# Secure Communication for Uplink Cellular Networks Assisted with Full-Duplex Device-to-Device User
## 2 System Model  
The system model is shown in Figure 1. We consider a network composed of a BS, a CU and a pair of D2D users (D1, D2). Among them, D1 is operated in FD and equipped with a transmitting antenna and a receiving antenna, CU and D2 are equipped with a single antenna. Due to long-distance transmission, CU and BS cannot communicate directly, and only an untrusted D2D device (D1) is relay assisted in communication.  
From Figure 1, CU and D2 can send their communication requests to BS with the assistance of D1. BS sends the control message to D1, and control information can be obtained by CU and D2 from D1. Initially, a signal combined with the confidential signal and the jamming signal is transmitted from the CU to D1. Then D1 forwards the signal from the CU to the BS, and at the same time communicates with D2. Since D2D reuses the spectrum resources of the cellular uplink, interference occurs between the D2D link and the cellular uplink.  
In addition, the channel gain model is adopted as follows:  
\[h_{ij}=g_{ij}d_{ij}^{-\theta} \tag{1}\]  
where \(i\in(C,1,B)\), \(j\in(1,2)\), \(g_{ij}\) is the channel coefficient, \(d_{ij}\) is the distance between node \(i\) and node \(j\), and \(\theta\) denotes the path loss exponent. All the channels are assumed to be narrow-band quasi-static and frequency flat fading.  
First, CU transmits the confidential signal \(x_{s}\) with power \(\beta P\) and the jamming signal \(x_{z}\) with power \((1-\beta)P\), where \(\beta\) represents the power allocation factor between \(x_{s}\) and \(x_{z}\) at CU. The signal \(y_{D1}\) received at the D1 can be written as:  
\[y_{D1}=\sqrt{\beta P_{C}}h_{C1}x_{s}+\sqrt{(1-\beta)P_{C}}h_{C1}x_{z}+\sqrt{ \kappa P_{D}}f_{1}x_{D}+n_{D1} \tag{2}\]  
where \(P_{C}\) and \(P_{D}\) are the transmit power from CU and D1, respectively, \(f_{1}\) is the self-interference channel, the parameter \(\kappa\in[0,1]\) is the cancellation coefficient, which is used to characterize the influence of self-interference on FD communication, \(x_{D}\) is the signal from D1, and \(n_{D1}\sim CN(0,\sigma^{2})\) is the additive noise at D1.  
Subsequently, D1 receives the signal from CU, and assigns part fraction \(\alpha\) of the available power to amplify and forward the signal to the BS, inhere \(\alpha\) is the power allocation factor at D1. The remaining  
Figure 1: Device-to-device (D2D) communication system based on full duplex (FD) relay.  
\(1-\alpha\) is used for D2D communication. We assume that the BS can eliminate the interference from D2D communication through successive interference cancellation technology when \(0\leq\alpha\leq 1/2\)[26; 27]. The signal \(y_{B}\) received at the BS can be written as:  
\[\begin{array}{ll}y_{B}&=Gh_{B1}y_{D1}+n_{B}\\ &=\sqrt{\beta P_{C}}Gh_{C1}h_{B1}x_{s}+\sqrt{(1-\beta)P_{C}}Gh_{C1}h_{B1}x_{z} +\sqrt{\kappa P_{D}}Gh_{B1}f_{1}x_{D}+Gh_{B1}u_{D1}+n_{B}\end{array} \tag{3}\]  
where \(n_{B}\sim CN(0,\sigma^{2})\) is the additive noise at BS, and the parameter \(G\) is denoted as the amplifying gain at D1, which can be considered by normalization of the received signal, i.e.,  
\[G=\sqrt{\frac{\alpha P_{D}}{P_{C}|h_{C1}|^{2}+\kappa P_{D}\big{|}f_{1}\big{|}^{ 2}+\sigma^{2}}} \tag{4}\]  
The signal \(y_{D2}\) received at the D2 can be written as:  
\[y_{D2}=\sqrt{(1-\alpha)P_{D}}h_{12}x_{D}+\sqrt{\beta P_{C}}h_{C2}x_{s}+\sqrt{ (1-\beta)P_{C}}h_{C2}x_{z}+\sqrt{\alpha P_{D}}h_{12}x_{D}+n_{D2} \tag{5}\]  
where \(n_{D2}\sim CN(0,\sigma^{2})\) is the additive noise at D2.