How to achieve a connected ad hoc network with homogeneous range assignment: an analytical study with consideration of border effects

The paper presents an analytical investigation of the connectivity of wireless ad hoc networks with randomly uniformly distributed nodes and homogeneous transmission range assignment The probability that a network is connected depends on the number of nodes, n, per area, A, and their transmission ranges, r₀. We derive an analytical expression that enables the determination of critical (r₀, n)-pairs that achieve, with high probability, a connected network in an area A. As opposed to prior analytical work on this topic (see Bettstetter, C., Proc. ACM Symp. on Mobile Ad Hoc Networks and Comp.-MobiHoc, 2002), we now consider border effects, which have significant impact on the obtained results. Furthermore, we calculate the expected node degree and the probability that the network has no isolated node. All three results are of practical value in simulation and system design of ad hoc and wireless sensor networks. While the paper considers a circular system area, the methods can also be applied to other shapes.