基于多参数加权分数阶傅里叶变换的星座预编码系统研究与实现

针对当前多参数加权分数阶傅里叶变换(Multiple Parameters Weighted-type FRactional Fourier Transform, MP-WFRFT)星座特征缺乏定量研究的缺限，该文提出一种新型的星座叠加数学模型。通过分别研究信号的时域及频域分量，给出了星座模糊及裂变的定性及定量分析结论，并搭建了基于MP-WFRFT的星座预编码系统。通过构建相关混合整数优化模型，并利用遗传算法进行模型优化，进而设计出符合预期通信需求的预编码系统。经仿真分析，验证了所提出的星座叠加数学模型及优化方案的正确性；同时通过USRP硬件平台测试表明了所搭建的基于MP-WFRFT星座预编码系统的可行性。

Analysis and Implementation of Constellation Precoding System Based on Multiple Parameters Weighted-type Fractional Fourier Transform

In view of the fact that there exists little research on the constellation characteristic of Multiple Parameters Weighted-type FRactional Fourier Transform (MP-WFRFT), a novel mathematical model based on constellation superposition is proposed. By analyzing the time domain and frequency domain components of the MP-WFRFT modulated signal, the quantitative and qualitative conclusions are provided, about the constellation splitting and Gaussian-like characteristics and the constellation precoding system is built based on MP-WFRFT. The related mixed integer optimization model is put forward and the Genetic Algorithm (GA) is used to solute the optimization, Then the desired MP-WFRFT-based precoding system is obtained. The simulation results demonstrate that the proposed constellation superposition model and its corresponding optimization model are correct. Besides, the tests obtained on USRP platforms also show that the constellation precoding system based on MP-WFRFT is practical.