Proportionate Minimum Error Entropy Algorithm for Sparse System Identification

Zongze Wu,Siyuan Peng,Jose Principe,Haiquan Zhao,Badong Chen

doi:10.3390/e17095995

Abstract

Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS) algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE) criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE) criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE) algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.

Highlights

Sparse system identification is an active research area at present, which finds various real-world applications in network echo cancelation, wireless multipath channels, underwater acoustic communications, and so on [1,2]
We propose a novel proportionate algorithm for sparse system identification, called the proportionate minimum error entropy (PMEE) algorithm
The PMEE algorithm may perform much better than the proportionate normalized least mean square (PNLMS) when identifying a sparse system with non-Gaussian noises

Summary

Introduction

Sparse system identification is an active research area at present, which finds various real-world applications in network echo cancelation, wireless multipath channels, underwater acoustic communications, and so on [1,2]. Most of the existing proportionate-type adaptive algorithms (such as PNLMS) are developed based on the well-known mean square error (MSE) criterion. In non-Gaussian situations, the proportionate-type NLMS algorithms may perform poorly especially in the presence of impulsive noises. Since entropy can capture higher-order statistics and information content of signals rather than their energy, the MEE based adaptive algorithms may achieve significant performance improvements in non-Gaussian situations. The PMEE algorithm may perform much better than the PNLMS when identifying a sparse system with non-Gaussian noises. In a recent paper [26], we proposed three sparse adaptive filtering algorithms under MEE criterion, namely. ZAMEE, RZAMEE, and CIMMEE, which are derived by incorporating a sparsity penalty term into the MEE criterion These algorithms perform well for sparse system identification with non-Gaussian noises.

Minimum Error Entropy Criterion

Proportionate Minimum Error Entropy

Energy Conservation Relation

Sufficient Condition for Mean Square Convergence

Simulation Results

Conclusions