The Capacity Region of Large Wireless Networks

The capacity region of a wireless network with $n$ nodes is the set of all simultaneously achievable rates between all possible $n^2$ node pairs. In this paper, we consider the question of determining the scaling, with respect to the number of nodes $n$, of the capacity region when the nodes are placed uniformly at random in a square region of area $n$ and they communicate over Gaussian channels. We identify this scaling of the capacity region in terms of $Theta(n)$, out of $2^n$ total possible, cuts. Our results are constructive and provide optimal (in the scaling sense) communication schemes. In the case of a restricted class of traffic requirement (permutation traffic), we determine the precise scaling in terms of a natural generalization of the transport capacity. 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.