Full frequency-phase synchronization for physical-layer distributed clocks

In wireless networks, the majority of cooperative communications rely on the high-accuracy timing synchronization among isolated nodes. However, most presented physical-layer distributed synchronization algorithms so far cannot satisfy the requirement for real applications. To realize frequency and phase synchronization of distributed clocks, i.e., full synchronization, inspired by the character of the proportional plus integral controller that it may help an unstable system be a no steady-state error one, a new loop structure of distributed discrete phase-locked loop (PLL) is designed. Furthermore, by using algebraic graph theory, the convergence of this scheme is analyzed for both directed and undirected networks, and full synchronization is proved to be reached. Simulation results are given to corroborate the proposed algorithm and analysis.