Abstract

In this work, the ergodic capacity performance for multiple-input/single-output (MISO) free-space optical (FSO) communications system with equal gain combining (EGC) reception is analyzed over gamma-gamma and misalignment fading channels, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.). Novel and analytical closed-form ergodic capacity expression is obtained in terms of H-Fox function by using the well-known inequality between arithmetic and geometric mean of positive random variables (RV) in order to obtain an approximate closed-form expression of the distribution of the sum of M gamma-gamma with pointing errors variates. In addition, we present an asymptotic ergodic capacity expression at high signal-to-noise ratio (SNR) for the ergodic capacity of MISO FSO systems. It can be concluded that the use of MISO technique can significantly reduce the effect of the atmospheric turbulence as well as pointing errors and, hence, provide significant capacity gain over the direct path link (DL). The impact of pointing errors on the MISO FSO system is also analyzed, which only depends on the number of laser sources and pointing error parameters. Moreover, it can be also concluded that the ergodic capacity performance is dramatically reduced as a consequence of the severity of pointing error effects. Simulation results are further demonstrated to confirm the analytical results.

© 2015 Optical Society of America

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References

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2015 (1)

I. Ansari, M.-S. Alouini, and J. Cheng, “Ergodic Capacity Analysis of Free-Space Optical Links with Nonzero Boresight Pointing Errors,” IEEE Trans. Wireless Communications PP(99), 1 (2015).
[Crossref]

2014 (2)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Communications Surveys Tutorials 16(4), 2231–2258 (2014).
[Crossref]

A. García-Zambrana, R. Boluda-Ruiz, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Transmit alternate laser selection with time diversity for FSO communications,” Opt. Express 22(20), 23,861–23,874 (2014).
[Crossref]

2013 (4)

2012 (1)

2011 (1)

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of gamma-gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59(5), 1298–1308 (2011).
[Crossref]

2010 (2)

2009 (5)

2008 (1)

2007 (2)

2005 (1)

H. Yuksel, S. Milner, and C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Commun. Netw. 4(8), 462–475 (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 (1)

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]

1999 (1)

1979 (1)

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]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16(6), 1417–1429 (1999).
[Crossref]

Alouini, M.

F. Benkhelifa, Z. Rezki, and M. Alouini, “Low SNR Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels,” IEEE Commun, Lett. 17(6), 1264–1267 (2013).
[Crossref]

I. Ansari, F. Yilmaz, and M. Alouini, “A unified performance of free-space optical links over Gamma-Gamma turbulence channels with pointing errors,” submitted to IEEE Transactions on Communications, technical report available at http://hdl.handle.net/10754/305353 (2015).

Alouini, M.-S.

I. Ansari, M.-S. Alouini, and J. Cheng, “Ergodic Capacity Analysis of Free-Space Optical Links with Nonzero Boresight Pointing Errors,” IEEE Trans. Wireless Communications PP(99), 1 (2015).
[Crossref]

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

F. Yilmaz and M.-S. Alouini, “Product of the powers of generalized Nakagami-m variates and performance of cascaded fading channels,” in Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE, pp. 1–8 (IEEE, 2009).
[Crossref]

Andrews, L.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications, vol. 99 (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]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16(6), 1417–1429 (1999).
[Crossref]

Anguita, J.

J. 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]

J. Anguita and J. E. Cisternas, “Experimental evaluation of transmitter and receiver diversity in a terrestrial FSO link,” in GLOBECOM Workshops (GC Wkshps), 2010 IEEE, pp. 1005–1009 (IEEE, 2010).
[Crossref]

Ansari, I.

I. Ansari, M.-S. Alouini, and J. Cheng, “Ergodic Capacity Analysis of Free-Space Optical Links with Nonzero Boresight Pointing Errors,” IEEE Trans. Wireless Communications PP(99), 1 (2015).
[Crossref]

I. Ansari, F. Yilmaz, and M. Alouini, “A unified performance of free-space optical links over Gamma-Gamma turbulence channels with pointing errors,” submitted to IEEE Transactions on Communications, technical report available at http://hdl.handle.net/10754/305353 (2015).

Arnon, S.

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]

Benkhelifa, F.

F. Benkhelifa, Z. Rezki, and M. Alouini, “Low SNR Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels,” IEEE Commun, Lett. 17(6), 1264–1267 (2013).
[Crossref]

Boluda-Ruiz, R.

