Abstract

The efficacy of spatial diversity in practical free-space optical communication systems is impaired by the fading correlation among the underlying subchannels. We consider in this paper the generation of correlated Gamma–Gamma random variables in view of evaluating the system outage probability and bit-error-rate under the condition of correlated fading. Considering the case of receive-diversity systems with intensity modulation and direct detection, we propose a set of criteria for setting the correlation coefficients on the small- and large-scale fading components based on scintillation theory. We verify these criteria using wave-optics simulations and further show through Monte Carlo simulations that we can effectively neglect the correlation corresponding to the small-scale turbulence in most practical systems, irrespective of the specific turbulence conditions. This has not been clarified before, to the best of our knowledge. We then present some numerical results to illustrate the effect of fading correlation on the system performance. Our conclusions can be generalized to the cases of multiple-beam and multiple-beam multiple-aperture systems.

© 2013 Optical Society of America

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    [CrossRef]
  5. E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22, 1896–1906 (2004).
    [CrossRef]
  6. S. G. Wilson, M. Brandt-Pearce, Q. L. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun. 23, 1901–1910 (2005).
    [CrossRef]
  7. N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 26, 3–12 (2008).
    [CrossRef]
  8. W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron. 2, 16–23 (2008).
    [CrossRef]
  9. W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol. 27, 967–973 (2009).
    [CrossRef]
  10. N. D. Chatzidiamantis, M. Uysal, T. A. Tsiftsis, and G. K. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol. 28, 1064–1070 (2010).
    [CrossRef]
  11. Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
    [CrossRef]
  12. X. M. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
    [CrossRef]
  13. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6, 2813–2819 (2007).
    [CrossRef]
  14. M. Uysal, S. M. Navidpour, and L. Jing, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett. 8, 635–637 (2004).
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  15. N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of Gamma–Gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59, 1298–1308 (2011).
    [CrossRef]
  16. K. P. Peppas, “A simple, accurate approximation to the sum of Gamma–Gamma variates and applications in MIMO free-space optical systems,” IEEE Photon. Technol. Lett. 23, 839–841 (2011).
    [CrossRef]
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    [CrossRef]
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  21. G. Yang, M. A. Khalighi, S. Bourennane, and Z. Ghassemlooy, “Approximation to the sum of two correlated Gamma–Gamma variates and its applications in free-space optical communications,” IEEE Wireless Commun. Lett. 1, 621–624 (2012).
    [CrossRef]
  22. M. A. Khalighi, F. Xu, Y. Jaafar, and S. Bourennane, “Double-laser differential signaling for reducing the effect of background radiation in free-space optical systems,” J. Opt. Commun. Netw. 3, 145–154 (2011).
    [CrossRef]
  23. F. Xu, M.-A. Khalighi, and S. Bourennane, “Impact of different noise sources on the performance of PIN- and APD-based FSO receivers,” in 11th International Conference on Telecommunications—ConTEL, Graz, Austria (2011), pp. 211–218.
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  25. C. Sim, “Generation of Poisson and Gamma random vectors with given marginals and covariance matrix,” J. Stat. Comput. Simul. 47, 1–10 (1993).
    [CrossRef]
  26. K. Zhang, Z. Song, and Y. L. Guan, “Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters,” IEEE Trans. Wireless Commun. 3, 1463–1468 (2004).
    [CrossRef]
  27. Q. T. Zhang, “A decomposition technique for efficient generation of correlated Nakagami fading channels,” IEEE J. Sel. Areas Commun. 18, 2385–2392 (2000).
    [CrossRef]
  28. R. Barrios and F. Dios, “Exponentiated weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 20, 13055–13064 (2012).
    [CrossRef]
  29. F. Xu, A. Khalighi, P. Caussé, and S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express 17, 872–887 (2009).
    [CrossRef]

2012 (3)

