Abstract

We investigate spatial diversity techniques for subcarrier phase-shift keying (PSK)-modulated optical wireless communication links over the Gamma–Gamma channels. Both repetition code and the Alamouti-type orthogonal space–time block code (OSTBC) are considered. Highly accurate series error rate expressions are derived by using a moment generating function approach with a series expansion of the modified Bessel function. Truncation error analyses and asymptotic error rate analyses are also presented. Our asymptotic analyses show that the diversity order of the studied system depends only on the effective number of small-scale cells of the scattering process in the atmosphere. Our performance analyses confirm that the repetition code outperforms OSTBC for subcarrier PSK-based systems over the Gamma–Gamma channels. The asymptotic performance loss of the Alamouti-coded system with respect to the repetition-coded system is also quantified analytically.

© 2013 Optical Society of America

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  1. W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun., vol.  E76-B, pp. 1169–1177, Sept. 1993.
  2. J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
    [CrossRef]
  3. W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol.  27, pp. 967–973, Apr. 2009.
    [CrossRef]
  4. N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Adaptive subcarrier PSK intensity modulation in free space optical systems,” IEEE Trans. Commun., vol.  59, pp. 1368–1377, May 2011.
    [CrossRef]
  5. X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, pp. 540–543, Apr. 2012.
    [CrossRef]
  6. Md. Z. Hassan, X. Song, and J. Cheng, “Subcarrier intensity modulated wireless optical communications with rectangular QAM,” J. Opt. Commun. Netw., vol.  4, pp. 522–532, June 2012.
    [CrossRef]
  7. X. Song and J. Cheng, “Optical communication using subcarrier intensity modulation in strong atmospheric turbulence,” J. Lightwave Technol., vol.  30, pp. 3484–3493, Nov. 2012.
    [CrossRef]
  8. X. Song, Md. Z. Hassan, and J. Cheng, “Subcarrier DQPSK modulated optical wireless communications in atmospheric turbulence,” Electron. Lett., vol.  48, pp. 1224–1225, Sept. 2012.
    [CrossRef]
  9. X. Song, F. Yang, and J. Cheng, “Subcarrier intensity modulated optical wireless communications in atmospheric turbulence with pointing errors,” J. Opt. Commun. Netw., vol.  5, pp. 349–358, Apr. 2013.
    [CrossRef]
  10. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  50, pp. 1293–1300, Aug. 2002.
    [CrossRef]
  11. S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
    [CrossRef]
  12. S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
    [CrossRef]
  13. E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
    [CrossRef]
  14. M. K. Simon and V. Vilnrotter, “Alamouti-type space–time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun., vol.  4, pp. 35–39, Jan. 2005.
    [CrossRef]
  15. A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett., vol.  11, pp. 390–392, May 2007.
    [CrossRef]
  16. M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection?” IEEE Trans. Wireless Commun., vol.  7, pp. 4445–4448, Nov. 2008.
    [CrossRef]
  17. E. Bayaki and R. Schober, “On space–time coding for free-space optical systems,” IEEE Trans. Commun., vol.  58, pp. 58–62, Jan. 2010.
    [CrossRef]
  18. J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in Gamma–Gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
    [CrossRef]
  19. X. Song and J. Cheng, “Performance of subcarrier intensity modulated MIMO wireless optical communications,” in 26th Queen’s Biennial Symp. on Communications, Kingston, Ontario, Canada, May 28–29, 2012.
  20. X. Song and J. Cheng, “Alamouti-type STBC for subcarrier intensity modulated wireless optical communications,” in IEEE Global Communications Conf. (GLOBECOM), Anaheim, CA, Dec. 3–7, 2012.
  21. L. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Philadelphia, PA: SPIE, 2001.
  22. 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., vol.  40, pp. 1554–1562, Aug. 2001.
    [CrossRef]
  23. E. Jakeman and P. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett., vol.  40, pp. 546–550, Feb. 1978.
    [CrossRef]
  24. E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A, vol.  13, pp. 31–48, Jan. 1980.
    [CrossRef]
  25. N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the Gamma–Gamma atmospheric turbulence model,” Opt. Express, vol.  18, pp. 12824–12831, June 2010.
    [CrossRef]
  26. G. P. Agrawal, Fiber-Optical Communication Systems, 3rd ed. New York: Wiley, 2002.
  27. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. San Diego: Academic, 2000.

