  This paper considers a wireless powered multiuser mobile edge computing (MEC)
system, in which a multi-antenna hybrid access point (AP) wirelessly charges
multiple users, and each user relies on the harvested energy to execute
computation tasks. We jointly optimize the energy beamforming and remote task
execution at the AP, as well as the local computing and task offloading, aiming
to minimize the total system energy consumption over a finite time horizon,
subject to causality constraints for both energy harvesting and task arrival at
the users. In particular, we consider a practical scenario with casual task
state information (TSI) and channel state information (CSI), i.e., only the
current and previous TSI and CSI are available, but the future TSI and CSI can
only be predicted subject to certain errors. To solve this real-time resource
allocation problem, we propose an offline-optimization inspired online design
approach. First, we consider the offline optimization case by assuming that the
TSI and CSI are perfectly known a-priori. In this case, the energy minimization
problem corresponds to a convex problem, for which the semi-closed-form optimal
solution is obtained via the Lagrange duality method. Next, inspired by the
optimal offline solution, we propose a sliding-window based online resource
allocation design in practical cases by integrating with the sequential
optimization. Finally, numerical results show that the proposed joint wireless
powered MEC designs significantly improve the system's energy efficiency, as
compared with the benchmark schemes that consider a sliding window of size one
or without such joint optimization.
