Abstract

Free-space optical (or optical wireless) communications represent an attractive technology for the realization of high-bandwidth wireless communications. However, for propagation through the atmosphere the characteristics of the optical signal are different from those of the signals from, e.g., fiber channels or radio-frequency wireless channels, and therefore the error characteristics on these links are also different. For evaluating fading mitigation techniques for optical wireless communications a channel model is needed that can be easily used by protocol designers. Existing channel models for optical wireless communications are based on atmospheric propagation theory and therefore require a deep physical understanding of the optical propagation through the atmosphere. The goal of this publication is to develop a simplified approach for modeling the received power dynamics of the atmospheric free-space optical channel. The proposed model consists of a random number generator and a low-pass filter and is therefore easy to implement and use. This approach is only valid for systems utilizing intensity modulation with direct detection, but this limitation is acceptable since most commercially available systems use this modulation format. The channel model is developed based on the statistics of received power measurements from a maritime-mobile link, a land-mobile link, and a satellite downlink.

© 2010 Optical Society of America

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  1. J. Horwath, M. Knapek, B. Epple, M. Brechtelsbauer, B. Wilkerson, “Broadband backhaul communication for stratospheric platforms: the stratospheric optical payload experiment (STROPEX),” Proc. SPIE, vol. 6304, paper 63041N, 2006.
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  3. D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.
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2008 (1)

H. Henniger, B. Epple, S. D. Milner, C. C. Davis, “Coding techniques to mitigate fading on free-space optical communication links,” Proc. SPIE, vol. 7091, paper 70910C, Aug. 2008.
[CrossRef]

2007 (3)

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

S. Jachner, K. G. v. d. Boogaart, T. Petzoldt, “Statistical methods for the qualitative assessment of dynamic models with time delay (R package qualV),” J. Stat. Software, vol. 22, no. 8, pp. 1–30, 2007.

F. Strömqvist Vetelino, C. Young, L. C. Andrews, “Fade statistics and aperture averaging for Gaussian beam waves in moderate-to-strong turbulence,” Appl. Opt., vol. 46, no. 18, p. 3780, June 2007.
[CrossRef]

2006 (1)

J. Horwath, M. Knapek, B. Epple, M. Brechtelsbauer, B. Wilkerson, “Broadband backhaul communication for stratospheric platforms: the stratospheric optical payload experiment (STROPEX),” Proc. SPIE, vol. 6304, paper 63041N, 2006.
[CrossRef]

2004 (2)

N. Perlot, D. Fritzsche, “Aperture-averaging—theory and measurements,” Proc. SPIE, vol. 5338, pp. 233–242, June 2004.
[CrossRef]

F. David, “Scintillation loss in free-space optic IM/DD systems,” Proc. SPIE, vol. 5338, pp. 66–75, Jan. 2004.

2003 (1)

R. Purvinskis, D. Giggenbach, H. Henniger, N. Perlot, F. David, “Multiple-wavelength free-space laser communications,” Proc. SPIE, vol. 4975, pp. 12–19, 2003.
[CrossRef]

2002 (1)

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, Aug. 2002.
[CrossRef]

2001 (1)

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol. 40, no. 8, pp. 1554–1562, Aug. 2001.
[CrossRef]

1992 (1)

1991 (1)

1981 (2)

L. C. Andrews, R. L. Phillips, “Measured statistics of laser-light scattering in atmospheric turbulence,” J. Opt. Soc. Am., vol. 71, no. 12, pp. 1440–1445, 1981.
[CrossRef]

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” J. Mod. Opt., vol. 28, no. 5, pp. 715–728, May 1981.
[CrossRef]

1968 (1)

U. G. Gujar, R. J. Kavanagh, “Generation of random signals with specified probability density functions and power density spectra,” IEEE Trans. Autom. Control, vol. 13, no. 6, pp. 716–719, Dec. 1968.
[CrossRef]

Abelson, D.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Airola, M. B.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol. 40, no. 8, pp. 1554–1562, Aug. 2001.
[CrossRef]

Amirfeiz, M.

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Andrews, L. C.

