Abstract

We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10<sup>-5</sup>. Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.

© 2007 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. D. J. Heatley, D. R. Wisely, I. Neild, P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 36, 72-82 (1998).
  2. S. Karp, R. Gagliardi, S. Moran, L. Stotts, Optical Channels (Plenum, 1988).
  3. L. C. Andrews, R. L. Phillips, C. Y. Hopen, M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Amer. A, Opt. Image Sci. 16, 1417-1429 (1999).
  4. M. A. Al-Habash, L. C. Andrews, R. L. Philips, "Mathematical model for the irradiance probability density function of a laser propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).
  5. J. D. Barry, G. S. Mecherle, "Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).
  6. C. C. Chen, C. S. Gardner, "Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links," IEEE Trans. Commun. 37, 252-260 (1989).
  7. S. Arnon, N. S. Kopeika, "Laser satellite communication network-vibration effect and possible solutions," Proc. IEEE 85, 1646-1661 (1997).
  8. S. Arnon, "Effects of atmospheric turbulence and building sway on optical wireless communication systems ," Opt. Lett. 28, 129-131 (2003).
  9. D. Kedar, S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt. 42, 4946-4954 (2003).
  10. S. Arnon, "Optimization of urban optical wireless communication systems," IEEE Trans. Commun. 2, 626-629 (2003).
  11. J. A. Anguita, I. B. Djordjevic, M. Neifeld, B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels ," OSA J. Opt. Netw. 4, 586-601 (2005).
  12. S. Haas, J. H. Shapiro, "Capacity of wireless optical communications," IEEE J. Sel. Areas Commun. 21, 1346-1357 (2003).
  13. L. Jing, M. Uysal, "Optical wireless communications: System model, capacity and coding," Proc. IEEE 58th Veh. Technol. Conf. (2003) pp. 168-172.
  14. X. Zhu, J. Kahn, "Free space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).
  15. X. Zhu, J. M. Kahn, "Performance bounds for coded free-space optical communications through atmospheric turbulence ," IEEE Trans. Commun. 51, 1233-1239 (2003).
  16. M. Uysal, J. Li, M. Yu, "Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels," IEEE Trans. Wireless Commun. 5, 1229-1233 (2006).
  17. E. Biglieri, J. Proakis, S. Shamai, "Fading channels: Information-theoretic and communications aspects," IEEE Trans. Inf. Theory 44, 2619-2692 (1998).
  18. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423 (1948).
  19. R. J. Hill, R. G. Frehlich, "Probability distribution of irradiance for the onset of strong scintillation," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 1530-1540 (1997).
  20. S. M. Flatte, C. Bracher, G. Y. Wang, "Probability density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulations," J. Opt. Soc. Amer. A, Opt. Image Sci. 11, 2080-2092 (1994).
  21. M. A. Naboulsi, H. Sizun, F. de Fornel, "Fog attenuation prediction for optical and infrared waves," Opt. Eng. 43, 319-329 (2004).
  22. I. Kim, B. McArthur, E. Korevaar, "Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications," Proc. SPIE 4214, 26-37 (2001).
  23. S. Muhammad, P. Köhldorfer, E. Leitgeb, "Channel modeling for terrestrial FSO links," Proc. IEEE Int. Conf. Transparent Opt. Netw. (2005) pp. 407-410.
  24. D. Bushuev, S. Arnon, "Analysis of the performance of a wireless optical multi-input to multi-output communication system ," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 1722-1730 (2006).
  25. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
  26. J. C. Ricklin, F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: Implications for free space laser communication," J. Opt. Soc. Amer. A, Opt. Image Sci. 19, 1794-1802 (2002).
  27. L. C. Andrews, Special Functions of Mathematics for Engineers (McGraw-Hill, 1992).
  28. E. Korevaar, I. I. Kim, B. McArthur, "Atmospheric propagation characteristics of highest importance to commercial free space optics ," Proc. SPIE 4976, 1-12 (2003).
  29. Maxim Integrated Products, Inc.Transimpedance Amplifier MAX3744 (2006) http://www.maxim-ic.com Data sheet.
  30. The Consultive Committee for Space Data Systems (CCSDS)TM Synchronization and Channel Coding (2006) http://public.ccsds.org/ Informational Rep., Issue 1: Green Book.
  31. T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory 47, 619-637 (2001).
  32. T. Richardson, R. Urbanke, "The renaissance of Gallager's low-density parity-check codes," IEEE Commun. Mag. 41, 126-131 (2003).
  33. I. B. Djordjevic, S. Sankaranarayanan, B. Vasic, "Irregular low-density parity-check codes for long-haul optical communications," IEEE Photon. Technol. Lett. 16, 338-340 (2004).
  34. I. B. Djordjevic, S. Sankaranarayanan, B. Vasic, "Projective-plane iteratively decodable block codes for WDM high-speed long-haul transmission systems," J. Lightw. Technol. 22, 695-702 (2004).
  35. S. Lin, D. J. Costello, Error Control Coding (Prentice-Hall, 2004).
  36. D. Divsalar, S. Dolinar, C. Jones, "Low-rate LDPC codes with simple protograph structure," Proc. IEEE Int. Symp. Inform. Theory (2005) pp. 1622-1626.

