  For downlink multi-user non-orthogonal multiple access (NOMA) systems with
successive interference cancellation (SIC) receivers, and a base-station not
possessing the instantaneous channel gains, the fundamental relationship
between the target rates and power allocation is investigated. It is proven
that the total interference from signals not removed by SIC has a fundamental
upper-limit which is a function of the target rates, and the outage probability
is one when exceeding this limit. The concept of well-behaved power allocation
strategies is defined, and its properties are proven to be derived solely based
on the target rates. The existence of power allocation strategies that enable
NOMA to outperform OMA in per-user outage probability is proven, and are always
well-behaved for the case when the outage probability performance of NOMA and
OMA are equal for all users. The proposed SIC decoding order is then shown to
the most energy efficient. The derivation of well-behaved power allocation
strategies that have improved outage probability performance over OMA for each
user is outlined. Simulations validate the theoretical results, demonstrating
that NOMA systems can always outperform OMA systems in outage probability
performance, without relying on the exact channel gains.
