Effect of Spatial Correlation on RIS-Assisted Wireless Systems Using Pilot-Aided Channel Estimation

In this paper, we investigate the effect of spatial correlation on the performance of wireless systems with reconfigurable intelligent surface (RIS) arrays using pilot-aided channel estimation. The RIS array is partitioned into several tiles, a pilot is inserted at or near the center of each tile, and the phase of the channel coefficient estimate at the pilot location is used to determine a common phase shift for configuring all RIS elements of that tile. The analysis shows that while a large number of pilots are needed in the absence of spatial correlation to approach the performance of optimally configured RIS arrays, a small number is sufficient in the presence of spatial correlation. The implication of this is that spatial correlation between the RIS array elements appears as a desirable feature, which not only reduces the number of pilots needed for channel estimation at the base station and the receiver complexity, but also the overhead involved in the feedback of the phase information for configuring the elements of the RIS array.