Joint Transmit Beamforming and Phase Shift Design for Reconfigurable Intelligent Surface Assisted MIMO Systems

Abstract

Reconfigurable intelligent surface (RIS) becomes an increasingly important technology in sixth-generation (6G). The key aspect of RIS is smartly configuring the wireless propagation environment and providing supplementary links to enhance the signal transmission between the BS and the UE. In recent years, there has been a surge of interest in RISs in joint active and passive beamforming design to improve the system performance of RIS-assisted systems with the assumption of uncorrelated environments. To date, far too little attention has been paid to the situations that consider the correlations among the antennas and RIS reflecting elements. In this article, we focus on an RIS-assisted multiple-input multiple-output (MIMO) system under spatial fading correlations, with the statistical channel state information (CSI) known at the transmitter and the RIS. We aim to maximize the ergodic spectral efficiency (SE) of this system. At first, we derive a tight upper bound on the ergodic SE. Concise upper bounds are also shown in special cases of independent and identically distributed (i.i.d.) Rician and Rayleigh, correlated Rayleigh as well as extreme Rician MIMO channels. Next, we propose a benchmark algorithm based on the semidefinite relaxation (SDR) technique to jointly optimize the beamforming vector at the transmitter and phase shift matrix of the RIS. Alternative manner is utilised until both arrive at convergence. Furthermore, we apply the dominant eigen direction transmission scheme to do beamforming in order to reduce the complexity of the algorithm, and consider the column control of the RIS to facilitate practical hardware implementation. Numerical results show the tightness of the upper bounds and the effectiveness of our proposed algorithm for improving the ergodic SE as well as the effects of freedom degrees on performances.