Connectivity of Large-Scale CSMA Networks

Wireless multi-hop networks are being increasingly used in military and civilian applications. Connectivity is a prerequisite in wireless multi-hop networks for providing many network functions. In a wireless network with many concurrent transmissions, signals transmitted at the same time will mutually interfere with each other. In this paper we consider the impact of interference on the connectivity of CSMA networks. Specifically, consider a network with n nodes uniformly and i.i.d. on a square [-√n/2, √n/2]² where a node can only transmit if the sensed power from any other active transmitter is below a threshold, i.e. subject to the carrier-sensing constraint, and the transmission is successful if and only if the SINR is greater than or equal to a predefined threshold. We provide a sufficient condition and a necessary condition, i.e. an upper bound and a lower bound on the transmission power, required for the above network to be asymptotically almost surely (a.a.s.)connected as n → ∞. The two bounds differ by a constant factor only as n → ∞. 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 (UDM) without interference. This result is also in stark contrast with previous results considering the connectivity of ALOHA networks under the SINR model.