  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.