A. García-Zambrana, R. Boluda-Ruiz, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Transmit alternate laser selection with time diversity for FSO communications,” Opt. Express 22(20), 23,861–23,874 (2014).
[Crossref]

Borah, D. K.

Brychkov, Y. A.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and series Volume 3: More Special Functions, vol. 3 (Gordon and Breach Science Publishers, 1999).

Castillo-Vázquez, B.

A. García-Zambrana, R. Boluda-Ruiz, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Transmit alternate laser selection with time diversity for FSO communications,” Opt. Express 22(20), 23,861–23,874 (2014).
[Crossref]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Asymptotic error-rate analysis of FSO links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(3), 2096–2109 (2012).
[Crossref] [PubMed]

Castillo-Vázquez, C.

A. García-Zambrana, R. Boluda-Ruiz, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Transmit alternate laser selection with time diversity for FSO communications,” Opt. Express 22(20), 23,861–23,874 (2014).
[Crossref]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Asymptotic error-rate analysis of FSO links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(3), 2096–2109 (2012).
[Crossref] [PubMed]

Castillo-Vázquez, M.

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]

Chatzidiamantis, N. D.

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of gamma-gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59(5), 1298–1308 (2011).
[Crossref]

Cheng, J.

Cisternas, J. E.

J. Anguita and J. E. Cisternas, “Experimental evaluation of transmitter and receiver diversity in a terrestrial FSO link,” in GLOBECOM Workshops (GC Wkshps), 2010 IEEE, pp. 1005–1009 (IEEE, 2010).
[Crossref]

Dai, L.

J. Zhang, L. Dai, Y. Han, Y. Zhang, and Z. Wang, “On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels,” IEEE J. Sel. Areas Commun. (to be published) (2015).
[Crossref]

Davis, C.

H. Yuksel, S. Milner, and C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Commun. Netw. 4(8), 462–475 (2005).
[Crossref]

Deng, P.

Fafalios, M. E.

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).

Galambos, J.

J. Galambos and I. Simonelli, Products of Random Variables: Applications to Problems of Physics and to Arithmetical Functions (CRC Press, 2004).

García-Zambrana, A.

A. García-Zambrana, R. Boluda-Ruiz, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Transmit alternate laser selection with time diversity for FSO communications,” Opt. Express 22(20), 23,861–23,874 (2014).
[Crossref]

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Asymptotic error-rate analysis of FSO links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(3), 2096–2109 (2012).
[Crossref] [PubMed]

Garrido-Balsells, J. M.

Gradshteyn, I. S.

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

Han, Y.

J. Zhang, L. Dai, Y. Han, Y. Zhang, and Z. Wang, “On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels,” IEEE J. Sel. Areas Commun. (to be published) (2015).
[Crossref]

Hassan, M. Z.

Hogge, C. B.

Hopen, C.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications, vol. 99 (SPIE press, 2001).
[Crossref]

Hopen, C. Y.

Hossain, M. J.

Hranilovic, S.

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).

Jain, V. K.

P. Kaur, V. K. Jain, and S. Kar, “Capacity of free space optical links with spatial diversity and aperture averaging,” in Communications (QBSC), 2014 27th Biennial Symposium on, pp. 14–18 (IEEE, 2014).
[Crossref]

Jurado-Navas, A.

Kar, S.

P. Kaur, V. K. Jain, and S. Kar, “Capacity of free space optical links with spatial diversity and aperture averaging,” in Communications (QBSC), 2014 27th Biennial Symposium on, pp. 14–18 (IEEE, 2014).
[Crossref]

Karagianni, E. A.

Karagiannidis, G. K.

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of gamma-gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59(5), 1298–1308 (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]

Kaur, P.

P. Kaur, V. K. Jain, and S. Kar, “Capacity of free space optical links with spatial diversity and aperture averaging,” in Communications (QBSC), 2014 27th Biennial Symposium on, pp. 14–18 (IEEE, 2014).
[Crossref]

Kavehrad, M.

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Communications Surveys Tutorials 16(4), 2231–2258 (2014).
[Crossref]

Kilbas, A. A.

A. A. Kilbas, H-transforms: Theory and Applications (CRC Press, 2004).
[Crossref]

Kim, I. I.

