The future 5G wireless networks aim to support high-rate data communications and high-speed mobile computing.To achieve this goal, the mobile edge computing (MEC)and device-to-device (D2D) communications have been recently developed, both of which take advantage of the proximity for better performance. In this paper, we integrate the D2D communications with MEC to further improve the computation capacity of the cellular networks, where the task of each device can be offloaded to an edge node and a nearby D2D device.We aim to maximize the number of devices supported by the cellular networks with the constraints of both communication and computation resources. The optimization problem is formulated as a mixed integer non-linear problem, which is not easy to solve in general. To tackle it, we decouple it into two sub problems. The first one minimizes the required edge computation resource fora given D2D pair, while the second one maximizes the number of supported devices via optimal D2D pairing. We prove that the optimal solutions to the two sub problems compose the optimal solution to the original problem. Then, the optimal algorithm to the original problem is developed by solving two sub problems,and some insightful results, such as the optimal transmit power allocation and the task offloading strategy, are also highlighted.Our proposal is finally tested by extensive numerical simulation results, which demonstrate that combining D2D communications with MEC can significantly enhance the computation capacity of the system.
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