Rain Attenuation Statistics Research Articles

Rain Attenuation Prediction Using Artificial Neural Network for Dynamic Rain Fade Mitigation

Atmospheric processes from which rainfall is formed are complex and cannot be accurately predicted using mathematical or statistical models. In this paper, the backpropagation neural network (BPNN) is trained to predict rainfall rates, and hence attenuation that is likely to be experienced on a link. This study is carried out over the sub-tropical region of Durban, South Africa (29.8587°S, 31.0218°E). Utilizing the non-linear mapping capability between inputs and outputs, the backpropagation neural network is trained using rainfall data collected from 2013 to 2016 to predict rainfall rates. Long-term rain attenuation statistics arising from predicted rain rates are compared with actual and ITU-R model, and results show a relatively small margin of error between predicted rain attenuation exceeded for 0.01 % of an average year. Furthermore, analysis of predicted and actual rain attenuation within individual rain events from different rainfall regimes was carried out and results show that the proposed model can be used to predict the state of the link. This is demonstrated when the trained BPNN was tested using unseen data that was collected from January 2017 to May 2018, a period that spans through all four different climatic seasons of summer, autumn, winter and spring. Results of the test show a correlation coefficient of 0.8298. Finally, the proposed rain prediction model was tested on rainfall data from Butare, Rwanda (2.6078°S, 29.7368°E), which is a tropical region and results obtained indicate the portability of the proposed model to other regions.

Rain attenuation statistics at Ka‐band estimated from weather radar observations in Belgium

SummaryThis paper presents rain attenuation statistics for satellite‐ground transmission links at Ka‐band based on 10‐year reflectivity observations from a C‐band weather radar. The ground receiving station and the radar are both located in Belgium. Only precipitation under the freezing level is considered, and the attenuation produced by hail is removed by applying a reflectivity threshold. The radar‐derived attenuations are analyzed to investigate the influence of elevation and azimuthal angles on the attenuation statistics. It is shown that the azimuthal dependence is extremely low. In contrast, the exceedance probability for a given attenuation threshold strongly increases with decreasing elevation angles, as foreseen by ITU‐R recommendations. The radar‐derived attenuations are used to estimate rain attenuation complementary cumulative distribution functions computed according to ITU‐R recommendations for a low Earth orbit satellite. The sensitivity to the hail reflectivity threshold is very limited. In contrast, our results show that reliable attenuation statistics cannot be obtained without taking carefully into account the height of the freezing level. Monthly averages of the freezing levels allow producing satisfactory results, but it is recommended to incorporate freezing level heights with high temporal and spatial resolutions.

Space-Time Stochastic Rain Fading Channel for Multiple LEO or MEO Satellite Slant Paths

In this letter, a novel time series synthesizer of rain attenuation is proposed which incorporates the spatial correlation of rain attenuation for multiple Low Earth Orbit or Medium Earth Orbit (MEO) satellite links. The model is based on the multi-dimensional stochastic differential equations (SDEs) and it extends the well-known Maseng–Bakken model for multiple Earth-LEO or MEO satellite links. Analytical expressions, for the prediction of the joint exceedance probability of rain attenuation induced in LEO or MEO slant paths, are given. Moreover, multi-dimensional SDEs are proposed and the solution of the SDEs is used for the generation of time series of rain attenuation for spatially time-dependent correlated slant paths correlated in spatial domain. The synthesizer is validated with the theoretical expressions for the calculation of joint first order statistics of rain attenuation in various diversity schemes.

Slant Path Ka-Band rain attenuation statistics in equatorial Malaysia obtained using stratiform convective-synthetic storm technique

In the design of satellite communication link, rain attenuation statistics is essential information for system designer to realistically determine link availability and provide means to combat system degradation. Due to the limitation of available measured data in equatorial regions especially for high frequencies (Ka-band and above), the prediction model is the best way to obtain rain attenuation statistics. This paper presents statistical analysis of rain attenuation at Ka-band by applying the Stratiform Convective-Synthetic Storm Technique (SC-SST) model taking advantage from local weather features from rain rate time series. The study on seasonal and diurnal variability is also presented in this paper to provide good insight in the design and implementation of fade margin.

