Sensor Array Signal Processing

I was cautious after reading the other reviewer's comments regarding this book's typography, but I decided to check it out since my school's library carried a copy. My graduate studies concern acoustic phased arrays, so this could've been one of my best references. I agree that the book's presentation is often unclear. Several diagrams depicting wavefronts and angles are incomprehensible -- I could deduce their associated equations, but only because I already knew the subject matter. The typesetting bothered me as well, but in principle I could live with it. IMHO book tries to convey too much in too little space. It reads like succint class notes intended to refresh one's memory, and not as a standalone reference to a previously unknown subject. It would be useful to Prof. Naidu's students, but it's of questionable value to other readers. I wish this review could've been more positive. With better editing, more detailed deductions and carefully drawn diagrams this could be one of the strongest references in the field of phased arrays. Regrettably, I can't recommend it. Sensor Array Signal Processing......Page 1 Copyright......Page 4 Prologue......Page 5 Contents......Page 9 Acknowledgment......Page 11 Dedication......Page 12 1.1 Types of Wavefields & Governing Equations......Page 13 1.2.1 Fourier Representation of Wave Field......Page 23 1.2.3 Apparent Propagation Speed......Page 26 1.2.4 Continuation of Wavefield......Page 29 1.2.5 Point Source......Page 30 1.2.6 Spatial Sampling & Aliasing......Page 34 1.2.7 Dispersion......Page 35 1.3.1 Ray Propagation......Page 38 1.3.2 Propagation in Channel--Ray Theory......Page 41 1.3.3 Propagation in Channel--Normal Mode Theory......Page 45 1.3.4 Propagation through Layered Medium......Page 47 1.4.1 Frequency-Wavenumber Spectrum......Page 51 1.4.2 Open Space......Page 53 1.4.3 Channel......Page 56 1.5.1 Random Filter Model......Page 61 Delay Diversity......Page 64 1.5.3 Local Scattering......Page 66 1.6.1 Acoustic Field......Page 71 1.6.2 Far Field Approximation......Page 75 1.6.3 Multisource Illumination......Page 77 1.6.4 Scattering of EM Field......Page 80 1.7 Exercises......Page 82 References......Page 83 2.1.1 Array Response......Page 86 2.1.2 Array Steering......Page 90 2.1.3 Broadband Source......Page 93 Angular Spectrum......Page 94 Slant Stacking......Page 97 2.1.4 Matrix Formulation......Page 98 Matrix......Page 100 Redundant sensors:......Page 105 Missing Sensors......Page 107 Random Array......Page 110 2.1.6 Flexible Array......Page 112 2.2.1 Uniform Planar Array (UPA)......Page 116 Random Array......Page 120 2.2.2 Uniform Circular Array (UCA)......Page 121 Boundary Array......Page 128 2.2.3 Distributed Dipoles......Page 131 Electric Dipole Array......Page 134 2.3.1 Bandwidth of Array......Page 136 2.3.2 Broadband Signals......Page 139 2.4 Source and Sensor Arrays......Page 142 2.4.1 Coarray......Page 143 2.4.3 Synthetic Aperture......Page 149 References......Page 154 3.1 Digital Filters in w-k Domain......Page 158 3.1.2 Fan Filters......Page 159 3.1.3 Fast Algorithm......Page 162 3.1.4 Quadrant Filter......Page 166 3.1.5 Weighted Least Squares Filter......Page 171 3.1.6 Aliasing Effect in Fan Filter & Quadrant Filter......Page 173 3.2.1 McClellan's Transformation......Page 175 3.2.2 Fan Filter......Page 180 3.3.1 Planar Array......Page 183 3.3.2 Frequency Domain......Page 187 3.3.3 Constrained Minimization......Page 190 3.4.1 Uniform Linear Array (ULA)......Page 192 3.4.2 Uniform Circular Array......Page 194 3.4.3 Robustification......Page 195 3.4.4 Levinson-Durbin Algorithm......Page 197 3.5 Predictive Noise Cancellation......Page 203 3.5.1 Signal Source in Near Field......Page 204 3.5.2 Source in Far Field......Page 206 3.5.3 Adaptive Filter......Page 211 3.6 Exercises......Page 214 References......Page 215 4.1.1 Spectral Representation of Wavefield......Page 217 4.1.2 Aliasing......Page 219 4.1.3 Spectral Matrix......Page 221 Propagation Matrix......Page 225 4.1.4 Eigenstructure......Page 226 4.1.6 Parametric Spectrum......Page 227 4.2.1 Beamformation......Page 229 Narrowband......Page 230 Window......Page 231 Rayleigh Resolution......Page 232 Sources of Error......Page 234 4.2.2 Broadband Beamformation......Page 236 Delayed Snapshots......Page 237 4.3 Capon's w-k Spectrum......Page 