Optimal Finite Horizon Sensing for Wirelessly Powered Devices

We are witnessing a significant advancements in the sensor technologies which has enabled a broad spectrum of applications. Often, the resolution of the produced data by the sensors significantly affects the output quality of an application. We study a sensing resolution optimization problem for a wireless powered device (WPD) that is powered by wireless power transfer (WPT) from an access point (AP). We study a class of harvest-first-transmit-later type of WPT policy, where an access point (AP) first employs RF power to recharge the WPD in the down-link, and then, collects the data from the WPD in the up-link. The WPD optimizes the sensing resolution, WPT duration and dynamic power control in the up-link to maximize an application dependant utility at the AP. The utility of a transmitted packet is only achieved if the data is delivered successfully within a finite time. Thus, we first study a finite horizon throughput maximization problem by jointly optimizing the WPT duration and power control. We prove that the optimal WPT duration obeys a time-dependent threshold form depending on the energy state of the WPD. In the subsequent data transmission stage, the optimal transmit power allocations for the WPD is shown to posses a channel-dependent fractional structure. Then, we optimize the sensing resolution of the WPD by using a Bayesian inference based multi armed bandit problem with fast convergence property to strike a balance between the quality of the sensed data and the probability of successfully delivering it.