Abstract

Underwater wireless optical communication (UWOC) systems are presented as a reliable alternative to typical underwater wireless systems (radio-frequency (RF) and acoustic waves) since they can provide much higher data rates with a higher level of communication security. Thus, a variety of potential applications have been recently proposed for UWOC systems, including offshore exploration, environmental monitoring, natural disaster precautions, or military operations. All of these must overcome the unpredictable nature of underwater channels due to scattering and turbulence processes associated with different factors, such as salinity, temperature, bubbles, or turbidity. Lately, a Weibull distribution has been demonstrated to have excellent agreement characterizing the fading of salinity-induced oceanic turbulence. Furthermore, an approximate closed-form expression is derived in this paper for the average bit error rate of any generic coding scheme by means of a Gauss-Laguerre quadrature. Numerical results obtained via Monte-Carlo simulation are provided to corroborate the validity of the derived analytical expressions.

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

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References

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2017 (2)

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

M. Elamassie, M. Uysal, Y. Baykal, M. Abdallah, and K. Qaraqe, “Effect of eddy diffusivity ratio on underwater optical scintillation index,” J. Opt. Soc. Am. A 34, 1969–1973 (2017).
[Crossref]

2016 (4)

M. C. Gökçe and Y. Baykal, “Scintillation analysis of multiple-input single-output underwater optical links,” Appl. Opt. 55, 6130–6136 (2016).
[Crossref] [PubMed]

C. Wang, H.-Y. Yu, and Y.-J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8, 1–11 (2016).
[Crossref]

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

2015 (1)

2014 (3)

L. J. Johnson, R. J. Green, and M. S. Leeson, “Underwater optical wireless communications: depth-dependent beam refraction,” Appl. Opt. 53, 7273–7277 (2014).
[Crossref] [PubMed]

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 Trans. Commun.,  62, 226–234 (2014).
[Crossref]

2013 (1)

2012 (5)

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 2, 13055–13064 (2012).
[Crossref]

A. Khalighi, C. Gabriel, and V. Rigaud, “Optical communication system for an underwater wireless sensor network,” EGU General Assembly 14, 2685 (2012).

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form expressions for the lower-bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels,” IET Commun. 6, 390–397 (2012).
[Crossref]

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22, 260–266 (2012).
[Crossref]

J. M. Garrido-Balsells, A. Jurado-Navas, J. Francisco Paris, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form BER analysis of variable weight MPPM coding under gamma-gamma scintillation for atmospheric optical communications,” Opt. Lett. 37, 719–721 (2012).
[Crossref]

2010 (1)

2006 (1)

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, “Variable weight MPPM technique for rate-adaptive optical wireless communications,” IET Electron. Lett. 42, 43–44 (2006).
[Crossref]

2004 (1)

H. Park and J. R. Barry, “Trellis-coded multiple-pulse-position modulation for wireless infrared communications,” IEEE Trans. Commun. 52, 643–651 (2004).
[Crossref]

2001 (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[Crossref]

2000 (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

1997 (1)

J.M. Kahn and J.R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

1963 (1)

P. Concus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Am. Math. Soc. 17, 245–256 (1963).

Abdallah, M.

Abdollahramezani, S.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Abolhassani, B.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[Crossref]

Alouini, M.-S.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Bean Propagation through Random Media (SPIE Press, 2005).
[Crossref]

Apel, J. R.

J. R. Apel, Principles of Ocean Physics (Academic Press, 1987).

Barrios, R.

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 2, 13055–13064 (2012).
[Crossref]

Barry, J. R.

H. Park and J. R. Barry, “Trellis-coded multiple-pulse-position modulation for wireless infrared communications,” IEEE Trans. Commun. 52, 643–651 (2004).
[Crossref]

Barry, J.R.

J.M. Kahn and J.R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Baykal, Y.

Bernotas, M. P.

M. P. Bernotas and C. Nelson, “Probability density function analysis for optical turbulence with applications to underwater communications systems,” in “SPIE Defense+ Security. International Society for Optics and Photonics” (2016), paper 98270D.

Bourennane, S.

Campos, M.

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

Cassatt, D.

