An Analysis of Spatial Correlation in RIS-Assisted Wireless Networks

In this paper, we analyze the impact of spatial correlation between the elements of reconfigurable intelligent surface (RIS) arrays considering both phase-optimized arrays providing a quadratic signal-to-noise ratio (SNR) gain as well as arrays without phase optimization providing a linear gain. The analysis shows that while spatial correlation degrades performance when the RIS array is phase-optimized, it significantly improves performance in the case of arrays without phase optimization. We develop analytic SNR expressions, which show that in RIS arrays without phase optimization, spatial correlation leads to the appearance of a quadratic term whose magnitude increases with the amount of correlation, and we provide simulation results, which corroborate the analytic results. Our findings suggest that spatial correlation can be exploited to reduce the number of pilots needed for channel estimation and signal detection, thus reducing both the receiver complexity and the overhead required for configuration of the RIS array.