Novel error variance estimation rule for nonparametric VSS-NLMS algorithm

Abstract

This paper presents a robust error variance estimation rule for the nonparametric variable step-size normalized least mean square (NPVSS-NLMS) algorithm. The proposed variance estimation rule accurately estimates the variance of the error signal. This is achieved by the variable exponential windowing parameter depending on the standard deviations of the sequential error signals. The accurate estimation of the error signal variance in the NPVSS-NLMS algorithm considerably improves the performance of the adaptive filter when compared to the classical NPVSS-NLMS algorithm. Moreover, the convergence and steady-state performances of the NPVSS-NLMS based on the proposed rule are analyzed in this study. The performance of the proposed algorithm is evaluated on system identification and acoustic echo canceling experiments and compared with that the classical NPVSS-NLMS algorithm. As a result, simulations show that the proposed algorithm with the help of the novel robust error variance estimation rule not only yields a dramatically reduced steady-state error but also achieves a faster convergence rate as compared with the classical counterparts. Furthermore, the theoretical results of the variable exponential windowing parameter used in the proposed rule are in very good agreement with its simulation results.