Abstract
This work presents modeling and performance analysis of beamforming in non-cooperative multi-user multiple-input multiple-output (MU-MIMO) cellular systems using stochastic geometry based abstraction models. Particularly, a downlink MU-MIMO system is investigated in which an array of antenna elements at the base stations (BS) serves several user devices. We derive the closed-form expression of the complimentary cumulative distribution function (CCDF) of signal-to-interference-plus-noise ratio (SINR) representing the coverage probability for orthogonal pilot sequences and thereby characterize a number of related special cases. Moreover, closed-form expressions are also obtained for the CCDF of signal-to-interference ratio (SIR) for non-orthogonal pilot sequences and we also derive useful special cases of it and identify the support region of our analysis. Lastly, we define the numerical expression of ergodic capacity and utilize a partial fraction expansion to solve a simple form. Our contribution in this work is twofold, we not only provide a pedagogical tutorial-like exposition of stochastic geometry technique to model terrestrial networks, but also augment the existing literature in the field with aspects of frequency reuse factor, an indicator function for pilot usage, and the effect of pilot contamination. Simulation results are presented to support the theoretical part.