ECE642 Detection and Estimation TheoryFall 2015

Goal:

To establish the essential signal detection and estimation background for engineering re-searchers and practitioners in areas such as communications, signal processing, image pro-cessing, radar and control.

Catalog Description:

Hypothesis testing; receiver operating characteristics; the Karhunen-Loeve representation;structure and performance of optimal discrete and continuous time detection, sequential de-tection; ML, minimumMSE, and MAP estimation; sufficient statistics and generalized boundson estimator performance; Kalman-Bucy filtering; multi-user detection; detection for multi-path fading channels, the RAKE receiver.

Prerequisites:

ECE541 or equivalent.

Instructor:

Dr. Majeed M. Hayat, ProfessorOffice: CHTM 139 (main); ECE 323B; Tel: 272-7095E-mail: hayat@chtm.unm.edu; Web: www.ece.unm.edu/faculty/hayat/main.htm

Classroom & time

MECH-220; MW: 9:30–10:45

Office hours

MW: 11:00–12:00, and by appointment.

Textbook:

H. V. Poor, An Introduction to Signal Detection and Estimation. Second Ed., Springer, 1994.

Class website: http://ece-research.unm.edu/hayat/ece642 15/mainpage.htm

Topics:

1. Hypothesis testing. Ch. 2Bayesian, Neyman-Pearson, and minimax hypothesis testing, composite testing, receiveroperating characteristics (ROC), locally optimum detectors.

2. Discrete-time signal detection: Structure and performance analysis. Ch. 3Optimal coherent detection of deterministic signals in colored noise, signal selection,non-coherent detection, sequential detection, asymptotic relative efficiency.

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3. Continuous-time signal detection. Ch. 5Grenander’s Theorem, Mercer’s Theorem, and the Karhunen-Loeve representation.Application to coherent detection.

4. Parameter estimation. Ch. 4Bayesian estimation: Maximum likelihood (ML), minimum-mean-square error, minimum-absolute-error, maximum a postriori (MAP) estimators.Sufficient statistics and the Blackwell-Rao Theorem, Cramer-Rao bound.The information inequality.Further properties and extensions of the ML estimator.Recursive estimation.

5. Signal estimation. Chs. 5, 7Linear estimation: The orthogonality principle, Wiener-Kolmogorov filtering and pre-diction (continuous and discrete time).Discrete-time Kalman-Bucy filtering.Estimation of continuous-time–signal parameters.Some remarks on optimal and non-optimal nonlinear filtering.

6. Detection of continuous-time stochastic signals in Gaussian noise. Ch. 5 &notesEstimator-correlator structure of the likelihood ratio.Connection to matched filtering.

7. Elements of large-deviation in communication theory Basic theorems; impor-tance sampling; application to detection.

8. Multi-user detection: NotesOptimum receivers for synchronous and asynchronous receivers.

9. Detection for multipath fading channels: NotesThe RAKE receiver: structure and performance.

Computer usage:

A number of homework assignments require the use of Matlab.

Course requirements

• 40% Homework & computer assignments.

• 30% Midterm examination.

• 30% Final examination.

• Each student is required to attend at least 90% of the lectures.

Examinations

Last class period: Wednesday, Dec. 2Midterm: TBA (mid October)Final examination: Monday, December 7, 9:30–10:30

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Bibliography

H. V. Poor, An Introduction to Signal Detection and Estimation. Second Ed., Springer-Verlag,1994. (Required Text)

H. L. Van Trees, Detection, Estimation, and Modulation Theory. Part I, Wiley Inter-Science,2001.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall,1998.

T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation. Prentice Hall, 2000.

S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Prentice Hall,1998.

J. Proakis, Digital Communications, Fourth Edition. McGraw Hill, 2001.

S. Verdu, Multiuser Detection, Cambridge University Press, 1998.

J. Bucklew, Introduction to Rare Event Simulation, Springer, 2003.

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