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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 5, SEPTEMBER 2000
Experimental Rain Attenuation Statistics Estimated from Radar Measurements Useful to Design Satellite Communication Systems for Mobile Terminals Emilio Matricciani
Abstract—Based on experimental data, we have reported a ( ) that rain reliable method to scale the cumulative time attenuation (dB) is exceeded in a fixed satellite system to the ( ) that it is exceeded in a satellite system for mobile time terminals. Zigzag routes and ring-roads simulated city patterns; ( ) can be straight routes simulated freeways. In all cases, expressed as ( ) = ( ) with a probability scaling factor independent of . The simulations have been made at 19.77 GHz with satellite elevation angle of 30.6 , 45 , 60 , 80 , and 90 . For the horizontal structure of rain, we have used a very large number of rain-rate maps of rain storms randomly observed in 1989–1992 by a meteorological radar placed at Spino d’Adda (Northern Italy). The vehicle speed was modeled as a log-normal random variable. We found: a) in zigzag routes, ( ) ( ), i.e., 1, with results depending on vehicle speed modeling and starting conditions; b) in ring-road, there is no difference between fixed and mobile systems ( = 1); and c) in straight freeways, ( ) ( )( 1); ( ) can change significantly in different straight lines and in opposite directions (anisotropy and asymmetry) for medium-large attenuation. When compared to zigzag routes or ring-roads, the performance in straight freeways is the most optimistic. For 30 6 and for the same pattern, is fairly independent of . Since the radar rain maps are a reliable estimate of the horizontal structure of rain, the findings, which can be considered frequency-independent, stand as a very good prediction of the results obtainable by experiments. Index Terms—Freeway traffic, mobile communication, radar, rain attenuation, ring-road traffic, satellite systems, zigzag traffic.
I. INTRODUCTION
F
UTURE satellite communication systems designed for mobile user applications will use extremely high-frequency carriers to provide more capacity and smaller equipment [1]–[6]. At these frequencies, the extra attenuation due to rain can be a limiting factor when low outage probabilities are required, e.g., below 10 (0.1% of the time in an average year). As a consequence, the designer needs reliable and long-term rain attenuation statistics applicable to terminals placed on moving vehicles. These statistics can be very different from those applicable to fixed terminals, linked to the same satellite, because of the relative motion of rainstorms and vehicles [7], [8]. Failure to consider this issue is a theoretical error and oversimplification
Manuscript received December 3, 1998; revised April 28, 1999. The author is with the Dipartimento di Elettronica e Informazione and Centro di Studio sulle Telecomunicazioni Spaziali (CSTS-CNR), Politecnico di Milano, Milan 20133 Italy (e-mail:
[email protected]). Publisher Item Identifier S 0018-9545(00)07879-8.
because rain attenuation statistics measured or predicted for the fixed system can lead to a large overdesign. Mobile satellite communication is affected, of course, not only by rain but also by shadowing, blockage, and multipath [6]. These disturbances can plague the channel for such a long time that they establish system performance for a large range of outage probabilities, including the very low ones when rain attenuation also contributes to the outage. This paper focuses on rain attenuation only. Notice, however, that at the end of a future technological breakthrough in “smart” antennas (phased arrays with a lot of signal processing), which may largely reduce the impact of multipath by ad hoc processing, rain will remain the irreducible cause of fading and system outage (if obstruction and shadowing are avoided) and must be considered. Following [7] and [8], we have investigated how, in the long term, the cumulative probability distribution of exceeding a given rain attenuation (dB) in a fixed satellite system is transformed into that applicable to a satellite system for working in the same geographical mobile terminals area, at the same carrier frequency and weather conditions. The results reported below allow such a transformation and are of general application. It is understood that a complete channel modeling must include the effects of shadowing, blockage, and multipath besides rain attenuation. We have investigated three general patterns, according to how vehicles are driven: a) zigzag routes and b) ring-roads to simulate city patterns and c) straight routes to simulate freeways. Vehicle speed was modeled as a log-normal random variable after the mathematical model derived from measurements performed in Europe [8]. As for rain, we have used a very large number of rain-rate maps, sampled every 90 s, of rain storms randomly observed in 1989, 1991, and 1992 by a 2.8-GHz meteorological radar located at Spino d’Adda (45.5 N, 9.5 E, 84 m above sea level), in flat countryside near Milan, Italy, within the Po Valley, and operated by Centro di Studio sulle Telecomunicazioni Spaziali of the Italian National Research Council (CSTS-CNR) for radio propagation experiments, the first of which was in the framework of satellite SIRIO experiment [9], [10]. To the author’s knowledge, this is one of the largest radar databases used for radio propagation studies. Moreover, this is a large database, per se, and as such it yields long-term results that are both reliable and of great value, as is shown in the following. On these maps, we superposed a grid of square cells to represent city blocks and streets in cases a) and b) and straight lines in
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MATRICCIANI: EXPERIMENTAL RAIN ATTENUATION STATISTICS
case c) mentioned above. Then we simulated moving terminals at 19.77 GHz with radio links toward a geostationary satellite located at 19 W, i.e., the former Olympus satellite orbital position, the 19.77-GHz beacon of which, in vertical polarization, was received at Spino d’Adda during CSTS propagation experi. To assess how ments, with slant path elevation angle of the elevation angle affects the results, we also simulated radio in the same links with elevation angles Olympus slant path. vertical plane of the While the results reported in [7] and [8] concern simulations based on simple models of the horizontal structure of precipitation, the results presently discussed are derived from measurements of the horizontal structure of rain. The results below have shown that the fixed system probability distribution compares very well with beacon measurements. This allows us also to be confident on the validity and reliability of mobile system results. In zigzag routes, we found that the cumulative time a given attenuation is exceeded in the mobile system is less than that in the fixed system. The detailed results depend on vehicle speed modeling and starting conditions. In ring-roads, we found that there is no significant difference between fixed and mobile systems. Straight freeways show more optimistic performance. The paper is divided into nine sections. Section II defines the probability distributions needed for system design, Section III summarizes the radar database available, and Section IV summarizes the simple modeling of the vertical structure of precipitation. Section V reports the results for zigzag routes and ring-roads, Section VI for freeways, and Section VII for different elevation angles. Section VIII compares the results to those obtained with the synthetic storm technique [7], [8], Section IX draws some conclusions. II. PROBABILITY DISTRIBUTION OF RAIN ATTENUATION FOR ANY VEHICLE When we consider a site and its fixed system , we imis applicable, in the long term, to plicitly assume that sites belonging to a more or less large geographical area centered at this site (neglecting possible orographic effects). Vehicles driven within this same area are affected by the same rain attenuation of the fixed terminals [7], [8] at any given location, but for different intervals of time. Hence, they experience different We wish to compare probability distributions with for the same rain attenuation . Since for the moving terminal the duration of fade does change, it follows that also the positive and negative time derivatives (rate of change) of fade change [7], and this fact can have a significant impact on those methods that dynamically adjust some system parameters according to the instantaneous rate of change of attenuation (e.g., power margin, bit rate, satellite tracking, etc.), in the past designed to cope with the fixed system rates of change. Now, in a geographical area, at any given time, a fraction of the total number of vehicles moving in it are started from inside the area (and eventually leave it, as in our simulations, by entering a contiguous area), and a fraction are driven into the area from its perimeter. These two mutually exclusive cases can yield two quite different distributions,
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Fig. 1. General view of the three full azimuth scans (not in scale) with constant elevation angle of 3 , 5 , and 7 , combined to obtain a pseudohorizontal circular map of reflectivity at about 1000 m of height.
