Abstract

A generic propagation model has been proposed recently and, from it, a new unifying statistical model has been obtained for the irradiance fluctuations due to a turbulent atmosphere. The statistical model presented, termed M distribution, can be written in a closed-form expression, and it contains most of the statistical models for the irradiance fluctuations that have been proposed in the literature. Relying on this generic model, in this paper, the performance of a subcarrier intensity-modulated free-space optical (SIM-FSO) communication system is investigated, and a novel closed-form analytical expression is derived for the average bit error rate of the system. Since the turbulence-induced fading is modeled by a generic distribution, the expression presented can be applied for performance analysis of SIM-FSO communication systems over most of the proposed statistical models derived so far.

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References

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  1. D. Keddar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May2004.
  2. L. Andrews, R. L. Philips, and C. Y. Hopen, Laser Beam Scintillation With Applications. SPIE Press, 2001.
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    [CrossRef]
  4. H. A. Al-Habash, L. C. Andrews, and 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]
  5. B. M. Uysal, J. T. Li, and 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.
    [CrossRef]
  6. J. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, and A. P. Notario, “A unifying statistical model for atmospheric optical scintillation,” arXiv.org, 2011 [Online]. Available: http://arxiv.org/abs/1102.1915v1.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. H. Samimi and P. Azmi, “Subcarrier intensity modulated free-space optical communications in K-distributed turbulence channels,” J. Opt. Commun. Netw., vol. 2, no. 8, pp. 625–632, Aug.2010.
    [CrossRef]
  11. C. K. Datsikas, K. P. Peppas, N. C. Sagias, and G. S. Tombras, “Serial free-space optical relaying communications over gamma–gamma atmospheric turbulence channels,” J. Opt. Commun. Netw., vol. 2, no. 8, pp. 576–586, Aug.2010.
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  13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed.Academic, New York, 1965.
  14. T. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series, Vol. 3: More Special Functions. Gordon and Breach Science Publishers, Amsterdam, 1986.
  15. V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in Proc. Int. Conf. on Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

2010 (2)

2009 (1)

2008 (1)

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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

2007 (1)

E. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1606, Aug.2007.
[CrossRef]

2005 (1)

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 (1)

D. Keddar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May2004.

2002 (1)

2001 (1)

H. A. Al-Habash, L. C. Andrews, and 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]

Adamchik, V. S.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in Proc. Int. Conf. on Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

Al-Habash, H. A.

H. A. Al-Habash, L. C. Andrews, and 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]

Allen, C. T.

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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

Andrews, L.

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

Andrews, L. C.

H. A. Al-Habash, L. C. Andrews, and 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]

Arnon, S.

D. Keddar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May2004.

Azmi, P.

Balsells, J. M. G.

J. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, and A. P. Notario, “A unifying statistical model for atmospheric optical scintillation,” arXiv.org, 2011 [Online]. Available: http://arxiv.org/abs/1102.1915v1.

Brychkov, Y. A.

T. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series, Vol. 3: More Special Functions. Gordon and Breach Science Publishers, Amsterdam, 1986.

Datsikas, C. K.

Demarest, K. R.

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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

Ghassemlooy, Z.

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol. 27, no. 8, pp. 967–973, Apr.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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed.Academic, New York, 1965.

Hopen, C. Y.

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

Huang, R.

Hui, R.

Jurado-Navas, J. A.

J. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, and A. P. Notario, “A unifying statistical model for atmospheric optical scintillation,” arXiv.org, 2011 [Online]. Available: http://arxiv.org/abs/1102.1915v1.

Keddar, D.

D. Keddar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May2004.

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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

Li, E. J.

E. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1606, Aug.2007.
[CrossRef]

Li, J. T.

B. M. Uysal, J. T. Li, and 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.
[CrossRef]

Liu, J. Q.

E. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1606, 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.

T. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series, Vol. 3: More Special Functions. Gordon and Breach Science Publishers, Amsterdam, 1986.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in Proc. Int. Conf. on Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

Notario, A. P.

J. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, and A. P. Notario, “A unifying statistical model for atmospheric optical scintillation,” arXiv.org, 2011 [Online]. Available: http://arxiv.org/abs/1102.1915v1.

Paris, J. F.

J. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, and A. P. Notario, “A unifying statistical model for atmospheric optical scintillation,” arXiv.org, 2011 [Online]. Available: http://arxiv.org/abs/1102.1915v1.

Peppas, K. P.

Philips, R. L.

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

Phillips, R. L.

H. A. Al-Habash, L. C. Andrews, and 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]

Popoola, W. O.

W. O. Popoola and Z. Ghassemlooy, “BPSK subcarrier modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol., vol. 27, no. 8, pp. 967–973, Apr.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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

Prudnikov, T. A. P.

T. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series, Vol. 3: More Special Functions. Gordon and Breach Science Publishers, Amsterdam, 1986.

Richards, D.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed.Academic, New York, 1965.

Sagias, N. C.

Samimi, H.

Taylor, D. P.

E. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1606, Aug.2007.
[CrossRef]

Tombras, G. S.

Uysal, B. M.

B. M. Uysal, J. T. Li, and 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.
[CrossRef]

Yu, M.

B. M. Uysal, J. T. Li, and 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.
[CrossRef]

Zhu, B.

IEEE Opt. Commun. (1)

D. Keddar and S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Opt. Commun., vol. 42, no. 5, pp. 51–57, May2004.

IEEE Trans. Commun. (1)

E. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 55, no. 8, pp. 1598–1606, Aug.2007.
[CrossRef]

IEEE Trans. Wireless Commun. (1)

B. M. Uysal, J. T. Li, and 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.
[CrossRef]

IET Optoelectron. (1)

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., vol. 2, no. 1, pp. 16–23, Feb.2008.
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Commun. Netw. (2)

J. Opt. Fiber Commun. Rep. (1)

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

Opt. Eng. (1)

H. A. Al-Habash, L. C. Andrews, and 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]

Other (5)

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

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed.Academic, New York, 1965.

T. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integral and Series, Vol. 3: More Special Functions. Gordon and Breach Science Publishers, Amsterdam, 1986.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in Proc. Int. Conf. on Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

J. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, and A. P. Notario, “A unifying statistical model for atmospheric optical scintillation,” arXiv.org, 2011 [Online]. Available: http://arxiv.org/abs/1102.1915v1.

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Figures (4)

Fig. 1
Fig. 1

(Color online) Proposed propagation scheme for M-distributed turbulence channels [6].

Fig. 2
Fig. 2

Scintillation index against parameter α for the case when ρ=1 (Gamma–Gamma distribution) and β={2,3}.

Fig. 3
Fig. 3

BER against average SNR for different values of the parameter ρ. In all curves, the transmitted power is normalized: Ω+2b0=1. The cases ρ=0 and ρ=1 correspond to the special cases of K and Gamma–Gamma distributions, respectively. Moreover, the case ρ=0,β=1,α corresponds to the negative exponential distribution.

Fig. 4
Fig. 4

BER against average SNR for different values of α, β, and ρ. Different behaviors are shown for the same intensity of turbulence (σI2=0.5). In all curves, the transmitted power is normalized, i.e., Ω+2b0=1.

Equations (9)

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

fI(I)=Ak=1βakIα+k21Kαk2αβIγβ+Ω,
A=2αα2γ1+α2Γ(α)γβγβ+Ωβ+α2,
ak=β1k1γβ+Ω1k2k1!Ωγk1αβk2,
Pe|I(I)=Qγ=QIR2σ,
Pe=0Pe|I(I)fI(I)dI=0QIR2σfI(I)dI.
Pe=Ak=1βak0QIR2σIα+k21Kαk2αβIγβ+ΩdI.
Pe=Ak=1βak00.5erfcIR2σIα+k21Kαk2αβIγβ+ΩdI.
Pe=2α18π3αβγβ+Ωα2k=1βPe(k),
Pe(k)=2kαβγβ+Ωk2akG5,22,44R2σ2αβγβ+Ω21α2,2α2,2k2,10,12.