I. I. Kim, B. McArthur, and E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Information Technologies 2000, pp. 26–37 (International Society for Optics and Photonics, 2001).

Korevaar, E. J.

I. I. Kim, B. McArthur, and E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Information Technologies 2000, pp. 26–37 (International Society for Optics and Photonics, 2001).

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]

Liu, C.

Liu, Z.

Loos, G. C.

Louthain, J. A.

Luong, D. A.

D. A. Luong, T. C. Thang, and A. T. Pham, “Average capacity of MIMO/FSO systems with equal gain combining over log-normal channels,” in Ubiquitous and Future Networks (ICUFN), 2013 Fifth International Conference on, pp. 306–309 (IEEE, 2013).
[Crossref]

D. A. Luong and A. T. Pham, “Average capacity of MIMO free-space optical gamma-gamma fading channel,” in Communications (ICC), 2014 IEEE International Conference on, pp. 3354–3358 (IEEE, 2014).
[Crossref]

Majumdar, A. K.

A. K. Majumdar and J. C. Ricklin, Free-space laser communications: principles and advances, vol. 2 (Springer Science & Business Media, 2010).

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]

Marichev, O. I.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and series Volume 3: More Special Functions, vol. 3 (Gordon and Breach Science Publishers, 1999).

McArthur, B.

I. I. Kim, B. McArthur, and E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Information Technologies 2000, pp. 26–37 (International Society for Optics and Photonics, 2001).

Milner, S.

H. Yuksel, S. Milner, and C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Commun. Netw. 4(8), 462–475 (2005).
[Crossref]

Neifeld, M. A.

Nistazakis, H. E.

Paris, J. F.

Pham, A. T.

D. A. Luong and A. T. Pham, “Average capacity of MIMO free-space optical gamma-gamma fading channel,” in Communications (ICC), 2014 IEEE International Conference on, pp. 3354–3358 (IEEE, 2014).
[Crossref]

D. A. Luong, T. C. Thang, and A. T. Pham, “Average capacity of MIMO/FSO systems with equal gain combining over log-normal channels,” in Ubiquitous and Future Networks (ICUFN), 2013 Fifth International Conference on, pp. 306–309 (IEEE, 2013).
[Crossref]

Phillips, R.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications, vol. 99 (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).
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L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am. A 16(6), 1417–1429 (1999).
[Crossref]

Prudnikov, A. P.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and series Volume 3: More Special Functions, vol. 3 (Gordon and Breach Science Publishers, 1999).

Puerta-Notario, A.

Rezki, Z.

F. Benkhelifa, Z. Rezki, and M. Alouini, “Low SNR Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels,” IEEE Commun, Lett. 17(6), 1264–1267 (2013).
[Crossref]

Ricklin, J. C.

A. K. Majumdar and J. C. Ricklin, Free-space laser communications: principles and advances, vol. 2 (Springer Science & Business Media, 2010).

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

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. 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]

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]

Simon, M. K.

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

Simonelli, I.

J. Galambos and I. Simonelli, Products of Random Variables: Applications to Problems of Physics and to Arithmetical Functions (CRC Press, 2004).

Sun, Y.

Thang, T. C.

D. A. Luong, T. C. Thang, and A. T. Pham, “Average capacity of MIMO/FSO systems with equal gain combining over log-normal channels,” in Ubiquitous and Future Networks (ICUFN), 2013 Fifth International Conference on, pp. 306–309 (IEEE, 2013).
[Crossref]

Tombras, G. S.

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]

Tsigopoulos, A. D.

Uysal, M.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Communications Surveys Tutorials 16(4), 2231–2258 (2014).
[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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J. Zhang, L. Dai, Y. Han, Y. Zhang, and Z. Wang, “On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels,” IEEE J. Sel. Areas Commun. (to be published) (2015).
[Crossref]

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M. D. Yacoub, “The α-μ distribution: A general fading distribution,” in Proc. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 2, pp. 629–633 (2002).
[Crossref]

Yao, Y.

Yilmaz, F.

F. Yilmaz and M.-S. Alouini, “Product of the powers of generalized Nakagami-m variates and performance of cascaded fading channels,” in Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE, pp. 1–8 (IEEE, 2009).
[Crossref]

I. Ansari, F. Yilmaz, and M. Alouini, “A unified performance of free-space optical links over Gamma-Gamma turbulence channels with pointing errors,” submitted to IEEE Transactions on Communications, technical report available at http://hdl.handle.net/10754/305353 (2015).

