A Transient Analysis for the Convex Combination of Adaptive Filters
Vítor H. Nascimento, Magno T. M. Silva and Jerónimo Arenas-Garcia
In: Statistical Signal Processing 2009(2009).
Combination schemes are gaining attention as an interesting way to
improve adaptive filter performance. In this paper we pay attention
to a particular convex combination scheme with nonlinear adaptation
that has recently been shown to be universal –i.e., to perform at
least as the best component filter– in steady-state; however, no theoretical
model for the transient has been provided yet. By relying
on Taylor Series approximations of the nonlinearities, we propose a
theoretical model for the transient behavior of such convex combinations.
In particular, we provide expressions for the time evolution of
the mean and the variance of the mixing parameter, as well as for the
mean square overall filter convergence. The accuracy of the model is
analyzed for the particular case of a combination of two LMS filters
with different step sizes, explaining also how our results can help the
designer to adjust the free parameters of the scheme.