Latency Minimization for mmWave D2D Mobile Edge Computing Systems: Joint Task Allocation and Hybrid Beamforming Design

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 assume partial offloading model and the task can be partitioned into two portions: the first part is computed locally at user A, while the second part is transmitted to the BS and computed by the MEC server. The computational results are then sent to user B through a D2D link and via the link from the BS to user B, respectively. To support computation offloading, both the users and the BS are equipped with multiple antennas and employ analog and digital (A/D) hybrid beamforming. Moreover, 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.