Closed-form solution for the max-min fairness problem in non-orthogonal multiple access systems

Abstract

Non-orthogonal multiple access (NOMA) can improve both the spectrum efficiency and the number of users in wireless communication systems. In the downlink of NOMA, the base station superimposes multiple data flows in the power domain and the users decode the information using successive interference cancellation SIC. The performance of downlink NOMA systems is highly dependent on the power allocation scheme for all users. This paper investigates the max-min fairness problem that maximizes the minimum achievable user rate, aiming to ensure fairness for all users in downlink NOMA systems. Although the max-min fairness problem in downlink NOMA systems is non-convex, we obtain its closed-form optimal solution in this paper. This result will be useful for the analysis and design of future NOMA systems. Numerical results validate the correctness and effectiveness of our closed-form optimal solution.