Abstract

Using an accurate exponential bound for the Gaussian Q-function, we derive simple approximate closed-form expressions for the average symbol error probability (ASEP) of a free-space optical communication link using subcarrier intensity modulation (SIM) with general-order rectangular quadrature amplitude modulation (QAM) over atmospheric turbulence channels. To model the atmospheric turbulence conditions, the log-normal and the gamma-gamma distribution are used. Extensive numerical and computer simulation results are presented in order to verify the accuracy of the proposed mathematical analysis.

© 2010 Optical Society of America

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  4. R. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.
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  6. D. L. Fried, G. E. Mevers, M. P. Keister, “Measurements of laser-beam scintillation in the atmosphere,” J. Opt. Soc. Am., vol. 59, pp. 1455–1460, Nov. 1969.
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  8. M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance PDF of a laser beam propagating through turbulent media,” Opt. Eng, vol. 40, no. 8, pp. 1554–1562, 2001.
    [CrossRef]
  9. L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves Random Media, vol. 11, no. 3, pp. 271–291, 2001.
    [CrossRef]
  10. M. Uysal, J. T. Li, M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 5, no. 6, pp. 1229–1233, June 2006.
    [CrossRef]
  11. T. Kamalakis, T. Sphicopoulos, S. S. Muhammad, E. Leitgeb, “Estimation of the power scintillation probability density function in free-space optical links by use of multicanonical Monte Carlo sampling,” Opt. Lett., vol. 31, no. 21, pp. 3077–3079, 2006.
    [CrossRef] [PubMed]
  12. F. S. Vetelino, S. Young, L. Andrews, “Fade statistics and aperture averaging for Gaussian beam waves in moderate to strong turbulence,” Appl. Opt., vol. 46, no. 18, pp. 3780–3789, 2007.
    [CrossRef] [PubMed]
  13. X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, Aug. 2002.
    [CrossRef]
  14. X. Zhu, J. M. Kahn, J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” IEEE Photon. Technol. Lett., vol. 15, no. 15, pp. 623–625, Apr. 2003.
    [CrossRef]
  15. S. M. Haas, J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1436–1357, Oct. 2003.
    [CrossRef]
  16. J. H. Shapiro, R. C. Harney, “Burst-mode atmospheric optical communication,” in Proc. Nat. Telecommun. Conf., 1980, pp. 27.5.1–27.5.7.
  17. J. Li, J. Q. Liu, D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1605, Aug. 2007.
    [CrossRef]
  18. W. Popoola, Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol. 27, no. 8, pp. 967–973, Apr. 2009.
    [CrossRef]
  19. W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
    [CrossRef]
  20. W. Popoola, Z. Ghassemlooy, E. Leitgeb, “BER performance of DPSK subcarrier modulated free space optics in fully developed speckle,” in 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, 2008, pp. 273–277.
  21. H. Rongqing, Z. Benyuan, H. Renxiang, T. Christopher, R. Kenneth, R. Douglas, “Subcarrier multiplexing for high-speed optical transmission,” J. Lightwave Technol., vol. 20, pp. 417–424, Mar. 2002.
    [CrossRef]
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  25. M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
    [CrossRef]
  26. M. Chiani, D. Dardari, M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, pp. 840–845, July 2003.
    [CrossRef]
  27. H. A. Suraweera, J. Armstrong, “A simple and accurate approximation to the SEP of rectangular QAM in arbitrary Nakagami-m fading channels,” IEEE Commun. Lett., vol. 11, no. 5, pp. 426–428, May 2007.
    [CrossRef]
  28. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1972.
  29. A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breech Science, 1990.
  30. H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol., vol. 27, no. 8, pp. 974–979, Apr. 2009.
    [CrossRef]
  31. M. Uysal, S. M. Navidpour, J. Li, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett., vol. 8, no. 10, pp. 635–637, Oct. 2004.
    [CrossRef]

