  While existing works about non-orthogonal multiple access (NOMA) have
indicated that NOMA can yield a significant performance gain over orthogonal
multiple access (OMA) with fixed resource allocation, it is not clear whether
such a performance gain will diminish when optimal resource
(Time/Frequency/Power) allocation is carried out. In this paper, the
performance comparison between NOMA and conventional OMA systems is
investigated, from an optimization point of view. Firstly, by using the idea of
power splitting, a closed-form expression for the optimum sum rate of NOMA
systems is derived. Then, with rigorous mathematical proofs, we reveal the fact
that NOMA can always outperform conventional OMA systems, even if both are
equipped with the optimal resource allocation policies. Finally, computer
simulations are conducted to validate the accuracy of the analytical results.
