Computer Science – Information Theory
Scientific paper
2009-08-17
Computer Science
Information Theory
Submitted to IEEE Transaction on Information Theory. The first version was uploaded on arxiv on 17 Aug 2009 with the following
Scientific paper
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 $\frac{KM}{K+M-1}$.
Gharan Shahab Oveis
Khandani Amir Keyvan
Maddah-Ali Mohammad-Ali
Motahari Abolfazl Seyed
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