Abstract

The impact of relay placement on diversity order in adaptive selective decode-and-forward (DF) cooperative strategies is here investigated in the context of free-space optical (FSO) communications over atmospheric turbulence channels with pointing errors when line of sight is available. The irradiance of the transmitted optical beam here considered is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) distribution together with a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Novel closed-form approximate bit error-rate (BER) expressions are obtained for a cooperative FSO communication setup with N relays, assuming that these relays are located in an area similar to an annulus around source or destination node. An analytical expression is here found that determines the best selection criterion based on the knowledge of the channel state information (CSI) of source-relay or relay-destination links in order to significantly increase the diversity order corresponding to the cooperative strategy under study. It is concluded that the highest diversity order is achieved when the relation βSRmin > βSD + βRminD is satisfied, wherein βSRmin, βRminD and βSD are parameters corresponding to the atmospheric turbulence conditions of source-relay and relay-destination link with the greatest scintillation index, and source-destination link, respectively.

© 2015 Optical Society of America

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References

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2014 (4)

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]

L. Yang, X. Gao, and M.-S. Alouini, “Performance Analysis of Free-Space Optical Communication Systems with Multiuser Diversity Over Atmospheric Turbulence Channels,” IEEE Photonics J. 6(2) 7901217 (2014).
[Crossref]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels,” The Scientific World Journal 2014213834 (2014).
[Crossref]

R. Boluda-Ruiz, A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, “Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels,” Opt. Express 22(13), 16,629–16,644 (2014).
[Crossref]

2013 (4)

2012 (3)

2011 (1)

2010 (3)

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

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Communications 4(12), 1423–1432 (2010).
[Crossref]

N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the gamma-gamma atmospheric turbulence model,” Opt. Express 18(12), 12824–12831 (2010).
[Crossref] [PubMed]

2009 (7)

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]

N. Letzepis and A. Guillen i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” Communications, IEEE Transactions on 57(12), 3682–3690 (2009).
[Crossref]

I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009).
[Crossref] [PubMed]

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]

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Light-waveTechnol. 27(24), 5639–5647 (2009).
[Crossref]

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

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

2008 (2)

2007 (1)

2006 (1)

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]

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]

Abdallah, M. M.

S. I. Hussain, M. M. Abdallah, and K. A. Qaraqe, “Power optimization and k th order selective relaying in free space optical networks,” in GCC Conference and Exhibition (GCC), 2013 7th IEEE, pp. 330–333 (IEEE, 2013).
[Crossref]

Abou-Rjeily, C.

C. Abou-Rjeily, “Performance Analysis of Selective Relaying in Cooperative Free-Space Optical Systems,” J. Lightwave Technol. 31(18), 2965–2973 (2013).
[Crossref]

C. Abou-Rjeily, “Achievable Diversity Orders of Decode-and-Forward Cooperative Protocols over Gamma-Gamma Fading FSO Links,” IEEE Trans. Commun. 61(9), 3919–3930 (2013).
[Crossref]

Al-Habash, M. A.

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

Alouini, M.-S.

L. Yang, X. Gao, and M.-S. Alouini, “Performance Analysis of Free-Space Optical Communication Systems with Multiuser Diversity Over Atmospheric Turbulence Channels,” IEEE Photonics J. 6(2) 7901217 (2014).
[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]

Anguita, J.

Bayaki, E.

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

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

Bhatnagar, M. R.

M. R. Bhatnagar, “Average BER analysis of relay selection based decode-and-forward cooperative communication over Gamma-Gamma fading FSO links,” in Communications (ICC), 2013 IEEE International Conference on, pp. 3142–3147 (IEEE, 2013).
[Crossref]

Boluda-Ruiz, R.

R. Boluda-Ruiz, A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, “Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels,” Opt. Express 22(13), 16,629–16,644 (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]

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and R. Boluda-Ruiz, “Bit detect and forward relaying for FSO links using equal gain combining over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(15), 16394–16409 (2012).
[Crossref]

Borah, D. K.

Brychkov, Y. A.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 2: Special Functions (CRC Press, 1986).

Castillo-Vazquez, B.

