A Fair Power Allocation Approach to NOMA in Multi-user SISO Systems

A non-orthogonal multiple access (NOMA) approach that always outperforms orthogonal multiple access (OMA) called Fair-NOMA is introduced. In Fair-NOMA, each mobile user is allocated its share of the transmit power such that its capacity is always greater than or equal to the capacity that can be achieved using OMA. For any slow-fading channel gains of the two users, the set of possible power allocation coefficients are derived. For the infimum and supremum of this set, the individual capacity gains and the sum-rate capacity gain are derived. It is shown that the ergodic sum-rate capacity gain approaches 1 b/s/Hz when the transmit power increases for the case when pairing two random users with i.i.d. channel gains. The outage probability of this approach is derived and shown to be better than OMA. The Fair-NOMA approach is applied to the case of pairing a near base-station user and a cell-edge user and the ergodic capacity gap is derived as a function of total number of users in the cell at high SNR. This is then compared to the conventional case of fixed-power NOMA with user-pairing. Finally, Fair-NOMA is extended to $K$ users and prove that the capacity can always be improved for each user, while using less than the total transmit power required to achieve OMA capacities per user.