A unified framework for multichannel fast QRD-LS adaptive filters based on backward prediction errors

Fast QR decomposition algorithms based on backward prediction errors are well known for their good numerical behavior and their low complexity when compared to similar algorithms with forward error update. Their application to multiple channel input signals generates more complex equations although the basic matrix expressions are similar. This paper presents a unified framework for a family of multichannel fast QRD-LS algorithms. This family comprises four algorithms - two basic algorithms with two different versions each. These algorithms are detailed in this work.