PREFACE ...................................................... xiii
CONTRIBUTORS ................................................. xvii
1 MIMO Radar — Diversity Means Superiority ..................... 1
Jian Li and Petre Stoica
1.1 Introduction ............................................ 1
1.2 Problem Formulation ..................................... 4
1.3 Parameter Identifiability ............................... 5
1.3.1 Preliminary Analysis ............................. 5
1.3.2 Sufficient and Necessary Conditions .............. 7
1.3.3 Numerical Examples ............................... 8
1.4 Nonparametric Adaptive Techniques for Parameter
Estimation ............................................. 11
1.4.1 Absence of Array Calibration Errors ............. 12
1.4.2 Presence of Array Calibration Errors ............ 15
1.4.3 Numerical Examples .............................. 18
1.5 Parametric Techniques for Parameter Estimation ......... 28
1.5.1 ML and BIC ...................................... 28
1.5.2 Numerical Examples .............................. 34
1.6 Transmit Beampattern Designs ........................... 35
1.6.1 Beampattern Matching Design ..................... 35
1.6.2 Minimum Sidelobe Beampattern Design ............. 38
1.6.3 Phased-Array Beampattern Design ................. 39
1.6.4 Numerical Examples .............................. 40
1.6.5 Application to Ultrasound Hyperthermia
Treatment of Breast Cancer ...................... 47
1.7 Conclusions ............................................ 56
Appendix 1A Generalized Likelihood Ratio Test ............... 57
Appendix 1В 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 Cramér-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
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 Kronecker and Tensor Products .................. 118
2H.1 Lexicographical Ordering ....................... 118
2H.2 Tensor and Kronecker 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
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 Cramér-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
4.7.1 General Model .................................. 182
4.7.2 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 TheSINR ........................................ 215
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
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
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: I × N MIMO ........................ 408
9D.3 General Case: M × N MIMO ........................ 408
Acknowledgments ............................................ 408
References ................................................. 408
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
INDEX ......................................................... 445
|
