Abstract

In this paper, we derive mathematical expressions for the evaluation of the average (ergodic) capacity of free-space optical (FSO) communication systems. Atmospheric turbulence conditions are modeled using the I-K distribution. Our newly derived expressions provide an efficient tool to assess the spectral efficiency of FSO communication systems. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

© 2012 OSA

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  1. D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. S1–S7, May2004.
  2. S. Arnon, “Optical wireless communications,” in Encyclopedia of Optical Engineering. New York, 2003, pp. 1866–1886.
  3. A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep., vol. 2, pp. 345–396, 2005.
    [CrossRef]
  4. S. M. Haas and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1346–1357, 2003.
    [CrossRef]
  5. H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.
  6. H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and 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]
  7. H. E. Nistazakis, V. D. Assimakopoulos, and G. S. Tombras, “Performance estimation of free space optical links over negative exponential atmospheric turbulence channels,” Optik, vol. 122, pp. 2191–2194, 2011.
    [CrossRef]
  8. C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
    [CrossRef]
  9. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol., vol. 25, no. 7, pp. 1702–1710, 2007.
    [CrossRef]
  10. L. C. Andrews and R. L. Phillips, “I-K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A, vol. 2, no. 2, pp. 160–163, Feb.1985.
    [CrossRef]
  11. L. C. Andrews and R. L. Philips, “Mathematical genesis of the I-K distribution for random optical fields,” J. Opt. Soc. Am. A, vol. 3, no. 11, pp. 1912–1919, 1986.
    [CrossRef]
  12. I. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 6th ed.Academic Press, New York, 2000.
  13. M. Abramovitz and I. Stegun, Eds., Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. Dover, New York, 1964.
  14. A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications. Springer, 2010.
  15. S. M. Navidpour, M. Uysal, and M. Kavehrad, “Performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug.2007.
    [CrossRef]
  16. X. Zhu and J. M. Kahn, “Free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, 2002.
    [CrossRef]
  17. L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.
  18. N. Letzepis and A. G. Fabregas, “Outage probability of the free space optical channel with doubly stochastic scintillation,” IEEE Trans. Commun., vol. 57, no. 10, pp. 2899–2902, Oct2009.
    [CrossRef]
  19. N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for the integrals ∫0∞e−x2f(x)dx and ∫0be−x2f(x)dx,” Math. Comput., vol. 23, no. 107, pp. 661–671, 1969.
  20. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breach Science Publishers, 1986.
  21. K. Peppas, “A new formula for the average bit error probability of dual-hop amplify-and-forward relaying systems over generalized shadowed fading channels,” IEEE Wireless Comm. Lett., vol. 1, no. 2, pp. 85–88, Apr.2012.
    [CrossRef]
  22. I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
    [CrossRef]
  23. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 1: Elementary Functions, 1st ed.CRC, 1992.

2012

K. Peppas, “A new formula for the average bit error probability of dual-hop amplify-and-forward relaying systems over generalized shadowed fading channels,” IEEE Wireless Comm. Lett., vol. 1, no. 2, pp. 85–88, Apr.2012.
[CrossRef]

2011

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

H. E. Nistazakis, V. D. Assimakopoulos, and G. S. Tombras, “Performance estimation of free space optical links over negative exponential atmospheric turbulence channels,” Optik, vol. 122, pp. 2191–2194, 2011.
[CrossRef]

2010

C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
[CrossRef]

2009

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and 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]

N. Letzepis and A. G. Fabregas, “Outage probability of the free space optical channel with doubly stochastic scintillation,” IEEE Trans. Commun., vol. 57, no. 10, pp. 2899–2902, Oct2009.
[CrossRef]

2007

S. M. Navidpour, M. Uysal, and M. Kavehrad, “Performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug.2007.
[CrossRef]

A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol., vol. 25, no. 7, pp. 1702–1710, 2007.
[CrossRef]

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. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. S1–S7, May2004.

2003

S. M. Haas and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1346–1357, 2003.
[CrossRef]

2002

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

2001

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.

1986

1985

L. C. Andrews and R. L. Phillips, “I-K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A, vol. 2, no. 2, pp. 160–163, Feb.1985.
[CrossRef]

1969

N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for the integrals ∫0∞e−x2f(x)dx and ∫0be−x2f(x)dx,” Math. Comput., vol. 23, no. 107, pp. 661–671, 1969.

Aidinis, C.

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

Al-Ahmadi, S.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

Al-Habash, M. A.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.

Alouini, M.-S.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

Andrews, L. C.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.

