-?. qS Synthetic Aperture Radar [Ising Non-Uniform Sampling by JoN¿IHEN ANOREW LECC Thesis submitted for the degree of Doctor of Philosophy Department of Electrical and Electronic Engineering Faculty of Engineering The University of Adelaide Adelaide, South Australia August 1997 Contents Abstract vu Declaration ix Acknowledgments xi List of Figures xrll List of Thbles xYll Glossary xtx Publications xxY I Introduction 1 l.l Motivation 1 I.2 Thesis Outline and Contributions 2 2 Background Information 7 2.I Synthetic Aperture Radar Fundamentals . 7 2.1.1 Range Information . 9 2.1.2 From Real to Synthetic Aperture l0 2.L3 Azimuthal Information 12 2.1.4 PRF Selection 13 2.2 Radar Moving Target Detection 15 2.3 The Effects of Moving Targets on SAR l6 2.4 Radar Waveforms l9 2.5 Existing SAR MTD Techniques 2t 2.6 Proposed SAR MTD Technique 29 ll CONTENTS 2.7 Non-Uniform Sampling 30 2.7.1 Heuristic Justification for Non-Uniform pRI SAR MTD 30 2.7.2 Introduction 31 2.7.3 Minimum SamplingRequiremeuts 55 2J.4 Pseudorandom Sampling JJ 2.7.5 SignalProcessing JJ 2.1.6 Timing Specifications 36 2.1.7 SAR Specifics 39 2.1.8 Non-UniformArrays 4t 2.7.9 Non-Uniform Sampling: Concluding Remarks 4t 2.8 Performance Requirements 42 2.9 Summary 42 3 Moving Thrget Ambiguity Function 43 3.1 Introduction 43 3.2 Ambiguity Function Derivation 44 3.2.1 Radar Scenario and Signals 44 3.2.2 RangeCompression 47 3.2.3 Slow Time Compression . 49 3.2.4 SAR Geometry 51 3.2.5 Stripmapping SAR Ambiguity Function . 52 3.3 Depth of Focus 54 3.4 Moving Target Focussing 55 '3.4.1 Linearity 56 3.4.2 Uniqueldentifiability 56 3.4.3 Squint Mode 58 3.5 Uniform Pzu . 59 3.5.1 Azimuthal Position/Range Velocity . 59 3.5.2 Azimuthal Position/Azimuthal Velocity 62 3.6 Non-UniformPRl 62 3.6.1 The Effect of Two Staggered PRIs . 65 3.7 The Ambiguity Function with Random Sampling 69 3.1.l Range Velocity/Azimuthal Position 1l 3.7.2 Azimuthal Velocity 76 CONTENTS lll 3.8 Conclusions 78 4 Moving Thrget Detection 79 4.1 Introduction 79 4.2 Data Model . 80 4.2.1 Azimuthal Signal 80 4.2.2 Hypotheses 80 4.2.3 Assumptions 8l 4.2.4 DisturbanceModelling 82 4.3 Optimal Detection 85 4.3.1 Numerical Examples . 89 4.3.2 Alternative Optimality Criterion 93 4.3.3 Signal-to-DisturbanceRatio Improvement 93 4.3.4 Receiver Operating Characteristic . 97 4.4 Moving Target Indication 102 4.5 ClutterCancellation 104 4.6 Practical Considerations 105 4.7 Conclusions 106 5 Moving Target Parameter Estimation 107 5.1 Introduction . 107 5.2 Signal Model . 108 5.3 Existing'Work . 111 5.4 Maximum Likelihood Estimation . 113 5.4.1 Bias . 115 5.4.2 Variance . rr7 5.5 Random Sampling . r2t 5.5.1 Example Sampling Distributions . r25 5.6 Simulations . t28 5.7 PracticalConsiderations . t29 5.8 Actual Unknown Parameters . 130 5.8.1 NumericalExamples . t32 5.9 Conclusions . t39 lv CONTENTS 6 Imaging r4t 6.1 Introduction l4t 6.2 Existing Work t42 6.3 Azimuthal Imaging Formulation r43 6.3.1 Focussing t46 6.4 ProcessingTechniques t47 6.4.1 Phase Corrections 148 6.4.2 Weighting 151 6.4.3 Maximum ISLR . t52 6.5 Effects of a Non-Uniform PRI 154 6.5.1 Resolution 156 6.6 The Azimuthal Response with Random Sampling 156 6.6.1 Case 1: Uniformly DistriburedTimes 157 6.6.2 Case 2: Uniformly Distributed Offsets 158 6.7 Conclusion 159 7 Application to Real Data t6l 7.1 Introduction 161 7.2 Moving Target Imaging r62 7.2.1 Non-Uniform PRI Simulation t6l 7.3 Moving Target Parameter Estimation 168 7.4 ClutterCancellation 170 7.5 Conclusions 17l I Summary 173 8.1 Summary of the SAR MTD Technique 173 8.2 Future Research 116 8.3 Conclusion 176 CONTENTS A Extended Ambiguity Function Properties 177 B SAR Clutter Modelling 181 8.1 Time Domain Clutter Modelling 181 8.2 Comparison between Doppler and Time Domain Models 184 C Biased Estimator Lower Variance Bounds 187 D The Complex Gaussian Fisher Information Matrix 189 E Notes Regarding the Optimal Tlansmission Times 193 E.1 Introduction . r93 8.2 Possible Schemes . t94 8.2.1 Deterministic: Heuristic . 194 8.2.2 Deterministic: Optimal . 194 8.2.3 Random Sampling Schemes . 195 E.3 Minimum Redundancy Sampling Scheme . r97 8.4 Conclusions . 