R. Boluda-Ruiz, A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, “Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels,” Opt. Express 22(13), 16,629–16,644 (2014).
[Crossref]

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and R. Boluda-Ruiz, “Bit detect and forward relaying for FSO links using equal gain combining over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(15), 16394–16409 (2012).
[Crossref]

Castillo-Vazquez, C.

R. Boluda-Ruiz, A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, “Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels,” Opt. Express 22(13), 16,629–16,644 (2014).
[Crossref]

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and R. Boluda-Ruiz, “Bit detect and forward relaying for FSO links using equal gain combining over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(15), 16394–16409 (2012).
[Crossref]

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, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels,” The Scientific World Journal 2014213834 (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]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[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, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels,” The Scientific World Journal 2014213834 (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]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[Crossref] [PubMed]

Chan, V. W. S.

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

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

Chatzidiamantis, N. D.

Chen, M.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Cheng, J.

Denic, S. Z.

Dhungana, Y.

Y. Dhungana and C. Tellambura, “New simple approximations for error probability and outage in fading,” IEEE Commun. Lett. 16(11), 1760–1763 (2012).
[Crossref]

Djordjevic, G. T.

Djordjevic, I.

Djordjevic, I. B.

Farid, A. A.

Gao, X.

L. Yang, X. Gao, and M.-S. Alouini, “Performance Analysis of Free-Space Optical Communication Systems with Multiuser Diversity Over Atmospheric Turbulence Channels,” IEEE Photonics J. 6(2) 7901217 (2014).
[Crossref]

Garcia-Zambrana, A.

R. Boluda-Ruiz, A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, “Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels,” Opt. Express 22(13), 16,629–16,644 (2014).
[Crossref]

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and R. Boluda-Ruiz, “Bit detect and forward relaying for FSO links using equal gain combining over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(15), 16394–16409 (2012).
[Crossref]

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, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels,” The Scientific World Journal 2014213834 (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]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[Crossref] [PubMed]

Gradshteyn, I. S.

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

Guan, R.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Guillen i Fabregas, A.

N. Letzepis and A. Guillen i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” Communications, IEEE Transactions on 57(12), 3682–3690 (2009).
[Crossref]

Gupta, P. R.

A. Jabeena, T. Jayabarathi, P. R. Gupta, G. Hazarika, and et al., “Cooperative Wireless Optical communication system using IWO based optimal relay placement,” in Advances in Electrical Engineering (ICAEE), 2014 International Conference on, pp. 1–6 (IEEE, 2014).
[Crossref]

Hazarika, G.

A. Jabeena, T. Jayabarathi, P. R. Gupta, G. Hazarika, and et al., “Cooperative Wireless Optical communication system using IWO based optimal relay placement,” in Advances in Electrical Engineering (ICAEE), 2014 International Conference on, pp. 1–6 (IEEE, 2014).
[Crossref]

Hopen, C.

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

Hranilovic, S.

Hu, Q.-S.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Huang, N.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Hussain, S. I.

S. I. Hussain, M. M. Abdallah, and K. A. Qaraqe, “Power optimization and k th order selective relaying in free space optical networks,” in GCC Conference and Exhibition (GCC), 2013 7th IEEE, pp. 330–333 (IEEE, 2013).
[Crossref]

Jabeena, A.

A. Jabeena, T. Jayabarathi, P. R. Gupta, G. Hazarika, and et al., “Cooperative Wireless Optical communication system using IWO based optimal relay placement,” in Advances in Electrical Engineering (ICAEE), 2014 International Conference on, pp. 1–6 (IEEE, 2014).
[Crossref]

Jayabarathi, T.

A. Jabeena, T. Jayabarathi, P. R. Gupta, G. Hazarika, and et al., “Cooperative Wireless Optical communication system using IWO based optimal relay placement,” in Advances in Electrical Engineering (ICAEE), 2014 International Conference on, pp. 1–6 (IEEE, 2014).
[Crossref]

Jia, L.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Karagiannidis, G. K.

Karimi, M.

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Communications 4(12), 1423–1432 (2010).
[Crossref]

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Light-waveTechnol. 27(24), 5639–5647 (2009).
[Crossref]

Kashani, M. A.

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).

Kriezis, E. E.

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]

Letzepis, N.

