Complex Kernel Risk-Sensitive Loss: Application to Robust Adaptive Filtering in Complex Domain

Abstract

Recently, the maximum complex correntropy criterion (MCCC) algorithm has shown its superiority for adaptive filter in complex domain. Compared with the traditional mean square error (MSE) criterion-based algorithms, MCCC uses complex correntropy as similarity measure, which is robust even in the presence of impulse noise. However, the error performance surface of complex correntropic loss (CC-loss) is not optimal, which is steep nearby the optimal solution and flat far from the optimal solution. In this paper, we propose a new similarity measure in complex domain, namely, complex kernel risk-sensitive loss (CKRSL). Based on CKRSL, we derive a new adaptive filter algorithm in the complex domain by using the gradient-based method, i.e., the CKRSL algorithm. Compared with the MCCC algorithm, the CKRSL algorithm has faster convergence rate and higher filtering accuracy. Meanwhile, it is robust against outlier. In addition, we provide the stability analysis and the steady-state excess MSE for the CKRSL algorithm. Simulation results confirm the correctness of the theoretical results and the superiority of the CKRSL algorithm.