On the Properties of the Reduction-by-Composition LMS Algorithm
نویسندگان
چکیده
The recently proposed low-complexity reduction-bycomposition 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 and an extra compensation step-size are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when is small enough and is properly chosen, the RCLMS algorithm has comparable performance to that of the DLMS algorithm. Simple working rules and ranges for and to make such comparability are provided. For the algorithm to converge, a tight bound for is also derived. The derived properties and conditions are verified by simulations.
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