F. Strömqvist Vetelino, C. Young, L. C. Andrews, “Fade statistics and aperture averaging for Gaussian beam waves in moderate-to-strong turbulence,” Appl. Opt., vol. 46, no. 18, p. 3780, June 2007.
[CrossRef]

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol. 40, no. 8, pp. 1554–1562, Aug. 2001.
[CrossRef]

L. C. Andrews, “Aperture-averaging factor for optical scintillations of plane and spherical waves in the atmosphere,” J. Opt. Soc. Am. A, vol. 9, no. 4, pp. 597–600, 1992.
[CrossRef]

L. C. Andrews, R. L. Phillips, “Measured statistics of laser-light scattering in atmospheric turbulence,” J. Opt. Soc. Am., vol. 71, no. 12, pp. 1440–1445, 1981.
[CrossRef]

L. C. Andrews, R. L. Phillips, Mathematical Techniques for Engineers and Scientists, SPIE Press Monograph Series. Bellingham, WA: SPIE Press, 2003, vol. PM118.
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed., SPIE Press Monograph Series. Bellingham, WA: SPIE Optical Engineering Press, 2005, vol. PM152.
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation With Applications, SPIE Press Monograph Series. Bellingham, WA: SPIE Optical Engineering Press, 2001, vol. PM99.
[CrossRef]

Biswas, A.

A. Biswas, S. Lee, “Ground-to-ground optical communications demonstration,” Jet Propulsion Laboratory, Pasadena, CA, Telecommunications and Mission Operations Progress Rep. 42-141, May 2000.

Boogaart, K. G. v. d.

S. Jachner, K. G. v. d. Boogaart, T. Petzoldt, “Statistical methods for the qualitative assessment of dynamic models with time delay (R package qualV),” J. Stat. Software, vol. 22, no. 8, pp. 1–30, 2007.

Brechtelsbauer, M.

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

J. Horwath, M. Knapek, B. Epple, M. Brechtelsbauer, B. Wilkerson, “Broadband backhaul communication for stratospheric platforms: the stratospheric optical payload experiment (STROPEX),” Proc. SPIE, vol. 6304, paper 63041N, 2006.
[CrossRef]

Churnside, J. H.

David, F.

F. David, “Scintillation loss in free-space optic IM/DD systems,” Proc. SPIE, vol. 5338, pp. 66–75, Jan. 2004.

R. Purvinskis, D. Giggenbach, H. Henniger, N. Perlot, F. David, “Multiple-wavelength free-space laser communications,” Proc. SPIE, vol. 4975, pp. 12–19, 2003.
[CrossRef]

Davis, C. C.

H. Henniger, B. Epple, S. D. Milner, C. C. Davis, “Coding techniques to mitigate fading on free-space optical communication links,” Proc. SPIE, vol. 7091, paper 70910C, Aug. 2008.
[CrossRef]

Di Nepi, G.

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Driver, D.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Epple, B.

H. Henniger, B. Epple, S. D. Milner, C. C. Davis, “Coding techniques to mitigate fading on free-space optical communication links,” Proc. SPIE, vol. 7091, paper 70910C, Aug. 2008.
[CrossRef]

J. Horwath, M. Knapek, B. Epple, M. Brechtelsbauer, B. Wilkerson, “Broadband backhaul communication for stratospheric platforms: the stratospheric optical payload experiment (STROPEX),” Proc. SPIE, vol. 6304, paper 63041N, 2006.
[CrossRef]

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Foshee, J.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Fritzsche, D.

N. Perlot, D. Fritzsche, “Aperture-averaging—theory and measurements,” Proc. SPIE, vol. 5338, pp. 233–242, June 2004.
[CrossRef]

Fuchs, C.

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Giggenbach, D.

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

R. Purvinskis, D. Giggenbach, H. Henniger, N. Perlot, F. David, “Multiple-wavelength free-space laser communications,” Proc. SPIE, vol. 4975, pp. 12–19, 2003.
[CrossRef]

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Gujar, U. G.

U. G. Gujar, R. J. Kavanagh, “Generation of random signals with specified probability density functions and power density spectra,” IEEE Trans. Autom. Control, vol. 13, no. 6, pp. 716–719, Dec. 1968.
[CrossRef]

Henniger, H.

H. Henniger, B. Epple, S. D. Milner, C. C. Davis, “Coding techniques to mitigate fading on free-space optical communication links,” Proc. SPIE, vol. 7091, paper 70910C, Aug. 2008.
[CrossRef]

R. Purvinskis, D. Giggenbach, H. Henniger, N. Perlot, F. David, “Multiple-wavelength free-space laser communications,” Proc. SPIE, vol. 4975, pp. 12–19, 2003.
[CrossRef]

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation With Applications, SPIE Press Monograph Series. Bellingham, WA: SPIE Optical Engineering Press, 2001, vol. PM99.
[CrossRef]

Horwath, J.

