  We investigate the secrecy performance of an underlay small-cell cognitive
radio network under unreliable backhaul connections. The small-cell network
shares the same spectrum with the primary network, ensuring that a desired
outage probability constraint is always met in the primary network. {To improve
the security of the small-cell cognitive network, we propose three sub-optimal
small-cell transmitter selection schemes,} namely sub-optimal transmitter
selection, minimal interference selection, and minimal eavesdropping selection.
Closed-form expressions of the non-zero secrecy rate, secrecy outage
probability, and ergodic secrecy capacity are provided for the schemes along
with asymptotic expressions. {We also propose an optimal selection scheme and
compare performances with the sub-optimal selection schemes.} {Computable
expressions for the non-zero secrecy rate and secrecy outage probability are
presented for the optimal selection scheme.} Our results show that by
increasing the primary transmitter's power and the number of small-cell
transmitters, the system performance improves. The selection scheme, the
backhaul reliability, and the primary user quality-of-service constraint also
have a significant impact on secrecy performance.