2013

2012

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, pp. 540–543, Apr. 2012.
[CrossRef]

Md. Z. Hassan, X. Song, and J. Cheng, “Subcarrier intensity modulated wireless optical communications with rectangular QAM,” J. Opt. Commun. Netw., vol.  4, pp. 522–532, June 2012.
[CrossRef]

X. Song and J. Cheng, “Optical communication using subcarrier intensity modulation in strong atmospheric turbulence,” J. Lightwave Technol., vol.  30, pp. 3484–3493, Nov. 2012.
[CrossRef]

X. Song, Md. Z. Hassan, and J. Cheng, “Subcarrier DQPSK modulated optical wireless communications in atmospheric turbulence,” Electron. Lett., vol.  48, pp. 1224–1225, Sept. 2012.
[CrossRef]

2011

N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Adaptive subcarrier PSK intensity modulation in free space optical systems,” IEEE Trans. Commun., vol.  59, pp. 1368–1377, May 2011.
[CrossRef]

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in Gamma–Gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

2010

E. Bayaki and R. Schober, “On space–time coding for free-space optical systems,” IEEE Trans. Commun., vol.  58, pp. 58–62, Jan. 2010.
[CrossRef]

N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the Gamma–Gamma atmospheric turbulence model,” Opt. Express, vol.  18, pp. 12824–12831, June 2010.
[CrossRef]

2009

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol.  27, pp. 967–973, Apr. 2009.
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

2008

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection?” IEEE Trans. Wireless Commun., vol.  7, pp. 4445–4448, Nov. 2008.
[CrossRef]

2007

A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett., vol.  11, pp. 390–392, May 2007.
[CrossRef]

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

2005

M. K. Simon and V. Vilnrotter, “Alamouti-type space–time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun., vol.  4, pp. 35–39, Jan. 2005.
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
[CrossRef]

2002

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

2001

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., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

1993

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun., vol.  E76-B, pp. 1169–1177, Sept. 1993.

1980

E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A, vol.  13, pp. 31–48, Jan. 1980.
[CrossRef]

1978

E. Jakeman and P. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett., vol.  40, pp. 546–550, Feb. 1978.
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optical Communication Systems, 3rd ed. New York: Wiley, 2002.

Al-Habash, A.

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., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

Andrews, L.

L. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Philadelphia, PA: SPIE, 2001.

Andrews, L. C.

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., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

Arnon, S.

N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Adaptive subcarrier PSK intensity modulation in free space optical systems,” IEEE Trans. Commun., vol.  59, pp. 1368–1377, May 2011.
[CrossRef]

Baedke, M.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
[CrossRef]

Bayaki, E.

E. Bayaki and R. Schober, “On space–time coding for free-space optical systems,” IEEE Trans. Commun., vol.  58, pp. 58–62, Jan. 2010.
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Brandt-Pearce, M.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
[CrossRef]

Cao, Q.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
[CrossRef]

Chatzidiamantis, N. D.

N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Adaptive subcarrier PSK intensity modulation in free space optical systems,” IEEE Trans. Commun., vol.  59, pp. 1368–1377, May 2011.
[CrossRef]

Cheng, J.

X. Song, F. Yang, and J. Cheng, “Subcarrier intensity modulated optical wireless communications in atmospheric turbulence with pointing errors,” J. Opt. Commun. Netw., vol.  5, pp. 349–358, Apr. 2013.
[CrossRef]

X. Song, Md. Z. Hassan, and J. Cheng, “Subcarrier DQPSK modulated optical wireless communications in atmospheric turbulence,” Electron. Lett., vol.  48, pp. 1224–1225, Sept. 2012.
[CrossRef]

Md. Z. Hassan, X. Song, and J. Cheng, “Subcarrier intensity modulated wireless optical communications with rectangular QAM,” J. Opt. Commun. Netw., vol.  4, pp. 522–532, June 2012.
[CrossRef]

X. Song and J. Cheng, “Optical communication using subcarrier intensity modulation in strong atmospheric turbulence,” J. Lightwave Technol., vol.  30, pp. 3484–3493, Nov. 2012.
[CrossRef]

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, pp. 540–543, Apr. 2012.
[CrossRef]

N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the Gamma–Gamma atmospheric turbulence model,” Opt. Express, vol.  18, pp. 12824–12831, June 2010.
[CrossRef]

X. Song and J. Cheng, “Performance of subcarrier intensity modulated MIMO wireless optical communications,” in 26th Queen’s Biennial Symp. on Communications, Kingston, Ontario, Canada, May 28–29, 2012.

