Coupling noise effect in self-synchronizing wireless sensor networks

Recent results have shown that the mathematical tools considered for modelling populations of coupled oscillators appearing in nature provide an appealing framework for designing self-syncronizing sensor networks. Trendy signal processing applications take advantage of these works by coupling the sensors in order to design reliable decision/estimation networks based on cheap and unreliable sensors. In this work, we extend those results to take into account that the coupling function might suffer from noise due to the need of estimating the states of the nearby sensors. The novelty of this paper is the introduction of the concept of frustration in the design of wireless sensor networks. Frustration implies that synchronization is only possible up to a certain variance standstill floor. We provide the analytic expression of this floor and discuss some limiting cases. In order to assess the performance of the self-synchronizing network, we propose a simple signal model for the transmission of states from node to node and study its Cramér-Rao Bound and the asymptotically efficient Maximum Likelihood estimator. Taking into consideration these achieved estimation variances, computer simulation results are provided discussing the coupling noise effect and the obtained theoretical lower bound.