N. Letzepis and A. Guillen i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” Communications, IEEE Transactions on 57(12), 3682–3690 (2009).
[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]

Marichev, O. I.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 2: Special Functions (CRC Press, 1986).

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).

Michalopoulos, D. S.

Nasiri-Kenari, M.

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Communications 4(12), 1423–1432 (2010).
[Crossref]

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Light-waveTechnol. 27(24), 5639–5647 (2009).
[Crossref]

Neifeld, M. A.

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).
[Crossref]

Prudnikov, A. P.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 2: Special Functions (CRC Press, 1986).

Qaraqe, K. A.

S. I. Hussain, M. M. Abdallah, and K. A. Qaraqe, “Power optimization and k th order selective relaying in free space optical networks,” in GCC Conference and Exhibition (GCC), 2013 7th IEEE, pp. 330–333 (IEEE, 2013).
[Crossref]

Ryzhik, I. M.

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

Safari, M.

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]

Schober, R.

N. D. Chatzidiamantis, D. S. Michalopoulos, E. E. Kriezis, G. K. Karagiannidis, and R. Schober, “Relay selection protocols for relay-assisted free-space optical systems,” J. Opt. Commun. Netw. 5(1), 92–103 (2013).
[Crossref]

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

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

Tellambura, C.

Y. Dhungana and C. Tellambura, “New simple approximations for error probability and outage in fading,” IEEE Commun. Lett. 16(11), 1760–1763 (2012).
[Crossref]

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]

Uysal, M.

M. A. Kashani, M. Safari, and M. Uysal, “Optimal relay placement and diversity analysis of relay-assisted free-space optical communication systems,” J. Opt. Commun. Netw. 5(1), 37–47 (2013).
[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]

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun. 7(12), 5441–5449 (2008).
[Crossref]

Vasic, B.

Voelz, D. G.

Wang, J.-B.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Wang, J.-Y.

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

Wang, N.

Yang, L.

L. Yang, X. Gao, and M.-S. Alouini, “Performance Analysis of Free-Space Optical Communication Systems with Multiuser Diversity Over Atmospheric Turbulence Channels,” IEEE Photonics J. 6(2) 7901217 (2014).
[Crossref]

Communications, IEEE Transactions on (1)

N. Letzepis and A. Guillen i Fabregas, “Outage probability of the Gaussian MIMO free-space optical channel with PPM,” Communications, IEEE Transactions on 57(12), 3682–3690 (2009).
[Crossref]

IEEE Commun. Lett. (1)

Y. Dhungana and C. Tellambura, “New simple approximations for error probability and outage in fading,” IEEE Commun. Lett. 16(11), 1760–1763 (2012).
[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 Photonics J. (1)

L. Yang, X. Gao, and M.-S. Alouini, “Performance Analysis of Free-Space Optical Communication Systems with Multiuser Diversity Over Atmospheric Turbulence Channels,” IEEE Photonics J. 6(2) 7901217 (2014).
[Crossref]

IEEE Trans. Commun. (3)

C. Abou-Rjeily, “Achievable Diversity Orders of Decode-and-Forward Cooperative Protocols over Gamma-Gamma Fading FSO Links,” IEEE Trans. Commun. 61(9), 3919–3930 (2013).
[Crossref]

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

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

IEEE Trans. Wireless Commun. (2)

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

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun. 7(12), 5441–5449 (2008).
[Crossref]

IET Communications (1)

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Communications 4(12), 1423–1432 (2010).
[Crossref]

J. Light-waveTechnol. (1)

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Light-waveTechnol. 27(24), 5639–5647 (2009).
[Crossref]

J. Lightwave Technol. (6)

J. Opt. Commun. Netw. (2)

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 (7)

R. Boluda-Ruiz, A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, “Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels,” Opt. Express 22(13), 16,629–16,644 (2014).
[Crossref]

N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the gamma-gamma atmospheric turbulence model,” Opt. Express 18(12), 12824–12831 (2010).
[Crossref] [PubMed]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[Crossref] [PubMed]

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]

A. Garcia-Zambrana, C. Castillo-Vazquez, B. Castillo-Vazquez, and R. Boluda-Ruiz, “Bit detect and forward relaying for FSO links using equal gain combining over gamma-gamma atmospheric turbulence channels with pointing errors,” Opt. Express 20(15), 16394–16409 (2012).
[Crossref]