X. Song and J. Cheng, “Alamouti-type STBC for subcarrier intensity modulated wireless optical communications,” in IEEE Global Communications Conf. (GLOBECOM), Anaheim, CA, Dec. 3–7, 2012.

García-Zambrana, A.

A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett., vol.  11, pp. 390–392, May 2007.
[CrossRef]

Ghassemlooy, Z.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. San Diego: Academic, 2000.

Hassan, Md. Z.

X. Song, Md. Z. Hassan, and J. Cheng, “Subcarrier DQPSK modulated optical wireless communications in atmospheric turbulence,” Electron. Lett., vol.  48, pp. 1224–1225, Sept. 2012.
[CrossRef]

Md. Z. Hassan, X. Song, and J. Cheng, “Subcarrier intensity modulated wireless optical communications with rectangular QAM,” J. Opt. Commun. Netw., vol.  4, pp. 522–532, June 2012.
[CrossRef]

Hopen, C. Y.

L. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Philadelphia, PA: SPIE, 2001.

Huang, W.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun., vol.  E76-B, pp. 1169–1177, Sept. 1993.

Jakeman, E.

E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A, vol.  13, pp. 31–48, Jan. 1980.
[CrossRef]

E. Jakeman and P. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett., vol.  40, pp. 546–550, Feb. 1978.
[CrossRef]

Kahn, J. M.

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

Karagiannidis, G. K.

N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Adaptive subcarrier PSK intensity modulation in free space optical systems,” IEEE Trans. Commun., vol.  59, pp. 1368–1377, May 2011.
[CrossRef]

Lee, E.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in Gamma–Gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

Leveque, J. H.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
[CrossRef]

Li, J.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

Lioumpas, A. S.

N. D. Chatzidiamantis, A. S. Lioumpas, G. K. Karagiannidis, and S. Arnon, “Adaptive subcarrier PSK intensity modulation in free space optical systems,” IEEE Trans. Commun., vol.  59, pp. 1368–1377, May 2011.
[CrossRef]

Liu, J. Q.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

Mallik, R. K.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Nakagawa, M.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun., vol.  E76-B, pp. 1169–1177, Sept. 1993.

Niu, M.

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, pp. 540–543, Apr. 2012.
[CrossRef]

Park, J.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in Gamma–Gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

Phillips, R. L.

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., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

L. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Philadelphia, PA: SPIE, 2001.

Popoola, W. O.

Pusey, P.

E. Jakeman and P. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett., vol.  40, pp. 546–550, Feb. 1978.
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. San Diego: Academic, 2000.

Safari, M.

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection?” IEEE Trans. Wireless Commun., vol.  7, pp. 4445–4448, Nov. 2008.
[CrossRef]

Sakanaka, T.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun., vol.  E76-B, pp. 1169–1177, Sept. 1993.

Schober, R.

E. Bayaki and R. Schober, “On space–time coding for free-space optical systems,” IEEE Trans. Commun., vol.  58, pp. 58–62, Jan. 2010.
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Simon, M. K.

M. K. Simon and V. Vilnrotter, “Alamouti-type space–time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun., vol.  4, pp. 35–39, Jan. 2005.
[CrossRef]

Song, X.

