Abstract

In this paper, the amplify and forward (AF) cooperative technique for one- and two-way relays has been implemented for underwater optical wireless communication (UOWC). UOWC suffers from scattering, absorption, and turbulence effects. The distance of communication between UOWC devices is typically within the range of 100 m. So relay-based UWOC has been proposed to improve the performance of device-to-device (D2D) based UWOC by increasing the effective link range. Performance analysis of unidirectional and bidirectional relay-based systems has been carried out in terms of outage probability and average symbol error probability (ASEP) for log-normal underwater fading channels. The analytical results have been validated by means of Monte Carlo simulations. Closed form expressions for ASEP have been obtained by using a mixture of gamma distributions, which was not possible using log-normal distributions. It has been observed that bidirectional relays, even though they have a better data rate than unidirectional relays, suffer in terms of outage probability.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
    [Crossref]
  2. P. Kaur, V. K. Jain, and S. Kar, “Performance analysis of FSO array receivers in presence of atmospheric turbulence,” IEEE Photonics Technology Letters 26, 1165–1168 (2014).
    [Crossref]
  3. W. Cox, Simulation, modeling, and design of underwater optical communication systems, (Ph.D. dissertation, North Carolina State University, Raleigh, 2012).
  4. M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.
  5. D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Communications Magazine 47, 97–102 (2009).
    [Crossref]
  6. L. J. Johnson, F. Jasman, R. J. Green, and M. S. Leeson, “Recent advances in underwater optical wireless communications,” Underwater Technol. 32, 167–175 (2014).
    [Crossref]
  7. S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Transactions on Communications 62, 226–234 (2014).
    [Crossref]
  8. W. Liu, Z. Xu, and L. Yang, “SIMO detection schemes for underwater optical wireless communication under turbulence,” Photon. Res. 3, 48–53 (2015).
    [Crossref]
  9. W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” Journal of Lightwave Technology 27, 967–973 (2009).
    [Crossref]
  10. M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Transactions on Communications 65, 1176–1192 (2017).
    [Crossref]
  11. K. A. N. Alhamawi and E. S. Altubaishi, “Capacity analysis of amplify-and-forward based dual-hop free space optical communication system with backup RF link,” in 2016 12th International Conference on Innovations in Information Technology (IIT), (2016), pp. 1–5.
  12. J. Liu and Y. Dong, “On capacity of underwater optical wireless links under weak oceanic turbulence,” in OCEANS 2016 - Shanghai, (2016), pp. 1–4.
  13. S. Lim and K. Ko, “Approximation of multi-hop relay to dual-hop relay and its error performance analysis,” IEEE Communications Letters 21, 342–345 (2017).
    [Crossref]
  14. L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
    [Crossref]
  15. M. O. Hasna and M. S. Alouini, “End-to-end performance of transmission systems with relays over rayleigh-fading channels,” IEEE Transactions on Wireless Communications 2, 1126–1131 (2003).
    [Crossref]
  16. L. W. Xu, T. T. L. H. Zhang, and T. A. Gulliver, “Performance analysis of the IAF relaying M2M cooperative networks over N-nakagami fading channels,” Journal of Communications 10, 185–191 (2015).
    [Crossref]
  17. J. Yang, P. Fan, T. Q. Duong, and X. Lei, “Exact performance of two-way AF relaying in Nakagami-m fading environment,” IEEE Transactions on Wireless Communications 10, 980–987 (2011).
    [Crossref]
  18. I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
    [Crossref]
  19. H. Cui, G. Wei, and Y. Wang, “Effects of CSI on ASEP based opportunistic DF relaying systems,” IEEE Transactions on Vehicular Technology 60, 1898–1904 (2011).
    [Crossref]
  20. A. Agrawal and R. S. Kshetrimayum, “Analysis of UWB communication over IEEE 802.15.3a channel by superseding lognormal shadowing by mixture of gamma distributions,” International Journal of Electronics and Communications pp. 1795–1799 (2015).
    [Crossref]
  21. D. Wang, Y. Cao, L. Zheng, and Z. Du, “A note on "performance analysis of UWB systems over the IEEE 802.15.3a channel model",” IEEE Transactions on Communications 60, 3909–3910 (2012).
    [Crossref]
  22. I. Gradshteyn, Table of Integrals, Series and Products (Academic Press, New York, NY, USA, 1994). ISBN 978-0-12-294760-5.
  23. A. Prudnikov, Integrals and Series: Special Functions, Additional Chapters (Fizmatlit Press, Moscow, Russia, 2003). ISBN 978-2881246821.
  24. M. D. Springer, The Algebra of random variables (wiley, Hoboken, NJ, USA, 1979).
  25. I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Performance analysis of free-space optical links over malaga (M) turbulence channels with pointing errors,” IEEE Transactions on Wireless Communications 15, 91–102 (2016).
    [Crossref]
  26. M. V. Jamali, F. Akhoundi, and J. A. Salehi, “Performance characterization of relay-assisted wireless optical CDMA networks in turbulent underwater channel,” IEEE Transactions on Wireless Communications 15, 4104–4116 (2016).
    [Crossref]

