Abstract

We study the average capacity performance for multiple-input multiple-output (MIMO) free-space optical (FSO) communication systems using multiple partially coherent beams propagating through non-Kolmogorov strong turbulence, assuming equal gain combining diversity configuration and the sum of multiple gamma-gamma random variables for multiple independent partially coherent beams. The closed-form expressions of scintillation and average capacity are derived and then used to analyze the dependence on the number of independent diversity branches, power law α, refractive-index structure parameter, propagation distance and spatial coherence length of source beams. Obtained results show that, the average capacity increases more significantly with the increase in the rank of MIMO channel matrix compared with the diversity order. The effect of the diversity order on the average capacity is independent of the power law, turbulence strength parameter and spatial coherence length, whereas these effects on average capacity are gradually mitigated as the diversity order increases. The average capacity increases and saturates with the decreasing spatial coherence length, at rates depending on the diversity order, power law and turbulence strength. There exist optimal values of the spatial coherence length and diversity configuration for maximizing the average capacity of MIMO FSO links over a variety of atmospheric turbulence conditions.

© 2013 OSA

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  1. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm.6(8), 2813–2819 (2007).
    [CrossRef]
  2. V. W. S. Chan, “Free-Space Optical Communications,” J. Lightwave Technol.24(12), 4750–4762 (2006).
    [CrossRef]
  3. J. A. Tellez and J. D. Schmidt, “Multibeam scintillation cumulative distribution function,” Opt. Lett.36(2), 286–288 (2011).
    [CrossRef] [PubMed]
  4. H. Guo, B. Luo, Y. Ren, S. Zhao, and A. Dang, “Influence of beam wander on uplink of ground-to-satellite laser communication and optimization for transmitter beam radius,” Opt. Lett.35(12), 1977–1979 (2010).
    [CrossRef] [PubMed]
  5. A. Tunick, “Optical turbulence parameters characterized via optical measurements over a 2.33 km free-space laser path,” Opt. Express16(19), 14645–14654 (2008).
    [CrossRef] [PubMed]
  6. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt.47(34), 6385–6391 (2008).
    [CrossRef] [PubMed]
  7. E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express18(10), 10650–10658 (2010).
    [CrossRef] [PubMed]
  8. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A19(9), 1794–1802 (2002).
    [CrossRef] [PubMed]
  9. O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004).
    [CrossRef]
  10. A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using diversity-combining techniques,” Opt. Express17(15), 12601–12611 (2009).
    [CrossRef] [PubMed]
  11. 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]
  12. Y. Baykal, H. T. Eyyuboğlu, and Y. J. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt.48(10), 1943–1954 (2009).
    [CrossRef] [PubMed]
  13. J. Cang and X. Liu, “Average capacity of free-space optical systems for a partially coherent beam propagating through non-Kolmogorov turbulence,” Opt. Lett.36(17), 3335–3337 (2011).
    [CrossRef] [PubMed]
  14. G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
    [CrossRef]
  15. D. K. Borah and D. G. Voelz, “Spatially partially coherent beam parameter optimization for free space optical communications,” Opt. Express18(20), 20746–20758 (2010).
    [CrossRef] [PubMed]
  16. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express19(14), 13480–13496 (2011).
    [CrossRef] [PubMed]
  17. K. P. Peppas, F. Lazarakis, A. Alexandridis, and K. Dangakis, “Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels,” Opt. Lett.37(15), 3243–3245 (2012).
    [CrossRef] [PubMed]
  18. X. Yi, Z. Liu, and P. Yue, “Formula for the average bit error rate of free-space optical systems with dual-branch equal-gain combining over gamma-gamma turbulence channels,” Opt. Lett.38(2), 208–210 (2013).
    [CrossRef] [PubMed]
  19. I. I. Kim, H. Hakakha, P. Adhikari, E. J. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Photonics West'97(International Society for Optics and Photonics, 1997), 102–113.
  20. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, Bellingham, 2005).
  21. N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun.7(5), 1744–1753 (2008).
    [CrossRef]
  22. 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]
  23. G. Yun and M. Kavehrad, “Spot-diffusing and fly-eye receivers for indoor infrared wireless communications,” in Proceedings of IEEE International Conference on Selected Topics in Wireless Communications(IEEE, 1992), 262–265.
    [CrossRef]
  24. Z. Hajjarian and M. Kavehrad, “Using MIMO Transmissions in Free Space Optical Communications in Presence of Clouds and Turbulence,” Proc. SPIE7199, 71990V, 71990V-12 (2009).
    [CrossRef]
  25. S. Jivkova and M. Kavehrad, “Transceiver design concept for cellular and multispot diffusing regimes of transmission,” Eurasip J Wirel Comm2005, 30–38 (2005).
  26. J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
    [CrossRef]
  27. 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 Commun5(6), 1229–1233 (2006).
    [CrossRef]
  28. 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), 1554–1562 (2001).
    [CrossRef]
  29. P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (2011).
    [CrossRef]
  30. P. Deng, X. Yuan, and D. Huang, “Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence,” Opt. Commun.285(6), 880–887 (2012).
    [CrossRef]
  31. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
    [CrossRef]
  32. N. D. Chatzidiamantis, G. K. Karagiannidis, and D. S. Michalopoulos, “On the distribution of the sum of gamma-gamma variates and application in MIMO optical wireless systems,” in IEEE Global Telecommunications Conference(IEEE, 2009), 1–6.
    [CrossRef]
  33. 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]
  34. G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun.6(3), 311–335 (1998).
    [CrossRef]
  35. B. Holter, “On the capacity of the MIMO channel: A tutorial introduction,” in Proc. IEEE Norwegian Symposium on Signal Processing(IEEE, 2001), 167–172.
  36. O. Oyman, R. U. Nabar, H. Bolcskei, and A. J. Paulraj, “Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels,” in IEEE Global Telecommunications Conference, GLOBECOM'02.(IEEE, 2002), 1172–1176.
    [CrossRef]
  37. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-interscience, New York, 2012).

