Abstract

A new upper bound on the capacity of power- and bandwidth-constrained optical wireless links using selection transmit diversity over exponential atmospheric turbulence channels with intensity modulation and direct detection is derived when non-uniform on-off keying (OOK) formats are used. In this strong turbulence free-space optical (FSO) scenario, average capacity is investigated subject to an average optical power constraint and not only to an average electrical power constraint when the transmit diversity technique assumed is based on the selection of the optical path with a greater value of irradiance. Simulation results for the mutual information are further demonstrated to confirm the analytical results for different diversity orders.

© 2010 Optical Society of America

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References

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  1. L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
    [CrossRef]
  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. Wirel. Comm. 8(2), 951–957 (2009).
    [CrossRef]
  3. 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]
  4. 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]
  5. 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]
  6. H. G. Sandalidis, and T. A. Tsiftsis, “Outage probability and ergodic capacity of free-space optical links over strong turbulence,” Electron. Lett. 44(1), 46–47 (2008).
    [CrossRef]
  7. H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
    [CrossRef]
  8. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “On the capacity of FSO links over gamma-gamma atmospheric turbulence channels using OOK signaling,” EURASIP J. Wireless Commun. Networking 2010), Article ID 127657, 9 pages doi:10.1155/2010/127657.
  9. 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]
  10. M. Simon, and V. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wirel. Comm. 4(1), 35–39 (2005).
    [CrossRef]
  11. 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 Comm. 26(6), 938–947 (2008).
    [CrossRef]
  12. W. O. Popoola, and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol. 27(8), 967–973 (2009).
    [CrossRef]
  13. N. Letzepis, K. Nguyen, and A. Guillen i Fabregas, “andW. Cowley, “Outage analysis of the hybrid free-space optical and radio-frequency channel,” IEEE J. Sel. Areas Comm. 27(9), 1709–1719 (2009).
    [CrossRef]
  14. K. Davaslioglu, E. Cagiral, and M. Koca, “Free-space optical ultra-wideband communications over atmospheric turbulence channels,” Opt. Express 18(16), 618–16,627 (2010).
  15. U. Madhow, Fundamentals of Digital Communication (Cambridge Univ. Press, 2008).
  16. T. M. Cover, and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley & Sons, 2006).
  17. A. J. Goldsmith, and P. P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inf. Theory 43(6), 1986–1992 (1997).
    [CrossRef]
  18. J. Li, and M. Uysal, “Optical wireless communications: system model, capacity and coding,” in Proc. VTC 2003-Fall Vehicular Technology Conference 2003 IEEE 58th, vol. 1, pp. 168–172 (2003).
  19. J. Li, and M. Uysal, “Achievable information rate for outdoor free space optical communication with intensity modulation and direct detection,” in Proc. IEEE Global Telecommunications Conference GLOBECOM ’03, vol. 5, pp. 2654–2658 (2003).
  20. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
    [CrossRef]
  21. J. Anguita, I. Djordjevic, M. Neifeld, and B. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. 4(9), 586–601 (2005).
    [CrossRef]
  22. A. A. Farid, and S. Hranilovic, “Design of non-uniform capacity-approaching signaling for optical wireless intensity channels,” in Proc. IEEE International Symposium on Information Theory ISIT 2008, pp. 2327–2331 (2008).
  23. A. A. Farid, and S. Hranilovic, “Outage capacity with non-uniform signaling for free-space optical channels,” in Proc. 24th Biennial Symposium on Communications, pp. 204–207 (2008).
  24. A. Farid, and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Comm. 27(9), 1553–1563 (2009).
    [CrossRef]
  25. S. Hranilovic, and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50(5), 784–795 (2004).
    [CrossRef]
  26. S. Z. Denic, I. Djordjevic, J. Anguita, B. Vasic, and M. A. Neifeld, “Information theoretic limits for free-space optical channels with and without memory,” J. Lightwave Technol. 26(19), 3376–3384 (2008).
    [CrossRef]
  27. I. S. Gradshteyn, and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic Press Inc., 2007).
  28. Wolfram Research, Inc., Mathematica, version 7.0 ed. (Wolfram Research, Inc., 2008).

2010 (1)

2009 (8)

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. Wirel. Comm. 8(2), 951–957 (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]

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]

N. Letzepis, K. Nguyen, and A. Guillen i Fabregas, “andW. Cowley, “Outage analysis of the hybrid free-space optical and radio-frequency channel,” IEEE J. Sel. Areas Comm. 27(9), 1709–1719 (2009).
[CrossRef]

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

A. Farid, and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Comm. 27(9), 1553–1563 (2009).
[CrossRef]

W. O. Popoola, and Z. Ghassemlooy, “BPSK subcarrier intensity modulated free-space optical communications in atmospheric turbulence,” J. Lightwave Technol. 27(8), 967–973 (2009).
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
[CrossRef]

2008 (3)

S. Z. Denic, I. Djordjevic, J. Anguita, B. Vasic, and M. A. Neifeld, “Information theoretic limits for free-space optical channels with and without memory,” J. Lightwave Technol. 26(19), 3376–3384 (2008).
[CrossRef]

