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Keywords:

  • radio propagation;
  • satellite;
  • U band

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[1] Long-term statistics of tropospheric attenuation were derived from almost 4 years of measurements made in the south of England using the ITALSAT F1 beacon signals at 49.5, 39.6, and 18.7 GHz; coincident rainfall rate measurements were made at the site of the receiving ground station. A method to remove the nonatmospheric changes of the beacon signals and to establish the reference levels from which to measure the excess and total attenuation has been presented in detail. The accuracy of fade level retrieval is estimated to be ∼±0.5 dB. A new method for predicting the annual total attenuation statistics has been proposed and validated against our data and data collected in Italy at 18.7, 39.6, and 49.5 GHz. For both locations, the new proposed method gives much better predictions compared with the established International Telecommunication Union recommendation method. A significant monthly and seasonal variation was observed in the attenuation and rainfall statistics and should be taken into consideration when planning the design and use of future slant path systems. We have seen that the attenuation statistics are subject to diurnal variations; however, for the period analyzed, this variation does not seem to follow a particular pattern.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[2] The increasing demand for more bandwidth for the numerous new services using Earth-space links, and the congestion of the lower-frequency bands, C (4–8 GHz) and Ku (12–18 GHz), is leading to the use of higher-frequency bands K (18–26 GHz), Ka (26–40 GHz) and U (40–60 GHz) or V (50–70 GHz). Services using systems operating at higher frequencies can benefit not only from the high data rates available at those frequencies but also from the smaller component sizes. The latter is an important factor for the expansion of satellite services in small business and direct to home applications.

[3] However, link quality and availability is likely to be severely degraded by the troposphere. In particular, rain attenuation, which increases rapidly with increasing frequency (at least for frequencies up to 100 GHz), is not the only propagation factor likely to degrade system performance as it is at the lower frequencies (Ku band). Light rain, clouds and gaseous attenuation, which have been neglected at the lower frequencies, can significantly limit the performance of Ka, U and V band Earth-space systems. Propagation experiments have been performed to measure, characterize and model the propagation effects on Earth-space paths. The first propagation experiment using satellite beacons occurred after NASA launched the ATS 5 and ATS 6 satellites in the 1970s [Ippolito, 1981]. Then a number of satellite experiments followed, mainly, in North America, Japan and Europe such as COMSTAR [Cox and Arnold, 1982], ETS-II [Yamada and Yokoi, 1974], SIRIO [Mauri, 1981], CS [Fukuchi et al., 1983], and the most recent OLYMPUS [Arbesser-Rastburg and Paraboni, 1997], ITALSAT [Paraboni et al., 2002], and ACTS [Davarian, 1996].

[4] The Radio Communications Research Unit (RCRU) of the Rutherford Appleton Laboratory (RAL) has made measurements of tropospheric induced fading by monitoring the 18.7, 39.6 and 49.5 GHz beacon signals carried on the geostationary Italian satellite, ITALSAT F1, for nearly four consecutive years. In addition, a 3 GHz multiparameter radar “CAMRa,” a microwave radiometer, a video camera, a ceilometer and a variety of other meteorological equipment provided information on the structure of rain and clouds. Measurements from this propagation experiment extended those already made using the beacons carried on the ESA satellite, Olympus, at frequencies near 12, 20 and 30 GHz [Ventouras et al., 1995]. Figure 1 shows an example of the comparative levels of attenuation experienced at Ku, K, Ka, and U band as measured at the receiving station of RCRU during the ITALSAT and Olympus propagation campaigns. The annual total attenuation statistics shown in Figure 1 were measured from April 1997 to March 1998 using the ITALSAT 49.5, 39.6 and 18.7 GHz beacons whereas the statistics for the Olympus 19.8 and 12.5 GHz frequencies were measured in 1993, the satellite's final operational year.

image

Figure 1. Total attenuation statistics measured in the south of England at Ku, K, Ka, and U frequency bands.

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[5] The severity of propagation impairments raises fundamental questions regarding the way in which Ka band and above services would be used and what system availability could be achieved. The rapid growth in Earth-space services using very small aperture terminals (VSAT), and ultra small aperture terminals (USAT), which necessarily have low fade margins, means that the impact of light rain, clouds and gaseous attenuation on these systems becomes a crucial consideration. Also, as the frequency increases, in a practical system subject to technological and economical limitations, the available fade margin alone is unlikely to compensate for the atmospheric attenuation. Therefore fade mitigation techniques might have to be employed. It is therefore very important to identify, measure and study all sources of loss along Earth-space paths for use in system design and the development of accurate propagation prediction methods.

[6] Section 2 of this paper describes the experimental characteristics and the processing of the recorded raw data from the ITALSAT propagation experiment. The algorithm used for the extraction of slant path attenuation from the received beacon signals is given in detail, as this is critical for the final outcome and conclusions. The results relating to long-term propagation measurements are discussed in section 3. These include attenuation and point rainfall statistics presented in annual, monthly, seasonal and diurnal format. The long-term attenuation statistics are compared with the current International Telecommunication Union recommendation (ITU-R) predictions and a new proposed prediction of total attenuation.

[7] Throughout this paper the attenuation is referred to as total or excess attenuation. The total attenuation is considered as the sum of two components: the gaseous attenuation due to oxygen and water vapor, which is always present, and the excess attenuation, which is sometimes present, due to clouds and rain.

2. Measurements and Data Processing

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

2.1. Measurements

[8] The Radio Communications Research Unit (RCRU) at RAL operated a receiving ground station, at Sparsholt in Hampshire (latitude 51°04′12″, latitude 01°26′W) from which it measured the signals of the beacons carried on ITALSAT F1 from April 1997 until the end of the satellite's operation in January 2001. ITALSAT F1 (owned and operated by the Italian Space Agency) was in a geostationary orbit at 13 degrees east, and it could be seen from the receiving station at an elevation angle of 30 degrees. The received 18.7 and 49.5 GHz signals were vertically polarized whereas the 39.6 GHz signal was circularly polarized [RHCP]. All receivers were sampled once a second. Details of the receiver design and operation can be found in work by Woodroffe et al. [1993]. For a number of years the control of satellite station keeping was reduced to preserve fuel supplies. North-south tracking of the satellite with the beacon receivers maintained ∼20 dB of dynamic range throughout most of this period. Alongside the beacon receivers, and pointing toward ITALSAT at an elevation angle of 30 degrees, were a digital camera to record the presence and structure of clouds occurring along the path, a Dicke switched radiometer operating at 51 GHz and a variety of meteorological instruments to measure temperature, humidity, pressure, rainfall and solar irradiance. The rainfall was measured using a drop counting rain gauge with sampling every 10 s. At Chilbolton, 7.5 km NNW of the receiver site, RCRU operates the multiparameter 3 GHz CAMRa radar, which provides information on the presence of rain, clouds and ice along the path to the satellite. Situated alongside the radar is a zenith pointing ceilometer operating at 905 nm, which provides information relating to the clouds base height. These additional measurements were used during data analysis to distinguish genuine fades from spurious outages, and to provide a baseline against which to estimate fade depth.