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

J. Horwath, M. Knapek, B. Epple, M. Brechtelsbauer, B. Wilkerson, “Broadband backhaul communication for stratospheric platforms: the stratospheric optical payload experiment (STROPEX),” Proc. SPIE, vol. 6304, paper 63041N, 2006.
[CrossRef]

Hurt, H.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Ishimaru, A.

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

Jachner, S.

S. Jachner, K. G. v. d. Boogaart, T. Petzoldt, “Statistical methods for the qualitative assessment of dynamic models with time delay (R package qualV),” J. Stat. Software, vol. 22, no. 8, pp. 1–30, 2007.

Jentile, M.

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Jono, T.

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

T. Jono, Y. Takayama, N. Perlot, Report on DLR-JAXA Joint Experiment—The Kirari Optical Downlink to Ober pfaffenhofen (KIODO). Japan Aerospace Exploration Agency, April 2007.

Juarez, J. C.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Kahn, J. M.

X. Zhu, J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, no. 8, pp. 1293–1300, Aug. 2002.
[CrossRef]

Kavanagh, R. J.

U. G. Gujar, R. J. Kavanagh, “Generation of random signals with specified probability density functions and power density spectra,” IEEE Trans. Autom. Control, vol. 13, no. 6, pp. 716–719, Dec. 1968.
[CrossRef]

Knapek, M.

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

J. Horwath, M. Knapek, B. Epple, M. Brechtelsbauer, B. Wilkerson, “Broadband backhaul communication for stratospheric platforms: the stratospheric optical payload experiment (STROPEX),” Proc. SPIE, vol. 6304, paper 63041N, 2006.
[CrossRef]

Lee, S.

A. Biswas, S. Lee, “Ground-to-ground optical communications demonstration,” Jet Propulsion Laboratory, Pasadena, CA, Telecommunications and Mission Operations Progress Rep. 42-141, May 2000.

Martini, G.

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

Mazzi, F.

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

McClaren, A.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Milner, S. D.

H. Henniger, B. Epple, S. D. Milner, C. C. Davis, “Coding techniques to mitigate fading on free-space optical communication links,” Proc. SPIE, vol. 7091, paper 70910C, Aug. 2008.
[CrossRef]

Northcott, M.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Papoulis, A.

A. Papoulis, S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed.McGraw-Hill, 2002.

Parry, G.

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” J. Mod. Opt., vol. 28, no. 5, pp. 715–728, May 1981.
[CrossRef]

Perlot, N.

N. Perlot, M. Knapek, D. Giggenbach, J. Horwath, M. Brechtelsbauer, Y. Takayama, T. Jono, “Results of the optical downlink experiment KIODO from OICETS satellite to optical ground station Oberpfaffenhofen (OGS-OP),” Proc. SPIE, vol. 6457, paper 645704, Mar. 2007.
[CrossRef]

N. Perlot, D. Fritzsche, “Aperture-averaging—theory and measurements,” Proc. SPIE, vol. 5338, pp. 233–242, June 2004.
[CrossRef]

R. Purvinskis, D. Giggenbach, H. Henniger, N. Perlot, F. David, “Multiple-wavelength free-space laser communications,” Proc. SPIE, vol. 4975, pp. 12–19, 2003.
[CrossRef]

T. Jono, Y. Takayama, N. Perlot, Report on DLR-JAXA Joint Experiment—The Kirari Optical Downlink to Ober pfaffenhofen (KIODO). Japan Aerospace Exploration Agency, April 2007.

Petzoldt, T.

S. Jachner, K. G. v. d. Boogaart, T. Petzoldt, “Statistical methods for the qualitative assessment of dynamic models with time delay (R package qualV),” J. Stat. Software, vol. 22, no. 8, pp. 1–30, 2007.

Phillips, J.

D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol. 40, no. 8, pp. 1554–1562, Aug. 2001.
[CrossRef]

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Appl. Opt. (2)

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IEEE Trans. Commun. (1)

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Opt. Eng. (1)

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[CrossRef]

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N. Perlot, D. Fritzsche, “Aperture-averaging—theory and measurements,” Proc. SPIE, vol. 5338, pp. 233–242, June 2004.
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[CrossRef]

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D. W. Young, J. E. Sluz, J. C. Juarez, M. B. Airola, R. M. Sova, H. Hurt, M. Northcott, J. Phillips, A. McClaren, D. Driver, D. Abelson, J. Foshee, “Demonstration of high data rate wavelength division multiplexed transmission over a 150 km free space optical link,” in IEEE Military Communications Conference, 2007. MILCOM 2007, Oct. 2007, pp. 1–6.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation With Applications, SPIE Press Monograph Series. Bellingham, WA: SPIE Optical Engineering Press, 2001, vol. PM99.
[CrossRef]

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[CrossRef]

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[CrossRef]

C. Fuchs, H. Henniger, B. Epple, D. Giggenbach, M. Amirfeiz, M. Jentile, G. Di Nepi, F. Mazzi, G. Martini, “Broadband communications for aeronautical networks: the ATENAA outer optical link validation,” in Proc. of 1st CEAS European Air and Space Conf., Sept. 2007.