I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009).
[Crossref] [PubMed]

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]

The Scientific World Journal (1)

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Improved BDF Relaying Scheme Using Time Diversity over Atmospheric Turbulence and Misalignment Fading Channels,” The Scientific World Journal 2014213834 (2014).
[Crossref]

Other (8)

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

J.-Y. Wang, J.-B. Wang, M. Chen, Q.-S. Hu, N. Huang, R. Guan, and L. Jia, “Free-space optical communications using all-optical relays over weak turbulence channels with pointing errors,” in Wireless Communications & Signal Processing (WCSP), 2013 International Conference on, pp. 1–6 (IEEE, 2013).

A. Jabeena, T. Jayabarathi, P. R. Gupta, G. Hazarika, and et al., “Cooperative Wireless Optical communication system using IWO based optimal relay placement,” in Advances in Electrical Engineering (ICAEE), 2014 International Conference on, pp. 1–6 (IEEE, 2014).
[Crossref]

S. I. Hussain, M. M. Abdallah, and K. A. Qaraqe, “Power optimization and k th order selective relaying in free space optical networks,” in GCC Conference and Exhibition (GCC), 2013 7th IEEE, pp. 330–333 (IEEE, 2013).
[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).

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

M. R. Bhatnagar, “Average BER analysis of relay selection based decode-and-forward cooperative communication over Gamma-Gamma fading FSO links,” in Communications (ICC), 2013 IEEE International Conference on, pp. 3142–3147 (IEEE, 2013).
[Crossref]

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series Volume 2: Special Functions (CRC Press, 1986).

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Figures (7)

Fig. 1
Fig. 1 Diagram showing the cooperative FSO communications system, where dSD is the source-destination link distance, Rk are the relay nodes for k = {1,2,...,N}, and (dSRk,θRk) represents the relay placement using polar coordinates.
Fig. 2
Fig. 2 Diversity order gain for a source-destination link distance of dSD=3 km when different weather conditions are assumed. Different relay locations are assumed together with values of normalized beam width and normalized jitter of (ωz/r,σs/r) = (7,1).
Fig. 3
Fig. 3 Maximum source-relay link distance when different weather conditions and different maximum relay-destination link distances are assumed, once the condition φ2 > β is satisfied for each link.
Fig. 4
Fig. 4 BER performance for a source-destination link distance of dSD=3 km when different number of relays are assumed. Different relay placement are assumed together with values of normalized beam width and normalized jitter of (ωz/r,σs/r) =(7,1) and (ωz/r,σs/r)=(10,1).
Fig. 5
Fig. 5 Diversity order gain for a source-destination link distance of dSD=3 km when values of normalized beam width of ωz/r = 7 and normalized jitter of σs/r = {1, 1.5, 2, 2.5, 3} are considered. Moderate turbulence conditions are assumed.
Fig. 6
Fig. 6 Optimum normalized beam width versus normalized jitter for a source-destination link distance of dSD = 3 km under moderate turbulence conditions.
Fig. 7
Fig. 7 BER performance when different number of relays N={2, 3} and source-destination link distance of dSD=3 km are assumed when a normalized beam width of ωz/r= 7 and normalized jitter of σs/r={1, 2, 3} are considered under moderate turbulence conditions, as well as the FSO scenario without pointing errors.

Equations (41)

