the properties of the illuminator and on the ability to suppress direct signal and noise in the receiver. However, it is expected that full-scale systems will have a performance near to the levels predicted here. Thus the PBR may be invoked to support quite a wide range of applications, provided they are consistent with the limitations imposed by the availability of illuminators. Indeed, the plethora of radio frequency radiation sources will undoubtedly increase still further and the case for the PBR becomes ever more compelling. Further more sophisticated processing techniques such as SAR, ISAR, interferometry and others can all be exploited.

7.3 PBR SYSTEM PROCESSING 7.3.1 Narrowband PBR Processing In this section the principal ingredients that make up a PBR radar system are examined. This is done for the three categories of narrowband, wideband and multistatic that were identified earlier. Narrowband PBR techniques approach the problem of target location from an unusual perspective. Rather than try to measure target range and bearing directly, as with a conventional radar, they aim to estimate the location of the target from those parameters that can be easily measured. In the case of analogue television-based radar, these are the Doppler shift of the target and, to a lesser extent, its bearing. Narrowband PBR processing is therefore concerned with the problem of estimating the location of aircraft from measurements of Doppler and bearing. The approaches adopted bear a close similarity to many of the target motion analysis (TMA) techniques used in passive sonar systems. In the simplest configuration, with a single receiver and single broadcast transmitter, it is necessary to have time histories of both Doppler shift and bearing in order to estimate the location of a target [7.32]. In multistatic configurations, with multiple transmitters, it is possible to estimate a target’s location from multiple Doppler measurements from each transmitter, although bearing is still valuable in the target association process and also improves the estimate [7.33]. In the context of the PBR, the approach has been most widely applied to measurements of the amplitude modulated vision carrier of the television signal, which contains up to 50 % of the transmitted power. However, it is more generally applicable to any waveform that includes a strong continuous wave component. With the SECAM television standard, the sound carrier is also amplitude modulated, and so it is also possible to apply these techniques to the sound carrier (but not so with the PAL and NTSC standards, which use an FM sound carrier). Narrowband

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PBR processing can be broken down into six main stages and these are described in the following sections. Much of the discussion below is based on the approach first published by Howland [7.34, 7.35]. 7.3.1.1 Direct Signal Cancellation

A common problem among all PBR systems is that the radar receiver must detect very low power target echoes in the presence of a very strong and continuous broadcast signal. Unlike a conventional radar system, a PBR system does not enjoy the luxury of a pulsed transmission and hence a period of transmitter silence in which to listen for echoes. A simple expression can be formulated for the amount of direct signal suppression required by calculating the ratio of the indirect received signal to the direct signal and requiring this to be at least the same value as that used to compute the maximum detection range. The simple assumption is made that a target can be seen above this level of direct signal breakthrough and hence that it approximates to the highest level of interference that is tolerable for single ‘pulse-like’ detection. There is, however, no benefit from integration as the direct leakage will also integrate up, and this may lead to a more stringent requirement needing to be set in practice. This places the direct leakage signal at the same level as the noise floor in the receiver and hence it has the attractive feature of proving equivalent performance to ‘single-pulse’ detection. Thus to achieve adequate suppression and hence maintenance of the full system dynamic range the direct signal must be cancelled by an amount given by the magnitude of the ratio of the indirect and directly received signals, e.g. Pr r 2 σb Pr = b2 2 > , Pd Pd 4πr1 r2

(7.7)

where Pr is the target echo signal, Pd is the direct signal and rb is the transmitter-to-receiver range (bistatic baseline). This expression is indicative only, and strictly speaking the direct signal should be below that of the noise floor after integration, if integration is employed. A numerical example is considered of the television transmitter located at Crystal Palace in South London and a receiver located at University College London. Assuming a 1 m2 target and a maximum detection range of 40 km, this equates to a requirement for suppression of direct signal leakage of some 120 dB, if this is to be taken down to the thermal noise level. It should be noted that as the detection range is reduced from the maximum the amount of direct signal breakthrough compared to the indirect signal will fall sharply. In addition, the leakage signal will be time varying and subjected to multiple scattering paths. This behaviour requires a thorough and detailed understanding to optimize the performance of a given design. There are several techniques that may be used to suppress this leakage. These include: (a) physical shielding, (b) adaptive cancellation and (c) Doppler (Fourier) processing. Each one of these techniques will provide different suppression characteristics over the θ – f plane; thus physical shielding or beam-forming techniques will provide suppression as a function of θ and Doppler processing or adaptive filtering will provide suppression as a function of f . The combination of high-gain antennas and adaptive beam-forming also enables multiple simultaneous transmissions to be exploited. In more detail we have: (a) Physical shielding. The simplest approach is simply to exploit distant transmitters, so that the signal is not received directly and any transmitter leakage into the receiver channels

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is due to lossy propagation mechanisms such as diffraction or tropospheric scattering. The disadvantage of this approach is that the transmitter and receiver only share a common coverage region at higher altitudes and hence low-altitude aircraft detection is not possible. This was the approach adopted by Howland in Reference [7.36]. The Manastash Ridge radar [7.9] provides an example of the use of physical shielding; in this case suppression is achieved by siting the receiver on the other side of a large mountain which provides the screening. In other cases some simpler more localized methods may be used such as appropriate deployment of absorbing material (RAM).

(b) Adaptive cancellation. A more sophisticated approach is to use a closer transmitter (and hence enjoy low-level coverage) and to have at least two channels in the receiver system, one to receive the target echoes and one to receive the transmitter signal directly. Assuming that the echo channel and the reference antennas are steered in different directions (ideally with the transmitter placed in a null in the echo antenna), it is possible to use a simple analogue canceller to subtract a delayed and scaled version of the reference signal from the echo signal, and hence cancel a proportion of the direct transmitter signal from the echo channel. A simple implementation of this was adopted by Poullin and Lesturgie in Reference [7.33]. Although this can be done most elegantly using digital adaptive signal processing techniques, it should ideally be done before sampling, to minimize the dynamic range requirements on the digital receiver. (c) Doppler (Fourier) processing. For the detection of moving targets Doppler or Fourier processing will automatically improve dynamic range, as the direct signal leakage will only occur at DC (with some spillover). However, it should be noted that significant sidelobe leakage due to inadequate suppression of very strong directly received signals will reduce the gain from Fourier processing and hence impair the dynamic range. In order to detect airborne targets and to measure the Doppler shift of their echoes, the narrowband PBR approach uses a narrowband receiver system to mix the signal from radio frequency down to baseband in a narrow bandwidth around the CW carrier, comparable to the range of Doppler shifts expected from the targets of interest. This is typically a few kilohertz for civilian aircraft with a UHF transmitter of opportunity. This signal is then sampled and digitized to allow digital signal processing. Target detection and Doppler measurement is then achieved by applying a fast Fourier transform (FFT) to time sequences of the sampled data. A sequence typically 1 or 2 seconds in length is used in order to maximize the signal processing gain and to provide good resolution of targets in the Doppler domain. For ideal integration, this gain is given by the time–bandwidth product: e.g. analysis of a 2 second sample of signal with a bandwidth of 5000 Hz would result in a time–bandwidth product of 10 000, or a gain of 40 dB. This large signal processing gain is critical to the operation of the PBR system and helps compensate for the lack of antenna gain compared with a conventional radar system. The maximum integration time is typically limited by the acceleration of the target – integrate for too long and the echo will simply smear across several Doppler bins and no further increase in the signal-to-noise ratio (SNR) will be seen. A window or weighting function can be applied to the time sequence before applying the FFT in order to reduce the Doppler sidelobes from strong target returns. This comes at the expense of a slightly decreased signal processing gain. If the television vision carrier is exploited then the signal after FFT processing will not only show the Doppler shifted target echoes of the vision carrier but also many periodic structures

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spaced at multiples of the television frame rate (50 Hz in Europe or 60 Hz in North America). These can be largely ameliorated by the cancellation process used before applying the FFT and any remaining structures can then be dealt with by the detection algorithm. The spectral analysis is repeated indefinitely on successive blocks of data, resulting in a time sequence of Doppler shifts for each target. Note that it is usually not necessary to receive a direct reference signal in order to estimate the Doppler shift, as this will be present in the echo signal. 7.3.1.2 Target Detection Having successfully removed the direct signal from the indirect channel the PBR system is then faced with the problem of target detection. Typically a Fourier transform is performed on a 1 second block of data. It is then necessary to identify which of the spectral lines are Dopplershifted echoes of the target from background clutter and interference. If the exploited transmitter is a clean continuous wave (CW) signal then the process is very simple, as any frequency-shifted component is a probable target. This is the case for simple amplitude-modulated sound carriers. In such a case, a very simple cell-averaging constant false alarm rate (CA-CFAR) algorithm can be used to detect the target returns. This is mathematically optimum when detecting targets against a background of white Gaussian noise, which is a good approximation in most cases. For more periodic signals, however, the problem is slightly more complex. In signals such as the television vision carrier, there are usually many frequency-shifted structures in the spectrum that are related to the periodicities in the signal and not target returns. Fortunately these tend to be at a constant frequency over time and hence can be removed by modifying the CA-CFAR algorithm to base the detection threshold on the time-averaged signal level in each Doppler cell. In this way, periodic structures that constantly occupy a particular Doppler cell will cause the threshold to be raised and hence will not be detected by the algorithm. This does, of course, result in a loss in sensitivity at these Doppler frequencies and so it is preferable to use it in conjunction with a direct signal cancellation approach. 7.3.1.3 Bearing Estimation

Measurements of bearing are essential when estimating the location of a target using a simple bistatic configuration and are very helpful in resolving the target association problem with multiple transmitters. Unfortunately, at the VHF and UHF frequencies used by most narrowband PBR systems, the accurate estimation of target bearing is difficult. First, for reasons of cost, most PBR systems tend to use fairly simple antenna systems – often no more than a pair of Yagi or log-periodic antennas spaced half a wavelength apart. Second, at these frequencies, multipath reflections from buildings and other objects in the environment can cause significant biases in the measurements of bearing. As a result, most narrowband PBR systems must contend with biased, noisy measurements of target bearing. The simplest (and cheapest) means of estimating bearing is to use a two-channel receiver system, with two antennas spaced half a wavelength apart. Phase interferometry can then be used to calculate the bearing of echoes from the phase difference of returns on the two channels. Simplistically the target bearing, θ , is determined using λ θ = sin−1 , (7.8) 2πd

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where λ is the wavelength, is the phase difference between the two channels and d is the antenna spacing. It is assumed that − sin−1 [λ/(2d)] < θ < sin−1 [λ/(2d)] to avoid directional ambiguities. The phase difference, , can be calculated directly from the phase terms of the complex numbers resulting from the FFT processing on each channel. If simple dipoles are used for the antennas then the expression above is usually sufficient. However, many implementations use directional antennas such as Yagi or log-periodic in order to benefit from the antenna gain. Such antennas suffer more significantly from issues of mutual coupling, particularly for signals arriving off-boresite, which cause significant differences in the relationship between the phase difference and angle compared with the expression above. In these cases it is far more accurate to generate a look-up table through numerical electromagnetic modelling or accurate calibration [7.34]. More sophisticated PBR systems use multiple antennas to provide a series of overlapping beams. Standard amplitude monopulse techniques can then be used to estimate the bearing of the target. Such an approach offers the benefits of antenna gain, good sector coverage and bearing measurements – but at the expense of increased numbers of receivers and processing load.

7.3.1.4 Target Association Target association processing is required to associate individual detections from each FFT and CFAR with individual aircraft. The process is analogous to the standard target tracking problem in conventional radars, in which individual target plots from each scan are combined over time to form tracks of individual aircraft. However, while a conventional radar tracker might take measurements of range and bearing and output aircraft tracks in Cartesian coordinates, in the narrowband PBR system the tracker takes plots in Doppler and bearing and also outputs tracks, also in Doppler and bearing. The conversion of these into aircraft tracks in Cartesian coordinates is usually performed in a second, distinct phase due to the difficulties of track initialization with only Doppler and bearing measurements. Target association in Doppler and bearing can be posed as a classical tracking problem, where the measurements are Doppler and bearing and the target state is Doppler, Doppler rate, bearing and bearing rate. Indeed, it is actually sufficient to associate purely in the Doppler domain, with a measurement of Doppler and a target state of just Doppler and Doppler rate. The accuracy of bearing measurements is usually sufficiently poor compared with the Doppler measurements that their omission from this tracking phase has little impact on the resulting association accuracy [7.34]. When viewed in the bistatic Doppler domain, even aircraft flying at a constant velocity have gently curved track histories, typically in a gentle ‘S’ shape, from positive Doppler through to negative as it passes towards the system, through the point of closest approach and then away again. Aircraft performing more complex manoeuvres will have more complex Doppler histories. As a result, target association is best performed using a tracking algorithm designed to cope with manoeuvring targets, even if the aircraft themselves are not manoeuvring. Early work used a standard Kalman filter with some manoeuvre detection logic that artificially increased the system covariance matrix whenever the normalized difference between the state estimate and measurement exceeded a certain threshold [7.34]. This allowed the tracker to maintain track on gently curved Doppler histories. However, such an approach can be slow to respond to the onset and end of manoeuvres and more recent tracking techniques such as the interacting

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multiple model (IMM) can offer better performance in such situations [7.37]. It is important to ensure that the target association process is as robust as possible, for short and broken target Doppler histories are usually insufficient to estimate the location of an aircraft accurately.

7.3.1.5 Target State Estimation The target state estimate is the critical (and unusual) part of narrowband PBR processing. In this step the target’s track parameters (such as location, heading and speed) are estimated from the measurements of Doppler and bearing. Different approaches are possible depending on the number of transmitters that are being simultaneously exploited. If there is only one illuminating transmitter it remains possible to estimate the location of an aircraft from the time history of its Doppler and bearing measurements, but at the expense of a delay of some tens of seconds before the track can be initialized [7.34]. If echoes are simultaneously available from four or more transmitters then it is possible to calculate the location of the aircraft directly from the Doppler measurements [7.33]. However, achieving simultaneous detection from four or more transmitters can be difficult to achieve in many regions and the problem of correctly associating multiple echoes from multiple transmitters with multiple targets is challenging. To understand the state estimation process, consider a target flying at constant velocity, from an initial location (x0 , y0 ) at time t0 , with components of velocity(x˙ , y˙ ). The receiver is assumed to be at the Cartesian origin and the transmitter at (0, L). If the radar calculates the Doppler spectrum every T seconds, then after n samples at time t = (t0 + nT), the Doppler shift and bearing of the target will be respectively 1 (x0 + nT x˙ )x˙ + (y0 + nT y˙ ) y˙ (x0 + nT x˙ )x˙ + [L − (y0 + nT y˙ )] y˙ F(n) = (7.9) + λ (x0 + nT x˙ )2 + (y0 + nT y˙ )2 (x0 + nT x˙ )2 + [L − (y0 + nT y˙ )]2 and θ(n) = tan−1

x0 + nT x˙ y0 + nT y˙

,

(7.10)

where λ is the radar wavelength. It is therefore apparent that the measurements of the Doppler and bearing are functions of several known parameters, n, T , L and λ, and the unknown track parameters x = (x0 , x˙ , y0 , y˙ ).

7.3.1.6 Batch Estimators It is possible to estimate the unknown track parameters (x0 , x˙ , y0 , y˙ ) from a sequence of measurements of Doppler, Fm (k), and bearing, θ m (k), for samples at times k = 0, . . . , m − 1, by posing the problem as a minimization problem. This is analogous to the high school problem of performing a least squares fit of a straight line (with unknown parameters m and c) to some noisy data points. To pose the problem as a minimization, consider a vector of the measurements, z T = (Fm (0), θm (0), Fm (1), θm (1), . . . , Fm (m − 1), θm (m − 1)), and a corresponding vector of state equations, hT (x) = (F(0), θ (0), F(1), θ(1), . . . , F(m − 1), θ (m − 1)). The problem is

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then one of attempting to minimize the least squares difference between the measurements and the state equations by selecting the best values of the track parameters, x. The difference is defined as JLS =

1 [z − h(x)]T [z − h(x)]. 2

(7.11)

This functional can be minimized by a number of standard least squares minimization algorithms, all of which adopt an iterative approach to determine the values of the parameters of x that minimize JLS in a least squares sense. Popular algorithms for this class of problem include the steepest descent algorithm, Gauss–Newton and Levenberg–Marquardt. Examples of their application to narrowband PBR processing are provided in Reference [7.34]. Note that in order to estimate the target’s track parameters, the least squares difference JLS must have a unique and well-defined minimum. In practice, the information content in the measurements of Doppler and bearing on the target track state is very low, and hence it is necessary to observe the evolution of Doppler and bearing with time for a number of seconds before there is sufficient information to uniquely estimate the target track parameters and hence for JLS to have a well-defined minimum. If too short a sequence of measurements is used, then any minimization algorithm will have great difficulty converging. Observation periods of the order of one minute were required for the system described in Reference [7.34], although the large separation between the transmitter and receiver in this case (424 km) would have exacerbated the problem of low information content in the Doppler measurements. Furthermore, to ensure correct convergence, the algorithms mentioned above all require a good initial estimate of the target state in order to converge on the correct minimum. This is because such algorithms are based on a linear approximation to the measurement equations; if an incorrect starting point is selected, this approximation is inaccurate and of little use in finding the minimum. Unfortunately, there is very little a priori information available on a target’s location, but it is possible to infer some basic information about the quadrant in which a target lies and the sign of x˙ from the measurement of bearing and the sign of the Doppler shift. Howland proposed using the following scheme [7.36]: x0initial

=

0, if |θ | < 15◦ , −50 sgn(θ ) otherwise,

y0initial = 50 sgn(90 − |θ |), x˙ 0initial = 0.2 sgn(Fθ ), y˙ 0initial = 0, where the values of 50 km and 0.2 km/s are arbitrary values chosen to ensure that the parameter lies clearly in the correct quadrant. As it is not possible to say anything a priori about the ycomponent of velocity, this is simply set to 0 km/s. In the absence of any other information, this approach at least ensures that the initial values are very approximately correct. In References [7.34] and [7.35], Howland describes the use of a genetic algorithm in order to search for the initial value of the estimate, before improving the value through a conventional minimization algorithm. The approach was quite effective, but somewhat elaborate and computationally expensive. It is unlikely to be of significant application in a real-time system.

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While a batch estimation approach, such as that described above, is good for initializing a track, it is computationally inefficient for track maintenance. Furthermore, because the equations assume that the target maintains a constant velocity throughout the sample period of a minute or so, it is incapable of following target manoeuvres. A better approach for track maintenance is therefore to use the extended Kalman filter. 7.3.1.7 Extended Kalman Filter

Because it requires many seconds of observations for the target state to become properly observable, it is always necessary to initialize a narrowband PBR track with some form of batch estimator, which explicitly takes account of the Doppler and bearing histories. However, once the track has been correctly initialized it is sufficient to use a more computationally efficient iterative approach to maintain the track. The Kalman filter is the obvious choice of estimator for this, but because the measurements of Doppler and bearing are related to the target’s state in a highly nonlinear fashion, it is necessary to use a nonlinear version of the Kalman filter. The simplest nonlinear form of the Kalman filter is the popular extended Kalman filter (EKF), which uses linear approximations to the measurement and state equations within the standard Kalman filter equations. However, this relies on an accurate initial estimate to ensure a good approximation in the linearization and it also assumes the measurement and state errors are Gaussian distributed. More recent techniques such as the unscented Kalman filter (UKF) [7.38] and the particle filter (PF) [7.11] may give more robust results, with relaxed requirements for the initialization. The UKF requires no linearization of the measurement and state equations and has a computational complexity similar to the EKF, but it still assumes Gaussian errors. The PF is completely general, requiring no linearization and no assumptions on the error distributions. However, it can be computationally expensive. Using the extended Kalman filter, the target’s state can be estimated from the Doppler and bearing measurements as follows [7.34, 7.35]: xˆ (tn ) = x(tn ) + K(tn )y(tn ) − h(x(tn ), tn ),

(7.12)

where y(tn ) is the vector of measurements (Doppler and bearing) at time tn , h(x(tn ), tn ) is the measurement that would be expected at time tn given the predicted state x(tn ) and K(tn ) is the Kalman gain at time tn . These are calculated using: x(tn ) = f (xˆ (tn−1 ), tn ), predicted track state at time tn , given its state at time tn−1 ,

−1 K(tn ) = Px (tn )MT (tn ) M(tn )Px (tn )MT (tn ) + Pv (tn ) , Kalman gain, where Px (tn ) = (tn )Px (tn−1 )T (tn ) + G, Px (tn−1 ) = I − K(tn−1 )M(tn−1 )Px (tn−1 ), ∂h(x(tn ), tn ) , ∂x ∂ f (xˆ (tn−1 ), tn ) (tn ) = , ∂x

M(tn ) =

covariance of the state prediction, x(tn ), covariance of the previous smoothed estimate, xˆ (tn−1 ), linearized measurement matrix, linearized state equations,

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and Pv (tn ) is the covariance matrix representing the measurement errors and G is a covariance matrix representing errors in the state equations. The measurement vector, h(x(tn ), tn ) is defined as (F, θ)T , where F and θ represent the measurements of Doppler and bearing respectively: 1 x x Y + yy Y yy Y + (L − y)y Y F =− , (7.13) + λ x 2 + y2 x 2 + (L − y)2 −1 x θ = tan (7.14) y and, assuming a simple linear model for target motion, the state equations are defined as

x(tn−1 ) + x Y (tn−1 )t f (ˆx(tn−1 ), tn ) = . (7.15) y(tn−1 ) + y Y (tn−1 )t Given an illuminator with a poor ambiguity function but a strong continuous wave component, it is therefore possible to detect and track an aircraft by observing the evolution of the Doppler shift and bearing of the echo over time. The information content in the Doppler and bearing measurements may be low, particularly for aircraft at longer ranges, and so it takes several tens of seconds before the target state becomes observable. In practice, it is difficult to make a robust PBR system using narrowband measurements alone. However, they make a very useful adjunct to a system that is also exploiting other transmitters that support wideband PBR processing. This is described in the next section.

7.3.2 Wideband PBR Processing In contrast to narrowband PBR processing, wideband PBR processing uses the full bandwidth of the transmitted signal and applies a conventional matched filter approach to the detection problem. It is applicable to any waveform that has a reasonable ambiguity function and can be applied to FM radio broadcast signals, as well as digital broadcast signals such as global system for mobile telecommunications (GSM), digital audio broadcast (DAB), digital video broadcast (DVB) and high-definition television (HDTV). Much of the signal processing is similar to narrowband PBR, the principal difference being the replacement of the FFT spectral analysis stage with an efficient cross-correlation implementation, to determine the range and Doppler of target returns. As a minimum, the system must comprise one reference channel and two echo channels. The approach can be summarized as follows:

r data collection on at least three channels; r signal conditioning of the reference signal; r cancellation of the unwanted broadcast signal received directly in the echo channels, either spatially by the antenna or by cancellation in the time domain;

r Doppler-sensitive matched filtering by cross-correlation of the reference signal with the echo channels;

PBR SYSTEM PROCESSING

r target detection using a constant false alarm rate (CFAR) algorithm; r target association in the range–Doppler–bearing space; r Target state estimation using a nonlinear filter.

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In some implementations, the target association and target state estimation stages can be combined into a single step. As with narrowband PBR processing, target bearing may either be estimated from two echo channels by interferometry after the detection stage or by using multiple receiver channels and using amplitude monopulse techniques with a number of overlapping beams. The processing is described in more detail in the sections that follow and is largely based on the approach described in Reference [7.36]. 7.3.2.1 Data Collection Requirements The principal requirement for the signal processing is the availability of a reference signal, received directly from the transmitter, against which to correlate the signals collected on the two or more echo channels. The principal limitation on detection performance tends to be the problem of the direction reception of the transmitter signal in the echo channels. This can be 80 or 90 dB greater in magnitude than the target echoes being sought and must be cancelled before attempting matched filtering. This drives the requirement for high dynamic range and highly linear receiving equipment with a low noise figure. In simple implementations it is necessary to try to steer the echo channel antennas to minimize direct reception of the transmitter signal and possibly to use some form of analogue canceller to reduce the signal further, before sampling. In more sophisticated implementations, analogue beam-forming techniques can be used to steer a null towards the transmitter. In rare instances, such as the Manastash Ridge radar [7.9], terrain features can be used to physically block the reception of the direct signal in the echo channels – but this then requires a remote, synchronized receiver for the reception of the reference signal, and limits radar detection to high-altitude targets. 7.3.2.2 Reference Signal Conditioning In order to perform the matched filtering stage, it is necessary to cross-correlate the echo channel signals with the reference signal. In some circumstances, it may be necessary to perform some signal processing on the reference signal to improve its quality. For a system exploiting FM radio stations, this conditioning is not essential, but channel equalization techniques can be used to remove unwanted multipath components within the signal. For other signal sources, however, this processing is essential. A good example of this is with digital audio broadcast (DAB) signals arising from a single frequency network (SFN). In this situation, the unprocessed reference signal would actually comprise the superposition of several identical, but time-shifted, copies of the reference signal from each transmitter within line-of-sight of the receiver. In this situation, it is necessary to exploit the multipath-resistant features of the coherent orthogonal frequency division multiplexed (COFDM) waveform and reconstruct a pure reference signal. If this is not done, then even a single aircraft would result in multiple detections when the reference signal was correlated [7.39].

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Another example of the need for some form of signal conditioning is when exploiting a digital waveform that contains some form of unwanted periodic structure, which causes ambiguities in the ambiguity function. By excising these structures from the reference signal before correlation, it is possible to improve the ambiguity function, but always at the expense of some loss in sensitivity. 7.3.2.3 Direct Signal and Clutter Cancellation The detection performance of wideband PBR systems tends to be fundamentally limited by the dynamic range of the receiver system and hence the masking of small target echoes by the unwanted reception of the transmitted signal in the same channel. Simple energy analysis using the radar and communications equations shows that in a typical bistatic configuration, the unwanted direct signal can be 90 dB or higher than the echo of a typical target at the 100 km range. Even after matched filter processing that may provide 50 dB of signal processing gain, the target echoes could still be 40 dB a more below the noise floor, which is set by the range and Doppler sidelobes of the unwanted signal. It is therefore essential for this direct signal to be removed before matched filter processing. The first stage in reducing the direct signal received in the echo channels is to try spatially to filter out the signal through the receiver antenna pattern. With simple antenna systems this is achieved by physically steering the antenna to ensure that the transmitter falls in a null or low sidelobe, and with more advanced antenna arrays the adaptive beam-forming approach can be applied. However, even after reducing the interference using the antenna pattern, it is necessary to filter the direct signal and clutter further by adaptive filtering in the time domain. The approach adopted in Reference [7.36] is to use an adaptive noise canceller structure, in which the signal from the reference antenna is used to estimate the interference and then remove it from the echo channels. This approach relies on a reference channel containing no echo signals; otherwise they would also be removed. The filter used comprised an adaptive M-stage lattice predictor followed by an adaptive tapped delay line. This relatively complex structure was required to ensure rapid convergence and hence support real-time operation. It was found effectively to remove the direct signal and also clutter signals received to ranges of about 50 km from the radar receiver. 7.3.2.4 Matched Filter Processing The matched filtering processing stage is the key difference between narrowband and wideband PBR processing. In this stage, the echo signal is correlated with Doppler-shifted copies of the reference signal in order to form a bank of filters matched to every possible Doppler shift. Such an approach is necessary due to the thumbtack nature of the ambiguity function of most transmitters of opportunity. While this means that unambiguous measurements of Doppler and range are possible, it also implies that the matched filter is intolerant to any Doppler shift of the echo. The matched filter stage serves two important purposes: the generation of sufficient signal processing gain to allow the targets to be detected above the noise floor and the estimation of the bistatic range and bistatic Doppler shift of the target echoes. An integration time of 1 second is again used, corresponding to a velocity resolution of around 1.5 m/s and a processing gain of 47 dB, for a typical FM radio station at 100 MHz with an average modulation bandwidth of around 50 kHz.

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This signal processing stage is analogous to the calculation of the ambiguity function and is defined as N −1 |(τ, υ)| = (7.16) e(n)d ∗ (n − τ )e j2πυ n/N , n=0 where denotes the range–Doppler surface that is to be calculated, e(n) is the filtered echo signal and d(n) is the reference signal, delayed by an amount τ seconds and Doppler shifted by υ Hz. It can be viewed as the cross-correlation of the echo signal with the Doppler-shifted reference signal. The reference signal can be weighted to reduce the range sidelobes, at the expense of reduced resolution. This processing stage is potentially very calculation intensive. With a 1 second sample of signal at a 200 kHz complex sample rate, and 500 possible Doppler shifts, this implies 500 complex cross-correlations of 200 000 complex samples every second. A significant performance improvement can be achieved by recognizing that correlation can be efficiently implemented as a multiplication in the frequency domain, allowing each correlation to be implemented as the multiplication of the FFT of the echo signal and the FFT of the reference signal, rotated by a number of samples to implement the Doppler shift. The inverse FFT is then applied to this product to return the correlation at that Doppler shift. The process is then repeated for every possible Doppler shift, noting that the FFT of the echo signal is identical each time (so only needs be performed once) and the Doppler-shifted reference is simply a different shift of the elements in the FFT of the original reference signal. Thus, the main calculation for each Doppler shift is the multiplication of the two FFT results, followed by calculation of the inverse transform. However, even this approach may be insufficient for real-time operation. A more efficient approach is to recognize that targets will not exist at every possible Doppler shift and hence to apply a decimation technique to correlation, to reduce significantly the size of the Doppler FFT that must be performed, with very little loss in processing gain [7.36]. This approach allows the performance to increase by a factor of around 15 when applied to the FM radio signal, bringing real-time computation within the reach of a few normal desktop computers. An even more efficient approach is to apply a signal processing approach similar to that used in FMCW processing. This algorithm recognizes that typical target returns will only be seen at delays of the order of 2 ms, and so the large, 1 second echo signal is divided into 512 segments of 2 ms each. Each of these is then correlated with a 1ms segment of (nonshifted) reference signal (starting at the same sample time as the first sample of the echo signal segment). These results in 512 separate range correlations, each calculated with a small, typically 256 or 512point FFT. The results of these are then (conceptually) used to form the rows of a matrix, and then 256 or 512 separate 512-point FFTs are performed across the columns of the matrix to calculate the Doppler spectrum in each range cell. This approach is highly efficient, and allows the real-time computation of the complete matched filter bank (or correlation surface) on a single personal computer. 7.3.2.5 Target Detection Having calculated the correlation surface, target detection is simply a matter of identifying which peaks cross a detection threshold. Providing the initial adaptive signal processing stage

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was effective and all significant reference signal leakages were removed, the target detection process is usually against a Gaussian noise floor. A simple constant false alarm rate (CFAR) algorithm is therefore very effective. In some circumstances, however, very large target returns can be observed for a few seconds. This is typically seen when a specular reflection is observed on a large jet aircraft, or when a target passes very close to the transmitter or receiver. In this case, the range and Doppler sidelobes of this large return can be sufficient to mask the other, smaller target returns on the correlation surface. Kulpa and Czeka/la [7.40] propose the iterative removal of such returns by estimating their position in range–Doppler, and then adaptively filtering them from the original data, before recalculating the correlation surface. The approach can be repeated for every strong return, but at the expense of nonreal-time operation in some instances. 7.3.2.6 Target Association The target association stage is very similar to that described for the narrowband PBR processing case. However, in this case a Kalman filter is used to track target returns in the range–Doppler space. A standard Kalman filter, with measurements of the range, Doppler and bearing and estimates of the range, Doppler, Doppler rate, bearing and bearing rate can be used effectively to associate the aircraft in this domain [7.38]. The fact that the system makes a high-quality estimate of Doppler (which is proportional to the range rate) means that the filter can very easily follow aircraft in the range–Doppler domain. A more sophisticated filter, such as the IMM, would prove more robust for highly manoeuvring aircraft, but the authors are unaware of any open literature publications describing this. 7.3.2.7 Target State Estimation Finally, the target state estimation process is again very similar to the extended Kalman filter approach described above for the narrowband PBR processing case. However, the wideband PBR system benefits from measurements of the bistatic range, in addition to the measurements of the bistatic Doppler and bearing. This makes the track initialization process much simpler, with no need for elaborate initialization schemes. In this case the measurement vector, h(x(tn ), tn ) is defined as (F, θ , R)T , where F and θ are defined as before, and the measurement of the bistatic range is R=

x 2 + y2 +

x 2 + (L − y)2 − L 2 .

(7.17)

All other equations in the EKF remain the same. Note that it would be perfectly possible to combine the target association and target state estimation phases into a single process, where the noisy measurements of the range, Doppler and bearing were directly passed into the EKF to estimate the target state, and then the target state prediction was used to predict the range, Doppler and bearing of the target at the next update. The process is likely to be more accurate than the two-stage process described above. However, in a practical wideband PBR system it is desirable to use multiple transmitters, and the problem of associating echoes from different transmitters with the correct targets is computationally very challenging, particularly in the presence of false alarms and missed

PBR SYSTEM PROCESSING

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detections. One way to minimize the magnitude of this computational problem is first to associate the targets from each transmitter in isolation and then associate the tracks from each individual transmitter. This allows false alarms to be rejected and also provides a means for extrapolating the values of the range, Doppler and bearing from each transmitter to the same time instant.

7.3.3 Multistatic PBR The descriptions of narrowband PBR and wideband PBR provided to this point have assumed the use of a single receiver and a single illuminator. In this situation, both systems rely heavily on the use of bearing to estimate the target’s location, followed by an elaborate tracking and estimation scheme to provide a smoothed track. In practice, the reliability and accuracy of a PBR system can be very significantly improved by exploiting multiple transmitters and, optionally, multiple receivers as well. If multiple transmitters are used then multiple independent measurements of the bistatic range and bistatic Doppler are obtained, as well as multiple measurements of the same bearing (as the bearing is due to the direction of the target and independent of the location of the illuminator). If multiple receivers are used, then all three measurements are different for a given target on different receivers. Multiple independent measurements of the range, Doppler and bearing of a target can be processed by extending the measurement vector of the EKF algorithm described above to encompass all the available measurements. The matrix equations remain unchanged. This rather minor change to the EKF causes dramatic improvements to the accuracy and robustness of the resulting PBR system. However, the technical challenge is one of data association. When multiple transmitters are used, the correct association of the echoes measured by each transmitter to target is not trivial. In simple terms, if two transmitters are used and two targets are present, then it is unclear how to pair the two echoes received from one transmitter with those received by the other transmitter – there are two possible pairings. If there are now n targets and two transmitters, then there are n 2 ways in which the returns can be paired (allowing for duplications). If the problem of false alarms and missed detections is now considered, it is clear that the problem can become extremely complex. If an accurate measurement of bearing is available then this can help reduce the number of possible pairings, as the correct pairings should have similar measurements of bearing. However, the problems of multipath and small apertures at VHF mean that the bearing measurements are rarely very accurate, limiting their usefulness. The bistatic range measurement represents an ellipse with the transmitter and receiver as its foci. Thus, when a pair of measurements have been associated, the target must lie close to the intersection of these ellipses (close, not on, due to errors in the measurements of range). However, a pair of ellipses will intersect in four locations in general, and so bearing is still required to help resolve this ambiguity. However, the advantage is that bearing is only required as a discriminant, and hence relatively large inaccuracies can be tolerated as the location accuracy will be dominated by the range accuracy. Determining the points of intersection of two ellipses is not a trivial mathematical problem, but computational solutions exist. One simple approach is to perform a grid search, testing each possible Cartesian solution to see whether an ellipse exists from each transmitter at that point. Alternatively, more analytical approaches can be used, such as writing the points on one ellipse in parametric form, x = x1 + a1 cos (θ) and y = y1 + b1 sin (θ), for an ellipse

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centred on (x1 , y1 ) with axes a and b. Points on the second ellipse (with foci at locations F1 and F2 and major axis α 1 ) will satisfy |F1 − p| + |F2 − p| − 2α1 = 0. Thus solutions for the intersection exist by substituting (x, y) for p and searching for those values of θ that solve the equation. The problem of locating a target and associating measurements is much easier if three or more transmitters are used. In the case of three transmitters illuminating a target, the three ellipses will usually only ever intersect in one location. The target’s location can thus be easily found, even without a measurement of bearing. The problem is then simply a matter of finding the locations at which three or more ellipses (one from each transmitter) intersect. Of course, once a track has been established in this way it can subsequently be maintained with intersections of just two ellipses, or the occasional single detection.

