Abstract

This paper shows that optical signal transmission over intersatellite links with swaying transmitters can be described as an equivalent fading model. In this model, the instantaneous signal-to-noise ratio is stochastic and follows the reciprocal Pareto distribution. With this model, we show that the transmitter power can be minimized, subject to a specified outage probability, by appropriately adjusting some system parameters, such as the transmitter gain.

© 2010 Optical Society of America

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References

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  1. N. Karafolas, S. Baroni, “Optical satellite networks,” J. Lightwave Technol. 18, 1792–1806 (2000).
    [CrossRef]
  2. J. M. Kahn, J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
    [CrossRef]
  3. S. Arnon, S. R. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
    [CrossRef]
  4. C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
    [CrossRef]
  5. X. Liu, “Optimization of the wireless optical system with Bessel pointing loss factor,” IEEE Commun. Lett. 12, 584–586 (2008).
    [CrossRef]
  6. E. Biglieri, J. Proakis, S. Shamai, “Fading channels: information-theoretic and communications aspects,” IEEE Trans. Inf. Theory 44, 2619–2692 (1998).
    [CrossRef]
  7. S. G. Lambert, W. L. Casey, Laser Communications in Space (Artech House, 1995).
  8. J. J. Degnan, B. J. Klein, “Optical antenna gain. 2: Receiving antennas,” Appl. Opt. 13, 2397–2401 (1974).
    [CrossRef] [PubMed]
  9. R. Otte, L. P. de Jong, A. H. M. Van Roermund, Low-Power Wireless Infrared Communications (Kluwer, 1999).
  10. J. C. Palais, Fiber Optic Communications, 5th ed. (Prentice Hall, 2005).
  11. X. Liu, “Outage behavior of the MISO optical inter-satellite link subject to correlated fading induced by transmitter vibration,” submitted to IEEE J. Sel. Areas Commun., Jan. 27, 2009.
  12. S. Arnon, “Minimization of outage probability of WiMAX link supported by laser link between a high-altitude platform and a satellite,” J. Opt. Soc. Am. A 26, 1545–1552 (2009).
    [CrossRef]
  13. K. Park and W. Willinger, eds., Self-Similar Network Traffic and Performance Evaluation (Wiley, 2000).
    [CrossRef]

2009 (1)

2008 (1)

X. Liu, “Optimization of the wireless optical system with Bessel pointing loss factor,” IEEE Commun. Lett. 12, 584–586 (2008).
[CrossRef]

2000 (1)

1998 (2)

E. Biglieri, J. Proakis, S. Shamai, “Fading channels: information-theoretic and communications aspects,” IEEE Trans. Inf. Theory 44, 2619–2692 (1998).
[CrossRef]

S. Arnon, S. R. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

1997 (1)

J. M. Kahn, J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

1989 (1)

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

1974 (1)

Arnon, S.

S. Arnon, “Minimization of outage probability of WiMAX link supported by laser link between a high-altitude platform and a satellite,” J. Opt. Soc. Am. A 26, 1545–1552 (2009).
[CrossRef]

S. Arnon, S. R. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

Baroni, S.

Barry, J. R.

J. M. Kahn, J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Biglieri, E.

E. Biglieri, J. Proakis, S. Shamai, “Fading channels: information-theoretic and communications aspects,” IEEE Trans. Inf. Theory 44, 2619–2692 (1998).
[CrossRef]

Casey, W. L.

S. G. Lambert, W. L. Casey, Laser Communications in Space (Artech House, 1995).

Chen, C. C.

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

de Jong, L. P.

R. Otte, L. P. de Jong, A. H. M. Van Roermund, Low-Power Wireless Infrared Communications (Kluwer, 1999).

Degnan, J. J.

Gardner, C. S.

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

Kahn, J. M.

J. M. Kahn, J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Karafolas, N.

Klein, B. J.

Kopeika, N. S.

S. Arnon, S. R. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

Lambert, S. G.

S. G. Lambert, W. L. Casey, Laser Communications in Space (Artech House, 1995).

Liu, X.

X. Liu, “Optimization of the wireless optical system with Bessel pointing loss factor,” IEEE Commun. Lett. 12, 584–586 (2008).
[CrossRef]

X. Liu, “Outage behavior of the MISO optical inter-satellite link subject to correlated fading induced by transmitter vibration,” submitted to IEEE J. Sel. Areas Commun., Jan. 27, 2009.

Otte, R.

R. Otte, L. P. de Jong, A. H. M. Van Roermund, Low-Power Wireless Infrared Communications (Kluwer, 1999).

Palais, J. C.

J. C. Palais, Fiber Optic Communications, 5th ed. (Prentice Hall, 2005).

Proakis, J.

E. Biglieri, J. Proakis, S. Shamai, “Fading channels: information-theoretic and communications aspects,” IEEE Trans. Inf. Theory 44, 2619–2692 (1998).
[CrossRef]

Rotman, S. R.

