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Secrecy capacity of hybrid FSO-RF communication links

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Abstract

In this paper, we analyze the secrecy capacity of hybrid communication links comprising cascaded free space optical (FSO) and radio frequency (RF) wireless systems. We consider the system in which FSO links are used as the medium of data transmission for the first hop followed by RF links for relaying the data to the destination. We consider Gamma–Gamma distributed channel gain for the FSO links and Nakagami-m fading distribution for the RF communication link. This takes care of both the line of sight (LOS) and non-LOS conditions for the RF link. We derive closed-form expressions for end-to-end secrecy capacity. The closed-form expressions are derived by representing the incomplete gamma function in the form of Meijer’s G-function. Further, closed-form solutions to the integrals involving the product of two Meijer’s G-functions are obtained. The analytical expressions have been validated through results obtained from simulations. A close agreement between the simulation and the analytical results is observed.

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References

  1. A.K. Pandey, Average capacity of FSO links over K-turbulence fading channels with pointing errors. J. Opt. 44(3), 305–309 (2015). https://doi.org/10.1007/s12596-015-0259-4

    Article  Google Scholar 

  2. R. Miglani, J.S. Malhotra, Evaluation of link-compensated 3240 gbit/s dwdm free space optical (FSO) transmission. J. Opt. 47(4), 467–474 (2018). https://doi.org/10.1007/s12596-018-0484-8

    Article  Google Scholar 

  3. H. Wu, J. Ma, P. Guo, Q. Wang, D. Kang, J. Yang, J. Wu, Secrecy outage probability analysis in a free-space optical system based on partially coherent beams through anisotropic non-Kolmogorov turbulent atmosphere. J. Opt. Soc. Am. B 39(5), 1378–1387 (2022). https://doi.org/10.1364/JOSAB.452857

    Article  ADS  Google Scholar 

  4. E. Zedini, M.-S. Alouini, On the performance of multihop heterodyne FSO systems with pointing errors. IEEE Photon. J. 7(2), 1–10 (2015). https://doi.org/10.1109/JPHOT.2015.2417867

    Article  Google Scholar 

  5. W. Gappmair, M. Flohberger, Error performance of coded FSO links in turbulent atmosphere modeled by gamma–gamma distributions. IEEE Transact. Wirel. Commun. 8(5), 2209–2213 (2009). https://doi.org/10.1109/TWC.2009.080076

    Article  Google Scholar 

  6. A. Das, B. Bag, C. Bose, A. Chandra, Free space optical links over Málaga turbulence channels with transmit and receive diversity. Opt. Commun. 456, 124591 (2020). https://doi.org/10.1016/j.optcom.2019.124591

    Article  Google Scholar 

  7. M. Cheng, J. Gao, W. Dan, Y. Zhang, Block error rate of fso links over non-kolmogorov turbulence with exponentiated weibull distribution. Optik 125(22), 6805–6809 (2014). https://doi.org/10.1016/j.ijleo.2014.07.101

    Article  ADS  Google Scholar 

  8. A.D. Wyner, The wire-tap channel. Bell Syst. Tech. J. 54(8), 1355–1387 (1975). https://doi.org/10.1002/j.1538-7305.1975.tb02040.x

    Article  MathSciNet  Google Scholar 

  9. A. Omri, M.O. Hasna, Average secrecy outage rate and average secrecy outage duration of wireless communication systems with diversity over Nakagami-m fading channels. IEEE Transact. Wirel. Commun. 17(6), 3822–3833 (2018)

    Article  Google Scholar 

  10. N. Yang, P.L. Yeoh, M. Elkashlan, R. Schober, I.B. Collings, Transmit antenna selection for security enhancement in MIMO wiretap channels. IEEE Transact. Commun. 61(1), 144–154 (2013). https://doi.org/10.1109/TCOMM.2012.12.110670

    Article  Google Scholar 

  11. H. Lei, H. Zhang, I.S. Ansari, C. Gao, Y. Guo, G. Pan, K.A. Qaraqe, Secrecy outage performance for SIMO underlay cognitive radio systems with generalized selection combining over Nakagami-channels. IEEE Transact. Veh. Technol. 65(12), 10126–10132 (2016). https://doi.org/10.1109/TVT.2016.2536801

