Implicit network timing synchronization with phase-only updates

Timing synchronization is a critical requirement for implementation of a number of performance-enhancing strategies in mesh networks, including Time Division Multiplexing (TDM) for more efficient resource usage, and sleep scheduling for power efficiency. In this paper, we propose a simple algorithm for overhead-free maintenance of timing synchronization and investigate its scalability with the size of the network. In the proposed scheme, the nodes only use information obtained from the timing of existing communication in the network: each node updates only its clock phase when it receives a packet, depending on the difference between the expected and actual packet arrival times. The uncompensated frequency differences across nodes lead to irreducible phase errors, which we bound by introducing the notion of an averaged system. We use a linear programming formulation to show that these phase errors can grow with the network size, thereby concluding that simple, phase-only adjustments might suffice to maintain synchrony in small networks, but additional frequency adjustments are necessary for larger networks.