Efficient Algorithms for RIS Aided Hybrid Beamforming With MSE Constraints.

In this paper, to stabilize the users’ quality of service (QoS), the symbol detection mean squared error (MSE) constrained hybrid analog and digital beamforming is proposed in millimeter wave (mmWave) system, and the reconfigurable intelligent surface (RIS) is proposed to assist the mmWave system. The inner majorization-minimization (iMM) method is proposed to obtain analog transmitter, RIS and analog receivers, and the alternating direction method of multipliers (ADMM) method is proposed to obtain digital transmitter. The proposed iMM and ADMM methods are faster than the semidefinite relaxation (SDR) and interior point methods, respectively. In order to counter against the changing large-scale path loss, the iMM method is helped by channel normalization to reduce the computational complexity, while the ADMM method is helped by the adaptive parameterizations to robust against the changing large-scale path loss. Simulation results show that the computational times of the proposed method are much faster than other methods, the proposed method is robust against the changing large-scale path loss, and the user’s bit error rate (BER) is stable under small to medium channel estimation errors.