Over-the-Air Time-Frequency Synchronization in Distributed ISAC Systems

A distributed integrated sensing and communication (D-ISAC) system offers significant cooperative gains for both sensing and communication performance. These gains, however, can only be fully realized when the distributed nodes are perfectly synchronized, which is a challenge that remains largely unaddressed in current ISAC research. In this paper, we propose an over-the-air time-frequency synchronization framework for the D-ISAC system, leveraging the reciprocity of bistatic sensing channels. This approach overcomes the impractical dependency of traditional methods on a direct line-of-sight (LoS) link, enabling the estimation of time offset (TO) and carrier frequency offset (CFO) between two ISAC nodes even in non-LoS (NLOS) scenarios. To achieve this, we introduce a bistatic signal matching (BSM) technique with delay-Doppler decoupling, which exploits offset reciprocity (OR) in bistatic observations. This method compresses multiple sensing links into a single offset for estimation. We further present off-grid super-resolution estimators for TO and CFO, including the maximum likelihood estimator (MLE) and the matrix pencil (MP) method, combined with BSM processing. These estimators provide accurate offset estimation compared to spectral cross-correlation techniques. Also, we extend the pairwise synchronization leveraging OR between two nodes to the synchronization of $N$ multiple distributed nodes, referred to as centralized pairwise synchronization. We analyze the Cramer-Rao bounds (CRBs) for TO and CFO estimates and evaluate the impact of D-ISAC synchronization on the bottom-line target localization performance. Simulation results validate the effectiveness of the proposed algorithm, confirm the theoretical analysis, and demonstrate that the proposed synchronization approach can recover up to 96% of the bottom-line target localization performance of the fully-synchronous D-ISAC.