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Summary
Summary
The first book to present a systematic and coherent picture of MIMO radars
Due to its potential to improve target detection and discrimination capability, Multiple-Input and Multiple-Output (MIMO) radar has generated significant attention and widespread interest in academia, industry, government labs, and funding agencies. This important new work fills the need for a comprehensive treatment of this emerging field.
Edited and authored by leading researchers in the field of MIMO radar research, this book introduces recent developments in the area of MIMO radar to stimulate new concepts, theories, and applications of the topic, and to foster further cross-fertilization of ideas with MIMO communications. Topical coverage includes:
Adaptive MIMO radar
Beampattern analysis and optimization for MIMO radar
MIMO radar for target detection, parameter estimation, tracking,association, and recognition
MIMO radar prototypes and measurements
Space-time codes for MIMO radar
Statistical MIMO radar
Waveform design for MIMO radar
Written in an easy-to-follow tutorial style, MIMO Radar Signal Processing serves as an excellent course book for graduate students and a valuable reference for researchers in academia and industry.
Author Notes
Jian Li, PhD, is Professor and Director of the Spectral Analysis Laboratory of the Department of Electrical and Computer Engineering at the University of Florida. She has coedited one book, coauthored one book and four book chapters, and published approximately 300 refereed technical conference contributions and journal papers, many of which are on topics related to array signal processing.
Petre Stoica, PhD, is Professor of System Modeling in the Information Technology Department at Uppsala University, Sweden. He has coedited two books, coauthored nine books, and published approximately 500 refereed technical conference contributions and journal papers, many of which are on topics related to array signal processing.
Table of Contents
Preface | p. xiii |
Contributors | p. xvii |
1 Mimo Radar - Diversity Means Superiority | p. 1 |
1.1 Introduction | p. 1 |
1.2 Problem Formulation | p. 4 |
1.3 Parameter Identifiability | p. 5 |
1.3.1 Preliminary Analysis | p. 5 |
1.3.2 Sufficient and Necessary Conditions | p. 7 |
1.3.3 Numerical Examples | p. 8 |
1.4 Nonparametric Adaptive Techniques for Parameter Estimation | p. 11 |
1.4.1 Absence of Array Calibration Errors | p. 12 |
1.4.2 Presence of Array Calibration Errors | p. 15 |
1.4.3 Numerical Examples | p. 18 |
1.5 Parametric Techniques for Parameter Estimation | p. 28 |
1.5.1 ML and BIC | p. 28 |
1.5.2 Numerical Examples | p. 34 |
1.6 Transmit Beampattern Designs | p. 35 |
1.6.1 Beampattern Matching Design | p. 35 |
1.6.2 Minimum Sidelobe Beampattern Design | p. 38 |
1.6.3 Phased-Array Beampattern Design | p. 39 |
1.6.4 Numerical Examples | p. 40 |
1.6.5 Application to Ultrasound Hyperthermia Treatment of Breast Cancer | p. 47 |
1.7 Conclusions | p. 56 |
Appendix IA Generalized Likelihood Ratio Test | p. 57 |
Appendix 1B Lemma and Proof | p. 59 |