2006 (2)

M. Uysal, J. Li, M. Yu, "Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels," IEEE Trans. Wireless Commun. 5, 1229-1233 (2006).

D. Bushuev, S. Arnon, "Analysis of the performance of a wireless optical multi-input to multi-output communication system ," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 1722-1730 (2006).

2005 (1)

J. A. Anguita, I. B. Djordjevic, M. Neifeld, B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels ," OSA J. Opt. Netw. 4, 586-601 (2005).

2004 (3)

M. A. Naboulsi, H. Sizun, F. de Fornel, "Fog attenuation prediction for optical and infrared waves," Opt. Eng. 43, 319-329 (2004).

I. B. Djordjevic, S. Sankaranarayanan, B. Vasic, "Irregular low-density parity-check codes for long-haul optical communications," IEEE Photon. Technol. Lett. 16, 338-340 (2004).

I. B. Djordjevic, S. Sankaranarayanan, B. Vasic, "Projective-plane iteratively decodable block codes for WDM high-speed long-haul transmission systems," J. Lightw. Technol. 22, 695-702 (2004).

2003 (7)

E. Korevaar, I. I. Kim, B. McArthur, "Atmospheric propagation characteristics of highest importance to commercial free space optics ," Proc. SPIE 4976, 1-12 (2003).

S. Haas, J. H. Shapiro, "Capacity of wireless optical communications," IEEE J. Sel. Areas Commun. 21, 1346-1357 (2003).

S. Arnon, "Optimization of urban optical wireless communication systems," IEEE Trans. Commun. 2, 626-629 (2003).

X. Zhu, J. M. Kahn, "Performance bounds for coded free-space optical communications through atmospheric turbulence ," IEEE Trans. Commun. 51, 1233-1239 (2003).

T. Richardson, R. Urbanke, "The renaissance of Gallager's low-density parity-check codes," IEEE Commun. Mag. 41, 126-131 (2003).

S. Arnon, "Effects of atmospheric turbulence and building sway on optical wireless communication systems ," Opt. Lett. 28, 129-131 (2003).

D. Kedar, S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt. 42, 4946-4954 (2003).

2002 (2)

X. Zhu, J. Kahn, "Free space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).

J. C. Ricklin, F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: Implications for free space laser communication," J. Opt. Soc. Amer. A, Opt. Image Sci. 19, 1794-1802 (2002).

2001 (3)

I. Kim, B. McArthur, E. Korevaar, "Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications," Proc. SPIE 4214, 26-37 (2001).

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory 47, 619-637 (2001).

M. A. Al-Habash, L. C. Andrews, R. L. Philips, "Mathematical model for the irradiance probability density function of a laser propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).

1999 (1)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Amer. A, Opt. Image Sci. 16, 1417-1429 (1999).

1998 (2)

D. J. Heatley, D. R. Wisely, I. Neild, P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 36, 72-82 (1998).

E. Biglieri, J. Proakis, S. Shamai, "Fading channels: Information-theoretic and communications aspects," IEEE Trans. Inf. Theory 44, 2619-2692 (1998).

1997 (2)

R. J. Hill, R. G. Frehlich, "Probability distribution of irradiance for the onset of strong scintillation," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 1530-1540 (1997).

S. Arnon, N. S. Kopeika, "Laser satellite communication network-vibration effect and possible solutions," Proc. IEEE 85, 1646-1661 (1997).

1994 (1)

S. M. Flatte, C. Bracher, G. Y. Wang, "Probability density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulations," J. Opt. Soc. Amer. A, Opt. Image Sci. 11, 2080-2092 (1994).

1989 (1)

C. C. Chen, C. S. Gardner, "Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links," IEEE Trans. Commun. 37, 252-260 (1989).

1985 (1)

J. D. Barry, G. S. Mecherle, "Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).

1948 (1)

C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423 (1948).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379-423 (1948).

IEEE Commun. Mag. (2)

T. Richardson, R. Urbanke, "The renaissance of Gallager's low-density parity-check codes," IEEE Commun. Mag. 41, 126-131 (2003).

D. J. Heatley, D. R. Wisely, I. Neild, P. Cochrane, "Optical wireless: The story so far," IEEE Commun. Mag. 36, 72-82 (1998).

IEEE J. Sel. Areas Commun. (1)

S. Haas, J. H. Shapiro, "Capacity of wireless optical communications," IEEE J. Sel. Areas Commun. 21, 1346-1357 (2003).

IEEE Photon. Technol. Lett. (1)

I. B. Djordjevic, S. Sankaranarayanan, B. Vasic, "Irregular low-density parity-check codes for long-haul optical communications," IEEE Photon. Technol. Lett. 16, 338-340 (2004).