2013

2012

2011

2010

2009

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using diversity-combining techniques,” Opt. Express17(15), 12601–12611 (2009).
[CrossRef] [PubMed]

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]

Y. Baykal, H. T. Eyyuboğlu, and Y. J. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt.48(10), 1943–1954 (2009).
[CrossRef] [PubMed]

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]

Z. Hajjarian and M. Kavehrad, “Using MIMO Transmissions in Free Space Optical Communications in Presence of Clouds and Turbulence,” Proc. SPIE7199, 71990V, 71990V-12 (2009).
[CrossRef]

2008

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun.7(5), 1744–1753 (2008).
[CrossRef]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
[CrossRef]

A. Tunick, “Optical turbulence parameters characterized via optical measurements over a 2.33 km free-space laser path,” Opt. Express16(19), 14645–14654 (2008).
[CrossRef] [PubMed]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt.47(34), 6385–6391 (2008).
[CrossRef] [PubMed]

2007

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

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]

2006

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 Commun5(6), 1229–1233 (2006).
[CrossRef]

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

2005

S. Jivkova and M. Kavehrad, “Transceiver design concept for cellular and multispot diffusing regimes of transmission,” Eurasip J Wirel Comm2005, 30–38 (2005).

2004

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004).
[CrossRef]

2002

2001

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), 1554–1562 (2001).
[CrossRef]

1998

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun.6(3), 311–335 (1998).
[CrossRef]

Alexandridis, A.

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), 1554–1562 (2001).
[CrossRef]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004).
[CrossRef]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng.40(8), 1554–1562 (2001).
[CrossRef]

Anguita, J. A.

Bayaki, E.

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]

Baykal, Y.

Belmonte, A.

Berman, G. P.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Bishop, A. R.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Bolcskei, H.

O. Oyman, R. U. Nabar, H. Bolcskei, and A. J. Paulraj, “Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels,” in IEEE Global Telecommunications Conference, GLOBECOM'02.(IEEE, 2002), 1172–1176.
[CrossRef]

Borah, D. K.

Cai, Y. J.

Cang, J.

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Chan, V. W. S.

Chatzidiamantis, N. D.

N. D. Chatzidiamantis, G. K. Karagiannidis, and D. S. Michalopoulos, “On the distribution of the sum of gamma-gamma variates and application in MIMO optical wireless systems,” in IEEE Global Telecommunications Conference(IEEE, 2009), 1–6.
[CrossRef]

Chernobrod, B. M.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Cowley, W.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun.7(5), 1744–1753 (2008).
[CrossRef]

Dang, A.

