On the Complex Kernel-based Adaptive Filter

A recent paper titled "The Complex Gaussian Kernel LMS Algorithm" published by Bouboulis and Theodoridis introduced a complex version of the Gaussian kernel LMS (KLMS) algorithm. In this paper, we extend the concepts of complex and complexified RKHS spaces to develop suitable complex Kernel based adaptive algorithms using the Affine projection algorithm (KAPA) method. We apply the complex Gaussian kernel here, as well as develop APA-based algorithms using other suitable complex kernels. We evaluate the performance of the new algorithms using practical simulation applications. The complex KAPA algorithms are seen to outperform their LMS-based counterparts, particularly for applications where convergence rate is important.