Abstract

In this Letter, closed-form expressions of ergodic capacity, outage probability, and outage rate are derived for an atmospheric optical communication link using intensity modulation and direct detection with unbounded optical wavefront propagating through a homogeneous and isotropic turbulent medium. The optical scintillation of the received signal is modeled with the recently proposed Málaga or M turbulence distribution. By taking advantage of this unifying statistical model, the expressions here presented are valid for all possible irradiance fluctuation conditions, leading to direct relationships between turbulence parameters and link capacity performance.

© 2013 Optical Society of America

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Corrections

José María Garrido-Balsells, Antonio Jurado-Navas, José Francisco Paris, Miguel Castillo-Vázquez, and Antonio Puerta-Notario, "On the capacity of M-distributed atmospheric optical channels: erratum," Opt. Lett. 39, 653-653 (2014)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-39-3-653

References

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  1. K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
    [CrossRef]
  2. X. Zhu and J. M. Kahn, IEEE Trans. Commun. 50, 1293 (2002).
    [CrossRef]
  3. S. Hranilovic, Wireless Optical Communication Systems (Springer, 2005).
  4. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
    [CrossRef]
  5. A. L. Afanas’ev, V. A. Banakh, and A. P. Rostov, Atmos. Oceanic Opt. 21, 102 (2008).
  6. H. G. Sandalidis and T. A. Tsiftsis, Electron. Lett. 44, 46 (2008).
    [CrossRef]
  7. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, IET Commun. 3, 1402 (2009).
  8. A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), p. 181.
  9. A. Jurado-Navas, J. M. G. Balsells, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, Opt. Lett. 36, 4095 (2011).
    [CrossRef]
  10. A. Goldsmith, Wireless Communications (Cambridge University, 2005).
  11. Wolfram functions, http://functions.wolfram.com .
  12. P. Billingsley, Convergence of Probability Measures (Wiley, 2005).

2011 (1)

2010 (1)

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

2009 (1)

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, IET Commun. 3, 1402 (2009).

2008 (2)

A. L. Afanas’ev, V. A. Banakh, and A. P. Rostov, Atmos. Oceanic Opt. 21, 102 (2008).

H. G. Sandalidis and T. A. Tsiftsis, Electron. Lett. 44, 46 (2008).
[CrossRef]

2002 (1)

X. Zhu and J. M. Kahn, IEEE Trans. Commun. 50, 1293 (2002).
[CrossRef]

2001 (1)

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

Afanas’ev, A. L.

A. L. Afanas’ev, V. A. Banakh, and A. P. Rostov, Atmos. Oceanic Opt. 21, 102 (2008).

Al-Habash, M. A.

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

Andrews, L. C.

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

Balsells, J. M. G.

Banakh, V. A.

A. L. Afanas’ev, V. A. Banakh, and A. P. Rostov, Atmos. Oceanic Opt. 21, 102 (2008).

Billingsley, P.

P. Billingsley, Convergence of Probability Measures (Wiley, 2005).

Castillo-Vázquez, M.

Garrido-Balsells, J. M.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), p. 181.

Goldsmith, A.

A. Goldsmith, Wireless Communications (Cambridge University, 2005).

Higashino, T.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

Hranilovic, S.

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

Jurado-Navas, A.

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

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), p. 181.

Kahn, J. M.

X. Zhu and J. M. Kahn, IEEE Trans. Commun. 50, 1293 (2002).
[CrossRef]

Kazaura, K.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

Komaki, S.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

Matsumoto, M.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

Nistazakis, H. E.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, IET Commun. 3, 1402 (2009).

Paris, J. F.

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

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), p. 181.

Phillips, R. L.

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

Puerta-Notario, A.

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

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), p. 181.

Rostov, A. P.

A. L. Afanas’ev, V. A. Banakh, and A. P. Rostov, Atmos. Oceanic Opt. 21, 102 (2008).

Sandalidis, H. G.

H. G. Sandalidis and T. A. Tsiftsis, Electron. Lett. 44, 46 (2008).
[CrossRef]

Tombras, G. S.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, IET Commun. 3, 1402 (2009).

Tsiftsis, T. A.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, IET Commun. 3, 1402 (2009).

H. G. Sandalidis and T. A. Tsiftsis, Electron. Lett. 44, 46 (2008).
[CrossRef]

Tsukamoto, K.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

Wakamori, K.

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

Zhu, X.

