Abstract

In this paper, we propose a secure transmission scheme to protect the confidential messages in a mixed free space optical-radio frequency (FSO-RF) relay network against malicious eavesdroppers. In the proposed scheme, the physical-layer key generation, encryption method and physical-layer wiretap coding are exploited to protect the FSO and RF links. Specifically, the overall transmission is divided into two time slots. In the first time slot, the transmitter and relay of the FSO link utilize the channel reciprocity of the FSO link to generate key packets. In the second time slot, the confidential messages will be securely transmitted from the transmitter to the receiver assisted by the relay over two phases. In the first phase, the transmitter sends the confidential messages to the relay through the FSO link encrypted by the generated key packets. In the second phase, the relay will forward these confidential messages to the receiver through the RF link protected by the physical-layer wiretap coding. For the proposed scheme, the key generation rate can be obtained. In addition, we analyze the performance of the connection outage probability and the secrecy outage probability, and optimally design the target transmission rate and secrecy rate such that the average secrecy rate is maximized. Numerical results are presented to demonstrate the performance superiority of the proposed scheme in terms of the average secrecy rate.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. D. J. T. Heatley, “Optical wireless: The story so far,” IIEEE Commun. Mag. 36(12), 72–74 (1988).
    [Crossref]
  3. E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
    [Crossref]
  4. I. S. Ansari, F. Yilmaz, and M.-S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” IEEE Wireless Commun. Lett. 2(3), 351–354 (2013).
    [Crossref]
  5. E. Zedini, H. Soury, and M. -S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. on Commun. 15(5), 3679–3689 (2016).
  6. I. S. Ansari, M. M. Abbdallah, M. -S. Alouini, and K. A. Qaraqe, “Outage performance analysis of underlay cognitive RF and FSO wireless channels,” The 3rd International Workshop in Optical Wireless Communications (IWOW) (2014).
  7. L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
    [Crossref]
  8. L. Yang, M. O. Hasna, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. 33(9), 1913–1924 (2015).
    [Crossref]
  9. S. Anees and M. R. Bhatnagar, “Performance of an amplify-and-forward dual-hop asymmetric RF-FSO communication system,” IEEE/OSA J. Opt. Commun. Networking 7(2), 124–135 (2015).
    [Crossref]
  10. A. M. Salhab, F. S. Al-Qahtani, R. M. Radaydeh, S. A. Zummo, and H. Alnuweiri, “Power allocation and performance of multiuser mixed RF/FSO relay networks with opportunistic scheduling and outdated channel information,” J. Lightwave Technol. 34(13), 3259–3272 (2016).
    [Crossref]
  11. N. I. Miridakis, M. Matthaiou, and G. K. Karagiannidis, “Multiuser relaying over mixed RF/FSO links,” IEEE Trans. on Commun. 62(5), 1634–1645 (2014).
    [Crossref]
  12. M. I. Petkovic, A. M. Cvetkovic, G. T. Djordjevic, and G. K. Karagiannidis, “Partial relay selection with outdated channel state estimation in mixed RF/FSO systems,” J. Lightwave Technol. 33(13), 2860–2867 (2015).
    [Crossref]
  13. B. Makki, T. Svensson, T. Eriksson, and M. -S. Alouini, “On the performance of RF-FSO links with and without hybrid ARQ,” IEEE Trans. on Wireless Commun. Accepted, (2016).
    [Crossref]
  14. L. Lai, Y. Lang, and W. Du, “Cooperative key generation in wireless networks,” IEEE J. Sel. Areas Commun. 30(8), 1578–1588 (2012).
    [Crossref]
  15. Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).
  16. H. V. Poor, “Information and inference in the wireless physical layer,” IEEE Commun. Mag. 19(1), 40–47 (2012).
  17. A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).
  18. N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
    [Crossref]
  19. F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
    [Crossref]
  20. G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
    [Crossref]
  21. A. A. Farid and S. Hranilovic, “Outage capacity optimization for frees pace optical links with pointing errors,” J. Lightw. Technol. 25(7), 1702–1710 (2007).
    [Crossref]
  22. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic2007).
  23. A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using diversity-combining techniques,” Opt. Express 17(15), 12601–12611 (2009).
    [Crossref] [PubMed]
  24. A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using atmospheric compensation techniques,” Opt. Express 17(4), 2763–2773 (2009).
    [Crossref] [PubMed]
  25. Q. Gao, C. Gong, and Z. Xu, “Joint transceiver and offset design for visible light communications with input-dependent shot noise,” Accepted by IEEE Trans. Wireless Commun. (2017).
    [Crossref]
  26. M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K -distributed turbulence,” IEEE Trans. Wireless Commun. 59(3), 664–668 (2011).
    [Crossref]
  27. B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
    [Crossref]
  28. Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “Spatial dimming scheme for optical OFDM based visible light communication,” Opt. Express,  24(28), 30254–30263 (2016).
    [Crossref]
  29. X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).
  30. M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011).
    [Crossref] [PubMed]

