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 μ and an extra compensation step-size α are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when α is small enough and α is properly chosen, the RCLMS algorithm has comparable performance to that of the DLMS algorithm. Simple working rules and ranges for α and μ to make such comparability are provided. For the algorithm to converge, a tight bound for α is also derived. The derived properties and conditions are verified by simulations.
|Number of pages||6|
|Journal||IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing|
|State||Published - 1 Dec 1999|