Integrating the reconfigurable intelligent surface (RIS) into a cell-free massive multiple-input multiple-output (CF-mMIMO) system is an effective solution to achieve high system capacity with low cost and power consumption. However, existing works of RIS-assisted systems mostly assumed perfect hardware, while the impact of hardware impairments (HWIs) is generally ignored. In this paper, we consider the general Rician fading channel and uplink transmission of the RIS-assisted CF-mMIMO system under transceiver impairments and RIS phase noise. To reduce the feedback overhead and power consumption, we propose a two-timescale transmission scheme to optimize the passive beamformers at RISs with statistical channel state information (CSI), while transmit beamformers at access points (APs) are designed based on instantaneous CSI. Also, the maximum ratio combining (MRC) detection is applied to the central processing unit (CPU). On this basis, we derive the closed-form approximate expression of the achievable rate, based on which the impact of HWIs and the power scaling laws are analyzed to draw useful theoretical insights. To maximize the users' sum rate or minimum rate, we first transform our rate expression into a tractable form, and then optimize the phase shifts of RISs based on an accelerated gradient ascent method. Finally, numerical results are presented to demonstrate the correctness of our derived expressions and validate the previous analysis, which provide some guidelines for the practical application of the imperfect RISs in the CF-mMIMO with transceiver HWIs.

翻译：将可重构智能表面（RIS）集成到无蜂窝大规模多输入多输出（CF-mMIMO）系统中，是一种以低成本和低功耗实现高系统容量的有效方案。然而，现有关于RIS辅助系统的工作大多假设理想硬件，而硬件损伤（HWI）的影响通常被忽略。本文考虑收发机损伤和RIS相位噪声条件下，RIS辅助CF-mMIMO系统上行链路传输及一般性莱斯衰落信道。为降低反馈开销和功耗，我们提出一种两时间尺度传输方案：利用统计信道状态信息（CSI）优化RIS处的无源波束赋形器，同时基于瞬时CSI设计接入点（AP）处的发射波束赋形器。此外，中央处理单元（CPU）采用最大比合并（MRC）检测。在此基础上，我们推导出可达速率的闭式近似表达式，并基于该表达式分析HWI的影响和功率缩放定律，以得出有用的理论洞察。为最大化用户的和速率或最小速率，我们首先将速率表达式转化为易处理形式，然后基于加速梯度上升法优化RIS的相移。最后，通过数值仿真验证所推导表达式的正确性及前期分析的有效性，为CF-mMIMO系统中存在收发机HWI时非理想RIS的实际应用提供指导准则。