2016 (4)

E. Zedini, H. Soury, and M. -S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. on Commun. 15(5), 3679–3689 (2016).

A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).

A. M. Salhab, F. S. Al-Qahtani, R. M. Radaydeh, S. A. Zummo, and H. Alnuweiri, “Power allocation and performance of multiuser mixed RF/FSO relay networks with opportunistic scheduling and outdated channel information,” J. Lightwave Technol. 34(13), 3259–3272 (2016).
[Crossref]

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “Spatial dimming scheme for optical OFDM based visible light communication,” Opt. Express,  24(28), 30254–30263 (2016).
[Crossref]

2015 (7)

M. I. Petkovic, A. M. Cvetkovic, G. T. Djordjevic, and G. K. Karagiannidis, “Partial relay selection with outdated channel state estimation in mixed RF/FSO systems,” J. Lightwave Technol. 33(13), 2860–2867 (2015).
[Crossref]

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
[Crossref]

B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
[Crossref]

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

L. Yang, M. O. Hasna, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. 33(9), 1913–1924 (2015).
[Crossref]

S. Anees and M. R. Bhatnagar, “Performance of an amplify-and-forward dual-hop asymmetric RF-FSO communication system,” IEEE/OSA J. Opt. Commun. Networking 7(2), 124–135 (2015).
[Crossref]

2014 (2)

N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
[Crossref]

N. I. Miridakis, M. Matthaiou, and G. K. Karagiannidis, “Multiuser relaying over mixed RF/FSO links,” IEEE Trans. on Commun. 62(5), 1634–1645 (2014).
[Crossref]

2013 (1)

I. S. Ansari, F. Yilmaz, and M.-S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” IEEE Wireless Commun. Lett. 2(3), 351–354 (2013).
[Crossref]

2012 (3)

L. Lai, Y. Lang, and W. Du, “Cooperative key generation in wireless networks,” IEEE J. Sel. Areas Commun. 30(8), 1578–1588 (2012).
[Crossref]

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

H. V. Poor, “Information and inference in the wireless physical layer,” IEEE Commun. Mag. 19(1), 40–47 (2012).

2011 (4)

M. Toyoshima, H. Takenaka, and Y. Takayama, “Atmospheric turbulence-induced fading channel model for space-to-ground laser communications links,” Opt. Express 19(17), 15965–15975 (2011).
[Crossref] [PubMed]

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K -distributed turbulence,” IEEE Trans. Wireless Commun. 59(3), 664–668 (2011).
[Crossref]

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
[Crossref]

2009 (2)

2007 (1)

A. A. Farid and S. Hranilovic, “Outage capacity optimization for frees pace optical links with pointing errors,” J. Lightw. Technol. 25(7), 1702–1710 (2007).
[Crossref]

2004 (1)

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

1988 (1)

D. J. T. Heatley, “Optical wireless: The story so far,” IIEEE Commun. Mag. 36(12), 72–74 (1988).
[Crossref]

Abbdallah, M. M.

I. S. Ansari, M. M. Abbdallah, M. -S. Alouini, and K. A. Qaraqe, “Outage performance analysis of underlay cognitive RF and FSO wireless channels,” The 3rd International Workshop in Optical Wireless Communications (IWOW) (2014).

Alnuweiri, H.

Alouini, M. -S.

E. Zedini, H. Soury, and M. -S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. on Commun. 15(5), 3679–3689 (2016).

A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).

