On the properties of the reduction-by-composition LMS algorithm

Abstract

The recently proposed low-complexity reduction-by-composition least-mean-square (LMS) algorithm (RCLMS) costs only half multiplications compared to that of the conventional direct-form LMS algorithm (DLMS), This work intends to characterize its properties and conditions for mean and mean-square convergence. Closed-form mean-square error (MSE) as a function of the LMS step-size mu and an extra compensation step-size alpha are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when mu is small enough and alpha is properly chosen, the RCLMS algorithm has comparable performance to that of the DLMS algorithm. Simple working rules and ranges for alpha and mu to make such comparability are provided. For the algorithm to converge, a tight hound for alpha is also derived. The derived properties and conditions are verified by simulations.