An Optimized LMS Algorithm
The least-mean-square (LMS) and the normalized least-mean-square (NLMS) algorithms require a trade-off between fast convergence and low misadjustment, obtained by choosing the control parameters. In general, time variable parameters are proposed according to different rules. Many studies on the optimization of the NLMS algorithm imply time variable control parameters according some specific criteria.
The optimized LMS (LMSO) algorithm  for system identification is developed in the context of a state variable model, assuming that the unknown system acts as a time-varying system, following a first-order Markov model .
The proposed algorithm follows an optimization problem and introduces a variable step-size in order to minimize the system misalignment
 A. G. Rusu, S. Ciochină, and C. Paleologu, “On the step-size optimization of the LMS algorithm,” in Proc. IEEE TSP, 2019, 6 pages.
 G. Enzner, H. Buchner, A. Favrot, and F. Kuech, “Acoustic echo control,” in Academic Press Library in Signal Processing, vol. 4, ch. 30, pp. 807–877, Academic Press 2014.
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