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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 16394–16409
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Bit detect and forward relaying for FSO links using equal gain combining over gamma-gamma atmospheric turbulence channels with pointing errors

Antonio García-Zambrana, Carmen Castillo-Vázquez, Beatriz Castillo-Vázquez, and Rubén Boluda-Ruiz  »View Author Affiliations


Optics Express, Vol. 20, Issue 15, pp. 16394-16409 (2012)
http://dx.doi.org/10.1364/OE.20.016394


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Abstract

An unsuitable alignment between transmitter and receiver together with fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence can severely degrade the performance of free-space optical (FSO) systems. In this paper, cooperative FSO communications with decode-and-forward (DF) relaying and equal gain combining (EGC) reception over atmospheric turbulence and misalignment fading channels is analyzed in order to mitigate these impairments. Novel closed-form asymptotic bit error-rate (BER) expressions are derived for a 3-way FSO communication setup when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), 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. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2β1/2 times the value of the pointing error displacement standard deviation at the receiver. It is contrasted that the available diversity order is strongly dependent on the relay location, achieving greater diversity gains when the diversity order is determined by βAC + βBC, where βAC and βBC are parameters corresponding to the turbulence of the source-destination and relay-destination links. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

© 2012 OSA

1. Introduction

In this paper, this approach is extended to FSO communication systems using IM/DD over atmospheric turbulence and misalignment fading channels, considering cooperative FSO communications with decode-and-forward (DF) relaying and equal gain combining (EGC) reception. Novel closed-form asymptotic bit error-rate (BER) expressions are derived for a 3-way FSO communication setup when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), following a gamma-gamma distribution of parameters α and β, or pointing errors, following a misalignment fading model, as in [14

14. 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]

, 15

15. H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun. 59(3), 669–674 (2011). [CrossRef]

], where the effect of beam width, detector size and jitter variance is considered. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2β1/2 times the value of the pointing error displacement standard deviation at the receiver. Moreover, it is contrasted that the available diversity order is strongly dependent on the relay location, achieving greater diversity gains when the diversity order is determined by βAC + βBC, where βAC and βBC are parameters corresponding to the turbulence of the source-destination and relay-destination links. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results, showing that asymptotic expressions here obtained lead to simple bounds on the bit error probability that get tighter over a wider range of signal-to-noise ratio (SNR) as the turbulence strength increases.

2. System and channel model

Fig. 1 Block diagram of the considered 3-way FSO communication system, where LAC is the A–C link distance and (xB, yB) represents the location of the node B.

3. Error-rate performance analysis

Fig. 2 Diversity order gain Gd for a 3-way FSO communication setup with BDF relaying and EGC reception for a source-destination link distance of (a) LAC = 3 km and (b) LAC = 6 km when different relay locations of yB={0.5 km, 1 km, 1.5 km, 2 km, 2.5 km} are assumed, once the condition φ2 > β is satisfied for each link.
Fig. 3 BER performance for a 3-way FSO communication setup with BDF relaying and EGC reception over atmospheric turbulence and misalignment fading channels, when different relay locations for source-destination link distances of (a) LAC = 3 km and (b) LAC = 6 km are assumed together with values of normalized beamwidth and normalized jitter of (ωz/r, σs/r) = (5, 1) and (ωz/r, σs/r) = (10, 2).

Fig. 4 (a) Diversity order gain Gd for a source-destination link distance of LAC = 2 km and vertical displacement of the relay node of yB={0.2 km} when values of normalized beamwidth of ωz/r = 7 and normalized jitter of σs/r = {1, 1.5, 1.75, 2, 3} are assumed. (b) BER performance is depicted for the same source-destination link distance and a relay location of (xB=0.8 km; yB=0.2 km) when values of normalized beamwidth of ωz/r = 7 and normalized jitter of σs/r = {1, 2, 3} are assumed as well as when no pointing errors are considered.

