A Fast Kernel Least Mean Square Algorithm

To deal with the problems in the nonlinear system, the kernel adaptive filter (KAF) was proposed by processing data in the reproducing kernel Hilbert space (RKHS). However, the kernel method dramatically improves the amount of calculation of the filter, which limits its application in practical problems. Furthermore, a critical factor in a large amount of KAF computation is due to its slow convergence speed, which requires a large amount of training data to participate in the calculation. If we can accelerate the convergence speed of KAF, the amount of training data can be reduced, thereby reducing the amount of KAF computation. This paper proposes a fast kernel least mean square algorithm (FAST-KLMS) by adaptively updating step size to address this issue. To verify the superiority of FAST-KLMS, we have applied it to the simulations of nonlinear channel equalization. The simulation results show that FAST-KLMS needs less training data to complete the convergence, which has improved the filtering performance of KAF.