2017 (3)

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
[Crossref]

M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Transactions on Communications 65, 1176–1192 (2017).
[Crossref]

S. Lim and K. Ko, “Approximation of multi-hop relay to dual-hop relay and its error performance analysis,” IEEE Communications Letters 21, 342–345 (2017).
[Crossref]

2016 (2)

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Performance analysis of free-space optical links over malaga (M) turbulence channels with pointing errors,” IEEE Transactions on Wireless Communications 15, 91–102 (2016).
[Crossref]

M. V. Jamali, F. Akhoundi, and J. A. Salehi, “Performance characterization of relay-assisted wireless optical CDMA networks in turbulent underwater channel,” IEEE Transactions on Wireless Communications 15, 4104–4116 (2016).
[Crossref]

2015 (3)

W. Liu, Z. Xu, and L. Yang, “SIMO detection schemes for underwater optical wireless communication under turbulence,” Photon. Res. 3, 48–53 (2015).
[Crossref]

L. W. Xu, T. T. L. H. Zhang, and T. A. Gulliver, “Performance analysis of the IAF relaying M2M cooperative networks over N-nakagami fading channels,” Journal of Communications 10, 185–191 (2015).
[Crossref]

L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
[Crossref]

2014 (3)

P. Kaur, V. K. Jain, and S. Kar, “Performance analysis of FSO array receivers in presence of atmospheric turbulence,” IEEE Photonics Technology Letters 26, 1165–1168 (2014).
[Crossref]

L. J. Johnson, F. Jasman, R. J. Green, and M. S. Leeson, “Recent advances in underwater optical wireless communications,” Underwater Technol. 32, 167–175 (2014).
[Crossref]

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Transactions on Communications 62, 226–234 (2014).
[Crossref]

2012 (1)

D. Wang, Y. Cao, L. Zheng, and Z. Du, “A note on "performance analysis of UWB systems over the IEEE 802.15.3a channel model",” IEEE Transactions on Communications 60, 3909–3910 (2012).
[Crossref]

2011 (3)

J. Yang, P. Fan, T. Q. Duong, and X. Lei, “Exact performance of two-way AF relaying in Nakagami-m fading environment,” IEEE Transactions on Wireless Communications 10, 980–987 (2011).
[Crossref]

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
[Crossref]

H. Cui, G. Wei, and Y. Wang, “Effects of CSI on ASEP based opportunistic DF relaying systems,” IEEE Transactions on Vehicular Technology 60, 1898–1904 (2011).
[Crossref]

2009 (2)

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” Journal of Lightwave Technology 27, 967–973 (2009).
[Crossref]

D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Communications Magazine 47, 97–102 (2009).
[Crossref]

2003 (1)

M. O. Hasna and M. S. Alouini, “End-to-end performance of transmission systems with relays over rayleigh-fading channels,” IEEE Transactions on Wireless Communications 2, 1126–1131 (2003).
[Crossref]

Agrawal, A.

A. Agrawal and R. S. Kshetrimayum, “Analysis of UWB communication over IEEE 802.15.3a channel by superseding lognormal shadowing by mixture of gamma distributions,” International Journal of Electronics and Communications pp. 1795–1799 (2015).
[Crossref]

Akhoundi, F.

