The Degrees of Freedom of Wireless Networks Via Cut-Set Integrals

It is shown that the capacity scaling of wireless net- works is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uni- formly an order of n users wishing to establish pairwise indepen- dent communications at fixed wavelength inside a two-dimensional domain of size of the order of n, there are an order of n commu- nication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of n, so the per-user information capacity must follow an inverse square-root of n law. This result shows that information-theoretic limits of wireless communication problems can be rigorously ob- tained without relying on stochastic fading channel models, but studying their physical geometric structure.