Pulse-coupled distributed PLLs in heterogeneous wireless networks

Decentralized time synchronization in ad hoc or sensor networks can be conveniently achieved via pulse-coupled discrete-time phase locked loops (PLLs). Previous work has characterized (frequency or phase) synchronous states and convergence conditions for homogeneous networks where all the nodes have the same power constraints. In this paper, we build on recent results on algebraic graph theory for generally non- bidirectional graphs, and address the asymptotic behavior of pulse-coupled PLLs in heterogeneous networks. We first derive necessary and sufficient conditions for global synchronization of the network. Then, we provide closed form expressions for the asymptotic frequency and phases, as a function of the network topology.