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Figures (4)

Fig. 1
Fig. 1

Exemplary plots for the fitting quality of the three distributions. Top left, ATENAA; top right, KIODO 40 cm; bottom left, KIODO 5 cm; bottom right, LCT-Marine. The lower tail ( P R x < = 1 ) of the CDF is plotted on a semilogarithmic scale for making the small fitting errors in this region visible. This region is of major interest for simulating the fading behavior of the received power.

Fig. 2
Fig. 2

Exemplary comparison of a measured PSD, the PSD according to theory (Tatarskii), and first-order (Bessel 1) and second-order Bessel filters (Bessel 2). This plot is taken from a LCT-Marine measurement.

Fig. 3
Fig. 3

Schematic drawing of the proposed algorithm for generating time series of received power.

Fig. 4
Fig. 4

Fade duration occurrence and exceedance probability plots. These are exemplary plots from all four scenarios to illustrate the achieved accuracy. Top left, ATENAA; top right, KIODO 40 cm; bottom left, KIODO 5 cm; bottom right, LCT-Marine.

Tables (4)

Tables Icon

Table 1 Evaluation of the Overall Fitting Quality of the Three Distributions a

Tables Icon

Table 2 Best-Fit Results Grouped by Measurement Campaign and Estimated Turbulence Regime a

Tables Icon

Table 3 Sets of Digital Filters Fitting the Analyzed Measurements

Tables Icon

Table 4 Derived Receiver Model Parameters for Selected Optical Receivers

Equations (29)

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σ P 2 = P R x 2 P R x 2 1 ,
PDF : f LN ( P R x ; μ , σ 2 ) = 1 P R x 2 π σ 2 e [ ln ( P R x ) μ ] 2 2 σ 2 ,
CDF : F LN ( P R x ; μ , σ 2 ) = 1 2 + 1 2 erf [ ln ( P R x ) μ 2 σ 2 ] ,
σ 2 = ln ( σ P 2 + 1 ) ,
μ = ln ( P R x ) σ 2 2 P R x = 1 σ 2 2 .
PDF : f G ( P R x ; k , θ ) = P R x k 1 e P R x θ 1 θ k Γ ( k ) ,
CDF : F G ( P R x ; k , θ ) = γ ( k , P R x θ ) Γ ( k ) ,
θ = σ P 2 ,
k = 1 σ P 2 .
PDF : f G G ( P R x ; α , β ) = 2 ( α β ) α + β 2 Γ ( α ) Γ ( β ) P R x α + β 2 1 K α β ( 2 α β P R x ) ,
σ P 2 = 1 α + 1 β + 1 α β .
β = r α , 0 r 1 ,
σ P 2 = 1 α + 1 r α + 1 r α 2 .
A AF = σ P 2 σ I 2 .
e = F M ( P R x ) F ( P R x ) ,
e rms = e 2 ,
e abs = max ( | e | ) ,
e rel = e F ( P R x ) .
f t = V L k ,
PDF : f N ( x ; μ , σ 2 ) = 1 2 π σ 2 e ( x μ ) 2 2 σ 2 ,
CDF : F N ( x ; μ , σ 2 ) = 1 2 + 1 2 erf ( x μ 2 σ 2 ) ,
P ( d F > D ) = N ( d F | d F > D ) N ( d F ) ,
F ( d F > D ) = i ( d F , i | d F , i > D ) i d F , i .
P ( P R x < P T ) = i d F , i D tot ,
BEP ( P R x ) = 1 2 erfc [ Q ( P R x ) 2 ]
Q ( P R x ) = P R x P 0 1 + 1 + ξ P R x P 0 .
Q ( BEP ) = 2 × erfc 1 ( 2 BEP ) ,
P R x = [ ξ Q ( BEP ) 2 + 2 Q ( BEP ) ] P 0 .
PLP ( P R x , n P ) = 1 [ 1 BEP ( P R x ) ] n P ,