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

2017; Institution of Engineering and Technology; Volume: 12; Issue: 4 Linguagem: Inglês

10.1049/iet-map.2017.0589

1751-8733

Flávio Jorge, Carlo Riva, Armando Rocha,

Soil Moisture and Remote Sensing

IET Microwaves, Antennas & PropagationVolume 12, Issue 4 p. 479-485 Special Issue: Selected Papers from the 11th European Conference on Antennas and Propagation (EuCAP 2017)Free Access Cross-polarisation discrimination models assessment and improvement on earth-space propagation paths at Ka and V-bands Flávio Jorge, Corresponding Author Flávio Jorge flaviojorge@ua.pt orcid.org/0000-0002-1656-7824 Instituto de Telecomunicações and Departamento de Electrónica Telecomunicações e Informática, Universidade de Aveiro, Campus Universitário de Santiago 3810–193, Aveiro, PortugalSearch for more papers by this authorCarlo Riva, Carlo Riva DEIB/Politecnico di Milano and IEIIT/CNR, Piazza Leonardo da Vinci, 20133 Milano, ItalySearch for more papers by this authorArmando Rocha, Armando Rocha Instituto de Telecomunicações and Departamento de Electrónica Telecomunicações e Informática, Universidade de Aveiro, Campus Universitário de Santiago 3810–193, Aveiro, PortugalSearch for more papers by this author Flávio Jorge, Corresponding Author Flávio Jorge flaviojorge@ua.pt orcid.org/0000-0002-1656-7824 Instituto de Telecomunicações and Departamento de Electrónica Telecomunicações e Informática, Universidade de Aveiro, Campus Universitário de Santiago 3810–193, Aveiro, PortugalSearch for more papers by this authorCarlo Riva, Carlo Riva DEIB/Politecnico di Milano and IEIIT/CNR, Piazza Leonardo da Vinci, 20133 Milano, ItalySearch for more papers by this authorArmando Rocha, Armando Rocha Instituto de Telecomunicações and Departamento de Electrónica Telecomunicações e Informática, Universidade de Aveiro, Campus Universitário de Santiago 3810–193, Aveiro, PortugalSearch for more papers by this author First published: 05 February 2018 https://doi.org/10.1049/iet-map.2017.0589Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract 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. 1 Introduction The performance of the satellite communication systems employing either polarisation diversity or frequency-reuse schemes to improve the spectral efficiency is degraded due to the depolarisation-induced interference caused by the interaction between the radiowave and the hydrometeors present along the Earth–Space propagation path, namely raindrops and ice particles [[1]]. Several models have been proposed in the literature for rain-induced depolarisation [[2]–[6]]. However, the ice plays also an important role in total depolarisation [[7], [8]], and consequently, both contributions must be considered. Two models account for both contributions: the International Telecommunication Union–Radiocommunications (ITU–R) model [[9]] and the Paraboni et al. model [[10]]. The ITU–R model, which is not updated since, at least, 1994, predicts the cumulative distribution function (CDF) of cross-polarisation discrimination (XPD) from the complementary CDF (CCDF) of rain attenuation; the empirically derived ice contribution is finally added. The relationship between XPD and co-polar attenuation (CPA), according to the ITU–R recommendation, is modelled assuming a normal distribution for the cross-polar to co-polar voltage ratio (CXVR), and it is fully statistically characterised through its mean and standard deviation (STD). For an attenuation exceeded for a given percentage of the time, p (%), the average value of CXVR is close to the value due to only rain not exceeded for the same percentage p. Its STD is almost constant for attenuations up to 8 dB. This approach assumes a correspondence between the values of rain attenuation and of CXVR at the same probability level. This assumption, in principle acceptable when only rain effects are considered, fails in the presence of ice-induced contributions, which are not correlated to attenuation. The ice, however, causes important effects on XPD at several attenuation levels, as shown in this contribution, therefore the Paraboni et al. model [[10]], which takes into account both rain and ice effects, is preferable because it does not predict the XPD–CPA relationship due to only rain. In this contribution, the ITU–R model [[9]] is first tested and improved for the prediction of the CDF of total, rain and ice-induced XPD. Then, the Paraboni et al. model [[10]], derived from data measured at the V-band, is validated by scaling the attenuation and XPD data, using a new long-term dataset at the Ka-band, to the V-band using the procedures