Yuan, X.

Yuksel, H.

H. Yuksel, S. Milner, and C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Commun. Netw. 4(8), 462–475 (2005).
[Crossref]

Zhang, J.

J. Zhang, L. Dai, Y. Han, Y. Zhang, and Z. Wang, “On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels,” IEEE J. Sel. Areas Commun. (to be published) (2015).
[Crossref]

Zhang, Y.

J. Zhang, L. Dai, Y. Han, Y. Zhang, and Z. Wang, “On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels,” IEEE J. Sel. Areas Commun. (to be published) (2015).
[Crossref]

Zhao, X.

Zhou, Z.

Appl. Opt. (2)

Chin. Opt. Lett. (1)

IEEE Commun, Lett. (1)

F. Benkhelifa, Z. Rezki, and M. Alouini, “Low SNR Capacity of FSO Links over Gamma-Gamma Atmospheric Turbulence Channels,” IEEE Commun, Lett. 17(6), 1264–1267 (2013).
[Crossref]

IEEE Communications Surveys Tutorials (1)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Communications Surveys Tutorials 16(4), 2231–2258 (2014).
[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 Trans. Commun. (2)

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]

N. D. Chatzidiamantis and G. K. Karagiannidis, “On the distribution of the sum of gamma-gamma variates and applications in RF and optical wireless communications,” IEEE Trans. Commun. 59(5), 1298–1308 (2011).
[Crossref]

IEEE Trans. Wireless Commun. (1)

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]

IEEE Trans. Wireless Communications (1)

I. Ansari, M.-S. Alouini, and J. Cheng, “Ergodic Capacity Analysis of Free-Space Optical Links with Nonzero Boresight Pointing Errors,” IEEE Trans. Wireless Communications PP(99), 1 (2015).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Commun. Netw. (1)

H. Yuksel, S. Milner, and C. Davis, “Aperture averaging for optimizing receiver design and system performance on free-space optical communication links,” J. Opt. Commun. Netw. 4(8), 462–475 (2005).
[Crossref]

J. Opt. Soc. Am. A (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 (6)

Opt. Lett. (2)

Other (18)

J. Anguita and J. E. Cisternas, “Experimental evaluation of transmitter and receiver diversity in a terrestrial FSO link,” in GLOBECOM Workshops (GC Wkshps), 2010 IEEE, pp. 1005–1009 (IEEE, 2010).
[Crossref]

I. I. Kim, B. McArthur, and E. J. Korevaar, “Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications,” in Information Technologies 2000, pp. 26–37 (International Society for Optics and Photonics, 2001).

P. Kaur, V. K. Jain, and S. Kar, “Capacity of free space optical links with spatial diversity and aperture averaging,” in Communications (QBSC), 2014 27th Biennial Symposium on, pp. 14–18 (IEEE, 2014).
[Crossref]

J. Zhang, L. Dai, Y. Han, Y. Zhang, and Z. Wang, “On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels,” IEEE J. Sel. Areas Commun. (to be published) (2015).
[Crossref]

M. D. Yacoub, “The α-μ distribution: A general fading distribution,” in Proc. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 2, pp. 629–633 (2002).
[Crossref]

A. K. Majumdar and J. C. Ricklin, Free-space laser communications: principles and advances, vol. 2 (Springer Science & Business Media, 2010).

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

J. Galambos and I. Simonelli, Products of Random Variables: Applications to Problems of Physics and to Arithmetical Functions (CRC Press, 2004).

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and series Volume 3: More Special Functions, vol. 3 (Gordon and Breach Science Publishers, 1999).