P. Concus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Am. Math. Soc. 17, 245–256 (1963).

Castillo-Vázquez, M.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form expressions for the lower-bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels,” IET Commun. 6, 390–397 (2012).
[Crossref]

J. M. Garrido-Balsells, A. Jurado-Navas, J. Francisco Paris, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form BER analysis of variable weight MPPM coding under gamma-gamma scintillation for atmospheric optical communications,” Opt. Lett. 37, 719–721 (2012).
[Crossref]

Chizari, A.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Cochenour, B.

L. Mullen, B. Cochenour, and A. Laux, “Spatial and temporal dispersion in high bandwidth underwater laser communication links,” Proc. IEEE Military Commun. Conf. (2008), pp. 1–7.

Concus, P.

P. Concus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Am. Math. Soc. 17, 245–256 (1963).

Costa, F.

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

Diniz, P.

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

Dios, F.

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 2, 13055–13064 (2012).
[Crossref]

Dong, Y.

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

ElAfandy, R. T.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Elamassie, M.

Farwell, N.

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22, 260–266 (2012).
[Crossref]

Francisco Paris, J.

Fu, S.

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

Gabriel, C.

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Commun. Netw. 5, 1–12 (2013).
[Crossref]

A. Khalighi, C. Gabriel, and V. Rigaud, “Optical communication system for an underwater wireless sensor network,” EGU General Assembly 14, 2685 (2012).

García-Zambrana, A.

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, “Variable weight MPPM technique for rate-adaptive optical wireless communications,” IET Electron. Lett. 42, 43–44 (2006).
[Crossref]

Garrido-Balsells, J. M.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form expressions for the lower-bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels,” IET Commun. 6, 390–397 (2012).
[Crossref]

J. M. Garrido-Balsells, A. Jurado-Navas, J. Francisco Paris, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form BER analysis of variable weight MPPM coding under gamma-gamma scintillation for atmospheric optical communications,” Opt. Lett. 37, 719–721 (2012).
[Crossref]

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, “Variable weight MPPM technique for rate-adaptive optical wireless communications,” IET Electron. Lett. 42, 43–44 (2006).
[Crossref]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), pp. 181–206.

Gois, J.

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

Gökçe, M. C.

Green, R. J.

L. J. Johnson, R. J. Green, and M. S. Leeson, “Underwater optical wireless communications: depth-dependent beam refraction,” Appl. Opt. 53, 7273–7277 (2014).
[Crossref] [PubMed]

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]

Gussen, C.

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

Hanson, F.

Jaehnig, G.

P. Concus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Am. Math. Soc. 17, 245–256 (1963).

Jamali, M. V.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

M. V. Jamali, P. Khorramshahi, and R. Ramírez, “Statistical distribution of intensity fluctuations for underwater wireless optical channels in the presence of air bubbles,” in Iran Workshop on Proceedings Communication and Information Theory (IWCIT) (2016).

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]

L. J. Johnson, R. J. Green, and M. S. Leeson, “Underwater optical wireless communications: depth-dependent beam refraction,” Appl. Opt. 53, 7273–7277 (2014).
[Crossref] [PubMed]

Jurado-Navas, A.

J. M. Garrido-Balsells, A. Jurado-Navas, J. Francisco Paris, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form BER analysis of variable weight MPPM coding under gamma-gamma scintillation for atmospheric optical communications,” Opt. Lett. 37, 719–721 (2012).
[Crossref]

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form expressions for the lower-bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels,” IET Commun. 6, 390–397 (2012).
[Crossref]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), pp. 181–206.

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Kahn, J.M.

J.M. Kahn and J.R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Kammoun, A.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Khalighi, A.

A. Khalighi, C. Gabriel, and V. Rigaud, “Optical communication system for an underwater wireless sensor network,” EGU General Assembly 14, 2685 (2012).

Khalighi, M.

Khorramshahi, P.

M. V. Jamali, P. Khorramshahi, and R. Ramírez, “Statistical distribution of intensity fluctuations for underwater wireless optical channels in the presence of air bubbles,” in Iran Workshop on Proceedings Communication and Information Theory (IWCIT) (2016).

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Korotkova, O.

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22, 260–266 (2012).
[Crossref]

Lasher, M.

Laux, A.

L. Mullen, B. Cochenour, and A. Laux, “Spatial and temporal dispersion in high bandwidth underwater laser communication links,” Proc. IEEE Military Commun. Conf. (2008), pp. 1–7.