2.2. Data Processing

[9] In order to extract the attenuation values from the recorded beacon signal values, a reference level, known as “zero dB reference level,” from which to measure the attenuation has to be defined. However, changes of the received beacon signal caused by atmospheric phenomena occur simultaneously with changes caused by the satellite and receiving terminal. Motion of the satellite in its geostationary orbit causes a diurnal variation of the received signal. This problem was quite severe especially in the later years of ITALSAT F1 propagation campaign as the control of satellite station keeping was reduced to preserve fuel supplies. In addition thermal shifts and resultant power fluctuations can cause a slow variation of the received signal from day to day whereas satellite maneuvers and outages while beacons are switched off during solar eclipse periods to conserve power can cause sudden changes of the signal level. As a result, it is not possible to establish an absolute reference level and the total or excess attenuation has to be estimated from the measured signal level values corresponding to “clear sky” (i.e., signal affected by gaseous attenuation only). Depending on the equipment available, not all atmospheric effects can be measured. Attenuation caused by atmospheric gases and some types of clouds is relatively slowly varying in time and is difficult to distinguish from the diurnal variation caused by satellite movements. Radiometry can determine quite accurately the atmospheric attenuation up to a few dB [Waters, 1976], [Westwater et al., 1990]. Attenuation derived from radiometer measurements is insensitive to equipment drifts.

[10] The simplest method to establish the “zero dB reference” is by linearly interpolating the recorded signal values before and after a propagation activity (event) affecting the signal. This method, which gives a measure of the excess attenuation only, can lead to significant errors especially for long-lasting propagation phenomena because it neglects the nonlinear behavior of the beacon signal as detected. Therefore it could not be applied for the analysis of ITALSAT data at RCRU due to the severe satellite diurnal movement.

[11] An alternative approach is to average the “clear-sky” values of the measured signal over several days and establish a template. However, this method requires repeatable diurnal variations of the received signal due to the satellite movements and as a consequence it is very sensitive to the day-to-day variation of the received signal. Therefore a method based on a single day is more appropriate.

[12] Using a radiometer operating at a frequency close to the beacon receiver Stutzman et al. [1994] developed a method that does not require examination of previous and subsequent days. In this method which has been used for the analysis of beacon data recorded at Blacksburg, VA, USA during the Olympus satellite propagation experiment [Stutzman et al., 1995] the radiometer data are used (1) to identify the non-clear-sky effects (rain, clouds) and remove them from the recorded time series (2) to adjust the recorded time series for clear-air effects. Then a polynomial of up to sixth order is fitted to the remaining data to remove the diurnal variations of the received signal.

[13] For the analysis of the Olympus satellite data collected at RCRU no radiometer or other radio-meteorological data were available and the zero dB reference level (with respect to clear sky) was established for each day by fitting a Fourier series to the received signal [Ventouras et al., 1995]. The method, which is explained in Appendix A, has a rigorous mathematical foundation and therefore the fitting accuracy depends only on the quality of the data. The achieved accuracy for the Olympus satellite experiment at RCRU was better than ±0.2 dB. Compared with the arbitrary choice of a polynomial of up to sixth order [Stutzman et al., 1994] it allows a considerable flexibility in fitting a curve to the data by variation of the number of terms allowed in the Fourier series. This method has also been applied successfully for the analysis of RCRU Olympus satellite data collected at Sparsholt [McEwan et al., 1996], and Chilton [Ventouras and Goddard, 1996] for depolarization studies.

[14] For the analysis of ITALSAT data the Fourier series method was developed further taking into account the characteristics of this new experiment in terms of the equipment that were available and the phenomena affecting the higher frequencies. The developed procedure to extract the “excess” and “total” attenuation values has four stages.

[15] Stage 1: Estimation of the attenuation due to oxygen and water vapor (gaseous attenuation) at all beacon and radiometer frequencies, plus the sky brightness temperature at the radiometer frequency.

[16] Stage 2: Identification of those occasions in the 49.5 GHz and 39.6 GHz data set, when the measured signal values suffer no loss apart from that caused by oxygen and water vapor. These periods are referred to in this paper as “clear-sky time points.”

[17] Stage 3: Establishment of zero dB reference level (removal of the diurnal variation of the signal due to satellite movements).

[18] Stage 4: Establish accuracy of beacon measured attenuation and identify genuine fades.

[19] The estimation of gaseous attenuation at each beacon frequency is required to establish total path attenuation. The sky brightness temperature is needed in stage 2 to aid the identification of clear-sky time points at 49.5 GHz and 39.6 GHz. Gaseous attenuation at the radiometer frequency is needed in stage 4.

2.2.1. Stage 1

[20] The gaseous attenuation (attenuation due to oxygen and water vapor) at all beacon and radiometer frequencies and the sky brightness temperature at the radiometer frequency were estimated from the time series of ground level measurements of temperature, pressure and relative humidity. As mentioned earlier radiometry can be used for estimating the gaseous attenuations quite accurately. However, for our experiment it was decided not to use the 51 GHz radiometer when estimating gaseous attenuation at 49.5 GHz because the level of oxygen absorption increases very rapidly with the frequency in that region, as a consequence the sky temperature observations are not representative of that at 49.5 GHz. For the purposes of the estimations the atmosphere is assumed to consist of horizontally stratified layers; the specific attenuation values at each level are estimated using the Liebe [1989] model from the temperature, pressure and water density at this level. Integration of the loss throughout the atmosphere is performed up to a height of 47 km, at an elevation angle of 30°. Layer depth is 0.25 km for the range [0–11] km and 0.5 km for the range [11–47] km. The mean annual global reference atmosphere [International Telecommunication Union (ITU), 1999a] is used to determine temperature, pressure and water vapor density as function of altitude from the surface measurements of temperature, pressure and relative humidity. The established ITU-R prediction method of gaseous attenuation [ITU, 2001] is currently based on the Liebe [1989] model; it has been tested, along with other models, against experimental data [Rosenkranz, 1998] where it appears to provide the most satisfactory overall representation of gaseous attenuation in the “window” regions of the spectrum. Measured water vapor density and air temperature profiles were available from radiosonde ascents made at a location 30 m to the west of Sparsholt. These occurred twice every morning on weekdays. The sparse nature of the radiosonde data meant that it was of limited value when establishing the level of gaseous attenuation which was estimated once every 10 s.

2.2.2. Stage 2

[21] The clear-sky time points are identified with reference to the measurements of sky brightness temperature from the 51 GHz radiometer by using the following procedure.

[22] 1. For each day the time series of the moving standard deviation, (SDM(ti)) of the measured sky brightness is estimated over a 10-min interval. For the time points where there were propagation phenomena along the path, the standard deviation values would be higher than those values under clear-sky conditions.

