MODELLING THE DYNAMIC PROPERTIES OF THE PROPAGATION CHANNEL Laurent Castanet and Max van de Kamp ONERA-DEMR, Toulouse, France emails:
[email protected],
[email protected] 1. INTRODUCTION Rain attenuation, caused by scattering and absorption by water droplets, is one of the most fundamental limitations to the performance of satellite communication links in the microwave region, causing large variations in the received signal power, with little predictability and many sudden changes. In the Ka- and V-bands, the attenuation caused by rain is too severe to be accounted for by a fixed margin in the link budget. In order to provide the same performance as in lower frequency bands, an excessively large margin would be required. This is why alternative methods to reduce outage due to rain fading have been developed. These fade countermeasures compensate for rain attenuation by adaptively improving the quality of the link when the signals are degraded. One of these countermeasures is adaptive power control, in which the transmitted power is increased to compensate for fading due to rain on the propagation path. For the development of adaptive fade countermeasure algorithms, information is needed on the dynamic behaviour of rain attenuation, to assess the required speed with which the system can track attenuation changes. This paper reviews various dynamic aspect of rain attenuation, explaining their meaning and their essence in the design of FMT systems, and presents recommended prediction models for these dynamic aspects.
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Fig. 1 shows an example of a graph of attenuation as a function of time, and defines the meaning of various parameters discussed in this paper: ‘event’, ‘episode’, ‘interval’, ‘threshold’, ‘fade slope’, and ‘fade duration’. Fade episodes
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Fig. 1. Features characterising the dynamics of fade events 2. FADE SLOPE The quantification of fade slope is important for the design of FMTs. The knowledge of the fade slope of the received signal is useful either to design a control loop that can follow signal variations, or to allow a better short term prediction of the propagation conditions. In both cases, the relevant information is the slope of the slow varying component of the signal (attenuation). It has already been demonstrated that fast fluctuations of signal, due in particular to tropospheric scintillation, are unpredictable, i.e. it is impossible to predict the level of the signal from the knowledge of its variation some seconds before [1]. This is because the autocorrelation function decreases very rapidly, so that the scintillation component is completely uncorrelated after only two seconds [2]. 2.1. Characterisation of fade slope distributions The fade slope probability distribution depends on climatic parameters, drop size distribution and therefore on the type of rain. The horizontal wind velocity perpendicular to the path is another climatic parameter of influence, determining the speed at which the horizontal rain profile passes across the propagation path. Also, the expected fade slope at a given
attenuation level is likely to decrease as path length increases due to the smoothing effect of summing different rain contributions, and, therefore, will increase as elevation angle increases on Earth-space paths. Furthermore, the measured fade slope is influenced by dynamic parameters, or time constants, of the receiving system. A receiver with a longer integrating time reduces the instantaneous fade change and spreads it over a longer period of time. To calculate the slope of the attenuation component from measured time series, it is necessary to remove the rapid component of the signal, consisting of both fast fluctuations of rain attenuation and scintillation. However, since there is no clear separation between the low- and high frequency parts of the spectra, the dynamic properties of the remaining signal will depend strongly on the threshold frequency used, and no ideal threshold frequency can be defined. Usually, a moving average filter is applied, the length of which can vary from 30 seconds to 2 minutes. More elaborated techniques such as the use of Butterworth filters have been sometimes applied with an equivalent time constant. Once the rapid component has been removed, thresholds in terms of attenuation levels are fixed (for instance every dB) and the fade slopes are calculated for each attenuation threshold. As shown in Fig. 1, the fade slope (t) is defined as the rate of change of rain attenuation A(t):
ζ (t ) =
A(t + ∆t ) − A(t ) ∆t
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Different experimenters have analysed fade slope measurements, and presented the statistical distributions usually as histograms or CDFs (Cumulative Distribution Functions). With histograms, fade slopes are sorted in intervals, and histograms are drawn which show the probability (or the number of occurrence) for a fade slope coinciding with a given attenuation to be situated in these intervals (see Fig. 2, left). A second type of representation for fade slope results is the CDF of fade slope with respect to time percentage (see Fig. 2, right). From these CDFs, it clearly appears that the fade slope increases with attenuation. The analysis of the results obtained by the experimenters has led to the following main conclusions [4]: • statistical distributions (obtained over a long period such as one month or one year) are symmetrical around a mean of 0 dB/s for small time lags (∆t < 200 s) • for a given interval of attenuation, there is no significant correlation between fade slope and carrier frequency; • the fade slope increases with attenuation level on a statistical basis, • there are indications that the fade slope might increase statistically with elevation angle, • even if probable, a clear dependency on climatic parameters has not been put into evidence for the moment.