M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Transactions on Communications 65, 1176–1192 (2017).
[Crossref]

M. V. Jamali, F. Akhoundi, and J. A. Salehi, “Performance characterization of relay-assisted wireless optical CDMA networks in turbulent underwater channel,” IEEE Transactions on Wireless Communications 15, 4104–4116 (2016).
[Crossref]

Akyildiz, I. F.

D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Communications Magazine 47, 97–102 (2009).
[Crossref]

Al-Ahmadi, S.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
[Crossref]

Alhamawi, K. A. N.

K. A. N. Alhamawi and E. S. Altubaishi, “Capacity analysis of amplify-and-forward based dual-hop free space optical communication system with backup RF link,” in 2016 12th International Conference on Innovations in Information Technology (IIT), (2016), pp. 1–5.

Alouini, M. S.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Performance analysis of free-space optical links over malaga (M) turbulence channels with pointing errors,” IEEE Transactions on Wireless Communications 15, 91–102 (2016).
[Crossref]

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
[Crossref]

M. O. Hasna and M. S. Alouini, “End-to-end performance of transmission systems with relays over rayleigh-fading channels,” IEEE Transactions on Wireless Communications 2, 1126–1131 (2003).
[Crossref]

Altubaishi, E. S.

K. A. N. Alhamawi and E. S. Altubaishi, “Capacity analysis of amplify-and-forward based dual-hop free space optical communication system with backup RF link,” in 2016 12th International Conference on Innovations in Information Technology (IIT), (2016), pp. 1–5.

Ansari, I. S.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Performance analysis of free-space optical links over malaga (M) turbulence channels with pointing errors,” IEEE Transactions on Wireless Communications 15, 91–102 (2016).
[Crossref]

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
[Crossref]

Bourennane, S.

M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.

Cao, Y.

D. Wang, Y. Cao, L. Zheng, and Z. Du, “A note on "performance analysis of UWB systems over the IEEE 802.15.3a channel model",” IEEE Transactions on Communications 60, 3909–3910 (2012).
[Crossref]

Cheng, J.

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
[Crossref]

Cox, W.

W. Cox, Simulation, modeling, and design of underwater optical communication systems, (Ph.D. dissertation, North Carolina State University, Raleigh, 2012).

Cui, H.

H. Cui, G. Wei, and Y. Wang, “Effects of CSI on ASEP based opportunistic DF relaying systems,” IEEE Transactions on Vehicular Technology 60, 1898–1904 (2011).
[Crossref]

Dong, Y.

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
[Crossref]

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Transactions on Communications 62, 226–234 (2014).
[Crossref]

J. Liu and Y. Dong, “On capacity of underwater optical wireless links under weak oceanic turbulence,” in OCEANS 2016 - Shanghai, (2016), pp. 1–4.

Du, Z.

D. Wang, Y. Cao, L. Zheng, and Z. Du, “A note on "performance analysis of UWB systems over the IEEE 802.15.3a channel model",” IEEE Transactions on Communications 60, 3909–3910 (2012).
[Crossref]

Duong, T. Q.

J. Yang, P. Fan, T. Q. Duong, and X. Lei, “Exact performance of two-way AF relaying in Nakagami-m fading environment,” IEEE Transactions on Wireless Communications 10, 980–987 (2011).
[Crossref]

Fan, P.

J. Yang, P. Fan, T. Q. Duong, and X. Lei, “Exact performance of two-way AF relaying in Nakagami-m fading environment,” IEEE Transactions on Wireless Communications 10, 980–987 (2011).
[Crossref]

Fu, S.

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
[Crossref]

Gabriel, C.

M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.

Ghassemlooy, Z.

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” Journal of Lightwave Technology 27, 967–973 (2009).
[Crossref]

Gradshteyn, I.

I. Gradshteyn, Table of Integrals, Series and Products (Academic Press, New York, NY, USA, 1994). ISBN 978-0-12-294760-5.

Green, R. J.

L. J. Johnson, F. Jasman, R. J. Green, and M. S. Leeson, “Recent advances in underwater optical wireless communications,” Underwater Technol. 32, 167–175 (2014).
[Crossref]

Gulliver, T. A.