H. G. Sandalidis, and T. A. Tsiftsis, “Outage probability and ergodic capacity of free-space optical links over strong turbulence,” Electron. Lett. 44(1), 46–47 (2008).
[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 Comm. 26(6), 938–947 (2008).
[CrossRef]

2005 (2)

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

J. Anguita, I. Djordjevic, M. Neifeld, and B. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. 4(9), 586–601 (2005).
[CrossRef]

2004 (1)

S. Hranilovic, and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50(5), 784–795 (2004).
[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, 8 (2001).
[CrossRef]

1997 (1)

A. J. Goldsmith, and P. P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inf. Theory 43(6), 1986–1992 (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 Comm. 26(6), 938–947 (2008).
[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]

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.

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]

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-Vazquez, C.

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-Vázquez, B.

Castillo-Vázquez, C.

Denic, S. Z.

Djordjevic, I.

Fafalios, M. E.

Farid, A.

A. Farid, and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Comm. 27(9), 1553–1563 (2009).
[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 Comm. 26(6), 938–947 (2008).
[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]

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]

García-Zambrana, A.

Ghassemlooy, Z.

Goldsmith, A. J.

A. J. Goldsmith, and P. P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inf. Theory 43(6), 1986–1992 (1997).
[CrossRef]

Guillen i Fabregas, A.

N. Letzepis, K. Nguyen, and A. Guillen i Fabregas, “andW. Cowley, “Outage analysis of the hybrid free-space optical and radio-frequency channel,” IEEE J. Sel. Areas Comm. 27(9), 1709–1719 (2009).
[CrossRef]

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]

Hranilovic, S.

A. Farid, and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Comm. 27(9), 1553–1563 (2009).
[CrossRef]

S. Hranilovic, and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50(5), 784–795 (2004).
[CrossRef]

Karagianni, E. A.

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. Wirel. Comm. 8(2), 951–957 (2009).
[CrossRef]

Kschischang, F. R.

S. Hranilovic, and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50(5), 784–795 (2004).
[CrossRef]

Letzepis, N.

N. Letzepis, K. Nguyen, and A. Guillen i Fabregas, “andW. Cowley, “Outage analysis of the hybrid free-space optical and radio-frequency channel,” IEEE J. Sel. Areas Comm. 27(9), 1709–1719 (2009).
[CrossRef]

Neifeld, M.

Neifeld, M. A.

Nguyen, K.

N. Letzepis, K. Nguyen, and A. Guillen i Fabregas, “andW. Cowley, “Outage analysis of the hybrid free-space optical and radio-frequency channel,” IEEE J. Sel. Areas Comm. 27(9), 1709–1719 (2009).
[CrossRef]

Nistazakis, H. E.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
[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]

Popoola, W. O.

Sandalidis, H. G.

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. Wirel. Comm. 8(2), 951–957 (2009).
[CrossRef]

H. G. Sandalidis, and T. A. Tsiftsis, “Outage probability and ergodic capacity of free-space optical links over strong turbulence,” Electron. Lett. 44(1), 46–47 (2008).
[CrossRef]

Simon, M.

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

Tombras, G. S.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. 27(8), 974–979 (2009).
[CrossRef]

Tsiftsis, T. A.

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (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. Wirel. Comm. 8(2), 951–957 (2009).
[CrossRef]

H. G. Sandalidis, and T. A. Tsiftsis, “Outage probability and ergodic capacity of free-space optical links over strong turbulence,” Electron. Lett. 44(1), 46–47 (2008).
[CrossRef]

Tsigopoulos, A. D.

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. Wirel. Comm. 8(2), 951–957 (2009).
[CrossRef]

Varaiya, P. P.

A. J. Goldsmith, and P. P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inf. Theory 43(6), 1986–1992 (1997).
[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. Wirel. Comm. 4(1), 35–39 (2005).
[CrossRef]

Electron. Lett. (2)

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]

H. G. Sandalidis, and T. A. Tsiftsis, “Outage probability and ergodic capacity of free-space optical links over strong turbulence,” Electron. Lett. 44(1), 46–47 (2008).
[CrossRef]

IEEE J. Sel. Areas Comm. (3)

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 Comm. 26(6), 938–947 (2008).
[CrossRef]

N. Letzepis, K. Nguyen, and A. Guillen i Fabregas, “andW. Cowley, “Outage analysis of the hybrid free-space optical and radio-frequency channel,” IEEE J. Sel. Areas Comm. 27(9), 1709–1719 (2009).
[CrossRef]

A. Farid, and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Comm. 27(9), 1553–1563 (2009).
[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. Inf. Theory (2)

A. J. Goldsmith, and P. P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inf. Theory 43(6), 1986–1992 (1997).
[CrossRef]

S. Hranilovic, and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50(5), 784–795 (2004).
[CrossRef]

IEEE Trans. Wirel. Comm. (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. Wirel. Comm. 8(2), 951–957 (2009).
[CrossRef]

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

IET Commun. (1)

H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. 3(8), 1402–1409 (2009).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. 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 (1)

Other (11)

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

Wolfram Research, Inc., Mathematica, version 7.0 ed. (Wolfram Research, Inc., 2008).