recommended in section 2.2.1.3.2 in [[9]]. After a full statistical characterisation of each XPD distribution as a function of the attenuation, new models are then proposed at the Ka-band for ice, rain and total XPD. Finally, a new approach for the conversion of the XPD CDF into the corresponding XPD–CPA relationship is presented. The paper is organised as follows: Section 2 describes the propagation campaign, during which the propagation data used in the study was measured. The ITU–R model is validated and improved in Section 3. In Section 4, the Paraboni et al. model is assessed and new models are proposed for the Ka-band. The base allowing the conversion of XPD CDF to the corresponding XPD–CPA relationship is investigated in Section 5 and, finally, some conclusions are drawn in Section 6. 2 Propagation campaign From September 2004 to June 2013 a propagation campaign was carried out in Aveiro, Portugal, by monitoring 1 sample/s the Eutelsat 13A satellite beacon at 19.7 GHz. In-excess attenuation (up to 25 dB) and XPD (from 40 dB) were derived, building up a database with an availability higher than 99.9% of the observation time. In fact, for 0.1% of the time, the system was offline, due to short-period maintenance activities, usually scheduled under clear-sky conditions. The receiver was phase-balanced to measure the phase of the cross-polarisation ratio [[11], [12]]. Concurrently, a radiometeorological station recorded the rainfall rate (up to 120 mm/h), the relative humidity, the wind speed and the air temperature. For this study, only complete years of measurements were considered: between January 2005 and December 2012. The main characteristics of the experiment are summarised in Table 1. Table 1. Experimental setup Parameter Value satellite name Eutelsat 13A satellite orbital position 13°E frequency 19.7 GHz elevation angle 38° polarisation linear-horizontal CNR0 53 dB polarisation tilt angle 23° earth station latitude 40.63°N earth station longitude 8.66°W earth station altitude a.m.s.l. 18 m In the framework of a previous study [[8]], the 2009 year was used to develop and test a physical method to separate ice and rain XPD contributions. A cautious inspection, on an event-basis, of the polar plot of the real and imaginary parts of the depolarisation ratio (corresponding, respectively, to the differential attenuation and differential phase shift caused by the medium anisotropy along its principal planes) and of the XPD–CPA scatter plot, was carried out. In this way, it was possible to assess if each event was mainly due to either ice or rain. To assure an accurate classification, each event was further divided into several sub-events (the 265 propagation events considered in this study originated 1035 classified sub-events). The general validity of these results is confirmed by the fact that the propagation characteristics of 2009 are close to the long-term period ones, as shown in Fig. 1, where the CCDF of rain attenuation and the CDF of XPD are plotted for 2009 and for 8 years database. Fig. 1Open in figure viewerPowerPoint First-order statistics of rain attenuation and XPD measured at Ka-band (full database), scaled to the V-band and measured in 2009 (a) CCDF of the rain attenuation, (b) CDF of the XPD and ITU–R model predictions 3 XPD first-order modelling The total XPD (combining both the rain and ice contributions) can be predicted by means of the ITU–R model [[9]], which is valid for a frequency between 6 and 55 GHz and for an elevation angle lower or equal to 60°. The model has, as input, the CCDF of the rain attenuation (Ap), which is used with the frequency to derive the attenuation-dependent term CA. It also considers a polarisation parameter Cτ, dependent on the polarisation tilt angle τ, a frequency parameter Cf, an elevation angle parameter Cθ and the parameter Cσ, function of the STD of raindrops canting angle distribution. From these parameters, the CDF of XPD due to rain (XPDrain) is computed as follows: (1) The ice contribution (Cice) is then added, depending on the XPDrain and on the time percentage p. The CDF of total XPD is finally computed (2) The measured CCDF of rain attenuation, the measured CDF of XPD and the XPD predictions provided by the described model, accordingly to the link specifications of Table 1, are depicted in Fig. 1. It is possible to observe that the ITU–R model always over-predicts the measured XPD, therefore the model improvement is required. To do that, the rain and ice classified events are used so that the attenuation-dependent parameter (which largely determines the shape of the XPD curve) is verified first and then the