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Influence of time interval and filter bandwidth on measured rain fade slope
Radio Science
Abstract
The rate of change of rain attenuation, or 'fade slope,' observed on a microwave link, is dependant on system parameters of the receiver. This paper assesses its dependence on two data processing parameters: the time interval over which the fade slope is defined, and the low-pass filter bandwidth used to remove tropospheric scintillation. A theoretical expression of this dependence is derived. The expression is compared with measured results, which show a good agreement. The results show that the time interval has a strong influence when it is larger than the inverse of the filter bandwidth, and the filter bandwidth has a strong influence when its inverse is larger than the time interval. In general, the fade slope always depends strongly on at least one of the two parameters.
... In the ONERA N-state Markov chain model, the transition probabilities between attenuation states are defined using the fade slope information. The transition matrix is filled with the ITU-R draft new recommendation on fade dynamics which relies on the van de Kamp fade slope model [13]. This model is well adapted to this purpose as it requires scintillation filtering cut-off frequency and sampling rate as inputs parameters. ...
... In order to quantify the dependence of fade slope standard deviation on filter bandwidth and time interval, van de Kamp and Clérivet [14] showed that the conditional fade slope standard deviation is proportional to the following expression: (10) where is the LPF bandwidth (Hz) and is the time interval (s). This function is plotted in Fig. 6. ...
An analysis is made of the measured distributions of the fade slope of rain attenuation, conditional for attenuation values, measured at Eindhoven University of Technology from the satellite Olympus. It is found that the distribution is similar for positive and negative fade slopes and independent of frequency in the range from 12 to 30 GHz. A distribution model for the conditional distribution is found. The only parameter of the distribution is the standard deviation, which is found to be proportional to attenuation level and dependent on rain type, on the low-pass filter bandwidth and on the time interval used in the slope calculation. The observed relation between the standard deviation and attenuation is compared with results from other measurement sites. From this comparison it is found that the fade slope standard deviation is likely to depend on elevation angle and on climate, through its dependence on rain type.
This paper presents results from the statistical analysis of fade slope in satellite and terrestrial links located throughout the Brazilian territory. The amount of data used in this study corresponds to 27 site-years. Among the presented results are the characterization of the probability density function of fade slope and the compilation of a prediction model for the Gaussian parameters based in site-specific parameters. Comparisons between results for satellite and terrestrial links are presented, as well as semi-empirical geo-climatic models for the behaviour of the mean and standard deviation of fade slope values with exceeded attenuation.
A key parameter of the statistics of the rate of change of rain attenuation (“fade slope”) on satellite links is the variance of relative fade slope. This paper shows how this parameter can be derived from rain rate measurements without the use of satellite beacon measurements. Relating rain rate directly to attenuation would give unrealistic results. A theoretical model to estimate the variance of relative fade slope is derived, using the integrating effect of rain rate variations along the propagation path and using as inputs several meteorological parameters only. The theoretical values are compared to measured results from a link in the United Kingdom at 50 GHz. The agreement is good on average and also in their correlation with the type of rain and with the rain height. With the wind speed, the theoretical values increase more strongly than the measured results, which may be due to the limited spatial resolution of the meteorological data.
Time series of rain attenuation on a slant path at 11.6 GHz are analysed with two digital filters to assess their influence on the statistics of the rate of change. It is found that the statistics depend on the measuring apparatus and that a normalisation to the median value reduces the dependence, efficiently permitting comparisons with statistics collected with different time resolutions. A cutoff in the rates is found at high attenuation level and the constancy of the log-normal variance found experimentally is discussed.
A mathematical model is presented which links the dynamical properties of microwave radio signal attenuation to the spatial rain rate structure of intensive showers. The theoretical relation found between attenuation and its rate of change is verified by radio wave propagation measurements on a satellite-earth path at 11.5 GHz.
Since 1969, continuous rain attenuation experiments have been conducted
on earth-satellite paths. The experiments were carried out at four New
Jersey sites, three Georgia sites, two Illinois sites, and two Colorado
sites. The measurement frequencies include 11.7, 13.6, 15.5, 17.8, 19,
and 28.5 GHz. For the convenience of system engineers, this paper
summarizes the new results and the previously published results and
discusses the implications of these data to the design of satellite
radio communication systems. The summary includes the geographic
dependence, the frequency dependence, the diurnal, monthly, and yearly
variations of rain attenuation statistics, the diversity improvement
factors, the fade duration distributions, the dynamic rain attenuation
behavior, the long-term (20 years) rain rate distribution for U.S.
