Performance analysis of a new variable step-size LMS algorithm with error nonlinearities

This paper introduces a new variable step size LMS algorithm in which the step size varies inversely with the squared norm of the error vector. With an appropriate choice of the value of the fixed step size in the proposed algorithm, a trade-off between speed of convergence and misadjustment can be achieved. The performance of the proposed algorithm is compared with one of the most significant algorithms that uses normalized data nonlinearity in the LMS adaptation, and with the normalized LMS (NLMS) algorithm as well. For short and long filter lengths in stationary environments, computer simulation results demonstrate substantial improvements in the speed of convergence of the proposed algorithm over other algorithms with the same small level of misadjustment. For nonstationary environments, we introduce a modified version of the proposed algorithm which provides an equivalent performance to that of other variable step-size and regular NLMS algorithms with low computational complexity.