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...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 2, Analog and digital signal processing Analog and digital signal processing, 1999-11, Vol.46 (11), p.1440-1445
Main Authors: Chen, Sau-Gee, Kao, Yung-An, Chen, Ching-Yeu
Format: Article
Language:English
Subjects:
Adaptive filters
Adaptive signal processing
Convergence
Costing
Costs
Councils
Filtering algorithms
Least squares approximation
Robustness
Signal processing algorithms
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Summary: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.
ISSN:1057-7130
1558-125X
DOI:10.1109/82.803485