and , respectively, which can be estimated separately, as shown in this paper. and for a given pattern, If we know then we can design the mobile satellite system for that pattern, regardless of the origin of the user, just by weighting the two to obtain the overall distributions according to the value of as probability distribution (1) must be estimated from traffic meaRealistic values of surements or models, as outlined by [11] and [12]. In this paper, we did not pursue this task, but estimated realistic values of and and then compared them with the for the difprobability distribution of the fixed system ferent patterns and elevation angles. Notice that (1) can be generalized to determine the probability distribution of rain attenuation in a larger area made up of smaller areas with homogeneous rain-rate statistics, or an area made up of probability distributions relative to different values of a parameter (e.g., pattern, elevation angle, speed model, outage probability due only to rain, etc.) by just adding many terms weighted accordingly. The lower limit to the linear extension of the geographical area is set by the projection to of the maximum slant path length expected to be the ground under rain at a site. For a circular area centered at a reference point, this limit is equal to 2 when the satellite can be seen at any azimuth. III. RADAR DATABASE The radar has a 3.6-m parabolic reflector (38 dB gain) and 2 angular resolution. Two radar bins of 75 m were averaged to yield 150-m slant range resolution. Pulse repetition frequency is 456 Hz, 64 consecutive echoes were averaged to yield about 20% standard deviation error (i.e., about 0.8 dB) in the estimation of the reflectivity factor , receiver noise figure of about 3 dB with a dynamic range 80 1 dB, equipped with a magnetron with 475-kW peak power. The recovery time is 3 s so that the circular area of 0.45-km radius could not be observed because of the finite time taken to switch the radar between the transmit and receive modes. The maximum unambiguous range is 329 km, but data were collected only up to 150 km. The data used in this study were obtained during 1989–1992 by three full azimuth scans with constant elevation of 3 , 5 , and 7 , respectively (Fig. 1). They were combined to obtain a pseu(mm /m ) dohorizontal circular map of reflectivity factor (e.g., [13]) at approximately 1000 m of height (so that clutter is minimized) to a range of 40-km radius from the radar site, to maintain a sufficient space resolution in azimuth (at 40 km, where data are collected above a height of about 1.4 km, the arc
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is about 1.4 km). The three scans provide data in polar coordinates in the range 0.45–9.5 km (calculated at the lowest angle, ), in the range 9.5–14.3 km ( – elevai.e., – elevation), and in the range greater than 14.3 km ( – tion). The three complete scans took 90 s. We can assume that in this interval the reflectivity field does not change (“frozen”). The measured values of reflectivity were then converted into the corresponding values of rain rate (mm/h) estimated (after the by the well-known relationship Marshall–Palmer raindrop size distribution, e.g., [13]), a relationship tested against long-term rain-rate measurements with a rain gauge at Spino d’Adda [14]. The minimum observable rain rate was 0.5 mm/h at the maximum distance of 40 km, with a signal-to-noise ratio of 10 dB at the minimum value of equal to 10 (18 dBZ). The original data were then routinely inspected by the technical personnel of CSTS, the clutter was identified, and its radar bins were labeled with negative values (“flags”). From these data in polar coordinates, further processing produced 25 600 square (Cartesian) cells of side 500 m (linear spatial resolution for our simulations) relative to a square area of side 80 km (160 160 square cells) in which the originally observed circular area is inscribed, with sides parallel to the north–south (N–S) and east–west (E–W) directions. In detail, the 0.25-km area of each square cell was divided into 64 (8 8) “pixels,” a compromise for a reasonable processing time. Then, the rain-rate values originally collected in polar coordinates, and found underneath the square cell superposed, were spatially averaged to yield a rain-rate estimate of the square cell of side 500 m. Cells outside the circular area were removed, and the border cells with less than half valid pixels were also excluded. The same method of validation was used for the inner cells affected partially by clutter. More details on data acquisition and processing can be found in [15]. However, for the present simulations, we assigned suitably extrapolated from the these inner cells a value of values of the surrounding cells with valid data: this procedure is necessary because we need retain as much as possible the continuity in the horizontal extent of rain. For this purpose, each map was scanned along four directions: N–S, E–W, and along the lines at 45 from the N–S direction. When a cell labeled as affected by clutter (identified by a negative value) was encountered, different methods were devised to interpolate the missing data from the nearby valid data, according to the size of the ground clutter. 1) If valid data were only on one side of the cell considered, as for the cells in the northern part of the map, where clutter is due to the pre-Alps and the only valid data were to the south, then the cell was assigned the rain rate of the southerly neighbor. 2) If along a given direction the cell had only one cell with valid data on both sides, then a linear interpolation provided an estimate of rain rate along that direction. 3) If along a given direction there were two neighbor cells with valid data on both sides, then a cubic interpolator (four-data interpolation) provided an estimate of rain rate along that direction (we took care of possible overshoots and negative values, due to this kind of interpolation, by
limiting the maximum rain rate to 200 mm/h and by removing negative values (flags), and then proceeding with a linear interpolation). The procedure could be repeated several times if the clutter extended over more than one contiguous cell. The procedure was also adopted for the “blind” area of 0.45-km radius around the radar site. Finally, the rain rate of the cluttered cell was obtained by averaging the values interpolated along the different directions. After this processing, the total number of useful cells amounts to 20 300 relative to an area of km . In the years 1989–1992, rain events were randomly sampled because of several factors, such as availability of personnel to operate the radar, equipment’s working properly, etc. The year 1990 was then excluded because of the very few rain events available. In total, we have 10 037 maps available for the year 1989 relative to 35 rainy events in 33 days, from February to December, and 10 051 maps available for the years 1991–1992, for 33 rainy events in 32 days, from January to December. Two rain events were considered distinct if at least 30 min elapsed between the two. The total database then consists of 20 088 maps relative to 68 minutes, rainy events, lasting a total time mm/h approximately) i.e., 502.2 h during which rain ( was present in a significant part of the observed area (the procedure to activate the radar acquisition was manual). IV. RAIN ATTENUATION CALCULATION Besides knowing the horizontal structure of precipitation (from the radar maps), we need to model its vertical structure so that rain attenuation in slant paths can be calculated. This structure has been modeled with two effective layers of precipitation of different depths, discussed in detail in [16]. Starting from ground, there is rain (hydrometeors in the form of raindrops, water temperature of 20 C, layer A) with uniform rain rate (i.e., the values obtained from radar), followed by a melting layer, i.e., melting hydrometeors at 0 C (layer B). With simple physical hypotheses, calculations also show that the precipitation rate in the melting layer, termed “apparent , can be supposed to be uniform and linked to rain rate” in layer A by the relationship [16]. of the precipitation (rain and melting The height layer) above sea level at a site is assumed to be the International Telecommunications Union, Radio (ITU-R) 0 C isotherm height above sea level [17], i.e., for northern latitudes, km, where is the site latitude ), m and in degrees. At Spino d’Adda ( the estimated average precipitation height above the ground m, according to ITU-R. The depth of is the melting layer (layer B) is 400 m, regardless of the latitude m is depth of rain of the site [16], so that alone (layer A). The two layers are used to describe, on the average and effectively, all rain events made up of the two main types of precipitation, i.e., stratiform and convective [16]–[18]. Notice, however, that if we used a different model of the vertical structure of the precipitation, although the absolute values of rain attenuation could change, the comparison we wish to make between the fixed and the mobile system, and the general
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conclusions discussed in Section IX would not change. In any case, the test carried out below has shown that our effective modeling of the vertical structure of precipitation with two layers, neglecting a possible third layer above layer with frozen particles, is statistically reliable for long-term statistics at frequencies up to at least 20 GHz. Rain attenuation (dB) is calculated as a line integral (approximated, of course, with a sum of discrete terms) of the spe(dB/km) [19] [in [19], is cific rain attenuation termed and is termed ], according to the values of rain rate found in the cells sampled by the projection at ground of the slant path, and to the layer (2) where
and
slant coordinate (at elevation angle ); slant length in layer A; slant length in layer B; specific rain attenuations in layer A and B, given by
(3) depend on the electromagnetic wave Parameters and (carrier) frequency and polarization, raindrop size distribution, and hydrometeor temperature. A discussion on using the same power law formula for computing the specific rain attenuation also in layer B is reported in [18]. For water temperature of 20 C, they are directly given by the ITU-R [20] as a function of frequency and polarization, after the Laws and Parson raindrop size distribution. The values for the melting layer (drops at 0 C) are given in [21], where there are also the 20 C values recommended by the ITU-R. The ITU-R provides also the formulas to interpolate in frequency and in polarization these parameters [20]. In the following, we have assumed circular polarization because it yields attenuation values in between those of the horizontal (larger) and vertical (smaller) polarization, and independent of slant path elevation angle, so that we need only four constants for our simulations. At 19.77 for layer GHz, we have calculated for layer B ( C). We A ( C) and know that the numerical values of and can change, even significantly, when they are calculated starting from different raindrop size distributions, or even rain-rate ranges, e.g., [19]. We have not pursued this theme deeper because our results refer to a mid-latitude site and any rain intensity, for which the ITU-R constants provide a general framework. Since in the real world both the fixed and moving terminals would measure the same value of rain attenuation , but for a different interval [7], [8], is calculated only once for each rain-rate map, by assuming that the fixed terminal was placed at the center of the radar square cell, i.e., at the intersections of streets. To force the moving terminal to measure the same value,
the vehicle was driven through the center of the cell, and its attenuation did not change along the distance through that cell. The quantity that changes from a vehicle to the fixed terminal is the duration of a given fade and its rate of change. Let us consider first the slant path to satellite Olympus, with elevation angle . The number of useful cells is less than 20 300 because we excluded some cells for the following argument, applicable to both the moving and the fixed terminals. toward Olympus is Since the path length in the precipitation m and its projection at ground is thus m, the cells from which it is not possible to integrate the specific attenuation for the entire path toward the satellite (which is to the southwest direction, about 32 counterclockwise from a vector pointing to the West) had to be excluded, because we wish to be sure that both the fixed and moving terminals could always “measure” a rain attenuation relative to the complete slant path, if rain were somewhere along the path. At last, we obtained 18 205 cells, i.e., we covered 4551 km and a geographical area of linear extent (approximately 80 km) much larger than , so that the patterns of the vehicles are of significant size and variability. The number of fixed terminals is 18 205, a very large number, more than sufficient to yield a . Besides the 30.6 reliable estimate of the fixed system slant path to Olympus, we simulated, in the same vertical plane, , and (zenith). radio links with The above discussion on how to obtain the number of useful could be repeated for each new elevation cells when and would lead, of course, to a larger number of useful cells, ) to 20 300 ( ). The passing from 18 205 ( comparison could then be partially misleading because of the different geographical area observed. We have preferred to consider the same 18 205 cells for any value of to make an unbiased comparison. We can test the fixed system results, at 19.77 GHz, against two sets of beacon experimental data collected at Spino d’Adda: 1) to satellite Olympus in the year August 1992–July 1993 (one year) and 2) to the geostationary satellite SIRIO (15 W) in the years 1980–1982 (three years) at 11.6 GHz [12] and scaled to 19.77 GHz with a scaling ratio equal to [22]. Since the orbital positions of Olympus and SIRIO are very close, the two slant paths are about the same path (the elevation angle was 30.6 for Olympus and 32.4 for SIRIO) so that the (scaled) experimental data of SIRIO can be used reliably for this purpose. Instead of cumulative probability distributions, Fig. 2 shows (minutes), that curves reporting the cumulative time the rain attenuation (dB) is exceeded for Olympus and SIRIO (in an average year, i.e., the total number of minutes a given was exceeded is divided, for SIRIO, by three and referred to the total time in a year, 525 600 min), and predicted with the radar simulations [in the following termed “standard” fixed ], as outlined above. Once divided by the total number of minutes of a common long term observation period (e.g., a year), these curves would yield estimates of the cumulative : there probability distributions usually considered, would be only a change in the ordinate scale. We have not done that because there is no such a common observation period since the radar data were randomly sampled, as mentioned
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Fig. 2. Cumulative time T (A) (minutes) that rain attenuation A (dB) in abscissa is exceeded for Olympus and SIRIO (in an average year, i.e., averaged over the years of observation) and predicted with the radar simulations. Frequency is 19.77 GHz, elevation angle = 30:6 .
