Statistical CSI-based design for RIS-assisted communication systems

Reconfigurable intelligent surfaces (RISs) have attracted considerable attention over the past years. A RIS can smartly adjust the phase of incident wavefronts and create anomalous reflections towards desired directions. In this letter, we consider a RIS-assisted large antenna system and investigate the ergodic spectral efficiency (SE). By considering a finite dimensional channel, we derive an upper bound on the ergodic SE. Based on this upper bound, we propose an optimal phase shift design by exploiting statistical channel state information. Specifically, we develop a semidefinite relaxation technique and Gaussian randomization procedure for continous phase shift design. Furthermore, an alternating optimization algorithm is applied to the discrete case. Numerical results verify the tightness of the upper bound and the effectiveness of our phase shift design. Considering hardware limitations, we find that a RIS of 2-bit phase adjustable elements achieves the same ergodic SE as the continous phase shift architecture.