4. Conclusions

In this paper, cooperative FSO communications with DF relaying and EGC reception using IM/DD over atmospheric turbulence channels with pointing errors are analyzed. Novel closed-form asymptotic BER expressions are derived for a 3-way FSO communication setup when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), 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. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2β1/2 times the value of the pointing error displacement standard deviation at the receiver. Moreover, it is contrasted that the available diversity order is strongly dependent on the relay location, achieving greater diversity gains when the diversity order is determined by βAC +βBC, where βAC and βBC are parameters corresponding to the turbulence of the source-destination and relay-destination links. Additionally, as previously reported by the authors [18

18. 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),480–496 (2011). [CrossRef]

], a relevant improvement in performance must be noted as a consequence of the pulse shape used, providing an increment in the average SNR of 10log10 ξ decibels. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results, showing that asymptotic expressions here obtained lead to simple bounds on the bit error probability that get tighter over a wider range of SNR as the turbulence strength increases. At last, it is verified that cooperative FSO communications with DF relaying and EGC reception can be applied to achieve spatial diversity without much increase in hardware or rate reduction at the destination node. From the relevant results here obtained, investigating the impact of the path loss on the coding gain Λc for different FSO setups as well as the incorporation of physics-based models (like a wave optics based approach) for representative FSO scenarios are interesting topics for future research in order to extend the analysis in this paper.

Acknowledgments

The authors are grateful for financial support from the Junta de Andalucía (research group “Communications Engineering (TIC-0102)”).

References and links

1.

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

2.

L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE 97(6), 1109–1127 (2009). [CrossRef]

3.

W. Lim, C. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express 17(6), 4479–4484 (2009). [CrossRef] [PubMed]

4.

L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001). [CrossRef]

5.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]

6.

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]

7.

I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel,” J. Lightwave Technol. 26(5), 478–487 (2008). [CrossRef]

8.

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]

9.

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]

10.

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

11.

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010). [CrossRef] [PubMed]

12.

A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 445–454 (2010). [CrossRef]

13.

S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett. 28(2), 129–131 (2003). [CrossRef] [PubMed]

14.

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]

15.

H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun. 59(3), 669–674 (2011). [CrossRef]

16.

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]

17.

W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett. 14(5), 468–470 (2010). [CrossRef]

18.

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),480–496 (2011). [CrossRef]

19.

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]

20.

A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity. Part I. System description,” IEEE Trans. Commun. 51(11), 1927 – 1938 (2003). [CrossRef]

21.

A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity. Part II. Implementation aspects and performance analysis,” IEEE Trans. Commun. 51(11), 1939 – 1948 (2003). [CrossRef]

22.

J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory 50(12), 3062 – 3080 (2004). [CrossRef]

23.

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

24.

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]

25.

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

26.

C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun. 59(3), 658 –663 (2011). [CrossRef]

27.

C. Abou-Rjeily and S. Haddad, “Cooperative FSO systems: performance analysis and optimal power allocation,” J. Lightwave Technol. 29(7), 1058 –1065 (2011). [CrossRef]

28.

M. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma-gamma fading channels,” IEEE Photon. Technol. Lett. 24(7), 545 –547 (2012). [CrossRef]

29.

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Rate-adaptive FSO links over atmospheric turbulence channels by jointly using repetition coding and silence periods,” Opt. Express 18(24),422–440 (2010). [CrossRef]

30.

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]

31.

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]

32.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 7th ed. (Academic Press Inc., 2007).

33.

N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the gamma-gamma atmospheric turbulence model.” Opt. Express 18(12), 824–831 (2010). [CrossRef]

34.

Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun. 51(8), 1389–1398 (2003). [CrossRef]

35.

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

36.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in Proc. Int. Conf. on Symbolic and Algebraic Computation, 212–224 (Tokyo, Japan, 1990).

