# Efficient Wireless Charger Deployment for Wireless Reshapeable Sensor Networks
## 1 Introduction  
A wireless rechargeable sensor network (WRSN) [1] consists of many rechargeable sensor nodes and one or more sink nodes. Sensor nodes are powered by batteries and can sense physical phenomena (e.g., temperature, humidity, atmospheric pressure, light intensity, and electromagnetic field strength) and forward the sensed data to the sink node(s) via multi-hop wireless communications. WRSNs are sustainable since they utilize energy harvesting technologies to replenish the batteries of sensor nodes. The replenishing is achieved by equipping every sensor node with an energy harvester to harvest energy from different sources [2; 3], such as solar power, thermal power, radio frequency (RF) waves, or air flow, as shown in Figure 1. Many recent studies [4; 5; 6; 7; 8; 9; 10; 11; 12; 13] focus on the WRSNs due to their sustainability. Some other studies [14; 15; 16; 17; 18; 19; 20] investigate battery-less or battery-free wireless sensor networks (WSNs) in which sensor nodes are powered by capacitors storing energy harvested through wireless power transmission (WPT), especially microwave power transmission (MPT). Without loss of generality, such WSNs are regarded as WRSNs in this paper. Energy harvesting technologies are generally divided into two classes: (1) charger-based energy harvesting and (2) ambient energy harvesting. The former technology deploys specific devices, called chargers, to emit energy, and utilizes harvesters to capture the energy. The latter technology applies ambient energy harvesting devices to capture energy from the ambient environment. Typical devices include solar panels, thermoelectric generators, and ambient RF harvesters to capture energies from TV,Wi-Fi, and 3G/4G stations. It is more difficult for the latter to control the amount of harvested energy due to the unstable nature of ambient energy sources (ESs). This is problematic if sensor nodes have to meet specific energy requirements. Therefore, this paper pays attention to WRSNs using charger-based energy harvesting technologies. It practically focuses on indoor WRSNs using the RF wireless energy harvesting technology. The deployment of \"RF wireless chargers\" (or \"chargers\" for short) is challenging, since every harvester needs to be covered by at least one charger and the charging space of chargers is usually limited. For example, the effective charging distance is 3-5 m and the effective charging angle is 30\({}^{\circ}\)-45\({}^{\circ}\) between the Powercast TX91501-3W-ID charger (Powercast Corp., Pittsburgh, PA, USA) [21] and the Powercast P2110-EVAL-02 harvester (Powercast Corp.) [22]. It is also a cost-consuming task, as wireless chargers are expensive. For example, the Powercast TX91501-3W-ID charger currently costs about 1,000 US dollars. This motivated the authors to study the wireless charger deployment optimization (WCDO) problem defined below. Given a set of WRSN sensor nodes equipped with harvesters, the WCDO addresses how to deploy as few as possible chargers to cover all sensor nodes for satisfying their energy requirements to make the WRSN sustainable. To the best of our knowledge, no research has addressed the same problem up to now. This paper proposes two algorithms for solving the WCDO problem. It is assumed that wireless chargers are equipped with directional antennas whose charging space is modeled as a cone and charging efficiency complies with the Friis free space transmission equation [23]. It is also assumed that chargers are deployed on grid points at a specific height and the sensor nodes equipped with wireless harvesters are distributed beneath the chargers on the floor or object surfaces. The proposed algorithms are the greedy cone covering (GCC) algorithm and the adaptive cone covering (ACC) algorithm. Both algorithms treat chargers as cones. The GCC (respectively, ACC) algorithm greedily (respectively, adaptively) generates candidate cones that can cover as many as possible sensor nodes.