Abstract

In this paper, we analytically investigate an optical signal detection scheme to mitigate the scintillation effect with the assistance of a co-propagating reference continuous wave (CW) light. Using the correlation coefficient between the intensities of the data light and the reference CW light, we mathematically derive their joint intensity distributions under two widely used atmospheric turbulence channel models, namely log-normal distributed channel model and Gamma-Gamma distributed channel model, respectively. We also carry out the Monte-Carlo (MC) simulation and show that theoretical results agree with simulation results well. Our analytical results reveal that when the correlation coefficient is 0.99, the power reductions to achieve BER of 10−3 are 12.3 dB and 20.4 dB under moderate and strong atmospheric turbulence conditions (i.e., Rytov variances of 1.0 and 4.0), respectively. In addition, the feasibility of the scheme applied to wavelength-division-multiplexed (WDM) free-space-optical (FSO) transmission systems is also investigated, where only a single reference CW light could be used to mitigate the scintillation effects on all WDM channels.

© 2012 OSA

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References

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  1. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
    [CrossRef] [PubMed]
  2. X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
    [CrossRef]
  3. N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
    [CrossRef]
  4. N. Cvijetc, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optical wireless transmission with coherent detection,” J. Lightwave Technol. 28(8), 1218–1227 (2010).
    [CrossRef]
  5. N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
    [CrossRef]
  6. A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient channel model for free space optical communications,” in IEEE Mediterranean Electrotechnical Conference, 2006. MELECON 2006 (IEEE, 2006), pp. 631–634.
  7. I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
    [CrossRef]
  8. X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Circle polarization shift keying with directed detection for free-space optical communication,” J. Opt. Commun. Netw. 1(4), 307–312 (2009).
    [CrossRef]
  9. W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
    [CrossRef]
  10. K. J. Grant, K. A. Corbett, B. A. Clare, J. E. Davies, B. D. Nener, and A. Boettcher-Hunt, “Dual wavelength free space optical communications,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuG3.
  11. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  12. T. Wang and J. W. Strohbehn, “Perturbed log-normal distribution of irradiance fluctuations,” J. Opt. Soc. Am. 64(7), 994–999 (1974).
    [CrossRef]
  13. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
    [CrossRef]
  14. C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
    [CrossRef]
  15. W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
    [CrossRef]
  16. G. R. Osche, Optical Detection Theory for Laser Applications (Wiley, 2002).
  17. 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 turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
    [CrossRef]
  18. T. D. Pham, A. Bekkali, K. Kazaura, K. Wakamori, and M. Matsumoto, “A universal platform for ubiquitous wireless communications using radio over FSO system,” J. Lightwave Technol. 28(16), 2258–2267 (2010).
    [CrossRef]
  19. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
  20. C. H. Edwards and D. E. Penny, Multivariable Calculus with Matrices (Prentice Hall, 2002).
  21. J. L. Devore, Probability Statistics for Engineering and the Sciences (Brooks/Cole, 2008).
  22. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
    [CrossRef]
  23. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley Inter-Science, 2002).
  24. J. G. Proakis, Digital Communications (McGraw-Hill, 2008).
  25. D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009).
    [CrossRef]
  26. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
    [CrossRef]
  27. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
    [CrossRef]
  28. N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space optical transmission using OFDM,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThD2.
  29. S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
    [CrossRef]
  30. A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
    [CrossRef]

2011 (2)

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (6)

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[CrossRef]

X. Zhao, Y. Yao, Y. Sun, and C. Liu, “Circle polarization shift keying with directed detection for free-space optical communication,” J. Opt. Commun. Netw. 1(4), 307–312 (2009).
[CrossRef]

D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009).
[CrossRef]

X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
[CrossRef]

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[CrossRef]

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

2008 (3)

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[CrossRef]

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[CrossRef]

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[CrossRef]

2007 (2)

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[CrossRef]

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[CrossRef]

2006 (1)

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[CrossRef]

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[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 turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[CrossRef]

1974 (1)

Abbou, F. M.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[CrossRef]

Abdullah, M.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[CrossRef]

Abushagur, A.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[CrossRef]

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 turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[CrossRef]

Allen, J.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[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 turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[CrossRef]

Bekkali, A.

Borah, D. K.

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Chang, F.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

Cowley, W.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[CrossRef]

Cvijetc, N.

Djordjevic, I. B.

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[CrossRef]

Flecker, B.

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[CrossRef]

Flohberger, M.

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[CrossRef]

Gao, S.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[CrossRef]

Gappmair, W.

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[CrossRef]

García-Zambrana, A.

Gebhart, M.

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[CrossRef]

Ghassemlooy, Z.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[CrossRef]

Holland, I.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[CrossRef]

Huang, Y.-K.

i Fabregas, A. G.

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[CrossRef]

Kahn, J. M.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

Kazaura, K.

Kwok, C. H.

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[CrossRef]

Leitgeb, E.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[CrossRef]

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[CrossRef]

Letzepis, N.

