Field Programmable Gate Array (FPGA) Implementation of Parallel Jacobi for Eigen-Decomposition in Direction of Arrival (DOA) Estimation Algorithm

The eigen-decomposition of a covariance matrix is a key step in the Direction of Arrival (DOA) estimation algorithms such as subspace classes. Eigen-decomposition using the parallel Jacobi algorithm implemented on FPGA offers excellent parallelism and real-time performance. Addressing the high complexity and resource consumption of the traditional parallel Jacobi algorithm implemented on FPGA, this study proposes an improved FPGA-based parallel Jacobi algorithm for eigen-decomposition. By analyzing the relationship between angle calculation and rotation during the Jacobi algorithm decomposition process, leveraging parallelism in the data processing, and based on the concepts of time-division multiplexing and parallel partition processing, this approach effectively reduces FPGA resource consumption. The improved parallel Jacobi algorithm is then applied to the classic DOA estimation algorithm, the MUSIC algorithm, and implemented on Xilinx’s Zynq FPGA. Experimental results demonstrate that this parallel approach can reduce resource consumption by approximately 75% compared to the traditional method but introduces little additional time consumption. The proposed method in this paper will solve the problem of great hardware consumption of eigen-decomposition based on FPGA in DOA applications.