Cross‐polarisation discrimination models assessment and improvement on earth‐space propagation paths at Ka and V‐bands

The performance of the satellite communication systems employing polarisation diversity or frequency-reuse schemes to improve the spectral efficiency is degraded due to the depolarisation-induced interference originated by raindrops and ice particles present along the Earth-Space propagation path. Two models account for both rain and ice contributions. One predicts the long-term cumulative distribution function (CDF) of cross-polarisation discrimination (XPD). The other predicts the relationship between XPD and co-polar attenuation (CPA) and it was derived considering exclusively data at the V-band. In this study, the former model is improved by considering the individual ice and rain contributions and their combined effects, while the latter is validated against new measurements at the Ka band. New models are then proposed for the XPD-CPA relationships at the Ka-band taking into account both rain and ice contributions and also their combined effects. Finally, the predictions provided by the first model are usually converted to the corresponding XPD-CPA relationship using the long-term first-order statistics of rain attenuation, (incorrectly) considering that the equiprobability hypothesis applies. A new approach for the conversion of the XPD CDF into the corresponding XPD-CPA relationship is presented.

Rain Attenuation Prediction Model Based on Hyperbolic Cosecant Copula for Multiple Site Diversity Systems in Satellite Communications

This paper presents a novel model for prediction of site diversity system performance in millimeter-wave satellite communications. The model predicts the joint exceedance probability of rain attenuation based on a new family of Archimedean copulas, called the hyperbolic cosecant copula. Furthermore, employing the hierarchical Archimedean copula structures, the proposed methodology can be used for the prediction of joint first-order statistics of rain attenuation for dual- and multiple-site diversity satellite communication systems. The proposed method has been tested on an extensive data set of site diversity experiments with various system configurations. Moreover, in addition to the common approaches, where the dependence of rain attenuation induced on multiple links is based solely on the distance between ground stations, elevation and baseline angle are also taken into account for the modeling of the dependence parameter. Both versions of the model outperform the existing model for two-site diversity systems given in the ITU-R Recommendation P.618-12. The version, which accounts for the system’s angles, shows a better performance also in comparison with the state-of-the-art models such as the models based on the Archimedean Clayton copula and the Gaussian copula.

Characterization of Rain Specific Attenuation and Frequency Scaling Method for Satellite Communication in South Korea

The attenuation induced by rain is prominent in the satellite communication at Ku and Ka bands. The paper studied the empirical determination of the power law coefficients which support the calculation of specific attenuation from the knowledge of rain rate at Ku and Ka band for Koreasat 6 and COMS1 in South Korea that are based on the three years of measurement. Rain rate data was measured through OTT Parsivel which shows the rain rate of about 50 mm/hr and attenuation of 10.7, 11.6, and 11.3 dB for 12.25, 19.8, and 20.73 GHz, respectively, for 0.01% of the time for the combined values of rain rate and rain attenuation statistics. Comparing with the measured data illustrates the suitability for estimation of signal attenuation in Ku and Ka band whose validation is done through the comparison with prominent rain attenuation models, namely, ITU-R P.618-12 and ITU-R P. 838-3 with the use of empirically determined coefficient sets. The result indicates the significance of the ITU-R recommended regression coefficients of rain specific attenuation. Furthermore, the overview of predicted year-wise rain attenuation estimation for Ka band in the same link as well as different link is studied which is obtained from the ITU-R P. 618-12 frequency scaling method.

Prediction of Joint Rain Attenuation Statistics Induced on Earth–Satellite Multiple Site Diversity Systems Using Gaussian Copula

A novel prediction model of the joint exceedance probability of rain attenuation in Earth–satellite site diversity systems based on the Gaussian copula is presented. The proposed model is based on a number of experimental data of two-site diversity systems with different configurations. The proposed model outperforms the existing model for two-site diversity given in Recommendation ITU-R P.618-12 and the recently presented model based on the Clayton copula. The method is generalized to multiple-site diversity prediction. Results for a few existing three-site diversity experiments are evaluated.

