Abstract

Atmospheric turbulence produces fluctuations in the irradiance of the transmitted optical beam, which is known as atmospheric scintillation, severely degrading the performance over free-space optical (FSO) links. Additionally, since FSO systems are usually installed on high buildings, building sway causes vibrations in the transmitted beam, leading to an unsuitable alignment between transmitter and receiver and, hence, a greater deterioration in performance. In this paper, the outage probability as a performance measure for multiple-input/multiple-output (MIMO) FSO communication systems with intensity modulation and direct detection (IM/DD) over strong atmospheric turbulence channels with pointing errors is analyzed. Novel closed-form expressions for the outage probability as well as their corresponding asymptotic expressions are presented when the irradiance of the transmitted optical beam is susceptible to either strong turbulence conditions, following a negative exponential distribution, and pointing error effects, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results show that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least twice the value of the pointing error displacement standard deviation at the receiver. Simulation results are further demonstrated to confirm the analytical results. Additionally, since proper FSO transmission requires transmitters with accurate control of their beamwidth, asymptotic expressions here obtained for different diversity techniques are used to find the optimum beamwidth that minimizes the outage performance.

© 2011 OSA

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    [CrossRef]
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2011 (1)

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

2010 (4)

2009 (6)

B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, “Closed-Form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels,” Electron. Lett. 45(23), 1185–1187 (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]

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]

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

W. Lim, C. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express 17(6), 4479–4484 (2009).
[CrossRef] [PubMed]

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]

2008 (4)

C. Abou-Rjeily and W. Fawaz, “Space-time codes for MIMO ultra-wideband communications and MIMO free-space optical communications with PPM,” IEEE J. Sel. Areas Commun. 26(6), 938–947 (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]

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]

2007 (2)

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[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]

2005 (1)

M. Simon and V. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[CrossRef]

2004 (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]

2003 (3)

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2(4), 626–629 (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]

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]

2002 (1)

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

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]

1997 (1)

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

Abou-Rjeily, C.

C. Abou-Rjeily and W. Fawaz, “Space-time codes for MIMO ultra-wideband communications and MIMO free-space optical communications with PPM,” IEEE J. Sel. Areas Commun. 26(6), 938–947 (2008).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 9th ed. (Dover, 1970).

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]

Alouini, M.-S.

M. K. Simon and M.-S. Alouini, Digital Communications over Fading Channels , 2nd ed. (Wiley-IEEE Press, 2005).

Andrews, L.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Andrews, L. C.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[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]

Anguita, J.

Arnon, S.

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2(4), 626–629 (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]

Barry, J. R.

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

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]

Borah, D. K.

Castillo-Vazquez, B.

B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, “Closed-Form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels,” Electron. Lett. 45(23), 1185–1187 (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]

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]

B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, “Closed-Form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels,” Electron. Lett. 45(23), 1185–1187 (2009).
[CrossRef]

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Chan, V. W. S.

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]

Cherry, P. C.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[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, 2010), pp. 1015–1019.
[CrossRef]

Fawaz, W.

C. Abou-Rjeily and W. Fawaz, “Space-time codes for MIMO ultra-wideband communications and MIMO free-space optical communications with PPM,” IEEE J. Sel. Areas Commun. 26(6), 938–947 (2008).
[CrossRef]

Foshee, J. J.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

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.

B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, “Closed-Form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels,” Electron. Lett. 45(23), 1185–1187 (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]

García-Zambrana, A.

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 (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, 2010), pp. 1015–1019.
[CrossRef]

Kahn, J. M.

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

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

Karagiannidis, G. K.

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]

Kavehrad, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[CrossRef]

Kim, K.

Kolodzy, P. J.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[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]

Lim, W.

McIntire, W. K.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

Nagaraja, H. N.

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

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[CrossRef]

Neifeld, M.

Northcott, M.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

Phillips, R.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Phillips, R. L.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[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]

Pike, H. A.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products , 7th ed. (Academic Press Inc., 2007).

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, 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]

Simon, M.

M. Simon and V. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[CrossRef]

Simon, M. K.

M. K. Simon and M.-S. Alouini, Digital Communications over Fading Channels , 2nd ed. (Wiley-IEEE Press, 2005).

Stadler, B.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 9th ed. (Dover, 1970).

Stotts, L. B.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
[CrossRef]

Tsiftsis, T. A.

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]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[CrossRef]

Vasic, B.

Vilnrotter, V.

M. Simon and V. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[CrossRef]

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]

Young, D. W.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009).
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Yun, C.

Zhu, X.

