Advances in Direction-of-Arrival Estimation Sathish Chandran Editor ARTECH HOUSE BOSTON LONDON artechhouse.com
Contents Preface xvii Acknowledgments xix Overview CHAPTER 1 Antenna Arrays for Direction-of-Arrival Estimation 3 1.1 Introduction 3 1.2 Spinning DF Antenna 4 1.3 Common DF Antennas 6 1.4 Antenna Arrays 7 1.4.1 Linear Arrays 8 1.4.2 Adcock Array 9 1.4.3 Array Element Spacing 10 1.4.4 Butler Matrix 12 1.4.5 Monopulse 15 1.4.6 Wullenweber Array 15 1.4.7 Planar Array 17 1.5 DF Algorithms and Arrays 18 References 19 CHAPTER 2 Detection-Estimation of Gaussian Sources by Nonuniform Linear Antenna Arrays: An Overview of the Generalized Likelihood-Ratio Test Approach 21 2.1 Introduction 21 2.2 GLRT Philosophy for the Detection-Estimation Problem 24 2.3 GLRT Detection-Estimation Results for Uniform and Sparse Antenna Arrays 30 2.3.1 Superior Case 30 2.3.2 Conventional Case 33 2.4 Conclusions 39 References 42
VIII Contents DOA Methods 47 CHAPTER 3 DOA Estimation of Wideband Signals 49 3.1 Incoherent Wideband DOA Estimation 52 3.2 Coherent Wideband DOA Estimation 52 3.2.1 Coherent Signal Subspace Method 53 3.2.2 BICSSM 54 3.2.3 WAVES 55 3.3 TOPS 56 3.3.1 Theory 57 3.3.2 Signal Subspace Projection 62 3.3.3 Performance Assessment 63 3.3.4 Modification of TOPS for Localization 66 3.4 Conclusions 67 Acknowledgments 68 References 68 CHAPTER 4 Coherent Broadband DOA Estimation Using Modal Space Processing 71 4.1 Introduction 71 4.2 System Model 72 4.3 Focusing Matrices for Coherent Wideband Processing 73 4.4 Spatial Resampling Method 74 4.5 Modal Decomposition 75 4.5.1 Linear Arrays 75 4.5.2 Modal Truncation 76 4.6 Modal Space Processing 77 4.6.1 Focusing Matrices 77 4.6.2 Spatial Resampling Matrices 78 4.7 Modal Space Algorithm 79 4.8 Simulation 80 4.8.1 A Group of Two Sources 80 4.8.2 Three Groups of Five Sources 82 4.9 Conclusions 85 References 85 CHAPTER 5 Target Localization in Three Dimensions 87 5.1 Direction-of-Arrival Estimation Method 87 5.1.1 Extraction of y,- 90 5.1.2 Extraction of z; 91 5.1.3 Extraction of d; 91 5.1.4 Pairing y ; -, г,, and dj 92 5.1.5 Complex Amplitude Estimation 92 5.1.6 Noisy Signals 92
Contents IX 5.2 Distance Estimation Method 93 5.3 Target Location Estimation and Simulation Results 96 5.4 Conclusions 101 References 101 CHAPTER 6 Polarimetrie Time-Frequency MUSIC for Direction Finding of Moving Sources with Time-Varying Polarizations 103 6.1 Introduction 103 6.2 Signal Model 105 6.2.1 Time-Frequency Distributions 105 6.2.2 Spatial Time-Frequency Distributions 105 6.3 Spatial Polarimetrie Time-Frequency Distributions 106 6.3.1 Polarimetrie Modeling 106 6.3.2 Polarimetrie Time-Frequency Distributions 108 6.3.3 Spatial Polarimetrie Time-Frequency Distributions 108 6.4 Polarimetrie Time-Frequency MUSIC 110 6.5 Spatio-Polarimetric Correlations 111 6.6 Moving Sources with Time-Varying Polarizations 112 6.6.1 Polarization Diversity and Selection of Data Samples 113 6.6.2 Polarization Diversity Consideration in PTF-MUSIC 114 6.7 Simulation Results 117 6.8 Conclusions 118 References 120 CHAPTER 7 A One-Dimensional Tree Structure-Based Algorithm for DOA-Delay Joint Estimation 123 7.1 Introduction 123 7.2 System Model 124 7.3 The Proposed Algorithm 127 7.3.1 S-ESPRIT 127 7.3.2 T-ESPRIT 128 7.3.3 TST-ESPRIT 131 7.4 Simulations and Discussions 138 7.5 Conclusions 141 References 141 Appendix 7.A Noise Property in (7.24) 142 CHAPTER 8 Direction-of-Arrival Estimation Approach Using Switched Parasitic Arrays 145 8.1 Introduction 145 8.2 Switched Parasitic Arrays 146 8.3 Wideband Direction-Finding Method for a Two-Path Model 148 8.3.1 Wideband Signaling in Multipath Environments 149 8.3.2 Method Description 149 8.3.3 Method Performance Analysis 151