240 Special Case......Page 242 4.3.1 Resolution......Page 243 4.3.2 Robust Beamformation......Page 246 4.3.3 High Resolution Capon Spectrum......Page 249 4.4.1 Maximum Entropy......Page 252 4.4.2 Resolution......Page 256 4.4.3 Finite Data Effects......Page 259 4.4.4 Iterative Inversion of Spectral Matrix......Page 261 4.5 Exercises......Page 262 References......Page 264 5.1 Subspace Methods (Narrowband)......Page 266 5.1.1 Music......Page 267 Signal Eigenvalues & Source Power......Page 269 Aliasing......Page 270 5.1.2 Correlated Sources......Page 273 5.1.3 Direct Estimation......Page 278 Root Music......Page 279 Subspace Rotation......Page 281 5.1.4 Diffused Source......Page 284 5.1.5 Adaptive Subspace......Page 285 5.2 Subspace Methods (Broadband)......Page 287 5.2.1 Wideband Focusing......Page 288 5.2.2 Spatial Resampling......Page 291 5.2.3 Spatio Temporal Covariance Matrix (STCM)......Page 293 5.2.4 Number of Sources......Page 297 5.3.1 Multitone Signal......Page 298 5.3.2 BPSK Signal......Page 303 Postcorrelation Covariance Matrix......Page 306 5.3.3 Cyclostationary Signals......Page 309 5.4.1 Amplitude & Phase Variation of Sensor......Page 314 5.4.2 Shape Estimation......Page 315 5.5 Source in Bounded Space......Page 317 5.5.1 Single Reflecting Surface......Page 318 5.5.2 Two Reflecting Surfaces......Page 320 5.6 Exercises......Page 323 References......Page 324 6.1 Wiener Filters......Page 328 Array Gain......Page 329 6.1.2 Two Source Case......Page 330 6.1.3 Linear Least Squares Estimate (LLSE)......Page 334 6.1.4 Effects of Errors in DOA......Page 337 6.2 Minimum Variance (Capon Method)......Page 340 6.2.1 Extended Source......Page 341 6.2.2 Single Point Source Case......Page 342 6.2.3 Two Source Case......Page 344 6.3.1 Null Steering......Page 348 6.3.2 Beam Steered Adaptive Array......Page 349 6.3.3 Adaptive Capon filter......Page 352 6.4 Beamformation with Coded Signals......Page 354 6.4.2 Estimation of All Direction Vectors......Page 355 6.4.3 Simulation Results......Page 356 6.4.4 Beamforming with Cyclostationary Signals......Page 357 6.5 Multipath Channel......Page 358 6.5.1 Known Channel......Page 360 6.5.2 Partially Known Channel......Page 364 6.6 Exercises......Page 368 References......Page 369 7.1.1 Absorption......Page 371 7.1.2 Filtered Backprojection Algorithm......Page 375 7.1.3 Algebraic Reconstruction......Page 377 Borehole Tomography......Page 379 Source/Sensor Array Design......Page 381 7.2 Diffracting Radiation......Page 382 Linear Array......Page 383 7.2.1 Filtered Backpropagation Algorithm......Page 385 Circular Array......Page 387 Verification of Fourier Diffraction Theorem......Page 389 7.2.3 Bilinear Interpolation Algorithm......Page 391 7.2.4 Imaging with Circular Array......Page 392 7.3.1 Spectrum Coverage......Page 395 7.3.2 Signal Processing Issues......Page 396 7.3.3 Cross Borehole Tomography......Page 399 7.3.4 Maximum Entropy Extrapolation......Page 402 7.4 Reflection Tomography......Page 403 7.4.1 Line Integral......Page 405 7.4.2 Spherical Wavefronts......Page 408 7.5 Object Shape Estimation......Page 410 7.5.1 Fourier Transform of Binary Convex Polygonal Object......Page 411 7.5.2 Pairing Algorithm......Page 413 7.5.3 Performance Analysis......Page 416 7.6 Exercises......Page 417 References......Page 419 8.1 Migration......Page 422 8.1.1 Imaging Conditions......Page 423 8.1.2 Downward Continuation of Sources & Sensors......Page 424 8.2 Exploding Reflector Model......Page 425 8.2.1 Initial Value Problem......Page 427 8.3.1 Downward Continuation......Page 428 8.3.2 Layered Medium......Page 430 8.3.3 Sloping Interface......Page 431 8.3.4 Depropagation of Wavefield......Page 433 8.3.5 Relation to Diffraction Tomography......Page 435 8.3.6 Continuation of Sources & Sensors......Page 437 8.4 Focused Beam......Page 438 8.4.1 Zero-Offset Wavefield......Page 439 Common Depth Point......Page 440 8.4.2 Layered Medium......Page 442 8.4.3 Focusing......Page 444 8.4.4 Depth of Focus......Page 446 8.4.5 Inclined Reflector......Page 447 8.4.6 Relation between Focusing & Downward Extrapolation......Page 449 8.4.7 Focused Beamformation for Imaging......Page 451 8.5.1 Wave Speed from CDP Gathers......Page 452 Interval Speed......Page 453 Maximum Likelihood......Page 454 8.5.3 Focusing with Optimum Wave Speed......Page 457 References......Page 459

