Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise

We consider a fading channel in which multiantenna transmitter communicates with multi-antenna receiver through reconfigurable intelligent surface (RIS) that is made of N passive scatterers impaired by phase noise. The beamforming vector at the transmitter, combining receiver, and shifts are optimized order to maximize signal-to-noise-ratio (SNR) receiver. By assuming Rayleigh (or line-of-sight propagation) on transmitter-RIS link RIS-receiver link, we prove SNR random variable equivalent distribution product three two) independent variables whose distributions approximated two one) gamma sum scaled non-central chi-square variables. proposed analytical framework allows us quantify robustness RIS-aided transmission channels. For example, amount experienced transmitter-RIS-receiver linearly decreases ? 1. This proves RISs large size can be effectively employed make less severe wireless channels more reliable.