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

## TL;DR

This paper analyzes the asymptotic behavior of the max-min SINR in RIS-assisted MISO systems, providing deterministic approximations and optimizing RIS phase shifts for different channel rank scenarios.

## Contribution

It introduces a novel asymptotic analysis of the minimum SINR in RIS-assisted MISO systems and develops deterministic approximations for optimal precoding and RIS phase optimization.

## Key findings

- RIS can outperform half-duplex relays with few elements
- Large RISs are required to outperform full-duplex relays
- Asymptotic approximations enable efficient RIS phase optimization

## Abstract

This work focuses on the downlink of a single-cell multi-user system in which a 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 offer unprecedented spectral efficiency gains by utilizing $N$ passive reflecting elements that induce phase shifts on the impinging electromagnetic waves to smartly reconfigure the signal propagation environment. We study the minimum signal-to-interference-plus-noise ratio (SINR) achieved by the optimal linear precoder (OLP), that maximizes the minimum SINR subject to a given power constraint for any given RIS phase matrix, for the cases where the LoS channel matrix between the BS and the RIS is of rank-one and of full-rank. In the former scenario, the minimum SINR achieved by the RIS-assisted link is bounded by a quantity that goes to zero with $K$. For the high-rank scenario, we develop accurate deterministic approximations for the parameters of the asymptotically OLP, which are then utilized to optimize the RIS phase matrix. Simulation results show that RISs can outperform half-duplex relays with a small number of passive reflecting elements while large RISs are needed to outperform full-duplex relays.