# Passive Beamforming and Trajectory Optimization for Reconfigurable Intelligent Surface-Assisted UAV Secure Communication

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## Abstract

**:**

## 1. Introduction

## 2. System Model

## 3. The RIS-Aided UAV Secure Transmission

Algorithm 1: The AO Algorithm for the Power Allocation and Phase Shift and Trajectory Design |

#### 3.1. BS’s Beamforming Strategy

- (1)
- Eavesdropping elimination method

- (2)
- Destination aiming method

#### 3.2. Phase Shift Optimization

- (1)
- Calculation of Riemannian gradient:Riemannianian gradient is the orthogonal projection of f of Euclidean gradient on the complex field as$$\mathrm{grad}f\left(\phi \right)=f\left(\phi \right)-\mathrm{Re}\left\{\nabla f\left(\phi \right)\circ {\mathrm{\Phi}}^{*}\right\}\circ \mathrm{\Phi}.$$
- (2)
- Tangent vector of search direction:$$\mathbf{d}=-\mathrm{grad}{f}_{\mathrm{C}}+{\tau}_{1}\mathcal{T}\left(\overline{\mathbf{d}}\right).$$$\mathcal{T}(\xb7)$ is the vector transfer function, which is defined as$$\mathcal{T}\left(\mathbf{d}\right)=\overline{\mathbf{d}}-\mathrm{Re}\left\{\mathbf{d}\circ {\mathrm{\Phi}}^{*}\right\}\circ \mathrm{\Phi}.$$
- (3)
- The tangent vector is projected onto a complex circular manifold:$${\mathrm{\Phi}}_{n}\leftarrow \frac{{\left(\mathrm{\Phi}+{\tau}_{2}\mathbf{d}\right)}_{n}}{\left|{\left(\mathrm{\Phi}+{\tau}_{2}\mathbf{d}\right)}_{n}\right|}.$$${\tau}_{2}$ is the size of the Armijo step [35] (We use the Armijo rule for descent in Riemannian manifolds, and provides a detailed description).

#### 3.3. UAV’s Trajectory Optimization

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Maximum average secure transmission rate with the reflective units on each RIS for different methods (P = 2.5 dbm).

Parameters | Values |
---|---|

Time slot | 1s |

Maximum speed of UAV | 10m/s |

Horizontal height of UAV | 100m |

Starting position of UAV | (100, −500) |

Ending position of UAV | (100, 500) |

Position of BS | (−50, 0) |

Position of EVE | (0, 0) |

Position of User | (200, 0) |

Path-loss for LoS channel | $35.6+22.0\times lg\left(d\right)$ |

Path-loss for NLoS channel | $32.6+36.7\times lg\left(d\right)$ |

Transmission bandwidth | 180 kHz |

Noise power spectral density | −170 dBm/Hz |

Maximum transmission power | 10 dBm |

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**MDPI and ACS Style**

Wang, D.; Zhao, Y.; He, Y.; Tang, X.; Li, L.; Zhang, R.; Zhai, D.
Passive Beamforming and Trajectory Optimization for Reconfigurable Intelligent Surface-Assisted UAV Secure Communication. *Remote Sens.* **2021**, *13*, 4286.
https://doi.org/10.3390/rs13214286

**AMA Style**

Wang D, Zhao Y, He Y, Tang X, Li L, Zhang R, Zhai D.
Passive Beamforming and Trajectory Optimization for Reconfigurable Intelligent Surface-Assisted UAV Secure Communication. *Remote Sensing*. 2021; 13(21):4286.
https://doi.org/10.3390/rs13214286

**Chicago/Turabian Style**

Wang, Dawei, Yang Zhao, Yixin He, Xiao Tang, Lixin Li, Ruonan Zhang, and Daosen Zhai.
2021. "Passive Beamforming and Trajectory Optimization for Reconfigurable Intelligent Surface-Assisted UAV Secure Communication" *Remote Sensing* 13, no. 21: 4286.
https://doi.org/10.3390/rs13214286