Abstract

In this Letter, we use laser beam intensity fluctuation measurements to model and describe the statistical properties of weak temperature-induced turbulence in underwater wireless optical communication (UWOC) channels. UWOC channels with temperature gradients are modeled by the generalized gamma distribution (GGD) with an excellent goodness of fit to the measured data under all channel conditions. Meanwhile, thermally uniform channels are perfectly described by the simple gamma distribution which is a special case of GGD. To the best of our knowledge, this is the first model that comprehensively describes both thermally uniform and gradient-based UWOC channels.

© 2017 Optical Society of America

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O. Korotkova, N. Farwell, and E. Shchepakina, Waves Random Complex Media 22, 260 (2012).
[Crossref]

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D. W. Scott, Wiley Interdiscip. Rev.: Comput. Stat. 1, 303 (2009).
[Crossref]

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[Crossref]

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K. M. Aly and E. Esmail, Opt. Mater. 2, 195 (1993).
[Crossref]

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E. A. Boyle and L. Keigwin, Nature 330, 35 (1987).
[Crossref]

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1977 (1)

1965 (1)

V. B. Parr and J. T. Webster, Technometrics 7, 1 (1965).
[Crossref]

AbdollahRamezani, S.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Alouini, M.-S.

Aly, K. M.

K. M. Aly and E. Esmail, Opt. Mater. 2, 195 (1993).
[Crossref]

Avery, W. H.

W. H. Avery and C. Wu, Renewable Energy from the Ocean: A Guide to OTEC (Oxford University, 1994).

Bahrani, S.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Bankman, I. N.

J. W. Giles and I. N. Bankman, in IEEE Military Communications Conference (MILCOM) (2005), Vol. 3, p. 1700.

Bissonnette, L. R.

Born, M.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 1999).

Boyle, E. A.

E. A. Boyle and L. Keigwin, Nature 330, 35 (1987).
[Crossref]

Chizari, A.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Deng, N.

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

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[Crossref]

Devore, J.

J. Devore, Probability and Statistics for Engineering and the Sciences, 8th ed. (Cengage Learning, 2011).

Esmail, E.

K. M. Aly and E. Esmail, Opt. Mater. 2, 195 (1993).
[Crossref]

Farwell, N.

O. Korotkova, N. Farwell, and E. Shchepakina, Waves Random Complex Media 22, 260 (2012).
[Crossref]

Fazelian, M.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Gerçekcioglu, H.

Giles, J. W.

J. W. Giles and I. N. Bankman, in IEEE Military Communications Conference (MILCOM) (2005), Vol. 3, p. 1700.

Guo, Y.

Han, J.

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, Opt. Express 24, 8097 (2016).
[Crossref]

Hanawa, M.

Hill, R. J.

Ho, K.-T.

Hou, W.

Jamali, M. V.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Keigwin, L.

E. A. Boyle and L. Keigwin, Nature 330, 35 (1987).
[Crossref]

Khorramshahi, P.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Kong, M.

J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, Opt. Express 24, 8097 (2016).
[Crossref]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

Korotkova, O.

O. Korotkova, N. Farwell, and E. Shchepakina, Waves Random Complex Media 22, 260 (2012).
[Crossref]

Li, C.

Li, Z.

Lin, A.

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, Opt. Express 24, 8097 (2016).
[Crossref]

Liu, G.

Liu, W.

Liu, Z.

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[Crossref]

Qu, F.

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

Salehi, J. A.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Scott, D. W.

D. W. Scott, Wiley Interdiscip. Rev.: Comput. Stat. 1, 303 (2009).
[Crossref]

Shahsavari, S.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Shchepakina, E.

O. Korotkova, N. Farwell, and E. Shchepakina, Waves Random Complex Media 22, 260 (2012).
[Crossref]

Shen, C.

Song, Y.

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, Opt. Express 24, 8097 (2016).
[Crossref]

Tashakori, A.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

Webster, J. T.

V. B. Parr and J. T. Webster, Technometrics 7, 1 (1965).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 1999).

Wu, C.

W. H. Avery and C. Wu, Renewable Energy from the Ocean: A Guide to OTEC (Oxford University, 1994).

Xu, J.

J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, Opt. Express 24, 8097 (2016).
[Crossref]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

Xu, Z.

Yang, L.

Yi, X.

Yu, X.

J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, Opt. Express 24, 8097 (2016).
[Crossref]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Nature (1)

E. A. Boyle and L. Keigwin, Nature 330, 35 (1987).
[Crossref]

Opt. Commun. (1)

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, Opt. Commun. 369, 100 (2016).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Opt. Mater. (1)

K. M. Aly and E. Esmail, Opt. Mater. 2, 195 (1993).
[Crossref]

Photon. Res. (1)

Technometrics (1)

V. B. Parr and J. T. Webster, Technometrics 7, 1 (1965).
[Crossref]

Waves Random Complex Media (1)

O. Korotkova, N. Farwell, and E. Shchepakina, Waves Random Complex Media 22, 260 (2012).
[Crossref]

Wiley Interdiscip. Rev.: Comput. Stat. (1)

D. W. Scott, Wiley Interdiscip. Rev.: Comput. Stat. 1, 303 (2009).
[Crossref]

Other (6)

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 1999).

http://www.maths.lth.se/matstat/wafo/documentation/wafodoc/wafo/wstats/index.html , accessed on April 10, 2017.

M. V. Jamali, P. Khorramshahi, A. Tashakori, A. Chizari, S. Shahsavari, S. AbdollahRamezani, M. Fazelian, S. Bahrani, and J. A. Salehi, Iran Workshop on Communication and Information Theory (IWCIT), Tehran, 2016, pp. 1–6.

J. W. Giles and I. N. Bankman, in IEEE Military Communications Conference (MILCOM) (2005), Vol. 3, p. 1700.

J. Devore, Probability and Statistics for Engineering and the Sciences, 8th ed. (Cengage Learning, 2011).

W. H. Avery and C. Wu, Renewable Energy from the Ocean: A Guide to OTEC (Oxford University, 1994).

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Figures (3)

Fig. 1.
Fig. 1.

Photograph of the experimental setup used to study thestatistics of the temperature-induced turbulence in an underwater wireless optical channel: LD, laser diode; PD, photodetector.

Fig. 2.
Fig. 2.

(a) Acquired data histogram along with the gamma PDF for 25°C water temperature— σ I _ measured 2 = 7.0622 × 10 4 , a = 1.412 × 10 3 , b = 7.0822 × 10 4 , and σ I 2 = 7.1649 × 10 4 . (b) Scintillation index as a function of water temperature (solid squares for measurements and closed circles for calculations). The dashed lines are guides to the eye.

Fig. 3.
Fig. 3.

Histograms of the measured data along with the PDF of various distributions under different temperature gradient levels: (a)  0.05 ° C · cm 1 , (b)  0.10 ° C · cm 1 , (c)  0.15 ° C · cm 1 , and (d)  0.20 ° C · cm 1 .

Tables (2)

Tables Icon

Table 1. Different Temperature Values Used to Create Temperature Gradients in the Water Channel

Tables Icon

Table 2. R 2 Test Measure Results for Different Distributions under Four Different Underwater Channel Temperature Gradient Levels

Equations (2)

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f ( I ; a , b , c ) = c I a c 1 b a c × exp ( ( I b ) c ) Γ , I > 0 ; a , b , c > 0 ,
σ I 2 = Γ ( a ) Γ ( a + 2 c ) Γ ( a + 1 c ) 1.

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