  In this paper, simultaneously transmitting and reflecting (STAR)
reconfigurable intelligent surface (RIS) is investigated in the multi-user
mobile edge computing (MEC) system to improve the computation rate. Compared
with traditional RIS-aided MEC, STAR-RIS extends the service coverage from
half-space to full-space and provides new flexibility for improving the
computation rate for end users. However, the STAR-RIS-aided MEC system design
is a challenging problem due to the non-smooth and non-convex binary amplitude
coefficients with coupled phase shifters. To fill this gap, this paper
formulates a computation rate maximization problem via the joint design of the
STAR-RIS phase shifts, reflection and transmission amplitude coefficients, the
receive beamforming vectors, and energy partition strategies for local
computing and offloading. To tackle the discontinuity caused by binary
variables, we propose an efficient smoothing-based method to decrease
convergence error, in contrast to the conventional penalty-based method, which
brings many undesired stationary points and local optima. Furthermore, a fast
iterative algorithm is proposed to obtain a stationary point for the joint
optimization problem, with each subproblem solved by a low-complexity
algorithm, making the proposed design scalable to a massive number of users and
STAR-RIS elements. Simulation results validate the strength of the proposed
smoothing-based method and show that the proposed fast iterative algorithm
achieves a higher computation rate than the conventional method while saving
the computation time by at least an order of magnitude. Moreover, the resultant
STAR-RIS-aided MEC system significantly improves the computation rate compared
to other baseline schemes with conventional reflect-only/transmit-only RIS.
