and/or destructively to suppress the co-channel interference, both leading to improved wireless link performance [@qqmag]. Hence, different from the conventional half-duplex amplify-and-forward (AF) relay, IRS achieves high beamforming gains by intelligent reflection in a *full-duplex* manner, without consuming any energy or requiring additional time/frequency resource for signal re-generation and re-transmission. Although passive reflect-array antennas have been widely applied in radar and satellite communication systems, their applications in mobile wireless communications are rather limited. This is because traditional passive arrays only allow for fixed phase-shift patterns once fabricated and are thus unable to adapt to the dynamic wireless channel induced by user mobility. Fortunately, the advances in radio frequency (RF) micro electromechanical systems (MEMS) and metamaterial (e.g., metasurface) have made it feasible to reconfigure the phase shifts in real time [@metasur], thus greatly enhancing the functionality and applicability of IRS for wireless communications.

Existing works on IRS [@qqtwc; @qqicassp; @debtwc; @mmwre; @irssw] mainly assume perfect channel state information (CSI) at the base station (BS)/IRS, based on which the design parameters are optimized to enhance the system performance. In [@debtwc2] and [@irsstatscsi], only statistical CSI is required for the design problem since large-scale antenna array systems are deployed and therefore deterministic equivalent 