above, and the beacon data refer to different years. However, this is by no means a limitation to the test or usefulness and reliability of the results and conclusions, as will be shown below. We can see, in fact, that the curve calculated from radar measurements is a very good estimate of Olympus measurements dB (even though the observation period is not the up to dB, the sample size of the experimental data same); for (one year) is so scarce that it is our opinion that, in this range, the radar simulations are more reliable than the Olympus measurements. This conclusion is very well supported by the fact that the radar curve is almost parallel to the SIRIO curve [which ]; can be considered a better estimate of the long-term i.e., the two curves yield about the same distribution when re. The radar has sampled so many slant ferred to the time paths (18 205), although for only 65 rainy days, that it can give the correct long-term distribution. These results confirm, once more, the well-known fact that even limited and random radar observation of the horizontal structure of rain yields very good long term statistics of point measurements, as rain rate, or line integrals, as rain attenuation. In conclusion, the radar simulation yields a good estimate of (in the form of cumulative time) for the the long-term Spino d’Adda area described above. As a consequence, we can , for a given pattern, can also confide that the long-term be a reliable estimate of real measurements, and it can thus be compared to the result of the fixed system. V. TERMINALS DRIVEN IN ZIGZAG ROUTES RING-ROADS
AND IN
A. Definition of Parameters To make the simulations simpler, but nevertheless significant, m, i.e., same we considered a grid of squares of side as radar cell dimensions, which simulates “city blocks” with . The streets intersection coincided with the center side of the radar cell, and, as mentioned above, the fixed terminal was placed at these intersections. A vehicle was driven with a
constant speed along a cell distance , independently from the previous or the following cell, and randomly extracted from a log-normal probability distribution with median value km/h, or km/h, and standard deviation equal to 0.221 Np for both (the average value of the Gaussian distribuand its standard deviation is 0.221), with maxtion is imum allowed values equal to 72 and 108 km/h, respectively. In Europe, these two probability distributions can model urban km/h) traffic in slow-speed routes (termed Model I, and suburban traffic in high-speed routes (Model II, km/h) [8]. We have not modeled the speed change in successive cells because this was not the task of our work; moreover, we are not aware of any general model. The vehicle starting point was chosen randomly and uniformly within the useful area (18 205 cells) (inside) or at its perimeter (outside): in the latter case, the vehicle was forced into the useful area for at least one cell. Notice, however, that the vehicle is supposed to be already running so that the “starting point” refers only to its position when we start observing both fixed and moving terminals, i.e., when we have the radar maps available. At each intersection, the “driver” decided where to go: we assumed that the vehicle was allowed to go straight with probability , or to turn to the right , or to the left , with equal , so that ; no probability U-turns or stops were allowed. These restricted conditions are, of course, arbitrary but nevertheless allow to appreciate the sensitivity of zigzag routes to these parameters. Square ring-roads within the area were also investigated (see Section V-D). When one map is over (after 90 s), space and time continuities are maintained by driving the vehicle in the same segment and in the new rain map. The attenuation measured in a cell by a vehicle is not sampled s. uniformly since it lasts, at most, a time interval Since is a log-normal random variable and is a constant, it follows that also the sampling interval is log-normal when the full distance is covered in a cell. is given a duration equal to the exact interval . A vehicle was not further considered as soon as 1) it left the useful area (and it “entered” a contiguous area) or 2) there were no radar maps left for the same rain storm. To obtain reliable statistics at a cumulative time as low as 10 min, we found that at least 50 independent vehicles must be driven in the zigzag and freeway routes (Sections V-B and VI) and 16 in the ring-roads (Section V-D). These tests are not shown for brevity since they are similar to those reported in [8]. In summary, the results below are averaged over 18 205 terminals for the fixed system, and over 50 or 16 terminals for the mobile system. The following cases were not considered. 1) Vehicles that stopped within the area, thus ending their journey, while it was still raining somewhere in the area. These cases should not be considered because the fixed system terminals do not “stop,” i.e., they are continuously observed for 24 hours a day. The vehicle counterpart is an indistinct running vehicle for 24 hours a day, not one in a garage. We must consider a vehicle only when the indistinct user must use its transceiver to communicate, i.e.,
MATRICCIANI: EXPERIMENTAL RAIN ATTENUATION STATISTICS
Fig. 3. Cumulative time (minutes) that rain attenuation A (dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems for p = 0:0; 0:5; 0:8; and 1. Vehicles started inside; urban traffic (Model I), D = d = 500 m.
