p Norm Constraint Leaky LMS Algorithm for Sparse System Identification

TL;DR

This paper introduces the Lp-LLMS algorithm, combining leaky LMS with a p-norm penalty to improve sparse system identification, especially under noisy conditions.

Contribution

It develops a novel Lp-LLMS algorithm that incorporates a p-norm penalty into leaky LMS, enhancing sparse system identification performance.

Findings

Improved filter performance in sparse systems.

Enhanced robustness to noisy inputs.

Better convergence behavior than standard LMS.

Abstract

This paper proposes a new leaky least mean square (leaky LMS, LLMS) algorithm in which a norm penalty is introduced to force the solution to be sparse in the application of system identification. The leaky LMS algorithm is derived because the performance ofthe standard LMS algorithm deteriorates when the input is highly correlated. However, both ofthem do not take the sparsity information into account to yield better behaviors. As a modification ofthe LLMS algorithm, the proposed algorithm, named Lp-LLMS, incorporates a p norm penalty into the cost function ofthe LLMS to obtain a shrinkage in the weight update equation, which then enhances the performance of the filter in system identification settings, especially when the impulse response is sparse. The simulation results verify that the proposed algorithm improves the performance ofthe filter in sparse system settings in the presence ofnoisy input signals.