Semester Offering: January
 

provide senior research students with a comprehensive understanding of discrete time statistical signal processing techniques with emphasis on applications in Wireless Communications.

 

Minimum Variance Unbiased Estimation, Cramer-Rao Lower Bound, General Minimum Variance Unbiased Estimation, Best Linear Unbiased Estimators, Maximum Likelihood Estimation, Least Squares, General Bayesian Estimators, Discrete Wiener Filters and Kalman Filters.

 

AT77.02 Signals and Systems , AT 77.9007 Statistical Communication Theory.

 

I  Minimum Variance Unbiased Estimation

1. Unbiased Estimators
2. Minimum Variance Criterion
3. Existence of the Minimum Variance Unbiased Estimator
4. Finding the Minimum Variance Unbiased Estimator
5. Extension to a Vector Parameter

II  Cramer-Rao Lower Bound

1. Estimator Accuracy Considerations
2. Cramer-Rao Lower Bound (CRLB)
3. General CRLB for Signals in White Gaussian Noise
4. Extension to a Vector Parameter
5. CRLB for the General Gaussian Case

III  General Minimum Variance Unbiased (MVU) Estimation

1. Sufficient Statistics
2. finding Sufficient Statistics
3. Using Sufficiency to Find MVU Estimator
4. Extension to a Vector Parameter

IV  Best Linear Unbiased Estimators (BLUE)

1. Definition of the BLUE
2. Finding the BLUE
3. Extension to a Vector Parameter
4. Applications

 

V  Maximum Likelihood Estimation (MLE)

1. Properties of the MLE
2. Extension to a Vector parameter
Applications
3. Applications in 3 rd and 4 th Generation Systems

VI  Least Squares

1. Linear Least Squares
2. Order-Recursive Least Squares
3. Sequential Least Squares
4. Constrained Least Squares
Applications

VII  General Bayesian Estimators

1. Prior Knoledge and Estimation
2. Bayesian Linear Model
3. Minimum Mean Square Error (MMSE) Estimators
4. Maximum A Posteriori (MAP) Estimators
Applications

VIII  Discrete Wiener Filters and Kalman Filters

1. Wiener-Hopf Equations
2. Error-Performance Surface
3. Linear Prediction
4. Levinson-Durbin Algorithm
5. Vector Kalman Filter
6. Kalman Versus Wiener Filters

 

 

Lecture Notes and Selected Papers.

 

Kay S.M. : Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, 1993
Kay S.M. : Fundamentals of Statistical Signal Processing: Detection Theory, Prentice Hall, 1998
Simon Haykin : Adaptive Filter Theory, Prentice Hall, 2 nd Edition, 1991
Harry L. Van Trees : Detection, Estimation, and Modulation Theory: Part I, John Wiley, 2001
William A. Gardner : Introduction to Random Processes, Macmillan, 1986
Athanasios Papoulis : Probability, Random Variables, and Stochastic Processes, Mc-Graw Hill, 2002, 4th Edition

 

IEEE Transactions on Communications/ Information Theory
IEEE Communications Letters
IEEE Transactions on Wireless Communications
IEEE Journal of Selected Areas in Communications
IEEE Transactions on Vehicular Technology (VT)
IEE Proceedings on Communications, IEE Electronics Letters

 

Assignments 50%
Mid Semester 25%
Final Exam 25%