The Bias-Compensated Proportionate NLMS Algorithm With Sparse Penalty Constraint

Zhan Jin,Longxiang Guo,Yingsong Li

doi:10.1109/access.2019.2962861

Abstract

For compensating the bias caused by the noisy input which is always ignored by ordinary algorithms, two novel algorithms with zero-attraction (ZA) penalties are proposed in this paper. The first one constructs a bias-compensated term in the updating recursion of the zero-attraction proportionate normalized least mean square (PNLMS) algorithm which is named BC-ZA-PNLMS algorithm. The second one employs the bias-compensated term and the correntropy induced metric (CIM) constraint to renew the updating recursion of the PNLMS algorithm which is named BC-CIM-PNLMS algorithm. Both of these two algorithms are derived on the basis of unbiased criterion. Simulation examples are carried out, and the results indicate that the two newly developed unbiased algorithms outperform the related algorithms previously presented in other literatures for combating noisy input and measurement noises.

Highlights

Normalized least-mean-square (NLMS) algorithm is one of the popular adaptive filtering algorithms which are widely used in signal processing field, such as echo cancellation, system identification and linear prediction [1], [2]
Besides the traditional zero-attractors obtained from different norm penalty, the correntropy induced metric (CIM) method has been considered to construct a zero-attractor in [20]–[26], which is to measure the similarity between the two different variables
The updating recursion of the proportionate normalized least mean square (PNLMS) algorithm with CIM penalty can be described as v(k )Q(k )e(k ) w (k + 1) = w (k) + μ vT (k)Q(k)v(k) + ε

Summary

INTRODUCTION

Normalized least-mean-square (NLMS) algorithm is one of the popular adaptive filtering algorithms which are widely used in signal processing field, such as echo cancellation, system identification and linear prediction [1], [2]. For the purpose of taking advantages of the sparse characteristics in these systems, the proportionate type algorithms which obtain fast convergence speed by assigning an independent step-size to each coefficient have been developed [6]–[11]. Among these algorithms, the most popular one is the proportionate normalized least mean square (PNLMS). The role of the sparse penalty is to attract the small value coefficients to zero, faster convergence speed can be obtained than that of original algorithms and even than that of the proportionate type algorithms. It is observed that the first two terms of the iteration are the same as those of the PNLMS algorithm, and the last term of the sign function with a zero attraction strength control parameter γ is the constructed zero attractor

REVIEW OF THE CIM

SIMULATION AND RESULT ANALYSIS

CONCLUSION