A prediction model that combines rain attenuation and otherpropagation impairments along Earth-satellite paths

The rapid growth of satellite services using higher frequency bands such as the Ka-band has highlighted a need for estimating the combined effect of different propagation impairments. Many projected Ka-band services will use very small terminals and, for some, rain effects may only form a relatively small part of the total propagation link margin. It is therefore necessary to identify and predict the overall impact of every significant attenuating effect along any given path. A procedure for predicting the combined effect of rain attenuation and several other propagation impairments (at frequencies between 4 and 35 GHz) along Earth-satellite paths is presented. Where an accurate model exist for some phenomena, these have been incorporated into the prediction procedure. New models were developed, however, for rain attenuation, cloud attenuation, and low-angle fading to provide more overall accuracy, particularly at very low elevation angles (<10°). In the absence of a detailed knowledge of the occurrence probabilities of different impairments, an empirical approach is taken in estimating their combined effects. An evaluation of the procedure is made using slant-path attenuation data that have been collected with simultaneous beacon and radiometer measurements which allow a near complete account of different impairments. Results indicate that the rain attenuation element of the model provides the best average accuracy globally between 10 and 30 GHz and that the combined procedure gives prediction accuracies comparable to uncertainties associated with the year-to-year variability of path attenuation     

A systematic comparison of rain attenuation prediction methods for terrestrial paths

The available rain attenuation prediction methods have been tested and compared, and the sensitivity to various input parameters regarding both the rain structure and the rainfall intensity measuring and processing techniques has been examined, on the basis of rain data collected in the northern and central parts of Italy. Starting from the same data, some considerations about the relationship between worst month/yearly cumulative rain attenuation distributions, and the diurnal influence on them are also given.     

Worst-month rain attenuation and XPD statistics for satellite paths at 12 GHz

Worst-month attenuation and XPD data are presented from a three year measurement program at Blacksburg, Virginia USA using the SIRIO 11.6 GHz beacon. The ratio of worst month to annual percentage occurrence levels (Q) for the attenuation and XPD data agree closely with each other. They also show excellent agreement to the CCIR model. Comparisons to previously reported experimental results are also given.     

Joint statistics of rain intensity in eight Italian locations for satellite communication networks

The aim of the letter is to investigate the statistical dependence of rainfall intensity for pairs of stations separated by at least 20 km. Sixteen pairs of stations, with separations ranging from about 20 to 700 km, have been considered by analysing tipping-bucket raingauge data collected during an average period of two years. The analysis shows that the hypothesis of statistical independence cannot be assumed below 150?200 km, while more realistic results can be obtained with reasonably simple procedures.     

Rain rate statistics and fade distributions at 20 and 30 GHzderived from a network of rain gauges in the mid-Atlantic coast over afive year period

The authors examine five years of rain rate and modeled slant path attenuation distributions at 20 and 30 GHz derived from a network of ten tipping bucket rain gauges located on the mid-Atlantic coast of the US in the vicinity of Wallops Island, VA. Distributions are derived from the variable integration time data from 1-min averages or rain rate time series. It is demonstrated that for realistic fade margins at 20 GHz and above, the variable integration time results are adequate to estimate slant path attenuations using models which require 1-min averages. An accurate empirical formula is developed to convert the variable integration time rain rates to 1-min averages. Rain rate and fade distributions corresponding to the overall network average, yearly network average, and site distributions averaged over the five-year period are derived. Significant differences in the distributions are noted for the year-to-year (temporal variability) and the worst year site-to-site (spatial variability) cases     

A general framework for developing and evaluating band-limitedfunction extrapolation methods

It is shown that the bandlimited function extrapolation can be considered as an approximation problem in operator space. Within this framework, the Papoulis-Gerchberg method and two other methods for extrapolation are analyzed. Particular attention is given to approximation using Taylor and Chebyschev series, and to approximation using the Lagrange interpolation method     

A new method for the prediction of fade duration statistics in satellite links above 10 GHz

A model for the statistical prediction of fade durations, applicable both to scintillation and rain-induced effects, is presented in this paper. It assumes that durations longer than about 1 minute are lognormally distributed whereas shorter durations follow a power-law distribution. The model is assessed using data contained in the CCIR data bank and from measurements performed with the SIRIO and Olympus satellites. The model is tested using the same data, and the results give multiplicative errors in the range from 0.6 to 1.8 (averages) and from 0.3 to 3.0 (r.m.s.) in the estimation of the fade durations exceeded for fixed probability.     