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]

L. J. Johnson, R. J. Green, and M. S. Leeson, “Underwater optical wireless communications: depth-dependent beam refraction,” Appl. Opt. 53, 7273–7277 (2014).
[Crossref] [PubMed]

Leon, P.

Liu, W.

Martins, W.

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

Melby, E.

P. Concus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Am. Math. Soc. 17, 245–256 (1963).

Mirani, A.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Mullen, L.

L. Mullen, B. Cochenour, and A. Laux, “Spatial and temporal dispersion in high bandwidth underwater laser communication links,” Proc. IEEE Military Commun. Conf. (2008), pp. 1–7.

Nabavi, P.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Nelson, C.

M. P. Bernotas and C. Nelson, “Probability density function analysis for optical turbulence with applications to underwater communications systems,” in “SPIE Defense+ Security. International Society for Optics and Photonics” (2016), paper 98270D.

Ng, T. K.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

Ooi, B. S.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Oubei, H. M.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Parenti, R. R.

R. R. Parenti and R. J. Sasiela, “Distribution models for optical scintillation due to atmospheric turbulence,” MIT Lincoln Laboratory Technical Report TR-1108 (2005).

Paris, J. F.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), pp. 181–206.

Park, H.

H. Park and J. R. Barry, “Trellis-coded multiple-pulse-position modulation for wireless infrared communications,” IEEE Trans. Commun. 52, 643–651 (2004).
[Crossref]

Parsay, A.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[Crossref]

L. C. Andrews and R. L. Phillips, Laser Bean Propagation through Random Media (SPIE Press, 2005).
[Crossref]

Puerta-Notario, A.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form expressions for the lower-bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels,” IET Commun. 6, 390–397 (2012).
[Crossref]

J. M. Garrido-Balsells, A. Jurado-Navas, J. Francisco Paris, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form BER analysis of variable weight MPPM coding under gamma-gamma scintillation for atmospheric optical communications,” Opt. Lett. 37, 719–721 (2012).
[Crossref]

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, “Variable weight MPPM technique for rate-adaptive optical wireless communications,” IET Electron. Lett. 42, 43–44 (2006).
[Crossref]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), pp. 181–206.

Qaraqe, K.

Ramírez, R.

M. V. Jamali, P. Khorramshahi, and R. Ramírez, “Statistical distribution of intensity fluctuations for underwater wireless optical channels in the presence of air bubbles,” in Iran Workshop on Proceedings Communication and Information Theory (IWCIT) (2016).

Rigaud, V.

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Commun. Netw. 5, 1–12 (2013).
[Crossref]

A. Khalighi, C. Gabriel, and V. Rigaud, “Optical communication system for an underwater wireless sensor network,” EGU General Assembly 14, 2685 (2012).

Rubinstein, R. Y.

R. Y. Rubinstein, Simulation and the Monte Carlo Method (Wiley, 1981).
[Crossref]

Salehi, J. A.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

Sasiela, R. J.

R. R. Parenti and R. J. Sasiela, “Distribution models for optical scintillation due to atmospheric turbulence,” MIT Lincoln Laboratory Technical Report TR-1108 (2005).

Shchepakina, E.

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22, 260–266 (2012).
[Crossref]

Tang, S.

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

Uysal, M.

Wang, C.

C. Wang, H.-Y. Yu, and Y.-J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8, 1–11 (2016).
[Crossref]

Xu, Z.

Yang, L.

Yu, H.-Y.

C. Wang, H.-Y. Yu, and Y.-J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8, 1–11 (2016).
[Crossref]

Zedini, E.

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

Zeng, Z.

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

Zhang, H.

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

Zhang, X.

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

Zhu, Y.-J.

C. Wang, H.-Y. Yu, and Y.-J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8, 1–11 (2016).
[Crossref]

Am. Math. Soc. (1)

P. Concus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Am. Math. Soc. 17, 245–256 (1963).

Appl. Opt. (3)

EGU General Assembly (1)

A. Khalighi, C. Gabriel, and V. Rigaud, “Optical communication system for an underwater wireless sensor network,” EGU General Assembly 14, 2685 (2012).

