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.
Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range to each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communication networks. Our main result shows that, despite the infinite range dependencies, percolation occurs in the model when the density of the Poisson point process is greater than the critical density value of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing). We study the impact of interferences on the connectivity of large-scale ad hoc networks, using percolation theory. We assume that a bi-directional connection can be set up between two nodes if the signal to noise ratio at the receiver is larger than some threshold. The noise is the sum of the contribution of interferences from all other nodes, weighted by a coefficient spl gamma , and of a background noise. We find that there is a critical value of spl gamma above which the network is made of disconnected clusters of nodes. We also prove that if spl gamma is nonzero but small enough, there exist node spatial densities for which the network contains a large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops. Since small values of spl gamma cannot be achieved without efficient CDMA codes, we investigate the use of a very simple TDMA scheme, where nodes can emit only every nth time slot. We show that it achieves connectivity similar to the previous system with a parameter spl gamma n.