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

G. Yang, M. A. Khalighi, S. Bourennane, and Z. Ghassemlooy, “Approximation to the sum of two correlated Gamma–Gamma variates and its applications in free-space optical communications,” IEEE Wireless Commun. Lett. 1, 621–624 (2012).
[CrossRef]

R. Barrios and F. Dios, “Exponentiated weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 20, 13055–13064 (2012).
[CrossRef]

2011 (5)

M. A. Khalighi, F. Xu, Y. Jaafar, and S. Bourennane, “Double-laser differential signaling for reducing the effect of background radiation in free-space optical systems,” J. Opt. Commun. Netw. 3, 145–154 (2011).
[CrossRef]

J. A. Tellez and J. D. Schmidt, “Multiple transmitter performance with appropriate amplitude modulation for free-space optical communication,” Appl. Opt. 50, 4737–4745 (2011).
[CrossRef]

K. P. Peppas, G. C. Alexandropoulos, C. K. Datsikas, and F. I. Lazarakis, “Multivariate Gamma–Gamma distribution with exponential correlation and its applications in radio frequency and optical wireless communications,” IET Microwaves Antennas Propag. 5, 364–371 (2011).
[CrossRef]

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of Gamma–Gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59, 1298–1308 (2011).
[CrossRef]

K. P. Peppas, “A simple, accurate approximation to the sum of Gamma–Gamma variates and applications in MIMO free-space optical systems,” IEEE Photon. Technol. Lett. 23, 839–841 (2011).
[CrossRef]

2010 (1)

2009 (3)

2008 (2)

N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 26, 3–12 (2008).
[CrossRef]

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

2007 (3)

2005 (1)

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

2004 (3)

K. Zhang, Z. Song, and Y. L. Guan, “Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters,” IEEE Trans. Wireless Commun. 3, 1463–1468 (2004).
[CrossRef]

M. Uysal, S. M. Navidpour, and L. Jing, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett. 8, 635–637 (2004).
[CrossRef]

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22, 1896–1906 (2004).
[CrossRef]

2002 (1)

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

2000 (1)

Q. T. Zhang, “A decomposition technique for efficient generation of correlated Nakagami fading channels,” IEEE J. Sel. Areas Commun. 18, 2385–2392 (2000).
[CrossRef]

1993 (1)

C. Sim, “Generation of Poisson and Gamma random vectors with given marginals and covariance matrix,” J. Stat. Comput. Simul. 47, 1–10 (1993).
[CrossRef]

Aitamer, N.

Alexandropoulos, G. C.

K. P. Peppas, G. C. Alexandropoulos, C. K. Datsikas, and F. I. Lazarakis, “Multivariate Gamma–Gamma distribution with exponential correlation and its applications in radio frequency and optical wireless communications,” IET Microwaves Antennas Propag. 5, 364–371 (2011).
[CrossRef]

Allen, J. I. H.

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

Andrews, L. C.

Anguita, J. A.

Baedke, M.

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

Barrios, R.

Bourennane, S.

G. Yang, M. A. Khalighi, S. Bourennane, and Z. Ghassemlooy, “Approximation to the sum of two correlated Gamma–Gamma variates and its applications in free-space optical communications,” IEEE Wireless Commun. Lett. 1, 621–624 (2012).
[CrossRef]

M. A. Khalighi, F. Xu, Y. Jaafar, and S. Bourennane, “Double-laser differential signaling for reducing the effect of background radiation in free-space optical systems,” J. Opt. Commun. Netw. 3, 145–154 (2011).
[CrossRef]

M. A. Khalighi, N. Schwartz, N. Aitamer, and S. Bourennane, “Fading reduction by aperture averaging and spatial diversity in optical wireless systems,” J. Opt. Commun. Netw. 1, 580–593 (2009).
[CrossRef]

F. Xu, A. Khalighi, P. Caussé, and S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express 17, 872–887 (2009).
[CrossRef]

F. Xu, M.-A. Khalighi, and S. Bourennane, “Impact of different noise sources on the performance of PIN- and APD-based FSO receivers,” in 11th International Conference on Telecommunications—ConTEL, Graz, Austria (2011), pp. 211–218.

