FPGA implementation method for Cholesky decomposition of positive definite matrix

Abstract

The present invention discloses an FPGA implementation method for Cholesky decomposition of a positive definite matrix. The method is mainly provided with: a top layer control module, for communication and control between modules; a data preprocessing module, for decomposing a positive definite matrix into two matrices for calculation operations in a matrix calculation module; and the matrix calculation module, for calculating two matrices obtained by the data preprocessing module to obtain a final Cholesky decomposition calculation result. Beneficial effects of the method disclosed by the present invention are that: by using the traditional hardware to directly implement Cholesky decomposition of the positive definite matrix, the algorithm is complex, the occupied area is large, and the resource consumption is more, and by using the rotation characteristic of the CORDIC algorithm to implement the Cholesky decomposition of the positive definite matrix, the implementation is simple, only the bit operation is needed, the resource consumption is less, and the computational complexity and the area of the gate circuit are effectively reduced.

Description

technical field [0001] The invention belongs to the field of digital signal processing, in particular to an FPGA realization method of Cholesky decomposition of a positive definite matrix. Background technique [0002] The Cholesky decomposition of a positive definite matrix is ​​a very important form of matrix triangulation decomposition, which is widely used in scientific computing, communication, and spectrum analysis. However, the Cholesky decomposition of a positive definite matrix with a scale of n×n requires a large number of multiplication and square root operations, and the computational complexity is O(n 3 / 6), therefore, under the condition that n is very large, the Cholesky decomposition calculation of the matrix has a huge amount of calculation, and the hardware implementation consumes a lot of resources. Contents of the invention [0003] In order to solve the computational complexity and resource consumption problems of the Cholesky decomposition of positiv...

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Problems solved by technology

[0003] In order to solve the computational complexity and resource consumption problems of the Cholesky decomposition of positive definite matrices, the present invention uses the rotation characteristics of the CORDIC algorithm to calculate the complex operations in the Cholesky calculation process. Since only bit operations are involved in the CORDIC calculation operations, the hardware implementation is simple and consumes resources. Less, the computational complexity is also reduced

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