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

The recently proposed low-complexity reduction-by-composition least-mean-square (LMS) algorithm (RCLMS) costs only half the 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 /spl mu/ and an extra compensation step-size /spl alpha/ are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when /spl mu/ is small enough and /spl alpha/ is properly chosen, the RCLMS algorithm has comparable performance to that of the DLMS algorithm. Simple working rules and ranges for /spl alpha/ and /spl mu/ to make such comparability are provided. For the algorithm to converge, a tight bound for /spl alpha/ is also derived. The derived properties and conditions are verified by simulations.