Max-Min Fairness Beamforming with Rate-Splitting Multiple Access: Optimization Without a Toolbox

We propose a max-min fairness (MMF) design method in a multi-antenna downlink network, where rate-splitting multiple access (RSMA) is adopted. A main aim in the considered MMF problem is providing uniformly good rates to users, by carefully controlling the rate of each private and common message, respectively. Solving this problem is challenging since multiple optimization variables, i.e., beamforming vectors and common message portions, are intricately intertwined in a non-tractable objective function. To resolve these obstacles, we first split a whole problem into two stages. In the first stage, we identify beamforming vectors given common message portion by exploiting the LogSumExp (LSE) approximation technique and the novel generalized power iteration (GPI) framework. In the second stage, we determine common message portions under fixed beamforming vectors. Iterating these two stages, we jointly design beamforming vectors and common message portion accordingly. Via simulations, we demonstrate that our method outperforms existing other frameworks in terms of the minimum rate, while requiring extremely small computational complexity.