Transient analysis of an output signal based combination of two NLMS adaptive filters

This paper investigates the convergence properties of a combination of two NLMS adaptive filters. The structure consists of two adaptive filters that adapt on the same input signal at the same time. One of the filters has a large and the other one has a small step size. The outputs of the filters are then combined together through a combination parameter λ: This combination is an interesting new way of achieving a fast initial convergence and a small steady state error of an adaptive filter at the same time. We compute the combination parameter from the output signals of the individual filters. In this paper we derive the expressions that characterize the time evolution of the mean square deviation and the excess mean square error of the combination scheme. The theoretical results are verified by simulations.