B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
[Crossref]

I. S. Ansari, M. M. Abbdallah, M. -S. Alouini, and K. A. Qaraqe, “Outage performance analysis of underlay cognitive RF and FSO wireless channels,” The 3rd International Workshop in Optical Wireless Communications (IWOW) (2014).

B. Makki, T. Svensson, T. Eriksson, and M. -S. Alouini, “On the performance of RF-FSO links with and without hybrid ARQ,” IEEE Trans. on Wireless Commun. Accepted, (2016).
[Crossref]

Alouini, M.-S.

I. S. Ansari, F. Yilmaz, and M.-S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” IEEE Wireless Commun. Lett. 2(3), 351–354 (2013).
[Crossref]

Al-Qahtani, F. S.

Anees, S.

S. Anees and M. R. Bhatnagar, “Performance of an amplify-and-forward dual-hop asymmetric RF-FSO communication system,” IEEE/OSA J. Opt. Commun. Networking 7(2), 124–135 (2015).
[Crossref]

Ansari, I. S.

I. S. Ansari, F. Yilmaz, and M.-S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” IEEE Wireless Commun. Lett. 2(3), 351–354 (2013).
[Crossref]

I. S. Ansari, M. M. Abbdallah, M. -S. Alouini, and K. A. Qaraqe, “Outage performance analysis of underlay cognitive RF and FSO wireless channels,” The 3rd International Workshop in Optical Wireless Communications (IWOW) (2014).

Arnon, S.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

Belmonte, A.

Bhatnagar, M. R.

S. Anees and M. R. Bhatnagar, “Performance of an amplify-and-forward dual-hop asymmetric RF-FSO communication system,” IEEE/OSA J. Opt. Commun. Networking 7(2), 124–135 (2015).
[Crossref]

Chang, S.

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

Chen, H.

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

Cheng, J.

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “Spatial dimming scheme for optical OFDM based visible light communication,” Opt. Express,  24(28), 30254–30263 (2016).
[Crossref]

B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
[Crossref]

N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
[Crossref]

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K -distributed turbulence,” IEEE Trans. Wireless Commun. 59(3), 664–668 (2011).
[Crossref]

Cvetkovic, A. M.

G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
[Crossref]

M. I. Petkovic, A. M. Cvetkovic, G. T. Djordjevic, and G. K. Karagiannidis, “Partial relay selection with outdated channel state estimation in mixed RF/FSO systems,” J. Lightwave Technol. 33(13), 2860–2867 (2015).
[Crossref]

Djordjevic, G. T.

M. I. Petkovic, A. M. Cvetkovic, G. T. Djordjevic, and G. K. Karagiannidis, “Partial relay selection with outdated channel state estimation in mixed RF/FSO systems,” J. Lightwave Technol. 33(13), 2860–2867 (2015).
[Crossref]

G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
[Crossref]

Du, W.

L. Lai, Y. Lang, and W. Du, “Cooperative key generation in wireless networks,” IEEE J. Sel. Areas Commun. 30(8), 1578–1588 (2012).
[Crossref]

El-Malek, A. H. A.

A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).

Eriksson, T.

B. Makki, T. Svensson, T. Eriksson, and M. -S. Alouini, “On the performance of RF-FSO links with and without hybrid ARQ,” IEEE Trans. on Wireless Commun. Accepted, (2016).
[Crossref]

Farid, A. A.

A. A. Farid and S. Hranilovic, “Outage capacity optimization for frees pace optical links with pointing errors,” J. Lightw. Technol. 25(7), 1702–1710 (2007).
[Crossref]

Gao, Q.

Q. Gao, C. Gong, and Z. Xu, “Joint transceiver and offset design for visible light communications with input-dependent shot noise,” Accepted by IEEE Trans. Wireless Commun. (2017).
[Crossref]

Gao, X.

L. Yang, M. O. Hasna, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. 33(9), 1913–1924 (2015).
[Crossref]

Garrido-Balsells, J. M.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

Ghassemlooy, Z.

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

Gomez, G.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

Gong, C.

Q. Gao, C. Gong, and Z. Xu, “Joint transceiver and offset design for visible light communications with input-dependent shot noise,” Accepted by IEEE Trans. Wireless Commun. (2017).
[Crossref]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic2007).

Guo, C.