2009

2008

W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

2007

F. S. Vetelino, S. Young, L. Andrews, “Fade statistics and aperture averaging for Gaussian beam waves in moderate to strong turbulence,” Appl. Opt., vol. 46, no. 18, pp. 3780–3789, 2007.
[CrossRef] [PubMed]

J. Li, J. Q. Liu, D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1605, Aug. 2007.
[CrossRef]

H. A. Suraweera, J. Armstrong, “A simple and accurate approximation to the SEP of rectangular QAM in arbitrary Nakagami-m fading channels,” IEEE Commun. Lett., vol. 11, no. 5, pp. 426–428, May 2007.
[CrossRef]

2006

M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
[CrossRef]

M. Uysal, J. T. Li, M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 5, no. 6, pp. 1229–1233, June 2006.
[CrossRef]

T. Kamalakis, T. Sphicopoulos, S. S. Muhammad, E. Leitgeb, “Estimation of the power scintillation probability density function in free-space optical links by use of multicanonical Monte Carlo sampling,” Opt. Lett., vol. 31, no. 21, pp. 3077–3079, 2006.
[CrossRef] [PubMed]

2005

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep., vol. 2, pp. 345–396, 2005.
[CrossRef]

2004

D. Keddar, S. Amon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May 2004.

M. Uysal, S. M. Navidpour, J. Li, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett., vol. 8, no. 10, pp. 635–637, Oct. 2004.
[CrossRef]

2003

M. Chiani, D. Dardari, M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, pp. 840–845, July 2003.
[CrossRef]

X. Zhu, J. M. Kahn, J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” IEEE Photon. Technol. Lett., vol. 15, no. 15, pp. 623–625, Apr. 2003.
[CrossRef]

S. M. Haas, J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1436–1357, Oct. 2003.
[CrossRef]

2002

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, Aug. 2002.
[CrossRef]

H. Rongqing, Z. Benyuan, H. Renxiang, T. Christopher, R. Kenneth, R. Douglas, “Subcarrier multiplexing for high-speed optical transmission,” J. Lightwave Technol., vol. 20, pp. 417–424, Mar. 2002.
[CrossRef]

2001

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance PDF of a laser beam propagating through turbulent media,” Opt. Eng, vol. 40, no. 8, pp. 1554–1562, 2001.
[CrossRef]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves Random Media, vol. 11, no. 3, pp. 271–291, 2001.
[CrossRef]

1998

I. I. Kim, E. Woodbridge, V. Chan, B. Strickland, “Scintillation measurements performed during the limited-visibility lasercom experiment,” Proc. SPIE, vol. 3266, pp. 209–220, 1998.
[CrossRef]

1969

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1972.

Agrawal, G.

G. Agrawal, Fiber-Optic Communication Systems. New York: Wiley-Interscience, 2002.
[CrossRef]

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance PDF of a laser beam propagating through turbulent media,” Opt. Eng, vol. 40, no. 8, pp. 1554–1562, 2001.
[CrossRef]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves Random Media, vol. 11, no. 3, pp. 271–291, 2001.
[CrossRef]

Allen, J.

W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Amon, S.

D. Keddar, S. Amon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May 2004.

Andrews, L.

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance PDF of a laser beam propagating through turbulent media,” Opt. Eng, vol. 40, no. 8, pp. 1554–1562, 2001.
[CrossRef]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves Random Media, vol. 11, no. 3, pp. 271–291, 2001.
[CrossRef]

Armstrong, J.

H. A. Suraweera, J. Armstrong, “A simple and accurate approximation to the SEP of rectangular QAM in arbitrary Nakagami-m fading channels,” IEEE Commun. Lett., vol. 11, no. 5, pp. 426–428, May 2007.
[CrossRef]

Benyuan, Z.

Brychkov, Y. A.

A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breech Science, 1990.

Chan, V.

I. I. Kim, E. Woodbridge, V. Chan, B. Strickland, “Scintillation measurements performed during the limited-visibility lasercom experiment,” Proc. SPIE, vol. 3266, pp. 209–220, 1998.
[CrossRef]

Chiani, M.

