1 Introduction 1.1 Review of Parts I and II 1.2 Random Signals in Noise 1.3 Signal Processing in Radar-Sonar Systems References 2 Detection of Gaussian Signals in White Gaussian Noise 2.1 Optimum Receivers 2.1.1 Canonical Realization No. 1: Estimator-Correlator 2.1.2 Canonical Realization No. 2: Filter-Correlator Receiver 2.1.3 Canonical Realization No. 3: Filter-Squarer-Inte-grator (FSI) Receiver 2.1.4 Canonical Realization No. 4: Optimum Realizable Filter Receiver 2.1.5 Canonical Realization No. 4S: State-variable Real-ization 2.1.6 Summary: Receiver Structures 2.2 Performance 2.2.1 Closed-form Expression for/a(s) 2.2.2 Approximate Error Expressions 2.2.3 An Alternative Expression for/uR(s) 2.2.4 Performance for a Typical System 2.3 Summary: Simple Binary Detection 2.4 Problems References 3 General Binary Detection: Gaussian Processes 3.1 Model and Problem Classification 3.2 Receiver Structures 3.2.1 Whitening Approach 3.2.2 Various Implementations of the Likelihood Ratio Test 3.2.3 Summary: Receiver Structures 3.3 Performance 3.4 Four Special Situations 3.4.1 Binary Symmetric Case 3.4.2 Non-zero Means 3.4.3 Stationary"Carrier-symmetric"Bandpass Problems 3.4.4 Error Probability for the Binary Symmetric Band-pass Problem 3.5 General Binary Case: White Noise Not Necessarily Pres-ent: Singular Tests 3.5.1 Receiver Derivation 3.5.2 Performance: General Binary Case 3.5.3 Singularity 3.6 Summary: General Binary Problem 3.7 Problems References 4 SpeciaICategoriesofDetectionProblerns 4.1 Stationary Processes: Long Observation Time 4.1.1 Simple Binary Problem 4.1.2 General Binary Problem 4.1.3 Summary: SPLOT Problem 4.2 Separable Kernels 4.2.1 Separable Kernel Model 4.2.2 Time Diversity 4.2.3 Frequency Diversity 4.2.4 Summary: Separable Kernels 4.3 Low-Energy-Coherence (LEC) Case 4.4 Summary 4.5 Problems References 5.1 Related Topics 5.1.1 M-ary Detection: Gaussian Signals in Noise 5.1.2 Suboptimum Receivers 5.1.3 Adaptive Receivers 5.1.4 Non-Gaussian Processes 5.1.5 Vector Gaussian Processes 5.2 Summary of Detection Theory 5.3 Problems References 6 Estimation of the Parameters of a Random Process 6.1 Parameter Estimation Model 6.2 Estimator Structure 6.2.1 Derivation of the Likelihood Function 6.2.2 Maximum Likelihood and Maximum A-Posteriori Probability Equations 6.3 Performance Analysis 6.3.1 A Lower Bound on the Variance 6.3.2 Calculation of J(2)(A) 6.3.3 Lower Bound on the Mean-Square Error 6.3.4 Improved Performance Bounds 6.4 Summary 6.5 Problems References 7 Special Categories of Estimation Problems 7.1 Stationary Processes: Long Observation Time 7.1.1 General Results 7.1.2 Performance of Truncated Estimates 7.1.3 Suboptimum Receivers 7.1.4 Summary 7.2 Finite-State Processes 7.3 Separable Kernels 7.4 Low-Energy-Coherence Case 7.5 Related Topics 7.5.1 Multiple-Parameter Estimation 7.5.2 Composite-Hypothesis Tests 7.6 Summary of Estimation Theory 7.7 Problems References 8 The Radar-sonar Problem References 9 Detection of Slowly Fluctuating Point Targets 9.1 Model of a Slowly Fluctuating Point Target 9.2 White Bandpass Noise 9.3 Colored Bandpass Noise 9.4 Colored Noise with a Finite State Representation 9.4.1 Differential-equation Representation of the Optimum Receiver and Its Performance: I 9.4.2 Differential-equation Representation of the Optimum Receiver and Its Performance: II 9.5 Optimal