High-Throughput FPGA Implementation of QR Decomposition

Abstract

This brief presents a hardware design to achieve high-throughput QR decomposition, using the Givens rotation method. It utilizes a new 2-D systolic array architecture with pipelined processing elements, which are based on the COordinate Rotation DIgital Computer (CORDIC) algorithm. CORDIC computes vector rotations through shifts and additions. This approach allows a continuous computation of QR factorizations with simple hardware. A fixed-point field-programmable gate array (FPGA) architecture for 4 $\times$ 4 matrices has been optimized by balancing the number of CORDIC iterations with the final error. As a result, compared with other previous proposals for FPGA, our design achieves at least 50% more throughput, as well as much less resource utilization.