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Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

机译：真正的干扰对准：开发单天线系统的潜力

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摘要

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine–Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the (X) channel. It is proved that the sum DoF of the (K) -user IC is (({K}/{2})) for almost all channel parameters. We also prove that the sum DoF of the (X) -channel with (K) transmitters and (M) receivers is (({KM}/{K+M-1})) for almost all channel parameters.
机译：在本文中，我们开发了真正的干扰对准机制。该机器在实现单天线系统的自由度（DoF）方面极为强大。实际干扰对准的方案基于设计用于在发射机处调制信息消息的单层和多层星座。我们展示了星座可以以与多个天线系统中的矢量类似的方式对齐，并且空间可以分解为分数维。信号方案的性能分析利用了Diophantine近似领域的最新结果，该结果表明Khintchine-Groshev定理的收敛部分适用于非简并流形上的点。使用实际干扰对准，我们获得两个模型通道的总DoF，即高斯干扰通道（IC）和（X）通道。事实证明，几乎所有通道参数的（K）用户IC的总DoF为（（{{K} / {2}））。我们还证明，对于几乎所有信道参数，具有（K）个发射机和（M）个接收机的（X）信道的总DoF为（（{{KM} / {K + M-1}））。

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