## 1 Introduction
### Motivation and Contribution  
Motivated by the discussion mentioned above,we investigate secure transmission in the dual-hop cognitive wiretap networks with FD receiver over Rayleigh fading channels under two different scenarios, in which the secondary transmitter ([PERSON]) aims to transmit confidential information to the secondary receiver ([PERSON]) in the presence of a multi-antenna relay (Relay), while the eavesdropper([PERSON]) is to eavesdrop the confidential information from [PERSON] and Relay. The randomize-and-forward (RaF) transmission protocol has been widely used in different phases of physical layer security in CRNs. Since there is the transmission heterogeneity of the two transmitters, the eavesdropper cannot merge the common information of the two phases [29; 30]. Relay is considered the half-duplex (HD) operation and Bob is considered the FD beamforming with AN operation to prevent overheard by the eavesdropper. To be specific, for the HD operation, the Relay utilize maximal-ratio combining (MRC) to pay more attention to the signal detection from [PERSON] and send data to [PERSON] by using maximal-ratio transmit (MRT) scheme, and then [PERSON] receives signals forwarded from the Relay through using the selection combining (SC) scheme. While for the FD operation, MRC-ZFB/MRT-SC-ZFB secure transmission schemes are proposed, Relay first adopts MRC scheme to receive the data forwarded from [PERSON] and at the same time [PERSON] uses the ZFB scheme to transmit AN signals to reduce the illegal wiretapping of users at the first phase. At the second phase, Relay utilizes MRT scheme to send security information to [PERSON], and then [PERSON] selects the best antenna to receive information from Relay and simultaneously transmits the jamming signal by utilizing the remaining antennas with FD operation. Our principal contributions are highlighted as follows:  
* We first derive closed-form and simple asymptotic expressions for the secrecy outage probability (SOP) and the secrecy throughput (ST) of the FD receiver cognitive wiretap networks with MRC-ZFB/MRT-SC-ZFB and MRC/MRT-SC schemes, respectively [31]. Moreover, we also explore the impact of the various system parameters on the SOP and ST, i.e., the number of antennas and the interference threshold at Relay and Bob. * We further derive the asymptotic closed-form expressions for the SOP and the secrecy diversity order and secrecy coding gain are achieved under two different scenarios, namely Scenario I: \(\overline{\tau}_{B}\rightarrow\infty\) and _fixed_\(\overline{\tau}_{E}\), and Scenario II: \(\overline{\tau}_{B}\rightarrow\infty\) and \(\overline{\tau}_{E}\rightarrow\infty\), which reveals that the influence of system performance under the high signal-to-noise ratio (SNR). Two distinct scenarios can achieve the same secrecy diversity (\(\min\left(N_{R},N_{R}N_{B}\right)\)) under Scenario I and zero secrecy diversity under Scenario II, where \(\overline{\tau}_{B}\) and \(\overline{\tau}_{E}\) denote the average SNR of the main channel and the eavesdropping channel, respectively. * Through the derivation and analysis of the SOP and ST, it has been verified that the MRC-ZFB/MRT-SC-ZFB scheme of FD operation at Bob outperforms MRC/MRT-SC scheme of HD operation in terms of enhancing secrecy performance of CRNs. The attained asymptotic expressions shed lights on the impact of distinct system parameters, i.e., increasing interference threshold of the primary network within a certain range and the number of antennas at the Relay and Bob. The beamforming of AN design can effectively improve the secrecy performance of the considered networks and the secrecy performance of the considered scheme with FD operation is mainly affected by the secrecy coding gain. The remainder of the paper is organized as follows. In Section 2, the proposed system model is described. The SOPs of the system for the secondary data transmission are analyzed in Section 3. In Section 4, we provide the SOPs of the system under the high SNR analysis and ST.