Fair Power Allocation Policies for Power-Domain Non-Orthogonal Multiple Access Transmission With Complete or Limited Successive Interference Cancellation

Power-Domain Non-Orthogonal Multiple Access (NOMA) transmission has been addressed in this paper with a proportional fairness optimization criterion (which includes MAX-MIN fairness as a special case) and an arbitrary number of users. The optimization of the power allocation coefficients required to achieve the optimum proportional fairness objective leads to a nonconvex optimization problem, which is generally hard to solve and may lead to multiple local optima. However, a simple optimality condition is characterized in the paper, leading to the solution of a nonlinear equation in a single variable. This equation reduces to polynomial form in the case of MAX-MIN fairness. Departing from the complete Successive Interference Cancellation (SIC) paradigm, typical of NOMA systems, a limited SIC technique is discussed and the relevant power allocation coefficients are obtained with the same optimization criterion. This approach eases the implementation of downlink NOMA when a large number of low-complexity hand-held terminals cannot sustain the computationally intensive task of complete SIC, at the cost of reduced their achievable rates. Numerical results are presented to illustrate the impact of complete and limited SIC, with power allocation optimization and two proportional fairness criteria. Among these results, the sum-rate loss due to proportional fairness and the impact of limited SIC on the system performance are illustrated.