Outage Constrained Transmit Optimization for Spatially Correlated RIS-Aided MIMO Systems With Imperfect CSI and Phase Errors

It is practically challenging to achieve perfect channel state information (CSI) and ideal reconfigurable intelligent surface (RIS) hardware for the transmission design of RIS-assisted multiple-input multiple-output (MIMO) systems. To address this issue, incorporating phase errors, spatial correlation, and imperfect CSI into a unified outage-constrained beamforming optimization framework can be extended from i.i.d. Rician model to correlated Rician model. Subsequently, the outage constrained power minimizing problem is first transformed into a convex problem through Bernstein-type inequality method. Then, precoder and reflection beamforming are iteratively optimized under the alternate optimization (AO) framework. Especially, the scheme adopts semidefinite relaxation (SDR) technology and element iteration method to optimize the passive beamforming and achieve better performance than Gaussian randomization scheme. The simulation results demonstrate the effectiveness of the proposed scheme in two models. Compared to i.i.d. model, which is more sensitive to CSI errors, correlated model can provide more robust QoS guarantees for large CSI uncertainty sets. Phase errors undermine transmission power under the two models, especially in the i.i.d. model. Further, deploying more RIS elements can effectively improve the transmission power. Ultimately, the proposed approach has the potential to improve transmission robustness in practical scenarios.