The Unicast and Multicast Capacity Regions of Large Wireless Networks

We consider the question of determining the scaling of the n-dimensional unicast and the n×2n-dimensional multicast capacity regions of a wireless network with n nodes placed uniformly at random in a square region of area n and communicating over Gaussian fading channels. We identify this scaling of both the unicast and multicast capacity regions in terms of Θ(n), out of 2n total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus can be readily evaluated. Our results are constructive and provide optimal (in the scaling sense) communication schemes. We illustrate the strength of these results by computing the capacity scaling in a number of scenarios with non-uniform traffic patterns for which no such results have been available before.