Abstract

The average bit error rate (BER) for binary phase-shift keying (BPSK) modulation in free-space optical (FSO) links over turbulence atmosphere modeled by the exponentiated Weibull (EW) distribution is investigated in detail. The effects of aperture averaging on the average BERs for BPSK modulation under weak-to-strong turbulence conditions are studied. The average BERs of EW distribution are compared with Lognormal (LN) and Gamma-Gamma (GG) distributions in weak and strong turbulence atmosphere, respectively. The outage probability is also obtained for different turbulence strengths and receiver aperture sizes. The analytical results deduced by the generalized Gauss-Laguerre quadrature rule are verified by the Monte Carlo simulation. This work is helpful for the design of receivers for FSO communication systems.

© 2014 Optical Society of America

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Subcarrier Intensity Modulated Free-Space Optical Communications in K-Distributed Turbulence Channels

Hossein Samimi and Paeiz Azmi
J. Opt. Commun. Netw. 2(8) 625-632 (2010)

References

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  1. P. Deng, M. Kavehrad, Z. W. Liu, Z. Zhou, and X. H. Yuan, “Capacity of MIMO free space optical communications using multiple partially coherent beams propagation through non-Kolmogorov strong turbulence,” Opt. Express 21(13), 15213–15229 (2013).
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    [Crossref]
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    [Crossref]
  28. X. G. Song, M. B. Niu, and J. L. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett. 16(4), 540–543 (2012).
    [Crossref]
  29. X. G. Song, F. Yang, and J. L. Cheng, “Subcarrier intensity modulated optical wireless communications in atmospheric turbulence with pointing error,” J. Opt. Commun. Netw. 5(4), 349–358 (2013).
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    [Crossref]
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    [Crossref] [PubMed]
  37. L. Q. Han, Q. Wang, and K. Shida, “Outage probability of free space optical communication over atmosphere turbulence,” in Proceeding of WASE International Conference on Information Engineering (2010), pp. 127–130.

2014 (1)

2013 (9)

I. E. Lee, Z. Ghassemlooy, W. P. Ng, and M. A. Khalighi, “Joint optimization of a partially coherent Gaussian beam for free-space optical communication over turbulent channels with pointing errors,” Opt. Lett. 38(3), 350–352 (2013).
[Crossref] [PubMed]

X. G. Song, F. Yang, and J. L. Cheng, “Subcarrier intensity modulated optical wireless communications in atmospheric turbulence with pointing error,” J. Opt. Commun. Netw. 5(4), 349–358 (2013).

X. G. Song and J. L. Cheng, “Subcarrier intensity modulated optical wireless communications using noncoherent and differentially coherent modulations,” J. Lightwave Technol. 31(12), 1906–1913 (2013).

P. Deng, M. Kavehrad, Z. W. Liu, Z. Zhou, and X. H. Yuan, “Capacity of MIMO free space optical communications using multiple partially coherent beams propagation through non-Kolmogorov strong turbulence,” Opt. Express 21(13), 15213–15229 (2013).
[Crossref] [PubMed]

X. G. Song and J. L. Cheng, “Subcarrier intensity modulated MIMO optical communications in atmospheric turbulence,” J. Opt. Commun. Netw. 5(9), 1001–1009 (2013).

A. E. Morra, H. S. Khallaf, H. M. H. Shalaby, and Z. Kawasaki, “Performance analysis of both shot- and thermal-noise limited multipulse PPM receivers in gamma-gamma atmospheric channels,” J. Lightwave Technol. 31(19), 3142–3150 (2013).
[Crossref]

J. M. Garrido-Balsells, A. Jurado-Navas, J. F. Paris, M. Castillo-Vázquez, and A. Puerta-Notario, “On the capacity of M-distributed atmospheric optical channels,” Opt. Lett. 38(20), 3984–3987 (2013).
[Crossref] [PubMed]

C. Y. Chen, H. M. Yang, Z. Zhou, W. Z. Zhang, M. Kavehrad, S. F. Tong, and T. S. Wang, “Effects of source spatial partial coherence on temporal fade statistics of irradiance flux in free-space optical links through atmospheric turbulence,” Opt. Express 21(24), 29731–29743 (2013).
[Crossref] [PubMed]

R. Barrios and F. Dios, “Exponentiated Weibull model for the irradiance probability density function of a laser beam propagating through atmospheric turbulence,” Opt. Laser Technol. 45, 13–20 (2013).
[Crossref]

2012 (6)

R. Barrios and F. Dios, “Probability of fade and BER performance of FSO links over the exponentiated Weibull fading channel under aperture averaging,” Proc. SPIE 8540, 85400D (2012).
[Crossref]

X. G. Song, M. B. Niu, and J. L. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett. 16(4), 540–543 (2012).
[Crossref]