Signal Design 9.6 Summary and Related Issues 9.7 Problems References 10 Parameter Estimation: Slowly Fluctuating Point Targets 10.1 Receiver Derivation and Signal Design 10.2 Performance of the Optimum Estimator 10.2.1 Local Accuracy 10.2.2 Global Accuracy (or Ambiguity) 10.2.3 Summary 10.3 Properties of Time-Frequency Autocorrelation Functions and Ambiguity Functions 10.4 Coded Pulse Sequences 10.4.1 On-off Sequences 10.4.2 Constant Power, Amplitude-modulated Wave-forms 10.4.3 Other Coded Sequences 10.5 Resolution 10.5.1 Resolution in a Discrete Environment: Model 10.5.2 Conventional Receivers 10.5.3 Optimum Receiver: Discrete Resolution Problem 10.5.4 Summary of Resolution Results 10.6 Summary and Related Topics 10.6.1 Summary 10.6.2 Related Topics 10.7 Problems References 1I Doppler-Spread Targets and Channels 11.1 Model for Doppler-Spread Target (or Channel) 11.2 Detection of Doppler-Spread Targets 11.2.1 Likelihood Ratio Test 11.2.2 Canonical Receiver Realizations 11.2.3 Performance of the Optimum Receiver 11.2.4 Classes of Processes 11.2.5 Summary 11.3 Communication Over Doppler-Spread Channels 11.3.1 Binary Communications Systems: Optimum Receiver and Performance 11.3.2 Performance Bounds for Optimized Binary Systems 11.3.3 Suboptimum Receivers 11.3.4 M-ary Systems 11.3.5 Summary: Communication over Doppler-spread Channels 11.4 Parameter Estimation: Doppler-Spread Targets 11.5 Summary: Doppler-Spread Targets and Channels 11.6 Problems References 12 Range-Spread Targets and Channels 12.1 Model and Intuitive Discussion 12.2 Detection of Range-Spread Targets 12.3 Time-Frequency Duality 12.3.1 Basic Duality Concepts 12.3.2 Dual Targets and Channels 12.3.3 Applications 12.4 Summary: Range-Spread Targets 12.5 Problems References 13 Doubly-Spread Targets and Channels 13.1 Model for a Doubly-Spread Target 13.1.1 Basic Model 13.1.2 Differential-Equation Model for a Doubly-Spread Target (or Channel) 13.1.3 Model Summary 13.2 Detection in the Presence of Reverberation or Clutter (Resolution in a Dense Environment) 13.2.1 Conventional Receiver 13.2.2 Optimum Receivers 13.2.3 Summary of the Reverberation Problem 13.3 Detection of Doubly-Spread Targets and Communica- tion over Doubly-Spread Channels 13.3.1 Problem Formulation 13.3.2 Approximate Models for Doubly-Spread Targets and Doubly-Spread Channels 13.3.3 Binary Communication over Doubly-Spread Channels 13.3.4 Detection under LEC Conditions 13.3.5 Related Topics 13.3.6 Summary of Detection of Doubly-Spread Signals 13.4 Parameter Estimation for Doubly-Spread Targets 13.4.1 Estimation under LEC Conditions 13.4.2 Amplitude Estimation 13.4.3 Estimation of Mean Range and Doppler 13.4.4 Summary 13.5 Summary of Doubly-Spread Targets and Channels 13.6 Problems References 14 Discussion 14.1 Summary: Signal Processing in Radar and Sonar Systems 14.2 Optimum Array Processing 14.3 Epilogue References Appendix: Complex Representation of Bandpass Signals, Systems, and Processes A.1 Deterministic Signals A.2 Bandpass Linear Systems A.2.1 Time-lnvariant Systems A.2.2 Time-Varying Systems A.2.3 State-Variable Systems A.3 Bandpass Random Processes A.3.1 Stationary Processes A.3.2 Nonstationary Processes A.3.3 Complex Finite-State Processes A.4 Summary A.5 Problems References Glossary Author Index Subject Index
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