Rain attenuation statistics over millimeter wave bands in South Korea

Rain induced degradations are significant for terrestrial microwave links operating at frequencies higher than 10GHz. Paper presents analyses done on rain attenuation and rainfall data for three years between 2013 till 2015, in 3.2km experimental link of 38GHz and 0.1km link at 75GHz. The less link distance is maintained for 75GHz operating frequency in order to have better recording of propagation effect as such attenuation induced by rain. OTT Parsivel is used for collection of rain rate database which show rain rate of about 50mm/h and attenuation values of 20.89 and 28.55dB are obtained at 0.01% of the time for vertical polarization under 38 and 75GHz respectively. Prediction models, namely, ITU-R P. 530-16, Da Silva Mello, Moupfouma, Abdulrahman, Lin and differential equation approach are analyzed. This studies help to identify most suitable rain attenuation model for higher microwave bands. While applying ITU-R P. 530-16, the relative error margin of about 3%, 38% and 42% along with 80, 70, 61% were obtained in 0.1%, 0.01% and 0.001% of the time for vertical polarization under 38 and 75GHz respectively. Interestingly, ITU-R P. 530-16 shows relatively closer estimation to measured rain attenuation at 75GHz with relatively less error probabilities and additionally, Abdulrahman and ITU-R P. 530-16 results in better estimation to the measured rain attenuation at 38GHz link. The performance of prominent rain attenuation models are judged with different error matrices as recommended by ITU-R P. 311-15. Furthermore, the efficacy of frequency scaling technique of rain attenuation between links distribution are also discussed. This study shall be useful for making good considerations in rain attenuation predictions for terrestrial link operating at higher frequencies.

Mitigating the effects of rain‐induced fading in satellite communications systems using time diversity in concert with maximal ratio combining

This paper reports on a preliminary study using EutelSat Hotbird 13A beacon data at 19.7 GHz and 29.5 GHz (scaled data) to evaluate the benefit of using Time Diversity (TD) and Maximal Ratio Combining (MRC) on an experimental next generation Ka-band (26.5–40 GHz) satellite link in the UK. The authors have used the 2nd generation of video broadcasting via satellite (DVB-S2) as the broadcasting standard to investigate the novel integration of TD and MRC. The benefit of the TD and MRC scheme was quantified in terms of percentage enhancement of the link availability. Long-term statistics of rain and atmospheric attenuation were derived from a period of three year’s measurements made in Pontypridd, South Wales and in Chilbolton, England, at 19.7 GHz. A hypothetical Ka-band satellite broadcast link between Pontypridd and Chilbolton has been designed to use 29.5 GHz as the uplink frequency while 19.7 GHz is used as the downlink frequency. The paper discusses the performance enhancement provided by TD and MRC during different types of fading events. The integration of TD and MRC into the DVB-S2 standard provides the capability to continue delivering services at lower carrier-to-noise (C/N) levels by lowering the bit error rate (BER).

Rain attenuation prediction during rain events in different climatic regions

A rain attenuation prediction method has been applied to different climatic regions to test the validity of the model. The significant difference in rain rate and attenuation statistics for the tropical and temperate region needs to be considered in developing channel model to predict time series of rain attenuation for earth space communication links. Model parameters obtained for a tropical location has been successfully applied to predict time series of rain attenuation at other tropical locations. Separate model parameters are derived from the experimental data obtained at a temperate location and these are used to predict rain attenuation during rain events for other temperate locations showing the effectiveness of the technique.

