A Comparison Between Kernel-based Adaptive Filters Including the Epanechnikov Function

Abstract

Kernel Adaptive Filtering is an effective solution for nonlinear channel equalization, offering remarkable results in scenarios where linear filters often fail. In this context, the Kernel Maximum Correntropy (KMC) is an efficient and resilient technique. In most cases, the Gaussian kernel is used to calculate correntropy. In this article, we propose to use the Epanechnikov kernel to estimate correntropy and analyze its performance. The filter performance is compared to the KMC with Gaussian kernel and also to the Kernel Least-Mean-Square algorithm.

New approaches for the Kernel-based Adaptive Filter with Epanechnikov kernel

“…where µ is the step size. Kernel width and step size effects on the algorithm have been studied in [7], [11].…”

“…As proposed in [7], the stochastic gradient, given by ( 5), can be computed using the Epanechnikov kernel (4) as follows:…”

“…In [7], it was observed that the KMC-EPA algorithm tends to diverge after a certain number of iterations, indicating potential numerical instability. This issue can arise due to the fact that the size of the network increases with the number of training data [4].…”

“…Among these criteria, the Maximum Correntropy Criterion (MCC) has gained attention due to its simplicity and robustness. The Kernel Maximum Correntropy (KMC) algorithm combines MCC with KAF and has shown promising performance, particularly in impulsive noise environments [7], [8].…”

“…In [7], a study considering different kernel functions for calculating the correntropy measure in the context of KAF was presented. The paper considered the classical Gaussian kernel and proposed the use of the Epanechnikov kernel.…”