Transient performance analysis of zero-attracting LMS

TL;DR

This paper provides a detailed mean and mean-square analysis of the zero-attracting LMS algorithm, which is used for sparse system identification, addressing the gap in understanding its transient behavior.

Contribution

It introduces a comprehensive analytical model for the transient performance of ZA-LMS, including its mean and mean-square behavior, validated by simulations.

Findings

The model accurately predicts the transient behavior of ZA-LMS.

Simulation results confirm the model's validity and show improved understanding.

Comparison with existing models demonstrates the proposed analysis's effectiveness.

Abstract

Zero-attracting least-mean-square (ZA-LMS) algorithm has been widely used for online sparse system identification. It combines the LMS framework and $\ell_1$-norm regularization to promote sparsity, and relies on subgradient iterations. Despite the significant interest in ZA-LMS, few works analyzed its transient behavior. The main difficulty lies in the nonlinearity of the update rule. In this work, a detailed analysis in the mean and mean-square sense is carried out in order to examine the behavior of the algorithm. Simulation results illustrate the accuracy of the model and highlight its performance through comparisons with an existing model.