Percolation in multi-hop wireless networks

Abstract

Models of wireless ad-hoc and sensor networks are often based on the geometric disc abstraction: transmission is assumed to be isotropic, and reliable communication channels are assumed to exist (apart from interference) between nodes closer than a given distance. In reality communication channels are unreliable and communication range is generally not rotationally symmetric. In this paper we examine how these issues affect network connectivity. We compare networks of geometric discs to other simple shapes and/or probabilistic connections, and we find that when transmission range and node density are normalized across experiments so as to preserve the expected number of connections (ENC) enjoyed by each node, discs are the “hardest ” shape to connect together. In other words, anisotropic radiation patterns and spotty coverage allow an unbounded connected component to appear at lower ENC levels than perfect circular coverage allows. This indicates that connectivity claims made in the literature using the geometric disc abstraction in general hold also for the more irregular shapes found in practice.