Detection of Signals in Noise

ContentsPrefaceAcknowledgementsChapter 1. Probability 1.1 Probability in Brief 1.2 Conditional Probability and Statistical Independence 1.3 Probability Distribution Functions 1.4 Continuous Random Variables 1.5 Functions of Random Variables 1.6 Characteristic Functions 1.7 Averages Exercises References Supplementary Bibliography Chapter 2. Random Processes 2.1 Introduction 2.2 Relation to Probability 2.3 Ensemble Correlation Functions 2.4 Time Averages 2.5 Time Correlation Functions 2.6 Power Spectral Density 2.7 Response of Linear Filters Exercises References Supplementary Bibliography Chapter 3. Narrowband Signals 3.1 Introduction 3.2 Deterministic Signal 3.3 Hilbert Transform 3.4 Signal Preenvelope 3.5 Narrowband Filters 3.6 Narrowband Processes 3.7 Fourier Series Representation Exercises References Supplementary Bibliography Chapter 4. Gaussian Derived Processes 4.1 Gaussian Properties 4.2 Sum of a Sine Wave and a Gaussian Process 4.3 Distribution of the Envelope of a Narrowband Gaussian Process 4.4 Envelope of a Sine Wave Plus Narrowband Noise 4.5 Envelope Squared of Narrowband Process 4.6 Chi-Squared Distribution 4.7 Envelope Squared of a Sine Wave Plus a Narrowband Process 4.8 Noncentral Chi-Squared Distribution Exercises References Supplementary Bibliography Chapter 5. Hypothesis Testing 5.1 Introduction 5.2 Hypothesis Testing 5.3 Bayes Criterion 5.4 Minimum Error Probability Criterion 5.5 Neyman-Pearson Criterion 5.6 Minimax Criterion 5.7 Multiple Measurements 5.8 Multiple Alternative Hypothesis Testing 5.9 Composite Hypothesis Testing 5.10 Unknown A Priori Information Exercises References Supplementary Bibliography Chapter 6. Detection of Known Signals 6.1 Introduction 6.2 A Binary Communication System 6.3 The Likelihood Functions 6.4 Matched Filters 6.5 An M-ary Communication System 6.6 Sampled Approach Exercises References Supplementary Bibliography Chapter 7. Detection of Signals with Random Parameters 7.1 Introduction 7.2 Signals with Random Phase 7.3 The Quadrature Receiver and Equivalent Forms 7.4 Receiver Operating Characteristics 7.5 Signals with Random Phase and Amplitude 7.6 Noncoherent Frequency Shift Keying 7.7 Signals with Random Frequency 7.8 Signals with Random Time of Arrival 7.9 Random Frequency and Time of Arrival 7.10 Sampled Approach Exercises References Supplementary Bibliography Chapter 8. Multiple Pulse Detection of Signals 8.1 Introduction 8.2 Known Signals 8.3 Signals with Random Parameters 8.4 Diversity Exercises References Supplementary Bibliography Chapter 9. Detection of Signals in Colored Gaussian Noise 9.1 Introduction 9.2 Karhunen-Loeve Expansion 9.3 Detection of Known Signals 9.4 Receiver Performance 9.5 Optimum Signal Waveform 9.6 The Likelihood Functions 9.7 Integral Equations 9.8 Detection of Signals with Unknown Phase Exercises References Supplementary Bibliography Chapter 10. Estimation of Signal Parameters 10.1 Introduction 10.2 Bayes Estimate 10.3 Maximum A Posteriori Estimate 10.4 Maximum-Likelihood Estimates 10.5 Properties of Estimators 10.6 Estimation in Presence of White Noise 10.7 Estimation of Specific Parameters 10.8 Estimation in Nonwhite Gaussian Noise 10.9 Generalized Likelihood Ratio Detection Exercises References Supplementary Bibliography Chapter 11. Extensions Using Matrix Formulation 11.1 Introduction 11.2 Matrix Preliminaries 11.3 Multivariate Complex Gaussian Distribution 11.4 Estimation 11.5 Best Linear Estimator 11.