Border effects on connectivity for randomly oriented directional antenna networks

We study the possibility of creating a fully con-nected ad-hoc network with bidirectional links between nodes equipped with randomly oriented directional antennas de-ployed in a circular planar region. The major contribution of our paper is to show that in the directional antenna setting there are always isolated nodes, no matter how high the transmission power of the antennas. We observe, however, that the isolated nodes are confined to a narrow annulus near the boundary of the region. We propose two solutions to achieve full connectivity in the directional setting: T-core that reorients isolated antennas towards the centre of the circular region, and Greedy that simply flips the antenna orientation. We show that the former heuristic, which needs information of the location of the centre of the region, achieves full connectivity with high probability and that, even the latter, which requires no extra information, is able to eliminate most of the isolation.