Rain attenuation prediction and modeling for line-of-sight links on terrestrial paths in South Africa

Transcription

1 RADIO SCIENCE, VOL. 42,, doi: /2007rs003618, 2007 Rain attenuation prediction and modeling for line-of-sight links on terrestrial paths in South Africa M. O. Fashuyi 1 and T. J. Afullo 1 Received 3 January 2007; revised 6 July 2007; accepted 30 July 2007; published 20 October [1] The different rain attenuation prediction models proposed by different authors on terrestrial paths are studied in this paper. Subsequently, for paths not exceeding 22 km, the rain attenuation exceeded for 0.01% of the time for these four geographical locations is estimated for South Africa using the ITU-R Model, the Crane Global model, and the Moupfouma model, at different frequencies. Finally, the predicted attenuation values are compared on a monthly basis, as well with the measured upper and lower attenuation bounds for a 6.73-km line-of-sight link operating at 19.5 GHz in Durban. Citation: Fashuyi, M. O., and T. J. Afullo (2007), Rain attenuation prediction and modeling for line-of-sight links on terrestrial paths in South Africa, Radio Sci., 42,, doi: /2007rs Introduction [2] Rainfall is a natural and time varying phenomenon that varies from location-to-location and from year-toyear. Above a certain threshold of frequency, attenuation due to rainfall becomes one of the most important limits of the performance of line-of-sight (LOS) microwave links [Moupfouma, 1984; Green, 2004]. In the temperate climates this frequency threshold is about 10 GHz, while in the tropical climates and in equatorial climate particularly, the incidence of rainfall on radio links becomes important for frequencies as low as about 7 GHz, since raindrops are larger than in the temperate climate [Moupfouma, 1984; Moupfouma and Tiffon, 1982]. Therefore, in the planning of terrestrial line-of sight systems, accurate prediction of rain induced attenuation on propagation paths is vital [Segal, 1986]. [3] The estimate of rain attenuation on terrestrial radio path is usually derived from observed rain rates in the geographical area considered [Moupfouma, 1984; Ajayi et al., 1996]. Most of the methods proposed for predicting rain induced attenuation make use of the rainfall cumulative distribution measured at a point [Moupfouma, 1984]. Certain authors have used the concept of equivalent path average rain rate which is obtained by multiplying the point rain rate for the time percentage of interest by a reduction factor, while other authors use an effective path length, the value of which is obtained by 1 School of Electrical, Electronic, and Computer Engineering, University of KwaZulu-Natal, Durban, South Africa. Copyright 2007 by the American Geophysical Union /07/2007RS multiplying the actual path length by a reduction coefficient [Moupfouma, 1984]. [4] In our previous paper [Fashuyi et al., 2006], the cumulative distribution of rainfall-rate in South Africa has been estimated using 1-hour rainfall rate statistics measured by the South African Weather Services (SAWS) in different climatic regions for the years for 12 different meteorological stations. This data has been processed and converted to the ITU-R recommended integration time of 1-minute for Durban [Fashuyi et al., 2006]. [5] For the purpose of this paper, three established attenuation models have been utilized for the prediction of rain attenuation in South Africa. These are: the ITU-R model, the Crane Global model, and the Moupfouma model. This is effected by using R 0.01, defined as the rain rate value that is exceeded in a region only 0.01% of the time, with a 1-minute integration time, averaged over a period of 5-years, for the different geographical locations in South Africa (Table 1). 2. Specific Rain Attenuation [6] A fundamental quantity in the calculation of rain attenuation statistics for terrestrial and earth-space paths is the specific attenuation g or attenuation per unit distance [Olsen et al., 1978]. Two general approaches have been used to calculate g by various authors: (1) a theoretical method employing a uniform distribution of raindrops modeled as water spheres or more complex shapes; and (2) an empirical procedure based on the approximate relation between g and rain rate R given as [Olsen et al., 1978]: g ¼ kr a ð1þ 1of15