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Fig. 4. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems for p = 0:0; 0:5; 0:8; and 1. Vehicles started inside; suburban traffic (Model II), D = d = 500 m.
he cannot use a fixed system facility. In the simulation, the vehicles start their journey at the first rain map as the fixed terminals do, so that it is like observing both for 24 hours a day. 2) Vehicles that, within their journey, stop and then go at an intersection, and so on. This situation is likely to occur in a zigzag route, and the stops will make the vehicles statistics closer to those of the fixed system. Unfortunately, we do not know the proportion of this time compared to that of a total trip. In any case, if this proportion were known, it could again be taken into account in (1) or (5) below, by introducing the fixed system statistic weighted accordingly. B. Zigzag Routes and a Useful Figure of Merit Fig. 3 shows the cumulative time (minutes) exceeded in the with Model I (urban traffic) and vemobile systems hicles started inside the useful area. Since the vehicles can be must be compared to the driven across any radar cell, standard cumulative time that the same value of is exceeded in , averaged over the 18 205 fixed the fixed system, i.e., terminals of the useful area. We notice the following. . 1) For a given value of , the smaller the value of 2) The higher the value of 3) For is not reduced significantly. These findings are sound: when a vehicle started inside is driven in zigzag routes with low values of , it is likely to stay longer in the area than a vehicle driven with high values of , so that the two measure different fade durations. for vehicles driven according to Fig. 4 shows Model II (suburban traffic) and started inside the useful area. The results are more favorable to the mobile system since the vehicles are more likely to leave the area earlier because of the higher speed.
Fig. 5. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems for p = 0:5, 0.8, and 1. Vehicles started on the perimeter; urban traffic (Model I), D = d = 500 m.
Fig. 5 shows for Model I (urban traffic) and vehicles driven from a point, randomly and uniformly selected along the perimeter of the useful area. The vehicle is forced into it for the first 500 m, randomly along the E–W, W–E, N–S, or S–N directions, according to its position along the perimeter. For these vehicles, performance is much better, i.e., they meafor the same rain attenuation . A similar sure a lower result, but more favorable to the mobile system, is also found for vehicles driven from the perimeter according to Model II (suburban traffic), Fig. 6. In both Models I and II, the performance is significantly insensitive to , and it is more favorable to the decreases (now a vehicle is more likely to mobile system as is low). leave the useful area when From the results shown in Figs. 3–6, we notice that for a given can be scaled from value of rain attenuation , any according to the simple expression (4)
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TABLE I AVERAGE VALUE OF THE PROBABILITY FACTOR FOR URBAN (MODEL I) AND SUBURBAN (MODEL II) TRAFFIC FOR VEHICLES STARTED FROM THE PERIMETER OF THE USEFUL AREA, D = 500 m, AS A FUNCTION OF IS AVERAGED IN THE THE PROBABILITY OF GOING STRAIGHT p . RANGE 1 < A 30 dB
Fig. 6. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems for p = 0:0; 0:5; 0:8; and 1. Vehicles started on the perimeter; suburban traffic (Model II), D = d = 500 m.
Fig. 7. Probability factor (A) as a function of rain attenuation A(dB), for p = 0:0; 0:5; 0:8; and 1. Vehicles started inside; urban traffic (Model I), D = d = 500 m (from Fig. 3).
with a probability scaling factor almost independent of attenuation, a result also found in the simulations performed with the synthetic storm technique [8]. obtained As an example, Fig. 7 shows the values of dB, is practifrom Fig. 3. We notice that for means that the cumulacally a constant. Now, a constant and referred to the time tive probability distributions of are identical, although the unconditional ones are not, as shown in Fig. 3: fixed and moving terminals measure the same rain attenuation and in the same time proportion. markedly increases only The probability scaling factor dB), a feature also found for for very low attenuation ( the other patterns simulated. The tendency toward unity, i.e., no distinction between the fixed and mobile terminals performance, is physically sound since a very low attenuation is likely to be induced by the very low rain rates of widespread rain, a type of rain which is likely to change very little within the
useful area and to be static, so that it affects all terminals in the same way. For instance, in the slant paths considered, a uniform 0.5-mm/h rain (the minimum rain rate detected by radar) yields dB. As a consequence, in geographical areas with predominant light and widespread rain, the mobile terminals should experience less optimistic rain attenuation statistics. can thus be obtained from by simply according to (4) with a constant value of scaling . These same observations can be made for the other cases shown above and in the following. This factor can be assumed as a figure of merit of the performance of the mobile system, compared to that of the fixed one, when they are affected by rain. This parameter is very useful because it is largely independent of frequency, so that the findings of this paper can be applied to systems working at carrier frequencies other than 19.77 GHz. calculated in the Table I shows the average values of dB (to avoid the situation that the peak range dB biases the almost constant value of found for for m, for vehicles started significant values of ) for from the perimeter, and for Models I and II. Values of have not been simulated because the vehicles would likely be driven out of the useful area after a very short time: for can be interpolated with a decreasing linear law to for . Tables II and III show the average values of for vehicles started inside the useful area (column m). of A constant and (4) allow us to write the overall only (1) as a function of (5) as a which is a useful expression that directly yields , for which many measurements or prediction function of methods are available. C. Sensitivity to Street Grid Dimension As for the sensitivity to street grid dimension , we have simulated zigzag routes in city blocks with sides multiple of m and m (the radar cells 500 m, i.e., of constant rain rate of 500-m side, of course, do not change),
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TABLE II AVERAGE VALUE OF THE PROBABILITY FACTOR FOR URBAN TRAFFIC (MODEL I) FOR VEHICLES STARTED INSIDE THE USEFUL AREA AS A FUNCTION OF STREET GRID DIMENSION D AND PROBABILITY OF GOING STRAIGHT p . IS AVERAGED IN THE RANGE 1 < A 30 dB
TABLE III AVERAGE VALUE OF THE PROBABILITY FACTOR FOR SUBURBAN TRAFFIC (MODEL II) FOR VEHICLES STARTED INSIDE THE USEFUL AREA AS A FUNCTION OF STREET GRID DIMENSION D AND PROBABILITY OF GOING STRAIGHT p . IS AVERAGED IN THE RANGE 1 < A 30 dB
Fig. 8. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems for the indicated ring-roads; urban traffic (Model I), results averaged in clockwise and counterclockwise.