IEEE Access (1)

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

IEEE Commun. Surveys Tutorials (1)

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

IEEE Photon. J. (1)

C. Wang, H.-Y. Yu, and Y.-J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8, 1–11 (2016).
[Crossref]

IEEE Trans. Commun. (2)

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

H. Park and J. R. Barry, “Trellis-coded multiple-pulse-position modulation for wireless infrared communications,” IEEE Trans. Commun. 52, 643–651 (2004).
[Crossref]

IET Commun. (1)

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, “Closed-form expressions for the lower-bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels,” IET Commun. 6, 390–397 (2012).
[Crossref]

IET Electron. Lett. (1)

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, “Variable weight MPPM technique for rate-adaptive optical wireless communications,” IET Electron. Lett. 42, 43–44 (2006).
[Crossref]

Int. J. Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuations of the sea-water refraction index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

J. Commun. Information Systems (1)

C. Gussen, P. Diniz, M. Campos, W. Martins, F. Costa, and J. Gois, “A survey of underwater wireless communication technologies,” J. Commun. Information Systems,  31, 242–255 (2016).
[Crossref]

J. Opt. Commun. Netw. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng. 40, 1554–1562 (2001).
[Crossref]

Opt. Express (1)

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 2, 13055–13064 (2012).
[Crossref]

Opt. Lett. (1)

Photon. Res. (1)

Proc. IEEE (1)

J.M. Kahn and J.R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Underwater Technol. (1)

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]

Waves Random Complex Media (1)

O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22, 260–266 (2012).
[Crossref]

Other (12)

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), pp. 181–206.

M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshahi, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations (long version),” arXiv:1801.07402 (2018)

M. P. Bernotas and C. Nelson, “Probability density function analysis for optical turbulence with applications to underwater communications systems,” in “SPIE Defense+ Security. International Society for Optics and Photonics” (2016), paper 98270D.

R. R. Parenti and R. J. Sasiela, “Distribution models for optical scintillation due to atmospheric turbulence,” MIT Lincoln Laboratory Technical Report TR-1108 (2005).

J. R. Apel, Principles of Ocean Physics (Academic Press, 1987).

L. Mullen, B. Cochenour, and A. Laux, “Spatial and temporal dispersion in high bandwidth underwater laser communication links,” Proc. IEEE Military Commun. Conf. (2008), pp. 1–7.

The Sonardyne Site, “BlueComm Underwater Optical Communications”. Sonardyne International Ltd. [retrieved 18 July 2018], http://www.sonardyne.com/products/all-products/instruments/1148-bluecomm-underwater-optical-modem.html .

L. C. Andrews and R. L. Phillips, Laser Bean Propagation through Random Media (SPIE Press, 2005).
[Crossref]

Wolfram, http://functions.wolfram.com/

H. M. Oubei, E. Zedini, R. T. ElAfandy, A. Kammoun, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “Efficient Weibull channel model for salinity induced turbulent underwater wireless optical communications,” in Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC) (2017).
[Crossref]

R. Y. Rubinstein, Simulation and the Monte Carlo Method (Wiley, 1981).
[Crossref]

M. V. Jamali, P. Khorramshahi, and R. Ramírez, “Statistical distribution of intensity fluctuations for underwater wireless optical channels in the presence of air bubbles,” in Iran Workshop on Proceedings Communication and Information Theory (IWCIT) (2016).

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Figures (4)