Han, D.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
[Crossref]

Hanzo, L.

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

Hasna, M. O.

L. Yang, M. O. Hasna, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. 33(9), 1913–1924 (2015).
[Crossref]

Heatley, D. J. T.

D. J. T. Heatley, “Optical wireless: The story so far,” IIEEE Commun. Mag. 36(12), 72–74 (1988).
[Crossref]

Holzman, J. F.

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K -distributed turbulence,” IEEE Trans. Wireless Commun. 59(3), 664–668 (2011).
[Crossref]

Hranilovic, S.

A. A. Farid and S. Hranilovic, “Outage capacity optimization for frees pace optical links with pointing errors,” J. Lightw. Technol. 25(7), 1702–1710 (2007).
[Crossref]

Huang, S.

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

Kahn, J. M.

Karagiannidis, G. K.

G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
[Crossref]

M. I. Petkovic, A. M. Cvetkovic, G. T. Djordjevic, and G. K. Karagiannidis, “Partial relay selection with outdated channel state estimation in mixed RF/FSO systems,” J. Lightwave Technol. 33(13), 2860–2867 (2015).
[Crossref]

N. I. Miridakis, M. Matthaiou, and G. K. Karagiannidis, “Multiuser relaying over mixed RF/FSO links,” IEEE Trans. on Commun. 62(5), 1634–1645 (2014).
[Crossref]

Kedar, D.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

Kong, L.

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

Lai, L.

L. Lai, Y. Lang, and W. Du, “Cooperative key generation in wireless networks,” IEEE J. Sel. Areas Commun. 30(8), 1578–1588 (2012).
[Crossref]

Lang, Y.

L. Lai, Y. Lang, and W. Du, “Cooperative key generation in wireless networks,” IEEE J. Sel. Areas Commun. 30(8), 1578–1588 (2012).
[Crossref]

Lee, C. G.

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

Lee, E.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
[Crossref]

Leung, V. C. M.

N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
[Crossref]

Lopez-Martinez, F. J.

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

Makki, B.

B. Makki, T. Svensson, T. Eriksson, and M. -S. Alouini, “On the performance of RF-FSO links with and without hybrid ARQ,” IEEE Trans. on Wireless Commun. Accepted, (2016).
[Crossref]

Matthaiou, M.

N. I. Miridakis, M. Matthaiou, and G. K. Karagiannidis, “Multiuser relaying over mixed RF/FSO links,” IEEE Trans. on Commun. 62(5), 1634–1645 (2014).
[Crossref]

Miridakis, N. I.

N. I. Miridakis, M. Matthaiou, and G. K. Karagiannidis, “Multiuser relaying over mixed RF/FSO links,” IEEE Trans. on Commun. 62(5), 1634–1645 (2014).
[Crossref]

Niu, M.

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K -distributed turbulence,” IEEE Trans. Wireless Commun. 59(3), 664–668 (2011).
[Crossref]

Park, J.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
[Crossref]

Petkovic, M. I.

M. I. Petkovic, A. M. Cvetkovic, G. T. Djordjevic, and G. K. Karagiannidis, “Partial relay selection with outdated channel state estimation in mixed RF/FSO systems,” J. Lightwave Technol. 33(13), 2860–2867 (2015).
[Crossref]

G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
[Crossref]

Poor, H. V.

H. V. Poor, “Information and inference in the wireless physical layer,” IEEE Commun. Mag. 19(1), 40–47 (2012).

Popoola, W. O.

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

Qaraqe, K. A.

I. S. Ansari, M. M. Abbdallah, M. -S. Alouini, and K. A. Qaraqe, “Outage performance analysis of underlay cognitive RF and FSO wireless channels,” The 3rd International Workshop in Optical Wireless Communications (IWOW) (2014).

Radaydeh, R. M.

Rajbhandari, S.

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic2007).

Salhab, A. M.

A. M. Salhab, F. S. Al-Qahtani, R. M. Radaydeh, S. A. Zummo, and H. Alnuweiri, “Power allocation and performance of multiuser mixed RF/FSO relay networks with opportunistic scheduling and outdated channel information,” J. Lightwave Technol. 34(13), 3259–3272 (2016).
[Crossref]

A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).

Shiu, Y.

