Cover image for Principles of signal detection and parameter estimation
Title:
Principles of signal detection and parameter estimation
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Publication Information:
New York, NY : Springer, 2008
Physical Description:
xviii, 639 p. : ill. ; 24 cm.
ISBN:
9780387765426

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30000010194102 TK5102.5 L484 2008 Open Access Book Book
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Summary

Summary

This textbook provides a comprehensive and current understanding of signal detection and estimation, including problems and solutions for each chapter. Signal detection plays an important role in fields such as radar, sonar, digital communications, image processing, and failure detection. The book explores both Gaussian detection and detection of Markov chains, presenting a unified treatment of coding and modulation topics. Addresses asymptotic of tests with the theory of large deviations, and robust detection. This text is appropriate for students of Electrical Engineering in graduate courses in Signal Detection and Estimation.


Table of Contents

1 Introductionp. 1
1.1 Book Organizationp. 3
1.2 Complementary Readingsp. 9
Referencesp. 10
Part I Foundations
2 Binary and M-ary Hypothesis Testingp. 15
2.1 Introductionp. 15
2.2 Bayesian Binary Hypothesis Testingp. 16
2.3 Sufficient Statisticsp. 25
2.4 Receiver Operating Characteristicp. 27
2.4.1 Neyman-Pearson Testsp. 29
2.4.2 ROC Propertiesp. 32
2.5 Minimax Hypothesis Testingp. 39
2.6 Gaussian Detectionp. 49
2.6.1 Known Signals in Gaussian Noisep. 50
2.6.2 Detection of a Zero-Mean Gaussian Signal in Noisep. 51
2.7 M-ary Hypothesis Testingp. 52
2.7.1 Bayesian M-ary Testsp. 52
2.7.2 Sufficient Statistics for M-ary Testsp. 56
2.7.3 Performance Analysisp. 59
2.7.4 Bounds Based on Pairwise Error Probabilityp. 62
2.8 Bibliographical Notesp. 63
2.9 Problemsp. 63
Referencesp. 71
3 Tests with Repeated Observationsp. 73
3.1 Introductionp. 73
3.2 Asymptotic Performance of Likelihood Ratio Testsp. 74
3.3 Bayesian Sequential Hypothesis Testingp. 88
3.4 Sequential Probability Ratio Testsp. 94
3.5 Optimality of SPRTsp. 100
3.6 Bibliographical Notesp. 102
3.7 Problemsp. 102
3.A Proof of Cramer's Theoremp. 108
Referencesp. 111
4 Parameter Estimation Theoryp. 113
4.1 Introductionp. 113
4.2 Bayesian Estimationp. 114
4.2.1 Optimum Bayesian Estimatorp. 117
4.2.2 Properties of the MSE Estimatorp. 123
4.3 Linear Least-squares Estimationp. 125
4.4 Estimation of Nonrandom Parametersp. 131
4.4.1 Biasp. 133
4.4.2 Sufficient Statisticp. 136
4.4.3 Cramer-Rao Lower Boundp. 138
4.4.4 Uniform Minimum Variance Unbiased Estimatesp. 150
4.5 Asymptotic Behavior of ML Estimatesp. 154
4.5.1 Consistencyp. 154
4.5.2 Asymptotic Distribution of the ML Estimatep. 157
4.6 Bibliographical Notesp. 159
4.7 Problemsp. 159
4.A Derivation of the RBLS Theoremp. 166
Referencesp. 167
5 Composite Hypothesis Testingp. 169
5.1 Introductionp. 169
5.2 Uniformly Most Powerful Testsp. 170
5.3 Invariant Testsp. 177
5.4 Linear Detection with Interfering Sourcesp. 194
5.5 Generalized Likelihood Ratio Testsp. 197
5.6 Asymptotic Optimality of the GLRTp. 204
5.6.1 Multinomial Distributionsp. 205
5.6.2 Exponential Familiesp. 216
5.7 Bibliographical Notesp. 221
5.8 Problemsp. 222
5.A Proof of Sanov's Theoremp. 231
Referencesp. 232
6 Robust Detectionp. 235
6.1 Introductionp. 235
6.2 Measures of Model Proximityp. 236
6.3 Robust Hypothesis Testingp. 239
6.3.1 Robust Bayesian and NP Testsp. 239
6.3.2 Clipped LR Testsp. 241
6.4 Asymptotic Robustnessp. 250
6.4.1 Least Favorable Densitiesp. 251
6.4.2 Robust Asymptotic Testp. 254
6.5 Robust Signal Detectionp. 257
6.5.1 Least-Favorable Densitiesp. 258
6.5.2 Receiver Structurep. 261
6.6 Bibliographical Notesp. 264
6.7 Problemsp. 265
Referencesp. 275
Part II Gaussian Detection
7 Karhunen-Loeve Expansion of Gaussian Processesp. 279
7.1 Introductionp. 279
7.2 Orthonormal Expansions of Deterministic Signalsp. 280
7.3 Eigenfunction Expansion of Covariance Kernelsp. 284
