COURSE TITLE: ECE 426 Signal Detection and Estimation

CATALOG DESCRIPTION: Simple-hypothesis detection problems, detection of signals with unknown parameters, Bayes’maximum likelihood estimation, estimation of signal parameters, detection of stochastic signals, nonparametric detection and estimation.

REQUIRED TEXT: A. D. Whalen, Detection of Signals in Noise, Academic Press, 2nd Ed.,1995.

REFERENCE TEXTS:

1. C. W. Helstrom, Statistical Theory of Signal Detection, Pergamon Press, 1968

2. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1, John Wiley, 1968

3. H. V. Poor, An Introduction to Signal Detection and Estimation, Springer-Verlag, 1988

COURSE DIRECTOR: Chung-Chieh Lee

COURSE GOALS: To study the fundamentals of signal detection and estimation.

PREREQUISITES BY COURSES: ECE 307 and ECE 422.

PREREQUISITES BY TOPIC:

1. Introduction to communication systems;

2. Fundamental background in analysis of random processes.

DETAILED COURSE TOPICS:

1. Background: Review of Gaussian variables and processes; problem formulation and objective of signal detection and signal parameter estimation.

2. Statistical Hypothesis Testing: Bayesian, minimax, and Neyman-Pearson optimum tests, likelihood ratio, receiver operating characteristics, locally optimum tests, detector comparison techniques, asymptotic relative efficiency.

3. Detection of a Known Signal: application of hypothesis testing to continuous-time detection problems. white Gaussian noise case, colored Gaussian noise case and Karhunen-Loeve expansion, pre-whitening techniques.

4. Radar Detection of a Signal with Random Parameters: a sinusoidal signal pulse with random phase, a sinusoidal pulse with random amplitude and phase, multiple-pulse radar signal detection and detector performance comparisons.

5. Nonparametric Detection: detection in the absence of complete statistical description of observations, the sign detector, the Wilcoxon detector, detectors based on quantized observations, robustness of detectors.

6. Estimation of Signal Parameters: Bayes estimation, properties of estimators, performance bound, the maximum likelihood estimate, continuous-time estimation of signal parameters.

7. Special Topics (if time permits): sequential detection, distributed detection.

COMPUTER USAGE: None.

LABORATORY PROJECTS: None.

GRADES:

Homeworks – 30%

Midterm exam – 30%

Final exam – 40%

COURSE OBJECTIVES: When a student completes this course, s/he should be able to:

1. formulate and solve the problems of signal detection and parameter estimation;

2. apply hypothesis testing.