Kernel recursive generalized mixed norm algorithm

This work studies the problem of kernel adaptive filtering (KAF) for nonlinear signal processing under non-Gaussian noise environments. A new KAF algorithm, called kernel recursive generalized mixed norm (KRGMN), is derived by minimizing the generalized mixed norm (GMN) cost instead of the well-known mean square error (MSE). A single error norm such as lp error norm can be used as a cost function in KAF to deal with non-Gaussian noises but it may exhibit slow convergence speed and poor misadjustments in some situations. To improve the convergence performance, the GMN cost is formed as a convex mixture of lp and lq norms to increase the convergence rate and substantially reduce the steady-state errors. The proposed KRGMN algorithm can solve efficiently the problems such as nonlinear channel equalization and system identification in non-Gaussian noises. Simulation results confirm the desirable performance of the new algorithm.