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On Irradiance Distributions for Weakly Turbulent FSO Links: Log-Normal vs. Gamma-Gamma

Carmen Álvarez Roa, Yunus Can Gültekin, Vincent van Vliet, Menno van den Hout, Chigo Okonkwo, Alex Alvarado

TL;DR

Problem addressed: the log-normal (LN) model may inadequately describe irradiance fluctuations in weak atmospheric turbulence, particularly in the intermediate regime $0.13<\text{SI}\le 1$. Approach: a 30-hour measurement campaign on a $4.6$ km urban FSO link, with data binned into one-minute windows to compute $\text{SI}$, normalized, and fitted using maximum-likelihood estimates for LN ($\sigma^2$) and Gamma-Gamma ($\alpha,\beta$) PDFs across representative $\text{SI}$ levels. Key findings: LN progressively misfits the empirical irradiance PDFs (notably under tails) while the Gamma-Gamma model provides a close match to the entire PDF, including tails, across $\text{SI}$ in $(0.13,1]$. Significance: results advocate using the Gamma-Gamma model for fade/outage probability estimation in FSO systems over a broad turbulence range, extending experimental validation into the intermediate weak regime and challenging the conventional LN assumption.

Abstract

Weak turbulence is commonly modeled using the log-normal distribution. Our experimental results show that this distribution fails to capture irradiance fluctuations in this regime. The Gamma-Gamma model is shown to be more accurate.

On Irradiance Distributions for Weakly Turbulent FSO Links: Log-Normal vs. Gamma-Gamma

TL;DR

Problem addressed: the log-normal (LN) model may inadequately describe irradiance fluctuations in weak atmospheric turbulence, particularly in the intermediate regime . Approach: a 30-hour measurement campaign on a km urban FSO link, with data binned into one-minute windows to compute , normalized, and fitted using maximum-likelihood estimates for LN () and Gamma-Gamma () PDFs across representative levels. Key findings: LN progressively misfits the empirical irradiance PDFs (notably under tails) while the Gamma-Gamma model provides a close match to the entire PDF, including tails, across in . Significance: results advocate using the Gamma-Gamma model for fade/outage probability estimation in FSO systems over a broad turbulence range, extending experimental validation into the intermediate weak regime and challenging the conventional LN assumption.

Abstract

Weak turbulence is commonly modeled using the log-normal distribution. Our experimental results show that this distribution fails to capture irradiance fluctuations in this regime. The Gamma-Gamma model is shown to be more accurate.
Paper Structure (4 sections, 2 equations, 3 figures)

This paper contains 4 sections, 2 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Experimental Setup and Signal Analysis
  3. Numerical Results
  4. Conclusions

Figures (3)

  • Figure 1: Experimental setup for an FSO link connecting Eindhoven University of Technology and the High Tech Campus over 4.6 km.
  • Figure 2: Sorted $\text{SI}_k$ and $\overline{\mu}_k$ (left), computed over one-minute windows and $\text{SI}_k$-$\overline{\mu}_k$ scatter plot (right).
  • Figure 3: PDF of the the normalized received optical power $f_Y(y)$ under weak turbulence for experimental data. Results for the LN and GG distributions are also shown. Columns correspond to $\hbox{$\text{SI} = 0.101$}$ (left), $\text{SI} = 0.486$ (middle), and $\text{SI} = 0.817$ (right).