p-norm-like Constraint Leaky LMS Algorithm for Sparse System Identification

TL;DR

This paper introduces a p-norm-like constrained leaky LMS algorithm that enhances sparse system identification performance by incorporating sparsity-aware penalties, outperforming traditional methods especially with noisy inputs.

Contribution

It proposes a novel sparse-aware LLMS algorithm with a p-norm-like penalty, improving adaptive filtering in sparse, noisy environments.

Findings

Enhanced performance in sparse system identification

Effective in noisy input conditions

Outperforms traditional LMS algorithms

Abstract

In this paper, we propose a novel leaky least mean square (leaky LMS, LLMS) algorithm which employs a p-norm-like constraint to force the solution to be sparse in the application of system identification. As an extension of the LMS algorithm which is the most widely-used adaptive filtering technique, the LLMS algorithm has been proposed for decades, due to the deteriorated performance of the standard LMS algorithm with highly correlated input. However, both ofthem do not consider the sparsity information to have better behaviors. As a sparse-aware modification of the LLMS, our proposed Lplike-LLMS algorithm, incorporates a p-norm-like penalty into the cost function of the LLMS to obtain a shrinkage in the weight update, which then enhances the performance in sparse system identification settings. The simulation results show that the proposed algorithm improves the performance of the filter in sparse system settings in the presence of noisy input signals.