Abstract

We analyze free-space optical links employing imaging receivers in the presence of misalignment and atmospheric effects, such as haze, fog or rain. We present a detailed propagation model based on the radiative transfer equation. We also compare the relative importance of two mechanisms by which these effects degrade link performance: signal attenuation and image blooming. We show that image blooming dominates over attenuation, except under medium-to-heavy fog conditions.

© 2012 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. D. Kedar and S. Arnon, “Optical wireless communication through fog in the presence of pointing errors,” Appl. Opt. 42(24), 4946–4954 (2003).
    [CrossRef] [PubMed]
  4. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
    [CrossRef]
  5. X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun. 51(8), 1233–1239 (2003).
    [CrossRef]
  6. A. A. Farid and S. Hranilovic, “Outage probability for free-space optical systems over slow fading channels with Pointing Errors,” in Proceedings of 19th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE LEOS, 2006), pp. 82–83.
  7. N. Perlot, “Turbulence-induced fading probability in coherent optical communication through the atmosphere,” Appl. Opt. 46(29), 7218–7226 (2007).
    [CrossRef] [PubMed]
  8. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consum. Electron. 50, 100–107 (2004).
  9. D. C. O'Brien, L. Zeng, H. Le-Minh, G. Faulkner, J. W. Walewski, and S. Randel, “Visible light communication: challenges and possibilities,” in Proceedings of IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE, 2008), pp. 1–5.
  10. J. Grubor, S. Randel, K. Langer, and J. W. Walewski, “Broadband information broadcasts using LED-based interior lighting,” J. Lightwave Technol. 26(24), 3883–3892 (2008).
    [CrossRef]
  11. N. Araki and H. Yashima, “A channel model of optical wireless communications during rainfall,” in Proceedings of 2nd International Symposium on Wireless Communication Systems (2005), pp. 205–209.
  12. M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).
  13. B. Wu, Z. Hajjarian, and M. Kavehrad, “Free space optical communications through clouds: analysis of signal characteristics,” Appl. Opt. 47(17), 3168–3176 (2008).
    [CrossRef] [PubMed]
  14. Z. Hajjarian and M. Kavehrad, “Using MIMO transmissions in free space optical communications in presence of clouds and turbulence,” Proc, SPIE 7199, 1–12 (2009).
  15. W. Popoola, Z. Ghassemlooy, M. S. Awan, and E. Leitgeb, “Atmospheric channel effects on terrestrial free-space optical communication links,” in Proceedings of 3rd International Conference on Electronics, Computers and Artificial Intelligence (2009), pp. 17–23.
  16. P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multi-beam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
    [CrossRef]
  17. S. Antyufeev, “Monte Carlo method for solving inverse problems of radiative transfer,” in Inverse and Ill-Posed Problem Series (VSP Publishers, 2000).
  18. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  19. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  20. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  21. W. E. K. Middleton, Vision through the Atmosphere (University of Toronto Press, Toronto, 1968).
  22. S. G. Narasimhan and S. K. Nayar, “Shedding light on the weather,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2003), pp. 665–672.
  23. S. Metari and F. Deschnes, “A new convolutional kernel for atmospheric point spread function applied to computer vision,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2003), pp. 1–8.
  24. A. P. Tang, J. M. Kahn, and K. P. Ho, “Wireless infrared communication links using multi-beam transmitters and imaging receivers,” in Proceedings of IEEE International Conference on Communications (IEEE, 1996), pp. 180–186.
  25. J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
    [CrossRef]
  26. A. A. Kokhanovsky, Cloud Optics (Springer, 2006).
  27. R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectral data sets,” Sol. Energy 30(6), 563–573 (1983).
    [CrossRef]

2009 (2)

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Z. Hajjarian and M. Kavehrad, “Using MIMO transmissions in free space optical communications in presence of clouds and turbulence,” Proc, SPIE 7199, 1–12 (2009).

2008 (2)

2007 (1)

2004 (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consum. Electron. 50, 100–107 (2004).

2003 (2)

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun. 51(8), 1233–1239 (2003).
[CrossRef]

D. Kedar and S. Arnon, “Optical wireless communication through fog in the presence of pointing errors,” Appl. Opt. 42(24), 4946–4954 (2003).
[CrossRef] [PubMed]

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

2000 (1)

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multi-beam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

1999 (1)

1997 (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

1985 (1)

1983 (1)

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectral data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Arnon, S.

Awan, M. S.

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

Bird, R. E.

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectral data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Chan, V.

Djahani, P.

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multi-beam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

Grubor, J.

Hajjarian, Z.

Z. Hajjarian and M. Kavehrad, “Using MIMO transmissions in free space optical communications in presence of clouds and turbulence,” Proc, SPIE 7199, 1–12 (2009).

