Refracting Reconfigurable Intelligent Surface Assisted URLLC for Millimeter Wave High-Speed Train Communication Coverage Enhancement

High-speed train (HST) has garnered significant attention from both academia and industry due to the rapid development of railways worldwide. Millimeter wave (mmWave) communication, known for its large bandwidth is an effective way to address performance bottlenecks in cellular network based HST wireless communication systems. However, mmWave signals suffer from significant path loss when traversing carriage, posing substantial challenges to cellular networks. To address this issue, reconfigurable intelligent surfaces (RIS) have gained considerable interest for its ability to enhance cell coverage by reflecting signals toward receiver. Ensuring communication reliability, a core performance indicators of ultra-reliable and low-latency communications (URLLC) in fifth-generation systems, is crucial for providing steady and reliable data transmissions along railways, particularly for delivering safety and control messages and monitoring HST signaling information. In this paper, we investigate a refracting RIS-assisted multi-user multiple-input single-output URLLC system in mmWave HST communications. We propose a sum rate maximization problem, subject to base station beamforming constraint, as well as refracting RIS discrete phase shifts and reliability constraints. To solve this optimization problem, we design a joint optimization algorithm based on alternating optimization method. This involves decoupling the original optimization problem into active beamforming design and packet error probability optimization subproblem, and discrete phase shift design subproblems. These subproblems are addressed exploiting Lagrangian dual method and the local search method, respectively. Simulation results demonstrate the fast convergence of the proposed algorithm and highlight the benefits of refracting RIS adoption for sum rate improvement in mmWave HST networks.