Comparative Study of LMS and NLMS Algorithms in Adaptive Equalizer

In this paper we provide a thorough ser( symbol error rate) analysis of two well known adaptive algorithms for equalization based on a novel least squares reference model that allows to treat the equalizer problem equivalently as system identification problem. An adaptive algorithm is a procedure for adjusting the parameters of an adaptive filter to minimize a cost function chosen for the task at hand. Here we firstly proposed a noise-robust optimal-step-size frequency domain LMS (least mean square) algorithm for estimating the equalizer coefficients and after the modified LMS algorithm which is an extension of the standard LMS (least mean square) algorithm which bypasses this issue by calculating maximum step size value. The proposed algorithms conclude that the stepsize ambiguity of the LMS (least mean square) algorithm is solved by the NLMS (normalized mean square) algorithm, which gives faster convergence speed as compared to the LMS (least mean square) algorithm. Computer simulation results a represented to show its improved performance for trained adaptive equalization. This paper focuses on the use of these two proposed algorithms to reduce this unwanted echo, thus increasing communication quality.