On the Connectivity of 2-D Random Networks with Anisotropically Radiating Nodes

We study the effect that anisotropic radiation has on the probability that a dense, two-dimensional (2-D) random network is fully connected. To this end, we provide a thorough analytical treatment of the connectivity of wireless ad hoc networks with beamforming using a newly established theory of connectivity reported in , where we assume the network experiences small-scale fading according to the well-known two-wave with diffuse power (TWDP) model. We calculate the connectivity mass related to various radiation patterns, and show that isotropic radiation is optimal when the path loss exponent is greater than two, but single-sector directed transmission yields superior performance for other cases. We exploit our analysis to design optimal radiation patterns in the sense that connectivity is maximized, which can be used as masks to perform antenna pattern synthesis. Our results exhibit a property of universality with respect to the small-scale fading model since they do not depend on the TWDP fading parameters.