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

A. A. Kilbas, H-transforms: Theory and Applications (CRC Press, 2004).
[Crossref]

F. Yilmaz and M.-S. Alouini, “Product of the powers of generalized Nakagami-m variates and performance of cascaded fading channels,” in Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE, pp. 1–8 (IEEE, 2009).
[Crossref]

D. A. Luong, T. C. Thang, and A. T. Pham, “Average capacity of MIMO/FSO systems with equal gain combining over log-normal channels,” in Ubiquitous and Future Networks (ICUFN), 2013 Fifth International Conference on, pp. 306–309 (IEEE, 2013).
[Crossref]

D. A. Luong and A. T. Pham, “Average capacity of MIMO free-space optical gamma-gamma fading channel,” in Communications (ICC), 2014 IEEE International Conference on, pp. 3354–3358 (IEEE, 2014).
[Crossref]

I. Ansari, F. Yilmaz, and M. Alouini, “A unified performance of free-space optical links over Gamma-Gamma turbulence channels with pointing errors,” submitted to IEEE Transactions on Communications, technical report available at http://hdl.handle.net/10754/305353 (2015).

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

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).

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation with Applications, vol. 99 (SPIE press, 2001).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Block diagram of the considered MISO FSO communications system.
Fig. 2
Fig. 2 Ergodic capacity for a source-destination link distance of dSD= 3 km when different weather conditions and values of normalized beam width and normalized jitter of (ωz/r, σs/r) =(5,1) and (ωz/r, σs/r)=(10,2) are assumed.
Fig. 3
Fig. 3 Gain for a source-destination link distance of dSD = 3 km when different weather conditions and a value of normalized beam width of ωz/r = 7 and values of normalized jitter of σs/r = {1, 3, 4} are assumed.
Fig. 4
Fig. 4 Ergodic capacity for a source-destination link distance of dSD = 3 km when different weather conditions and a value of normalized beam width of ωz/r = 7 and values of normalized jitter of σs/r = {1, 3} are assumed.

Equations (33)

