Rate Loss of Hybrid Beamforming with Imperfect Phase Shifters in Millimeter Wave Systems

In millimeter massive MIMO systems, hybrid beamforming algorithms with fewer RF chain are widely applied as they can save power and cut down on hardware costs. Hybrid beamforming can be divided into two stages: analog beamforming in the RF domain usually implemented with phase shifters and digital beamforming in the baseband domain. Phase shifters have rms phase error and rms gain error which are random and unknown so they can’t be compensated by the digital beamforming. In this paper, we study the influence of rms phase error and rms gain error upon the performance of the mmWave communication system. We derive the closed-form expression of the loss of spectral efficiency in point to point scenario and the loss of achievable sum rate in multiuser scenario. The result can be applied to both sparse channel and rich-scattering channel and all kinds of hybrid beamforming algorithms. The derived expression and simulation results are in good agreements. From the results in both theory and simulation, we can see that considering the phase shifters with an rms phase error of 0.5◦ and rms gain error of 1-dB, the loss ratio of the spectral efficiency is 40% in point to point scenario and the loss ratio of the achievable sum rate is 35% in multiuser scenario when signal-to-noise ratio is 15dB and will increase when the signal-to-noise ratio grows up. The loss of performance is serious and cann’t be neglected.