Hermite矩阵特征值分解的硬件加速  

Hardware Acceleration of Hermite Matrix Eigenvalue Decomposition

作　　者：王卫江[1,2] 李泽英 薛丞博 李翔南 任仕伟 WANG Weijiang;LI Zeying;XUE Chengbo;LI Xiangnan;REN Shiwei(School of Integrated Circuits and Electronics,Beijing Institute of Technology,Beijing 100081,China;Chongqing Center for Microelectronics and Microsystems,Beijing Institute of Technology,Chongqing 401332,China;School of Information and Electronics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学集成电路与电子学院,北京100081 [2]北京理工大学重庆微电子中心,重庆401332 [3]北京理工大学信息与电子学院,北京100081

出　　处：《北京理工大学学报》2023年第9期988-994,共7页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(62201039)。

摘　　要：在数字信号处理领域,Hermite矩阵的特征值分解有着非常广泛的应用.为了解决其硬件实现问题,提出了一种基于复数域Jacobi算法的硬件加速架构,该设计方案可适用于不同大小的Hermite矩阵.为了在计算精度、计算速度和资源占用之间取得平衡,在Matlab平台上对定点运算的小数位量化位宽进行了仿真,以8×8大小的Hermite矩阵为例,确定了15位的小数位量化为最佳.分别介绍了复数域Jacobi算法硬件加速中寻找最大非对角线元素、构造酉矩阵和更新特征值矩阵和特征向量矩阵的硬件电路结构.在Zynq-7000系列FPGA开发板上进行了实现,仅需要17 438LUTs和24 650Registers即可在34.42μs内完成对8×8大小的Hermite矩阵的特征值分解.In the field of digital signal processing,the eigenvalue decomposition of Hermitian matrices possesses a very wide range of applications.To solve the problem of its hardware implementation,a hardware acceleration architecture was proposed based on Jacobi algorithm in complex domain,and the design scheme was arranged to be applied to Hermite matrices with different sizes.In order to achieve a balance among calculation accuracy,calculation speed and resource occupancy,the quantization bit width of the fixed-point operation was simulated on the Matlab platform firstly.Taking the Hermite matrix of size 8×8 as an example,the quantization of 15-bit decimal places was determined as the best.Then,the hardware circuit structure was introduced respectively for finding the largest off-diagonal element,constructing unitary matrix and updating eigenvalue matrix and eigenvector matrix in hardware acceleration of Jacobi algorithm for complex number domain.Finally,the hardware acceleration method was implemented on the Zynq-7000 series FPGA development board,taking only 17438 LUTs and 24650 Registers to complete the eigenvalue decomposition of an 8×8 Hermite matrix in 34.42μs.

关 键 词：HERMITE矩阵 特征值分解 Jacobi算法 硬件加速 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程]