G. Yang, M. A. Khalighi, and S. Bourennane, “Performance of receive diversity FSO systems under realistic beam propagation conditions,” in IEEE, IET International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Poznan, Poland (2012), pp. 1–5.

Brandt-Pearce, M.

N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 26, 3–12 (2008).
[CrossRef]

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

Cao, Q. L.

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

Caussé, P.

Chan, V. W. S.

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22, 1896–1906 (2004).
[CrossRef]

Chatzidiamantis, N. D.

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of Gamma–Gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59, 1298–1308 (2011).
[CrossRef]

N. D. Chatzidiamantis, M. Uysal, T. A. Tsiftsis, and G. K. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol. 28, 1064–1070 (2010).
[CrossRef]

Chen, Z.

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

Cvijetic, N.

N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 26, 3–12 (2008).
[CrossRef]

Datsikas, C. K.

K. P. Peppas, G. C. Alexandropoulos, C. K. Datsikas, and F. I. Lazarakis, “Multivariate Gamma–Gamma distribution with exponential correlation and its applications in radio frequency and optical wireless communications,” IET Microwaves Antennas Propag. 5, 364–371 (2011).
[CrossRef]

Dios, F.

Gao, S.

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

Ghassemlooy, Z.

G. Yang, M. A. Khalighi, S. Bourennane, and Z. Ghassemlooy, “Approximation to the sum of two correlated Gamma–Gamma variates and its applications in free-space optical communications,” IEEE Wireless Commun. Lett. 1, 621–624 (2012).
[CrossRef]

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

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

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB (CRC Press, 2013).

Gu, W.

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

Guan, Y. L.

K. Zhang, Z. Song, and Y. L. Guan, “Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters,” IEEE Trans. Wireless Commun. 3, 1463–1468 (2004).
[CrossRef]

Jaafar, Y.

Jing, L.

M. Uysal, S. M. Navidpour, and L. Jing, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett. 8, 635–637 (2004).
[CrossRef]

Kahn, J. M.

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

Karagiannidis, G. K.

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of Gamma–Gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59, 1298–1308 (2011).
[CrossRef]

N. D. Chatzidiamantis, M. Uysal, T. A. Tsiftsis, and G. K. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol. 28, 1064–1070 (2010).
[CrossRef]

Kavehrad, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6, 2813–2819 (2007).
[CrossRef]

Khalighi, A.

Khalighi, M. A.

G. Yang, M. A. Khalighi, S. Bourennane, and Z. Ghassemlooy, “Approximation to the sum of two correlated Gamma–Gamma variates and its applications in free-space optical communications,” IEEE Wireless Commun. Lett. 1, 621–624 (2012).
[CrossRef]

M. A. Khalighi, F. Xu, Y. Jaafar, and S. Bourennane, “Double-laser differential signaling for reducing the effect of background radiation in free-space optical systems,” J. Opt. Commun. Netw. 3, 145–154 (2011).
[CrossRef]

M. A. Khalighi, N. Schwartz, N. Aitamer, and S. Bourennane, “Fading reduction by aperture averaging and spatial diversity in optical wireless systems,” J. Opt. Commun. Netw. 1, 580–593 (2009).
[CrossRef]

G. Yang, M. A. Khalighi, and S. Bourennane, “Performance of receive diversity FSO systems under realistic beam propagation conditions,” in IEEE, IET International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Poznan, Poland (2012), pp. 1–5.

Khalighi, M.-A.

F. Xu, M.-A. Khalighi, and S. Bourennane, “Impact of different noise sources on the performance of PIN- and APD-based FSO receivers,” in 11th International Conference on Telecommunications—ConTEL, Graz, Austria (2011), pp. 211–218.

