Impact of Hardware Impairment on the Joint Reconfigurable Intelligent Surface and Robust Transceiver Design in MU-MIMO System

Reconfigurable intelligent surface (RIS) is a revolutionary passive radio technique to facilitate capacity enhancement beyond the current massive multiple-input multiple-output (MIMO) transmission. However, the potential hardware impairment (HWI) of the RIS usually causes inevitable performance degradation and the amplification of imperfect CSI. These impacts still lack full investigation in the RIS-assisted wireless network. This paper developed a robust joint RIS and transceiver design algorithm to minimize the worst-case mean square error (MSE) of the received signal under the HWI effect and imperfect channel state information (CSI) in the RIS-assisted multi-user MIMO (MU-MIMO) wireless network. Specifically, since the proposed robust joint RIS and transceiver design problem yields non-convex characteristics under severe HWI, an iterative three-step convex algorithm is developed to approach the optimality by relaxation and convex transformation. Compared with the state-of-the-art baselines that ignore the HWI, the proposed robust algorithm inhibits the destruction of HWI while raising the worst-case MSE effectively in several numerical simulations. Moreover, due to the properties of the HWI, the performance loss is notable under the magnification of the number of reflected elements in the RIS-assisted MU-MIMO wireless network.