Capacity Scaling of Wireless Ad Hoc Networks: Shannon Meets Maxwell

TL;DR

This paper precisely characterizes the capacity scaling laws of wireless ad hoc networks using Maxwell's equations, resolving previous conflicts and establishing conditions under which linear scaling is achievable.

Contribution

It introduces an exact channel model from Maxwell's equations and derives capacity scaling laws, reconciling prior conflicting results in the literature.

Findings

Capacity scales as min(n, degrees of freedom limit) in dense networks.

Capacity scales as min(n, sqrt(n) * lambda^{-1}) in extended networks.

Modified hierarchical cooperation achieves the derived capacity bounds.

Abstract

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 \"{O}zg\"{u}r et al. and the degrees of freedom limit given as the ratio of the network diameter and the wavelength $\lambda$ by Franceschetti et al. 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 $\sqrt{n}\lambda^{-1}$ to within an arbitrarily small exponent. Hence, we recover the linear capacity scaling by \"{O}zg\"{u}r et al. 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 et al. 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.