A Fixed-Point Implementation for QR Decomposition

Abstract

Matrix triangularization and orthogonalization are prerequisites to solving least square problems and find applications in a wide variety of communication systems and signal processing applications such as MIMO systems and matrix inversion. QR decomposition using modified Gram-Schmidt (MGS) orthogonalization is one of the numerically stable techniques used in this regard. This paper presents a fixed point implementation of QR decomposition based on MGS algorithm using a novel LUT based approach. The proposed architecture is based on log-domain arithmetic operations. The error performance of various fixed-point arithmetic operations has been discussed and optimum LUT sizes are presented based on simulation results for various fractional-precisions. The proposed architecture also paves way for an efficient parallel VLSI implementation of QR decomposition using MGS