## Keywords

Laser beam propagation, Scintillation, Fade statistics, Atmospheric parameters, PDF of irradiance fluctuations, Atmospheric turbulence

## Abstract

The performance of lasercom systems operating in the atmosphere is reduced by optical turbulence, which causes irradiance fluctuations in the received signal. The result is a randomly fading signal. Fade statistics for lasercom systems are determined from the probability density function (PDF) of the irradiance fluctuations. The expected number of fades per second and their mean fade time require the joint PDF of the fluctuating irradiance and its time derivative. Theoretical integral expressions, as well as closed form, analytical approximations, were developed for the joint PDF of a gamma-gamma distributed irradiance and its time derivative, and the corresponding expression for the expected number of fades per second. The new approximation for the conditional PDF of the time derivative of a gamma-gamma irradiance is a zero mean Gaussian distribution, with a complicated irradiance depending variance. Fade statistics obtained from experimental data were compared to theoretical predictions based on the lognormal and gamma-gamma distributions. A Gaussian beam wave was propagated through the atmosphere along a horizontal path, near ground, in the moderate-to-strong optical turbulence. To characterize the propagation path, a new method that infers atmospheric propagation parameters was developed. Scintillation theory combined with a numerical scheme was used to infer the structure constant, Cn2, the inner scale and the outer scale from the optical measurements. The inferred parameters were used in calculations for the theoretical PDFs. It was found that fade predictions made by the gamma-gamma and lognormal distributions provide an upper and lower bound, respectively, for the probability of fade and the number of fades per second for irradiance data collected in the moderate-to-strong fluctuation regime. Aperture averaging effects on the PDF of the irradiance fluctuations were investigated by comparing the irradiance distributions for the three receiver apertures at two different values of the structure parameter and, hence, different values of the coherence radius. For the moderate-to-strong fluctuation regime, the gamma-gamma distribution provides a good fit to the irradiance fluctuations collected by finite-sized apertures that are significantly smaller than the coherence radius. For apertures larger than or equal to the coherence radius, the irradiance fluctuations appear to be lognormally distributed.

## Notes

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## Graduation Date

2006

## Semester

Fall

## Advisor

Young, Cynthia

## Degree

Doctor of Philosophy (Ph.D.)

## College

College of Sciences

## Department

Mathematics

## Degree Program

Mathematics

## Format

application/pdf

## Identifier

CFE0001440

## URL

http://purl.fcla.edu/fcla/etd/CFE0001440

## Language

English

## Length of Campus-only Access

None

## Access Status

Doctoral Dissertation (Open Access)

## STARS Citation

Stromqvist Vetelino, Frida, "Fade Statistics For A Lasercom System And The Joint Pdf Of A Gamma-gamma Distributed Irradiance And Its Time Derivative" (2006). *Electronic Theses and Dissertations*. 824.

https://stars.library.ucf.edu/etd/824