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This work focuses on the downlink of a single-cell multi-user system in whicha base station (BS) equipped with $M$ antennas communicates with $K$single-antenna users through a reconfigurable intelligent surface (RIS)installed in the line-of-sight (LoS) of the BS. RIS is envisioned to offerunprecedented spectral efficiency gains by utilizing $N$ passive reflectingelements that induce phase shifts on the impinging electromagnetic waves tosmartly reconfigure the signal propagation environment. We study the minimumsignal-to-interference-plus-noise ratio (SINR) achieved by the optimal linearprecoder (OLP), that maximizes the minimum SINR subject to a given powerconstraint for any given RIS phase matrix, for the cases where the LoS channelmatrix between the BS and the RIS is of rank-one and of full-rank. In theformer scenario, the minimum SINR achieved by the RIS-assisted link is boundedby a quantity that goes to zero with $K$. For the high-rank scenario, wedevelop accurate deterministic approximations for the parameters of theasymptotically OLP, which are then utilized to optimize the RIS phase matrix.Simulation results show that RISs can outperform half-duplex relays with asmall number of passive reflecting elements while large RISs are needed tooutperform full-duplex relays.

Asymptotic Max-Min SINR Analysis of Reconfigurable Intelligent Surface Assisted MISO Systems