  In mobile edge computing (MEC) systems, the wireless channel condition is a
critical factor affecting both the communication power consumption and
computation rate of the offloading tasks. This paper exploits the idea of
cooperative transmission and employing reconfigurable intelligent surface (RIS)
in MEC to improve the channel condition and maximize computation efficiency
(CE). The resulting problem couples various wireless resources in both uplink
and downlink, which calls for the joint design of the user association,
receive/downlink beamforming vectors, transmit power of users, task partition
strategies for local computing and offloading, and uplink/downlink phase shifts
at the RIS. To tackle the challenges brought by the combinatorial optimization
problem, the group sparsity structure of the beamforming vectors determined by
user association is exploited. Furthermore, while the CE does not explicitly
depend on the downlink phase shifts, instead of simply finding a feasible
solution, we exploit the hidden relationship between them and convert this
relationship into an explicit form for optimization. Then the resulting problem
is solved via the alternating maximization framework, and the nonconvexity of
each subproblem is handled individually. Simulation results show that
cooperative transmission and RIS deployment can significantly improve the CE
and demonstrate the importance of optimizing the downlink phase shifts with an
explicit form.
