Mobile edge computing (MEC) is considered as an efficient method to relieve the computation burden of mobile devices. In order to reduce the energy consumption and time delay of mobile devices (MDs) in MEC, multiple users multiple input and multiple output (MU-MIMO) communications is considered to be applied to the MEC system. The purpose of this paper is to minimize the weighted sum of energy consumption and time delay of MDs by jointly considering the offloading decision and MU-MIMO beamforming problems. And the resulting optimization problem is a mixed-integer non-linear programming problem, which is NP-hard. To solve the optimization problem, a semidefinite relaxation based algorithm is proposed to solve the offloading decision problem. Then, the MU-MIMO beamforming design problem is handled with a newly proposed fractional programming method. Simulation results show that the proposed algorithms can effectively reduce the energy consumption and time delay of the computation offloading.
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