## Scintillation index and performance analysis of wireless optical links over non-Kolmogorov weak turbulence based on generalized atmospheric spectral model |

Optics Express, Vol. 19, Issue 20, pp. 19067-19077 (2011)

http://dx.doi.org/10.1364/OE.19.019067

Acrobat PDF (1237 KB)

### Abstract

Based on the generalized spectral model for non-Kolmogorov atmospheric turbulence, analytic expressions of the scintillation index (SI) are derived for plane, spherical optical waves and a partially coherent Gaussian beam propagating through non-Kolmogorov turbulence horizontally in the weak fluctuation regime. The new expressions relate the SI to the finite turbulence inner and outer scales, spatial coherence of the source and spectral power-law and then used to analyze the effects of atmospheric condition and link length on the performance of wireless optical communication links.

© 2011 OSA

## 1. Introduction

1. A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res. **2**(4), 345–396 (2005). [CrossRef]

2. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. **3**(8), 1402–1409 (2009). [CrossRef]

3. H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. **27**(8), 974–979 (2009). [CrossRef]

6. O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. **43**(2), 330–341 (2004). [CrossRef]

9. G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. **35**(5), 715–717 (2010). [CrossRef] [PubMed]

11. D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE **2120**, 43–55 (1994). [CrossRef]

14. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. **47**(34), 6385–6391 (2008). [CrossRef] [PubMed]

15. N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE **7588**, 758808 (2010). [CrossRef]

17. L. Y. Cui, B. D. Xue, X. G. Cao, J. K. Dong, and J. N. Wang, “Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence,” Opt. Express **18**(20), 21269–21283 (2010). [CrossRef] [PubMed]

18. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE **6457**, 64570T (2007). [CrossRef]

20. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. **57**(6), 1783–1788 (2009). [CrossRef]

21. L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express **18**(2), 451–462 (2010). [CrossRef] [PubMed]

22. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. **283**(7), 1229–1235 (2010). [CrossRef]

23. B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence,” Opt. Express **19**(9), 8433–8443 (2011). [CrossRef] [PubMed]

24. B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Generalized modified atmospheric spectral model for optical wave propagating through non-Kolmogorov turbulence,” J. Opt. Soc. Am. A **28**(5), 912–916 (2011). [CrossRef] [PubMed]

## 3. Variance of irradiance fluctuations

*l*

_{c}is the spatial coherence length of the source. The values Θ

_{1}and Λ

_{1}are the curvature parameter and Fresnel ratio at the receiver plane for vacuum propagation, which given in terms of their respective values at the source plane are

*L*is the propagation distance,

*F*

_{0}is the initial radius of curvature,

*W*

_{0}is the initial beam waist, and

*k*= 2π/

*λ*is the wavenumber.

*ρ*=0) or when Λ=0, while the longitudinal component

25. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A **11**(10), 2719–2726 (1994). [CrossRef]

25. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A **11**(10), 2719–2726 (1994). [CrossRef]

*H*

_{j}. where

*I*

_{0}in the form of Maclaurin series, we can obtainwhere

25. W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A **11**(10), 2719–2726 (1994). [CrossRef]

## 4. Optical communication link performance statistics

2. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. **3**(8), 1402–1409 (2009). [CrossRef]

*ηIx*+

*n*where

*ηI*is the instantaneous intensity gain,

*η*is the effective photo-current conversion ratio at the receiver,

*I*is the irradiance,

*x*is the modulation signal taking values 0 or 1 and

*n*is the AWGN with zero mean and variance

*N*

_{0}/2. For weak-to-moderate atmospheric fluctuation conditions, the turbulence-induced fading is assumed to be a random process following the log-normal distribution.

### 4.1 Outage probability

*μ*=(

*ηI*)

^{2}/

*N*

_{0}, the average electrical SNR will be given by

*I*is normalized to unity, and after a power transformation of the RV

*I*in above model, the electrical SNR PDF can be rewritten as:

*μ*

_{th}, which corresponds to sensitivity limit of the receiver. Thus, the outage probability for weak-to-moderate fluctuation regime is obtained from the log-normal distribution model, given by [2

2. H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. **3**(8), 1402–1409 (2009). [CrossRef]

### 4.2 Mean Bit-Error-Rate (BER) performance

### 4.3 Average channel capacity

**3**(8), 1402–1409 (2009). [CrossRef]

**3**(8), 1402–1409 (2009). [CrossRef]

## 5. Numerical results and discussion

*L*, spectral index alpha, turbulence inner and outer scales. The transmitted beam is taken to be collimated partially coherent Gaussian beams with parameters of λ=1.55μm, Θ

_{0}=1,

*W*

_{0}=2.5cm,

*l*

_{c}=0.02m; the coefficients of the spectrum are set to be

*a*

_{1}=1.802,

*b*

_{1}=0.254, and

*β*=7/6; and the turbulence strength is

*L*=4km,

*l*

_{0}(

*l*

_{0}. As the path length increases,

*L*=200m, the size of Fresnel zone

*L*=4km, the size of Fresnel zone

*L*=200m), SI obtains maximum value when α=3.2; while for longer propagation distance (

*L*=4km), SI has maximum value when α=3.27. The alpha value corresponding to maximum value of SI is unchanged for different inner scale values. For alpha values higher than α=11/3, or close to 3, the scintillation index decreases, and therefore it will lead to a gain in the performance of FSO communication systems. The physical interpretation of alpha approaching 3 is that turbulence tends to vanish and the explanation for alpha approaching 4 is that the power spectrum contains fewer eddies of high wave numbers, i.e. the wavefront tilt is the primary aberration.

