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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