A Robust Complex α-Sigmoid Affine Projection Algorithm Under Non-Gaussian Noise

To address the performance degradation of traditional adaptive filtering algorithms in environments with correlated input signals and non-Gaussian noise, this paper proposes a complex-valued affine projection algorithm based on the α-Sigmoid cost function (α-CSAP). The algorithm leverages the nonlinear characteristics of the α-Sigmoid function and implicitly achieves variable step-size updates by introducing a normalization factor, which effectively suppresses impulsive noise interference and avoids matrix inversion, thereby reducing computational complexity. Theoretical analysis derives the steady-state mean square deviation (MSD) expression for the algorithm. Simulation results demonstrate that the proposed α-CSAP algorithm exhibits superior performance compared to traditional complex adaptive filtering algorithms in both system identification and beamforming application scenarios.