MIMO雷达信号处理电子书

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1.6.4 Numerical Examples 40
1.6.5 Application to Ultrasound Hyperthermia
Treatment of Breast Cancer 47
1.7 Conclusions 56
Appendix IA Generalized Likelihood Ratio Test 57
Appendix 1B Lemma and Proof 59
Acknowledgments 60
References 60
2 MIMO Radar: Concepts, Performance Enhancements,
and Applications 65
Keith W. Forsythe and Daniel W. Bliss
2.1 Introduction 65
2.1.1 A Short History of Radar 65
2.1.2 Definition and Characteristics of MIMO Radar 66
2.1.3 Uses of MIMO Radar 68
2.1.4 The Current State of MIMO Radar Research 70
2.1.5 Chapter Outline 71
2.2 Notation 72
2.3 MIMO Radar Virtual Aperture 73
2.3.1 MIMO Channel 73
2.3.2 MIMO Virtual Array: Resolution and Sidelobes 74
2.4 MIMO Radar in Clutter-Free Environments 77
2.4.1 Limitations of Crame´r –Rao Estimation Bounds 77
2.4.2 Signal Model 77
2.4.3 Fisher Information Matrix 79
2.4.4 Waveform Correlation Optimization 82
2.4.5 Examples 85
2.5 Optimality of MIMO Radar for Detection 87
2.5.1 Detection 88
2.5.2 High SNR 89
2.5.3 Weak-Signal Regime 90
2.5.4 Optimal Beamforming without Search 92
2.5.5 Nonfading Targets 92
2.5.6 Some Additional Benefits of MIMO Radar 93
2.6 MIMO Radar with Moving Targets in Clutter: GMTI Radars 93
2.6.1 Signal Model 93
2.6.2 Localization and Adapted SNR 96
2.6.3 Inner Products and Beamwidths 101
2.6.4 SNR Loss 103
vi CONTENTS
2.6.5 SNR Loss and Waveform Optimization 107
2.6.6 Area Search Rates 109
2.6.7 Some Examples 109
2.7 Summary 111
Appendix 2A A Localization Principle 111
Appendix 2B Bounds on R(N) 114
Appendix 2C An Operator Norm Inequality 115
Appendix 2D Negligible Terms 115
Appendix 2E Bound on Eigenvalues 115
Appendix 2F Some Inner Products 116
Appendix 2G An Invariant Inner Product 117
Appendix 2H Kro¨necker and Tensor Products 118
2H.1 Lexicographical Ordering 118
2H.2 Tensor and Kro¨necker Products 118
2H.3 Properties 119
Acknowledgments 119
References 120
3 Generalized MIMO Radar Ambiguity Functions 123
Geoffrey San Antonio, Daniel R. Fuhrmann, and Frank C. Robey
3.1 Introduction 123
3.2 Background 124
3.3 MIMO Signal Model 127
3.4 MIMO Parametric Channel Model 131
3.4.1 Transmit Signal Model 131
3.4.2 Channel and Target Models 132
3.4.3 Received Signal Parametric Model 133
3.5 MIMO Ambiguity Function 134
3.5.1 MIMO Ambiguity
Function Composition 137
3.5.2 Cross-Correlation Function under
Model Simplifications 138
3.5.3 Autocorrelation Function and Transmit
Beampatterns 141
3.6 Results and Examples 143
3.6.1 Orthogonal Signals 143
3.6.2 Coherent Signals 147
3.7 Conclusion 149
References 150
CONTENTS vii
4 Performance Bounds and Techniques for Target Localization
Using MIMO Radars 153
Joseph Tabrikian
4.1 Introduction 153
4.2 Problem Formulation 155
4.3 Properties 158
4.3.1 Virtual Aperture Extension 159
4.3.2 Spatial Coverage and Probability of Exposure 162
4.3.3 Beampattern Improvement 163
4.4 Target Localization 165
4.4.1 Maximum-Likelihood Estimation 165
4.4.2 Transmission Diversity Smoothing 167
4.5 Performance Lower Bound for Target Localization 170
4.5.1 Crame´r –Rao Bound 170
4.5.2 The Barankin Bound 173
4.6 Simulation Results 175
4.7 Discussion and Conclusions 180
Appendix 4A Log-Likelihood Derivation 181
4A.1 General Model 182
4A.2 Single Range –Doppler with
No Interference 184
Appendix 4B Transmit –Receive Pattern Derivation 185
Appendix 4C Fisher Information Matrix Derivation 186
References 189
5 Adaptive Signal Design For MIMO Radars 193
Benjamin Friedlander
5.1 Introduction 193
5.2 Problem Formulation 195
5.2.1 Signal Model with Reduced Number of
Range Cells 199
5.2.2 Multipulse and Doppler Effects 200
5.2.3 The Complete Model 203
5.2.4 The Statistical Model 203
5.3 Estimation 203
5.3.1 Beamforming Solution 204
5.3.2 Least-Squares Solutions 210
5.3.3 Waveform Design for Estimation 210
5.4 Detection 214
5.4.1 The Optimal Detector 214
5.4.2 The SINR 215
viii CONTENTS
5.4.3 Optimal Waveform Design 217
5.4.4 Suboptimal Waveform Design 218
5.4.5 Constrained Design 219
5.4.6 The Target and Clutter Models 220
5.4.7 Numerical Examples 221
5.5 MIMO Radar and Phased Arrays 226
5.5.1 Scan Transmit Beam after Receive 228
5.5.2 Adaptation of Transmit Beampattern 229
5.5.3 Combined Transmit –Receive Beamforming 229
