On a combination of M adaptive filters

In this paper we consider a combination of arbitrary number of LMS adaptive filters. The filters are connected in parallel and use the same input and desired signals. They differ by the step sizes, which gives the structure ability to achieve fast initial convergence together with gradually diminishing steady state error level. In the paper we show that the straightforward problem statement leads to a necessity to solve a singular linear system of equations. We therefore propose a regularization approach to deal with the problem. Results of the transient analysis of the resulting algorithm are presented together with some simulation results.