Convergence and steady-state analysis of a variable step-size NLMS algorithm

In this paper, a simple and robust variable step-size normalized LMS (VSS-NLMS) adaptive algorithm is proposed. The NLMS algorithm with a fixed step-size usually results in a trade-off between the residual error and the convergence speed of the algorithm. The variable step-size NLMS algorithm presented here will eliminate much of this trade-off. 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 fixed step-size case. We derive here the proposed algorithm and analyze its steady-state performance. Computer simulation shows that the analytical results obtained in this paper are closely verified. In particular, our simulation results show that the proposed VSS-NLMS algorithm outperforms the traditional NLMS algorithm both in terms of convergence speed and steady-state error.