in Tables II and III the average values of (in the range dB) for Model I (urban traffic) and Model II (suburban traffic). The better performance in larger blocks clearly appears in the smaller values of . Notice that when approaches unity there is little distinction in the values of . D. Ring-Roads
and only for vehicles started inside the useful area. These new simulations can be seen as special cases of the simulation with m: for instance, when m, a vehicle is driven in a straight line for four elementary cells with the same speed, and only at the fourth cell does it have to choose where to go, , and and can change according to values assumed by its speed. This simulation does change the process of successive values of speed by introducing a deterministic relationship in the values that speed takes in the four contiguous elementary cells. In the case of 1000 m, two contiguous cells are, of course, considered. and speed modeling, the general results as For a given , and are similar to those found with a function of m, but with a more optimistic performance (lower values of ) compared to the standard fixed system. For the , the results concerning difsame modeling of are more favorable to the mobile terminal ferent values of as increases from 500 to 2000 m (lower values of ). In this case, the better performance for larger values of is due to the longer average distance covered in straight routes, and thus to a higher probability of leaving the area sooner. These results are confirmed by those obtained in the freeway routes with urban traffic (Section VI). Instead of showing curves of cumulative time (of the same nature as those shown in Figs. 7–10), we have preferred to report
The ring-roads simulated are square rings centered at the radar site of side length 8, 16, 20, 25, 30, and 40 km. The km (64 cells) to perimeter ranges from km (320 cells). This pattern can represent the kind of circular routes that public buses (or trains) follow in a small–medium or large European city, such as Milan. The simulations have been performed only on the 1991–1992 database, but nevertheless the insight we get is very clear, as will be shown in the following. Vehicles are driven according to Model I (urban traffic) with speed changed, as above, every 500 m, in clockwise and counterclockwise directions. for the different ring-roads, averFig. 8 shows aged in clockwise and counterclockwise directions for each , i.e., calcuring-road, and compared to the standard calculated in 1991–1992 lated for the total database [ is almost coincident with the standard curve]. We have averaged the results of clockwise and counterclockwise routes because there is no significant difference between the two (not shown for brevity). While the inner ring-roads (8–16–20 km) yield larger values , for a given , the outer ones (25–30–40 km) yield of and, more interestvalues almost equal to the standard ingly, they show that there is no significant difference between fixed and moving terminals. The outer routes yield results closer because they sample more cells that are to the standard more distant, and thus can match more closely the sample size of the total useful area. In the case of a deterministic route, such as fixed ring-roads, it to a fixed system cumulative is significant to compare , time averaged over the same cells of the ring-road,
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Fig. 9. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed system (dots) and in the fixed systems of the indicated ring-roads.
Fig. 10. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems. Freeway slow traffic (Model I) for the indicated directions.
since the vehicles must always be driven along these same cells. for the ring-roads and the standard Fig. 9 shows . Notice that the are not significantly difand, more interestingly, they are not different from , Fig. 8. ferent from the corresponding In conclusion, moving and fixed terminals perform in the same way. Ring-roads make the vehicle measure a given rain attenuation for the same time intervals, on the average, of the fixed receivers. In the limit, the performance of a fixed receiver can be imagined as the performance of a receiver on a vehicle driven in a ring-road with a radius approaching zero. VI. FREEWAY ROUTES In these simulations, the vehicles always enter the useful area from the perimeter, according to different directions, and are driven along a straight line through the radar site, at a constant speed extracted from a log-normal probability distribution with km/h and Np, a model median value (Model III) valid for (fast) freeway traffic [8], with maximum speed limited to 180 km/h. Simulations have been also conducted with Model I (urban traffic) at a constant speed to simulate the heavy and steady traffic in freeways near or in big cities in the busy hours. Eventually, the vehicle leaves the area. Of is defined, being always. Notice that course, only this type of simulation, with a convenient speed model, can also be applied to ships or trains. The routes simulated are: 1) from north to south (NS) and from south to north (SN); 2) east–west (EW) and west–east (WE); 3) 45 measured counterclockwise with respect to east [i.e., vehicles driven from southwest (SW) to northeast (NE)], and 225 (NE to SW); 4) 135 (SE to NW) and 315 (NW to SE); 5) north to south (N–S) and south to north (S–N); 6) east to west (E–W) and west to east (W–E). for the indicated routes and Figs. 10 and 11 show for speed Model I. Figs. 12 and 13 show results for Model reported is the standard curve III. The fixed system
Fig. 11. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems. Freeway slow traffic (Model I) for the indicated directions.
(18 205 cells) because the fixed system distributions averaged over the cells covered by the vehicles in their deterministic patterns are not significantly different from the standard curve (Fig. 14). From these figures, we can conclude the following. 1) Model I predicts a less favorable performance than Model III, as expected. – dB), there is no 2) For low values of attenuation ( significant difference between routes (there is isotropy) and directions (there is symmetry), a result physically sound because of the low and widespread rain involved. Notice, however, that symmetry and isotropy are much more pronounced for Model III than for Model I, a result due to the higher speeds, which “compress” time; we can describe this behavior as apparent isotropy and symmetry, both functions of speed modeling and rain attenuation. dB), 3) For medium–high values of attenuation ( asymmetry and anisotropy may appear, even in the Model III results, e.g., along the S–N direction (Fig. 13).
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Fig. 12. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems. Freeway fast traffic (Model III) for the indicated directions. The two unlabeled coincident curves refer to the SE–NW and SW–NE directions.
Fig. 13. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed (dots) and in the mobile systems. Freeway fast traffic (Model III) for the indicated directions. The three unlabeled coincident curves refer to the N–S, E–W, and W–E directions.
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Fig. 14. Cumulative time (minutes) that rain attenuation A(dB) in abscissa is exceeded in the standard fixed system (dots) and in freeway fixed systems. The unlabeled coincident two curves above the standard refer to N–S and E–W routes.
Fig. 15. Cumulatived time (minutes) that rain attenuation A in abscissa is exceeded in the standard fixed system (dots) and in the mobile system. Results averaged over all directions for Model I and Model III.
When compared to zigzag routes or ring-roads, these results are more optimistic. Figs. 10–13 show that there is a very small probability factor , as clearly appears from the curves shown averaged over all the in Figs. 15 and 16, which report eight directions for both Models I and III. We can assume, on for Model I and for Model III. average, that Notice, finally, that since the rate of change of attenuation measured by a vehicle is equal to that measured by the fixed system divided by [7], the moving terminals must face rates of change up to 20 times (1/0.05) those of the fixed system. VII. SIMULATIONS IN SLANT PATHS WITH HIGHER ELEVATION ANGLES To assess how the elevation angle affects the results, we ( have also simulated radio links with m, m), ( m, m), 80
Fig. 16. Probability factor (A) as a function of rain attenuation A(dB) from Fig. 15.
