Abstract

Atmospheric turbulence can cause a significant performance degradation in free-space optical communication systems. It is well known that the effect of turbulence can be reduced by performing aperture averaging and/or employing spatial diversity at the receiver. In this paper, we provide a synthesis on the effectiveness of these techniques under different atmospheric turbulence conditions from a telecommunication point of view. In particular, we quantify the performance improvement in terms of average bit error rate (BER) and outage capacity, which are among important parameters in practice. The efficiency of channel coding and the feasibility of exploiting time diversity in aperture averaging receivers are discussed as well. We also compare single- and multiple-aperture systems from the point of view of fading reduction by considering uncorrelated fading on adjacent apertures for the latter case. We show that when the receiver is background noise limited, the use of multiple apertures is largely preferred to a single large aperture under strong turbulence conditions. A single aperture is likely to be preferred under moderate turbulence conditions, however. When the receiver is thermal noise limited, even under strong turbulence conditions, the use of multiple apertures is interesting only when working at a very low BER. We also provide discussions on several practical issues related to system implementation.

© 2009 Optical Society of America

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T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 951–957, Feb. 2009.
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F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express, vol. 17, no. 2, pp. 872–887, Jan. 2009.
[CrossRef] [PubMed]

2008 (1)

2007 (5)

2006 (3)

2005 (5)

H. Yuksel, S. Milner, C. C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Netw., vol. 4, no. 8, pp. 462–475, Aug. 2005.
[CrossRef]

M. Razavi, J. H. Shapiro, “Wireless optical communications via diversity reception and optical preamplification,” IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 975–983, May 2005.
[CrossRef]

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

L. M. Wasiczko, C. C. Davis, “Aperture averaging of optical scintillations in the atmosphere: experimental results,” Proc. SPIE, vol. 5793, pp. 197–208, 2005.
[CrossRef]

S. G. Wilson, M. B. Pearce, Q. L. Cao, M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. 1901–1910, Sept. 2005.
[CrossRef]

2004 (3)

D. Kedar, S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, no. 5, pp. 2–7, May 2004.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

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

2003 (1)

2002 (3)

M. A. Khalighi, K. Raoof, G. Jourdain, “Capacity of wireless communication systems employing antenna arrays, a tutorial study,” Wireless Personal Communications, vol. 23, no. 3, paper 321352, Dec. 2002.
[CrossRef]

C. C. Davis, I. I. Smolyaninov, “The effect of atmospheric turbulence on bit-error-rate in an on-off-keyed optical wireless system,” Proc. SPIE, vol. 4489, pp. 126–137, 2002.
[CrossRef]

X. Zhu, J. M. Kahn, “Pilot-symbol assisted modulation for correlated turbulent free-space optical channels,” Proc. SPIE, vol. 4489, pp. 138–145, 2002.
[CrossRef]

2001 (2)

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

C. Ruilier, F. Cassaing, “Coupling of large telescopes and single-mode waveguides: application to stellar interferometry,” J. Opt. Soc. Am. A, vol. 18, no. 1, pp. 143–149, Jan. 2001.
[CrossRef]

2000 (1)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum,” Waves Random Media, vol. 10, pp. 53–70, 2000.
[CrossRef]

1994 (1)

J. Salz, J. H. Winters, “Effect of fading correlation on adaptive arrays in digital mobile communication systems,” IEEE Trans. Veh. Technol., vol. 43, no. 4, pp. 1049–1057, Nov. 1994.
[CrossRef]

1993 (1)

1992 (1)

1991 (1)

1988 (1)

1983 (1)

1981 (1)

J. L. Massey, “Capacity, cutoff rate, and coding for a direct-detection optical channel,” IEEE Trans. Commun., vol. 29, no. 11, pp. 1651–1621, Nov. 1981.
[CrossRef]

1966 (1)

Aitamer, N.

M. A. Khalighi, N. Aitamer, N. Schwartz, S. Bourennane, “Turbulence mitigation by aperture averaging in wireless optical systems,” Proc. of ConTEL Conf., Zagreb, Croatia, 2008, pp. 59–66.

Al-Habash, M. A.

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

Andrews, L. C.

