Reconfigurable Intelligent Surfaces Assisted MIMO-MAC with Partial CSI

This paper considers the application of reconfigurable intelligent surfaces (RISs) to assist multiuser multipleinput multiple-output multiple access channel (MIMO-MAC) systems. In contrast to most existing works on RIS-assisted systems assuming the availability of full channel state information (CSI), only partial CSI is required in our investigation, including the instantaneous CSI of the channel from a RIS to a base station and the statistical CSI of the channels from user terminals (UTs) to the RIS. We investigate the joint design of both the transmit covariance matrices of the UTs and the RIS phase shift matrix under the system global energy efficiency (GEE) maximization criterion. To maximize the GEE, we first obtain closed-form solutions for the eigenvectors of the optimal transmit covariance matrices of the UTs. Then, we derive an asymptotic expression of the objective function with the aid of random matrix theory to reduce the computational cost. We further propose a lowcomplexity algorithm to tackle the GEE maximization problem with guaranteed convergence, capitalizing on the approaches of alternating optimization, fractional programming, and sequential optimization. Numerical results substantiate the effectiveness of the proposed approach as well as the GEE performance gains provided by RIS-assisted MIMO-MAC systems.