Dangakis, K.

Davidson, F. M.

Deng, P.

P. Deng, X. Yuan, and D. Huang, “Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence,” Opt. Commun.285(6), 880–887 (2012).
[CrossRef]

P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (2011).
[CrossRef]

Djahani, P.

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

Eyyuboglu, H. T.

Fafalios, M. E.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
[CrossRef]

Foschini, G. J.

G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun.6(3), 311–335 (1998).
[CrossRef]

Gans, M. J.

G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun.6(3), 311–335 (1998).
[CrossRef]

García-Zambrana, A.

Golbraikh, E.

Gorshkov, V. N.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Guo, H.

Hajjarian, Z.

Z. Hajjarian and M. Kavehrad, “Using MIMO Transmissions in Free Space Optical Communications in Presence of Clouds and Turbulence,” Proc. SPIE7199, 71990V, 71990V-12 (2009).
[CrossRef]

Holland, I.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun.7(5), 1744–1753 (2008).
[CrossRef]

Holter, B.

B. Holter, “On the capacity of the MIMO channel: A tutorial introduction,” in Proc. IEEE Norwegian Symposium on Signal Processing(IEEE, 2001), 167–172.

Huang, D.

P. Deng, X. Yuan, and D. Huang, “Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence,” Opt. Commun.285(6), 880–887 (2012).
[CrossRef]

Jivkova, S.

S. Jivkova and M. Kavehrad, “Transceiver design concept for cellular and multispot diffusing regimes of transmission,” Eurasip J Wirel Comm2005, 30–38 (2005).

Kahn, J. M.

A. Belmonte and J. M. Kahn, “Capacity of coherent free-space optical links using diversity-combining techniques,” Opt. Express17(15), 12601–12611 (2009).
[CrossRef] [PubMed]

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

Karagianni, E. A.

Karagiannidis, G. K.

N. D. Chatzidiamantis, G. K. Karagiannidis, and D. S. Michalopoulos, “On the distribution of the sum of gamma-gamma variates and application in MIMO optical wireless systems,” in IEEE Global Telecommunications Conference(IEEE, 2009), 1–6.
[CrossRef]

Kavehrad, M.

Z. Hajjarian and M. Kavehrad, “Using MIMO Transmissions in Free Space Optical Communications in Presence of Clouds and Turbulence,” Proc. SPIE7199, 71990V, 71990V-12 (2009).
[CrossRef]

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

S. Jivkova and M. Kavehrad, “Transceiver design concept for cellular and multispot diffusing regimes of transmission,” Eurasip J Wirel Comm2005, 30–38 (2005).

G. Yun and M. Kavehrad, “Spot-diffusing and fly-eye receivers for indoor infrared wireless communications,” in Proceedings of IEEE International Conference on Selected Topics in Wireless Communications(IEEE, 1992), 262–265.
[CrossRef]

Kopeika, N. S.

Korotkova, O.

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express18(10), 10650–10658 (2010).
[CrossRef] [PubMed]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004).
[CrossRef]

Lazarakis, F.

Letzepis, N.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun.7(5), 1744–1753 (2008).
[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 Commun5(6), 1229–1233 (2006).
[CrossRef]

Liu, X.

Liu, Z.

Lizon, D. C.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Luo, B.

Luo, H.

P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (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]

Michalopoulos, D. S.

N. D. Chatzidiamantis, G. K. Karagiannidis, and D. S. Michalopoulos, “On the distribution of the sum of gamma-gamma variates and application in MIMO optical wireless systems,” in IEEE Global Telecommunications Conference(IEEE, 2009), 1–6.
[CrossRef]

Moody, D. I.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Nabar, R. U.

O. Oyman, R. U. Nabar, H. Bolcskei, and A. J. Paulraj, “Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels,” in IEEE Global Telecommunications Conference, GLOBECOM'02.(IEEE, 2002), 1172–1176.
[CrossRef]

Navidpour, S. M.

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

Neifeld, M. A.

Nguyen, D. C.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Nistazakis, H. E.

Oyman, O.

O. Oyman, R. U. Nabar, H. Bolcskei, and A. J. Paulraj, “Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels,” in IEEE Global Telecommunications Conference, GLOBECOM'02.(IEEE, 2002), 1172–1176.
[CrossRef]

Paulraj, A. J.

