## 1 Introduction
### Background  
Due to the open nature of CRNs, they are vulnerable to illegal attacking and malicious eavesdropping, which would result in many challenging issues, especially security. Traditional security policies are not applicable to meet the security requirements of CRNs. Motivated by the problem, physical layer security (PLS) has been conceived as a new paradigm to guarantee secure transmissions while overcoming the vulnerabilities of traditional higher layer cryptography. For enhancing the PLS of wireless transmissions, many works have been explored. The orthogonal frequency-division multiplexing of CRNs as the medium access technique is put forward to show the performance of PLS in [6]. In [7, 8], the authors proposed multiuser scheduling-aided energy harvesting to improve PLS in CRNs. The maximizing secrecy capacity of CRNs through zero forcing beamforming (ZFB) was investigated in [9]. There is still a lot of previous work that has been done on PLS of CRNs. In [10], the security strategy deployment for switches on core network is proposed to enhance network's performance in cognitive internet of vehicles. In [3, 11, 12], the authors proposed different protocols to enhance the secrecy performance of CRNs. The device-to-device (D2D), the non-orthogonal multiple access (NOMA), buffer-aided technology and millimeter-wave (mmWave) were also used to improve the communication quality of CRNs [13, 14, 15, 16, 17]. With the maturity of self-interference cancellation technology, full-duplex (FD) technology is becoming more widely used. It is worth highlighting that lots of scholars are focusing on the full-duplex (FD) and have extensively applied it in many areas. On the one hand, the FD technique is proposed for the sake of enhancing the performance of the traditional cooperative jamming scheme (TCJS). The core part of full-duplex jamming scheme (FDJS) is that the FD user is able to transmit jamming signal and receive the required signal at the same time, and has been widely used in 5G communication systems [18]. In [19, 20], authors have fully demonstrated the application of FD technology in CRNs. Different from TCJS, FDJS is much easier and more reliable to realize. In [12], the authors designed different antenna reception schemes of FD operations, where the secrecy performance of system is enhanced through transmitting jamming signals and receiving legal signal at the same time. In [21], the authors analyzed the different relay selection schemes for the FD heterogeneous networks with multiple cognitive radio eavesdroppers to improve the secrecy performance of system. In [22], the authors analyzed collaboration interference (CI) transmission scheme of the FD wireless wiretap networks for improving PLS in CRNs. In [23], the authors explored that receiving antenna can send jamming signals at the time of receiving information and energy to degrade the eavesdropper's decoding capacity through FD operation, which was put forward to enhance the PLS. On the other hand, the beamforming with artificial noise (AN) of FD operation can effectively decrease the eavesdropping efficiency of eavesdropping users by sending interfering signals. However, beamforming with AN is different from beamforming in traditional networks because there are following aspects should be considered in CRNs. First, the interference power of PU should be taken into consideration in the process of designing beamforming scheme, that is, the quality of service (QoS) of PUs are ensured. Second, in [24, 25, 26], the SU transmitter can obtain SU receiver channel state information (CSI) through a pilot signal transmitted by SU receiver. Secure transmission in a multiple-input single-output multi-eavesdropper CRNs was investigated in [26] with the aim of maximizing the ergodic secrecy rate by beamforming and AN. In [27], AN was introduced in D2D to interfere with illegal eavesdropping of eavesdropping nodes, and the closed-form expression of SOP was further obtained to verify the impact on system performance.