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[CrossRef]

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[CrossRef]

Li, J.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[CrossRef]

Liu, C.

Liu, J. Q.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[CrossRef]

Liu, X.

X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
[CrossRef]

Matsumoto, M.

Misran, N.

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[CrossRef]

Mizuochi, T.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

Muhammad, S. S.

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[CrossRef]

Neifeld, M. A.

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[CrossRef]

Nistazakis, H. E.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

Onohara, K.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

Penty, R. V.

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[CrossRef]

Pham, T. D.

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 turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[CrossRef]

Popoola, W. O.

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[CrossRef]

Qian, D.

Strohbehn, J. W.

Sun, Y.

Taylor, D. P.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[CrossRef]

Tombras, G. S.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

Tsiftsis, T. A.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

Vasic, B.

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[CrossRef]

Voelz, D. G.

Wakamori, K.

Wang, T.

White, I. H.

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[CrossRef]

Yao, Y.

Yu, J.

Zhao, X.

Zhu, X.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

IEEE Commun. Mag. (1)

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

I. B. Djordjevic, B. Vasic, and M. A. Neifeld, “Multilevel coding in free-space optical MIMO transmission with Q-ary PPM over the atmospheric turbulence channel,” IEEE Photon. Technol. Lett. 18(14), 1491–1493 (2006).
[CrossRef]

C. H. Kwok, R. V. Penty, and I. H. White, “Link reliability improvement for optical wireless communication systems with temporal-domain diversity reception,” IEEE Photon. Technol. Lett. 20(9), 700–702 (2008).
[CrossRef]

IEEE Trans. Commun. (4)

N. Letzepis and A. G. i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” IEEE Trans. Commun. 57(12), 3682–3690 (2009).
[CrossRef]

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communications using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

X. Liu, “Free-space optics optimization models for building sway and atmospheric interference using variable wavelength,” IEEE Trans. Commun. 57(2), 492–498 (2009).
[CrossRef]

IEEE Trans. Wirel. Comm. (2)

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wirel. Comm. 7(5), 1744–1753 (2008).
[CrossRef]

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by Gamma-Gamma distribution,” IEEE Trans. Wirel. Comm. 8(5), 2209–2213 (2009).
[CrossRef]

IET Commun. (1)

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

IET Optoelectron. (1)

W. O. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2(1), 16–23 (2008).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (1)

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

S. S. Muhammad, B. Flecker, E. Leitgeb, and M. Gebhart, “Characterization of fog attenuation in terrestrial free space optical links,” Opt. Eng. 46(6), 066001 (2007).
[CrossRef]

A. Abushagur, F. M. Abbou, M. Abdullah, and N. Misran, “Performance analysis of a free-space terrestrial optical system in the presence of absorption, scattering, and pointing error,” Opt. Eng. 50(7), 075007 (2011).
[CrossRef]

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 turbulence media,” Opt. Eng. 40(8), 1554–1562 (2001).
[CrossRef]

Opt. Express (1)

Other (10)

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

C. H. Edwards and D. E. Penny, Multivariable Calculus with Matrices (Prentice Hall, 2002).

J. L. Devore, Probability Statistics for Engineering and the Sciences (Brooks/Cole, 2008).

N. Cvijetic, D. Qian, and T. Wang, “10Gb/s free-space optical transmission using OFDM,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThD2.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley Inter-Science, 2002).

J. G. Proakis, Digital Communications (McGraw-Hill, 2008).

G. R. Osche, Optical Detection Theory for Laser Applications (Wiley, 2002).

A. Jurado-Navas, A. Garcia-Zambrana, and A. Puerta-Notario, “Efficient channel model for free space optical communications,” in IEEE Mediterranean Electrotechnical Conference, 2006. MELECON 2006 (IEEE, 2006), pp. 631–634.

K. J. Grant, K. A. Corbett, B. A. Clare, J. E. Davies, B. D. Nener, and A. Boettcher-Hunt, “Dual wavelength free space optical communications,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CTuG3.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

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Figures (6)

Fig. 1
Fig. 1

Schematic of an OOK FSO communication system with a reference CW light to mitigate the scintillation effect.

Fig. 2
Fig. 2

PDFs of the normalized intensity (amplitude) of the data light (signal) under moderate atmospheric turbulence condition with Rytov variance of 1.0: (a) before and (b) after the signal processing by the division circuit.

Fig. 3
Fig. 3

BER improvement of OOK FSO system by a reference CW light under moderate atmospheric turbulence condition with Rytov variance of 1.0: (a) correlation coefficient is 0.85 and (b) correlation coefficient is 0.99.

Fig. 4
Fig. 4

PDFs and histograms of the normalized intensity (amplitude) of the data light (signal) under strong atmospheric turbulence condition with Rytov variance of 4.0: (a) before signal processing, (b) after signal processing with correlation coefficient is 0.85 and (c) after signal processing with correlation coefficient is 0.99.

