Relationship Between Criteria Based on Correntropy and Second Order Statistics for Equalization of Communication Channels

Correntropy has been successfully used for signal processing in a large variety of applications. Usually, correntropy estimator uses a Gaussian kernel, which leads to a measure that takes into account all even order statistical moments of the underlying signal. In this paper we analyze correntropy implemented with the Epanechnikov kernel, which is given by a second order polynomial. Considering an equalization scenario, we compare such criterion with the one obtained through the use of the Gaussian kernel and also the Correlation Retrieval Criterion. We discuss similarities and differences, theoretically and through simulations, between the three criteria.