# Physical Layer Intercept Probability in Wireless Sensor Networks over Fisher–Snedecor \({\mathcal{F}}\) Fading Channels

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- Novel, highly general exact intercept probability expressions for WSN security in the presence of an unauthorized node, under RS, OP, and CS scheduling methods, are derived.
- Asymptotic expressions in simpler form, showing good accuracy in the region of medium-to-high SNR values at the sink, are also determined with the aim to enable the evaluation of the security metrics required for optimal system design.
- Novel SRT analysis is identified, and the intercept probability is additionally quantified by the outage threshold.
- Numerical and simulation results verify the presented analysis and illustrate the influence of channel and system parameters against eavesdropping in WSN.

## 2. System and Channel Model

## 3. Intercept Probability Based on Sensor Scheduling

#### 3.1. Exact Analysis

#### 3.2. Asymptotic Analysis

## 4. Security–Reliability Tradeoff

## 5. Numerical Results and Simulation

^{®}, according to the fact that the exact expressions are in the form of special Meijer’s G functions, which are built-in functions in this software package. Along with the analytical results, independent Monte Carlo simulations are also shown. One ${P}_{\mathrm{int}}^{i}$ value is estimated on the basis of ${10}^{8}$ generated samples, in $\mathit{Matlab}$

^{®}. For the sake of simplicity, we assume i.i.d. main or/and wiretap links, in the analysis that follows.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

* | designates: s for sink, e for eavesdropper |

${\gamma}_{\ast i}$, SNR | signal-to-noise ratio at the sink (or eavesdropper), from the i-th sensor |

N | number of sensors in the network |

${h}_{\ast i}$ | channel fading amplitude for the i-th link |

${P}_{s}$ | signal power emitted from each sensor |

${d}_{\ast i}$ | distance between the i-th sensor and the sink (or eavesdropper) |

$\xi $ | path loss parameter |

${\sigma}_{N}^{2}$ | variance of additive white Gaussian noise |

${C}_{\ast i}$ | channel capacity of the i-th link (or wiretap channel) |

${p}_{{\gamma}_{\ast i}}$, PDF | probability density function of SNR at receiver |

