The instrumental variable multichannel FAP-RLS and FAP algorithms

The LMS and affine projection algorithms (APA) and its fast version (FAP) may suffer convergence slowdown in the presence of strong correlation between the input samples (colored input signals). In the case multichannel adaptive filtering, this problem may be compounded by strong correlation between the channel signals. Recently, improved multichannel APA´s have been introduced (without a FAP counterpart), involving decorrelation operations between the channels. We show a connection between the improved APA and a certain choice of instrumental variable (IV) in an IV version of multichannel APA. There is also a connection to fast Newton transversal filters (FNTF´s). We suggest a particular choice for the IV that will make fast multichannel IV APA possible and derive multichannel IV FAPs for the case of IVs with the usual shift-invariance structure. Whereas we have introduced a single channel IV FAP before, based on the fast transversal filter (FTF) algorithm, we propose here a multichannel IV FAP based on the numerically more robust RLS algorithm.