  In this paper, we derive the optimal user pairing and power allocation in
uplink non orthogonal multiple access (NOMA) networks. The optimal power
allocation that maximizes the sum rate is found for two user NOMA networks,
while ensuring that the individual rates of NOMA users are at least equal to
those they would achieve with orthogonal multiple access (OMA). Next, we prove
that in a 2K user network and when the optimal power allocation is used, the
optimal pairing reduces to pairing the user with index k to the user with index
2K-k+1, i.e., the user with the best channel condition and the one with the
worst channel condition are paired together, the second best with the second
worst and so on. Finally, the expressions of the corresponding optimal NOMA
power coefficients are derived analytically for networks with more than two
users. With these expressions at hand, our simulation results validate the
superiority of NOMA over OMA in terms of sum rates.