ice-dependent term is improved. The CDF of the total XPD and of each contribution, in 2009, are depicted in Fig. 2. As it is possible to see, the ice contribution dominates the XPD distribution from 40 to 20 dB, whereas the rain contribution becomes more important for XPD values lower than 20 dB. The rain-induced XPD is worse than 40 dB for 0.3% of the time, whereas the ice-induced one is worse than 40 dB for 0.8%. Fig. 2Open in figure viewerPowerPoint CDF of XPD measured at Ka-band in 2009, the CDF of its contributions, the ITU–R model predictions, and their improvement In what concerns the rain-induced XPD, it turns clear that its CDF is overestimated by the ITU–R model. To improve the prediction, the attenuation-dependent term CA was derived from the data by inverting (1), as is shown in Fig. 3. It is possible to see that the parameter CA, derived from the measured data, is significantly lower than the ITU–R one, which is given by (3) where V(f) is a multiplicative frequency-dependent factor and f is the frequency. Better results are achieved by using a modified expression (4) Fig. 3Open in figure viewerPowerPoint CA parameter as predicted by the ITU–R model, extracted from data and the improved version The achieved improvement, in predicting the CDF of the rain-induced XPD by using (4), can be assessed in Fig. 2. The improved parameter enables a much more accurate prediction of the rain contribution comparatively to its original version. To quantify its performance, the absolute value of the logarithmic error was calculated for each time percentage as follows: (5) The root-mean-square error (RMSE) and STD values of ɛ for the ITU–R model are, respectively, 14.0 and 4.2; the two parameters are significantly smaller (2.2 and 1.0, respectively) when the improved model of (4) is considered. After the improvement of the rain-induced XPD, it is possible to improve the ice-dependent term. The parameter Cice in the ITU–R model is given by (6) The same parameter can be retrieved from the data by inverting (2) and, dividing it by the measured rain-induced XPD, it is possible to calculate (7) By fitting the experimental results in Fig. 4, better results are achieved by using a modified expression for Cice (8) Fig. 4Open in figure viewerPowerPoint Cice parameter modelling and evaluation on the prediction of the CDF of XPD (a) Cice extracted from data and its modelling, (b) Total XPD measured in 2009 and its prediction using the modelled parameter Fig. 4 shows the total XPD predicted by using the measured rain-induced XPD and the modelled contribution of ice in (8). As it can be seen, the new predictions follow quite well the measured XPD. Finally, making use of the new and parameters, the expressions (1) and (2) were used to predict the CDF of the total XPD as presented in Fig. 5, where also the ITU–R model predictions are depicted. It is evident that the significant improvement is achieved. The RMSE and STD values of (5) are 7.9 and 5.7, respectively, for the ITU–R model and 3.0 and 1.5, respectively, for the improved model. Fig. 5Open in figure viewerPowerPoint Total XPD prediction and evaluation (a) Total XPD in 2009, predictions according to the original ITU–R model and prediction after the model improvement, (b) Predictions’ evaluation 4 XPD high-order modelling As stressed by Paraboni et al. in [[10]], for communications systems design the usually available parameter is the CPA and, therefore, the XPD–CPA relationship is of most interest. 4.1 XPD–CPA relationship at V-band Considering circular polarisation and the frequency of 49.5 GHz, Paraboni et al. [[10]] proposed for the XPD–CPA relationship the following first-order polynomial expression: (9) To verify the model, both the attenuation and the XPD measured at the Ka-band were scaled accordingly to the procedures described in section 2.2.1.3.2 of [[9]]. The attenuation scaling method is valid for frequencies from 7 to 55 GHz, but the XPD scaling method is only valid up to 30 GHz. It is considered here that depolarisation induced by rain and ice populations have the same frequency dependence and so the model can be extended up to the frequency of interest. The method also considers the polarisation-scaling as the polarisation tilt angle has a critical impact on the measured XPD. The difference between the elevation angles of the experiment in Aveiro and of the experiment reported in [[10]], on the other hand, is negligible (0.3°), and therefore its scaling was not considered. The V-band attenuation CCDF scaled from the Ka-band CCDF and the V-band scaled (in polarisation and frequency) CDF of XPD are presented in Fig. 1. The scaling