Steady-state behavior and design of the Gaussian KLMS algorithm

The Kernel Least Mean Square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. A Gaussian KLMS has two design parameters; the step size and the kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the stability limits of the Gaussian KLMS algorithm for Gaussian inputs. Design guidelines for the choice of the step size and the kernel bandwidth are then proposed based on the analysis results. A design example is presented which validates the theoretical analysis and illustrates its application.