Adaptive Parameters Adjustment for Group Reweighted Zero-Attracting LMS

TL;DR

This paper proposes a variable-parameter approach for group zero-attracting LMS algorithms, optimizing step size and regularization to improve sparsity and convergence in system identification tasks.

Contribution

It introduces a novel adaptive parameter adjustment method based on transient behavior modeling, providing closed-form solutions for optimal parameters.

Findings

Enhanced sparsity and estimation accuracy

Improved convergence speed and steady-state performance

Validated effectiveness through simulations

Abstract

Group zero-attracting LMS and its reweighted form have been proposed for addressing system identification problems with structural group sparsity in the parameters to estimate. Both algorithms however suffer from a trade-off between sparsity degree and estimation bias and, in addition, between convergence speed and steady-state performance like most adaptive filtering algorithms. It is therefore necessary to properly set their step size and regularization parameter. Based on a model of their transient behavior, we introduce a variable-parameter variant of both algorithms to address this issue. By minimizing their mean-square deviation at each time instant, we obtain closed-form expressions of the optimal step size and regularization parameter. Simulation results illustrate the effectiveness of the proposed algorithms.