S. Arnon, S. R. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

Shamai, S.

E. Biglieri, J. Proakis, S. Shamai, “Fading channels: information-theoretic and communications aspects,” IEEE Trans. Inf. Theory 44, 2619–2692 (1998).
[CrossRef]

Van Roermund, A. H. M.

R. Otte, L. P. de Jong, A. H. M. Van Roermund, Low-Power Wireless Infrared Communications (Kluwer, 1999).

Appl. Opt. (1)

IEEE Commun. Lett. (1)

X. Liu, “Optimization of the wireless optical system with Bessel pointing loss factor,” IEEE Commun. Lett. 12, 584–586 (2008).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

S. Arnon, S. R. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

IEEE Trans. Commun. (1)

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

IEEE Trans. Inf. Theory (1)

E. Biglieri, J. Proakis, S. Shamai, “Fading channels: information-theoretic and communications aspects,” IEEE Trans. Inf. Theory 44, 2619–2692 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Proc. IEEE (1)

J. M. Kahn, J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Other (5)

S. G. Lambert, W. L. Casey, Laser Communications in Space (Artech House, 1995).

R. Otte, L. P. de Jong, A. H. M. Van Roermund, Low-Power Wireless Infrared Communications (Kluwer, 1999).

J. C. Palais, Fiber Optic Communications, 5th ed. (Prentice Hall, 2005).

X. Liu, “Outage behavior of the MISO optical inter-satellite link subject to correlated fading induced by transmitter vibration,” submitted to IEEE J. Sel. Areas Commun., Jan. 27, 2009.

K. Park and W. Willinger, eds., Self-Similar Network Traffic and Performance Evaluation (Wiley, 2000).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Normalized minimum transmitter power versus the pointing error deviation and the outage probability ( wavelength = 850 nm ).

Fig. 2
Fig. 2

Normalized minimum transmitter power versus the pointing error deviation and the outage probability ( wavelength = 1550 nm ).

Equations (23)

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f Θ ( θ ) = ( θ σ 2 ) exp ( θ 2 2 σ 2 ) , ( θ 0 ) ,
F Θ ( θ ) = 1 exp ( θ 2 2 σ 2 ) .
P R = M P T G T G R ( λ 4 π d ) 2 η T η R L T ( G T , Θ ) L R ( G R , Γ ) .
R = η q λ / ( h c ) ,
μ = R P R ,
U = P s 2 σ N 2 = A exp ( 2 G T Θ 2 ) , ( 0 < U A ) ,
A = 1 2 σ N 2 ( λ 4 π d ) 4 ( R M P T G T G R η T η R ) 2 .
F U ( u ) = P ( U u ) = P [ A exp ( 2 G T Θ 2 ) u ] = P [ Θ 1 2 G T | ln ( u A ) | ] = 1 F Θ [ 1 2 G T | ln ( u A ) | ] = exp [ 1 4 σ 2 G T ln ( u A ) ] = ( u A ) 1 4 σ 2 G T , ( u < A ) .
F Z ( z ) = P ( Z z ) = P ( 1 U z ) = P ( U 1 z ) = 1 F U ( 1 z ) = 1 ( 1 A z ) 1 4 σ 2 G T , ( z 1 / A ) .
P a = P ( U a ) = ( a A ) 1 4 σ 2 G T .
α = ( R M 2 σ N 2 ) η T η R ( λ 4 π d ) 2 G R .
P a = ( a 4 ) 1 4 x ( 1 x y ) 1 2 x .
minimize     y , subject to     P a = b ; ( b < 1 ) ,
( a 4 ) 1 4 x ( 1 x y ) 1 2 x = b , or y = a 2 x b 2 x .
d y d x = a 4 ( 1 + 2 x ln b x 2 b 2 x ) = a 4 ( 2 x ln ( 1 / b ) 1 x 2 b 2 x ) .
x s = 1 2 ln ( 1 / b ) .
d y d x = a 4 ( 2 x ln ( 1 / b ) 1 x 2 b 2 x ) = a 4 ( 1 x b 2 x ) [ 2 ln ( 1 b ) 1 x ] = y [ 2 ln ( 1 b ) 1 x ] .
d 2 y d x 2 = d y d x [ 2 ln ( 1 b ) 1 x ] + y x 2 .
y min = b ( 1 / ln b ) a ln ( 1 b ) .
α P T , min σ 2 = b ( 1 / ln b ) a ln ( 1 b ) .
P M = def M P T , min 2 σ N a = b ( 1 / ln b ) σ 2 2 R η T η R G R ( 4 π d λ ) 2 ln ( 1 b ) ( watt / ampere ) .
P M = h c b ( 1 / ln b ) σ 2 2 η q λ η T η R ( 4 d D R ) 2 ln ( 1 b ) ( watt / ampere ) .
P T a = def η q η T η R D R 2 P M 16 d 2 h c 2 = b ( 1 / ln b ) σ 2 λ ln ( 1 b ) ( rad 2 / m ) .

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