Sensors arrays are used in diverse applications across a broad range of disciplines. Regardless of the application, however, the tools of sensor array signal processing remain the same. Furthermore, whether your interest is in acoustic, seismic, mechanical, or electromagnetic wavefields, they all have a common mathematical framework. Mastering this framework and those tools lays a strong foundation for more specialized study and research.

Sensor Array Signal Processing helps build that foundation. It unravels the underlying principles of the subject without reference to any particular application. Instead, the author focuses on the common threads that exist in wavefield analysis. After introducing the basic equations governing different wavefields, the treatment includes topics from simple beamformation, spatial filtering, and high resolution DOA estimation to imaging and reflector mapping. It studies different types of sensor configurations, but focuses on the uniform linear and circular arrays-the most useful configurations for understanding array systems in practice.

Unique in its approach, depth, and quantitative focus, Sensor Array Signal Processing offers the ideal starting point and an outstanding reference for those working or interested in medical imaging, astronomy, radar, communications, sonar, seismology-any field that studies propagating wavefields. Its clear exposition, numerical examples, exercises, and wide applicability impart a broad picture of array signal processing unmatched by any other text on the market.

This introduction and reference to sensor array signal processing is written to be widely applicable and useable for those working or interested in medical imaging, astronomy, radar, communications, sonar, seismology, and any field that studies propagating wavefields. Emphasizes the underlying principles in the field without reference to any particular application. An overview of wavefields is followed by treatment of sensor array systems, frequency wavenumber processing, source localization (including both frequency wavenumber spectrum and subspace methods), source estimation, tomographic imaging, and imaging by wavefield extrapolation. Annotation copyrighted by Book News, Inc., Portland, OR This text unravels the basic principles of array signal processing, without reference to a particular application, and provides a quantitative understanding of its concepts. Both traditional and modern topics are covered, and there are illustrative examples and exercises in each chapter