Robust Beamforming Design for Energy Efficiency and Fairness Maximization in RIS-Assisted mmWave Communications

The use of reconfigurable intelligent surfaces (RISs) has been proposed in the past few years to achieve a better communication system performance by creating a programmable wireless propagation environment. In this paper, we target maximizing both energy efficiency and user fairness in RIS-assisted millimeter-wave systems with imperfect channel state information. We formulate the energy efficiency and fairness maximization problem as a multi-objective optimization problem. We split the corresponding multi-objective optimization problem into two stages using a lexicographic approach. In the first stage, the energy efficiency is maximized; then in the second stage, the fairness is maximized subject to a maximum reduction in the optimal value of the energy efficiency. We propose a projected gradient ascent based alternating optimization procedure to solve the optimization problem in each stage. We further employ the penalty dual decomposition method to address the challenging energy efficiency constraint in the second stage. Simulation results show that the proposed algorithm can achieve a better trade-off between energy efficiency and fairness compared to the methods that target only one of those metrics.