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

Intelligent reflecting surfaces (IRS) have emerged as a promising technology to enhance the performance of wireless communication systems. By actively manipulating the wireless propagation environment, IRS enables efficient signal transmission and reception. In recent years, the integration of IRS with full-duplex (FD) communication has garnered significant attention due to its potential to further improve spectral and energy efficiencies. IRS-assisted FD systems combine the benefits of both IRS and FD technologies, providing a powerful solution for the next generation of cellular systems. In this manuscript, we present a novel approach to jointly optimize active and passive beamforming in a multiple-input-multiple-output (MIMO) FD system assisted by an IRS for weighted sum rate (WSR) maximization. Given the inherent difficulty in obtaining perfect channel state information (CSI) in practical scenarios, we consider imperfect CSI and propose a statistically robust beamforming strategy to maximize the ergodic WSR. Additionally, we analyze the achievable WSR for an IRS-assisted MIMO FD system under imperfect CSI by deriving both the lower and upper bounds. To tackle the problem of ergodic WSR maximization, we employ the concept of expected weighted minimum mean squared error (EWMMSE), which exploits the information of the expected error covariance matrices and ensures convergence to a local optimum. We evaluate the effectiveness of our proposed design through extensive simulations. The results demonstrate that our robust approach yields significant performance improvements compared to the simplistic beamforming approach that disregards CSI errors, while also outperforming the robust half-duplex (HD) system considerably.