A New Definition of Fairness for Non-Orthogonal Multiple Access

Fairness in non-orthogonal multiple access (NOMA) may be defined in different ways, taking into account the physical layer alone or also including the process of radio resource management. The latter has been frequently used in the recent literature, implying a significant advantage of this technique compared with conventional orthogonal multiple access (OMA). In this letter, we look at the fairness issue from another angle and introduce a fundamental definition of fairness, which measures the difference between the rates that can be achieved by the users and the fair rates suggested by the power distribution among them. With this definition, the fairness issue is inexistent in OMA and it appears as a NOMA-specific problem due to interference between users and the detection process. The new fairness index we advocate incorporates the power distribution of different users. Thus, in a cell with a non-uniform power distribution, fairness implies that a user with a higher power should get a higher rate, and hence, the index should measure the rate of each user by accounting for the fraction of total power allocated to it. Our index achieves its maximum value of 1 only when all users get their fair rates, and it goes to zero when one user gets all resources in the case of uniform power distribution. We provide an asymptotic analysis of fairness at high and low signal-to-noise ratio (SNR) values and give a comprehensive illustration in the two-user case.