A fixed budget implementation of a new variable step size kernel proportionate NLMS algorithm

In this paper, a fixed-budget implementation of the kernel proportionate normalized least mean square (KPNLMS) algorithm using a variable step size scheme is proposed. The similarity between the equations of the NLMS algorithm and those of the kernel proportionate NLMS algorithm with coherence criterion is emphasized and the reason of using the proportionate coefficients for the KPNLMS algorithm is given. It is shown that applying the proportionality principle to the kernel outputs leads to better convergence properties than applying it to the weights of the nonlinear filter. The effect of the step size on the convergence properties of KPNLMS is exemplified. Also, and the effect of SNR on the dictionary size of the KPNLMS algorithm is proved for channel equalization and forward prediction examples. The influence of the dictionary size on the performance of the fixed budget KPNLMS algorithm is demonstrated. Therefore, a simple variable step size scheme is proposed in order to improve the convergence properties of fixed-budget KPNLMS algorithm for channel equalization of a multi-path Rayleigh fading channel and forward prediction applications. It is also proved that the additional computational complexity burden of the proposed algorithms is very small.