Channel Estimation Method and Phase Shift Design for Reconfigurable Intelligent Surface Assisted MIMO Networks

This paper deals with channel estimation in reconfigurable intelligent surface (RIS) aided multiple-input multiple-output (MIMO) time-division duplexing systems. In a typical RIS assisted communication, an RIS is deployed in the close proximity of communication devices, thus resulting in ill-conditioned low-rank channel matrices. To effectively estimate these channels, we propose a two-stage channel estimation method. Specifically, in the first stage, the direct MIMO channel between the end terminals is estimated by utilizing the conventional uplink training approach. In the second stage, after the training process, it is noticed that the RIS channel estimation problem becomes equivalent to a well-known dictionary learning problem. Therefore, we propose to use a bilinear adaptive vector approximate message passing (BAdVAMP) algorithm to estimate RIS channels, which has been shown to be accurate and robust for ill-conditioned dictionary learning problems in compressed sensing. We also propose a phase shift design (passive beamforming) for the RIS by formulating an optimization problem that maximizes the total channel gain at the receiver. Due to its non-convex nature, an approximate closed-form solution is proposed to obtain the phase shift matrix. Numerical results show that the proposed BAdVAMP based RIS channel estimation performs better than its counterpart bilinear generalized AMP (BiGAMP) scheme.