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

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