factors, which can be inferred from Fig. 6, were used to scale both the Ka-band attenuation and the XPD time series to the V-band. The joint histogram was then computed considering 0.2 dB spaced bins for the attenuation and 0.5 dB for the XPD. The results are compared with the model [[10]] in Fig. 7. Fig. 6Open in figure viewerPowerPoint V-band scaled XPD and attenuation from the corresponding measured data Fig. 7Open in figure viewerPowerPoint Average and STD of XPD–CPA relationship from scaled data, considering all data, truncated data (XPD < 40 dB) and the proposed model As it can be seen, the model only slightly deviates from the scaled data for attenuation higher than about 10 dB, becoming less correlated to lower attenuation values. It shall be emphasised, however, that the V-band scaled XPD is about 10 dB smaller than the Ka-band measured XPD, and so only from an XPD of 30 dB the results depicted in Fig. 7 can be considered due to the measurement accuracy (receiver and satellite cross-polarisation ratio residuals are hard to remove). The remaining differences, at higher attenuation values, can be because the proposed model has been derived considering only 131 events whose XPD was additionally adaptively filtered. Indeed, the correlation can be improved by removing the data above 40 dB (Fig. 7), suggesting that truncating the data can have a non-negligible impact on the XPD–CPA modelling. Moreover, the different depolarising populations shall have different frequency scaling factors, but in this verification, they were assumed equal, as it was observed for frequencies up to 30 GHz [[9]]. In turn, the STD is fairly constant with the attenuation, ranging from 7.8 dB, at an attenuation value of 8.7, to 5 dB, for an attenuation of 25 dB, in perfect agreement with [[10]]. 4.2 XPD–CPA relationships at Ka-band When investigating the data at the Ka-band, it turns clear that a first-order polynomial, as proposed in [[10]], does not fit the data, while a better agreement is obtained with a second-order polynomial (10) This is an equivalent XPD–CPA relationship to that proposed by Paraboni et al. [[10]], retrieved for the Ka-band by considering the full database as reported earlier. The results are depicted in Fig. 8. It is possible to observe that the STD increases up to a maximum value of 5.6 dB, at an attenuation of 3.5 dB, then decreases to 2.3 dB, at an attenuation of about 15 dB and remains essentially constant for higher attenuation values. Fig. 8Open in figure viewerPowerPoint Average of measured XPD–CPA relationship (full data) (a) Proposed model and STD, (b) XPD–CPA histogram, its average value (black curve) and the proposed model (blue dash-dot curve) The performance of the model here proposed can be evaluated considering also Fig. 8 (blue dash-dot curve), where the model is compared with the measured XPD–CPA histogram (more intense colours representing a bigger number of points) and to the average XPD. Considering the total XPD and its contributions in 2009, the XPD–CPA relationships are presented in Fig. 9. As it is possible to see, the average XPD–CPA begins to follow closely the average XPD–CPA of events caused by ice, approaching then the one caused by rain and following it from 8 dB of attenuation. This is evidence that the ice contribution is mainly present at lower attenuation values, whereas the rain assumes the main importance for higher attenuations. The STD of the XPD–CPA relationship caused by ice also reaches bigger values comparatively to that caused by rain, indicating a worse correlation between XPD and CPA in the presence of ice than that caused by rain. Fig. 9Open in figure viewerPowerPoint XPD–CPA relationship for total XPD, rain-induced XPD, and ice-induced XPD (a) Average and STD of measured data in 2009, (b) Modelling of the XPD–CPA relationships caused by rain and ice Considering the XPD–CPA due to rain events, the following expression was derived from the data: (11) Whereas regarding that due to ice the following one was obtained: (12) These models are also superimposed over the data in Fig. 9. 