Beyond-Diagonal Reconfigurable Intelligent Surface Enhanced NOMA Systems

In this letter, we investigate how the beyond-diagonal reconfigurable intelligent surface (BD-RIS) can enhance non-orthogonal multiple access (NOMA) systems. Specifically, we analyze the BD-RIS enhancement performance in terms of sum-rate maximization (SRM), asymptotic received signal-to-noise ratio (SNR), and quasi-degradation region of the channel. In general, the SRM problem is tricky due to the complex structure of the phase-shift matrix of the BD-RIS. To address the resulting problem, we develop an effective variable separation algorithm to optimize the precoding vector and phase-shift matrix for maximizing the multiuser sum rate. It is worth mentioning that our proposed algorithm is well-compatible with the phase-shift design of existing BD-RIS structures. Furthermore, we analyze the asymptotic SNR and derive the quasi-degradation condition in BD-RIS-assisted NOMA systems. Simulation results demonstrate that the BD-RIS can achieve a higher square law of SNR than the diagonal RIS (D-RIS), higher spectral efficiency compared to OMA and D-RIS systems, and a larger NOMA quasi-degradation region than D-RIS and systems without RIS.