NLOS-Aided Joint OTA Synchronization and Off-Grid Imaging for Distributed MIMO Systems

Distributed multiple-input multiple-output (MIMO) architectures enable large-scale integrated sensing and communication (ISAC) by providing high spatial resolution and robustness through spatial diversity. However, practical phase-coherent sensing is challenged by phase synchronization errors and modeling mismatch caused by grid discretization. Existing over-the-air (OTA) synchronization methods typically treat synchronization and sensing tasks separately, which may lead to inaccurate phase alignment when multipath components are used for imaging. In this paper, we propose a non-line-of-sight (NLOS)-aided joint OTA synchronization and off-grid imaging framework for distributed MIMO ISAC systems. First, a line-of-sight (LOS)-assisted coarse synchronization is performed to establish initial phase coherence across distributed links. Subsequently, an iterative refinement stage exploits reconstructed NLOS components obtained from imaging results. By modeling off-grid effects via a first-order Taylor expansion, we transform measurements with nonlinear off-grid offset into an augmented linear model with jointly sparse reflectivity and off-set variables. The imaging problem is reformulated as a structured sparse recovery task and solved using a tailored off-grid approximate message passing (OG-AMP) algorithm. The imaging and synchronization modules are coupled within a closed-loop alternative optimization framework, where improved imaging enables more accurate phase refinement, and vice versa. Numerical results show that the proposed framework achieves accurate synchronization and imaging under phase errors. Compared with conventional approaches, it shows superior robustness and accuracy.