Phase synchronization for distributed sensor networks in feedback bit errors

Abstract

It has been reported recently that phase synchronization in distributed sensor networks can be achieved by adjusting the phase in sensors randomly with a single bit feedback from the receiver (base station) to the sensors. It has been shown that such algorithm leads asymptotic phase coherence with probability one for a broad class of distributions for the random phase adjustments. However, the effects of errors in the feedback bit and phase noise/uncertainty at the sensors were not explored in the algorithm. In this paper, we design a synchronization algorithm with the presence of communication errors in the feedback bit and phase noise at the sensors. Each sensor adaptively adjusts the phase by random phase perturbations by two stages. The first stage, the phase is adjusted according the best received signal strength available; and in the second stage, the adjusting is based on the previous received signal. By alternating between these two stages, the convergence is guaranteed and robust to the feedback bit errors. The convergence time is roughly linear in the number of sensors. Simulations have shown that the proposed algorithm provides satisfactory performance with the feedback bit errors and phase noise at the sensors.