Abstract

By means of numerical simulations we analyze the statistical properties of the power fluctuations induced by the incoherent superposition of multiple transmitted laser beams in a terrestrial free-space optical communication link. The measured signals arising from different transmitted optical beams are found to be statistically correlated. This channel correlation increases with receiver aperture and propagation distance. We find a simple scaling rule for the spatial correlation coefficient in terms of the propagation distance and we are able to predict the scintillation reduction in previously reported experiments with good accuracy. We propose an approximation to the probability density function of the received power of a spatially correlated multiple-beam system in terms of the parameters of the single-channel gamma–gamma function. A bit-error-rate evaluation is also presented to demonstrate the improvement of a multibeam system over its single-beam counterpart.

© 2007 Optical Society of America

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References

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  1. S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).
  2. J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Netw. 4, 586-601 (2005).
    [CrossRef]
  3. J. H. Churnside, "Aperture averaging of optical scintillations in the turbulent atmosphere," Appl. Opt. 30, 1982-1994 (1991).
    [CrossRef] [PubMed]
  4. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
    [CrossRef]
  5. J. C. Ricklin and F. M. Davidson, "Atmospheric optical communication with a Gaussian Schell beam," J. Opt. Soc. Am. A 20, 856-866 (2003).
    [CrossRef]
  6. O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43, 330-341 (2004).
    [CrossRef]
  7. A. Belmonte, A. Comeron, J. A. Rubio, J. Bara, and E. Fernandez, "Atmospheric-turbulence-induced power-fade statistics for a multiaperture optical receiver," Appl. Opt. 36, 8632-8638 (1997).
    [CrossRef]
  8. X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
    [CrossRef]
  9. V. Vilnrotter, C.-W. Lau, M. Srinivasan, K. Andrews, and R. Mukai, "Optical array receiver for communication through atmospheric turbulence," J. Lightwave Technol. 23, 1664-1675 (2005).
    [CrossRef]
  10. M. Razavi and J. H. Shapiro, "Wireless optical communications via diversity reception and optical amplification," IEEE Trans. Wireless Commun. 4, 975-983 (2005).
    [CrossRef]
  11. S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
    [CrossRef]
  12. S. M. Navidpour, M. Uysal, and J. Li, "BER performance of MIMO free-space optical links," in Proceedings of IEEE Conference on Vehicular Technology (IEEE 2004), p. 3378.
  13. M. K. Simon and V. A. Vilnrotter, "Alamouti-type space-time coding for free-space optical communication with direct detection," IEEE Trans. Wireless Comm. 4, 35-39 (2005).
    [CrossRef]
  14. L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
    [CrossRef]
  15. H. Yuksel, S. Milner, and C. Davis, "Aperture averaging for optimizing receiver design and system performance on free-space optical communication links," J. Opt. Netw. 4, 462-475 (2005).
    [CrossRef]
  16. A. Biswas and M. W. Wright, "Mountain-top-to-mountain-top optical link demonstration: part I," IPN Progress Report 42-149 (Jet Propulsion Laboratory, 2002).
  17. P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
    [CrossRef]
  18. I. Kim, P. Adhikari, E. Korevaar, and A. Majumdar, "Scintillation reduction using multiple transmitters," Proc. SPIE 2990, 102-113 (1997).
    [CrossRef]
  19. C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
    [CrossRef]
  20. H. Willebrand, "Multibeam-multipath terrestrial lasercom terminal," Proc. SPIE 3532, 16-21 (1999).
    [CrossRef]
  21. A. Belmonte, "Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance," Appl. Opt. 39, 5426-5445 (2000).
    [CrossRef]
  22. L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
    [CrossRef]
  23. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  24. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
    [CrossRef]
  25. A. Tiker, N. Yarkoni, N. Blaunstein, A. Zilberman, and N. Kopeika, "Prediction of data stream parameters in atmospheric turbulent wireless communication links," Appl. Opt. 46, 190-199 (2007).
    [CrossRef] [PubMed]
  26. N. Perlot, "Evaluation of the scintillation loss for optical communications systems with direct detection," SPIE Opt. Eng. 46, 025003 (2007).
  27. J. C. Dainty, M. J. Northcott, and D.-N. Qu, "Measurements of the temporal correlation of images at La Palma," J. Mod. Opt. 37, 1247-1254 (1990).
    [CrossRef]
  28. R. J. McEliece and W. E. Stark, "Channels with Block Interference," IEEE Trans. Inf. Theory 30, 44-53 (1984).
    [CrossRef]

