Globally Optimal Spectrum- and Energy-Efficient Beamforming for Rate Splitting Multiple Access

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.