L. C. Andrews and R. L. Philips, “Mathematical genesis of the I-K distribution for random optical fields,” J. Opt. Soc. Am. A, vol. 3, no. 11, pp. 1912–1919, 1986.
[CrossRef]

L. C. Andrews and R. L. Phillips, “I-K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A, vol. 2, no. 2, pp. 160–163, Feb.1985.
[CrossRef]

Ansari, I. S.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

Arnon, S.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. S1–S7, May2004.

S. Arnon, “Optical wireless communications,” in Encyclopedia of Optical Engineering. New York, 2003, pp. 1866–1886.

Assimakopoulos, V. D.

H. E. Nistazakis, V. D. Assimakopoulos, and G. S. Tombras, “Performance estimation of free space optical links over negative exponential atmospheric turbulence channels,” Optik, vol. 122, pp. 2191–2194, 2011.
[CrossRef]

Brychkov, Y. A.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 1: Elementary Functions, 1st ed.CRC, 1992.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breach Science Publishers, 1986.

Byrne, G. D.

N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for the integrals ∫0∞e−x2f(x)dx and ∫0be−x2f(x)dx,” Math. Comput., vol. 23, no. 107, pp. 661–671, 1969.

Fabregas, A. G.

N. Letzepis and A. G. Fabregas, “Outage probability of the free space optical channel with doubly stochastic scintillation,” IEEE Trans. Commun., vol. 57, no. 10, pp. 2899–2902, Oct2009.
[CrossRef]

Fafalios, M. E.

Farid, A.

Gelbard, E. M.

N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for the integrals ∫0∞e−x2f(x)dx and ∫0be−x2f(x)dx,” Math. Comput., vol. 23, no. 107, pp. 661–671, 1969.

Gradshteyn, I.

I. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 6th ed.Academic Press, New York, 2000.

Haas, S. M.

S. M. Haas and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1346–1357, 2003.
[CrossRef]

Hanias, M. P.

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

Haubold, H. J.

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications. Springer, 2010.

Hopen, C. Y.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.

Hranilovic, S.

Kahn, J. M.

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

Karagianni, E. A.

Kavehrad, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “Performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug.2007.
[CrossRef]

Kedar, D.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. S1–S7, May2004.

Letzepis, N.

N. Letzepis and A. G. Fabregas, “Outage probability of the free space optical channel with doubly stochastic scintillation,” IEEE Trans. Commun., vol. 57, no. 10, pp. 2899–2902, Oct2009.
[CrossRef]

Liu, C.

C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
[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, and O. I. Marichev, Integrals and Series Volume 1: Elementary Functions, 1st ed.CRC, 1992.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breach Science Publishers, 1986.

Marinos, D.

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

Mathai, A.

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications. Springer, 2010.

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “Performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug.2007.
[CrossRef]

Nistazakis, H. E.

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

H. E. Nistazakis, V. D. Assimakopoulos, and G. S. Tombras, “Performance estimation of free space optical links over negative exponential atmospheric turbulence channels,” Optik, vol. 122, pp. 2191–2194, 2011.
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and 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]

Peppas, K.

K. Peppas, “A new formula for the average bit error probability of dual-hop amplify-and-forward relaying systems over generalized shadowed fading channels,” IEEE Wireless Comm. Lett., vol. 1, no. 2, pp. 85–88, Apr.2012.
[CrossRef]

Philips, R. L.

Phillips, R. L.

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.

L. C. Andrews and R. L. Phillips, “I-K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A, vol. 2, no. 2, pp. 160–163, Feb.1985.
[CrossRef]

Prudnikov, A. P.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 3: More Special Functions, 1st ed.Gordon and Breach Science Publishers, 1986.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 1: Elementary Functions, 1st ed.CRC, 1992.

Psychogios, C. D.

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

Ryzhik, I. M.

I. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 6th ed.Academic Press, New York, 2000.

Saxena, R. K.

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications. Springer, 2010.

Shapiro, J. H.

S. M. Haas and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1346–1357, 2003.
[CrossRef]

Steen, N. M.

N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for the integrals ∫0∞e−x2f(x)dx and ∫0be−x2f(x)dx,” Math. Comput., vol. 23, no. 107, pp. 661–671, 1969.

Sun, Y.

C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
[CrossRef]

Tombras, G. S.

H. E. Nistazakis, V. D. Assimakopoulos, and G. S. Tombras, “Performance estimation of free space optical links over negative exponential atmospheric turbulence channels,” Optik, vol. 122, pp. 2191–2194, 2011.
[CrossRef]

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and 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]

Tsigopoulos, A. D.

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and 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]

Uysal, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “Performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug.2007.
[CrossRef]

Yanikomeroglu, H.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

Yao, Y.

