Abstract

Since free-space optical (FSO) systems are usually installed on high buildings and building sway may cause vibrations in the transmitted beam, an unsuitable alignment between transmitter and receiver together with fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence can severely degrade the performance of optical wireless communication systems. In this paper, asymptotic bit error-rate (BER) performance for FSO communication systems using transmit laser selection over atmospheric turbulence channels with pointing errors is analyzed. Novel closed-form asymptotic expressions are derived when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), following a gamma-gamma distribution of parameters α and β, or pointing errors, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2(min{α,β})1/2 times the value of the pointing error displacement standard deviation at the receiver. Moreover, since proper FSO transmission requires transmitters with accurate control of their beamwidth, asymptotic expressions are used to find the optimum beamwidth that minimizes the BER at different turbulence conditions. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results, showing that asymptotic expressions here obtained lead to simple bounds on the bit error probability that get tighter over a wider range of signal-to-noise ratio (SNR) as the turbulence strength increases.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. W. S. Chan, “Free-Space Optical Communications,” J. Lightwave Technol. 24(12), 4750–4762 (2006).
    [CrossRef]
  2. L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001).
    [CrossRef]
  3. E. J. Lee and V. W. S. Chan, “Part 1: optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22(9), 1896–1906 (2004).
    [CrossRef]
  4. I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel,” J. Lightwave Technol. 26(5), 478–487 (2008).
    [CrossRef]
  5. T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
    [CrossRef]
  6. E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Commun. 57(11), 3415–3424 (2009).
    [CrossRef]
  7. E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
    [CrossRef]
  8. A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
    [CrossRef]
  9. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
    [CrossRef] [PubMed]
  10. A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20,445–20,454 (2010).
    [CrossRef]
  11. C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
    [CrossRef]
  12. H. Samimi, “Performance analysis of free-space optical links with transmit laser selection diversity over strong turbulence channels,” IET Communications 5(8), 1039–1043 (2011).
    [CrossRef]
  13. S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28(2), 129–131 (2003).
    [CrossRef] [PubMed]
  14. A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol. 25(7), 1702–1710 (2007).
    [CrossRef]
  15. H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun. 59(3), 669–674 (2011).
    [CrossRef]
  16. D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009).
    [CrossRef]
  17. H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, “Optical wireless communications with heterodyne detection over turbulence channels with pointing errors,” J. Lightwave Technol. 27(20), 4440–4445 (2009).
    [CrossRef]
  18. W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010).
    [CrossRef]
  19. C. Liu, Y. Yao, Y. X. Sun, J. J. Xiao, and X. H. Zhao, “Average capacity optimization in free-space optical communication system over atmospheric turbulence channels with pointing errors,” Opt. Lett. 35(19), 3171–3173 (2010).
    [CrossRef] [PubMed]
  20. A. A. Farid and S. Hranilovic, “Diversity gains for MIMO wireless optical intensity channels with atmospheric fading and misalignment,” in Proc. IEEE GLOBECOM Workshops (GC Wkshps), pp. 1015–1019 (2010).
  21. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13,480–13,496 (2011).
    [CrossRef]
  22. A. F. Molisch and M. Z. Win, “MIMO systems with antenna selection,” IEEE Microwave Magazine 5(1), 46–56 (2004).
    [CrossRef]
  23. 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, 8 (2001).
    [CrossRef]
  24. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 7th ed. (Academic Press Inc., 2007).
  25. M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 5(6), 1229–1233 (2006).
    [CrossRef]
  26. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Spatial correlation and irradiance statistics in a multiple-beam terrestrial free-space optical communication link,” Appl. Opt. 46(26), 6561–6571 (2007).
    [CrossRef] [PubMed]
  27. Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun. 51(8), 1389–1398 (2003).
    [CrossRef]
  28. Wolfram Research Inc., “The Wolfram functions site,” URL http://functions.wolfram.com .
  29. H. A. David and H. N. Nagaraja, Order statistics, 3rd ed. (John Wiley and Sons Inc., 2003).
    [CrossRef]
  30. M. K. Simon and M.-S. Alouini, Digital communications over fading channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).
  31. H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
    [CrossRef]
  32. H. G. Sandalidis, “Optimization models for misalignment fading mitigation in optical wireless links,” IEEE Commun. Lett. 12(5), 395–397 (2008).
    [CrossRef]
  33. X. Liu, “Optimisation of satellite optical transmission with correlated sways,” IET Communications 5(8), 1107–1112 (2011).
    [CrossRef]
  34. Wolfram Research Inc., Mathematica, version 8.0.1. ed. (Wolfram Research, Inc., Champaign, Illinois, 2011).
  35. H. Samimi and P. Azmi, “Subcarrier intensity modulated free-space optical communications in K-distributed turbulence channels,” J. Opt. Commun. Netw. 2(8), 625–632 (2010).
    [CrossRef]

