The Balanced Unicast and Multicast Capacity Regions of Large Wireless Networks

TL;DR

This paper characterizes the scaling of balanced unicast and multicast capacity regions in large wireless networks with randomly placed nodes, providing geometric-based, optimal communication schemes.

Contribution

It identifies the capacity region scaling in terms of cuts based on node geometry, offering a constructive and optimal communication scheme.

Findings

Capacity regions scale as Θ(n) out of 2^n possible cuts.

Capacity depends only on source-destination geometry and traffic demands.

Provides scalable, optimal communication schemes.

Abstract

We consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $\Theta(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus can be readily evaluated. Our results are constructive and provide optimal (in the scaling sense) communication schemes.