${F}_{{\gamma}_{\ast i}}$, CDF | cumulative distribution function of SNR |

${m}_{\ast i}$ | fading severity |

${k}_{\ast i}$ | shadowing factor |

${P}_{\mathrm{int}}$ | intercept probability |

$\mathsf{\Lambda}$ | secrecy diversity order |

${\lambda}_{i}$, MER | main-to-eavesdropper’s signal ratio for i-th sensor |

CSI | channel state information |

## Appendix A. Derivation of Exact ${\mathit{P}}_{\mathit{int}}^{\mathbf{CS}}$

## Appendix B. Derivation of Asymptotic ${\mathit{P}}_{\mathit{int}}$

## References

- Rani, S.; Maheswar, R.; Kanagachidambaresan, G.; Jayarajan, P. Integration of WSN and IoT for Smart Cities; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar]
- Gaddam, A.; Wilkin, T.; Angelova, M.; Gaddam, J. Detecting Sensor Faults, Anomalies and Outliers in the Internet of Things: A Survey on the Challenges and Solutions. Electronics
**2020**, 9, 511. [Google Scholar] [CrossRef] [Green Version] - Gungor, V.C.; Lu, B.; Hancke, G.P. Opportunities and Challenges of Wireless Sensor Networks in Smart Grid. IEEE Trans. Ind. Electron.
**2010**, 57, 3557–3564. [Google Scholar] [CrossRef] [Green Version] - Fahmy, H.M.A. Wireless Sensor Networks: Concepts, Applications, Experimentation and Analysis; Springer Nature: Berlin/Heidelberg, Germany, 2020. [Google Scholar]
- Malik, N.N.; Alosaimi, W.; Uddin, M.I.; Alouffi, B.; Alyami, H. Wireless Sensor Network Applications in Healthcare and Precision Agriculture. J. Healthc. Eng.
**2020**, 2020, 8836613. [Google Scholar] [CrossRef] - Zhu, J.; Zou, Y.; Zheng, B. Physical-Layer Security and Reliability Challenges for Industrial Wireless Sensor Networks. IEEE Access
**2017**, 5, 5313–5320. [Google Scholar] [CrossRef] - Mukherjee, A. Physical-Layer Security in the Internet of Things: Sensing and Communication Confidentiality Under Resource Constraints. Proc. IEEE
**2015**, 103, 1747–1761. [Google Scholar] [CrossRef] - Shakiba-Herfeh, M.; Chorti, A.; Poor, H.V. Physical Layer Security: Authentication, Integrity, and Confidentiality. In Physical Layer Security; Springer: Cham, Switzerland, 2021. [Google Scholar] [CrossRef]
- Zou, Y.; Zhu, J.; Wang, X.; Hanzo, L. A Survey on Wireless Security: Technical Challenges, Recent Advances, and Future Trends. Proc. IEEE
**2016**, 104, 1727–1765. [Google Scholar] [CrossRef] [Green Version] - Wu, Y.; Khisti, A.; Xiao, C.; Caire, G.; Wong, K.K.; Gao, X. A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead. IEEE J. Sel. Areas Commun.
**2018**, 36, 679–695. [Google Scholar] [CrossRef] [Green Version] - Shannon, C.E. Communication theory of secrecy systems. Bell Syst. Tech. J.
**1949**, 28, 656–715. [Google Scholar] [CrossRef] - Wyner, A.D. The wire-tap channel. Bell Syst. Tech. J.
**1975**, 54, 1355–1387. [Google Scholar] [CrossRef] - Badarneh, O.S.; Sofotasios, P.C.; Muhaidat, S.; Cotton, S.L.; Rabie, K.; Al-Dhahir, N. On the Secrecy Capacity of Fisher–Snedecor F Fading Channels. In Proceedings of the 2018 14th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), Limassol, Cyprus, 15–17 October 2018; pp. 102–107. [Google Scholar] [CrossRef] [Green Version]
- Yoo, S.K.; Cotton, S.L.; Sofotasios, P.C.; Matthaiou, M.; Valkama, M.; Karagiannidis, G.K. The Fisher–Snedecor $\mathcal{F}$ Distribution: A Simple and Accurate Composite Fading Model. IEEE Commun. Lett.
**2017**, 21, 1661–1664. [Google Scholar] [CrossRef] [Green Version] - Kong, L.; Kaddoum, G. On Physical Layer Security Over the Fisher-Snedecor $\mathcal{F}$ Wiretap Fading Channels. IEEE Access
**2018**, 6, 39466–39472. [Google Scholar] [CrossRef] - Badarneh, O.S.; Sofotasios, P.C.; Muhaidat, S.; Cotton, S.L.; Rabie, K.M.; Aldhahir, N. Achievable Physical-Layer Security Over Composite Fading Channels. IEEE Access
**2020**, 8, 195772–195787. [Google Scholar] [CrossRef] - Kong, L.; Ai, Y.; He, J.; Rajatheva, N.; Kaddoum, G. Intercept Probability Analysis over the Cascaded Fisher-Snedecor $\mathcal{F}$ Fading Wiretap Channels. In Proceedings of the 2019 16th International Symposium on Wireless Communication Systems (ISWCS), Oulu, Finland, 27–30 August 2019; pp. 672–676. [Google Scholar]
- Goel, S.; Negi, R. Guaranteeing secrecy using artificial noise. IEEE Trans. Wirel. Commun.
**2008**, 7, 2180–2189. [Google Scholar] [CrossRef] - Zou, Y.; Wang, X.; Shen, W. Optimal relay selection for physical-layer security in cooperative wireless networks. IEEE J. Sel. Areas Commun.
**2013**, 31, 2099–2111. [Google Scholar] [CrossRef] [Green Version] - Zou, Y.; Wang, G. Intercept behavior analysis of industrial wireless sensor networks in the presence of eavesdropping attack. IEEE Trans. Ind. Inform.
**2015**, 12, 780–787. [Google Scholar] [CrossRef] [Green Version] - Park, D.; Seo, H.; Kwon, H.; Lee, B.G. Wireless packet scheduling based on the cumulative distribution function of user transmission rates. IEEE Trans. Commun.
**2005**, 53, 1919–1929. [Google Scholar] [CrossRef] - Ge, X.; Wu, P.; Jin, H.; Leung, V.C. Secrecy analysis of multiuser downlink wiretap networks with opportunistic scheduling. In Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK, 8–12 June 2015; pp. 7370–7375. [Google Scholar]
- Anastasov, J.A.; Cvetković, A.M.; Milović, D.M.; Milić, D.N.; Djordjević, G.T. On physical layer security in WSN over GK fading channels during intercept events. Telecommun. Syst.
**2020**, 74, 95–102. [Google Scholar] [CrossRef] - Zou, Y.; Wang, X.; Shen, W.; Hanzo, L. Security versus reliability analysis of opportunistic relaying. IEEE Trans. Veh. Technol.
**2013**, 63, 2653–2661. [Google Scholar] [CrossRef] [Green Version] - Li, B.; Zou, Y.; Zhu, J.; Cao, W. Impact of Hardware Impairment and Co-Channel Interference on Security-Reliability Trade-Off for Wireless Sensor Networks. IEEE Trans. Wirel. Commun.
**2021**. [Google Scholar] [CrossRef] - Gradshteyn, I.S.; Ryzhik, I.M. Table of Integrals, Series, and Products, 6th ed.; Academic Press: New York, NY, USA, 2000. [Google Scholar]
- Adamchik, V.; Marichev, O. The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system. In Proceedings of the International Symposium on Symbolic and Algebraic Computation, Tokyo, Japan, 20–24 August 1990; pp. 212–224. [Google Scholar]
- Hoang An, N.; Tran, M.; Nguyen, T.N.; Ha, D.H. Physical Layer Security in a Hybrid TPSR Two-Way Half-Duplex Relaying Network over a Rayleigh Fading Channel: Outage and Intercept Probability Analysis. Electronics
**2020**, 9, 428. [Google Scholar] [CrossRef] [Green Version] - Wolfram Research Inc. The Mathematical Functions Site; Wolfram Research Inc.: Champaign, IL, USA, 2020. [Google Scholar]

