基于QR分解自适应波束形成算法的FPGA实现

为了在当前的通信环境中选择合适的QR分解算法来硬件实现矩阵的求逆，需要提前了解该算法的硬件性能。分析常用于复数QR分解的Givens rotation法和Modified Gram—Schmidt正交法的算法原理和硬件实现。在Xilinx公司的ISE软件上进行两种算法的底层设计和硬件仿真，经过综合在Xilinx的Kintex-7系列的XC7K325T芯片上实现了整个设计。通过对比两种算法的硬件性能后发现，在输入数据宽度相同的前提下，两种算法的误差值相差很小，其中MGS算法的实时性比GR算法差，但是硬件资源消耗更小。因此在对系统实时性要求较高的环境中，选择GR算法更好一些。

FPGA Implementations of QR Decomposition based Adaptive Beamforming Algorithm

To choose a better QR decomposition to be applied to the communication environment , the hardware performance of the algorithms needs to be known before they are implemented. The commonly QR decomposition algorithms including the Gram -Schmidt and Givens rotation are introdueed briefly. The implementation of these QR decomposition algorithms with FPGA are offered in detail. Using the ISE software of the company Xilinx as the design tool, most parts of the algorithms are accomplished by using VHDL. The design of the system is realizes in the chip Kintex - 7 XCTK325T. The hardware performance and the cost of these algorithms are compared. Under the condition of the same input data＇s length, the errors of these two algorithms are almost the same. Compared with GR, MGS has a lower resource cost, as well as a inferior real - time. Therefore, GR algorithm is better to get the QR decomposition in the condition which has a strict requirement of the system real - time.