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Generalization of critical transmission range for connectivity to wireless multihop network models including interference

The connectivity of wireless multihop networks has mostly been studied neglecting interference, assuming that all network nodes have a common transmission range within which they can form direct links. Under this assumption, the critical transmission range for connectivity of a given network equals the greatest edge length in the Euclidean minimum spanning tree of the network nodes. While the impact of interferences on the percolation phenomena of infinite networks has been studied [1], little is known about the graph connectivity of finite networks under more realistic network models. In this paper, we generalize the critical range for connectivity to two network models presented earlier which are both based on a minimum required signal-to-noise-and-interference ratio for successful communication. As these models have more than one free parameters, the critical range generalizes into a boundary in the space of these parameters; we show how to determine this boundary for a given network. The connectivity boundary implies tradeoffs between different parameters dictating network performance. Our results allow studying the connectivity of interferences-limited networks by simulation and give insight on the sensitivity of connectivity to different network parameters.