ESPRIT算法广义逆矩阵求解的快速FPGA实现

在基于旋转不变子空间的信号参数估计（estimating signal parameter via rotational invariance techniques,ESPRIT）算法中涉及到求解信号子空间矩阵的逆矩阵，针对常用方法计算复杂度高，实时性差等问题，提出使用广义逆公式对信号子空间矩阵进行求解的方法. 在FPGA平台上设计并实现了由复数矩阵乘法、矩阵LU分解、下三角矩阵求逆等子模块构成的广义逆矩阵求解系统. 利用该系统求解广义逆矩阵所用的时间约为2.18 ms，与在MATLAB上对同样矩阵进行广义逆求解的平均用时15.7 ms减少了7.2倍. 使用该系统的结果在MATLAB上完成后续仿真，对ESPRIT算法最终所得角度进行误差分析，最终所得角度的平均估计误差约为0.04°. 结果表明，该系统能在保证结果精确度的同时有效减少运算时间. 

Fast FPGA Implementation of Solving Moore-Penrose Inverse Matrices in ESPRIT Algorithm

The estimating signal parameter via rotational invariance techniques (ESPRIT) algorithm involves solving the inverse matrix of the signal subspace matrix. To overcome the shortcomings of commonly used algorithms, such as high computational complexity and poor real-time performance, a generalized inverse formula-based method was proposed to solve the signal subspace matrix. Firstly, a generalized inverse matrix solution system was implemented on FPGA platform, composed with complex matrix multiplication sub-module, matrix LU decomposition sub-module, and lower triangular matrix inversion sub-module. The calculation time with this system to solve the generalized inverse matrix is about 2.18ms, reducing by 7.2 times compared with the same matrix on MATLAB, average time 15.7ms. And then, a subsequent simulation of the results was completed on MATLAB, and the error of the final angle obtained by ESPRIT algorithm was analyzed. The average estimation error of the final angle is about 0.04 °. The results demonstrate that the proposed method can effectively reduce the operation time, while improving the estimation accuracy.