Abstract
This work studies the capacity limits of multi-input multiple-output (MIMO) systems using beyond diagonal (BD) reconfigurable intelligent surface (RIS), a.k.a., MIMO-BD-RIS systems, in Rician fading channels, when the number of transmit antennas, N_(t) , or receive antennas, Nᵣ , is asymptotically large. More specifically, we first derive a novel asymptotic approximation of the MIMO-BD-RIS capacity for the large N_(t) or Nᵣ regime that is then used to greatly simplify the optimization process of the BD-RIS reflection pattern in this scenario, since we prove that it simply boils down to solving a classic MIMO beamforming problem with extra constraints. Numerical simulations validate both the correctness of our capacity approximation for different types of BD-RIS reflection patterns as well as the effectiveness of our simplified MIMO-BD-RIS optimization method. They also show that the relative share of the capacity related to BD-RIS reflection pattern optimization in the overall capacity decreases as the minimum value between N_(t), Nᵣ , and the number of RIS elements increases, making optimization less pertinent in this case.