On the hop count statistics for randomly deployed wireless sensor networks

In this paper we focus on exploiting the information provided by a generally accepted and largely ignored hypothesis (the random deployment of the nodes of an ad hoc or wireless sensor network) to design improved networking protocols. Specifically, we derive the relationship between the number of hops separating two nodes and the physical distance between them (one- and two- dimensional topologies). In this way, distance estimates between nodes are made available without the use of any distance measuring hardware. We conclude the paper showing how the obtained statistical results can be applied to improve the performance of distributed localisation protocols while simplifying their implementation.