2007 (2)

A. Tiker, N. Yarkoni, N. Blaunstein, A. Zilberman, and N. Kopeika, "Prediction of data stream parameters in atmospheric turbulent wireless communication links," Appl. Opt. 46, 190-199 (2007).
[CrossRef] [PubMed]

N. Perlot, "Evaluation of the scintillation loss for optical communications systems with direct detection," SPIE Opt. Eng. 46, 025003 (2007).

2005 (6)

M. K. Simon and V. A. Vilnrotter, "Alamouti-type space-time coding for free-space optical communication with direct detection," IEEE Trans. Wireless Comm. 4, 35-39 (2005).
[CrossRef]

J. A. Anguita, I. B. Djordjevic, M. A. Neifeld, and B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels," J. Opt. Netw. 4, 586-601 (2005).
[CrossRef]

V. Vilnrotter, C.-W. Lau, M. Srinivasan, K. Andrews, and R. Mukai, "Optical array receiver for communication through atmospheric turbulence," J. Lightwave Technol. 23, 1664-1675 (2005).
[CrossRef]

M. Razavi and J. H. Shapiro, "Wireless optical communications via diversity reception and optical amplification," IEEE Trans. Wireless Commun. 4, 975-983 (2005).
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
[CrossRef]

H. Yuksel, S. Milner, and C. Davis, "Aperture averaging for optimizing receiver design and system performance on free-space optical communication links," J. Opt. Netw. 4, 462-475 (2005).
[CrossRef]

2004 (2)

S. M. Navidpour, M. Uysal, and J. Li, "BER performance of MIMO free-space optical links," in Proceedings of IEEE Conference on Vehicular Technology (IEEE 2004), p. 3378.

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43, 330-341 (2004).
[CrossRef]

2003 (1)

2002 (2)

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

A. Biswas and M. W. Wright, "Mountain-top-to-mountain-top optical link demonstration: part I," IPN Progress Report 42-149 (Jet Propulsion Laboratory, 2002).

2001 (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

2000 (2)

A. Belmonte, "Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance," Appl. Opt. 39, 5426-5445 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

1999 (3)

P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

H. Willebrand, "Multibeam-multipath terrestrial lasercom terminal," Proc. SPIE 3532, 16-21 (1999).
[CrossRef]

1998 (1)

C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
[CrossRef]

1997 (2)

1996 (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

1992 (1)

L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
[CrossRef]

1991 (1)

1990 (1)

J. C. Dainty, M. J. Northcott, and D.-N. Qu, "Measurements of the temporal correlation of images at La Palma," J. Mod. Opt. 37, 1247-1254 (1990).
[CrossRef]

1988 (1)

S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).

1984 (1)

R. J. McEliece and W. E. Stark, "Channels with Block Interference," IEEE Trans. Inf. Theory 30, 44-53 (1984).
[CrossRef]

Adhikari, P.

I. Kim, P. Adhikari, E. Korevaar, and A. Majumdar, "Scintillation reduction using multiple transmitters," Proc. SPIE 2990, 102-113 (1997).
[CrossRef]

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

Andrews, K.

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43, 330-341 (2004).
[CrossRef]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
[CrossRef]

Anguita, J. A.

Baedke, M.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
[CrossRef]

Bara, J.

Barclay, H.

C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
[CrossRef]

Belmonte, A.

Biliman, K.

C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
[CrossRef]

Biswas, A.

A. Biswas and M. W. Wright, "Mountain-top-to-mountain-top optical link demonstration: part I," IPN Progress Report 42-149 (Jet Propulsion Laboratory, 2002).

Blaunstein, N.

Brandt-Pearce, M.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
[CrossRef]

Cao, Q.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
[CrossRef]

Churnside, J. H.

Comeron, A.

Cusumano, S.

C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
[CrossRef]

Dainty, J. C.

J. C. Dainty, M. J. Northcott, and D.-N. Qu, "Measurements of the temporal correlation of images at La Palma," J. Mod. Opt. 37, 1247-1254 (1990).
[CrossRef]

Davidson, F. M.

