From Partitioning to Fully-Connected RIS: A Beyond Diagonal-RIS–Based Multiuser Wireless Transmission Perspective

Abstract

This study presents a generalized design framework for beyond-diagonal reconfigurable intelligent surface (BD-RIS)-based multiuser wireless transmitters capable of serving multiple users simultaneously via spatial beamforming. The proposed system provides an energy-efficient alternative to conventional multi-antenna transmitters, as both multiuser data modulation and beamforming are implemented through a passive BD-RIS, thereby eliminating the need for multiple active RF chains and antenna arrays. As a baseline design, we first propose a partitioned RIS-based transmitter that serves multiple downlink users independently, and subsequently introduce a more general non-partitioned design that achieves markedly improved performance under both correlated and uncorrelated user channels. We show that a conventional diagonal-RIS, due to its architectural constraints, can realize only a row-wise non-uniformly scaled version of a desired beamforming matrix. To address this limitation, BD-RIS-based transmitters employing group- and fully-connected architectures are proposed, whose performance approaches that of conventional multi-antenna transmitters. In this context, we develop a scattering-matrix design algorithm that configures the BD-RIS to realize arbitrary beamforming and modulation across all considered architectures. Extensive computer simulations evaluate the error performance of the proposed designs under various channel-aware beamforming schemes and examine the impact of BD-RIS architecture, RIS size, and group size, providing practical design insights. Theoretical error performance under Rayleigh fading is also analyzed.