Performance Analysis of RIS-Assisted Communications With Element Grouping and Spatial Correlation

We investigate the performance of a reconfigurable intelligent surface (RIS) assisted single-input single-output (SISO) communication system where RIS elements are narrowly spaced so that the channels between the RIS elements and receiver are spatially correlated. Adjacent RIS elements are grouped together to reduce the channel estimation overhead. The statistical properties of the optimal received SNR are analytically derived and these are used to characterize the coverage probability of the system. An analytical upper bound for the average achievable rate is also derived. This analysis provides insight into the impact of the grouping strategy and element spatial channel correlation level on the coverage probability and the achievable rate of the system. Numerical results validate the tightness of the closed-form expressions. Our results show that the average achievable rate for a given group size is higher for the spatially correlated RIS elements as compared to the uncorrelated configuration.