Table Of Contents:
Preface xv
Acknowledgments xvii
Chapter 1 Probability Concepts 1(74)

1.1 Introduction 1(1)

1.2 Sets and Probability 1(16)

1.2.1 Basic Definitions 1(2)

1.2.2 Venn Diagrams and Some Laws 3(3)

1.2.3 Basic Notions of Probability 6(2)

1.2.4 Some Methods of Counting 8(4)

1.2.5 Properties, Conditional Probability, and Bayes' Rule 12(5)

1.3 Random Variables 17(6)

1.3.1 Step and Impulse Functions 17(1)

1.3.2 Discrete Random Variables 18(2)

1.3.3 Continuous Random Variables 20(2)

1.3.4 Mixed Random Variables 22(1)

1.4 Moments 23(8)

1.4.1 Expectations 23(3)

1.4.2 Moment Generating Function and Characteristic Function 26(3)

1.4.3 Upper Bounds on Probabilities and Law of Large Numbers 29(2)

1.5 Two- and Higher-Dimensional Random Variables 31(17)

1.5.1 Conditional Distributions 33(8)

1.5.2 Expectations and Correlations 41(3)

1.5.3 Joint Characteristic Functions 44(4)

1.6 Transformation of Random Variables 48(17)

1.6.1 Functions of One Random Variable 49(3)

1.6.2 Functions of Two Random Variables 52(7)

1.6.3 Two Functions of Two Random Variables 59(6)

1.7 Summary 65(1)

Problems 65(8)

Reference 73(1)

Selected Bibliography 73(2)
Chapter 2 Distributions 75(66)

2.1 Introduction 75(1)

2.2 Discrete Random Variables 75(13)

2.2.1 The Bernoulli, Binomial, and Multinomial Distributions 75(3)

2.2.2 The Geometric and Pascal Distributions 78(4)

2.2.3 The Hypergeometric Distribution 82(3)

2.2.4 The Poisson Distribution 85(3)

2.3 Continuous Random Variables 88(33)

2.3.1 The Uniform Distribution 88(1)

2.3.2 The Normal Distribution 89(7)

2.3.3 The Exponential and Laplace Distributions 96(2)

2.3.4 The Gamma and Beta Distributions 98(3)

2.3.5 The Chi-Square Distribution 101(5)

2.3.6 The Rayleigh, Rice, and Maxwell Distributions 106(9)

2.3.7 The Nakagami m-Distribution 115(1)

2.3.8 The Student's t- and F-Distributions 115(5)

2.3.9 The Cauchy Distribution 120(1)

2.4 Some Special Distributions 121(15)

2.4.1 The Bivariate and Multivariate Gaussian Distributions 121(8)

2.4.2 The Weibull Distribution 129(2)

2.4.3 The Log-Normal Distribution 131(1)

2.4.4 The K-Distribution 132(3)

2.4.5 The Generalized Compound Distribution 135(1)

2.5 Summary 136(1)

Problems 137(2)

Reference 139(1)

Selected Bibliography 139(2)
Chapter 3 Random Processes 141(82)

3.1 Introduction and Definitions 141(4)

3.2 Expectations 145(8)

3.3 Properties of Correlation Functions 153(3)

3.3.1 Autocorrelation Function 153(1)

3.3.2 Cross-Correlation Function 153(1)

3.3.3 Wide-Sense Stationary 154(2)

3.4 Some Random Processes 156(18)

3.4.1 A Single Pulse of Known Shape but Random Amplitude and Arrival Time 156(1)

3.4.2 Multiple Pulses 157(1)

3.4.3 Periodic Random Processes 158(3)

3.4.4 The Gaussian Process 161(2)

3.4.5 The Poisson Process 163(3)

3.4.6 The Bernoulli and Binomial Processes 166(2)

3.4.7 The Random Walk and Wiener Processes 168(4)

3.4.8 The Markov Process 172(2)

3.5 Power Spectral Density 174(4)

3.6 Linear Time-Invariant Systems 178(8)

3.6.1 Stochastic Signals 179(6)

3.6.2 Systems with Multiple Terminals 185(1)

3.7 Ergodicity 186(3)

3.7.1 Ergodicity in the Mean 186(1)

3.7.2 Ergodicity in the Autocorrelation 187(1)

3.7.3 Ergodicity of the First-Order Distribution 188(1)

3.7.4 Ergodicity of Power Spectral Density 188(1)

3.8 Sampling Theorem 189(5)

3.9 Continuity, Differentiation, and Integration 194(7)

3.9.1 Continuity 194(2)

3.9.2 Differentiation 196(3)

3.9.3 Integrals 199(2)

3.10 Hilbert Transform and Analytic Signals 201(4)

3.11 Thermal Noise 205(6)

3.12 Summary 211(1)

Problems 212(9)