X. Song, F. Yang, and J. Cheng, “Subcarrier intensity modulated optical wireless communications in atmospheric turbulence with pointing errors,” J. Opt. Commun. Netw., vol.  5, pp. 349–358, Apr. 2013.
[CrossRef]

X. Song, Md. Z. Hassan, and J. Cheng, “Subcarrier DQPSK modulated optical wireless communications in atmospheric turbulence,” Electron. Lett., vol.  48, pp. 1224–1225, Sept. 2012.
[CrossRef]

X. Song and J. Cheng, “Optical communication using subcarrier intensity modulation in strong atmospheric turbulence,” J. Lightwave Technol., vol.  30, pp. 3484–3493, Nov. 2012.
[CrossRef]

Md. Z. Hassan, X. Song, and J. Cheng, “Subcarrier intensity modulated wireless optical communications with rectangular QAM,” J. Opt. Commun. Netw., vol.  4, pp. 522–532, June 2012.
[CrossRef]

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, pp. 540–543, Apr. 2012.
[CrossRef]

X. Song and J. Cheng, “Performance of subcarrier intensity modulated MIMO wireless optical communications,” in 26th Queen’s Biennial Symp. on Communications, Kingston, Ontario, Canada, May 28–29, 2012.

X. Song and J. Cheng, “Alamouti-type STBC for subcarrier intensity modulated wireless optical communications,” in IEEE Global Communications Conf. (GLOBECOM), Anaheim, CA, Dec. 3–7, 2012.

Takayanagi, J.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun., vol.  E76-B, pp. 1169–1177, Sept. 1993.

Tayler, D. P.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

Uysal, M.

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection?” IEEE Trans. Wireless Commun., vol.  7, pp. 4445–4448, Nov. 2008.
[CrossRef]

Vilnrotter, V.

M. K. Simon and V. Vilnrotter, “Alamouti-type space–time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun., vol.  4, pp. 35–39, Jan. 2005.
[CrossRef]

Wang, N.

Wilson, S. G.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
[CrossRef]

Yang, F.

Yoon, G.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in Gamma–Gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

Zhu, X.

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

Electron. Lett.

X. Song, Md. Z. Hassan, and J. Cheng, “Subcarrier DQPSK modulated optical wireless communications in atmospheric turbulence,” Electron. Lett., vol.  48, pp. 1224–1225, Sept. 2012.
[CrossRef]

IEEE Commun. Lett.

X. Song, M. Niu, and J. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett., vol.  16, pp. 540–543, Apr. 2012.
[CrossRef]

A. García-Zambrana, “Error rate performance for STBC in free-space optical communications through strong atmospheric turbulence,” IEEE Commun. Lett., vol.  11, pp. 390–392, May 2007.
[CrossRef]

IEEE J. Sel. Areas Commun.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol.  23, pp. 1901–1910, Sept. 2005.
[CrossRef]

IEEE Photon. Technol. Lett.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in Gamma–Gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

IEEE Trans. Commun.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

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

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol.  53, pp. 1402–1412, Aug. 2005.
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Block diagram of a subcarrier intensity-modulated SISO OWC system.

Fig. 2.
Fig. 2.

Block diagram of a subcarrier intensity-modulated MIMO OWC system.

Fig. 3.
Fig. 3.

BERs of subcarrier BPSK-modulated SISO/MIMO OWC systems over a Gamma–Gamma channel with α = 5.05 , β = 1.16 , and J = 20 .

Fig. 4.
Fig. 4.

BERs of subcarrier BPSK-modulated SISO and MIMO OWC systems over a Gamma–Gamma channel with α = 11.65 and β = 10.12 .

Fig. 5.
Fig. 5.

SNR loss in decibels for an Alamouti-coded system with respect to a repetition-coded system as a function of L for different α and β values.

Equations (51)

