Simultaneous Generalized Triangular Decomposition and SIC Decoding for RIS-Aided MIMO-NOMA Uplink

Recently, simultaneous generalized triangular decomposition (SGTD) has emerged as an effective matrix decomposition technique for multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems. In this paper, we extend SGTD to a two-user MIMO uplink setting where each user is assisted by a dedicated reconfigurable intelligent surface (RIS), enabling user-specific channel control. Both the conventional diagonal RIS (D-RIS) and the more general beyond-diagonal RIS (BD-RIS) are considered. For both designs, we derive low-SNR and high-SNR approximations of the sum-rate expressions, enabling lightweight optimization problems that are solved using either Riemannian manifold optimization (RMO) or quasi-Newton-based methods. In addition, a low-complexity scheme based on closed-form approximations is also provided. Simulation results and detailed complexity analysis demonstrate that the proposed schemes, which solve lightweight optimization problems, achieve significantly higher sum rates than benchmarks, while the proposed closed-form scheme still outperforms the benchmarks with substantially reduced computational complexity.