Fig. 2. Example of fade slope histograms (left) and CDF of positive fade slopes (right) at Ka-band obtained during the OPEX at 30 GHz [3].
2.2. Fade slope modelling A fade slope prediction model has been approved by ITU-R Study Group 3 (‘Propagation Issues’) as a draft new recommendation [5]. The model is in the process of approval by the administrations, which should be finished at the end of April 2003. This model was developed by Van de Kamp [6] [7], and calculates the PDF (Probability Density Function) and the CDF of fade slope depending on the attenuation, the time lag ∆t used in equation (1), and on the receiver filter bandwidth. The model does not give a dependency with respect to frequency, elevation and climate area. The model has been developed using measurements collected over 16 months at Eindhoven University of Technology from the satellite Olympus (ε = 26.78o), at 12.5, 20 and 30 GHz, and tested using data from other sites in the UK, France, Belgium, Italy and the US, at frequencies from 12 to 50 GHz and elevation angles from 5° to 52° [7]. The following parameters are required as input to the model: A attenuation level (dB): 0-20 dB fB 3dB cut-off frequency of the low pass filter (Hz): 0.001-1 Hz ∆t time interval length over which fade slope is calculated (s): 2-200 s. Calculations of fade slope distributions (PDF and CDF) have been performed dependent on these three input parameters. Fig. 3 shows examples of the modelled pdf and cdf of fade slope, conditional to several attenuation thresholds. These values are valid for a receiver filter bandwidth of 0.02 Hz which is the recommended value for a good filtering of fast fluctuations of scintillation and rain attenuation and for a time lag of 1 s (fade slope calculated over two consecutive samples separated by 1 s) appropriate for a FMT fast control loop.
Fig. 3. Modelled pdf and cdf of fade slope for different attenuation thresholds Fig. 4 shows examples of the distributions of fade slope for different time lags ∆t. These values are valid for a receiver filter bandwidth of 0.02 Hz and for an attenuation threshold of 5 dB. A time lag of 1 s is appropriate for a rapid control loop possibly implemented in a terminal using ULPC, whereas a 1 min time lag should be more convenient for a slower control loop that could be used in a NCC for resource management. As can be seen in the figure, the dependence is only significant for time lags longer than 1/2fB = 25 s. Fig. 4 also shows examples of the distributions of fade slope for different filter bandwidths. These values are valid for a time lag of 1 s and for an attenuation threshold of 5 dB. A 0.01 Hz filter bandwidth corresponds to a good filtering of fast fluctuations, therefore the obtained signal presents only the slow variations of attenuation and fade slopes are low. On the contrary, a 0.5 Hz filter bandwidth corresponds to a filtering of only the most rapid component of scintillation, therefore the obtained signal exhibits fast variations and fade slopes are high.
Fig. 4. Modelled cdf of fade slope for different time lags (left) and different receiver filter bandwidths (right). 3. FADE DURATION Fade duration is defined as the period of time between two consecutive crossings of the received signal on the same attenuation threshold (Fig. 1). This is an important parameter to be taken into account into system design for several reasons: • system unavailability: fade duration gives information on outage periods or system unavailability due to propagation on a given link and service, • sharing of the system resource: it is important for the operator point of view to have an insight into the statistical duration of an event in order to assign the resource for other users, • FMTs: fade duration is of concern to define statistical duration for the system to stay in a compensation configuration before coming back to its nominal mode, • system waveform: fade duration is a key element in the process of choosing FEC codes and best modulation schemes; for SatCom systems, the propagation channel does not produce independent errors but blocks of errors. Fade duration impacts directly on the choice of the coding scheme (size of the coding word in block codes, interleaving in concatenated codes, …). 3.1. Characterisation of fade duration distributions Differently from fade slope, it is not necessary to separate the low and the rapid components of the received signal, this separation being implicit with respect to the fade duration considered. Since the European action COST205 [8], the standard has been to consider on the one hand long fade duration (>32 sec) caused by attenuation and on the other hand short fade duration due essentially to scintillation (with low attenuation level) and fast fluctuations during rain (associated with strong attenuation level). Results from fade duration analyses are usually presented as either statistics of the number of fade events above a given attenuation threshold and longer than a given fade duration (see Fig. 5, left), or statistics of the total composite time of all fade events above a given attenuation threshold and longer or shorter than a given fade duration (see Fig. 5, right). Both statistics can also be represented as fractions of the total number of events, or the total fade time, for the same attenuation threshold. Results obtained by the experimenters have led to the following general conclusions [4]: • Statistical distribution obtained for both short and long fades are independent on the location and therefore on climatic parameters, • Statistical distribution obtained for both short and long fades are dependent on the attenuation level.
