  In this paper, we aim at maximizing the weighted sum-rate (WSR) of rate
splitting multiple access (RSMA) in multi-user multi-antenna transmission
networks through the joint optimization of rate allocation and beamforming.
Unlike conventional methods like weighted minimum mean square error (WMMSE) and
standard fractional programming (FP), which tackle the non-convex WSR problem
iteratively using disciplined convex subproblems and optimization toolboxes,
our work pioneers a novel toolbox-free approach. For the first time, we
identify the optimal beamforming structure and common rate allocation for WSR
maximization in RSMA by leveraging FP and Lagrangian duality. Then we propose
an algorithm based on FP and fixed point iteration to optimize the beamforming
and common rate allocation without the need for optimization toolboxes. Our
numerical results demonstrate that the proposed algorithm attains the same
performance as standard FP and classical WMMSE methods while significantly
reducing computational time.