7.4 WAVEFORM PROPERTIES Resolution and ambiguity in both range and Doppler are parameters of fundamental importance in the design and subsequent performance of any radar system. In passive bistatic radar (PBR) systems these properties are determined by the transmitted waveform, the location of the transmitter, the location of the receiver and the location of the target. Consequently, the scope for radar design and optimization would seem to be severely restricted as many factors are not within the control of the radar designer. Here, practical measurements of transmitted waveforms are use to illustrate their effects on the resulting system design and performance. In particular, the ‘self-ambiguity’ is computed, which enables the limits on range and Doppler resolutions to be evaluated. The bistatic form of the ambiguity function is subsequently presented and used to illustrate how these best-case parameters vary as a function of transmitter, receiver and target locations. Understanding the forms that these functions can take and subsequently the implications for system performance is most important if this type of radar is to be used effectively. Then it is shown that the radar designer does in fact have some freedoms to improve system performance. Finally, the implications of transmitter waveform and bistatic geometry on target detection, location and imaging are discussed.

7.4.1 Introduction In Section 7.2 of this chapter the sensitivity of a number of exemplar PBR systems was computed and showed that useful detection ranges can be expected, leading to a considerable number of possible applications. To realize these applications it is important to understand fully the performance limitations that exist. In a PBR system the range and Doppler resolutions and ambiguities have a number of unique characteristics that require careful consideration. In particular they are highly dependent on the (time-varying) form of the transmitted signal, which is not under the control of the radar designer. These require direct measurement in order to evaluate the range and Doppler properties of PBR systems. Range resolution is the ability of a radar system to distinguish two closely spaced targets at differing ranges. In monostatic radar this is primarily a function of pulse length or modulation bandwidth. Azimuth and elevation resolutions distinguish between two targets in angle space and are determined by antenna dimensions and operating wavelength. Together these specify

WAVEFORM PROPERTIES

• 275

the three-dimensional spatial resolution of any radar system. Doppler resolution is the ability to distinguish two targets by virtue of their differing velocities. In a monostatic radar system this is primarily a function of wavelength, waveform and target illumination time. It is important to understand the range and Doppler resolutions of any radar system in order that overall performance may be reliably estimated. Examples might include ensuring that tracking performance is adequate for a particular application or that image quality metrics result in two-dimensional target signatures suitable for further processing tasks such as classification. In monostatic radar systems these parameters are routinely established as part of the design process and can be easily pre-determined by the radar designer to be tailored to the chosen application. However, in bistatic radar systems, and more particularly in PBR systems, they cease to be of a routine nature and considerable care needs to be exercised in these aspects of design. Indeed, in the case of the PBR the lack of design control over the form, nature and origin of the transmitted waveform seems to imply severe restrictions. In practice, however, there are more freedoms than might be apparent at first sight as usually more than one transmitter may be used at any given instant of time. This is an aspect not exploited in monostatic radar systems. Nevertheless, separation of the transmitter and receiver and the time-varying properties of qualifying illuminations of opportunity do result in important differences that must be thoroughly understood if PBR system design methods are to evolve to similar levels of maturity to that of monostatic radar. In this section these fundamental aspects of PBR radar design that determine subsequent performance are analyzed. Practical measurements of transmissions of opportunity show detailed, time-dependent, behaviours that require careful consideration when developing an overall system design. Specifically, the ambiguity function has long been used to evaluate range and Doppler resolutions as well as range and Doppler ambiguities. However, it was developed to capture these aspects of performance for monostatic radar systems only. Here the ambiguity function and in particular its bistatic formulation are reviewed. This highlights the importance of system geometry with respect to target position. Results of the bistatic ‘self-ambiguity’ of ‘on-air’ signals are used to demonstrate waveform variability and its effect on the range and Doppler resolutions as well as detection performance. These give the best possible range and Doppler resolutions and are geometry independent. The more general description of ambiguity in a bistatic system introduces a geometrical dependence between the transmitter, receiver and target that determines the range and Doppler resolutions. This dependence is computed and used to illustrate regions where system operation is likely to be compromised. Also illustrated is how the use of multiple transmitters coupled with appropriate signal processing may enable the coverage of PBR to be improved. These characteristics also have a significant impact on detection, location and imaging, and this issue is also discussed.

7.4.2 Range and Doppler Resolution – ‘Self-Ambiguity’ The range and Doppler resolutions are fundamentally important parameters in the design of any radar system as they govern the ability to distinguish between two or more targets by virtue of spatial or frequency (i.e. radial velocity) differences. The nature of the transmitted waveform determines these properties, which may be evaluated via the ambiguity function [7.24]. In the case of the PBR the waveform and the location and direction of its transmission are not in the control of the radar designer and may even be derived from a number of differing transmissions and transmitters. These include analogue and digital VHF radio, UHF television

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as well as signals from telephone basestations or even GPS satellites. Typically the range of frequencies may span from a few tens of MHz to a few GHz. For example, FM broadcasting in Europe uses the frequency range 88–108 MHz and the specified peak frequency deviation (i.e. bandwidth) is ±75 kHz, which gives a range resolution in the region of 1–2 km. DAB operates at a transmit frequency of around 220 MHz and has a variable bandwidth of the order of 100 kHz. It is therefore necessary to evaluate the range and Doppler resolution and ambiguous behaviour of these waveforms in terms of the ambiguity function in order to understand the resulting radar performance. The importance of this, for example, may be appreciated by a simple consideration of the nature of analogue television. This has a 64 μs line repetition rate, which generates strong ambiguities [7.3] and consequently implies a severe restriction in its utility. It is also necessary to know how the ambiguity behaviour varies as a function of the instantaneous modulation of a particular signal and how this may vary with time (which is a particular feature of waveforms likely to be exploited by a PBR system). The range and Doppler resolutions are initially computed by matched filtering the directly received transmitter signal. In a PBR system this would be the signal used to provide a ‘reference’ waveform for correlation with the indirect target scattering. This is termed the ‘self-ambiguity function’, as it does not take into account the relative positions of the target, transmitter and receiver and effectively mimics a monostatic geometry. This enables the best achievable resolutions to be evaluated and the time-varying properties to be investigated. These have an important bearing on the overall range and Doppler resolutions as will be seen later. The ambiguity function represents the output of a matched filter and may be written as ψ (TR , f d )2 =

∞

−∞

st (t)st∗ (t

2 + TR ) exp[j2π f d t]dt

(7.18)

where ψ(TR , f d ) = ambiguity response at the delay range TR and Doppler f d , s(t) = directly received transmitted signal. Computation of this function results in a three-dimensional plot for which one axis is the time delay (or range), the second is Doppler frequency or radial velocity and the third is the output power of the matched filter (usually normalized to unity). The extent of the ambiguity function peak in the TR and the f d dimensions determines the range and Doppler resolution respectively. As only the directly received signal is used this is termed ‘self-ambiguity’ as there is no inclusion of any system geometry dependence on the transmitter and receiver locations. These properties have been measured using a simple digital receiving system, as shown schematically in Figure 7.8, with Figure 7.9 showing the experimental equipment. The receiving system was based on a Yagi antenna feeding an HP8565A spectrum analyser. Although the noise figure of the spectrum analyser is relatively poor the signal level received was sufficiently high to ensure that separation from receiver noise was straightforward. The spectrum analyser also provides downconversion to an intermediate frequency of 21.4 MHz. The output bandwidth of the spectrum analyser is controlled in order to provide the optimum integration gain. This signal is then digitized directly at 32.5 MHz using an Echotek ECDR-214-PCI digitizer card, converted to baseband and stored in the memory of a standard PC. This makes a

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WAVEFORM PROPERTIES

Pre-amplifier Stage

Spectrum Analyser

Computer

Antenna

Signal Generator

Digitised signal as Data file

Digitiser Card

Signal Generator

Figure 7.8 Experimental equipment showing the spectrum analyser

very flexible system as the spectrum analyser can operate linearly over a wide frequency range and captured data can be processed offline and the self-ambiguity function computed. Some sample results were reported in Reference [7.22] illustrating different waveform properties. Here the ambiguity function properties are investigated in greater detail via computation of the self-ambiguity function described by Equation (7.18) to illustrate the variability of responses. Examples of these are shown in Figures 7.10 to 7.13. Figure 7.10(a) shows an unweighted self-ambiguity function for a BBC Radio 4 transmission for which the signal

Figure 7.9 Schematic of the experimental equipment

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Amplitude/dB

PASSIVE BISTATIC RADAR SYSTEMS

0 −20

−40 500 400 300 200 100 0 −100 −200

Doppler Frequency/Hz

−300 −400 −500 −1.5

−4

−0.5

0

0.5

1

1.5 x 105

Range/metres (a)

Figure 7.10 (a) The ambiguity function for a BBC radio 4 transmission at 93.5 MHz. (b) The range and (c) Doppler resolution for the BBC Radio 4 transmission

comprises speech (in this instance an announcer reading the news). The peak of the ambiguity function is reasonably well-defined but a lot of fine, semi-random structure can be seen in the regions away from the main peak, which are a function of the detailed modulation present in this component of the waveform. This does not show pure noise-like behaviour but is consistent with the correlation that might be expected in a speech-type signal. Cuts taken at zero range and Doppler are also shown in Figures 7.10(b) and 7.10(c) to demonstrate the range and Doppler resolutions more clearly. Sidelobe levels are very good with nearly −50 dB in the frequency domain and around −25 dB for the range. If a number of speech collections are analysed it can be seen that performance is not consistent. This is illustrated in Table 7.3, which shows the bandwidth in kHz for ten waveform samples. The bandwidth is seen to vary from 500 Hz to 22.2 kHz. This is important in two respects. The first is that by no means all of the 150 kHz modulation bandwidth is being used (in this case it is only 15 % of the available bandwidth). Second, as the bandwidth is a function of time the performance of the radar system will also be

• 279

Amplitude/dB

WAVEFORM PROPERTIES

0 −10 −20 −30

−40 500 400 300 200 100 0 −100 −200 −300 −400 −500 −1.5

−1

−0.5

0

0.5

1

1.5 5

× 10

Range/metres (a)

Figure 7.11 (a) The ambiguity function for ‘fast tempo Jazz’. (b) The range and (c) Doppler resolution for the ‘fast tempo jazz’

a function of time. The effects this may have on system performance are considered in more detail in a later section. Figure 7.11 shows a similar plot but this time for an FM broadcast containing ‘fast tempo jazz’ modulation. The ambiguity function plot shows a narrower (better) defined peak and exhibits faster fluctuating detail in the sidelobe regions. This indicates a wider bandwidth, and a more noise-like waveform. This again seems consistent with what might be expected for jazz music as compared to speech. Again the range and Doppler cuts show sidelobes to be usefully low and this time there is improved performance in the range domain. The improvement in range resolution reflects the higher rate modulation in the jazz waveform than for speech.

• Amplitude/dB

280

PASSIVE BISTATIC RADAR SYSTEMS

0 −20 −40 500 400 300 200 100

0 −100 −200 −300 −400 Doppler Frequency/Hz −500

1.5 1 0.5

5

× 10

0 −0.5 −1

Range/metres

−1.5 (a)

Figure 7.12 (a) The ambiguity function for a GSM 1800 communication signal. (b) The range and (c) Doppler resolution for a GSM 1800 communications signal

Table 7.4 examines the time-dependent bandwidth of this waveform type. Generally the values of bandwidth are greater and the variation less but still significant. Note, that the modulation bandwidth measured is still only 24 % of that available. An alternative signal of opportunity for exploitation in a PBR system and one used in a system like CELLDAR [7.8] are GSM transmissions. Figure 7.12(a) shows the ambiguity function for a GSM 1800 communications signal. The code modulation results in a lot of detailed structure in the sidelobes and results in them being suppressed to a level of −30 dB. There are repetitive high sidelobes, equispaced at 200 Hz, in the range domain caused by the bit rate modulation used. The bit rate at a particular instant of measurement depends on what is being transmitted and on the occupied bandwidth. In GSM the total bit rate is 270.8 kbits/s for each 200 Hz carrier. In addition, the modulation bandwidths of a time sequence of GSM

• 281

Amplitude/dB

WAVEFORM PROPERTIES

0 −20 −40 1.5 1 0.5 × 105

0 −0.5

Range/metres

−1 −1.5 500

400

300

200

100

0

−100

−200

−300

−400

−500

Doppler Frequency/Hz (a)

Figure 7.13 (a) The ambiguity function for analogue UHF television signals. (b) The range and (c) Doppler resolution for analogue UHF television signals

waveforms are generally larger (approximately 57 kHz) and are more stable. The sidelobe levels are higher and will require weighting which may, at least in part, offset the benefits of the larger modulation bandwidth. The repetitive and highly ambiguous sidelobes will need to be carefully taken into account in any systems attempting to exploit this form of transmission. Table 7.5 summarizes the measured ambiguity function performance of a range of measured signals. A third form of signal that can be exploited by the PBR are analogue UHF TV transmissions and Figure 7.13 shows a typical ambiguity function for the vision carrier signal component. As mentioned earlier, the effect of the 64 μs line repetition flyback time is to create range ambiguities at 19.2 km. This is shown very clearly in the range cut at zero Doppler (Figure 7.13(c)). The relatively short range and severity of this ambiguity makes exploitation of this type of

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PASSIVE BISTATIC RADAR SYSTEMS Table 7.4 Bandwidth variation of fast tempo jazz Collection number

Bandwidth (kHz)

1 2 3 4 5 6 7 8 9 10

25.7 13.8 22.9 21.0 24.5 31.2 17.2 17.7 35.1 35.1

Average bandwidth /(kHz)

24.4

Table 7.5 Bandwidth variation for GSM 1800 waveforms Collection number

Bandwidth (kHz)

1 2 3 4 5 6 7 8 9 10

52.0 45.1 57.2 52.0 57.3 57.5 57.2 57.2 57.3 57.3

Average bandwidth (kHz)

55.0

waveform much more complicated and consequently its application is much more likely to be limited. It should also be noted that the range resolution is significantly worse than in the previous examples. Indeed, the bandwidth varies with time between approximately 10 and 370 Hz. The other main class of signals that could be exploited are digital audio broadcasts (DAB). These have similar properties to the FM modulations although they exhibit a less deterministic structure in the sidelobe regions. Bandwidths vary widely, typically between 20 and 100 kHz around a carrier of 220 MHz. In general these waveforms exhibit slightly improved properties. Overall it is clear that there is considerable variability in the waveforms to be exploited, with dependence on the type of transmission, its content and the time of transmission. For example, if there is a long pause on an FM speech channel then effectively all range resolution information will be lost. This is illustrated in Figure 7.14, which compares the range resolution as a function of time (sample) for a number of differing transmission types. The two ‘news’ channels show a high degree of temporal variability in range resolution compared to the music channels as predicted. Overall the range resolution varies approximately between 1.5 and

• 283

WAVEFORM PROPERTIES

0

2

4

6

Collection Number 8 10

12

14

16

0

Range Resolution/m

20000 40000

Pop Classical

60000

Rock Medium Jazz

80000

Dance BBC Radio 3 News BBC Radio 4 News

100000 120000 140000

Figure 7.14 Variation of range resolution with media content

16.5 km. The pop and dance channels exhibit the least variation, rock and jazz have slightly inferior performance and classical music is degraded a little further. The important conclusion is that the performance tends to have quite a considerable variation and that the effect on overall system performance will require careful consideration. The rate of fluctuation of the bandwidth of the signals is governed by the content and hence occurs on a relatively slow timescale (i.e. seconds). This will also have a certain predictability which offers the opportunity for intelligent processing to recognize changes in signal structure and take appropriate action.

7.4.3 Range and Doppler Resolution – ‘Bistatic and Multistatic Ambiguity’ So far only ‘self-ambiguity’ has been considered. This has been defined as the output of the matched filter response of the direct signal. Hence it may be thought of as a condition that mimics the performance of a monostatic radar system with the same waveform. In effect this yields the best possible range and Doppler resolutions with any given waveform. However, in PBR and more generally in bistatic radar the relative positions of the target, transmitter and receiver govern the actual resolutions that can be achieved. Here the formulation presented in Reference [7.41] is used to compute the bistatic ambiguity function, which uses the transmitter at Alexandra Palace with the receiver located at University College London. From Reference [7.41] the bistatic form of the ambiguity function can be written as ψ(RRH , RRa , VH , Va , θR , L)2 =

∞ −∞

2 , × exp[j2π f DH (RRH , VH , θR , L) − 2π f Da (RRa , Va , θR , L)t]dt

st (t − τa (RRa , θR , L))st∗ (t + τR (RRH , θR , L))

(7.19)

• 284

PASSIVE BISTATIC RADAR SYSTEMS

where RRH and RRa = hypothesized and actual ranges (delays) from the receiver to the target, VH and Va = hypothesized and actual radial velocities of the target with respect to the receiver, f DH and f Da = hypothesized and actual Doppler frequencies, θR = angle from the receiver to the target with respect to ‘north’, L = length of the baseline formed by the transmitter and receiver. The expression assumes the reference point of the PBR geometry to be the receiver and is essentially a straight change of variables with Equation (7.18). The important difference is that the geometrical layout of the transmitter, receiver and target are now taken into account. This can have a significant effect on the form of the ambiguity function and the resulting range and Doppler resolutions. Plates 7 to 9 in the colour section illustrate the range of possible behaviours for a simulation representing the present exemplar case. The frequency of transmission is 100 MHz and the bandwidth of modulation is 150 kHz. Plate 7 shows the ambiguity behaviour when a target is located on an extension to the baseline such that it is further from the transmitter than the receiver and is 5 km from the receiver. Here the resolution is almost the same as in the self-ambiguity case. The range resolution is quite poor (around 8 km) as expected and the Doppler resolution good with a minimum detectable radial velocity of approximately 0.2 m/s. The effects of changes in the target position with respect to the transmitter receiver baseline are now considered. As the target position changes to make an angle of 90◦ with respect to the baseline the resolution degrades the Doppler resolution slightly and the range resolution more, as shown in Plate 8. The degradation in Doppler is not too severe and may be quite acceptable in many applications but the range resolution, which degrades by a much greater amount, will have a more significant effect on performance. As the target is located at ever-increasing angles with respect to the baseline the resolutions degrade further. Eventually, when the target is situated directly between the transmitter and receiver (i.e. on the baseline) there is no effective resolution at all in either range or Doppler. This situation is shown in Plate 9 and the effect on radar performance will be very significant. It should also be noted that this will be a function of the relative lengths of the radar baseline and target range. Indeed, if a target is much further away than the length of the baseline then the bistatic ambiguity function begins to approximate that of the monostatic case. Overall, though, it may be concluded that there are regions of potentially unacceptable performance and that great care needs to be taken when designing the PBR system. Variations in the range resolution can be considered in more detail via the ‘traffic light’ plot of Plate 10. Here the range resolution only is being plotted as a function of the target position. Green corresponds approximately to a range resolution of up to one and a half that of the self-ambiguity case. Amber corresponds to a resolution of two-thirds of that of the selfambiguity case and red is greater than twice. The scale on the left hand side of the plot indicates this on a continuous colour change basis. This shows that there are significant areas where the resolution is severely degraded. There are several strategies for taking this into account in the design of the system. Two possibilities might be either to adjust the signal processing depending on the application or simply to declare a ‘no-go’ region where radar operation is not attempted. As the no-go area coincides with the direction of the directly received transmissions, this may be the preferred option as it aids the problem of suppression of the directly received signal.

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WAVEFORM PROPERTIES

This would seem to be a significant limitation of the PBR approach. However, it should be borne in mind once again that it is quite likely that multiple transmitters will be exploited and their spatial spread will alter the simple bistatic case considered above. Plate 11 shows an extension to this simple situation. Here the transmitter at Crystal Palace has been added to the example system. The geometry has been adjusted from the true case to make the second transmitter lie along the baseline (which is quite close to the actual geometry). For simplicity the same frequency of operation and waveform properties are assumed for both the Alexandra Palace and Crystal Palace transmissions. Plate 11 shows that the area of green and amber is now extended and the regions of ‘no-go’ are very limited. This illustrates two important points. The first is that multiple transmitter sites can be used to improve the overall range resolution performance. The second is that this performance is still very much governed by the locations of the additional transmitters and is a function of the angles made by the multiple baselines. In practice the location of transmitters and receivers will be known and hence the resolution performance as a function of the target position can be predetermined. This opens the way to detection strategies that are now a function of known variations in system performance. This gives some flexibility to the designer although the fixed positions of the transmitters are not under his or her control. Plates 12 and 13 also show similar behaviour for Doppler resolution. Note, however, that here the degradation in resolution is much more severe and the addition of the second transmitter has a correspondingly greater benefit.

7.4.4 Influence of Waveform Properties on Design and Performance Suitable waveforms available for exploitation in a PBR system are often relatively narrowband, as exemplified by those reported in this section. It has also been shown that the characteristics of these waveforms are themselves a function of time due to the changing content of the signal transmitted. These two features will play an important role in determining the design approach and resulting performance of a PBR system. In addition, the bistatic geometry in which only the receiver position is under some control of the designer will also need to be carefully chosen due to the effects on the range and Doppler resolutions and ambiguity. This can be further complicated by the use of multiple transmitters, not all of which will be contributing to the radar performance all of the time. The role of directly received radiation from the transmitter also needs to be taken into account as this will ultimately limit the system dynamic range and hence overall sensitivity [7.8]. The effects of these factors on detection, location, tracking and imaging are now considered. Earlier the maximum processing gain was defined to be G p = TMAX B,

(7.20)

where B = signal bandwidth (Hz), TMAX = maximum coherent processing time (s). Table 7.3 shows that the bandwidth of the transmitted signal may vary (in this example) from 500 Hz to 22.2 kHz. This translates to a variation in processing gain of over 16 dB and will consequently can have quite a significant impact on detection, and one that is time varying. Although noncoherent integration will begin to average this out it should be carefully factored into an assessment of the likely system performance.

• 286

PASSIVE BISTATIC RADAR SYSTEMS Table 7.3 Bandwidth variation of speech waveforms Collection number 1 2 3 4 5 6 7 8 9 10 Average bandwidth (kHz)

Bandwidth (kHz) 22.2 0.5 14.8 9.1 10.1 0.8 12.2 4.2 1.0 5.3 8.0

The narrowband continuous wave nature of the signals generally exploited by the PBR mean that detection of spatially limited targets such as aircraft will be via segmentation of the waveform into discrete-time components followed by correlation after an appropriate delay. The signal-to-noise ratio will be improved by subsequent coherent and noncoherent integration. The relative roles of coherent and noncoherent integration will be a function of the coherency (i.e. amplitude and phase stability) of the target signature to be detected as well as the coherency of competing clutter and noise signals. Consequently TMAX can also be a time-varying quantity and will need care in its choice. The large size of range resolution cells means there will be contributions due to clutter. Ultimately this can limit both the range and minimum radial velocity of targets that can be detected, particularly where the clutter has the properties of a very large backscatter fixed object. Fourier integration is likely to yield the biggest gains where moving aircraft can be detected in spectral regions away from static clutter. As seen in the earlier ambiguity plots, the Doppler properties of many of the waveforms available for exploitation are well suited to Doppler processing. Additionally, care will also need to be taken when processing returns that are from multiple transmitters. The independent nature of these multiple waveforms is likely to necessitate detection being carried out for each transmitter separately and the results then combined noncoherently. It is likely that for each transmitter the target and clutter coherence times are different, and this will require different implementations of a detection algorithm. At the very least this may imply different coherent and noncoherent integration times. In juxtaposition to the detection of discrete targets it may be argued that the relatively large spatial resolution makes this form of transmission especially suited to applications where the target is spatially extended. The Manastash Ridge radar [7.9] used to measure properties of the ionosphere is an excellent example of this. Here, too, the methods of providing sufficient detection sensitivity will depend on the form of the signal to be detected and the clutter to be rejected. The time-varying nature of the resulting radar performance will still need to be separated from that of any properties of the volume being measured. For example, if the bandwidth decreases over the measurement interval the total backscatter return can increase (assuming a uniform distribution of scatterers). This must be separated from, say, an increase in electron density that may also increase backscatter. One approach may be a simple normalization where the bandwidth fluctuation in the directly received signal is used to provide the appropriate factor. The effect on target detection is difficult to predict, depending on the precise nature of the

WAVEFORM PROPERTIES

• 287

clutter contributions. In general the detection of spatially limited targets will be reduced as the clutter contribution increases while the measurement of Doppler is likely to improve. In both cases the fact that the bandwidth is constantly subject to change will result in performance being constantly modulated. Multiple transmitters may in part ameliorate this, providing that on average a consistent bandwidth signal is available for exploitation for a particular target. It should also be noted that the seemingly poor ambiguity properties of analogue TV transmissions can be partly overcome by using a subset of the available waveforms. For example, the sound carrier has much improved ambiguity characteristics. If system sensitivity or range performance is to be extended to the limit then it may be important to exploit every usefully available waveform. The target location is usually evaluated using a combination of the range and Doppler within a beam. The poor range resolution means that alternative techniques are likely to have to be considered. For example, Howland [7.19] uses angle and Doppler to form tracks in a PBR radar exploiting TV transmissions. The inherently narrowband nature of the signals makes this approach attractive although temporal fluctuations in bandwidth will again modulate the performance. The precise effect of this will depend upon waveform properties and system geometry. A reduction in bandwidth is again likely to reduce sensitivity but may be compensated, at least in part, by a superior Doppler estimation. Monopulse techniques can be applied conventionally at the receiver to improve angular resolution. If multiple transmitters are used then more sophisticated forms of triangulation could be adopted and could result in high angular accuracies. If this were to be combined with monopulse then an array antenna at the receiver would be required that was capable of forming multiple simultaneous beams. A comprehensive analysis of these effects is beyond the scope of this chapter. Imaging with PBR-type systems has been reported [7.42, 7.43] where digital TV transmissions have been used. These have a centre frequency of 1.5 GHz and a bandwidth of 4 MHz. However, the proposed integration times of up to half a day impose severe requirements on the coherency of the scene to be imaged. Lanterman et al. [7.44] discuss the use of back-projection techniques using different look angles to generate high-resolution imagery. The multiple transmitter nature of the PBR lends itself to this approach. However, unless sufficient numbers of transmitters can be exploited image ambiguities may well result. Alternatively, if moving targets are to be imaged then techniques based on multiple ISAR imaging could be used. For example, a PBR system comprising two orthogonal baselines imaging a moving target with a trajectory that makes an angle of around 45◦ to both baselines will enable two near orthogonal image projection planes to be generated and hence a high-resolution two-dimensional image could be produced, although this may still be subject to ambiguities.

7.4.5 Conclusions In this section the form and nature of PBR transmissions have been investigated. In general many of them are found to be relatively narrowband and time-varying based on instantaneous modulation. This provides quite good Doppler resolution but poor range resolution. The range and Doppler resolutions are further influenced by the relative positions of the transmitters, the receiver and the target. Hence the received signal is a function of both time and space, although the spatial effects are constant for a given fixed receiver site. These effects will need to be factored into any radar design in order to predict performance confidently. For example, the time-varying nature means that the bandwidth can reduce, which tends to hinder the detection of

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PASSIVE BISTATIC RADAR SYSTEMS

discrete moving targets but improves sensitivity to volumetric scattering. However, the benefits to volumetric scattering applications may be offset by the need to ‘unscramble’ time-varying effects of the radar from time-varying effects of the volumetric properties being measured. The range of design freedoms inherent in the PBR have also been explored and were found to be less restrictive due to the potential exploitation of multiple transmissions. Overall it may be concluded that readily available waveforms of opportunity lend themselves well to exploitation by a PBR system. Equally, the detailed and time-varying behaviours of the waveforms must be fully understood for a given geometrical configuration to arrive at solutions capable of robust and reliable performance.

7.5 EXPERIMENTS AND RESULTS 7.5.1 Experimental Overview In this section the design, processing approach and performance are described of an experimental PBR system developed at the NATO C3 Agency in the Netherlands. This system was built on a low budget and is one of the simplest architectures that can be used to explore this technology. Nevertheless, it highlights all the important issues in the design and operation of PBR radar systems. Figure 7.15 illustrates the complete processing chain. The signal is collected by a digital receiver system comprising at least three channels. This allows for one reference channel and two surveillance channels. Two surveillance channels allow direction finding. Digital data from the three channels are fed to the range–Doppler processor, which outputs, approximately once every five seconds, two amplitude–range–Doppler (ARD) surfaces (one for each surveillance channel). A conventional constant false alarm rate (CFAR) detection scheme is then applied to the combination of ARD surfaces to determine the range and Doppler of each target. The complex amplitude of a target’s echo received by each surveillance channel is then fed to the direction-finding processor. With only two surveillance channels, the direction-finding system uses phase interferometry or amplitude monopulse techniques to estimate the target bearing. At this stage in the processing the system has determined the range, bearing and Doppler of a number of targets. In order to further process the data it is necessary to associate this plot data with individual targets, and this is performed using some form of conventional Kalman filter tracker in the box marked ‘frequency line tracker’. Having associated plots-to-targets, the range–Doppler–bearing data for each target are processed by a nonlinear estimator to determine the target’s location, speed and heading. Use of a nonlinear estimator allows optimum use of the Doppler information in this tracking process. In a more complex system with multiple surveillance channels, it may be advantageous to do the beamforming before the range–Doppler or CFAR processing stages. This would allow additional processing gain before the detection process and hence improve the probability of detection, but at the expense of increased processing load.

7.5.2 Expected System Performance In the system a single, vertically polarized FM radio transmitter is exploited, located at Lopik in the Netherlands, some 50 km behind the receiver. The transmitter has a mean emitted radiated power (ERP) of 50 kW and frequency of 96.8 MHz. The transmitter is located on a 375 m mast and provides excellent long-range low-level illumination.

Reference Antenna

Interferometer

Ch2 (I,Q)

Ref (I,Q)

Ch2

Ref

receivers

VXI-3570A

Ch1 (I,Q)

Ch1

Range/

r,fd

r,fd

Generate Range/Doppler Surface

Refs

Processing

Ch2 Doppler

Ch1

CFAR

Target Detection

r,fd

r,fd

r,fd

r,fd Direction Finding

Bearing Estimation

r,fd

r,fd r

fd

fd Frequency r Line Tracker

Plot-to-Target Association

r

fd

Standard CA-CFAR processing is sufficient here

Ch2

Ch1

fd

Figure 7.15 Wideband PCL processing scheme (single illuminator)

Ch2

Ch1

Simple phase-interferometry is adequate with two channels. Need to take proper account of mutual coupling.

This is a critical phase of the processing where many targets can be lost. Suggest use IMMJPDAF for this processing. The aim here is to associate plots to targets. Bistatic range and bearing can be used as broad discriminants and Doppler for fine target resolution.

Int.fd

Integrator

vy

vy

Estimate target location from range, bearing and integrated Doppler shift

y vx

Int.fd` x Non-Linear y r Estimator vx

x Display

Use Particle Filter or Unscented Kalman Filter to estimate target state.

lntegrating Doppler gives relative range plus an unknown constant of integration. We need to estimate both (x, y) and C in the non-linear estimator.

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The receiver comprises two vertically polarized half-wave dipoles over a wire-mesh backplane 1.5 wavelengths by 1.5 wavelengths in size. The receiver antenna is steered in order to try to place the transmitter in a null in the antenna pattern to reduce the unwanted direct signal. The radar surveys a sector approximately 120◦ in azimuth and is steered at an angle 45◦ west of true North, looking over the North Sea towards the United Kingdom. Assuming a target with a radar cross-section of 10 m2 and a cross-correlation processing gain of 47 dB, surveillance over the region is predicted as shown in Figure 7.16. The upper illustration shows contours of coverage above the 15 dB signal-to-noise ratio, while the lower illustration shows a slice in elevation along the boresight. Both figures include a simple model for the elevation lobing effects of both the transmitter and receiver, which result in the breakup of the coverage at longer ranges. This modelling seems reasonably accurate as aircraft are observed at ranges of up to 150 km from the receiver, the range of the first deep null in the coverage in the figure. As previously discussed, the limiting factor in the performance of any PBR system is the direct-path interference received from the transmitter. This interference is up to 90 dB greater SNIR Above 15 dB

150

100

50

0

−50

−100 −200 30 25 20 15 10 5 0

0

−100

50

0

100

Figure 7.16 Predicted system coverage

100

150

200

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Signal-10-Inteference Radio (dB)

−90dB

150 Tx ERP Tx height Tx-Rx distance RCS Int. Time. Rx ant. gain Rx height Noise fig.

50dBW 375m 50km

−80dB

−85dB

100

−75dB −70dB 15

10m2 1s 8dB 75m 15dB

50

−50

0 −25

−75

−50

−55

15 −35

−95dB

−31 −91

−100 −200

−100

0

100

Figure 7.17 Predicted signal-to-interference ratio

than the echo that would be expected from a 10 m2 aircraft at a range of 150 km and illustrates the need for good interference rejection. The signal-to-interference ratio, after taking account of the antenna suppression, but before correlation or filtering, is shown in Figure 7.17.

7.5.3 Data Collection Data are collected on all three antennas which are connected to Cubic Communications VXI3570A digital receivers, which sample the data in quadrature in a bandwidth of 110 kHz. These data are then transmitted in real-time over a gigabit local area network (LAN) to the processing cluster. In this configuration, 1.342 seconds worth of data from all three receivers is collected and then processed every 5 seconds, the current bottleneck in the processing being a combination of the performance of the LAN and the adaptive signal cancellation (which is not parallelizable). The design of the data acquisition system is presented in Figure 7.18 and has the following features:

r eight inputs, r multistatic data collection, a sequential re-tuning of digital receivers, r interface for any pre-processing algorithm (e.g. beam-forming), r configuration flexibility.

