The degrees of freedom of wireless networks

Abstract

It is shown using electromagnetic wave theory and without relying on stochastic fading channel models, that the number of independent information channels available in planar wireless networks embedded in a three-dimensional propagation environment is limited by the spatial size of the cut that divides the environment into two parts. Specifically, in the case of propagation inside a cylinder of height h and base area n, containing n communicating source-destination node pairs, the number of available channels is at most proportional to hradicn and hence, as the number of nodes increases, the per-user information capacity must follow an inverse square-root of n law.