Contents 8.4 A Modified MUSIC Algorithm for Switched Parasitic Arrays 153 8.4.1 Method Performance Analysis 155 8.5 Conclusions 157 References 159 CHAPTER 9 DOA Estimation for Noncircular Signals: Performance Bounds and Algorithms 161 9.1 Introduction 161 9.2 Array Signal Model 162 9.3 MUSIC-Like Algorithms 163 9.3.1 MUSIC-Like Algorithms Built Only from R^T 163 9.3.2 MUSIC-Like Algorithms Built from Both Ry' >T and R;, T 164 9.4 Asymptotically Minimum Variance Estimation 170 9.5 Stochastic Cramer-Rao Bound for Noncircular Gaussian Signals 173 9.6 Stochastic Cramer-Rao Bound for BPSK Signals 175 9.7 Illustrative Examples 177 9.8 Conclusions 187 References 188 CHAPTER 10 Localization of Scattered Sources 191 10.1 Introduction 191 10.2 Array Model 192 10.2.1 Coherently Distributed Source Model 193 10.2.2 Incoherently Distributed Source Model 195 10.3 Parameter Estimation Techniques 197 10.3.1 Estimation Techniques for CD Sources 197 10.3.2 Estimation Techniques for ID Sources 200 10.4 Conclusions 209 References 209 Source Localization Problems 211 CHAPTER 11 Direct Position Determination of Multiple Radio Transmitters 213 11.1 Introduction 213 11.2 Mathematical Preliminaries 215 11.3 Position Determination 217 11.3.1 Unknown Waveforms Signals 217 11.3.2 Known Waveform Signals 219 11.4 Numerical Examples 222 11.4.1 Example 1 222 11.4.2 Example 2 223
XI ПАЗ Example 3 223 11.4.4 Example 4 225 11.4.5 Example 5 225 11.5 Conclusions 225 References 227 Appendix 11.A Cramer-Rao Bound for Known Waveforms 228 Appendix 11.В CRB for Unknown Gaussian Waveforms 230 Appendix 11.С DPD Performance Analysis for Unknown Waveforms 233 ll.c.l Expressions for ft 234 11.C.2 Expressions for Ф 235 11.C.3 Special Case: Uniform Linear Array 237 Appendix ll.d The Frequency Domain Representation of Finite Length Observations 238 CHAPTER 12 Direction-of-Arrival Estimation Under Uncertainty 241 12.1 Introduction 241 12.2 Basic DOA Estimation Signal Model 242 12.3 Uncertainties in Signal Model and System Parameters 244 12.3.1 Sources of Uncertainty 245 12.3.2 Improving the Robustness 245 12.4 Uncertainty in Noise Model 247 12.4.1 Qualitative and Quantitative Robustness 248 12.4.2 Robust Procedures 250 12.5 Array Processing Examples 254 12.6 Conclusions 255 References 256 CHAPTER 13 Coupling Model in DOA Antenna Arrays 259 13.1 Introduction 259 13.2 Antenna Steering Vector Model 260 13.3 Steering Vector Errors and Their Influence in DOA Estimation 264 13.4 Coupling Model 266 13.5 Coupling Influence in DOA Estimation 272 13.6 Error Compensation 273 13.7 Conclusions 278 References 280 PART IV Specific Applications of DOA Estimation 283 CHAPTER 14 Maximum Likelihood Estimate of Target Angular Coordinates Under Main Beam Interference: Application to Recorded Live Data 285 14.1 Introduction 285
XII Contents 14.2 MLE Algorithm for Estimation of Target Angular Coordinates 286 14.3 CRLB of Estimation of Target Angular Coordinates 288 14.4 MLE Algorithm Simulation Results 292 14.5 Test on Recorded Live Data 294 14.5.1 Description of the Radar for Data Capture 295 14.5.2 Data Capture Experimental Setup 296 14.5.3 Comparison Between the Theoretical and Real Radar Beams 297 14.5.4 MLE on Recorded Live Data 301 14.6 Conclusions 301 References 302 CHAPTER 15 Direction Estimation of Broadband Sources for Auditory Localization and Spatially Selective Listening 305 15.1 Introduction 305 15.2 Scenario and Model 306 15.3 Characteristics of Natural Sound Sources 307 15.4 Decomposing into Spectral Components 308 15.5 DOA Estimation Based on Time Delays and Relative Attenuation 308 15.5.1 General Approach 309 15.5.2 DOA Estimation Using Time Delay Between the Sensors 309 15.5.3 Subspace Methods in a Reverberant Room 310 15.5.4 DOA Estimation Using Relative Attenuation Between the Sensors 311 15.6 Spectrally Weighted DOA Estimate 313 15.7 Source Separation Algorithm 314 15.8 Experimental Results 316 15.8.1 Parameter Values Used in the Implementation 316 15.8.2 Performance of the Algorithm When the Sources Are Sinusoidal 318 15.8.3 Performance of the Algorithm with Increasing Number of Sources 318 15.8.4 Performance of the Algorithm When the Sensor Spacing Is Varied 319 15.8.5 Resolvability of the Algorithm When Sources Are Closely Spaced 320 15.8.6 Performance of the Sound Source Separation from Real Two Sensor Array Recordings in Multitalker Scenario 320 15.8.7 Performance Measure for Listening Tests 321 15.8.8 Performance of the Algorithm with Headlike Structure 322 15.9 Conclusions 323 References 323 Selected Bibliography 324 CHAPTER 16 Multiple Target Estimation in a Surveillance Radar System with a Mechanically Rotating Antenna 327 16.1 Introduction 327
