EEC264 – Estimation And Detection Of Signals In Noise

4 units – Fall Quarter; alternate years

Lecture: 3 hours

Discussion: 1 hour

Prerequisite: EEC 260

Grading: Letter; problem sets (10%), MATLAB assignments (10%), midterm exam (35%), final exam (45%).

Catalog Description:

Introduction to parameter estimation and detection of signals in noise. Bayes and Neyman-Pearson likelihood-ratio tests for signal detection. Maximum-likelihood parameter estimation. Detection of known and Gaussian signals in white or colored noise. Applications to communications, radar, signal processing.

Expanded Course Description:

  1. Hypothesis Testing (2 weeks)
    1. Bayesian likelihood ratio tests for binary decisions
    2. Receiver operating characteristic
    3. Non-Bayesian minimax and Neyman-Pearson tests
    4. M-ary hypothesis testing
  2. Parameter Estimation (2 weeks)
    1. Bayesian, maximum a posteriori, and maximum-likelihood estimation of parameter vectors
    2. Cramer-Rao lower bound, bias, efficient estimates
    3. Linear least-squares estimation and its geometric interpretation
  3. Orthogonal Expansion of Gaussian Processes (1 week)
    1. Orthogonal expansion of deterministic signals
    2. Karhunen-Loeve expansion of discrete and continuous-time Gaussian processes
  4. Detection of Known Signals (2-1/2 weeks)
    1. Detection of known signals in white Gaussian noise (WGN)
    2. Sufficient statistics
    3. Correlator and matched filter receiver implementations
    4. Performance evaluation
    5. M-ary detection in WGN
    6. Detection of known signals in colored noise: resolvent and whitening filter approaches.
  5. Detection of Signals with Unknown/Random Parameters (2 weeks)
    1. Detection of signals with unwanted parameters. Composite hypothesis testing
    2. Estimation of waveform parameters in noise
    3. Application to the estimation of pulse amplitude and delay and sinewave amplitude, phase and frequency.
    4. Joint estimation and detection, generalized likelihood ratio test (GLRT)
    5. Detection of signals with random parameters. Detection of signals with incoherent phases and/or random amplitudes. Envelope detectors
  6. Detection of Gaussian Signals in WGN (1/2 week)
    1. Generalized correlator receiver structure for detecting Gaussian signals in WGN


  1. R. N. McDonough and A. D. Whalen, Detection of Signals in Noise 2nd Edition, Academic Press, 1995.

Instructors: Ding, Levy


Last revised: January 2001