Max-Min Fairness Precoder Design using A Generalized Power Iteration Approach in Rate-Splitting Multiple Access

In this paper, we study a max-min fairness (MMF) beamforming design method in a multiple-user downlink network utilizing rate-splitting multiple access (RSMA). A main objective of the MMF problem is to provide users with uniformly good rates by appropriately adjusting the rates of common and private message, respectively. Since the optimization of the objective function with respect to beamforming vectors and common message rates for each users is intricate and difficult to solve, we divide a whole problem into two stages. In the first stage, we utilize the LogSumExp (LSE) approximation technique and the novel generalized power iteration (GPI) framework to find a beamforming vector given a common message portion. In the second stage, we allocate common message rate for each user for given fixed beamforming vectors. By repeating these two stages, we jointly design the optimal beamforming vectors and common message rates for each users. Through simulation, we show that our method outperforms existing approaches in terms of the worst-case user's rate with extremely low complexity cost.