Widely Linear Complex-valued Logarithmic Hyperbolic Cosine Adaptive Filtering Algorithm and Its Performance Analysis

Widely linear complex-valued adaptive filtering (WL-CAF) has been extensively studied to solve noncircular input noises in the complex domain. However, the performance of the existing WL-CAF algorithms will be deteriorated when the noise is non-Gaussian. To solve this problem, a novel robust algorithm called widely linear complex-valued logarithmic hyperbolic cosine adaptive filtering (WL-CLHCAF) algorithm is first proposed to fully consider second-order statistical information of the complex-valued signal. In WL-CLHCAF algorithm, the logarithmic hyperbolic cosine function is utilized as the cost function to combat non-Gaussian noises. Then, the mean convergence, mean-square transient performance, and mean-square steady-state performance of the proposed WL-CLHCAF algorithm are analyzed theoretically. Finally, the simulation results indicate the performance superiority of the proposed WL-CLHCAF algorithm and confirm the correctness of the obtained theoretical results.