对称矩阵特征值分解的FPGA实现  

Implementation of symmetric matrix eigenvalue decomposition with FPGA

作　　者：刘永勤[1,2] LIU Yongqin(School of Automation and Information Engineering,Xi’an University of Technology,Xi’an 710048,China;School of Mathematics and Physics,Weinan Normal University,Weinan 714099,China)

机构地区：[1]西安理工大学自动化与信息工程学院,陕西西安710048 [2]渭南师范学院数学与物理学院,陕西渭南714099

出　　处：《现代电子技术》2017年第12期15-18,共4页Modern Electronics Technique

基　　金：国家自然科学基金(61377080;60977054;61271110);陕西省军民融合研究基金项目(15JMR11);渭南师范学院自然科学基金项目(15YKF002);渭南师范学院特色学科建设项目(14TSXK07)

摘　　要：针对应用于MUSIC DOA估计的数据协方差矩阵特征值分解的需要,给出一个特征值分解的硬件实现方案,并阐述了基本思想。设计采用基于CORDIC的Jacobi算法实现实对称矩阵特征值分解,并在FPGA上对5×5矩阵进行了硬件仿真,经过理论分析和实验验证,该设计可以计算出全部特征值和特征向量,为MUSIC算法的FPGA实现奠定了基础。Aiming at the needs of the data covariance matrix eigenvalue decomposition used in DOA estimation such as MUSIC,a hardware implementation scheme of the eigenvalue decomposition is provided and the basic idea is described in this paper.The Jacobi algorithm based on CORDIC is adopted in the design to achieve real symmetric matrix eigenvalue decomposition,and conduct the hardware emulation for5×5matrix in FPGA.The results of theoretical analysis and experimental verification show that the design can calculate all eigenvalues and eigenvectors,and has laid the foundation for FPGA implementation of MUSIC algorithm.

关 键 词：MUSIC算法 特征值分解 Jacobi算法 CORDIC算法 FPGA 

分 类 号：TN911.34[电子电信—通信与信息系统] TN929.1[电子电信—信息与通信工程]