Limiting Performance of Millimeter-Wave Communications in the Presence of a 3D Random Waypoint Mobility Model

—This paper proposes a mathematical framework for evaluating the limiting capacity of a millimeter-wave (mmWave) communication involving a mobile user (MU) and a cellular base station. The investigation is realized considering a three-dimensional (3D) space in which the random waypoint mobility model is used to probabilistically identify the location of the MUs. Besides, the analysis is developed accounting for path-loss atten- uation, directional antenna gains, shadowing, and modulation scheme. Closed-form formulas for the received signal power, the Shannon capacity, and the bit error rate (BER) are obtained for both line-of-sight (LoS) and non-LoS scenarios in the presence of a noise-limited operating regime. The conceived theoretical model is firstly checked by Monte Carlo validations, and then employed to explore the influence of the antenna gain and of the cell radius on the capacity and on the BER of a fifth-generation (5G) link in a 3D environment, taking into account both the 28 and 73 GHz mmWave bands.