MEASURES OF TRACKING PERFORMANCE FOR THE LMS ALGORITHM

Two measures of tracking performance for the LMS algorithm are compared and contrasted. These are the conventional time-average or temporal mean of the nonstationary mean-squared error (MSE) in excess of the minimum attainable MSE, and the novel temporal root-mean-squared value of the excess MSE, which takes into account the temporal variance as well as the temporal mean of the non-stationary MSE. These measures are evaluated for the LMS algorithm applied to two time-variant system identification problems, one involving a random Markov system and the other a periodic system. Optimal step-size parameters and minimum misadjustments are evaluated. It is shown that the conventional time-average performance measure is adequate only when the degree of nonstationarity is sufficiently low. For higher degrees of nonstationarity, the time-average performance measure can be misleading in studies of the tracking behavior of the LMS algorithm. © 1990 IEEE