  In distributed massive multiple-input multiple-output (MIMO) systems,
multiple geographically separated access points (APs) communicate
simultaneously with a user, leveraging the benefits of multi-antenna coherent
MIMO processing and macro-diversity gains from the distributed setups. However,
time and frequency synchronization of the multiple APs is crucial to achieve
good performance and enable joint precoding. In this paper, we analyze the
synchronization requirement among multiple APs from a reciprocity perspective,
taking into account the multiplicative impairments caused by mismatches in
radio frequency (RF) hardware. We demonstrate that a phase calibration of
reciprocity-calibrated APs is sufficient for the joint coherent transmission of
data to the user. To achieve synchronization, we propose a novel over-the-air
synchronization protocol, named BeamSync, to calibrate the geographically
separated APs without sending any measurements to the central processing unit
(CPU) through fronthaul. We show that sending the synchronization signal in the
dominant direction of the channel between APs is optimal. Additionally, we
derive the optimal phase and frequency offset estimators. Simulation results
indicate that the proposed BeamSync method enhances performance by 3 dB when
the number of antennas at the APs is doubled. Moreover, the method performs
well compared to traditional beamforming techniques.