[23] 2. For the same day we estimate the time series of the moving standard deviation over a 10-min interval, SDE(ti), of the estimated sky brightness temperature at 51 GHz under clear-sky condition (stage 1) and take their maximum value USD = max(SDE(ti)). Time points ti that satisfy the condition SDM(ti) ≤ USD are identified as clear-sky points.

[24] If radiometer data are not available a similar but less accurate technique can be applied. The time series SDM(ti) is derived from the beacon measurements and the threshold USD is established by examining the standard deviation values at time points when we know there were no propagation phenomena along the path. Data from the radar, the video camera and the ceilometer were used to provide information regarding the presence of rain and cloud along the path to the satellite.

2.2.3. Stage 3

[25] The establishment of a “zero dB reference level” for each beacon frequency is performed on a daily basis and uses the recorded signal values at clear-sky points for 49.5 GHz and 39.6 GHz signals (details of the method employed follow). The signal samples at the identified clear-sky time points include only diurnal variations due to the satellite movement and slow variation due to oxygen and water vapor absorption. To remove the variation due to oxygen and water vapor absorption, the gaseous attenuation estimated in stage 1 at the beacon frequency is added to the measured signal level values, then the zero dB reference level relative to vacuum is estimated over 10-min intervals. From the zero dB reference level relative to vacuum the zero dB reference level relative to clear sky is estimated by subtracting the gaseous attenuation.

[26] The procedure to establish the “zero dB reference level” at 49.5 GHz and 39.6 GHz has to cope with the difficulty that there are some days which have few clear-sky periods, and sometimes there are whole days without any clear sky. In order to minimize this problem, a set of N consecutive days is selected with the first and last having many clear-sky points. For the analysis of our data N was never greater than 30. Each day is divided into 144 (=86400/600) 10-min intervals and a representative value, which is the average of the signal level values at the identified clear-sky points within the interval, is calculated. If there are no clear-sky time points in the 10-min interval there is a gap. So at every 10-min interval of a set of N consecutive days (tiji = 1, 2, …, N, j = 1, 2, …, 144) corresponds to either (1) a signal value S(tij) which is affected only by the movement of the satellite:

  • equation image

where Sclear_sky(tij) is the signal value at the clear-sky points and agaseous(tij) the gaseous attenuation, or (2) a gap if there were propagation phenomena along the path to the satellite.

[27] By taking the same 10-min interval for each day from the set of consecutive days we define 144 time series that have the same number of time points N each. The signal values S(tij) within each of these time series (i = 1, …, N, j is constant within the series) do not experience any variation due to the diurnal movement of the satellite as they refer to the same 10-min interval of a day. Bearing in mind that the signal (relative to vacuum) is expected to undergo only a slow variation from day to day (thermal shifts, power fluctuations etc as mentioned earlier) the gaps in each time series can be filled by linear interpolation.

[28] Unfortunately this procedure does not always fill the gaps with sufficient accuracy. To remedy this we revert to the daily time series in which the original gaps have now been filled with first approximations to the vacuum levels. We seek to improve these by fitting a Fourier series See Appendix A and the fitted values used as a zero dB level. For the Fourier series fitting the number of series term are chosen by the operator. Typical values for our experiment are 5 or 7. Also it is possible to apply a fitting in a part of the day to overcome specific problems (i.e., jumps in signal level).

[29] For the 18.7 GHz zero dB reference level, the time series of the beacon signal values are converted into 10-min time series by taking the median value and then the iterative Fourier series fitting is applied (see Appendix A). This method is similar to that, which was applied for the analysis of data from the beacons on the Olympus satellite [Ventouras et al., 1995].

2.2.4. Stage 4

[30] The accuracy of the measured attenuation at 49.5 GHz is checked by comparing it to the 51 GHz radiometer-derived excess attenuation, and the independently extracted 49.5 GHz beacon excess attenuation, at the lower attenuation levels. From radiometer measurements we estimate the total attenuation at the radiometer frequency A(dB), using the formula [Ulaby et al., 1981]

  • equation image

where

Tmeas

radiometer measured temperature;

T0

cosmic background temperature which is taken to be 2.7 K;

Teff

effective medium temperature.

[31] Wu [1979] defined Teff as quoted by Ulaby et al. [1981] as

  • equation image

where Kcls(K) is the clear-sky temperature (not including the cosmic background temperature), and Npcls(Np) is the clear-sky attenuation (gaseous attenuation) respectively at the radiometer frequency as estimated from the ground measurements of temperature, pressure and relative humidity using the Liebe model (stage 1). The radiometer-derived attenuation relative to clear sky can be obtained by subtracting the estimated gaseous attenuation at 51 GHz from the total attenuation.

[32] Figure 2 shows in the first plot the time series of 49.5 GHz signal and zero dB reference level relative to vacuum (top curve) and clear sky (bottom curve) for 26 June 1997. The second plot of Figure 2 shows the time series of the excess attenuation at 49.5 GHz and excess radiometer-derived attenuation for the same day. The good agreement between the radiometer-derived excess attenuation and the independently extracted 49.5 GHz beacon excess attenuation, at the lower attenuation levels, confirms the accuracy of our zero dB reference level estimation procedure. During the analysis of our data, the difference between the beacon 49.5 GHz excess attenuation time series and the 51 GHz–derived excess attenuation time series was within ±0.5 dB. The accuracy of 39.6 GHz attenuation measurements, because the method to establish the “zero dB reference level” is the same as that applied for the 49.5 GHz data, was ±0.5 dB as well. For the 18.7 GHz “zero dB reference level” the accuracy as described in Appendix A can be about ±0.2 dB.

image

Figure 2. (top) 49.5 GHz signal (black), zero dB reference level (dashed curves) relative to vacuum and clear sky and (bottom) excess beacon attenuation (black) in comparison with the radiometer-derived excess attenuation (gray) at 51 GHz.

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[33] The effective medium temperature Teff as obtained by equation (2) seems to be appropriate for low-level attenuation levels to make predictions from radiometer measurements at 51 GHz. Figure 3 illustrates the sensitivity of the derived attenuation to Teff. Each curve is for a different value of Tmeas. The lowest curve is for Tmeas equal to the estimated clear-sky brightness temperature for ground temperature (7°C), pressure (1005 mbar), and water vapor density (8 gr/m3) at 51 GHz, and elevation angle of 30°. For each curve the uncertainty in the attenuation prediction is less than 0.5 dB.

image

Figure 3. Radiometer-derived total attenuation versus the effective temperature Teff for Tmeas = Tcls51, Tcls51 + 1, Tcls51 + 2, …, Tcls51 + 20 K at 51 GHz. Tcls51 is the estimated clear-sky brightness temperature for ground temperature 7°C, pressure 1005 mbar, and water vapor density 8 gr/m3 at 51 GHz and elevation angle 30°. Each line is for each Tmeas temperature. The lowest line is for Tmeas = Tcls51.

