Network connectivity in non-convex domains with reflections

TL;DR

This paper develops a new analytical framework to analyze wireless network connectivity in non-convex domains with boundary reflections, especially considering external nodes outside the convex region, which traditional models overlook.

Contribution

It introduces a novel analytical approach that accounts for non-convex geometries and boundary reflections, extending connectivity analysis beyond line-of-sight assumptions.

Findings

Derived analytical expressions in 2D and 3D for non-convex domains.

Confirmed the model's accuracy with numerical simulations under Rician fading.

Highlighted the importance of boundary reflections for external node connectivity.

Abstract

Recent research has demonstrated the importance of boundary effects on the overall connection probability of wireless networks but has largely focused on convex deployment regions. We consider here a scenario of practical importance to wireless communications, in which one or more nodes are located outside the convex space where the remaining nodes reside. We call these `external nodes', and assume that they play some essential role in the macro network functionality e.g. a gateway to a dense self-contained mesh network cloud. Conventional approaches with the underlying assumption of only line-of-sight (LOS) or direct connections between nodes, fail to provide the correct analysis for such a network setup. To this end we present a novel analytical framework that accommodates for the non-convexity of the domain and explicitly considers the effects of non-LOS nodes through reflections from the domain boundaries. We obtain analytical expressions in 2D and 3D which are confirmed numerically for Rician channel fading statistics and discuss possible extensions and applications.