Selected Bibliography 221(2)
Chapter 4 Discrete-Time Random Processes 223(66)

4.1 Introduction 223(1)

4.2 Matrix and Linear Algebra 224(21)

4.2.1 Algebraic Matrix Operations 224(8)

4.2.2 Matrices with Special Forms 232(4)

4.2.3 Eigenvalues and Eigenvectors 236(9)

4.3 Definitions 245(8)

4.4 AR, MA, and ARMA Random Processes 253(13)

4.4.1 AR Processes 254(8)

4.4.2 MA Processes 262(2)

4.4.3 ARMA Processes 264(2)

4.5 Markov Chains 266(18)

4.5.1 Discrete-Time Markov Chains 267(9)

4.5.2 Continuous-Time Markov Chains 276(8)

4.6 Summary 284(1)

Problems 284(3)

References 287(1)

Selected Bibliography 288(1)
Chapter 5 Statistical Decision Theory 289(56)

5.1 Introduction 289(2)

5.2 Bayes' Criterion 291(22)

5.2.1 Binary Hypothesis Testing 291(12)

5.2.2 Mu-ary Hypothesis Testing 303(10)

5.3 Minimax Criterion 313(4)

5.4 Neyman-Pearson Criterion 317(9)

5.5 Composite Hypothesis Testing 326(6)

5.5.1 Θ Random Variable 327(2)

5.5.2 theta Nonrandom and Unknown 329(3)

5.6 Sequential Detection 332(5)

5.7 Summary 337(1)

Problems 338(5)

Selected Bibliography 343(2)
Chapter 6 Parameter Estimation 345(54)

6.1 Introduction 345(1)

6.2 Maximum Likelihood Estimation 346(2)

6.3 Generalized Likelihood Ratio Test 348(5)

6.4 Some Criteria for Good Estimators 353(2)

6.5 Bayes' Estimation 355(9)

6.5.1 Minimum Mean-Square Error Estimate 357(1)

6.5.2 Minimum Mean Absolute Value of Error Estimate 358(1)

6.5.3 Maximum A Posteriori Estimate 359(5)

6.6 Cramer-Rao Inequality 364(7)

6.7 Multiple Parameter Estimation 371(7)

6.7.1 theta Nonrandom 371(5)

6.7.2 theta Random Vector 376(2)

6.8 Best Linear Unbiased Estimator 378(10)

6.8.1 One Parameter Linear Mean-Square Estimation 379(2)

6.8.2 theta Random Vector 381(2)

6.8.3 BLUE in White Gaussian Noise 383(5)

6.9 Least-Square Estimation 388(3)

6.10 Recursive Least-Square Estimator 391(2)

6.11 Summary 393(1)

Problems 394(4)

References 398(1)

Selected Bibliography 398(1)
Chapter 7 Filtering 399(50)

7.1 Introduction 399(1)

7.2 Linear Transformation and Orthogonality Principle 400(9)

7.3 Wiener Filters 409(15)

7.3.1 The Optimum Unrealizable Filter 410(6)

7.3.2 The Optimum Realizable Filter 416(8)

7.4 Discrete Wiener Filters 424(12)

7.4.1 Unrealizable Filter 425(1)

7.4.2 Realizable Filter 426(10)

7.5 Kalman Filter 436(9)

7.5.1 Innovations 437(3)

7.5.2 Prediction and Filtering 440(5)

7.6 Summary 445(1)

Problems 445(3)

References 448(1)

Selected Bibliography 448(1)
Chapter 8 Representation of Signals 449(54)