Diurnal and Seasonal Variations of Rain Rate and Rain Attenuation on Ku-Band Satellite Systems in a Tropical Region: A Synthetic Storm Techniques Approach

In this paper, a time-varying rain characterization and diurnal variation in the Ku-band satellite systems simulated with synthetic storm techniques (SST) over a tropical location in Nigeria have been presented. Three years’ rain rate time-series data measured by a raingauge located inside the Federal University of Technology Akure, Nigeria were utilized for the purpose of this work. The analysis is based on the CDF of one-minute rain rate; time-series simulated annual/seasonal and diurnal rain rate, rain attenuation statistics and fade margins observed over four time intervals: 00:00-06:00, 06:00-12:00, 12:00-18:00 and 18:00-24:00. In addition, comparison was also made between the synthesized values and rain attenuation statistics, at 12.245 GHz for a hypothetical downlink from EUTELSAT W4/W7 satellite in the area. It could be observed that at 99.99% link availability, the fade margin as high as ~20 dB may be required at Ku band uplink frequency bands in this area. We also observed that the communication downlinks working in the early morning and early to late in the evening hours must be compensated with an appropriate Down-Link Power Control (DLPC) for optimum performances during severe atmospheric influences in the region.

Advanced time series synthesizer for simulation of joint rain attenuation conditions

AbstractThis contribution presents a model to generate time series of rain attenuation by adapting a large set of rain attenuation measurements to different locations. The proposed model allows generating rainy and not rainy conditions for multiple stations in a large geographical area, reproducing the actual spatial and temporal variability of the rain process, with limited computational effort. Single site and joint statistics of rain attenuation obtained by the time series of measurements are discussed. The model is used to show the effectiveness, in terms of link margin, of gateway networks in smart diversity arrangement, for different separation distances among sites.

Analysis of Fade Dynamic at Ku-Band in Malaysia

This work investigates fade dynamics of satellite communication systems in equatorial heavy rain region based on a one year of Ku-band propagation measurement campaign carried out in Universiti Teknologi Malaysia (UTM), Johor, Malaysia. First order statistics of rain attenuation are deduced and the results are found to be in good agreement with those obtained from other beacon measurements gathered within the same area (Kuala Lumpur). Moreover, the fade duration and slope statistics of the satellite signal variations are also carefully derived and subsequently compared with the ITU-R recommendation model. Such information is useful for the system operator and radio communication engineer for the design of appropriate fade mitigation techniques as well as the quality of service that could be offered to the user (according to the time interval for a typical day). Further evaluation on the performances of several ITU-R models in the heavy rain region are needed based on the measurement database available of this climatic region.

Inter‐annual variability, risk and confidence intervals associated with propagation statistics. Part I: theory of estimation

SUMMARYThis set of two companion papers aims at providing a statistical framework to quantify the inter‐annual variability observed on the statistics of rain attenuation or rainfall rate derived from Earth‐space propagation measurements. This part I is more specifically devoted to the theoretical study of the variance of estimation of empirical complementary cumulative distribution functions (ECCDFs) derived from Earth‐space rain attenuation or rainfall rate time series. To focus the analysis on the statistical variability but without loss of generality, synthetic rain attenuation time series are considered. A large variability on the ECCDFs, which depends on the duration of the synthetic data, is first put into evidence. The variance of estimation is then derived from the properties of the statistical estimator. The formulation is validated numerically, by comparison with the ECCDF variances derived from the synthetic data. The variance of the fluctuations around the CCDF is then shown to be dependent on the average of the correlation function of the time series, on the probability level and on the measurement duration. This variance of estimation is needed as a prerequisite in conjunction with the knowledge of the climatic variability to characterize the yearly fluctuations of propagation statistics computed from experimental time series. The extensions from simulations to experiments as well as the application to system planning are detailed in part II. Copyright © 2013 John Wiley & Sons, Ltd.

New physical‐mathematical model for predicting slant‐path rain attenuation statistics based on inverse Gaussian distribution

A new physical-mathematical model for predicting first-order rain attenuation statistics for slant-path links is presented in this study. It is assumed that point rain rate and slant-path rain attenuation follow the inverse Gaussian (IG) distribution. The statistical parameters of the IG distribution of the induced rain attenuation on a slant path are calculated in terms of the rain rate statistical parameters by adopting a spatial inhomogeneity model for specific rain attenuation. The method is validated using experimental data taken from Database of Study Group 3 (radiowave propagation) of International Telecommunication Union-Radio (ITU-R), hereafter named DBSG3 and with simulated rain attenuation data using the Synthetic Storm Technique on recent rain rate measurements in Athens, Greece. Its performance is also compared to the ITU-R P. 618-10 model. The proposed model shows better performance comparing to the ITU-R model and the results are very encouraging.

