We propose a tractable expression for the
outage probability in single-cell uplink non-orthogonal multiple access (NOMA) systems serving an arbitrary number of
users. The expression is obtained by approximating the interuser interference using a shifted-gamma distributed random
variable. We then formulate and propose an efficient iterative
algorithm for the outage-constrained min–max power allocation
problem for the NOMA system. To give a rigorous comparison, we solve the outage-constrained min–max power allocation
problem for the orthogonal multiple access (OMA) counterpart
where both the user power allocation and the radio resource
division pattern are optimized. Simulations confirm the accuracy
of the derived outage probability expression for the NOMA
system. Also, we demonstrate that fairness among users in terms
of transmission power can be achieved by NOMA. Moreover,
NOMA can bring significant power savings to the users as
compared with OMA