2011 (5)

H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun. 59(3), 669–674 (2011).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13,480–13,496 (2011).
[CrossRef]

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[CrossRef]

H. Samimi, “Performance analysis of free-space optical links with transmit laser selection diversity over strong turbulence channels,” IET Communications 5(8), 1039–1043 (2011).
[CrossRef]

X. Liu, “Optimisation of satellite optical transmission with correlated sways,” IET Communications 5(8), 1107–1112 (2011).
[CrossRef]

2010 (6)

W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010).
[CrossRef]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[CrossRef]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20,445–20,454 (2010).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
[CrossRef] [PubMed]

H. Samimi and P. Azmi, “Subcarrier intensity modulated free-space optical communications in K-distributed turbulence channels,” J. Opt. Commun. Netw. 2(8), 625–632 (2010).
[CrossRef]

C. Liu, Y. Yao, Y. X. Sun, J. J. Xiao, and X. H. Zhao, “Average capacity optimization in free-space optical communication system over atmospheric turbulence channels with pointing errors,” Opt. Lett. 35(19), 3171–3173 (2010).
[CrossRef] [PubMed]

2009 (5)

D. K. Borah and D. G. Voelz, “Pointing error effects on free-space optical communication links in the presence of atmospheric turbulence,” J. Lightwave Technol. 27(18), 3965–3973 (2009).
[CrossRef]

H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, “Optical wireless communications with heterodyne detection over turbulence channels with pointing errors,” J. Lightwave Technol. 27(20), 4440–4445 (2009).
[CrossRef]

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
[CrossRef]

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Commun. 57(11), 3415–3424 (2009).
[CrossRef]

2008 (3)

H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
[CrossRef]

H. G. Sandalidis, “Optimization models for misalignment fading mitigation in optical wireless links,” IEEE Commun. Lett. 12(5), 395–397 (2008).
[CrossRef]

I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel,” J. Lightwave Technol. 26(5), 478–487 (2008).
[CrossRef]

2007 (2)

2006 (2)

V. W. S. Chan, “Free-Space Optical Communications,” J. Lightwave Technol. 24(12), 4750–4762 (2006).
[CrossRef]

M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 5(6), 1229–1233 (2006).
[CrossRef]

2004 (2)

E. J. Lee and V. W. S. Chan, “Part 1: optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22(9), 1896–1906 (2004).
[CrossRef]

A. F. Molisch and M. Z. Win, “MIMO systems with antenna selection,” IEEE Microwave Magazine 5(1), 46–56 (2004).
[CrossRef]

2003 (2)

Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun. 51(8), 1389–1398 (2003).
[CrossRef]

S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28(2), 129–131 (2003).
[CrossRef] [PubMed]

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, 8 (2001).
[CrossRef]

Abou-Rjeily, C.

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[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, 8 (2001).
[CrossRef]

Alouini, M.-S.

M. K. Simon and M.-S. Alouini, Digital communications over fading channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

Andrews, L.

L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001).
[CrossRef]

Andrews, L. C.

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, 8 (2001).
[CrossRef]

Anguita, J.

Anguita, J. A.

Arnon, S.

Azmi, P.

Bayaki, E.

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Commun. 57(11), 3415–3424 (2009).
[CrossRef]

Borah, D. K.

Castillo-Vazquez, B.

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
[CrossRef]

Castillo-Vazquez, C.

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
[CrossRef]

Castillo-Vázquez, B.

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13,480–13,496 (2011).
[CrossRef]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20,445–20,454 (2010).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
[CrossRef] [PubMed]

Castillo-Vázquez, C.

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13,480–13,496 (2011).
[CrossRef]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20,445–20,454 (2010).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
[CrossRef] [PubMed]

Chan, V. W. S.

V. W. S. Chan, “Free-Space Optical Communications,” J. Lightwave Technol. 24(12), 4750–4762 (2006).
[CrossRef]

E. J. Lee and V. W. S. Chan, “Part 1: optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22(9), 1896–1906 (2004).
[CrossRef]

David, H. A.

H. A. David and H. N. Nagaraja, Order statistics, 3rd ed. (John Wiley and Sons Inc., 2003).
[CrossRef]

Denic, S.