IEEE Trans. Commun. (4)

C. C. Chen, C. S. Gardner, "Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links," IEEE Trans. Commun. 37, 252-260 (1989).

S. Arnon, "Optimization of urban optical wireless communication systems," IEEE Trans. Commun. 2, 626-629 (2003).

X. Zhu, J. Kahn, "Free space optical communication through atmospheric turbulence channels," IEEE Trans. Commun. 50, 1293-1300 (2002).

X. Zhu, J. M. Kahn, "Performance bounds for coded free-space optical communications through atmospheric turbulence ," IEEE Trans. Commun. 51, 1233-1239 (2003).

IEEE Trans. Inf. Theory (2)

E. Biglieri, J. Proakis, S. Shamai, "Fading channels: Information-theoretic and communications aspects," IEEE Trans. Inf. Theory 44, 2619-2692 (1998).

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory 47, 619-637 (2001).

IEEE Trans. Wireless Commun. (1)

M. Uysal, J. Li, M. Yu, "Error rate performance analysis of coded free-space optical links over gamma-gamma atmospheric turbulence channels," IEEE Trans. Wireless Commun. 5, 1229-1233 (2006).

J. Lightw. Technol. (1)

I. B. Djordjevic, S. Sankaranarayanan, B. Vasic, "Projective-plane iteratively decodable block codes for WDM high-speed long-haul transmission systems," J. Lightw. Technol. 22, 695-702 (2004).

J. Opt. Soc. Amer. A, Opt. Image Sci. (5)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Amer. A, Opt. Image Sci. 16, 1417-1429 (1999).

D. Bushuev, S. Arnon, "Analysis of the performance of a wireless optical multi-input to multi-output communication system ," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 1722-1730 (2006).

J. C. Ricklin, F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: Implications for free space laser communication," J. Opt. Soc. Amer. A, Opt. Image Sci. 19, 1794-1802 (2002).

R. J. Hill, R. G. Frehlich, "Probability distribution of irradiance for the onset of strong scintillation," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 1530-1540 (1997).

S. M. Flatte, C. Bracher, G. Y. Wang, "Probability density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulations," J. Opt. Soc. Amer. A, Opt. Image Sci. 11, 2080-2092 (1994).

Opt. Eng. (3)

M. A. Naboulsi, H. Sizun, F. de Fornel, "Fog attenuation prediction for optical and infrared waves," Opt. Eng. 43, 319-329 (2004).

M. A. Al-Habash, L. C. Andrews, R. L. Philips, "Mathematical model for the irradiance probability density function of a laser propagating through turbulent media," Opt. Eng. 40, 1554-1562 (2001).

J. D. Barry, G. S. Mecherle, "Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems," Opt. Eng. 24, 1049-1054 (1985).

Opt. Lett. (1)

OSA J. Opt. Netw. (1)

J. A. Anguita, I. B. Djordjevic, M. Neifeld, B. V. Vasic, "Shannon capacities and error-correction codes for optical atmospheric turbulent channels ," OSA J. Opt. Netw. 4, 586-601 (2005).

Proc. IEEE (1)

S. Arnon, N. S. Kopeika, "Laser satellite communication network-vibration effect and possible solutions," Proc. IEEE 85, 1646-1661 (1997).

Proc. SPIE (2)

I. Kim, B. McArthur, E. Korevaar, "Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze for optical wireless communications," Proc. SPIE 4214, 26-37 (2001).

E. Korevaar, I. I. Kim, B. McArthur, "Atmospheric propagation characteristics of highest importance to commercial free space optics ," Proc. SPIE 4976, 1-12 (2003).

Other (9)

Maxim Integrated Products, Inc.Transimpedance Amplifier MAX3744 (2006) http://www.maxim-ic.com Data sheet.

The Consultive Committee for Space Data Systems (CCSDS)TM Synchronization and Channel Coding (2006) http://public.ccsds.org/ Informational Rep., Issue 1: Green Book.

L. C. Andrews, Special Functions of Mathematics for Engineers (McGraw-Hill, 1992).

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

S. Muhammad, P. Köhldorfer, E. Leitgeb, "Channel modeling for terrestrial FSO links," Proc. IEEE Int. Conf. Transparent Opt. Netw. (2005) pp. 407-410.

L. Jing, M. Uysal, "Optical wireless communications: System model, capacity and coding," Proc. IEEE 58th Veh. Technol. Conf. (2003) pp. 168-172.

S. Lin, D. J. Costello, Error Control Coding (Prentice-Hall, 2004).

D. Divsalar, S. Dolinar, C. Jones, "Low-rate LDPC codes with simple protograph structure," Proc. IEEE Int. Symp. Inform. Theory (2005) pp. 1622-1626.

S. Karp, R. Gagliardi, S. Moran, L. Stotts, Optical Channels (Plenum, 1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.