Automatic LMS equalizer algorithms with fast rate of convergence

Abstract

In high speed voiceband modems, as in many other data transmission systems, linear distortion and additive noise are important degrading factors. The tapped-delay-line equalizers designed to minimize the mean-square-error cost function are commonly used to compensate these undesired effects. Among the several algorithms which minimizes the mean-square-error cost function stochastic gradient algorithm is the most popular because of its simplicity in implementation. However, for highly distorted channels stochastic gradient algorithm converges slowly and, therefore, a long training period which causes a fall in the overall performance of the system is required. Instead, more complicated algorithms with faster rate of convergence have been developed in the last years: Kalman/Godard, Fast Kalman and lattice algorithms. In this thesis, the rate of convergence of stochastic gradient, Kalman/Godard and Fast Kalman algorithms are analyzed and their computational, complexities are examined. The analysis is extended to the complex domain in order to cover equalization of quadrature-amplitude-modulated signals. Furthermore, a computer program package which simulates several telephone channels, a quadrature-amplitude-modulatiqn. system and the equalization algorithms is written. Them, the performance of the different equalizatIon algorithms over a wide range of channels are compared.