Radio Science, Volume 32, Number 5, Pages , September-October 1997

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1 Radio Science, Volume 32, Number 5, Pages , September-October 1997 Scintillation and simultaneous rain attenuation at 12.5 GHz to satellite Olympus Emilio Matricciani, Mario Maud, and Carlo Riva Dipartimento di Elettronica e Informazione and CNR-CSTS, Politecnico di Milano, Milan, Italy Abstract. This paper reports the statistical relationship between 1-s averaged rain attenuation (A, in decibels) and standar deviation (c, in decibels) of simultaneous tropospheric scintillation in 1-s intervals, derived from high-resolution (50 samples/s) experimental 12.5-GHz attenuation time series recorded at Spino d'adda (45.4øN) in a 30.6 ø slant path to satellite Olympus during an observation time of approximately 1 year. The statistical relationship can be fitted by the power law cr = 0.068A " 2 derivable from a thin turbulent layer model. A similarelationship was also previously obtained in the same slant path at GHz. As a consequence, we have concluded that at least up to 20 GHz, the modeling is independent of frequency. 1. Introduction Satellite communication systems designed with low power margins must be examined for the statistical relationship between concurrent rain attenuation and scintillation. Such knowledge could improve the instantaneous frequency scaling of attenuation by separating rain effects from turbulenceffects (e.g., in up-link power control). Concurrent rain attenuation and scintillation have been studied in the literature: Karasawa and Matsudo [1991] and Dintelmann et al. [1993] observed scintillation during rain and concluded that a statistical relationship between the two phenomena exists. Matricciani et al. [1996] prove theoretically, and verify experimentally, that the two phenomenare statistically linked at a carrier frequency (19.77 GHz) for which scattering due to hydrometeors is not yet comparable to turbulence scintillation [e.g., see Haddon and Vilar, 1986]. In this paper we have analyzed the attenuation time series, recorded at 12.5 GHz, of 31 rain events in a 30.6 ø slant path to satellite Olympus with an antenna diameter of 3.5 m, to separate rain fade and scintillation effects. The attenuation time series recorded at GHz during the same rain events were previously used by the authors to derive the following statistical relationship between rain attenuation A (in decibels), Copyright 1997 by the American Geophysical Union. Paper number 97RS /97/97RS averaged over 1 s, and the standard deviation of simultaneous tropospheric scintillation o (in decibels), calculated for 1-s intervals by using 50 samples: ty = CA 5/'2 (1) where C is a constant, equal to Equation (1) was derived as sketched in the following. We first need a relationship between A and the average rainy path L; then we need a similar relationship between c and L. By using Taylor's hypothesis of "frozen flow," rain attenuation can be modeled as the convolution of a rectangular unit function L kilometers wide with the specific attenuation (decibels/kilometer) calculated from rain rate (millimeters/hour) time series recorded at a rain gauge [Matricciani, 1996]. By using Fourier transforms and assuming that the "path transfer function" [Matricciani, 1996] is an all-pass ideal filter, rain attenuation turns out to be proportional to L A = E 1L (2) where C is a constant. As for c, after Tatarski [ 1961 ], the expression of scintillation variance in presence of a thin uniform turbulent layer aloft is given by o '2 = 42.25Dk TM Cn L 'w (3) where k=2rd) (per meter) is the wave number, ) (meters) is the wavelength, C (m-2/3) is the structure constant of the turbulence, L (meters) is the rainy slant path, and D (meters) is the actual turbulent path length, located aloft between L-D and L with D<<L. Substituting (2) into (3), we get (1). Equation (1) seems to be physically reasonable since high attenuation values are associated with intense rain, 1861

2 1862 MATRICCIANI ET AL.: SCINTILLATION AND RAIN ATTENUATION which often comes with strong wind gusts and consequently intense turbulence phenomena. We anticipate that the results presented in this paper seem to confirm the validity of (1) also at 12.5 GHz. Following this introduction, in section 2 we describe the statistical method used in the analysis; in section 3 we report the model which fits the experimental results; and in section 4 we draw some conclusions. 