Study of Sparsity-Aware Subband Adaptive Filtering Algorithms with Adjustable Penalties

TL;DR

This paper introduces two new sparsity-aware subband adaptive filtering algorithms that leverage l1-norm penalties to improve sparse system identification, with lower complexity and adaptive penalty adjustment, validated through theoretical analysis and simulations.

Contribution

The paper presents novel sparsity-aware NSAF algorithms with adaptive penalty tuning and comprehensive statistical models, enhancing sparse system identification performance.

Findings

Lower computational complexity compared to prior methods

Effective identification of sparse systems demonstrated in simulations

Adaptive adjustment of sparsity penalty improves performance

Abstract

We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter coefficients. This l1-norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady -state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results.