# Secure Transmission in mmWave Wiretap Channels: On Sector Guard Zone and Blockages
## 4 Performance Analysis
### Direct Transmission
Based on Equations (12) and (16), the SOP is derived as  
\[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]2 \[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]3  
Substituting Equations (11) and (17) into Equation (4), the secrecy throughput \(\eta_{a}\) is derived as  
\[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]4 \[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]5 \[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]6  
**Remark 1**. : _It can be deduced from Equation (11) that the COP is a decreasing function of \(P\), this implies that the reliability performance of system is strengthened as \(P\) increases. For the case of \(E\in\Phi_{1}\), Equation (17) shows that the SOP increases with \(P\) when the sector secrecy guard zone is invariant. Correspondingly, when \(P\) is fixed, the secrecy performance becomes better with the increase of the sector secrecy guard zone. It means that, in this case, increasing power makes it possible to leak confidential information to eavesdroppers, and, at the same time, using the sector guard zone to keep eavesdroppers away from legitimate user. In addition, from Equation (18), it can be deduced that, in addition to \(P\) and \(\lambda_{E}\), the secrecy throughput has a close relationship with radius \(r\) and central angle \(\theta_{S}\) of the secrecy guard zone._  
In the case of \(E\in\Phi_{2}\), i.e., eavesdroppers may reside anywhere except in the signal beam where the sector secrecy guard zone is located. Substituting Equation (7) into Equation (2), the SOP is derived as  
\[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]7  
Substituting Equations (11) and (24) into Equation (4), the secrecy throughput is derived as  
\[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]8 \[=\sum\limits_{i\in\left\{L,N\right\}}\left(\frac{\mathrm{Y}\left( N_{i},\frac{\left(2^{R_{B}}-1\right)\sigma_{D}^{2}}{PM_{S}L\left(r_{D}\right)}N_{i} \right)}{\Gamma\left(N_{i}\right)}\right)P_{i}\left(r_{D}\right), \tag{11}\]9 \[p_{soa}=\Pr\left(\gamma_{E_{A}}>2^{R_{B}-R_{S}}-1\right)=\int_{2^{R_{B}-R_{S}} -1}^{\infty}f_{\gamma_{E_{A}}}\left(x\right)dx, \tag{12}\]0  
**Remark 2**. : _In the case of \(E\in\Phi_{2}\), the eavesdroppers are not in the beam where the sector secrecy guard zone is located; security threats come mainly from sidelobe. Referecne Equation (24) shows that the SOP is an increasing function of \(P\) and \(m_{S}\), which indicates that the secrecy performance becomes better as \(P\) and \(m_{S}\) decreases. It means that, when the eavesdroppers are in the sidelobe, increasing power \(P\) and \(m_{S}\) may lead to a leakage of confidential information. At the same time, increasing the central angle \(\theta_{S}\) of the sector guard zone can reduce the risk of eavesdropping.