Two-Timescale-Based Beam Training for RIS-Aided Millimeter-Wave Multi-User MISO Systems

Reconfigurable intelligent surfaces (RISs), as a promising technology for 6 G communications, have received considerable attention. Herein, we investigate the downlink precoding in the RIS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) system, where the access point (AP) uses hybrid digital and analog precoders. Due to the constraints of practical hardware and the difficulty of acquiring channel state information, we consider codebook-based passive beamforming and analog beamforming, and then formulate the downlink precoding problem as a mixed-integer nonlinear programming (MINLP) problem. To solve this NP-hard MINLP problem with low channel estimation overheads, we investigate beam training for the codebook-based passive beamforming and analog beamforming, and the MINLP problem is then reduced to a traditional MU-MISO precoding problem. To further reduce the beam training overheads, we propose a two-timescale-based beam training (TT-BT) algorithm. We prove that the TT-BT algorithm achieves the maximum codebook-based passive and analog beamforming gain. To avoid the limitations imposed the use of the TT property, we design the analog precoder by aligning the analog beamforming to RISs. Moreover, we characterize the rate loss due to codebook-based quantization. Compared with the empirical BT (EBT) algorithm, the proposed TT-BT algorithm achieves better performance with significantly lower training and feedback overheads.