MIMO Communications with 1-bit RIS: Asymptotic Analysis and Over-the-Air Channel Diagonalization

This paper presents an asymptotic analysis of Multiple-Input Multiple-Output (MIMO) systems assisted by a 1-bit Reconfigurable Intelligent Surface (RIS) under Ricean fading conditions. Using random matrix theory, we show that, in the asymptotic regime, the dominant singular values and vectors of the transmitter-RIS and RIS-receiver channels converge to their deterministic Line-of-Sight (LoS) components, almost irrespective of the Ricean factors. This enables RIS phase configuration using only LoS information through a closed-form Sign Alignment (SA) rule that maximizes the channel gain. Furthermore, when the RIS is asymptotically larger than the transceiver arrays, proper RIS configuration can render the end-to-end MIMO channel in the capacity formula asymptotically diagonal, thereby eliminating inter-stream interference and enabling Over-The-Air (OTA) spatial multiplexing without channel knowledge at the transmitter. Building on this result, a waterfilling-inspired SA algorithm that allocates RIS elements to spatial streams, based on the asymptotic singular values and statistical channel parameters, is proposed. Simulation results validate the theoretical analyses, demonstrating that the proposed schemes achieve performance comparable to conventional Riemannian manifold optimization, but with orders of magnitude lower runtime.