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

Electron. Lett. (1)

B. Castillo-Vazquez, A. Garcia-Zambrana, and C. Castillo-Vazquez, “Closed-Form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels,” Electron. Lett. 45(23), 1185–1187 (2009).
[CrossRef]

IEEE Commun. Lett. (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]

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]

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

IEEE J. Sel. Areas Commun. (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]

C. Abou-Rjeily and W. Fawaz, “Space-time codes for MIMO ultra-wideband communications and MIMO free-space optical communications with PPM,” IEEE J. Sel. Areas Commun. 26(6), 938–947 (2008).
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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).
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IEEE Trans. Commun. (4)

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

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

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

IEEE Trans. Wireless Commun. (4)

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[CrossRef]

M. Simon and V. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[CrossRef]

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2(4), 626–629 (2003).
[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]

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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, 1554–1562 (2001).
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Figures (5)

Fig. 1
Fig. 1

Probability of outage versus normalized average SNR in FSO IM/DD links over the exponential atmospheric turbulence channel with pointing errors, assuming different values of normalized beamwidth, ωz /r, and normalized jitter, σs /r.

Fig. 2
Fig. 2

Probability of outage versus normalized average SNR in MISO and SIMO FSO IM/DD links over the exponential atmospheric turbulence channel with pointing errors, assuming a normalized beamwidth of ωz /r = 5 and values of normalized jitter of (a) σs /r = 1 and (b) σs /r = 4.

Fig. 3
Fig. 3

Coding gain advantage for the SC scheme relative to the EGC scheme, assuming a normalized beamwidth of ωz /r = 10 and values of normalized jitter of 6, 7, 8 and 9, corresponding to values of φ of 0.83, 0.71, 0.62 and 0.55, respectively.

Fig. 4
Fig. 4

Probability of outage versus normalized average SNR in MIMO FSO IM/DD links over the exponential atmospheric turbulence channel with pointing errors, assuming a normalized beamwidth of ωz /r = 5 with a normalized jitter of σs /r = 1 and a normalized beamwidth of ωz /r = 10 with a normalized jitter of σs /r = 7, corresponding to values of φ of 2.55 and 0.71, respectively. Additionally, results assuming the optimum beamwidth corresponding to values of jitter of σs /r = 1 and σs /r = 7 are also included for L = 4 and M = 2.

Fig. 5
Fig. 5

Optimum normalized beamwidth versus normalized jitter, σs /r in FSO IM/DD links over the exponential atmospheric turbulence channel with pointing errors.

Equations (48)