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[34] Associated with each data set (49.5, 39.6, and 18.7 GHz), an information file is created for each day, which contains flags to indicate where the data are valid, where the extracted attenuation is not genuine, where there are gaps (data acquisition gaps or the system was off), or there is “loss of lock.” The extracted zero dB reference level and the information files are stored in additional files for further processing.

3. Attenuation and Rainfall Statistics

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[35] From the attenuation and the coincident rain time series the daily cumulative distributions of attenuation and rainfall rate were estimated and stored as number of seconds for which the attenuation/rain thresholds were exceeded. The attenuation threshold intervals are 0.5 dB whereas the rainfall rate threshold intervals are 1 mm/h. For comparison with the ITU-R prediction methods the rain time series were averaged over 1-min intervals to produce cumulative distributions with an integration time of 1 min. For the study of diurnal variation of attenuation, the daily cumulative distributions for every hour during the day were estimated and stored. From these daily files the cumulative distributions for a selected period can be readily derived.

3.1. Measured Annual Attenuation and Rainfall Statistics

[36] Figure 4 shows annual rainfall statistics as measured during the ITALSAT propagation campaign in comparison with the ITU [2003b] model. The prediction is in good agreement with the experimental data at the higher percentages whereas at the lower percentages the discrepancies are less than the variability from year to year.

image

Figure 4. Measured annual rainfall statistics in comparison with the ITU-R prediction.

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[37] The measured annual total attenuation statistics at 18.7, 39.6, and 49.5 GHz are shown in Figures 5, 6, and 7, respectively. In the figures are also shown the average annual statistics related to 3 and 4 single years of measurements for 18.7, 39.6 and 49.5 GHz, respectively. At 18.7 GHz, the years April 1997 to March 1998 and August 1999 to July 2000 have similar total attenuation statistics whereas in the year August 2000 to July 2001 the measured attenuation for percentages lower than ∼0.1% is less compared with the attenuation measured the two previous years. On the other hand the concurrent rain statistics for these years (see Figure 4) are similar. The lower than expected (according to measured rain rates) values of attenuation measured from August 2000 to July 2001 may result from the way the intense rain is distributed along the path. For example, more attenuation would be expected because of a rain cell moving along the path than a rain cell of similar intensity that crosses the path. However, an extensive number of consecutive years of beacon and rain measurements in conjunction with wind speed and direction measurements are required to confirm this conclusion. Recent work [Callaghan and Vilar, 2003] has indicated that the shape of rain cells is impacted by the wind speed and direction. It appears that the wind “compresses” the rain cells along the line parallel to the direction of the wind, and the rain cells are elongated along a line perpendicular to the direction of the wind.

image

Figure 5. Annual measured total attenuation statistics for each year and average over 3 years at 18.7 GHz.

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image

Figure 6. Annual measured total attenuation statistics for each year and average over 4 years at 39.6 GHz.

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image

Figure 7. Annual measured total attenuation statistics for each year and average over 4 years at 49.5 GHz.

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[38] The maximum measurable attenuation for both 39.6 GHz and 49.5 GHz beacon signals was ∼20 dB. In this range, which corresponds for percentages greater than ∼0.05%, no significant variability was observed in the measured annual total attenuation statistics from year to year. This may result from the following reasons.

[39] 1. The variability of the rain statistics results from the variability of the occurrence of more severe rain events from year to year which contribute to the lower percentages. These events cause attenuation at U band signals higher than our maximum measurable attenuation.

[40] 2. U band signals suffer from significant attenuation due to clouds and light rain [Ventouras et al., 1998], which are present during most of the year.

[41] The impact on system design due to annual variability of yearly attenuation statistics can be seen if the attenuation axis in Figures 5, 6, and 7 is interpreted as the fade margin of a radio link. Then the curves yield the link outage caused by troposphere attenuation. As an example for an outage 0.1% (i.e., for an availability 99.9%) the required fade margin at 18.7 GHz (see Figure 5) ranges from 3.3 to 4.8 dB and at 39.6 GHz (see Figure 6) from 13.8 to 16.5 dB. At 49.5 GHz the required fade margin is greater than 20 dB.

3.2. Comparison of Measured Total Attenuation Annual Statistics With Predictions

[42] Propagation impairments act alone or in combination along the path to the satellite. Therefore a reliable system design requires not only accurate estimates of the individual impairments but also an estimate of the statistics of their combined effects especially at higher frequencies (Ka/V band) where the contributions from light rain, clouds and gases are more severe [Rogers et al., 1997]. In this paper two combination methods are applied. The ITU-R combination method [ITU, 2003a] and the method proposed recently [Ventouras and Wrench, 2002]. A detailed description of this method is given in Appendix B. The statistics for the individual effects are predicted from the ITU-R models.

3.2.1. Rain Attenuation

[43] Rain attenuation statistics are predicted from ITU [2003a] which uses the rain rate at the percentage 0.01%. For comparison rain attenuation statistics are predicted also using the rain rate at the probability of interest (use of the whole rain rate distribution) as has been proposed recently by Gibbins and Walden [2003] and ITU [2003c]. This new approach is described in Appendix C. Rain statistics are predicted by Recommendation P.837-4 [ITU, 2003b]. Table 1 gives the predicted rain attenuation statistics along the path to the ITALSAT satellite at the percentages 20,10,5, 1, 0.5 and 0.1% for the location of Sparsholt at 49.5, 39.6 and 18.7 GHz.

Table 1. Predicted Rain Attenuation Statistics at 49.5, 39.6, and 18.7 GHz for Sparsholt, UK, Elevation Angle 30°a
Outage, %Rain Attenuation, dB
49.5 GHz39.6 GHz18.7 GHz
R0.01%All DistR0.01%All DistR0.01%All Dist
  • a

    R0.01% is prediction using the rain rate at 0.01%; All Dist is prediction using the whole rain distribution.

200.4800.3600.060
100.8400.6300.120
51.441.261.090.790.220.12
14.377.903.365.600.751.16
0.56.7010.815.198.001.201.74
0.116.0019.0412.5914.763.23.69
3.2.2. Cloud Attenuation

[44] Cloud attenuation statistics are predicted using Recommendation P.840-3 [ITU, 1999c] in the range from 50% to 0.1%. For lower percentages than 0.1%, the ITU-R combination method assumes the value of rain attenuation at 0.1%. Table 2 gives the predicted values of cloud attenuation statistics at 20%, 10%, 5%, 1%, 0.5% and 0.1% for Sparsholt at the three beacon frequencies, 49.5, 39.6 and 18.7 GHz.

