Vertical beamforming for three-dimensional user placement

Full-dimensional multiple input multiple output (FD-MIMO) is a practical implementation of massive MIMO in cellular communication systems. FD-MIMO relies on a planar array of active antenna systems (AAS) at the base stations to harvest the benefits of both azimuth and vertical beamforming. In this paper, we analyze the network performance of per-user vertical beamforming with a special focus on the three-dimensional placement of the base stations and the users. We use tools from stochastic geometry to analyze the coverage performance of cellular networks with a three-dimensional radiation pattern at the base stations, using AAS. We show that the directionality achieved via dynamic antenna tilting provides multi-fold improvement in network performance as compared to omni-directional digital beamforming. We draw insights on the performance of the network as a function of the height difference between the base stations and the users, the number of antennas at the base station, and the various characteristics of the radiation pattern.