    Article  Google Scholar 

  12. H. Lei, C. Gao, I.S. Ansari, Y. Guo, Y. Zou, G. Pan, K.A. Qaraqe, Secrecy outage performance of transmit antenna selection for MIMO underlay cognitive radio systems over Nakagami-channels. IEEE Transact. Veh. Technol. 66(3), 2237–2250 (2017). https://doi.org/10.1109/TVT.2016.2574315

    Article  Google Scholar 

  13. J. Si, Z. Li, J. Cheng, C. Zhong, Asymptotic secrecy outage performance for tas/mrc over correlated Nakagami-fading channels. IEEE Transact. Commun. 67(11), 7700–7714 (2019)

    Article  Google Scholar 

  14. H.K. Sharma, B. Kumbhani, Secrecy analysis of mrc diversity schemes over Nakagami-m fading channels, in 2019 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), pp. 1–5 (2019)

  15. W.M.R. Shakir, Physical layer security performance analysis of hybrid FSO/RF communication system. IEEE Access 9, 18948–18961 (2021). https://doi.org/10.1109/ACCESS.2020.3048614

    Article  Google Scholar 

  16. N. Vishwakarma, R. Swaminathan, Performance analysis of hybrid FSO/RF communication over generalized fading models. Opt. Commun. 487, 126796 (2021). https://doi.org/10.1016/j.optcom.2021.126796

    Article  Google Scholar 

  17. K.O. Odeyemi, P.A. Owolawi, Selection combining hybrid FSO/RF systems over generalized induced-fading channels. Opt. Commun. 433, 159–167 (2019). https://doi.org/10.1016/j.optcom.2018.10.009

    Article  ADS  Google Scholar 

  18. H. Liang, Y. Li, M. Miao, C. Gao, X. Li, Analysis of selection combining hybrid FSO/RF systems considering physical layer security and interference. Opt. Commun. 497, 127146 (2021). https://doi.org/10.1016/j.optcom.2021.127146

    Article  Google Scholar 

  19. Z. Jing, Z. Shang-hong, Z. Wei-hu, C. Ke-fan, Performance analysis for mixed FSO/RF Nakagami-m and exponentiated Weibull dual-hop airborne systems. Opt. Commun. 392, 294–299 (2017). https://doi.org/10.1016/j.optcom.2017.01.033

    Article  ADS  Google Scholar 

  20. V.K. Tonk, V.K. Dwivedi, A. Upadhya, S.P. Singh, P.K. Yadav, New results in secrecy analysis of mixed RF/FSO cooperative relaying networks. Opt. Commun. 503, 127376 (2022). https://doi.org/10.1016/j.optcom.2021.127376

    Article  Google Scholar 

  21. S. Ghatwal, H. Saini, Investigations on challenges faced by hybrid FSO/RF high-speed networks. J. Opt. 52(2), 924–934 (2023). https://doi.org/10.1007/s12596-022-00898-w

    Article  Google Scholar 

  22. D. Bykhovsky, Simple generation of Gamma, Gamma-Gamma, and K distributions with exponential autocorrelation function. J. Lightw. Technol. 34(9), 2106–2110 (2016). https://doi.org/10.1109/JLT.2016.2525781

    Article  ADS  Google Scholar 

  23. A. Bhowal, R.S. Kshetrimayum, Advanced Spatial Modulation Systems (Springer, Singapore, 2021). https://doi.org/10.1007/978-981-15-9960-6

    Book  Google Scholar 

  24. M.K. Simon, M.-S. Alouini, Digital Communication over Fading Channels (Wiley, Hoboken, 2005)

    Google Scholar 

  25. B. Kumbhani, R.S. Kshetrimayum, MIMO Wireless Communications over Generalized Fading Channels (CRC Press, Florida, 2017)

    Book  Google Scholar 

  26. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 7th edn. (Academic Press, New York, 2007)

    Google Scholar 

Download references

Funding

This work has been partially supported by the Indo-Austria grant number DST/IC/Austria/P-12/2021.

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Correspondence to Brijesh Kumbhani.

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Sharma, H.K., Kumbhani, B. Secrecy capacity of hybrid FSO-RF communication links. J Opt (2024). https://doi.org/10.1007/s12596-023-01593-0

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