Exponentiated weibull fading channel model in free-space optical communications under atmospheric turbulence
Authors:   , Barrios Porras Ricardo 
Published: October 2023

Free-space optical (FSO) communications is drawing increasing attention as a promising technology to overcome bandwidth shortage, of an evermore crowded wireless marketplace. Currently radio-frequency (RF) technology struggles to cope with the ever increasing demand for high-bandwidth data. Moreover, as the number of users increases, the RF spectrum is getting so crowded that there is virtually no room for new wireless services, with the additional inconvenient of limited bandwidth restriction for using a RF band and the license fees that have to be paid for such bands. FSO communications offer clear advantages over other alternatives such as narrower and more secure beams, virtually limitless bandwidth and no regulatory policies for using optical frequencies and bandwidth. Moreover, in the space sector FSO technology is becoming more attractive for satellite communication systems due to the less mass and power requirements --compared to RF.

The major drawback for deploying wireless links based on FSO technology is the perturbation of the optical wave as it propagates through the turbulent atmosphere. Many effects are produced, of which the most noticeable is the random fluctuations of the signal-carrying laser beam irradiance (intensity), phenomenon known as scintillation and quantified by the scintillation index (SI). The statistical analysis of the random irradiance fluctuations in FSO links is conducted through the probability density function (PDF), from which one can obtain other statistical tools to measure link performance such as the probability of fade and the bit error-rate (BER). Nowadays, the most widespread models for the irradiance data are, by far, the Lognormal (LN) and Gamma-Gamma (GG) distributions. Although both models comply with actual data in most scenarios neither of them is capable of fitting the irradiance data under all conditions of atmospheric turbulence for finite receiving aperture sizes, i.e. in the presence of aperture averaging. Furthermore, there are several cases where neither the LN or the GG model seem to accurately fit the irradiance data, specially in the left tail of the PDF.

The work presented in this thesis is devoted to propose a new model for the irradiance fluctuations in FSO links under atmospheric turbulence, in the presence of aperture averaging; resulting in the exponentiated Weibull (EW) distribution. A physical justification for the appearance of the new model is provided along with numerous test scenarios in the weak-to-strong turbulence regime --including numerical simulations and experimental data-- to assess its suitability to model the irradiance data in terms of the PDF and probability of fade. Here, a semi-heuristic approach is used to find a set of equations relating the EW parameters directly to the SI. Such expressions were tested offering a fairly good fitting the actual PDF of irradiance data. Furthermore, for all the scenarios tested a best fit version of the EW PDF is obtained and always presents itself as an excellent fit to the PDF data. The new model has been compared to the LN and GG distributions proving to cope to the predictions made by those and, in some cases, even outperforming their predictions. Additionally, a new closed-form expression has been derived for estimating the BER performance under EW turbulence, for intensity-modulation/direct-detection (IM/DD) systems using on-off keying (OOK) modulation. Moreover, this expression has been extended to include pointing errors. Finally, the exponentiated Weibull PDF has been proved to be valid with fully and partially coherent beams.

The results presented here suggest that the EW distribution presents the better fit for data under different scenarios, thus, the exponentiated Weibull distribution becomes an excellent alternative to model the PDF of irradiance data under all conditions of atmospheric turbulence in the presence of aperture averaging.