Lazarakis, F. I.

K. P. Peppas, G. C. Alexandropoulos, C. K. Datsikas, and F. I. Lazarakis, “Multivariate Gamma–Gamma distribution with exponential correlation and its applications in radio frequency and optical wireless communications,” IET Microwaves Antennas Propag. 5, 364–371 (2011).
[CrossRef]

Lee, E. J.

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22, 1896–1906 (2004).
[CrossRef]

Leitgeb, E.

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

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6, 2813–2819 (2007).
[CrossRef]

M. Uysal, S. M. Navidpour, and L. Jing, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett. 8, 635–637 (2004).
[CrossRef]

Neifeld, M. A.

Peppas, K. P.

K. P. Peppas, “A simple, accurate approximation to the sum of Gamma–Gamma variates and applications in MIMO free-space optical systems,” IEEE Photon. Technol. Lett. 23, 839–841 (2011).
[CrossRef]

K. P. Peppas, G. C. Alexandropoulos, C. K. Datsikas, and F. I. Lazarakis, “Multivariate Gamma–Gamma distribution with exponential correlation and its applications in radio frequency and optical wireless communications,” IET Microwaves Antennas Propag. 5, 364–371 (2011).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).

Popoola, W.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB (CRC Press, 2013).

Popoola, W. O.

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

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

Rajbhandari, S.

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB (CRC Press, 2013).

Recolons, J.

Schmidt, J. D.

Schwartz, N.

Sim, C.

C. Sim, “Generation of Poisson and Gamma random vectors with given marginals and covariance matrix,” J. Stat. Comput. Simul. 47, 1–10 (1993).
[CrossRef]

Song, Z.

K. Zhang, Z. Song, and Y. L. Guan, “Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters,” IEEE Trans. Wireless Commun. 3, 1463–1468 (2004).
[CrossRef]

Tellez, J. A.

Tsiftsis, T. A.

Uysal, M.

N. D. Chatzidiamantis, M. Uysal, T. A. Tsiftsis, and G. K. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol. 28, 1064–1070 (2010).
[CrossRef]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6, 2813–2819 (2007).
[CrossRef]

M. Uysal, S. M. Navidpour, and L. Jing, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett. 8, 635–637 (2004).
[CrossRef]

Vasic, B. V.

Vetelino, F. S.

Wang, S.

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

Wang, T.

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

Wilson, S. G.

N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 26, 3–12 (2008).
[CrossRef]

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

Wu, G.

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

Xu, F.

Yang, G.

G. Yang, M. A. Khalighi, S. Bourennane, and Z. Ghassemlooy, “Approximation to the sum of two correlated Gamma–Gamma variates and its applications in free-space optical communications,” IEEE Wireless Commun. Lett. 1, 621–624 (2012).
[CrossRef]

G. Yang, M. A. Khalighi, and S. Bourennane, “Performance of receive diversity FSO systems under realistic beam propagation conditions,” in IEEE, IET International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Poznan, Poland (2012), pp. 1–5.

Young, C.

Yu, S.

Z. Chen, S. Yu, T. Wang, G. Wu, S. Wang, and W. Gu, “Channel correlation in aperture receiver diversity systems for free-space optical communication,” J. Opt. 14, 1–7 (2012).
[CrossRef]

Zhang, K.

K. Zhang, Z. Song, and Y. L. Guan, “Simulation of Nakagami fading channels with arbitrary cross-correlation and fading parameters,” IEEE Trans. Wireless Commun. 3, 1463–1468 (2004).
[CrossRef]

Zhang, Q. T.

Q. T. Zhang, “A decomposition technique for efficient generation of correlated Nakagami fading channels,” IEEE J. Sel. Areas Commun. 18, 2385–2392 (2000).
[CrossRef]

Zhu, X. M.

