Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves.

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.

[1]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[2]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[3]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[4]  Petr Beckmann,et al.  Probability in communication engineering , 1967 .

[5]  D. Schleher,et al.  Radar Detection in Weibull Clutter , 1976, IEEE Transactions on Aerospace and Electronic Systems.

[6]  E. Jakeman,et al.  Significance of K Distributions in Scattering Experiments , 1978 .

[7]  L. Andrews,et al.  I–K distribution as a universal propagation model of laser beams in atmospheric turbulence , 1985 .

[8]  James H. Churnside,et al.  Probability density of irradiance scintillations for strong path-integrated refractive turbulence , 1987 .

[9]  R. Lane,et al.  Simulation of a Kolmogorov phase screen , 1992 .

[10]  Malcolm E. Turner,et al.  Modeling particle size distributions by the Weibull distribution function , 1993 .

[11]  G. S. Mudholkar,et al.  Exponentiated Weibull family for analyzing bathtub failure-rate data , 1993 .

[12]  L. Andrews,et al.  Laser Beam Propagation Through Random Media , 1998 .

[13]  R. Lane,et al.  Fast simulation of a kolmogorov phase screen. , 1999, Applied optics.

[14]  T. W. Lambert,et al.  Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis , 2000 .

[15]  Mohamed-Slim Alouini,et al.  Performance of generalized selection combining over Weibull fading channels , 2001, IEEE 54th Vehicular Technology Conference. VTC Fall 2001. Proceedings (Cat. No.01CH37211).

[16]  L. Andrews,et al.  Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media , 2001 .

[17]  Nicolas Perlot,et al.  Aperture averaging: theory and measurements , 2004, SPIE LASE.

[18]  Saralees Nadarajah,et al.  On the Moments of the Exponentiated Weibull Distribution , 2005 .

[19]  Federico Dios,et al.  Accurate calculation of phase screens for the modelling of laser beam propagation through atmospheric turbulence , 2005, SPIE Optics + Photonics.

[20]  R. Sasiela,et al.  Distribution Models for Optical Scintillation Due to Atmospheric Turbulence , 2005 .

[21]  Frida Strömqvist Vetelino,et al.  Fade statistics and aperture averaging for Gaussian beam waves in moderate-to-strong turbulence. , 2007, Applied optics.

[22]  L. Andrews,et al.  Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence. , 2007, Applied optics.

[23]  Mqhele E. Dlodlo,et al.  Performance of MIMO system in Weibull fading channel - Channel capacity analysis , 2009, IEEE EUROCON 2009.

[24]  Stephen D. Lyke,et al.  Probability density of aperture-averaged irradiance fluctuations for long range free space optical communication links. , 2009, Applied optics.

[25]  Ricardo Barrios,et al.  Aperture averaging in a laser Gaussian beam: simulations and experiments , 2010, Optical Engineering + Applications.

[26]  Larry C. Andrews,et al.  Comparing the Log-Normal and Gamma-Gamma model to experimental probability density functions of aperture averaging data , 2010, Optical Engineering + Applications.

[27]  Michail Matthaiou,et al.  New results on turbulence modeling for free-space optical systems , 2010, 2010 17th International Conference on Telecommunications.

[28]  Bernhard Epple.  Simplified Channel Model for Simulation of Free-Space Optical Communications , 2010, IEEE/OSA Journal of Optical Communications and Networking.