Momentum-Accelerated Phase Synchronization for UAV Swarm Collaborative Beamforming

Distributed beamforming in UAV swarms requires fast and accurate carrier-phase alignment under sparse connectivity and propagation-induced phase bias. This paper proposes a physics-aware decentralized synchronization framework for quasi-static UAV swarm beamforming by integrating momentum-accelerated Metropolis–Hastings consensus with position-aided phase pre-compensation. To preserve phase evolution on the circular manifold, a sinusoidal coupling law is adopted, while the momentum term improves convergence in sparse random geometric graphs. A propagation model is further established to characterize how geometric separation and ranging uncertainty translate into residual phase error and coherent power loss. Under small-signal conditions, local stability is analyzed, and Monte Carlo simulations are conducted to evaluate convergence, synchronization accuracy, robustness, and beam-focusing performance. Results show that, at 2.4 GHz with low-centimeter ranging uncertainty, the proposed method achieves sub-wavelength synchronization accuracy while providing an effective balance among convergence speed, accuracy, and complexity. Compared with standard Metropolis–Hastings, fixed-weight, and other accelerated consensus methods, the proposed scheme converges faster over most sparse topologies. Although its steady-state accuracy is slightly lower than that of filter-based predictive methods such as KF-DFPC in some cases, those schemes incur higher implementation and computational overhead. Therefore, from the perspectives of decentralized realization and practical deployment, the proposed method is more suitable for lightweight phase synchronization in distributed UAV swarms.