Algorithmically engineered fast multichannel adaptive filter based on QR-RLS

Abstract

A fast version of the multichannel QR algorithm for RLS adaptive filtering, with channel filters of unequal length, is derived. This is achieved by applying the techniques of algorithmic engineering to a signal flow graph representation of the basic QR RLS algorithm. By virtue of this graphical approach, the derivation is relatively straightforward and circumvents the complex and notationally verbose matrix algebra usually involved in the derivation of fast RLS algorithms in general and the previously published, unequal-length, multichannel RLS lattice algorithm in particular.