Active IRS-Aided MIMO Communications: How Much Gain Can We Get?

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, where 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 paper, 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 characterization 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. Interesting physical insights regarding the advantage of active IRSs over their passive counterparts and the optimal power allocation between the transmitter and IRS are unveiled.