8.1 Introduction 449(1)

8.2 Orthogonal Functions 449(17)

8.2.1 Generalized Fourier Series 451(4)

8.2.2 Gram-Schmidt Orthogonalization Procedure 455(3)

8.2.3 Geometric Representation 458(5)

8.2.4 Fourier Series 463(3)

8.3 Linear Differential Operators and Integral Equations 466(14)

8.3.1 Green's Function 470(1)

8.3.2 Integral Equations 471(8)

8.3.3 Matrix Analogy 479(1)

8.4 Representation of Random Processes 480(15)

8.4.1 The Gaussian Process 483(4)

8.4.2 Rational Power Spectral Densities 487(5)

8.4.3 The Wiener Process 492(1)

8.4.4 The White Noise Process 493(2)

8.5 Summary 495(1)

Problems 496(4)

References 500(1)

Selected Bibliography 500(3)
Chapter 9 The General Gaussian Problem 503(30)

9.1 Introduction 503(1)

9.2 Binary Detection 503(2)

9.3 Same Covariance 505(13)

9.3.1 Diagonal Covariance Matrix 508(3)

9.3.2 Nondiagonal Covariance Matrix 511(7)

9.4 Same Mean 518(6)

9.4.1 Uncorrelated Signal Components and Equal Variances 519(3)

9.4.2 Uncorrelated Signal Components and Unequal Variances 522(2)

9.5 Same Mean and Symmetric Hypotheses 524(5)

9.5.1 Uncorrelated Signal Components and Equal Variances 526(2)

9.5.2 Uncorrelated Signal Components and Unequal Variances 528(1)

9.6 Summary 529(1)

Problems 530(2)

Reference 532(1)

Selected Bibliography 532(1)
Chapter 10 Detection and Parameter Estimation 533(94)

10.1 Introduction 533(1)

10.2 Binary Detection 534(22)

10.2.1 Simple Binary Detection 534(9)

10.2.2 General Binary Detection 543(13)

10.3 M-ary Detection 556(16)

10.3.1 Correlation Receiver 557(10)

10.3.2 Matched Filter Receiver 567(5)

10.4 Linear Estimation 572(4)

10.4.1 ML Estimation 573(2)

10.4.2 MAP Estimation 575(1)

10.5 Nonlinear Estimation 576(4)

10.5.1 ML Estimation 576(3)

10.5.2 MAP Estimation 579(1)

10.6 General Binary Detection with Unwanted Parameters 580(26)

10.6.1 Signals with Random Phase 583(12)

10.6.2 Signals with Random Phase and Amplitude 595(3)

10.6.3 Signals with Random Parameters 598(8)

10.7 Binary Detection in Colored Noise 606(11)

10.7.1 Karhunen-Lo猫ve Expansion Approach 607(4)

10.7.2 Whitening Approach 611(4)

10.7.3 Detection Performance 615(2)

10.8 Summary 617(1)

Problems 618(8)

Reference 626(1)

Selected Bibliography 626(1)
Chapter 11 Adaptive Thresholding CFAR Detection 627(38)

11.1 Introduction 627(2)

11.2 Radar Elementary Concepts 629(5)

11.2.1 Range, Range Resolution, and Unambiguous Range 631(2)

11.2.2 Doppler Shift 633(1)

11.3 Principles of Adaptive CFAR Detection 634(14)

11.3.1 Target Models 640(2)

11.3.2 Review of Some CFAR Detectors 642(6)

11.4 Adaptive Thresholding in Code Acquisition of Direct-Sequence Spread Spectrum Signals 648(12)

11.4.1 Pseudonoise or Direct Sequences 649(3)

11.4.2 Direct-Sequence Spread Spectrum Modulation 652(3)

11.4.3 Frequency-Hopped Spread Spectrum Modulation 655(1)

11.4.4 Synchronization of Spread Spectrum Systems 655(4)

11.4.5 Adaptive Thresholding with False Alarm Constraint 659(1)

11.5 Summary 660(1)

References 661(4)
Chapter 12 Distributed CFAR Detection 665(10)

12.1 Introduction 665(1)

12.2 Distributed CA-CFAR Detection 666(4)

12.3 Further Results 670(1)

12.4 Summary 671(1)

References 672(3)
Appendix 675(8)
About the Author 683(2)
Index 685