Fundamentals of Statistical Signal Processing: Detection Theory, Volume 2
The most comprehensive overview of signal detection available.
This is a thorough, up-to-date introduction to optimizing detection algorithms for implementation on digital computers. It focuses extensively on real-world signal processing applications, including state-of-the-art speech and communications technology as well as traditional sonar/radar systems.
Start with a quick review of the fundamental issues associated with mathematical detection, as well as the most important probability density functions and their properties. Next, review Gaussian, Chi-Squared, F, Rayleigh, and Rician PDFs, quadratic forms of Gaussian random variables, asymptotic Gaussian PDFs, and Monte Carlo Performance Evaluations.
Three chapters introduce the basics of detection based on simple hypothesis testing, including the Neyman-Pearson Theorem, handling irrelevant data, Bayes Risk, multiple hypothesis testing, and both deterministic and random signals.
The author then presents exceptionally detailed coverage of composite hypothesis testing to accommodate unknown signal and noise parameters. These chapters will be especially useful for those building detectors that must work with real, physical data. Other topics covered include:
- Detection in nonGaussian noise, including nonGaussian noise characteristics, known deterministic signals, and deterministic signals with unknown parameters
- Detection of model changes, including maneuver detection and time-varying PSD detection
- Complex extensions, vector generalization, and array processing
The book makes extensive use of MATLAB, and program listings are included wherever appropriate. Designed for practicing electrical engineers, researchers, and advanced students, it is an ideal complement to Steven M. Kay's Fundamentals of Statistical Signal Processing, Vol. 1: Estimation Theory (Prentice Hall PTR, 1993, ISBN: 0-13-345711-7).
Why Read This Book
You will get a thorough, mathematically rigorous guide to hypothesis testing and detector design that connects theory to practical performance evaluation. The book emphasizes real-world signal models (Gaussian and non-Gaussian), likelihood-ratio and generalized tests, and Monte Carlo techniques so you can design and analyze detectors used in radar, communications, and speech systems.
Who Will Benefit
Graduate students, researchers, and practicing engineers working on detection problems in radar, communications, audio/speech, or general statistical signal processing who need a solid theoretical and practical foundation.
Level: Advanced — Prerequisites: Undergraduate probability and random processes, linear algebra, basic signal processing and statistical estimation theory; comfort with mathematical derivations and integrals.
Key Takeaways
- Derive and apply likelihood-ratio and Neyman-Pearson detectors for binary and multi-hypothesis problems.
- Design and analyze optimal detectors in Gaussian noise including matched filters, correlators, and quadratic detectors.
- Formulate and implement generalized likelihood ratio tests (GLRT) and locally optimal detectors for composite hypotheses and unknown parameters.
- Evaluate detector performance using ROC curves, false-alarm/detection probabilities, asymptotic approximations, and Monte Carlo simulation.
- Analyze detection under non-Gaussian models (e.g., Rayleigh, Rician, chi-square) and understand quadratic forms of Gaussian variables.
- Apply statistical detection principles to practical problems in radar, sonar, communications, and speech activity detection.
Topics Covered
- Introduction and Fundamental Concepts in Detection
- Binary Hypothesis Testing and Likelihood Ratio Tests
- Neyman-Pearson Criteria and Bayesian Detection
- Performance Metrics: ROC Curves, Probability of Detection and False Alarm
- Detection in Gaussian Noise: Matched Filters and Correlators
- Quadratic Detectors and Quadratic Forms of Gaussian Variables
- Composite Hypotheses and the Generalized Likelihood Ratio Test (GLRT)
- Locally Optimum Detectors and Nonlinear Detection
- Detection with Unknown Parameters and Adaptive Approaches
- Non-Gaussian Models: Rayleigh, Rician, Chi-Squared, and F Distributions
- Asymptotic Approximations and Monte Carlo Performance Evaluation
- Extensions: Multi-hypothesis Testing, Sequential Detection, and Practical Considerations
Languages, Platforms & Tools
How It Compares
More accessible and application-oriented than Van Trees' multivolume treatment and more modern/practical than classical texts like Helstrom; complementary to Poor's or Van Trees for alternative perspectives on Bayesian vs. classical methods.