**Figure 3.**The intercept probability of the eavesdropped WSN vs. the fading severity over the main links.

**Figure 5.**The intercept probability for different fading/shadowing conditions over wiretap channels.

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**MDPI and ACS Style**

Maričić, S.; Milošević, N.; Drajić, D.; Milić, D.; Anastasov, J.
Physical Layer Intercept Probability in Wireless Sensor Networks over Fisher–Snedecor \({\mathcal{F}}\) Fading Channels. *Electronics* **2021**, *10*, 1368.
https://doi.org/10.3390/electronics10121368

**AMA Style**

Maričić S, Milošević N, Drajić D, Milić D, Anastasov J.
Physical Layer Intercept Probability in Wireless Sensor Networks over Fisher–Snedecor \({\mathcal{F}}\) Fading Channels. *Electronics*. 2021; 10(12):1368.
https://doi.org/10.3390/electronics10121368

**Chicago/Turabian Style**

Maričić, Srđan, Nenad Milošević, Dejan Drajić, Dejan Milić, and Jelena Anastasov.
2021. "Physical Layer Intercept Probability in Wireless Sensor Networks over Fisher–Snedecor \({\mathcal{F}}\) Fading Channels" *Electronics* 10, no. 12: 1368.
https://doi.org/10.3390/electronics10121368