Capacity Scaling of Wireless Ad Hoc Networks: Shannon Meets Maxwell.

In this paper, we characterize the information-theoretic capacity scaling of wireless ad hoc networks with n randomly distributed nodes. By using an exact channel model from Maxwell's equations, we successfully resolve the conflict in the literature between the linear capacity scaling by Özgür and the degrees of freedom limit given as the ratio of the network diameter and the wavelength \lambda by Franceschetti In dense networks where the network area is fixed, the capacity scaling is given as the minimum of n and the degrees of freedom limit \lambda^-1 to within an arbitrarily small exponent. In extended networks where the network area is linear in n, the capacity scaling is given as the minimum of n and the degrees of freedom limit \sqrtn\lambda^-1 to within an arbitrarily small exponent. Hence, we recover the linear capacity scaling by Özgür if \lambda=O(n^-1) in dense networks and if \lambda=O(n^-1/2) in extended networks. Otherwise, the capacity scaling is given as the degrees of freedom limit characterized by Franceschetti For achievability, a modified hierarchical cooperation is proposed based on a lower bound on the capacity of multiple-input multiple-output channel between two node clusters using our channel model. [ABSTRACT FROM AUTHOR]