SPARLS: A Low Complexity Recursive $\mathcal{L}_1$-Regularized Least Squares Algorithm

TL;DR

The paper introduces SPARLS, a recursive algorithm for sparse signal estimation that improves accuracy and reduces complexity over traditional methods in adaptive filtering, especially for wireless channel estimation.

Contribution

It presents a novel recursive $ ext{L}_1$-regularized least squares algorithm that efficiently estimates sparse vectors using an EM-type approach.

Findings

SPARLS outperforms RLS in mean squared error.

SPARLS reduces computational complexity.

Effective in multi-path wireless channel estimation.

Abstract

We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an Expectation-Maximization type algorithm. Simulation studies in the context of channel estimation, employing multi-path wireless channels, show that the SPARLS algorithm has significant improvement over the conventional widely-used Recursive Least Squares (RLS) algorithm, in terms of both mean squared error (MSE) and computational complexity.