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y m ( t ) = η i m ( t ) x m ( t ) + z m ( t ) ,
f I m ( i ) a m i b m 1 e i c m a m .
f I m ( i ) { φ m 2 ( α m β m ) β m Γ ( α m β m ) ( A 0 L m ) β m Γ ( α m ) Γ ( β m ) ( φ m 2 β m ) i β m 1 e i α m β m ( φ m 2 β m ) ( A 0 L m ) 1 ( α m β m 1 ) ( β m β m φ m 2 + 1 ) , φ m 2 > β m φ m 2 ( α m β m ) φ m 2 Γ ( α m φ m 2 ) Γ ( β m φ m 2 ) ( A 0 L m ) φ m 2 Γ ( α m ) Γ ( β m ) i φ m 2 1 , φ m 2 < β m
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
Y 0 = X I SD + Z SD , X { 0 , d E } , Z SD ~ N ( 0 , N 0 / 2 ) I R k D < I SD
Y 1 = 1 2 X I SD + X * I R k D + Z SD + Z R k D , Z R k D ~ N ( 0 , N 0 / 2 ) I R k D > I SD
P b SD RD ( I SD ) = Q ( d E 2 i 2 / 2 N 0 ) = Q ( 2 γ ξ i ) ,
P b SD RD 0 Q ( 2 γ ξ i ) j = 1 N F I R j D ( i ) f I SD ( i ) d i .
F I m ( i ) a m b m i b m e i c m b m a m ( b m + 1 ) ,
P b SD RD a RD T Γ ( ( b RD T + 1 ) / 2 ) ( γ ξ ) b RD T / 2 2 b RD T π F 2 2 ( b RD T 2 , b RD T + 1 2 ; b RD T + 2 2 , 1 2 ; c RD T 2 4 a RD T 2 γ ξ ) + c RD T Γ ( ( b RD T + 2 ) / 2 ) ( γ ξ ) ( b RD T + 1 ) / 2 2 ( b RD T + 1 ) π F 2 2 ( b RD T + 1 2 , b RD T + 2 2 ; b RD T + 3 2 , 3 2 ; c RD T 2 4 α RD T 2 γ ξ ) ,
a RD T = a SD i = 1 N a R i D i = 1 N b R i D , b RD T = b SD + i = 1 N b R i D , c RD T a RD T = c SD a SD + i = 1 N c R i D b R i D a R i D ( b R i D + 1 ) .
P b DL = 0 Q ( 2 γ ξ i ) f I SD ( i ) d i .
P b DL a SD Γ ( ( b SD + 1 ) / 2 ) ( γ ξ ) b SD / 2 2 b SD π F 2 2 ( b SD 2 , b SD + 1 2 ; b SD + 2 2 , 1 2 ; c SD 2 4 a SD 2 γ ξ ) + c SD Γ ( ( b SD + 2 ) / 2 ) ( γ ξ ) ( b SD + 1 ) / 2 ( b SD + 1 ) π F 2 2 ( b SD + 1 2 , b SD + 2 2 ; b SD + 3 2 , 3 2 ; c SD 2 4 α SD 2 γ ξ ) .
Y 1 = 1 2 X ( I SD + 2 I R k D ) + Z SD + Z R k D , X * = X
P b DF k 0 ( I SD , I R k D ) = Q ( γ ξ 4 ( i 1 + 2 i 2 ) ) ,
P b DF k 0 = 0 0 Q ( γ ξ 4 ( i i + 2 i 2 ) ) f I SD ( i 1 ) F I SD ( i 2 ) j = 1 j k N F I R j D ( i 2 ) f I R k D ( i 2 ) d i 1 d i 2 .
f I RD max ( i ) a SD b R k D j = 1 N a R j D b SD j = 1 N b R j D i b SD + j = 1 N b R j D 1 e i ( c R k D a R k D + c SD b SD a SD ( b SD + 1 ) + j = 1 j k N c R j D b R j D a R j D ( b R j D + 1 ) ) .
f I DF T a SD a RD max Γ ( b SD ) Γ ( b RD max ) 2 b RD max Γ ( b SD + b RD max ) i b SD + b RD max 1 e i ( 2 a RD max b SD c SD + a SD b RD max c RD max 2 a SD a RD max ( b SD + b RD max ) ) .
P b DF k 0 = 0 Q ( γ ξ 4 i ) f I DF T ( i ) d i .
