Statistical Analysis of the Pulse-Coupled Synchronization Strategy for Wireless Sensor Networks

Pulse-coupled synchronization is attracting increased attention in the sensor network community. Yet its properties have not been fully investigated. Using statistical analysis, we prove analytically that by controlling the number of connections at each node, synchronization can be guaranteed for generally pulse-coupled oscillators even in the presence of a refractory period. The approach does not require the initial phases to reside in half an oscillation cycle, which improves existing results. We also find that a refractory period can be strategically included to reduce idle listening at nearly no sacrifice to the synchronization probability. Given that reduced idle listening leads to higher energy efficiency in the synchronization process, the strategically added refractory period makes the synchronization scheme appealing to cheap sensor nodes, for which energy is a precious system resource. We also analyzed the pulse-coupled synchronization in the presence of unreliable communication links and obtained similar results. QualNet experimental results are given to confirm the effectiveness of the theoretical predictions.