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 users 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.
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