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.
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