H. E. Nistazakis and G. S. Tombras, “On the use of wavelength and time diversity in optical wireless communication systems over gamma-gamma turbulence channels,” Opt. Laser Technol. 44(7), 2088–2094 (2012).
[Crossref]

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 20(12), 13055–13064 (2012).
[Crossref] [PubMed]

X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Coherent heterodyne multilevel polarization shift keying with spatial diversity in a free-space optical turbulence channel,” J. Lightwave Technol. 30(16), 2689–2695 (2012).
[Crossref]

X. Yi, Z. J. Liu, and P. Yue, “Average BER of free-space optical systems in turbulent atmosphere with exponentiated Weibull distribution,” Opt. Lett. 37(24), 5142–5144 (2012).
[Crossref] [PubMed]

2010 (2)

2009 (2)

2007 (5)

F. S. Vetelino, C. Young, L. Andrews, and J. Recolons, “Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence,” Appl. Opt. 46(11), 2099–2108 (2007).
[Crossref] [PubMed]

F. S. Vetelino, C. Young, and L. Andrews, “Fade statistics and aperture averaging for Gaussian beam waves in moderate-to-strong turbulence,” Appl. Opt. 46(18), 3780–3789 (2007).
[Crossref] [PubMed]

G. K. Karagiannidis and S. Lioumpas, “An improved approximation for the Gaussian Q-function,” IEEE Commun. Lett. 11(8), 644–646 (2007).
[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]

J. Li, J. Q. Lin, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

2006 (2)

2005 (1)

2004 (1)

N. Perlot and D. Fritzsche, “Aperture-averaging: theory and measurements,” Proc. SPIE 5338, 233–242 (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), 1554–1562 (2001).
[Crossref]

1963 (1)

P. Conçus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Math. Comput. 17(83), 245–256 (1963).

Aitamer, N.

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.

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), 1554–1562 (2001).
[Crossref]

Azmi, P.

Barrios, R.

R. Barrios and F. Dios, “Exponentiated Weibull model for the irradiance probability density function of a laser beam propagating through atmospheric turbulence,” Opt. Laser Technol. 45, 13–20 (2013).
[Crossref]

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 20(12), 13055–13064 (2012).
[Crossref] [PubMed]

R. Barrios and F. Dios, “Probability of fade and BER performance of FSO links over the exponentiated Weibull fading channel under aperture averaging,” Proc. SPIE 8540, 85400D (2012).
[Crossref]

Bourennane, S.

Cassatt, D.

P. Conçus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Math. Comput. 17(83), 245–256 (1963).

Castillo-Vázquez, M.

Chan, V. W. S.

Chen, C. Y.

Cheng, J. L.

Conçus, P.

P. Conçus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Math. Comput. 17(83), 245–256 (1963).

Davis, C. C.

Deng, P.

Dios, F.

R. Barrios and F. Dios, “Exponentiated Weibull model for the irradiance probability density function of a laser beam propagating through atmospheric turbulence,” Opt. Laser Technol. 45, 13–20 (2013).
[Crossref]

R. Barrios and F. Dios, “Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves,” Opt. Express 20(12), 13055–13064 (2012).
[Crossref] [PubMed]

R. Barrios and F. Dios, “Probability of fade and BER performance of FSO links over the exponentiated Weibull fading channel under aperture averaging,” Proc. SPIE 8540, 85400D (2012).
[Crossref]

Epple, B.

Fritzsche, D.

N. Perlot and D. Fritzsche, “Aperture-averaging: theory and measurements,” Proc. SPIE 5338, 233–242 (2004).
[Crossref]

Garrido-Balsells, J. M.

Ghassemlooy, Z.

Hulea, M.

Jaehnig, G.

P. Conçus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Math. Comput. 17(83), 245–256 (1963).

Jurado-Navas, A.

Karagiannidis, G. K.

G. K. Karagiannidis and S. Lioumpas, “An improved approximation for the Gaussian Q-function,” IEEE Commun. Lett. 11(8), 644–646 (2007).
[Crossref]

Kavehrad, M.

Kawasaki, Z.

Khalighi, M. A.

Khallaf, H. S.

Kiasaleh, K.

Lee, C. G.

Lee, I. E.

Li, J.

J. Li, J. Q. Lin, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Lin, J. Q.

J. Li, J. Q. Lin, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Lioumpas, S.

G. K. Karagiannidis and S. Lioumpas, “An improved approximation for the Gaussian Q-function,” IEEE Commun. Lett. 11(8), 644–646 (2007).
[Crossref]

Liu, Z. J.

Liu, Z. W.

Melby, E.

P. Conçus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Math. Comput. 17(83), 245–256 (1963).

Milner, S.

Morra, A. E.

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]

Ng, W. P.

Nistazakis, H. E.

