Impact of Interferences on Connectivity in Ad Hoc Networks

We study the impact of interferences on the connectivity of large-scale ad-hoc networks, using percolation theory. We assume that a bi-directional connection can be set up between two nodes if the signal to noise ratio at reception is larger than some threshold. The noise is the sum of the contribution of interferences from all other nodes, weighted by a coefficient g, and of a background noise. We find that there is a critical value of g above which the network is made of disconnected clusters of nodes. We also prove that if g is non zero but small enough, there exist node spatial densities at which the network contains an large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops. Since small values of g cannot be achieved without efficient CDMA codes, we investigate the use of a very simple TDMA scheme, where nodes can emit only every n-th time slot. We show qualitatively that it even achieves a better connectivity than the previous system with a parameter g/n.