Abstract

In this paper, a novel adaptive cooperative protocol with multiple relays using detect-and-forward (DF) over atmospheric turbulence channels with pointing errors is proposed. The adaptive DF cooperative protocol here analyzed is based on the selection of the optical path, source-destination or different source-relay links, with a greater value of fading gain or irradiance, maintaining a high diversity order. Closed-form asymptotic bit error-rate (BER) expressions are obtained for a cooperative free-space optical (FSO) communication system with Nr relays, when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions, following a gamma-gamma distribution of parameters α and β, or pointing errors, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. A greater robustness for different link distances and pointing errors is corroborated by the obtained results if compared with similar cooperative schemes or equivalent multiple-input multiple-output (MIMO) systems. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  20. 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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2014 (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]

2013 (4)

2012 (2)

2010 (2)

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]

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

2009 (3)

2008 (1)

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

2007 (1)

2006 (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]

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

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

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 IEEE International Conference on Communications (ICC), pp. 3142–3147 (2013).

Boluda-Ruiz, R.

Borah, D. K.

Castillo-Vazquez, B.

Castillo-Vazquez, C.

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Celik, Y.

Y. Celik and N. Odabasioglu, “On relay selection for cooperative free-space optical communication,” in Networks and Optical Communications (NOC), 2012 17th European Conference on, pp. 1–5 (IEEE, 2012).
[Crossref]

Chan, V. W. S.

Chatzidiamantis, N. D.

Cheng, J.

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.

García-Zambrana, A.

Gradshteyn, I. S.

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

Hopen, C.

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

Hranilovic, S.

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]

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-wave Technol. 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.

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-wave Technol. 27(24), 5639–5647 (2009).
[Crossref]

Odabasioglu, N.

Y. Celik and N. Odabasioglu, “On relay selection for cooperative free-space optical communication,” in Networks and Optical Communications (NOC), 2012 17th European Conference on, pp. 1–5 (IEEE, 2012).
[Crossref]

Phillips, R.

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

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.

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

Sandalidis, H. G.

Schober, R.

Tsiftsis, T. A.

Uysal, M.

M. A. Kashani and M. Uysal, “Outage performance and diversity gain analysis of free-space optical multi-hop parallel relaying,” J. Opt. Commun. Netw. 5(8), 901–909 (2013).
[Crossref]

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

Voelz, D. G.

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]

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. (1)

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]

IEEE Trans. Wireless Commun. (1)

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-wave Technol. (1)

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

J. Lightwave Technol. (5)

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 (3)

Other (6)

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]

Y. Celik and N. Odabasioglu, “On relay selection for cooperative free-space optical communication,” in Networks and Optical Communications (NOC), 2012 17th European Conference on, pp. 1–5 (IEEE, 2012).
[Crossref]

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

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

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

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).

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Figures (5)

Fig. 1
Fig. 1 Block diagram of the cooperative FSO system under study, where dSD is the source-destination link distance, Rk are the relays nodes for k = {1, 2,...,Nr}, and (dRkD,ϕRk) represents the relay location using polar coordinates.
Fig. 2
Fig. 2 Diversity order gain Gd for the ADF cooperative protocol for a source-destination link distance of dSD=3 km when different weather conditions and relay locations are assumed. (a) (ωz/r,σs/r)=(5,1) for each link and (b) (ωz/r,σs/r)=(5,1) for the S-Rk and Rk-D links, and (ωz/r,σs/r)=(5,3) for the S-D link.
Fig. 3
Fig. 3 BER performance when different number of relays Nr={1, 2, 3} and source-destination link distance of dSD=3 km are assumed. Different relay locations of (a) dRD=0.3dSD and (b) dRD=0.8dSD are assumed together with values of normalized beam width and normalized jitter of (ωz/r, σs/r) = {(5, 1), (10, 2)}.
Fig. 4
Fig. 4 Diversity order gain Gd for the Adaptive-DF cooperative protocol for a source-destination link distance of dSD=3 km when (a) 1, (b) 2 and (c) 3 relays are assumed together with different values of normalized beam width of ωz/r= 5 and normalized jitter of σs/r={1, 2, 3}.
Fig. 5
Fig. 5 BER performance when different number of relays Nr={1, 2, 3} and source-destination link distance of dSD=3 km are assumed when dRD=0.2dSD together with a normalized beam width of ωz/r= 5 and normalized jitter of σs/r={1, 2, 3} as well as the FSO scenario without pointing errors.

Tables (1)

Tables Icon

Table 1 ADF cooperative protocol with multiple relays when the message s = {s1, s2,..., sn} is transmitted, being Rmax the relay selected by the source node.

Equations (34)