Davis, C.

De La Rue, I. A.

P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
[CrossRef]

Djordjevic, I. B.

Fernandez, E.

Fugatea, R. Q.

P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
[CrossRef]

Gagliardi, R.

S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Higgs, C.

C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
[CrossRef]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

Kahn, J. M.

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

Karp, S.

S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).

Kim, I.

I. Kim, P. Adhikari, E. Korevaar, and A. Majumdar, "Scintillation reduction using multiple transmitters," Proc. SPIE 2990, 102-113 (1997).
[CrossRef]

Kopeika, N.

Korevaar, E.

I. Kim, P. Adhikari, E. Korevaar, and A. Majumdar, "Scintillation reduction using multiple transmitters," Proc. SPIE 2990, 102-113 (1997).
[CrossRef]

Korotkova, O.

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43, 330-341 (2004).
[CrossRef]

Lau, C.-W.

Li, J.

S. M. Navidpour, M. Uysal, and J. Li, "BER performance of MIMO free-space optical links," in Proceedings of IEEE Conference on Vehicular Technology (IEEE 2004), p. 3378.

Lowrey, W. H.

P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
[CrossRef]

Majumdar, A.

I. Kim, P. Adhikari, E. Korevaar, and A. Majumdar, "Scintillation reduction using multiple transmitters," Proc. SPIE 2990, 102-113 (1997).
[CrossRef]

McEliece, R. J.

R. J. McEliece and W. E. Stark, "Channels with Block Interference," IEEE Trans. Inf. Theory 30, 44-53 (1984).
[CrossRef]

Milner, S.

Moran, S. E.

S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).

Mukai, R.

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and J. Li, "BER performance of MIMO free-space optical links," in Proceedings of IEEE Conference on Vehicular Technology (IEEE 2004), p. 3378.

Neifeld, M. A.

Northcott, M. J.

J. C. Dainty, M. J. Northcott, and D.-N. Qu, "Measurements of the temporal correlation of images at La Palma," J. Mod. Opt. 37, 1247-1254 (1990).
[CrossRef]

Perlot, N.

N. Perlot, "Evaluation of the scintillation loss for optical communications systems with direct detection," SPIE Opt. Eng. 46, 025003 (2007).

Phillips, R. L.

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43, 330-341 (2004).
[CrossRef]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999).
[CrossRef]

Qu, D.-N.

J. C. Dainty, M. J. Northcott, and D.-N. Qu, "Measurements of the temporal correlation of images at La Palma," J. Mod. Opt. 37, 1247-1254 (1990).
[CrossRef]

Razavi, M.

M. Razavi and J. H. Shapiro, "Wireless optical communications via diversity reception and optical amplification," IEEE Trans. Wireless Commun. 4, 975-983 (2005).
[CrossRef]

Ricklin, J. C.

Rubio, J. A.

Ryan, P. T.

P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
[CrossRef]

Shapiro, J. H.

M. Razavi and J. H. Shapiro, "Wireless optical communications via diversity reception and optical amplification," IEEE Trans. Wireless Commun. 4, 975-983 (2005).
[CrossRef]

Simon, M. K.

M. K. Simon and V. A. Vilnrotter, "Alamouti-type space-time coding for free-space optical communication with direct detection," IEEE Trans. Wireless Comm. 4, 35-39 (2005).
[CrossRef]

Srinivasan, M.

Stark, W. E.

R. J. McEliece and W. E. Stark, "Channels with Block Interference," IEEE Trans. Inf. Theory 30, 44-53 (1984).
[CrossRef]

Stotts, L. B.

S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).

Tiker, A.

Uysal, M.

S. M. Navidpour, M. Uysal, and J. Li, "BER performance of MIMO free-space optical links," in Proceedings of IEEE Conference on Vehicular Technology (IEEE 2004), p. 3378.

Vasic, B. V.

Vilnrotter, V.

Vilnrotter, V. A.

M. K. Simon and V. A. Vilnrotter, "Alamouti-type space-time coding for free-space optical communication with direct detection," IEEE Trans. Wireless Comm. 4, 35-39 (2005).
[CrossRef]

Willebrand, H.

