# Residual Energy Analysis in Cognitive Radios with Energy Harvesting UAV under Reliability and Secrecy Constraints

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## Abstract

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## 1. Introduction

#### 1.1. Contributions

- We consider the energy management aspect of the energy harvesting CR-based UAV with limited-energy budget. The closed-form expressions of the total residual energy, connection outage probability, and secrecy outage probability are derived under a circular flight condition.
- We aim to extend the on-board battery life-time for UAV by maximizing the energy obtained through the EH and minimizing the transmission energy consumption. Thus, the optimal lengths of sensing phase and the transmit powers are obtained by solving the formulated optimization problems of maximum residual energy under the constraints of connection and secrecy outage probabilities with perfect sensing approximation.
- The analytical results are verified through the numerical simulations including imperfect sensing. Based on the results, we provide guidelines in designing an energy harvesting UAV-based CR system with the reliable and secure communications under scenarios without and with an eavesdropper, respectively.

#### 1.2. Paper Organization

## 2. System Model

## 3. Sensing Procedure and Signal Modeling

## 4. Residual Energy Analysis

#### 4.1. Sensing Phase

#### 4.2. Transmission Phase

#### 4.3. Total Residual Energy

## 5. Connection and Secrecy Outage Probabilities

#### 5.1. Connection Outage Probability

#### 5.2. Secrecy Outage Probability

## 6. Maximization of Total Residual Energy

#### 6.1. Residual Energy Maximization under Connection Outage Constraint

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

**Lemma**

**3.**

**Proof.**

**Lemma**

**4.**

**Proof.**

#### 6.2. Residual Energy Maximization under Secrecy Outage Constraint

**Lemma**

**5.**

**Proof.**

**Lemma**

**6.**

**Proof.**

## 7. Numerical Results and Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Total residual energy, connection and secrecy outage probabilities, and their approximation under perfect sensing with respect to (

**a**) length of sensing phase (duration) with a fixed transmit power, (

**b**) transmit power for a fixed length of sensing phase.

**Figure 3.**Total residual energy and its approximation with respect to energy harvesting (EH) power splitting ratio for $\theta =\{\pi /2,\pi \}$ and ${P}_{tx}=\{50,90\}$ mW.

**Figure 4.**Monotonic functions of connection outage probability, secrecy outage probability vs. (

**a**) mean (expectation) of $|{h}_{l}{|}^{2}$ and (

**b**) target rates.

**Figure 5.**Exact and approximated total residual energy as a function of $\theta $ for EH-unmanned aerial vehicle (UAV) under (

**a**) connection outage constraint, (

**b**) secrecy outage constraint.

**Figure 6.**Exact and approximated total residual energy as a function of ${P}_{tx}$ for EH-UAV under (

**a**) connection outage constraint, (

**b**) secrecy outage constraint.

**Figure 7.**Optimal lengths of sensing phase (duration) and optimal transmit powers for EH-UAV over (

**a**) connection outage threshold (${\phi}_{1}$), (

**b**) secrecy outage threshold (${\phi}_{2}$).

Symbol | Description |
---|---|

${\mathcal{P}}_{off},{\mathcal{P}}_{on}$ | 0.50 ( fair model of channel occupancy) |

${P}_{x}$ | 1.05 W |

${\mathcal{P}}_{d}$ | 0.85 (interference probability to PT is 15% or less for the imperfect sensing) |

${\omega}_{p}$ | 0.95 |

${\omega}_{e}$ | 0.82 |

${\omega}_{l}$ | 0.55 |

$\eta $ | 0.80 |

$\rho $ | 0.10 |

h | 100m |

${\sigma}^{2}$ | 0.10 W |

${\sigma}_{sr}^{2}$ | 0.78 W |

${\sigma}_{e}^{2}$ | 0.22 W |

${P}_{w},{P}_{\delta}$ | 0.50 mW |

${f}_{s}$ | 50 kHz |

${R}_{S1}$ | 0.30 bps/Hz |

${R}_{S2}$ | 0.60 bps/Hz |

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**MDPI and ACS Style**

Khalid, W.; Yu, H.; Noh, S.
Residual Energy Analysis in Cognitive Radios with Energy Harvesting UAV under Reliability and Secrecy Constraints. *Sensors* **2020**, *20*, 2998.
https://doi.org/10.3390/s20102998

**AMA Style**

Khalid W, Yu H, Noh S.
Residual Energy Analysis in Cognitive Radios with Energy Harvesting UAV under Reliability and Secrecy Constraints. *Sensors*. 2020; 20(10):2998.
https://doi.org/10.3390/s20102998

**Chicago/Turabian Style**

Khalid, Waqas, Heejung Yu, and Song Noh.
2020. "Residual Energy Analysis in Cognitive Radios with Energy Harvesting UAV under Reliability and Secrecy Constraints" *Sensors* 20, no. 10: 2998.
https://doi.org/10.3390/s20102998