基于浮点数的Cholesky分解FPGA实现

FPGA Implementation of Cholesky Decomposition Based on Floating Point Number

在阵列信号抗干扰算法中,常常需要求解协方差矩阵的逆矩阵。Cholesky分解利用了协方差矩阵的厄米特(Hermitian)正定的特性,大大简化了矩阵求逆运算的计算量。论文介绍了Cholesky分解数学原理,并提出了一种适合FPGA实现的结构。基于浮点数的算法实现相比传统的定点数,大大提高了结果的精度。由于Cholesky分解需要涉及浮点数的开方运算,论文引入了平方根倒数法来提高开方运算的速度。通过仿真与实测,选取了最优的资源与速度的实现方案。

In the anti-jamming algorithm of array signal,it is often necessary to solve the inverse matrix of covariance matrix.Cholesky decomposition makes use of the Hermitian positive definite property of covariance matrix,which greatly simplifies the calculation of matrix inversion.This paper introduces the mathematical principle of Cholesky decomposition and proposes a structure suitable for FPGA implementation.Compared with the traditional fixed-point number,the algorithm based on floating-point number greatly improves the accuracy of the results.Because Cholesky decomposition needs to involve the square root operation of floating-point numbers,this paper introduces the inverse square root method to improve the speed of square root operation.Through simulation and measurement,the optimal implementation scheme of resources and speed is selected.