J. Li, and M. Uysal, “Optical wireless communications: system model, capacity and coding,” in Proc. VTC 2003-Fall Vehicular Technology Conference 2003 IEEE 58th, vol. 1, pp. 168–172 (2003).

J. Li, and M. Uysal, “Achievable information rate for outdoor free space optical communication with intensity modulation and direct detection,” in Proc. IEEE Global Telecommunications Conference GLOBECOM ’03, vol. 5, pp. 2654–2658 (2003).

A. A. Farid, and S. Hranilovic, “Design of non-uniform capacity-approaching signaling for optical wireless intensity channels,” in Proc. IEEE International Symposium on Information Theory ISIT 2008, pp. 2327–2331 (2008).

A. A. Farid, and S. Hranilovic, “Outage capacity with non-uniform signaling for free-space optical channels,” in Proc. 24th Biennial Symposium on Communications, pp. 204–207 (2008).

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

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “On the capacity of FSO links over gamma-gamma atmospheric turbulence channels using OOK signaling,” EURASIP J. Wireless Commun. Networking 2010), Article ID 127657, 9 pages doi:10.1155/2010/127657.

K. Davaslioglu, E. Cagiral, and M. Koca, “Free-space optical ultra-wideband communications over atmospheric turbulence channels,” Opt. Express 18(16), 618–16,627 (2010).

U. Madhow, Fundamentals of Digital Communication (Cambridge Univ. Press, 2008).

T. M. Cover, and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley & Sons, 2006).

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Figures (3)

Fig. 1.
Fig. 1.

Maximization over the input distribution p of the capacity bound, i.e. C 1(γ) in (13), and mutual information, i.e. C 2(γ) in (17), for the atmospheric turbulent optical channel and the non-turbulent case when κ = 20, a rectangular pulse shape with ξ = 1 and different diversity orders are adopted.

Fig. 2.
Fig. 2.

Mutual information in (16) versus the input distribution p for values of SNR of γ = −5 dB 2(a) and γ = −10 dB 2(b) and different diversity orders together with the non-turbulent case.

Fig. 3.
Fig. 3.

Mean value (E[Im ]) 3(a) and equivalent scintillation index (SIm ) 3(b) of the equivalent turbulence model configured by the MISO system under study versus the number of laser sources L.

Equations (20)

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

I m = max j = 1 , 2 , L I j
y ( t ) = η i m ( t ) x ( t ) h ( t ) + z ( t )
f I j ( i j ) = e i j , i j 0
f I m ( i m ) = L Σ n = 1 L ( L 1 n 1 ) ( 1 ) n 1 e n i m
x ( t ) = Σ k = a k ( 1 p ) T b P opt G ( f = 0 ) g ( t k T b ) = Σ k = a k ( 1 p ) P opt T b E g G ( f = 0 ) ϕ ( t k T b )
d = ( 1 p ) P opt T b ξ
θ = W W 1 E g G ( f ) 2 d f
C = max p 0 I ( X ; Y i m ) f I m ( i m ) d i m
I ( X ; Y i m ) 1 2 log 2 ( 1 + σ X rx 2 N o 2 )
I ( X ; Y i m ) 1 2 log 2 ( 1 + ( ( 1 p ) 1 ) P opt 2 i m 2 T b ξ θ N o 2 )
C ( γ , p ) 0 1 2 log 2 ( 1 + ( 1 p 1 ) κ ξ θ γ 2 i m 2 ) f I m ( i m ) d i m H B ( p )
C ( γ , p ) 2 L Σ n = 1 L ( 1 ) n 1 ( L 1 n 1 ) ( si ( n h ( p , γ ) ) sin ( n h ( p , γ ) ) + ci ( n h ( p , γ ) ) cos ( n h ( p , γ ) ) ) n ln ( 4 )
C 1 ( γ ) = max p C ( γ , p )
Y = A X I m + Z , X { 0 , 1 } ,     Z ~ N ( 0 , 1 )
I ( X ; Y i m ) = Σ x = 0 1 P X ( x ) f Y ( y x , i m ) log 2 ( f Y ( y x , i m ) Σ r = 0 , 1 P X ( r ) f Y ( y x = r , i m ) ) d y
I ( X ; Y ) = 0 I ( X ; Y i m ) f I m ( i m ) d i m
C 2 ( γ ) = max p I ( X ; Y )
θ = κ 2 T b κ 2 T b T b sin 2 ( π T b f ) ( π T b f ) 2 d f
E [ I m ] = L Σ n = 1 L ( 1 ) n 1 ( L 1 n 1 ) 0 i m e n i m d i m = Σ n = 1 L ( 1 ) n 1 n ( L n ) = Σ n = 1 L 1 n
E [ I m 2 ] = L Σ n = 1 L ( 1 ) n 1 ( L 1 n 1 ) 0 i m 2 e n i m d i m = 2 Σ n = 1 L ( 1 ) n 1 n 2 ( L n )

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