Robust Widely linear complex-valued combined step-size algorithm for beamforming

In non-circular signals, the drawback of the fixed step-size of the widely linear complex-valued least mean square (WL-CNLMS) algorithm results in the algorithm being suboptimal. To address this problem, we introduce a combined step-size (CSS) strategy in the WL-CNLMS algorithm to improve the convergence performance. Also, to overcome the negative effects of non-Gaussian impulsive noise, we use a modified Huber (MH) function to improve the robustness of the algorithm. Finally, we propose a robust combined step-size WL-CNLMS algorithm and apply it to beamforming. Simulation results show that the proposed algorithm not only enhances the convergence performance of the adaptive beamformer but also greatly improves its robustness.