Optimal Energy Allocation and Task Offloading Policy for Wireless Powered Mobile Edge Computing Systems

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 & x2019;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.