Gometz−la−Ville 20 GHz
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Fig. 5. Examples of statistics of the number of fade events longer than D (left), and of the composite time of fades shorter than D (right), both obtained in Gometz-la-Ville, in the Olympus experiment, at 20 GHz. 3.2. Fade duration modelling A global model for fade duration distribution is recommended by ITU-R Study Group 3 [5]. This model was developed by Paraboni and Riva [9], from both theoretical aspects and experimental results obtained during the Sirio and Olympus propagation experiments. It has been tested also with the ITU-R DBSG5 databank. This model enables the calculation of the statistics of fade duration due to the combined effects of attenuation (gases, clouds and rain) and scintillation on Earth-space paths. In this model, long fades follow a log-normal distribution, while short fades follow a power-law. The following parameters are required as input to the model: f frequency (GHz): 10-50 GHz ϕ elevation angle (degrees): 5-60° A attenuation threshold (dB) The total outage time Ttot(A) corresponding to a given attenuation threshold is also necessary. To obtain this parameter, conventional rain attenuation prediction method such as ITU-R Rec. P.618 can be used. The model gives fade duration statistics expressed in quantities equivalent to the representations of Fig. 5: • The number of fades, during which attenuation exceeds A dB, and which are longer than D s. • The probability of fade events, during which attenuation exceeds A dB, to last longer than D s. • The composite fade time of all fades above A dB and lasting longer than D s. • The relative composite fade time of all fades above A dB and lasting longer than D s, relative to the total time of all fades above A dB. This quantity is equal to the probability for any sample measured above A dB to be part of a fade longer than D s. Calculations of fade duration distributions have been performed using the model, for several attenuation thresholds; the results are shown in Fig. 6. This figure shows that the probability of occurrence of a given fade duration decreases with the attenuation level, similarly as the total fraction of fade time of a given fade duration. Fig. 7 presents fade duration distributions dependent on elevation and carrier frequency. 3.3. Interfade duration Apart from fade duration statistics, it is also interesting to characterise period of time between two fades, referred to as ‘interfade duration’. For users of a service supplied through an Earth-space link, once the level of the received signal has just crossed back the margin threshold after an outage event, it is essential for the operator point of view to know statistically how much time the system is going to work properly before another outage event. Fig. 8 gives some statistical results of interfade duration obtained during the OPEX project. No recommended model is available yet.
Fig. 6. Distributions of fade duration for several attenuation thresholds. Left: probability of events; right: relative composite event time.
Fig. 7. Dependence of probability of events on elevation (left) and frequency (right).
Fig. 8. Relative composite time of interfade periods shorter than the ordinate, obtained in Albertslund, Denmark, at 20 and 30 GHz [10].
