Maximizing Harvested Energy in Natural Energy Powered RF WPT with Nonlinear EH Model

In the typical radio frequency (RF)-based wireless power transfer (WPT) system, the wireless power station (WPS) connected to the grid transmits energy to charge low-power sensors via radio signals. Such a system may not be green and also difficult to deploy in some special areas including deserts and mountainous areas, because it depends on the grid. To achieve a green RF WPT system design, this paper considers that the WPS is powered by natural energy sources rather than the grid. To explore the maximal total amount of the energy that can be harvested by the sensors, we focus on the offline setting, so similar to many existing works on offline optimization, we assume that the WPS knows prior knowledge about energy arrivals and channel changes, and then formulate an optimization problem to maximize the total harvested energy via optimizing the WPS's time-domain transmit power subject to multiple constraints, including the finite battery capacity at the WPS, the causal relationship between the natural energy harvesting and the WPT, and the transmit power budget of the WPS, where for practicality, the nonlinear energy harvesting (EH) model is also taken into account. To solve this non-convex problem, we first equivalently transform it by using the epigraph reformulation and the variable substitution, and then use the first-order Taylor expansion to get an approximate convex version. Then, we present a successive convex approximation (SCA)-based algorithm to improve the accuracy of the obtained solution for approaching the optimal one. For the special case with a single sensor, we further propose a branch and bound (BB)-based algorithm that is able to get a more accurate solution with lower complexity than the SCA-based one. Numerical results demonstrate that the proposed algorithms are able to achieve the near-global optimal solution. As the average recharge rate increases, compared with the other two baselines, i.e., the greedy power (GP) policy and the constant power (CP) policy, the total harvested energy achieved by the SCA-based algorithm is up to about 2.48 times and 1.37 times that of the baselines respectively. For the single-sensor case, the BB-based algorithm always outperforms the SCA-based one in terms of the total harvested energy while reducing the running time required for solving by about 90% on average.