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

Song, X.

N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
[Crossref]

Soury, H.

E. Zedini, H. Soury, and M. -S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. on Commun. 15(5), 3679–3689 (2016).

Svensson, T.

B. Makki, T. Svensson, T. Eriksson, and M. -S. Alouini, “On the performance of RF-FSO links with and without hybrid ARQ,” IEEE Trans. on Wireless Commun. Accepted, (2016).
[Crossref]

Takayama, Y.

Takenaka, H.

Tang, X.

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

Toyoshima, M.

Wang, N.

N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
[Crossref]

Wu, H.

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

Wu, L.

B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
[Crossref]

Xu, W.

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

Xu, Z.

Q. Gao, C. Gong, and Z. Xu, “Joint transceiver and offset design for visible light communications with input-dependent shot noise,” Accepted by IEEE Trans. Wireless Commun. (2017).
[Crossref]

Yang, L.

L. Yang, M. O. Hasna, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. 33(9), 1913–1924 (2015).
[Crossref]

Yang, Y.

Yilmaz, F.

I. S. Ansari, F. Yilmaz, and M.-S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” IEEE Wireless Commun. Lett. 2(3), 351–354 (2013).
[Crossref]

Yoon, G.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
[Crossref]

Zedini, E.

E. Zedini, H. Soury, and M. -S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. on Commun. 15(5), 3679–3689 (2016).

Zeng, Z.

Zhang, H.

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

Zhao, C.

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

Zhu, B.

B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
[Crossref]

Zummo, S. A.

A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).

A. M. Salhab, F. S. Al-Qahtani, R. M. Radaydeh, S. A. Zummo, and H. Alnuweiri, “Power allocation and performance of multiuser mixed RF/FSO relay networks with opportunistic scheduling and outdated channel information,” J. Lightwave Technol. 34(13), 3259–3272 (2016).
[Crossref]

Amer. J. Eng. Appl. Sci. (1)

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent polarization shift keying modulated free space optical links over a Gamma-Gamma turbulence channel,” Amer. J. Eng. Appl. Sci. 4(4), 520–530 (2012).

IEEE Commun. Mag. (3)

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag. 42(5), S2–S7 (2004).
[Crossref]

Y. Shiu, S. Chang, H. Wu, S. Huang, and H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Commun. Mag. 18(2), 66–74 (2011).

H. V. Poor, “Information and inference in the wireless physical layer,” IEEE Commun. Mag. 19(1), 40–47 (2012).

IEEE J. Sel. Areas Commun. (3)

G. T. Djordjevic, M. I. Petkovic, A. M. Cvetkovic, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. 33(9), 1935–1948 (2015).
[Crossref]

L. Yang, M. O. Hasna, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. 33(9), 1913–1924 (2015).
[Crossref]

L. Lai, Y. Lang, and W. Du, “Cooperative key generation in wireless networks,” IEEE J. Sel. Areas Commun. 30(8), 1578–1588 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (1)

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett. 23(21), 1642–1644 (2011).
[Crossref]

IEEE Photonics J. (2)

L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 64(6), 1–19 (2015).
[Crossref]

F. J. Lopez-Martinez, G. Gomez, and J. M. Garrido-Balsells, “Physical-layer security in free-space optical communications,” IEEE Photonics J. 7(2), 1–14 (2015).
[Crossref]

IEEE Trans. on Commun. (3)

N. I. Miridakis, M. Matthaiou, and G. K. Karagiannidis, “Multiuser relaying over mixed RF/FSO links,” IEEE Trans. on Commun. 62(5), 1634–1645 (2014).
[Crossref]

E. Zedini, H. Soury, and M. -S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. on Commun. 15(5), 3679–3689 (2016).

A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M. -S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. on Commun. 15(9), 5904–5918 (2016).

