Efficient Channel Estimation for RIS

We propose a two-stage channel estimation procedure for a multi-antenna base station (BS) assisted by a reconfigurable intelligent surface (RIS). In Stage 1, the BS estimates the direct link from the user to BS and the UE-to-RIS link using partial knowledge of the RIS-to-BS channel. To reduce pilot overhead, the UE-to-RIS channel state information (CSI) is interpolated from channel estimates for a subset of active RIS elements. CSI obtained in Stage 1 is then used to inform the RIS phase design and form an initial estimate of the global channel, which is refined with more pilot symbols in Stage 2 and subsequently used to perform uplink processing during data transmission. We examine the normalised mean squared error of the global channel estimate from Stage 1 under various channel conditions, and the spectral efficiency (SE) following Stage 2. Using physically-motivated models, we are able to study the impact of ray angular spread, RIS size, and inter-element spacing on the global channel estimation accuracy, and reveal the detrimental effect of errors in the RIS-to-BS channel knowledge. The SE following Stage 2 approaches the performance achieved with perfect CSI, revealing the greater importance of CSI accuracy for processing as opposed to RIS design.