Stochastic geometry analysis of the average error probability of downlink cellular networks

In this paper, we introduce a mathematical framework for computing the average error probability of downlink cellular networks in the presence of other-cell interference, Rayleigh fading, and thermal noise. A stochastic geometry based abstraction model for the locations of the Base Stations (BSs) is used, hence the BSs are modeled as points of a homogeneous spatial Poisson Point Process (PPP). The Mobile Terminal (MT) is assumed to be served by the BS that is closest to it. The technical contribution of this paper is twofold: 1) we provide an exact closed-form expression of the Characteristic Function (CF) of the aggregate other-cell interference at the MT, which takes into account the shortest distance based cell association mechanism; and 2) by relying on the Gil-Pelaez inversion theorem, we provide an exact closed-form expression of the Average Pairwise Error Probability (APEP), which accounts for Rayleigh fading and for the spatial distribution of the BSs. From the APEP, the Average Symbol Error Probability (ASEP) is obtained by using the Nearest Neighbor (NN) approximation, which is shown to provide accurate estimates. Finally, the mathematical framework is substantiated through extensive Monte Carlo simulations and insights on the achievable performance are discussed.