F. S. Vetelino, C. Young, L. C. Andrews, J. Recolons, “Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence,” Appl. Opt., vol. 46, no. 11, pp. 2099–2108, Apr. 2007.
[CrossRef] [PubMed]

F. S. 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, pp. 3780–3789, June 2007.
[CrossRef] [PubMed]

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

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

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum,” Waves Random Media, vol. 10, pp. 53–70, 2000.
[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, Apr. 1992.
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. Bellingham, Washington: SPIE Press, 2005.
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications. Bellingham, Washington: SPIE Press, 2001.
[CrossRef]

Anguita, J. A.

Arnon, S.

D. Bushuev, S. Arnon, “Analysis of the performance of a wireless optical multi-input to multi-output communication system,” J. Opt. Soc. Am. A, vol. 23, no. 7, pp. 1722–1730, July 2006.
[CrossRef]

D. Kedar, S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, no. 5, pp. 2–7, May 2004.
[CrossRef]

Baedke, M.

S. G. Wilson, M. B. Pearce, Q. L. Cao, M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. 1901–1910, Sept. 2005.
[CrossRef]

Bastin, G. L.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Batet, O.

Bloom, S.

Borbath, M. R.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Bourennane, S.

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express, vol. 17, no. 2, pp. 872–887, Jan. 2009.
[CrossRef] [PubMed]

M. A. Khalighi, N. Aitamer, N. Schwartz, S. Bourennane, “Turbulence mitigation by aperture averaging in wireless optical systems,” Proc. of ConTEL Conf., Zagreb, Croatia, 2008, pp. 59–66.

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Performance of coded time-diversity free-space optical links,” in Queen’s 24th Biennial Symp. on Communications (QSBC), Kingston, Canada, 2008, pp. 146–149.

Burdge, G. L.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Bushuev, D.

Cao, Q. L.

S. G. Wilson, M. B. Pearce, Q. L. Cao, M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. 1901–1910, Sept. 2005.
[CrossRef]

Cassaing, F.

Caussé, P.

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express, vol. 17, no. 2, pp. 872–887, Jan. 2009.
[CrossRef] [PubMed]

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Performance of coded time-diversity free-space optical links,” in Queen’s 24th Biennial Symp. on Communications (QSBC), Kingston, Canada, 2008, pp. 146–149.

Chan, V. W. S.

V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol., vol. 24, no. 12, pp. 4750–4762, Dec. 2006.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” IEEE Int. Conf. Communications, 2007, pp. 2485–2492.

Chin, P. G.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Churnside, J. H.

Cochetti, E.

Consortini, A.

Davis, C. C.

H. Yuksel, S. Milner, C. C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Netw., vol. 4, no. 8, pp. 462–475, Aug. 2005.
[CrossRef]

L. M. Wasiczko, C. C. Davis, “Aperture averaging of optical scintillations in the atmosphere: experimental results,” Proc. SPIE, vol. 5793, pp. 197–208, 2005.
[CrossRef]

C. C. Davis, I. I. Smolyaninov, “The effect of atmospheric turbulence on bit-error-rate in an on-off-keyed optical wireless system,” Proc. SPIE, vol. 4489, pp. 126–137, 2002.
[CrossRef]

Dios, F.

Faulkner, G. E.

D. C. O’Brien, S. Quasem, S. Zikic, G. E. Faulkner, “Multiple input multiple output systems for optical wireless: challenges and possibilities,” Proc. SPIE, vol. 6304, pp. 16-1–16-7, 2006.

Ferrell, B. A.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Flatté, S. M.

Fried, D. L.

Fritzsche, D.

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

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications, 2nd ed.Wiley, 1995.

Galus, D. J.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Harris, W. G.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Hemmati, H.

H. Hemmati, Deep Space Optical Communications. Wiley, 2006.
[CrossRef]

Hill, R. J.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum,” Waves Random Media, vol. 10, pp. 53–70, 2000.
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications. Bellingham, Washington: SPIE Press, 2001.
[CrossRef]

Hranilovic, S.

S. Hranilovic, Wireless Optical Communication Systems. Springer-Verlag, 2005.

Jourdain, G.

