Passive Beamforming and Information Transfer Design for Reconfigurable Intelligent Surfaces Aided Multiuser MIMO Systems

This paper investigates the passive beamforming and information transfer (PBIT) technique for the multiuser multiple-input multiple-output (MIMO) systems with the aid of a reconfigurable intelligent surface (RIS), where the RIS enhances the primary communication via passive beamforming and at the same time delivers additional information by the spatial modulation (which adjusts the on-off states of the reflecting elements). For the passive beamforming design, we propose to maximize the sum channel capacity of the RIS-aided multiuser MIMO channel and formulate the problem as a two-step stochastic program. A sample average approximation (SAA) based iterative algorithm is developed for the efficient passive beamforming design of the considered scheme. To strike a balance between complexity and performance, we then propose a simplified beamforming algorithm by approximating the stochastic program as a deterministic alternating optimization problem. For the receiver design, the signal detection at the receiver is a bilinear estimation problem since the RIS information is multiplicatively modulated onto the reflected signals of the reflecting elements. To solve this bilinear estimation problem, we develop a turbo message passing (TMP) algorithm in which the factor graph associated with the problem is divided into two modules: one for the estimation of the user signals and the other for the estimation of the RIS's on-off states. The two modules are executed iteratively to yield a near-optimal low-complexity solution. Furthermore, we extend the design of the multiuser MIMO PBIT scheme from single-RIS to multi-RIS, by leveraging the similarity between the single-RIS and multi-RIS system models. Extensive simulation results are provided to demonstrate the advantages of our passive beamforming and receiver designs.