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Fig. 17. Cumulative time (minutes) exceeded in fixed systems as a function of elevation angle, averaged over the 18 205 cells of the useful area, for the indicated slant-path elevation angles.
Fig. 18. Cumulative time (minutes) exceeded in fixed systems as a function of elevation angle for the indicated rain attenuation A(dB).
( m, m) in the same vertical plane of the 30.6 slant path to Olympus, and paths with 90 ( m) elevation angle (zenith). For this study, we have used the 1991–1992 database only. Fig. 17 shows the cumulative time exceeded in fixed systems as a function of elevation angle (the 80 curve is just above the 90 curve, so it is not shown) and averaged over the 18 205 cells of the useful area. For a given cumulative time, decreases as increases, as expected; for a given , the cumulative time decreases as increases. Fig. 18 shows for some values of . We notice, in particular, that the total decreases as increases from 30.6 time for which ranges from to 90 : the ratio , when , to , , i.e., at most a reduction of about 20% comwhen ). The ratio is a steeper pared to the Olympus path ( decreasing function as increases because the higher the elevation angle, the shorter the rainy path length and the less likely that a rainy area is intercepted with intense rain.
Fig. 19. Ratio between the rain attenuation exceeded in the slant path with the indicated elevation angle and that exceeded in the Olympus path ( = 30:6 ), as a function of the cumulative time (minutes). Horizontal lines represent the simple scaling model.
Often, to scale measured in a slant path with elevation angle to that predicted for a slant path in the same vertical plane, but with a different elevation angle, designers use a simple model that assumes a rain, of a given height, infinitely extended horizontally. In this modeling, turns out to be proportional to path length so that the ratio between the two at, with tenuations can be written as in our case. Fig. 19 shows the ratios obtained from the simulations and calculated according to the formula just mentioned. This comparison shows that as long as we (obviously) consider cumulain both slant paths, the theoretical tive times for which model (horizontal lines) is a first good approximation only for elevation angles not too different (e.g., 45 ) and that it overestimates the ratio for low values of time, i.e., large values of attenuation, in the other cases. As for the mobile system, we wish to assess whether the changes or not, compared to that probability scaling factor for found for the reference elevation angle. Fig. 20 shows vehicles started inside or outside the useful area, driven according to Model I (urban traffic) in zigzag routes with m and , compared to the results obtained in same cases . The probability factor does not and database with (this anomaly may change significantly, except for arise because of sampling rain cells of particular extension). Similar results have also been obtained for freeway routes, not shown for brevity. In conclusion, to a first good approximation and for , the probability scaling factor is fairly independent of elis scaled to , we can apply the evation angle. Once to the new slant path to obtain from values of . VIII. COMPARISON WITH RESULTS OBTAINED WITH SYNTHETIC STORM TECHNIQUE In [8], we used the synthetic storm technique [18] to estimate the probability scaling factor in the case of speed Model I,
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IX. CONCLUSION
Fig. 20. Probability factor (A) as a function of rain attenuation A(dB) for the different elevation angles (dots represent the reference case, = 30:6 ). Upper set of curves: vehicles started inside; lower set: vehicles started on the perimeter. Urban traffic (Model I), D = 500 m, p = 0:5.
zigzag routes, with m and the same values of . , in Those simulations show that is around 0.2–0.3 for the optimistic case in which the probability of encountering rain is the same for all observers (fixed or in motion). This numerical result is very similar to that presently found for vehicles started m (Table I). outside the useful area with The probability scaling factor could be doubled when the probability that a vehicle encounters rain is twice that of the fixed receiver. As a consequence, may easily reach values around 0.6: these values are within the upper values presently found with speed Model I and vehicles started inside, (Table II, m). As for the freeways, the values presently obtained with Model III and Model I (Figs. 15 and 16) agree very well with those found with the simple rectilinear motion simulations for Model III and first studied (see [7, Fig. 4]), i.e., – for Model I, once the same speed modeling is used, for 1) the “most favorable” case, in which rain storms and vehicles move along the same straight lines but in opposite directions, or 2) for the case in which the vehicles move in straight lines, the direction of which is uniformly distributed in the 0–360 range, and the rain storms move also in straight lines with direction uniformly distributed in 0–180 range. We can provisionally conclude that, given a model for , the synthetic storm technique can be used to predict a first estimate of the performance of moving terminals. In zigzag routes, the values of estimated by assuming the same probability of encountering rain (optimistic case), for both fixed and moving observers, can stand as the values presently obtained when vehicles are driven from the perimeter of the useful area. When doubled (pessimistic case), the values of can stand for those presently obtained when vehicles are driven from inside the area. Ring-roads (“loops”) were not considered: now, we know that moving terminals in ring-roads do perform as the fixed terminals (Section V-D). In rectilinear motion, the simple simulations performed in [7] for the “most favorable” case can yield reliable average results for freeways.
