矩阵特征值分解的算法研究与FPGA实现  

Algorithm research and FPGA implementation of matrixeigenvalue decomposition

作　　者：黄家俊 王建新[1] HUANG Jiajun;WANG Jianxin(School of Electronic and Optical Engineering,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学电子工程与光电技术学院,江苏南京210094

出　　处：《电子设计工程》2021年第16期50-54,共5页Electronic Design Engineering

摘　　要：特征值分解是阵列信号处理中一种常用的信息提取方法,在多种信号分离算法中都有应用。针对复信号协方差矩阵的特征值分解问题进行了研究,通过两步解决了复Hermitian矩阵特征值分解问题。第一步先将复Hermitian矩阵转化为实对称矩阵,根据不同的情况,给出了两种将复Hermitian矩阵转化为实对称矩阵的方法。第二步利用Jacobi旋转法求解实对称矩阵的特征值分解。整个特征值分解模块在ISE软件上利用Cordic IP核以及脉动阵列结构矩阵乘法器实现,计算误差小、性能良好。Eigenvalue decomposition is a kind of information extraction method commonly used in array signal processing,and it is applied in various signal separation algorithms.The eigenvalue decomposition of the complex signal covariance matrix is stuided,the eigenvalue decomposition of the complex Hermitian matrix in two steps is solved.The first step is to convert the complex Hermitian matrix into a real symmetric matrix.According to different situations,two methods for converting the complex Hermitian matrix into a real symmetric matrix are given.The second step uses Jacobi rotation method to solve the eigenvalue decomposition of real symmetric matrix.The entire eigenvalue decomposition module is implemented on the ISE software using Cordic IP core and matrix array multiplier with systolic array structure.The calculation error is small and the performance is good.

关 键 词：复Hermitian矩阵 特征值分解 Jacobi旋转法 脉动阵列 FPGA 

分 类 号：TN911.7[电子电信—通信与信息系统]