Effect of users height distribution on the coverage of mmwave cellular networks with 3d beamforming

In this paper, we study the effect of users\u27 height distribution on the coverage probability of millimeter-wave (mmWave) cellular networks that utilize three-dimensional beamforming (3DBF). The users and base stations (BSs) are equipped with multiple antennas and both line-of-sight (LOS) and non-LOS links exist in the channel which are, respectively, modeled by the Nakagami-m and Rayleigh distribution. In this setup, we investigate the tilt angle optimization of the BS antenna arrays for maximizing the coverage probability under two regimes of noise limited and interference limitedd. In both cases, by adopting a stochastic geometry approach, we analytically derive the coverage probability, and then, find the optimal tilt angle that maximizes this probability. In addition, in the noise limited regime, we show that the optimal tilt angle depends on the average distance between each user and its serving BS and also their effective height. In the interference-limited regime, we further consider different rules for associating users to the BSs. Meanwhile, since in this regime, the tilt angle optimization is very complex, we propose a low complexity approach to find the optimal tilt angle that has a performance close to the optimal solution. We further study the asymptotic behavior when the density of the BSs or signal-To-interference ratio tends to infinity or zero. Finally, through the numerical simulations, we show that using the 3DBF and also incorporating the users\u27 height distribution in the tilt angle optimization lead to a substantial improvement in the coverage probability of the mmWave cellular networks