Distributed Synchronization on Weakly Connected Networks

Distributed synchronization for wireless networks is based on the mutual exchange of the same chirp-signature by nodes. Collisions of these signatures drive the system toward time and (carrier) frequency synchronization using distributed consensus algorithms. This letter investigates the convergence and the asymptotic distortion properties on noisy networks when neighboring clusters of nodes are weakly connected to each other only through a subset of nodes and bridging links. These heavily connected clusters act as macroagents, and the consensus properties of the ensemble depend on the number of bridge links between them. The convergence rate and mean square synchronization deviation are derived as functions of the number of bridge links for different examples of weakly connected noisy networks via the analytic calculation of Laplacian spectra. Our approach facilitates the study of network topology optimization for distributed synchronization.