Degrees of freedom of large planar wireless networks embedded in a 3D domain

It is shown using first physical principles and without relying on stochastic fading channel models, that the number of spatial degrees of freedom 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 h√n and hence, as the number of nodes increases, the per-user information capacity must follow an inverse square-root of n law.