Reconfigurable Intelligent Surface Aided Communications: Asymptotic Analysis under Imperfect CSI

This work studies the asymptotic sum-rate performance of a multi-user reconfigurable intelligent surface (RIS) assisted-multiple-input single-output (MISO) downlink system under imperfect CSI and Rayleigh and Rician fading. We first extend the existing least squares (LS) ON/OFF channel estimation protocol to a multi-user system, where we derive minimum mean squared error (MMSE) estimates of all RIS-assisted channels over multiple sub-phases. We also consider a low-complexity direct estimation (DE) scheme, where the BS obtains the MMSE estimate of the overall channel in a single sub-phase. Under both protocols, the BS implements maximum ratio transmission (MRT) precoding while the RIS phases are studied in the large system limit, where we derive deterministic equivalents of the signal- to-interference-plus-noise ratio (SINR) and the sum-rate. The derived asymptotic expressions reveal that under Rayleigh fading, the RIS phase-shift values do not play a significant role in improving the sum-rate but the RIS still provides an array gain. However, under Rician fading, we show that RIS provides both array and reflect beamforming gains. A projected gradient ascent-based algorithm is used to optimize the phase-shifts under both ON/OFF and DE protocol. Simulation results show that the DE of the overall channel yields better downlink performance when considering large systems.