An inequality by which to adjust the LMS algorithm step-size (Q2726598)

The authors deal with the Least Mean Square algorithm, a standard method to track slowly varying parameters of a signal system. The paper describes an algorithm for automatic step size adjustment to both improve the convergence rate and reduce steady-state parameter estimation errors of this method. Based on the mean square values of the output estimation errors, a set of inequalities are defined, which provides information on the transient or steady-state operation of the Least Mean Square algorithm. A modified Least Mean Square algorithm, which uses these inequalities to control the step size is given in the paper. A simulation example demonstrates the performance of the method, i.e., faster convergence and smaller steady-state mean square errors in comparison with the fixed step size Least Mean Square algorithm.