Two-Timescale Design for Simultaneous Transmitting and Reflecting RIS-Assisted Massive MIMO Systems with Imperfect CSI

This paper investigates the performance of simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted massive multiple-input multiple-output (MIMO) systems with Rician fading channels and channel estimation errors. We adopt the two-timescale scheme to design the systems, namely, applying the instantaneous channel state information (CSI) to design the base station (BS) beamforming and leveraging the statistical CSI to design the phase shifts of the STAR-RIS. Specifically, we estimate the overall channels based on the linear minimum mean-squared error (LMMSE) estimator and derive the closed-form expression of the average achievable rate. Based on the derived rate, we analyze the power scaling laws in which the transmit power is respectively reduced inversely proportional to the number of BS antennas and STAR-RIS elements. Besides, we draw insights from the comparison between STAR-RIS and conventional RIS under the same condition and the power scaling laws of STAR-RIS and optimize the phase shifts of the STAR-RIS to maximize the sum rate using an accelerated gradient ascent-based algorithm. Finally, numerical results are provided to validate our theoretical insights. In particular, we also compare the two-timescale scheme with the instantaneous CSI scheme in the simulation. We show that STAR-RIS outperforms conventional RIS, and the two-timescale-based scheme outperforms the instantaneous CSI-based scheme. Furthermore, we draw insight into this phenomenon.