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f I ( I ) = 2 ( α β ) α + β 2 Γ ( α ) Γ ( β ) I α + β 2 1 K α β ( 2 α β I ) , I > 0 ,
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 ,
P ( t ) = P [ 1 + ξ m ( t ) ] ,
i ( t ) = P R I ( t ) [ 1 + ξ m ( t ) ] + n ( t ) ,
γ = ( P R ξ ) 2 σ n 2 I 2 = γ ¯ I 2 ,
i l ( t ) = P R [ 1 + ξ m ( t ) ] K k = 1 K I k l + n l ( t ) , l = 1 , 2 , , L ,
i r ( t ) = P R [ 1 + ξ m ( t ) ] K k = 1 K l = 1 L I k l I R + l = 1 L n l ( t ) z ( t ) = P R I R [ 1 + ξ m ( t ) ] K + z ( t ) ,
γ R = ( P R ξ ) 2 K 2 L σ n 2 I R 2 = γ ¯ K 2 L I R 2 .
i 11 = P R [ I 11 ( 1 + ξ m 1 ) + I 21 ( 1 + ξ m 2 ) ] K + n 11 ,
i 12 = P R [ I 12 ( 1 + ξ m 1 ) + I 22 ( 1 + ξ m 2 ) ] K + n 12 ,
i 21 = P R [ I 11 ( 1 ξ m 2 ) + I 21 ( 1 + ξ m 1 ) ] K + n 21 ,
i 22 = P R [ I 12 ( 1 ξ m 2 ) + I 22 ( 1 + ξ m 1 ) ] K + n 22 ,
i ˜ 1 = P R ξ m 1 K k = 1 K l = 1 L I k l 2 U + I 11 n 11 + I 12 n 12 + I 21 n 21 + I 22 n 22 v 1 = P R ξ m 1 U K + v 1 .
i ˜ 2 = P R ξ m 2 K k = 1 K l = 1 L I k l 2 + I 21 n 11 + I 22 n 12 + I 11 n 21 + I 12 n 22 v 2 = P R ξ m 2 U K + v 2 .
γ A = ( P R ξ ) 2 U 2 K 2 U σ n 2 = γ ¯ K 2 U .
γ A = γ ¯ K 2 k = 1 K l = 1 L I k l 2 Y A .
K ν ( x ) = π 2 sin ( π ν ) p = 0 [ ( x / 2 ) 2 p ν Γ ( p ν + 1 ) p ! ( x / 2 ) 2 p + ν Γ ( p + ν + 1 ) p ! ] ,
M I ( s ) E [ exp ( s I ) ] = p = 0 [ a p ( α , β ) ( s α β ) ( p + β ) + a p ( β , α ) ( s α β ) ( p + α ) ] ,
a p ( α , β ) Γ ( α β ) Γ ( 1 α + β ) Γ ( p + β ) Γ ( α ) Γ ( β ) Γ ( p α + β + 1 ) p ! .
M I R ( s ) = [ M I ( s ) ] K L = m = 0 K L ( K L m ) p = 0 b p ( K L m , m ) ( s α β ) 2 G d ,
b p ( i , j ) a p ( i ) ( α , β ) * a p ( j ) ( β , α )
f I R ( I R ) = m = 0 K L ( K L m ) p = 0 b p ( K L m , m ) ( α β ) 2 G d Γ ( 2 G d ) I R 2 G d 1 .
M Y R ( s ) = m = 0 K L ( K L m ) p = 0 b p ( K L m , m ) Γ ( G d ) 2 Γ ( 2 G d ) ( s α 2 β 2 ) G d .
P e , R = 1 π 0 ( M 1 ) π M M Y R ( sin 2 ( π M ) γ ¯ K 2 L sin 2 θ ) d θ = m = 0 K L ( K L m ) p = 0 b p ( K L m , m ) Γ ( G d ) 2 π Γ ( 2 G d ) ( λ R γ ¯ ) G d × 0 η π ( sin θ ) p + ( K L m ) β + m α d θ ,
g p ( x , η ) 0 η π ( sin θ ) p + x d θ ;
g p ( x , η ) = π Γ ( 1 + p + x 2 ) 2 Γ ( 1 + p + x 2 ) cos ( η π ) F [ 1 2 , 1 p x 2 ; 3 2 ; cos 2 ( η π ) ] ,
P e , R = m = 0 K L ( K L m ) × p = 0 b p ( K L m , m ) Γ ( G d ) g p ( 2 G d p , η ) 2 π Γ ( 2 G d ) ( λ R γ ¯ ) G d .
g p ( x , 1 2 ) = π Γ ( 1 + p + x 2 ) 2 Γ ( 1 + p + x 2 ) .