2. Database The attenuation time series of 31 rainy events span the period from August 1992 to June 1993 at 12.5 GHz (vertical polarization), for a total time of hours, in a 30.6 ø slant path to the geostationary satellite Olympus (19øW). The data were recorded at Spino d'adda (northern Italy, 45.4øN, 84 m above sea level) with an antenna of 3.5 m diameter, at the high sampling rate of 50 samples/s, so that the unknown high-frequency content of rain attenuation and scintillation power spectra is measured reliably. The same 31 rainy events were used by Matricciani et al. [1996] to derive (1) for the same slant path, but at GHz. The carrier-tonoise ratio (CNR) of the receiver in clear-sky conditions is 54.9 db in 1 Hz [Adamou et al., 1989]. 3. Data Processing To distinguish between rain attenuation (i.e., signal amplitude variation caused by absorption and scattering by hydrometeors) and scintillation (i.e., signal amplitude variation caused by tropospheric turbulence), we must separate the two effects as much as possible by filtering the experimental time series. After Matricciani et al. [1996], we have thus analyzed the power spectra of attenuation time series to assess the frequency range in which there is a change in the nature of the physical phenomenon causing amplitude fluctuations. As rain attenuation has most of its power at the lowest frequencies and in this range this power is much larger than that of scintillation, disjoint blocks of 50 samples were averaged and decimated to yield 1 sample/s time series, i.e., the conventional rain attenuation time series usually recorded. With S, (f) being the power spectrum of a single rain event attenuation, the average power spectra of the 31 events is given by the following equation: 1 N _ og,o s, S (f) = 10 '--' (4) which maintains constant the logarithmic slopes and thus allows us to compare the experimental results with! db/decade O frequency [Hz] Figure 1. Average power spectral density of 31 events (original data averaged over 1 s; frequency, 12.5 GHz; antenna diameter, 3.5 m; slant path elevation, 30.6ø); total time is hours.

3 MATRICCIANI ET AL.' SCINTILLATION AND RAIN ATTENUATION 1863 theory (equation also used by Matricciani et al. [1996]), as in the following. The result is shown in Figure 1. Notice that on the average, the theoretical -20 db/decade slope due to rain [Matricciani, 1994] is valid up to about 0.02 or 0.03 Hz, as given by Matricciani et al. [1996], beyond which other effects are prevalent, as confirmed by the change in spectrum slope. Figure 2 shows an example of a power spectrum of a single event, in which turbulence with a spectrum slope of-80/3 db/decade (i.e., f-8/3 in natural units [Tatarski, 1961; Karasawa and Matsudo, 1991 ]) is evident. We have then estimated bulk rain attenuation time series from the original time series (50 samples/s) by a low-pass filter (Butterworth filter of the fifth order) with a cutoff frequency of Hz. After the low-pass filtering, disjoint blocks of 50 samples of the time series were averaged and decimated to yield 1 sample/s time series (A in decibels). In the end, we produced 1 sample/s time series with the nominal highest frequency equal to Hz. In the following we will refer to these low-pass filtered time series as "rain attenuation." To complement the previous analysis, the original time series (50 sample/s) were filtered by high-pass filter (Butterworth of the fifth order) with a cutoff frequency Hz. Intervals of scintillation stationarity (71 in total) were identified by visual inspection, for each interval, of the probability distribution of the amplitude, to assess that it is well modeled by the Gaussian probability distribution with zero mean, as predicted by theory and experiments [Tatarski, 1961; Ortgies, 1985; Banjo and Vilar, 1986]. Finally, the average power spectrum was calculated, according to equation (4). The result is shown in Figure 3. From Figure 3 we notice that the receiver CNR permits observation of frequency components up to about 3 Hz, beyond which the receiver (white) noise appears. We also notice a decay very close to the theoretical f-s/3 above 0.03 Hz while the smoother decay below 0.03 Hz is likely due to changes in the scintillation spectrum from one event to another [Matricciani et al., 1996]. As a consequence, we filtered out the high-frequency noise by using a low-pass filter (Butterworth of the fifth order) with a cutoff frequency of 3 Hz. In the end we produced two concurrent 1 sample/s time series, one for "rain attenuation" only and one for "scintillation" standardeviation only, the latter obtained by the band-pass time series ( Hz). We can now assess whether the relationship found by 10 4 r 102 r r loo r 20 db/decade 80/3 db/decade 10-2 '. 1 o -4-1 o -6 r '4 1 0 '3 1 0 '2 1 0 '1 1 0 o frequency [H z] Figure 2. Power spectral density of attenuation for one event (original data averaged over 1 s; frequency, 12.5 GHz; antenna diameter, 3.5 m; slant path elevation, 30.6ø); date is September 21, 1992.

