  Rate splitting multiple access (RSMA) is a promising non-orthogonal
transmission strategy for next-generation wireless networks. It has been shown
to outperform existing multiple access schemes in terms of spectral and energy
efficiency when suboptimal beamforming schemes are employed. In this work, we
fill the gap between suboptimal and truly optimal beamforming schemes and
conclusively establish the superior spectral and energy efficiency of RSMA. To
this end, we propose a successive incumbent transcending (SIT) branch and bound
(BB) algorithm to find globally optimal beamforming solutions that maximize the
weighted sum rate or energy efficiency of RSMA in Gaussian multiple-input
single-output (MISO) broadcast channels. Numerical results show that RSMA
exhibits an explicit globally optimal spectral and energy efficiency gain over
conventional multi-user linear precoding (MU-LP) and power-domain
non-orthogonal multiple access (NOMA). Compared to existing globally optimal
beamforming algorithms for MU-LP, the proposed SIT BB not only improves the
numerical stability but also achieves faster convergence. Moreover, for the
first time, we show that the spectral/energy efficiency of RSMA achieved by
suboptimal beamforming schemes (including weighted minimum mean squared error
(WMMSE) and successive convex approximation) almost coincides with the
corresponding globally optimal performance, making it a valid choice for
performance comparisons. The globally optimal results provided in this work are
imperative to the ongoing research on RSMA as they serve as benchmarks for
existing suboptimal beamforming strategies and those to be developed in
multi-antenna broadcast channels.