locations, and a simple empirical model for rain attenuation
A dynamic mathematical model of rain attenuation has been developed and is presented in this paper. This model permits the expression of analytic relationships between parameters commonly used to describe the properties of interest for communication. The dynamic model is based on the lognormal distribution of rain attenuation and utilizes a memoryless nonlinear device to transform attenuation and rain intensity into a one-dimensional Gaussian stationary Markov process. Hence, only one parameter is required to introduce the dynamic properties of rain attenuation into the model. Experimental results and the known properties of rain have been used to derive and to verify the model; comparative results are presented and demonstrate good correspondence. The application of the model to the statistical analysis of the performance of communications systems is illustrated in the paper. The use of a dynamic rain attenuation model is necessary in order to analyze radio communication systems with transmit power control to offset the effects of rain attenuation, and where the finite response time of the control system affects the performance. An advantage of the model is the simplicity with which it allows simulation of communication link performance under the influence of rain attenuation. Such simulations are of great interest for complex models of adaptive networks where several deteriorating effects, including finite response times, are present.
Positive and negative rates of change of attenuation are studied jointly with the in-between fade duration using Sirio 11.6 GHz beacon four-year data for several attenuation thresholds, collected in northern Italy. The letter shows that the rate conditional distributions are log-normal, and that little correlation exists between negative and positive rates and durations.
Fade slope statistics for negative and positive slopes are
presented which are obtained by propagation measurements of the 40 GHz
beacon signal of the Italian satellite ITALSAT. Especially, the fade
slope and the 3 dB time duration introduced here are evaluated. Measured
fade slopes of up to 3.2 dB/s were recorded. However, in 99.99% of the
fading event time the fade slopes are <1.9 dB's
The author presents a physical-mathematical model of the dynamics
of rain attenuation and applies it to predict the power spectrum of
attenuation. Compared to experimental data at 19.77 GHz (beacon from
satellite Olympus) the prediction is very good
A comprehensive set of propagation experiments was performed using
the Olympus satellite 12, 20, and 30 GHz beacons. This set of
experiments is unique in North America because of simultaneous reception
of signals spanning the Ku- and Ka-bands from the same orbital slot,
which permits direct inference of the frequency behavior of signal
variations. The elevation angle from the receiving site in Blacksburg,
VA, to the satellite was 14 degrees. Beacon, radiometric, and weather
data for one year were analyzed. The statistical results for rain rate,
beacon attenuation, attenuation ratios, radiometrically derived
attenuation, fade duration and fade slope are presented. They are
important to the design of Ku- and Ka-band satellite communication
systems. The beacon attenuation results include cumulative statistics
for attenuation with respect to free space and with respect to clear
air. Attenuation ratio data are presented using attenuation with respect
to clear air to focus on rain effects. Instantaneous attenuation ratios
computed from instantaneous beacon levels were found to be nearly
identical to statistical attenuation ratios obtained from cumulative
attenuation statistics at each frequency
The dynamics of rain-induced fades on radio links is studied by
evaluating the rate at which the first Fresnel zone volume fills with
rain. The amount of water in this volume determines the fade depth, and
the rate at which it fills establishes the fade slope. A compact
expression for fade slope on a terrestrial path is derived. This
expression shows that once the rain rate is specified, fade slope is
very sensitive to differences in rain velocity. Thus, there is no unique
relationship between fade slope and rain rate
This paper analyzes fade slope for the Alaska, Florida, and New
Mexico Advanced Communications Technology Satellite (ACTS) propagation
data at 20 and 27.5 GHz for the first two years of the experiment
(December 1, 1993-November 30, 1995). The propagation experiment will
continue to collect data for at least another 21 months. Fade slope is
examined on a statistical basis for the three sites. The Florida and New
Mexico receiver sites have very different weather characteristics but
almost identical elevation angles, while the Alaska receiver terminal
has an extremely low elevation angle. The cumulative statistics
illustrate the relationship between fade slope, fade level, transmission
frequency, and elevation angle for all three sites
Fade slope modeling for the satellite com-munication in the Ka-and V-band, graduation report Radio wave propagation modelling for SatCom services at Ku-band and above, final report of COST Action 255
- P Clé
Clé, P. (2001), Fade slope modeling for the satellite com-munication in the Ka-and V-band, graduation report, INSA Rennes/ONERA Toulouse, France. COST255 (2002), Radio wave propagation modelling for SatCom services at Ku-band and above, final report of COST Action 255, chap. 5.3, SP-1252, Eur. Space Agency, Paris.
Climatic radiowave propaga-tion models for the design of satellite communication sys-tems
- Van
- M M J L Kamp
van de Kamp, M. M. J. L. (1999), Climatic radiowave propaga-tion models for the design of satellite communication sys-tems, Ph.D. thesis, Eindhoven Univ. of Technol., Eindhoven, Netherlands. ÀÀÀÀÀÀÀÀÀÀÀ À P. Clé, IN-SNEC, 91940 les Ulis, France.
Fade slope modeling for the satellite communication in the Ka- and V-band graduation report
- P Clérivet
Fade slope modeling for the satellite communication in the Ka- and V-band INSA
- P Clérivet