Table 2. Predicted Cloud Attenuation Statistics at 49.5, 39.6, and 18.7 GHz for Sparsholt, UK, Elevation Angle 30°
Outage, %Cloud Attenuation, dB
49.5 GHz39.6 GHz18.7 GHz
200.370.260.06
101.130.770.19
51.851.260.31
13.002.050.50
0.53.382.310.56
0.14.132.820.69
3.2.3. Gaseous Attenuation

[45] Gaseous attenuation statistics and annual mean gaseous attenuation values are predicted using Recommendation P.676-5 [ITU, 2001]. Gaseous attenuation statistics are predicted in the range from 50% to 0.1%. When gaseous attenuation is estimated from ground measurements of air temperature, pressure and relative humidity, as described earlier in section 2.2, it showed only a small degree of variation. Figure 8 shows the observed distribution of gaseous attenuation values at 49.5 GHz, 39.6 GHz and 18.7 GHz for a typical year, 1 April 1998 to 31 March 1999. As depicted in Figure 8, gaseous attenuation values, at all three frequencies are distributed symmetrically with a small spread around an average value. The mean value and standard deviation together with the median and 99%, 90%, 10% and 1% boundary values of these distributions are listed in Table 3. For comparison, Table 3 includes also the mean annual values of gaseous attenuation as predicted from ITU-R Recommendation P.676-5.

image

Figure 8. Distribution of gaseous attenuation values at 49.5, 39.6, and 18.7 GHz along the path to the ITALSAT satellite as measured from ground measurements of air temperature, relative humidity, and pressure.

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Table 3. Parameters of the Distribution of Gaseous Attenuation at 49.5, 39.6, and 18.7 GHz Along the Path to the Satellite (30° Elevation Angle) as Measured From 1 April 1998 to 31 March 1999 Together With the Mean Values of Gaseous Attenuation as Estimated From ITU-R Model
 Mean, dBStandard Deviation, dBMedian, dB99%, dB90%, dB10%, dB1%, dBITU-R, dB
49.5 GHz2.670.092.672.462.552.882.802.63
39.6 GHz0.750.070.740.610.650.850.920.72
18.7 GHz0.340.070.330.220.250.430.490.33

[46] As can be derived from Tables 2 and 3 clouds and atmospheric gases cause significant attenuation that increases with the frequency. For example at 0.1% the cloud attenuation exceeds the value of ∼4 dB at 49.5 GHz whereas at 18.7 GHz exceeds the value of ∼0.7 dB. Also (see Table 1) there is a difference between the two predictions of rain attenuation statistics that increases as the frequency increases. The prediction that relies on the rain rate at 0.01% of the time [ITU, 2003a], exhibits nonzero attenuation for time percentages when there is no rain. This “nonzero” attenuation can be neglected at 18.7 GHz but not at 39.6 and 49.5 GHz. As can be derived from Tables 2 and 3, the difference between the two rain attenuation models is comparable to the clouds and gaseous attenuation or even greater.

[47] As far as the predictions of total attenuation statistics are concerned the ITU-R established method combines the individual statistics on an equiprobable basis. This approach gives an upper bound on the total attenuation for each time percentage [Rogers et al., 1997] and not a total attenuation prediction. Therefore the ITU-R combination method (1) can in many cases lead to system over design and (2) cannot be used for predicting the total attenuation statistics especially at higher frequencies where the attenuation from the clouds and gases is more severe. On the other hand the new method based on a rigorous mathematical foundation and reasonable assumptions (which can be applied globally) overcomes all these problems and can highlight potential improvements which may be needed for cloud or rain attenuation predictions at higher frequencies.

[48] To compare the predictions with the measurements for each experimental data set, four predictions were made.

[49] 1. Estimating the rain attenuation statistics using the rate rain at 0.01% (current ITU-R method Recommendation 618-8) and the current ITU-R (Recommendation 618-8) combination method (labeled “ITU-R, 0.01%” in the following plots).

[50] 2. Estimating the rain attenuation statistics using the whole rate rain distribution and the current ITU-R (Recommendation 618-8) combination method (labeled “ITU-R, all distribution” in the following plots).

[51] 3. Estimating the rain attenuation statistics using the rate rain at 0.01% (current ITU-R method Recommendation 618-8) and the proposed combination method (labeled “New Method, 0.01%” in the following plots).

[52] 4. Estimating the rain attenuation statistics using the whole rate rain distribution and the proposed combination method (labeled “New Method, all distribution” in the following plots).

[53] Figure 9 shows the comparisons at 49.5 GHz between the measured and predicted total attenuation statistics. The measured statistics is the average over the 4 single years.

image

Figure 9. Annual measured (average over 4 years) and predicted total attenuation statistics at 49.5 GHz, Sparsholt, UK.

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3.2.4. Using the ITU-R Combination Method

[54] “ITU-R, 0.01%” prediction is close to experimental data whereas it should overestimate if the individual statistics were correct. On the other hand “ITU-R, all distribution” over estimates as it should. Therefore there is an indication that the current ITU-R method for rain attenuation statistics underestimates the rain attenuation. This underestimation compensates the overestimation from the ITU-R combination method and as a result the “ITU-R, 0.01%” prediction is close to experimental data.

3.2.5. Using the New Combination Method

[55] When the single statistics are combined with the proposed method the “New Method, all distribution” is very close to the measured statistics whereas the “New Method, 0.01%” significantly underestimates. This is an indication again that the current ITU-R method for rain attenuation statistics underestimates the rain attenuation.

[56] Similar results were obtained at 39.6 and 18.7 GHz as depicted in Figures 10 and 11, respectively. The differences between the different predictions are getting smaller as the frequency decreases. Table 4 illustrates the comparisons between the measured (average) and the predicted total attenuation statistics for Sparsholt UK at the three beacon frequencies. The predicted statistics were obtained using the “ITU-R, 0.01%” method which is the current ITU-R method and the “New Method, all distribution” method. To validate the new proposed methods of combination and rain attenuation statistics Table 5 illustrates the comparisons between the measured (average) and the predicted total attenuation statistics for Spino d'Adda (Italy). The data from Italy refer to 7 years (from 1994 to 2000) of measurements using the three beacons on ITALSAT satellite at the elevation angle of 37.7°. Further details of these measurements can be found in work by Riva [2004]. For both locations the new proposed method gives much better predictions than the established ITU-R method Recommendation P 618-8.

image

Figure 10. Annual measured (average over 4 years) and predicted total attenuation statistics at 39.6 GHz, Sparsholt, UK.

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image

Figure 11. Annual measured (average over 3 years) and predicted total attenuation statistics at 18.7 GHz, Sparsholt, UK.

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Table 4. Annual Measured and Predicted Total Attenuation Statistics for Sparsholt, UKa
Outage, %Total Attenuation, dB
49.5 GHz39.6 GHz18.7 GHz
MeasuredITU-R, 0.01%New Method, All DistributionMeasuredITU-R, 0.01%New Method, All DistributionMeasuredITU-R, 0.01%New Method, All Distribution
  • a

    For measured statistics, 49.5 and 39.6 GHz were averaged over 4 years, and 18.7 GHz was averaged over 3 years. For predicted statistics, ITU-R, 0.01% refers to Recommendation P.618-8, and New Method, All Distribution is a proposed combination method, whole rain distribution for rain attenuation statistics.

