Abstract: Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, prob- abilistic techniques have been developed in the last decade to provide communication-theoretic results accounting for the network's random geometrical conguration. I will review the statisti- cal characterization of the interference process and show how tools from spatial point processes, random geometric graphs, and stochastic geometry, can be used to characterize the connectivity, outage probability, and information capacity of wireless networks. I will also mention some open problems which are of interest from both the mathematical and the engineering point of view. The presentation is mostly based on material contained in the following reviews.

References

[1] M. Franceschetti, R. Meester (2007) Random Networks for Communication, Cambridge Uni- versity Press.

[2] M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti (2009), Stochastic Geometry and Random Graphs for the Analysis and Design of Wireless Networks, IEEE Journal on Selected Areas in Communications. (Invited) Sept. 2009.