C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
[CrossRef]

Yilmaz, F.

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

Zhao, X.

C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
[CrossRef]

Zhu, X.

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

J. Opt. Soc. Am. A

L. C. Andrews and R. L. Phillips, “I-K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A, vol. 2, no. 2, pp. 160–163, Feb.1985.
[CrossRef]

Electron. Lett.

C. Liu, Y. Yao, Y. Sun, and X. Zhao, “Average capacity for heterodyne FSO communication systems over gamma–gamma turbulence channels with pointing errors,” Electron. Lett., vol. 46, no. 12, pp. 851–853, 2010.
[CrossRef]

IEEE J. Sel. Areas Commun.

S. M. Haas and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun., vol. 21, no. 8, pp. 1346–1357, 2003.
[CrossRef]

IEEE Opt. Commun.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. S1–S7, May2004.

IEEE Trans. Commun.

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

N. Letzepis and A. G. Fabregas, “Outage probability of the free space optical channel with doubly stochastic scintillation,” IEEE Trans. Commun., vol. 57, no. 10, pp. 2899–2902, Oct2009.
[CrossRef]

I. S. Ansari, S. Al-Ahmadi, F. Yilmaz, M.-S. Alouini, and H. Yanikomeroglu, “A new formula for the BER of binary modulations with dual-brance selection over generalized-K composite fading channels,” IEEE Trans. Commun., vol. 59, no. 10, pp. 2654–2658, Oct.2011.
[CrossRef]

IEEE Trans. Wireless Commun.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “Performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug.2007.
[CrossRef]

IEEE Wireless Comm. Lett.

K. Peppas, “A new formula for the average bit error probability of dual-hop amplify-and-forward relaying systems over generalized shadowed fading channels,” IEEE Wireless Comm. Lett., vol. 1, no. 2, pp. 85–88, Apr.2012.
[CrossRef]

J. Lightwave Technol.

J. Opt. Fiber Commun. Rep.

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

J. Opt. Soc. Am. A

Math. Comput.

N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for the integrals ∫0∞e−x2f(x)dx and ∫0be−x2f(x)dx,” Math. Comput., vol. 23, no. 107, pp. 661–671, 1969.

Optik

H. E. Nistazakis, V. D. Assimakopoulos, and G. S. Tombras, “Performance estimation of free space optical links over negative exponential atmospheric turbulence channels,” Optik, vol. 122, pp. 2191–2194, 2011.
[CrossRef]

Radioengineering

H. E. Nistazakis, A. D. Tsigopoulos, M. P. Hanias, C. D. Psychogios, D. Marinos, C. Aidinis, and G. S. Tombras, “Estimation of outage capacity for free space optical links over I-K and K turbulent channels,” Radioengineering, vol. 20, no. 2, pp. 493–498, 2011.

Waves in Random Media

L. C. Andrews, M. A. Al-Habash, C. Y. Hopen, and R. L. Phillips, “Theory of optical scintillation: Gaussian beam wave model,” Waves in Random Media, vol. 11, pp. 271–291, 2001.

Other

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Figures (2)

Fig. 1
Fig. 1

Average channel capacity of I-K distributed optical wireless links as a function of the average electrical SNR ξ for values of a and ρ, assuming arbitrary positive real values of a.

Fig. 2
Fig. 2

Average channel capacity of I-K distributed optical wireless links as a function of the average electrical SNR ξ, assuming half-integer values of a ( a = M + 1 / 2 ), for values of M and ρ.

Equations (38)

