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Edge networks offer a promising solution for satisfying the increasing energy and computation needs of user devices with new data intensive services. A mutil-access edge computing (MEC) system with collocated MEC servers and base-stations/access points (BS/AP) has the ability to support multiple users for both data computation and wireless charging. We propose an integrated solution for wireless charging with computation offloading to satisfy the largest feasible proportion of requested wireless charging while keeping the total energy consumption at the minimum, subject to the MEC-AP transmit power and latency constraints. We design a novel nested algorithm to optimally solve the resulting non-convex problem in order to jointly perform data partitioning, time allocation, transmit power control and design the optimal energy beamforming for wireless charging. The proposed resource allocation scheme offers minimal energy consumption compared to other schemes while also delivering a higher amount of wirelessly transferred charge to the users. The results also show that compared to other solutions, the energy charging beams for minimum consumption have a wider main lobe, smaller side lobes, with an absence of the back lobe. Even with data offloading, the proposed solution shows significant charging performance, comparable to the case of charging alone, hence showing the effectiveness of performing partial computation offloading jointly with wireless charging.
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