Research on the method of fast inverse realisation of Vandermonde matrix based on FPGA

摘要

With the rapid development of science and technology, the operation and calculation in synthetic aperture radar (SAR) imaging systems require high throughput, and the system has high requirement for real-time performance. At the same time, in the SAR imaging technology, many Vandermonde matrix inversion operations are used in places where the weight coefficients are calculated. Especially when multi-channel inverse filtering is performed, the use of the Vandermonde matrix inversion operation is a crucial step. In this study, the authors worked hard to find a high speed and accurate Vandermonde matrix inversion algorithm for complex SAR imaging systems. Considering the field-programmable gate array (FPGA) can be parallel computing and its computing speed is high, the authors chose FPGA to achieve a large number of Vandermonde matrix inversion calculation, and it can meet the requirements of high speed and real time. So, first the realisation method of the fast inversion of the Vandermonde matrix based on Lagrange interpolation polynomial is discussed in this study, which includes preprocessing module, u matrix calculation module, v matrix calculation module, p' vector calculation module and post-processing module. Then, the simulation results of the design are compared and analysed, which proved the correctness and feasibility of the rapid inversion method of Vandermonde matrix.