198 VI Abstract Synthetic aperture radar is a well established technique for imaging the ground to one side of an airborne platform. Moving target detection is a very useful capability for a long range sensor. The combination of synthetic aperture radar and moving target detection has the potential to produce high resolution ground imagery with superimposed moving target information. Un- fortunately, using conventional imaging data for detecting moving targets leads to ambiguities in the targets' positions and velocities. By utilising a non-uniform pulse repetition interval, the proposed ground imaging / moving target detection radar overcomes this limitation and allows the azimuthal data to be focussed at any velocity of interest, whilst collecting data at the same average rate as a conventional synthetic aperture radar. This approach permits the flexible use of a multimode radar, relaxes the specifications of data acquisition systems, affords a degree of protection against electronic countermeasures and retains alarge unambiguous range swath, but with the added complexity of processing the non-uniform samples. This thesis investigates the technique in detail, incorporating optimal target detection strategies and azimuthal beampatterns, and demonstrates it using simulations of non-uniform transmissions with real data. vil vlll X Acknowledgments I wish to thank a number of people and organisations, without whom this thesis would not exist. Dr Alan Bolton is a colleague and friend who provided the original inspiration for this work and gave continual support and encouragement throughout its duration. Prof. Douglas Gray, my Ph.D. supervisor, changed my attitude from one of 'try it and see' to one of careful and thorough analysis. His expertise in sonar beamforming provided me with useful insights regarding the treatment of synthetic aperture radar as a phased array. Dr Don Sinnott, as Chief of Microwave Radar Division, approved my sponsorship through the Defence Science and Technology Organisation, Salisbury. My MRD supervisor, Mar- ian Viola, kindly decided he could do without me during the period of my candidature and eagerly awaited its completion. The Cooperative Research Centre for Sensor Signal and Information Processing provided excellent facilities and great people to work with. I will never forget the superlative morning teas. My family, and particularly my darling Jan, provided encouragement regarding the further- ing of my career. Jan was quite happy for me to work hard during the weekends! XI xll List of Figures 2.1 Simplified stripmapping SAR geometry 8 2.2 An overview of SAR processing. 8 2.3 The first order effects of moving targets on a SAR image 18 2.4 A moving target's return after being processed as if the target were stationary 19 2.5 The distances to two targets seen by the radar 30 2.6 Radar azimuthal phase returns. 3l 2.7 Radar azimuthal phase returns; non-uniform PR[. 32 2.8 Correlation filtering of non-uniformly sampled data. 35 2.9 Estimated spectrum; uniform sampling 37 2.ro Estimated spectrum; random offsets. 38 2.tt Non-uniform sampling notation 38 2.t2 Estimated spectrum; random intervals. 39 3.1 A block diagram of the radar model M 3.2 The SAR antenna pattern 45 3.3 SAR imaging scenario 49 3.4 The range velocitylazimuthal position ambiguity function . 60 3.5 The peak of the range velocitylazimuthal position AF . 60 3.6 The azimuthal velocity/azimuthal position AF . 62 3.1 The peak azimuthal velocitylazimuthal position AF . 63 3.8 The range velocitylazimuthal position AF; non-uniform PRI 63 3.9 Slices of the non-uniform PRI range velocitylazimuthal position AF 64 3.10 The non-uniform PRI azimuthal velocity/azimuthal position AF 64 3.1 l The peak non-uniform PRI azimuthal velocitylazimuthal position AF . ' 65 3.12 The normalised SAR azimuthal AF with one PRI plotted against range velocity. 67 3.r3 The normalised AF with superimposed sample times. 68 xiii XIV LIST OFFIGURES 3.t4 The normalised AF with two PRIs: the first is 0.3 x the nominal value. 68 3. r5 The normalised AF with two alternating PRIs: the first is 0.5 x the nominal value. 69 3.16 The expected range velocity/azimuthal position ambiguity function for uni- formly distributed sampling l2 3.t] The peak of the expected range velocitylazimuthal position ambiguity function for uniformly distributed sampling t3 3.18 The expected range velocity/azimuthal position ambiguity function for uni- formly distributed offsets 75 3.19 The normalised AF with randomly chosen PRIs . 16 4.1 Moving target detection spectra; high PRF 9l 4.2 MTD spectra; high PRF, non-uniform PRI 9l 4.3 MTD spectra;low PRF 92 4.4 MTD spectra; low PRF, non-uniform PRI 92 4.5 Signal to disturbance ratio improvement; high PRF 95 4.6 SDR improvement; high PRF, non-uniform PRI 96 4.7 SDR improvement; low PRF 96 4.8 SDR improvement; low PRF, non-uniform PRI 97 4.9 Receiver operating characteristics for an optimal filter, high PRF r0l 4.to ROC for an optimal filter,low PRF 101 4.tt ROC for a matched filter, low PRF .