Method for implementing Hermitian matrix decomposition by using FPGA (field programmable gate array)

Abstract

The invention discloses a method for implementing Hermitian matrix decomposition by using FPGA (field programmable gate array) and provides a method for implementing a Jacobi algorithm by using the FPGA. A complex Hermitian matrix received by an array antenna is decomposed by adopting the Jacobi algorithm, the Jacobi algorithm is implemented by using the FPGA on hardware implementation, complex multiplication and division operations in the Jacobi algorithm are all replaced by CORDIC cores according to certain rules, and finally feature values and feature vectors of the Hermitian matrix are acquired. The feature values and the feature vectors of the Hermitian matrix are calculated by using the FPGA, almost all the CORDIC cores are used on the related matrix operations, the CORDIC cores arereused, multiplication and division operations are saved greatly, FPGA resources are saved, and the method is fast in processing time, good in parallelism and broad in application prospect in array signal processing.

Description

technical field [0001] The invention relates to a method for realizing Hermitian matrix decomposition by using FPGA. Background technique [0002] In array signal processing, the signals received by multiple antennas often need to be decomposed into a matrix to obtain the eigenvalues ​​and eigenvectors of the matrix in order to estimate the direction of the signal source. Traditional matrix decomposition is realized by DSP (Digital Signal Processor), which is time-consuming. FPGA, as a field programmable gate array, has the advantages of parallel computing and fast processing time. It is gradually used to implement complex array signal processing algorithms. However, FPGA also has disadvantages, that is, it is particularly complicated to perform nonlinear operations. Therefore, in order to make full use of the advantages of FPGA while taking into account the disadvantages of FPGA, FPGA uses Jacobi algorithm with good parallelism instead of QR algorithm for matrix decompositi...

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Problems solved by technology

Traditional matrix decomposition is realized by DSP (Digital Signal Processor), which is time-consuming. FPGA, as a field programmable gate array, has the advantages of parallel computing and fast processing time. It is gradually used to implement complex array signal processing algorithms. However, FPGA also has disadvantages, that is, it is particularly complicated to perform nonlinear operations, so in order to make full use of the advantages of FPGA while taking into account the disadvantages of FPGA, FPGA uses Jacobi algorithm with good parallelism instead of QR algorithm for matrix decomposition

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