O. Oyman, R. U. Nabar, H. Bolcskei, and A. J. Paulraj, “Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels,” in IEEE Global Telecommunications Conference, GLOBECOM'02.(IEEE, 2002), 1172–1176.
[CrossRef]

Peppas, K. P.

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004).
[CrossRef]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng.40(8), 1554–1562 (2001).
[CrossRef]

Ren, Y.

Ricklin, J. C.

Schmidt, J. D.

Schober, R.

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]

Shchepakina, E.

Tang, A.

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

Teik, B. K.

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

Tellez, J. A.

Tombras, G. S.

Torous, S. V.

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
[CrossRef]

Tsigopoulos, A. D.

Tunick, A.

Uysal, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm.6(8), 2813–2819 (2007).
[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 Commun5(6), 1229–1233 (2006).
[CrossRef]

Vasic, B. V.

Voelz, D. G.

Weisbin, A. G.

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

Yi, X.

You, R.

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

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 Commun5(6), 1229–1233 (2006).
[CrossRef]

Yuan, X.

P. Deng, X. Yuan, and D. Huang, “Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence,” Opt. Commun.285(6), 880–887 (2012).
[CrossRef]

P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (2011).
[CrossRef]

Yue, P.

Yun, G.

G. Yun and M. Kavehrad, “Spot-diffusing and fly-eye receivers for indoor infrared wireless communications,” in Proceedings of IEEE International Conference on Selected Topics in Wireless Communications(IEEE, 1992), 262–265.
[CrossRef]

Zeng, Y.

P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (2011).
[CrossRef]

Zhao, M.

P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (2011).
[CrossRef]

Zhao, S.

Zilberman, A.

Appl. Opt.

Eurasip J Wirel Comm

S. Jivkova and M. Kavehrad, “Transceiver design concept for cellular and multispot diffusing regimes of transmission,” Eurasip J Wirel Comm2005, 30–38 (2005).

IEEE Commun. Mag.

J. M. Kahn, R. You, P. Djahani, A. G. Weisbin, B. K. Teik, and A. Tang, “Imaging diversity receivers for high-speed infrared wireless communication,” IEEE Commun. Mag.36(12), 88–94 (1998).
[CrossRef]

IEEE Trans. Commun.

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]

IEEE Trans. Wirel. Comm.

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

IEEE Trans. Wireless Commun

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 Commun5(6), 1229–1233 (2006).
[CrossRef]

IEEE Trans. Wireless Commun.

N. Letzepis, I. Holland, and W. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun.7(5), 1744–1753 (2008).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Phys. B

G. P. Berman, A. R. Bishop, B. M. Chernobrod, V. N. Gorshkov, D. C. Lizon, D. I. Moody, D. C. Nguyen, and S. V. Torous, “Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam,” J. Phys. B42(22), 225403 (2009).
[CrossRef]

J. Phys. Conf. Ser.

P. Deng, X. Yuan, Y. Zeng, M. Zhao, and H. Luo, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non kolmogorov strong turbulence,” J. Phys. Conf. Ser.276, 012056 (2011).
[CrossRef]

Opt. Commun.

P. Deng, X. Yuan, and D. Huang, “Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence,” Opt. Commun.285(6), 880–887 (2012).
[CrossRef]

Opt. Eng.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng.47(2), 026003–026009 (2008).
[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(8), 1554–1562 (2001).
[CrossRef]

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

Z. Hajjarian and M. Kavehrad, “Using MIMO Transmissions in Free Space Optical Communications in Presence of Clouds and Turbulence,” Proc. SPIE7199, 71990V, 71990V-12 (2009).
[CrossRef]

Wirel. Pers. Commun.

G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun.6(3), 311–335 (1998).
[CrossRef]

Other

B. Holter, “On the capacity of the MIMO channel: A tutorial introduction,” in Proc. IEEE Norwegian Symposium on Signal Processing(IEEE, 2001), 167–172.

O. Oyman, R. U. Nabar, H. Bolcskei, and A. J. Paulraj, “Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels,” in IEEE Global Telecommunications Conference, GLOBECOM'02.(IEEE, 2002), 1172–1176.
[CrossRef]

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-interscience, New York, 2012).