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VXI FRAMES

DATA ACQ PC

CH1 CH2

GC214TS

From antennas

CH3 CH4 CH5

GC214TS 8xVXI3570A 1x MXI/2

CH6

GC214TS

1Gbit LAN to PCR Engine

GC214TS

CH7

MXI/2 PCI

CH8

Stable LO 1.6 GHz 20 MHz 10 MHz

Stable LO 65 MHz

Figure 7.18 New data acquisition system

7.5.4 Adaptive Filtering of the Signal Although the cross-correlation processing between the reference and surveillance channels causes any unwanted reference signal in the surveillance channel to be confined to the zeroDoppler and zero-range bin, the range and Doppler sidelobes of this autocorrelation function remain significant. At best, with a 1 second integration time and 50 kHz effective bandwidth, these will be 47 dB below the main autocorrelation peak. However, given that the direct signal may be 80–90 dB greater than the echoes themselves, this means that the sidelobes remain some 30–40 dB higher than the echoes that are sought. In the experimental system, this is compounded by strong surface clutter returns from the sea surface to a bistatic range of around 50 km. It is therefore critical that the direct signal and clutter are removed from the surveillance channels before cross-correlation processing is attempted. An adaptive noise canceller like that in Figure 7.19 is used. The goal of the canceller is to estimate the desired signal d(n) from a noisy observation: x(n) = d(n) + w1 (n), recorded by the surveillance antenna, where w1 (n) is the unwanted interference. The signal from the reference antenna w2 (n) is used to estimate interference. The task of the adaptive filter is to estimate w ˆ 1 (n) from w2 (n). Then, this estimate is subtracted from the signal from the primary sensor leaving only an estimate of the true echo signal: e(n) = x(n) − w ˆ 1 (n).

(7.21)

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EXPERIMENTS AND RESULTS

Surveillance antenna Reflected signal

Σ

x(n) = d(n) + w1(n)

d(n)

e(n) = x(n) − wˆ 1(n)

w(n)

FM transmitter

Reference antenna w(n)

Adaptive filter w ˆ 1(n)

w2(n)

Figure 7.19 Adaptive noise canceller structure

To implement the adaptive filter the joint process estimator algorithm is used. The structure of the filter is presented in Figure 7.20 and consists of two parts:

r an adaptive M-stage lattice predictor; r an adaptive tapped delay line. The structure of the M-stage lattice predictor is shown in Figure 7.21. The output signals at the mth stage are: f m (n) = f m−1 (n) + κm∗ bm−1 (n − 1), bm (n) = κm f m−1 (n) + bm−1 (n − 1),

m = 1, 2, . . . , M, m = 1, 2, . . . , M,

(7.22) (7.23)

w1(n)

M-stage lattice predictor

Noisy reference signal

Backward prediction errors b0(n)

b1(n)

bM(n)

e(n) Estimated echo signal

Tapped delay line

Estimated reference signal wˆ 1(n)

Figure 7.20 Joint process estimator

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PASSIVE BISTATIC RADAR SYSTEMS

f0(n)

fM(n)

Σ κ

u(n) κ* b0(n)

bM (n)

Σ

z-1 Stage 1

Stage 2

Stage M

Figure 7.21 Lattice predictor structure

where M is the predictor order. The variables f m (n) and bm (n) are the mth forward prediction error and the mth backward prediction error respectively. The coefficient κm is the mth reflection coefficient. From each stage of the filter, the backward prediction error bm (n), m = 0, 1, . . . , M, is connected to the input of a finite impulse response (FIR) filter. The M-stage lattice predictor transforms the sequence of the correlated input samples x(n), x(n − 1), . . . , x(n − M) into a sequence of uncorrelated prediction errors b0 (n), b1 (n), . . . , b M (n). The second part of the filter uses the backward prediction to estimate the desired signal y(n). The first part of the filter is equivalent to the Gram–Schmidt algorithm; the second part of the filter is equivalent to a multiple regression filter. Mathematically, the joint process estimator is described by two algorithms. The first algorithm, called the gradient adaptive lattice (GAL), is used to adjust the coefficients κm in the lattice predictor structure. In the second filter, the coefficients h(n) are updated using the normalized LMS (NLMS) algorithm. Based on Reference [7.45] these two algorithms can be summarized as follows:

r The GAL algorithm. Parameters: M = final prediction order, μ < 0.1, step sizes, m = 1, 2, . . . , p, β ∈ (0, 1), δ and α-small positive constant. Initialization: For prediction order m = 1, 2, . . . , M, put f 0 (n) = 0, b0 (n) = 0, ξm−1 (0) = α, κm (0) = 0. Computation: For time step n = 1, 2, . . . , put f 0 (n) = b0 (n) = u(n), u(n), lattice predictor input. For prediction order m = 1, 2, . . . , M and time step n = 1, 2, . . . ,put ξm−1 (n) = βξm−1 (n − 1) + (1 − β) | f m−1 (n)|2 + |bm−1 (n)|2 , f m (n) = f m−1 (n) + κm (n)bm−1 (n − 1), bm (n) = bm−1 (n − 1) + κm∗ (n) f m−1 (n), μm κm (n) = κm (n − 1) [ f m (n)bm∗ (n − 1) + bm∗ (n) f m−1 (n)]. ξm−1 (n)

EXPERIMENTS AND RESULTS

r The NLMS algorithm.

• 295

Parameters: ε = 0.001, a small constant that prevents division by zero, 0 < β < 2, normalized step size. Initialization: For m = 0, 1, . . . , M, h(m) = 0. Computation: For time step n = 1, 2, . . ., calculate b∗m (n) h(n + 1) = h(n) + β e(n), ε + bm (n) 2 w ˆ 1 (n) = bm (n)H h(n), e(n) = w2 (n) − w ˆ 1 (n). Although the filter structure may appear excessively complex, it has been found experimentally that the eigenvalue spread in the correlation matrix prevents the direct use of simpler algorithms, because the convergence rate is too slow. The lattice predictor decorrelates the input data vector; thus the spread of the eigenvalues is smaller, the convergence rate of the filter is faster and the reference signal is removed from echoes properly. The selection of the prediction order M for the filter does not necessarily use any formal method, like Akaike’s information theoretic criterion or minimum description length criterion, but may instead rely on empirical observation. A value of M = 50 has been found to be optimum for this system. It completely removes sea clutter within an acceptable computation time. In order to test the algorithm, a reference FM modulated waveform was generated. An echo signal was constructed as a sum of reflections from two (point) targets and a portion of the reference signal that comes through a backlobe of the surveillance antenna. Targets were at range R1 and velocity v1 , and at range R2 and velocity v2 respectively. The amplitude of the breakthrough signal was −20 dB below the reference level and the amplitude of the reflected signal was −70 dB below the reference level, which shows the results of calculations of a range–Doppler surface without adaptive filtering. The presence of the reference signal in the echo manifests itself on the surface as a peak at zero range and zero Doppler. The targets are completely masked by the direct breakthrough signal, illustrating the significance of this aspect of PBR radar system design. After applying the adaptive filter, the results are as shown in Plate 14. The direct signal is removed and the targets are clearly visible with a signal-to-noise ratio of 35 dB. In total, the adaptive filter is able to suppress interference by almost 75 dB and its performance is clearly crucial to the performance of the whole PBR demonstrator.

7.5.5 Target Detection by Cross-Correlation Having adaptively filtered out the direct path signal it is necessary to search for the Dopplershifted and time-delayed echoes of the targets. This processing step serves two distinct purposes within the radar:

r to act as a matched filter for the radar system and provide the necessary signal processing gain to allow detection of the target echo;

r to estimate the bistatic range and Doppler shift of the target.

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This results in a range resolution (with one transmitter) of approximately 2–3 km (depending on the instantaneous modulation of the signal, which depends on the radio programme content). The Doppler resolution is the reciprocal of the coherent integration time, and so typically is 1 Hz, corresponding to a velocity resolution of around 1.5 m/s. For all intents and purposes there is no minimum or maximum unambiguous range or Doppler. The maximum range is set by the integration time (1 second gives a maximum range of 150 000 km) and the maximum Doppler by half the sample rate of the signal, thus typically 150 kHz or so, or about 750 times the speed of sound! When implementing the radar receiver, the designer can select the subset of ranges and Doppler shifts of interest. In practice, the coherent integration time is limited by migration of the target out of the Doppler, and sometimes the range, cell of interest. An integration time of around 1 second is optimal for most civilian air traffic and provides a processing gain of around 47 dB. In the next sections, three different algorithms for computation of the range–Doppler surface of increasing efficiency are described. First there is a conceptually simple algorithm for crosscorrelation of two complex valued data vectors. Then a description is given of how the efficiency of this approach can be improved through the use of decimation techniques. Finally, the final solution is given, which is a much more efficient approach that uses processing techniques analogous to those used on conventional FMCW radar systems.

7.5.6 Long-Integration Time 7.5.6.1 Algorithmic Description The long-integration method of a range–Doppler estimation is illustrated in Figure 7.22. The algorithm operates on a large 1 second sample of data (required to achieve the necessary processing gain) and generates main Doppler-shifted copies of the reference signal to act as a bank of matched filters, each matched to a different target velocity. The Doppler shift is assumed constant during the 1 second duration of integration, which presents a limit on the duration of the signal that can be integrated. 1 second ( eg. 400,000 samples)

Rx 1 1 second

Ref Create Dopplershifted copies Do p

−fd Hz

rre co

g. (e

ple r

la

) es pi co

te

2 51

0 Hz + fd Hz 1 second

Figure 7.22 Long-integration method of range–Doppler processing

r a ng

e

EXPERIMENTS AND RESULTS

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To implement the correlation the frequency-domain method is used as described in Section 7.5.4 and hence the fast Fourier transform (FFT) of the received echo signal and the reference signal is calculated, the complex conjugate of the echo is multiplied by the reference and then the inverse FFT is used to obtain the correlation in the time domain. The processing is analogous to the calculation of the ambiguity function described earlier, and can be written in discrete-time notation as N −1 ∗ j2πνn/N |(τ, ν)| = (7.24) e(n)d (n − τ )e , n=0 where now denotes the amplitude–range–Doppler (ARD) surface that is to be calculated, e(n) denotes the filtered echo signal and d(n) represents the reference signal. The variable τ denotes the time delay corresponding to the bistatic time difference of arrival (TDOA) of interest and ν denotes the Doppler shift of interest. This definition naturally leads to two different approaches for efficiently calculating the ARD surface, |(τ, ν)|. The first way of looking at the definition is to view |(τ, ν)| as the cross-correlation between e (n) and d (n) ej2πν(n/N ) . The second way of looking at the definition is to view |(τ ,ν|) as the discrete Fourier transform of e(n)d ∗ (n − τ ). The two viewpoints result in different computational algorithms. In both algorithms, the reference signal d(n) can be weighted using a standard weighting function (such as those defined in Reference [7.46]) before calculation of the ARD surface in order to reduce the range and Doppler sidelobes, at the expense of a broadened main peak and slight loss in processing gain. This is advisable in order to ensure that small targets are not masked by the range or Doppler sidelobes of larger targets. Therefore, in the work that follows, assume that d(n) actually represents d(n)w(n), where w(n) is the weighting function (in the case of no weighting, w(n) = 1 for all n).

7.5.6.2 Cross-Correlation Approach This approach seeks to calculate the efficient cross-correlation between e(n) and d(n)ej2πν(n/N ) . Note that d(n)ej2πν(n/N ) represents a frequency-shifted version of d(n). This can either be implemented directly by multiplying d(n) by the complex vector ej2πν(n/N ) , or more efficiently by simply calculating the FFT of d(n) and then rotating the elements of the transform the appropriate number of places to impose the correct frequency shift. This is far more efficient. The algorithm therefore comprises the following steps:

r Calculate the FFT of e(n) and denote this E(n). r Calculate the FFT of d(n) and denote this D(n). Then for each Doppler shift of interest:

r Rotate the elements of D(n) to obtain the required Doppler shift. r Multiply the rotated D(n) by E(n).

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PASSIVE BISTATIC RADAR SYSTEMS

r Inverse the FFT to obtain the cross-correlation of e(n) with the Doppler-shifted d(n) for all possible delays 0 < τ < N .

r Discard data from ranges not of interest. This algorithm allows the calculation of a limited number of Doppler shifts, but all possible ranges (in the case of a 1 second integration, this means ranges up to 150 × 108 m). Note that, the sequences e(n) or d(n) are not zero-padded in order to implement linear crosscorrelation. Although this is, strictly speaking, incorrect, to do so would double the size of the FFT of an already massive 512k points to 1024k points. In this case, the circular correlation can be regarded as an acceptable approximation to the linear correlation as there is only interest in the first four hundred or so points – a fraction of the total 512k. With these relatively small shifts, the overall difference between the circular and linear correlation is negligible.

7.5.6.3 Discrete Fourier Transform Approach This approach seeks to calculate efficiently the discrete Fourier transform of e(n)d ∗ (n − τ ). To compute the ARD surface, for each range of interest:

r Rotate the elements of d(n) and conjugate to obtain the required time delay, d ∗ (n − τ ). r Multiply the rotated d(n) by e(n). r Calculate the FFT of e(n)d ∗ (n − τ ). r Discard data from Doppler bins not of interest. This algorithm allows the calculation of a limited number of ranges, but all possible Doppler shifts (in the case of a 360 kHz sample frequency, this means Doppler shifts between ±180 kHz). This approach can be understood by thinking of e(n)d ∗ (n − τ ) as calculating the ‘beat frequencies’ between the original signal and the Doppler shifted echoes. The Fourier transform then extracts these beat frequencies.

7.5.6.4 Comparison of the Cross-Correlation and Fourier Transform Methods The two approaches to calculating the cross-correlation have similar computational loads per ‘slice’ through the ARD surface, but can be used in different ways. The cross-correlation viewpoint allows only slices through the ARD surface to be calculated at the Doppler shifts of interest, whereas the Fourier viewpoint allows only slices through the ARD surface at the ranges of interest to be calculated. As a consequence, it is clear that the former approach is more efficient when the number of Doppler shifts of interest is less than the number of range cells, and vice versa. In practice, both algorithms might need to be implemented and the most efficient approach might be dynamically chosen depending on the current mode of operation of the PBR system.

EXPERIMENTS AND RESULTS

7.5.6.5 Processing Requirements

• 299

A data collection bandwidth of 110 kHz requires a sample rate of 195k complex (I/Q) samples per second. If an integration time of 1.342 seconds is assumed this gives 262 144 samples, equivalent to 218 samples, that can be efficiently Fourier transformed using the radix-2 algorithm (hence the strange choice of integration time!). As an example, a target travelling at 360 m/s generates a Doppler shift of up to ±240 Hz at 100 MHz, suggesting that 646 Doppler bins are of interest with a 1.342 second integration time. Similarly, with a range resolution of 1364 m, a range coverage of 0–300 km implies 220 range bins. With these assumptions, both algorithms are of similar computational complexity and require the calculation of approximately 256k-point complex FFTs and 220 multiplications of a pair of 256k vectors per second. A radix-2 FFT requires N log2 N multiples and hence the processing load is approximately 220 × [218 × log2 (218 ) + 218 ] = 1.096 × 109 complex multiples per second (1.1 GFLOPS). Another way of thinking of this is that the system must be capable of multiplying a pair of 256k vectors and performing a 256k-point complex FFT within 4.55 ms. If more than one surveillance receiver is used, then the processing requirement scales proportionally; thus processing the two surveillance receivers used to support interferometry requires almost 2.2 GFLOPS of processing power, or a 256k-point FFT in 2.275 ms. In practice, the load could be reduced if the number of range bins or Doppler bins could be reduced. For instance, if targets are expected only to the 150 km range then this implies only 110 range bins and hence a 256k-point complex FFT within 9.1 ms per channel.

7.5.7 Use of Decimation to Improve Efficiency 7.5.7.1 Algorithmic Description The major drawback of the approach described above is the excessive processing load due to calculations of the fast Fourier transforms for long input signals. This may be resloved by applying a decimation technique that allows data to be discarded at Doppler frequencies where it is known that targets do not exist, before calculating the Fourier transform. This modified integration algorithm utilizes some extra processing steps to decimate the signal, but greatly reduces the overall computation complexity with almost no loss in signal processing gain. 7.5.7.2 Processing Summary The algorithm can be summarized as follows: Parameters:

r d(n), the reference signal, r e(n), the echo signal, r p, the initial time delay, which plays an important role in the distributed version of the algorithm; for a single CPU p = 0,

r Nb , number of range bins, r R, decimation factor.

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Computation:

r dm (n) = conjugate(delay by(d(n), p)), r NF = e¨ N/R u,ˆ the number of points in the FFT after decimation. For k = 1, 2, . . . , Nb :

r s(n) = dm (n)e(n), product of a conjugated, time-delayed reference signal and an echo signal, r sd (n) = CIC(s(n), R), decimation by factor R, r sd (n) = LPF(sd (n)), out-of-band filtering, r S = FFT(sd (n), NF ), computation of the Doppler velocities, r delay by(dm (n),1), delay reference signal in the time domain by one sample, r Rd (k) = S, building up a range–Doppler surface end. The main difference between the basic algorithms and this modification is the presence of two additional functions in the processing path: a cascaded integrator–comb (CIC) filter and a lowpass FIR filter (LPF). The CIC is a very efficient implementation of a decimation filter and is described in References [7.46] and [7.47]. The algorithm works as follows. First, the product of the conjugated, time-delayed reference signal with the echo signal is calculated. The signal, s(n), enters the CIC structure where it is integrated using a one-stage integrator, decimated by factor R, and then differentiated in a onestage comb section. The integrator operates at the original sampling rate f s . After decimation, the comb section operates at the reduced sampling rate of f ns = f s /R. Therefore, the length of the output vector from the filter is a factor of R smaller. Next, the decimated signal sd (n) is lowpass filtered in order to remove out-of-band frequencies. Finally, calculating the FFT algorithm on the filtered data vector sd (n) results in all the Doppler velocities for all targets from a specific range of frequencies at that range. In the present system the following parameters are typical:

r Receiver bandwidth, BW = 110 kHz. r Input signals are quadrature sampled at fs = 195.313 kHz. r Decimation factor, R = 128. r Sampling frequency after decimation fns = 1525.88 Hz. r Cut-off frequency for the fifth-order lowpass (symmetric) FIR filter, r fc = 300 Hz. The difference in computational complexity between the original and modified versions of the algorithm is as follows:

r O(CIC), N complex additions for the one-stage integrator, with Nd = N/R additions for the one-stage comb integrator;

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EXPERIMENTS AND RESULTS

r O(FFT), Nd log2 (Nd ) complex operations; r O(LPF), 5Nd complex multiplications and 5Nd additions. The computation cost of the extra steps is: Ot = O(CIC) + O(LPF) + O(FFT).

For N = 218 = 262 144 samples, R = 128 and Nd = 2048, the value of Ot is 218 + 2048 log2 (2048) + 10 × 2048 ≈ 305 123 operations per slice in the range–Doppler surface and 220 × 305 123 = 67 127 060 operation (67,1 MFLOPS) for the whole range–Doppler surface. The complexity of the algorithm described is OFFT = N log2 (N ) = 218 log2 (218 ) = 4 718 592 operations (one slice in the range–Doppler surface). Therefore, the speed-up factor Sf is Sf =

OFFT = 15.46. Ot

To increase the processing speed further, the algorithm is parallelized by spreading the computation of different sets of time delays, p, among different computers. It was possible to perform a 1 second coherent integration in just under 1 second by using this algorithm and six 2.6 GHz Pentium-4 machines in parallel.

7.5.8 An FMCW-Like Approach 7.5.8.1 Algorithmic Description It is possible to achieve even greater computational efficiencies through the use of a shortintegration time method of a range–Doppler estimation, as illustrated in Figures 7.23 and 7.24. 1 second Rx 1

Ref

Repeat over whole data sequence Power

2ms correlate

Figure 7.23 Calculating a range snapshot

range

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FFT over each rangebin

T FF T FF

T FF T FF T FF

Power Power Power Power Power Power Power Power Power Power Power

1

co se

nd

Do

pp

range range

ler

rang

e

Figure 7.24 Determining the Doppler components in the data

The processing is analogous to the traditional radar processing method used for frequencymodulated continuous wave (FMCW) signals, in which a number of snapshots of amplitudeversus-range data are calculated, and then a Fourier transform is used over each range bin to determine the Doppler shifts of targets at each range. Typically, the range snapshots are calculated using segments of signal of lengths that provide the desired unambiguous range. By using a 2 ms snapshot of the reference signal and a 4 ms snapshot of the echo signal, an unambiguous range of 300 km is obtained, with an effective Doppler sample rate of 500 Hz, allowing an unambiguous Doppler of ±250 Hz. It is also possible to cross-correlate the 2 ms snapshot of the reference signal against larger snapshots of the echo signal, to increase the unambiguous range. The length of the reference signal determines the Doppler ambiguity and the difference between the lengths of the echo and reference signals determines the unambiguous range. One problem with this approach is that Doppler-shifted echoes will decorrelate with the reference signal and this will result in a loss of detection of the echo for fast-moving targets before Fourier processing is attempted. This decorrelation is because noise only correlates with itself. With an infinite sample of noise the noise is completely decorrelated with even the smallest Doppler-shifted version of itself. With a finite sample of noise, of length T, the noise retains some correlation with Doppler-shifted copies of itself, provided that the Doppler shift falls within the same Doppler resolution cell – of about 1/T Hz. Therefore with a 2 ms sample of echo, significant processing gain would still be expected to be achieved for targets with Doppler shifts of up to 500 Hz. The use of an FM signal is likely to improve Doppler tolerance further (as noise is the worst case), and the use of a weighting function to reduce sidelobes also broadens the Doppler resolution and enhances the Doppler tolerance. 7.5.8.2 Processing Summary The algorithm can be summarized as follows:

r Take the first 1 ms of reference signal, apply a weighting and denote this d(n). r Take the first 2 ms of echo signal and denote this e(n).

EXPERIMENTS AND RESULTS

• 303

r Cross-correlate d(n) and e(n) for time delays of 0 to 2 ms (denoting bistatic ranges from 0 to 300 km). For efficiency, this correlation is calculated using the FFT, noting that the reference signal must be zero padded to give a total length of 4 ms. Call the result a ‘range snapshot’.

r Store the result. r Discard the first 2 ms of the reference and echo signals and then repeat the first four steps

above. Keep repeating until 512 range snapshots have been generated (using approximately 1s of data in total).

r For each range bin, take the 512 consecutive samples and perform an FFT to calculate the Doppler spectrum at each range. A weighting can be applied across these 512 samples if required in order, to reduce the Doppler sidelobes.

7.5.8.3 Processing Requirements The data collection bandwidth of 110 kHz requires a sample rate of 195k complex (I/Q) samples per second. Each 4 ms range snapshot requires two FFTs and one inverse FFT of length 781 with this sample rate. If instead of 4 ms, a 5.25 ms sample of echo is taken, then a 1024-point radix-2 FFT can be used. Calculation of 512 range snapshots then requires 512 × [3 × 210 × log2 (210 ) + 210 ] = 16 252 928 complex multipliers in 512 × 2 ms = 1.024 seconds. A further 512 1024-point FFTs are then required to calculate the Doppler components in each range bin, giving 512 × [210 × log2 (210 )] = 5 242 880 complex multipliers in 1.024 seconds. This gives a total of 21 495 808 complex multipliers in 1.024 seconds or 21 495 808 complex multipliers per second, per receiver channel. This is 50 times more efficient than the long-correlation processing method (with similar range and Doppler extents) and is equivalent to demanding approximately one 1024-point FFT in 0.48 ms – well within the capabilities of an office PC, let alone specialized digital signal processing hardware. Plate 15 shows a typical amplitude–range–Doppler surface created using the adaptive interference and clutter processing and cross-correlation processing, described above. Target echoes are visible in this figure as the bright returns at different bistatic ranges and Doppler shifts. Having generated the ARD surface it is then necessary to detect automatically the range and Doppler bins in which valid targets lie. This is performed using a constant false alarm rate (CFAR) algorithm.

7.5.9 Constant False Alarm Rate (CFAR) Detection In order to maintain a constant probability of false alarm, the detection threshold changes according to an estimate of the noise variance. The conventional cell-averaging constant false alarm rate with guarded cells algorithm (CA-CFAR) is used [7.48]. The algorithm operates on the full ARD surface, first in the range domain and then in the Doppler. The optimum parameters were found empirically to be:

r number of cells for averaging M = 10, M/2 cells at each side of the cell under test; r threshold level K 0 = 3 dB.

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7.5.10 Direction Finding For the initial system, a simple angle estimation process is implemented using phase interferometry. The angle of arrival of a target echo, , is related to the phase difference of the received signal at the two surveillance antennas, , by =

2πd sin(), λ

(7.25)

where d is a distance between the dipoles and λ is the wavelength. In order to minimize any angular ambiguities the antennas are mounted half a wavelength apart. This gives a 180◦ ambiguity – targets behind the antenna and in front of the antenna cannot be distinguished – but in practice this is acceptable due to the reasonable front-to-back ratio of the antenna gain pattern, which means targets behind the antenna are rarely detected. The phase of each echo on the ARD surface is calculated using the argument of their complex value. Any phase mismatch between the two channels is removed in software using a simple calibration coefficient.

7.5.11 Plot-to-Plot Association Although many conventional air surveillance radars output raw detection data for tracking by an external system, it is better for a passive radar to track aircraft detections from each transmitter internally. This tracking is performed in the range–Doppler–bearing domain. By using an internal tracker, the system is then able to forward the associated plot data for:

r association of returns from different transmitters of the same target (in a multistatic system); r target state estimation (described below). In the experimental system the basic Kalman filter described in Section 1.5 of Reference [7.48] is used. The measurement vector comprises measurements of the range, Rk , Doppler, Fk , and bearing, k , from the ambiguity surface, and the state vector comprises the range, range rate, Doppler, Doppler rate, bearing and bearing rate: z(k) = (Rk Fk k ) , ˙ x(k) = r (k) f (k) ˙f (k)φ(k)φ(k) .

(7.26) (7.27)

The fact is exploited that the measurements of Doppler are proportional to the rate of change of the range and a modified form of the state prediction equation is used: ⎛

1 −λτ ⎜0 1 ⎜ 0 0 F(k) = ⎜ ⎜ ⎝0 0 0 0

0 τ 1 0 0

⎞ 0 0 0 0⎟ ⎟ 0 0⎟ ⎟, 1 τ⎠ 0 1

x(k + 1|k) = F(k)xˆ (k|k),

(7.28)

(7.29)

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EXPERIMENTS AND RESULTS

where τ is the update rate and λ is the wavelength. The fact that the Doppler is proportional to the rate of change of the range means that it is particularly easy for even the basic Kalman filter to track targets in the range–Doppler space. For updating the state prediction covariance matrix, the standard definition of the state transition matrix is used, as follows: ⎛

1 ⎜0 ⎜ F(k) = ( ) ⎜ ⎜0 ⎝0 0

0 0 1 τ 0 1 0 0 0 0

0 0 0 1 0

⎞ 0 0⎟ ⎟ 0⎟ ⎟, τ⎠ 1

P(k + 1|k) = F(k)P(k|k)F(k) + Q(k).

(7.30)

(7.31)

The tracker uses a standard four-out-of-five track initiation logic. A track is ‘preliminary’ until it has satisfied this condition, after which it is ‘confirmed’. The association gate is defined according to [z − zˆ (x + 1|k)] S(k + 1)−1 [z − zˆ (x + 1|k)] ≤ γ .

(7.32)

The gate threshold γ is set as (7.32), corresponding to a probability of 0.99 with three degrees of freedom. When maintaining preliminary tracks, the gate size is increased by a factor of 1.5 to increase the probability of association. To reduce the computational load associated with Equation (7.32), an ‘early gate’ is first applied to all the plots under consideration, to reject distance outliers. This simple gate simply rejects any plot more than 10.0 Hz, 3.0 km or 1 radian away from zˆ (k + 1|k). The basic logic of the tracker is:

r Update all confirmed tracks with the closest plot to zˆ (k + 1|k) falling within the association gate defined in Equation (7.32). If no plots are present, rate-aid the track.

r Using any remaining plots, update all preliminary tracks with the closest plot to zˆ (k + 1|k) falling within the association gate. If no plots are present, rate-aid the track.

r Using any remaining plots, initiate new tracks.

A graphical display of the filter’s predictions and covariance estimates was used to tune the filter parameters. Using this, the initial value of the covariance matrix was set as ⎛

⎞ 5.0 0 0 0 0 ⎜ 0 0.04 0 0 0 ⎟ ⎜ ⎟ 0 0 0.1 0 0 ⎟ Pinit (0|0) = ⎜ ⎜ ⎟ ⎝0 0 0 0.8 0 ⎠ 0 0 0 0 0.06

(7.33)

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PASSIVE BISTATIC RADAR SYSTEMS

and the covariance matrix modelling process error was set as ⎛ ⎞ 3.0 0 0 0 0 ⎜ 0 0.2 0 0 0 ⎟ ⎜ ⎟ ⎜ 0 0.05 0 0 ⎟ Q(k) = ⎜ 0 ⎟, ⎝0 0 0 0.8 0 ⎠ 0 0 0 0 0.06

(7.34)

where the basic units of measurement are km, Hz and radians. Note that the bearing parameters are still preliminary and will undoubtedly benefit from additional tuning. Example results of this tracking process are shown in Plate 16. In this display an error ellipse is displayed around each track estimate, together with an arrow indicating the track prediction. Preliminary tracks are shown in light grey, while confirmed tracks are coloured. The majority of preliminary tracks are due to false alarms and are never promoted into confirmed tracks. Even without any special logic or modifications of the tracker to cope with manoeuvring targets, the basic filter has been found to be extremely robust and original plans to implement an interacting multiple model (IMM) filter have not proved necessary in this case.

7.5.12 Target State Estimation A simple trigonometrical transformation from the bistatic range and bearing into a local Cartesian coordinate scheme is used to display the target on a geographical map. Example results are shown in Plate 17. While this serves to show the detections on a map quickly, it effectively discards all the excellent Doppler information provided by the system. More recent modifications to the system to exploit multistatic data from multiple transmitters are now estimating target location using range, Doppler and bearing within an extended Kalman filter.

7.5.13 Plot-to-Target Association (Multiple Illuminator Case) 7.5.13.1 Introduction When multiple FM illuminators are used with a single receiver to detect and track targets, the plot-to-target association problem becomes considerably more complex. It is assumed that each transmitter–receiver pair will form a correlation surface and track targets on that range– Doppler surface in the same way as the simple bistatic case. However, there is then the issue of determining which range–Doppler track from one transmitter–receiver pair corresponds to the same target as the range–Doppler track from a different transmitter–receiver pair. It is known that the bistatic range measured by one transmitter–receiver pair defines an ellipse (with the transmitter and receiver at its foci) on which the target lies. Similarly, the bistatic range of the same target measured using a different transmitter will define a second ellipse that shares one common focus (the receiver location) and one different focus (the transmitter location) on which the target also lies. Obviously the two ellipses will intersect at the target’s location – as well as up to three other ‘ghost’ locations. However, because the two ellipses share a common focus, in most cases they only intersect in two locations: the correct location and a ghost location. An attempt is made to exploit this property in order to solve the multistatic target association problem.

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100

y (Km)

50

−150

−100

−50

AMSTERDAM

NC3A x (Km)

50 LOPIK

100

−50 GOES

−100

Figure 7.25 Simultaneous bistatic range ellipses in the future system

There is no attribute of the received signal or the processing thereof that permits direct correlation of the track report data from one receiver–transmitter pair with another. Hence, geometrical and statistical methods must be employed to develop a module capable of fusing the tracks from multiple receivers and transmitters. When multiple transmitters are used, the actual target location can be quickly determined using ellipse intersections alone. Figure 7.25 shows the bistatic range ellipses plotted for a target 35 km northwest of the NC3A site (at Cartesian coordinates (−25,25)), with the system receiving signals from transmitters in Amsterdam, Lopik and Goes. There is an explosion in the number of potential combinations of tracks when data from multiple tracks are fused. Figure 7.26 shows the possible ellipse intersections for just six targets for the same three transmitters. Recent work at the NATO C3 Agency has developed algorithms to associate these multistatic data. These algorithms borrow efficient techniques from the computer graphics world to identify locations efficiently where two or three ellipses intersect, or almost intersect. These are combined with bearing information to allow accurate multistatic tracks to be initialized with either one or two bistatic range measurements and a measurement of bearing, or three bistatic range measurements and no bearing. Once initialized, these combinatorial contraints can be relaxed to maintain a track.

• 308

PASSIVE BISTATIC RADAR SYSTEMS

100

y (Km)

50

–150

–100

–50 x (Km)

NC3AS +10002

AMTERDAM

50 LOPIK

100

+10004 +10003 –50 GOES +10006 +10005 +10000

–100

Figure 7.26 Multiple-target tracking in the future system

7.5.14 Verification of System Performance To verify the detection performance of the system a live civil air traffic control data feed may be used. These data may be fed into a display program, filtered to cover geographically only the region in which the system detects targets and then displayed on a map (Plate 18). These data may also be used to calculate the bistatic range and Doppler shifts that each target would present to the system. These can be placed on a separate range–Doppler display (Plate 19) with their Mode 3/A identifiers. Selecting an aircraft’s range–Doppler plot highlights the same aircraft on the map. Selected tracks on both displays are shown as red squares. The truth data can also be overlaid directly on the system’s range–Doppler display (Plate 20) as a quick check of which aircraft have been detected. These techniques provide a real-time verification of the system’s performance. In the examples provided here, it is possible to compare the detections in Plate 20 with the truth tracks in Plate 19. The latter tracks can then be directly related to the aircrafts’ locations by comparing Mode 3/A codes between Plates 18 and 20, or simply by looking for tracks highlighted with the red squares. Furthermore, it is possible to compare the output of the passive radar’s target association tracker in Plate 20 with the truth tracks in Plate 19 In both cases, the results are encouraging.

ABBREVIATIONS

• 309

Using this approach, it has been verified that the radar is able to detect and track aircraft reliably at bistatic ranges of beyond 300 km, corresponding to ranges of up to 150 km from the receiver. Track initiation is reliable and false target tracks are rarely observed.

7.6 SUMMARY AND CONCLUSIONS In this chapter the design and performance of PBR radar systems has been examined. It has been shown that they have the potential to operate with excellent detection ranges and, good low-level coverage and are able to detect and track a wide variety of targets. These systems offer both a stand-alone and a complementary capability to existing installations such as those for air traffic management and air defence. Indeed they can offer a low-cost route to an air traffic management infrastructure to countries when none currently exists. Further, it has been shown that the performance of PBR radar systems is strongly dependent on the geometry and waveform utilized. This also highlights the importance of the role of direct signal interference whose mitigation is vital if the full dynamic range of the system is to be realized, as it is a fundamental limit on sensitivity and dynamic range. However, as has been shown, it is perfectly possible to remove this interference using relatively simple and accessible techniques. Areas for future exploration include verification of three-dimensional localization of targets, full bandwidth exploitation for high-range resolution, ISAR imaging for high cross-range resolution and perhaps even detection of ground-moving targets. Overall the increasing plethora of available signals with suitable power levels and waveforms led to a continued upsurge of interest in this technique with an ever increasing range of types and applications.