## 6. Conclusions

## References and links

1. | A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res. |

2. | H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun. |

3. | H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol. |

4. | L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE |

5. | L. C. Andrews and R. L. Phillips, |

6. | O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. |

7. | C. Y. Chen, H. M. Yang, X. Feng, and H. Wang, “Optimization criterion for initial coherence degree of lasers in free-space optical links through atmospheric turbulence,” Opt. Lett. |

8. | D. K. Borah and D. G. Voelz, “Spatially partially coherent beam parameter optimization for free space optical communications,” Opt. Express |

9. | G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. |

10. | V. I. Tatarskii, |

11. | D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE |

12. | B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE |

13. | M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE |

14. | A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. |

15. | N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE |

16. | I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE |

17. | L. Y. Cui, B. D. Xue, X. G. Cao, J. K. Dong, and J. N. Wang, “Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence,” Opt. Express |

18. | I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE |

19. | I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE |

20. | I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag. |

21. | L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express |

22. | A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun. |

23. | B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence,” Opt. Express |

24. | B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Generalized modified atmospheric spectral model for optical wave propagating through non-Kolmogorov turbulence,” J. Opt. Soc. Am. A |

25. | W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A |

26. | L. C. Andrews, |

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: June 30, 2011

Revised Manuscript: August 12, 2011

Manuscript Accepted: September 2, 2011

Published: September 15, 2011

**Citation**

Ji Cang and Xu Liu, "Scintillation index and performance analysis of wireless optical links over non-Kolmogorov weak turbulence based on generalized atmospheric spectral model," Opt. Express **19**, 19067-19077 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19067

Sort: Year | Journal | Reset

### References

- A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Res.2(4), 345–396 (2005). [CrossRef]
- H. E. Nistazakis, T. A. Tsiftsis, and G. S. Tombras, “Performance analysis of free-space optical communication systems over atmospheric turbulence channels,” IET Commun.3(8), 1402–1409 (2009). [CrossRef]
- H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E. Fafalios, and G. S. Tombras, “Average capacity of optical wireless communication systems over atmospheric turbulence channels,” J. Lightwave Technol.27(8), 974–979 (2009). [CrossRef]
- L. C. Andrews and R. L. Phillips, “Impact of scintillation on laser communication systems: recent advances in modeling,” Proc. SPIE4489, 23–34 (2002). [CrossRef]
- L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Optical Engineering Press, 2005).
- O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng.43(2), 330–341 (2004). [CrossRef]
- C. Y. Chen, H. M. Yang, X. Feng, and H. Wang, “Optimization criterion for initial coherence degree of lasers in free-space optical links through atmospheric turbulence,” Opt. Lett.34(4), 419–421 (2009). [CrossRef] [PubMed]
- D. K. Borah and D. G. Voelz, “Spatially partially coherent beam parameter optimization for free space optical communications,” Opt. Express18(20), 20746–20758 (2010). [CrossRef] [PubMed]
- G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett.35(5), 715–717 (2010). [CrossRef] [PubMed]
- V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Trans. NOAA by Israel Program for Scientific Translations, 1971).
- D. T. Kyrazis, J. Wissler, D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE2120, 43–55 (1994). [CrossRef]
- B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical Propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE2471, 181–196 (1995). [CrossRef]
- M. S. Belen’kii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE3126, 113–123 (1997). [CrossRef]
- A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt.47(34), 6385–6391 (2008). [CrossRef] [PubMed]
- N. S. Kopeika, A. Zilberman, and E. Golbraikh, “Generalized atmospheric turbulence: implications regarding imaging and communications,” Proc. SPIE7588, 758808 (2010). [CrossRef]
- I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE6551, 65510E (2007). [CrossRef]
- L. Y. Cui, B. D. Xue, X. G. Cao, J. K. Dong, and J. N. Wang, “Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence,” Opt. Express18(20), 21269–21283 (2010). [CrossRef] [PubMed]
- I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE6457, 64570T (2007). [CrossRef]
- I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non Kolmogorov moderate-strong turbulence,” Proc. SPIE6747, 67470B (2007). [CrossRef]
- I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free space optical system performance for a Gaussian beam propagating through non-Kolmogorov weak turbulence,” IEEE Trans. Antenn. Propag.57(6), 1783–1788 (2009). [CrossRef]
- L. Tan, W. Du, J. Ma, S. Yu, and Q. Han, “Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence,” Opt. Express18(2), 451–462 (2010). [CrossRef] [PubMed]
- A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence,” Opt. Commun.283(7), 1229–1235 (2010). [CrossRef]
- B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence,” Opt. Express19(9), 8433–8443 (2011). [CrossRef] [PubMed]
- B. D. Xue, L. Y. Cui, W. F. Xue, X. Z. Bai, and F. G. Zhou, “Generalized modified atmospheric spectral model for optical wave propagating through non-Kolmogorov turbulence,” J. Opt. Soc. Am. A28(5), 912–916 (2011). [CrossRef] [PubMed]
- W. B. Miller, J. C. Ricklin, and L. C. Andrews, “Effects of the refractive index spectral model on the irradiance variance of a Gaussian beam,” J. Opt. Soc. Am. A11(10), 2719–2726 (1994). [CrossRef]
- L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (SPIE Optical Engineering Press, 1998).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.