4. FREQUENCY SCALING Frequency scaling concerns the variation of propagation effects characteristics with respect to frequency. The objective of frequency scaling studies is to estimate the magnitude of a propagation effect (attenuation, scintillation, depolarisation) at a given frequency from the knowledge of its magnitude at another frequency, generally a lower one. Two general interests of using such kind of information can be identified: • to study the influence of propagation effects on the design of systems operating at high frequency bands (for instance Ka or V-band) from the knowledge of the performances of current systems operating at conventional frequency bands (Ku-band), • to design Fade Mitigation Techniques in an open-loop configuration such as uplink power control where the attenuation on the link (for instance the uplink) is estimated from the measurement of the attenuation at another frequency (for instance beacon measurement in a lower frequency band). Frequency scaling can also reflect time variations of the physical characteristics of the propagation medium and consequently can lead to a better comprehension and therefore to a better modelling of the physical phenomena which affect radiowave propagation. For instance, the variation with time of the frequency scaling ratio during a rain event provides valuable information about the drop size distribution. Two kinds of frequency scaling methods can be defined. The first one is related to long-term variations and uses cumulative distributions of propagation effects for the same percentage of exceedance. The second one aims at studying the instantaneous ratio of attenuation, scintillation log-amplitude or discrimination in polarisation at two distinct frequencies. 4.1. Long-term frequency scaling It is recommended to use the ITU-R Recommendation P.618 [18] to calculate the long-term frequency scaling ratio of rain attenuation. This model uses as inputs: the two frequencies, and the attenuation exceeded for a certain probability at one frequency; and provides the factor to multiply with the attenuation to obtain the attenuation at the other frequency exceeded for the same probability. Current state-of-the-art in terms of frequency scaling leads to the conclusion that available models allow good predictions of the long-term frequency scaling ratio. In general, the accuracy of long-term frequency scaling prediction models is in the order of magnitude of 10-15 %. It should be borne in mind that the accuracy of attenuation prediction models is rather in the range 30-35 % [11]. This means that if attenuation statistics are available at a given frequency, to estimate statistics at another frequency, it is more reliable to use frequency scaling algorithms than directly attenuation prediction methods. Apart from rain attenuation, at frequency bands higher than 20 GHz different effects have to be considered which do not exhibit the same behaviour with respect to frequency. Gaseous, cloud and melting layer attenuation as well as scintillation (in both clear sky and clouds) and depolarisation (due to rain and ice) must be considered. The total ratio becomes significantly lower for small attenuation due to gas and clouds. For instance, the 30/20 GHz frequency scaling ratio obtained in Darmstadt during the Olympus campaign varied between 1 and 1.8 for attenuation lower than 3 dB whereas the rain frequency scaling ratio is about 2 for the same attenuation levels. Some methods have been proposed to calculate the frequency scaling ratio of attenuation due to gas and clouds [19] and of depolarisation [20]. The frequency scaling ratio of scintillation can be derived from ITU-R Recommendation P.618 [18] or Karasawa et al. [21]. To date the ITU-R only proposes a fixed value for this scaling factor, however, there is experimental evidence that the ratio is strongly variable. Models that take into account the variability of the frequency scaling factor of scintillation are useful in advanced detection schemes relying on a variable detection margin. As the frequency scaling ratio of rain attenuation and scintillation are different, it is necessary to separate them, using low / high pass filters, before applying their own frequency scaling processes.
4.2. Instantaneous frequency scaling of rain attenuation For the purpose of FMT design it is not the long-term but rather the instantaneous frequency scaling ratio that has to be considered. The frequency scaling ratio can exhibit strong variations during an event, specially during convective rain. When looking into propagation data, plots of the attenuation at a given frequency with respect to the attenuation at another frequency inside the same rain event present a typical hysteresis behaviour [12] [10] as shown in Fig. 9 (left). The phenomenon is caused by dynamic variations of the drop size distribution (DSD) during a rain event [13]. This can be shown by plotting theoretical specific attenuation at two distinct frequencies corresponding to different DSD (Marshall-Palmer, Laws-Parsons, Joss-drizzle, Joss-thunderstorm, …) in the same graph, as in Fig. 9 (right). This figure shows that, especially below a rain rate of 50 mm/hr, the ratio between attenuations at 20 and 30 GHz is larger for the drizzle than for the thunderstorm DSD. Consequently, if at the beginning of a rain event the DSD is different than at the end (at the same rain rate), the frequency scaling ratio of attenuation may be different for the same rain rate, and a hysteresis as in the left graph will be observed.