L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
[Crossref]

L. W. Xu, T. T. L. H. Zhang, and T. A. Gulliver, “Performance analysis of the IAF relaying M2M cooperative networks over N-nakagami fading channels,” Journal of Communications 10, 185–191 (2015).
[Crossref]

Hamza, T.

M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.

Hasna, M. O.

M. O. Hasna and M. S. Alouini, “End-to-end performance of transmission systems with relays over rayleigh-fading channels,” IEEE Transactions on Wireless Communications 2, 1126–1131 (2003).
[Crossref]

Jain, V. K.

P. Kaur, V. K. Jain, and S. Kar, “Performance analysis of FSO array receivers in presence of atmospheric turbulence,” IEEE Photonics Technology Letters 26, 1165–1168 (2014).
[Crossref]

Jamali, M. V.

M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Transactions on Communications 65, 1176–1192 (2017).
[Crossref]

M. V. Jamali, F. Akhoundi, and J. A. Salehi, “Performance characterization of relay-assisted wireless optical CDMA networks in turbulent underwater channel,” IEEE Transactions on Wireless Communications 15, 4104–4116 (2016).
[Crossref]

Jasman, F.

L. J. Johnson, F. Jasman, R. J. Green, and M. S. Leeson, “Recent advances in underwater optical wireless communications,” Underwater Technol. 32, 167–175 (2014).
[Crossref]

Johnson, L. J.

L. J. Johnson, F. Jasman, R. J. Green, and M. S. Leeson, “Recent advances in underwater optical wireless communications,” Underwater Technol. 32, 167–175 (2014).
[Crossref]

Kar, S.

P. Kaur, V. K. Jain, and S. Kar, “Performance analysis of FSO array receivers in presence of atmospheric turbulence,” IEEE Photonics Technology Letters 26, 1165–1168 (2014).
[Crossref]

Kaur, P.

P. Kaur, V. K. Jain, and S. Kar, “Performance analysis of FSO array receivers in presence of atmospheric turbulence,” IEEE Photonics Technology Letters 26, 1165–1168 (2014).
[Crossref]

Khalighi, M. A.

M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.

Ko, K.

S. Lim and K. Ko, “Approximation of multi-hop relay to dual-hop relay and its error performance analysis,” IEEE Communications Letters 21, 342–345 (2017).
[Crossref]

Kshetrimayum, R. S.

A. Agrawal and R. S. Kshetrimayum, “Analysis of UWB communication over IEEE 802.15.3a channel by superseding lognormal shadowing by mixture of gamma distributions,” International Journal of Electronics and Communications pp. 1795–1799 (2015).
[Crossref]

Leeson, M. S.

L. J. Johnson, F. Jasman, R. J. Green, and M. S. Leeson, “Recent advances in underwater optical wireless communications,” Underwater Technol. 32, 167–175 (2014).
[Crossref]

Lei, X.

J. Yang, P. Fan, T. Q. Duong, and X. Lei, “Exact performance of two-way AF relaying in Nakagami-m fading environment,” IEEE Transactions on Wireless Communications 10, 980–987 (2011).
[Crossref]

Léon, P.

M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.

Lim, S.

S. Lim and K. Ko, “Approximation of multi-hop relay to dual-hop relay and its error performance analysis,” IEEE Communications Letters 21, 342–345 (2017).
[Crossref]

Liu, J.

J. Liu and Y. Dong, “On capacity of underwater optical wireless links under weak oceanic turbulence,” in OCEANS 2016 - Shanghai, (2016), pp. 1–4.

Liu, W.

Pompili, D.

D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Communications Magazine 47, 97–102 (2009).
[Crossref]

Popoola, W. O.

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” Journal of Lightwave Technology 27, 967–973 (2009).
[Crossref]

Prudnikov, A.

A. Prudnikov, Integrals and Series: Special Functions, Additional Chapters (Fizmatlit Press, Moscow, Russia, 2003). ISBN 978-2881246821.

Rigaud, V.

M. A. Khalighi, C. Gabriel, T. Hamza, S. Bourennane, P. Léon, and V. Rigaud, “Underwater wireless optical communication; recent advances and remaining challenges,” in 2014 16th International Conference on Transparent Optical Networks (ICTON), (2014), pp. 1–4.

Salehi, J. A.

