Multi-channel design for random CSMA wireless networks: A stochastic geometry approach

Topological randomness is an intrinsic characteristic of large scale ad-hoc and sensor networks. For networks with random topologies, choosing the operating parameters that govern the performance metrics is very challenging. Calculating the minimum number of channels required to accommodate a certain population of co-existing star connected networks (SCNs), or quantifying the performance degradation if the minimum number of channels in not available is the main focus of this paper. The main performance metric in our analysis is the self admission failure probability (blocking probability). We relax the single channel assumption that has always been used in the stochastic geometry analysis of random wireless networks. We show that the intensity of the coexisting networks does not increase linearly with the number of channels, and that the rate of increase of the intensity of the coexisting networks decreases with the number of channels. By using graph theory, we bound the number of channels required for accommodating a certain intensity of coexisting SCNs and provide a good initial point for the numerical optimization problem.