A fast variable step-size LMS algorithm with system identification

A fast variable step-size least-mean-square algorithm (MRVSS) is proposed and analyzed in this paper. The main features of the new algorithm include the twofold. 1) It eliminates the influence of the power of the measurement noise on the steady-state misadjustment, unlike a number of variable step-size LMS algorithms previously proposed. Therefore, the new algorithm is more flexible to work in the environment with noise uncertainties. 2) It provides faster adaptation speed as well as smaller misadjustment. The mean and mean-square convergence conditions, and steady-state misadjustment of the new algorithm are analyzed. Simulation results for system identification are provided to support the theoretical analysis and to compare the new algorithm with the existing variable step-size LMS algorithms, the conventional LMS algorithm (FSS) in various conditions. They show a superior performance of the new algorithm in stationary environment and an equivalent performance in nonstationary environment.