# Jointly Optimize the Residual Energy of Multiple Mobile Devices in the MEC-WPT System
## 1 Introduction  
With the explosive development of the mobile devices and mobile communication, mobile devices (MDs) are becoming more and more widely used, the novel mobile applications emerge continuously. These emerging latency-sensitive applications rely heavily on real-time communication and computation of wireless devices [1]. However, most MDs have low computing capability and finite battery capacity, and cannot meet the massive demand for physical resources of current applications, which will be a crucial and breakthrough challenge. To resolve this issue, mobile edge computing (MEC) has emerged as a promising technique by providing cloud-like computing at the edge of mobile networks via integrated MEC servers at wireless access points (APs) [2]. Leveraging MEC, MDs with limited resources can offload their computation tasks to APs, and remotely compute and offload tasks on the MEC server. Generally, there are two different methods for computation, namely binary offloading and partial offloading. When using binary offloading, the division of tasks is not allowed. The entire task is required to be executed locally on the MD or remotely on the edge server. As for partial offloading, the task can be divided into two parts, one part is executed locally and the otherpart is executed on the edge server [3]. Meanwhile, because MEC technology can promote low-power devices to perform computing tasks in real-time, and MEC technology has attracted growing research interests in both academia and industry. In addition to improving the computation capability and reducing power consumption of MDs, another challenge is how to provide a sustainable and cost-effective energy supply to massive computation-heavy MDs is another challenge. The development of radio frequency (RF)-based wireless power transmission (WPT) technology brings a new solution to solve the problem of insufficient battery energy [4]. It was shown that user quality of experience (QoE) can be improved by integrating wireless powered techniques into MEC networks since the duration of having MEC services is extended [5]. By integrating WPT with the AP, the dedicated energy transmitter can be deployed to spread energy wirelessly to continuously power the battery of remote energy harvesting (EH) devices [6]. Deploying multiple antennas on the energy transmitter can be used for multiple devices at the same time, which helps to improve the efficiency of WPT, thereby it can satisfy more MDs' energy supply requests. In this article, we study the integration of WPT into MEC where multiple MDs collect energy in each time block and perform computationally intensive tasks simultaneously on edge servers and local devices. The key contributions of this article are as follows. 1. We adopting the case of multiple MDs, leveraging multiple antennas on the AP to perform energy transmission and charging multiple MDs at the same time so that each MD completes the corresponding computing task based on the harvested energy. Using partial offloading, each MD arbitrarily divides the computing task into two independent parts, which are used for local computing and task offloading. In addition, our proposed scheme uses Time Division Multiple Access (TDMA) protocol to coordinate computation offloading, where different users offload their respective tasks to the AP over orthogonal time slots. 2. In the integrated system, we focus on the joint optimization of the communication and computing resources of the partial computation offloading system. Taking the multi-period execution tasks of MDs into account, we achieve the goal of maximizing the remaining energy under multiple MDs and multi-slots, which requires maximizing energy harvesting and minimizing energy consumption. Therefore, we jointly optimize the task offloading size, task offloading time, energy harvesting time and CPU frequency of the MDs. 3. We established the system model and formalized the residual energy maximum problem.