Asymptotic Sum-Capacity of Random Gaussian Interference Networks Using Interference Alignment

TL;DR

This paper analyzes the asymptotic sum-capacity of dense random Gaussian interference networks, demonstrating convergence to a specific value using interference alignment and bottleneck link arguments.

Contribution

It provides the first asymptotic capacity bound for large random interference networks using interference alignment and bottleneck link techniques.

Findings

Sum-capacity per user converges to 1/2 E log(1 + 2SNR)

Achievability follows from interference alignment schemes

Converse bound established via bottleneck link analysis

Abstract

We consider a dense n-user Gaussian interference network formed by paired transmitters and receivers placed independently at random in Euclidean space. Under natural conditions on the node position distributions and signal attenuation, we prove convergence in probability of the average per-user capacity C_Sigma/n to 1/2 E log(1 + 2SNR). The achievability result follows directly from results based on an interference alignment scheme presented in recent work of Nazer et al. Our main contribution comes through the converse result, motivated by ideas of `bottleneck links' developed in recent work of Jafar. An information theoretic argument gives a capacity bound on such bottleneck links, and probabilistic counting arguments show there are sufficiently many such links to tightly bound the sum-capacity of the whole network.