Exact Outage Analysis for Stochastic Cellular Networks under Multi-User MIMO

The next generations of cellular wireless systems promise an improved user experience with respect to the throughput, reliability, latency, and connectivity. To this end, multiple-input multiple-output (MIMO) and massive MIMO systems hold enormous potential. Moreover, due to heterogeneity and densification, user and base station locations are increasingly random. Thus, in this paper, we characterize the performance of a typical downlink user within a massive MIMO Voronoi cell when the base stations employ matched filter based precoding in the downlink We consider a typical Voronoi cell where the base stations follow a Poisson point process (PPP), and also consider the users to be randomly distributed according to a PPP independent from the base stations. Furthermore, a wireless channel with log-distance path loss and Rayleigh fading is assumed. Using a novel framework to model the signal to noise ratio, the outage probability of a user is derived in closed-form while taking into account full and partial loading for the cell's base station due to the randomness of user numbers. Numerical results show that the outage probability is heavily dependent on the base station density, and that the performance decreases when the maximum number of users served by a base station increases.