Achievable Rate Lower Bound and Bottleneck Analysis for IRS-Assisted MISO Systems With Channel Estimation Errors

Abstract

Intelligent reflecting surfaces (IRSs) have attracted extensive research interest for their passive beamforming gains. However, practical IRS-assisted systems rely heavily on accurate channel state information (CSI), which inevitably suffers from estimation errors. Motivated by this challenge, we first investigate the impact of channel estimation errors on IRS-assisted multiple-input single-output (MISO) downlink systems. Specifically, based on the estimated CSI used for transmission design, we derive a rigorous achievable rate lower bound and exactly decompose the residual variance entering the bound into direct and cascaded components. We further derive a threshold for the number of IRS elements to identify which residual component dominates the average mean-square error (MSE) of the effective channel vector. Under equal normalized error variances, simulations show a transition from direct residual dominance near the access point (AP) to cascaded residual dominance as the user approaches the IRS or the number of IRS elements increases. Under unequal absolute error variances, the direct residual component can instead become dominant in the considered setting.