Reduced Complexity Solution for Weight Extraction in QRD-LSL Algorithms

QR-decomposition-based least-squares lattice (QRD-LSL) algorithms do not provide the transversal weight vector in explicit form. These weights can be computed from the variables of the QRD-LSL algorithm using the Levinson-Durbin (LD) recursion. If the prediction coefficients do not vary over time, a reduced complexity but approximate solution can be obtained. Nonetheless, this approximate solution requires algorithm convergence and infinite memory support (forgetting factor equal to one). To obtain the exact weights at any time instant and for any choice of the forgetting factor, the computational complexity of the true LD recursion increases by an order of magnitude. In this letter, we show that an exact solution can be obtained with a reduced computational complexity and without any added restriction. Simulation results show that the solutions obtained using the proposed method and the exact LD recursion are the same up to the precision used, whereas the weights from the approximate method always deviate from the true solution.