M. Chiani, D. Dardari, M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, pp. 840–845, July 2003.
[CrossRef]

Christopher, T.

Cvijetic, N.

N. Cvijetic, T. Wang, “WiMAX over free-space optics—evaluating OFDM multi-subcarrier modulation in optical wireless channels,” in Sarnoff Symp., IEEE, 27–28 March 2006, pp. 1–4.

Dardari, D.

M. Chiani, D. Dardari, M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, pp. 840–845, July 2003.
[CrossRef]

Douglas, R.

Fafalios, M. E.

Fried, D. L.

Gagliardi, R.

R. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.

Gao, S.

W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Ghassemlooy, Z.

W. Popoola, Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol. 27, no. 8, pp. 967–973, Apr. 2009.
[CrossRef]

W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

W. Popoola, Z. Ghassemlooy, E. Leitgeb, “BER performance of DPSK subcarrier modulated free space optics in fully developed speckle,” in 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, 2008, pp. 273–277.

Haas, S. M.

S. M. Haas, J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1436–1357, Oct. 2003.
[CrossRef]

Harney, R. C.

J. H. Shapiro, R. C. Harney, “Burst-mode atmospheric optical communication,” in Proc. Nat. Telecommun. Conf., 1980, pp. 27.5.1–27.5.7.

Hongou, J.

M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
[CrossRef]

Hopen, C. Y.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves Random Media, vol. 11, no. 3, pp. 271–291, 2001.
[CrossRef]

L. Andrews, R. L. Philips, C. Y. Hopen, Laser Beam Scintillation With Applications. SPIE Press, 2001.
[CrossRef]

Kahn, J. M.

X. Zhu, J. M. Kahn, J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” IEEE Photon. Technol. Lett., vol. 15, no. 15, pp. 623–625, Apr. 2003.
[CrossRef]

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, Aug. 2002.
[CrossRef]

Kamalakis, T.

Karagianni, E. A.

Karp, S.

R. Gagliardi, S. Karp, Optical Communications. New York: Wiley, 1995.

Kasai, K.

M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
[CrossRef]

Keddar, D.

D. Keddar, S. Amon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May 2004.

Keister, M. P.

Kenneth, R.

Kim, I. I.

I. I. Kim, E. Woodbridge, V. Chan, B. Strickland, “Scintillation measurements performed during the limited-visibility lasercom experiment,” Proc. SPIE, vol. 3266, pp. 209–220, 1998.
[CrossRef]

Leitgeb, E.

W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

T. Kamalakis, T. Sphicopoulos, S. S. Muhammad, E. Leitgeb, “Estimation of the power scintillation probability density function in free-space optical links by use of multicanonical Monte Carlo sampling,” Opt. Lett., vol. 31, no. 21, pp. 3077–3079, 2006.
[CrossRef] [PubMed]

W. Popoola, Z. Ghassemlooy, E. Leitgeb, “BER performance of DPSK subcarrier modulated free space optics in fully developed speckle,” in 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, 2008, pp. 273–277.

Li, J.

J. Li, J. Q. Liu, D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1605, Aug. 2007.
[CrossRef]

M. Uysal, S. M. Navidpour, J. Li, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett., vol. 8, no. 10, pp. 635–637, Oct. 2004.
[CrossRef]

Li, J. T.

M. Uysal, J. T. Li, M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 5, no. 6, pp. 1229–1233, June 2006.
[CrossRef]

Liu, J. Q.

J. Li, J. Q. Liu, D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1605, Aug. 2007.
[CrossRef]

Majumdar, A. K.

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep., vol. 2, pp. 345–396, 2005.
[CrossRef]

Marichev, O. I.

A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breech Science, 1990.

Mevers, G. E.

Muhammad, S. S.

Nakazawa, M.

M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
[CrossRef]

Navidpour, S. M.

