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 allocation of users, the power-splitting ratios, and scattering matrix of the BD-RIS, under the assumption of imperfect channel state information (CSI). Additionally, to better capture practical hardware behavior, we incorporate a nonlinear energy harvesting model and ensure that the resulting system satisfies all energy harvesting constraints. In the considered system, we design a robust optimization framework to maximize the system sum-rate, while explicitly accounting for the worst-case impact of CSI uncertainties. To tackle the inherent non-convexity of the problem, we introduce an alternating optimization framework that partitions the problem into several blocks, which are optimized in an iterative manner. More specifically, the transmit precoding vectors are optimized by reformulating the problem as a convex semidefinite programming problem through successive-convex approximation (SCA), whereas the inherently convex 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 simulations are conducted to evaluate the performance of the proposed scheme, revealing significant performance improvements over existing benchmarks and demonstrating rapid convergence within a reasonable number of iterations.