M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Transactions on Communications 65, 1176–1192 (2017).
[Crossref]

M. V. Jamali, F. Akhoundi, and J. A. Salehi, “Performance characterization of relay-assisted wireless optical CDMA networks in turbulent underwater channel,” IEEE Transactions on Wireless Communications 15, 4104–4116 (2016).
[Crossref]

Shi, W.

L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
[Crossref]

Springer, M. D.

M. D. Springer, The Algebra of random variables (wiley, Hoboken, NJ, USA, 1979).

Tang, S.

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Transactions on Communications 62, 226–234 (2014).
[Crossref]

Wang, D.

D. Wang, Y. Cao, L. Zheng, and Z. Du, “A note on "performance analysis of UWB systems over the IEEE 802.15.3a channel model",” IEEE Transactions on Communications 60, 3909–3910 (2012).
[Crossref]

Wang, J.

L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
[Crossref]

Wang, Y.

H. Cui, G. Wei, and Y. Wang, “Effects of CSI on ASEP based opportunistic DF relaying systems,” IEEE Transactions on Vehicular Technology 60, 1898–1904 (2011).
[Crossref]

Wei, G.

H. Cui, G. Wei, and Y. Wang, “Effects of CSI on ASEP based opportunistic DF relaying systems,” IEEE Transactions on Vehicular Technology 60, 1898–1904 (2011).
[Crossref]

Xu, L.

L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
[Crossref]

Xu, L. W.

L. W. Xu, T. T. L. H. Zhang, and T. A. Gulliver, “Performance analysis of the IAF relaying M2M cooperative networks over N-nakagami fading channels,” Journal of Communications 10, 185–191 (2015).
[Crossref]

Xu, Z.

Yang, J.

J. Yang, P. Fan, T. Q. Duong, and X. Lei, “Exact performance of two-way AF relaying in Nakagami-m fading environment,” IEEE Transactions on Wireless Communications 10, 980–987 (2011).
[Crossref]

Yang, L.

Yanikomeroglu, H.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
[Crossref]

Yilmaz, F.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Performance analysis of free-space optical links over malaga (M) turbulence channels with pointing errors,” IEEE Transactions on Wireless Communications 15, 91–102 (2016).
[Crossref]

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M. S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-branch selection over generalized-K composite fading channels,” IEEE Transactions on Communications 59, 2654–2658 (2011).
[Crossref]

Zeng, Z.

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
[Crossref]

Zhang, H.

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Communications Surveys Tutorials 19, 204–238 (2017).
[Crossref]

L. Xu, H. Zhang, J. Wang, W. Shi, and T. A. Gulliver, “End-to-end performance analysis of AF relaying M2M cooperative system,” International Journal of Multimedia and Ubiquitous Engineering 10, 211–224 (2015).
[Crossref]

Zhang, T. T. L. H.

L. W. Xu, T. T. L. H. Zhang, and T. A. Gulliver, “Performance analysis of the IAF relaying M2M cooperative networks over N-nakagami fading channels,” Journal of Communications 10, 185–191 (2015).
[Crossref]

Zhang, X.

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Transactions on Communications 62, 226–234 (2014).
[Crossref]

Zheng, L.

D. Wang, Y. Cao, L. Zheng, and Z. Du, “A note on "performance analysis of UWB systems over the IEEE 802.15.3a channel model",” IEEE Transactions on Communications 60, 3909–3910 (2012).
[Crossref]

IEEE Communications Letters (1)

S. Lim and K. Ko, “Approximation of multi-hop relay to dual-hop relay and its error performance analysis,” IEEE Communications Letters 21, 342–345 (2017).
[Crossref]

IEEE Communications Magazine (1)

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Figures (8)

Figure 1
Figure 1 Practical system model for UOWC (dashed line represent bidirectional optical links).
Figure 2
Figure 2 System model for OWR based UOWC.
Figure 3
Figure 3 System model for UOWC_TWR.
Figure 4
Figure 4 Block diagram of Monte Carlo simulation model.
Figure 5
Figure 5 Outage probability for amplify and forward relay based UOWC.
Figure 6
Figure 6 Comparison between log-normal and different MG distributions.
Figure 7
Figure 7 Outage probability for OWR based UOWC using 5-MG distributions for different values of σ (solid line represents analytical results, dashed line represents asymptotic results, and * represents simulation results).
Figure 8
Figure 8 ASEP of OWR based UOWC (Solid line represents analytical results using log-normal distribution, dashed line represents analytical results using 5-MG distribution, and * represents simulation results using log-normal distribution).

