Complex Correntropy Function: properties, and application to a channel equalization problem

TL;DR

This paper formalizes the properties of complex correntropy, a new similarity measure for complex data, and demonstrates its effectiveness in channel equalization compared to traditional algorithms.

Contribution

It introduces the formal properties of complex correntropy and applies it successfully to a channel equalization problem, showing advantages over existing methods.

Findings

Complex correntropy is effective for channel equalization.

It outperforms CLMS, CRLS, and LAD algorithms in experiments.

Properties of complex correntropy are rigorously formalized.

Abstract

The use of correntropy as a similarity measure has been increasing in different scenarios due to the well-known ability to extract high-order statistic information from data. Recently, a new similarity measure between complex random variables was defined and called complex correntropy. Based on a Gaussian kernel, it extends the benefits of correntropy to complex-valued data. However, its properties have not yet been formalized. This paper studies the properties of this new similarity measure and extends this definition to positive-definite kernels. Complex correntropy is applied to a channel equalization problem as good results are achieved when compared with other algorithms such as the complex least mean square (CLMS), complex recursive least squares (CRLS), and least absolute deviation (LAD).