7.3.1 Properties of Covariance Kernelsp. 285
7.3.2 Decomposition of Covariance Matrices/Kernelsp. 289
7.4 Differential Characterization of the Eigenfunctionsp. 294
7.4.1 Gaussian Reciprocal Processesp. 294
7.4.2 Partially Observed Gaussian Reciprocal/Markov Processesp. 307
7.4.3 Rational Stationary Gaussian Processesp. 310
7.5 Karhunen-Loeve Decompositionp. 313
7.6 Asymptotic Expansion of Stationary Gaussian Processesp. 315
7.7 Bibliographical Notesp. 316
7.8 Problemsp. 317
Referencesp. 324
8 Detection of Known Signals in Gaussian Noisep. 327
8.1 Introductionp. 327
8.2 Binary Detection of Known Signals in WGNp. 328
8.2.1 Detection of a Single Signalp. 328
8.2.2 General Binary Detection Problemp. 332
8.3 M-ary Detection of Known Signals in WGNp. 338
8.4 Detection of Known Signals in Colored Gaussian Noisep. 344
8.4.1 Singular and Nonsingular CT Detectionp. 346
8.4.2 Generalized Matched Filter Implementationp. 348
8.4.3 Computation of the Distorted Signal g(t)p. 352
8.4.4 Noise Whitening Receiverp. 356
8.5 Bibliographical Notesp. 362
8.6 Problemsp. 362
Referencesp. 368
9 Detection of Signals with Unknown Parametersp. 371
9.1 Introductionp. 371
9.2 Detection of Signals with Unknown Phasep. 372
9.2.1 Signal Space Representationp. 373
9.2.2 Bayesian Formulationp. 374
9.2.3 GLR Testp. 377
9.2.4 Detector Implementationp. 378
9.3 Detection of DPSK Signalsp. 381
9.4 Detection of Signals with Unknown Amplitude and Phasep. 386
9.4.1 Bayesian Formulationp. 387
9.4.2 GLR Testp. 389
9.5 Detection with Arbitrary Unknown Parametersp. 389
9.6 Waveform Parameter Estimationp. 395
9.7 Detection of Radar Signalsp. 402
9.7.1 Equivalent Baseband Detection Problemp. 403
9.7.2 Cramer-Rao Boundp. 406
9.7.3 ML Estimates and GLR Detectorp. 409
9.7.4 Ambiguity Function Propertiesp. 412
9.8 Bibliographical Notesp. 420
9.9 Problemsp. 421
Referencesp. 431
10 Detection of Gaussian Signals in WGNp. 433
10.1 Introductionp. 433
10.2 Noncausal Receiverp. 434
10.2.1 Receiver Structurep. 435
10.2.2 Smoother Implementationp. 442
10.3 Causal Receiverp. 448
10.4 Asymptotic Stationary Gaussian Test Performancep. 456
10.4.1 Asymptotic Equivalence of Toeplitz and Circulant Matricesp. 457
10.4.2 Mean-square Convergence of S[subscript T]p. 459
10.4.3 Large Deviations Analysis of the LRTp. 461
10.4.4 Detection in WGNp. 466
10.5 Bibliographical Notesp. 473
10.6 Problemsp. 473
Referencesp. 480
11 EM Estimation and Detection of Gaussian Signals with Unknown Parametersp. 483
11.1 Introductionp. 483
11.2 Gaussian Signal of Unknown Amplitude in WGN of Unknown Powerp. 485
11.3 EM Parameter Estimation Methodp. 486
11.3.1 Motonicity Propertyp. 488
11.3.2 Examplep. 489
11.3.3 Convergence Ratep. 492
11.3.4 Large-Sample Covariance Matrixp. 498
11.4 Parameter Estimation of Hidden Gauss-Markov Modelsp. 500
11.4.1 EM iterationp. 501
11.4.2 Double-sweep smootherp. 504
11.4.3 Examplep. 507
11.5 GLRT Implementationp. 511
11.6 Bibliographical Notesp. 515
11.7 Problemsp. 516
Referencesp. 522
Part III Markov Chain Detection
12 Detection of Markov Chains with Known Parametersp. 527
12.1 Introductionp. 527
12.2 Detection of Completely Observed Markov Chainsp. 528
12.2.1 Notation and Backgroundp. 528
12.2.2 Binary Hypothesis Testingp. 533
12.2.3 Asymptotic Performancep. 534
12.3 Detection of Partially Observed Markov Chainsp. 543
12.3.1 MAP Sequence Detectionp. 546
12.3.2 Pointwise MAP Detectionp. 563
12.4 Example: Channel Equalizationp. 571
12.4.1 Markov Chain Modelp. 571
12.4.2 Performance Analysisp. 574
12.5 Bibliographical Notesp. 585
12.6 Problemsp. 585
Referencesp. 589
13 Detection of Markov Chains with Unknown Parametersp. 593
13.1 Introductionp. 593
13.2 GLR Detectorp. 595
13.2.1 Modelp. 595
13.2.2 GLR Testp. 597
13.3 Per Survivor Processingp. 599
13.3.1 Path Extensionp. 599
13.3.2 Parameter Vector Updatep. 599
13.4 EM Detectorp. 605
13.4.1 Forward-backward EMp. 608
13.4.2 EM Viterbi Detectorp. 613
13.5 Example: Blind Equalizationp. 619
13.5.1 Convergence Analysisp. 621
13.5.2 Convergence Ratep. 623
13.6 Bibliographical Notesp. 628
13.7 Problemsp. 628
Referencesp. 631
Indexp. 633