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y = η I x + n ,
C = 0 ln ( 1 + γ ) f γ ( γ ) d γ .
f γ ( γ ) = { a ( 1 + ρ ) ( 1 + ρ ρ ) a 1 2 γ a 3 4 ξ a + 1 4 K a 1 ( 2 a ρ ) × I a 1 ( 2 a ( 1 + ρ ) γ ξ ) if  γ < ρ 2 ξ ( 1 + ρ ) 2 a ( 1 + ρ ) ( 1 + ρ ρ ) a 1 2 γ a 3 4 ξ a + 1 4 I a 1 ( 2 a ρ ) × K a 1 ( 2 a ( 1 + ρ ) γ ξ ) if  γ > ρ 2 ξ ( 1 + ρ ) 2 ,
C = a ( 1 + ρ ) ( ξ ) a + 1 2 ( 1 + ρ ρ ) a 1 2 I a 1 ( 2 a ρ ) × I ( ρ 2 ξ ( 1 + ρ ) 2 , a , ρ , ξ ) + a ( 1 + ρ ) ( ξ ) a + 1 2 ( 1 + ρ ρ ) a 1 2 K a 1 ( 2 a ρ ) × J ( ρ 2 ξ ( 1 + ρ ) 2 , a , ρ , ξ ) ,
I ( A , a , ρ , ξ ) = A x a 3 4 ln ( 1 + x ) K a 1 ( 2 Ξ x 1 4 ) d x
J ( A , a , ρ , ξ ) = 0 A x a 3 4 ln ( 1 + x ) I a 1 ( 2 Ξ x 1 4 ) d x ,
I ( A , a , ρ , ξ ) = 2 1 a Ξ a + 1 2 0 ( t + 2 A 1 4 Ξ ) a × ln [ 1 + ( t + 2 A 1 4 Ξ ) 4 16 Ξ 2 ] K a 1 ( t + 2 A 1 4 Ξ ) d t .
I ( A , a , ρ , ξ ) = 0 e x 2 f ( A , a , ρ , ξ , x ) d x ,
f ( A , a , ρ , ξ , x ) = 2 π e 2 a ρ Ξ a + 1 2 ln [ 1 + ( x 2 + 2 a ρ ) 4 ξ 16 a 2 ( 1 + ρ ) 2 ] × x ( x 2 + 2 a ρ ) 2 a 1 Ψ ( a 1 2 , 2 a 1 , 4 a ρ + 2 x 2 ) .
0 e x 2 f ( x ) d x j = 1 Q ω j f ( x j ) ,
C = a ( 1 + ρ ) ( ξ ) a + 1 2 ( 1 + ρ ρ ) a 1 2 I a 1 ( 2 a ρ ) I ( ρ 2 ξ ( 1 + ρ ) 2 , a , ρ , ξ ) + 2 a ( 1 + ρ ) ( ξ ) a + 1 2 ( 1 + ρ ρ ) a 1 2 K a 1 ( 2 a ρ ) Ξ a 1 2 k = 0 Ξ k ( ρ 2 ξ ( 1 + ρ ) 2 ) a + k 2 k ! Γ ( a + k + 1 ) [ ln ( ρ 2 ξ ( 1 + ρ ) 2 + 1 ) ρ 2 ξ ( 1 + ρ ) 2 Φ ( ρ 2 ξ ( 1 + ρ ) 2 , 1 , a + k 2 + 1 ) ]
C = ( M + 1 2 ) 3 / 4 ρ 1 4 M 2 ( 1 + ρ ) M + 1 2 2 π ξ M + 1 4 K M 1 2 ( 2 a ρ ) × [ k = 0 M 1 ( M 1 + k ) ! ( 1 ) k k ! ( M 1 k ) ! 2 2 k Ξ k 2 × K ( M k , 2 Ξ , ρ 2 ξ ( 1 + ρ ) 2 ) + ( 1 ) M k = 0 M 1 ( M 1 + k ) ! k ! ( M 1 k ) ! 2 2 k × Ξ k 2 K ( M k , 2 Ξ , ρ 2 ξ ( 1 + ρ ) 2 ) ] + ( M + 1 2 ) 3 / 4 ( 1 + ρ ) M + 1 2 ξ M + 1 4 ρ 1 2 M 4 I M 1 2 ( 2 a ρ ) × π k = 0 M 1 ( M 1 + k ) ! 2 2 k 1 Ξ k / 2 k ! ( M 1 k ) ! × L ( M k , 2 Ξ , ρ 2 ξ ( 1 + ρ ) 2 ) ,
K ( n , c , A ) = 0 A x n 3 4 ln ( 1 + x ) e c x 4 d x
L ( n , c , A ) = A x n 3 4 ln ( 1 + x ) e c x 4 d x .
K a 1 ( 2 Ξ x 1 4 ) = 1 4 π ı σ 1 ı σ 1 + ı Γ ( a 1 2 + s ) × Γ ( 1 a 2 + s ) Ξ s x s / 2 d s , σ 1 = { s } > | a | 2
ln ( 1 + x ) = 1 2 π ı σ 2 ı σ 2 + ı Γ ( 1 + t ) Γ 2 ( t ) Γ ( 1 t ) x t d t , 1 < { t } < 0 ,
I ( A , a , ρ , ξ ) = 1 2 ( 1 4 π 2 ) σ 1 ı σ 1 + ı σ 2 ı σ 2 + ı Γ ( a 1 2 + s ) × Γ ( 1 a 2 + s ) Ξ s Γ ( 1 + t ) Γ 2 ( t ) Γ ( 1 t ) [ A x a 3 4 t s 2 d x ] d s d t .