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

Appl. Opt. (3)

IEEE Commun. Lett. (1)

M. Uysal, S. M. Navidpour, and L. Jing, “Error rate performance of coded free-space optical links over strong turbulence channels,” IEEE Commun. Lett. 8, 635–637 (2004).
[CrossRef]

IEEE J. Sel. Areas Commun. (4)

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22, 1896–1906 (2004).
[CrossRef]

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

N. Cvijetic, S. G. Wilson, and M. Brandt-Pearce, “Performance bounds for free-space optical MIMO systems with APD receivers in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 26, 3–12 (2008).
[CrossRef]

Q. T. Zhang, “A decomposition technique for efficient generation of correlated Nakagami fading channels,” IEEE J. Sel. Areas Commun. 18, 2385–2392 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. P. Peppas, “A simple, accurate approximation to the sum of Gamma–Gamma variates and applications in MIMO free-space optical systems,” IEEE Photon. Technol. Lett. 23, 839–841 (2011).
[CrossRef]

IEEE Trans. Commun. (2)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of an FSO link with a triple-aperture receiver. The receiver geometry is depicted on the right.

Fig. 2.
Fig. 2.

Flow chart of the verification method for the proposed criteria to set ρX and ρY.

Fig. 3.
Fig. 3.

PDFs of normalized ln(I) for three link distances of Z=1, 1.3, and 2 km for single- and triple-aperture systems with DR=5cm. PDFWO denotes the PDF obtained via wave-optics simulations for a subchannel, and PDFΓΓ,fit is the ΓΓ best-fit to it; PDFEGC is the PDF obtained by summing the received intensities from wave-optics simulations; and PDFΓΓ1 and PDFΓΓ2 denote the PDFs obtained by summing the generated correlated ΓΓ RVs according to [ρY=0] and [ρX=ρY] solutions, respectively. The calculated fading correlation coefficients for the (1×3) case and the best-fit α and β parameters for the (1×1) case are indicated on each figure. (a) Z=1.0km, ΔE=0; (b) Z=1.0km, ΔE=1cm; (c) Z=1.3km, ΔE=0; (d) Z=1.3km, ΔE=1cm; (e) Z=2.0km, ΔE=0; (f) Z=2.0km, ΔE=1cm.

Fig. 4.
Fig. 4.

Contrasting the system performance for the two solutions of [ρY=0] and [ρX=ρY] for Z=1 and 2 km with DR=5cm and ΔE=0. ρ=0.11 for Z=1km and ρ=0.21 for Z=2km. (a) Outage probability versus normalized SNR threshold. (b) Average BER versus average SNR.

Fig. 5.
Fig. 5.

Contrasting system performances for (1×3) system with the two solutions of [ρY=0] and [ρX=ρY] for Z=5km. ρ=0.31, which corresponds to (DR=5cm with ΔE=2cm), (DR=3cm with ΔE=2cm), and (DR=2cm with ΔE=2cm), from wave-optics simulations. (a) Outage probability versus normalized SNR threshold. (b) Average BER versus average SNR.

Fig. 6.
Fig. 6.

System performance for the (1×3) system with Z=5km, DR=5cm, and ΔC ranging from 5 to 12 cm. (a) Outage probability versus normalized SNR threshold. (b) Average BER versus average SNR.

Tables (2)

Tables Icon

Table 1. Scale Sizes for Different Link Distances Z

Tables Icon

Table 2. Criteria for Setting ρX and ρY Depending on Scintillation Parameters

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

p(I)=2(αβ)(α+β)/2Γ(α)Γ(β)I(α+β)21Kαβ(2αβI),I>0.
σμ,ν2=Φθ(κμ,ν)Δκ2=2πk2δZΦn(κμ,ν)Δκ2.
ρ=αρY+βρX+ρXρYα+β+1.
h=XY,
Rh=αRY+βRX+RXRYα+β+1,
lX=max(2,3),lY=min(1,2).

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