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

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 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 demonstrate 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 estimate 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.