MIMO Radar Signal Processing

MIMO RADAR SIGNAL PROCESSING......Page 3
CONTENTS......Page 7
PREFACE......Page 15
CONTRIBUTORS......Page 19
1.1 Introduction......Page 21
1.2 Problem Formulation......Page 24
1.3.1 Preliminary Analysis......Page 25
1.3.2 Sufficient and Necessary Conditions......Page 27
1.3.3 Numerical Examples......Page 28
1.4 Nonparametric Adaptive Techniques for Parameter Estimation......Page 31
1.4.1 Absence of Array Calibration Errors......Page 32
1.4.2 Presence of Array Calibration Errors......Page 35
1.4.3 Numerical Examples......Page 38
1.5.1 ML and BIC......Page 48
1.5.2 Numerical Examples......Page 54
1.6.1 Beampattern Matching Design......Page 55
1.6.2 Minimum Sidelobe Beampattern Design......Page 58
1.6.3 Phased-Array Beampattern Design......Page 59
1.6.4 Numerical Examples......Page 60
1.6.5 Application to Ultrasound Hyperthermia Treatment of Breast Cancer......Page 67
1.7 Conclusions......Page 76
Appendix IA Generalized Likelihood Ratio Test......Page 77
Appendix 1B Lemma and Proof......Page 79
References......Page 80
2.1.1 A Short History of Radar......Page 85
2.1.2 Definition and Characteristics of MIMO Radar......Page 86
2.1.3 Uses of MIMO Radar......Page 88
2.1.4 The Current State of MIMO Radar Research......Page 90
2.1.5 Chapter Outline......Page 91
2.2 Notation......Page 92
2.3.1 MIMO Channel......Page 93
2.3.2 MIMO Virtual Array: Resolution and Sidelobes......Page 94
2.4.2 Signal Model......Page 97
2.4.3 Fisher Information Matrix......Page 99
2.4.4 Waveform Correlation Optimization......Page 102
2.4.5 Examples......Page 105
2.5 Optimality of MIMO Radar for Detection......Page 107
2.5.1 Detection......Page 108
2.5.2 High SNR......Page 109
2.5.3 Weak-Signal Regime......Page 110
2.5.5 Nonfading Targets......Page 112
2.6.1 Signal Model......Page 113
2.6.2 Localization and Adapted SNR......Page 116
2.6.3 Inner Products and Beamwidths......Page 121
2.6.4 SNR Loss......Page 123
2.6.5 SNR Loss and Waveform Optimization......Page 127
2.6.7 Some Examples......Page 129
Appendix 2A A Localization Principle......Page 131
Appendix 2B Bounds on R(N)......Page 134
Appendix 2E Bound on Eigenvalues......Page 135
Appendix 2F Some Inner Products......Page 136
Appendix 2G An Invariant Inner Product......Page 137
2H.2 Tensor and Krönecker Products......Page 138
Acknowledgments......Page 139
References......Page 140
3.1 Introduction......Page 143
3.2 Background......Page 144
3.3 MIMO Signal Model......Page 147
3.4.1 Transmit Signal Model......Page 151
3.4.2 Channel and Target Models......Page 152
3.4.3 Received Signal Parametric Model......Page 153
3.5 MIMO Ambiguity Function......Page 154
3.5.1 MIMO Ambiguity Function Composition......Page 157
3.5.2 Cross-Correlation Function under Model Simplifications......Page 158
3.5.3 Autocorrelation Function and Transmit Beampatterns......Page 161
3.6.1 Orthogonal Signals......Page 163
3.6.2 Coherent Signals......Page 167
3.7 Conclusion......Page 169
References......Page 170
4.1 Introduction......Page 173
4.2 Problem Formulation......Page 175
4.3 Properties......Page 178
4.3.1 Virtual Aperture Extension......Page 179
4.3.2 Spatial Coverage and Probability of Exposure......Page 182
4.3.3 Beampattern Improvement......Page 183
4.4.1 Maximum-Likelihood Estimation......Page 185
4.4.2 Transmission Diversity Smoothing......Page 187
4.5.1 Cramér–Rao Bound......Page 190
4.5.2 The Barankin Bound......Page 193
4.6 Simulation Results......Page 195
4.7 Discussion and Conclusions......Page 200
Appendix 4A Log-Likelihood Derivation......Page 201
4A.1 General Model......Page 202
4A.2 Single Range–Doppler with No Interference......Page 204
Appendix 4B Transmit–Receive Pattern Derivation......Page 205
Appendix 4C Fisher Information Matrix Derivation......Page 206
References......Page 209
5.1 Introduction......Page 213
5.2 Problem Formulation......Page 215
5.2.1 Signal Model with Reduced Number of Range Cells......Page 219
5.2.2 Multipulse and Doppler Effects......Page 220
5.3 Estimation......Page 223
5.3.1 Beamforming Solution......Page 224
5.3.3 Waveform Design for Estimation......Page 230
5.4.1 The Optimal Detector......Page 234
5.4.2 The SINR......Page 235
5.4.3 Optimal Waveform Design......Page 237
5.4.4 Suboptimal Waveform Design......Page 238
