This paper studies a single-user wireless powered mobile edge computing (MEC) system, in which one multi-antenna energy transmitter (ET) employs energy beamforming for wireless power transfer (WPT) towards the user, and the user relies on the harvested energy to locally execute a portion of tasks and offload the other portion to an access point (AP) integrated with an MEC server for remote execution. Different from prior works considering static wireless channels and computation tasks at the user, this paper considers both energy and task causality constraints due to the channel fluctuations and dynamic task arrivals over time. Towards an energy-efficient joint-WPT-MEC design, we minimize the total transmission energy consumption at the ET over a particular finite horizon while ensuring the user’s successful task execution, by jointly optimizing the transmission energy allocation at the ET for WPT and the task allocation at the user for local computing and offloading over a particular finite horizon. First, in order to characterize the fundamental performance limit, we consider the offline optimization by assuming that the perfect knowledge of channel state information (CSI) and task state information (TSI) (i.e., task arrival timing and amounts) is known a-priori. In this case, we obtain the well-structured optimal solution to the energy minimization problem by using convex optimization techniques. The optimal solution shows that in the scenario with static channels, the ET should allocate the transmission energy uniformly over time, and the user should employ staircase task allocation for both local computing and offloading, with the number of executed task input-bits monotonically increasing over time. It also shows that in the scenario with time-varying channels, the ET should transmit energy sporadically at slots with causally dominating channel power gains, and the user should apply the staircase task allocation for local computing and staircase water-filling task allocation for offloading with monotonically increasing computation levels over time. Next, inspired by the structured offline solutions obtained above, we develop heuristic online designs for the joint energy and task allocation when the knowledge of CSI/TSI is only causally known. Finally, numerical results show that the proposed joint energy and task allocation designs achieve significantly smaller energy consumption than benchmark schemes with only local computing or full offloading at the user, and the proposed heuristic online designs perform close to the optimal offline solutions and considerably outperform the conventional myopic designs.

中文翻译：

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无线供电移动边缘计算系统的最佳能量分配和任务卸载策略

本文研究了一种单用户无线供电移动边缘计算 (MEC) 系统，其中一个多天线能量发射器 (ET) 采用能量波束成形向用户进行无线功率传输 (WPT)，用户依赖于收集的能量在本地执行一部分任务并将另一部分卸载到与 MEC 服务器集成的接入点 (AP) 以进行远程执行。与考虑静态无线信道和用户计算任务的先前工作不同，本文考虑了由于信道波动和动态任务随时间到达而引起的能量和任务因果关系约束。为了实现节能的联合 WPT-MEC 设计，我们在确保用户成功执行任务的同时，最大限度地减少了特定有限范围内 ET 的总传输能耗，通过联合优化 WPT 的 ET 传输能量分配和用户的任务分配，用于本地计算和特定有限范围内的卸载。首先，为了表征基本性能限制，我们通过假设信道状态信息 (CSI) 和任务状态信息 (TSI)（即任务到达时间和数量）的完美知识是先验已知的来考虑离线优化. 在这种情况下，我们通过使用凸优化技术获得能量最小化问题的结构良好的最优解。最优方案表明，在静态信道场景下，ET应随时间均匀分配传输能量，用户应采用阶梯式任务分配进行本地计算和卸载，随着执行的任务输入位数随着时间的推移单调增加。它还表明，在具有时变信道的场景中，ET 应该在具有因果支配信道功率增益的时隙上零星地传输能量，并且用户应该应用楼梯任务分配进行本地计算和楼梯注水任务分配进行卸载随着时间的推移单调增加计算水平。接下来，受上面获得的结构化离线解决方案的启发，当 CSI/TSI 的知识只是因果已知时，我们为联合能量和任务分配开发了启发式在线设计。最后，数值结果表明，所提出的联合能量和任务分配设计比仅在用户本地计算或完全卸载的基准方案实现了显着更小的能耗，