Evaluating SIR in 3D mmWave Deployments: Direct Modeling and Feasible Approximations

Recently, new opportunities for utilizing the extremely high frequencies have become instrumental to design the fifthgeneration (5G) mobile technology. The use of highly directional antennas in millimeter-wave (mmWave) bands poses an important question of whether 2D modeling suffices to capture the resulting system performance accurately. In this work, we develop a novel mathematical framework for performance assessment of the emerging 3D mmWave communication scenarios, which takes into account vertical and planar directivities at both ends of a radio link, blockage effects in three dimensions, and random heights of communicating entities. We also formulate models having different levels of details and verify their accuracy for a wide range of system parameters. We show that capturing the randomness of both Tx and Rx heights as well as the vertical antenna directivities becomes crucial for accurate system characterization. The conventional planar models provide overly optimistic results that overestimate performance. For instance, the model with fixed heights that disregards the effect of vertical exposure is utterly pessimistic. Other two models, one having random heights and neglecting vertical exposure and another one characterized by fixed heights and capturing vertical exposure are less computationally expensive and can be used as feasible approximations for certain ranges of input parameters.