Contents Kill 16.2 Data Model and Problem Statement 328 16.3 The Estimation Algorithm 329 16.3.1 Asymptotic Maximum Likelihood Estimation 329 16.3.2 The AML-RELAX Estimator 332 16.4 Numerical Performance Analysis 334 16.5 Conclusions 342 References 342 CHAPTER 17 Joint DOA/DOD/DTOA Estimation System for UWB Double Directional Channel Modeling 345 17.1 Introduction 345 17.2 UWB Double Directional Channel Sounding System 346 17.3 Parametric Multipath Modeling for UWB 347 17.3.1 Multipath Model 347 17.3.2 Subband Model 349 17.3.3 Spherical Wave Model 349 17.3.4 Two Single Directional Measurements, Pairing, and Clusterization 350 17.4 ML-Based Parameter Estimation for UWB Directional Channel 351 17.4.1 Maximum Likelihood Parameter Estimation 352 17.4.2 Expectation Maximization Algorithm 352 17.4.3 SAGE Algorithm 353 17.4.4 Successive Interference Cancellation-Type Procedure 354 17.4.5 Consideration About the Subband 356 17.4.6 Deconvolution of Antenna Directivity 356 17.5 Experiments 356 17.5.1 Specification of Measurement Equipment 356 17.5.2 Measurement Environment 357 17.5.3 Results 357 17.6 Conclusions 358 References 360 CHAPTER 18 Conventional Method Improvement by Signal Property Exploitation 363 18.1 Cyclostationarity 363 18.2 Data Model 364 18.3 High-Resolution Techniques 365 18.3.1 Cyclic MUSIC Algorithm 365 18.3.2 Extended Cyclic MUSIC Algorithm 365 18.3.3 Root Cyclic MUSIC Algorithm 369 18.4 Nonselective Beamforming Techniques 372 18.4.1 Data Model 373 18.4.2 Beamforming for Cyclostationary Signals 374
XIV Contents 18.4.3 Minimum Variance Beamforming for Cyclostationary Signals 374 18.4.4 Discussion 375 18.4.5 Simulations 375 18.5 Conclusions 376 References 377 Experimental Setup and Results 379 CHAPTER 19 DOA Antenna Array Measurement and System Calibration 381 19.1 Introduction 381 19.2 Steering Vector Model 382 19.3 Calibration Process 386 19.3.1 Coupling Through Terminals 387 19.3.2 Radiation Pattern Measurements 388 19.3.3 Calibration Process for the RF Subsystem 389 19.3.4 Application Example 391 19.4 Conclusions 392 References 393 CHAPTER 20 ESPAR Antenna Signal Processing for DOA Estimation 395 20.1 Introduction 395 20.2 ESPAR Antenna Fundamentals 397 20.2.1 Structure and Formulation 397 20.2.2 Signal Model 400 20.3 High-Precision DOA Estimation 401 20.3.1 Correlation Matrix for Single-Port Antennas 402 20.3.2 Reactance-Domain Signal Processing 403 20.3.3 Computer Simulations 405 20.3.4 Experimental Verification 408 20.4 Practical System Applications 412 20.4.1 Satellite Attitude and Direction Control 412 20.4.2 Wireless Locator and Homing System 413 20.4.3 Wireless Ad Hoc Network 414 20.5 Conclusions 414 Acknowledgments 415 References 415 CHAPTER 21 A New DOA Estimation Method for Pulsed Doppler Radar 419 21.1 Introduction 419 21.2 Review of MUSIC and BS-MUSIC 421 21.3 Model for HF Radar 423
Contents xv 21.4 Two-Dimensional Prefiltering-Based MUSIC 423 21.5 Algorithm Summary for 2DP-MUSIC 427 21.6 Performance Analysis 427 21.6.1 Formulation of Sample Null Spectra for MUSIC, BS-MUSIC, and 2DP-MUSIC 428 21.6.2 Expectation of 2DP-MUSIC's Null Spectrum 429 21.6.3 Resolution Threshold 430 21.7 Simulations 431 21.8 Experimental Result 433 21.9 Conclusions 435 References 435 Appendix 21.A Derivation of (21.24) 437 Appendix 21.В Resolution of Spectral MUSIC 438 List of Symbols 441 Acronyms 443 About the Authors 445 Index 459