Non-Orthogonal Multiple Access (NOMA) is an essential enabling
technology that is expected to help future broadband wireless networks
meet their higher system throughput requirements. However, in addition,
NOMA should also aim to provide a desired trade-off between system
throughput and user fairness, as fairness is an equally important aspect
that should go hand in hand with system throughput. In order to achieve
such a desired trade-off, in this paper, we derive optimal power
allocation (PA) coefficients at the NOMA transmitter, by formulating and
solving a joint sum rate and fairness optimization problem. To the best
of our knowledge, such a work is missing in the literature.
Additionally, along with the usual transmitter power budget and Quality
of Service (QoS) constraints, we also consider the minimum transmit
power gap between users, that is required for successful signal decoding
of a user in a SIC receiver, a constraint ignored at large in the
literature. The weighted sum method is used to convert the joint
objective optimization problem into a single-objective optimization
problem to make it analytically solvable and also provide the desired
trade-off between the conflicting objectives. As part of the validation
process, we present simulation results and also compare the performance
of the derived system with a system that considers only the sum rate
objective.