Two-Timescale Hybrid Analog-Digital Beamforming for mmWave Full-Duplex MIMO Multiple-Relay Aided Systems

Due to the severe pathloss experienced by electromagnetic waves in the millimeter wave (mmWave) band, a substantial challenge in their design is to have an adequate coverage area. With the objective of improving the coverage area and the sum rate attained, we conceive new full-duplex (FD) mmWave multiple-input multiple-output (MIMO) multiple-relay systems. Specifically, we propose a novel two-timescale analog-digital hybrid beamforming scheme for maximizing the sum rate, while reducing the system's complexity and the channel state information (CSI) signalling overhead, as well as mitigating both the effects of self-interference and that of outdated CSIs caused by the associated delays. In the proposed scheme, the long-timescale analog beamforming matrices are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. By contrast, the short-timescale digital beamforming matrices are optimized more frequently - namely for each time slot - based on the low-dimensional effective CSI matrices available on a real-time basis. We develop both an efficient analog beamforming algorithm based on the cut-set bound as well as on stochastic successive convex approximation (SSCA) and an innovative digital beamforming algorithm that relies on the theory of penalty dual decomposition (PDD), where our design objective is to maximize the system's sum rate. Both the convergence properties and the computational complexity of the proposed algorithms are also examined. Our simulation results show that the proposed two-timescale hybrid beamforming design significantly outperforms the conventional beamformers both in terms of requiring a lower CSI-signalling overhead and a higher sum rate in the face of realistic outdated CSIs.