ESPRIT 算法广义逆矩阵求解的快速 FPGA 实现

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.