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y m ( t ) = η i m ( t ) x m ( t ) + z m ( t ) ,
f I l m ( i ) = α m β m φ m 2 A 0 L m Γ ( α m ) Γ ( β m ) G 1 , 3 3 , 0 ( α m β m A 0 L m i | φ m 2 φ m 2 1 , α m 1 , β m 1 ) , 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
f I m ( i ) a m i b m 1 = 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 , φ m 2 > β m
f I m ( i ) a m i b m 1 = 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
Y SD = X I SD + Z SD , X { 0 , d E } , Z SD ~ N ( 0 , N 0 / 2 ) .
P b SD ( E | I SD ) = Q ( d E 2 i 2 / 2 N 0 ) = Q ( 2 γ ξ i ) ,
P b SD ( E ) = 0 Q ( 2 γ ξ i ) f I SD ( i ) d i .
P b SD ( E ) a SD Γ ( ( b SD + 1 ) / 2 ) 2 b SD π ( γ ξ ) b SD / 2 ,
Y ADF 0 = 1 2 X I SD + Z SD + X * I R max D + Z R max D , I SR max > I SD
Y ADF 1 = X I SD + Z SD , I SR max < I SD
Y ADF 0 = ( 1 / 2 ) X ( I SD + 2 I R Max D ) + Z SD + Z R Max D , X * = X
Y ADF 0 = ( 1 / 2 ) X ( I SD 2 I R Max D ) + d E I R Max D + Z SD + Z R Max D , X * = d E X
P b ADF ( E | I SD , I SR k , I R k D ) = k = 1 N r P b BDF k ( E | I SD , I SR k , I R k D ) F I SD ( I SR k ) j = 1 j k N r F I SR j ( I SR k ) + P b SD ( E | I SD ) j = 1 N r F I SR j ( I SD ) ,
P b BDF k ( E | I SD , I SR k , I R k D ) = P b BDF k 0 ( E | I SD , I R k D ) ( 1 P b SR k ( E | I SR k ) ) + P b BDF k 1 ( E | I SD , I R k D ) P b SR k ( E | I SR k ) = Q ( ( γ / 4 ) ξ ( i SD + 2 i R k D ) ) ( 1 Q ( ( γ / 2 ) ξ i SR k ) ) + Q ( ( γ / 4 ) ξ ( i SD 2 i R k D ) ) Q ( ( γ / 2 ) ξ i SR k ) .
P b ADF ( E ) = k = 1 N r ( P b BDF k 0 ( E ) P b SR k ADF 0 ( E ) + P b BDF k 1 ( E ) P b SR k ADF 1 ( E ) ) + P b SD ADF ( E ) = k = 1 N r P b BDF k 0 ( E ) 0 [ 1 P b SR k ( E | I SR k ) ] F I SD ( i ) j = 1 j k N r F I SR k ( i ) f I SR k ( i ) d i . + k = 1 N r P b BDF k 1 ( E ) 0 P b SR k ( E | I SR k ) F I SD ( i ) j = 1 j k N r F I SR j ( i ) f I SR k ( i ) d i . + 0 P b SD ( E | I SD ) j = 1 N r F I SR j ( i ) f I SD ( i ) d i .
0 Q ( c γ ξ i ) n = 1 n m N r F I n ( i ) f I m ( i ) d i , c +
P b SD ADF ( E ) = 0 P b SD ( E | I SD ) j = 1 N r F I SR j ( i ) f I SD ( i ) d i .
P b SR k ADF 1 ( E ) = 0 P b SR k ( E | I SR k ) F I SD ( i ) j = 1 j k N r F I SR j ( i ) f I SR k ( i ) d i .
P b SD ADF ( E ) a SD Π i = 1 N r a SR i Γ ( ( 1 + b SD + i = 1 N r b SR i ) / 2 ) ( γ ξ ) ( b SD + i = 1 N r b SR i ) / 2 Π i = 1 N r b SR i 2 π ( b SD + i = 1 N r b SR i )
P b SR k ADF 1 ( E ) b SR k b SD 2 ( b SD + i = 1 N r b SR i ) P b SD ADF ( E ) ,
P b SR k ADF 0 ( E ) = 0 [ 1 P b SR k ( E | I SR k ) ] F I SD ( i ) j = 1 j k N r F I SR j ( i ) f I SR k ( i ) d i .
P b SR k ADF 0 ( E ) 0 j = 1 j k N r F I SR j ( i ) F I SD ( i ) f I SR k ( i ) d i .
P b BDF k 0 ( E ) a SD a R k D Γ ( b SD ) Γ ( b R k D ) ( γ ξ ) ( b SD + b R k D ) / 2 2 ( b SD + b R k D ) / 2 2 Γ ( ( b SD + b R k D + 2 ) / 2 ) ,
P b BDF k 1 ( E ) 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 ADF ( E ) P b BDF min 0 ( E ) P b SR min ADF 0 ( E ) , b R min D < i = 1 N r b SR i
P b ADF ( E ) ( 1 = 2 ( b SD + i = 1 N r b SR i ) b SD k = 1 N r b SR k P b BDF k 1 ( E ) ) P b SD ADF ( E ) , b R min D > i = 1 N r b SR i
G d ( N r ) = 1 + min ( b R min D , i = 1 N r b SR i ) b SD .
G d ( N r ) = 1 + min ( φ RD 2 , N r φ SR 2 ) φ SD 2 = 1 + min ( φ 2 , N r φ 2 ) φ 2 = 2 ,
P b ADF ( E ) ( 1 + 2 ( β SD + i = 1 N r β SR i ) β SD k = 1 N r β SR k P b BDF k 1 ( E ) ) P b SD ADF npe ( E ) ,
a m npe = ( α m β m ) β m Γ ( α m β m ) L m β m Γ ( α m ) Γ ( β m ) .
D pe [ d B ] 20 β SD + i = 1 N r β SR i log 10 ( φ SD 2 A 0 β SD ( φ SD 2 β SD ) i = 1 N r φ SR i 2 A 0 β SR i ( φ SR i 2 β SR i ) ) .
D pe [ d B ] 20 ( N r + 1 ) β SD log 10 ( A 0 β SD φ SD 2 φ SD 2 β SD ) N r + 1 = 20 β SD log 10 ( A 0 β SD φ SD 2 φ SD 2 β SD ) ,

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