Appendix 5A Theoretical SINR Calculation 231
References 232
6 MIMO Radar Spacetime Adaptive Processing and Signal Design 235
Chun-Yang Chen and P. P. Vaidyanathan
6.1 Introduction 236
6.1.1 Notations 238
6.2 The Virtual Array Concept 238
6.3 Spacetime Adaptive Processing in MIMO Radar 242
6.3.1 Signal Model 243
6.3.2 Fully Adaptive MIMO-STAP 246
6.3.3 Comparison with SIMO System 247
6.3.4 The Virtual Array in STAP 248
6.4 Clutter Subspace in MIMO Radar 249
6.4.1 Clutter Rank in MIMO Radar: MIMO Extension
of Brennan’s Rule 250
6.4.2 Data-Independent Estimation of the Clutter Subspace
with PSWF 253
6.5 New STAP Method for MIMO Radar 257
6.5.1 The Proposed Method 258
6.5.2 Complexity of the New Method 259
6.5.3 Estimation of the Covariance Matrices 259
6.5.4 Zero-Forcing Method 260
6.5.5 Comparison with Other Methods 260
6.6 Numerical Examples 261
6.7 Signal Design of the STAP Radar System 265
6.7.1 MIMO Radar Ambiguity Function 265
6.7.2 Some Properties of the MIMO Ambiguity Function 267
6.7.3 The MIMO Ambiguity Function of Periodic
Pulse Radar Signals 272
6.7.4 Frequency-Multiplexed LFM Signals 274
6.7.5 Frequency-Hopping Signals 276
CONTENTS ix
6.8 Conclusions 278
Acknowledgments 279
References 279
7 Slow-Time MIMO SpaceTime Adaptive Processing 283
Vito F. Mecca, Dinesh Ramakrishnan, Frank C. Robey,
and Jeffrey L. Krolik
7.1 Introduction 283
7.1.1 MIMO Radar and Spatial Diversity 284
7.1.2 MIMO and Target Fading 286
7.1.3 MIMO and Processing Gain 286
7.2 SIMO Radar Modeling and Processing 289
7.2.1 Generalized Transmitted Radar Waveform 289
7.2.2 SIMO Target Model 290
7.2.3 SIMO Covariance Models 291
7.2.4 SIMO Radar Processing 292
7.3 Slow-Time MIMO Radar Modeling 293
7.3.1 Slow-Time MIMO Target Model 293
7.3.2 Slow-Time MIMO Covariance Model 295
7.4 Slow-Time MIMO Radar Processing 297
7.4.1 Slow-Time MIMO Beampattern and VSWR 299
7.4.2 Subarray Slow-Time MIMO 301
7.4.3 SIMO versus Slow-Time MIMO Design Comparisons 301
7.4.4 MIMO Radar Estimation of Transmit –Receive
Directionality Spectrum 302
7.5 OTHr Propagation and Clutter Model 303
7.6 Simulations Examples 307
7.6.1 Postreceive/Transmit Beamforming 307
7.6.2 SINR Performance 311
7.6.3 Transmit –Receive Spectrum 315
7.7 Conclusion 316
Acknowledgment 316
References 316
8 MIMO as a Distributed Radar System 319
H. D. Griffiths, C. J. Baker, P. F. Sammartino, and M. Rangaswamy
8.1 Introduction 319
8.2 Systems 321
8.2.1 Signal Model 323
8.2.2 Spatial MIMO System 325
x CONTENTS
8.2.3 Netted Radar Systems 325
8.2.4 Decentralized Radar Network (DRN) 327
8.3 Performance 329
8.3.1 False-Alarm Rate (FAR) 329
8.3.2 Probability of Detection (Pd) 336
8.3.3 Jamming Tolerance 348
8.3.4 Coverage 352
8.4 Conclusions 359
Acknowledgment 361
References 361
9 Concepts and Applications of A MIMO Radar System
with Widely Separated Antennas 365
Hana Godrich, Alexander M. Haimovich, and Rick S. Blum
9.1 Background 365
9.2 MIMO Radar Concept 369
9.2.1 Signal Model 369
9.2.2 Spatial Decorrelation 373
9.2.3 Other Multiple Antenna Radars 375
9.3 NonCoherent MIMO Radar Applications 377
9.3.1 Diversity Gain 377
9.3.2 Moving-Target Detection 380
9.4 Coherent MIMO Radar Applications 383
9.4.1 Ambiguity Function 385
9.4.2 CRLB 388
9.4.3 MLE Target Localization 390
9.4.4 BLUE Target Localization 393
9.4.5 GDOP 395
9.4.6 Discussion 399
9.5 Chapter Summary 399
Appendix 9A Deriving the FIM 400
Appendix 9B Deriving the CRLB on the Location
Estimate Error 403
Appendix 9C MLE of Time Delays — Error Statistics 405
Appendix 9D Deriving the Lowest GDOP for Special Cases 407
9D.1 Special Case: N  N MIMO 407
9D.2 Special Case: 1  N MIMO 408
9D.3 General Case: M  N MIMO 408
Acknowledgments 408
References 408
CONTENTS xi
10 SpaceTime Coding for MIMO Radar 411
Antonio De Maio and Marco Lops
10.1 Introduction 411
10.2 System Model 415
10.3 Detection In MIMO Radars 417
10.3.1 Full-Rank Code Matrix 419
10.3.2 Rank 1 Code Matrix 420
10.4 Spacetime Code Design 421
10.4.1 Chernoff-Bound-Based (CBB) Code Construction 423
10.4.2 SCR-Based Code Construction 426
10.4.3 Mutual-Information-Based (MIB) Code Construction 427
10.5 The Interplay Between STC and Detection Performance 429
10.6 Numerical Results 431
10.7 Adaptive Implementation 437
10.8 Conclusions 441
Acknowledgment 442
References 442