Convergence Analysis of a Fixed Point Algorithm Under Maximum Complex Correntropy Criterion

With the emergence of complex correntropy, the maximum complex correntropy criterion (MCCC) has been applied to the complex-domain adaptive filtering. The MCCC uses the fixed point method to find the optimal solution, which provides good robustness in the non-Gaussian noise environment, especially for the impulse noise. However, the convergence analysis for the fixed point method is limited to the real-domain filtering. In this letter, we provide the convergence analysis of fixed point based MCCC algorithm in complex-domain filtering. First, by using the matrix inversion lemma, we rewrite the MCCC algorithm to a gradient-like version. In addition, we provide two computationally efficient versions of MCCC. Then, we provide the stability analysis and obtain the excess mean square error for MCCC. Finally, simulation results confirm the correctness of the convergence analysis in this letter.