On the number of active links in random wireless networks

TL;DR

This paper analyzes the maximum number of simultaneous high-rate transmissions in large random wireless networks, showing it scales as the fourth root of the number of nodes under Rayleigh fading and Poisson node distribution.

Contribution

It provides a new asymptotic scaling law for the number of active links in large wireless networks with Rayleigh fading and Poisson-distributed nodes.

Findings

Number of active links scales as O(n^{1/4})

Results hold with high probability as network size grows

Simulation confirms theoretical scaling law

Abstract

This paper presents results on the typical number of simultaneous point-to-point transmissions above a minimum rate that can be sustained in a network with $n$ transmitter-receiver node pairs when all transmitting nodes can potentially interfere with all receivers. In particular we obtain a scaling law when the fading gains are independent Rayleigh distributed random variables and the transmitters over different realizations are located at the points of a stationary Poisson field in the plane. We show that asymptotically with probability approaching 1, the number of simultaneous transmissions (links that can transmit at greater than a minimum rate) is of the order of $O(n^{\frac{1}{4}})$. These asymptotic results are confirmed from simulations.