Active reconfigurable intelligent surface (RIS) has attracted significant attention as a recently proposed RIS architecture. Owing to its capability to amplify the incident signals, active RIS can mitigate the multiplicative fading effect inherent in the passive RIS-aided system. In this paper, we consider an active RIS-aided uplink multi-user massive multiple-input multiple-output (MIMO) system in the presence of phase noise at the active RIS. Specifically, we employ a two-timescale scheme, where the beamforming at the base station (BS) is adjusted based on the instantaneous aggregated channel state information (CSI) and the statistical CSI serves as the basis for designing the phase shifts at the active RIS, so that the feedback overhead and computational complexity can be significantly reduced. The aggregated channel composed of the cascaded and direct channels is estimated by utilizing the linear minimum mean square error (LMMSE) technique. Based on the estimated channel, we derive the analytical closed-form expression of a lower bound of the achievable rate. The power scaling laws in the active RIS-aided system are investigated based on the theoretical expressions. When the transmit power of each user is scaled down by the number of BS antennas M or reflecting elements N, we find that the thermal noise will cause the lower bound of the achievable rate to approach zero, as the number of M or N increases to infinity. Moreover, an optimization approach based on genetic algorithms (GA) is introduced to tackle the phase shift optimization problem. Numerical results reveal that the active RIS can greatly enhance the performance of the considered system under various settings.

翻译：有源可重构智能表面（RIS）作为近年来提出的新型RIS架构，因其具备放大入射信号的能力而受到广泛关注。有源RIS可有效缓解传统无源RIS辅助系统中固有的乘性衰落效应。本文研究了存在有源RIS相位噪声条件下的上行多用户大规模多输入多输出（MIMO）系统。具体而言，采用双时间尺度方案：基站（BS）根据瞬时聚合信道状态信息（CSI）调整波束赋形，同时利用统计CSI设计有源RIS的相移配置，从而显著降低反馈开销和计算复杂度。通过线性最小均方误差（LMMSE）技术估计由级联信道和直达信道构成的聚合信道。基于信道估计结果，推导了可达速率下界的解析闭式表达式，并据此分析有源RIS辅助系统的功率缩放规律。研究发现，当每个用户的发射功率按基站天线数M或反射单元数N的倒数进行缩放时，热噪声将导致可达速率下界在M或N趋于无穷时趋近于零。此外，采用基于遗传算法（GA）的优化方法解决相移优化问题。数值结果表明，在不同系统配置下，有源RIS均可显著提升系统的性能表现。