Tables (2)

Tables Icon

Table 1 Parameter values

Tables Icon

Table 2 Comparison of lower bounds on outage probability for σ 2 = 0.09

Equations (34)

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f ( h ) = 1 h 2 π σ 2 exp ( ( l n ( h ) μ ) 2 2 σ 2 )
f γ ( γ ) = 1 32 π γ σ exp ( ( l n ( γ γ ¯ ) + 8 σ 2 ) 2 32 σ 2 )
F γ ( γ ) = 1 1 2 e r f c ( l n ( γ γ ¯ ) + 8 σ 2 32 σ )
r S R = E R e h S R x + n S R
r R D = c E R e h S R h R D x + n R D
c = R e E / N 0 1 + R e | h S R | 2 E / N 0 + R e | h R D | 2 E / N 0
γ S R D = γ S R γ R D 1 + γ S R + γ R D
γ S R = R e | h S R | 2 E N 0 γ R D = R e | h R D | 2 E N 0
γ S R D = γ S R γ R D 1 + γ S R + γ R D 1 2 2 1 γ S R + 1 γ R D = γ a p p r o x
γ a p p r o x < γ u p = m i n ( γ S R , γ R D )
F l o w e r ( γ ) = P ( γ S R < γ ) + P ( γ R D < γ ) P ( γ S R < γ ) P ( γ R D < γ )
= 1 1 4 e r f c ( l n ( 2 R 1 R e γ ¯ S R ) + 8 σ S R 2 32 σ S R ) e r f c ( l n ( 2 R 1 R e γ ¯ R D ) + 8 σ R D 2 32 σ R D )
F l o w e r ( γ ) = 1 1 4 e r f c ( l n ( γ R e γ ¯ S R ) + 8 σ S R 2 32 σ S R ) e r f c ( l n ( γ R e γ ¯ R D ) + 8 σ R D 2 32 σ R D )
f l o w e r ( γ ) = 1 8 2 π γ [ 1 σ S R exp ( ( l n ( γ R e γ ¯ S R ) + 8 σ S R 2 ) 2 32 σ S R 2 ) e r f c ( ( l n ( γ R e γ ¯ R D ) + 8 σ R D 2 ) 32 σ R D ) + 1 σ R D exp ( ( l n ( γ R e γ ¯ R D ) + 8 σ R D 2 ) 2 32 σ R D 2 ) e r f c ( ( l n ( γ R e γ ¯ S R ) + 8 σ S R 2 ) 32 σ S R ) ]
γ S R D = γ S R γ R D 1 + γ S R + 2 γ R D
γ S R D = γ S R γ R D 1 + γ S R + 2 γ R D 1 2 2 2 γ S R + 1 γ R D = γ a p p r o x
F l o w e r ( γ ) = P { 1 2 m i n ( γ S R , 2 γ R D ) < γ }
P o u t ( γ t h ) = P { 1 2 m i n ( γ S R , 2 γ R D ) < γ t h } = 1 1 4 e r f c ( l n ( 2 * 2 R 1 R e γ ¯ S R ) + 8 σ S R 2 32 σ S R ) e r f c ( l n ( 2 R 1 R e γ ¯ R D ) + 8 σ R D 2 32 σ R D )
F l o w e r ( γ ) = 1 1 4 e r f c ( l n ( 2 * γ R e γ ¯ S R ) + 8 σ S R 2 32 σ S R ) e r f c ( l n ( γ R e γ ¯ R D ) + 8 σ R D 2 32 σ R D )
f l o w e r ( γ ) = 1 8 2 π γ [ 1 σ S R exp ( ( l n ( 2 γ R e γ ¯ S R ) + 8 σ S R 2 ) 2 32 σ S R 2 ) e r f c ( ( l n ( γ R e γ ¯ R D ) + 8 σ R D 2 ) 32 σ R D ) + 1 σ R D exp ( ( l n ( γ R e γ ¯ R D ) + 8 σ R D 2 ) 2 32 σ R D 2 ) e r f c ( ( l n ( 2 γ R e γ ¯ S R ) + 8 σ S R 2 ) 32 σ S R ) ]