Fig. 1
Fig. 1 Analytical (solid lines average bit error rate and Monte Carlo simulation results (circles) vs SNR0 for uncoding OOK formats under weak ( σ I 2 = 0.0496), weak-to-moderate ( σ I 2 = 0.1015), moderate-to-strong ( σ I 2 = 0.7885) and strong ( σ I 2 = 1.0652) salinity induced turbulence. Scenarios and values of irradiance variances taken from acquired data presented in [35]. As a reference, the ideal AWGN channel is depicted in dashed line.
Fig. 2
Fig. 2 Analytical (solid lines) average bit error rate and Monte Carlo simulation results (circles) vs SNR0 for a vw-MPPM format with code rate of 2/3 under weak ( σ I 2 = 0.0496), weak-to-moderate ( σ I 2 = 0.1015), moderate-to-strong ( σ I 2 = 0.7885) and strong ( σ I 2 = 1.0652) salinity induced turbulence. Scenarios and values of irradiance variances taken from acquired data presented in [35]. As a reference, the ideal AWGN channel is depicted in dashed line.
Fig. 3
Fig. 3 Analytical (solid lines) average bit error rate and Monte Carlo simulation results (circles) vs SNR0 for a vw-MPPM format with code rate of 6/12 under weak ( σ I 2 = 0.0496), weak-to-moderate ( σ I 2 = 0.1015), moderate-to-strong ( σ I 2 = 0.7885) and strong ( σ I 2 = 1.0652) salinity induced turbulence. Scenarios and values of irradiance variances taken from acquired data presented in [35]. As a reference, the ideal AWGN channel is depicted in dashed line.
Fig. 4
Fig. 4 Analytical (solid lines) average bit error rate and Monte Carlo simulation results (circles) vs SNR0 for a vw-MPPM format with code rate of 9/36 under weak ( σ I 2 = 0.0496), weak-to-moderate σ I 2 = 0.1015), moderate-to-strong ( σ I 2 = 0.7885) and strong ( σ I 2 = 1.0652) salinity induced turbulence. Scenarios and values of irradiance variances taken from acquired data presented in [35]. As a reference, the ideal AWGN channel is depicted in dashed line.

Tables (1)

Tables Icon

Table 1 Hyperexponential Fitting Parameters a, b and c in Absence of Turbulence

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

f I ( I ) = K λ ( I λ ) K 1 exp [ ( I λ ) K ] ,
λ = 1 Γ ( 1 + 1 / K )
σ I 2 Γ ( 1 + 2 / K ) Γ ( 1 + 1 / K ) 2 1 K 11 / 6
i = i S + i N = α RIP t + i N ,
P b ( e | I ) = 1 2 erfc ( i S 0 I 2 2 σ N ) = 1 2 erfc ( SNR 0 I 2 2 ) ,
P b = 0 1 2 erfc ( SNR 0 I 2 2 ) f I ( I ) d I .
P b = ( P b ( e | I ) F I ( I ) ) | 0 0 d d I [ P b ( e | I ) ] F I ( I ) d I .
P b = 0 d d I [ 1 2 erfc ( SNR 0 I 2 2 ) ] F I ( I ) d I ,
F I ( I ) = 1 exp [ ( I λ ) K ] .
d d I [ P b ( e | I ) ] = SNR 0 2 2 π exp [ ( SNR 0 I 2 2 ) 2 ] .
0 x β e x f ( x ) d x = i = 1 n H i f ( x i ) + E n ,
L n β = m = 0 n ( n + β n m ) ( x ) m m ! .
H i = Γ ( n + β + 1 ) x i n ! ( n + 1 ) 2 [ L n + 1 β ( x i ) ] 2 , ( i = 1 , 2 , , n ) .
P b = 1 2 π 0 x 1 2 exp ( x ) ( 1 exp [ ( 2 2 λ SNR 0 x ) K ] ) d x
x = ( SNR 0 2 2 ) 2 I 2 ; d x = 2 ( SNR 0 2 2 ) 2 I d I .
P b = 1 2 π i = 1 n H i { 1 exp [ ( 2 2 λ SNR 0 x i ) K ] }
C ˜ N = ( i = 0 x 1 C n , i ) C ˜ n , x ,
2 k i = 0 x 1 ( n i )
CBER ( I , γ 0 ) = P b ( e | I ) a exp [ b ( γ 0 I 2 ) c ]
P b = 0 a exp [ b ( γ 0 I 2 ) c ] f I ( I ) d I .
d d I [ a exp [ b ( ( SNR 0 I ) 2 ) c ] ] = 2 a b c SNR 0 2 c I 2 c 1 exp [ b ( ( SNR 0 I ) 2 ) c ]
P b = a i = 1 n H i { 1 exp [ ( x i 1 2 c σ N b 1 2 c R P t λ ) κ ] }
f I ( I ) = α K λ ( I λ ) K 1 exp [ ( I λ ) K ] { 1 exp [ ( I λ ) K ] } α 1 ,
F I ( I ) = { 1 exp [ ( I λ ) K ] } α .
P b = 1 2 π 0 x 1 2 exp ( x ) ( 1 exp [ ( 2 2 λ SNR 0 x ) K ] ) α d x
P b = 1 2 π i = 1 n H i { 1 exp [ ( 2 2 λ SNR 0 x i ) K ] } α