Prediction of monthly rainfall statistics from data with long integration time

Conversion models, originally devised to turn yearly rainfall statistics from long (e.g. 30 or 60 min) to short integration time T (i.e. 1 min), are assessed for their ability to also predict monthly 1-min integrated statistics, P(R)1m, knowledge of which may be beneficial for specific services (e.g. reconfigurable systems) and for the definition of a reliable approach to estimate monthly (hence worst month) rain attenuation statistics. Tests, performed for 5 ≤ T ≤ 60 min against monthly raingauge-derived rainfall data collected in some sites worldwide, indicate that the EXponential CELL rainfall statistics conversion (EXCELL RSC) and Lavergnat-Golé models, in force of their physical soundness, provide a good performance when used to predict 1-min integrated rainfall statistics both on yearly and on monthly bases.

Tropospheric Scintillation With Concurrent Rain Attenuation at 50 GHz in Madrid

Tropospheric scintillation can become a significant impairment in satellite communication systems, especially in those with low fade-margin. Moreover, fast amplitude fluctuations due to scintillation are even larger when rain is present on the propagation path. Few studies of scintillation during rain have been reported and the statistical characterization is still not totally clear. This paper presents experimental results on the relationship between scintillation and rain attenuation obtained from slant-path attenuation measurements at 50 GHz. The study is focused on the probability density function (PDF) of various scintillation parameters. It is shown that scintillation intensity, measured as the standard deviation of the amplitude fluctuations, increases with rain attenuation; in the range 1-10 dB this relationship can be expressed by power-law or linear equations. The PDFs of scintillation intensity conditioned to a given rain attenuation level are lognormal, while the overall long-term PDF is well fitted by a generalized extreme value (GEV) distribution. The short-term PDFs of amplitude conditioned to a given intensity are normal, although skewness effects are observed for the strongest intensities. A procedure is given to derive numerically the overall PDF of scintillation amplitude using a combination of conditional PDFs and local statistics of rain attenuation.

Investigation of Rain Attenuation in Equatorial Kuala Lumpur

This letter investigates rain attenuation in Kuala Lumpur, Malaysia, by exploiting local drop size distribution (DSD) measurements. Coefficients for the well-established power-law model relating rain rate and specific attenuation are derived for frequencies in the Ku-, Ka-, and Q/V-bands based on three years of disdrometer data. We analyze the diurnal variation of rainfall rate for four time intervals and, moreover, we present statistics of rain attenuation for slant-path Earth-space links estimated by means of a new model (Stratiform-Convective SST) that combines the advantages of the Dual-Layer Synthetic Storm Technique (SST) and the SC EXCELL model. The predicted statistics are in good agreement with those obtained from beacon measurements (MEASAT-1 satellite at 12 GHz). Finally, the diurnal variation of the slant-path rain attenuation is presented to provide system operators and radio communication engineers with useful information on the quality of service (QoS) that can be achieved during a typical day on an Earth-space link.

Estimation of Path Length Reduction Factor by Using One Year Rain Attenuation Statistics over a Line of Sight Link Operating at 28.75 GHz in Amritsar (INDIA)

The effect of environmental factors in general and rain droplets in particular, on microwave propagation is a very well known fact now. If the rain droplets are present in an inhomogeneous way across the path length of the microwave communication system then, a new concept of path length reduction factor is introduced which accounts for the inhomogeneous nature of the rain droplets along the path length of the microwave signal. The present paper presents results of path length reduction factor using data on attenuation levels obtained on a LOS link operating at 28.75 GHz in Amritsar region and its comparison with Crane’s and ITU-R’s model.