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.

翻译：在分布式大规模多输入多输出（MIMO）系统中，多个地理上分离的接入点（AP）与用户同时通信，充分利用了多天线相干MIMO处理带来的优势以及分布式部署产生的宏分集增益。然而，多个AP之间的时间和频率同步是实现良好性能并实现联合预编码的关键。本文从互易性角度分析了多AP间的同步需求，并考虑了射频（RF）硬件失配导致的乘性损伤。我们证明，对经过互易校准的AP进行相位校准，足以实现面向用户的联合相干数据传输。为实现同步，我们提出了一种新型空中同步协议，命名为BeamSync，该协议无需通过前传链路向中央处理单元（CPU）发送任何测量值即可校准地理上分离的AP。理论分析表明，沿AP间信道主方向发送同步信号是最优的。此外，我们推导了最优的相位和频率偏移估计器。仿真结果表明，当AP天线数量加倍时，所提BeamSync方法可提升3 dB的性能。同时，与传统的波束赋形技术相比，该方法表现出良好的性能优势。