Wireless Power Transfer for Distributed Estimation in Wireless Passive Sensor Networks

Recent advances in wireless power transfer (WPT) technology enable over-the-air charging of passive sensor devices and allow sensors to be active on demand without concern of their battery lifetime. This work examines the beam pattern selection and charging power allocation problems for distributed estimation applications in wireless passive sensor networks (WPSNs) that employ WPT to replenish sensors. The charging operation consists of two-phases: an exploration phase and a replenishment-and-transmission phase. In the exploration phase, radio-frequency (RF) energy chargers first scan the network in turn using different beam patterns and sensors that harvest sufficient energy based on these beams emit pilot signals to enable channel estimation at the fusion center. In the replenishment-and-transmission phase, beam patterns and charging powers are first chosen based on the available channel state information (CSI) and then used to emit RF charging signals to replenish the sensors. The sensors utilize the harvested RF energy to make local observations of the underlying parameter of interest and transmit them to the fusion center, where the final estimate is computed. In this paper, the beam pattern selection and charging power allocation are first jointly optimized with the goal of minimizing the mean-square error (MSE) of the final estimate under perfect CSI. For tractability, an MSE upper bound is used as the objective function and the problem is solved efficiently using the block successive upper bound minimization (BSUM) method. The impact of the exploration threshold and duration on the MSE is then examined for the imperfect CSI case. Simulation results demonstrate the effectiveness of the proposed scheme.