Robust Transmission Design for RIS-Assisted High-Speed Train Communication Coverage Enhancement With Imperfect Cascaded Channels

Reconfigurable intelligent surface (RIS) has recently been gained attention as an effective technique improving the coverage and performance of communication systems by creating additional communication links. Deployment of RIS is crucial for overcoming signal coverage limitations, especially in high-speed train (HST) scenarios. Considerable research has been performed assuming perfect channel state information (CSI). However, due to the rapidly time-varying fading channels and feedback delays, achieving perfect CSI at the base station (BS) is not feasible in the HST scenarios. To tackle this problem, this paper investigates a robust design strategy for RIS-aided HST communication coverage enhancement, particularly focusing on cascaded BS-RIS-user channels at BS (CBRUB). The study explores the optimization problem under two types distinct of models: centered on minimizing transmit power subject to worst-case rate constraints within the bounded CSI error (BCSIE) model, and the other focusing on outage probability (OP) constraints under the statistical CSI error (SCSIE) model. We use the S-procedure to approximate the non-convex (NC) constraints, converting the worst-case rate constraints into linear matrix inequalities. Additionally, the Bernstein-type inequality is applied to transform the OP constraints into second-order cone constraints and linear inequalities. The simulation analysis results show that CBRUB errors have a significant effect on system performance compared to direct CSI errors.