M. A. Khalighi, K. Raoof, G. Jourdain, “Capacity of wireless communication systems employing antenna arrays, a tutorial study,” Wireless Personal Communications, vol. 23, no. 3, paper 321352, Dec. 2002.
[CrossRef]

Kahn, J. M.

X. Zhu, J. M. Kahn, “Pilot-symbol assisted modulation for correlated turbulent free-space optical channels,” Proc. SPIE, vol. 4489, pp. 138–145, 2002.
[CrossRef]

Karagiannidis, G. K.

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 951–957, Feb. 2009.
[CrossRef]

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications, 2nd ed.Wiley, 1995.

Kavehrad, M.

S. M. Navidpour, M. Uysal, M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug. 2007.
[CrossRef]

Kedar, D.

D. Kedar, S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, no. 5, pp. 2–7, May 2004.
[CrossRef]

Khalighi, M. A.

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express, vol. 17, no. 2, pp. 872–887, Jan. 2009.
[CrossRef] [PubMed]

M. A. Khalighi, K. Raoof, G. Jourdain, “Capacity of wireless communication systems employing antenna arrays, a tutorial study,” Wireless Personal Communications, vol. 23, no. 3, paper 321352, Dec. 2002.
[CrossRef]

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Performance of coded time-diversity free-space optical links,” in Queen’s 24th Biennial Symp. on Communications (QSBC), Kingston, Canada, 2008, pp. 146–149.

M. A. Khalighi, N. Aitamer, N. Schwartz, S. Bourennane, “Turbulence mitigation by aperture averaging in wireless optical systems,” Proc. of ConTEL Conf., Zagreb, Croatia, 2008, pp. 59–66.

Klein, L.

Korevaar, E.

Lee, E. J.

E. J. Lee, V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” IEEE Int. Conf. Communications, 2007, pp. 2485–2492.

Majumdar, A. K.

A. K. Majumdar, J. C. Ricklin, Free-Space Laser Communications: Principles and Advances. Springer-Verlag, 2007.

Marín, J. A.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Martin, J. M.

Massey, J. L.

J. L. Massey, “Capacity, cutoff rate, and coding for a direct-detection optical channel,” IEEE Trans. Commun., vol. 29, no. 11, pp. 1651–1621, Nov. 1981.
[CrossRef]

McKinley, W. G.

Milner, S.

Moloney, J.

Navidpour, S. M.

S. M. Navidpour, M. Uysal, M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug. 2007.
[CrossRef]

Neifeld, M. A.

Nelson, R. A.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

O’Brien, D. C.

D. C. O’Brien, S. Quasem, S. Zikic, G. E. Faulkner, “Multiple input multiple output systems for optical wireless: challenges and possibilities,” Proc. SPIE, vol. 6304, pp. 16-1–16-7, 2006.

Pearce, M. B.

S. G. Wilson, M. B. Pearce, Q. L. Cao, M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. 1901–1910, Sept. 2005.
[CrossRef]

Peleg, A.

Perlot, N.

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

Pescatore, R.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Philips, R. L.

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

Phillips, R. L.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum,” Waves Random Media, vol. 10, pp. 53–70, 2000.
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. Bellingham, Washington: SPIE Press, 2005.
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications. Bellingham, Washington: SPIE Press, 2001.
[CrossRef]

Polynkin, P.

Quasem, S.

D. C. O’Brien, S. Quasem, S. Zikic, G. E. Faulkner, “Multiple input multiple output systems for optical wireless: challenges and possibilities,” Proc. SPIE, vol. 6304, pp. 16-1–16-7, 2006.

Raoof, K.

M. A. Khalighi, K. Raoof, G. Jourdain, “Capacity of wireless communication systems employing antenna arrays, a tutorial study,” Wireless Personal Communications, vol. 23, no. 3, paper 321352, Dec. 2002.
[CrossRef]

Razavi, M.

M. Razavi, J. H. Shapiro, “Wireless optical communications via diversity reception and optical preamplification,” IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 975–983, May 2005.
[CrossRef]

Recolons, J.

Rhoadarmer, T.

