Convergence evaluation of variable step-size NLMS algorithm in adaptive channel equalization

The use of two simple and robust variable step-size approaches in the adaptation process of the Normalized Least Mean Square (NLMS) algorithm (VSS-NLMS) in the adaptive channel equalization is investigated. The NLMS algorithm with a fixed step-size (FSS-NLMS) usually results in a trade-off between the residual error and the convergence speed of the algorithm. It is proved by computer simulation that the VSS-NLMS algorithms presented here eliminate much of this trade-off. In this paper the Mean-Square Error (MSE) performance of using the VSS-NLMS algorithms in the adaptation process of adaptive channel equalization is investigated. The step-size variation makes it possible for the VSS-NLMS algorithm to converge faster and to a lower steady state error than in the FSS-NLMS case.

1. INTRODUCTION

Adaptive filtering algorithms have been widely applied to solve many problems in digital communication systems [1]–[4]. The Least-Mean Square (LMS) algorithm has been widely used for adaptive filters, due to its simplicity and numerical robustness. On the other hand, the Normalized LMS (NLMS) algorithm is known that it gives better convergence characteristics than the LMS, because the NLMS uses a variable step-size parameter in which a fixed step-size parameter is divided by the input vector power at each iteration. However, a critical issue associated with both algorithms is the choice of the step-size parameter that is the trade-off between the steady-state misadjustment and the speed of adaptation. Recent studies have thus presented the idea of variable step-size NLMS algorithm to remedy this issue [5], [6]. Also, many other adaptive algorithms based upon non-mean-square cost function can also be defined to improve the adaptation performance. For example, the use of the error to the power Four has been investigated [4], [7] and the Least-Mean-Fourth adaptive algorithm (LMF) results. The use of the switching algorithm in adaptive channel equalization has also been studied [8], [9].