Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization with Shrinkage

TL;DR

This paper introduces a new sparsity-aware adaptive filtering method using alternating optimization with shrinkage, improving convergence and tracking in system identification tasks.

Contribution

It presents a novel two-stage adaptive filtering scheme with an alternating optimization approach and shrinkage, enhancing performance over existing methods.

Findings

Outperforms existing sparsity-aware algorithms in convergence

Demonstrates improved tracking in simulations

Analyzes mean-square error of the proposed algorithms

Abstract

This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating optimization of a diagonally-structured matrix that speeds up the convergence and an adaptive filter with a shrinkage function that forces the coefficients with small magnitudes to zero. We devise alternating optimization least-mean square (LMS) algorithms for the proposed scheme and analyze its mean-square error. Simulations for a system identification application show that the proposed scheme and algorithms outperform in convergence and tracking existing sparsity-aware algorithms.