How many users are needed for non-trivial performance of random beamforming in highly-directional mm-wave MIMO downlink?

In this paper, the multi-user (MU) gain and the impact of training are investigated for random beamforming (RBF) in highly-directional millimeter-wave (mm-wave) MU multiple-input multiple-output (MIMO) downlink which is considered as one of the major technological thrusts for 5G communications. To do so, the uniform random line-of-sight (UR-LoS) channel model suitable for highly-directional mm-wave radio propagation channels is adopted. Based on the UR-LOS channel model, the performance of RBF and the MU gain in mm-wave MIMO systems are analyzed. It is shown that there exists a transition point on the number of users relative to the number of transmit antennas for non-trivial performance of the RBF scheme. Furthermore, in case of training, the number of training beams relative to the number of antennas required for asymptotically good performance of the RBF scheme is specified when the number of users relative to the number of antennas is given. The provided results in this paper yields insights into the MU gain with partial CSI and the amount of required training in highly-directional mm-wave channels.