Blind Channel Equalization for SISO and SIMO Channels Using Second Order Statistics

Abstract

<p> In this thesis we develop several approaches to the problem of blind channel equalization based on second-order statistics (808). We consider the single-input singleoutput (8180) system with minimum phase channel where the received signal is sampled at the symbol rate (T-spaced equalizer). We formulate the equalizer design criterion as a simple convex optimization problem, where the equalizer can be obtained efficiently avoiding the local minima problem. </p> <p> We also extend the problem to the single-input multiple-output (8IMO) systems where the received signal is sampled at an integer multiple of the symbol rate. We formulate the problem as a convex optimization problem using the features existing in the channel matrix structure. The problem can be solved efficiently to obtain the equalizer where a global minima is guaranteed. Moreover, we modify this formulation and deduce a closed form solution to the equalizer. Although both methods are sensitive to the channel order as well as existing subspace methods, they perform better than the subspace methods when the channel matrix is close to being singular. Furthermore, we propose an efficient direct minimum mean square error (MM8E) approach to estimate the equalizer. The method does not rely on the channel order and utilizes the channel matrix structure in SIMO systems. Therefore, it outperforms existing algorithms including the previously proposed methods. However, due to the large amount of computations involved in this method we present a new algorithm that belongs to the same class with moderate computational complexity and acceptable performance loss with respect to the latter algorithm. </p>