Active reconfigurable intelligent surfaces (RISs) employ amplification to overcome attenuation caused by the RIS cascaded link. In this paper, we analyze the effects of phase errors and channel aging in active simultaneously transmitting and reflecting (STAR) RIS-assisted cell-free massive multiple-input multiple-output (MIMO) systems. By leveraging a spatially correlated Rayleigh fading model, this paper derives minimum mean square error estimate-based channel estimates and formulates closed-form expressions for downlink spectral efficiency. This analytical framework enables a comprehensive evaluation of the effects of channel aging and uniformly distributed phase errors on system performance. The results demonstrate that active STAR-RISs can effectively compensate for the adverse effects of phase errors and channel aging. To counteract the impact of channel aging, we propose practical guidelines for resource-block-length design. Also, an increase in APs and STAR-RIS elements, along with a larger amplification factor, can alleviate performance degradation.

翻译：主动可重构智能表面通过引入放大机制来克服级联链路引起的衰减。本文分析了主动同时透射反射型可重构智能表面辅助的无蜂窝大规模多输入多输出系统中相位误差与信道老化的影响。基于空间相关瑞利衰落信道模型，本文推导了基于最小均方误差估计的信道估计方法，并建立了下行频谱效率的闭式表达式。该分析框架能够全面评估信道老化与均匀分布相位误差对系统性能的影响。结果表明，主动STAR-RIS能有效补偿相位误差与信道老化带来的负面影响。为应对信道老化效应，我们提出了资源块长度设计的实用准则。此外，增加接入点与STAR-RIS单元数量，以及采用更大的放大因子，均可缓解系统性能的下降。