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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。
In order to select the proper QR decomposition algorithm in the current communication environment to realize the matrix inversion in hardware, it is required to know the hardware performance of the algorithm in advance. The algorithm principle and hardware implementation of Givens rotation method and Modified Gram-Schmidt orthogonal method which are commonly used in complex QR decomposition are analyzed. The underlying design and hardware simulations of both algorithms were performed on ISE software from Xilinx and integrated into Xilinx’s Kintex-7 family of XC7K325T chips. By comparing the hardware performance of the two algorithms, it is found that the error of the two algorithms is very small when the input data width is the same, among them, the real-time performance of the MGS algorithm is worse than that of the GR algorithm, but the hardware resource consumption is smaller. Therefore, in the real-time requirements of the system higher environment, select the GR algorithm is better.