Ricklin, J. C.

A. K. Majumdar, J. C. Ricklin, Free-Space Laser Communications: Principles and Advances. Springer-Verlag, 2007.

Rodriguez, A.

Ruilier, C.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics. Wiley, 1991.
[CrossRef]

Salz, J.

J. Salz, J. H. Winters, “Effect of fading correlation on adaptive arrays in digital mobile communication systems,” IEEE Trans. Veh. Technol., vol. 43, no. 4, pp. 1049–1057, Nov. 1994.
[CrossRef]

Sandalidis, H. G.

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 951–957, Feb. 2009.
[CrossRef]

Schuster, J.

Schwartz, N.

M. A. Khalighi, N. Aitamer, N. Schwartz, S. Bourennane, “Turbulence mitigation by aperture averaging in wireless optical systems,” Proc. of ConTEL Conf., Zagreb, Croatia, 2008, pp. 59–66.

Shapiro, J. H.

M. Razavi, J. H. Shapiro, “Wireless optical communications via diversity reception and optical preamplification,” IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 975–983, May 2005.
[CrossRef]

Smolyaninov, I. I.

C. C. Davis, I. I. Smolyaninov, “The effect of atmospheric turbulence on bit-error-rate in an on-off-keyed optical wireless system,” Proc. SPIE, vol. 4489, pp. 126–137, 2002.
[CrossRef]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics. Wiley, 1991.
[CrossRef]

Tsiftsis, T. A.

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 951–957, Feb. 2009.
[CrossRef]

Uysal, M.

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 951–957, Feb. 2009.
[CrossRef]

S. M. Navidpour, M. Uysal, M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug. 2007.
[CrossRef]

Vasic, B. V.

Vetelino, F. S.

Wasiczko, L. M.

L. M. Wasiczko, C. C. Davis, “Aperture averaging of optical scintillations in the atmosphere: experimental results,” Proc. SPIE, vol. 5793, pp. 197–208, 2005.
[CrossRef]

Wayne, D.

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

Willebrand, H.

Wilson, S. G.

S. G. Wilson, M. B. Pearce, Q. L. Cao, M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. 1901–1910, Sept. 2005.
[CrossRef]

Winters, J. H.

J. Salz, J. H. Winters, “Effect of fading correlation on adaptive arrays in digital mobile communication systems,” IEEE Trans. Veh. Technol., vol. 43, no. 4, pp. 1049–1057, Nov. 1994.
[CrossRef]

Xu, F.

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Channel coding and time-diversity for optical wireless links,” Opt. Express, vol. 17, no. 2, pp. 872–887, Jan. 2009.
[CrossRef] [PubMed]

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Performance of coded time-diversity free-space optical links,” in Queen’s 24th Biennial Symp. on Communications (QSBC), Kingston, Canada, 2008, pp. 146–149.

Young, C.

Yuksel, H.

Yura, H. T.

Zhu, X.

X. Zhu, J. M. Kahn, “Pilot-symbol assisted modulation for correlated turbulent free-space optical channels,” Proc. SPIE, vol. 4489, pp. 138–145, 2002.
[CrossRef]

Zikic, S.

D. C. O’Brien, S. Quasem, S. Zikic, G. E. Faulkner, “Multiple input multiple output systems for optical wireless: challenges and possibilities,” Proc. SPIE, vol. 6304, pp. 16-1–16-7, 2006.

Appl. Opt. (6)

IEEE Commun. Mag. (1)

D. Kedar, S. Arnon, “Urban optical wireless communication networks: the main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, no. 5, pp. 2–7, May 2004.
[CrossRef]

IEEE J. Sel. Areas Commun. (2)

S. G. Wilson, M. B. Pearce, Q. L. Cao, M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. 1901–1910, Sept. 2005.
[CrossRef]

E. J. Lee, V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

IEEE Trans. Commun. (1)

J. L. Massey, “Capacity, cutoff rate, and coding for a direct-detection optical channel,” IEEE Trans. Commun., vol. 29, no. 11, pp. 1651–1621, Nov. 1981.
[CrossRef]

IEEE Trans. Veh. Technol. (1)

