Title:
Principles of signal detection and parameter estimation
Personal Author:
Publication Information:
New York, NY : Springer, 2008
Physical Description:
xviii, 639 p. : ill. ; 24 cm.
ISBN:
9780387765426
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010194102 | TK5102.5 L484 2008 | Open Access Book | Book | Searching... |
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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 Introduction | p. 1 |
1.1 Book Organization | p. 3 |
1.2 Complementary Readings | p. 9 |
References | p. 10 |
Part I Foundations | |
2 Binary and M-ary Hypothesis Testing | p. 15 |
2.1 Introduction | p. 15 |
2.2 Bayesian Binary Hypothesis Testing | p. 16 |
2.3 Sufficient Statistics | p. 25 |
2.4 Receiver Operating Characteristic | p. 27 |
2.4.1 Neyman-Pearson Tests | p. 29 |
2.4.2 ROC Properties | p. 32 |
2.5 Minimax Hypothesis Testing | p. 39 |
2.6 Gaussian Detection | p. 49 |
2.6.1 Known Signals in Gaussian Noise | p. 50 |
2.6.2 Detection of a Zero-Mean Gaussian Signal in Noise | p. 51 |
2.7 M-ary Hypothesis Testing | p. 52 |
2.7.1 Bayesian M-ary Tests | p. 52 |
2.7.2 Sufficient Statistics for M-ary Tests | p. 56 |
2.7.3 Performance Analysis | p. 59 |
2.7.4 Bounds Based on Pairwise Error Probability | p. 62 |
2.8 Bibliographical Notes | p. 63 |
2.9 Problems | p. 63 |
References | p. 71 |
3 Tests with Repeated Observations | p. 73 |
3.1 Introduction | p. 73 |
3.2 Asymptotic Performance of Likelihood Ratio Tests | p. 74 |
3.3 Bayesian Sequential Hypothesis Testing | p. 88 |
3.4 Sequential Probability Ratio Tests | p. 94 |
3.5 Optimality of SPRTs | p. 100 |
3.6 Bibliographical Notes | p. 102 |
3.7 Problems | p. 102 |
3.A Proof of Cramer's Theorem | p. 108 |
References | p. 111 |
4 Parameter Estimation Theory | p. 113 |
4.1 Introduction | p. 113 |
4.2 Bayesian Estimation | p. 114 |
4.2.1 Optimum Bayesian Estimator | p. 117 |
4.2.2 Properties of the MSE Estimator | p. 123 |
4.3 Linear Least-squares Estimation | p. 125 |
4.4 Estimation of Nonrandom Parameters | p. 131 |
4.4.1 Bias | p. 133 |
4.4.2 Sufficient Statistic | p. 136 |
4.4.3 Cramer-Rao Lower Bound | p. 138 |
4.4.4 Uniform Minimum Variance Unbiased Estimates | p. 150 |
4.5 Asymptotic Behavior of ML Estimates | p. 154 |
4.5.1 Consistency | p. 154 |
4.5.2 Asymptotic Distribution of the ML Estimate | p. 157 |
4.6 Bibliographical Notes | p. 159 |
4.7 Problems | p. 159 |
4.A Derivation of the RBLS Theorem | p. 166 |
References | p. 167 |
5 Composite Hypothesis Testing | p. 169 |
5.1 Introduction | p. 169 |
5.2 Uniformly Most Powerful Tests | p. 170 |
5.3 Invariant Tests | p. 177 |
5.4 Linear Detection with Interfering Sources | p. 194 |
5.5 Generalized Likelihood Ratio Tests | p. 197 |
5.6 Asymptotic Optimality of the GLRT | p. 204 |
5.6.1 Multinomial Distributions | p. 205 |
5.6.2 Exponential Families | p. 216 |
5.7 Bibliographical Notes | p. 221 |
5.8 Problems | p. 222 |
5.A Proof of Sanov's Theorem | p. 231 |
References | p. 232 |
6 Robust Detection | p. 235 |
6.1 Introduction | p. 235 |
6.2 Measures of Model Proximity | p. 236 |
6.3 Robust Hypothesis Testing | p. 239 |
6.3.1 Robust Bayesian and NP Tests | p. 239 |
6.3.2 Clipped LR Tests | p. 241 |
6.4 Asymptotic Robustness | p. 250 |
6.4.1 Least Favorable Densities | p. 251 |
6.4.2 Robust Asymptotic Test | p. 254 |
6.5 Robust Signal Detection | p. 257 |
6.5.1 Least-Favorable Densities | p. 258 |
6.5.2 Receiver Structure | p. 261 |
6.6 Bibliographical Notes | p. 264 |
6.7 Problems | p. 265 |
References | p. 275 |
Part II Gaussian Detection | |
7 Karhunen-Loeve Expansion of Gaussian Processes | p. 279 |
7.1 Introduction | p. 279 |
7.2 Orthonormal Expansions of Deterministic Signals | p. 280 |
7.3 Eigenfunction Expansion of Covariance Kernels | p. 284 |
7.3.1 Properties of Covariance Kernels | p. 285 |
7.3.2 Decomposition of Covariance Matrices/Kernels | p. 289 |
7.4 Differential Characterization of the Eigenfunctions | p. 294 |
7.4.1 Gaussian Reciprocal Processes | p. 294 |
7.4.2 Partially Observed Gaussian Reciprocal/Markov Processes | p. 307 |
7.4.3 Rational Stationary Gaussian Processes | p. 310 |
7.5 Karhunen-Loeve Decomposition | p. 313 |
7.6 Asymptotic Expansion of Stationary Gaussian Processes | p. 315 |