ABBREVIATIONS ADC ARD CA-CFAR CDMA CFAR DAB DSP DVB ERP FDMA FKF FM FMCW GAL GMTI GPS GSM HDTV

analogue-to-digital convertor amplitude range Doppler cell-averaging constant false alarm rate code division multiple access constant false alarm rate digital audio broadcast digital signal processor digital video broadcast emitted radiated power frequency division multiple access extended kalman filter frequency modulation frequency modulated continuous wave gradient adaptive lattice ground Moving Target Indication global positioning satellite global system for mobile communications high definition TV

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PASSIVE BISTATIC RADAR SYSTEMS

IMM interacting multiple model ISAR inverse synthetic aperture radar LAN local area network NLMS normalized least mean squares NTSC national TV standards committee OFCOM Office of Communication PAL phase alternating line PF particle filter RAM radar absorbing material PBR passive bistatic radar RCS radar cross-section RF radio frequency SAR synthetic aperture radar SECAM sequential colour and memory TDMA time division multiple access UHF ultra high frequency VHF very high frequency

VARIABLES AR B d d(n) F Gr Gt k L L (≤1) Pd Pn Pr Pt Pv (tn ) rb r1 r2 TMAX T0 y(tn ) θR λ σb ψ(TR , f d )

radial component of target acceleration receiver effective bandwidth target linear dimension reference signal receiver effective noise figure receive antenna gain transmit antenna gain Boltzmann’s constant length of the baseline formed by the transmitter and receiver system losses direct signal power receiver noise power received signal power transmit power covariance matrix transmitter-to-receiver range (bistatic baseline) transmitter-to-target range target-to-receiver range maximum coherent processing time noise reference temperature, 290 K vector of measurements phase difference angle from the receiver to the target with respect to ‘North’ signal wavelength target bistatic radar cross-section ambiguity response range–Doppler surface

REFERENCES

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7.1 Willis, N.J. (1991) Bistatic Radar, Artech House, Norwood, Massachusetts. 7.2 Willis, N.J. and Griffiths, H.D. (eds) (2007) Advances in Bistatic Radar, SciTech Publishing Inc., Raleigh, North Carolina, ISBN 1891121480, April 2007. 7.3 Griffiths, H. D. and Long, N.R.W. (1986) Television based bistatic radar, IEE Proc.-F, 133(7), 649–657, December. 7.4 Long, N. R. W. and Griffiths, H.D. (1985) A television-based bistatic radar system, Final Report, Research Agreement 2047/0105 RSRE, Microwave Research Unit, University College London, November 1985. 7.5 Baniak, J., Baker, G., Cunningham, A.M. and Martin, L. (1999) Silent sentry passive surveillance, Aviation and Space Technology, 7 June 1999. 7.6 Cherniakov, M., Nezlin, D. and Kubin, K. (2002) Air target detection via bistatic radar based on LEOS communication systems, IEE Proc. Radar, Sonar and Navigation, 149, 33–38, February. 7.7 Griffiths, H. D., Baker, C. J., Baubert, J., Kitchen, N. and Treagust, M. (2002) Bistatic radar using spaceborne illuminator of opportunity, in Proceedings of the Radar Conference, Edinburgh; IEE Conference Publication 490, 15–17 October 2002, pp 1–5. 7.8 http://www.roke.co.uk/sensors/stealth/celldar.asp 7.9 Sahr, J.D. and Lind, F.D. (1997) The Manastash Ridge radar: a passive bistatic radar for upper atmospheric radio science, Radio Science, 32, 2345–2358, November–December. 7.10 Zoeller, C.L., Budge Jr, M.C., and Moody, M. (2002) Passive coherent location radar demonstration, in Proceedings of the Thirty-Fourth Southeastern Symposium on System Theory, 18–19 March 2002, pp. 358–62. 7.11 Ristic, B., Arulampalam, S. and Gordon, N. (2004) Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House, Norwood, Massachusetts, ISBN 158053631X. 7.12 Griffiths, H.D., Garnett, A.J., Baker, C.J. and Keaveny, S. (1992) Bistatic radar using satellite illuminators of opportunity, in Proceedings of the International Radar Conference, Brighton, IEE Conference Publication 365, 12–13 October 1992, pp. 276–9. 7.13 Griffiths, H.D. (2003) From a different perspective: principles, practice and potential of bistatic radar, in Proceedings of the International Radar Conference, Adelaide, Australia, 3–5 September 2003, pp. 1–7. 7.14 Hawkins, J.M. (1997) An opportunistic bistatic radar, in Proceedings of the International Radar Conference, Edinburgh, IEE Conference Publication 449, 14–16 October 1997, pp. 318–22. 7.15 Trizna, D. and Gordon, J. (2002) Results of a bistatic HF radar surface wave sea scatter experiment, in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS’02), 24–28 June 2002, Vol. 3, pp. 1902–4. 7.16 Greneker, E.F. and Geisheimer, J.L. (2003) The use of passive radar for mapping lightning channels in a thunderstorm, in Proceedings of the IEEE Radar Conference, 5– 8 May 2003, Philadelphia pp. 28–33. 7.17 Yakubov, V.P., Antipov, V.B., Losev, D.N. and Yuriev, I.A. (1999) Passive radar detection of radioactive pollution, Application of the Conversion Research Results for International Cooperation, SIBCONVERS ’99, in the third International Symposium, 18–20 May 1999, Vol. 2, pp. 397–9.

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7.18 Meyer, M. and Sahr, J.D. (2004) Passive coherent radar scatter interferometer implementation, observations and analysis, Radio Science, 39, RS3008, doi: 0.1029/2003RS002985, May. 7.19 Howland, P.E. (1999) Target tracking using television based bistatic radar, IEE Proc. Radar, Sonar and Navigation, 146(3), 166–74. 7.20 Herman, S. and Moulin, P.M. (2002) A particle filtering approach to passive radar tracking and automatic target recognition, in Proceedings of the IEEE Aerospace Conference, 9– 16 March 2002, Vol. 4, pp. 4-1789–4-1808. 7.21 Ehrman, L.M. and Lanterman, A.D. (2004) A robust algorithm for automatic target recognition using passive radar, in Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory, 14-16 March 2004, pp. 102–106. 7.22 Griffiths, H.D., Baker, C.J., Ghaleb, H., Ramakrishnan, R. and Willlman, E. (2003) Measurement and analysis of ambiguity functions of off-air signals for passive coherent location, Electronics Letters, 39(13), 1005–7, 26 June 2003. 7.23 Baker, C.J., Griffiths, H.D. and Papoutsis, I. (2005) Passive coherent radar systems – Part II: waveform properties, IEE Proc. Radar, Sonar and Navigation, Special Issue on Passive Radar, 152(3), 160–168, June. 7.24 Woodward, P.M. (1953) Probability and Information Theory, with Applications to Radar, Pergamon Press, New York, 1953; reprinted by Artech House, 1980. 7.25 http://www.bbc.co.uk/reception/. 7.26 http://www.sitefinder.radio.gov.uk/. 7.27 Jackson, M.C. (1986) The geometry of bistatic radar systems, IEE Proc.-F, 133(7), 604–12. 7.28 Kell, R.E. (1965) On the derivation of bistatic RCS from monostatic measurements, Proc. IEEE, 53, 983–8. 7.29 Larson, R.W., Maffett, A.L., Heimiller, R.C., Fromm, A.F., Johansen, E. L., Rawson, R.F. and Smith F.L. (1978) Bistatic clutter measurements, IEEE Trans. Antennas and Propagation, AP-26 (6), 801–4. 7.30 Wicks, M., Stremler, F. and Anthony, S. (1988) Airborne ground clutter measurement system design considerations, IEEE AES Magazine, 27–31, October. 7.31 McLaughlin, D. M., Boltniew, E., Wu, Y. and Raghavan, R. S. (1994) Low grazing angle bistatic NRCS of forested clutter, Electronics Letters, 30(18), 1532–3, September. 7.32 Howland, P.E. (1994) A passive metric radar using a transmitter of opportunity, in International Conference on Radar, Paris, May 1994, pp. 251–6. 7.33 Poullin, D. and Lesturgie, M. (1994) Radar multistatic a` e´ missions non-coop´eratives, in International Conference on Radar, Paris, May 1994, pp. 370–5. 7.34 Howland, P.E. (1997) Television-based bistatic radar, PhD Thesis, School of Electronic and Electrical Engineering, University of Birmingham, September 1997. 7.35 Howland, P.E. (1999) Target tracking using television-based bistatic radar, IEE Proc. Radar, Sonar and Navigation, 146(3), June. 7.36 Howland, P.E., Maksimiuk, D. and Reitsma, G. (2005) FM radio based bistatic radar, IEE Proc. Radar, Sonar and Navigation, 152 (3), 107–15, June. 7.37 Bar-Shalom, Y. and Li, Xiao-Rong, (1995) Multitarget-Multisensor Tracking Principles and Techniques, YBS, Storrs, Connecticut, 615 pp., ISBN 0-9648312-0-1. 7.38 Wan, E.A. and van der Merwe, R. (2001) Kalman Filtering and Neural Networks (ed. S. Haykin), Chapter 7, John Wiley & Sons, Inc., New York.

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7.39 Poullin, D. (2005) Passive detection using digital broadcasters (DAB, DVB) with COFDM modulation, IEE Proc. Radar, Sonar and Navigation, 152(3), pp. 143–52, June. 7.40 Kulpa, K.S. and Czekaa, Z. (2005) Masking effect and its removal in PCL radar, IEE Proc. Radar, Sonar and Navigation, 152(3), 174–8, June. 7.41 Tsao, T., Slamani, M., Varshney, P., Weiner, D., Schwarzlander, H. and Borek, S. (1997) Ambiguity function for a bistatic radar, IEEE Trans. Aerospace and Electronic Systems, 33(3), 1041–51, July. 7.42 Prati, C., Rocca, F., Giancola. D. and Monti Guarnieri, A. (1988) Passive geosynchronous SAR system reusing backscattered digital audio broadcasting signals, IEEE Trans. Geoscience and Remote Sensing, 36(6), 1973–6, November. 7.43 Cazzani, L., Colestani, C., Leva, D., Nesti, G., Prati, C., Rocca, F. and Tarchi, D. (2000) A ground-based parasitic SAR experiment, IEEE Trans. Geoscience and Remote Sensing, 38(5), 2132–41, September. 7.44 Lanterman, A.D., Munson Jr, D.C. and Wu, Y. (2003) Wide-angle radar imaging using time-frequency distributions, IEE Proc. Radar, Sonar and Navigation, 150(4), 203–11, August. 7.45 Haykin, S. (2002) Adaptive Filter Theory, 4th edn, Prentice-Hall, Upper Saddle River, New Jersey. 7.46 Harris, F.J. (1978) On the use of windows for harmonic analysis with the discrete fourier transform, Proc. IEEE, 66, 51–8, January. 7.47 Hogenauer, E.B. (1981) An economical class of digital filters for decimation and interpolation, IEEE Trans. Acoustics, Speech, and Signal Processing, ASSP-29(2), 155–62, April. 7.48 Nitzberg, R.K. (1999) Radar Signal Processing and Adaptive Systems, Artech House, London.

8 Ambiguity Function Correction in Passive Radar: DTV-T Signal Mikhail Cherniakov

8.1 INTRODUCTION The key parameters of any passive bistatic radar system (PBRS) are specified by the adopted external waveform that is used as the ranging signal. For many years, analogue television (ATV) stations have been considered to be one of the best candidates for passive radar applications due to their high power and wide availability [8.1–8.4]. Currently, however, ATV is being replaced by terrestrial digital video broadcasting systems (DTV-T), and this implies a new set of studies: PBRS based on DTV-T. The fundamental difference between ATV and DTV-T is the transmitting signal modulation. Occupying a similar frequency band, DTV-T signals utilize an essentially different method of modulation compared to ATV, which is orthogonal frequency division multiplexing (OFDM), incorporated with channel coding and interleaving, i.e. Coded OFDM or COFDM [8.5]. A simplified block diagram of a DTV-T based radar is shown in Figure 8.1. It is essential that the reference (heterodyne) signal is in place at the reception side which, after appropriate processing, may be correlated with the radar echo signal. Therefore, the receiving part of the radar consists of the radar and the heterodyne channels, where the radar channel is used for the reception of the reflected signal from an observation area. In general, waveforms used in radars with transmitters of opportunity do not correspond to those commonly used in traditional radars. These signals should be accepted as they are and instead the developing radar should be adapted to these signals. Consequently, the major radar parameters are totally dependent on these waveforms. In the considered case, this waveform is the DTV-T signal and will be characterized by the ambiguity function (AF), the most common method of radar signal analysis since its introduction in Reference [8.6]. This function was also used in previous chapters of this book. The optimal signal processing against additive white Gaussian noise (AWGN) comprises linear-matched filtering, which technically may be carried out at the matched filter or the Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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Radar channel

Heterodyne channel

DTV-T Transmitter

Receiver

Figure 8.1 DTV-T-based passive radar block diagram. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

correlator. This matched filter output may be presented as ∞ g ∗ (ξ )g(ξ − τ )ejωd ξ dξ , χ (τ, ωd ) =

(8.1)

−∞

where g(.) is the transmitting waveform, g ∗ (.) is its complex conjugate and τ and ωd are the signal delay and Doppler frequency shift respectively. The function |χ (τ, ωd |2 is referred to as an ambiguity function (AF) of the appropriate signal [8.7] and |χ (τ, ωd | is called the uncertainty function (UF). Both the AF and UF have an identical physical sense and are based on the integral (8.1). It should also be borne in mind that the Equation (8.1) cross-section at ωd = 0 is equal to the autocorrelation function (ACF) of the complex envelope: ∞ χ (τ, 0) = g ∗ (ξ )g(ξ − τ )dξ (8.2) −∞

and the cross-section τ = 0 is the Fourier transform of the squared complex envelope: ∞ |g(ξ )|2 ejωd ξ dξ . χ (0, ωd ) = (8.3) −∞

It is important to mention here that so-called ‘mismatch filters’ are used in some circumstances. The extent to which a filter response can deviate from the corresponding matched filter and remain characterized as ‘mismatched’ is difficult to specify. Nevertheless, it can be assumed that the pulse response of the mismatched filter has a close relationship with the transmitted waveform. Denoting this response as gm (ξ ), Equation (8.1) can be rewritten as ∞ ∗ χm (τ, ωd ) = gm (ξ )g(ξ − τ )e jωd ξ dξ . (8.4) −∞

For this mismatched filter a power loss should be specified in comparison to the appropriate matched filter. It is known that the matched filter’s output signal reaches maximum when τ = 0, ωd = 0, and is related to the real signal energy as 2Es [8.7]. In general, it is expected that signals at the mismatched filter output will reach their maximum in the vicinity of this point and they cannot exceed 2Es . Assuming that Equation (8.4) is maximal at τε = 0 ± ε and

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ωdε = 0 ± ι, where and ι are small parameters including zero, the mismatching loss could be specified as χ = χ (0, 0) − χm (±ε, ±ι).

(8.5)

In general, the signal at the output of the mismatched filter will be close to, but will not directly correspond to, the AF. Using some mismatching in the correlation procedure, the signal ambiguity function can be ‘corrected’ according to a specified criterion, but at the expense of some power loss. This mismatching will be used for DTV-T signal processing later in the section.

8.2 DTV-T SIGNAL SPECIFICATION The parameters and modulation methods of DTV-T signals have been specified by a set of criteria pertaining to TV broadcasting. Nevertheless, it is possible to predict the suitability of DTV-T signals for a radar application. This prediction is based on the fact that due to its signal modulation, coding and interleaving features, this process is close to being purely random. The use of random signals in radar has been discussed and the attractive peculiarities, as well as problems, behind their application are known [8.8]. There are a number of publications dedicated to DTV-T, the use of digital audio broadcasting (DAB) signals in bistatic radar, as well as to OFDM modulated signals specifically developed for radar applications [8.9–8.11]. The following section represents an exploration of the area of DTV-T signals, bearing in mind that the actual DTV-T signal standards deviate from region to region. A simplified block diagram of the DTV-T transmission system is shown in Figure 8.2 [8.5, 8.12, 8.13]. It can be seen that the video signal compressed according to the MPEG-2 standard is error encoded and interleaved with further OFDM modulation prior to transmission. COFDM involves the error-coded serial bit stream data followed by the modulation over evenly spaced orthogonal subcarriers. The COFDM symbol consists of a number of discrete subcarrier frequencies transmitted together for a particular length of time, TU . This time period corresponds closely to the duration of the transmitted symbol. The subcarrier frequency in DTV-T signals is separated by FC = 1/TU . In the United Kingdom, 1705 subcarrier frequencies with TU = 224 μs are used. Each subcarrier is 16 or 64 quadrature amplitude DTV - T signal

MPEG-2 signal

OFDM Modulation

Random Signal

Coding and Interleaving

Upconverter

Guard Intervals Pilot Signals and TPS

DTV-T Baseband Signal

Figure 8.2 DTV-T transmission system. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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modulated (QAM) by baseband data. One DTV-T signal occupies an approximate frequency band of 7.61 MHz. The OFDM modulator output is the point where the occurrence of a purely random signal is expected. Coding, interleaving and modulation should effectively randomize any, even highly correlated, data streams. The MEPEG-2 signal itself is not likely to have a correlation between the data bits, as the video signal compression procedure is inherently based on redundancy mitigation; i.e. correlation removal between the signal components. The summation of an essential number of noncorrelated signals in the process of forming the DTVT signal normalizes this process. It is therefore expected that the baseband stationary white Gaussian process will form the process at the OFDM modulator output. The next step in generating the DTV-T signal is the introduction of special control signals to the video data. At this stage, about 10 % of carrier frequencies are modulated by control data. These data are different in comparison to the video stream methods of modulation. The DTV-T control signal contains pilot carriers and transport parameter signalling (TPS) carriers, which are used for receiver synchronization and estimating the transmission parameters respectively. There are two types of pilot carriers in a COFDM symbol, scattered pilot (SP) and continuous pilot (CP). In addition to the special control signals that occupy some carriers, guard intervals between symbols are added. Time intervals TU , plus the guard interval, form one symbol. A COFDM frame is thus made up of 68 COFDM symbols. Four frames introduce one super frame. The pilot and TPS carriers are scattered at given frequencies and according to a known rule [8.14]. The modulation of all data and TPS carriers is normalized to have an average power, E d = 1. The pilot carriers are transmitted at an enhanced power level, that is E PC = 16/9E d . All these added signals introduce some regularity into the random video data stream. Consequently, a deviation of the DTV-T signal AF from the appropriate function of a purely random process can be expected. This will be discussed in detail later on.

8.2.1 Scattered Pilot Carrier A frame of a DTV-T signal is shown in Figure 8.3 as a matrix with different carrier frequencies along the columns and the number of transmitting symbols along the rows. The SPs in each symbol occupy the carriers separated by 12 FC within each symbol. There is also mutual shift by 3 FC between the appropriate positions in the neighbouring symbols in a frame. Consequently, the positions of the scattered pilot carriers are repeated after every four symbols. Binary phase shift keying (BPSK) modulation is used at SP carriers. The modulation data is an 11-stage pseudo-random binary sequence (PRBS). In one symbol 143 carriers are occupied by the SP signal.

8.2.2 Continuous Pilot Carrier In contrast to the deterministic position of the SP carrier, the frequency positions occupied by the continuous pilot are pseudo-random. Each carrier position number is a multiple of three, within the symbol duration. The CP frequency and the corresponding signal phase are the same for all symbols. The continuous pilot carriers are also BPSK modulated with the reference bits derived from a PRBS generator expressed as pkc = πbkc ,

(8.6)

• 319

DTV-T SIGNAL SPECIFICATION

NΔFC (Frequency)

Carrier Position K min=0 X OOOOOOOOOOOXOOOOOOOOOOOXOOO OOOXOOOOOOOOOOOXOOOOOOOOOOOX OOOOOOXOOOOOOOOOOOXOOOOOOOOO OOOOOOOOOXOOOOOOOOOOOXOOOOOO XOOOOOOOOOOOXOOOOOOOOOOOXOOO

Symbol 0 Symbol 1 Symbol 2 Symbol 3 Symbol 4

XOOOOOOOOOOOXOOOOOOOOOOOXOOO - - - - - Symbol 67 “X”→ Scattered Pilot Signals “O”→ Video Data

KTS (Time)

Figure 8.3 Scattered pilot positions in a COFDM frame

where bkc is a corresponding PRBS bit. In the United Kingdom, the position of DTV-T standard 45 CP carriers is specified (see Table 8.1).

8.2.3 Transport Parameter Signalling Carrier The transport parameter signalling (TPS) bits are transmitted using differential BPSK (D-BPSK) modulation. This modulation implies that the information itself is carried out by the phase difference between the consecutive bits. If the phase of a particular TPS carrier differs from one symbol to the next by π , then the data bit is ‘1’; in the case of the continuous phase the data bit is ‘0’. Each symbol contains 17 TPS carriers that have the same phases. Consequently, the signal carriers could have the same or 180◦ mutually shifted phases in the neighbouring symbols. TPS carriers are randomly spread within the same symbol and occupy the same position in all symbols (see Table 8.1). Therefore TPS signal power is equal to the mainstream data, D-BPSK modulation is applied from symbol to symbol and the TPS carriers Table 8.1 CP and TPS carrier position numbers Position occupied by CP carriers 0000 0255 0531 0873 1101 1323

0048 0279 0618 0888 1107 1377

0054 0282 0636 0918 1110 1491

0087 0333 0714 0939 1137 1683

0141 0432 0759 0942 1140 1704

0156 0450 0765 0969 1146

0192 0483 0780 0984 1206

0201 0525 0804 1050 1269

0569 1286

0595 1469

0688 1594

Position occupied by TPS carriers 0034 0790 1687

0050 0901

0209 1073

0346 1219

0413 1262

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TS

TU

Δ Guard Interval

Figure 8.4 The guard interval

are randomly spread along symbols. By considering these peculiarities it can be predicted that TPS will not affect the AF of the random part of the DTV-T signal. This will be shown later.

8.2.4 Guard Intervals The COFDM symbol also has a guard interval. It is a segment of duration , added at the beginning of the COFDM symbol (see Figure 8.4). This segment is identical to the segment of the same length at the end of the symbol. The duration of the GI ranges from 3 to 25 % of TU , depending upon the expected level of multipath in a channel. In the United Kingdom, the DTV-T standard ∼3 % TU is used. Therefore, the total duration of the symbol increases from TU to TS = TU + . Thus, if the DTV-T signal itself at the COFDM modulator output is expected to be a random process, the transmitted signal contains some deterministic or quasi-deterministic components. As will be shown, this essentially affects the signal’s ambiguity function. The main parameters of the DTV-T signal used in the United Kingdom are shown in Table 8.2.

8.3 DTV-T SIGNAL AMBIGUITY FUNCTION The universal approach to radar signal analysis, based on the consideration of the ambiguity function, has been discussed above. Fundamentally there are at least three ways to study the AF: an analytical description, a computer simulation and an experimental study. In Reference [8.13] a detailed analytical analysis of the DTV-T signal AF was carried out which corresponds well to the computer simulation results. To avoid the presentation of extremely tedious analytical equations only the simulation approach will be considered, with further experimental confirmation of the main simulation results. Nevertheless, readers may wish to refer to Reference [8.13], to compare the analytical and the modelling results. The computer simulation approach used in Reference [8.12] will be followed. Table 8.2 Main parameters of the DTV-T signals (UK) Mode (K) 2

Carrier number

TU (μs)

GI (μs)

Carrier modulation

Total bandwidth (MHz)

Number of SP

Number of CP

Number of TPS

1705

224

7

64-QAM

7.61

143

45

17

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DTV-T SIGNAL AMBIGUITY FUNCTION

8.3.1 The DTV-T Signal Model

For radar application, the ambiguity function represents a particular area of interest. In terms of delay, one millisecond corresponds to a 150 km maximal range. This figure fits well into the practical power budget of DTV-T-based radar with 10 kW transmitters operating in surveillance mode [8.13]. The Doppler range is specified by the maximal speed of air targets and the transmitter carrier frequency. Assuming the typical DTV-T frequency is about 500 MHz, a 4 kHz Doppler shift corresponding to a target speed of ∼1000 m/s can be expected. Later in this chapter a carrier frequency of 631.25 MHz will be referred to. This frequency corresponds to channel 41, which was used during experimentation. The next parameter to be specified for DTV-T signal AF analysis is the signal integration time. The maximal coherent and post-detector integration time essentially depend on the particular radar signal processing algorithms, as well as the operational mode and the target dynamics. However, the goal of the presented material is to analyse the signal AF, rather than the radar itself. The DVT-T signal bandwidth is known, i.e. 7 MHz, and the integration time can be evaluated, where the AF floor will be well below the main lobe. This level may be specified as −50 dB and the corresponding integration time is about 20 ms. More precisely, a level of −55 dB RMS sidelobes will occur after the integration time interval; this will be used for future reference. This coherent integration time may be viewed as a practical one. For the DTV-Tbased surveillance radar, the range resolution is expected to be about R ∼ 20 m. An aircraft with a maximal speed of 1000 m/s, as mentioned above, will cross this cell over the 20 ms time interval and this may be considered as the shortest integration time. A further increase in the integration time will reduce the floor level in the random signal ambiguity function. For AF analysis, a computer model will be used that effectively repeats the process of generating the DTV-T signal (see Table 8.2), using the coding, interleaving and modulation procedure in accordance with the appropriate standard [8.14]. 8.3.1.1 Experimental Setup For experimental confirmation of the analytical study, a single-channel linear receiver was used. A simplified block diagram of this receiver is shown in Figure 8.5. This is a super heterodyne receiver which converts the signal into the baseband via two downconversion stages. The output baseband signal is digitized and stored in a memory and then transferred to a personal computer hard-drive for further processing.

fc = 631.25MHz

RF part

IF Part

BPF1

BPF2

'a' Low noise amplifier

+10 dBm 568 MHz

LO 1

M1

Baseband Part

'b' A2 +10 dBm 63.25 MHz

M2

LPF

'c'

A/D conversion

LO 2

Figure 8.5 Block diagram of the receiver. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

In this experimental setup a 25 dB gain amplifier is used with a 1.5 dB noise figure. The signal passed through the bandpass filter BPF1 with a passband of 42 MHz at a level of –3 dB is then downconverted to the 70 MHz intermediate frequency (IF). It is then passed through the standard DTV-T IF surface acoustic wave (SAW) filter, BPF2, with the passband of 8 MHz. Finally, the signal is converted to a baseband where all the spectrum components outside the DTV signal band are filtered out by the lowpass filter (LPF) with the cut-off frequency of 10.7 MHz at the –1 dB level. The signals stored by the computer were then used for experimentation. Low-frequency spectral components up to about 100 kHz, as well as spectral components above 6 MHz, were cut off by a software filter. To unify the computer generated and experimentally obtained signal, the same software filter was used in both cases. Thus, these two signals, computer generated and experimentally obtained real DTV-T signals, are ready to use for further study.

8.3.2 AF of DTV-T Signal Random Components The AF of a random process with a uniform spectrum has a thumbtack shape [8.8]. Therefore, the DTV-T signal’s random component can also be expected to have a similar shape. This may be verified by a computer simulation as was used in Reference [8.12]. The signal is generated according to the DTV-T standard, but neither the CP or SP carriers nor the guard intervals were added, yet TPS is present in this model. The time and frequency positions occupied by the pilot carriers or guard intervals are filed with the video data. The introduction of TPS after modulation may or may not prove that TPS signals are acting in a similar way to the random components of the DTV-T signal. As was discussed above, the expectation is that the MPEG-2 coded signal corresponds to a baseband white random process with the correlation interval specified by its spectrum. Moreover, further coding, interleaving and OFDM modulation should remove any correlations between the MPEG bits. This can be proven by modelling an unrealistic, but worst-case, scenario. Instead of using the MPEG-2 data at the COFDM modulator input, a periodical deterministic stream of 1 and 0 was used. This bit stream was then processed according to the DTV-T modulation standard. Figure 8.6 shows the ACF of this test bit stream at the input and at the output of the COFMD modulator. It is seen that the channel coding, interleaving and modulation fully randomize the signal. It is also concluded that the quasi-deterministic components of the TPS signal do not generate any ambiguity, at least in the ACF. This was also analytically proven in Reference [8.13]. In Figure 8.7 the UF of the output signal is shown over a 1 ms delay and 4 kHz Doppler shift. From this figure, it can be seen that the AF of the DTV-T random component does not contain any ambiguities in the considered delay–Doppler domain.

8.4 IMPACT OF DTV-T SIGNAL DETERMINISTIC COMPONENTS ON THE SIGNAL AMBIGUITY FUNCTION At the beginning of the previous sections an assumption was made that, by being pre-processed and modulated according to the DTV standard, the video data itself acts as a random signal.

• 323

0

0

−10

−10 | χ(τ,0)| (dB)

| χ(τ,0)| (dB)

IMPACT OF DTV-T SIGNAL DETERMINISTIC COMPONENTS

−20 −30

−20 −30

−40

−40

−50

−50

−60 −1

−0.5

0 τ(msec)

−0.2

1

0.5

0

0.2

−3

0.4

0.6

0.8

1

τ(msec)

X 10

(b)

(a)

Figure 8.6 The test signal autocorrelation function: (a) at the COFDM modulator input and (b) at its output. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

During the course of the study it was demonstrated that this assumption is true and this waveform has a thumbtack ambiguity function. In the same way, an assumption is now made that the presence of guard intervals and control signals (at least CP and SP) introduce some deterministic repetitive components into the random signal considered above. As a result, a number of supplementary and unwanted deterministic peaks can be expected in the DTV-T signal ambiguity function. This will be proven below.

0

| χ (τ,ω)|, dB

−20 −40 −60 −80 −100 −120 4 3 ω, kHz

2 1 0

0.2

0.4

0.6

0.8

1

τ, msec

Figure 8.7 UF of DTV signal random components. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

0

| χ(τ,0)|, dB

−10

Intra-symbol pilot peaks

Inter-symbol pilot peaks

Gurad interval peak

−20 −30 −40 −50

−0.2

0

0.2

0.4

0.6

0.8

1

τ, msec

Figure 8.8 ACF of the computer modelled DTV-T signal. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

8.4.1 Autocorrelation Function (ωd = 0) The ACF of the DTV-T is shown in Figure 8.8. The modelled waveform contains a complete set of deterministic components: guard interval, pilot and TPS carriers. As already discussed, the TPS carriers do not influence the AF due to their quasi-random positions and specific type of modulations. Nevertheless, in all experiments TPS carriers are present. The sidelobes generated by the GI occur at τ = TU = 224 μs, which is the guard interval period. The peaks generated by pilot carriers could be divided conditionally into two categories: intrasymbol peaks and intersymbol peaks. The first group occupy a time interval between 0 ≤ τ ≤ TS = 231 μs, which is the symbol duration; the second group is delayed at a time τ > TS = 231 μs. Figure 8.8 clearly demonstrates that the introduction of a guard interval and pilot carriers generate deterministic sidelobes in the ACF with essential amplitudes. These sidelobes could mask desired signals and generate false targets. In more general terms, the presence of deterministic components in the DTV-T waveform clutter the observation area.

8.4.2 Complex Envelope Spectrum (τ = 0) The complex envelope spectrum, i.e. the cross-section of the DTV-T signal AF (τ = 0) could be expressed by Equation (8.3), i.e. the Fourier transform of the square of the DTV-T complex envelope. This does not depend on a particular modulation. The DTV-T signal has a constant average power over Tc and its spectrum as expected follows the ‘sinc’ function: χ (0, ωd ) =

sin π Tc ωd , π Tc ωd

where χ (0,ωd ) obtained by the modelling for Tc = 20 ms is shown in Figure 8.9.

(8.7)

• 325

IMPACT OF DTV-T SIGNAL DETERMINISTIC COMPONENTS

(a)

| χ(0,v)| (dB)

0 –20 –40 –60 –4

–3

–2

0 ω (kHz)

1

2

3

4

(b)

| χ(0,v)| (dB)

0 –10 –20 –30 –40 –0.2

–0.15

–0.1

0 ω (kHz)

0.05

0.1

0.15

0.2

Figure 8.9 (a) DTV-T signal complex envelope spectrum over the ± 4 kHz band and (b) the zoomed main lobe. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

8.4.3 Ambiguity Function of the DTV-T Signal Finally, the DTV-T signal was modelled according to its standard and the AF was evaluated over the considered time–frequency interval. Figure 8.10 shows the UF of this waveform. It is seen that a number of deterministic sidelobes occur over the entire delay–Doppler domain.

8.4.4 Experimental Confirmation of the Modelling Results To confirm the results, the ACF (Figure 8.11(a)) obtained from a real DTV-T signal, stored at the output of the experimental setup (Figure 8.5), may be compared with the ACF of the modelled signal (Figure 8.13 (b)). It can be seen that there is an extremely high level of similarity between the two. At this point of the study it can be concluded that:

r The DTV-T signals could be considered as a random passband white noise with the appropriate thumbtack ambiguity function.

r This thumbtack ambiguity function is cluttered by the presence of a guard interval and pilot signals carriers in the DTV-T waveforms.

r The clutter sidelobes levels have amplitudes of −20–30 dB relevant to the main lobe of the ambiguity function and consequently essentially reduce the system’s dynamic range.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

Inter-symbol pilot peaks

Guard interval peaks

Intra-symbol pilot peaks 0

| χ (τ,ω)|, dB

−20 −40 −60 −80 −100 −120 4 3 ω, kHz

2 1

0.4

0.2

0

1

0.8

0.6 τ, msec

Figure 8.10 UF of the DTV-T signal. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

This conclusion raises the question of whether it is possible to modify the DTV-T signal processing algorithm at the reception side in such a way as to remove, or at least essentially reduce, the level of these unwanted sidelobes. The answer to this question is positive and may be achieved through the use of some mismatching in the signal processing algorithms. The next sections are dedicated to this problem. Ideally, the proper signal processing algorithms should be synthesized, but this is too complex a task. Instead, an empirical way will be found to identify the signal processing that minimizes the unwanted sidelobes level. (a)

−10

−10

−20

−20

−30 −40

−30 −40 −50

−50 −0.2

(b)

0

| χ(τ,0)| (dB)

| χ(τ,0)| (dB)

0

0

0.2

0.4 τ(msec)

0.6

0.8

1

−0.2

0

0.2

0.4

0.6

0.8

1

τ(msec)

Figure 8.11 ACF of the DTV-T signal: (a) experimental and (b) modelled. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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MISMATCHED SIGNAL PROCESSING

8.5 MISMATCHED SIGNAL PROCESSING

The ambiguity function of a DTV-T signal contains a large number of deterministic sidelobes outside the main lobe area. This situation can be improved by the introduction of some mismatching between the heterodyne channel and the radar channel at the receiver. This could be achieved by modifying the heterodyne reference signal. Let stv (t) be the transmitted DTV-T signal. The optimal signal processing at a background of the AWGN assumes matched filtering (8.1), i.e. the correlation of the input signal with its complex conjugate copy stv∗ (t). Applying the mismatching, a function sm∗ (t) should be specified, which should be selected in a way that minimizes the level of unwanted sidelobes. Following Equation (8.4), the DTV-T signal generalized ambiguity function (GAF) can be specified [8.15]. The physical sense of the generalized ambiguity function (GAF) corresponds to the waveform at the matched (in this case a mismatched) filter output: ∞ 2 |χm (τ, ωd )|2 = sm∗ (t)stv (t − τ )e jωd t dt . (8.8) −∞

Following the definition above, the function |χm (τ, ωd )| could be referred to as the generalized uncertainty function (GUF) and ideally coincides with that shown in Figure 8.7. As the cause of the unwanted peaks in the AF of the DTV-T signal is known, the heterodyne channel signal can now be modified in such a way as to have a thumbtack GAF. In subsequent sections, modification of the heterodyne channel signal is discussed in detail.

