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 cancelation (SIC) to efficiently decode all users' offloaded tasks for remote execution. In particular, we pursue energy-efficient MEC designs by considering two cases with partial and binary offloading, respectively. 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 mixed Boolean convex optimization 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.