Acknowledgments | p. 60 |
References | p. 60 |
2 MIMO Radar: Concepts, Performance Enhancements, and Applications | p. 65 |
2.1 Introduction | p. 65 |
2.1.1 A Short History of Radar | p. 65 |
2.1.2 Definition and Characteristics of MIMO Radar | p. 66 |
2.1.3 Uses of MIMO Radar | p. 68 |
2.1.4 The Current State of MIMO Radar Research | p. 70 |
2.1.5 Chapter Outline | p. 71 |
2.2 Notation | p. 72 |
2.3 MIMO Radar Virtual Aperture | p. 73 |
2.3.1 MIMO Channel | p. 73 |
2.3.2 MIMO Virtual Array: Resolution and Sidelobes | p. 74 |
2.4 MIMO Radar in Clutter-Free Environments | p. 77 |
2.4.1 Limitations of Cramer-Rao Estimation Bounds | p. 77 |
2.4.2 Signal Model | p. 77 |
2.4.3 Fisher Information Matrix | p. 79 |
2.4.4 Waveform Correlation Optimization | p. 82 |
2.4.5 Examples | p. 85 |
2.5 Optimality of MIMO Radar for Detection | p. 87 |
2.5.1 Detection | p. 88 |
2.5.2 High SNR | p. 89 |
2.5.3 Weak-Signal Regime | p. 90 |
2.5.4 Optimal Beamforming without Search | p. 92 |
2.5.5 Nonfading Targets | p. 92 |
2.5.6 Some Additional Benefits of MIMO Radar | p. 93 |
2.6 MIMO Radar with Moving Targets in Clutter: GMTI Radars | p. 93 |
2.6.1 Signal Model | p. 93 |
2.6.2 Localization and Adapted SNR | p. 96 |
2.6.3 Inner Products and Beamwidths | p. 101 |
2.6.4 SNR Loss | p. 103 |
2.6.5 SNR Loss and Waveform Optimization | p. 107 |
2.6.6 Area Search Rates | p. 109 |
2.6.7 Some Examples | p. 109 |
2.7 Summary | p. 111 |
Appendix 2A A Localization Principle | p. 111 |
Appendix 2B Bounds on R(N) | p. 114 |
Appendix 2C An Operator Norm Inequality | p. 115 |
Appendix 2D Negligible Terms | p. 115 |
Appendix 2E Bound on Eigenvalues | p. 115 |
Appendix 2F Some Inner Products | p. 116 |
Appendix 2G An Invariant Inner Product | p. 117 |
Appendix 2H Kronecker and Tensor Products | p. 118 |
2H.1 Lexicographical Ordering | p. 118 |
2H.2 Tensor and Kronecker Products | p. 118 |
2H.3 Properties | p. 119 |
Acknowledgments | p. 119 |
References | p. 120 |
3 Generalized MIMO Radar Ambiguity Functions | p. 123 |
3.1 Introduction | p. 123 |
3.2 Background | p. 124 |
3.3 MIMO Signal Model | p. 127 |
3.4 MIMO Parametric Channel Model | p. 131 |
3.4.1 Transmit Signal Model | p. 131 |
3.4.2 Channel and Target Models | p. 132 |
3.4.3 Received Signal Parametric Model | p. 133 |
3.5 MIMO Ambiguity Function | p. 134 |
3.5.1 MIMO Ambiguity Function Composition | p. 137 |
3.5.2 Cross-Correlation Function under Model Simplifications | p. 138 |
3.5.3 Autocorrelation Function and Transmit Beampatterns | p. 141 |
3.6 Results and Examples | p. 143 |
3.6.1 Orthogonal Signals | p. 143 |
3.6.2 Coherent Signals | p. 147 |
3.7 Conclusion | p. 149 |
References | p. 150 |
4 Performance Bounds and Techniques for Target Localization Using MIMO Radars | p. 153 |
4.1 Introduction | p. 153 |
4.2 Problem Formulation | p. 155 |
4.3 Properties | p. 158 |
4.3.1 Virtual Aperture Extension | p. 159 |
4.3.2 Spatial Coverage and Probability of Exposure | p. 162 |
4.3.3 Beampattern Improvement | p. 163 |
4.4 Target Localization | p. 165 |
4.4.1 Maximum-Likelihood Estimation | p. 165 |
4.4.2 Transmission Diversity Smoothing | p. 167 |