J. Salz, J. H. Winters, “Effect of fading correlation on adaptive arrays in digital mobile communication systems,” IEEE Trans. Veh. Technol., vol. 43, no. 4, pp. 1049–1057, Nov. 1994.
[CrossRef]

IEEE Trans. Wireless Commun. (3)

S. M. Navidpour, M. Uysal, M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2813–2819, Aug. 2007.
[CrossRef]

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 951–957, Feb. 2009.
[CrossRef]

M. Razavi, J. H. Shapiro, “Wireless optical communications via diversity reception and optical preamplification,” IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 975–983, May 2005.
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Netw. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Eng. (1)

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

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (6)

D. C. O’Brien, S. Quasem, S. Zikic, G. E. Faulkner, “Multiple input multiple output systems for optical wireless: challenges and possibilities,” Proc. SPIE, vol. 6304, pp. 16-1–16-7, 2006.

C. C. Davis, I. I. Smolyaninov, “The effect of atmospheric turbulence on bit-error-rate in an on-off-keyed optical wireless system,” Proc. SPIE, vol. 4489, pp. 126–137, 2002.
[CrossRef]

X. Zhu, J. M. Kahn, “Pilot-symbol assisted modulation for correlated turbulent free-space optical channels,” Proc. SPIE, vol. 4489, pp. 138–145, 2002.
[CrossRef]

G. L. Bastin, L. C. Andrews, R. L. Phillips, R. A. Nelson, B. A. Ferrell, M. R. Borbath, D. J. Galus, P. G. Chin, W. G. Harris, J. A. Marín, G. L. Burdge, D. Wayne, R. Pescatore, “Measurements of aperture averaging on bit-error-rate,” Proc. SPIE, vol. 5891, no. 02, pp. 1–12, 2005.

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

L. M. Wasiczko, C. C. Davis, “Aperture averaging of optical scintillations in the atmosphere: experimental results,” Proc. SPIE, vol. 5793, pp. 197–208, 2005.
[CrossRef]

Waves Random Media (1)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, “Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum,” Waves Random Media, vol. 10, pp. 53–70, 2000.
[CrossRef]

Wireless Personal Communications (1)

M. A. Khalighi, K. Raoof, G. Jourdain, “Capacity of wireless communication systems employing antenna arrays, a tutorial study,” Wireless Personal Communications, vol. 23, no. 3, paper 321352, Dec. 2002.
[CrossRef]

Other (12)

S. Hranilovic, Wireless Optical Communication Systems. Springer-Verlag, 2005.

“Design concepts of the FlightStrata optical wireless system with beam tracking and automatic power control,” LightPointe, White Paper, 2004, http://www.lightpointe.com.

M. A. Khalighi, N. Aitamer, N. Schwartz, S. Bourennane, “Turbulence mitigation by aperture averaging in wireless optical systems,” Proc. of ConTEL Conf., Zagreb, Croatia, 2008, pp. 59–66.

E. J. Lee, V. W. S. Chan, “Diversity coherent receivers for optical communication over the clear turbulent atmosphere,” IEEE Int. Conf. Communications, 2007, pp. 2485–2492.

R. M. Gagliardi, S. Karp, Optical Communications, 2nd ed.Wiley, 1995.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications. Bellingham, Washington: SPIE Press, 2001.
[CrossRef]

A. K. Majumdar, J. C. Ricklin, Free-Space Laser Communications: Principles and Advances. Springer-Verlag, 2007.

S. Bloom, “The physics of free-space optics,” AirFiber Inc., White Paper, May 2002.

H. Hemmati, Deep Space Optical Communications. Wiley, 2006.
[CrossRef]

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics. Wiley, 1991.
[CrossRef]

L. C. Andrews, R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. Bellingham, Washington: SPIE Press, 2005.
[CrossRef]

F. Xu, M. A. Khalighi, P. Caussé, S. Bourennane, “Performance of coded time-diversity free-space optical links,” in Queen’s 24th Biennial Symp. on Communications (QSBC), Kingston, Canada, 2008, pp. 146–149.

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Figures (11)

Fig. 1
Fig. 1

Aperture averaging factor, plane-wave propagation.

