Robust Transmission Design for IRS Aided Distributed MISO with Imperfect Cascaded CSIT

In this paper, we propose the robust transmission design for an intelligent reflecting surface (IRS) aided distributed multi-antenna system under imperfect cascaded channel state information at transmitter (CSIT). The active transmit beamforming at access points and reflection coefficients at IRS are jointly optimized to maximize the worst-case sum rate subject to the transmit power constraint and unit-modulus reflection coefficients for all possible channel realizations in the uncertainty region. We propose the conservative approximation (CA) based robust optimization. Under the framework of alternative optimization algorithm, the transmit beamforming is first solved via weighted minimum mean square error method with the fixed reflection coefficients, and then the reflection coefficients are optimized via nearest point projection method. Since the CA method can introduce the rate saturation for non-scaling CSIT as signal-to-noise ratio scales, we investigate another robust optimization algorithm, cutting-set (CS) method, which solves the problem by alternating between an optimization step for a finite subset of the uncertainty region, and a pessimization step for updating the subset. The numerical simulation results illustrate that the CS method can reap better sum-rate performance than CA, and the deleterious effect of imperfect cascaded CSIT on the performance becomes more significant with the increase of the reflecting elements.