  In this paper, we propose two beamforming designs for a multiple-input
single-output non-orthogonal multiple access system considering the energy
efficiency (EE) fairness between users. In particular, two quantitative
fairness-based designs are developed to maintain fairness between the users in
terms of achieved EE: max-min energy efficiency (MMEE) and proportional
fairness (PF) designs. While the MMEE-based design aims to maximize the minimum
EE of the users in the system, the PF-based design aims to seek a good balance
between the global energy efficiency of the system and the EE fairness between
the users. Detailed simulation results indicate that our proposed designs offer
many-fold EE improvements over the existing energy-efficient beamforming
designs.
