Mixture Complex Correntropy for Adaptive Filter

Abstract

With the development of adaptive filtering theory and its application, the research on complex domain has attracted more attention. As a measure of local similarity, complex correntropy has been applied to adaptive filtering in the complex domain. The choice of kernel function plays a very important role in the performance of corresponding algorithms. Generally, Gaussian function is used as the kernel function since it has some attractive properties, e.g., positive definiteness and convexity. However, Gaussian function is not always the best choice. In order to further improve the performance of adaptive filtering algorithm in the complex domain, this brief employs the mixture Gaussian function as the kernel function, and proposes a new fixed point algorithm based on the maximum mixture complex correntropy criterion (MMCCC). In addition, we derive the excess mean square error of the proposed fixed point algorithm for theoretical analysis. Simulation results illustrate the superiority of the MMCCC algorithm and the correctness of the theoretical analysis in this brief.