5 High-order XPD–CPA relationship retrieval from first-order statistics Regardless of its performance, the ITU–R model described in Section 3 is usually employed to derive the XPD–CPA relationship by using the rain attenuation CCDF on an equiprobable base. The equiprobability is a reasonable hypothesis, provided that the XPD is, at least, very well correlated to CPA (ideally the relationship should be univocal) and so the XPD–CPA relationship derived under such conditions only accounts for the rain-induced effects. Nevertheless, the ice-induced contribution to the XPD is important, as demonstrated in Section 3. Fig. 8 shows that, for a given attenuation, the XPD varies significantly; the variation is larger when attenuation decreases, as confirmed by the STD depicted in Fig. 8, and where the ice-induced depolarisation is more important as demonstrated previously in Fig. 9. From Fig. 9, it turns also clear that the ice-induced XPD has a larger spread than that due to rain up to an attenuation of about 15 dB. Therefore, the equiprobability principle is not valid, as it can be seen in Fig. 10, where both the XPD–CPA relationships measured and derived from the CDF of total XPD employing equiprobability are depicted. The same data simply do not match, due to the data spreading observed in Fig. 8. On the contrary, the XPD–CPA relationship, derived on an equiprobability basis, is closer to the measured curve for higher attenuations, where the data spreading is less pronounced, as shown in Fig. 10. Fig. 10Open in figure viewerPowerPoint XPD–CPA relationship retrieval employing equiprobability and the proposed conversion model which is superimposed on the actual average XPD–CPA relationship (a) Total XPD, (b) Rain events, (c) Ice events From this analysis, it is clear that a new conversion base is required, where a conversion factor (CF) can be employed to calculate the attenuation probability to be used for the XPD calculation. The novel proposed CF has been derived by finding, for each measured XPD value, the relationship between the time percentage at which it is not exceeded (that would be used to find out the corresponding attenuation in the case of equiprobability) and the time percentage at which the attenuation shall actually be read. The CF for the total XPD is plotted in Fig. 11, together with the following model: (13) Fig. 11Open in figure viewerPowerPoint CF modelling (a) Total XPD, (b) Rain-induced XPD, (c) Ice-induced XPD The time percentage, pa, at which the attenuation is retrieved, is then given by (14) The predictions of the proposed model, which is valid for time percentages up to 1%, are quite close to the measured data, as shown in Fig. 10. To further assess the equiprobability principle, each individual contribution to the XPD in 2009 is also investigated. The XPD–CPA relationship caused by rain events is depicted in Fig. 10, where it is possible to see a good correlation between the XPD–CPA relationships derived using equiprobability and the actually measured one. A small deviation occurs, however, for low attenuation where either the limited data or the population's retrieval limitations can impair the results. Nevertheless, the good correlation is also evident when attempting to derive a CF similar to (13) (15) The values given by the proposed CF for rain-induced XPD, valid up to 0.3% of the time, are around 1 for a wide range of probability values, as it can be seen in Fig. 11. Nevertheless, an improvement is achieved by using (15) as it can be seen in Fig. 10. On the other hand, the measured XPD–CPA relationship due to ice events has no evident correlation to that derived using equiprobability as presented in Fig. 10. Therefore, the CF in (16), valid up to 0.85% of the time and presented in Fig. 11, is needed. This CF performs quite well as it can be seen in Fig. 10, where the CDF of ice-induced XPD is converted to the corresponding XPD–CPA relationship (16) To further illustrate the need for an appropriate CF, several time percentages were taken as an example. The corresponding CF and the relative error (RE) that the true time percentage deviates from the one that would be used in case of equiprobability are presented in Table 2. As it can be seen, the rain CF holds±0.1 around 1.0, meaning a RE of 11.0%, along a significant interval of time percentages, deviating from the one-to-one relationship for higher or lower time percentages. For the same time percentages, the ice CF is much more important as the RE is significantly bigger comparatively to that of rain, turning clear the need for a CF when ice effects are present. This evidence is also clarified when considering the average CF required for rain (0.96) with respect to that of ice (0.76). Considering the total XPD, when both contributions are present, the equiprobability basis also fails, as an average CF of 0.41 is needed to mitigate an average RE of 57.7% if the equiprobability would be in use. Table 2. CFs and RE that the true time percentage deviates from the one retrieved using equiprobability Time, % CF RE, % CF RE, % CF RE, % Total Rain Ice 0.01 0.6 37.2 0.4 55.7 1.0 0.0 0.02 0.6 44.1 1.1 12.3 0.9 11.0 0.03 0.4 55.7 0.9 11.0 0.9 11.0 0.05 0.4 60.6 0.9 11.0 0.6 