B. Wu, Z. Hajjarian, and M. Kavehrad, “Free space optical communications through clouds: analysis of signal characteristics,” Appl. Opt. 47(17), 3168–3176 (2008).
[CrossRef] [PubMed]

Horwath, L. C.

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Hulstrom, R. L.

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectral data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Kahn, J. M.

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun. 51(8), 1233–1239 (2003).
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multi-beam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

Kavehrad, M.

Z. Hajjarian and M. Kavehrad, “Using MIMO transmissions in free space optical communications in presence of clouds and turbulence,” Proc, SPIE 7199, 1–12 (2009).

B. Wu, Z. Hajjarian, and M. Kavehrad, “Free space optical communications through clouds: analysis of signal characteristics,” Appl. Opt. 47(17), 3168–3176 (2008).
[CrossRef] [PubMed]

Kedar, D.

Khan, M. S.

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Komine, T.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consum. Electron. 50, 100–107 (2004).

Langer, K.

Lavan, M. J.

Leitgeb, E.

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Lewis, L. J.

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectral data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Majumdar, A. K.

Muhammad, S. S.

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Nadeem, F.

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

Nakagawa, M.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consum. Electron. 50, 100–107 (2004).

Perlot, N.

Randel, S.

Strickland, B. R.

Walewski, J. W.

Woodbridge, E.

Wu, B.

Zhu, X.

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun. 51(8), 1233–1239 (2003).
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

Appl. Opt. (5)

IEEE Trans. Commun. (3)

P. Djahani and J. M. Kahn, “Analysis of infrared wireless links employing multi-beam transmitters and imaging diversity receivers,” IEEE Trans. Commun. 48(12), 2077–2088 (2000).
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002).
[CrossRef]

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun. 51(8), 1233–1239 (2003).
[CrossRef]

IEEE Trans. on Consum. Electron. (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consum. Electron. 50, 100–107 (2004).

J. Commun. (1)

M. S. Awan, L. C. Horwath, S. S. Muhammad, E. Leitgeb, F. Nadeem, and M. S. Khan, “Characterization of fog and snow attenuations for free-space optical propagation,” J. Commun. 4, 533–545 (2009).

J. Lightwave Technol. (1)

Proc, SPIE (1)

Z. Hajjarian and M. Kavehrad, “Using MIMO transmissions in free space optical communications in presence of clouds and turbulence,” Proc, SPIE 7199, 1–12 (2009).

Proc. IEEE (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[CrossRef]

Sol. Energy (1)

R. E. Bird, R. L. Hulstrom, and L. J. Lewis, “Terrestrial solar spectral data sets,” Sol. Energy 30(6), 563–573 (1983).
[CrossRef]

Other (13)

N. Araki and H. Yashima, “A channel model of optical wireless communications during rainfall,” in Proceedings of 2nd International Symposium on Wireless Communication Systems (2005), pp. 205–209.

A. A. Kokhanovsky, Cloud Optics (Springer, 2006).

W. Popoola, Z. Ghassemlooy, M. S. Awan, and E. Leitgeb, “Atmospheric channel effects on terrestrial free-space optical communication links,” in Proceedings of 3rd International Conference on Electronics, Computers and Artificial Intelligence (2009), pp. 17–23.

D. C. O'Brien, L. Zeng, H. Le-Minh, G. Faulkner, J. W. Walewski, and S. Randel, “Visible light communication: challenges and possibilities,” in Proceedings of IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE, 2008), pp. 1–5.

A. A. Farid and S. Hranilovic, “Outage probability for free-space optical systems over slow fading channels with Pointing Errors,” in Proceedings of 19th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE LEOS, 2006), pp. 82–83.

S. Antyufeev, “Monte Carlo method for solving inverse problems of radiative transfer,” in Inverse and Ill-Posed Problem Series (VSP Publishers, 2000).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

W. E. K. Middleton, Vision through the Atmosphere (University of Toronto Press, Toronto, 1968).

S. G. Narasimhan and S. K. Nayar, “Shedding light on the weather,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2003), pp. 665–672.

S. Metari and F. Deschnes, “A new convolutional kernel for atmospheric point spread function applied to computer vision,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2003), pp. 1–8.

A. P. Tang, J. M. Kahn, and K. P. Ho, “Wireless infrared communication links using multi-beam transmitters and imaging receivers,” in Proceedings of IEEE International Conference on Communications (IEEE, 1996), pp. 180–186.

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Figures (7)

Fig. 1
Fig. 1

As a result of the multiple scattering of light in the atmosphere, the image of a point source spreads out into a spot known as the atmospheric point spread function. When the distance between the transmitter and receiver is much larger than the focal length of the receiver lens, we can assume that multiple scattering only happens within a sphere around the source that fits into the FOV of the receiver (region of significant multiple scattering), and that the effect of propagation through the rest of the atmosphere is merely attenuation.

