Connectivity of Wireless CSMA Multi-hop Networks

In this paper we consider the impact of interference on the connectivity of CSMA networks. First, it is shown that the aggregate interference experienced by any receiver in a CSMA network with arbitrarily distributed nodes is upper bounded. Then, we derive an equivalent transmission range for CSMA networks where any pair of nodes whose Euclidean distance is smaller than or equal to the transmission range are directly connected. Finally we give a sufficient condition on the transmission power required for a CSMA network with a total of n nodes i.i.d. on a root n x root n square following a uniform distribution to be asymptotically almost surely connected as n -> infinity under the SINR model. It is shown that the transmission power only needs to be increased by a constant factor to combat interference and maintain connectivity compared with that considering a unit disk model without interference. This result is also in sharp contrast with previous results considering the connectivity of ALOHA networks under the SINR model.