Researching on the relationships among different multiple weighted type fractional Fourier transform (multi-WFRFT) schemes, we in this paper provide the modulation order relation of different multi-WFRFT in theory. Moreover, we also prove that the two matrix spaces (i.e., 4-WFRFT and multi-WFRFT) are equivalent. To apply multi-WFRFT into the wireless communication, we design the implementation structure of multi-WFRFT (in particular, for 2 n -WFRFT scheme). Furthermore, the generalized hybrid carrier modulation (GHCM) system has been proposed in this paper, which can be degenerated to the classical hybrid carrier modulation (HCM) system with special parameters. We also verify the modulation order relationship between multi-WFRFT by numerical simulations. Leveraging the theory and structure of multi-WFRFT, we finally discuss its potential applications over secure communication and multiple input multiple output (MIMO) system.
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机译：通过研究不同的多重加权类型分数阶傅里叶变换（multi-WFRFT）方案之间的关系，我们在理论上提供了不同的multi-WFRFT的调制阶数关系。此外，我们还证明了两个矩阵空间（即4-WFRFT和multi-WFRFT）是等效的。为了将multi-WFRFT应用于无线通信，我们设计了multi-WFRFT的实现结构（特别是对于2 n -WFRFT方案）。此外，本文提出了广义混合载波调制（GHCM）系统，可以将其退化为具有特殊参数的经典混合载波调制（HCM）系统。我们还通过数值模拟验证了多WFRFT之间的调制阶数关系。利用多WFRFT的理论和结构，我们最终讨论其在安全通信和多输入多输出（MIMO）系统上的潜在应用。
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