Two-Timescale Design for Reconfigurable Intelligent Surface-Aided URLLC

In this paper, to tackle the blockage issue in massive multiple-input-multiple-output (mMIMO) systems, a reconfigurable intelligent surface (RIS) is seamlessly deployed to support devices with ultra-reliable and low-latency communications (URLLC). The transmission power of the base station and the phase shifts of the RIS are jointly devised to maximize the weighted sum rate while considering the spatially correlation and channel estimation errors. Firstly, \textcolor{black}{the relationship between the channel estimation error and spatially correlated RIS's elements is revealed by using the linear minimum mean square error}. Secondly, based on the maximum-ratio transmission precoding, a tight lower bound of the rate under short packet transmission is derived. Finally, the NP-hard problem is decomposed into two optimization problems, where the transmission power is obtained by geometric programming and phase shifts are designed by using gradient ascent method. Besides, we have rigorously proved that the proposed algorithm can rapidly converge to a sub-optimal solution with low complexity. Simulation results confirm the tightness between the analytic results and Monte Carlo simulations. Furthermore, the two-timescale scheme provides a practical solution for the short packet transmission.