A modified QRD for smoothing and a QRD-LSL smoothing algorithm

This paper introduces a modified QR-decomposition (QRD) that extends the method of QRD to a more general case to solve the least-squares lattice smoothing problems. We show that the conventional QRD is a special form of the modified QRD that occurs when no future data values are used. Within the framework of the modified QRD procedure, an order-recursive QRD based least-squares lattice (QRD-LSL) smoothing algorithm is formulated. The algorithm combines all the desirable features of the standard QRD-LSL filtering algorithm with a more accurate smoothing process. The results of some computer simulations of a channel equalizer are also presented.