A new variable tap-length LMS algorithm with variable step size

A new variable tap-length LMS algorithm is proposed which updates the step size and the tap-length simultaneously at each iteration in the update of the coefficients. The tap length is adjusted according to the fractional tap-length (FT) algorithm and the step size is derived to be an approximately optimal variable step size algorithm which can obtain the largest decrease of the mean square deviation (MSD). Simulations are performed under high noise and low noise conditions to show the improved performance of the proposed scheme.