# Performance Analysis of Artificial Noise-Assisted Location-Based Beamforming in Rician Wiretap Channels

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## Abstract

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## 1. Introduction

- Based on the location information of the legitimate user and the eavesdropper, the signal to interference plus noise ratio (SINR) expressions have been derived for both the user and the eavesdropper, and the impact of AN has been considered. Close approximations of the probability density functions (PDFs) of SINRs have been proposed for Rician channels.
- The expectations of SINRs have been derived in closed-form expressions. Moreover, the bit error rate (BER) expressions are derived using Gaussian-Laguerre (GL) approximation.
- A quality of service (QoS)-based beamforming scheme is proposed to minimize the SINR of the eavesdropper and ensure the minimum SINR requirement of the legitimate user. Simulation results show that, when eight antennas are used at the base station, the block error rate (BLER) of eavesdroppers located 5° away from the legitimate user reaches 1.

## 2. System Model

## 3. Performance Analysis

#### 3.1. Distribution of the SINR

#### 3.2. Expectation of SINR

#### 3.3. BER Analysis

## 4. Optimal Location-Based Beamforming

Algorithm 1 Algorithm to Determine ${\psi}_{b}^{\ast}$, ${\psi}_{\mathrm{AN}}^{\ast}$, ${g}_{b}^{\ast}$ for Location-based Beamforming |

Require: ${\theta}_{b}$, ${\theta}_{e}$Ensure: ${\psi}_{b}^{\ast}$, ${\psi}_{\mathrm{AN}}^{\ast}$, ${g}_{b}^{\ast}$1: for $0\le {\psi}_{b},{\psi}_{\mathrm{AN}}\le \pi $ with step size ${\delta}_{\psi}$ do3: while $0<{g}_{b}\le 1$ with step size ${\delta}_{g}$ do4: calculate $\mathbb{E}\left[{\mathrm{SINR}}_{b}\right]$ using (29) 5: if $\mathbb{E}\left[{\mathrm{SINR}}_{b}\right]\ge {\widehat{\gamma}}_{b}$ then6: ${g}_{b,tmp}={g}_{b}$ 7: calculate $\mathbb{E}\left[{\mathrm{SINR}}_{e}\right]$ using (29) and the parameters of Eve 8: ${\gamma}_{e,tmp}=\mathbb{E}\left[{\mathrm{SINR}}_{e}\right]$ 9: break10: end if11: end while12: end for13: Choose ${\psi}_{b}^{\ast}$, ${\psi}_{\mathrm{AN}}^{\ast}$ that achieve the minimum ${\gamma}_{e,tmp}$, ${g}_{b}^{\ast}$ takes the value of the corresponding ${g}_{b,tmp}$. |

## 5. Simulation Results

^{th}generation (5G) mobile communication systems [47]. Polar code has been adopted for enhanced mobile broadband (eMBB) control channels. We set the rate of the code $R=4$, $\u03f5=0.15$, and the length of information as 128. It can be seen from Figure 11 that the BLER of Bob remains 0 and the BLER of Eve increases with ${\theta}_{e}$. When $M=8$, the BLER of Eve reaches 1 for ${\theta}_{e}={50}^{\circ}$, which means that eavesdroppers beyond 5° cannot decode the information. When the number of antennas reaches 32, eavesdroppers beyond 1° also cannot decode the message.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The expectation of ${\mathrm{SINR}}_{b}$ and ${\mathrm{SINR}}_{e}$ in the function of ${g}_{\mathrm{AN}}$ for $M\in \{8,16,32,64,100\}$.

**Figure 3.**The expectation of ${\mathrm{SINR}}_{b}$ and ${\mathrm{SINR}}_{e}$ with optimal beamforming in the function of the location of Eve ${\theta}_{e}$.

**Figure 4.**The expectation of the power of the desired signal and AN received by Eve, with different numbers of receive antennas at Eve.

**Figure 6.**The expectation of ${\mathrm{SINR}}_{e}$ without using AN in the function of the location of Eve ${\theta}_{e}$.

**Figure 7.**The simulated BERs of Eve without using AN in the function of the location of Eve ${\theta}_{e}$.

**Figure 8.**The expectations of ${\mathrm{SINR}}_{b}$ and ${\mathrm{SINR}}_{e}$ when the ergodic secrecy rate is maximized in the function of the location of Eve ${\theta}_{e}$.

**Figure 9.**The simulated BERs when the ergodic secrecy rate is maximized in the function of the location of Eve ${\theta}_{e}$.

**Figure 10.**The expectation of ${\mathrm{SINR}}_{b}$ and ${\mathrm{SINR}}_{e}$ for ${K}_{b}=\{10,14.8\}$ dB in the function of the location of Eve ${\theta}_{e}$.

**Figure 11.**The simulated BLERs of Bob and Eve in the function of the location of Eve ${\theta}_{e}$.

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**MDPI and ACS Style**

Fu, H.; Zhang, X.; Peng, L.
Performance Analysis of Artificial Noise-Assisted Location-Based Beamforming in Rician Wiretap Channels. *Entropy* **2023**, *25*, 1626.
https://doi.org/10.3390/e25121626

**AMA Style**

Fu H, Zhang X, Peng L.
Performance Analysis of Artificial Noise-Assisted Location-Based Beamforming in Rician Wiretap Channels. *Entropy*. 2023; 25(12):1626.
https://doi.org/10.3390/e25121626

**Chicago/Turabian Style**

Fu, Hua, Xiaoyu Zhang, and Linning Peng.
2023. "Performance Analysis of Artificial Noise-Assisted Location-Based Beamforming in Rician Wiretap Channels" *Entropy* 25, no. 12: 1626.
https://doi.org/10.3390/e25121626