Abstract
A modified version of the QR-decomposition (QRD) is presented. It uses approximate Givens rotations instead of exact Givens rotations, i.e., a matrix entry usually annihilated with an exact rotation by an angle (sigma) is only reduced by using an approximate rotation by an angle (sigma) . The approximation of the rotations is based on the idea of CORDIC. Evaluating a CORDIC-based approximate rotation is to determine the angle (sigma) equals (sigma) t equals arctan 2-t, which is closest to the exact rotation angle (sigma) . This angle (sigma) t is applied instead of (sigma) . Using approximate rotations for computing the QRD results in an iterative version of the original QRD. A recursive version of this QRD using CORDIC-based approximate rotations is applied to adaptive RLS filtering. Only a few angles of the CORDIC sequence, r say (r << b, where b is the word length), work as well as using exact rotations (r equals b, original CORDIC). The misadjustment error decreases as r increases. The convergence of the QRD-RLS algorithm, however, is insensitive to the value of r. Adapting the approximation accuracy during the course of the QRD-RLS algorithm is also discussed. Simulations (channel equalization) confirm the results.