7.7 Bibliographical Notes | p. 316 |
7.8 Problems | p. 317 |
References | p. 324 |
8 Detection of Known Signals in Gaussian Noise | p. 327 |
8.1 Introduction | p. 327 |
8.2 Binary Detection of Known Signals in WGN | p. 328 |
8.2.1 Detection of a Single Signal | p. 328 |
8.2.2 General Binary Detection Problem | p. 332 |
8.3 M-ary Detection of Known Signals in WGN | p. 338 |
8.4 Detection of Known Signals in Colored Gaussian Noise | p. 344 |
8.4.1 Singular and Nonsingular CT Detection | p. 346 |
8.4.2 Generalized Matched Filter Implementation | p. 348 |
8.4.3 Computation of the Distorted Signal g(t) | p. 352 |
8.4.4 Noise Whitening Receiver | p. 356 |
8.5 Bibliographical Notes | p. 362 |
8.6 Problems | p. 362 |
References | p. 368 |
9 Detection of Signals with Unknown Parameters | p. 371 |
9.1 Introduction | p. 371 |
9.2 Detection of Signals with Unknown Phase | p. 372 |
9.2.1 Signal Space Representation | p. 373 |
9.2.2 Bayesian Formulation | p. 374 |
9.2.3 GLR Test | p. 377 |
9.2.4 Detector Implementation | p. 378 |
9.3 Detection of DPSK Signals | p. 381 |
9.4 Detection of Signals with Unknown Amplitude and Phase | p. 386 |
9.4.1 Bayesian Formulation | p. 387 |
9.4.2 GLR Test | p. 389 |
9.5 Detection with Arbitrary Unknown Parameters | p. 389 |
9.6 Waveform Parameter Estimation | p. 395 |
9.7 Detection of Radar Signals | p. 402 |
9.7.1 Equivalent Baseband Detection Problem | p. 403 |
9.7.2 Cramer-Rao Bound | p. 406 |
9.7.3 ML Estimates and GLR Detector | p. 409 |
9.7.4 Ambiguity Function Properties | p. 412 |
9.8 Bibliographical Notes | p. 420 |
9.9 Problems | p. 421 |
References | p. 431 |
10 Detection of Gaussian Signals in WGN | p. 433 |
10.1 Introduction | p. 433 |
10.2 Noncausal Receiver | p. 434 |
10.2.1 Receiver Structure | p. 435 |
10.2.2 Smoother Implementation | p. 442 |
10.3 Causal Receiver | p. 448 |
10.4 Asymptotic Stationary Gaussian Test Performance | p. 456 |
10.4.1 Asymptotic Equivalence of Toeplitz and Circulant Matrices | p. 457 |
10.4.2 Mean-square Convergence of S[subscript T] | p. 459 |
10.4.3 Large Deviations Analysis of the LRT | p. 461 |
10.4.4 Detection in WGN | p. 466 |
10.5 Bibliographical Notes | p. 473 |
10.6 Problems | p. 473 |
References | p. 480 |
11 EM Estimation and Detection of Gaussian Signals with Unknown Parameters | p. 483 |
11.1 Introduction | p. 483 |
11.2 Gaussian Signal of Unknown Amplitude in WGN of Unknown Power | p. 485 |
11.3 EM Parameter Estimation Method | p. 486 |
11.3.1 Motonicity Property | p. 488 |
11.3.2 Example | p. 489 |
11.3.3 Convergence Rate | p. 492 |
11.3.4 Large-Sample Covariance Matrix | p. 498 |
11.4 Parameter Estimation of Hidden Gauss-Markov Models | p. 500 |
11.4.1 EM iteration | p. 501 |
11.4.2 Double-sweep smoother | p. 504 |
11.4.3 Example | p. 507 |
11.5 GLRT Implementation | p. 511 |
11.6 Bibliographical Notes | p. 515 |
11.7 Problems | p. 516 |
References | p. 522 |
Part III Markov Chain Detection | |
12 Detection of Markov Chains with Known Parameters | p. 527 |
12.1 Introduction | p. 527 |
12.2 Detection of Completely Observed Markov Chains | p. 528 |
12.2.1 Notation and Background | p. 528 |
12.2.2 Binary Hypothesis Testing | p. 533 |
12.2.3 Asymptotic Performance | p. 534 |
12.3 Detection of Partially Observed Markov Chains | p. 543 |
12.3.1 MAP Sequence Detection | p. 546 |
12.3.2 Pointwise MAP Detection | p. 563 |
12.4 Example: Channel Equalization | p. 571 |
12.4.1 Markov Chain Model | p. 571 |
12.4.2 Performance Analysis | p. 574 |
12.5 Bibliographical Notes | p. 585 |
12.6 Problems | p. 585 |
References | p. 589 |
13 Detection of Markov Chains with Unknown Parameters | p. 593 |
13.1 Introduction | p. 593 |
13.2 GLR Detector | p. 595 |
13.2.1 Model | p. 595 |
13.2.2 GLR Test | p. 597 |
13.3 Per Survivor Processing | p. 599 |
13.3.1 Path Extension | p. 599 |
13.3.2 Parameter Vector Update | p. 599 |
13.4 EM Detector | p. 605 |
13.4.1 Forward-backward EM | p. 608 |
13.4.2 EM Viterbi Detector | p. 613 |
13.5 Example: Blind Equalization | p. 619 |
13.5.1 Convergence Analysis | p. 621 |
13.5.2 Convergence Rate | p. 623 |
13.6 Bibliographical Notes | p. 628 |
13.7 Problems | p. 628 |
References | p. 631 |
Index | p. 633 |