Efficient WMMSE beamforming for 5G mmWave cellular networks exploiting the effect of antenna array geometries

Millimetre wave (mmWave) transmission is considered as one of the potential technologies in fifth generation (5G) cellular networks that could allocate more bandwidth to support the rapid growth of mobile data services. However, mmWave signals experience large path loss which can overcome by employing directional beamforming with high-dimensional antenna arrays. In this study, a downlink multiuser multiple-input multiple-output beamforming optimisation problem is considered for maximising the system utility subject to per-user quality-of-service constraint as well as per-antenna and base station transmit power constraints. The difficulty of this problem lies in its non-convex nature. To address this challenge, a weighted minimum mean square error (WMMSE)-based solution is proposed to reformulate the non-convex problem into equivalent convex one. Then, the block coordinate descent method is used to determine beamforming vectors. Moreover, the different antenna array geometries either two-dimensional (2D) such as planar array and circular array (CiA), or 3D such as conformal array and conical array (CoA) are designed at the base station and their effect on the system performance is exploited. Extensive simulations show that the performance of the proposed WMMSE-based solution with CiA and CoA geometries outperforms the comparable algorithms in terms of system throughput, system power consumption and access rate.