  The fundamental power allocation requirements for NOMA systems with minimum
quality of service (QoS) requirements are investigated. For any minimum QoS
rate $R_0$, the limits on the power allocation coefficients for each user are
derived, such that any power allocation coefficient outside of these limits
creates an outage with probability equal to 1. The power allocation
coefficients that facilitate each user's success of performing successive
interference cancellation (SIC) and decoding its own signal are derived, and
are found to depend only on the target rate $R_0$ and the number of total users
$K$. It is then proven that using these power allocation coefficients create
the same outage event as if using orthogonal multiple access (OMA), which
proves that the outage performance of NOMA with a fixed-power scheme can
matched that of OMA for all users simultaneously. Simulations confirm the
theoretical results, and also demonstrate that a power allocation strategy
exists that can improve the outage performance of NOMA over OMA, even with a
fixed-power strategy.
