A class of adaptive filtering algorithms based on improper complex correntropy

As a robust online learning approach, adaptive filtering based on correntropy has attracted more attentions. Recently, researchers have made efforts to develop complex correntropy to deal with adaptive filtering issues in complex domain. However, most of the literature on complex cor-rentropy lack details regarding the processing of noncircular signals. Up to now, the maximum improper complex correntropy criterion (MICCC) algorithm for noncircular and widely-linear (WL) adaptive filtering utilizes the gradient descent method to find the maximum of the objec-tive function. However, the MICCC algorithm fails to guarantee both low steady-state weight error power and fast convergence. To overcome this defect, this paper proposes a class of adaptive filtering algorithms which are based on fixed-point instead of gradient descent. It is worth noting that we manage to avoid the massive calculation of matrix inversion in traditional fixed-point based methods by utilizing the lemma of matrix inversion properly and further provide two alternative recursive algorithms. Finally, the local convergence analysis of mean and mean square is performed, and the simulated results offer strong evidences for the superior performance of the proposed algorithms over widely-linear complex least mean square (WL-CLMS), widely-linear recursive least square (WL-RLS) and MICCC.

Automated summary

This paper proposes a class of adaptive filtering algorithms based on fixed-point instead of gradient descent to overcome the limitations of current algorithms in weight error and convergence speed. By properly utilizing the lemma of matrix inversion, the massive calculation of matrix inversion in traditional fixed-point based methods is avoided, and two alternative recursive algorithms are provided. Local convergence analysis of mean and mean square is performed, and simulated results show strong evidence for the superior performance of the proposed algorithms over WL-CLMS, WL-RLS, and MICCC.