H. E. Nistazakis and G. S. Tombras, “On the use of wavelength and time diversity in optical wireless communication systems over gamma-gamma turbulence channels,” Opt. Laser Technol. 44(7), 2088–2094 (2012).
[Crossref]

Niu, M. B.

X. G. Song, M. B. Niu, and J. L. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett. 16(4), 540–543 (2012).
[Crossref]

Paris, J. F.

Perlot, N.

N. Perlot and D. Fritzsche, “Aperture-averaging: theory and measurements,” Proc. SPIE 5338, 233–242 (2004).
[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), 1554–1562 (2001).
[Crossref]

Popoola, W. O.

Puerta-Notario, A.

Rajbhandari, S.

Recolons, J.

Samimi, H.

Schwartz, N.

Shalaby, H. M. H.

Song, X. G.

Tang, X.

Taylor, D. P.

J. Li, J. Q. Lin, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

Tombras, G. S.

H. E. Nistazakis and G. S. Tombras, “On the use of wavelength and time diversity in optical wireless communication systems over gamma-gamma turbulence channels,” Opt. Laser Technol. 44(7), 2088–2094 (2012).
[Crossref]

Tong, S. F.

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]

Vetelino, F. S.

Wang, T. S.

Yang, F.

Yang, H. M.

Yi, X.

Young, C.

Yuan, X. H.

Yue, P.

Yuksel, H.

Zhang, W. Z.

Zhou, Z.

Appl. Opt. (2)

IEEE Commun. Lett. (2)

X. G. Song, M. B. Niu, and J. L. Cheng, “Error rate of subcarrier intensity modulations for wireless optical communications,” IEEE Commun. Lett. 16(4), 540–543 (2012).
[Crossref]

G. K. Karagiannidis and S. Lioumpas, “An improved approximation for the Gaussian Q-function,” IEEE Commun. Lett. 11(8), 644–646 (2007).
[Crossref]

IEEE Trans. Commun. (1)

J. Li, J. Q. Lin, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55(8), 1598–1606 (2007).
[Crossref]

IEEE Trans. Wirel. Comm. (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]

J. Lightwave Technol. (6)

J. Opt. Commun. Netw. (5)

J. Opt. Netw. (1)

J. Opt. Soc. Am. A (1)

Math. Comput. (1)

P. Conçus, D. Cassatt, G. Jaehnig, and E. Melby, “Tables for the evaluation of ∫0∞xβe−xf(x)dx by Gauss-Laguerre quadrature,” Math. Comput. 17(83), 245–256 (1963).

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), 1554–1562 (2001).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (2)

R. Barrios and F. Dios, “Exponentiated Weibull model for the irradiance probability density function of a laser beam propagating through atmospheric turbulence,” Opt. Laser Technol. 45, 13–20 (2013).
[Crossref]

H. E. Nistazakis and G. S. Tombras, “On the use of wavelength and time diversity in optical wireless communication systems over gamma-gamma turbulence channels,” Opt. Laser Technol. 44(7), 2088–2094 (2012).
[Crossref]

Opt. Lett. (3)

Proc. SPIE (2)

N. Perlot and D. Fritzsche, “Aperture-averaging: theory and measurements,” Proc. SPIE 5338, 233–242 (2004).
[Crossref]

R. Barrios and F. Dios, “Probability of fade and BER performance of FSO links over the exponentiated Weibull fading channel under aperture averaging,” Proc. SPIE 8540, 85400D (2012).
[Crossref]

Other (6)

W. O. Popoola, “Subcarrier intensity modulated free-space optical communication systems,” Diss. Northumbria Univ. (2009).

V. Xarcha, A. N. Stassinakis, H. E. Nistazakis, G. P. Latsas, M. P. Hanias, G. S. Tombras, and A. Tsigopoulos, “Wavelength diversity for Free Space Optical Systems: Performance evaluation over log normal turbulence channels,” in Proceeding of IEEE on Microwave Radar and Wireless Communications (IEEE 2012), pp. 678–683.
[Crossref]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1992).

M. K. Simon and M. S. Alouini, in Digital Communication Over Fading Channels: A Unified Approach to Perform Analysis (John Wiley, 2000).

Wolfram, http://mathworld.wolfram.com .

L. Q. Han, Q. Wang, and K. Shida, “Outage probability of free space optical communication over atmosphere turbulence,” in Proceeding of WASE International Conference on Information Engineering (2010), pp. 127–130.

