Improper Gaussian Signaling Based Robust Transmission Design for RIS-Assisted Communication Systems

Reconfigurable intelligent surface (RIS), with passive reflection elements, has the potential to enhance future wireless communications due to its exceptional flexibility and broad compatibility. However, the performance deteriorates when exact channel state information (CSI) is unavailable, and this effect is even exacerbated when the base station (BS) with only a few transmit antennas serves relatively more users. Fortunately, this issue can be mitigated by utilizing improper Gaussian signaling (IGS). This work explores the robust IGS based resource allocation approach for multi-user communication systems with RIS under conditions of imperfect CSI. Specifically, we formulate a joint optimization framework to design the widely linear beamforming and reflection phase shifts. The objective is to maximize the worst achievable IGS based transmission rate across all users under the bounded model of CSI errors. The formulated non-convex optimization problem involves infinite constraints of CSI errors, along with the RIS's unit-modulus and IGS based rate optimization, which present significant challenges. To address the problem, the non-convex achievable rate of IGS is linearized, and semi-infinite constraints caused by imperfect CSI are converted into tractable linear matrix inequalities. Moreover, the joint resource allocation scheme is obtained via alternatively optimizing beamforming and phase shifts. Numerical experiments verify the proposed approach in enhancing the robustness and performance in various scenarios.