## Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves |

Optics Express, Vol. 20, Issue 12, pp. 13055-13064 (2012)

http://dx.doi.org/10.1364/OE.20.013055

Enhanced HTML Acrobat PDF (1347 KB)

### Abstract

Nowadays, the search for a distribution capable of modeling the probability density function (PDF) of irradiance data under all conditions of atmospheric turbulence in the presence of aperture averaging still continues. Here, a family of PDFs alternative to the widely accepted Log-Normal and Gamma-Gamma distributions is proposed to model the PDF of the received optical power in free-space optical communications, namely, the Weibull and the exponentiated Weibull (EW) distribution. Particularly, it is shown how the proposed EW distribution offers an excellent fit to simulation and experimental data under all aperture averaging conditions, under weak and moderate turbulence conditions, as well as for point-like apertures. Another very attractive property of these distributions is the simple closed form expression of their respective PDF and cumulative distribution function.

© 2012 OSA

**OCIS Codes**

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: February 2, 2012

Revised Manuscript: March 28, 2012

Manuscript Accepted: March 28, 2012

Published: May 25, 2012

**Citation**

Ricardo Barrios and Federico Dios, "Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves," Opt. Express **20**, 13055-13064 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-13055

Sort: Year | Journal | Reset

### References

- D. T. Wayne, R. L. Phillips, and L. C. Andrews, “Comparing the log-normal and gamma-gamma model to experimental probability density functions of aperture averaging data,” Proc. SPIE7814, 78140K (2010). [CrossRef]
- 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, 1554–1562 (2001). [CrossRef]
- P. Beckmann, Probability in Communication Engineering, (Harcourt, Brace & World, 1967).
- J. H. Churnside and R. J. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence,” J. Opt. Soc. Am. A4, 727–737 (1987). [CrossRef]
- L. C. Andrews and R. L. Phillips, “I – K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A2, 160–163 (1985). [CrossRef]
- E. Jakeman and P. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett.40, 546–550 (1978). [CrossRef]
- 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, 3780–3790 (2007). [CrossRef] [PubMed]
- N. Perlot and D. Fritzsche, “Aperture-averaging: theory and measurements,” Proc. SPIE5338, 233–242 (2004).
- B. Epple, “Simplified channel model for simulation of free-space optical communications,” J. Opt. Commun. Netw.2(5), 293–304 (2010). [CrossRef]
- N. Chatzidiamantis, H. Sandalidis, G. Karagiannidis, S. Kotsopoulos, and M. Matthaiou, “New results on turbulence modeling for free-space optical systems,” in Telecommunications (ICT), 2010 IEEE 17th International Conference on, (Doha, Qatar, 2010), pp. 487–492.
- M.-S. Alouini and M. Simon, “Performance of generalized selection combining over Weibull fading channels,” in Vehicular Technology Conf., (Atlantic City, NJ, USA, 2001), pp. 1735–1739.
- M. Lupupa and M. Dlodlo, “Performance of MIMO system in Weibull fading channel—channel capacity analysis,” in EUROCON 2009, EUROCON ’09. IEEE, (St. Petersburg, Russia, 2009), pp. 1735–1740. [CrossRef] [PubMed]
- W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech.-Trans. ASME18, 293–297 (1951).
- J. V. Seguro and T. W. Lambert, “Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis,” J Wind. Eng. Ind. Aerod.85, 75–84 (2000). [CrossRef]
- Z. Fang, B. R. Patterson, and M. E. Turner, “Modeling particle size distributions by the Weibull distribution function,” Mater. Charact.31, 177–182 (1993). [CrossRef]
- D. Schleher, “Radar detection in Weibull clutter,” IEEE Trans. Aerosp. Electron. Syst.AES-12, 736–743 (1976). [CrossRef]
- G. Mudholkar and D. Srivastava, “Exponentiated Weibull family for analyzing bathtub failure-rate data,” IEEE Trans. Reliab.42, 299–302 (1993). [CrossRef]
- L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE Press, 2005). [CrossRef]
- R. R. Parenti and R. J. Sasiela, “Distribution models for optical scintillation due to atmospheric turbulence,” MIT Lincoln Laboratory Technical Report TR-1108, (2005).
- S. Nadarajah and A. K. Gupta, “On the moments of the exponentiated Weibull distribution,” Comm. Statist. Theory Methods34, 253–256 (2005).
- C. M. Harding, R. A. Johnston, and R. G. Lane, “Fast simulation of a Kolmogorov phase screen,” Appl. Opt.38, 2161–2160 (1999). [CrossRef]
- R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media2, 209–224 (1992). [CrossRef]
- J. Recolons and F. Dios, “Accurate calculation of phase screens for the modeling of laser beam propagation through atmospheric turbulence,” Proc. SPIE5891, 51–62 (2005).
- F. S. Vetelino, C. Young, L. C. Andrews, and J. Recolons, “Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence,” Appl. Opt.46, 2099–2109 (2007). [CrossRef] [PubMed]
- K. Levenberg, “A method for the solution of certain problems in least squares,” Quart. Appl. Math.2, 164–168 (1944).
- D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math.11, 431–441 (1963). [CrossRef]
- R. Barrios, F. Dios, J. Recolons, and A. Rodríguez, “Aperture averaging in a laser gaussian beam: simulations and experiments,” Proc. SPIE7814, 78140C (2010). [CrossRef]
- S. D. Lyke, D. G. Voelz, and M. C. Roggemann, “Probability density of aperture-averaged irradiance fluctuations for long range free space optical communication links,” Appl. Opt.48, 6511–6527 (2009). [CrossRef] [PubMed]
- R. J. Hill, R. G. Frehlich, and W. D. Otto, “The probability distribution of irradiance scintillation,” National Oceanic and Atmospheric Administration (NOAA) Technical Report ETL-270, (1997).

## 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.