  Recently, spectrum sharing has been considered as a promising solution to
improve the spectrum utilization. It however may be vulnerable to security
problems as the primary and secondary network access the same resource.
Therefore, in this paper, we focus on the performance analysis of a cognitive
radio network in the presence of an eavesdropper (EAV) who illegally listens to
the primary user (PU) communication in which the transmit power of the
secondary transmitter (SU-Tx) is subject to the joint constraint of peak
transmit power of the SU-Tx and outage probability of the PU. Accordingly, an
adaptive transmit power policy and an analytical expression of symbol error
probability are derived for the SU. Most importantly, security evaluations of
primary network in terms of the probability of existence of non-zero secrecy
capacity and outage probability of secrecy capacity are obtained. Numerical
results reveal a fact that the security of the primary network does not only
depends on the channel mean powers between primary and secondary networks, but
also strongly depends on the channel condition of the SU-Tx to EAV link and
transmit power policy of the SU-Tx.