8.5.1 Receiver Stricture The modern approach to signal processing in radar technology is mainly based on a software solution. Here, to enable better visualization, a signal processing procedure will be introduced in terms of block diagrams. In practice these block diagrams represent software algorithms rather than hardware subsystems. In Figure 8.12 a simplified block diagram of the radar signal processing subsystem in the DTV-T-based passive radar is shown. The DTV-T signal at the reception side is not known beforehand, and to form the reference signal the radar has two channels, the radar and the heterodyne channels, with two dedicated antennas. The HC antenna assumes a medium gain and may be directed towards the TV station. It is expected that the received signal will not be Radar channel Sampling and A/D conversion

fc Heterodyne channel

Multi-Channel Correlator

stv(t) Sampling and A/D conversion

Heterodyne signal pre-processing

sm(t)

Figure 8.12 The radar receiver structure. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

MULTI-CHANNEL CORRELATOR Range-Frequency Cells ω1 ω2

ωn

ω1 ω2

Bank of Bandpass Filters

ωn

ω1 ω2

ωn

Bank of Bandpass Filters

Bank of Bandpass Filters

Radar Channel Heterodyne Channel

τ1

τ2

τn

Figure 8.13 Time-domain multichannel correlator. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

distorted and will have a high signal-to-noise ratio. The output signals from these two antennas are downconverted to baseband. Having been received in the heterodyne channel, stv (t) should be pre-processed and converted into a new reference signal sm (t). The core of further signal processing is the correlation of the radar signal with the HC reference. The heterodyne signal is delayed for each range resolution cell in the multichannel correlator, as shown in Figure 8.13. The delay τ corresponds to a range resolution cell, whereas ωn corresponds to a particular Doppler frequency filter. The Fourier transform could be used as the filter bank. Moreover, the proposed correlation algorithms could be realized not only in the time domain but also in the frequency domain. If the correlator reference signal is a replica of the receiving signal, then the output of this multichannel correlator corresponds to the appropriate signal AF. Where the heterodyne signal is modified, the appropriate outputs correspond to the GAF specified above. The goal is now to find the heterodyne signal ‘pre-processing’ procedure as a way to remove deterministic sidelobes from the GAF.

8.5.2 Signal Pre-processing in the Receiver 8.5.2.1 Guard Intervals A straightforward method of mitigating deterministic sidelobes, which occur due to the guard interval (GI) presence, i.e. GI peaks, is to form the heterodyne signal with zero amplitude during the GI in the radar channel. This is an easy and technically achievable procedure and the GI tracking subsystem can be found in any DTV receiver. The appropriate waveform with blocked GI is shown in Figure 8.14. When this signal is used as the heterodyne, in the appropriate GUF (Figure 8.15), the strong GI peaks (see Figure 8.10) are absent. However, this occurs at the expense of new sidelobes appearing at Doppler frequency ∼4 kHz, that is 1/TS . This result is predictable, as there is a

• 329

MISMATCHED SIGNAL PROCESSING

100 80 60 40 20 0 −20 −40 −60 −80 −100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time(msec)

Figure 8.14 DTV-T waveform with blocked GI.

new regularity in the heterodyne channel. The deterministic sidelobes that are 4 kHz apart from the AF function main lobe are not considered to be detrimental for most radar applications, as they correspond to a speed of nearly 1000 m/s for the radial target. Moreover, it will be shown later that these new guard intervals in the GUF can also be mitigated. 8.5.2.2 Pilot Carriers Pilot carriers, which are deterministic components of a DTV-T signal, have boosted power levels and introduce some periodicity in the DTV-T signal. As discussed above, two types Due to guard interval blanking 0

| χm (τ,ω)|, dB

−20 −40 −60 −80 −100 −120 4 3 ω, kHz

2 1 0

0.2

0.4

0.6

0.8

1

τ, (msec)

Figure 8.15 GUF with the GI blocked in the heterodyne channel. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

Scattered pilot peaks Suppression SP1

Digital Equaliser (Switchable coefficients)

Continuous pilot peak Suppression Digital Equaliser (Fixed coefficients)

Start of Frame Pulse

Heterodyne channel

To Multi-Channel Correlator Selection (SP1 or SP2)

TPS Decoder Start of Frame Pulse Blanking guard interval

SP2

Digital Filter (Switchable coefficients)

Digital Filter (Fixed coefficients)

Figure 8.16 Block diagram of the heterodyne signal pre-processing. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p.133–142. Reproduced by permission of IET.

of sidelobes are generated in the AF of the DTV-T signal: intrasymbol and intersymbol. To mitigate these peaks in the GAF, two complementary procedures are proposed. The first is the power equalization of the pilot carriers in the heterodyne channel signal. As will be shown later, this mitigates the intrasymbol peaks. The second procedure is the filtering-out of the pilot carrier components in the heterodyne channel prior to correlation, in order to suppress the intersymbol sidelobes. These two algorithms cannot be applied simultaneously as they counteract each other. To resolve this contradiction, two parallel signal processing channels can be used, as shown in Figure 8.16. In the first (upper) channel, the signal processing procedure is given the conditional name, SP1. SP1 comprises two consecutive amplitude equalizers that are lowpass digital filters with a flat frequency response and a reduced gain at the pilot signal carrier frequencies. In the second (lower) channel, the signal processing algorithm, SP2, is used. SP2 includes two multiband notch filters that fully suppress the pilot carrier frequencies. The first filters in both channels are for correcting the scattered pilot carrier frequencies in HC. Scattered pilot carriers depend on the symbol position in the DTV-T signal frame. Consequently, the appropriate filters (see Figure 8.16) in SP1 and SP2 have time-variant parameters that should be synchronized with the receiving signal frame.

8.5.3 Pilot Carrier Equalization Thus, the equalizers have a frequency response to adjust the power of the pilot carriers to the video data level. The frequency response of the equalizer is shown conditionally in Figure 8.17. The digital equalizer, with switchable coefficients, tunes the equalizer to the appropriate frequencies from symbol-to-symbol over a period of four symbols, i.e. frame duration. To start the process of amplitude equalization of the scattered pilot carriers, the beginning of the frame of the received DTV-T signal should be tracked. This is necessary to control the

• 331

MISMATCHED SIGNAL PROCESSING

| H(f )|SP1

Ideal response Inaccurate response

3/4 Deviation

f2

f1

f

fn

Figure 8.17 Equalizer frequency response in the SP1 channel. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p.133–142. Reproduced by permission of IET.

coefficients of the scattered pilot equalizer. The information regarding the DTV-T signal frame can be extracted from the TPS. Hence a TPS decoder, similar to those used in a conventional DTV-T receiver, should be used for this tracking. Unlike the scattered pilots, the continuous pilot carrier frequency positions are the same for all the symbols and the equalizer has a time-invariant frequency response. The equalizer output is correlated with the radar channel signal and contains no intrasymbol peaks, but still have intersymbol peaks in the GAF. The modelled GUF is shown in Figure 8.18. Guard interval peaks

Intersymbol peaks

0

| χm (τ,ω)|, dB

−20 −40 −60 −80 −100 −120 4 3

1 2

ω, kHz

1 0

0.2

0.4

0.6

0.8

τ, msec

Figure 8.18 GUF of the DTV-T signal with equalized power in the heterodyne signal. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

Intra-Symbol Peak Attenuation (dB)

0 –10 –20 –30 –40 –50 –60 0

2

4

6 8 10 12 14 16 Equaliser response inaccuracy (%)

18

20

Figure 8.19 Intrasymbol sidelobes attenuation versus equalizer frequency response inaccuracy. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

This fact is clearly seen by comparison of the GUF, which was obtained by correlating the received signal waveform modified according to SP1 reference signal, and the UF of the DTV-T signal (Figure 8.12). This shows that the intrasymbol sidelobes are cancelled when the intersymbol sidelobes are presented with a reduced magnitude of about 4 dB. The graph shown in Figure 8.18 illustrates the ideal case, i.e. the equalizer perfectly adjusts the amplitude of the pilot carriers to the video data power level. Using this algorithm in practice, the equalizer frequency response could still deviate from this ideal scenario. This situation was modelled and the results are shown in Figure 8.19. This figure shows the intrasymbol sidelobe level as a function of inaccuracy in the equalizer frequency response. The +100 % point on the horizontal axis corresponds to the pilot carrier power level, which is twice that of the data carrier. The 0 dB point on the y axis refers to the absence of equalization. For example, to obtain −40 dB intrasymbol sidelobe suppression, the equalizer should have not more than about 2 % inaccuracy in its response, i.e. the level of pilot signals should not deviate more than about 2 % in comparison with the main data stream power level.

8.5.4 Pilot Carrier Filtering The intersymbol peaks are generated due to the repetition of the pilot carrier positions from one symbol to another. An essential reduction of these sidelobes can be expected by filtering out the appropriate carrier frequencies; this filtering is the function of the SP2. The two digital filters shown in Figure 8.16 have a zero frequency response level at the pilot signal carrier frequencies. Similar to SP1, the first filter has time-variant coefficients to mitigate the scatter pilot carriers, whereas the second is for continuous pilots and has a time-invariant frequency response. The SP2 filter frequency response is shown conditionally in Figure 8.20.

• 333

MISMATCHED SIGNAL PROCESSING

| H(f )|SP2

Ideal frequency response Nonideal frequency response

1

Deviation

0

f1

f2

f

fn

Figure 8.20 SP2 notch filters frequency response. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

Figure 8.21 shows the GUF of the DTV-T waveform when the reference signal was processed according to SP2 algorithms and a blank guard interval. Comparing this figure with Figure 8.10, it can be seen that the intersymbol sidelobes are fully mitigated. As with the discussion of the practical application of the equalization algorithm, the required accuracy of the notch filters should be evaluated. Deviation from the ideal filter frequency response would result in some remaining level of intersymbol peaks. Figure 8.22 shows the modelling results for the intersymbol peak attenuation as a function of the inaccuracy (notch frequency shift) in the filter frequency response. A 0 dB level on the attenuation axis represents Due to guard interval blanking

No inter-symbol sidelobes present

0

| χm (τ,ω)|, dB

−20 −40 −60 −80 −100 −120 4 3 ω, kHz

2 1 0

0.2

0.4

0.6

0.8

1

τ, msec

Figure 8.21 GUF of the DTV-T waveform with a blanked guard interval and filtered-out pilot signals in the heterodyne signal. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

Inter-Symbol Peak Attenuation (dB)

0 –10 –20 –30 –40 –50 –60

0

2

4

6

10 12 14 8 Filter Inaccuracy (%)

16

18

20

Figure 8.22 Intersymbol peak attenuation versus filter response inaccuracy. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

the case when no filtering is applied. For example, a 2 % inaccuracy in this case corresponds to about a −34 dB intersymbol peak attenuation [8.16]. 8.5.4.1 Two channels combining Comparing Figures 8.18 and 8.21, it can be seen that unwanted deterministic sidelobes are still present in the GUFs even when the heterodyne channel signal is pre-processed according to SP1 or SP2. However, these peaks correspond to different delays between the reference and the radar signals. As a result, a simple rule of heterodyne channel signal selection can be derived, which introduces no peaks outside the main lobe of the GUF (Figure 8.23). This rule is given below:

r For all delays corresponding to intrasymbol peaks the output of the equalizers in the heterodyne channel is selected as the reference signal, for correlation with the radar channel.

r For delays corresponding to the intersymbol peak and delay related to the guard interval peak, the output of the filters in the heterodyne channel is selected. This selection procedure gives a GUF without any unwanted peaks. 8.5.4.2 Mismatching Loss The discussion of mismatched signal processing begins with the statement that, at least in the case of signal reception at the background of AWGN, any mismatching in the signal processing leads to some signal-to-noise ratio degradation. This is the penalty demanded for the corrections made in the GAF. In the present case, due to the modifications of the heterodyne channel signal, there is a reduction in the reference signal power in comparison with the matched filter case,

• 335

SUMMARY

0

| χm (τ,ω)|, dB

−20 −40 −60 −80 −100 −120 4 3 ω, kHz

0.8

2 1 0

0.2

0.4

1

0.6 τ, msec

Figure 8.23 GUF of the DTV-T waveform after the mismatched signal processing. This figure was published in Saini, R. & Cherniakov, M., 2005. DTV signal ambiguity function analysis for radar application. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 133–142. Reproduced by permission of IET.

whereas the noise level remains the same. The guard interval occupies about 3 % of the total symbol duration and the pilot carriers occupy approximately 10 % of the total carrier positions in the DTV-T COFDM symbol. Therefore, filtering the pilot carriers and guard interval blanking can cause a total of up to 13 % of power. This can be seen as a reasonable price to pay for the significant improvements made in the AF.

8.6 SUMMARY This chapter is finalized with the following statement: radar performance essentially depends on the ranging signal parameters. When a transmitter of opportunity is used the ‘hijacked’ waveform has to be accepted as it is and this waveform essentially specifies the radar’s characteristics. It is not possible to fundamentally alter this situation. Nevertheless, the radar performance can be essentially corrected by means of signal processing algorithms. These algorithms are essentially different, depend on the correction criteria and cannot be applied for general cases. In the presented material it has been demonstrated how to improve the DTV-T waveform ambiguity function, i.e. at the cost of a reduction of 0.5 dB in the power budget. The negative effect of the presence of the deterministic components on the signal ambiguity function have been fully mitigated. The general approach in the appropriate signal processing was the introduction of some mismatching at the reception side. Moreover, all modifications were carried out in the reference (heterodyne) channel, which is technically easy to perform in comparison with signal processing in the radar channel. This approach could be recommended for other applications of bistatic radar with transmitters of opportunity.

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AMBIGUITY FUNCTION CORRECTION IN PASSIVE RADAR

ABBREVIATIONS ACF autocorrelation function AF ambiguity function ATV analogue television AWGN additive white Gaussian noise BPF bandpass filter BPSK binary phase shift keying COFDM Coded OFDM CP continuous pilot signal DAB digital audio broadcasting D-BPSK differential BPSK DTV-T terrestrial digital video broadcasting systems GAF generalized ambiguity function GI guard interval GUF generalized uncertainty function IF intermediate frequency LO local oscillators LPF lowpass filter MPEG Moving Picture Experts Group OFDM orthogonal frequency division multiplexing PCL passive coherent location PBRS passive bistatic radar system QAM quadrature amplitude modulated RMS root mean square SAW surface acoustic wave SP scattered pilot signal TPS transport parameter signalling UF uncertainty function

VARIABLES bkc B Ed g(.) ∗ g (.) pkc Tc TS TU FC R χ χ (τ, 0) |χ (τ, ω|

pseudo-random bit value occupied frequency band signal average energy signal waveform signal complex conjugate pseudo-random code bit coherent integration time symbol duration time interval frequency intervals between carriers range resolution function deviation autocorrelation function uncertainty function

χ(0, ω) |χ(τ, ω|2 |χm (τ, ωd )| |χm (τ, ωd )|2 τ τε ωd ωdε

• 337

REFERENCES

complex envelope spectrum ambiguity function generalized uncertainty function generalized ambiguity function time delay small time deviation Doppler frequency small frequency deviation

REFERENCES 8.1 Griffiths, H. D. and Long, B. A. (1986) Television based bistatic radar, IEE Proc.-F, Radar and Signal Processing, 133, 649–57. 8.2 Griffiths, H. D., Garnett, A. J., Baker, C. J. and Keaveney, S. (1992) Bistatic radar using satellite-borne illuminator of opportunity, in IEE International Radar Conferance, UK, pp. 276–9. 8.3 Howland, P. E. (1999) Target tracking using television-based bistatic radar, IEE Proc. Radar, Sonar and Navigation, 146, 166–174. 8.4 Poullin, D. and Lesturgie, M. (1994) Multistatic radar using non cooperative transmitters, in International Radar Conferance, Paris, pp. 370–5. 8.5 Collins, G. W. (2000) Fundamentals of Digital Television Transmission, John Wiley & Sons, Inc., New York. 8.6 Woodward, P. M. (1953) Probability and Information Theory, with Applications to Radar, Pergamon Press, New York (second printing, 1960). 8.7 Peebles Jr, P. Z. (1998) Radar Principles, John Wiley & Sons, Inc., New York. 8.8 Guo-Sui Liu, Hong Gu, Wei-Min Su, Hong-Bo Sun and Jian-Hui Zhang (2003) Random signal radar – a winner in both the military and civilian operating environments, IEEE Trans. AES, 39 (2), 489–98. 8.9 Poullin, D. (2001) On the use of COFDM modulation (DAB, DVB) for passive radar application, in Symposium on Passive Radar LPI Radio Frequency Sensors, NATO RTO, Poland. 8.10 Guner, A., Temple, M. A. and Claypoole, R. L. (2003) Direct-path filtering of DAB waveform from PCL receiver target channel, IEE Electronic Letters, 39 (13), 118–9. 8.11 Levanon, N. (2000) Multifrequency radar signal, in International Radar Conference, Alexandria, USA, 683–8. 8.12 Saini, R. and Cherniakov, M. (2005) DTV signal ambiguity function analysis for radar application, IEE Proc. Radar, Sonar and Navigation, 152 (3), 133–42. 8.13 Saini, R. (2005) Digital television based radar, PhD Thesis, University of Birmingham, UK. 8.14 European Telecommunications Standard Institute (1997) Digital video broadcasting (DVB) framing structure, channel coding and modulation for digital terrestrial television, ETS 300 744, France. 8.15 Soliman, S. S. and Scholtz, R. A. (1998) Spread ambiguity function. IEEE Trans. Information Theory, 34 (2), 343–7. 8.16 Smith, S. W. (1997) The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, California.

9 Passive Bistatic SAR with GNSS Transmitters Mikhail Cherniakov and Tao Zeng

Chapter 6 is dedicated to the analysis of a newly introduced class of SAR, namely the spacesurface BSAR [9.1–9.3]. The SS-BSAR topology is well suited to be combined with a transmitter of opportunity. Launching a dedicated satellite, and specifically a satellite constellation, for SS-BSAR implementation may be economically unaffordable. One possible solution is to use electromagnetic energy emitted by existing communications, broadcasting, navigation satellites or radar satellites, and a number of options have been discussed in the literature [9.2, 9.4–9.7]. In this section the SS-BSAR based on global navigation satellite systems (GNSSs) are considered. GNSSs, i.e. GPS (US), GLONASS (Russia) and Galileo1 (EU), utilize constellations of high-orbit satellites. Between four and eight satellites of each system are simultaneously visible above the horizon from any point on the Earth. As discussed in Chapter 6, satellite diversity is extremely important for SS-BSAR to minimize spatial resolution reduction in comparison with its monostatic counterpart. The simplified topology of an airborne SS-BSAR with a GNSS as a transmitter of opportunity is shown in Figure 9.1. To use the GNSS as an illuminator in the SS-BSAR case, a condition should be satisfied that is common for all radar systems: the reflected signal must be strong enough to be detected at the background of noise and interferences. Systems with a transmitter of opportunity have at least one peculiarity in comparison with the traditional systems with dedicated transmitters – the transmitting signal power is predefined and has to be accepted whether it is suitable or not. Consequently, the power budget analysis is the first step for PBRS system design. As for the GNSS-based SS-BSAR, the problem of intrasystem interferences has to be dealt with. This comes from the fact that all satellites within the same GNSS operate with continuous periodic signals occupying the same or at least overlapping frequency bands. As a result, a number of inherent interferences are acting in the system and the signal has to be detected against their background. Hence, the signal-to-interference ratio (SIR) should be evaluated. 1

Scheduled to reach operational capacity in 2008.

Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

Z

GNSS Satellite Transmitter

VTr

DPI API

RT

Airborne Receiver

VRr

RR X

Target Area

–Y

Ground Plane

Figure 9.1 GNSS-based SS-BSAR topology

The first interference – the direct path interference (DPI) (see Figure 9.1) – is the signal transmitted from the illuminating satellite and received by the radar antenna, presumably via the antenna sidelobes. The DPI and the reflected signal (RS) have absolutely the same structure, but come to the receiver input with a different time delay and possibly have a different phase history. The second type of interferences – the adjacent path interference (API) – is due to the fact that GNSS satellites operate at the same frequency bands using code division multiple access (CDMA) between the satellites. Hence, the RS signal will also always be received at the background of API. It is important to mention here that these interferences, being extremely strong in relation to the signal level, are still less than the thermal noise level in the linear part of the receiver. This reduces the problem of the receiver nonlinearity as the noise randomizes the system.

9.1 GLOBAL NAVIGATION SATELLITE SYSTEMS All three exiting GNSSs have a similar architecture and basic principles of operation. The GPS constellation consists of 24 satellites that orbit the Earth in about 12 hours at an orbit altitude of 20 180 km. The satellites occupy six orbital planes with four space vehicles in each 60◦ equally separated with a 55◦ orbit inclination relevant to the equatorial plane [9.8]. GLONASS utilizes 24 satellites in three orbital planes shifted by 120◦ and each plane contains eight equally spaced satellites. Each satellite operates in a circular 19 130 km altitude orbit at an inclination angle of 64.8◦ and each satellite completes an orbit in approximately 11 hours 15 minutes. The Galileo system will comprise 30 satellites orbiting the Earth at an altitude of 23 222 km. Ten satellites will occupy each of three orbital planes inclined at an angle of 56◦ to the equator. The satellites will be spread equally around each plane and will take about 14 hours to orbit the Earth. All GNSSs operate in a relatively low frequency band, between 1 and 2 GHz, introducing about the same power flux density near the Earth’s surface of 10−13 –10−14 W/m2 order. The main GNSS–air interface parameters are presented in Table 9.1.

a

15 P-code

1575.42 1.023 C/A-code 10.23 P-code 13.5 50 26.5 −158 2.7 × 10−14

L1

GPS

13.5 50 26.5 −158

1227.60 10.23 P-code

L2

30 P-code

L2

11 50 25–27 −167

1246–1257 5.11 P-code

GLONASS

1602.563–1615.5 0.511 C/A-code 5.11 P-code 11 50 25–27 −161 1.4 × 10−14

L1

Minimum power received by omnidirectional antenna on the Earth’s surface.

Satellite antenna gain (dBi) Power output (W) EIRP (dB W) Minimum powera (dB W) Minimum estimated power flux density (W/m2 ) Potential range resolution (m)

Central frequency (MHz) Chip rate – ChR (M/s)

Channel

GNSS

Table 9.1 Parameters of GNSS satellite transmitters

15 50 29.7 −154

30

8 (a + b)

1278.75 5.11

E6

15 50 29.7 −157 3.0 × 10−14

1191.795 10.23 × 2

E5 (a + b)

Galileo

75

15 50 29.5 −156

1575.42 2.04

L1

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

Power flux density, introduced in the Table 9.1, which corresponds to the minimal guaranteed level, is one of the most important parameters of a GNSS-based SS-BSAR system. Selecting a particular satellite, this power could be at least 6–7 dB bigger in comparison with that presented in the table due to the nonuniform power flux distribution across the surface. Another vitally important parameter of the GNSS transmitting signals in terms of radar applications is their occupied bandwidth. This bandwidth specifies the potential SAR range resolution. This bandwidth and the appropriate resolution could be easy recalculated from the signal chip rates: R ≈

C , 2B

(9.1)

where C is the speed of electromagnetic waves and B is the ranging signal baseband bandwidth related directly to the transmitting code chip rate. The corresponding potential range resolution of a quasi-monostatic SAR system for different signals of the GNSS system is also shown in Table 9.1. It is interesting to mention here that the Galileo E5 band transmission includes two signals located in the E5a and E5b bands respectively, which can be processed jointly in the total bandwidth, improving the range resolution in comparison with a single E5 channel or GPS P-code [9.9, 9.10]. For the bistatic SAR case, the range resolution declines with the bistatic angle β as R =

C 1 , 2B cos (β/2)

(9.2)

where the direction of the range resolution is along the direction of the bisector of the bistatic plane. Figure 9.2 shows the potential range resolution for four different GNSS signals. 180 GLONASS P-code GPS P-code & Galileo E5a Galileo E5

160

Range resolution (m)

140 120 100 80 60 40 20 0 0

20

40

60

80

100

120

140

160

Bistatic angle (degree)

Figure 9.2 Range resolution versus bistatic angle for the SS-BSAR using GNSS

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POWER BUDGET ANALYSIS

When the SS-SAR utilizes an airbornes receiver and GNSS transmitter, the satellite can be considered nearly stationary during the observation time. As a result, only the receiver motion generates the synthetic aperture. The potential azimuth resolution az for the bistatic SAR can be written as [9.3, 9.11–9.13] az =

λRR λRR = , Lc V Tc

(9.3)

where λ is the wavelength, Lc is a length of the synthetic aperture and RR is the distance from the aircraft to the target. For a given physical antenna size, the maximum length of the aperture is given by L max = (λ/D)RR , where D is the effective length of the real antenna. Substituting Lmax for Lc in Equation (9.3), the minimum resolution in the focused bistatic case is found to be az = D.

(9.4)

This means that the inherent azimuth resolution for a GNSS-based SS-BSAR is the physical antenna length, which is twice as bad in comparison as its monostatic counterpart. The coherent integration time, Tc , required to achieve the minimum resolution is implied by various aircraft flight parameters: Tc =

λRR . V az

(9.5)

This parameter is very important for the power budget analysis, which will be presented in the next section. Thus, from the GNSS-based SS-SAR the potential spatial resolution cell can be expected to be about 1 m × 8 m, which is practical for a number of applications. The second question focuses on finding the operational range of such a system. The answer to this question may be found in the next section.

9.2 POWER BUDGET ANALYSIS Power budget analysis in the SS-BSAR was considered in References [9.13] and [9.14]. The SNR is calculated for the time of aperture synthesis. Here only targets that are frequency and angle independent from the radar cross-section (RCS) will be considered. After the range and azimuth compression, the final signal-to-noise ratio (SNR) can be written, following Skolnik in his Radar Handbook [9.15], as S Pt G t τi PRF RR λ Ar σ 1 η, = N 4πRT2 τcp V az 4πRR2 K Tβ0 Fn

(9.6)

where Pt Gt is the transmitter equivalent radiating power, RT is the transmitter target range and PRF is the pulse repetition frequency. The first term introducing the power flux density near the Earth’s surface, produced, in this case, by a GNSS transmitter, is assumed to be Pt G t /(4πRT2 ) = 1 ≈ 3.0 × 10−14 Wt/m2 for a one-channel Galileo signal (see Table 9.1). Equation (9.6) was originally derived for the pulse compression waveform with the compressed pulse duration, τcp , and uncompressed signal duration, τ i . Hence the second term in the equation, i.e. τi /τcp ,

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

is the SNR gain after range compression within a period, which in the present case is the correlation between the reflected signal and reference signal obtained via the receiver and the transmitter synchronization. The third term, i.e. PRF RR λ/(V · az ) = PRF Tc , is the number of integrated signals during the time of aperture synthesis, namely the SNR gain brought by the azimuth compression. Assuming that the receiver bandwidth and the transmitting signal’s bandwidth are matched, then β0 τcp ≈ 1, e.g. β0 ≈ B. The other notations in Equation (9.6) are rather common: Ar is the receiving antenna effective area, σ is a target RCS, K is the Boltzman constant, Fn is the receiver noise factor, which in this calculation will be considered as 1 dB, T is the physical temperature in Kelvin and finally η is the loss factor, which is assumed to be η = 0.5. For the considered system topology (see Figure 9.1), the equation to calculate the signalto-noise ratio is S 1 Ar σ tc PRF λη , = N 4πRR Fn KTVaz

(9.7)

where tc is the period of transmitting signal code. Consider as a practical example that the physical aperture of the aircraft aerial is S = 1.0 m × 0.7 m (1 m along the fuselage). The aerial efficiency is supposed to be ka = 0.7; hence the antenna effective area can be calculated as Ar ≈ 0.5 m2 . The calculations will be performed for the fixed value of the azimuth resolution az = D = 1 m. The rest of the parameters in Equation (9.7) could be considered as variables. If account is taken on the fact that the continuous transmitting signal is being dealt with, and hence the signal is integrated in the receiver over all the aperture synthesis time and that az is fixed, Equation (9.7) can be rewritten as S σ 1 Aλη = . N 4πFn K T az RR V

(9.8)

The first term of this equation is a constant and for the values given above S σ = 3.0 × 104 × . N RR V

(9.9)

Using Equation (9.9) it is easy to calculate the SNR for different parameters σ , R and V. Some results of the calculation are presented in Table 9.2. The far right column is derived for the case where the power flux density corresponds to the favourable satellite position choice, i.e. approximately 6 dB above the minimal guaranteed flux level. It is also important to draw attention here to the fact that the SNR degrades in the SS-BSAR as 1/RR . This is an unusual dependence for conventional radars and is a consequence of the nearly uniformed power flux density on the surface generated by the spaceborne transmitter. From this table it can be seen that the operational range is also reasonable for a number of applications. One further vitally important question must be addressed here: can the reflecting signal be detected at the background of the intrasystem interferences, which are inherent features of the GNSS-based SS-BSAR? The next section is dedicated to this analysis.

• 345

ANALYSIS OF THE SIGNAL-TO-INTERFERENCE RATIO Table 9.2 The power budget of the Galileo-based SS-BSAR RCS (m2 )

Distance of receiver–target (km)

Receiver (aircraft) speed (m/s)

Integration time (s)

Minimal SNR (dB)

Achievable (dB)

10 50 50 50 50 250 250

3 3 6 10 10 10 15

25 (90 k/h) 25 25 25 50 (180 k/h) 25 50

30 30 61 102 51 102 76

6.2 13.2 10.2 7.9 4.9 14.9 10.2

12.2 19.2 16.2 13.9 10.9 20.9 16.2

9.3 ANALYSIS OF THE SIGNAL-TO-INTERFERENCE RATIO Consider the signal-to-interference ratio (SIR) and its improvements at the different stages of signal processing, starting from the receiving antenna selectivity, then the interference ambiguity functions and the aperture synthesis algorithm. Detailed analysis of this problem is presented in References [9.13] and [9.14].

9.3.1 SIR at the Antenna Output In GNSS the satellites transmitting antenna patterns are shaped in such a way as to introduce a uniform power flux density near the surface that is irrelevant for satellite elevations down to 10◦ . Hence it can be assumed that the DPI and API power density in the target – receiver areas are nearly equal. As a result, the signal-to-interference ratio at the output of the antenna can be simply introduced by SIR =

σ G0 , 4πRR2 G 1

(9.10)

where G0 , G1 are the receiving antenna gains in the direction of the reflected signal and the interference respectively. Assuming that interferences are received via sidelobes of the receiving antenna pattern and/or that the radar channel can use the orthogonal to the transmitting signal polarization, the ratio G0 /G1 is about 15–20 dB [9.1]. Hence the SIR can be evaluated as a function of the receiver-to-target range for a set of practical RCSs. Results of the appropriate calculations are presented in Figure 9.3.

9.3.2 Analysis of the SIR Improvement Factor In order to simplify the analysis, the satellite, targets and the receiver are supposed to be coplanar. W 1 , W 0 and W r are the coordinate vectors of the satellite, target and the receiver respectively. It will be seen that this assumption does not affect the numerical results or lead to a loss of generality.

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

0

RCS=100 RCS=10 RCS=1900

SIR at the antenna output (dB)

–10

–20

–30

–40

–50

–60 1

2

3

4

5

6

7

8

9

10

Distance from receiver to target (km)

Figure 9.3 SIR at the antenna output versus receiver-to-target range

For the Galileo system the navigation signal uses gold codes (GC) for signal spreading. Denoting the GC sequence as A(m) and the normalized complex envelope of the navigation signal as a(t), this can be presented as t − (mT0 + n M T0 ) a (t) = , A(m)Rect T0 n=−(N +1)/2 m=−(M+1)/2 (N +1)/2

(M+1) /2

(9.11)

where Rect (t) =

1,

−1/2 ≤ t ≤ 1/2

0,

otherwise

,

and T0 and M are the period of the chip and the length of the gold code sequence respectively. This timing concept of the GC is shown in Figure 9.4. For Galileo T0 is about 0.1 μs and N is the number of cycles of the gold code sequences during the coherent integrating interval in the SS-BSAR system, which is the time of the aperture synthesis. The received signal of the SS-BSAR is the sum of signals reflected by the target and the interference. The appropriate waveform can be written as s(t) = k0 a(t − τ0 (t)) exp [j2π f c τ0 (t)] + k1 a(t − τ1 (t)) exp [ j2π f c τ1 (t)],

(9.12)

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ANALYSIS OF THE SIGNAL-TO-INTERFERENCE RATIO

M

Figure 9.4 Timing diagram of the Galileo signal

where fc is the carrier frequency, k0 is the amplitude of the target, k1 is the amplitude of the interference and τ 0 and τ 1 are the delays of the echo of the target and the interference respectively: |W 1 − W 0 | + |W r − W 0 | , c |W 1 − W r | τ1 (t) = , c

τ0 (t) =

(9.13)

where c is the speed of the light. The time delay can be approximated by two orders multinomial of t: 1 1 2 τi (t) ≈ τ i + vμi t + gi t , i = 0, 1, (9.14) c 2 where τ 0 and τ 1 are the delays of the target echo and the direct interference respectively (when t = 0). The expressions of the symbols μi and gi are shown in Table 9.3. In the table x, y are the coordinates of the target, Rs is the distance between the coordinate origin and the satellite and Va and Vs are the velocity of the aircraft and the satellite respectively. The SS-BSAR imaging procedure is in fact the correlation of the received signal and the reference signal. As a result the pixel of the complex SS-BSAR image can be written as

T /2 −T /2

s(t)s0∗ (t) dt,

where T = NMT0 is the coherent integration time of the SS-BSAR system and, s0 (t) is the reference signal, i.e. the baseband signal reflected by an ideal point target at the geometric position corresponding to the image pixel: s0 (t) = a(t − τ0 (t)) exp[j2π f c τ0 (t)]. Table 9.3 Expressions for the symbols μi and gi Parameter

Airborne receiver

μ0

μ0 =

μ1

0

−x x 2 + y2

Stationary receiver μ0 = −

x Rs

0 Va2 y 2

g0

g0 =

g1

g1 = Va2 /Rs

x 2 + y2

3/2

g0 = Vs2 /Rs g1 = Vs2 /Rs

(9.15)

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

Define the SIR improvement factor γ as γ =

signal-to-interference ratio after the imaging processing . signal-to-interference ratio before the imaging processing

From the signal model, γ can be calculated as

T/2

∗

1

−T/2 s0 (t)s0 (t) dt

, γ = T/2

= T/2

∗

∗ s (t)s (t) dt

/T 1 −T/2 s1 (t)s0 (t) dt 0 −T /2

(9.16)

(9.17)

where s1 (t) is the normalized baseband waveform of the interference: s1 (t) = a(t − τ1 (t)) exp [j2π f c τ1 (t)].

