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

Sau-Gee Chen, Yung An Kao, Ching Yeu Chen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1440-1445
Number of pages6
JournalIEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
Issue number11
StatePublished - 1 Dec 1999

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