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This paper presents a controllable analysis framework for evaluating the reliability and security of underlay cognitive radio networks (CRs) relying on non-orthogonal multiple access (NOMA). In such systems, a secondary base station (BS) transmits confidential information to multiple secondary users uniformly distributed in the presence of a nearby located external eavesdropper. Moreover, transmit power constraints are introduced to limit the interference to the primary imposed by cognitive base stations. As an effective approach of multiple input single output (MISO) systems, the transmit antenna selection (TAS) is selected in the BS to improve the secrecy performance of the primary networks. Furthermore, we first consider the impact of quadrature-phase imbalance (IQI) to characterize the secure performance of the considered network in practice. Then, the degraded performance is evaluated in terms of outage …