(9.18)

Equation (9.17) indicates that the SIR improvement factor of the imaging processing is the reciprocal of the correlation coefficient between s0 (t) and s1 (t). In the next section, it will be shown that γ can be divided into two components, i.e. the time-domain improvement factor and the Doppler-domain improvement factor. If the signal is sampled at frequency 1/T0 , there will be in total M∗ N samples over the aperture synthesis time. Dividing the samples into N groups, each group has M samples and t can be presented in a discrete format as

M +1 N +1 (9.19) t = m− T0 + n − M T0 , 2 2 for m = −(M + 1)/2, . . . , (M + 1)/2

and n = −(N + 1)/2, . . . , (N + 1)/2.

The discrete counterpart of si (t) is written as si (m, n) = exp (j2πτ¯i )A(m − L i (n)) exp (j2π f di (n)mT0 ) exp [jβi (n)],

i = 0, 1,

(9.20)

where f di (n) =

vμi gi n M T0 fc + fc, c c

vμi n M T0 πgi (n M T0 )2 fc + fc, c c τ¯i + 1c vμi n M T0 + 12 gi (n M T0 )2 L i (n) = . T0 βi (n) = 2π

(9.21) (9.22) (9.23)

Thus, the correlation coefficient is

T/2

∗ (N +1)/2

−T/2 s1 (t)s0 (t) dt 1

exp{j[β1 (n) − β0 (n)]}χ (L 0 (n) − L 1 (n), f d1 (n) − f d0 (n)) ,

≈

N n=−(N +1) 2

T / (9.24)

ANALYSIS OF THE SIGNAL-TO-INTERFERENCE RATIO

where χ (n, f )is the ambiguity function of the gold code sequence: χ (n, f ) =

1 M

(M+1) /2

A(m)A∗ (m − n) exp (j2π fmT0 ).

• 349

(9.25)

m=−(M+1)/2

In practical scenarios, if the proper parameters are chosen, the variation of χ(L 0 (n) − L 1 (n), f d1 (n) − f d0 (n)) with respect to n is statistically very small and is negligible. As a result

T/2

∗

−T/2 s1 (t)s0 (t) dt

≈ |χ (L 0 (0) − L 1 (0), f d1 (0) − f d0 (0))| |η( f , κ , M T0 )| ,

T

(9.26)

where η( f , κ , M T0 ) =

=

1 N 1 N

(N +1)/2

exp{ j[β1 (n) − β0 (n)]}

n=−(N +1)/2 (N +1)/2

exp{j[2π f (n M T0 ) + πκ (n M T0 )2 ]}

(9.27)

n=−(N +1)/2

and f , κ (see Table 9.4) can be considered as the difference of the central frequency and the frequency-dependent ratio (fdr ) between the target echo and the direct interference respectively. The meanings of the symbols in Table 9.4 are the same as in Table 9.3. Equation (9.26) indicates that the correlation coefficient is the product of two terms. This is consistent with the SAR imaging procedure that composes the range and the azimuth compressions. As a result, the improvement factor, γ , can be written as a productγ = γt γ f , where 1 , |χ (L 0 (0) − L 1 (0), f d1 (0) − f d0 (0))| 1 γf = , |η( f , κ , M T0 )| γt =

Table 9.4 Expressions for the symbols f and κ Airborne receiver f =

−x f c Va c x 2 + y2

κ = −

−Va2 y 2 fc fc g0 = c c x 2 + y 2 3/2

(9.28)

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

The time-domain improvement factor γt comes from the difference between the delay of the signal reflected by the target and the delay of the interference, as well as the average Doppler frequency √ shift. The quantity of γ t depends on the GC length and can be conservatively estimated by M [9.16]. For the DPI this will be proportional to the sidelobes of the two-dimensional (time, frequency) autocorrelation function, while for the API case this will be proportional to the two-dimensional cross-correlation function between two different signals. The Doppler domain improvement factor γ f is related to N and essentially reflects the phase history of the signal and the interferences. The difference between the improvement factors for the two considered scenarios, airborne and stationary receivers, arises from slightly different physical backgrounds. For the airborne receiver, γ f , comes from the difference between the Doppler history (both central frequency and f dr ) of the signal reflected by the target and the interference, while the stationary receiver, γ f , comes mainly from the difference between the Doppler central frequency of the signal reflected by the target and the interference. Therefore, exp{j[β1 (n) − β0 (n)]} at this configuration turns into nearly single frequency signals. These can be seen from Table 9.4 and Figure 9.5. It should be mentioned that if the variation of χ (L 0 (n) − L 1 (n), f d1 (n) − f d0 (n)) with respect to n is bigger than the chip duration, T0 , the improvement factor will change randomly due to the quality of the two-dimensional cross-correlation function. 1

the phase of echo signal-Airborne Receiver

0.5 0 –0.5 –1 –5000 –4000 –3000 –2000 –1000 0 1000 2000 3000 4000 5000 the phase of direct interference signal-Airborne Receiver 1 0.9998 0.9996 0.9994 –5000 –4000 –3000 –2000 –1000 0 1000 2000 3000 4000 5000 the phase difference 1 0.5 0 0.5 –1 –5000 –4000 –3000 –2000 –1000 0 1000 2000 3000 4000 5000 synthetic aperture-n

Figure 9.5 The phase of the echo signal and the interference signal. This figure was published in He, X., Cherniakov, M. and Zeng, T., 2005. Signal detectability in SS-BSAR with GNSS non-cooperative transmitter. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 124–132. Reproduced by permission of IET.

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ANALYSIS OF THE SIGNAL-TO-INTERFERENCE RATIO Table 9.5 The simulation parameters Parameters

Value

Code period (T0 ) Primary code length Secondary code length Navigation message length Sample rate ( f s ) Centre frequency Speed of airplane Satellite velocity

10−7 s 10 230 4 256 107 Hz 1207.14 MHz 50 m/s 3500 m/s

9.3.3 Simulation Results Equations derived in the previous sections introduce the improvement of SIR for general cases. Consider improvement factors in numerical results for some practical situations using a simulation in MATLAB. For the modelling of the Galileo signal E5-b was used [9.17]. It is assumed that for the airborne receiver the main synthesis is due to the airplane motion over an interval of 10 seconds, with a carrier speed of 50 m/s. The navigation message in the modelling is assumed to be an M sequence for some sort of upper boundary of the system’s performance. Simulation parameters are collected in Table 9.5. The setting of the scene is shown in Figure 9.6. The receiver is positioned at the coordinate origin and the two satellites are in the same orbits. The simulation results are shown in Figure 9.7. Here, N is chosen to be 2000, and the horizontal axis is the distance between the receiver and the target. The first curve of Figure 9.7(a) introduces the DPI improvement factor for the airborne case. Figure 9.7(b) compares DPI with y Satellite (0,RS )

Receiver, Va x R

Rrt Target (x,y)

Figure 9.6 Simplified topology of the modelling configurations. This figure was published in He, X., Cherniakov, M. and Zeng, T., 2005. Signal detectability in SS-BSAR with GNSS non-cooperative transmitter. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 124–132. Reproduced by permission of IET.

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

120

DPI Airborne receiver

the signal to DPI ratio, dB

110 100 90 80 70 60 50 40 0

100 200 300 400 500 600 700 800 900 1000 the distance between the target and the receiver, m

(a) 120

Airborne receiver

110 100

dB

90 80 70 60 the signal to API ratio the signal to DPI ratio

50 40 0

100 200 300 400 500 600 700 800 900 1000 the distance between the target and the receiver, m

(b) 120

API Airborne receiver

110 100

dB

90 80 70 60 the signal to API ratio the signal to DPI ratio

50

40 0 100 200 300 400 500 600 700 800 900 1000 the distance between the target and the receiver, m

(c) Figure 9.7 The influence of the target position relevant to the airborne receiver: (a) signal to DPI ratio, (b) API at the same position, (c) API at another position. This figure was published in He, X., Cherniakov, M. and Zeng, T., 2005. Signal detectability in SS-BSAR with GNSS non-cooperative transmitter. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 124–132. Reproduced by permission of IET.

ANALYSIS OF THE SIGNAL-TO-INTERFERENCE RATIO

• 353

API factors for a hypothetical case where the DPI and the API are transmitted from the same satellite. Figure 9.7(c) compares the improvement factors for the DPI and API, transmitted from another satellite, where the angle between these two satellites is about 1◦ . It can be seen that when the target gets further away from the receiver, the improvement factor becomes better for the DPI. For the API, improvement does not directly depend on this distance and follows to the level of cross-correlations between signals from different satellites. For the DPI the dependence has a simple explanation. When the distance of the receiver – target tends to zero (a hypothetical case) the phase history of the RS and DPI is the same and the only improvement is due to the autocorrelation function peculiarity. The two-dimensional cor√ relation function level outside the mainlobe, which is statistically proportional to 1/ 10 230, is about −40 dB. Subsequently, due to the phase history difference, the improvement factor becomes better via SAR signal processing. The API level is statistically derived from the length of the integrated sequence; in the present case that is 2000 times more than the GC period, and hence a level of 75 dB can be expected. As soon as the API transmitting satellite position does not coincide with the DPI transmitting satellite, in the practical case, the API level does not depend on the satellite position. The improvement factor is fully specified by the two-dimensional cross-correlation function and is about 75 dB for the considered parameters, irrelevant to the distance between DPI and API transmitting satellites. The API introduces a quasi-random signal relevant to the desired signal. If the radar receiver is synchronized for the ranging signal, then the API has at least two differences in comparison with the ranging signal: another GC sequence is used and another navigation message is transmitted. Consequently, it is expected that by increasing an integration time, at least until Airborne receiver 130

the signal to API ratio, dB

120

110

100

90

80

70

60 0

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 the azimuth accumulate number N

Figure 9.8 Signal-to-API ratio versus the signal coherent integration time. This figure was published in He, X., Cherniakov, M. and Zeng, T., 2005. Signal detectability in SS-BSAR with GNSS non-cooperative transmitter. IEE Proceedings – Radar, Sonar and Navigation, 152(3), p. 124–132. Reproduced by permission of IET.

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PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

√ the duration of the navigation message frame, the API level will decrease statistically as 1/ N . Modelling results shown in Figure 9.8 for the case of the airborne receiver clearly demonstrate this. With the integration time increased to about 10 s, the API improvement factor for the airborne receiver tends to 100 dB. The absolute difference between these factor values reflects the fact that there is some difference in the signal phase history occurring in the two considered systems configurations.

9.4 RESULTS DISCUSSION Two major components of the signal detectability analysis in the SS-BSAR with a noncooperative transmitter (NCT) are considered in this paper: target detection against a thermal noise background and against the system’s interferences. Utilization of a GNSS as the energyemitting sources makes this analysis critically important, as the transmitting signal power and the interference level are given. Other main conclusions that can be made from the study are:

r The power budget of the SS-BSAR with GNSS NCT is noise rather than interference limited. Two mechanisms of SIR improvement are identified: a correlation property of the DPI and API as well as different phase histories of the signals and interferences. These essentially reduce the interference levels.

r For the airborne receiver the signal detection, and consequently imaging range, is practically

restricted by about 5–10 km for a typical 50 m2 RCS target (a small vehicle, for example). This low-power budget specifies an SS-BSAR application for light, presumably autonomous, aircrafts for search and rescue missions, natural disaster damage assessment and similar purposes.

r The adjacent path interferences have a quasi-random nature that is relevant to the ranging

signal and are well below the signal level irrelevant to the receiver – observation area range.

r The DPI can potentially introduce a bigger threat to target detection as the two-dimensional

autocorrelation level limits the minimum improvement factor. Nevertheless, in most practical situations the DPI level is still essentially below the signal level after the SAR signal processing. Taking into account that only one satellite is the source of the DPI, the traditional adaptive sidelobe cancellation methods can be applied for further DPI suppression. The restricted power budget of the considered systems specifies their application to short to medium range radars. For airborne receivers UAVs as platforms could be recommended. In this section the SS-BSAR with GNSS transmitters of opportunity were analysed at analytical and modelling levels. The parameters and performance of this or similar systems correspond to a number of practical needs and their technical feasibility are of great interest. This will be the subject of the next section.

9.5 EXPERIMENTAL STUDY OF THE SS-BSAR In a number of publications [9.18–9.22] the experimental study of the SS-BSAR based on GLONASS GNSS is discussed. Figure 9.9 shows the experimental system topology. The navigation satellite is positioned as shown, the angles θ A and θ E being, respectively, the azimuth and elevation angles of the

• 355

EXPERIMENTAL STUDY OF THE SS-BSAR

z RT L Altitude

y Rx motion direction

θE

β

φ θA

Imaging Area

x

RR

Figure 9.9 Three-dimensional system geometry

satellite relative to the receiver, which is moving in the (0, y, z) plane, parallel to the y axis. The observation area is located in the (x, y, 0) plane. The bistatic angle, β, is the angle between the target illumination and echo propagation paths. As per the definition of the bistatic radar, the transmitter and receiver are separated by the distance L. The distance from the transmitter to the target is RT and the distance from the receiver to the target is RR . As the transmitter and receiver are in motion, RT , RR and L are functions of time. The utilized signal-processing algorithm for the SS-BSAR is a modification of the traditional range–doppler algorithm (RDA) (see Figure 9.10). The only difference between the standard RDA and the proposed algorithm is in the design of azimuth filter, which is derived from the instantaneous bistatic triangle formed by the transmitter, the receiver and the target, as shown in Figure 9.9.

Received signal

Range FFT

Range IFFT

Reference signal

Range FFT

Azimuth FFT

Computer Generated Azimuth Filter

Azimuth FFT

Azimuth IFFT (Image) Standard RDA algorithm

Receivertarget range estimates

Figure 9.10 SS-BSAR proposed algorithm

• 356

PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

The following assumptions were made in developing the algorithm for the experimental study:

r A moderate aperture length is considered (30 m for experimentation), allowing the range migration step of the normal RDA to be ignored.

r Targets at short ranges are considered (maximum range ∼600 metres). r For experimentation, a two-channel receiver is considered: the radar channel used for receiving the reflected signal from the observation area and the heterodyne (reference) channel receiving a signal directly from the satellite. The radar channel antenna is mounted on a flight imitator for array synthesis but, at this stage, the heterodyne channel is stationary (see Figure 9.11). The different components of the modified RDA are shown below: 1. Reference signal. For the considered GNSS GLONASS, the P-code (5.11 MHz bandwidth) is used for the purpose of imaging, as it provides adequate range resolution (30 m in the quasi-bistatic case) and is not encrypted. The locally generated P-code has been synchronized (in time and Doppler) with the P-code signal received by the heterodyne channel before it was correlated with the radar channel signal (see Figure 9.11(a)). This is to maintain the phase coherence between the radar channel and the locally generated P-code. Successful synchronization using a GLONASS satellite has been reported in Reference [9.5]. 2. Range compression. Figure 9.12 shows the simplified two-dimensional diagram forming the bistatic triangle. As mentioned earlier, the locally generated signal is synchronized to the heterodyne channel signal. Therefore, after range correlation, a target at distance RR from the receiver is located by the radar at the range RT + RR (u), where RT = RT (t) − L(t) and u is the slow time. For each range bin, RT is constant. This is due to negligible angular variation of the satellite during the time-of-flight and the moderate aperture length. 3. Azimuth compression. Doppler shift is evident along different paths in the bistatic triangle. As a stationary heterodyne channel and targets at short ranges are being considered, the Doppler shifts due to satellite motion (Fs ) in the heterodyne channel and transmitter-totarget paths are similar. The azimuth phase variation is due to the receiver motion only (RR variation). Therefore, in order to design an appropriate azimuth filter, for each range bin RR needs to be found from RT + RR . This can be estimated by solving the bistatic triangle of Figure 9.12, which in turn requires estimates of L(t) and φ. The synchronization algorithm tracks the satellite in delay and hence provides an estimate of L. The angle φ can be measured using an off-the-shelf GNSS receiver, which provides the satellite’s coordinates (azimuth and elevation angles). 4. Flight imitator. An experiment was conducted using the flight imitator installed on the rooftop of a five-storey building (Figure 9.11(b)). A GLONASS satellite was selected in such a way that the ‘transmitter–receiver–target’ topology corresponds to a quasi-bistatic case. The satellite selection was carried out using a commercial GNSS receiver. Table 9.6 shows the different experimental parameters of Figure 9.9.

• 357

EXPERIMENTAL STUDY OF THE SS-BSAR

Stationary heterodyne channel

Radar Channel

Observation area

30 m

Locally Generated P-code

Moving platform for aperture synthesis

Image Processing

Synchronisation (delay, Doppler)

(a)

Synchronised Locally Generated P-code

(b)

Figure 9.11 Experiment setup

Plate 21 (in the colour section) shows the image obtained using a real satellite. The radar images have been rescaled and superimposed on an aerial photograph of the same region for comparison. It is seen that a building (at a range of 250 m) and part of the structure of a greenhouse (in the range interval of 350–400 m) are clearly identified. The grassy areas appear as shades of blue (low intensity), as expected. It can be seen from the figure that there is no evidence of image corruption by the DPI or API.

• 358

PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

Height axis z

Tx

RT (t), FS L(t), FS Heterodyne Channel RT (t)-L(t)

ϕ Radar Channel

Target

FS+FR

Rx

RR FS: Doppler Due to Satellite Motion FD: Doppler due to Moving receiver L(t): Transmitter-to-Heterodyne Range RT: Transmitter -to -Target Range

Slant range axis x

Figure 9.12 Two-dimensional system geometry

Table 9.6 Parameters of the experiment Frequency channel θA θE β Satellite altitude Aperture length Receiver velocity Integration time

10 (1607.625 MHz) 178.4914◦ 11.3558◦ ∼11◦ ∼23 000 km 30 m 0.6 m/s 45 s

9.6 SUMMARY As discussed previously, the SS-BSAR is a brand new class of SAR and a lot of work is yet to be done to understand the potential of this radar class. In this section one particular kind of SSBSAR, i.e. the SS-BSAR with the GNSS satellite as a transmitter of opportunity and an airborne receiver is discussed. This system was investigated at the analytical, computer modelling and experimental level with rather good correspondence between these three approaches. The true SS-BSAR image can be seen in Plate 21 (colour section), as well as similar images published in References [9.19] to [9.23]. Therefore, the feasibility of one particular class of this radar is proven and with some degree of optimism the authors can predict a bright future for the SS-BSAR.

ABBREVIATIONS API CDMA DPI GC GNSS GPS NCT PCL RCS RDA RS SAR SIR SNR SS-BSAR UAV

• 359

VARIABLES

adjacent path interference code division multiple access direct path interference gold codes global navigation satellite system global positioning system noncooperative transmitter passive coherent location radar cross-section range–Doppler algorithm reflected signal synthetic aperture radar signal-to-interference ratio signal-to-noise ratio space-surface bistatic synthetic aperture radar unmanned aerial vehicle

VARIABLES a(t) normalized complex envelope of the navigation signal A(m) GC sequence Ar receiving antenna effective area B bandwidth c speed of light D effective length of the real antenna fc carrier frequency fdr frequency dependent ratio f difference of the central frequency Fn receiver noise factor receiving antenna gain in the direction of the reflected signal G0 G1 receiving antenna gain in the direction of the interference k0 amplitude of the target amplitude of the interference k1 K Boltzman constant Lc length of the synthetic aperture Lmax maximum length of the aperture M length of the gold code sequence N number of cycles of the gold code sequence Pt Gt transmitter equivalent radiating power RR distance from the aircraft to the target Rs distance between the coordinate origin and the satellite RT transmitter target range

• 360

s0 (t) tc T Tc T0 Va Vs Wr W0 W1 β γ γf γt az R η θA θE λ σ τ cp τi τ0 τ1 τ¯0 τ¯1 χ (n, f)

PASSIVE BISTATIC SAR WITH GNSS TRANSMITTERS

reference signal period of transmitting signal code physical temperature coherent integration time period of the chip velocity of the aircraft velocity of the satellite coordinate vectors of the receiver coordinate vectors of target coordinate vectors of the satellite bistatic angle SIR improvement factor Doppler domain improvement factor time domain improvement factor azimuth resolution range resolution loss factor azimuth angle of the satellite relative to the receiver elevation angle of the satellite relative to the receiver wavelength target RCS compressed pulse duration uncompressed signal duration delay of the echo of the target delay of the echo of the interference delays of the target echo (when t = 0) delays of the direct interference (when t = 0) ambiguity function of the gold code sequence

REFERENCES 9.1 Cherniakov, M. (2002) Space-surface bistatic synthetic aperture radar– prospective and problems, in International Radar Conference, Edinburgh, UK, pp. 22–6. 9.2 Cherniakov, M., Nezlin, D. and Kubik, K. (2002) Air target detection via bistatic radar based on LEOS communication signals, IEE Proc. Radar, Sonar and Navigation, 149 (1), 33–8. 9.3 Tao, Z., Cherniakov, M. and Teng, L. (2005) Generalized approach to resolution analysis in BSAR, IEEE Trans., AES-41 (2), 461–74. 9.4 Armatys, M., Axelrad, P. and Masters, D. (2001) GPS-based remote sensing of oceansurface wind speed from space, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS’01), July, vol. 6, pp. 2522–4. 9.5 Zavorotny, V. U. and Voronovich, A.G. (2000) Bistatic GPS signal reflections at various polarizations from rough land surface with moisture content, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS’00), pp. 2852–4.

REFERENCES

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9.6 Basili, P., Bonafoni, S., Mattioli, V., Ciotti, P. and d’Auria, G. (2002) Monitoring atmospheric water vapour using GPS measurements during precipitation events, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS’02), June, vol. 1, pp. 24–8. 9.7 Keydel, W. (2003) Perspectives and vision for future SAR systems, IEE Proc. Radar, Sonar and Navigation, 150 (3), 97–103. 9.8 Guochang, X. (2003) GPS: Theory, Algorithms and Applications, Springer, Berlin. 9.9 Guenter, W., Hein, J.G., Jean, L.I., Martin, J.C., Philippe, E., Rafael, L.R. and Tony, P. (2003) Status of Galileo frequency and signal design, Members of the Galileo Signal Task Force of the European Commission, Brussels. 9.10 Moccia, A., Vetrella, S. and Ponte, S. (1994) Passive and active calibrator characterization using a spaceborne SAR system simulator, IEEE Trans., GRS-32 (3), 715–21. 9.11 Willis, N.J. (1991) Bistatic Radar, Technology Service Corporation, US. 9.12 Cherniakov, M., Tao, Z. and Plakidis, E. (2003) Analysis of space-surface interferometric bistatic radar, in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS’03), pp. 778–80. 9.13 He, X., Cherniakov, M. and Tao, Z. (2005) Signal detectability in SS-BSAR with GNSS non-cooperative transmitter, IEE Proc. Radar, Sonar and Navigation, 152 (3), 124–32. 9.14 He, X., Tao, Z. and Cherniakov, M. (2004) Interference level evaluation in SS-BSAR with GNSS non-cooperative transmitter, IEE Electronic Letters, 40 (19), 1222–3. 9.15 Skolnik, M. (1990) Radar Handbook, McGraw Hill, New York. 9.16 Pestriakov, B. (ed.) (1973) Pseudo Random Signals in Data Transmission Systems. Soviet Radio, Moscow [in Russian]. 9.17 ESA (2002) Galileo system test bed V2 navigation signal-in-space ICD, ESA-APPNGGSTBV2-SS-SPEC-PL-00271. 9.18 Cherniakov, M., Saini, R., Zuo, R. and Antoniou, M. (2005) Bistatic synthetic aperture radar (BSAR) with transmitters of opportunity, J. of Defence Science, 10 (3), 136–40. 9.19 Cherniakov, M., Saini, R., Antoniou, M., Zuo, R. and Edwards, J. (2006) SS-BSAR with transmitter of opportunity – practical aspects, in 3rd EMRS DTC Technical Conference, Edinburgh, UK. 9.20 Cherniakov, M., Saini, R., Antoniou, M., Zuo, R. and Edwards, J. (2006) Modified range– Doppler algorithm for space-surface BSAR imaging, in Radar Conference, China. 9.21 Cherniakov, M., Antoniou, M., Saini, R., Zuo, R. and Edwards, J. (2006) Space-surface BSAR – analytical and experimental study, in EuSAR Conference, Dresden, Germany. 9.22 Cherniakov, M., Saini, R., Antoniou, M., Zuo, R. and Edwards, J. (2006) SS-BSAR with Transmitter of opportunity – practical aspect, in DTC Conference, Edinburgh, UK (A2). 9.23 Antoniou, M. Saini, R., Cherniakov, M. (2007) Results of a Space-Surface Bistatic SAR image formation algorithm, IEEE Trans., GRS-45, 3359–3371.

10 Ionospheric Studies John D. Sahr

10.1 INTRODUCTION In 1901 Marconi succeeded in communicating across the Atlantic using radio waves. This remarkable feat presented an immediate puzzle, because there was no propagation path known that was strong enough to support the communications link. In 1902 Kenelly and Heaviside independently suggested the existence of a conducting layer in the upper atmosphere that could redirect radio waves back to the Earth’s surface. In modern terms the ionized portion of the Earth’s atmosphere is called the ionosphere, but a strong theory of the radio frequency behaviour of ionized gases was not available until the works of Debye and Landau in the 1920s and 1930s. The radio methods of the early 1900s nevertheless permitted strong inference about the ionosphere. The useful reception of radio signals from large distances implied the existence of some refractive or reflective or scattering mechanism in the upper atmosphere that could redirect sky waves back to the Earth’s surface. The majority of wave redirection occurred at altitudes above 100 km, which could be inferred from estimates of angle of arrival. More direct, time-of-flight measurements with pulsed radar systems began in 1926 with Breit and Tuve [10.1]. The descendents of that instrument are known collectively as ionosondes [10.2]; they are widely distributed and have been in constant use for decades.1 The earliest ionospheric instruments (including that of Breit and Tuve) were bistatic by necessity; technology limitations precluded sharing a single antenna for transmit and receive. Furthermore, radio communications technology is intrinsically bistatic. By the Second World War, necessary technologies for monostatic radar had improved greatly, and indeed monostatic radar dominates today’s radar technology. Monostatic radars have a tremendous logistic advantage and are now generally simpler than bistatic systems. However, recent technology 1

Ionosonde data from the past 50 years is available from the National Geophysical Data Center, http:// www.ngdc.noaa.gov/stp/IONO/ionogram.html.

Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

Edited by M. Cherniakov

• 364

IONOSPHERIC STUDIES

developments have addressed several cost and complexity issues associated with bistatic radar systems:

r global positioning system satellites, which tremendously simplify time and frequency transport over planetary scales;

r very high speed, high dynamic range analogue-to-digital converters; r digital receivers, which replace analogue components with ‘exact’ digital calculations; r tremendous improvements in computing power. Improvements in computational power have made it possible to forego the transmitter altogether, by using transmitters of opportunity. Such radar systems are called ‘passive,’ although their data product arises by the same mechanism as in active radars: a target scatters incident radio waves and the scattered waves contain information about the location, size and motion of the target. Although a passive system is in some ways more complex than a conventional radar, it costs little to procure and little to operate, it is safe, it generates no radio interference and ultimately passes the ‘radar Turing test’ in that the data product is indistinguishable from that of a conventional radar. It is important that the aerospace community be aware of the ionospheric applications of passive radar. The scattering cross-section of ionospheric turbulence is comparable to that of large aircraft, and because the illumination is continuous, ionospheric clutter will be observed over all ranges when it is present. The concept of Swerling target models [10.3] is not frequently used in ionospheric physics. However, for the purposes of this document, ionospheric targets could be loosely considered to be intermediate between Swerling models 3 and 4. The target will certainly decorrelate during a time period of any mechanically scanned antenna, but may be sufficiently correlated to permit some coherent processing. Typical correlation times at 100 MHz are 5 to 50 ms. Aerospace radars are often sufficiently sensitive to detect large- and small-scale density structures in the ionized gases found in the upper atmosphere, or ionosphere. Most of the time the ionosphere is fairly benign, because most long-range radars operate at relatively high frequencies, well above the ‘plasma frequency’ associated with refraction and reflection detected by medium-frequency (MF) ionosondes. When the ionosphere becomes turbulent it can be a source of very strong radio scatter – useful and interesting for the ionospheric physicist, but generally deleterious for aerospace radar operations. Ground-based HF, VHF and UHF radars provide some of the best coverage and richest data sets for ionospheric studies, for which the scientific record is approaching a century’s duration. Radar is particularly useful for study of the ionosphere below 250 km, because atmospheric drag restricts the duration of satellite missions. Although the study of ionospheric radio scatter is fascinating in its own right, this volume is intended to serve the aerospace radar systems community. Emphasis will be given to the principle features of the ionosphere which will affect sensitive, long-range radar systems. Most of the comments will apply equally to monostatic and bistatic radar systems, although there are some subtle issues that separate bistatic and monostatic operations. The content of this chapter can be summarized as follows:

r Large radar systems whose power–aperture product exceeds about 1010 W m2 will experience the (weak) effect of Thomson, or incoherent scatter, at all times. The effects will be most noticable throughout the VHF and UHF spectrum.

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r Radar systems whose operating frequency is less than 50 MHz will experience significant bulk refraction, especially in daytime, and especially at low latitudes.

r Radar systems whose operating frequency is less than 100 MHz will occasionally experience severe daytime absorption associated with bright X-ray flares from the Sun, and occasionally from very bright X-ray emissions from elsewhere in the galaxy.

r Radar systems whose operating frequency is less than 3 GHz will occasionally experience

very strong scatter from the ionosphere. This scatter arises from ‘field-aligned irregularities’. This plasma turbulence is highly anisotropic, and quite variable; it depends upon time of day, time of year, latitude, longitude and solar wind parameters. The phenomenon is much stronger at low frequencies than at high frequencies. In this chapter emphasis will be put on the role of field-aligned irregularities (FAI) that have a very large scattering cross-section. Then a description of the large-scale structure of the ionosphere will be given, followed by small-scale field-aligned irregularities. Then a short tour of radio wave propagation will be provided through a collisional magneto-plasma, and the Bragg scatter mechanism will be introduced. A summary of ionospheric observation instruments and capabilities will be presented, as well as a tour of indices of ionospheric activity.

10.2 THE IONOSPHERE AND UPPER ATMOSPHERE The ionosphere envelopes the Earth, coexisting with the neutral atmosphere, and is detectable by radio methods at altitudes above about 75 km. A remarkable variety of quantum mechanical, chemical, photochemical, acoustic, electromagnetic and dynamical behaviour occur in the ionosphere. These processes affect the operation of long-range radar systems in various ways. The main features of the ionosphere can be explained as follows:

r Plasma is created primarily through X-ray and ultraviolet photons from the Sun; additional plasma is created by energetic particle precipitation and meteor ablation provides a minor source of ionization; very energetic X-ray bursts on other stars can create detectable ionization.

r Plasma is destroyed through chemical reactions, the rates of which depend very strongly upon the ion species and neutral density.

r Large-scale plasma density structures significantly refract radio waves at frequencies up to about 50 MHz.

r Small-scale, magnetic field aligned plasma density irregularities scatter radio waves through large angles at frequencies up to 1 GHz.

r Plasma is transported and circulated at horizontal speeds that may exceed 1 km/s, and at vertical speeds that may exceed 100 m/s. Sources of transport include co-rotation of plasma, diurnal thermal forcing and solar wind perturbations.

r Plasma instabilities cause spontaneous, natural emission of electromagnetic waves. r Low-altitude plasmas can be very lossy to radio waves traversing the region, causing significant absorption.

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The structure of the ionosphere is briefly summarized below. Interested readers should refer to a number of textbooks [10.4–10.7].

10.2.1 Gross Structure of the Ionosphere In this section the vertical and latitudinal structure of the ionosphere is briefly described. Extended discussion of the material in this section can be found in References [10.4] to [10.6]. 10.2.1.1 Vertical Structure The first satisfying theory of the vertical distribution of plasma in the ionosphere was developed by Chapman in 1931 [10.8, 10.9]. Fundamentally, solar ultraviolet and X-ray photons ionize atoms and molecules in the upper atmosphere, while the neutral gas catalyses chemical recombination of ions and electrons. An equilibrium distribution results from the limited budget of ionizing photons available, and the exponentially increasing density of the neutral atmosphere (with depth). Chapman’s theory predicts a distribution of plasma with height: N (z + z M ) = N0 exp(1 − z/H − e−z/H ).

(10.1)

Here N0 is the peak electron concentration (approximately 1 × 1012 m−3 , H is the ‘scale height’ (approximately 10 km) of the atmosphere and z M is the altitude of the peak density (about 350 km). Chapman’s theory produces a very good first model of ionospheric density, with the following main features: a slowly decaying topside density and a rapid reduction in the bottomside density. In reality the ionospheric profiles are more complicated, perhaps with several local maxima, for photochemical and dynamical reasons described below. Nevertheless, Chapman’s theory has proved durable, and it is common to use functions of the form of Equation (10.1) for ionospheric models such as the international reference ionosphere (IRI) [10.10] (see Section 10.2.2). A sketch of the ionospheric density profile is provided in Figure 10.1. The D region The D region is the lowest region of ionization in the atmosphere, which has a conventional upper boundary at an altitude of about 90 km. It is rarely present at night, because it requires an ample supply of photons to provide any ionization. In this altitude region, most ions are molecular; some are even aerosols, and these aerosols may have net negative charge. In the upper D region a significant fraction of the ions are atomic metals, notably sodium and iron (easily detected by optical means from the ground), which are deposited by meteor ablation. As monatomic metallic species with low ionization potentials, the metallic ions are much longer lived than the molecular ions, and thus are especially prevalent during the night. D region concentration, and radio absorption, is enhanced by bright solar X-ray flares. Occasionally gamma ray flares from beyond the solar system are bright enough to enhance ionization in the D region.2 Charged particles in the D region collide very frequently with the 2

On 27 December 2004, a tremendous gamma ray burst on the opposite side of the Milky Way and iononized the D region at a significant level; see http://www.physorg.com/news3113.html [10.11].

