An Adaptive Upper Threshold Based Gain Function for the ZA-PNLMS Algorithm

Abstract

The recently proposed Zero-Attracting Proportionate Normalized Least Mean Square (ZA-PNLMS) algorithm improves the performance of the PNLMS algorithm for identifying sparse systems. In particular, it keeps the fast initial convergence rate of the PNLMS algorithm, and improves its transient performance by arresting the fall in the convergence rate at the later stage of the adaptation process, and it also improves the steady-state mean square error (MSE). However, the improvement in the steady-state performance is marginal. In this brief, we propose a novel gain function for the ZA-PNLMS algorithm by introducing an adaptive upper threshold parameter. It has two fold implications. First, the proposed threshold parameter truncates the proportional gains of highly active taps when they approach to their steady-states and helps the lesser active taps to converge faster by providing them more gains, and thereby the overall transient performance is further improved. Secondly, it also improves steady-state MSE significantly by reducing the fluctuation of the active taps at the steady-state. Extensive simulation studies have been carried out to justify the improvement obtained by the proposed algorithm.