A newly derived variable degree variable step size LMS algorithm

A new least-mean-squares-(LMS-)type algorithm that employs a time-varying variable step size in the standard LMS weight update recursion is introduced in this paper. The work is aimed at improving the directional estimate, in searching for the global minimum of the mean-square-error surface, in an effort to increase the algorithm's speed of convergence. First-order convergence analysis of the algorithm is developed. Additionally, expressions for the ith time constant and algorithm misadjustment are introduced. Several simulation examples are presented to compare the new algorithm with the LMS and other existing variable step size algorithms. Comparisons illustrate the new algorithm's possession of better convergence properties, under stationary and non-stationary signal conditions, when compared with the other algorithms.