Capacity Analysis of Cascaded BD-RIS Assisted MIMO Systems

Abstract: This paper examines the cascaded deployment of beyond diagonal (BD) reconfigurable intelligent surfaces (RISs) and explores its potential to enhance the performance of MIMO systems. We first derive the jointly optimal closed form solutions for the RISs in cascade with SVD water filling (SVD WF) and uniform power allocation (UPA) precoding strategies. The optimally configured cascaded-RIS with UPA is shown to achieve performance comparable to that with the SVD WF approach, suggesting that cascaded-RISs can also aid in reducing transmitter complexity. Furthermore, the approximate ergodic capacity for UPA is derived, along with its high SNR approximation which provides multiple useful insights into the dimension and deployment of cascaded RISs. The analytical results establish a clear tradeoff among transmit power, RIS size, and achievable capacity, providing insights for practical deployment in high SNR cascaded RIS MIMO systems.