Singular value decomposition algorithm of rectangular complex matrix based on FPGA

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.