Statistical characterization of uplink interference in two-tier co-channel femtocell networks

Femtocell (FC) is a new networking paradigm that differs from the traditional, macrocell (MC) network in many ways: size/coverage, random deployment, autonomous operation, signal propagation environment, etc. Inter-cell interference is a major issue in FCs operating over the same channel as the underlying MC. In this paper, we present an analytic study of the uplink (UL) physical interference and other related metrics, namely the signal to interference ratio (SIR) and the outage probability in FCs. We consider a stochastic model in which the spatial distribution of the femto users (FUs) and the macro users (MUs) is described by two independent, homogeneous Poisson Point Processes (PPPs). We first characterize the UL interference at the FC by deriving its first and second order statistics, its probability density function (PDF) and its tail distribution. Second, we derive the PDF of the per-FU SIR, its temporal autocorrelation and the outage probability. Finally, we validate the derived outage probability via Monte-Carlo simulations and show how this probability constrains the system capacity in terms of number (or density) of FUs that could be accepted in the MC.