A transient analysis for the convex combination of adaptive filters

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.