The Influence of Canyon Shadowing on Device-to-Device Connectivity in Urban Scenario

TL;DR

This paper uses percolation theory and a Poisson-Voronoi tessellation model to analyze large-scale device-to-device network connectivity in urban environments with canyon shadowing, identifying critical relay and user density thresholds.

Contribution

It introduces a novel percolation-based model for urban D2D networks with canyon shadowing and quantifies thresholds for relay and user densities necessary for connectivity.

Findings

Existence of a relay threshold at approximately 71.3% for large-scale connectivity.

Identification of a street length threshold at about 74.3% of communication range affecting connectivity.

Demonstration that increasing relay deployment can compensate for low user density in certain urban scenarios.

Abstract

In this work, we use percolation theory to study the feasibility of large-scale connectivity of relay-augmented device-to-device (D2D) networks in an urban scenario, featuring a haphazard system of streets and canyon shadowing allowing only for line-of-sight (LOS) communications in a limited finite range. We use a homogeneous Poisson-Voronoi tessellation (PVT) model of streets with homogeneous Poisson users (devices) on its edges and independent Bernoulli relays on the vertices. Using this model, we demonstrated the existence of a minimal threshold for relays below which large-scale connectivity of the network is not possible, regardless of all other network parameters. Through simulations, we estimated this threshold to 71.3%. Moreover, if the mean street length is not larger than some threshold (predicted to 74.3% of the communication range; which might be the case in a typical urban scenario) then any (whatever small) density of users can be compensated by equipping more crossroads with relays. Above this latter threshold, good connectivity requires some minimal density of users, compensated by the relays in a way we make explicit. The existence of the above regimes brings interesting qualitative arguments to the discussion on the possible D2D deployment scenarios.