Achievable Rate in RIS-Aided MU-MIMO System Using Location Information for Phase Shift Design

Reconfigurable intelligent surface (RIS) is a promising technology for wireless communication systems. In order to design the beam from RIS to users, the users' positions are usually adopted to calculate the angle of departure (AoD) and angle of arrival (AoA) information. The users' positions from GPS or other localization system may not be accurate, thus degrades the performance of RIS-aided communication system. To this end, we analyze the achievable rate using the observed users' positions for beamforming design in multi-user multiple-input multiple-output (MU-MIMO) system. Based on the observed users' positions, approximate beamforming from RIS to users is designed. Moreover, a user-side analog combining vector based on users' positions is designed to maximize the received signal strength. Furthermore, the closed-form expression of the achievable rate is derived when the users' position errors follow Gaussian distributions. To verify the impact of observed users' positions, simulations demonstrate the derived closed-form achievable rate and numerical rate versus the mean and variance of position error, as well as the number of user antennas, respectively.