Does white input give better convergence speed in adaptive filtering?

In this paper, we present an exact performances analysis of adaptive filtering without any unrealistic hypothesis. In particular, we demonstarte that convergence rate depends on the high order statistics of the input. Consequently, in some cases, adaptive algorithms with decor-relating properties do not speed up the convergence as expected. In fact, we give example showing that the convergence for correlated input is more important than iid one.