N. D. Chatzidiamantis, G. K. Karagiannidis, and D. S. Michalopoulos, “On the distribution of the sum of gamma-gamma variates and application in MIMO optical wireless systems,” in IEEE Global Telecommunications Conference(IEEE, 2009), 1–6.
[CrossRef]

G. Yun and M. Kavehrad, “Spot-diffusing and fly-eye receivers for indoor infrared wireless communications,” in Proceedings of IEEE International Conference on Selected Topics in Wireless Communications(IEEE, 1992), 262–265.
[CrossRef]

I. I. Kim, H. Hakakha, P. Adhikari, E. J. Korevaar, and A. K. Majumdar, “Scintillation reduction using multiple transmitters,” in Photonics West'97(International Society for Optics and Photonics, 1997), 102–113.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, Bellingham, 2005).

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Figures (4)

Fig. 1
Fig. 1

Average channel capacity versus average SNR for MIMOFSO IM/DD links with multiple partially coherent beams in Gamma–Gamma atmospheric turbulence. Performance is shown for different values of: (a) the number of transmit and receive apertures number M × N, (b) the spatial coherence length lc of the beam source with different diversity configurations, (c) the power law ��of non-Kolmogorov turbulence with various diversity orders and (d) the power law �� with different spatial coherence length.

Fig. 2
Fig. 2

Average channel capacity versus power law �� for MIMOFSO IM/DD links with multiple partially coherent beams in Gamma–Gamma atmospheric turbulence channels. Performance is shown for different values of: (a) the number of transmit and receive apertures M × N, (b) scintillation index as a function of ��, (c) the spatial coherence length lc of the beam source with various diversity configurations and the turbulence strength parameter Cn2 with different diversity orders.

Fig. 3
Fig. 3

Average channel capacity versus propagation distance for MIMOFSO IM/DD links with multiple partially coherent beams in Gamma–Gamma atmospheric turbulence channels. Performance is shown for different values of: (a) the number of transmit and receive apertures M × N, (b) scintillation index as a function of distance L, (c) the spatial coherence length lc of the beam source with various diversity orders and (d) the power law �� with different diversity configurations.

Fig. 4
Fig. 4

Average channel capacity versus spatial coherence length of partially coherent beams for MIMOFSO IM/DD links in Gamma–Gamma atmospheric turbulence channels. Performance is shown for the various values of: (a) the number of transmit and receive apertures M × N, (b) the special case M = 2 N = 2, (c)the power law �� in the case M = 2 N = 2,(d) the turbulence structure parameter Cn2in the case M = 2 N = 2, (e) the longitude scintillation index as a function of coherence length and (f) the large scale and small scale log-irradiance variance as a function of coherence length.

Equations (37)

