Overcoming the Independence Assumption in LMS Filtering

The learning process of the LMS algorithm remains understood only very poorly. Despite three decades of intensive research, very few results have been found to overcome the classical independence assumption in which the sequence of driving regression vectors is assumed to be statistically independent. While giving relatively precise results for processes of little correlation, the results obtained in other cases are far off from the true values. In this paper, a new approach is taken to investigate the learning behavior of the LMS algorithm using much milder conditions than in the classical independence theory. It is shown that our conditions lead to much better results, in particular for correlated driving processes when compared with the classical independence assumption.