Multichannel fast QRD-RLS adaptive filtering: Block-channel and sequential-channel algorithms based on updating backward prediction errors

Fast QR decomposition recursive least-squares (FQRD-RLS) algorithms are well known for their fast convergence and reduced computational complexity. A considerable research effort has been devoted to the investigation of single-channel versions of the FQRD-RLS algorithms, while the multichannel counterparts have not received the same attention. The goal of this paper is to broaden the study of the efficient and low complexity family of multichannel RLS adaptive filters, and to offer new algorithm options. We present a generalized approach for block-type multichannel FQRD-RLS (MC-FQRD-RLS) algorithms that includes both cases of equal and multiple order. We also introduce new versions for block-channel and sequential-channel processing, details of their derivations, and a comparison in terms of computational complexity. The proposed algorithms are based on the updating of backward a priori and a posteriori error vectors, which are known to be numerically robust.