  In this paper, we study a mobile edge computing (MEC) system with the mobile
device aided by multiple relay nodes for offloading data to an edge server.
Specifically, the modes of decode-and-forward (DF) with
time-division-multiple-access (TDMA) and frequency-division-multiple-access
(FDMA), and the mode of amplify-and-forward (AF) are investigated, which are
denoted as DF-TDMA, DF-FDMA, and AF, respectively. Our target is to minimize
the total energy consumption of the mobile device and multiple relay nodes
through optimizing the allocation of computation and communication resources.
Optimization problems under the three considered modes are formulated and shown
to be non-convex. For DF-TDMA mode, we transform the original non-convex
problem to be a convex one and further develop a low computation complexity yet
optimal solution. In DF-FDMA mode, with some transformation on the original
problem, we prove the mathematical equivalence between the transformed problem
in DF-FDMA mode and the problem under DF-TDMA mode. In AF mode, the associated
optimization problem is decomposed into two levels, in which monotonic
optimization is utilized in upper level and successive convex approximation
(SCA) is adopted to find the convergent solution in the lower level. Numerical
results prove the effectiveness of our proposed methods under various working
modes.
