Abstract

In this paper, the performance of the variable weight multiple pulse-position modulation (MPPM) coding technique in an atmospheric optical communication environment under gamma-gamma optical scintillation is analyzed, proposing a closed-form expression for the average bit error rate (BER). This study is based on a hyperexponential fitting of the conditional BER in absence of turbulence fluctuations, leading to closed-form expressions that characterize the behavior of this nonlinear coding scheme. Finally, conditional and average BER expressions proposed here are corroborated with Monte Carlo simulations results.

© 2012 Optical Society of America

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  1. K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
    [CrossRef]
  2. A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Express 18, 17346 (2010).
    [CrossRef]
  3. S. Hranilovic, Wireless Optical Communication Systems (Springer, 2005).
  4. W. Gappmair and M. Flohberger, IEEE Trans. Wireless Commun. 8, 2209 (2009).
    [CrossRef]
  5. L. Zhang, Z. Wu, S. Gao, and M. Cui, in Proceedings of the International Conference on Electronics and Optoelectronics (ICEOE) (IEEE, 2011), Vol. 3, pp. 90–93.
  6. F. Xu, M. A. Khalighi, and S. Bourennane, J. Opt. Commun. Netw. 1, 404 (2009).
    [CrossRef]
  7. A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).
  8. J. M. Kahn and J. R. Barry, Proc. IEEE 85, 265 (1997).
    [CrossRef]
  9. J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, IEE Electron. Lett. 42, 43 (2006).
    [CrossRef]
  10. M. A. Al-Habash, L. C. Adrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
    [CrossRef]
  11. S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, 2004).
  12. D. V. Duong, G. E. Øien, and K. J. Hole, IEEE Trans. Veh. Technol. 55, 458 (2006).
    [CrossRef]
  13. Oberhettinger, Tables of Mellin Transforms (Springer-Verlag, 1974).
  14. A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists (Springer, 2008).
  15. F. Yilmaz and M. S. Alouini, in Proceedings of the 17th International Conference on Telecommunications (ICT) (IEEE, 2010), pp. 260–265.

2010 (2)

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Express 18, 17346 (2010).
[CrossRef]

2009 (2)

F. Xu, M. A. Khalighi, and S. Bourennane, J. Opt. Commun. Netw. 1, 404 (2009).
[CrossRef]

W. Gappmair and M. Flohberger, IEEE Trans. Wireless Commun. 8, 2209 (2009).
[CrossRef]

2006 (2)

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, IEE Electron. Lett. 42, 43 (2006).
[CrossRef]

D. V. Duong, G. E. Øien, and K. J. Hole, IEEE Trans. Veh. Technol. 55, 458 (2006).
[CrossRef]

2001 (1)

M. A. Al-Habash, L. C. Adrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

1997 (1)

J. M. Kahn and J. R. Barry, Proc. IEEE 85, 265 (1997).
[CrossRef]

Adrews, L. C.

M. A. Al-Habash, L. C. Adrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Al-Habash, M. A.

M. A. Al-Habash, L. C. Adrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Alouini, M. S.

F. Yilmaz and M. S. Alouini, in Proceedings of the 17th International Conference on Telecommunications (ICT) (IEEE, 2010), pp. 260–265.

Barry, J. R.

J. M. Kahn and J. R. Barry, Proc. IEEE 85, 265 (1997).
[CrossRef]

Bourennane, S.

Castillo-Vázquez, M.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Express 18, 17346 (2010).
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).

Costello, D. J.

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, 2004).

Cui, M.

L. Zhang, Z. Wu, S. Gao, and M. Cui, in Proceedings of the International Conference on Electronics and Optoelectronics (ICEOE) (IEEE, 2011), Vol. 3, pp. 90–93.

Duong, D. V.

D. V. Duong, G. E. Øien, and K. J. Hole, IEEE Trans. Veh. Technol. 55, 458 (2006).
[CrossRef]

Flohberger, M.

W. Gappmair and M. Flohberger, IEEE Trans. Wireless Commun. 8, 2209 (2009).
[CrossRef]

Gao, S.

L. Zhang, Z. Wu, S. Gao, and M. Cui, in Proceedings of the International Conference on Electronics and Optoelectronics (ICEOE) (IEEE, 2011), Vol. 3, pp. 90–93.

Gappmair, W.

W. Gappmair and M. Flohberger, IEEE Trans. Wireless Commun. 8, 2209 (2009).
[CrossRef]

García-Zambrana, A.

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, IEE Electron. Lett. 42, 43 (2006).
[CrossRef]

Garrido-Balsells, J. M.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Express 18, 17346 (2010).
[CrossRef]

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, IEE Electron. Lett. 42, 43 (2006).
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).

Haubold, H. J.

A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists (Springer, 2008).

Higashino, T.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

Hole, K. J.

D. V. Duong, G. E. Øien, and K. J. Hole, IEEE Trans. Veh. Technol. 55, 458 (2006).
[CrossRef]

Hranilovic, S.

S. Hranilovic, Wireless Optical Communication Systems (Springer, 2005).

Jurado-Navas, A.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Express 18, 17346 (2010).
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).

Kahn, J. M.

J. M. Kahn and J. R. Barry, Proc. IEEE 85, 265 (1997).
[CrossRef]

Kazaura, K.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

Khalighi, M. A.

