This paper presents a theoretical model for estimating the uplink capacity of a communication in a three-dimensional(3D) millimeter-wave (mmWave) scenario. The model is developed considering realistic channel conditions, including path-loss attenuation, shadowing, and angular dispersion, which comply with recent measurement campaigns carried out in mmWave environment. The analysis also incorporates the effects of interference and noise, additionally accounting in detail for the actual shapes of the transmitting/receiving antenna patterns. Analytical expressions for the statistics of the interference power are derived, in order to enable a low-complexity evaluation of the capture probability and of the Shannon capacity for an interfered uplink communication. The conceived 3D mathematical framework, whose reliability is verified by Monte Carlo validations, is used to investigate some insights concerning the application of beamforming in dense mmWave scenarios.
