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.

翻译：本文旨在通过联合优化速率分配与波束成形，最大化多用户多天线传输网络中速率分裂多址接入（RSMA）的加权和速率（WSR）。与传统方法（如加权最小均方误差（WMMSE）和标准分数规划（FP））需借助凸子问题与优化工具箱迭代求解非凸WSR问题不同，本文首创性地提出一种无需工具箱的方法。首次通过结合FP与拉格朗日对偶性，揭示了RSMA中WSR最大化的最优波束成形结构与公共速率分配机制。进而提出基于FP和不动点迭代的算法，无需优化工具箱即可实现波束成形与公共速率分配的优化。数值结果表明，该算法在显著降低计算时间的同时，能达到与标准FP及经典WMMSE方法相同的性能。