Djordjevic, I. B.

Farid, A. A.

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol. 25(7), 1702–1710 (2007).
[CrossRef]

A. A. Farid and S. Hranilovic, “Diversity gains for MIMO wireless optical intensity channels with atmospheric fading and misalignment,” in Proc. IEEE GLOBECOM Workshops (GC Wkshps), pp. 1015–1019 (2010).

Gappmair, W.

W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010).
[CrossRef]

Garcia-Zambrana, A.

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
[CrossRef]

García-Zambrana, A.

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13,480–13,496 (2011).
[CrossRef]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20,445–20,454 (2010).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
[CrossRef] [PubMed]

Giannakis, G. B.

Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun. 51(8), 1389–1398 (2003).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 7th ed. (Academic Press Inc., 2007).

Hiniesta-Gomez, A.

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
[CrossRef]

Hopen, C.

L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001).
[CrossRef]

Hranilovic, S.

W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010).
[CrossRef]

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol. 25(7), 1702–1710 (2007).
[CrossRef]

A. A. Farid and S. Hranilovic, “Diversity gains for MIMO wireless optical intensity channels with atmospheric fading and misalignment,” in Proc. IEEE GLOBECOM Workshops (GC Wkshps), pp. 1015–1019 (2010).

Karagiannidis, G. K.

H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, “Optical wireless communications with heterodyne detection over turbulence channels with pointing errors,” J. Lightwave Technol. 27(20), 4440–4445 (2009).
[CrossRef]

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
[CrossRef]

H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
[CrossRef]

Lee, E. J.

E. J. Lee and V. W. S. Chan, “Part 1: optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22(9), 1896–1906 (2004).
[CrossRef]

Leitgeb, E.

W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010).
[CrossRef]

Li, J.

M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 5(6), 1229–1233 (2006).
[CrossRef]

Liu, C.

Liu, X.

X. Liu, “Optimisation of satellite optical transmission with correlated sways,” IET Communications 5(8), 1107–1112 (2011).
[CrossRef]

Mallik, R. K.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Commun. 57(11), 3415–3424 (2009).
[CrossRef]

Molisch, A. F.

A. F. Molisch and M. Z. Win, “MIMO systems with antenna selection,” IEEE Microwave Magazine 5(1), 46–56 (2004).
[CrossRef]

Nagaraja, H. N.

H. A. David and H. N. Nagaraja, Order statistics, 3rd ed. (John Wiley and Sons Inc., 2003).
[CrossRef]

Neifeld, M.

Neifeld, M. A.

Phillips, R.

L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001).
[CrossRef]

Phillips, R. L.

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, 8 (2001).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 7th ed. (Academic Press Inc., 2007).

Samimi, H.

H. Samimi, “Performance analysis of free-space optical links with transmit laser selection diversity over strong turbulence channels,” IET Communications 5(8), 1039–1043 (2011).
[CrossRef]

H. Samimi and P. Azmi, “Subcarrier intensity modulated free-space optical communications in K-distributed turbulence channels,” J. Opt. Commun. Netw. 2(8), 625–632 (2010).
[CrossRef]

Sandalidis, H. G.

H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun. 59(3), 669–674 (2011).
[CrossRef]

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
[CrossRef]

H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, “Optical wireless communications with heterodyne detection over turbulence channels with pointing errors,” J. Lightwave Technol. 27(20), 4440–4445 (2009).
[CrossRef]

H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
[CrossRef]

H. G. Sandalidis, “Optimization models for misalignment fading mitigation in optical wireless links,” IEEE Commun. Lett. 12(5), 395–397 (2008).
[CrossRef]

Schober, R.

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Commun. 57(11), 3415–3424 (2009).
[CrossRef]

Simon, M. K.

M. K. Simon and M.-S. Alouini, Digital communications over fading channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

Sun, Y. X.

Tsiftsis, T. A.

H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, “Optical wireless communications with heterodyne detection over turbulence channels with pointing errors,” J. Lightwave Technol. 27(20), 4440–4445 (2009).
[CrossRef]

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
[CrossRef]

H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
[CrossRef]

Uysal, M.

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
[CrossRef]

H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
[CrossRef]

M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 5(6), 1229–1233 (2006).
[CrossRef]

Vasic, B.

Vasic, B. V.

Voelz, D. G.

Wang, Z.

Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun. 51(8), 1389–1398 (2003).
[CrossRef]

Win, M. Z.

A. F. Molisch and M. Z. Win, “MIMO systems with antenna selection,” IEEE Microwave Magazine 5(1), 46–56 (2004).
[CrossRef]

Xiao, J. J.