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f I ( i ) = φ 2 i 1 Γ ( α ) Γ ( β ) G 1 , 3 3 , 0 ( α β A 0 L i | φ 2 + 1 φ 2 , α , β ) , i 0
α = [ exp ( 0.49 σ R 2 / ( 1 + 1.11 σ R 12 / 5 ) 7 / 6 ) 1 ] 1 ,
β = [ exp ( 0.51 σ R 2 / ( 1 + 0.69 σ R 12 / 5 ) 5 / 6 ) 1 ] 1 .
θ 0 = ( 2.91 κ 2 0 d C n 2 ( z ) z 5 / 3 d z ) 3 / 5 = 0.94 ( κ 2 C n 2 d 8 / 3 ) 3 / 5 .
Y = X 1 M k = 1 M I k + Z , X { 0 , 2 P opt } , Z ~ N ( 0 , N 0 / 2 ) ,
γ MISO = 1 2 ( 2 P opt / M ) 2 σ n 2 ( k = 1 M I k ) 2 = 4 P opt 2 I T 2 M 2 N 0 = 4 γ 0 M 2 I T 2 ,
C MISO = B 2 ln ( 2 ) 0 ln ( 1 + 4 γ 0 M 2 i 2 ) f I T ( i ) d i ,
AM GM ,
I T = k = 1 M I k M F k = 1 M I k M = M F I LB M .
C MISO B ln ( 4 ) 0 ln ( 1 + 4 γ 0 ( i F ) 2 M ) f I LB ( i ) d i .
f I LB ( i ) = i 1 k = 1 M φ k 2 G M , 3 M 3 M , 0 ( k = 1 M α m β k A k L k i | φ 1 2 + 1 , , φ M 2 + 1 φ 1 2 , α 1 , β , , φ M 2 , α M , β M ) k = 1 M Γ ( α k ) Γ ( β k ) .
C MISO B k = 1 M φ k 2 H 2 + 3 M , 2 + M 1 , 2 + 3 M ( 4 γ 0 F M ( k = 1 M A k L k α k β k ) 2 M | ( 1 , 1 ) , ( 1 , 1 ) , ξ 1 ( 1 , 1 ) , ξ 2 ( 0 , 1 ) ) ln ( 4 ) k = 1 M Γ ( α k ) Γ ( β k ) ,
C MISO H B ln ( 4 γ 0 ) ln ( 4 ) + B ln ( F ) M ln ( 2 ) + B M ln ( 2 ) k = 1 M 0 ln ( i k ) f I k ( i k ) d i k .
ln ( z ) = z ln ( z ) z 1 ln ( z ) z 1 .
C MISO H B ln ( 4 γ 0 ) ln ( 4 ) + B ln ( F ) M ln ( 2 ) + B M ln ( 2 ) ( k = 1 M 0 i k G 2 , 2 2 , 2 ( i k | 0 , 0 0 , 0 ) f I k ( i k ) d i k k = 1 M 0 G 2 , 2 2 , 2 ( i k | 0 , 0 0 , 0 ) f I k ( i k ) d i k ) .
C MISO H B ln ( 4 γ 0 ) ln ( 4 ) + B ln ( F ) M ln ( 2 ) + B M ln ( 2 ) k = 1 M φ k 2 Γ ( α k ) Γ ( β k ) × ( G 3 , 5 5 , 2 ( α k β k A k L k | 0 , 0 , φ k 2 + 1 φ k 2 , α k , β k , 0 , 0 ) G 3 , 5 5 , 2 ( α k β k A k L k | 1 , 1 , φ k 2 + 1 φ k 2 , α k , β k , 1 , 1 ) ) .
C MISO H B ln ( 4 γ 0 ) ln ( 4 ) + B ln ( F ) M ln ( 2 ) + B M ln ( 2 ) k = 1 M ψ ( α k ) + ψ ( β k ) 1 φ k 2 ln ( α k β k A k L k ) ,
γ MISO th [ d B ] = 20 ln ( 10 ) ( ln ( F ) M + ln ( 2 ) + 1 M k = 1 M ψ ( α k ) + ψ ( β k ) ln ( α k β k A k L k ) 1 φ k 2 ) .
γ DL th [ d B ] = 20 ln ( 10 ) ( ln ( 2 ) + ψ ( α DL ) + ψ ( β DL ) ln ( α DL β DL A DL L DL ) 1 φ DL 2 ) ,
G MISO [ d B ] = γ DL th [ d B ] γ MISO th [ d B ] = 20 ln ( F ) M ln ( 10 ) .
k = 1 M lim φ k 2 + Γ ( φ k 2 + 1 ) Γ ( φ k 2 2 s M ) Γ ( φ k 2 ) Γ ( 1 + φ k 2 2 s M ) = k = 1 M lim φ k 2 + M φ k 2 M φ k 2 2 s = 1 .
C MISO npe B H 2 + 2 M , 2 1 , 2 + 2 M ( 4 γ 0 F npe M ( k = 1 M L k α k β k ) 2 M | ( 1 , 1 ) , ( 1 , 1 ) , ξ 3 ( 1 , 1 ) , ( 0 , 1 ) ) ln ( 4 ) k = 1 M Γ ( α k ) Γ ( β k ) ,
C MISO H npe B ln ( 4 γ 0 ) ln ( 4 ) + B ln ( F npe ) M ln ( 2 ) + B M ln ( 2 ) k = 1 M ψ ( α k ) + ψ ( β k ) ln ( α k β k L k ) .
γ MISO th npe [ d B ] = 20 ln ( 10 ) ( ln ( F npe ) M + ln ( 2 ) + 1 M k = 1 M ψ ( α k ) + ψ ( β k ) ln ( α k β k L k ) ) .
D pe [ d B ] γ MISO th [ d B ] γ MISO th npe [ d B ] = 20 M ln ( 10 ) ( ln ( F npe F ) + k = 1 M 1 φ k 2 ln ( A k ) ) .
D pe [ d B ] 20 ln ( 10 ) ( M ln ( M φ 2 M φ 2 + 1 ) + ln ( φ 2 + 1 φ 2 ) + 1 φ 2 ln ( A 0 ) ) .
F = 𝔼 [ I T ] M M M 𝔼 [ I LB M ] M .
𝔼 [ I k ] = 0 i f I k ( i ) d i .
𝔼 [ I T ] = k = 1 M A k L k φ k 2 1 + φ k 2 .
𝔼 [ I k M ] = 0 i 1 / M f I k ( i ) d i .
𝔼 [ I LB M ] = k = 1 M M φ k 2 Γ ( α k + 1 M ) Γ ( β k + 1 M ) Γ ( α k ) Γ ( β k ) ( M φ k 2 + 1 ) ( α k β k A k L k ) 1 / M .
𝔼 [ I T ] npe = k = 1 M L k ,
𝔼 [ I LB M ] npe = k = 1 M Γ ( α k + 1 M ) Γ ( β k + 1 M ) Γ ( α k ) Γ ( β k ) ( α k β k L k ) 1 / M .

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