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Detection and Estimation for Communication and Radar Systems

Book Description

Covering the fundamentals of detection and estimation theory, this systematic guide describes statistical tools that can be used to analyze, design, implement and optimize real-world systems. Detailed derivations of the various statistical methods are provided, ensuring a deeper understanding of the basics. Packed with practical insights, it uses extensive examples from communication, telecommunication and radar engineering to illustrate how theoretical results are derived and applied in practice. A unique blend of theory and applications and over 80 analytical and computational end-of-chapter problems make this an ideal resource for both graduate students and professional engineers.

Table of Contents

  1. Cover
  2. Half title
  3. Epigraph
  4. Title
  5. Copyright
  6. Dedication
  7. Table of Contents
  8. Preface
  9. Chapter 1: Introduction and motivation to detection and estimation
    1. 1.1 Introduction
    2. 1.2 A simple binary decision problem
    3. 1.3 A simple correlation receiver
    4. 1.4 Importance of SNR and geometry of the signal vectors in detection theory
    5. 1.5 BPSK communication systems for different ranges
    6. 1.6 Estimation problems
      1. 1.6.1 Two simple estimation problems
      2. 1.6.2 Least-absolute-error criterion
      3. 1.6.3 Least-square-error criterion
      4. 1.6.4 Estimation robustness
      5. 1.6.5 Minimum mean-square-error criterion
    7. 1.7 Conclusions
    8. 1.8 Comments
    9. References
    10. Problems
  10. Chapter 2: Review of probability and random processes
    1. 2.1 Review of probability
    2. 2.2 Gaussian random vectors
      1. 2.2.1 Marginal and conditional pdfs of Gaussian random vectors
    3. 2.3 Random processes (stochastic processes)
    4. 2.4 Stationarity
    5. 2.5 Gaussian random process
    6. 2.6 Ensemble averaging, time averaging, and ergodicity
    7. 2.7 WSS random sequence
    8. 2.8 Conclusions
    9. 2.9 Comments
    10. 2.A Proof of Theorem
    11. 2.B Proof of Theorem
    12. References
    13. Problems
  11. Chapter 3: Hypothesis testing
    1. 3.1 Simple hypothesis testing
    2. 3.2 Bayes criterion
    3. 3.3 Maximum a posteriori probability criterion
    4. 3.4 Minimax criterion
    5. 3.5 Neyman-Pearson criterion
    6. 3.6 Simple hypothesis test for vector measurements
    7. 3.7 Additional topics in hypothesis testing (*)
      1. 3.7.1 Sequential likelihood ratio test (SLRT)
      2. 3.7.2 Uniformly most powerful test
      3. 3.7.3 Non-parametric sign test
    8. 3.8 Conclusions
    9. 3.9 Comments
    10. References
    11. Problems
  12. Chapter 4: Detection of known binary deterministic signals in Gaussian noises
    1. 4.1 Detection of known binary signal vectors in WGN
    2. 4.2 Detection of known binary signal waveforms in WGN
    3. 4.3 Detection of known deterministic binary signal vectors in colored Gaussian noise
    4. 4.4 Whitening filter interpretation of the CGN detector
    5. 4.5 Complete orthonormal series expansion
    6. 4.6 Karhunen-Loève expansion for random processes
    7. 4.7 Detection of binary known signal waveforms in CGN via the KL expansion method
    8. 4.8 Applying the WGN detection method on CGN channel received(*)
      1. 4.8.1 Optimization for evaluating the worst loss of performance
    9. 4.9 Interpretation of a correlation receiver as a matched filter receiver
    10. 4.10 Conclusions
    11. 4.11 Comments
    12. 4.A
    13. 4.B
    14. References
    15. Problems
  13. Chapter 5: M-ary detection and classification of deterministic signals
    1. 5.1 Introduction
    2. 5.2 Gram-Schmidt orthonormalization method and orthonormal expansion
    3. 5.3 M-ary detection
    4. 5.4 Optimal signal design for M-ary systems
    5. 5.5 Classification of M patterns
      1. 5.5.1 Introduction to pattern recognition and classification
      2. 5.5.2 Deterministic pattern recognition
    6. 5.6 Conclusions
    7. 5.7 Comments
    8. References
    9. Problems
  14. Chapter 6: Non-coherent detection in communication and radar systems
    1. 6.1 Binary detection of a sinusoid with a random phase
    2. 6.2 Performance analysis of the binary non-coherent detection system
    3. 6.3 Non-coherent detection in radar receivers
      1. 6.3.1 Coherent integration in radar
      2. 6.3.2 Post detection integration in a radar system
      3. 6.3.3 Double-threshold detection in a radar system
      4. 6.3.4 Constant False Alarm Rate (CFAR)
    4. 6.4 Conclusions
    5. 6.5 Comments
    6. References
    7. Problems
  15. Chapter 7: Parameter estimation
    1. 7.1 Introduction
    2. 7.2 Mean-square estimation
      1. 7.2.1 Non-linear mean-square estimation and conditional expectation
      2. 7.2.2 Geometry of the orthogonal principle and mean-square estimation
      3. 7.2.3 Block and recursive mean-square estimations
    3. 7.3 Linear LS and LAE estimation and related robustness and sparse solutions
      1. 7.3.1 LS estimation
      2. 7.3.2 Robustness to outlier (*) of LAE solution relative to LS solution
      3. 7.3.3 Minimization based on l[sub(2)] and l[sub(1)] norms for solving linear system of equations (*)
    4. 7.4 Basic properties of statistical parameter estimation
      1. 7.4.1 Cramér-Rao Bound
      2. 7.4.2 Maximum likelihood estimator
      3. 7.4.3 Maximum a posteriori estimator
      4. 7.4.4 Bayes estimator
    5. 7.5 Conclusions
    6. 7.6 Comments
    7. 7.A Proof of Theorem 7.3.3.1 of Section 7.3.3
    8. 7.B Proof of Theorem 7.4.1.1 of Section 7.4.1
    9. References
    10. Problems
  16. Chapter 8: Analytical and simulation methods for system performance analysis
    1. 8.1 Analysis of receiver performance with Gaussian noise
    2. 8.2 Analysis of receiver performance with Gaussian noise and other random interferences
      1. 8.2.1 Evaluation of P[sub(e)] based on moment bound method
    3. 8.3 Analysis of receiver performance with non-Gaussian noises
      1. 8.3.1 Noises with heavy tails
      2. 8.3.2 Fading channel modeling and performance analysis
      3. 8.3.3 Probabilities of false alarm and detection with robustness constraint
    4. 8.4 Monte Carlo simulation and importance sampling in communication/radar performance analysis
      1. 8.4.1 Introduction to Monte Carlo simulation
      2. 8.4.2 MC importance sampling simulation method
    5. 8.5 Conclusions
    6. 8.6 Comments
    7. 8.A Generation of pseudo-random numbers
      1. 8.A.1 Uniformly distributed pseudo-random number generation
      2. 8.A.2 Gaussian distributed pseudo-random number generation
      3. 8.A.3 Pseudo-random generation of sequences with arbitrary distributions
    8. 8.B Explicit solution of p[sub(V)](·)
    9. References
    10. Problems
  17. Index