|M.Sc Student||Ofer Saferman|
|Subject||The EM Algorithm: Towards a Unified Method for Channel|
Estimation, Detection and Iterative Decoding
|Department||Department of Electrical Engineering||Supervisor||Professor Emeritus Bar-David Israel|
The EM algorithm has been invented in the 1960’s as a method to perform maximum-likelihood (ML) estimation in an iterative manner for problems where direct ML is intractable. Although the algorithm’s implementation can be very complex, the fact that it assures a monotone increase in the likelihood function and convergence to a stationary point (which can be, unfortunately, to a local maximum) make it very attractive.
Since then the algorithm has been used extensively in many areas and application like: economics, genetics, speech recognition, electromagnetics, general estimation of parameters, image processing, communications, etc. The algorithm became popular for use in communications applications about 10 years ago. Since then it found its use in almost all aspects of communication, like: channel estimation, channel decoding, channel modeling, multi-user detection, direction of arrival estimation, etc.
This work surveys the application of the EM algorithm and its variants to joint blind channel estimation and data detection for Intersymbol Interference (ISI) channels which in general are time-varying. It shows that many important and successful methods for channel estimation and channel modeling can are derived as sub-optimal variants of the EM algorithm. We show that modeling by use of hidden Markov models (HMM) emerges as the dominant and most promising method because of its ability to model a wide family of stochastic processes. Training these models is done by the Baum-Welch algorithm (BWA), which is a special implementation of the EM algorithm. We also show the important connection between EM channel estimation algorithms and iterative decoding, and in fact we use iterative decoding as a raison d’etre for EM channel based estimation.