4 1864 MATRICCIANI ET AL.' SCINTILLATION AND RAIN ATYENUATION '1-80/3 db/decade 10'2 10' frequency [H z] Figure 3. Average power spectral density of scintillation for the 71 intervals of stationarity. Original time series is at 50 samples/s, high-pass filtered with cutoff frequency of Hz; frequency, 12.5 GHz; antenna diameter, 3.5 m; slant path elevation, 30.6 ø. Matricciani et al. [1996] at GHz is confirmed or not at 12.5 GHz. 4. Results We obtained a bivariate histogram between 1-s rain attenuation (1 db class width) and 1-s standard deviation of scintillation (0.1 db class width). Dots in Figure 4 show the average value of scintillation standard deviation c (in decibels) for each rain attenuation center class value A (in decibels). Though the highest attenuation measured was 17 db, the receiver CNR ratio allows a reliable estimation of scintillation standard deviation for attenuation below about 13 db (value estimated by equation (1) of Matricciani et al. [1996]). From Figure 4 it is evident that the two phenomen are correlated, even though the data are dispersed. Notice that when A approaches zero (no rain along the path), c must approach a finite value, obviously determined by the "residual turbulence" associated with clouds or clear sky; a rough estimate of this limit can be derived from the minimum attenuation shown in Figure 4, i.e., A=l.5 db, for which c =0.09 db. The values shown in Figure 4 must be increased if we use smaller antennas, as in very small aperture terminals systems (VSAT) or in lower elevation paths. For example, if we consider a communication link at 50 GHz with an antenna diameter of 0.5 m, efficiency 0.6, and an elevation angle of 10 ø and scale c =0.09 db to the new link ,,,,,,,, I rain attenuation [db] Figure 4. Experimental average standard deviation of scintillation (solid circles) as a function of "rain attenuation" (frequency, 12.5 GHz; antenna diameter, 3.5 m; slant path elevation, 30.6ø); the solid line is the thin layer turbulent model (equation(5)). ß.

5 , MATRICCIANI ET AL.: SCINTILLATION AND RAIN ATTENUATION 1865 characteristics, after International Telecommunication Union-Radiocommunication (ITU-R) [ 1992a], we obtain o=0.36 db, which can give rise to extreme _+3 standard deviation of carrier amplitude variations equal to _+1.1 db. Since 0.36 db represents an average value of (, even more ample fluctuations can be impressed to the carrier amplitude if we consider the statistics of ( (e.g., as those reported in Table 1 of Matricciani et al. [1996]). Let us now determine if the thin turbulent layer model can represent the experimental data of Figure 4: By fitting the power law (1) to the experimental curve between A=l.5 and 12.5 db, we found C=0.068; hence cr = 0.068A5/ 2 (5) which is plotted as the solid line in Figure 4. The fit is satisfactory up to about 10 db. As an exercise, let us now assess how the carrier frequency affects the results, by comparing equation (5) with the following relationship: 5/12 O'19.77 : 0-039A19.77 (6) obtained by Matricciani et al. [1996] at GHz. From (6) we obtain ( 19.77=0.039 db for A19.77=1 db. If we scale A19.77 = 1 db to 12.5 GHz, according to Drufuca [1974] :(f2/tm A 2,- - ) A (7) 12.5 = D&7/ (9) , I, I, I, I, frequency [GHz] Figure 5. Structure constant of the turbulence C, estimated starting from the standard deviation of scintillation at 12.5 GHz, calculated by means of the thin layer model (equation(5)) at various frequencies and elevation angle of 30.6 ø (solid line). The solid circle gives the value of C estimated from the thin layer model (equation (6)) at GHz. With L=6357 m (calculated from the ITU-R [1992b] rain height formula at Spino d'adda for an elevation angle of 30.6ø), D=786 m (a vertical depth of 400 m), and o12.5= db, calculated with (5) when A 2.5=0.7 db (rain attenuation value scaled from 1.5 db at GHz, used by Matricciani et al. [1996]), from (9) we obtain Cn as a function of frequency, as shown in Figure 5. At GHz we get Cn =6.2 x m -2/3 which must compared with Cn =3.82x 10-4m -2/3 obtained for A=l.5 db at GHz by Matricciani et al. [1996]. Now considering that this parameter ranges from to 10-1ø m '2/3(e.g., for Milan, a site