# Secure Transmission of Terahertz Signals with Multiple Eavesdroppers

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## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. Signal Model

#### 2.2. Highly Directive Channel

#### 2.3. Scatter Channel

## 3. Secrecy Performance

#### 3.1. Performance Metrics

#### 3.2. Non-Colluding Eavesdroppers

#### 3.3. Colluding Eavesdroppers

## 4. Security Analysis

#### 4.1. Eve’s Attack

#### 4.2. AN as a Countermeasure

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**System model. (

**a**) Alice transmits a highly directive THz signal $\mathit{x}$ to Bob with or without AN $\mathit{w}$. A PEC (orange cylinder) located at the edge of beam can scatter the incident THz wave to Eves in all directions. (

**b**) The spatial distribution of Eves is modeled as PPP in a circle region. The objects in this indoor scene can scatter THz signals.

**Figure 2.**The scattered fields of PEC for (

**a**) a = 20 mm, ${d}_{3}$ = 2 m (

**b**) a = 40 mm, ${d}_{3}$ = 2 m (

**c**) a = 40 mm, ${d}_{3}$ = 1.5 m. The maximum values were cut off at 8 since only a few values exceed it.

**Figure 3.**Secure transmission probability (STP) under different ${R}_{S}$ and ${\lambda}_{p}$ for (

**a**) non-colluding case and (

**b**) colluding case. Parameters are given by: G = 25 dBi; N = 5; f = 300 GHz; and P = −10 dBm.

**Figure 4.**The normalized secrecy capacity as a function of ${d}_{2}$ in the non-colluding and colluding cases. Here, all the eavesdroppers have the same distance ${d}_{2}$ to the PEC and the channel fading is ignored. Other parameters are given by: G = 25 dBi; f = 300 GHz; P = −10 dBm; ${R}_{S}$ = 15 m; and ${d}_{3}$ = 1 m.

**Figure 5.**Ergodic secrecy capacity (ESC) as a function of ${d}_{1}$ (Alice–Bob) and ${d}_{3}$ (Alice–PEC) for (

**a**) non-colluding eavesdroppers and (

**b**) colluding eavesdroppers. Other parameters are given by: $G=25$ dBi; N = 3; f = 300 GHz; P = −10 dBm; ${R}_{S}$ = 15 m; and ${\lambda}_{p}$ = 0.015.

**Figure 6.**(

**a**) Influence of radius a on STP. (

**b**) ESC versus radius a under different PEC location ${d}_{3}$. The solid line describes the non-colluding case while the dashed line describes the colluding case. Other parameters are given by: G = 25 dBi; N = 3; f = 300 GHz; P = −10 dBm; ${R}_{S}$ = 15 m; and ${\lambda}_{p}$ = 0.04.

**Figure 7.**The benefit of AN on STP for (

**a**) a non-colluding case; and a (

**b**) colluding case. Other parameters are given by: G = 25 dBi, N = 3, f = 300 GHz, P = −10 dBm, ${R}_{S}$ = 15 m, $\eta $ = 0.3.

**Figure 8.**The optimal $\eta $ under different ${\lambda}_{p}$ and N. The solid line describes non-colluding cases while the dashed line describes colluding cases. The main figure for N = 2 while the inset for N = 6. Other parameters are given by: G = 27 dBi; f = 300 GHz; P = −10 dBm; and ${R}_{S}$ = 15 m.

**Figure 9.**Secrecy performance in a non-colluding case. (

**a**) The ECS as a function of $\eta $ and f with $P=-$10 dBm; (

**b**) The ECS as a function of $\eta $ and P with f = 300 GHz. Other parameters are given by: G = 25 dBi, N = 3, ${R}_{S}$ = 15 m, ${\lambda}_{p}$ = 0.02.

Side | Symbol | Parameter Setting | Value |
---|---|---|---|

Alice | P | Transmitting power | −10 dBm |

${G}_{t}$ | Antenna gain | 25/27 dBi | |

N | Antenna number | Independent variable | |

$\eta $ | Power allocation ratio | Independent variable | |

Channel | ${R}_{S}$ | Covering radius | 10/15 m |

${\lambda}_{p}$ | Density of eavesdroppers | Independent variable | |

${N}_{E}$ | Number of eavesdroppers | Independent variable | |

a | Radius of cylinder | Independent variable | |

${d}_{2}$ | Distance between Eve and PEC | Independent variable | |

${d}_{3}$ | Distance between Alice and PEC | Independent variable | |

m | Nakagami fading parameters | 2 | |

Bob | ${d}_{1}$ | Distance between Alice and Bob | Independent variable |

${G}_{r}$ | Antenna gain | 25/27 dBi | |

Other | c | Speed of light | 3 × 10${}^{8}$ m/s |

f | Frequency | Independent variable | |

${P}_{N}$ | Noise power | −75 dBm | |

W | Bandwidth | 50 GHz | |

N-C | Non-colluding case | - | |

C | Colluding case | - |

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**MDPI and ACS Style**

He, Y.; Zhang, L.; Liu, S.; Zhang, H.; Yu, X.
Secure Transmission of Terahertz Signals with Multiple Eavesdroppers. *Micromachines* **2022**, *13*, 1300.
https://doi.org/10.3390/mi13081300

**AMA Style**

He Y, Zhang L, Liu S, Zhang H, Yu X.
Secure Transmission of Terahertz Signals with Multiple Eavesdroppers. *Micromachines*. 2022; 13(8):1300.
https://doi.org/10.3390/mi13081300

**Chicago/Turabian Style**

He, Yuqian, Lu Zhang, Shanyun Liu, Hongqi Zhang, and Xianbin Yu.
2022. "Secure Transmission of Terahertz Signals with Multiple Eavesdroppers" *Micromachines* 13, no. 8: 1300.
https://doi.org/10.3390/mi13081300