P b DF k 0 a DF T Γ ( ( b DF T + 1 ) / 2 ) ( γ ξ ) b DF T / 2 2 ( 2 3 b DF T ) / 2 b DF T π F 2 2 ( b DF T 2 , b DF T + 1 2 ; b DF T + 2 2 , 1 2 ; 2 c DF T 2 a DF T 2 γ ξ ) + c DF T Γ ( ( b DF T + 2 ) / 2 ) ( γ ξ ) ( b D F T + 1 ) / 2 2 ( 3 b DF T + 1 ) / 2 ( b DF T + 1 ) π F 2 2 ( b DF T + 1 2 , b DF T + 2 2 ; b DF T + 3 2 , 3 2 ; 2 c DF T 2 a DF T 2 γ ξ ) .
Y 1 = 1 2 X ( I SD 2 I R k D ) + d E I R k D + Z SD + Z R k D , X * = d E X
P b DF k 1 ( I SD , I R k D ) = Q ( γ ξ 4 ( i 1 2 i 2 ) ) .
P b DF k 1 = 0 0 Q ( γ ξ 4 ( i 1 2 i 2 ) ) f I SD ( i 1 ) F I SD ( i 2 ) j = 1 j k N F I R j D ( i 2 ) f I R k D ( i 2 ) d i 1 d i 2 .
P b DF k 1 = ˙ 0 0 2 i 2 f I SD ( i 1 ) F I SD ( i 2 ) j = 1 j k N F I R j D ( i 2 ) f I R k D ( i 2 ) d i 1 d i 2 .
P b SR k RD Γ ( ( b SR k + 1 ) / 2 ) ( γ ξ ) b SR k / 2 ( a SR k ) 1 2 ( 1 b SR k ) b SR k π F 2 2 ( b SR k 2 , b SR k + 1 2 ; b SR k + 2 2 , 1 2 ; c SR k 2 a SR k 2 γ ξ ) + Γ ( ( b SR k + 2 ) / 2 ) ( γ ξ ) ( b SR k + 1 ) / 2 ( c SR k ) 1 2 b SR k ( b SR k + 1 ) π F 2 2 ( b SR k + 1 2 , b SR k + 2 2 ; b SR k + 3 2 , 3 2 ; c SR k 2 a SR k 2 γ ξ ) ,
P b RD = P b SD RD + k = 1 N P b DF k 0 ( 1 P b SR k RD ) + k = 1 N P b DF k 1 P b SR k RD .
P b RD = ˙ { P b DF min 1 P b SR min RD , b SR min < b SD + i = 1 N b R i D P b SD RD , b SR min > b SD + i = 1 N b R i D
G d RD = min ( b SR min , b SD + i = 1 N b R i D ) / b SD .
G d SR = 1 + min ( b R min D , i = 1 N b SR i ) / b SD .
G d = { G d RD , b SR min > b SD + b R min D G d SR , b SR min < b SD + b R min D
d SR max ( km ) = ( 1 1.23 C n 2 κ 7 / 6 ) 6 / 11 ( ln 6 / 11 ( 1 + 1 β SD + β R min D ) ( 0.44 0.69 ln 6 / 5 ( 1 + 1 β SD + β R min D ) ) 5 / 11 ) × 10 3 ,
ω z / r optimum 4.013 σ s / r 0.153 .
D pe [ dB ] ( 20 / β SD ) log 10 ( φ SD 2 / ( A 0 β SD ( φ SD 2 β SD ) ) ) .
P b SR = P b SD SR + k = 1 N P b BDF k 0 P b SR k 0 SR + k = 1 N P b BDF k 1 P b SR k 1 SR .
a SR T = a SD i = 1 N a SR i i = 1 N b SR i , b SR T = b SD + i = 1 N b SR i , c SR T a SR T = c SD a SD + i = 1 N c SR i b SR i a SR i ( b SR i + 1 ) .
P b SR k 1 SR ( b SR k / b SD ) 2 ( b SD + i = 1 N b SR i ) P b SD SR .
P b SR k 0 0 j = 1 j k N F I SR j ( i ) F I SD ( i ) f I SR k ( i ) d i .
a BDF T = a SD a R k Γ ( b SD ) Γ ( b R k D ) 2 b R k D Γ ( b SD + b R k D ) , b BDF T = b SD + b R k D , c BDF T a BDF T = 2 a R k D b SD c SD + a SD b R k D c R k D 2 a SD a R k D ( b SD + b R k D ) .
P b BDF k 1 0 0 2 i 2 f I SD ( i 1 ) f I R k D ( i 2 ) d i 1 d i 2 .
P b SR { P b BDF min 0 P b SR min 0 b R min D < i = 1 N b SR i ( 1 + 2 ( b SD + i = 1 N b SR i ) b SD k = 1 N b SR k P b BDF k 1 ) P b SD SR b R min D > i = 1 N b SR i

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