A x a 3 4 t s 2 d x = 4 A 1 + a 4 t s 2 2 s + 4 t a 1 = 4 A 1 + a 4 t s 2 Γ ( 1 + a 2 s 4 t ) Γ ( 2 + a 2 s 4 t ) , { a 2 s 4 t } < 1 .
I ( A , a , ρ , ξ ) = 2 A 1 + a 4 4 π 2 σ 1 ı σ 1 + ı σ 2 ı σ 2 + ı Γ ( a 1 2 + s ) × Γ ( 1 a 2 + s ) Γ ( 1 + t ) Γ 2 ( t ) Γ ( 1 t ) Γ ( 1 + a 2 s 4 t ) Γ ( 2 + a 2 s 4 t ) × ( Ξ A ) s A t d s d t .
I ( A , a , ρ , ξ ) = 2 A 1 + a 4 × H 01 : 20 ; 12 11 : 02 ; 22 [ Ξ A A | ( a ; 2 , 4 ) : ; ( 1 , 1 ) , ( 1 , 1 ) ; ( a 1 ; 2 , 4 ) : ( a 1 2 , 1 ) , ( 1 a 2 , 1 ) ; ( 1 , 1 ) , ( 0 , 1 ) ; ] .
J ( A , a , ρ , ξ ) = Ξ a 1 2 k = 0 Ξ k k ! Γ ( a + k ) 0 A x a + k 2 1 ln ( 1 + x ) d x .
J ( A , a , ρ , ξ ) = 2 Ξ a 1 2 k = 0 Ξ k A a + k 2 k ! Γ ( a + k + 1 ) [ ln ( A + 1 ) A Φ ( A , 1 , a + k 2 + 1 ) ] .
K ( n , c , A ) = 4 0 A 4 y n ln ( 1 + y 4 ) e c y d y .
K ( n , c , A ) = 4 e c A 4 ln ( 1 + A ) j = 0 n ( 1 ) j j ! c j + 1 ( n j ) A n j 4 16 j = 0 n ( 1 ) j j ! c j + 1 ( n j ) 0 A 4 y n j + 3 e c y 1 + y 4 d y .
K 1 = n j + 3 c n j + 3 0 A 4 e c y 1 + y 4 d y .
K 2 = 1 2 { i = 1 2 e c s i s i [ Ei ( c s i + c A 4 ) Ei ( c s i ) ] } ,
g ( N ) ( x ) U ( B , C , N , x ) = B N e B x Ei ( C x ) + e ( B + C ) x × q = 1 N ( N q ) B N q p = 0 q C q p 1 ( q + 1 ) p x p + 1 .
K ( n , c , A ) = 4 e c A 4 ln ( 1 + A ) j = 0 n ( 1 ) j j ! c j + 1 ( n j ) A n j 4 8 j = 0 n ( 1 ) j j ! c j + 1 ( n j ) { i = 1 2 s i [ U ( s i , s i + A 4 , n j + 3 , c ) U ( s i , s i , n j + 3 , c ) ] } .
L ( n , c , A ) = 4 A 4 y n ln ( 1 + y 4 ) e c y d y .
L ( n , c , A ) = 4 e c A 4 ln ( 1 + A ) j = 0 n j ! c j + 1 ( n j ) A n j 4 + 16 j = 0 n j ! c j + 1 ( n j ) A 4 y n j + 3 e c y 1 + y 4 d y .
L 1 = ( 1 ) n j + 3 n j + 3 c n j + 3 A 4 e c y 1 + y 4 d y .
L 2 = 1 2 { i = 1 2 e c s i s i E 1 ( c s i + c A 4 ) } ,
h ( N ) ( x ) V ( B , C , N , x ) = B N e B x E 1 ( C x ) + e ( B C ) x × q = 1 N ( 1 ) q ( N q ) B N q p = 0 q C q p 1 ( 1 ) p ( q + 1 ) p x p + 1 .
L ( n , c , A ) = 4 e c A 4 ln ( 1 + A ) j = 0 n j ! c j + 1 ( n j ) A n j 4 8 j = 0 n ( 1 ) n j j ! c j + 1 ( n j ) × { i = 1 2 s i V ( s i , s i + A 4 , n j + 3 , c ) } .
f I ( I ) = 0 p 1 ( I | b ) p 2 ( b ) d b ,
p 1 ( I | b ) = a b ( I B ) a 1 e a ( B 2 + I ) b I a 1 ( 2 a B b I )
p 2 ( b ) = 1 b 0 e b b 0 .
f X ( x ; ν , λ ) = 1 2 e ( x + λ ) / 2 ( x λ ) ν / 4 1 / 2 I ν / 2 1 ( λ x ) , x 0 .