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1000

Altitude, km

Night

Day

600

350 150 100

F region E valley E region D region

104 105 106 Electron Concentration, cm−3

Figure 10.1 Representative daytime (solid) and night-time (dashed) plasma concentration at midlatitudes. The actual concentration can vary widely from these values during magnetic storms

far more dense neutral gas. For this reason, D region plasmas exhibit little of the complex plasma physics processes found at higher altitudes. Because the loss of tangent of collisional plasmas is greatest at low frequencies, D region effects should be negligible for radars operating at frequencies above 100 MHz. However, HF over-the-horizon (OTH) radars may be severely affected by absorption from enhanced D region ionization. The E region During the daytime, the plasma at altitudes of 90 to 150 km is predominantly a molecular plasma consisting of NO+ and O+ 2 in approximately equal concentration. Molecular nitrogen is the dominant neutral species at this altitude, but fast chemical reactions rapidly remove N+ 2 [10.4]. Daytime plasma concentration is of the order 1011 m−3 and the ion temperature varies between 250 K at 90 km and 1000 K at 200 km. The temperature and composition lead to an ion sound speed of the order of 400 m/s near 100 km. At night photoionization ceases and the molecular ions rapidly recombine, removing much of the plasma. This process takes place in a few seconds to a few minutes. At high latitudes new plasma can be created through impact ionization by energetic particles streaming in from higher altitudes. Long-lived metallic plasmas can occasionally be found in surprisingly dense, thin layers in the lower E region (ca. 100 km). These plasmas are composed of materials deposited by meteor ablation. As the metal ions are atomic and easily ionized, their recombination rates are slow [10.4]. Furthermore, neutral wind shears and tilted magnetic fields create a dynamical ‘sweeping’ effect, which can concentrate the metallic plasma into layers whose thickness is a few hundred metres. These layers are sometimes called ‘sporadic E’ layers in the context of radio observations via ionosondes [10.2]. Sodium and other metals may also be observed using ground-based fluorescence lidar systems [10.12].

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The E region has sufficiently high plasma concentration and sufficiently low collision frequencies that plasma electrodynamic processes occur. Below about 130 km, the ions collide frequently with the background neutral gas, but the electrons are strongly magnetized. Thus when an electric field is applied to the E region, a strong electron Hall current flows. If the applied electric field is sufficiently large (about 20 mV/m at high latitude and about 10 mV/m at the equator), the electron Hall drift speed can exceed the ion acoustic speed. The F region The F region extends from about 150 km up to about 1200 km, merging smoothly into the protonosphere above. The F region is primarily an atomic plasma, consisting of O+ below 800 km and H+ above. Recently significant He+ layers have been detected with incoherent scatter radars [10.13]. The ionosphere is never hot enough to support a significant population of doubly ionized species. The F region contains the highest electron concentration, at a peak that is typically 300– 450 km in altitude (lower in the daytime, higher at night). During the daytime, the plasma production is greatest at about 200 km, but during the night time recombination erodes the bottom of the F region, leaving the high-altitude plasma through the night. It is worth mentioning that low Earth orbit satellites are immersed in the F region, and that the F region is well-probed in situ with satellites.3 The protonosphere At even higher altitudes (i.e. above 1200 km or so) the ionosphere consists of a more tenuous hydrogen plasma – protons and electrons. This plasma is only weakly affected by collisions and is strongly affected by direct electrodynamic and thermal forcing from the magnetosphere. The protonosphere is the highest altitude plasma that co-rotates with the Earth; it contains the van Allen radiation belts4 [10.7], which are regions of very high temperature plasma that are trapped via the natural magnetic bottle5 of the Earth’s ionosphere. The protonosphere should have a neglible affect on almost all radio systems, but the van Allen belts are a significant radiation exposure challenge for spacecraft traversing these regions.

10.2.1.2 Magnetic Latitude The ionospheric plasma near the Earth is a ‘low beta’ plasma, which means that the Earth’s magnetic field is strong enough to sweep the plasma along with the rotation of the Earth. The magnetic field of the Earth is (to first order) an offset, tilted dipole; the north magnetic pole lies about 10◦ away from the rotational magnetic pole, in northern Canada, while the south magnetic pole lies about 25◦ from the pole.6

3 4 5 6

A reasonably up-to-date list of satellites that sample the ionosphere can be found at http://space.rice.edu/ISTP/\#Sat. cf. http://en.wikipedia.org/wiki/Van Allen Belts. A configuration of magnetic field in which a central weak magnetic field is bordered by strong magnetic fields. See maps of the magnetic field strength, declination and ‘dip angle’ in Reference [10.14].

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The Earth’s magnetic field wanders, and occasionally reverses sign. Since 1950 it has been frequently measured and modelled. The international geomagnetic reference field (IGRF) is the principal model of the Earth’s magnetic field used in geophysics;7 it is reasonably accurate, and widely used. The magnetic latitude is (roughly) the latitude computed with respect to the magnetic poles, rather than the rotational poles. Because the north magnetic pole is tilted towards the American sector, phenomena such as the Northern Lights are common as far south as the US–Canada border (49 N) while very rarely observed at the same latitude in the Asian sector. The magnetic field orientation is critically important in understanding the occurrence and location of field aligned irregularites (see Section 10.2.3). High latitudes At magnetic latitudes greater than about 65 N and 65 S, the magnetic field lines are ‘open’ and extend deeply into the Earth’s magnetotail. Very strong, generally anti-sunward convection of the plasma occurs in this region. Because the magnetic field lines are so steeply inclined, only HF OTH radars will detect field-aligned irregularities. The SuperDARN OTH radar system8 provides excellent coverage of high-latitude convection, by tracking decameter-scale field-aligned irregularities in F region plasma. The auroral oval The auroral oval marks the transition from open to closed magnetic field lines. The electric fields may be quite large (e.g. greater than 20 mV/m), leading to plasma drifts greater than 300 m/s. In the E region, the ions are collisionally bound but the electrons are not. This leads to substantial generation of large-amplitude density perturbations of metre and decametre size. The auroral zone is not fixed in latitude. When the solar wind

r increases in concentration, r increases in velocity, r changes from mostly northward to mostly southward orientation, then the auroral ovals (north and south) move towards the equator. Such events correspond to ‘magnetic storms/substorms’ and there are increases in the values of several geomagnetic activity indices, such as the K and Kp indices9 ). The subauroral zone Immediately equatorward of the auroral oval is a region of closed field lines, which are nevertheless strongly influenced by the high electric fields and convection of the auroral oval. In recent years the phenomena of subauroral polarization streams (SAPS) has been identified as a frequent feature of the American sector [10.15]. This phenomenon appears to be a significant 7 8 9

See http://modelweb.gsfc.nasa.gov/models/igrf.html. See http://superdarn.jhuapl.edu/. See http://www.sec.noaa.gov/info/Kindex.html.

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source of scatter observed by coherent scatter radars near the US–Canada border, certinly including the Manastash Ridge radar, as well as some operations of the Cornell University portable radar interferometer (CUPRI). Midlatitudes In magnetic latitudes ranging from about 15 to 45◦ north and south of the magnetic equator, the ionosphere is usually less susceptible to disturbance. At E region altitudes it is possible to find sporadic E layers, as well as the recently identified ‘quasi-periodic echoes’ with decametre wavelengths, but on the whole the midlatitude ionosphere is relatively benign. Equatorial zone The equatorial region of the ionosphere might be expected to be even more calm than midlatitudes, but the opposite is true. The nearly horizontal magnetic field provides a platform upon which the ionospheric plasma can rest. Interactions between the neutral atmosphere and the ionosphere create E and F region dynamos, which lead to the creation of remarkably high amplitude field-aligned irregularities in both the E and F regions.

10.2.2 Ionospheric Models Standard models of the ionosphere have been created to serve a variety of purposes. They can be classified as empirical, semi-empirical, physics-based and data-driven. An extensive list of models is available from the NASA Goddard Space Flight Center.10 Empirical models such as the international reference ionosphere (IRI)11 are fairly useful for obtaining a general idea of the ionospheric structure, but it should be emphasized that IRI is an average model derived from observations. The substantial variability of the ionosphere means that an average parameter value may be less meaningful than hoped, in the sense that the toss of a fair coin is not well described by an average value. The thermospheric general circulation model (TGCM) is a physics-based global circulation model for the upper atmosphere, which does a reasonably good job of modelling the ionosphere, although it does require high-performance computers to run with useful speed.12

10.2.3 Fine Structure, Field-Aligned Density Irregularities Plasma density irregularities in the ionosphere cause large-angle Bragg-like scatter of radio waves at frequencies up to and beyond 1 GHz [10.16]. Although these irregularities provide a fascinating opportunity for research, these phenomena are generally deleterious to transionospheric radio communications and navigation, as well as a source of clutter to HF, VHF and UHF radars.

10 11 12

See http://modelweb.gsfc.nasa.gov/. See http://modelweb.gsfc.nasa.gov/ionos/iri.html. See http://web.hao.ucar.edu/public/research/tiso/tgcm/tgcm.html.

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Here the main ionospheric features that result in high-amplitude scatter in the ionosphere are described. Rather than dwelling on the details of plasma theory, the main physical processes will be indicated and the results summarized. 10.2.3.1 Electron and Ion Dynamics Although the plasma physics of the ionosphere is rich, complicated and still under study, the strong scatter of HF, VHF and UHF scatter results from the following (simplified) situation:

r The

electron fluid is highly magnetized, and thus the electron mobility is extremely anisotropic. In particular, the electrons can move freely along the ambient magnetic field.

r The enormous mobility of the electrons creates highly elongated density structures parallel to the magnetic field, called ‘field-aligned irregularities’.

r Incident radio waves drive displacement currents in the electron fluid, and these currents are scattered by the density irregularities, resulting in large-angle Bragg scatter. 10.2.3.2 E Region Plasma Irregularities In the lower ionosphere, large-amplitude plasma sound waves can arise from the Farley– Buneman instability [10.17–10.19], in which a magnetized electron fluid undergoes a large Hall drift through a relatively stationary ion fluid. When an electric field is imposed upon the lower ionosphere the electron fluid drifts through the ion fluid at the Hall drift speed, which is given as follows: vH =

E×B . |B|2

(10.2)

The magnitude of the Hall drift is E/B; at high latitudes B ∼ 55 000 nT and near the Earth’s equator the magnetic field is about half as strong, about 27 000 nT. The plasma will be stable as long as the Hall drift is slower than the local ion acoustic speed Cs , given by kB γi Ti + kB γe Te Cs = , (10.3) mi where kB is Boltzmann’s constant, γe,i are the specific heat ratios for electrons (∼5/3) and ions (∼1) and Te,i are the temperatures of the electron and ion fluids (which can be quite different). + The ion mass m i reflects that of the principle E region ions, O+ 2 and NO , with a mass of about 30 AMU. Typical values for the ion acoustic speed are 300–400 m/s near 105 km. Given these magnetic field strengths and ion acoustic speeds, it can be seen that the threshold electric field for irregularities at high latitudes is about 20 mV/m, and at low latitudes, about 10 mV/m. At high latitudes, such electric fields are frequently found in the auroral oval (about 65 N and 65 S), especially in the evening sector (ca. 2000–2400 local time) and somewhat less frequently just after midnight (0000–0400 local time). This region of high current is often called the auroral electrojet.

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Near the Earth’s magnetic equator the conditions for the Farley–Buneman instability occur essentially every day, in a region known as the equatorial electrojet. The region of instability extends for about 200 km north and south of the magnetic equator. During magnetically disturbed periods (from solar wind forcing), the auroral ovals expand towards the equator, bringing the irregularities with them and making the irregularities occur over more hours of local time. 10.2.3.3 Midlatitude Sporadic E Given the physical mechanisms described above, it would not ordinarily be expected that many irregularities exist at midlatitudes. However, deposition of meteoritic metallic ions and wind shears can conspire to create relatively thin, relatively dense ionization layers. Although the ambient electric fields are relatively low, sharp density gradients provide another source of free energy that can drive irregularities. Unlike the Hall instability, however, a density gradient favours longer wavelength irregularity generation; fairly sensitive radars are needed to detect midlatitude sporadic E layer irregularities at frequencies above 50 MHz [10.20, 10.21]. Because the microphysics are similar, sporadic E region irregularities are highly field aligned. Occasionally the sporadic E echoes occur with a several minute quasi-periodicity, perhaps associated with internal gravity (bouyancy) waves in the mesosphere. The quasiperiodic echoes (QPE) are nevertheless midlatitude sporadic E irregularities [10.22]. 10.2.3.4 F Region Irregularities, ‘Spread F’ A completely different field-aligned plasma instability occurs at higher altitudes and low (magnetic) latitudes. Roughly speaking, the irregularity arises as a ‘heavy fluid over light fluid’ instability; the plasma ‘falls’ and voids or bubbles rise up through it (see Reference [10.23]). The phenomenon is frequently divided into two classes: the ‘bottomside’ and ‘topside’ forms. The physics of the bottomside and topside differ to some extent, with the bottomside (below 350 km altitude) irregularities having ‘collisional’ dynamics and the topside (above 350 km altitude) irregularities having ‘inertial’ dynamics. When the phenomenon occurs in a strong form, it is possible for metre-scale irregularities to exist from 200 to perhaps 1500 km in altitude; it is a spectacular phenomenon. In recent years the radio imaging of these irregularities has become quite sophisticated [10.24]; however, the precise origin of the irregularities has resisted solution. The basic issue is that the present understanding of the plasma physics leads to instability growth rates that are too slow to account for the echoes; some large amplitude seed must provoke the echoes. This ‘seeding’ phenomenon has not been identified. Finally, F region irregularities are quite seasonally dependent, and the seasonal dependence itself varies with magnitic longitude. For example, in the American sector, spread F occurs primarily near the equinoxes; however, the seasonal dependence is different in other longitudes. Scintillations F region plasma irregularities are the principal source of ionospheric scintillations, or fluctuations in signal strength of radio waves traversing the ionosphere. Such scintillations have been studied for decades and remain important as they deleteriously affect transionospheric communications, navigation, surveillance and radio astronomy applications.

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The United States is planning to launch a new satellite instrument with a low inclination F region orbit, specially designed to study this plasma environment.13

10.2.3.5 Meteors and Meteor Trails Each year, several million kg of meteoritic material impacts the Earth [10.25, 10.26]. Fortunately, most of the influx is in the form of dust particles whose mass is well under a microgram. With typical velocities of the order 50 km/s, these meteors nevertheless release significant energy into the upper atmosphere. Among other things, they form plasma columns many km long as they strike the upper atmosphere. The influx of meteors is sufficiently high to support reliable transport of modest data rates over thousand-kilometre links,14 and considering its antiquity, meteor burst communications is a surprisingly robust field. Micrometeors occur most frequently at dawn, where they are swept up by the Earth in its orbital path, and least frequently at dusk. Very high performance radars (e.g. Arecibo, Jicamarca, ALTAIR) can detect scatter from the compact plasmoid around the decelerating meteor – the ‘head echo’ – whereas more modest radars will primarily observe the plasma wake or trail. Radio scatter from a meteor trail occurs by two mechanisms: Fresnel or specular scatter from the whole trail and Bragg scatter from irregularities that emerge on the very high density gradients produced by the trail. Interestingly, high-performance radars do not observe elevated scatter rates from head echoes during meteor showers,15 whereas meteor scatter radars that observe the trails do observe additional scatter during showers. This may very well be due to the small field-ofview of high-performance radars and the large field-of-view of smaller, coherent radars.

10.2.4 Radio Interaction with the Ionosphere 10.2.4.1 Absorption In the D region, electron collisions with the neutral gas occur at a high enough rate to cause significant ohmic loss of radio waves under two conditions:

r There must be higher than usual electron concentration in the D region. r The radio frequency must be lower than about 50 MHz. This phenomenon will be well known to operators of HF over-the-horizon (OTH) radars. It is, however, useful to point out that high D region electron concentration usually occurs on the dayside of the Earth. When strong X-ray bursts occur on the Sun, the excess ionizing radiation can introduce substantial new free electron production. On occasion, bright gamma ray bursts from other stars can modify the structure of the ionosphere; there was a recent example in December 2004 [10.27, 10.28]. 13 14 15

See the Communication/Navigation Outage Forecasting System (C/NOFS), http://www.vs.afrl.af.mil/Product Lines/CNOFS. See http://en.wikipedia.org/wiki/Meteor scatter. An excellent meteor shower calendar is provided by Gary Kronk at http://comets.amsmeteors.org.

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At high latitudes it is possible for energetic particles streaming along field lines to create excess low altitude ionization. There are calibrated radio receivers that measure the relative ionospheric opacity (riometers) to detect absorption in the ionosphere [10.2, 10.29]. Also, a fairly nice absorption data product is provided by the NOAA SEC.16

10.2.4.2 Refraction The presence of significant quantities of magnetized free electrons in the ionosphere provides significant opportunity for refraction and reflection. The details are quite complex at frequencies below about 50 MHz, as the electromagnetic normal modes and polarizations are not degenerate (as they are in air or vacuum). The details are certainly well known to the HF OTH community, and a classical presentation of the issues can be found in the text by Budden [10.30]. For radio waves with a frequency greater than about 50 MHz, the high-frequency limit of the effect of bulk, large-scale ionization can be expressed in the dielectric function of plasmas, as follows: 2 fp n ≈ 1− , (10.4) f f p ≈ 9 Ne .

(10.5)

Here Ne is the plasma concentration in MKS units (m−3 ), and f p is the ‘plasma frequency’, which is of the order 10 MHz at the peak daytime density of the ionosphere. At frequencies below the plasma frequency, radio waves will experience total internal reflection and return to the Earth’s surface.

10.2.4.3 Bragg Scatter The total internal reflection mechanism is not capable of explaining the large-angle scatter, and indeed backscatter, of radio waves at frequencies up to and beyond 1 GHz. Also, the plasma cannot support concentration gradients that are large enough to permit substantial Fresnel reflection from step changes in dielectric strength. Thus, the observation of large angle scatter at VHF and UHF frequencies requires a new physical mechanism. Ionospheric plasma can become structured with ion acoustic turbulence, and this density structure then provides a basis for Bragg scatter. Given an incident plane wave with the wavevector ki and frequency ωi , there will be a significant amount of electromagnetic scattering at wavenumber ks and frequency ωs from an acoustic density perturbation with wavenumber ka and frequency ωa when the following conditions hold: ki = ks + ka , ωi = ωs + ωa . 16

See http://sec.noaa.gov/tr plots/dregion.html.

(10.6) (10.7)

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These have a quantum mechanical analog as conservation of momentum and energy. As ωi,s ωa , this means that ωi ∼ ωs . Because the incident and scattered waves are electromagnetic and their frequencies are nearly the same, this implies further that ki ∼ ks . In the case of backscatter, ki = −ks so that ka = 2ki . In other words, radio waves with wavelength λ are strongly backscattered from acoustic waves with wavelength λ/2. Although the argument looks casual, it can be justified in mathematical detail [10.31]. In general, radio waves whose frequency is considerably higher than the plasma frequency can be scattered by plasma density turbulence whose scale size is comparable to the wavelength. Field alignedness

The ionosphere above 80 km altitude has highly magnetized electrons. The magnetic field impedes the flow of current across the magnetic field lines, but the electrons can stream easily along the magnetic field lines. Any plasma density perturbation will rapidly diffuse along the magnetic field, but only slowly diffuse across the magnetic field. Thus, all ionospheric density irregularities become highly elongated and are said to be ‘field-aligned’. The amount of alignment can be quite extreme; kilometre-scale irregularities are known to stretch many thousands of km from the northern to southern hemispheres, producing approximate mirror images in auroral forms and airglow. Very precise interferometric observations at Jicamarca [10.32] show that the vast majority of metre-scale E region irregularities are aligned within about half a degree of the magnetic field. The alignment is even stronger in the F region. The strong implications of field-alignedness are evident in Figure 10.2. Estimates of scattering cross-section Smaller HF and VHF radars are rarely well calibrated in amplitude, but it is possible to compare the relative scattering cross-section with other targets. The CUPRI radar frequently observed commercial aircraft at ranges of 100 km and auroral turbulence having comparable scattered signal strength at ranges beyond 500 km. Assuming that the auroral turbulence and aircraft were point scatterers, this implies that the larger meteor scatter cross-section was of the order of 25 dB greater than that of commercial aircraft, perhaps104 m2 or +40 dB sm. However, as a volume scatterer, this estimate must be qualified by the size of the scattering volume. The scattering volume for plasma irregularities is ill-determined. The limits of the scattering volume are almost certainly between 100 and 120 km altitude, and the slant range is well determined by the radar operating mode, but coherent radars frequently have a fairly wide field of view in the azimuth. A question is, therefore: do the irregularities fill the beam in the azimuth or not? Some interferometric experiments suggest that the azimuth is constrained to just a few km. Ultimately the scattering volume is, for a radar like CUPRI, perhaps 1000 cubic km, or about 1012 m2 . Thus the volume-scattering cross-section would be about σv ≈ 10−8

m2 m2 = 10 . m3 km3

(10.8)

It is worth comparing this scattering cross-section to the background Thomson scattering cross-section. For a background electron concentration of 1011 e/m3 and an electron scattering

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225° 60°

IONOSPHERIC STUDIES

230°

235°

240°

245°

250°

255° 60°

1

1

1200

00

12

55°

0

55° 0

1

00

12

1

1

1 400

50°

50°

0 –1

400

Seattle TX

Ellensburg RX

45° 225°

230°

235°

240°

245°

250°

45° 255°

Figure 10.2 A map of the bistatic range and magnetic aspect angle. There are two sets of curves. The elliptical curves with Seattle TX and Ellensburg RX as foci are curves of a constant bistatic range at 200, 400, . . . , 1200 km. The ovals centred on the BC–Alberta border are curves of constant aspect angle for scatter at 100 km altitude, marked in 1◦ increments. Although scatterers may fill the entire region, the strongly field-aligned nature of the irregularities implies that all the echoes likely arrive from the ±1◦ band

cross-section of 6.3 × 10−29 m2 /m3 , a Thomson scattering cross-section of approximately σis ≈ 6.3 × 10−18 m2 /m3 would be expected, which is about 8 orders of magnitude smaller than the coherent scatter cross-section. It is possible that the effective scattering volume of coherent scatter is significantly overstated by large factors (100 or more), which would lead to significantly larger scattering cross-sections. However, the fact remains that coherent scatter is far stronger than Thomson or thermal scatter [10.33].

Doppler characteristics Metre-scale E region irregularities are essentially sound waves, with typical velocities of about 400 m/s. Because the sound waves have a very large amplitude, they interact in a nonlinear fashion, which causes spectral broadening and coupling to ordinarily damped waves. Hamza and St-Maurice [10.34, 10.35] have proposed a fairly simple model that (expressed in velocity units) captures this behaviour: V02 + V 2 = Cs2 .

(10.9)

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At frequencies below 50 MHz it is possible for the mean velocity to be very low, V02 Cs2 , but at frequencies of 100 MHz and higher, observations of very low Doppler velocities are rare. At UHF radar frequencies, the mean Doppler velocity seems to conform well to the cosine law, V = k · V d , where V is the observed Doppler velocity, k is the wave vector of the sound wave and V d , is the electron Hall drift velocity vector. This property permits mapping of E region electric fields by UHF radars. (HF radars (e.g. SuperDARN) can map convection fields in the F region by similar reasoning, although the physics is very different.) The minimum Doppler width can be quite small, of the order of 10 m/s; this corresponds to about 15 Hz (at radio wavelengths of 3 m). Equivalently (and importantly for distributed passive radar), this means that the target coherence time is not more than about one tenth of a second. Although meteor trails are caused by 50 km/s particles, the trails themselves drift with the speed of the local wind, which is of the order of 100 m/s in the mesosphere. Ionospheric indices

The complex behaviour of the ionosphere is summarized in a variety of indices derived from spacecraft and ground-based magnetometer measurements. A nice summary of the indices is available.17 To date, no indices are available that directly indicate the presence of scatterers. There is a set of indices derived from perturbations in the Earth’s magnetic field due to large electric currents flowing in the ionosphere and magnetosphere. At high latitude, the auroral or ‘A’ indices are appropriate, with ‘Ae’ being the most useful. At midlatitudes, especially in North America, the Kp index is quite helpful. When Kp exceeds 6, it is likely that E region irregularities can be found near the US–Canada border; when it exceeds 8, the irregularities can be further south. At low (but not equatorial) latitudes, the Dst index provides an indication of magnetic storms due to an enhanced ring current.18

10.2.4.4 Thomson Scatter VHF and UHF radars with very large transmitter power and antenna aperture product will be able to detect scatter from the ambient plasma at all times. In particular, if PT Aeff > 109 W m2 then the radar operators must become familiar with the phenomenon. At operating frequencies above about 3 GHz the phenomenon is less noticeable because the target bandwidth increases tremendously; however, the scattering cross-section is large.

10.2.4.5 Faraday Rotation The magnetized plasma of the ionosphere is a strong Faraday rotating medium, especially at frequencies below about 1 GHz. Long-range radar operators should be aware of this phenomenon for any ray paths that penetrate the ionosphere.

17 18

See http://www.oulu.fi/∼spaceweb/textbook/indices.html. See http://en.wikipedia.org/wiki/Ring current.

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10.3 BISTATIC, PASSIVE RADAR STUDIES 10.3.1 Bistatic Radar Observations of the Ionosphere Almost all ionospheric radars are monostatic for reasons of cost, convenience and logistical complexity. However, there are some bistatic ionospheric radars worth mentioning [10.2]. Bistatic operations can be divided into ‘strong’ and ‘weak’ forms. The latter are not coherent among stations (STARE, SABRE, SuperDARN) but rather fuse data from independent radars with overlapping fields-of-view. However, there are others (SAPPHIRE, EISCAT UHF) that are truly coherent VHF bistatic systems.

10.3.2 The Manastash Ridge Radar The Manastash Ridge Radar19 is also a coherent bistatic radar, but rather than observing scatter from a dedicated transmitter, it observes the scatter of use of transmitters of opportunity at VHF, in particular commercial FM broadcasts. Commercial FM broadcasts are quite useful for ionospheric irregularity research:

r Frequencies below 50 MHz suffer considerable ionospheric refraction. r The scattering cross-section scales roughly as λ4 , so the relatively large wavelength of FM broadcasts is desirable. In principle an analogue TV at VHF and UHF could be used, but the analogue TV signal is highly range-ambiguous due to the high-amplitude horizontal sync pulse. Digital TV broadcasts at 600 MHz have very high ERP and a superb ambiguity function, but the scattering crosssection is low. Also, the high bandwidth requires a substantial increase in computation to extract the signal. From a geophysical perspective, 100 MHz is also interesting because there is a certain disagreement between the extant 50 and 150 MHz data sets. Thus there was a real incentive to look at scatter at an intermediate frequency. As mentioned above, E region irregularity Doppler spectra have a Doppler content up to about 1 kHz, with correlation times in the range of 5–50 ms. Griffiths et al. [10.36] have made a comparative study of the ambiguity functions of a variety of broadcast waveforms. Sahr et al. (personal communication, 2005) have made a fairly detailed study of the short-time ambiguity function of several days’ worth of FM broadcasts. The net result of these studies is that commercial FM broadcasts of music (as opposed to speech) almost always offer excellent range–Doppler ambiguity, with range resolution of the order of 1.5 km or better. 10.3.2.1 Basic Principles of Operation The basic principles of operation for a distributed passive radar for detection of deep fluctuating targets were described by Sahr and Lind in 1997 [10.37]. They built an instrument that began detecting auroral E region scatter in 1998, and upgraded it subsequently in 2001. 19

See \texttt{http://rrsl.ee.washington.edu}.

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By 1997 passive radar had been developed for aerospace applications, in particular by Lockheed Martin, as well as by Griffiths and Howland and coworkers. However, the application to ionospheric physics was novel, and Sahr and coworkers developed a somewhat different strategy for addressing the fundamental engineering challenge of very high dynamic range requirements. To estimate the dynamic range requirements, consider a 20 dB sm target at a range of 100 km from a transmitter, with a passive radar receiver 20 km from the transmitter. If (for the moment) it is assumed that the passive radar receiving antenna is also omnidirectional, then the ratio of the scattered to direct signal is nearly −100 dB. Sahr considered this performance requirement beyond the skill of his laboratory, and so he and his coworkers split the passive radar receiver into two pieces:

r One receiver would be placed near the transmitters, to make a clean copy of the illumination. r Additional receivers would be placed in locations that were not strongly exposed to the direct transmit path, but were exposed to the scattered signal. Sahr and coworkers installed one receiver at the Seattle campus of the University of Washington and a second receiver 150 km to the east, beyond the Cascade Mountains, at the Manastash Ridge (astronomical) Observatory (see Figure 10.3). The resulting system has become known as the Manastash Ridge radar (MRR). Auroral Scatter

Broadcast Transmitter

Cascade Mountains block direct path

Interferometric Scatter Receiver

Reference Receiver internet

Computing at UW

internet

Figure 10.3 A sketch of the coherent distributed receiver system of the Manastash Ridge radar. A commercial FM broadcaster illuminates a reference receiver as well as auroral turbulence. The Cascade Mountain Range largely shields the interferometric scatter receivers, which can then retrieve the weak scatter from the aurora. Control and data transport are provided by computers at the University of Washington

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GPS Synchronization With the wide separation of the receivers, some effort is required to operate the receiver system coherently. This coherence was achieved relatively simply by using global positioning system (GPS) receivers to provide a time and frequency reference. The GPSs that were used provided absolute time accuracy of the order of 100 ns, with a suitably quiet reference oscillator to drive the data acquisition system. As mentioned above, the VHF and UHF ionospheric irregularities have a coherence time that does not exceed one-tenth of a second. Among other things, this means that the coherence time of a distributed system need not exceed one-tenth of a second for entry-level operations. Prior to GPS technology, the standard technique for introducing coherence among distributed systems was to maintain high precision clocks at each site and to have at least one additional ‘traveling clock’ to transfer time and frequency among them. This was an expensive, awkward procedure, which the GPS has largely eliminated. Internet Data Transport For ionospheric applications it is usually not important to achieve low latency, so the data can be time-tagged, recorded to some large capacity medium and then periodically transported for offline processing. However, this is less convenient than immediate electronic transport. The Manastash Ridge Observatory (MRO) is located in a relatively hostile environment and is not continuously staffed. It is a 4 hour drive from Seattle, and the final 10 km are fairly rugged roads. Since electricity is available year round and there is a line-of-sight path to Ellensburg, Washington, and the Central Washington University, a microwave link was installed that permits a 500 kbps full-duplex link. This is insufficient to support the data generating capacity of the receiver (approaching 1 Gbps). However, in a routine surveillance mode, the MRR takes 10 second data bursts each 4 minutes. These data can be continuously downloaded to Seattle for processing. When the ionosphere is especially active, much higher data acquisition is written to disk at the Observatory, which can absorb several days of multiple antenna, 75% duty cycle coverage. These data can then be downloaded gradually after the event. The current practice is to retain full precision (16 bit) in phase and quadrature samples, at a sample rate of 100 ksamples/s, with an effective receiver bandwidth of about 65 kHz. It is well known that the 16 bit samples are excessive; 8 bit and 4 bit samples work extremely well, since the direct transmission is significantly suppressed by the shielding of the Cascade Mountains. 10.3.2.2 Signal Processing As mentioned above, Sahr and Lind [10.37] described the mathematical basis for detecting the power spectrum of a deep fluctuating target, using an analysis based upon correlations in continuous time. Subsequently, Ringer et al. [10.38] made a related study oriented towards discrete point targets in discrete time. The two studies achieve similar results but are clearly geared towards different audiences. Cross ambiguity/range–Doppler estimates The analysis of Sahr and Lind considered the FM signal to be a band-limited Gaussian process, which is white over a bandwidth of approximately 100 kHz. In what follows, x(t) is the

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transmitter illumination and y(t) is the scattered signal. The detection algorithm can proceed in several ways. The report of Sahr and Lind suggests forming the target correlation function by range, but that is computationally inefficient (and essentially intractable as presented). The actual approach taken by the MRR is to perform a decimation or coherent average, followed by a conventional periodogram. Pre-decimation The transmitter bandwidth is of the order of 100 kHz whereas the target bandwidth is of the order of 2 kHz. Thus, the received signal can be coherently averaged by a factor of order 50: yx(t; r ) =

50

y(t + τ )x ∗ (t + τ − r ).

(10.10)

τ =0

It can be shown that yx(t; r ) is a noisy but unbiased estimate of the target scattering amplitude. It is possible to address some spectral shaping by using a window of some kind, but the MRR uses a uniform window for the accumulated samples. The signal yx(t; r ) can then be passed into a conventional periodogram power spectral estimator for each range; an example is shown in Plate 22 (in the colour section). Interferometry for azimuth resolution If the scattered signal is detected on several antennas, then these signals can be cross-correlated in a manner suggested by Farley et al. [10.39], and which has lately become a very mature and powerful technique [10.40]. Meyer and Sahr have implemented this with the MRR [10.41]; an example from the MRR website is provided in Plate 23. The interferometer shows superb azimuth resolution of about 1.5 km at a range of 1000 km, achieved with a baseline of 16λ. Data truncation As mentioned above, when the scattered signal y(t) is relatively free of the transmitter illumination, it is possible to truncate the precision of the scattered signal. There is essentially no penalty for truncating to 8 or 4 bit samples, and even sign-bit-only samples yield very usable spectra. It is important to recall that the geophysical information is carried in the statistics of the scatter more than the particular amplitude of the scatter. Parallel algorithms In the late 1990s when the MRR was first developed, computers were considerably slower. Sahr and Lind used a cluster of computers to compute the cross-ambiguity; the algorithm splits very simply by dicing the processing into subsets of ranges r in yx(t; r ). In typical operation the MRR processes 800 ranges, so there is a large opportunity for straightforward parallelization. By about 2004, desktop computers had become sufficiently fast so that it was no longer necessary for routine operation of the MRR.

