Different from conventional passive reconfigurable intelligent surfaces (RISs), incident signals and thermal noise can be amplified at active RISs. By exploiting the amplifying capability of active RISs, noticeable performance improvement can be expected when precise channel state information (CSI) is available. Since obtaining perfect CSI related to an RIS is difficult in practice, a robust transmission design is proposed in this paper to tackle the channel uncertainty issue, which will be more severe for active RIS-aided systems. To account for the worst-case scenario, the minimum achievable rate of each user is derived under a statistical CSI error model. Subsequently, an optimization problem is formulated to maximize the sum of the minimum achievable rate. Since the objective function is non-concave, the formulated problem is transformed into a tractable lower bound maximization problem, which is solved using an alternating optimization method. Numerical results show that the proposed robust design outperforms a baseline scheme that only exploits estimated CSI.

翻译：与传统无源可重构智能反射面不同，有源智能反射面能够放大入射信号与热噪声。当精确的信道状态信息可用时，利用有源智能反射面的放大能力有望获得显著的性能提升。由于在实际中获取与智能反射面相关的完美信道状态信息较为困难，本文提出一种鲁棒传输设计以应对信道不确定性问题，该问题在有源智能反射面辅助系统中将更为严重。为考虑最坏情况，本文在统计信道状态信息误差模型下推导了每个用户的最小可达速率。随后，构建了一个优化问题以最大化最小可达速率之和。由于目标函数非凹，将原问题转化为一个可处理的下界最大化问题，并采用交替优化方法进行求解。数值结果表明，所提出的鲁棒设计优于仅利用估计信道状态信息的基准方案。