Yao, Y.

Yu, M.

M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 5(6), 1229–1233 (2006).
[CrossRef]

Zhao, X. H.

Appl. Opt. (1)

IEEE Commun. Lett. (4)

H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, “BER performance of FSO links over strong atmospheric turbulence channels with pointing errors,” IEEE Commun. Lett. 12(1), 44–46 (2008).
[CrossRef]

H. G. Sandalidis, “Optimization models for misalignment fading mitigation in optical wireless links,” IEEE Commun. Lett. 12(5), 395–397 (2008).
[CrossRef]

W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010).
[CrossRef]

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

E. J. Lee and V. W. S. Chan, “Part 1: optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun. 22(9), 1896–1906 (2004).
[CrossRef]

IEEE Microwave Magazine (1)

A. F. Molisch and M. Z. Win, “MIMO systems with antenna selection,” IEEE Microwave Magazine 5(1), 46–56 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and A. Hiniesta-Gomez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photon. Technol. Lett. 21(14), 1017–1019 (2009).
[CrossRef]

IEEE Trans. Commun. (4)

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma-gamma fading,” IEEE Trans. Commun. 57(11), 3415–3424 (2009).
[CrossRef]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[CrossRef]

H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun. 59(3), 669–674 (2011).
[CrossRef]

Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun. 51(8), 1389–1398 (2003).
[CrossRef]

IEEE Trans. Wireless Commun. (2)

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 8(2), 951–957 (2009).
[CrossRef]

M. Uysal, J. Li, and M. Yu, “Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels,” IEEE Trans. Wireless Commun. 5(6), 1229–1233 (2006).
[CrossRef]

IET Communications (2)

X. Liu, “Optimisation of satellite optical transmission with correlated sways,” IET Communications 5(8), 1107–1112 (2011).
[CrossRef]

H. Samimi, “Performance analysis of free-space optical links with transmit laser selection diversity over strong turbulence channels,” IET Communications 5(8), 1039–1043 (2011).
[CrossRef]

J. Lightwave Technol. (5)

J. Opt. Commun. Netw. (1)

Opt. Eng. (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, 8 (2001).
[CrossRef]

Opt. Express (3)

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13,480–13,496 (2011).
[CrossRef]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20,445–20,454 (2010).
[CrossRef]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
[CrossRef] [PubMed]

Opt. Lett. (2)

Other (7)

Wolfram Research Inc., Mathematica, version 8.0.1. ed. (Wolfram Research, Inc., Champaign, Illinois, 2011).

L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001).
[CrossRef]

A. A. Farid and S. Hranilovic, “Diversity gains for MIMO wireless optical intensity channels with atmospheric fading and misalignment,” in Proc. IEEE GLOBECOM Workshops (GC Wkshps), pp. 1015–1019 (2010).

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 7th ed. (Academic Press Inc., 2007).

Wolfram Research Inc., “The Wolfram functions site,” URL http://functions.wolfram.com .

H. A. David and H. N. Nagaraja, Order statistics, 3rd ed. (John Wiley and Sons Inc., 2003).
[CrossRef]

M. K. Simon and M.-S. Alouini, Digital communications over fading channels, 2nd ed. (Wiley-IEEE Press, New Jersey, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

FSO system with transmit laser selection.

Fig. 2
Fig. 2

BER performance in FSO IM/DD links using transmit laser selection over gamma-gamma atmospheric and misalignment fading channels, when different levels of turbulence (a) (α,β) = (6,3), (b) (α,β) = (4,2) and (c) (α,β) = (2,1) are assumed together with values of normalized jitter of σs/r = {1,2,3} and a normalized beamwidth of ωz/r = 5. BER results corresponding to the same FSO scenario without pointing errors and the non-turbulence case are also included.

Fig. 3
Fig. 3

BER performance in FSO links using transmit laser selection over gamma-gamma atmospheric with/without pointing errors, assuming M = {1,4} and values of normalized jitter of σs/r = {1,3} and normalized beamwidth of ωz/r = {5,10}. BER result corresponding to the non-turbulence case is also included as a reference.

Fig. 4
Fig. 4

Coding gain disadvantage D in Eq. (15) as a function of the distance L between transmitter and receiver in FSO links over gamma-gamma atmospheric when λ = 1550 nm, C n 2 = 1.7 × 10 14 m 2 / 3, and D/L → 0, assuming a normalized jitter of σs/r = 1.5 and values of normalized beamwidth of ωz/r = {4.75,5,5.25}.

