Feedback-Based Closed-Loop Carrier Synchronization: A Sharp Asymptotic Bound, an Asymptotically Optimal Approach, Simulations, and Experiments

We derive an asymptotically sharp bound on the synchronization speed of a randomized black box optimization technique for closed-loop feedback-based distributed adaptive beamforming in wireless sensor networks. We also show that the feedback function that guides this synchronization process is strong multimodal. Given this knowledge that no local optimum exists, we consider an approach to locally compute the phase offset of each individual carrier signal. With this design objective, an asymptotically optimal algorithm is derived. Additionally, we discuss the concept to reduce the optimization time and energy consumption by hierarchically clustering the network into subsets of nodes that achieve beamforming successively over all clusters. For the approaches discussed, we demonstrate their practical feasibility in simulations and experiments.