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Non-orthogonal multiple access (NOMA) and coordinated multi-point (CoMP) are two fundamental techniques considered for the fifth generation (5 G) of wireless communications. In this paper, a hybrid satellite-unmanned aerial vehicle (UAV) relay network (HSURN) is proposed where the UAV relays (URs) employ CoMP transmission to serve the terrestrial users (UEs). Furthermore, all UEs associated with the CoMP-URs form a single NOMA cluster. For this model, an optimization problem is formulated subject to the minimum quality of services (QoSs) requirements of the UEs, transmission power budgets and, successive interference cancellation (SIC), to select URs and allocate their transmission powers for the energy efficiency (EE) maximization. With this insight, first, a computationally efficient sub-optimal UR selection scheme is proposed. Then, the powers are allocated to the selected URs via the Lagrange …