Martin Grabner

The wavelength dependent model of extinction in fog and haze for free space optical communication

The wavelength dependence of the extinction coefficient in fog and haze is investigated using Mie single scattering theory. It is shown that the effective radius of drop size distribution determines the slope of the log-log dependence of the extinction on wavelengths in the interval between 0.2 and 2 microns. The relation between the atmospheric visibility and the effective radius is derived from the empirical relationship of liquid water content and extinction. Based on these results, the model of the relationship between visibility and the extinction coefficient with different effective radii for fog and for haze conditions is proposed.

Multiple Scattering in Rain and Fog on Free-Space Optical Links

The multiple scattering effects of light propagation in rain and fog are investigated by means of numerical Monte Carlo photon propagation simulations. Rain and fog consisting of water droplets are described by realistic drop size distributions with parameters related to physical parameters of hydrometeors such as rain intensity, liquid water content, effective droplet radius of fog and atmospheric visibility. Simulations show that optical attenuation due to rain is about two times lower than predicted by single scattering approach. Fog attenuation is also reduced for the lowest visibilities. An impulse response of optical channel in rain and fog is obtained and the explicit models for the delay spread dependence are provided. Under realistic conditions, the RMS delay spread due to rain on 1 km long free space optics (FSO) path is limited below 10 ps. Moderate and dense fog can cause the delay spread about 50 ps or more. Frequency characteristics of the FSO channel impaired by rain and fog are given.

Estimation of the Refractivity Structure of the Lower Troposphere From Measurements on a Terrestrial Multiple-Receiver Radio Link

A matched field technique is used for remote sensing of refractivity profile. The method relies on electromagnetic propagation simulation to estimate the height profile of radio refractivity in the lower atmosphere by comparing theoretical predictions with measurements on a terrestrial radio link. The objective is to discover whether small variations of the airs refractive index can be detected in the lowest part of atmosphere, up to 150 m above the ground. The resultant estimations of the height profile of refractivity are compared with the measured refractivity profile obtained from meteorological sensors at different heights. The results show a close agreement between the estimated and measured refractivity profiles during periods of deep fading events.

Fog attenuation dependence on atmospheric visibility at two wavelengths for FSO link planning

Performance of the models of dependence between fog attenuation and atmospheric visibility is investigated using two-year experimental data measured on parallel FSO links with wavelengths of 830 and 1550 nm. Models fitted to measured data provide better estimation of attenuation for FSO link planning.

Atmospheric Refraction and Propagation in Lower Troposphere

Influence of atmospheric refraction on the propagation of electromagnetic waves has been studied from the beginnings of radio wave technology (Kerr, 1987). It has been proved that the path bending of electromagnetic waves due to inhomogeneous spatial distribution of the refractive index of air causes adverse effects such as multipath fading and interference, attenuation due to diffraction on the terrain obstacles or so called radio holes (Lavergnat & Sylvain, 2000). These effects significantly impair radio communication, navigation and radar systems. Atmospheric refractivity is dependent on physical parameters of air such as pressure, temperature and water content. It varies in space and time due the physical processes in atmosphere that are often difficult to describe in a deterministic way and have to be, to some extent, considered as random with its probabilistic characteristics. Current research of refractivity effects utilizes both the experimental results obtained from in situ measurements of atmospheric refractivity and the computational methods to simulate the refractivity related propagation effects. The two following areas are mainly addressed. First, a more complete statistical description of refractivity distribution is sought using the finer space and time scales in order to get data not only for typical current applications such as radio path planning, but also to describe adverse propagation in detail. For example, multipath propagation can be caused by atmospheric layers of width of several meters. During severe multipath propagation conditions, received signal changes on time scales of minutes or seconds. Therefore, for example, the vertical profiles of meteorological parameters measured every 6 hours by radiosondes are not sufficient for all modelling purposes. The second main topic of an ongoing research is a development and application of inverse propagation methods that are intended to obtain refractivity fields from electromagnetic measurements. In the chapter, recent experimental and modelling results are presented that are related to atmospheric refractivity effects on the propagation of microwaves in the lowest troposphere. The chapter is organized as follows. Basic facts about atmospheric refractivity are introduced in the Section 2. The current experimental measurement of the vertical distribution of refractivity is described in the Section 3. Long term statistics of atmospheric refractivity parameters are presented in the Section 4. Finally, the methods of propagation modelling of EM waves in the lowest troposphere with inhomogeneous refractivity are discussed in the Section 5.

