A Correntropy-Based Proportionate Affine Projection Algorithm for Estimating Sparse Channels with Impulsive Noise.

Zhengxiong Jiang,Xinqi Huang,Yingsong Li

doi:10.3390/e21060555

Abstract

A novel robust proportionate affine projection (AP) algorithm is devised for estimating sparse channels, which often occur in network echo and wireless communication channels. The newly proposed algorithm is realized by using the maximum correntropy criterion (MCC) and the data reusing scheme used in AP to overcome the identification performance degradation of the traditional PAP algorithm in impulsive noise environments. The proposed algorithm is referred to as the proportionate affine projection maximum correntropy criterion (PAPMCC) algorithm, which is derived in the context of channel estimation framework. Many simulation results were obtained to verify that the PAPMCC algorithm is superior to early reported AP algorithms with different input signals under impulsive noise environments.

Highlights

A class of adaptive filtering (AF) algorithms are extensively considered in use in channel estimation (CE), echo cancellation, noise elimination, etc. [1,2,3,4,5,6,7,8,9,10]
From the inspiration of the well-known PNLMS algorithm, the proportionate AP (PAP) algorithm integrates the proportionate idea into the affine projection (AP) algorithm to modify the gain allocation method, and realizes a dynamic step size (STS) based on the magnitudes of the channel coefficients that are included in the unknown channels
Since the α-stable distribution can well construct the non-Gaussian phenomenon, which is ubiquitous in practice, it was chosen to model the impulsive noise in the simulations

Summary

Introduction

A class of adaptive filtering (AF) algorithms are extensively considered in use in channel estimation (CE), echo cancellation, noise elimination, etc. [1,2,3,4,5,6,7,8,9,10]. The computation burden of the AP is between the LMS and RLS algorithms, and the AP algorithm has a fast convergence, especially for colored or speech signal input signals [13] In many engineerings, such as speech signal processing and real-time traffic predictions, noise often exhibits strongly impulsive characteristics [14,15]. Traditional NLMS and AP algorithms, which use the minimum-mean-square-error (MMSE) criterion to construct an expected cost function, will suffer from performance degradation in those impulsive noise environments. Inspired by the PNLMS, the proportionate AP (PAP) algorithm has been proposed by using the idea in PNLMS to fully use the sparse structure-information of the echo channels [31] based on the data reusing principle. The AP scheme and MCC are considered together to construct a new cost function to enhance the PAP algorithm in impulsive noise environments, which is denoted as proportionate affine projection maximum correntropy criterion (PAPMCC) algorithm. Experimental results verify that the PAPMCC provides a lower steady state error than AP, ZA-AP, RZA-AP, and PAP algorithms with different inputs

Review of the PAP Algorithm

AP Algorithm

PAP Algorithm

Proposed PAPMCC Algorithm

Experimental Results

Conclusions