In this letter, we investigate the price-based power allocation with rate proportional fairness constraint in downlink non-orthogonal multiple access (NOMA) systems. The Stackelberg game is utilized to model the interaction between the base station (BS) and users. The revenue maximization problem of the BS is first converted to rate allocation problem, then the optimal rate allocation for each user is obtained by variable substitution. Finally, a price-based power allocation with rate proportional fairness (PAPF) algorithm is proposed based on the relationship between rate and transmit power. Simulation results show that the proposed PAPF algorithm is superior to the previous price-based power allocation algorithm in terms of fairness index and minimum normalized user (MNU) rate.

In this letter, we consider the power allocation scheme with rate proportional fairness to maximize energy efficiency in the downlink the non-orthogonal multiple access (NOMA) systems. The optimization problem of energy efficiency is a non-convex optimization problem, and the fractional programming is used to transform the original problem into a series of optimization sub-problems. A two-layer iterative algorithm is proposed to solve these sub-problems, in which power allocation with the fixed energy efficiency is achieved in the inner layer, and the optimal energy efficiency of the system is obtained by the bisection method in the outer layer. Simulation results show the effectiveness of the proposed algorithm.