Practical RIS-Aided Multiuser Communications With Imperfect CSI: Practical Model, Amplitude Feedback, and Beamforming Optimization

Reconfigurable intelligent surfaces (RIS) can dynamically reconstruct wireless environments to enhance spectral efficiency. However, most existing studies have ignored the impact of the phase error and imperfect amplitude gain of the RIS. In this paper, we investigate the practical RIS-aided multiuser communication systems by maximizing the sum of users' average achievable rate, filling the current research gap. Specifically, a novel RIS phase shift design approach, namely amplitude feedback (AF), is proposed by utilizing the coupling relationship between the amplitude and phase to derive the optimal phase shift under the worst phase error. The feasibility of AF is demonstrated by proving the measurability of amplitude response through the electromagnetic theory. We propose a channel estimation design with low pilot overhead and provide an effective closed-form achievable rate to approximate the average achievable rate. Moreover, an efficient optimization algorithm is proposed to achieve the optimal closed-form precoding at the base station and the optimal trade-off design between the amplitude and phase of RIS, and the algorithm is extended to active RIS systems. Numerical results demonstrate that our proposed AF method and optimization algorithm can efficiently improve the performance in terms of achievable sum rate compared to existing methods.