A Zero-attracting Quaternion-valued Least Mean Square Algorithm for Sparse System Identification

TL;DR

This paper introduces a novel quaternion-valued LMS algorithm that leverages sparsity via the $l_1$ norm to enhance convergence speed in sparse system identification, marking the first such study in quaternion signal processing.

Contribution

The paper presents the first quaternion-valued sparse system identification method using a zero-attracting LMS algorithm incorporating $l_1$ norm regularization.

Findings

Faster convergence speed demonstrated through simulations

Effective incorporation of sparsity information in quaternion LMS

First study on quaternion-valued sparse system identification

Abstract

Recently, quaternion-valued signal processing has received more and more attention. In this paper, the quaternion-valued sparse system identification problem is studied for the first time and a zero-attracting quaternion-valued least mean square (LMS) algorithm is derived by considering the $l_1$ norm of the quaternion-valued adaptive weight vector. By incorporating the sparsity information of the system into the update process, a faster convergence speed is achieved, as verified by simulation results.