Optimal step-size update equation in nonstationary environment and OVS-LMSII algorithm

The least mean square (LMS) algorithm is the most widely used adaptive signal processing algorithm. Many variable step-size LMS algorithms are developed to increase the convergence and lower the steady-state mean-square error (MSE). The optimal variable step-size LMS (OVS-LMS) algorithm exerts its best performance and its convergence rate is nearly the same as the theoretical limit of variable step-size algorithm in the stationary environment. This paper develops the optimal step-size update equation that fits for unknown system changes. Then the robust condition of this equation is analyzed. Finally, the OVS-LMS II, which uses an optimal step-size in the nonstationary environment, is constructed. The computer simulation shows that its rate of convergence and of tracking is nearly the same as the theoretical limit of the variable step-size LMS algorithm.