基于FPGA的复数长方阵SVD算法  

Singular Value Decomposition Algorithm of Rectangular Complex Matrix Based on FPGA

作　　者：阎波[1] 张威威[1] 林水生[1] 

机构地区：[1]电子科技大学通信与信息工程学院,成都611731

出　　处：《电子科技大学学报》2015年第4期481-486,共6页Journal of University of Electronic Science and Technology of China

基　　金：国家自然科学基金(61301155;61176025);中央高校基本科研业务费专项资金(ZYGX2012J003)

摘　　要：在OFDM和MIMO系统中普遍使用长方形矩阵复数奇异值分解运算。针对传统算法运算量大,迭代次数多的问题,提出了一种基于householder和双边Jacobi的混合优化算法。该算法首先通过householder变换将矩阵化解为二对角矩阵;然后提取2×2复矩阵;再进行改进型复数双边Jacobi变换。兼具有QR算法的高精度和Jacobi算法的低硬件实现成本的优点。给出了2×8的CSVD的FPGA硬件实现方案并进行了板级测试。测试结果表明,该混合优化算法较传统算法在硬件资源上节省26%,延时缩短10倍,在同等位宽下计算精度至少提高了一个数量级。Rectangular matrix complex singular value decomposition（CSVD） is widely used in orthogonal frequency division multiplexing（OFDM） and multiple input and multiple output（MIMO） systems. In view of large iteration computation of traditional algorithms, a householder and Jacobi based mixed optimized algorithm is proposed which diagonalizes a general complex matrix and carry out an improved complex two-sided Jacobi transform. This method combines the advantages of high precision of QR and the simple hardware structure of Jacobi. A 2×8 CSVD design is implemented on field programmable gate array（FPGA） by using MATLAB simulation and Xilinx platform. Compared with traditional algorithms, the mixed optimized algorithm saves 26% hardware resources, shortens delay time by 10 and improve the accuracy of calculation at least one order of magnitude under the same bit width.

关 键 词：复数奇异值分解 可编程逻辑阵列 householder JACOBI 长方矩阵 

分 类 号：TP33[自动化与计算机技术—计算机系统结构] TN4[自动化与计算机技术—计算机科学与技术]