Connectivity of Ad Hoc Networks with Link Asymmetries Induced by Shadowing

The aim of this letter is to determine the minimum node density to achieve a connected large-scale ad hoc network, where every node has the same transmitting and receiving capabilities. Due to the log-normal shadowing, links are unidirectional in general. Contrary to the prevailing opinion, we argue that such asymmetries result into a "reduced" connectivity graph, which, from the point of view of MAC and routing protocols, is to be considered the true or effective connectivity graph. Accordingly, we derive a new formula for the connection probability between two nodes in order to compute global connectivity. Finally, theoretical findings, borrowed from random graphs theory, are compared to numerical simulation results in synthetic wireless network scenarios.