Komaki, S.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

Lin, S.

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, 2004).

Mathai, A. M.

A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists (Springer, 2008).

Matsumoto, M.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

Oberhettinger,

Oberhettinger, Tables of Mellin Transforms (Springer-Verlag, 1974).

Øien, G. E.

D. V. Duong, G. E. Øien, and K. J. Hole, IEEE Trans. Veh. Technol. 55, 458 (2006).
[CrossRef]

Paris, J. F.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).

Phillips, R. L.

M. A. Al-Habash, L. C. Adrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Puerta-Notario, A.

A. Jurado-Navas, J. M. Garrido-Balsells, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Express 18, 17346 (2010).
[CrossRef]

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, IEE Electron. Lett. 42, 43 (2006).
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).

Tsukamoto, K.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

Wakamori, K.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

Wu, Z.

L. Zhang, Z. Wu, S. Gao, and M. Cui, in Proceedings of the International Conference on Electronics and Optoelectronics (ICEOE) (IEEE, 2011), Vol. 3, pp. 90–93.

Xu, F.

Yilmaz, F.

F. Yilmaz and M. S. Alouini, in Proceedings of the 17th International Conference on Telecommunications (ICT) (IEEE, 2010), pp. 260–265.

Zhang, L.

L. Zhang, Z. Wu, S. Gao, and M. Cui, in Proceedings of the International Conference on Electronics and Optoelectronics (ICEOE) (IEEE, 2011), Vol. 3, pp. 90–93.

IEE Electron. Lett. (1)

J. M. Garrido-Balsells, A. García-Zambrana, and A. Puerta-Notario, IEE Electron. Lett. 42, 43 (2006).
[CrossRef]

IEEE Commun. Mag. (1)

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48, 130 (2010).
[CrossRef]

IEEE Trans. Veh. Technol. (1)

D. V. Duong, G. E. Øien, and K. J. Hole, IEEE Trans. Veh. Technol. 55, 458 (2006).
[CrossRef]

IEEE Trans. Wireless Commun. (1)

W. Gappmair and M. Flohberger, IEEE Trans. Wireless Commun. 8, 2209 (2009).
[CrossRef]

J. Opt. Commun. Netw. (1)

Opt. Eng. (1)

M. A. Al-Habash, L. C. Adrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Opt. Express (1)

Proc. IEEE (1)

J. M. Kahn and J. R. Barry, Proc. IEEE 85, 265 (1997).
[CrossRef]

Other (7)

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett.36, 4095 (2011).

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, 2004).

Oberhettinger, Tables of Mellin Transforms (Springer-Verlag, 1974).

A. M. Mathai and H. J. Haubold, Special Functions for Applied Scientists (Springer, 2008).

F. Yilmaz and M. S. Alouini, in Proceedings of the 17th International Conference on Telecommunications (ICT) (IEEE, 2010), pp. 260–265.

S. Hranilovic, Wireless Optical Communication Systems (Springer, 2005).

L. Zhang, Z. Wu, S. Gao, and M. Cui, in Proceedings of the International Conference on Electronics and Optoelectronics (ICEOE) (IEEE, 2011), Vol. 3, pp. 90–93.

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Figures (2)

Fig. 1.
Fig. 1.

CBER hyperexponential fitting (solid lines) and simulation results for relevant vw-MPPM code rates, in absence of atmospheric turbulence.

Fig. 2.
Fig. 2.

Analytical average BER and Monte Carlo simulation results for relevant vw-MPPM code rates under weak, moderate, and strong atmospheric turbulence.

Tables (1)

Tables Icon

Table 1. vw-MPPM Code-Dependent Hyperexponential Fitting Parameters a, b, and c in Absence of Turbulence

Equations (12)

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

fI(I)=2(αβ)(α+β)/2Γ(α)Γ(β)Iα+β21Kαβ(2αβI),
Pb=0CBER(I;γ0)fI(I)dI,
CBER(I;γ0)aexp[b(γ0I2)c],
Pbaμ0Iα+β21exp(b˜I2c)Kαβ(σI)dI,
I(x)0tα+β21exp(b˜t2c)Kαβ(xt)dt,
M[I(x);z]=M[Kαβ(x);z]M[exp(b˜x2c);α+β2z].
M[Kαβ(x);z]=22z1Γ(z+αβ2)×Γ(zαβ2),
M[exp(b˜x2c);z]=b˜z2c2cΓ(z2c).
M[I(x);z]=b˜α+β4c4c(4b˜12c)zΓ(z+αβ2)×Γ(zαβ2)Γ(α+β4cz2c),
M[Hp,qm,n(x|(a1,α1),,(ap,αp)(b1,β1),,(bq,βq));z]=(j=1mΓ(bj+βjz))(j=1nΓ(1ajαjz))(j=m+1qΓ(1bjβjz))(j=n+1pΓ(aj+αjz)),
I(x)=b˜α+β4c4cH1,22,1(x4b˜1/2c|(1α+β4c,12c)(αβ2,1),(αβ2,1)).
Pba2c(αβ)α+β2Γ(α)Γ(β)(γ0b1/c)α+β2×H1,22,1(αβγ0b1/c|(1α+β4c,12c)(αβ2,1),(αβ2,1)),

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