Network Synchronization of Random Signals

This paper presents a unified mathematical model for studying the behavior of various network synchronization techniques, e.g., plesiochronous or independent clocks, hierarchical master-slave, delay-compensated and uncompensated network models are presented in the form of a set of nonlinear space-time matrix equations in which network interconnection matrices are manifested. Each equation in the set characterizes the diffusion of phase (time) and frequency generated at each network node. The matrices of this model define the topological structure of the network. The time-frequency model is used to characterize the timefrequency stability of the network clock ensemble. Expressions for the steady-state network frequency and the time differences between nodal clocks are derived and compared for plesiochronous, delay compensated and uncompensated networks. A network frequency stability measure is introduced, evaluated and performance comparisons are made for specific network configurations. Finally, we illustrate the steady-state frequency stability achievable when subnetworks are connected to form a larger network.