基于FPGA的复数长方阵SVD算法

Singular Value Decomposition Algorithm of Rectangular Complex Matrix Based on FPGA

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.