Physical-layer distributed synchronization in wireless networks and applications

Physical-layer (pulse-coupled) techniques for distributed synchronization in wireless networks are attracting significant attention for their efficiency and scalability. In this paper, the model of pulse-coupled discrete Phase Locked Loops is reviewed and further investigated in two directions. At first, we extend the characterization of (frequency or phase) synchronous states and convergence conditions from homogeneous networks, where all the nodes have the same power constraints, to more general heterogeneous networks. Towards this goal, we build on recent results on algebraic graph theory for generally non-bidirectional graphs, and derive: (i) necessary and sufficient conditions for global synchronization of the network; (ii) closed-form expressions for the asymptotic values of frequency and phases, as a function of the network topology. In the second part of the paper, an application of pulse-coupled synchronization is considered, namely data collection in a sensor network. The energy efficiency of two medium access protocols for data collection from a set of randomly located sensors to an access point is compared: (i) basic ALOHA (which does not require time synchronization among the sensors); (ii) slotted ALOHA, where time synchronization is achieved via pulse-coupled clocks. Analysis shows that the energy spent for maintaining synchronization in slotted ALOHA pays off in terms of total energy consumption with respect to basic ALOHA provided that the number of sensors is sufficiently small. Moreover, the energy gain is proved to depend explicitly on the system load (in terms of packets /s), hardware and topology of the network.