l_0 Norm Constraint LMS Algorithm for Sparse System Identification

TL;DR

This paper introduces a new LMS-based adaptive algorithm that incorporates an $l_0$ norm approximation to exploit system sparsity, enhancing convergence and performance in sparse system identification.

Contribution

The paper proposes a novel $l_0$ norm constrained LMS algorithm that improves convergence speed and accuracy for sparse systems, with reduced computational complexity.

Findings

Enhanced convergence rate for small coefficients

Effective identification of sparse systems

Reduced computational complexity through partial updating

Abstract

In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on $l_0$ norm -- a typical metric of system sparsity, is proposed and integrated into the cost function of the LMS algorithm. This integration is equivalent to add a zero attractor in the iterations, by which the convergence rate of small coefficients, that dominate the sparse system, can be effectively improved. Moreover, using partial updating method, the computational complexity is reduced. The simulations demonstrate that the proposed algorithm can effectively improve the performance of LMS-based identification algorithms on sparse system.