On the rain attenuation dynamics: spatial‐temporal analysis of rainfall rate and fade duration statistics

Knowledge about the dynamic characteristics of rain attenuation is of utmost importance for many applications in terrestrial and satellite communication systems operating at frequencies above 10 GHz. Long‐term rain rate statistics and rain rate duration statistics are usually available from meteorological data. In this paper, a spatial–temporal analysis is employed in order to evaluate the rain attenuation power spectrum of a terrestrial/satellite path. The predicted power spectrum is compared with experimental data. Based on the spectral analysis of rainfall rate a method for converting rain rate duration statistics to link fade duration statistics is also proposed. Fade duration statistics are presented for terrestrial and satellite links and compared with available experimental data. The agreement between the predicted results and the experimental data has been found to be quite encouraging. Finally, numerical results are presented for various climatic zones, elevation angles and frequencies. Some very useful conclusions concerning the dynamic properties of rain attenuation for a microwave path are deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Real-time prediction of attenuation for applications to fade countermeasures in satellite communications

The author has simulated the behaviour of a fade countermeasure control system that predicts the attenuation level on the satellite link on the basis of previous attenuation samples, using the experimental rain attenuation data measured at 11.6 GHz in three Italian stations with the Sirio satellite. Some dynamic characteristics of fading are investigated and the performances of prediction algorithms based on linear regression are evaluated.<>     

Analysis of rain fade slope for Ka and V-band satellite links in Southern England

The fade slope of rain attenuation at Sparsholt, U.K. has been measured for a link with the ITALSAT F1 and F2 satellites at frequencies of 18.7, 39.6, and 49.5 GHz and compared with the corresponding ITU-R model. The model fits the data well visually with a tendency to be less accurate with increasing frequency due to the assumption of constant scaling of equiprobable attenuations being less accurate at higher frequencies. The probability distribution used in the model fails a chi-squared test for all confidence levels when compared with the data. Conditional statistics of fade slope on a diurnal and seasonal basis are also analyzed and reveal that the autumn season has higher fade slopes than any other, which can in part be attributed to the higher ratio of stratiform to convective rain in the autumn season. Fade slope was found to have slightly higher values during midday.     

Theoretical random process for prediction of rain attenuation statistics in site diversity satellite links above 10 GHz

Site diversity systems are foreseen for earth-to-satellite links in localities with high rain-induced attenuation operating at frequencies above 10 GHz. An analytical model for the rain-rate statistical process is developed using radar-derived information on the rain structure collected at Spino d'Adda in the framework of the Sirio experiment. The procedure for estimating rain attenuation in both single and site diversity systems is outlined in a general formulation which makes it applicable to different situations. The model gives results very similar to experimental ones.     

Prediction methods for rain attenuation statistics at variable path angles and carrier frequencies between 13 and 100 Ghz

Fade depth and space diversity statistics of propagation along earth-satellite paths have been calculated from radar reflectivity data of rain using modeling procedures. The reflectivity data base was obtained during the summer of 1973 at Wallops Island, Va., using a high resolutionSband radar interfaced with a computer and digital processing system. Fade statistics have been calculated for various path angles at several frequencies between 13 and 100 GHz. Subsequent analysis has demonstrated the ability to predict the following: 1) fade statistics at other path elevation angles given similar type statistics at a particular path angle, 2) space diversity statistics at other frequencies, given similar type statistics at a particular frequency, and 3) fade statistics at a third frequency given similar type statistics at two other frequencies. Although a specific data base was used pertaining to the climatology at Wallops Island, the techniques developed are general and may be applied to existing or future "fade measurements" at other climatological locations.     