X. Zhu and J. M. Kahn, IEEE Trans. Commun. 50, 1293 (2002).
[CrossRef]

Atmos. Oceanic Opt. (1)

A. L. Afanas’ev, V. A. Banakh, and A. P. Rostov, Atmos. Oceanic Opt. 21, 102 (2008).

Electron. Lett. (1)

H. G. Sandalidis and T. A. Tsiftsis, Electron. Lett. 44, 46 (2008).
[CrossRef]

IEEE Commun. Mag. (1)

K. Kazaura, K. Wakamori, M. Matsumoto, T. Higashino, K. Tsukamoto, and S. Komaki, IEEE Commun. Mag. 48(2), 130 (2010).
[CrossRef]

IEEE Trans. Commun. (1)

X. Zhu and J. M. Kahn, IEEE Trans. Commun. 50, 1293 (2002).
[CrossRef]

IET Commun. (1)

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, IET Commun. 3, 1402 (2009).

Opt. Eng. (1)

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

Opt. Lett. (1)

Other (5)

A. Goldsmith, Wireless Communications (Cambridge University, 2005).

Wolfram functions, http://functions.wolfram.com .

P. Billingsley, Convergence of Probability Measures (Wiley, 2005).

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, Numerical Simulations of Physical and Engineering Processes (In-Tech, 2011), p. 181.

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

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Figures (4)

Fig. 1.
Fig. 1.

Laser beam propagation scheme under a M -distributed free space optical link.

Fig. 2.
Fig. 2.

Ergodic capacity per channel use against the received electrical SNR in absence of turbulence, γ 0 , for different values of ρ .

Fig. 3.
Fig. 3.

Outage probability against normalized electrical SNR received in absence of turbulence, γ n , for different values of ρ .

Fig. 4.
Fig. 4.

Outage rate against outage probability for different values of ρ and electrical received SNR γ 0 [ dB ] = 10 , 20, and 30 dB.

Equations (15)

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γ = ( R I 0 I ) 2 / σ n 2 = γ 0 I 2 ,
f I ( I ) = A k = 1 β a k I α + k 2 1 K α k ( 2 α β I ξ g β + Ω ) ,
{ A 2 α α 2 ξ g 1 + α 2 Γ ( α ) ( ξ g β ξ g β + Ω ) β + α 2 , a k ( β 1 k 1 ) ( ξ g β + Ω ) 1 k 2 Γ ( k ) ( Ω ξ g ) k 1 ( α β ) k 2 .
f I ( I ) = A ( G ) k = 1 a k ( G ) I α + k 2 1 K α k ( 2 α I ξ g ) ,
{ A ( G ) 2 α α 2 ξ g 1 + α 2 Γ ( α ) ( ξ g β ξ g β + Ω ) β , a k ( G ) ( β ) k 1 ( α ξ g ) k 2 [ ( k 1 ) ! ] 2 ξ g k 1 ( Ω + ξ g β ) k 1 ,
C ( I ) = log 2 ( 1 + γ 0 I 2 ) .
C erg = 0 log 2 ( 1 + γ 0 I 2 ) f I ( I ) d I ,
C erg = A α ( 2 B ) α 2 π ln ( 2 ) k = 1 β ( β 1 k 1 ) 2 k Γ ( k ) ( Ω ξ g β ) k 1 × G 6 , 2 1 , 6 ( 16 B 2 γ 0 | 1 , 1 , 1 α 2 , 2 α 2 , 1 k 2 , 2 k 2 1 , 0 ) ,
C erg = A ( G ) 8 π ln ( 2 ) ( 4 ξ g α ) α 2 k = 1 a k ( G ) ( 4 ξ g α ) k 2 × G 6 , 2 1 , 6 ( 4 ξ g α γ 0 | 1 , 1 , 1 α 2 , 2 α 2 , 1 k 2 , 2 k 2 1 , 0 ) .
P out = Pr [ γ γ th ] = Pr [ P b P b , th ] .
C out = log 2 ( 1 + γ th ) .
P out = Pr [ I γ th γ 0 ] = Pr [ I 1 γ n ] = F I [ 1 γ n ] ,
P out = A k = 1 β a k ( γ n ) α + k 2 × G 1 , 3 2 , 1 ( 1 B γ n | 1 α + k 2 α k 2 , α k 2 , α + k 2 ) ,
P out = A ( G ) k = 1 a k ( G ) ( γ n ) α + k 2 × G 1 , 3 2 , 1 ( α ξ g γ n | 1 α + k 2 α k 2 , α k 2 , α + k 2 ) ,
R out = ( 1 P out ) log 2 ( 1 + γ th ) .

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