Widely Linear Maximum Complex Correntropy Criterion Affine Projection Algorithm and Its Performance Analysis

Recently, affine projection algorithm has been extensively studied in the Gaussian noise environment. However, the performance of affine projection algorithm will deteriorate rapidly in the presence of impulsive noise and other non-Gaussian noise. To address this issue, this paper proposes a novel affine projection algorithm based on the complex Gaussian kernel function, called widely linear maximum complex correntropy criterion affine projection algorithm (WL-MCCC-APA). With the maximum complex correntropy criterion (MCCC), the robustness of affine projection algorithm is improved significantly in the non-Gaussian noise environment, especially in the presence of impulsive noise. Meanwhile, a variable step size WL-MCCC-APA (VSS-WL-MCCC-APA) method based on fixed-point theory is proposed to further balance the convergence rate and steady-state misalignment of the algorithm. Finally, the step size boundary analysis and steady-state analysis are presented for theoretical analysis. Simulation results verify the correctness of obtained theoretical results and the superiority of the proposed WL-MCCC-APA and VSS-WL -MCCC-APA.