P e 0 a Q ( e γ ) f l o w e r ( γ ) d γ
f M G ( x ) = i = 1 n P i x α i 1 β i   α i T ( α i ) e x β i Ω
F M G ( x ) = i = 1 n P i ( 1 1 T ( α i ) G 1 , 2 2 , 0 [ 1 0 , α i | β i x ] )
P o u t = i = 1 n P i ( 1 1 T ( α i ) G 1 , 2 2 , 0 [ 1 0 , α i | β i γ t h R e γ ¯ ] )
P t o t a l n i = 1 P i ( 1 P i ) 1 T ( α i ) π G 2 , 2 2 , 1 ( 1 α i , 1 0 , 1 2 | γ ¯ R e β i ) + n i = 1 P i 2 ( T ( α i ) ) 2 π G 1 , 0 : 1 , 2 : 1 , 2 0 , 1 : 2 , 0 : 2 , 0 ( 1 α i | 1 0 , α i | 1 0 , 1 2 | 1 , γ ¯ R e β i )
f E 2 E ( γ ) = f ( γ S R ) + f ( γ R D ) f ( γ S R ) F ( γ R D ) f ( γ R D ) F ( γ S R ) = f ( γ S R ) ( 1 F ( γ R D ) ) + f ( γ R D ) ( 1 F ( γ S R ) )
f E 2 E ( γ ) = 2 f ( γ ) ( 1 F ( γ ) ) = 2 f ( γ ) n i = 1 [ ( 1 P i ) + P i T [ α ] G 1 , 2 2 , 0 ( 1 0 , α | γ β i γ ¯ R e ) ]
P e = 0 f E 2 E ( γ ) Q ( 2 γ ) d γ
Q ( 2 x ) = 1 2 π G 1 , 2 2 , 0 ( 1 0 , 1 / 2 | x )
f 1 = 0 i = 1 n P i ( 1 P i ) γ α i 1 β i α i T ( α i ) e β i γ 1 π G 1 , 2 2 , 0 ( 1 0 , 1 / 2 | γ ) d γ = i = 1 n P i ( 1 P i ) 0 β i α i T ( α i ) π γ α i 1 G 0 , 1 1 , 0 ( 0 | β i γ γ ¯ R e ) G 1 , 2 2 , 0 ( 1 0 , 1 / 2 | γ ) d y = i = 1 n P i ( 1 P i ) T ( α i ) π G 2 , 2 2 , 1 ( 1 α i , 1 0 , 1 / 2 | γ ¯ R e β i )
f 2 = 0 i = 1 n P i γ α i 1 β i α i T ( α i ) T ( α i ) e β i γ 1 π P i G 1 , 2 2 , 0 ( 1 0 , α i | β i γ γ ¯ R e ) G 1 , 2 2 , 0 ( 1 0 , 1 / 2 | γ ) d γ = 0 i = 1 n P i γ α i 1 β i α i T ( α i ) T ( α i ) G 0 , 1 1 , 0 ( 0 | β i γ γ ¯ R e ) 1 π P i G 1 , 2 2 , 0 ( 1 0 , α i | β i γ γ ¯ R e ) G 1 , 2 2 , 0 ( 1 0 , 1 / 2 | γ ) d γ = i = 1 n P i 2 ( T ( α i ) ) 2 π G 1 , 0 : 1 , 2 : 1 , 2 0 , 1 : 2 , 0 : 2 , 0 ( 1 α i | 1 0 , α i | 1 0 , 1 2 | 1 , γ ¯ R e β i )
P o u t = i = 1 n P i ( 1 1 T ( α i ) G 1 , 2 2 , 0 [ 1 0 , α i | β i γ t h R e γ ¯ ] )
P o u t = i = 1 n P i ( 1 1 T ( α i ) G 2 , 1 0 , 2 [ 1 , 1 α i 0 | R e γ ¯ β i γ t h ] )
P o u t = i = 1 n P i ( 1 1 T ( α i ) k = 1 2 z a k 1 l = 1 , l k 2 T ( a k a l ) l = 1 1 T ( a k b l ) )

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