A Mathematical Framework to the Computation of the Error Probability of Downlink MIMO Cellular Networks by Using Stochastic Geometry

In this paper, a mathematical framework to the computation of the error probability of downlink cellular networks is introduced. It is based on the Poisson point process (PPP)-based abstraction for modeling the spatial locations of the base stations (BSs), and it exploits results from stochastic geometry for characterizing the distribution of the other-cell interference. The framework is applicable to spatial multiplexing multiple-input-multiple-output (MIMO) systems with an arbitrary number of antennas at the transmitter (N_t) and at the receiver (N_r). If N_t = N_r = 1, the mathematical approach can be used for arbitrary fading distributions on both useful and interfering links. If either N_t > 1 or N_r > 1, it can be applied to arbitrary fading distributions on the useful link and to Rayleigh fading on the interfering links. It is shown that the proposed approach leads to easy-to-compute integral expressions, which reduce to closed-form formulas in some asymptotic regimes. Furthermore, the framework is shown to provide insights for system design and optimization. The accuracy of the mathematical analysis is substantiated through extensive Monte Carlo simulations for various cellular network setups.