4.5 Performance Lower Bound for Target Localization | p. 170 |
4.5.1 Cramer-Rao Bound | p. 170 |
4.5.2 The Barankin Bound | p. 173 |
4.6 Simulation Results | p. 175 |
4.7 Discussion and Conclusions | p. 180 |
Appendix 4A Log-Likelihood Derivation | p. 181 |
4A.1 General Model | p. 182 |
4A.2 Single Range-Doppler with No Interference | p. 184 |
Appendix 4B Transmit-Receive Pattern Derivation | p. 185 |
Appendix 4C Fisher Information Matrix Derivation | p. 186 |
References | p. 189 |
5 Adaptive Signal Design For MIMO Radars | p. 193 |
5.1 Introduction | p. 193 |
5.2 Problem Formulation | p. 195 |
5.2.1 Signal Model with Reduced Number of Range Cells | p. 199 |
5.2.2 Multipulse and Doppler Effects | p. 200 |
5.2.3 The Complete Model | p. 203 |
5.2.4 The Statistical Model | p. 203 |
5.3 Estimation | p. 203 |
5.3.1 Beamforming Solution | p. 204 |
5.3.2 Least-Squares Solutions | p. 210 |
5.3.3 Waveform Design for Estimation | p. 210 |
5.4 Detection | p. 214 |
5.4.1 The Optimal Detector | p. 214 |
5.4.2 The SINR | p. 215 |
5.4.3 Optimal Waveform Design | p. 217 |
5.4.4 Suboptimal Waveform Design | p. 218 |
5.4.5 Constrained Design | p. 219 |
5.4.6 The Target and Clutter Models | p. 220 |
5.4.7 Numerical Examples | p. 221 |
5.5 MIMO Radar and Phased Arrays | p. 226 |
5.5.1 Scan Transmit Beam after Receive | p. 228 |
5.5.2 Adaptation of Transmit Beampattern | p. 229 |
5.5.3 Combined Transmit-Receive Beamforming | p. 229 |
Appendix 5A Theoretical SINR Calculation | p. 231 |
References | p. 232 |
6 MIMO Radar Spacetime Adaptive Processing and Signal Design | p. 235 |
6.1 Introduction | p. 236 |
6.1.1 Notations | p. 238 |
6.2 The Virtual Array Concept | p. 238 |
6.3 Spacetime Adaptive Processing in MIMO Radar | p. 242 |
6.3.1 Signal Model | p. 243 |
6.3.2 Fully Adaptive MIMO-STAP | p. 246 |
6.3.3 Comparison with SIMO System | p. 247 |
6.3.4 The Virtual Array in STAP | p. 248 |
6.4 Clutter Subspace in MIMO Radar | p. 249 |
6.4.1 Clutter Rank in MIMO Radar: MIMO Extension of Brennan's Rule | p. 250 |
6.4.2 Data-Independent Estimation of the Clutter Subspace with PSWF | p. 253 |
6.5 New STAP Method for MIMO Radar | p. 257 |
6.5.1 The Proposed Method | p. 258 |
6.5.2 Complexity of the New Method | p. 259 |
6.5.3 Estimation of the Covariance Matrices | p. 259 |
6.5.4 Zero-Forcing Method | p. 260 |
6.5.5 Comparison with Other Methods | p. 260 |
6.6 Numerical Examples | p. 261 |
6.7 Signal Design of the STAP Radar System | p. 265 |
6.7.1 MIMO Radar Ambiguity Function | p. 265 |
6.7.2 Some Properties of the MIMO Ambiguity Function | p. 267 |
6.7.3 The MIMO Ambiguity Function of Periodic Pulse Radar Signals | p. 272 |
6.7.4 Frequency-Multiplexed LFM Signals | p. 274 |
6.7.5 Frequency-Hopping Signals | p. 276 |
6.8 Conclusions | p. 278 |
Acknowledgments | p. 279 |
References | p. 279 |
7 Slow-Time MIMO SpaceTime Adaptive Processing | p. 283 |
7.1 Introduction | p. 283 |
7.1.1 MIMO Radar and Spatial Diversity | p. 284 |
7.1.2 MIMO and Target Fading | p. 286 |
7.1.3 MIMO and Processing Gain | p. 286 |
7.2 SIMO Radar Modeling and Processing | p. 289 |
