A variable step size LMS algorithm

A new LMS-type adaptive filter with a variable step size is introduced. The step size increases or decreases as the mean-square error increases or decreases, allowing the adaptive filter to track changes in the system as well as produce a small steady state error. The convergence and steady state behavior of the algorithm are analyzed. These results reduce to well-known ones when specialized to the constant step size case. Simulation results are presented to support the analysis and to compare the performance of the new algorithm with the usual LMS algorithm and another variable step algorithm. They show that the performance of the new algorithm compares favorably with these existing algorithms.