Detection and Estimation in Engineering Systems
Catalog Data: 

Graduate Course Information



ECE 639 Detection and Estimation in Engineering Systems


UA Catalog Description:

ECE 639 – Detection and Estimation in Engineering Systems  (3 units)

Description:  Communication, detection and estimation as statistical inference problems. Optimal detection in the presence of Gaussian noise. Extraction of signals in noise via MAP and MMSE techniques


Grading:  Regular grades are awarded for this course: A B C D E.


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

Course Topics: 

1.     Introduction: random processes, narrowband signals, and Gaussian derived processes

2.     Hypothesis testing: formulation, detection problem, Neyman-Pearson criterion, Bayes’ criterion, minimum error probability criterion, minimax criterion, multiple measurements, multiple alternative hypothesis testing, composite hypothesis testing with minimum cost, uniformly most powerful tests, unknown a priori information and nonoptimal tests,  sufficient statistics.

3.     Detection of known signals: two completely known signals in additive Gaussian noise, application to radar, application to binary communications, the likelihood functions, matched filters, the general discrete matched filter, an M-ary communication system, the discrete Gaussian problem.

4.     Detection of signals with random parameters: narrowband signals processing, detection of signals with unknown carrier phase, quadrature receivers and equivalent forms, operating characteristics of receivers, signals with random phase and amplitude, noncoherent FSK, signals with random frequency, signals with random time of arrival.

5.     Detection of signals in colored Gaussian noise: matrix formulation, discrete spectral factorization, continuous time spectral decomposition, finite observation time and Karhunen-Loève expansion, detection of known signals with finite reservation time, receiver performance, optimum signal waveform, integral equations, detection of signals with unknown phase. 

6.     Estimation of signal parameters: Bayes estimation, the conditional mean as Bayes estimator, maximum a posteriori estimation, maximum likelihood estimation, estimators properties, Cramér-Rao bound, parameters of signals in additive Gaussian noise, simultaneous estimation of time and frequency, estimation in nonwhite Gaussian noise, generalized likelihood detection, linear minimum variance estimation, discrete Kalman filters.  

7.     Multiple pulse detection of signals: known signals, signals with unknown phase, quadratic detector, Gram-Charlier series, linear detector, unknown phase and known unequal amplitudes, unknown amplitude and phase, diversity reception

Prepared by: 
Ivan B. Djordjevic
Prepared Date: 
April 2013

University of Arizona College of Engineering