# Secure Transmission in mmWave Wiretap Channels: On Sector Guard Zone and Blockages
## 2 System Description and Performance Metrics  
### System Description  
Let's consider a mmWave wiretap network, which consists of a transmitter, a legitimate receiver and multiple random distributed eavesdroppers, as shown in Figure 1. The transmitter equipped with \(M\) multiple antennas uses directional beamforming for transmitting the confidential information. Both the legitimate receiver and the eavesdroppers equip a single antenna [31]. Furthermore, the locations of eavesdroppers, denoted by \(\Phi_{E}\), are modeled as an independent homogeneous Poisson point process (HPPP) with density \(\lambda_{E}\). Without loss of generality, similar to [32], a sector model is used to analyze the beam pattern in this paper, particularly  
\[G_{S}\left(\theta\right)=\left\{ \begin{array}{ll}M_{S},&if\left|\theta\right| \leq\theta_{S},\\ m_{S},&otherwise,\end{array} \right. \tag{1}\]  
where \(M_{S}\) represents the main lobe gain with the beam width \(\theta_{S}\), and \(m_{S}\) represents the array gain of side lobe. We assume that the transmitter can get the perfect channel state information (CSI) of the legitimate receiver; then, they can trim their antenna steering orientation array to their legitimate receiver and maximize the directivity gains. In practical terms, estimating the CSI may be a nontrivial task, so our work actually provides an upper bound on achievable secrecy performance. In this model, the eavesdroppers have been in the attempt to intercept the confidential information of the system, the CSIs of eavesdroppers are assumed to be unknown at the transmitter. The nearest eavesdropper is not necessarily the most detrimental one, but the one possessing the best channel to the transmitter. In addition, we consider non-colluding eavesdroppers in this work. The secrecy performance of the system is further improved by using the sector secrecy guard zone and AN. It is assumed that the eavesdroppers can be detected by scanning nearby eavesdropping devices before transmission [17; 18], provided that they are close enough to the transmitter. Therefore,a sector secrecy guard zone having a radius of \(r\) is introduced, and the eavesdroppers may be in or out of the sector secrecy guard zone. Therefore, a sector secrecy guard zone having a radius of \(r\) is introduced, and the eavesdroppers may be in or out of the sector secrecy guard zone. Similar to the secrecy guard zone mechanism in Referec [17], considering the characteristics of mmWave beam pattern, we model the finite range around the transmitter as a sector secrecy guard zone with radius \(r\) and central angle \(\theta_{S}\). Considering the generalized fading environment, mmWave communication channel is modeled as a Nakagami fading model. It is different from [33], which studied the secrecy performance of random multiple-input multiple- output (MIMO) wireless networks based on homogeneous Poisson point process (HPPP) over the \(\alpha\)-\(\mu\) fading channel. It is worth pointing out that the estimation of mmWave channel is more consistent with the actual communication system, but it is beyond the scope of this paper. According to the characteristics of mmWave in an outdoor scenario, the confidential information reaches to the legitimate receiver may be via LOS or NLOS [26]. According to 3 GPP standards and the blockage model with random shape theory [34], the probability of a LOS with distance \(r_{d}\) is represented by \(P_{L}\left(r_{d}\right)\), while the NLOS probability is \(P_{N}\left(r_{d}\right)\). The probability \(P_{L}\left(r_{d}\right)\) and \(P_{N}\left(r_{d}\right)\) are given as \(P_{L}\left(r_{d}\right)=e^{-\beta r_{d}}\) or \(P_{N}\left(r_{d}\right)=1-e^{-\beta r_{d}}\), which can be acquired from stochastic blockage models or field measurements, where \(\beta\) is the blockage density.