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Figures (8)

Fig. 1
Fig. 1 Generic complex form of SIM-FSO system.
Fig. 2
Fig. 2 Analytical and simulation results for average BER of subcarrier BPSK modulated FSO system over the EW turbulence channels against average electrical SNR under weak turbulence condition σ R 2 =0.15 . Link distance L=375m and coherence radius ρ 0 =18.89mm .
Fig. 3
Fig. 3 Analytical and simulation results for average BER of subcarrier BPSK modulated FSO system over the EW turbulence channels against average electrical SNR under moderate turbulence condition σ R 2 =1.35 . Link distance L=1225m and coherence radius ρ 0 =9.27mm .
Fig. 4
Fig. 4 Analytical and simulation results for average BERs of subcarrier BPSK modulated FSO systems over the EW turbulence channels against average electrical SNR under strong turbulence condition σ R 2 =19.2 . Link distance L=1500m and coherence radius ρ 0 =2.94mm .
Fig. 5
Fig. 5 Analytical and simulation results for average BERs of subcarrier BPSK and MPSK modulated FSO systems over the EW turbulence channels against average electrical SNR under weak turbulence condition σ R 2 =0.15 .
Fig. 6
Fig. 6 The average BERs for subcarrier BPSK modulated FSO system over the EW and LN turbulence channels against average SNR under weak turbulence condition.
Fig. 7
Fig. 7 The average BER for subcarrier BPSK modulated FSO system over the EW and GG turbulence channels against average SNR under strong turbulence condition.
Fig. 8
Fig. 8 The outage probability against the normalized electrical SNR.

Tables (2)

Tables Icon

Table 1 Parameters for the LN and EW distributions used in Fig. 6.

Tables Icon

Table 2 Parameters for the GG and EW distributions used in Fig. 7.

Equations (30)

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

P t =P[1+ξm(t)],
i r (t)=RPI(t)[1+ξm(t)]+n(t),
γ b = γ ¯ b I 2 = R 2 P ¯ 2 ξ 2 I 2 σ n 2 ,
f I (I)= αβ η ( I η ) β1 exp[ ( I η ) β ]× {1exp[ ( I η ) β ]} α1 ,I0
F I (I)= {1exp[ ( I η ) β ]} α ,
P ¯ b = 0 P b (I) f I (I)dI ,
P ¯ b = 0 P b (I) F I (I)dI,
P b,BPSK (I)= 1 2 erfc( γ b ),
P b,BPSK (I)= γ ¯ b π exp( γ ¯ b I 2 ),
P ¯ b,BPSK = 0 γ ¯ b π exp( γ ¯ b I 2 )× {1exp[ ( I η ) β ]} α dI ,
P ¯ b,BPSK = 1 2 π 0 x 1/2 exp(x)× {1exp[ ( x η γ ¯ b ) β ]} α dx.
P ¯ b,BPSK 1 2 π k=1 n H k {1exp[ ( x k η γ ¯ b ) β ]} α ,
H k = Γ(n+1/2 ) x k n! (n+1) 2 [ L n+1 ( 1 2 ) ( x k )] 2 .
P b,MPSK = 2 log 2 M Q( 2 γ b log 2 M sin π M ),
P b,MPSK = 2sin( π M ) γ ¯ b π log 2 M exp( γ ¯ b I 2 sin 2 π M log 2 M).
P ¯ b,MPSK = 2sin( π M ) γ ¯ b π log 2 M 0 exp( γ ¯ b I 2 sin 2 π M log 2 M)× {1exp[ ( I η ) β ]} α dI ,
P ¯ b,MPSK = 1 π log 2 M 0 x 1/2 exp(x)× {1exp[ ( x ηsin( π M ) γ ¯ b log 2 M ) β ]} α dx,
P ¯ b,MPSK 1 π log 2 M k=1 n H k {1exp[ ( x k ηsin( π M ) γ ¯ b log 2 M ) β ]} α ,
P out = P r ( γ b γ th )= P r (I γ th γ ¯ b ),
P out = 0 γ th γ ¯ b f I (I)d I.
P out == F I ( γ th γ ¯ b )= {1exp[ ( 1 η γ n ) β ]} α ,
P b,BPSK (I)= 1 2 erfc( γ b ),
P b,BPSK (I)= d P b,BPSK (I) dI = 1 2 d dI erfc( γ ¯ b I),
P b,BPSK (I)= 1 2 d[erfc( γ ¯ b I)] d( γ ¯ b I) d( γ ¯ b I) dI ,
P b,BPSK (I)= γ ¯ b π exp( γ ¯ b I 2 ).
P b,MPSK = 2 log 2 M Q( 2 γ b log 2 M sin π M ),
P b,MPSK = 1 log 2 M erfc( γ ¯ b log 2 M Isin π M ).
P b,MPSK = d P b,MPSK dI = 1 log 2 M d dI erfc( γ ¯ b log 2 M Isin π M ),
P b,MPSK = 1 log 2 M d[erfc(z)] dz dz dI ,
P b,MPSK = 2 γ ¯ b sin π M π log 2 M exp( γ ¯ b I 2 sin 2 π M log 2 M).

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