An Adaptive Setting Method of Step-Size Parameter in NLMS Algorithms

Abstract

A major, and yet unresolved, problem has been the choice of the step-size in some parameter tracking algorithms. This paper presents an adaptive setting method of step-size parameter for tracking time-varying parameters when normalized least mean square (NLMS) algorithm is used. The usual method suggested by Benveniste et al is to adjust the step-size so as to minimize the performance measure defined by the mean squares of prediction error. The weak point of this method is that the performance measure converges only on a local minimum.
The main object of this paper is to give a solution for this problem. The solution obtained is that the performance measure converges on the global minimum through the minimization of another performance measure. As a result, the proposed algorithm becomes asymptotically optimal.
Numerical examples indicate acceptable performance of the proposed method.