We have investigated how the cumulative time , (dB) measured in a fixed satellite a given rain attenuation , applicable to a system, is transformed to time mobile satellite system. We have investigated three general patterns according to how vehicles are driven: zigzag routes and ring-roads to simulate city patterns and straight routes to simulate freeways. The vehicles’ speed was modeled as a lognormal random variable after the mathematical models derived from measurements. In zigzag routes, for a given value of rain attenuation , we . The detailed results depend found that on vehicle speed modeling and starting conditions, i.e., inside the area or from the perimeter. These two mutually exclusive situations must be both studied and known to design mobile satellite communication systems [(1)]. In ring-roads, there is no improvement compared to the fixed system. As for straight freeways, the results have shown that ; can change significantly in different straight lines and in opposite directions (anisotropy and asymmetry) for medium–large attenuation; only at low attenuation, directions and routes are indistinguishable (isotropy and symmetry). When compared to zigzag routes or ring-roads, the performance of vehicles driven in freeways is the most optimistic. When the elevation angle is changed, the probability scaling . Once is factor is fairly independent of , for , we can apply the values of to the new slant scaled to from . path to obtain Since the radar rain maps used for the simulations are reliable estimates of the horizontal structure of rain, we think that the estimated results can stand as experimental results, as for the fixed system (Fig. 5). These simulations are very useful because they yield design statistics for geographical areas with weather characteristics similar to that found in the Po Valley, otherwise very difficult, lengthy, and costly to obtain from beacon measurements. Mobile satellite communication is not affected only by rain but also by shadowing, blockage, and multipath. These disturbances can plague the channel for such a long time that they establish system performance for a large range of outage probabilities, including the very low ones, when also rain attenuation contributes to the outage. However, at the end of a future technological breakthrough in “smart” antennas (which supposedly will largely reduce the impact of multipath by ad hoc processing), and in absence of significant obstructions and shadowing (as may be the case with nongeostationary satellites), rain will still be there to plague the system and be the irreducible cause of fading and system outage. ACKNOWLEDGMENT The author would like to thank F. Anelli, M. Scotti, and D. Terreni, who ran the simulations as part of their graduation theses in electronics engineering at Politecnico di Milano.
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REFERENCES [1] A. C. Densmore and V. Jamnejad, “A satellite-tracking K- and K -band mobile vehicle antenna system,” IEEE Trans. Veh. Technol., vol. 42, pp. 502–513, 1993. [2] K. S. Miles, K. Dessouky, B. Levitt, and W. Rafferty, “A satellite-based personal communication system for the 21st century,” in Proc. 3rd Int. Mobile Satellite Conf., Ottawa, Ont., Canada, 1990, pp. 56–63. [3] S. K. Barton and J. R. Norbury, “Future mobile satellite communication concepts at 20/30 GHz,” in Proc. 3rd Int. Mobile Satellite Conf., Ottawa, Ont., Canada, 1990, pp. 64–69. [4] W. W. Wu, E. F. Miller, W. L. Pritchard, and R. L. Pickholtz, “Mobile satellite communications,” Proc. IEEE, vol. 82, pp. 1431–1447, 1994. [5] S. Ohmori and M. Matsumoto, “Global multimedia mobile satellite communications system (GMMSS),” in Proc. 5th Int. Mobile Satellite Conf., Pasadena, CA, 1997, pp. 421–426. [6] C. Loo and J. S. Butterworth, “Land mobile satellite channel measurements and modeling,” Proc. IEEE, vol. 86, pp. 1442–1462, 1998. [7] E. Matricciani, “Transformation of rain attenuation statistics from fixed to mobile satellite communication systems,” Trans. Veh. Technol., pp. 565–569, 1995. [8] E. Matricciani and S. Moretti, “Rain attenuation statistics useful for the design of mobile satellite communication systems,” IEEE Trans. Veh. Technol., vol. 47, pp. 637–648, 1998. [9] C. Capsoni, A. Pawlina, and M. Politi, “Performance of the meteorological radar at Spino d’Adda as a device for propagation studies,” Alta Frequenza, vol. 48, pp. 392–396, 1979. [10] “Special issue on the SIRIO program in the tenth year of satellite life,” Alta Frequenza, vol. 56, pp. 5–184, 1987. [11] D. Lam, D. C. Cox, and J. Widom, “Teletraffic modeling for personal communications services,” IEEE Commun. Mag., pp. 79–87, Feb. 1997. [12] C. Rose and R. Yates, “Location uncertainty in mobile networks: A theoretical framework,” IEEE Commun. Mag., pp. 94–101, Feb. 1997. [13] R. J. Doviak and D. S. Zrnic, Doppler Radar and Weather Observations. San Diego, CA: Academic, 1984. [14] C. Capsoni, M. Mauri, E. Matricciani, A. Paraboni, A. Pawlina, and J. P. V. Poiares Baptista, “Radar data analyses for propagation studies,”, Final Rep. ESTEC 4680/81/NL/MS(SC), Sept. 1983. [15] A. Pawlina Bonati, “Strutture piovose orizzontali sulle mappe radar: Nuove caratteristiche basate sulla nuova collezione dati” (in Italian), in Proc. RADME 94, Rome, Italy, 1994, pp. 238–252.
[16] E. Matricciani, “Rain attenuation predicted with a two-layer rain model,” Eur. Trans. Telecommun. Related Technol., vol. 2, pp. 715–727, 1991. [17] ITU-R, “Rain height model for prediction methods,” in Propagation in Non-Ionized Media, Rec. 839, Geneva, Switzerland, 1992. [18] E. Matricciani, “Physical-mathematical model of the dynamics of rain attenuation based on rain rate time series and a two-layer vertical structure of precipitation,” Radio Sci., vol. 31, pp. 281–295, 1996. [19] R. L. Olsen, D. V. Rogers, and D. B. Hodge, “The aR relation in the calculation of rain attenuation,” IEEE Trans. Antennas Propagat., vol. AP-26, pp. 318–329, 1978. [20] ITU-R, “Specific attenuation model for rain for use in prediction methods,” in Propagation in Non-Ionized Media, Rec. 838, Geneva, Switzerland, 1992. [21] D. Maggiori, “Computed transmission through rain in the 1–400 GHz frequency range for spherical and elliptical drops and any polarization,” Alta Frequenza, vol. 50, pp. 262–273, 1981. [22] G. Drufuca, “Rain attenuation statistics for frequencies above 10 GHz,” J. Rech. Atmos., vol. 1–2, pp. 399–411, 1974.
Emilio Matricciani was born in Italy in 1952. After serving in the army, he received the Laurea degree in electronics engineering from Politecnico di Milano, Milan, Italy, in 1978. That year, he joined the same university as a recipient of a research scholarship. In 1981, he became an Assistant Professor of electrical communications. In 1987, he joined the Università di Padova, Padua, Italy, as Associate Professor of microwaves. Since 1991, he has been with Politecnico di Milano as Associate Professor of electrical communications. His research activity is mainly in the field of satellite communications at frequencies above 10 GHz, both for fixed (SIRIO, Olympus, and Italsat satellites experiments) and mobile systems. Besides institutional activities (lectures and research), he teaches technical writing to students in short courses. He is interested in the general aspects of communicating scientific and technical information.