H. Willebrand, "Multibeam-multipath terrestrial lasercom terminal," Proc. SPIE 3532, 16-21 (1999).
[CrossRef]

Wilson, S. G.

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
[CrossRef]

Wright, M. W.

A. Biswas and M. W. Wright, "Mountain-top-to-mountain-top optical link demonstration: part I," IPN Progress Report 42-149 (Jet Propulsion Laboratory, 2002).

Yarkoni, N.

Yuksel, H.

Zhu, X.

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

Zilberman, A.

Appl. Opt. (4)

IEEE J. Sel. Areas Commun. (1)

S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, "Optical repetition MIMO transmission with multipulse PPM," IEEE J. Sel. Areas Commun. 23, 1901-1910 (2005).
[CrossRef]

IEEE Trans. Commun. (1)

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

IEEE Trans. Inf. Theory (1)

R. J. McEliece and W. E. Stark, "Channels with Block Interference," IEEE Trans. Inf. Theory 30, 44-53 (1984).
[CrossRef]

IEEE Trans. Wireless Comm. (1)

M. K. Simon and V. A. Vilnrotter, "Alamouti-type space-time coding for free-space optical communication with direct detection," IEEE Trans. Wireless Comm. 4, 35-39 (2005).
[CrossRef]

IEEE Trans. Wireless Commun. (1)

M. Razavi and J. H. Shapiro, "Wireless optical communications via diversity reception and optical amplification," IEEE Trans. Wireless Commun. 4, 975-983 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (2)

L. C. Andrews, "An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere," J. Mod. Opt. 39, 1849-1853 (1992).
[CrossRef]

J. C. Dainty, M. J. Northcott, and D.-N. Qu, "Measurements of the temporal correlation of images at La Palma," J. Mod. Opt. 37, 1247-1254 (1990).
[CrossRef]

J. Opt. Netw. (2)

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

O. Korotkova, L. C. Andrews, and R. L. Phillips, "Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom," Opt. Eng. 43, 330-341 (2004).
[CrossRef]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
[CrossRef]

Proc. SPIE (4)

P. T. Ryan, W. H. Lowrey, I. A. De La Rue, and R. Q. Fugatea, "Scintillation characterization for multiple beams," Proc. SPIE 3763, 210-217 (1999).
[CrossRef]

I. Kim, P. Adhikari, E. Korevaar, and A. Majumdar, "Scintillation reduction using multiple transmitters," Proc. SPIE 2990, 102-113 (1997).
[CrossRef]

C. Higgs, H. Barclay, S. Cusumano, and K. Biliman, "Active tracking using multibeam illumination," Proc. SPIE 3381, 160-167 (1998).
[CrossRef]

H. Willebrand, "Multibeam-multipath terrestrial lasercom terminal," Proc. SPIE 3532, 16-21 (1999).
[CrossRef]

SPIE Opt. Eng. (1)

N. Perlot, "Evaluation of the scintillation loss for optical communications systems with direct detection," SPIE Opt. Eng. 46, 025003 (2007).

Waves Random Media (1)

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, "Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum," Waves Random Media 10, 53-70 (2000).
[CrossRef]

Other (4)

S. Karp, R. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Plenum, 1988).

S. M. Navidpour, M. Uysal, and J. Li, "BER performance of MIMO free-space optical links," in Proceedings of IEEE Conference on Vehicular Technology (IEEE 2004), p. 3378.

A. Biswas and M. W. Wright, "Mountain-top-to-mountain-top optical link demonstration: part I," IPN Progress Report 42-149 (Jet Propulsion Laboratory, 2002).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (8)

Fig. 1
Fig. 1

(Color online) Diagram of a four-beam–single-receiver FSO link.

Fig. 2
Fig. 2

Example of a (a) collimated Gaussian beam with w 0 = 4   cm , (b) after 1 km propagating in turbulent air with C n 2 = 10 13 m 2 / 3 , and (c) the (zoomed-in) point-spread function at the focal plane of the collecting lens whose area is marked in (b).

Fig. 3
Fig. 3

(Color online) Average correlation coefficient between pairs of converging beams on a single receiver, with receiver aperture D = (a) 1, (b) 3, (c) 5, and (d) 7 cm.

