Beamforming Saturation in Two-Timescale RIS-assisted Communication

Abstract: This paper considers wireless communication assisted by a reconfigurable intelligent surface (RIS), focusing on the two-timescale approach, in which the RIS phase shifts are optimized based on channel statistics to mitigate the overheads associated with channel estimation. It is shown that, while the power captured by the RIS scales linearly with the number of its elements, the two-timescale beamforming gain upon re-radiation towards the receiver saturates rapidly as the number of RIS elements increases, for a broad class of power angular spectra (PAS). The ultimate achievable gain is determined by the decay rate of the PAS in the angular domain, which directly influences how rapidly spatial correlations between RIS elements diminish. The implications of this saturation on the effectiveness of RIS-assisted communications are discussed.