Maximum Total Improper Complex Correntropy Algorithm for Widely Linear Adaptive Filtering

The maximum total complex correntropy (MTCC) algorithm improves the performance of adaptive filtering under the error in variable (EIV) model by integrating both input and output noise information into the total complex correntropy. However, the MTCC algorithm cannot be applied to the widely linear model, directly. Compared with a strictly linear model, the widely linear model provides the complete statistical information of signals for adaptive filtering. This paper first constructs a novel cost function for the widely linear model by incorporating the input and output noise information into the improper complex correntropy. Then, a novel widely linear adaptive filter algorithm named widely linear maximum total improper complex correntropy (WL-MTICC) is proposed using the gradient descent method under the maximum total improper correntropy criterion. Finally, the analysis of local stability and convergence in the mean sense regarding the proposed WL-MTICC algorithm is provided. Simulations are used to show the performance advantage of the proposed WL-MTICC algorithm in the presence of both input and output noises.