On pulse-coupled discrete-time phase locked loops forwireless networks

Mutual clock synchronization over a wireless channel has been recently studied in the framework of pulse-coupled oscillators using either models borrowed from mathematical biology or the model of coupled discrete-time Phase Locked Loops (PLLs). In this paper, we focus on the latter case and extend previous analyses by considering frequency-asynchronous clocks, second-order PLLs and by addressing the issues of propagation delays, finite pulse resolution and half-duplex constraints. Moreover, we provide a steady-state and convergence analysis of the system under the ideal assumption of infinite-resolution time error detectors, exploiting some results from the literature on consensus of multi-agents networks. Finally, numerical examples are discussed that corroborate the analysis and show the impact of system parameters such as transmit/ receive switching time and oversampling factor at the receiver.