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arXiv · 0908.2282

Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

Abolfazl Seyed Motahari·Shahab Oveis Gharan·Mohammad-Ali Maddah-Ali·Amir Keyvan Khandani
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Abstract

In this paper, the available spatial Degrees-Of-Freedoms (DOF) in single antenna systems is exploited. A new coding scheme is proposed in which several data streams having fractional multiplexing gains are sent by transmitters and interfering streams are aligned at receivers. Viewed as a field over rational numbers, a received signal has infinite fractional DOFs, allowing simultaneous interference alignment of any finite number of signals at any finite number of receivers. The coding scheme is backed up by a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on non-degenerate manifolds. The proposed coding scheme is proved to be optimal for three communication channels, namely the Gaussian Interference Channel (GIC), the uplink channel in cellular systems, and the $X$ channel. It is proved that the total DOF of the $K$-user GIC is $\frac{K}{2}$ almost surely, i.e. each user enjoys half of its maximum DOF. Having $K$ cells and $M$ users within each cell in a cellular system, the total DOF of the uplink channel is proved to be $\frac{KM}{M+1}$. Finally, the total DOF of the $X$ channel with $K$ transmitters and $M$ receivers is shown to be $\frac{KM}{K+M-1}$.

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Abolfazl Seyed Motahari, Shahab Oveis Gharan, Mohammad-Ali Maddah-Ali, Amir Keyvan Khandani. 2009-08-17. Real Interference Alignment: Exploiting the Potential of Single Antenna Systems. https://doi.org/10.1109/tit.2014.2329865

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