  Reconfigurable intelligent surface (RIS) has emerged as a promising
technology for achieving high spectrum and energy efficiency in future wireless
communication networks. In this paper, we investigate an RIS-aided single-cell
multi-user mobile edge computing (MEC) system where an RIS is deployed to
support the communication between a base station (BS) equipped with MEC servers
and multiple single-antenna users. To utilize the scarce frequency resource
efficiently, we assume that users communicate with BS based on a non-orthogonal
multiple access (NOMA) protocol. Each user has a computation task which can be
computed locally or partially/fully offloaded to the BS. We aim to minimize the
sum energy consumption of all users by jointly optimizing the passive phase
shifters, the size of transmission data, transmission rate, power control,
transmission time and the decoding order. Since the resulting problem is
non-convex, we use the block coordinate descent method to alternately optimize
two separated subproblems. More specifically, we use the dual method to tackle
a subproblem with given phase shift and obtain the closed-form solution; and
then we utilize penalty method to solve another subproblem for given power
control. Moreover, in order to demonstrate the effectiveness of our proposed
algorithm, we propose three benchmark schemes: the time-division multiple
access (TDMA)-MEC scheme, the full local computing scheme and the full
offloading scheme. We use an alternating 1-D search method and the dual method
that can solve the TDMA-based transmission problem well. Numerical results
demonstrate that the proposed scheme can increase the energy efficiency and
achieve significant performance gains over the three benchmark schemes.