P 2 , R = m = 0 K L ( K L m ) p = 0 b p ( K L m , m ) Γ ( G d + 1 2 ) 2 π Γ ( 2 G d + 1 ) ( λ R γ ¯ ) G d ,
P 4 , R = m = 0 K L ( K L m ) p = 0 b p ( K L m , m ) Γ ( G d ) 2 π Γ ( 2 G d ) × [ 2 g p ( 2 G d p , 1 2 ) g p ( 2 G d p , 1 4 ) ] ( λ R γ ¯ ) G d ,
g p ( x , 1 4 ) = F ( 1 2 , p + x + 1 2 ; p + x + 3 2 ; 1 2 ) 2 p + x + 1 2 ( p + x + 1 )
ε R ( J ) m = 0 K L ( K L m ) p = J + 1 u p , R ( m , η ) ( 1 λ R γ ¯ ) p ,
u p , R ( m , η ) b p ( K L m , m ) Γ ( G d ) g p ( 2 G d p , η ) 2 π Γ ( 2 G d ) × ( 1 λ R γ ¯ ) ( K L m ) β + m α .
ε R ( J ) 1 ( λ R γ ¯ 1 ) ( λ R γ ¯ ) J m = 0 K L ( K L m ) × max p > J { u p , R ( m , η ) } .
P e , R = g 0 ( K L β , η ) Γ ( K L β 2 ) 2 π Γ ( K L β ) ( Γ ( α β ) Γ ( α ) ) K L ( K L α β sin π M ) K L β γ ¯ K L β 2 .
P 2 , R = Γ ( K L β + 1 2 ) ( K β ) K L β 1 α K L β L K L β 2 1 2 π Γ ( K L β ) ( Γ ( α β ) Γ ( α ) ) K L γ ¯ K L β 2 .
M X ( s ) E [ exp ( s X ) ] = p = 0 [ d p ( α , β ) ( s α 2 β 2 ) p + β 2 + d p ( β , α ) ( s α 2 β 2 ) p + α 2 ] ,
d p ( α , β ) Γ ( α β ) Γ ( 1 α + β ) Γ ( p + β 2 ) 2 Γ ( α ) Γ ( β ) Γ ( p α + β + 1 ) p ! .
M Y A ( s ) = [ M X ( s ) ] K L = m = 0 K L ( K L m ) p = 0 c p ( K L m , m ) ( s α 2 β 2 ) G d ,
c p ( i , j ) d p ( i ) ( α , β ) * d p ( j ) ( β , α )
P e , A = 1 π 0 ( M 1 ) π M M Y A ( sin 2 ( π M ) γ ¯ K 2 sin 2 θ ) d θ = 1 π m = 0 K L ( K L m ) p = 0 c p ( K L m , m ) ( λ A γ ¯ ) G d × 0 η π ( sin θ ) p + ( K L m ) β + m α d θ ,
P e , A = 1 π m = 0 K L ( K L m ) p = 0 c p ( K L m , m ) × g p ( 2 G d p , η ) ( λ A γ ¯ ) G d .
P 2 , A = 1 2 π m = 0 K L ( K L m ) × p = 0 c p ( K L m , m ) Γ ( G d + 1 2 ) Γ ( G d + 1 ) ( λ A γ ¯ ) G d .
P 4 , A = 1 π m = 0 K L ( K L m ) p = 0 c p ( K L m , m ) × { 2 g p ( 2 G d p , 1 2 ) g p ( 2 G d p , 1 4 ) } ( λ A γ ¯ ) G d .
ε A ( J ) 1 π m = 0 K L ( K L m ) p = J + 1 u p , A ( m , η ) ( 1 λ A γ ¯ ) p ,
u p , A ( m , η ) c p ( K L m , m ) × g p ( 2 G d p , η ) ( 1 λ A γ ¯ ) ( K L m ) β + m α .
ε A ( J ) 1 π ( λ A γ ¯ 1 ) ( λ A γ ¯ ) J m = 0 K L ( K L m ) max p > J { u p , A ( m , η ) } .
P e , A = g 0 ( K L β , η ) 2 K L π ( Γ ( α β ) Γ ( β 2 ) Γ ( α ) Γ ( β ) ) K L ( K α β sin π M ) K L β γ ¯ K L β 2 .
P 2 , A = Γ ( K L β + 1 2 ) ( K β ) K L β 1 α K L β 2 K L L π Γ ( K L β 2 ) ( Γ ( α β ) Γ ( β 2 ) Γ ( α ) Γ ( β ) ) K L γ ¯ K L β 2 .
SNR A R = 2 β [ 10 log ( Γ ( β 2 ) Γ ( β ) ) + 10 K L log ( Γ ( K L β ) Γ ( K L β 2 ) ) 10 log ( 2 ) ( K L 1 ) K L ] 10 log ( L ) ,