M. Uysal, S. M. Navidpour, J. Li, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett., vol. 8, no. 10, pp. 635–637, Oct. 2004.
[CrossRef]

Nistazakis, H. E.

Philips, R. L.

L. Andrews, R. L. Philips, C. Y. Hopen, Laser Beam Scintillation With Applications. SPIE Press, 2001.
[CrossRef]

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance PDF of a laser beam propagating through turbulent media,” Opt. Eng, vol. 40, no. 8, pp. 1554–1562, 2001.
[CrossRef]

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves Random Media, vol. 11, no. 3, pp. 271–291, 2001.
[CrossRef]

Popoola, W.

W. Popoola, Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol. 27, no. 8, pp. 967–973, Apr. 2009.
[CrossRef]

W. Popoola, Z. Ghassemlooy, J. Allen, E. Leitgeb, S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol. 2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

W. Popoola, Z. Ghassemlooy, E. Leitgeb, “BER performance of DPSK subcarrier modulated free space optics in fully developed speckle,” in 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, 2008, pp. 273–277.

Prudnikov, A. P.

A. P. Prudnikov, Y. A. Brychkov, O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breech Science, 1990.

Renxiang, H.

Rongqing, H.

Shapiro, J. H.

S. M. Haas, J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1436–1357, Oct. 2003.
[CrossRef]

J. H. Shapiro, R. C. Harney, “Burst-mode atmospheric optical communication,” in Proc. Nat. Telecommun. Conf., 1980, pp. 27.5.1–27.5.7.

Simon, M. K.

M. Chiani, D. Dardari, M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Trans. Wireless Commun., vol. 2, pp. 840–845, July 2003.
[CrossRef]

Sphicopoulos, T.

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1972.

Strickland, B.

I. I. Kim, E. Woodbridge, V. Chan, B. Strickland, “Scintillation measurements performed during the limited-visibility lasercom experiment,” Proc. SPIE, vol. 3266, pp. 209–220, 1998.
[CrossRef]

Suraweera, H. A.

H. A. Suraweera, J. Armstrong, “A simple and accurate approximation to the SEP of rectangular QAM in arbitrary Nakagami-m fading channels,” IEEE Commun. Lett., vol. 11, no. 5, pp. 426–428, May 2007.
[CrossRef]

Taylor, D. P.

J. Li, J. Q. Liu, D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1605, Aug. 2007.
[CrossRef]

Tombras, G. S.

Tsigopoulos, A. D.

Uysal, M.

M. Uysal, J. T. Li, M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 5, no. 6, pp. 1229–1233, June 2006.
[CrossRef]

M. Uysal, S. M. Navidpour, J. Li, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett., vol. 8, no. 10, pp. 635–637, Oct. 2004.
[CrossRef]

Vetelino, F. S.

Wang, J.

X. Zhu, J. M. Kahn, J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” IEEE Photon. Technol. Lett., vol. 15, no. 15, pp. 623–625, Apr. 2003.
[CrossRef]

Wang, T.

N. Cvijetic, T. Wang, “WiMAX over free-space optics—evaluating OFDM multi-subcarrier modulation in optical wireless channels,” in Sarnoff Symp., IEEE, 27–28 March 2006, pp. 1–4.

Woodbridge, E.

I. I. Kim, E. Woodbridge, V. Chan, B. Strickland, “Scintillation measurements performed during the limited-visibility lasercom experiment,” Proc. SPIE, vol. 3266, pp. 209–220, 1998.
[CrossRef]

Yoshida, M.

M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
[CrossRef]

Young, S.

Yu, M.

M. Uysal, J. T. Li, M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 5, no. 6, pp. 1229–1233, June 2006.
[CrossRef]

Zhu, X.

X. Zhu, J. M. Kahn, J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” IEEE Photon. Technol. Lett., vol. 15, no. 15, pp. 623–625, Apr. 2003.
[CrossRef]

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, Aug. 2002.
[CrossRef]

Appl. Opt.