303.053.092.960.991.060.940.460.420.38
203.403.673.501.311.461.290.610.540.46
104.384.894.421.962.331.930.840.780.61
55.876.305.483.003.342.640.961.050.76
37.117.386.473.844.143.301.101.260.89
28.148.487.864.544.954.301.361.461.01
110.3410.5310.586.036.506.381.851.851.50
0.5013.2812.8613.457.988.338.662.452.302.09
0.3015.9915.1615.789.8310.1510.542.912.772.59
0.2018.5017.3917.8011.4711.9212.203.253.253.06
0.1023.4522.1721.6914.9515.7315.493.914.304.02
0.050   19.2320.6319.495.215.725.28
0.030   23.0424.9823.006.467.046.42
0.020      7.508.267.51
0.010      9.9110.719.75
0.005      12.9113.5912.42
0.003      15.0415.9514.58
0.002      16.6217.9316.34
0.001      17.8721.4217.52
Table 5. Annual Measured and Predicted Total Attenuation Statistics for Spino d'Adda, Italya
Outage, %Total Attenuation, dB
49.5 GHz39.6 GHz18.7 GHz
MeasuredITU-R, 0.01%New Method, All DistributionMeasuredITU-R, 0.01%New Method, All DistributionMeasuredITU-R, 0.01%New Method, All Distribution
  • a

    For measured statistics, 49.5, 39.6, and 18.7 GHz were averaged over 7 years. For predicted statistics, ITU-R, 0.01% refers to Recommendation P.618-8, and New Method, All Distribution is a proposed combination method, whole rain distribution for rain attenuation statistics.

302.542.902.390.891.100.730.390.380.35
202.713.242.551.031.350.820.460.450.38
103.204.152.971.362.021.120.560.630.42
54.055.493.751.963.021.630.690.870.53
35.246.765.542.783.972.761.001.100.69
26.767.877.663.854.824.271.391.300.99
110.010.7910.896.147.056.722.301.851.57
0.5013.414.3114.378.899.819.453.212.542.27
0.3017.917.7317.2311.1612.5211.773.943.242.89
0.2020.921.0319.7813.2615.1413.874.613.943.50
0.1026.428.0024.8117.6920.7018.166.005.494.80
0.05033.236.7530.9722.7227.7623.567.747.556.57
0.030   26.8933.9528.339.619.448.21
0.020   30.7239.4232.5111.3211.179.75
0.010      14.3414.5912.67
0.005      17.4618.5515.71
0.003      19.6621.7517.89
0.002      21.6424.4019.55
0.001      24.8428.9923.7

3.3. Monthly Statistics

[57] Annual statistics of path loss and rainfall rate are the average values collected over a period of 12 consecutive calendar months. Our measurements show that within a year the monthly statistics can vary significantly. To illustrate this the maximum and minimum monthly statistics have been established as follows.

[58] 1. The maximum monthly statistics for a preselected threshold (of attenuation or rain) are the statistics of the month during which the threshold is exceeded for the longest time.

[59] 2. The minimum monthly statistics for a preselected threshold (of attenuation or rain) are the statistics of the month during which the threshold is exceeded for the shortest time.

[60] The maximum (known as “worst month” within Recommendation P851-2 [ITU, 1999b] and the minimum months are not necessarily the same for all attenuation levels.

[61] Figure 12a is a composite plot showing the maximum and minimum monthly statistical total attenuation values measured during 1 year, at 18.7 and 39.6 GHz, respectively. The concurrent rainfall statistics are depicted in Figure 12b. These data are representative of a typical year at the Sparsholt receiving station and illustrates significant variation in monthly statistics at both frequencies. For 0.1% of the time, attenuation level (i.e., the required fade margin) varies from ∼1.5 dB to ∼8 dB at K band; while at Ka band the attenuation levels vary from ∼5 dB to well over 20 dB, beyond the dynamic range of our receivers. Figure 13 shows the monthly total attenuation statistics at 39.6 GHz. For each month the presented statistics are the averages over the 4 years of measurements. It seems that the highest values of attenuation were experienced during the summer and autumn months (June-July-August, September-October-November). Analysis of 18.7, 49.5 GHz and rainfall data showed similar trends. A similar pattern of results have been obtained by other experimenters using the beacons on the ITALSAT satellite in Italy [Riva, 2004], and Germany [Fiebig and Riva, 2004]. At both locations as in the southern United Kingdom high rain rates are almost never observed in winter (December-January-February). A detailed study regarding the monthly rain rate and attenuation statistics can be found in work by Konefal et al. [2000]

image

Figure 12. Annual, maximum, and minimum monthly values of (a) attenuation at 39.6 and 18.7 GHz and (b) rainfall.

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image

Figure 13. Averaged monthly statistics of total attenuation at 39.6 GHz for (a) January–June and (b) July–December.

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[62] At Ka and U band the results seem to show that designing a system based on worst month statistics would be uneconomical or, most likely, impractical (i.e., large fade margin). For this reason it will be necessary to use new methods of system planning taking into account observed seasonal and diurnal characteristics. For example on the basis of our data a system operating at 39.6 GHz with fade margin of 15 dB is expected to experience outages of 0.1% of a year (i.e., 526.6 min a year) due to tropospheric attenuation. As can be derived from Figure 13 with this fade margin, of the 526.6 min, statistically, 111.6 min will occur in August (outage time 0.25%) and only 1.2 min (outage time 0.003%) in February.

3.4. Seasonal Variation

[63] As shown above the monthly statistics can vary significantly within a period of 1 year. For the purposes of seasonal analysis the data were grouped into summer (June, July, August), autumn (September, October, November), winter (December, January, February) and spring (March, April, May) periods. Figure 14 presents an example of the annual and seasonal statistics of 39.6 GHz total attenuation and rain rate as observed from June 1997 to May 1998. The variation of total attenuation and rain rate statistics from season to season are much larger than from year to year (Figures 6 and 4, respectively). The analysis of the whole database shows that the highest level of attenuation and rain rate occurs during either the summer or autumn, whereas the lowest is during the winter or spring. The impact that seasonal variation could have on system planning is highlighted in Figure 15. Figure 15 shows the fraction of annual exceedance time (outage) versus the total attenuation at 49.5 GHz for each season, and for the worst {summer and autumn} and best {winter and spring} periods of the year October 1998 to September 1999. As depicted in Figure 15, the outage at 10 dB was distributed: 11% in spring, 15% in winter, 26% in summer and 48% in autumn or 26% in spring and winter and 74% in summer and autumn. The seasonal variation of attenuation increases with the increase of the attenuation level. At the larger attenuation level of 15 dB, 14% of the annual outage time occurred in winter and spring and 86% in summer and autumn. Higher values of attenuation (greater than ∼10 dB) are mainly due to rain whereas light rain and clouds together with the atmospheric gases contribute significantly at the lower attenuation levels. The latter are present for a large fraction of the average year, in contrast, the heavy rain events are significantly shorter in duration and occur usually in summer and autumn months. This explains the increasing seasonal variation of the attenuation statistics with increasing attenuation level. Such characteristics will be dependent on locality and to make optimal use of a system it will be necessary to know how atmospheric propagation varies at each site.

image

Figure 14. Annual and seasonal statistics: (a) attenuation at 39.6 GHz and (b) rain rate integration time 1 min. Observation period is June 1997 to May 1998.

