Proportionate Adaptive Filtering for Block Sparse System Identification

TL;DR

This paper introduces new proportionate adaptive filtering algorithms tailored for block-sparse system identification, enhancing performance over existing methods with minimal added complexity.

Contribution

The paper proposes the BS-PNLMS and BS-IPNLMS algorithms, which optimize a mixed l2,1 norm and unify previous algorithms as special cases, improving block-sparse system identification.

Findings

BS-PNLMS outperforms NLMS, PNLMS, and IPNLMS in simulations.

Proposed algorithms have modest computational complexity increase.

Algorithms effectively identify block-sparse and dispersive impulse responses.

Abstract

In this paper, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed l2,1 norm of the adaptive filter coefficients. It is demonstrated that both the NLMS and the traditional PNLMS are special cases of BS-PNLMS. Meanwhile, a block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Simulation results demonstrate that the proposed BS-PNLMS and BS-IPNLMS algorithms outperformed the NLMS, PNLMS and IPNLMS algorithms with only a modest increase in computational complexity.