37.2 0.07 0.3 68.7 0.9 11.0 0.6 44.1 0.1 0.3 68.7 0.9 11.0 0.7 29.5 0.2 0.3 68.7 1.6 59.2 0.6 44.1 average 0.41 57.67 0.96 24.46 0.76 25.27 STD 0.13 12.78 0.36 22.57 0.17 17.87 6 Conclusions The XPD models accounting for the combined effects of rain and ice on depolarisation were reviewed, tested and improved. The ITU–R model, predicting either the CDF of XPD or the rain-induced XPD, was not in good agreement with the measured data. The attenuation-dependent term was thus improved, enabling then the upgrade of the ice contribution estimation. The new parameters were then used together in order to evaluate the performance of the complete model. The new predictions are in much better agreement with the measured data. The measured data at the Ka-band were scaled to the V-band in order to verify the recently proposed model [[10]] on the XPD–CPA relationship. The model proved to perform quite well when considering higher attenuations, where the scaling method can be employed with some degree of confidence. The small deviation from the measured data is probably associated with the limited database used in the model development and to the different scaling factors for rain and ice effects, which have been assumed equal. Considering eight complete years of data, the full statistical characterisation of the XPD distribution along the attenuation was presented and discussed, and a new model for the XPD–CPA relationship has been proposed for the Ka-band, based on a second-order polynomial. The data spread is higher at lower attenuations due to the ice effects. By using one average year of XPD events, classified as having been caused by rain or ice, this evidence was further verified after the statistical characterisation of the XPD–CPA relationships due to rain and ice have been executed: the spread of the XPD caused by ice is more pronounced than that caused by rain. Models for the XPD–CPA relationship were then derived by considering individually each population. The total XPD–CPA follows the ice one at lower attenuations and that of rain at higher attenuations, putting in evidence that ice contribution is predominant for low attenuation and the rain one at higher attenuation values. As a consequence of the data spreading, the equiprobability principle, largely employed for the conversion of the CDF of XPD to the XPD–CPA relationship, cannot be used. Therefore, a novel approach and a new conversion base have been then proposed for total XPD, rain-induced XPD, and ice-induced XPD, enabling the prediction of the actual high-order XPD–CPA relationship from the corresponding first-order predictions for which widely accepted models exist. 7 References [1]van de Kamp, M.M.J.L.: ‘Depolarization due to rain: the XPD–CPA relation’, Int. J. Satell. Commun., 2001, 19, (3), pp. 285– 301 [2]Stutzman, W.L., Runyon, D.L.: ‘The relationship of rain-induced cross-polarization discrimination’, IEEE Trans. Antennas Propag., 1984, AP-32, (7), pp. 705– 710 [3]Dissanayake, A., Haworth, D.P., Watson, P.A.: ‘Analytical models for cross-polarization on earth-space radio paths for frequency range 9–30 GHz’, Ann. Télécommun., 1980, 35, (11), pp. 398– 404 [4]Nowland, W.L., Olsen, R.L., Shkarofsky, I.P.: ‘Theoretical relationship between rain depolarization and attenuation’, Electron. Lett., 1977, 13, pp. 676– 678 [5]Chu, T.S.: ‘A semi-empirical formula for microwave depolarization versus rain attenuation on Earth–Space paths’, IEEE Trans. Commun., 1982, 30, (12), pp. 2550– 2554 [6]van de Kamp, M.M.J.L.: Climatic radiowave propagation models for the design of satellite communication systems, November. 1999 [7]Jorge, F.: ‘ Separação das contribuições de chuva e gelo para o XPD na banda Ka’ ( Universidade de Aveiro, Aveiro, 2012) [8]Rocha, A., Jorge, F.: ‘Separation of rain and ice contributions for depolarization at Ka band’. European Conf. on Antennas and Propagation, 2013, pp. 57– 60 [9]‘ ITU–R P.618–12: ‘Propagation data and prediction methods required for the design of Earth–Space telecommunication systems,’ Geneva, 2015 [10]Paraboni, A., Martellucci, A., Capsoni, C., et al.: ‘The physical basis of atmospheric depolarization in slant paths in the V band: theory, italsat experiment and models’, IEEE Trans. Antennas Propag., 2011, 59, (11), pp. 4301– 4314 [11]Rocha, A., Sousa, M., Cupido, L.: ‘A Ka-band propagation beacon receiver’. ESA Work Shop MWTA, Helsinki, Finland, May 2003, pp. 177– 182 [12]Rocha, A.: ‘Propagation experiment at Ka band’. Ka and Broadband Communications Conf., Vicenza, Italy, October 2004, pp. 127– 133 Citing Literature Volume12, Issue4March 2018Pages 479-485 FiguresReferencesRelatedInformation