Signal Detection and Estimation -- Contents vii -- Preface xv -- Acknowledgments xvii -- Chapter 1 Probability Concepts 1 -- 1.2 SETS AND PROBABILITY 1 -- 1.3 RANDOM VARIABLES 17 -- 1.4 MOMENTS 23 -- 1.5 TWO- AND HIGHER-DIMENSIONAL RANDOM VARIABLES 31 -- 1.6 TRANSFORMATION OF RANDOM VARIABLES 48 -- 1.7 SUMMARY 65 -- PROBLEMS 65 -- Reference 73 -- Selected Bibliography 73 -- Chapter 2 Distributions 75 -- 2.1 INTRODUCTION 75 -- 2.2 DISCRETE RANDOM VARIABLES 75 -- 2.3 CONTINUOUS RANDOM VARIABLES 88 -- 2.4 SOME SPECIAL DISTRIBUTIONS 121 -- 2.5 SUMMARY 136 -- PROBLEMS 137 -- Reference 139 -- Selected Bibliography 139 -- Chapter 3 Random Processes 141 -- 3.1 INTRODUCTION AND DEFINITIONS 141 -- 3.2 EXPECTATIONS 145 -- 3.3 PROPERTIES OF CORRELATION FUNCTIONS 153 -- 3.4 SOME RANDOM PROCESSES 156 -- 3.5 POWER SPECTRAL DENSITY 174 -- 3 .6 LINEAR TIME-INVARIANT SYSTEMS 178 -- 3.7 ERGODICITY 186 -- 3.8 SAMPLING THEOREM 189 -- 3.9 CONTINUITY, DIFFERENTIATION, AND INTEGRATION 194 -- 3.10 HILBERT TRANSFORM AND ANALYTIC SIGNALS 201 -- 3.11 THERMAL NOISE 205 -- 3.12 SUMMARY 211 -- PROBLEMS 212 -- Selected Bibliography 221 -- Chapter 4 Discrete-Time Random Processes 223 -- 4.1 INTRODUCTION 223 -- 4.2 MATRIX AND LINEAR ALGEBRA 224 -- 4.3 DEFINITIONS 245 -- 4.4 AR, MA, AND ARMA RANDOM PROCESSES 253 -- 4.5 MARKOV CHAINS 266 -- 4.6 SUMMARY 284 -- PROBLEMS 284 -- References 287 -- Selected Bibliography 288 -- Chapter 5 Statistical Decision Theory 289 -- 5.1 INTRODUCTION 289 -- 5.2 BAYES' CRITERION 291 -- 5.3 MINIMAX CRITERION 313 -- 5.5 COMPOSITE HYPOTHESIS TESTING 326 -- 5.6 SEQUENTIAL DETECTION 332 -- 5.7 SUMMARY 337 -- PROBLEMS 338 -- Selected Bibliography 343 -- Chapter 6 Parameter Estimation 345 -- 6.1 INTRODUCTION 345 -- 6.2 MAXIMUM LIKELIHOOD ESTIMATION 346 -- 6.3 GENERALIZED LIKELIHOOD RATIO TEST 348 -- 6.4 SOME CRITERIA FOR GOOD ESTIMATORS 353.

6.5 BAYES' ESTIMATION 355 -- 6.6 CRAMER-RAO INEQUALITY 364 -- 6.7 MULTIPLE PARAMETER ESTIMATION 371 -- 6.8 BEST LINEAR UNBIASED ESTIMATOR 378 -- 6.9 LEAST-SQUARE ESTIMATION 388 -- 6.10 RECURSIVE LEAST-SQUARE ESTIMATOR 391 -- 6.11 SUMMARY 393 -- PROBLEMS 394 -- References 398 -- Selected Bibliography 398 -- Chapter 7 Filtering 399 -- 7.1 INTRODUCTION 399 -- 7.2 LINEAR TRANSFORMATION AND ORTHOGONALITY PRINCIPLE 400 -- 7.3 WIENER FILTERS 409 -- 7.4 DISCRETE WIENER FILTERS 424 -- 7.5 KALMAN FILTER 436 -- 7.6 SUMMARY 445 -- PROBLEMS 445 -- References 448 -- Selected Bibliography 448 -- Chapter 8 Representation of Signals 449 -- 8.1 INTRODUCTION 449 -- 8.2 ORTHOGONAL FUNCTIONS 449 -- 8.3 LINEAR DIFFERENTIAL OPERATORS AND INTEGRAL EQUATIONS 466 -- 8.4 REPRESENTATION OF RANDOM PROCESSES 480 -- 8.5 SUMMARY 495 -- PROBLEMS 496 -- References 500 -- Selected Bibliography 500 -- Chapter 9 The General Gaussian Problem 503 -- 9.1 INTRODUCTION 503 -- 9.2 BINARY DETECTION 503 -- 9.3 SAME COVARIANCE 505 -- 9.4 SAME MEAN 518 -- 9.5 SAME MEAN AND SYMMETRIC HYPOTHESES 524 -- 9.6 SUMMARY 529 -- PROBLEMS 530 -- Reference 532 -- Selected Bibliography 532 -- Chapter 10 Detection and Parameter Estimation 533 -- 10.1 INTRODUCTION 533 -- 10.2 BINARY DETECTION 534 -- 10.3 M-ARY DETECTION 556 -- 10.4 LINEAR ESTIMATION 572 -- 10.5 NONLINEAR ESTIMATION 576 -- 10.6 GENERAL BINARY DETECTION WITH UNWANTED PARAMETERS 580 -- 10.7 BINARY DETECTION IN COLORED NOISE 606 -- 10.8 SUMMARY 617 -- PROBLEMS 618 -- Reference 626 -- Selected Bibliography 626 -- Chapter 11 Adaptive Thresholding CFAR Detection 627 -- 11.1 INTRODUCTION 627 -- 11.2 RADAR ELEMENTARY CONCEPTS 629 -- 11.3 PRINCIPLES OF ADAPTIVE CFAR DETECTION 634 -- 11.4 ADAPTIVE THRESHOLDING IN CODE ACQUISITION OF DIRECT-SEQUENCE SPREAD SPECTRUM SIGNALS 648 -- 11.5 SUMMARY 660 -- References 661.

Chapter 12 Distributed CFAR Detection 665 -- 12.1 INTRODUCTION 665 -- 12.2 DISTRIBUTED CA-CFAR DETECTION 666 -- 12.3 FURTHER RESULTS 670 -- 12.4 SUMMARY 671 -- References 672 -- Appendix 675 -- References 677 -- About the Author 683 -- Index 385.