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image

Figure 15. Fraction of annual outage time for each season at 49.5 GHz versus the attenuation exceeded threshold. Observation period is October 1998 to September 1999.

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3.5. Diurnal Variation

[64] Atmospheric attenuation is subject not only to seasonal but also to diurnal variation. Over 1 year the spread of attenuation statistics at 49.5 GHz established by selecting different time intervals during each day is shown in Figure 16. For a selected time slot, shifting the slot in steps of one hour derives 24 separate plots of attenuation statistics. Then the maximum and minimum statistics throughout the year were derived for each attenuation threshold. (The maximum and minimum values do not necessarily refer to the same time slot position in the day.) It can be seen that the attenuation statistics experience significant variation as the selected time slot shifts through a day. Also the spread of the statistics reduces as the time slot width increases. For instance during the displayed year, for a system operating with a 2-hour time slot and 99% availability, the fade margin varies from 9 dB to 13 dB. However, operating an 8-hour time slot with the same availability, the fade margin varies from 9.5 dB to 11.2 dB. It would be possible to take advantage of this diurnal variation in the design and use of a slant path communications system if the variation were repeatable. Figure 17 shows the observed level of diurnal variation of those periods for which slant path total attenuation at 49.5 GHz exceeds levels of 5 dB, 10 dB, 15 dB and 20 dB during the years from October 1997 to September 1998 and from October 1998 to September 1999. For this analysis the moving time slot has a width of 4 hours and each point on the plots refers to the starting hour of the time slot. It can be seen that there is a significant variation as the attenuation threshold increases but for the 2 years analyzed it is difficult to distinguish a repeated pattern. Similar results were observed using the 39.6 GHz data. On the other hand analysis of data using the 39.6 GHz beacon on ITALSAT satellite in Italy [Riva, 2004] and Germany [Fiebig and Riva, 2004] showed a strong diurnal variation for Germany and a moderate one for Italy. Whereas all three locations experienced significant monthly and seasonal variation of the attenuation statistics for the diurnal variations different trends were reported. However, our results refer to 2 years of data whereas the results from Italy and Germany refer to 7 and 4 years, respectively.

image

Figure 16. Spread of annual diurnal variation at 49.5 GHz total attenuation statistics for different moving time slots in comparison with the annual statistics of the full day.

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image

Figure 17. Diurnal variation of exceedance time at 49.5 GHz for (a) October 1997 to September 1998 and (b) October 1998 to September 1999.

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4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[65] We have presented the long-term total attenuation statistics from the analysis of almost 4 years beacon signal measurements at 49.5, 39.6 and 18.7 GHz and coincident rainfall rate data; these data have been collected in the south of England from the geostationary satellite ITALSAT F1. A comparison of the attenuation statistics at 39.6 GHz (Ka band) and 49.5 GHz (U band) with those from the 18.7 GHz beacon (K band) highlights the significantly increased attenuation levels that are experienced when using high-frequency slant path communication systems.

[66] In any propagation experiment using satellite beacons, the received signals undergo changes originating from behavior of the satellite and/or receiving station. These changes occur simultaneously with the atmospheric phenomena and can bias the measured attenuation if they are not removed from the received signals. A method to remove the nonatmospheric changes of the beacon signals, and to establish the reference levels from which to measure the excess and total attenuation, has been presented in detail. The accuracy of fade level retrieval is estimated to be ∼±0.5 dB.

[67] A new method for predicting the annual total attenuation statistics has been proposed and validated against our data and data collected in Italy at 18.7, 39.6 and 49.5 GHz. For both locations the new proposed method gives much better predictions compared with the established ITU-R method Recommendation P.618-8.

[68] The significant monthly variation that was observed in the attenuation and rain rate statistics should be taken into consideration when planning the design and use of future slant path systems. A design based only on annual and worst month statistics would give uneconomical or impractical solutions, and would not give any insight into potential advantages to be obtained by operating services during specific time slots. Summer and autumn were found to be the seasons with the most rain and attenuation. We have seen that the attenuation statistics are subject to diurnal variations; however, for the period analyzed, this variation does not seem to follow a particular pattern.

Appendix A:: Fourier Series Fitting

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[69] The received beacon signal S(t) at the instant t can be expressed as

  • equation image

where rv(t) is the zero dB reference signal with respect to a vacuum, which will be slowly varying because of the satellite movements, ga(t) is the gaseous attenuation, and is also slowly varying, whereas a(t) the attenuation due to rain, clouds and scintillation, generally with much faster variation than the two other quantities. Combining components with similar characteristics, the above equation can be written as

  • equation image

where rc(t) is the zero dB reference signal with respect to clear sky (rc(t) = rv(t) − ga(t)). The method is based on the mathematical fact that any continuous functions with its first derivative also a continuous function can be expanded in to a Fourier series [Jeffreys and Jeffreys, 1972].

[70] Taking one day, or 86400 s, as a base interval, rc(t) (the received signal in absence of any rain, clouds and scintillation) and its derivative, being regarded as continuous functions, can be expanded in any interval T1 to T1 + 86400 s by the Fourier series

  • equation image

where w = T1 + 2π(tT1)/86400.

[71] The number of terms that are required for the expansion can be determined by examining days without propagation events. A fitting of the truncated Fourier series to a measured data set over the interval T1 to T1 + 86400 s will fail where there are propagation events. In mathematical terms the propagation events can be regarded as discontinuities of the received signal as they cause faster variations of the received signal than the movement of the satellite. Taking advantage of this the Fourier fitting can be applied iteratively, as described below, to remove the propagation events gradually and set the zero dB reference level.

[72] The reference level can be estimated between the time T1 and any time T within the interval (usually T = T1 + 86400 unless there are jumps or offsets in the signal) by a two-step process.

[73] 1. Choosing a number of coefficients (k) (with k = 3, 5, 7, …) and fitting the above equation (A3) to an experimental set of data S(ti) i = 1, 2, …, N1 (with T1tiT) (by the method of least squares) we obtain an estimated set of values of the received signal: Se(ti) = equation image0 + equation image1 cos(w) + equation image2 sin(w) + … + equation imagek−2 cosequation image + equation imagek−1 sinequation image, i = 1, 2, …, N1, where equation image0, equation image1, …, equation imagek−1 are the estimates of the Fourier series coefficients.

