Adaptive Combination of l0 LMS Adaptive Filters for Sparse System Identification in Fluctuating Noise Power

TL;DR

This paper introduces adaptive combinations of l0-LMS filters with varying parameters to robustly identify sparse systems under fluctuating noise conditions, improving performance and computational efficiency.

Contribution

It proposes a novel adaptive combination framework for l0-LMS filters, including partial updates and RLS-type parameter updates, extending to multiple filters for enhanced results.

Findings

Performance is robust across varying SNR conditions.

Partial update scheme reduces computation and improves performance.

Combining multiple filters yields further accuracy improvements.

Abstract

Recently, the l0-least mean square (l0-LMS) algorithm has been proposed to identify sparse linear systems by employing a sparsity-promoting continuous function as an approximation of l0 pseudonorm penalty. However, the performance of this algorithm is sensitive to the appropriate choice of the some parameter responsible for the zero-attracting intensity. The optimum choice for this parameter depends on the signal-to-noise ratio (SNR) prevailing in the system. Thus, it becomes difficult to fix a suitable value for this parameter, particularly in a situation where SNR fluctuates over time. In this work, we propose several adaptive combinations of differently parameterized l0-LMS to get an overall satisfactory performance independent of the SNR, and discuss some issues relevant to these combination structures. We also demonstrate an efficient partial update scheme which not only reduces the number of computations per iteration, but also achieves some interesting performance gain compared with the full update case. Then, we propose a new recursive least squares (RLS)-type rule to update the combining parameter more efficiently. Finally, we extend the combination of two filters to a combination of M number adaptive filters, which manifests further improvement for M > 2.