close to Spino d'adda [Marzano et al., 1994]), an order of magnitude may not be a significant difference, and hence Figure 5 shows that the thin turbulent layer where A1 and A2 are the attenuation values at f and f2, respectively, we obtain A12.5=0.45 db, which, when introduced in (5) gives o 2.5=0.048 db. By scaling o 2.5=0.048 db to GHz [ITU-R, 1992a], we obtain ( 9.77=0.061 db, which is of the same order of magnitude of db in (6). Since both (7) and the ITU-R scaling formula give, of course, estimates, we modeling is substantially independent of frequency, as it conclude that equation (5) is consistent with equation should be. (6). To further supporthis conclusion, let us estimate the 5. Conclusions value of the structure constant of the turbulence, Cn ß We can use (5) to calculate at any significant The analysis of 71 time series (50 samples/s) of rain frequency other than 12.5 GHz by scaling A 2.5 with (7). attenuation and scintillation recorded at 12.5 GHz to We obtain satellite Olympus (elevation 30.6 ø) has shown that a relationship between "bulk" rain attenuation (in O'19.77 = O'12.5 ' (8) decibels), averaged over 1-s intervals, and simultaneous standard deviation of scintillation (in decibels), and can finally estimate the value of Cn from (3) and calculated over 50 samples every second, can be well (8) as fitted by a power law of the type given by Matricciani et al. [1996], which models a turbulent thin layer aloft. The results are consistent with those obtained in the previous analysis of dat at GHz in the same path.

6 1866 MATRICCIANI ET AL.: SCINTILLATION AND RAIN ATFENUATION We conclude that at least up to 20 GHz, the modeling is independent of frequency. References Adamou, A., F. Barbaliscia, A. Florio, F. Martinino, L. Ordano, and A. Paraboni, Esperimento di propagazione nel programma del satellite Olympus, Riv. Tec. Selenia, 11, , Banjo, O.P., and E. Vilar, Measurement and modelling of amplitude scintillations on low-elevation earth-space paths and impact on communication systems, IEEE Trans. on Commun., 34, , Dintelmann, F., G. Ortgies, F. Rt cker, and R. Jakoby, Results from 12- to 30-GHz German propagation experiments carried out with radiometers and the Olympus satellite, Proc. of the IEEE, 81, , Drufuca, G., Rain attenuation statistics for frequencies above 10 GHz from raingauges observation, J. Rech. Atmos., 1-2, , Haddon, J., and E. Vilar, Scattering induced microwave scintillations from clear air and rain on Earth-space paths and the influence of antenna aperture, IEEE Trans. Antennas Propag., 34, , International Telecommunication Union- Radiocommunication, Rain height model for prediction methods: Propagation in non-ionized media, ITU-R Rec , Geneva, 1992a. International Telecommunication Union- Radiocommunication, Rain height model for prediction methods, Propagation in non-ionized media, ITU-R Rec. 839, Geneva, 1992b. Karasawa, Y., and T. Matsudo, Characteristics of fading on low-elevation angle Earth-space paths with concurrent rain attenuation and scintillation, IEEE Trans. Antennas Propag., 39, ,1991. Marzano, F.S., G. Cesari, and G. D'Auria, Metodo predittivo di scintillazioni troposferiche in collegamenti a microonde via satellite, paper presented at the X Riunione Nazionale di Elettromagnetismo, Cesena, Italy, Sept , Matficciani, E., Physical-mathematical model of the dynamics of rain attenuation with application to power spectrum, Electron. Lett., 30, , Matficciani, E., Physical-mathematical model of the dynamics of rain attenuation based on rain rate time series and a twolayer vertical structure of precipitation, Radio Sci., 31, , Matficciani, E., M. Mauri, and C. Riva, Relationship between scintillation and rain attenuation at GHz. Radio Sci., 31, , Ortgies, G., Probability density function of amplitude scintillations, Electron. Lett., 21, , Tatarski, V.I., Wave Propagation in a Turbulent Medium, McGraw-Hill, New York, E. Matficciani, M. Mauri, and C. Riva, Dipartimento di Elettronica e Informazione and CNR-CSTS, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy. ( elet.polimi.it; elet.polimi.it; riva@elet.polimi.it) (Received November 18, 1996; revised April 2, 1997; accepted May 19, 1997.)