Analysis of steady-state excess mean-square-error of the least mean kurtosis adaptive algorithm

In this paper, the average of the steady state excess mean square error (ASEMSE) of the least mean kurtosis (LMK) adaptive algorithm is theoretically derived. It is done by applying the energy conservation behavior of adaptive filters and it is based on the n-th order correlations and cumulants theory. By doing so, the behavior of the recently proposed LMK can be predicted, so that it can be widely used. The behavior is compared with the various adaptive algorithms. Our study shows that it is possible to adjust the performance of the LMK. When the step size μ is carefully selected, the performance of the LMK can outperform the LMS.