On the power scaling law of MIMO-RIS in Rician fading

This paper characterizes the power scaling law of multi-input multiple-output (MIMO)-reconfigurable intelligent surface (RIS) communication systems, i.e., how the channel gain of MIMO-RIS scales with the number of RIS elements, M , as M grows asymptotically large, when considering Rician fading as well as possible intra-element coupling at the RIS. We first propose a novel and insightful way of expressing the MIMO-RIS capacity that sheds light on the structure of the MIMO-RIS power scaling law, regardless of the type of channels, before deriving new approximations and bounds of the power scaling gains of MIMO-RIS for Rician fading channels, where both the line-of-sight (LOS) and non-LOS (NLOS) gains are characterized. Both these gains are typically linear in M without optimization and intra-element coupling at the RIS, such that the capacity of a MIMO-RIS system is equivalent to the capacity of a classic MIMO system with a boost in channel gain of M in this case. This remains true when the number of transmit antennas, Nt, and/or receive antennas, Nr, is large compared to M , even if complex optimization relying on full channel state information (CSI) is performed at the RIS. Otherwise, the LOS power gain scales at best quadratically with M , while the NLOS power gain is up to linear in M in the absence of CSI, and it scales at best with M 1.7 with full CSI and no intra-element coupling at the RIS for Nt, Nr ≥ 4, based on our simulation results.