Distributed Clock Phase and Frequency Synchronization in Half-Duplex TDMA Networks

High clock synchronization accuracy across the nodes in wireless networks is a prerequisite for facilitating high-rate data transmission. Accurate clock synchronization is a particularly challenging goal in networks implementing time division multiple access (tdma) via half-duplex (hd) communications, as in such networks the updates are temporally sparse, and consequently, clock frequency differences induce significant phase drifts between subsequent updates. Thus, accurate clock synchronization in hd tdma networks requires synchronizing both clock phases and clock frequencies across the nodes, which is the focus of this work. We consider pulse-coupling (pc)-based distributed clock synchronization, where each node implements its synchronization processing independently, based on its own received clock phases and power measurements. These measurements are then weighted to generate the phase and the frequency correction signals. We first analyze this synchronization framework and motivate decoupling the phase and frequency updates. We then analyze the resulting decoupled structure and derive the asymptotic synchronization accuracy, which is shown to be a function of the weighting coefficients and the unknown propagation delays. This motivates on-line learning of the optimal weights. To that aim, we introduce a novel initialization scheme with unsupervised online training. Simulation results show that the new scheme exhibits excellent synchronization accuracy, which is significantly better than previously proposed schemes, as well as robustness to clock resets and to node mobility.