  Joint optimization for common rate allocation and beamforming design have
been widely studied in rate splitting multiple access (RSMA) empowered
multiuser multi-antenna transmission networks. Due to the highly coupled
optimization variables and non-convexity of the joint optimization problems,
emerging algorithms such as weighted minimum mean square error (WMMSE) and
successive convex approximation (SCA) have been applied to RSMA which typically
approximate the original problem with a sequence of disciplined convex
subproblems and solve each subproblem by an optimization toolbox. While these
approaches are capable of finding a viable solution, they are unable to offer a
comprehensive understanding of the solution structure and are burdened by high
computational complexity. In this work, for the first time, we identify the
optimal beamforming structure and common rate allocation for the weighted
sum-rate (WSR) maximization problem of RSMA. We then propose a computationally
efficient optimization algorithm that jointly optimizes the beamforming and
common rate allocation without relying on any toolbox. Specifically, we first
approximate the original WSR maximization problem with a sequence of convex
subproblems based on fractional programming (FP). Numerical results show that
the proposed algorithm achieves the same performance but takes only 0.5\% or
less simulation time compared with the state-of-the-art WMMSE, SCA, and FP
algorithms. Experimental results show that the proposed two methods have
similar mean square error (MSE) performance compared with traditional method
using CVX optimization tool, however, computational complexities are greatly
reduced. The proposed algorithms pave the way for the practical and efficient
optimization algorithm design for RSMA and its applications in 6G.