5.4.5 Constrained Design......Page 239
5.4.6 The Target and Clutter Models......Page 240
5.4.7 Numerical Examples......Page 241
5.5 MIMO Radar and Phased Arrays......Page 246
5.5.1 Scan Transmit Beam after Receive......Page 248
5.5.3 Combined Transmit–Receive Beamforming......Page 249
Appendix 5A Theoretical SINR Calculation......Page 251
References......Page 252
6 MIMO Radar Spacetime Adaptive Processing and Signal Design......Page 255
6.1 Introduction......Page 256
6.2 The Virtual Array Concept......Page 258
6.3 Spacetime Adaptive Processing in MIMO Radar......Page 262
6.3.1 Signal Model......Page 263
6.3.2 Fully Adaptive MIMO-STAP......Page 266
6.3.3 Comparison with SIMO System......Page 267
6.3.4 The Virtual Array in STAP......Page 268
6.4 Clutter Subspace in MIMO Radar......Page 269
6.4.1 Clutter Rank in MIMO Radar: MIMO Extension of Brennan’s Rule......Page 270
6.4.2 Data-Independent Estimation of the Clutter Subspace with PSWF......Page 273
6.5 New STAP Method for MIMO Radar......Page 277
6.5.1 The Proposed Method......Page 278
6.5.3 Estimation of the Covariance Matrices......Page 279
6.5.5 Comparison with Other Methods......Page 280
6.6 Numerical Examples......Page 281
6.7.1 MIMO Radar Ambiguity Function......Page 285
6.7.2 Some Properties of the MIMO Ambiguity Function......Page 287
6.7.3 The MIMO Ambiguity Function of Periodic Pulse Radar Signals......Page 292
6.7.4 Frequency-Multiplexed LFM Signals......Page 294
6.7.5 Frequency-Hopping Signals......Page 296
6.8 Conclusions......Page 298
References......Page 299
7.1 Introduction......Page 303
7.1.1 MIMO Radar and Spatial Diversity......Page 304
7.1.3 MIMO and Processing Gain......Page 306
7.2.1 Generalized Transmitted Radar Waveform......Page 309
7.2.2 SIMO Target Model......Page 310
7.2.3 SIMO Covariance Models......Page 311
7.2.4 SIMO Radar Processing......Page 312
7.3.1 Slow-Time MIMO Target Model......Page 313
7.3.2 Slow-Time MIMO Covariance Model......Page 315
7.4 Slow-Time MIMO Radar Processing......Page 317
7.4.1 Slow-Time MIMO Beampattern and VSWR......Page 319
7.4.3 SIMO versus Slow-Time MIMO Design Comparisons......Page 321
7.4.4 MIMO Radar Estimation of Transmit–Receive Directionality Spectrum......Page 322
7.5 OTHr Propagation and Clutter Model......Page 323
7.6.1 Postreceive/Transmit Beamforming......Page 327
7.6.2 SINR Performance......Page 331
7.6.3 Transmit–Receive Spectrum......Page 335
References......Page 336
8.1 Introduction......Page 339
8.2 Systems......Page 341
8.2.1 Signal Model......Page 343
8.2.3 Netted Radar Systems......Page 345
8.2.4 Decentralized Radar Network (DRN)......Page 347
8.3.1 False-Alarm Rate (FAR)......Page 349
8.3.2 Probability of Detection (P(d))......Page 356
8.3.3 Jamming Tolerance......Page 368
8.3.4 Coverage......Page 372
8.4 Conclusions......Page 379
References......Page 381
9.1 Background......Page 385
9.2.1 Signal Model......Page 389
9.2.2 Spatial Decorrelation......Page 393
9.2.3 Other Multiple Antenna Radars......Page 395
9.3.1 Diversity Gain......Page 397
9.3.2 Moving-Target Detection......Page 400
9.4 Coherent MIMO Radar Applications......Page 403
9.4.1 Ambiguity Function......Page 405
9.4.2 CRLB......Page 408
9.4.3 MLE Target Localization......Page 410
9.4.4 BLUE Target Localization......Page 413
9.4.5 GDOP......Page 415
9.5 Chapter Summary......Page 419
Appendix 9A Deriving the FIM......Page 420
Appendix 9B Deriving the CRLB on the Location Estimate Error......Page 423
Appendix 9C MLE of Time Delays — Error Statistics......Page 425
9D.1 Special Case: N × N MIMO......Page 427
References......Page 428
10.1 Introduction......Page 431
10.2 System Model......Page 435
10.3 Detection In MIMO Radars......Page 437
10.3.1 Full-Rank Code Matrix......Page 439
10.3.2 Rank 1 Code Matrix......Page 440
10.4 Spacetime Code Design......Page 441
10.4.1 Chernoff-Bound-Based (CBB) Code Construction......Page 443
10.4.2 SCR-Based Code Construction......Page 446
10.4.3 Mutual-Information-Based (MIB) Code Construction......Page 447
10.5 The Interplay Between STC and Detection Performance......Page 449
10.6 Numerical Results......Page 451
10.7 Adaptive Implementation......Page 457
10.8 Conclusions......Page 461
References......Page 462
INDEX......Page 465