Interference alignment-based sum capacity bounds for random dense Gaussian interference networks

TL;DR

This paper establishes sum capacity bounds for dense Gaussian interference networks using interference alignment and bottleneck capacity concepts, showing convergence of per-user capacity under random node placement.

Contribution

It introduces a novel upper bound on sum capacity based on physical location control and bottleneck links, extending interference alignment analysis to random dense networks.

Findings

Per-user capacity converges to half the expected log(1 + 2 SNR)

Achievability follows from interference alignment schemes

Upper bounds are derived using bottleneck capacity ideas

Abstract

We consider a dense $K$ user Gaussian interference network formed by paired transmitters and receivers placed independently at random in a fixed spatial region. Under natural conditions on the node position distributions and signal attenuation, we prove convergence in probability of the average per-user capacity $\csum/K$ to $\half \ep \log(1 + 2 \SNR)$. 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 an upper bound, motivated by ideas of `bottleneck capacity' developed in recent work of Jafar. By controlling the physical location of transmitter--receiver pairs, we can match a large proportion of these pairs to form so-called $\epsilon$-bottleneck links, with consequent control of the sum capacity.