IEEE Trans. Wireless Commun. (2)

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K -distributed turbulence,” IEEE Trans. Wireless Commun. 59(3), 664–668 (2011).
[Crossref]

B. Zhu, J. Cheng, M. -S. Alouini, and L. Wu, “Relay placement for FSO multihop DF systems with link obstacles and infeasible regions,” IEEE Trans. Wireless Commun. 14(9), 5240–5250 (2015).
[Crossref]

IEEE Wireless Commun. Lett. (1)

I. S. Ansari, F. Yilmaz, and M.-S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” IEEE Wireless Commun. Lett. 2(3), 351–354 (2013).
[Crossref]

IEEE/OSA J. Opt. Commun. Networking (2)

S. Anees and M. R. Bhatnagar, “Performance of an amplify-and-forward dual-hop asymmetric RF-FSO communication system,” IEEE/OSA J. Opt. Commun. Networking 7(2), 124–135 (2015).
[Crossref]

N. Wang, X. Song, J. Cheng, and V. C. M. Leung, “Enhancing the security of free-space optical communications with secret sharing and key agreement,” IEEE/OSA J. Opt. Commun. Networking 6(12), 1072–1081 (2014).
[Crossref]

IIEEE Commun. Mag. (1)

D. J. T. Heatley, “Optical wireless: The story so far,” IIEEE Commun. Mag. 36(12), 72–74 (1988).
[Crossref]

J. Lightw. Technol. (1)

A. A. Farid and S. Hranilovic, “Outage capacity optimization for frees pace optical links with pointing errors,” J. Lightw. Technol. 25(7), 1702–1710 (2007).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (4)

Other (4)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic2007).

Q. Gao, C. Gong, and Z. Xu, “Joint transceiver and offset design for visible light communications with input-dependent shot noise,” Accepted by IEEE Trans. Wireless Commun. (2017).
[Crossref]

B. Makki, T. Svensson, T. Eriksson, and M. -S. Alouini, “On the performance of RF-FSO links with and without hybrid ARQ,” IEEE Trans. on Wireless Commun. Accepted, (2016).
[Crossref]

I. S. Ansari, M. M. Abbdallah, M. -S. Alouini, and K. A. Qaraqe, “Outage performance analysis of underlay cognitive RF and FSO wireless channels,” The 3rd International Workshop in Optical Wireless Communications (IWOW) (2014).

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Figures (5)

Fig. 1
Fig. 1

The mixed FSO-RF relay system model.

Fig. 2
Fig. 2

Two time slots required to transmit one data packet from Alice to Bob via Relay.

Fig. 3
Fig. 3

The key generation rate of the proposed scheme is a function of Alice’s transmit power pa.

Fig. 4
Fig. 4

The average secrecy rate of the proposed scheme is a function of Relay’s transmit power pr.

Fig. 5
Fig. 5

The average secrecy rate of the proposed scheme is a function of the maximum permitted COP.

Equations (30)

