Minimum total complex error entropy for adaptive filter

As a powerful tool, the minimum error entropy (MEE) criterion has aroused extensive attention within the field of adaptive filtering recently. However, most MEE-based methods cannot be applied to the complex domain. Although the maximum total complex correntropy (MTCC) algorithm has been applied in errors-in-variables (EIV) model successfully when the noise is impulsive, it would degenerate obviously in some non-Gaussian noise cases, especially in the multi-peak distributed noise case. In this paper, we take the EIV model and complex domain into consideration and then propose a minimum total complex error entropy (MTCEE) algorithm. More importantly, the local stability and steady-state behavior of MTCEE are analyzed theoretically. Finally, we apply the MTCEE algorithm to the system identification and channel estimation, considering situations where noise affects both input and output. Through these applications, we demonstrate the effectiveness and superiority of MTCEE under EIV model in complex domain.