Connectivity of ad hoc wireless networks: an alternative to graph-theoretic approaches

Connectivity in wireless ad hoc and sensor networks is typically analyzed using a graph-theoretic approach. In this paper, we investigate an alternative communication-theoretic approach for determining the minimum transmit power required for achieving connectivity. Our results show that, if there is significant multipath fading and/or multiple access interference in the network, then graph-theoretic approaches can substantially underestimate the minimum transmit power required for connectivity. This is due to the fact that graph-theoretic approaches do not take the route quality into consideration. Therefore, while in scenarios with line-of-sight (LOS) communications a graph-theoretic approach could be adequate for determining the minimum transmit power required for connectivity, in scenarios with strong multipath fading and/or multiple access interference a communication-theoretic approach could yield much more accurate results and, therefore, be preferable.