Fig. 9. Left: Simultaneous attenuation measurements at 20 and 30 GHz in Spino d’Adda, Italy [10]. Right: Specific attenuation vs. rain rate for Joss-drizzle (J-D) and Joss-thunderstorm (J-T) DSD [14]. Fig. 9 also shows a decreasing frequency scaling ratio of large attenuation, possibly also due to changing DSD during the event. This effect is also found from the long-term frequency scaling ratio which decreases for low percentages of time (and therefore for high attenuation). It is possible to calculate, for a given 20 GHz attenuation, the value of the instantaneous frequency scaling ratio not exceeded for a given percentage of time (for instance 10, 50 and 90 %). From Fig. 10 (left), it appears that the median curve is of the same order of magnitude as the long-term ratio. These curves are relatively flat with respect to attenuation, and the long-term frequency scaling ratio can therefore be used in FMT control loops as a rough estimate of the instantaneous frequency scaling ratio [15]. However, the instantaneous frequency scaling ratio variability remains large. If only a constant frequency scaling ratio is considered in a control loop, significant errors can occur when predicting attenuation at the highest frequency from the attenuation measurement at the lowest one. Fig. 10 (right) presents statistics of the instantaneous frequency scaling ratio obtained in the Olympus campaign. For instance, if the 20 GHz measured attenuation is 10 dB, the corresponding 30 GHz attenuation, median value 20 dB, varies between 16 and 23 dB in 80% of the cases. Other results have shown that errors due to the use of fixed frequency scaling ratio can reach up to ± 4 dB [16] for high attenuation levels. An improvement of the method can be achieved either by the introduction of a variable frequency scaling ratio, or by modelling of the inhomogeneity of the medium from differential attenuation and phase measurements.
Fig. 10. Left: Comparison of long-term frequency scaling ratio (RAS) with median instantaneous frequency scaling ratio (RA-50%) [15]. Right: 30 GHz attenuation exceeded for 10, 50 and 90 % of the time with respect to simultaneous 20 GHz attenuation (30 months period in Darmstadt, Germany) [10]. Grémont and Filip [14] theoretically derived distribution of instantaneous frequency scaling ratio, empirically calibrated. This model considers the impact of the stochastic temporal variations in rain drop size distribution (DSD) on the standard deviation of the instantaneous frequency scaling ratio of rain. In this model, the DSD is supposed to vary between two boundaries constituted by the Joss-Drizzle (J-D) and Joss thunderstorm (J-T) DSD. This model gives results in good accordance with measurements [2] [17]. It is recommended to use this model if instantaneous frequency scaling is required. The following parameters are required as input to the model: AD the attenuation at the lower frequency (dB) P the probability that AU is not exceeded (%) R the rain intensity (mm/hr) PDSD the probability (%) of the specific attenuation to be between the two theoretical extremes of the Jossthunderstorm and Joss-drizzle DSDs. After optimisation, PDSD was set to 97.8% [14]. 5. CONCLUSIONS Several dynamic aspects of rain attenuation have been defined and described: fade slope, fade and interfade duration, frequency scaling of attenuation and autocorrelation of attenuation. For fade slope, fade duration and frequency scaling, the influencing parameters have been defined, prediction models have been described and some typical results have been shown. These are important information in the design of Fade Mitigation Techniques. Fade slope depends on the attenuation level, the bandwidth of the filter used to remove scintillation, and time interval used to define the fade slope. It does not depend on frequency in the range 12-50 GHz. Possible dependencies on elevation angle and on climate are expected, but are not yet included in the recommended model. The model gives the pdf or the cdf of fade slope to be expected at a given attenuation level. Fade durations show a power-law distribution for short fades, and a lognormal distribution for long fades. According to the recommended model, the distribution is dependent on the attenuation threshold used in the definition of a fade, the frequency and the elevation angle. The model gives the number of fades longer than a specified duration, or the composite time of fades longer than a specified duration. Long-term frequency scaling can be used to scale the statistics of attenuation from one frequency to another. A model is presented, giving the ratio of attenuation at the two frequencies, depending on the two frequencies and the attenuation at the lower frequency. Instantaneous frequency scaling can be used to predict the momentary attenuation value from that measured at another frequency. It depends on attenuation and on the frequencies, but also on the drop size distribution. A hysteresis effect of
