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Intelligent reflecting surfaces (IRS) have emerged as a promising technologyto enhance the performance of wireless communication systems. By activelymanipulating the wireless propagation environment, IRS enables efficient signaltransmission and reception. In recent years, the integration of IRS withfull-duplex (FD) communication has garnered significant attention due to itspotential to further improve spectral and energy efficiencies. IRS-assisted FDsystems combine the benefits of both IRS and FD technologies, providing apowerful solution for the next generation of cellular systems. In thismanuscript, we present a novel approach to jointly optimize active and passivebeamforming in a multiple-input-multiple-output (MIMO) FD system assisted by anIRS for weighted sum rate (WSR) maximization. Given the inherent difficulty inobtaining perfect channel state information (CSI) in practical scenarios, weconsider imperfect CSI and propose a statistically robust beamforming strategyto maximize the ergodic WSR. Additionally, we analyze the achievable WSR for anIRS-assisted MIMO FD system under imperfect CSI by deriving both the lower andupper bounds. To tackle the problem of ergodic WSR maximization, we employ theconcept of expected weighted minimum mean squared error (EWMMSE), whichexploits the information of the expected error covariance matrices and ensuresconvergence to a local optimum. We evaluate the effectiveness of our proposeddesign through extensive simulations. The results demonstrate that our robustapproach yields significant performance improvements compared to the simplisticbeamforming approach that disregards CSI errors, while also outperforming therobust half-duplex (HD) system considerably

IRS Assisted MIMO Full Duplex: Rate Analysis and Beamforming Under Imperfect CSI