Fig. 2
Fig. 2

The phase function P(cosα) is the ratio of the intensity of light scattered at an angleα to the intensity of the incident light.

Fig. 3
Fig. 3

Cross section of the APSF for (a) a thin atmosphere (T = 1.2) and (b) a thick atmosphere (T = 4.1). In a thick atmosphere, where the density of scatterers is high, the FWHM of the ASPF is almost independent of the value of the forward scattering parameterq. By contrast, in a thin atmosphere, where the density of the scatterers is low, the FWHM of the APSF is larger for smaller values of q.

Fig. 4
Fig. 4

Geometry of an FSO link.

Fig. 5
Fig. 5

SNR losses caused by image blooming and attenuation under different weather conditions (clear air to heavy rain) for receivers employing different numbers of pixels when the distance between the transmitter and receiver is (a) 8 m and (b) 50 m. Image blooming loss exceeds attenuation loss, except under medium-to-heavy fog conditions.

Fig. 6
Fig. 6

SNR losses caused by image blooming and attenuation under three different weather conditions (haze, light fog and heavy fog) for an imaging receiver with 169 pixels, versus link distance. Image blooming loss exceeds attenuation loss except under heavy fog conditions at distances beyond 43 m.

Fig. 7
Fig. 7

Average SNR versus link distance in the presence of (a) thermal noise only or (b) thermal noise and ambient-light shot noise. The receiver employs 1, 25 or 169 pixels with MRC. Atmospheric conditions include no fog, light fog or heavy fog. For each curve shown, the SNR represents an average over 100 different transmitter locations within the receiver FOV. The horizontal line indicates the minimum SNR required to achieve a BER<10−5.

Equations (31)

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P( cosα )=P( θ,φ; θ , φ )= I( θ,φ ) I( θ , φ ) ,
cosα=μ μ + (1 μ 2 )(1 μ 2 ) cos(φ φ ),
dI σds =IF,
σ= 3.912 V (m 1 ).
F(θ,φ)= 1 4π 0 2π 0 π P(cosα)I( θ , φ )d θ d φ .
dR=cosθds      and         Rdθ=sinθds.
cosθ I R sinθ R I θ =σ[ I(R,θ)F(R,θ) ].
μ I T + 1 μ 2 T I μ =I(T,μ)+ 1 4π 0 2π 1 1 P(cosα)I(T, μ )d μ d θ .
P(cosα)= 1 q 2 ( 1+ q 2 2qcosα ) 3/2 .
I(T,μ)= I 0 n=0 ( g n (T)+ g n+1 (T) ) L n (μ) ,
g 0 (T)=0 g n (T)=exp( β n T α n lnT ),n0 α n =n+1 β n = 2n+1 n ( 1 q n1 ).
APSF(x,y)=APSF(ρ)= I( T,μ(ρ) ) I 0 e T ( m 2 ),
μ(ρ)=cos( θ(ρ) ) θ(ρ)=φ+ψ= tan 1 ( ρ f )+ sin 1 ( h R ) h= b b 2 ac a a= ρ 2 + f 2 b=dfρ c=( d 2 R 2 ) ρ 2 R=dsin( FOV 2 ).
P rec =I(φ,d) T F (ψ) T L (ψ)Acosψ,
A=π ( f 2 N f ) 2 .
I(φ,d)= P Tx (n+1) 2π d 2 cos n φ( W/m 2 ),
I rec (x,y)=L(S, P rec ,f,d,ψ,θ,φ) (W/m 2 ),
I rec,fog (x,y)= I rec (x,y)APSF(x,y),
P rec,i = s i (x,y) I rec,fog (x,y)dxdy i=1,2,,N,
s i (x,y)={ 1, if(x,y)intheinteriorofthe i th pixel 0, otherwise
σ tot, i 2 = σ shot, i 2 + σ th, i 2 i=1,2,,N,
σ shot, i 2 =2er P b,i Δ f n ,
P b,i 4πA B sky Δλ T F ( ψ i ) T L ( ψ i )cos ψ i sin 2 ( Ψ a,i 2 ),
Ψ a,i =2 sin 1 ( 1 N sin( FOV 2 ) ),
FOV=2 tan 1 ( w 2f ),
σ th, i 2 = 4kT R F F n Δ f n ,
σ th, i 2 = 8πkT G η A d F n BΔ f n ,
SN R SB = max i ( r 2 P rec,i 2 σ tot,i 2 )= max i SNR i 1iN.
SN R MRC = ( i=1 N ω i r P rec,i ) 2 i=1 N ω i 2 σ tot,i 2 = i=1 N r 2 P rec,i 2 σ tot,i 2 = i=1 N SN R i .
δ att =20 log 10 ( P fog P air )(dB),
δ bloom =10 log 10 ( SN R MRC, fog SN R MRC, air ) =10 log 10 ( N eff, air N eff, fog )(dB).

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