A closed-form solution for energy-efficiency optimization in multi-user downlink NOMA

This paper investigates the energy efficiency of a multi-user downlink non-orthogonal multiple access (NOMA) system. The energy-efficiency maximization representing the tradeoff between the sum rate versus the overall power consumption is formulated as a bi-criterion optimization problem; being convex, scalarization is suitable for its solution. Assuming that each individual user has a minimum quality of service constraint, we prove that the solution of the scalarized objective can be obtained in closed form. Hence, our solution characterizes the entire Pareto-optimal boundary of the rate vs. power tradeoffs. In the special case of maximizing the ratio sum rate vs. overall power, our solution reduces the complexity of the Dinkelbach procedure to a univariate bisection method. At last, our simulation results highlight the benefit of NOMA over OMA in terms of the rate vs. power optimal tradeoff.