# Joint Power Charging and Routing in Wireless
## 1 Introduction  
Because of the wide applications of wireless sensor networks (WSNs) in environmental monitoring, ecosystem surveillance, and physical hazard prevention, WSNs have attracted a flourish of research efforts from both the industry and academia in the last decade. However, most WSNs still face a limited operating time, as they are powered by battery. In order to prolong the network lifetime, extensive research efforts have been focused on low-power hardware architecture [1], low-complexity software implementation [2], power-efficient wireless communication [3], topology control [4], and dynamic routing techniques [5]. Although these solutions can extend the network lifetime to some extent, the limited battery remains a paramount hurdle to the development of large-scale applications. Some other solutions have resorted to energy harvesting sources, such as solar, wind, hydroelectric, and thermoelectric. However, these harvesting sources are generally expensive and with a large size, requiring an additional energy harvesting component, and they may not always be accessible because of the environment dynamics [6]. For example, the availability of a solar-based harvesting system drastically varies with time and weather, and these cannot provide enough energy for duty-cycle applications [7]. In place of conventional energy harvesting techniques, the recent breakthrough in the area of wireless power transfer (WPT) has opened up a promising alternative to power devices using radio frequency (RF) signals over the air. It was shown in an Intel research report that a wireless identificationand sensing platform (WISP) can harvest energy to power the operation of micro-controller unit (MCU) [8]. In their study, WPT was performed by harvesting energy from the ambient RF signals radiated by the surrounding transmitters, and they also showed that WPT technology is fully adjustable in its transmit power, waveforms, and resource blocks. Regarding the energy harvesting efficiency, the results in [9] showed that nearly 40 \(\upmu\)W can be transferred over a distance of 10 m with a transmit power of 3 W, which is sufficient to power the operations of many low-power devices, such as sensors and RF identification (RFID) tags. As a result of the inherent energy harvesting characteristic of the WPT technique, a relatively short transmission distance and multiple simultaneous transmissions in WSNs, wireless rechargeable sensor networks (WRSNs) can be a promising solution to achieve high energy efficiency, and they have attracted much attention recently [10]. In WRSNs, the rechargeable sensors are capable of harvesting energy from the RF signals transmitted by energy sources to power the data sensing from the environment and data delivered to the sink. In most applications, these energy sources are mobile chargers carried by autonomous vehicles [11] to tackle the dynamic topology problem. With the moving speed and the predefined charging capacity, the modeling, characterization and optimization of charging in WRSNs becomes extremely important. There has been some research focusing on charging optimization in WRSNs. In [12], by importing the concept of a renewable energy cycle, an optimal traveling path for a mobile charging vehicle is designed. In [13], velocity control with a predefined charging trajectory is designed to satisfy the traveling time constraint. In [14], as a result of the redundant deployment of sensors, the optimal energy replenishment joint with coverage control is designed to achieve the balance between the coverage rate and the energy partitioning. However, all these works assume that the data-gathering tree is predefined before energy harvesting. In [15], a joint routing and charging schedule was proposed to prolong the network lifetime.