Switching Step-Size Based Widely Linear Adaptive Filtering Algorithms

The widely linear complex-valued least mean square (WL-CNLMS) algorithm is extensively used for processing complex-valued signals, but it exists performance compromise between convergence rate and steady-state misadjustment. In response to this problem, we incorporate the idea of switching step-size (SSS), that is, selecting an optimal step-size at each iteration by comparing the mean-square deviation trends of the WL-CNLMS algorithm with pre-set different step-sizes and then proposing the SSS based WL-NLMS algorithm. Meanwhile, to keep the robustness of the algorithm in the impulsive noise environment, a robust variant of it is proposed by utilizing the modified Huber function instead of the quadratic function. Through extensive simulations in the contexts of system identification and beamforming, we have verified the effectiveness of the proposed algorithms.