Optimal online sensing scheduling for energy harvesting sensors with infinite and finite batteries

In this paper, we study the optimal sensing scheduling problem for an energy harvesting sensor. The objective is to strategically select the sensing time such that the long-term time-average sensing performance is optimized. In the sensing system, it is assumed that the sensing performance depends on the time durations between two consecutive sensing epochs. Example applications include reconstructing a wide-sense stationary random process by using discrete-time samples collected by a sensor. We consider both scenarios where the battery size is infinite and finite, assuming the energy harvesting process is a Poisson random process. We first study the infinite battery case and identify a performance limit on the long-term time average sensing performance of the system. Motivated by the structure of the performance limit, we propose a best-effort uniform sensing policy, and prove that it achieves the limit asymptotically, thus it is optimal. We then study the finite battery case, and propose an energy-aware adaptive sensing scheduling policy. The policy dynamically chooses the next sensing epoch based on the battery level at the current sensing epoch. We show that as the battery size increases, the sensing performance under the adaptive sensing policy asymptotically converges to the limit achievable by the system with infinite battery, thus it is asymptotically optimal. The convergence rate is also analytically characterized.