Electron. Lett.

M. Nakazawa, M. Yoshida, K. Kasai, J. Hongou, “20 Msymbol∕s, 64 and 128 QAM coherent optical transmission over 525 km using heterodyne detection with frequency-stabilised laser,” Electron. Lett., vol. 42, no. 12, pp. 710–712, June 2006.
[CrossRef]

IEEE Commun. Lett.

H. A. Suraweera, J. Armstrong, “A simple and accurate approximation to the SEP of rectangular QAM in arbitrary Nakagami-m fading channels,” IEEE Commun. Lett., vol. 11, no. 5, pp. 426–428, May 2007.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

An optical communication system operating over atmospheric turbulence channels.

Fig. 2
Fig. 2

ASEP of optical communication systems employing subcarrier general-order rectangular QAM versus the average electrical SNR, for weak turbulence strength and for various values of r and L.

Fig. 3
Fig. 3

ASEP of optical communication systems employing subcarrier general-order rectangular QAM versus the average electrical SNR, for strong turbulence strength, r = 1 , and for various values of a and b.

Fig. 4
Fig. 4

ASEP of optical communication systems employing subcarrier general-order rectangular QAM versus the average electrical SNR, for medium turbulence strength, r = ( 21 5 ) 1 2 , and for various values of L.

Fig. 5
Fig. 5

ASEP of optical communication systems employing subcarrier general-order rectangular QAM versus the average electrical SNR, for strong turbulence strength, r = ( 21 5 ) 1 2 , and for various values of L.

Fig. 6
Fig. 6

ASEP of optical communication systems employing subcarrier general-order rectangular QAM versus the average electrical SNR, for medium turbulence strength, r = 1 , and for various values of L.

Fig. 7
Fig. 7

ASEP of optical communication systems employing subcarrier general-order rectangular QAM versus the average electrical SNR, for strong turbulence strength, r = 1 , and for various values of L.

Equations (35)

