Complex Correntropy with Variable Center: Definition, Properties, and Application to Adaptive Filtering

• Main Authors: Fei Dong, Guobing Qian, Shiyuan Wang
• Format: Article
• Language: English
• Published: MDPI AG 2020-01-01
• Series: Entropy
• Subjects: complex; mccc-vc; variable center; stability; emse
• Online Access: https://www.mdpi.com/1099-4300/22/1/70

The complex correntropy has been successfully applied to complex domain adaptive filtering, and the corresponding maximum complex correntropy criterion (MCCC) algorithm has been proved to be robust to non-Gaussian noises. However, the kernel function of the complex correntropy is usually limited to a Gaussian function whose center is zero. In order to improve the performance of MCCC in a non-zero mean noise environment, we firstly define a complex correntropy with variable center and provide its probability explanation. Then, we propose a maximum complex correntropy criterion with variable center (MCCC-VC), and apply it to the complex domain adaptive filtering. Next, we use the gradient descent approach to search the minimum of the cost function. We also propose a feasible method to optimize the center and the kernel width of MCCC-VC. It is very important that we further provide the bound for the learning rate and derive the theoretical value of the steady-state excess mean square error (EMSE). Finally, we perform some simulations to show the validity of the theoretical steady-state EMSE and the better performance of MCCC-VC.