  This paper studies a multiuser mobile edge computing (MEC) system, in which
one base station (BS) serves multiple users with intensive computation tasks.
We exploit the multi-antenna non-orthogonal multiple access (NOMA) technique
for multiuser computation offloading, such that different users can
simultaneously offload their computation tasks to the multi-antenna BS over the
same time/frequency resources, and the BS can employ successive interference
cancellation (SIC) to efficiently decode all users' offloaded tasks for remote
execution. We aim to minimize the weighted sum-energy consumption at all users
subject to their computation latency constraints, by jointly optimizing the
communication and computation resource allocation as well as the BS's decoding
order for SIC. For the case with partial offloading, the weighted sum-energy
minimization is a convex optimization problem, for which an efficient algorithm
based on the Lagrange duality method is presented to obtain the globally
optimal solution. For the case with binary offloading, the weighted sum-energy
minimization corresponds to a {\em mixed Boolean convex problem} that is
generally more difficult to be solved. We first use the branch-and-bound (BnB)
method to obtain the globally optimal solution, and then develop two
low-complexity algorithms based on the greedy method and the convex relaxation,
respectively, to find suboptimal solutions with high quality in practice. Via
numerical results, it is shown that the proposed NOMA-based computation
offloading design significantly improves the energy efficiency of the multiuser
MEC system as compared to other benchmark schemes. It is also shown that for
the case with binary offloading, the proposed greedy method performs close to
the optimal BnB based solution, and the convex relaxation based solution
achieves a suboptimal performance but with lower implementation complexity.
