Interference Alignment and the Degrees of Freedom of Wireless Networks
Cadambe, V.R.; Jafar, S.A.
Information Theory, IEEE Transactions on
Volume 55, Issue 9, Sept. 2009 Page(s):3893 - 3908
Digital Object Identifier   10.1109/TIT.2009.2025541
Summary:We explore the degrees of freedom of M times N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to [(MN)/(M+N-1)] per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M=2 or N=2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1) . For these cases the degrees of freedom outer bound is exactly achievable.

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