Convergence of output signal based combination of two LMS adaptive filters

In this paper we investigate a combination of two LMS adaptive algorithms, one with large and another one with small step size. Large step size of one of the filters allows fast initial convergence and small step size of the other filter allows a small steady state mean square error. The outputs of the two filters are combined together via a combination parameter λ. We compute this parameter using the output signals of the individual filters. In the paper we derive formulae that predict the entire learning curve of the combination of two LMS adaptive filters. The theoretical findings are confirmed in our simulation study.