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

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3 Author(s)
Sau-Gee Chen ; Dept. of Electron. Eng. & Inst. of Electron., Nat. Chiao Tung Univ., Hsinchu, Taiwan ; Yung-An Kao ; Ching-Yeu Chen

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 μ and an extra compensation step-size α are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when μ 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

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IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing  (Volume:46 ,  Issue: 11 )