Low-Complexity Set-Membership Normalized LMS Algorithm for Sparse System Modeling

TL;DR

This paper introduces two low-complexity set-membership normalized LMS algorithms that efficiently exploit system sparsity, reducing computational costs while maintaining performance comparable to existing methods.

Contribution

The paper proposes novel low-complexity set-membership NLMS algorithms that effectively leverage sparsity with reduced computational complexity.

Findings

Algorithms achieve similar performance to state-of-the-art methods.

Proposed methods require lower computational cost.

Numerical results validate effectiveness and efficiency.

Abstract

In this work, we propose two low-complexity set-membership normalized least-mean-square (LCSM-NLMS1 and LCSM-NLMS2) algorithms to exploit the sparsity of an unknown system. For this purpose, in the LCSM-NLMS1 algorithm, we employ a function called the discard function to the adaptive coefficients in order to neglect the coefficients close to zero in the update process. Moreover, in the LCSM-NLMS2 algorithm, to decrease the overall number of computations needed even further, we substitute small coefficients with zero. Numerical results present similar performance of these algorithms when comparing them with some state-of-the-art sparsity-aware algorithms, whereas the proposed algorithms need lower computational cost.