Behavior of the ε-normalized LMS algorithm with Gaussian inputs

The first and second moment behavior of one variation of the normalized LMS (ε-NLMS) algorithm is investigated for a white covariance matrix and Gaussian statistics for the data. For this model, it is shown that the ε-NLMS algorithm has neither behavior independent of the input data power nor a performance significantly better than the LMS algorithm for which the input power level also must be known a priori. Hence, based upon the results of the analysis, it is recommended that the algorithm not be used in place of the LMS for known input power levels or in place of the NLMS for unknown input power levels.