Reconfigurable intelligent surface (RIS) has emerged as a cost-effective solution to improve wireless communication performance through just passive reflection. Recently, the concept of simultaneously transmitting and reflecting RIS (STAR-RIS) has appeared but the study of minimum signal-to-interference-plus-noise ratio (SINR) and the impact of hardware impairments (HWIs) remain open. In addition to previous works on STAR-RIS, we consider a massive multiple-input multiple-output (mMIMO) base station (BS) serving multiple user equipments (UEs) at both sides of the RIS. Specifically, in this work, focusing on the downlink of a single cell, we derive the minimum SINR obtained by the optimal linear precoder (OLP) with HWIs in closed form. The OLP maximises the minimum SINR subject to a given power constraint for any given passive beamforming matrix (PBM). Next, we obtain deterministic equivalents (DEs) for the OLP and the minimum SINR, which are then used to optimise the PBM. Notably, based on the DEs and statistical channel state information (CSI), we optimise simultaneously the amplitude and phase shift by using a projected gradient ascent algorithm (PGAM) for both energy splitting (ES) and mode switching (MS) STAR-RIS operation protocols with reduced feedback, \textcolor{black}{which is quite crucial for STAR-RIS systems that include the double number or variables compared to reflecting only RIS.} Simulations verify the analytical results, shed light on the impact of HWIs, and demonstrate the better performance of STAR-RIS compared to conventional RIS.

翻译：可重构智能表面（RIS）作为一种通过被动反射提升无线通信性能的经济高效解决方案已受到广泛关注。近年来，同时传输与反射RIS（STAR-RIS）的概念已经出现，但其最小信干噪比（SINR）分析及硬件损伤（HWIs）影响的研究仍属空白。与现有STAR-RIS研究不同，我们考虑一个大规模多输入多输出（mMIMO）基站（BS）在RIS两侧同时服务多个用户设备（UEs）的场景。具体而言，本文聚焦单小区下行链路，推导了硬件损伤条件下最优线性预编码器（OLP）所达到的最小SINR闭合表达式。该OLP在任意给定无源波束赋形矩阵（PBM）的功率约束下最大化最小SINR。随后，我们获得了OLP及最小SINR的确定性等价（DEs），并基于此优化PBM。值得注意的是，基于DEs和统计信道状态信息（CSI），我们采用投影梯度上升算法（PGAM）同步优化能量分裂（ES）与模式切换（MS）两种STAR-RIS工作协议下的幅度和相移，该算法通过降维反馈实现——这对包含相较纯反射RIS双倍变量数的STAR-RIS系统至关重要。仿真验证了理论分析结果，揭示了硬件损伤的影响，并证明了STAR-RIS相较于传统RIS的优越性能。