The combination of mobile edge computing (MEC) and wireless power transfer (WPT) is recognized as a promising technology to solve the problem of limited battery capacities and insufficient computation capabilities of mobile devices. This technology can transfer energy to users by radio frequency (RF) in wireless powered mobile edge computing. The user converts the harvested energy, stores it in the battery, and utilizes the harvested energy to execute corresponding local computing and offloading tasks. This paper adopts the Frequency Division Multiple Access (FDMA) technique to achieve task offloading from multiple mobile devices to the MEC server simultaneously. Our objective is to study multiuser dynamic joint optimization of computation and wireless resource allocation under multiple time blocks to solve the problem of maximizing residual energy. To this end, we formalize it as a nonconvex problem that jointly optimizes the number of offloaded bits, energy harvesting time, and transmission bandwidth. We adopt convex optimization technology, combine with Karush–Kuhn–Tucker (KKT) conditions, and finally transform the problem into a univariate constrained convex optimization problem. Furthermore, to solve the problem, we propose a combined method of Bisection method and sequential unconstrained minimization based on Reformulation-Linearization Technique (RLT). Numerical results demonstrate that the performance of our joint optimization method outperforms other benchmark schemes for the residual energy maximization problem. Besides, the algorithm can maximize the residual energy, reduce the computation complexity, and improve computation efficiency.

With the rapid popularity of mobile devices (MDs), mobile edge computing (MEC) networks and wireless power transmission (WPT) will receive more attention. Naturally, by integrating these two technologies, the inherent energy consumption during task execution can be effectively reduced, and the collected energy can be provided to charge the MD. In this article, our research focuses on extending the battery time of MDs by maximizing the harvested energy and minimizing the consumed energy in the MEC–WPT system, which is formulated as a residual energy maximization problem and also a non-convex optimization problem. On the basis of study on maximizing the residual energy under multi-users and multi-time blocks, we propose an effective jointly optimization method (i.e., jointly optimize the energy harvesting time, task-offloading time, task-offloading size and the MDs’ CPU frequency), which combines the convex optimization method and the augmented Lagrangian to solve the residual energy maximum problem. We leverage Time Division Multiple Access (TMDA) mode to coordinate computation offloading. Simulation results show that our scheme has better performance than the benchmark schemes on maximizing residual energy. In particular, our proposed scheme is outstanding in the failure rate of multiple MDs and can adapt to the task size to minimize the failure rate.

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