Fig. 5
Fig. 5

BER improvement of OOK FSO system by a reference CW light under strong atmospheric turbulence condition with Rytov variance of 4.0: (a) correlation coefficient is 0.85 and (b) correlation coefficient is 0.99.

Fig. 6
Fig. 6

Power reductions for achieving BER of 10−3 in WDM-FSO system under moderate atmospheric turbulence condition (i.e., Rytov variance of 1.0).

Equations (33)

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f LN ( I S )= 1 2π σ R 2 I S exp{ [ ln( I S I 0 )+ 1 2 σ R 2 ] 2 / ( 2 σ R 2 ) },
σ R 2 =1.23 C n 2 k 7/6 L 11/6 ,
f GG ( I S )= 2 (αβ) α+β 2 Γ(α)Γ(β) I S α+β2 2 K αβ (2 αβ I S ),
α= { exp[ 0.49 σ R 2 / ( 1+1.11 σ R 12/5 ) 7/6 ]1 } 1 ,
β= { exp[ 0.51 σ R 2 / ( 1+0.69 σ R 12/5 ) 5/6 ]1 } 1 .
f( I P )= 0 I R f( I S , I R ) d I R = 0 I R f( I R I P , I R ) d I R ,
f x ( x )= 1 2π σ 1 exp( ( x μ 1 ) 2 2 σ 1 2 ).
f xy ( x,y )= 1 2π σ 1 σ 2 1 ρ N 2 exp( 1 2( 1 ρ N 2 ) ( ( x μ 1 ) 2 σ 1 2 2 ρ N ( x μ 1 )( y μ 2 ) σ 1 σ 2 + ( y μ 2 ) 2 σ 2 2 ) ).
ρ N = cov( x,y ) D( x )D( y ) = E( xy )E( x )E( y ) D( x )D( y ) ,
u=exp( x ),
v=exp( y ).
J 1 =| x u x v y u y v |=| 1 u 0 0 1 v |= 1 uv .
f uv ( u,v )= J 1 f xy ( x,y )= 1 uv f xy ( x,y )= 1 2π σ 1 σ 2 1 ρ N 2 uv exp( 1 2( 1 ρ N 2 ) ( ( ln( u ) μ 1 ) 2 σ 1 2 2 ρ N ( ln( u ) μ 1 )( ln( v ) μ 2 ) σ 1 σ 2 + ( ln( v ) μ 2 ) 2 σ 2 2 ) ).
ρ LN = cov( u,v ) D( u )D( v ) = E( uv )E( u )E( v ) D( u )D( v ) .
cov( u,v )=E( uv )E( u )E( v ) =exp( μ 1 + μ 2 )exp( σ 1 2 + σ 2 2 2 )( exp( ρ N σ 1 σ 2 )1 ),
D( u )=E( u 2 ) ( E( u ) ) 2 =exp( 2 μ 1 + σ 1 2 )( exp( σ 1 2 )1 ),
D( v )=E( v 2 ) ( E( v ) ) 2 =exp( 2 μ 2 + σ 2 2 )( exp( σ 2 2 )1 ).
ρ N = ln( ρ LN ( exp( σ 1 2 )1 )( exp( σ 2 2 )1 ) +1 ) σ 1 σ 2 .
J 2 =| u w u z v w v z |=| u w 0 0 v z |= du dw dv dz .
f wz ( w,z )= J 2 f uv ( u,v )= du dw dv dz f uv ( u,v ).
J 3 = du dw = f GG (w) f LN (u) ,
J 4 = dv dz = f GG (z) f LN (v) .
u= h w ( w ).
v= h z ( z ).
f wz ( w,z )= f GG (w) f GG (z) f LN (u) f LN (v) f uv ( u,v ) = f GG (w) f GG (z) f LN [ h w ( w ) ] f LN [ h z ( z ) ] f uv [ h w ( w ), h z ( z ) ].
ρ GG = cov( w,z ) D( w )D( z ) = n( wz )( w )( z ) [ n( w 2 ) ( w ) 2 ][ n( z 2 ) ( z ) 2 ] ,
P e =P( 0 )P( error|0 )+P( 1 )P( error|1 ),
P( error|0 )= I th 1 2π σ n 2 exp( r 2 2 σ n 2 )dr =Q( I th σ n ),
P( error|1 )= I th 1 2π σ n 2 exp( ( rI ) 2 2 σ n 2 )f( I )drdI = Q( I I th σ n )f( I )dI ,
Λ= 1 2π σ n 2 exp( ( I th I ) 2 2 σ n 2 )f( I )dI / ( 1 2π σ n 2 exp( I th 2 2 σ n 2 ) ) = exp( ( I th I ) 2 + α 2 2 σ n 2 )f( I )dI =1.
P e = 1 2 ( Q( I th σ n )+ Q( I I th σ n )f( I )dI ).
σ R_R 2 = σ R_S 2 ( λ S / λ R ) 7/6 .
P R ( L )= P T ( 0 )exp( AL ),

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