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10.3.2.3 System Features and Requirements Since 2001 the MRR receivers have begun to use digital receivers. The RF signals at 100 MHz are directly sampled by digitizers sampling at 56 or 72 MHz. These sample frequencies permit the FM broadcast band to appear unaliased within the Nyquist bandwidth of the samplers. Subsequently, IQ detection and downsampling are performed entirely in the digital domain. When properly operated, it is possible to achieve an instantaneous dynamic range exceeding 90 dB with these digital receiver systems. Proper operation of the data acquisition system requires two signals: a clean sample clock and a precise time reference. Both are provided by dedicated GPS receivers. Moderate-quality GPS receivers are capable of providing an absolute time with an uncertainty of 100 ns or better; this corresponds to a range uncertainty of about 15 metres. As the range resolution of FM is about 1.5 km, this range error is entirely acceptable. Similarly, moderate-quality GPS receivers provide a frequency reference that is accurate to one part in 109 or better. At 100 MHz this corresponds to a 0.1 Hz error, or about 0.15 m/s, which is completely negligible with respect to the typical resolution of about 8 Hz. As a practical matter, the absolute frequency of the reference oscillator is less important than the spectral noise power, as jitter in the sample clock can introduce a very substantial noise floor in high dynamic range systems. Antennas In the split receiver system, antennas of modest gain suffice. For the reference receiver a simple half-wave dipole or discone is completely adequate, as the transmitter signal is quite strong. For the scatter receiver, several antenna types have been used, including a 5 dB i log periodic dipole array (LPDA), a 15-element Yagi–Uda parasitic array (used for interferometry) and more discones. The small LPDA has been the most useful to date because it was placed in a location that protects it from co-channel interference from other broadcasters. The Yagi has been problematic; it is located at the top of a 40 foot tower so that it is exposed to co-channel interference, and it also ‘sails’ in the frequent winds so that it is almost always pointed improperly. Computation The basic signal processing algorithm described above consists of an initial coherent detection followed by an FFT-based periodogram. The digital receivers are operated in such a way that they produce 100 ksamples/s, each sample of which consists of 16 bit inphase and quadrature samples; thus the data rate is 400 kbytes per second, per channel, per antenna. The associated computational burden is dominated by the coherent detection step: 800 ranges of 100 kHz complex multiply–add operations, about 320 million multiply–add operations per second. These can be (and are) carried out in integer arithmetic. Although there is not a tremendous speed advantage for integer versus floating-point mathematics, the use of 16 bit integers, at least initially, halves the data volume that must be brought to the CPU. Once the initial coherent detection is performed, the data are converted to a single precision floating point, for ease of implementation of the FFT. To date there has been no need to perform any space–time adaptive processing (STAP) (e.g. see Reference [10.42]) to remove direct illumination and ground clutter. First, the extended

ABBREVIATIONS

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baseline (150 km and mountain range) reduces the direct illumination to a tolerable level. Second, the ground clutter is undetectable at ranges beyond 200 km, whereas the auroral signatures do not appear before a bistatic slant range of about 350 km. Nevertheless, STAP techniques will be added to the system [10.43]. Site requirements

A useful site will provide sufficient electric power, an appropriate radio field-of-view and network connectivity. In the case of the Manastash Ridge Observatory, the network connectivity is quite limited – about 60 kbytes/s – which is only about a tenth of the bandwidth needed for a single channel. Thus, in routine operations the radar takes data for 10 seconds every 4 minutes. This provides a moderate latency, real-time surveillance mode for auroral scatter. When the ionosphere is active, data are taken almost continuously and buffered up on to local hard disks, which can then be gradually downloaded over several days.

10.4 TRENDS FOR IONOSPHERIC RESEARCH The MRR passive ionospheric radar system has profited from the availability of powerful desktop computers, GPS receivers digital receivers and widespread internet connectivity. More broadly, in ionospheric physics and ‘space weather’ research, there is a growing awareness that computer models are strongly limited by a paucity of real-time data distributed over the globe.20 Passive radar systems provide one attactive means to gather such data cost-effectively, growing on the example of the real-time total electron content (TEC) maps developed from a substantial ground-based GPS receiver system.21

ABBREVIATIONS ALTAIR ARPA CPU CUPRI CWU DASI DB dB sm EISCAT FAI FFT FM GPS HF 20 21

ARPA long-range tracking and identification radar Advanced Research Projects Agency central processing unit Cornell University portable radar interferometer Central Washington University distributed arrays of scientific instruments decibel decibel scattering cross-section referenced to 1 square metre European Incoherent Scatter Consortium field-aligned irregularities fast Fourier transform frequency modulation global positioning system high frequency, 3–30 MHz

See the US National Academies of Science report on ‘Distributed arrays of scientific instruments’, http:// www7.nationalacademies.org/ssb/DASI.pdf. See http://iono.jpl.nasa.gov/latest rti global.html.

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IGRF IRI JPL km Kp LPDA MF MRO MRR NASA NOAA NSF nT OTH QPE RF SABRE SAPPHIRE

international geomagnetic reference field international reference ionosphere Jet Propulsion Laboratory kilometre planetary K index for high-latitude magnetic field disturbance log periodic dipole array medium frequency, 0.3–3 MHz Manastash Ridge Observatory Manastash Ridge radar National Aeronautic and Space Administration National Oceanic and Atmospheric Administration National Science Foundation nanotesla over-the-horizon (radar) quasi-periodic echoes radio frequency Sweden and Britain Radar Experiment Saskatchewan Auroral Polarimetric Phased Array Ionospheric Radar Experiment SAPS subauroral polarization stream STAP space–time adaptive processing STARE Scandinavian Twin Auroral Radar Experiment SuperDARN Super Dual Auroral Radar Network TEC total electron content TGCM thermospheric global circulation model TIEGCM thermosphere ionosphere electrodynamic general circulation model UHF ultra high frequency, 300–3000 MHz UW University of Washington VHF very high frequency, 30–300 MHz

VARIABLES Aeff B Cs E f fp H kB ki,s,a m e,i N0 PT Te,i Vd

effective antenna area magnetic field strength ion acoustic speed electric field strength wave frequency (Hz) plasma frequency scale height Boltzmann’s constant (1.38 × 10−23 J/K) wave number for incident, scattered and irregularities (rad/m) electron and ion mass background or peak electron density (concentration) transmitter power electron and ion temperatures electron drift velocity; mean observed Doppler velocity of irregularities

REFERENCES

VH x(t) y(t) yx(t; r ) γe,i V λ σv σis ωi,s,a

Hall drift velocity signal representing the transmitter illumination scattered signal downsampled time series for the slant range r specific heat ratio for electrons and ions spectral width of coherent scatter, in velocity units wavelength volume scattering cross-section (m2 /m3 ) incoherent (Thomson) scattering cross-section radian frequency for incident, scattered and irregularities (rad/s)

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ACKNOWLEDGEMENTS The author is deeply grateful to the National Science Foundation for its long support of the passive radar effort at the University of Washington, most recently through Grant ATM0310233. Additional support is gratefully acknowledged from NATO NC3 and AFOSR.

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10.12 Friedman, J. S., Tepley, C. A., Raizada, S., Zhou, Q. H., Hedin, J. and Delgado, R. (2003) Potassium Doppler-resonance lidar for the study of the mesosphere and lower thermosphere at the Arecibo Observatory, J. Atmos. Solar-Terr. Phys., 65 (16), 1411–24. 10.13 Gonzalez S. and Sulzer, M. P. (1996) Detection of {He+} layering in the topside ionosphere over Arecibo during equinox solar minimum conditions, Geophysical Research Letters, 23, 2509–12. 10.14 Jursa, A. S. (1985) Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, Washington DC. 10.15 Foster, J. C., Erickson, P. J., Coster, A. J., Goldstein, J. and Rich, F. J. (2002) Ionospheric signatures of plasmaspheric tails, Geophysical Research Letters, DOI: 29(3):10.1029/2002GL015067. 10.16 Leadabrand, R. L., Schlobohm, J. C. and Barron, M. J. (1965) Simultaneous very high frequency and ultra high frequency observations of the aurora at Fraserburgh, Scotland, J. Geophysical Research, 70, 4235. 10.17 Buneman, O. (1963) Excitation of field aligned sound waves by electron streams, Phys. Rev. Letters, 10, 285–7. 10.18 Farley, D. T. (1963) A plasma instability resulting in field-aligned irregularities in the ionosphere, J. Geophysical Research, 68, 6083–97. 10.19 Farley, D. T. (1963) Two-stream plasma instability as a source of irregularities in the ionsphere, Phys. Rev. Letters, 10, 279. 10.20 Chau, J. L. and Woodman, R. F. (1999) Low-latitude quasiperiodic echoes observed with the piura vhf radar in the {E}-region, Geophysical Research Letters, 26, 2167–70. 10.21 Riggin, D., Swartz, W. E., Providakes, J. and Farley, D. T. (1986) Radar studies of long-wavelength waves associated with mid-latitude sporadic E layers, J. Geophysical Research, 91, 8011–24. 10.22 Tsunoda, R. T., Fukao, S. and Yamamoto, M. (1994) On the origin of quasi-periodic radar backscatter from midlatitude sporadic E, Radio Science, 29, 349–65. 10.23 Fejer, B. G. and Kelley, M. C. (1980) Ionospheric irregularities, Rev. Geophysical, 18, 401–54. 10.24 Hysell, D. L. and Woodman, R. F. (1997) Imaging coherent backscatter radar observations of topside equatorial Spread F, Radio Science, 32, 2309. 10.25 Ceplecha, Z., Borovida, J., Elford, W. G., Revelle, D. O., Hawkes, R. L., Porubcan, V. and Simek, M. (1998) Meteor phenomena and bodies, Space Sci. Rev., 84, 327–471. 10.26 Mathews, J. D., Janches, D., Meisel, D. D. and Zhou, Q.-H. (2001) The micrometeoroid mass flux into the upper atmosphere: Arecibo results and a comparison with prior estimates, Geophysical Research Letters, 28, 1929–32. 10.27 Gaenster, B. M., Kouvellotou, C., Gelfand, J. D., Taylor, G. B., Eichler, D., Wijers, R. A. M. J., Granot, J., Ramirez-Ruiz, E., Lyubarsky, Y. E., Hunstead, R. W., CampbellWilson, D., van der Horst, A. J., McLaughlin, M. A., Fender, R. P., Garrett, M. L., Newton-McGee, K. J., Palmer, D. M., Gehrels, N. and Woods, P. M. (2006) An expanding radio nebula produced by a giant flare from the magnetar sgr 1806–20, Nature, 15 (7037), 1104–6. 10.28 Hurley, K., Boggs, S. E., Smith, D. M., Duncan, R. C., Lin, R., Zoglauer, Z., Krucker, S., Hurford, G., Hudson, H., Wigger, C., Hajdas, W., Thompson, C., Mitrofanov, I., Sanin, A., Boynton, W., Fellows, C., von Kienlin, A., Licht, G., Rau, A. and Cline, T.

REFERENCES

10.29

10.30 10.31 10.32 10.33

10.34 10.35

10.36

10.37 10.38

10.39 10.40 10.41

10.42 10.43

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(2005) An exceptionally bright flare from sgr 1806 20 and the origins of short-duration gamma ray bursts, Nature, 434, 1098–103. Hagfors, T., Grill, M. and Honary, F. (2003) Performance comparison of cross correlation and filled aperture imaging riometers, Radio Science, 38 (6), 1109, DOI:10.1029/2003RS002958. Budden, K. G. (1988) The Propagation of Radio Waves, Cambridge University Press. Ishimaru, A. (1978) Wave Propagation and Scattering in Random Media, Academic Press, New York. Kudeki E. and Farley, D. T. (1989) Aspect sensitivity of equatorial electrojet irregularities and theoretical implications, J. Geophysical Research, 94, 426. Foster, J. C., Tetenbaum, D., del Pozo, C. F., St.-Maurice, J.-P. and Moorcroft, D. R. (1992) Aspect angle variations in intensity, phase velocity, and altitude for high-latitude 34-cm E region irregularities, J. Geophysical Research, 97, 8601–17. Hamza A. M. and St.-Maurice, J.-P. (1993) A self consistent fully turbulent theory of auroral E region irregularities, J. Geophysical Research, 98, 11 601. Hamza A. M. and St.-Maurice, J.-P. (1993) A turbulent theoretical framework for the study of current-driven E region irregularities at high latitudes: basic derivation and application to gradient-free situations, J. Geophysical Research, 98, 11 587. Griffiths, H. D., Baker, C. J., Ghaleb, H., Ramakrishnam, R. and Willman, E. (2003) Measurement and analysis of ambiguity functions of off-air signals for passive coherent location, Electronics Letters, 39 (13), 1005–7. Sahr, J. D. and Lind, F. D. (1997) The Manastash Ridge Radar: a passive bistatic radar for upper atmospheric radio science, Radio Science, 32, 2345–58. Ringer, M. A., Frazer, G. J. and Anderson, S. J. (1999) Waveform analysis of transmitters of opportunity for passive radar, Technical Report DSTO-TR-0809, DSTO Electronics and Surveillance Research Laboratory. Farley, D. T., Ierkic, H. M. and Fejer, B. G. (1981) Radar interferometry: a new technique for studying plasma turbulence in the ionosphere, J. Geophysical Research, 86, 1467. Hysell, D. L. (1999) Imaging coherent backscatter radar studies of equatorial spread F, J. Atmos. Solar-Terr. Phys., 61, 701–16. Meyer M. G. and Sahr, J. D. (2004) Passive coherent scatter radar interferometer implementation, observations, and analysis, Radio Science, 39, DOI: 10.1029/2003RS002985. Klemm, R. (2004) Applications of Space-Time Adaptive Processing, IEE, London. Zhou, C. C. (2003) Application and extension of space–time adaptive processing to passive FM radar, PhD Thesis, University of Washington, Seattle, Washington.

Index absolute parallax, defined, 16 Across track time invariant configuration, 162 adaptive cancellation, 262 adaptive noise canceller, 270, 292–293 adjacent path interferences, 354 airborne bistatic SAR, 159–210 Allan variance, 110 along-track interferometry, 69, 95, 98–99, 116, 143–144, 146, 159, 162, 200 along-track time invariant configuration, 161–162 ambiguities, 101, 104, 106, 115, 117, 120, 128–133, 139–142, 252, 264, 270, 275, 287, 304, 322 ambiguity function, 2, 12, 218, 222–223, 228–238, 248, 251, 268, 270–271, 274–284, 297, 315–335, 345, 349, 378 analogue canceller, 262, 269 analogue television, 249–250, 252, 260, 276, 315 antenna synthesis, 216 antenna-fixed reference frame (ARF), 14 aperture synthesis, 169, 215–218, 221, 234, 343–346, 348 Arecibo Observatory, 373 artificial Earth satellites, 215 aspect angle, 208, 376 attitude manoeuvring, 29 Auroral Oval, 369 Auroral Zone, 369 autocorrelation function, 221, 291, 316, 323–324, 350, 353 autofocus techniques, 218 azimuth compression, 343–344, 349, 356

Bistatic Radar: Emerging Technology C 2008 John Wiley & Sons, Ltd

azimuth resolution, 2, 6–9, 12, 37, 78, 88, 124, 140–141, 163, 165, 198, 223, 234–235, 240–241, 343–344 azimuth steering, 36–39, 54, 57, 75, 78–79, 82, 131 baseline estimation, 125–127 batch estimator, 266–267 bearing estimation, 263–264 behavioural philosophy, 40 binary phase shift keying, 318 BISSAT (BIstatic SAR SATellite) mission attitude design and radar pointing design, 78–86 orbit design, 76–78 payload characteristics and architecture, 70–76 radar performance, 86–91 scientific rationale and technical approach, 68–70 BISSAT attitude, 79 BISSAT2000 antenna, 69, 75–76, 81–84 BISSAT2000 polarization, 72 bistatic angle effect on the scattering, 209 bistatic azimuth resolution, 8, 163 bistatic Doppler, 12, 124, 131, 163, 265, 271–273 bistatic image geometry, 12, 19, 185–188 bistatic observation, 1–3, 5, 10, 13, 18, 20, 30, 32, 34, 68, 76, 85–86, 88, 91 bistatic processing, 170 bistatic radar cross section, 1, 68, 159, 252–254 bistatic radar equation, 2, 162, 251–253

Edited by M. Cherniakov

• 390

bistatic radar altimeters, 28 elevation angle, 53 bistatic SAR, 159–210, 219, 235, 285 bistatic synthetic aperture radar (BSAR) geometric parameters and resolutions, 2–8 scientific applications, 8–20 transmitter-target-receiver angle, 2 bistatic time difference of arrival, 297 bistatic triangle, 355–356 body-fixed reference frame (BRF), 14 Bragg resonance condition, 11 Bragg-resonant sea-wave cross-track component, 12 Bragg-scatter, 12, 365, 371, 374–377 broadcast services, 251 bus-based (pitch and yaw), 38 Calibration, 12, 73, 97, 104, 114, 122, 127, 143, 146, 185, 203, 206–208, 264, 304 Carnot and sines theorems, 5 cartwheel concept, 30, 45–48, 161 Cascade Mountains, 379–380 cellphone transmission, 252, 255 central frequency, 73, 204, 341, 349–350 change detection, 11, 98, 144–145 chip rate, 341–342 clock drift, 165, 167, 185, 190–196, 206–207, 210 Clohessy-Wiltshire equations, 49 clutters sidelobes coherence, 98–99, 115–122, 133, 135, 138, 144, 201, 207, 286, 356, 377, 380 coherent integrating interval, 346 coherent orthogonal frequency division multiplexed, 270 coherent processing, 13, 255, 286, 364 collision risks, 41, 103 complex envelope, 219–220, 316, 324–325, 346 computer simulation, 86, 320, 322 continuous pilot, 318–319, 330–331 control signals, 318, 323 COSMO-SkyMed, 28, 32, 67–70, 74, 76–79, 85–86, 88 critical baseline, 100–101, 105, 124, 133, 162, 201 cross ambiguity, 380–381 cross-correlation, 11, 268–269, 271, 290–292, 295–298, 303, 350, 353 cross-platform bistatic interferometric images, 209–210

Index cross-track interferometry, 97–99, 127, 139, 146–147, 159–160, 162 cross-track swath separation, 31, 36–38 2-D correlation function, 350, 353 2-D cross correlation, 350, 353 D region, 366–367 data collection, 162, 219, 269, 291, 299, 303 data vector, 295–296, 300 delay difference, 230–232 delay-Doppler domain, 322, 325 differential BPSK, 318–319 differential ranging, 133 digital audio broadcast, 28, 251, 258, 268, 270, 282, 317 digital beamforming, 115 digital conversion, 73, 247 digital elevation model (DEM), 9, 96–99, 103–105, 111, 113, 116, 125–128, 132–133, 135, 138–139, 143, 145–147, 159–160, 172–173, 175, 179, 188, 194 digital signal processors, 248, 250 digital video broadcast, 268, 315 direct path interference, 290, 340, 345, 350–354 direct signal, 254–257, 260–263, 270, 288, 292, 295, 309 Doppler centroid, 10, 15, 88, 110, 124, 131, 141–142, 161 Doppler frequency, 1, 12, 30, 88, 110, 131, 170–172, 175–176, 179, 186, 190, 225, 276, 278, 280–281, 316, 328–329, 350 Doppler frequency maps, 1 Doppler frequency, at the boresight, 30 Doppler resolution, 224, 240, 248, 274–276, 278–280, 283–287, 296, 302 Doppler shifts, 230, 247, 262–263, 271, 296, 298, 302, 308, 356 Doppler spectrum, 130, 265, 272, 303 Doppler-based resolution, 234 downdusk orbit, 69 dynamic range, 9, 11, 254, 261–262, 269–270, 285, 309, 325, 364, 379, 382 E region, 367–368 E valley, 367 Earth fixed reference frames, 15 Earth’s oblateness, 49 Earth-based receiver, 27–28 Earth-based systems, 27

• 391

Index echo effective bandwidth, 167, 252, 255–256, 292 EKF algorithm, 273 electrojet, 371–372 electronic units’ thermal control, 70, 72 elevation angle, 31, 35, 50, 52–54, 56–58, 76, 79–85, 88, 90, 354, 356 elevation swaths, 53 Engineering Pre-Qualification Model, 69 enhanced payload-based (azimuth and yaw), 38 enhanced payload-based (enpay) mission, 52 enhanced payload-based option, 36–37, 39, 54, 57, 79 Envisat ASAR data, 27 Envisat, 29 equatorial spread F, 372–373 ERS-1 SAR echo ERS-1 SAR, 27, 29 Euler angles, of antenna, 14 F region, 368 Farley-Buneman instability, 371–372 finite impulse response, 294 flux distribution, 342 fly bistatic radars, 44 FM radio, 250, 252, 256–257, 268, 271 Fourier processing, 262, 302 free-flying spacecraft, 29 frequency band, between, 339 Frequency Generator Unit (FGU), 71 frequency modulated, FM radio stations, 250 Galileo system, 340, 346 Gaussian noise, 119, 263, 272, 315 GEO satellite transmitter, 216–217 geometric distortion model, 3, 17–18, 185–188 geostationary Earth orbits (GEO), 216 geosynchronous SAR system, 28 geosynchronous satellite, 27 German TerraSAR-X, 28 global navigation satellite signals, 28 global navigation satellite systems, 339–343 GPS, 2, 12–13, 17, 28, 41–42, 72–73, 76, 110, 126–127, 185, 205, 217–218, 250, 276, 339–340, 342, 380, 382 GPS techniques, 41 gradient drift instability grating lobes, 219 ground moving target indication (GMTI), 95, 97, 99, 105–106, 115, 163, 165

ground range resolutions, of monostatic and bistatic SAR, 3 GSM transmissions, 280 guard intervals, 317–318, 320, 322–323, 328–329

height accuracy, 97, 120, 124–128 height of ambiguity (also: ambiguous height), 114, 116, 124–127, 132–133 Helix concept, 103–104, 106, 116, 124, 144–145 (pls add this term) heterodyne channels, 315, 327–330, 334, 356–358 heterodyne reference, 327 heterodyne synchronization, 12 high resolution imaging, 249 high resolution wide swath imaging, 142, 147 HypSEO Earth Observation Mission, 74 integration time, 88–89, 108–111, 161, 163, 165, 170, 176, 197, 255–256, 260, 263, 271, 286–287, 292, 296–299, 301, 321, 343, 347, 353–354 inertial navigation systems (INS), 218 inertial reference frame (IRF), 13 interacting multiple model, 265, 306 interference, 95, 112, 115, 139, 160, 251, 254, 257, 261, 263, 270, 290–291, 293, 295, 309, 339–340, 344, 364, 382 interferometric cartwheel, 104–105, 139, 161 interferometric image pair registration, 19 interferometric missions, 28 interferometry, 10, 13, 27–28, 30, 45, 69, 97–101, 159–160, 162, 185, 193, 201, 207, 381–382 ion-acoustic waves, 374 ionosphere, 363, 365–377 irregularities iso-Doppler contour, 235 isorange ellipses eccentricity, 5 i–th cartwheel satellite, 45–46 i–th receiver satellite, 45 J2 secular perturbations, 76 Jacobian determinant, 236 Jicamarca Radar Observatory, 373, 375 Kalman filter, 265, 267–268, 272, 288, 304–306 Keplerian circular orbit, 45 Keplerian dynamics, in Taylor series, 45 Keplerian mean motion, 45, 47 Kirchhoff model, 10

• 392

Lagrangian points, 40 lattice predictor, 270, 293–295 L-band GPS signals, 12 leader-follower philosophy, 40 long-integration method, 296 magnetic equator, 370, 372 magnetic latitude, 368–370 matched filter, 12, 247, 268–272, 276, 283, 295–296, 315–317, 327, 334 microsatellites, 28, 45, 95–96, 104, 137, 139 MIL HDBK 340A handbook, 32 mismatch filters, 316 mismatching loss, 317, 334–335 MMSU dimensions, 74 monopulse techniques, 264, 269, 287–288 monostatic radar, 8, 11–12, 27, 159, 197–198, 248–249, 275, 283, 363 monostatic SAR ambiguity function, 218–223 motion compensation for bistatic airborne SAR, 165, 174, 177–184 moving target indicator, 249 multi-baseline multipath, 41, 254, 264, 270, 273, 320 multiple transmitters, 259, 261, 263, 265, 273, 275, 285–286, 307 multistatic configurations, 95–96, 115, 136–137, 139, 261 multistatic PBR, 273–274 multistatic, 95 mutual coupling, 264, 289 narrowband PBR, 260–268 navigation signal, 346 noise equivalent sigma zero (NESZ), 117–118, 136 noise figures, 73, 116, 118, 128, 252, 254–257, 260, 269, 277, 322 non-cooperative LEO (Low Earth Orbit) commercial satellites, 28 non-cooperative microwave illuminators, 28 non-cooperative radar, 248 non-geostationary satellites, 215 non-zero datum, 17 operational mode, 34, 71–72, 112–115, 321 opportunistic radar, 248 orbit configurations, of Spaceborne BSAR, 29–32 orthogonal frequency division multiplexing, 251, 315, 317–318, 322

Index oscillator (USO), 71, 107, 110, 146 ovals of Cassini, 256 parallel orbits, 30, 33, 41–42, 44, 49, 60, 67, 76, 91 Parseval’s theorem, 230 passive bistatic radar, 247–309 passive coherent location, 248, 250 path difference, 233 payload duty cycle, 31, 34 payload operational modes, 71–72 payload-based (azimuth), 38 pendulum concept, 30, 49 phase noise, 107–108, 111, 114, 120, 127–128, 204–205 physical antenna length, 343 pilot carriers, 318–319, 322, 324, 330–335 PING PONG mode transmitted polarization, 72 pitch angles, 36, 86, 205 pitch-yaw-roll attitude rotation, 56 planet-based transmitter, 27 pointing angles, 14–17, 19, 49–50, 52, 54, 56–57, 60 pointing design, 49–60, 78–86 polarimetric SAR interferometry (PolInSAR), 98–99, 134–136 power budget, 28, 33, 74–76, 321, 343–345 power flux density, 340, 343–345 pre-decimation, 381 ProtoFlight Model, 69 protonosphere, 368 pulse duration, 108, 118, 222, 227, 343 quadrature amplitude modulated, 317–318, 320 quantization, 104, 116–117, 119 quasi monostatic versus monostatic configuration, 208–210 radar equation, 2, 162, 229, 251–253, 255–256, 260 grammetric techniques, 16 resolution capability, 217, 239 Radar Signal Receiver S/S, 70, 73 radargrammetry, 10, 17, 143 Radarsat-2/3, 97 radiation, 219, 232, 237, 252, 254, 260, 285, 368, 373 random signal, 317–318, 321–323, 353 range-Doppler processor, 12, 288 range-Doppler-bearing space, 269 range-rate resolution, 224–226

• 393

Index range resolution, 3–5, 7, 100, 115, 118, 124, 162–163, 165, 167, 182, 199, 202, 218–219, 223–226, 235, 240, 249, 275, 279, 282–287, 296, 299, 342–343, 356, 378, 382 real-time surveillance, 250, 383 receive antenna, 118, 129, 131, 141, 199–200, 252, 256 receiver to target range, 345–346 receiving antenna, 1–2, 27, 73, 85, 100, 161, 188, 344–345, 379 reference absolute parallax, defined, 17 reference signal, 71, 220, 262–263, 269–272, 291, 293, 295–297, 300, 302–303, 327–328, 332–334, 344, 347, 355–356 remote sensing, 1–3, 20, 28, 31–33, 40, 42, 47, 67, 69, 97, 142–143, 159, 215 resolution cell, 10, 12, 100, 120, 138, 142, 164–165, 220, 226–227, 235, 239, 286, 302, 328, 343 resolution performances for bistatic SAR, 163–165, 219, 235, 285 resolution, in BSAR, 223–228 retro-reflector effects, 9 RF emissions, 250 riometer, 374 Rx antenna azimuth angle, 54 Rx spacecraft, 31 Rx -only antenna, 3, 7–8, 13–15 SAR ambiguity function, 222–223 SAR antenna dimensions, 70 satellite formation, 29, 96–98, 101–106 satellite navigation system, 218, 250 satellites horizontal separation, 42 in geostationary Earth orbits (GEO), 216 in medium and low Earth orbits (MEO and LEO), 216 interlink, 41 manoeuvring, 37–38 trajectory, 46 scattered pilot, 318–319, 330–331 self-ambiguity, 248, 274–285 semi-active sidelobe echo, 42 sidelobe levels, 75, 131, 182, 218, 279, 281, 332 signal to interference ratio, 345–354 signal-to-noise ratio, 3, 36, 75, 80, 101, 117, 202–203, 206, 256–257, 260, 263, 286, 290, 295, 328, 334, 343

single-pass interferometry, 27 spaceborne BSAR design issues functional and technological issues, 40–42 impact of bistatic observation on mission and system design, 32–34 payload-bus performance trade-off, 35–40 trade-offs in configuration, 29–32 mission analysis antenna design, 49–60 orbit design, 42–49 spaceborne geometry, 5 spaceborne remote sensing, 20, 32 spaceborne SAR interferometry, 30, 97–101 spaceborne systems, 17, 27 spacecraft dynamics, 73 Space-Surface Bistatic SAR (SS-BSAR), 28 Space-Surface Bistatic SAR spatial resolution, 217–228 SS-BSAR resolution, 228–237 system overview, 215–217 sparse aperture, 97, 137, 139, 144, 147 spatial resolution, 142, 144, 217–228, 232, 243, 275, 286, 339, 343 specular reflection, 253, 272 spherical Earth surface, 5 sporadic E, 367, 370, 372 spotlight mode, 37–38, 78, 198 spread F, 372–373 SS-BSAR resolution, 228–237 SS-BSAR topology, 216, 229, 339–340 stereoradargrammetric techniques, 16 stripmapping modes, 72 sub-carriers frequency, 317 sunsynchronicity condition, 33 sunsynchronous orbits, 44, 217 super-resolution, 142, 147 surveillance applications of bistatic radar, 1 surveillance radar, 198, 304, 321 ‘swath-driven’ yaw angles, 86 swath separation, 31, 36–38 symbol duration, 318, 324, 334 synchronisation, 96, 216, 357 synchronization algorithm, 42, 356 synthetic aperture radar (SAR), 148 system performance, 248, 250, 274, 279, 280, 285–290, 308–309 T/R off-nadir angle, 85 TanDEM-X missions, 103, 115–128 TanDEM-X, 32, 97, 111, 115–128

• 394

target detection, 11, 27–28, 160, 197, 250, 253, 257, 262–263, 269, 272, 274, 286, 295–296, 354 Taylor expansion, of delay difference, 230 TechSAT 21, 97, 105 temporal decorrelation, 95, 98–99, 104, 113, 117, 121–122, 136–139, 143 TerraSAR, 28, 100–101, 115, 118, 124, 128–136 terrestrial digital video broadcasting, 315–335 Thales/Finmeccanica Company, 67 Thomson scattering, 375–376 time-bandwidth product, 263 tomography, 137–139, 142, 145 TOPSAT mission, 30 traffic monitoring, 98, 144 transmitted signal power, 229 transmitted waveform, 12, 221, 248, 274–276, 316 transmitters of opportunity, 247–248, 271, 315, 335, 354, 364, 378 trigonometric relations, 19 Trinodal Pendulum, 106, 128, 133–134, 139 two-channel receiver, 264, 356 Tx /Rx and Rx satellites, 29, 31, 33

Index Tx /Rx Tx /Rx Tx /Rx Tx /Rx

antenna off-nadir angle, 3 antenna-fixed Reference Frame (TRF), 14 elevation angle, 53 elevation plane, 76

Ultra Stable Oscillator (USO), 71 uncertainty function, 316, 322, 325–327, 332 Unmanned Aerial Vehicle (UAV), 234 vertical-plane radiation patterns, 252 volume decorrelation, 101, 117, 119, 120–121, 125, 134 waveform, 274–288 wavelength, 10, 13, 27, 110, 118, 141–142, 173, 252, 264–265, 275, 304–305, 343, 370, 372, 375, 377–378 wideband PBR, 268–273 Woodward’s ambiguity function, 232 X-band SAR (SAR2000), 67 X-band surveys, 9 yaw steering manoeuvre, 30, 37, 42, 79–80, 83, 86 yaw-rotate Rx satellite, 76

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Plate 1 Time series of focused azimuth responses in a bistatic SAR. The fast change of the grey levels in the curve on the top shows the temporal variation of the mainlobe phase which varies by multiples of π (vsat = 7 km/s, r0 = 800 km, λ = 3.1 cm).

Plate 2 Quasi-monostatic configuration, superposition of monostatic and bistatic images. The planes are flying from left to right at the top of the images. One can clearly detect the large shift (in both directions) between the two images. This shift is linked to the drift between the two clocks and can be computed by performing sub-image correlation along the image.

Plate 3 Comparison between the monostatic and the quasi monostatic images (a) on the top row, and color composite of the two images (b).

a

b

c

RAMSES E-SAR

Bistatic Shadow

Plate 4 Comparison between the different bistatic images. (a) steep angle; (b) quasi-monostatic; (c) grazing angle configuration. The colour composition was obtained by coding (a) in red, (b) in blue and (c) in green. In the drawing the shadow length is illustrated for monostatic and steep angle configuration. The steep angle configuration shadow is shown to be longer, as observed on the data.

Plate 5 Bistatic interferometric image associated with the grazing configuration: The colours are coding the terrain elevation. Two villages can be seen in this image, Garons on the top left and Bouillargues on the top right of this image. The tree hedges, characteristic of agriculture in this windy area are clearly visible. The transponder strong signal appears as a bright spot on the right of the image.

Plate 6 Cross-platform interferometric bistatic image: The pair of images was acquired in the quasi monostatic configuration. One image is monostatic while the other is bistatic. During the processing, an average underlying topography was removed to highlight the manmade constructions, appearing in pink. The Garons airfield is clearly visible in the top part of the image. A freeway, crossing the image is set below the surrounding ground. Doppler Hz × 104

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Plate 7 Ambiguity plot showing range and Doppler resolution for a target positioned on the baseline Doppler × 104

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Plate 8 Plot showing the change in resolution when a target is at an angle of 90◦ to the baseline

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Plate 9 Plot showing the collapse in resolution as the target approaches a position

Range resolution in Radar

Range resolution in Radar

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Vertical displacement in km

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Plate 10 Traffic light plot of normalised range resolution variation for a bistatic PCL system

Plate 11 Traffic light plot of normalised range resolution variation for a multi static PCL system

Plate 12 Traffic light plot of normalised Doppler resolution variation for a bistatic PCL system

Plate 13 Traffic light plot of normalised Doppler resolution variation for a multi static PCL system

Plate 14 filtering

Range-Doppler surface after adaptive

Plate 16 Example target tracks in RangeDoppler space

Plate 15 Example results of cross-correlation processing

Plate 17

Example target tracks overlaid on map

Plate 18 Simulated tracks with corresponding association numbers added

Plate 19 Civil ATC truth data converted to range/Doppler space for comparison

Plate 20 Example of detection showing overlaid civil ATC data

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–10 –15 –20 –25 –30 –35

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Plate 21 SS-BSAR with GLONASS GNSS image vs aerial photo UT20031030_024700_F965_D560_B100

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Plate 22 Example of a Range-Doppler distribution. The horizontal axis is bistatic slant range, from 0 to 1200 km. The vertical axis is Doppler Velocity, +/−1500 m/s. To the left, at ranges below 150 km, signals from ground clutter and aircraft can be seen. At ranges from 600 to 1000 km, an extended region of auroral turbulence can be seen, with Doppler content ranging from 300 to 900 m/s.

Plate 23 Example of passive radar interferometry. The left panel is a range-Doppler distribution (range is now the vertical axis). The right panel is the position and size of the scattering region in range (vertical) and azimuth (horizontal). The interferometer baseline was 16 wavelengths, and thus significantly overmoded. However, other geophysical evidence permits identifying the absolute direction.