Fig. 5
Fig. 5

Optimum normalized beamwidth versus normalized jitter, σs/r in FSO links over gamma-gamma atmospheric when λ = 1550 nm, C n 2 = 1.7 × 10 14 m 2 / 3, D/L → 0 and distances between transmitter and receiver of L = {3,5,7} km.

Fig. 6
Fig. 6

Combining gain advantage, GTLS, of TLS over RC-EGC versus the distance L between transmitter and receiver in FSO links and gamma-gamma fading when λ = 1550 nm, C n 2 = 1.7 × 10 14 m 2 / 3, and D/L → 0, assuming M trasmit lasers with the TLS scheme and the same diversity order as in RC-EGC scheme.

Equations (20)

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

y m ( t ) = η i m ( t ) x ( t ) + z ( t )
f I m ( a ) ( 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 = [ exp ( 0.49 χ 2 ( 1 + 0.18 d 2 + 0.56 χ 12 / 5 ) 7 / 6 ) 1 ] 1
β = [ exp ( 0.51 χ 2 ( 1 + 0.69 χ 12 / 5 ) 5 / 6 ( 1 + 0.9 d 2 + 0.62 d 2 χ 12 / 5 ) 7 / 6 ) 1 ] 1
S I = E [ I ] 2 ( E [ I ] ) 2 1 = 1 α + 1 β + 1 α β .
f I m ( p ) ( i ) = φ 2 A 0 φ 2 i φ 2 1 , 0 i A 0
f I l m ( i ) = α β φ 2 A 0 Γ ( α ) Γ ( β ) G 1 , 3 3 , 0 ( α β A 0 i | φ 2 φ 2 1 , α 1 , β 1 ) , i 0
f I m ( i ) φ 2 ( α β ) min { α , β } Γ ( | α β | ) A 0 min { α , β } Γ ( α ) Γ ( β ) ( φ 2 min { α , β } ) i min { α , β } 1 , φ 2 > min { α , β }
f I m ( i ) φ 2 ( α β ) φ 2 Γ ( α φ 2 ) Γ ( β φ 2 ) A 0 φ 2 Γ ( α ) Γ ( β ) i φ 2 1 , φ 2 < min { α , β }
Y = X I max + Z , X { 0 , d } , Z N ( 0 , N 0 / 2 )
P b ( E | I max ) = Q ( d 2 i 2 / 2 N 0 )
P b ( E ) = 0 Q ( 2 γ ξ i ) f I max ( i ) d i .
f I max ( i ) ( ( Ω min M ) 1 / M ( A 0 1 α β ) Ω min φ 2 Γ ( | α β | ) Γ ( Ω max ) ( φ 2 Ω min ) Γ ( Ω min + 1 ) ) M i M Ω min 1 , φ 2 > Ω min
f I max ( i ) ( ( φ 2 M ) 1 / M ( A 0 1 α β ) φ 2 Γ ( α φ 2 ) Γ ( β φ 2 ) Γ ( α ) Γ ( β ) ) M i M φ 2 1 , φ 2 < Ω min
P b ( E ) ( ( φ 2 ( A 0 1 α β ) Ω min Γ ( | α β | ) Γ ( M Ω min + 1 2 ) 1 / M ( φ 2 Ω min ) ( 2 π ) 1 / M Γ ( Ω max ) Γ ( Ω min + 1 ) ) 2 Ω min γ ξ ) M Ω min 2 , φ 2 > Ω min
P b ( E ) ( ( ( A 0 1 α β ) φ 2 Γ ( α φ 2 ) Γ ( β φ 2 ) Γ ( M φ 2 + 1 2 ) 1 / M ( 2 π ) 1 / M Γ ( α ) Γ ( β ) ) 2 φ 2 γ ξ ) M φ 2 2 , φ 2 < Ω min
P b ( E ) ( ( ( α β ) Ω min Γ ( | α β | ) Γ ( M Ω min + 1 2 ) 1 / M ( 2 π ) 1 / M Γ ( Ω max ) Γ ( Ω min + 1 ) ) 2 Ω min γ ξ ) M Ω min 2 .
D [ d B ] 20 Ω min log 10 ( φ 2 A 0 Ω min ( φ 2 Ω min ) ) .
ω z / r optimum ( 0.034 Ω min 2 + 0.72 Ω min + 2.15 ) σ s / r
G TLS [ dB ] 20 Ω min log 10 ( M Ω min Γ ( Ω min + 1 ) Γ ( M Ω min + 1 ) 1 / M )

Metrics