On the Step-Size optimization of the 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. In this paper, we develop an optimized LMS algorithm, in the context of a state variable model. The proposed algorithm follows an optimization problem and introduces a variable step-size in order to minimize the system misalignment. The simulations confirm the theoretical results and show the good features of the algorithm.