Robust Design of Beyond-Diagonal Reconfigurable Intelligent Surface Empowered RSMA-SWIPT System Under Channel Estimation Errors

This work explores the integration of rate-splitting multiple access (RSMA), simultaneous wireless information and power transfer (SWIPT), and beyond-diagonal reconfigurable intelligent surface (BD-RIS) to enhance the spectral-efficiency, energy-efficiency, coverage, and connectivity of future sixth-generation (6G) communication networks. Specifically, with a multiuser BD-RIS-empowered RSMA-SWIPT system, we jointly optimize the transmit precoding vectors, the common rate proportion of users, the power-splitting ratios, and scattering matrix of BD-RIS node, under the assumption of imperfect channel state information (CSI). Additionally, to better capture practical hardware behavior, we incorporate a nonlinear energy harvesting model under energy harvesting constraints. We design a robust optimization framework to maximize the system sum-rate, while explicitly accounting for the worst-case impact of CSI uncertainties. Further, we introduce an alternating optimization framework that partitions the problem into several blocks, which are optimized iteratively. More specifically, the transmit precoding vectors are optimized by reformulating the problem as a convex semidefinite programming through successive-convex approximation (SCA), whereas the power-splitting problem is solved using the MOSEK-enabled CVX toolbox. Subsequently, to optimize the scattering matrix of the BD-RIS, we first employ SCA to reformulate the problem into a convex form, and then design a manifold optimization strategy based on the Conjugate-Gradient method. Finally, numerical simulation results reveal that the proposed scheme provides significant performance improvements over existing benchmarks and demonstrates rapid convergence within a reasonable number of iterations.