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h ar l = exp ( λ L )
f h ar ( x ) = ξ 2 α β A 0 h ar l Γ ( α ) Γ ( β ) G 1 , 3 3 , 0 ( α β A 0 h ar l x | ξ 2 ξ 2 1 , α 1 , β 1 )
Y R = p a h ar S A + n R
Y A = p r h ar S R + n A
Y R = p a h ar S A + n R h ˜ ar , r = S A T p a | S A | Y R = h ar + N R
Y A = p r h ar S R + n A h ˜ ar , a = S R T p a | S R | Y A = h ar + N A
Y E 1 = p a h ae S A + n E 1
Y E 2 = p r h re S R + n E 2
f h ˜ ar ( x ) = f h ar ( x ) * f N R ( x )
f N R ( x ) = 1 2 π σ N R exp ( x 2 2 σ N R 2 )
f h ˜ ar ( x ) = ξ 2 α β A 0 h ar l Γ ( α ) Γ ( β ) G 1 , 3 3 , 0 ( α β A 0 h ar l x | ξ 2 ξ 2 1 , α 1 , β 1 ) * 1 2 π σ N R exp ( x 2 2 σ N R 2 ) = ξ 2 α β 2 π σ N R A 0 h ar l Γ ( α ) Γ ( β ) 0 G 1 , 3 3 , 0 ( α β A 0 h ar l t | ξ 2 ξ 2 1 , α 1 , β 1 ) × exp ( ( x t ) 2 2 σ N R 2 ) d t = ξ 2 α β A 0 h sr l Γ ( α ) Γ ( β ) 0 0 Γ ( ξ 2 1 s ) Γ ( α 1 s ) Γ ( β 1 s ) 2 π i Γ ( ξ 2 s ) × ( α β A 0 h sr l t ) s exp ( x 2 2 x t + t 2 2 σ N a 2 ) d s d t = ( a ) ξ 2 α β A 0 h sr l Γ ( α ) Γ ( β ) 0 Γ ( ξ 2 1 s ) Γ ( α 1 s ) Γ ( β 1 s ) 2 π i Γ ( ξ 2 s ) × ( α β A 0 h sr l ) s ( 1 σ N a 2 ) s + 1 2 Γ ( s + 1 ) exp ( x 2 4 σ N a 2 ) D ( s + 1 ) ( x σ N a ) d s
D ( s + 1 ) ( x σ N a ) = 2 s + 1 2 exp ( x 2 4 σ N a 2 ) ( π Γ ( s + 2 2 ) Φ ( s + 1 2 , 1 2 ; x 2 2 σ N a 2 ) + 2 π x σ N a Γ ( s + 1 2 ) Φ ( s + 2 2 , 3 2 ; x 2 2 σ N a 2 ) )
f h ˜ h ˜ ar ( x ) = σ N a ξ 2 α β 2 A 0 h sr l Γ ( α ) Γ ( β ) 0 G 1 , 3 3 , 0 ( α β A 0 h sr l t | ξ 2 ξ 2 1 , α 1 , β 1 ) × ( π Γ ( s + 2 2 ) Φ ( s + 1 2 , 1 2 ; x 2 2 σ N a 2 ) + 2 π x σ N a Γ ( s + 1 2 ) Φ ( s + 2 2 , 3 2 ; x 2 2 σ N a 2 ) ) d s .
R k = T 1 T I ( h ˜ ar , h ˜ ra ) = T 1 T ( H ( h ˜ ar ) H ( h ˜ ra | h ˜ ra ) ) = T 1 T ( H ( h ˜ ar ) H ( h ˜ ra S R T | S R | n A + S A T | S A | n R | h ˜ ra ) ) .
R k = T 1 T ( H ( h ˜ ar ) H ( h ˜ ra | h ˜ ra ) H ( S R T | S R | n A | h ˜ ra ) H ( S A T | S A | n R | h ˜ ra ) ) = T 1 T ( H ( h ˜ ar ) H ( S R T | S R | n A ) H ( S A T | S A | n R ) ) = T 1 T ( H ( h ˜ ar ) H ( S R T | S R | n A + S A T | S A | n R ) )
H ( h ˜ ar ) = f h ˜ ar ( x ) log 2 f h ˜ ar ( x ) d x
H ( S R T | S R | n A + S A T | S A | n R ) = 1 2 log 2 ( 2 π e σ N A 2 N f + 2 π e σ N R 2 N f )
R ar T 2 2 T log 2 ( 1 + p a RA h ar q Δ f )
R rb = T 2 2 T log 2 ( 1 + p r g rb N 0 ) .
R re = T 2 2 T log 2 ( 1 + p r g re N 0 ) .
R sec 2 = ( R rb R re ) +
R sec = min ( R ar , ( R rb R re ) + ) .
P cop , ar = Pr ( R ar < R b ) = ξ 2 Γ ( α ) Γ ( β ) G 2 , 4 3 , 1 ( ξ 2 α β ξ 2 + 1 R ^ b μ | 1 , ξ 2 + 1 ξ 2 , α , β , 0 )
P cop , rb = Pr ( R rb < R b ) = 1 exp ( R ˇ b P r σ rb 2 )
P cop = 1 ( 1 P cop , ar ) ( 1 P cop , rb ) .
P sop = Pr ( R re R e ) = exp ( R ^ e P r σ re 2 )
P 1 : max R b , R s R s ( 1 P sop ) s . t . P cop < P upper , R s min { R b , R ar } R k
P 2 : min R b P sop s . t . P cop < P upper , R s min { R b , R ar } R k .
P 3 : min R s R s ( 1 P sop ) s . t . R s min { R b max , R ar } R k .
{ d F d R s = 1 ( 1 + R s p r σ re 2 ) exp ( R b max R s P r σ re 2 ) , d 2 F d R s 2 = ( 2 R s p r σ re 2 + R s p r 2 σ re 4 ) exp ( R b max R s P r σ re 2 ) .

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