Energy Efficient Optimum Sensing with Energy Harvesting Power Sources

In this paper, we study the optimum estimation of a band-unlimited continuous-time random process using discrete-time samples taken by a sensor powered by energy harvesting devices. In order to accurately represent a band-unlimited random process, a large sampling rate is needed, and this may yield a huge amount of data to be collected and transmitted. In the mean time, the energy required for sensing and transmitting the data must satisfy the constraints imposed by stochastic energy harvesting sources. To cope with these challenges, we propose a family of the best-effort random sensing policies. The best-effort random sensing schemes define a set of randomly chosen candidate sensing instants, and the sensor performs sensing at a given candidate sensing instant only if there is sufficient energy available. Otherwise an energy outage is declared and the sensor remains silent. It is shown through asymptotic analysis that the probability of energy outage during sensing is determined by the ratio between the energy harvesting rate and the energy consumption rate. For a given average energy harvesting rate, less samples per-unit time means a weaker temporal correlation between two adjacent samples, but a smaller energy outage probability, less data, and more energy per sample. Such a tradeoff relationship is captured by developing a closed-form expression of the estimation mean squared error (MSE), which analytically identifies the interactions among the various system parameters. The estimation MSE is minimized by optimizing the tradeoff among system parameters. The proposed optimum sensing scheme can asymptotically achieve the same performance as a system with the conventional energy sources, and significantly reduce the amount of data to be collected and transmitted.