Pairwise Base Station Synchronization via Joint Tensor Decomposition for Networked ISAC

This letter proposes a tensor-based framework for estimating the timing offset (TO) and carrier frequency offset (CFO) between base stations (BSs) in a networked integrated sensing and communication (ISAC) system. Unlike a recently introduced super-resolution offset estimation by matrix pencil (SOE-MP) method that compresses the received signal matrix in BS-BS links into a vector, the proposed framework employs canonical polyadic decomposition (CPD) to preserve and exploit the spatial-time-frequency structure of the data. Through CPD, our framework separates multipath channel components, enabling TO estimation that is robust against multipath delay interference, a major limitation of the SOE-MP method. The proposed CPD framework operates in a joint manner, where the CFO-related factor matrix is shared between two CPDs based on a reciprocity in BS-BS links. The framework also incorporates a Vandermonde structural constraint on the TO- and CFO-related factor matrices. These structured factors can be efficiently optimized via a correlation-based scheme. The Cramér-Rao bound for offset estimation and the uniqueness conditions for the Vandermonde structured CPDs are provided to characterize the theoretical performance limit. Simulation results demonstrate the superior estimation performance of the proposed tensor-based method compared to the conventional approach.