Optimizing femtocell densities for spectrum allocation in cellular networks

In this work we analyze a spectrum allocation problem between two classes of users. We study the problem from the perspective of a cellular network with an underlaid femtocell network. Femtocells are deployed by the end-user, and thus the topology of femtocell networks is highly dynamic and stochastic in nature. One way of managing the interference is to control the population size of the network. By fixing the spectrum resources available to the femtocell network, an optimal density of femtocells can be found that maximizes the performance of the network in terms of the achievable sum rate.