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This paper addresses over-the-air synchronization of two distributed receivers connected to a fusion center via digital links. We distinguish between received signals&#x2019; synchronization and receiving channels&#x2019; synchronization. The applications are digital receive beamforming (BF) and radio source localization, respectively. We introduce the system and signal models and propose a synchronization procedure. The scheme for signal synchronization includes estimating and compensating for the instantaneous phase and time offsets between the received user signals. This is achieved by utilizing wideband and narrowband pilots sent by a beacon transmitter, along with a wideband preamble sent by the user transmitter. Optionally, the scheme allows for equalization of the user signal, employing a narrowband pilot signal sent by the user transmitter. For channel synchronization, the procedure involves estimating and compensating for the instantaneous phase and time offsets between the receiving channels using pilot signals sent by the beacon transmitter. We assume variable frequency and constant time offsets during the observation interval. Additionally, we propose a novel adaptive algorithm for instantaneous phase offset estimation. We demonstrate the performance of the synchronization procedure and the proposed algorithms through Monte Carlo simulations and experiments using USRPs (Universal Software Radio Peripheral). With a 20 dB signal-to-noise ratio and realistic frequency offset amplitude and dynamics, the 0.9-quantiles for time estimation error and instantaneous phase estimation error are one 20th of the sampling interval and 10 degrees, respectively. The total error is reduced almost to the noise-only error.

Over-the-air Synchronization of Time, Phase and Frequency in a Distributed Receiving System