Rain attenuation at 58 GHz: prediction versus long-term trial results

Electromagnetic wave propagation research in frequency band 58 GHz was started at TESTCOM in Praha due to lack of experimentally obtained results needed for a realistic calculation of quality and availability of point-to-point fixed systems. Rain attenuation data obtained from a path at 58 GHz with V polarization located in Praha was processed over a 5-year period. Rainfall intensities have been measured by means of a heated siphon rain gauge. In parallel, rainfall intensity data from rain gauge records was statistically processed over the same year periods as the rain attenuation data. Cumulative distributions of rainfall intensities obtained as well as cumulative distributions of rain attenuation obtained are compared with the calculated ones in accordance with relevant ITU-R recommendations. The results obtained can be used as the primary basis for the possible extension of the ITU-R recommendation for calculating rain attenuation distributions up to 60 GHz. The obtained dependence of percentages of time of the average year on the percentages of time of the average worst month is also compared with the relevant ITU-R recommendation. The results obtained are discussed.

On the relation between atmospheric visibility and optical wave attenuation

The knowledge about the relationship between atmospheric visibility and optical wave attenuation in the atmosphere is essential in order to predict the performance of free space optical communication links. In this paper, a study of the available models of visibility -attenuation relation is presented. Visibility and attenuation are measured on an experimental free space optical link with a wavelength of 830 nm. New models are proposed based on the least square fitting of data from this measurement.

Statistics of lower atmosphere refractivity in Czechia

Atmospheric refractivity influences significantly the propagation of electromagnetic waves in atmosphere. ITU-R recommends using statistics of a refractivity vertical gradient in the lowest 65 meters above the ground for estimation of multipath fading incidence on the terrestrial fixed wireless links. In this paper, results of the measurement of atmospheric refractivity in a lower 80 m layer of atmosphere are presented. Daily and monthly variability of refractivity and of its vertical gradient is shown. Refractivity statistics are compared with the quantiles obtained from the ITU-R world map.

Further results on fog modeling for terrestrial free-space optical links

Recent measurement campaigns in Prague, Czech Republic have recorded the specific attenuation caused by fog in terrestrial free-space optical (FSO) links along with visibility, liquid water content (LWC), and integrated particle surface area for operational wavelengths of 1550 and 830 nm. Data recorded during 5 months of measurements has been analyzed in an attempt to validate and improve the empirical models for LWC and visibility-based attenuation and the probability density function (PDF) estimation of the received signal strength (RSS). The results strongly suggest that further attempts in refinement of the empirical modeling for visibility-based attenuation or LWC-based attenuation shall move towards the establishment of a global data bank of fog attenuation measurements in different climatic regions. This data bank can then help develop generic models which could lead to better system design of future terrestrial FSO links. The PDF estimation of RSS puts forth the Kumaraswamy distribution as the best fit for settled continental fog conditions.

Propagation study of 850nm/58 GHz hybrid municipal system

The paper deals with the results of a propagation study on a fixed hybrid Free Space Optical (FSO) and Radio Frequency (RF) system operating in 850 nm / 58 GHz bands. Propagation models for the availability assessment of both FSO and RF links were examined against a comprehensive database of meteorological attenuation events. The influences of individual hydrometeors were analyzed and the availability performances of the simulated FSO/MMW hybrid link were evaluated. The study pointed out that visibility and rainfall measurements can be only used for the raw assessment of availability performance due to the concurrent occurrence of different attenuation effect.