Application of synthetic storm data to evaluate simpler techniques for predicting rain attenuation statistics

The concept of employing synthetic storm data to evaluate simpler attenuation prediction techniques based on cumulative distributions of point rain rate is introduced. As examples, several versions of the «path average rain rate technique» and a new method developed by Crane are tested using 10-year rain rate data bases from several Canadian locations. The results indicate that there is no universal relationship for the ratio of the path average to the point rain rate in terms of either rain rate or percentage of time. However, Crane’s new method appears to be an improvement over earlier versions of the path average rain rate technique.     

Comparison of attenuation statistics at 19 and 37 GHz for Sun-Earth paths

For 0.2% of the observing time during May-August 1970, the attenuations at 19 and 37 GHz were about 3.8 and 10.2 dB, respectively, the larger value being the maximum measurable with the technique used in the investigation. Previous attenuation statistics published for 19 GHz are updated to cover the period June 1968-August 1970.     

Comparison of a one- and a two-frequency technique for frequency scaling of rain attenuation statistics

The theory underlying Hogg's technique for the frequency scaling of rain attenuation statistics at two frequencies is presented, and the inherent approximations given. The technique is compared theoretically and numerically with a new method for scaling single frequency statistics recently proposed by the authors.     

Efficient numerical techniques for solving Pocklington's equation and their relationships to other methods

It is shown that testing Pocklington's equation with piecewise sinusoidal functions yields an integro-difference equation whose numerical solution is identical to that of the point-matched Hallen's equation when a common set of basis functions is used with each. For any choice of basis functions, the integro-difference equation has the simple kernel, the fast convergence, the simplicity of point-matching, and the adequate treatment of rapidly varying incident fields, but none of the additional unknowns normally associated with Hallen's equation. Furthermore, for the special choice of piecewise sinusoids as the basis functions, the method reduces to Richmond's piecewise sinusoidal reaction matching technique, or Galerkin's method. It is also shown that testing with piecewise linear (triangle) functions yields an integro-difference equation whose solution converges asymptotically at the same rate as that of Hallen's equation. The resulting equation is essentially that obtained by approximating the second derivative in Pocklington's equation by its finite difference equivalent. The authors suggest a simple and highly efficient method for solving Pocklington's equation. This approach is contrasted to the point-matched solution of Pocklington's equation and the reasons for the poor convergence of the latter are examined.     

A normal approximation to distributions of likelihood ratio statistics in life testing,reliability and multivariate analysis of variance

A general approach to normal approximation of distributions of some likelihood ratio statistics in life testing, reliability and the multivariate analysis of variance (MANOVA) is discussed. A few special cases are considered for illustration.     

A novel method for the statistical prediction of rain attenuation in site diversity systems: theory and comparative testing against experimental data

Site diversity is a promising technique to overcome severe attenuation on earth–space communication links. This technique is based on the experimental evidence that intense rain cells are limited in extent, so that the replacement of one station with two or more stations separated by a few kilometres may substantially reduce the outage probability of the communication system. In this paper the physical EXCELL rain cell model, developed at our laboratory for the prediction of single-site rain attenuation statistics, has been extended to the case of diversity configuration systems. For comparison purposes, two among the best-performing models found in the literature, proposed by Hodge and Matricciani, have been considered. The values predicted by the three models have been compared against data of 41 experiments with a maximum separation distance between ground stations of 15 km, collected both from the ITU-R databank and from the open literature. This site separation range is the most interesting one, because attenuations in diversity paths tend to be uncorrelated above 20–30 km and hence the benefit obtained by a diversity scheme becomes marginal. The measured and predicted ‘relative diversity gains’ at various time percentages have been compared: the RMS values of relative gain error show that EXCELL is the best-performing model. © 1998 John Wiley & Sons, Ltd.