Block-Sparsity-Induced Adaptive Filter for Multi-Clustering System Identification

TL;DR

This paper introduces a new block-sparse LMS algorithm that enhances adaptive filtering for block-sparse systems by incorporating a block-sparsity penalty, with theoretical analysis and simulations confirming improved convergence and performance.

Contribution

The paper proposes the BS-LMS algorithm with a block-sparsity penalty and provides theoretical analysis of its convergence and steady-state behavior, demonstrating its advantages over existing methods.

Findings

BS-LMS outperforms l0-LMS in convergence behavior.

Theoretical expressions match simulation results.

BS-LMS achieves lower misadjustment with better convergence.

Abstract

In order to improve the performance of least mean square (LMS)-based adaptive filtering for identifying block-sparse systems, a new adaptive algorithm called block-sparse LMS (BS-LMS) is proposed in this paper. The basis of the proposed algorithm is to insert a penalty of block-sparsity, which is a mixed \$l_{2, 0}\$ norm of adaptive tap-weights with equal group partition sizes, into the cost function of traditional LMS algorithm. To describe a block-sparse system response, we first propose a Markov-Gaussian model, which can generate a kind of system responses of arbitrary average sparsity and arbitrary average block length using given parameters. Then we present theoretical expressions of the steady-state misadjustment and transient convergence behavior of BS-LMS with an appropriate group partition size for white Gaussian input data. Based on the above results, we theoretically demonstrate that BS-LMS has much better convergence behavior than \$l_0\$-LMS with the same small level of misadjustment. Finally, numerical experiments verify that all of the theoretical analysis agrees well with simulation results in a large range of parameters.