On the Relationship Between Relay and Infrastructure Densities in Geometrically Bounded Relay-Assisted Wireless Networks

Abstract

In this paper, we study the connectivity between two fixed terminal nodes within a geometrically bounded network of relay nodes and fixed infrastructure nodes. We assume that a communication path, between the terminal nodes, can be established by direct connection (1-hop), via a relay node (2-hop) or via the infrastructure network; the choice is based on link viability in a Rayleigh fading environment. We adopt a probabilistic approach to our analysis considering a homogeneous spatial distribution of relay nodes and an inhomogeneous spatial distribution of infrastructure nodes. Our analysis of the relationship between relay and infrastructure densities for a prescribed outage probability shows that reliance on infrastructure connectivity can be appreciably reduced by employing direct and 2-hop connectivity. We further show that, as the relay density increases, optimum connectivity is achieved by employing a non uniform spatial thinning of the infrastructure, which is dependent upon the geometric extent of the network. Our analysis provides an insight into multi-mode connectivity in bounded network domains and has application in many fields including cellular and vehicle-to-infrastructure (V2X), which are often modelled as having finite extent and where reducing the reliance on fixed infrastructure can effectively reduce operating expenditure costs.