A New Performance Measure of the Normalized LMS Adaptive Filter

The paper provides a new performance measure of the normalized LMS algorithm. The performance measure is based on the time evolution of the component of the weight deviation vector in the direction of the regressor. This is the only component that contributes to the excess estimation error at the output of the adaptive filter. The main advantage of the proposed measure is that it enables a rigorous establishment of the algorithm convergence under weak assumptions. The assumptions do not include restrictions on the dependence between successive regressors, the dependence among the regressor elements, the length of the adaptive filter, the distributions of the filter input and the noise. Moreover, the proposed measure enables also a convergence analysis without the usual restriction of small step size of the algorithm.