the attenuation at the two frequencies can be observed within an event. The recommended model gives the probability distribution of the scaling ratio between the two frequencies, depending on the frequencies, the attenuation at the lower frequency and the rain rate. 6. REFERENCES [1] Gremont, B. C., A. P. Gallois and S. Bate: “Efficient fade compensation for Ka-band VSAT systems”, 2nd Ka-band Utilization Conference, Florence, Italy, 1996, pp 439-443, 1996. [2] Castanet, L.: Fade Mitigation Techniques for new SatCom systems operating at Ka and V bands, Ph’D thesis of SUPAERO, Toulouse, France, December 2001. [3] Ventouras, S.: “Fade slope characteristics”, NRPP Research Note n°157, July 1995. [4] Van de Kamp, M.M.J.L. and L. Castanet: “Fade dynamics review”, First COST 280 Workshop, doc. PM3-018, Malvern, UK, July 2002. [5] ITU-R: Draft new Recommendation ITU-R P.[FADE] – “Prediction method of fade dynamics on Earth-space paths”, Document P.3/BL/49, Radiocommunication Study Group 3, December 2002. [6] van de Kamp, M.M.J.L.: Climatic Radiowave Propagation Models for the design of Satellite Communication Systems, Ph.D. Thesis, Eindhoven University of Technology, ISBN 90-386-1700-3, November 1999. [7] Van de Kamp, M.M.J.L.: “Statistical Analysis of Rain Fade Slope”, IEEE Trans. Antennas Propagat., in press. [8] COST205: Influence of the atmosphere on radiopropagation on satellite earth paths at frequencies above 10 GHz, COST Project 205, Report EUR 9923 EN, ISBN 92-825-5412-0, Sections 5.3 and 5.6, 1985. [9] Paraboni, A. and C. Riva: “A new method for the prediction of fade duration statistics in satellite links above 10 GHz”, Int. J. Sat. Com., 12, pp. 387-394, 1994. [10] Poiares Baptista, J.P.V., and P. G. Davies (editors): “OPEX; Volume 1: Reference Book on Attenuation Measurement and Prediction”, Second Workshop of the OLYMPUS Propagation Experimenters, ESA/ESTEC, Noordwijk, the Netherlands, WPP-083, 1994. [11] Castanet, L., D. Mertens and M. Bousquet: “Simulation of the performance of a Ka-band VSAT videoconferencing system with uplink power control and data rate reduction to mitigate atmospheric propagation effects”, Int. J. Sat. Com., 20(4), pp. 231-249, 2002. [12] Sweeney, D.G. and C.W. Bostian: “The dynamics of rain-induced fades”, IEEE Trans. Antennas Propagat., 40(3), pp. 275-278, 1992. [13] Dintelman, F., G. Ortgies and R. Jakoby: “Results from 21- to 30-GHz German propagation experiments carried out with radiometers and the Olympus satellite”, Proc. IEEE, 81(6), pp. 876-883, 1993. [14] Grémont, B. C. and M. Filip: “Modelling and Applications of the Instantaneous Frequency Scaling Factor (IFSF) of Rain Attenuation”, COST255 First International Workshop on Radiowave Propagation Modelling for SatCom Services at Ku-band and Above, Noordwijk, the Netherlands, WPP-146, ISSN 1022-6656, 1998, pp. 269-276. [15] Laster, J. D. and W. L. Stutzman: “Frequency scaling of rain attenuation for satellite communication links”, IEEE Trans. Antennas Propagat., AP-43(11), pp. 1207-1216, 1995. [16] Ortgies, G.: “Event-based analysis of tropospheric attenuation”, Olympus Utilisation Conference, Sevilla, Spain, WPP-60, pp. 515-520, April 1993. [17] COST255: Radiowave propagation modelling for new satcom services at Ku-band and above, COST 255 Final Report, Chapter 2.2 "Rain attenuation"”, ESA Publications Division, SP-1252, March 2002. [18] ITU-R: “Propagation data and prediction methods required for the design of earth-space telecommunications systems”, Recommendations of the ITU-R, 5(F), Rec. ITU-R P.618-7, 2001. [19] Salonen, E., S. Karhu, S. Uppala, and R. Hyvönen: “Study of improved propagation predictions”, Final Report for ESA/ESTEC Contract 9455/91/NL/LC(SC), Helsinki University of Technology and Finnish Meteorological Institute, 1994. [20] Dintelmann, F. (editor), “OPEX; Volume 2: Reference Book on Depolarisation”, Second Workshop of the OLYMPUS Propagation Experimenters, WPP-083, ESA/ESTEC, Noordwijk, the Netherlands, 1994. [21] Karasawa, Y., M. Yamada and J. E. Allnutt: “A New Prediction Method for Tropospheric Scintillation on EarthSpace Paths”, IEEE Trans. Antennas Propagat., 36(11), pp. 1608-1614, 1988.