Fig. 2
Fig. 2

Spatial spectrum W I of intensity fluctuations normalized by the Rytov variance σ R 2 for (a) weak turbulence regime and (b) strong turbulence regime. Spectra are obtained via simulating wave propagation through turbulence using the phase screens method.

Fig. 3
Fig. 3

Average BER performance in the strong turbulence regime with σ R 2 = 19.18 , plane-wave propagation.

Fig. 4
Fig. 4

Average BER performance in the moderate turbulence regime with σ R 2 = 2.56 , plane-wave propagation.

Fig. 5
Fig. 5

Average BER performance in the weak turbulence regime with σ R 2 = 0.004 , plane-wave propagation model. “Pt Rx” denotes the point receiver case ( D = 0 ) .

Fig. 6
Fig. 6

Gain in E b N 0 (with respect to a point receiver) versus receiver lens diameter D for BPPM, 4PPM, and 8PPM. Moderate turbulence regime with σ R 2 = 2.56 , plane-wave propagation, l 0 = 4.6 mm , BER = 10 5 .

Fig. 7
Fig. 7

Gain in E b N 0 (with respect to a point receiver without coding) versus receiver lens diameter D for the three cases of turbulence, plane-wave propagation, l 0 = 4.6 mm , BER = 10 5 . Dashed curves, aperture averaging without coding: solid curves, aperture averaging + RSC ( 1 , 15 17 ) coding.

Fig. 8
Fig. 8

Outage capacity C out (in bits per channel use) versus lens diameter D for three turbulence regimes. P out = 10 9 , OOK modulation, plane-wave propagation, l 0 = 0 . Note that the abscissa is in linear scale for (a) and in logarithmic scale for (b) and (c).

Fig. 9
Fig. 9

Average BER performance for multiple- and single-aperture systems for background-noise-limited receivers, OOK modulation, plane-wave propagation, l 0 = 0 .

Fig. 10
Fig. 10

Outage capacity versus the diameter of lenses for a four-aperture receiver, P out = 10 9 , OOK modulation, background-noise-limited receivers, plane-wave propagation, l 0 = 0 .

Fig. 11
Fig. 11

Average BER performance for multiple- and single-aperture systems for thermal-noise-limited receivers, strong turbulence regime, OOK modulation, plane-wave propagation, l 0 = 0 .

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

r = η I + n ,
σ R 2 = 1.23 C n 2 k 7 6 L 11 6 ,
P ( I ) = 2 ( α β ) ( α + β ) 2 Γ ( α ) Γ ( β ) I ( α + β ) 2 1 K α β [ 2 ( α β I ) 1 2 ] , I > 0 ,
σ I , PL 2 ( D ) = exp [ 0.49 σ R 2 ( 1 + 0.653 d 2 + 1.11 σ R 12 5 ) 7 6 + 0.51 σ R 2 ( 1 + 0.69 σ R 12 5 ) 5 6 1 + 0.9 d 2 + 0.621 d 2 σ R 12 5 ] 1 ,
A = σ I 2 ( D ) σ I 2 ( 0 ) ,
A [ 1 + 1.062 ( D 2 4 k L ) ] 7 6 .
C = max P B ( b ) I ( b ; r ) .
C OOK = + b = 0 , 1 P B ( b ) f R ( r ) log 2 ( f R ( r | b ) b = 0 1 P B ( b ) f R ( r | b ) ) d r ,
C OOK = 1 2 2 π + e t 2 2 log 2 ( 1 + 2 e θ 2 2 sinh ( θ t ) + e θ 2 ) d t ,
P out = Prob { I < I T } .
P out , LN = 1 2 [ 1 + erf ( 1 2 σ ln I 2 + ln I T 2 σ ln I ) ] .
P out , Γ Γ = π Γ ( α ) Γ ( β ) sin [ π ( α β ) ] × { ( α β ) β β Γ ( β α + 1 ) I T β F 2 1 [ β ; β + 1 , β α + 1 ; α β I T ] ( α β ) α α Γ ( α β + 1 ) I T α F 2 1 [ α ; α + 1 , α β + 1 ; α β I T ] } .