7.2.1 Generalized Transmitted Radar Waveform | p. 289 |
7.2.2 SIMO Target Model | p. 290 |
7.2.3 SIMO Covariance Models | p. 291 |
7.2.4 SIMO Radar Processing | p. 292 |
7.3 Slow-Time MIMO Radar Modeling | p. 293 |
7.3.1 Slow-Time MIMO Target Model | p. 293 |
7.3.2 Slow-Time MIMO Covariance Model | p. 295 |
7.4 Slow-Time MIMO Radar Processing | p. 297 |
7.4.1 Slow-Time MIMO Beampattern and VSWR | p. 299 |
7.4.2 Subarray Slow-Time MIMO | p. 301 |
7.4.3 SIMO versus Slow-Time MIMO Design Comparisons | p. 301 |
7.4.4 MIMO Radar Estimation of Transmit-Receive Directionality Spectrum | p. 302 |
7.5 OTHr Propagation and Clutter Model | p. 303 |
7.6 Simulations Examples | p. 307 |
7.6.1 Postreceive/Transmit Beamforming | p. 307 |
7.6.2 SINR Performance | p. 311 |
7.6.3 Transmit-Receive Spectrum | p. 315 |
7.7 Conclusion | p. 316 |
Acknowledgment | p. 316 |
References | p. 316 |
8 MIMO as a Distributed Radar System | p. 319 |
8.1 Introduction | p. 319 |
8.2 Systems | p. 321 |
8.2.1 Signal Model | p. 323 |
8.2.2 Spatial MIMO System | p. 325 |
8.2.3 Netted Radar Systems | p. 325 |
8.2.4 Decentralized Radar Network (DRN) | p. 327 |
8.3 Performance | p. 329 |
8.3.1 False-Alarm Rate (FAR) | p. 329 |
8.3.2 Probability of Detection (P[subscript d]) | p. 336 |
8.3.3 Jamming Tolerance | p. 348 |
8.3.4 Coverage | p. 352 |
8.4 Conclusions | p. 359 |
Acknowledgment | p. 361 |
References | p. 361 |
9 Concepts and Applications of A MIMO Radar System with Widely Separated Antennas | p. 365 |
9.1 Background | p. 365 |
9.2 MIMO Radar Concept | p. 369 |
9.2.1 Signal Model | p. 369 |
9.2.2 Spatial Decorrelation | p. 373 |
9.2.3 Other Multiple Antenna Radars | p. 375 |
9.3 NonCoherent MIMO Radar Applications | p. 377 |
9.3.1 Diversity Gain | p. 377 |
9.3.2 Moving-Target Detection | p. 380 |
9.4 Coherent MIMO Radar Applications | p. 383 |
9.4.1 Ambiguity Function | p. 385 |
9.4.2 CRLB | p. 388 |
9.4.3 MLE Target Localization | p. 390 |
9.4.4 BLUE Target Localization | p. 393 |
9.4.5 GDOP | p. 395 |
9.4.6 Discussion | p. 399 |
9.5 Chapter Summary | p. 399 |
Appendix 9A Deriving the FIM | p. 400 |
Appendix 9B Deriving the CRLB on the Location Estimate Error | p. 403 |
Appendix 9C MLE of Time Delays - Error Statistics | p. 405 |
Appendix 9D Deriving the Lowest GDOP for Special Cases | p. 407 |
9D.1 Special Case: N x N MIMO | p. 407 |
9D.2 Special Case: 1 x N MIMO | p. 408 |
9D.3 General Case: M x N MIMO | p. 408 |
Acknowledgments | p. 408 |
References | p. 408 |
10 SpaceTime Coding for MIMO Radar | p. 411 |
10.1 Introduction | p. 411 |
10.2 System Model | p. 415 |
10.3 Detection In MIMO Radars | p. 417 |
10.3.1 Full-Rank Code Matrix | p. 419 |
10.3.2 Rank 1 Code Matrix | p. 420 |
10.4 Spacetime Code Design | p. 421 |
10.4.1 Chernoff-Bound-Based (CBB) Code Construction | p. 423 |
10.4.2 SCR-Based Code Construction | p. 426 |
10.4.3 Mutual-Information-Based (MIB) Code Construction | p. 427 |
10.5 The Interplay Between STC and Detection Performance | p. 429 |
10.6 Numerical Results | p. 431 |
10.7 Adaptive Implementation | p. 437 |
10.8 Conclusions | p. 441 |
Acknowledgment | p. 442 |
References | p. 442 |
Index | p. 445 |