The Generalized Complex Kernel Affine Projection Algorithms

Abstract The complex kernel adaptive filter (CKAF) has been widely applied to the complex-valued nonlinear problem in signal processing and machine learning. However, most of CKAF applications involve least mean square (CKLMS) algorithms, which work a pure or complexified reproducing Hilbert space (RKHS). In this paper, we propose generalized affine projection (GCKAP) algorithms linear RKHS (WL-RKHS). proposed have two main notable features. One is that they provide complete solution for both circular non-circular problems show many performance improvements over CKAP algorithms. other GCKAP inherit simplicity CKLMS algorithm while reducing its gradient noise boosting convergence. second-order statistical characteristics WL-RKHS also developed. An augmented Gram matrix consists standard pseudo-Gram matrix. This decomposition provides more underlying information when real imaginary parts are correlated learning independent. addition, some online sparsification criteria compared comprehensively including novelty criterion, coherence angle criterion. Finally, channel equalization experiments with inputs presented illustrate