Fig. 4
Fig. 4

(Color online) Average correlation coefficient versus receiver aperture diameter for C n 2 = (a) 2 × 10 15 m 2 / 3 , (b) 5 × 10 14 m 2 / 3 , (c) 2 × 10 13 m 2 / 3 , and (d) 8 × 10 13 m 2 / 3 .

Fig. 5
Fig. 5

(Color online) Average correlation coefficient among pairs of beams at 1, 2, 4, and 9   km with σ R 2 = 16 . Correlation estimates (dotted curves) for 2, 4, and 9   km are obtained by using the data from the 1   km curve and Eq. (7).

Fig. 6
Fig. 6

(Color online) (a) Scintillation versus σ R for five system configurations: (i) single-beam–point-receiver; (ii) single-beam, receiver aperture D = { 3 , 7 } cm and 50 μm detector; (iii) four beams, receiver aperture D = { 3 , 7 } cm and 50   μm detector. (b) Aperture averaging factor A D and total averaging factor A D F B versus receiver aperture D. For both (a) and (b), z = 1   km , w 0 = 2.2   cm , L 0 = 10   m , l 0 = 5   mm , and d = 15   cm .

Fig. 7
Fig. 7

(Color online) Histograms of intensity fluctuations and ΓΓ fit. The ΓΓ density curve for the four-beam case is predicted using the beam factor F B . (a) C n 2 = 5 × 10 14 m 2 / 3 , D = 3   mm , d = 5   cm . (b) C n 2 = 5 × 10 14 m 2 / 3 , D = 3   mm , d = 15   cm . (c) C n 2 = 2 × 10 13 m 2 / 3 , D = 1   cm , d = 5   cm . (d) C n 2 = 2 × 10 13 m 2 / 3 , D = 1   cm , d = 15   cm .

Fig. 8
Fig. 8

(Color online) Bit-error-rate comparison of a single-beam system and a four-beam system as a function of electrical SNR in decibels with channel conditions as given in Table 5.

Tables (5)

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Table 1 F B −1 at Beam Separation d = {5, 7.5, 10, 12.5} cm a

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Table 2 Prediction of F B −1 for the 46.8 km Eight-Beam Experiment a

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Table 3 Prediction of F B −1 for the 10.4 km 16-Beam Experiments a

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Table 4 Prediction of F B −1 for the 5.4 km Nine-Beam Experiment a

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Table 5 Parameters Used in the Monte Carlo Simulations to Determine BER

Equations (17)

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ϕ ( κ ) = 0.033 C n 2 ( κ 2 + 1 / L 0 2 ) 11 / 6 f ( κ , l 0 ) ,
f ( κ , l 0 ) = exp ( κ 2 / κ l 2 ) [ 1 + 1.802 ( κ / κ l ) 0.254 ( κ / κ l ) 7 / 6 ] ,
κ l = 3.3 / l 0 ,
h i = p R x ( i ) p T x ( i ) = u = u 0 u 1 v = v 0 v 1 I r ( i ) ( u , v ) u = u 0 u 1 v = v 0 v 1 I t ( i ) ( u , v ) .
r ^ i j = h i h j h i h j s i s j ,
σ R 2 = 1.23 C n 2 k 7 / 6 z 11 / 6 ,
d = d 0 z / z 0 ,
r = exp ( C d 0 ) ,
r = exp ( C d z / z 0 ) .
σ I 2 = ( p R x ( i ) p R x ( i ) ) 2 p R x ( i ) 2 = p R x 2 ( i ) p R x ( i ) 2 1 ,
σ I 2 = σ h 2 M ,
A D = σ I 2 ( D ) σ I 2 ( 0 ) , F B = σ I 4 2 ( D ) σ I 2 ( D ) ,
σ I M 2 = 1 M ( 1 + 2 M p P r p ) σ I 2 ,
F B 1 = M ( 1 + 2 M p P r p ) 1 ,
f ( I ) = 2 ( α β ) ( α + β ) / 2 Γ ( α ) Γ ( β ) I ( α + β ) / 2 1 K α β ( 2 α β I ) , I > 0 ,
α = F B 1 α 1 , β = F B 1 β 1 ,
y ( j ) = h ( j ) x ( j ) + n ( j ) ,

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