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r n =xη m=1 M I mn + υ n ,n=1,...N
p I ( I mn , α 1 , β 1 )= 2 ( α 1 β 1 ) ( α 1 + β 1 )/2 Γ( α 1 )Γ( β 1 ) ( I mn ) ( α 1 + β 1 )/21 K α 1 β 1 ( 2 α 1 β 1 I mn ), I mn >0
α 1 = 1 σ X 2 = 1 exp( σ lnX 2 )1 , β 1 = 1 σ Y 2 = 1 exp( σ lnY 2 )1
Φ n (κ,α)=A( α ) C ˜ n 2 κ α ,2π/ L 0 κ2π/ l 0 ,3<α<4.
σ lnX 2 ( L,α )= 0.49 σ ˜ B 2 [1+ f x (α, Θ ¯ ed ) σ ˜ R 4 α2 ] 3 α 2
f x (α, Θ ¯ ed )= ( V(α, Θ ¯ ed )Z(α, Θ ¯ ed ) 0.98 × σ ˜ R 2 σ ˜ B 2 ) 2 α6
V(α, Θ ¯ ed )= 8 π 2 A(α) 1.23R(α)(α2) Γ( 6α α2 )B (α, Θ ¯ ed ) α6 α2
B(α, Θ ¯ ed )= π 2 1.23 4 2 α 2 Γ(1α/2) Γ(α/2) A(α) R(α) 1 Θ ¯ ed (α1)
Z(α, Θ ¯ ed )= 0 1 ξ α4 (1 Θ ¯ ed ξ) 2 [ (1 Θ ¯ ed ξ) α2 (1 Θ ¯ ed ) α1 ] 6α α2 dξ .
σ ˜ R 2 (α)=6.5 π 2 A(α)Γ(1 α 2 ) 1 α sin(α π 4 )×1.23 C ˜ n 2 k 3 α 2 L α 2
σ ˜ B 2 (α)= 1 α1 A(α) C ˜ n 2 π 2 k 3 α 2 L α/2 Γ( 2α 2 ) ×{ Λ ed α 2 1 Re[ 2α2 α i α2 α F 2 1 ( 2α 2 , α 2 ; 2+α 2 ; Θ ¯ ed +i Λ ed )]}
σ lnY 2 (α)= 0.51 σ ˜ B 2 (α) (1+ f Y (α) σ ˜ R 4 α2 ) α2 2
r= 1 MN n=1 N r n = xη MN n=1 N m=1 M I mn +υ.
I S = i=1 S=M×N I i = i=1 S x i y i
I S = 1 S ( i=1 S x i )( i=1 S y i )+ 1 S ( i=1 S1 j=i+1 S ( x i x j )( y i y j )
ε S =(S1) 0.1270.95 α 1 0.0058 β 1 1+0.00124 α 1 +0.98 β 1
α S =S α 1 + ε S , β S =S β 1
σ lnXs 2 =ln(1+ 1 α S ), σ lnYs 2 =ln(1+ 1 β S )
σ I S 2 =exp( σ lnXs 2 + σ lnYs 2 )1 = 1 α S β S + 1 α S + 1 β S ,0 σ R 2
p I S ( I s , α S , β S )= 2 ( α S β S ) α S + β S 2 Γ( α S )Γ( β S ) I s ( I s MN ) α S + β S 2 K α S β S ( 2 α S β S I s MN )
C MN = log 2 det( I N + u M H H )
C MN = log 2 det( I N + u M UΣ Σ U )
C MN = log 2 det(U U + u M UΣ Σ U ) = log 2 det( I N + u M Σ Σ ) = log 2 i=1 N m (1+ u M σ i 2 )
N m =rank(H)min(M,N).
C MN = i=1 N m log 2 (1+ u M σ i 2 ) N m log 2 (1+ u M N m i=1 N m σ i 2 )
C MN N m log 2 (1+ u M N m Tr[H H ]) = N m log 2 (1+ 1 M N m i=1 N j=1 M u ij )
h ij =a+jb = a 2 + b 2 e jarctan b a =| h ij | e j ϕ ij
C MN N m log 2 (1+ 1 M N m i=1 N j=1 M u ij )
C 11 log 2 (1+ u 11 )
C 1N log 2 (1+ i=1 N u i )
C M1 log 2 (1+ 1 M i=1 M u i )
C NN N log 2 (1+ 1 N 2 i=1 N u i )
C MN E{ N m log 2 (1+ 1 M N m i=1 N j=1 M u ij ) } N m 0 log 2 (1+ u s M N m ) p u s ( u s )d u s
p u S ( u s )= ( α S β S ) ( α S + β S )/2 u s ( α S + β S )/41 Γ( α S )Γ( β S ) u ¯ s ( α S + β S )/4 K α S β S ( 2 α S β S u s u ¯ s )
C MN max = N m ( α S β S ) ( α S + β S )/2 4πΓ( α S )Γ( β S )ln2 u ¯ s ( α S + β S )/4 × 0 ln(1+ u s M N m ) u s ( α S + β S )/41 K α S β S ( 2 α S β S u s u ¯ s )d u s
C MN max = N m ( α S β S ) ( α S + β S )/2 4πΓ( α S )Γ( β S )ln2 ( u ¯ m ) ( α S + β S )/4 × 0 ln(1+ u m ) ( u m ) ( α S + β S )/41 K α S β S ( 2 α S β S u m u ¯ m )d u m
< C MN > max = N m ( α S β S ) ( α S + β S )/2 4πΓ( α S )Γ( β S )ln(2) ( μ ¯ m ) ( α S + β S )/4 × G 2,6 6,1 [ ( α S β S ) 2 16 μ ¯ m | α S + β S 4 , α S + β S 4 +1 α S β S 4 , α S β S +2 4 , α S β S 4 , ( α S β S )+2 4 , α S + β S 4 , α S + β S 4 ]

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