On the asymptotic equivalence between stochastic and deterministic energy sources in energy harvesting sensing systems

In this paper, we seek answer to the question: can a wireless sensing system with energy harvesting power supplies perform as well as the one with conventional power supplies? Conventional sensing systems with deterministic energy sources usually employ uniform sampling. However, due to the stochastic nature of the energy harvested from the ambient environment, uniform sampling is usually infeasible for energy harvesting sensing systems. We thus propose a simple best-effort sensing scheme, which defines a set of equally spaced candidate sensing instants. At a given candidate sensing instant, the sensor will perform sensing if there is sufficient energy available, and it will remain silent otherwise. It is analytically shown that the percentage of silent candidate sensing instants goes to zero as time increases, if and only if the average energy harvesting rate is no less than the average energy consumption rate. Therefore, the difference between the best-effort sensing policy and the uniform sensing policy diminishes as time evolves. The theoretical results are then used to guide the design of a practical sensing system that monitors a time-varying event. Both analysis and simulations show that the energy harvesting system with the best-effort sensing scheme can asymptotically achieve the same mean squared error (MSE) performance as the one with uniform sensing and deterministic energy sources. Therefore, we provide a positive answer to the question by establishing the asymptotic equivalence between stochastic and deterministic energy sources, from both theoretical and practical aspects.