  Mobile edge computing (MEC) and millimeter wave (mmWave) communications are
capable of significantly reducing the network's delay and enhancing its
capacity. In this paper we investigate a mmWave and device-to-device (D2D)
assisted MEC system, in which user A carries out some computational tasks and
shares the results with user B with the aid of a base station (BS). We propose
a novel two-timescale joint hybrid beamforming and task allocation algorithm to
reduce the system latency whilst cut down the required signaling overhead.
Specifically, the high-dimensional analog beamforming matrices are updated in a
frame-based manner based on the channel state information (CSI) samples, where
each frame consists of a number of time slots, while the low-dimensional
digital beamforming matrices and the offloading ratio are optimized more
frequently relied on the low-dimensional effective channel matrices in each
time slot. A stochastic successive convex approximation (SSCA) based algorithm
is developed to design the long-term analog beamforming matrices. As for the
short-term variables, the digital beamforming matrices are optimized relying on
the innovative penalty-concave convex procedure (penalty-CCCP) for handling the
mmWave non-linear transmit power constraint, and the offloading ratio can be
obtained via the derived closed-form solution. Simulation results verify the
effectiveness of the proposed algorithm by comparing the benchmarks.
