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 n² 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 2ⁿ 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.