Intelligent reflecting surfaces (IRSs) have emerged as a promising technology to improve the efficiency of wireless communication systems. However, passive IRSs suffer from the ``multiplicative fading" effect, because the transmit signal will go through two fading hops. With the ability to amplify and reflect signals, active IRSs offer a potential way to tackle this issue, where the amplification energy only experiences the second hop. However, the fundamental limit and system design for active IRSs have not been fully understood, especially for multiple-input multiple-output (MIMO) systems. In this work, we consider the analysis and design for the large-scale active IRS-aided MIMO system assuming only statistical channel state information (CSI) at the transmitter and the IRS. The evaluation of the fundamental limit, i.e., ergodic rate, turns out to be a very difficult problem. To this end, we leverage random matrix theory (RMT) to derive the deterministic approximation (DA) for the ergodic rate, and then design an algorithm to jointly optimize the transmit covariance matrix at the transmitter and the reflection matrix at the active IRS. Numerical results demonstrate the accuracy of the derived DA and the effectiveness of the proposed optimization algorithm. The results in this work reveal interesting physical insights with respect to the advantage of active IRSs over their passive counterparts.

翻译：智能反射面（IRS）已成为提高无线通信系统效率的一种有前景的技术。然而，无源IRS存在“乘性衰落”效应，因为发射信号会经历两次衰落跳变。有源IRS具有放大和反射信号的能力，为解决这一问题提供了潜在途径，其放大能量仅经历第二次跳变。然而，有源IRS的基本极限和系统设计尚未被充分理解，尤其是对于多输入多输出（MIMO）系统。本文考虑在发射端和IRS仅已知统计信道状态信息（CSI）的情况下，对大规模有源IRS辅助的MIMO系统进行分析与设计。基本极限（即遍历速率）的评估是一个极具挑战的问题。为此，我们利用随机矩阵理论（RMT）推导了遍历速率的确定性近似（DA），并设计了一种算法来联合优化发射端的发射协方差矩阵和有源IRS的反射矩阵。数值结果证明了所推导的DA的准确性以及所提优化算法的有效性。本文的结果揭示了有源IRS相对于无源IRS优势的深刻物理见解。