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y lm ( t ) = η i lm ( t ) x ( t ) + z m ( t )
f I lm ( a ) ( i ) = e i , i 0.
f I lm ( p ) ( i ) = φ 2 A 0 φ 2 i φ 2 1 , 0 i A 0
f I lm ( i ) = φ 2 A 0 φ 2 i φ 2 1 Γ ( 1 φ 2 , i A 0 ) , i 0
P out = Prob ( γ T γ th ) = 0 γ th f γ T ( γ T ) d γ T = F γ T ( γ th )
Y = XI + Z , X { 0 , d } , Z N ( 0 , N 0 / 2 ) .
γ T SISO ( i ) = 1 2 d 2 N 0 / 2 i 2 = 4 P opt 2 T b ξ N 0 i 2 = γ ξ i 2
P out = Prob ( γ ξ i 2 γ th ) = Prob ( i 2 γ th ξ γ ) = F I ( 1 ξ γ th γ )
F I ( i ) = 1 ( i A 0 ) φ 2 φ 2 Γ ( φ 2 , i A 0 ) , i 0
P out ( φ 4 ( 1 φ 2 ) 2 A 0 2 ξ γ th γ ) 1 / 2 + ( Γ ( 1 φ 2 ) 2 φ 2 A 0 2 ξ γ th γ ) φ 2 / 2 .
P out ( φ 4 ( 1 φ 2 ) 2 A 0 2 ξ γ th γ ) 1 / 2 , φ > 1
P out ( Γ ( 1 φ 2 ) 2 / φ 2 A 0 2 ξ γ th γ ) φ 2 / 2 , φ < 1
D [ dB ] 20 log 10 ( φ 2 A 0 ( φ 2 1 ) ) .
Y = X 1 L l = 1 L I l + Z , X { 0 , d } , Z N ( 0 , N 0 / 2 )
γ T MISO-RC = γ ξ 1 L 2 ( l = 1 L i l ) 2 = γ ξ 1 L 2 i T 2
P out = F I T ( L 1 ξ γ th γ )
f I lm ( i ) φ 2 A 0 ( φ 2 1 ) , φ > 1
f I lm ( i ) φ 2 Γ ( 1 φ 2 ) A 0 φ 2 i φ 2 1 , φ < 1
F I T ( i ) 1 Γ ( L + 1 ) ( φ 2 A 0 ( φ 2 1 ) ) L i L , φ > 1
F I T ( i ) Γ ( 1 + φ 2 ) L Γ ( 1 + L φ 2 ) ( Γ ( 1 φ 2 ) A 0 φ 2 ) L i L φ 2 , φ < 1
P out ( L 2 Γ ( L + 1 ) 2 / L φ 4 A 0 2 ( 1 φ 2 ) 2 ξ γ th γ ) L / 2 , φ > 1
P out ( L 2 Γ ( 1 + φ 2 ) 2 / φ 2 Γ ( 1 + L φ 2 ) 2 / L φ 2 Γ ( 1 φ 2 ) 2 / φ 2 A 0 2 ξ γ th γ ) L φ 2 / 2 , φ < 1
Y = X I max + Z , X { 0 , d } , Z N ( 0 , N 0 / 2 )
P out = F I max ( 1 ξ γ th γ ) = ( F I ( 1 ξ γ th γ ) ) L
P out ( φ 4 ( 1 φ 2 ) 2 A 0 2 ξ γ th γ ) L / 2 , φ > 1
P out ( Γ ( 1 φ 2 ) 2 / φ 2 A 0 2 ξ γ th γ ) L φ 2 / 2 , φ < 1
A TLS [ dB ] 10 log 10 ( L 2 Γ ( L + 1 ) 2 / L ) , φ > 1
A TLS [ dB ] 10 log 10 ( L 2 Γ ( 1 + φ 2 ) 2 / φ 2 Γ ( 1 + L φ 2 ) 2 / L φ 2 ) , φ < 1
Y = X 1 M m = 1 M I m + Z EGC , X { 0 , d } , Z EGC N ( 0 , N 0 / 2 )
Y = X 1 M I max + Z SC , X { 0 , d } , Z SC N ( 0 , N 0 / 2 M )
γ T SIMO-SC = γ ξ 1 M I max 2
P out = F I max ( M ξ γ th γ ) = ( F I ( M ξ γ th γ ) ) M .
P out ( M φ 4 ( 1 φ 2 ) 2 A 0 2 ξ γ th γ ) M / 2 , φ > 1
P out ( M Γ ( 1 φ 2 ) 2 / φ 2 A 0 2 ξ γ th γ ) M φ 2 / 2 , φ < 1
A EGC [ dB ] 10 log 10 ( Γ ( M + 1 ) 2 / M M ) , φ > 1
A SC [ dB ] 10 log 10 ( M Γ ( 1 + φ 2 ) 2 / φ 2 Γ ( 1 + M φ 2 ) 2 / M φ 2 ) , φ < 1
Y = X 1 M m = 1 M I m + Z EGC , X { 0 , d } , Z EGC N ( 0 , N 0 / 2 )
γ T MIMO = γ ξ 1 M 2 ( m = 1 M i m ) 2 = γ ξ 1 M 2 i T 2
P out = F I T ( M 1 ξ γ th γ )
f I m ( i ) L ( φ 2 ( φ 2 1 ) A 0 ) L i L 1 , φ > 1
f I m ( i ) L φ 2 ( Γ ( 1 φ 2 ) A 0 φ 2 ) L i L φ 2 1 , φ < 1
F I T ( i ) ( L Γ ( L ) ) M Γ ( LM + 1 ) ( φ 2 ( φ 2 1 ) A 0 ) LM i LM , φ > 1
F I T ( i ) Γ ( L φ 2 + 1 ) M Γ ( LM φ 2 + 1 ) ( Γ ( 1 φ 2 ) A 0 φ 2 ) LM i LM φ 2 , φ < 1
P out ( ( M 2 Γ ( L + 1 ) 2 / L Γ ( LM + 1 ) 2 / LM φ 4 ( φ 2 1 ) 2 A 0 2 ξ γ th γ ) LM 2 , φ > 1
P out ( M 2 Γ ( L φ 2 + 1 ) 2 / L φ 2 Γ ( LM φ 2 + 1 ) 2 / LM φ 2 Γ ( 1 φ 2 ) 2 / φ 2 A 0 2 ξ γ th γ ) LM φ 2 / 2 , φ < 1
D MIMO [ dB ] 20 log 10 ( M Γ ( O d / M + 1 ) M / O d Γ ( O d + 1 ) 1 / O d ) .
ω z / r optimum 2.85 ( σ s / r 1 ) + 2.6
x ( t ) = k = a k 2 T b P opt G ( f = 0 ) g ( t k T b )

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