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s ( t ) = 1 + α [ s I ( t ) cos ( 2 π f c t ) s Q ( t ) sin ( 2 π f c t ) ] ,
P ( t ) = A 0 I ( u , t ) { 1 + α [ s I ( t ) cos ( 2 π f c t ) s Q ( t ) sin ( 2 π f c t ) ] } ,
r ( t ) = I ( u , t ) + α I ( u , t ) [ s I ( t ) cos ( 2 π f c t ) s Q ( t ) sin ( 2 π f c t ) ] + n I ( t ) cos ( 2 π f c t ) n Q ( t ) sin ( 2 π f c t ) ,
r I ( t ) = α I ( u , t ) s I ( t ) + n I ( t )
r Q ( t ) = α I ( u , t ) s Q ( t ) + n Q ( t ) .
P s e = 0 P e ( μ ) f μ ( μ ) d μ ,
P e ( μ ) = 2 ( 1 1 M I ) Q ( A I μ ) + 2 ( 1 1 M Q ) Q ( A Q μ ) 4 ( 1 1 M I ) ( 1 1 M Q ) Q ( A I μ ) Q ( A Q μ ) ,
Q ( x ) 1 2 π x exp ( t 2 2 ) d t ,
A I = 6 [ ( M I 2 1 ) + r 2 ( M Q 2 1 ) ] ⁢,
A Q = 6 r 2 [ ( M I 2 1 ) + r 2 ( M Q 2 1 ) ] .
Q ( x ) = 1 2 erfc ( x 2 ) .
p I ( I ) = 1 I σ 2 π exp { [ ln ( I ) + σ 2 2 ] 2 2 σ 2 } ,
σ 2 = exp [ 0.49 σ 2 2 ( 1 + 0.18 d 2 + 0.56 σ 2 12 5 ) 7 6 + 0.51 σ 2 2 ( 1 + 0.69 σ 2 12 5 ) 5 6 1 + 0.90 d 2 + 0.62 d 2 σ 2 12 5 ] 1 .
σ 2 2 = 0.492 C n 2 k 7 6 L 11 6 .
C n 2 = 0.00594 ( υ 27 ) 2 ( 10 5 h ) 10 exp ( h 1000 ) + 2.7 × 10 16 exp ( h 1500 ) + C n 2 ( 0 ) exp ( h 100 ) ,
f μ ( μ ) = 1 μ Σ 2 π exp [ ( ln μ M ) 2 2 Σ 2 ] ,
erfc ( x ) 1 6 e x 2 + 1 2 e 4 x 2 3 .
P s e = 2 ( 1 1 M I ) i = 1 2 a i Υ ( σ , μ ¯ , b i A I 2 ) + 2 ( 1 1 M Q ) i = 1 2 a i Υ ( σ , μ ¯ , b i A Q 2 ) 4 ( 1 1 M I ) ( 1 1 M Q ) i = 1 4 c i Υ ( σ , μ ¯ , d i ) ,
a 1 = 1 12 , a 2 = 1 4 ,
b 1 = 1 2 , b 2 = 2 3 ,
c 1 = 1 144 , c 2 = c 3 = 1 48 , c 4 = 1 16 ,
d 1 = A I 2 + A Q 2 2 , d 2 = A I 2 2 + 2 A Q 2 3 ,
d 3 = 2 A I 2 3 + A Q 2 2 , d 4 = 2 A I 2 + 2 A Q 2 3 ,
Υ ( σ , μ ¯ , S ) 0 e S μ μ Σ 2 π exp [ ( ln μ M ) 2 2 Σ 2 ] d μ ,
Υ ( σ , μ , S ) = 1 π exp ( t 2 ) e S exp ( t 2 Σ + M ) d t .
Υ ( σ , μ , S ) 1 π i = 1 N W i f ( x i ) ,
f I ( I ) = 2 ( a b ) ( a + b ) 2 Γ ( a ) Γ ( b ) I ¯ ( I I ¯ ) ( a + b ) 2 1 K a b [ 2 a b ( I I ¯ ) ] ,
a = { exp [ 0.49 σ 2 2 ( 1 + 0.18 d 2 + 0.56 σ 2 12 5 ) 7 6 ] 1 } 1 ,
b = { exp [ 0.51 σ 2 2 ( 1 + 0.69 σ 2 12 5 ) 5 6 1 + 0.90 d 2 + 0.62 d 2 σ 2 12 5 ] 1 } 1 ,
f μ ( μ ) = ( a b ) ( a + b ) 2 Γ ( a ) Γ ( b ) μ ¯ μ ( μ μ ¯ ) ( a + b ) 2 1 × K a b [ 2 a b μ μ ¯ ] ,
P s e = ( 1 1 M I ) F ( a , b , μ ¯ , A I 2 ) + ( 1 1 M Q ) F ( a , b , μ ¯ , A Q 2 ) 4 ( 1 1 M I ) ( 1 1 M Q ) i = 1 4 c i G ( a , b , μ ¯ , d i ) ,
F ( a , b , μ ¯ , s ) = 0 erfc ( s μ ) f μ ( μ ) d μ ,
G ( a , b , μ ¯ , s ) = 0 exp ( s μ ) f μ ( μ ) d μ ,
F ( a , b , μ ¯ , s ) = Ξ a + b s ( a + b ) 4 4 π 3 2 Γ ( a ) Γ ( b ) × G 2 , 5 4 , 2 [ a 2 b 2 16 μ ¯ s 1 a + b 4 , 1 2 a + b 4 1 2 + a b 4 , a b 4 , 1 2 + b a 4 , b a 4 , a + b 4 ] ,
G ( a , b , μ ¯ , s ) = Ξ a + b s ( a + b ) 4 4 π Γ ( a ) Γ ( b ) × G 1 , 4 4 , 1 [ a 2 b 2 16 μ ¯ s 1 a + b 4 1 2 + a b 4 , a b 4 , 1 2 + b a 4 , b a 4 ] .