  In this paper, non-orthogonal multiple access (NOMA) is applied to
large-scale underlay cognitive radio (CR) networks with randomly deployed
users. In order to characterize the performance of the considered network, new
closed-form expressions of the outage probability are derived using
stochastic-geometry. More importantly, by carrying out the diversity analysis,
new insights are obtained under the two scenarios with different power
constraints: 1) fixed transmit power of the primary transmitters (PTs), and 2)
transmit power of the PTs being proportional to that of the secondary base
station. For the first scenario, a diversity order of $m$ is experienced at the
$m$-th ordered NOMA user. For the second scenario, there is an asymptotic error
floor for the outage probability. Simulation results are provided to verify the
accuracy of the derived results. A pivotal conclusion is reached that by
carefully designing target data rates and power allocation coefficients of
users, NOMA can outperform conventional orthogonal multiple access in underlay
CR networks.
