The independence assumption: A dispensable tool in adaptive filter theory

The well-known expression for the weight-error correlation matrix in a fully adapted LMS-type transversal filter is derived for a small step size and a white additive noise at the channel output, without use of the ''independence assumption''. It is shown that for small step sizes the independence assumption (which is illicit for a tapped-delay line) is equivalent to a white additive output noise in that both assumptions lead to the same weight-error correlation matrix. (C) 1997 Elsevier Science B.V.