Convergence analysis of a variable step-size normalized LMS adaptive filter algorithm

This paper investigates the convergence properties of a variable step normalized LMS (VSNLMS) adaptive filter algorithm. Instead of a fixed step-size used in the conventional normalized LMS algorithm, the step-size of the algorithm under study is updated in each iteration, based on an expression related to the output errors. The variable step-size improves the convergence speed, while sacrificing little in complexity. For an application where the adaptive filter is used to track a time varying channel it is shown that the step-size converges towards its optimum value. Simulation results are presented to support the analysis.