Kernel affine projection sign algorithms for combating impulse interference

The kernel method has been successfully applied to nonlinear adaptive filtering. This brief presents a kernel affine projection sign algorithm (KAPSA), which is a nonlinear extension of the affine projection sign algorithm (APSA). The proposed KAPSA combines the benefits of the kernel method and the APSA, and is robust against non-Gaussian impulse interference. In order to further improve the filtering performance, a variable step-size adjustment is incorporated into the KAPSA, resulting in a new variable step-size kernel APSA (VSS-KAPSA) without increasing the computational burden. Simulations in the context of time-series prediction show that both the KAPSA and the VSS-KAPSA are robust against impulse interference and that both outperform other affine projection algorithms in terms of steady-state mean square errors.