"Small-World" effects of shadowing in pulse-coupled distributed time synchronization

Performance of pulse-coupled distributed synchronization in wireless ad hoc networks is known to depend critically on the topology of the corresponding connectivity graph. This paper evaluates the impact of log-normal shadowing on the convergence of distributed discrete-time phase locked loops (PLLs). It is argued that the beneficial effect of shadowing on distributed synchronization can be seen as an instance of the "small-world" phenomenon. Evidence of this is further provided by evaluating average path length and clustering coefficient of the wireless network through simulations.