OCIS Codes
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(060.4510) Fiber optics and optical communications : Optical communications
(060.2605) Fiber optics and optical communications : Free-space optical communication

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 14, 2012
Revised Manuscript: June 27, 2012
Manuscript Accepted: June 27, 2012
Published: July 3, 2012

Citation
Antonio García-Zambrana, Carmen Castillo-Vázquez, Beatriz Castillo-Vázquez, and Rubén 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, 16394-16409 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16394


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References

  1. V. W. S. Chan, “Free-Space Optical Communications,” J. Lightwave Technol.24(12), 4750–4762 (2006). [CrossRef]
  2. L. B. Stotts, L. C. Andrews, P. C. Cherry, J. J. Foshee, P. J. Kolodzy, W. K. McIntire, M. Northcott, R. L. Phillips, H. A. Pike, B. Stadler, and D. W. Young, “Hybrid optical RF airborne communications,” Proc. IEEE97(6), 1109–1127 (2009). [CrossRef]
  3. W. Lim, C. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express17(6), 4479–4484 (2009). [CrossRef] [PubMed]
  4. L. Andrews, R. Phillips, and C. Hopen, Laser beam scintillation with applications (Bellingham, WA: SPIE Press, 2001). [CrossRef]
  5. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun.50(8), 1293–1300 (2002). [CrossRef]
  6. 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]
  7. I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel,” J. Lightwave Technol.26(5), 478–487 (2008). [CrossRef]
  8. 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]
  9. 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]
  10. E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun.58(1), 58–62 (2010). [CrossRef]
  11. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express18(6), 5356–5366 (2010). [CrossRef] [PubMed]
  12. A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express18(19), 445–454 (2010). [CrossRef]
  13. S. Arnon, “Effects of atmospheric turbulence and building sway on optical wireless-communication systems,” Opt. Lett.28(2), 129–131 (2003). [CrossRef] [PubMed]
  14. 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]
  15. H. G. Sandalidis, “Coded free-space optical links over strong turbulence and misalignment fading channels,” IEEE Trans. Commun.59(3), 669–674 (2011). [CrossRef]
  16. 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]
  17. W. Gappmair, S. Hranilovic, and E. Leitgeb, “Performance of PPM on terrestrial FSO links with turbulence and pointing errors,” IEEE Commun. Lett.14(5), 468–470 (2010). [CrossRef]
  18. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express19(14),480–496 (2011). [CrossRef]
  19. 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. Express20(3), 2096–2109 (2012). [CrossRef] [PubMed]
  20. A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity. Part I. System description,” IEEE Trans. Commun.51(11), 1927 – 1938 (2003). [CrossRef]
  21. A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity. Part II. Implementation aspects and performance analysis,” IEEE Trans. Commun.51(11), 1939 – 1948 (2003). [CrossRef]
  22. J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory50(12), 3062 – 3080 (2004). [CrossRef]
  23. M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun.7(12), 5441–5449 (2008). [CrossRef]
  24. 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]
  25. M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Communications4(12), 1423 –1432 (2010). [CrossRef]
  26. C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun.59(3), 658 –663 (2011). [CrossRef]
  27. C. Abou-Rjeily and S. Haddad, “Cooperative FSO systems: performance analysis and optimal power allocation,” J. Lightwave Technol.29(7), 1058 –1065 (2011). [CrossRef]
  28. M. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma-gamma fading channels,” IEEE Photon. Technol. Lett.24(7), 545 –547 (2012). [CrossRef]
  29. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Rate-adaptive FSO links over atmospheric turbulence channels by jointly using repetition coding and silence periods,” Opt. Express18(24),422–440 (2010). [CrossRef]
  30. 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]
  31. 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]
  32. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, 7th ed. (Academic Press Inc., 2007).
  33. N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the gamma-gamma atmospheric turbulence model.” Opt. Express18(12), 824–831 (2010). [CrossRef]
  34. Z. Wang and G. B. Giannakis, “A simple and general parameterization quantifying performance in fading channels,” IEEE Trans. Commun.51(8), 1389–1398 (2003). [CrossRef]
  35. Wolfram Research Inc., “The Wolfram functions site,” URL http://functions.wolfram.com .
  36. V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system,” in Proc. Int. Conf. on Symbolic and Algebraic Computation, 212–224 (Tokyo, Japan, 1990).

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