The FPGA Implementation Of Matrix Calculation In Signal Processing

Matrix decomposition algorithm has a wide range of applications in signal processing.Its high-speed implementation technology,especially Field-Programmable Gate Array?FPGA?,has always been a research hotspot.In this thesis,we investigate the FPGA implementation technology of complex matrix eigenvalue decomposition,QR decomposition,inversion,and the two-dimensional direction of arrival estimation system.The key points of this thesis are as following:?1?A FPGA implementation technique based on Jacobian iterative method is proposed,which can be used in the eigenvalue decomposition of Hermitian matrices with different dimensions.By adding the function of element jump and expansion,improving the iteration method of element traversing,the accuracy of calculation is improved.Based on the hardware structure of pipelining and logical multiplexing,an eigenvalue decomposition of arbitrary dimensional Hermitian matrices with 7%resource consumption and10^-8 calculation accuracy is realized.?2?A FPGA implementation technique for complex matrix QR decomposition based on Givens transform is proposed.A cordic module with vector and rotation mode is designed.Making use of systolic array architecture with column input,a QR decomposition with10^-6 calculation accuracy,7%minimum resource consumption and 103 MMatrices/s highest data throughput rate is realized.?3?A FPGA implementation technique for matrix inversion based on Cordic-GJ elimination method is proposed.Using dual-mode cordic instead of multiplication and division unit to solve the fixed-point division overflow when the diagonal element is small.An arbitrary-dimensional matrix inversion module with high precision and throughput is realized through a semi-parallel barrel-pipeline hardware structure.?4?A FPGA hardware architecture of 2D-MUSIC DOA estimation system is realized.A novel modified Gerschgorin Disk source number estimation technique based on Jacobi method is proposed.It can be implemented in FPGA easily.A kind of spatial division and parallel computing technology is put forward to improving the search speed.A complete 2D-MUSIC DOA estimation system is implemented on FPGA,including the calculation of the covariance matrix,the estimation of the number of signal sources,the calculation of the noise subspace,the calculation of the two-dimensional music spectrum and the peak search.The system can be adapted to different antenna array structures in two-dimensional plane and three-dimensional space with high flexibility and estimation accuracy.