[74] 2. Choosing an upper U and a lower threshold L we obtain a reduced set of data which satisfy the condition L < Se(tj) − S(tj) < U where j = 1, 2, …, N2 (with N2N1). The process is iterated using successively more exacting thresholds and the signal excursions caused by rain etc are gradually removed. It is not necessary for the number of coefficients to remain constant from iteration to iteration and can be increased slightly as the fitting is forced through more valid points for improved accuracy up to about ±0.2 dB. The method can be adapted for periods of more than one day. Also, the times T1 and T can be chosen to take into account jumps or offsets in the signal which have occurred because of system changes. An advantage of the method is that there are no restrictions for data points on which the fitting is applied. For example the data points need not be equally spaced in time or free from gaps. Also after estimating the Fourier series coefficients the zero dB level can be estimated at any point in the interval from T1 to T.

Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[75] Consider two stochastic variables X and Y and their scatterplot on the xy plane (x the horizontal axis). The combined X + Y statistics depend on how the scatter points are distributed on the x-y plane. By definition [Papoulis, 1965] the exceedance probabilities P(Xa), P(Ya) and P(X + Ya) for a given threshold a are given by the number of points to the right of the line x = a, above the line y = a and to the right of the line x + y = a, respectively, divided by the total number of scatterplot points.

[76] Bearing in mind that in beacon attenuation measurements it is difficult to distinguish rain attenuation from its associated raining clouds attenuation and as a consequence rain prediction models include also raining clouds attenuation, the combined attenuation due to rain and clouds (Arain+cloud) can be written as the sum of two components; the rain and raining clouds attenuation component (Arain) and the nonraining clouds attenuation component (Acloud). This implies a (Arain, Acloud) scatterplot with points only on the two axes. This gives according to the aforementioned (Arain is the X and Acloud is the Y)

  • equation image

where P(Arain+clouda), P(Araina) and P(Aclouda) are the exceedance probabilities of Arain+cloud, Arain and Acloud, respectively, at the attenuation threshold of a dB.

[77] Gaseous attenuation, in contrast with clouds and rain attenuation, is always present. Our measurements have shown that, in southern England, gaseous attenuation values are distributed symmetrically with a small spread around an average value as illustrated in Table 3. For example at 49.5 GHz the spread was less than 0.3 dB on either side of the average value.

[78] Figure B1 shows the integrated water vapor statistics (zenith) for Sparsholt, UK; Spino D'Adda, Italy (longitude 9.5°E, latitude 45.4°N); and a tropical location (longitude 100°E, latitude 5°N) as obtained from the ITU-R Recommendation P.676-5. The corresponding zenith (gaseous) attenuation statistics for these three locations at the frequencies 22.23, 39.6 and 49.5 GHz as obtained from Recommendation P.676-5 are shown in Figure B2. In the whole range from 50% to 0.1% the fluctuation of attenuation levels around an average value is less than 0.25 dB for all frequencies, even for 22.23 GHz at which the gaseous attenuation is very sensitive to water vapor variations. Therefore the gaseous attenuation can be considered as a constant in the whole range of the time percentage of interest.

image

Figure B1. Annual statistics of zenith integrated water vapor for Sparsholt, UK; Spino D'Adda, Italy; and a tropical location (100°E, 5°N) as obtained from ITU-R Recommendation P.676-5.

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image

Figure B2. Annual statistics of zenith attenuation for Sparsholt, UK; Spino D'Adda, Italy; and a tropical location (100°E, 5°N) as obtained from ITU-R Recommendation P.676-5 at the frequencies 22.236, 39.6, and 49.5 GHz.

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[79] As a result the probability of total attenuation (Atotal) to exceed a dB can be given by

  • equation image

where mgaseous is the mean value of gaseous attenuation and can be obtained from Recommendation P.676-5.

Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information

[80] The model can be defined as follows [ITU, 2003c], using the same terminology as in Recommendation P.618-8, with the rain assumed to extend from the ground, at a height hS above mean sea level, up to the rain height, hR. These heights may be obtained from ITU-R Recommendations P.1511 and P.839-3, respectively.

[81] The slant path length, LS, from the Earth station to the rain height is determined from

  • equation image

where θ is the elevation angle of the slant path.

[82] The horizontal projection of the slant path length along the ground is given by

  • equation image

The specific attenuation due to rain is obtained from

  • equation image

where R is the rainfall rate at the required time percentage.

[83] The horizontal path length adjustment factor is then given by the expression

  • equation image

The effective path length along the slant path can then be defined as

  • equation image

where ν is a vertical adjustment factor, and the slant path attenuation is then given by

  • equation image

The vertical adjustment factor is given by the expression

  • equation image

For rain rates less than 1 mm/h, a value of 1 mm/h should be used.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information
  • Arbesser-Rastburg, B. R., and A. Paraboni (1997), European research on Ka-band slant path propagation, Proc. IEEE, 85, 843852.
  • Callaghan, S. A., and E. Vilar (2003), Analysis of the fractal dimension of rain rate contours with reference to wide area coverage of satellite communications, Foreign Radioelectronics, vol. 6, Successes of Modern Radioelectronics, Radiotechnika, Moscow.
  • Cox, D. C., and H. W. Arnold (1982), Results from the 19- and 28-GHz COMSTAR satellite propagation experiments at Crawford Hill, Proc. IEEE, 70, 458488.
  • Davarian, F. (1996), Ka-band propagation research using ACTS, Int. J. Satell. Commun., 14(3), 267282.
  • Fiebig, U., and C. Riva (2004), Impact of seasonal and diurnal variations on satellite system design in V band, IEEE Trans. Antennas Propag., 52, 923932.
  • Fukuchi, H., T. Kozu, K. Nakamura, J. Awaka, H. Inomata, and Y. Otsu (1983), Centimeter wave propagation experiments using the beacon signals of CS and BSE satellites, IEEE Trans. Antennas Propag., 31, 603613.
  • Gibbins, C. J., and C. J. Walden (2003), A study into the derivation of improved rain attenuation regression coefficients, Radiocommun. Agency Rep. AY4359, Ofcom, London.
  • International Telecommunication Union (ITU) (1999a), Recommendation ITU-R P.835-3, Reference standard atmospheres, P series, Geneva, Switzerland.
  • International Telecommunication Union (ITU) (1999b), Recommendation ITU-R P.851-2, The concept of “worst month,” P series, Geneva, Switzerland.
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Measurements and Data Processing
  5. 3. Attenuation and Rainfall Statistics
  6. 4. Conclusions
  7. Appendix A:: Fourier Series Fitting
  8. Appendix B:: Statistical Combination of Individual Tropospheric Effects to Obtain the Total Attenuation Statistics
  9. Appendix C:: Rain Attenuation Statistics Using the Full Rainfall Distribution
  10. References
  11. Supporting Information
FilenameFormatSizeDescription
rds5213-sup-0001-t01.txtplain text document1KTab-delimited Table 1.
rds5213-sup-0002-t02.txtplain text document0KTab-delimited Table 2.
rds5213-sup-0003-t03.txtplain text document1KTab-delimited Table 3.
rds5213-sup-0004-t04.txtplain text document1KTab-delimited Table 4.
rds5213-sup-0005-t05.txtplain text document1KTab-delimited Table 5.

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