2 Table 1. Annual and Averaged R 0.01 Statistics for Each Geographical Location Location 2000, mm/h 2001, mm/h 2002, mm/h 2003, mm/h 2004, mm/h , mm/h ITU-R P.837-1, mm/h ITU-R P.837-4, mm/h Durban Cape Town Pretoria Brandvlei Equation (1) is known as the power-law form of rain specific attenuation [Zhang and Moayeri, 1999], where R is the rain rate in mm/h, k and a are power law parameters, which depend on frequency, raindrop size distribution, rain temperature, and polarization. This form is the method adopted in this paper to compute the specific attenuation. Values for k and a for the frequency range GHz were calculated for raindrops with the assumed shape of oblate spheroids, at the temperature of 20, using the drop size distribution proposed by Laws and Parsons [1943], terminal velocity following Gunn and Kinzer [1949], and refractive index values according to the model of Ray. These values were adopted by the ITU-R recommendation [ITU-R, 2003]. [7] To find the total path attenuation due to rain, it is necessary to know the specific attenuation or the rain rate exceeded for the percentage of time of interest and the raindrop size distribution upon which the coefficient k and a depend [Ajayi et al., 1996]. 3. Existing Attenuation Prediction Models 3.1. ITU-R Rain Attenuation Model [8] The ITU-R P [ITU-R, 2001] gives a simple technique that may be used for estimating the long-term statistics of rain attenuation. The path attenuation is obtained from: A 0:01 ¼ g R d eff ¼ g R rd db ð2þ Here d eff is the effective path length of the link by multiplying the actual path length d by a distance factor r, given by: d eff ¼ rd ð3þ r is a factor which reduces in magnitude as d increases. It is given by: r ¼ 1 1 þ d=d 0 ð4þ d 0 is a rainfall-rate-dependent factor, introduced to reflect the fact that the greater the intensity of rainfall in a storm, the smaller the physical dimensions of the storm are. It is given by [ITU-R, 2001; Hall et al., 1996; Pozar, 1988]: d 0 ¼ 35e 0:015 R 0:01 ð5þ This is valid for R mm/h. For R 0.01 > 100 mm/h, the value 100 mm/h is used in place of R The prediction procedure outlined above is considered to be valid in all parts of the world at least for frequencies up to 40 GHz and path lengths up to 60 km Moupfouma Rain Attenuation Model [9] Moupfouma [1984] proposed an empirical model for predicting rain-induced attenuation on terrestrial paths from the knowledge of 1-minute rain intensities recorded in a broad range of geographical areas and the corresponding percentages of time p during which these rain rates are exceeded. The rain induced attenuation on a line-of-sight path can be expressed as [Moupfouma, 1984]: AdB ð Þ ¼ kr a d eff ð6þ with d (km) the actual path length, d eff the effective path length, and r a reduction factor coefficient, here taking the form: r ¼ d eff ¼ rd ð7þ 1 1 þ Cd m ð8þ The attenuation A(dB) and the 1-min rain rate R (mm/h) are calculated for the same time percentage, k and a are the regression coefficients depending on frequency and polarization. To derive C and m, experimental data obtained were used. It was found that C depends on probability level p (in percentage) of interest for which data are available, and m depends on the radio link path length and its frequency. The resultant formula for the path length reduction factor is given by: 1 r ¼ p 1 þ 0:03 0:01 bd m ð9þ 2of15

3 Figure 1. Rain attenuation prediction models for terrestrial line-of-sight links for Cape Town. with mf; ð dþ ¼ 1 þ YðFÞlog e d YðFÞ ¼ 1: F 1:76 ð10þ ð11þ [10] Here F is the frequency in GHz. The b coefficient is given as a result of a best fit by: 9 d < 50 km b ¼ 0:45 for 0:001 p 0:01 >= b ¼ 0:6 for 0:01 p 0:1 ð12þ d 50 km b ¼ 0:36 for 0:001 p 0:01 >; b ¼ 0:6 for 0:01 p 0: Crane s Global Rain Attenuation Model [11] The Crane Global attenuation model was developed for use on either Earth-space or terrestrial paths. It is based entirely on geophysical observations of rain rate, rain structure, and the vertical variation of atmospheric temperature [Crane, 1996, 2003]. Rain is characteristically inhomogeneous in the horizontal, and a statistical model is required to provide an estimate of the effect of the homogeneity on the estimation of attenuation [Crane, 1996; De Miranda et al., 1998]. Crane accomplished this model by a piecewise representation of the path profile by exponential functions. An adequate model results when two exponential functions are used to span the 0 to 22.5 km distance range, one from 0 to d(r) km, the other from d(r) to 22.5 km [Crane, 1996; De Miranda et al., 1998]. The resulting attenuation model for a given rain rate is given by [Crane, 1996]: A T A T ðr; dþ ¼gðRÞ e ydðrþ 1 y dðrþ < d < 22:5 ðr; dþ ¼ gðrþ e ydðrþ 1 y þ e zd e ydðrþ e ab z 0 < d < dðrþ where A T = horizontal path attenuation (db); R = rain rate (mm/hr); g(r) = specific attenuation = kr a (db/km). ð13þ 3of15

4 Figure 2. Rain attenuation prediction models for terrestrial line-of-sight links for Pretoria. The remaining coefficients are the empirical constants of the piecewise exponential model: 9 B ¼ lnðbþ ¼ 0:83 0:17 lnðrþ c ¼ 0:026 0:03 lnðrþ dðrþ ¼ 3:8 0:6lnðRÞ u ¼ B dðrþ þ c y ¼ au z ¼ ac >= >; ð14þ 4. Estimation of Path Attenuation Using Existing Models [12] The specific rain attenuation predicted for the 4 climatic regions above may not be too adequate for the estimation of attenuation along a radio link path [Crane, 1996, 1980]. This is because of the nonuniformity of rain along a radio link and the spatial inhomogeneity present in rain. This makes it unlikely that the reference rainfall rate will extend uniformly over the length of the transmission path, unless this is very short [ITU-R, 2001]. The longer the path, the less likely it is that rain will extend over the full length of the path [Crane, 1996; Moupfouma, 1984; Crane, 1980]. [13] In this section, an estimation of the rain induced attenuation on a line-of-sight (LOS) path is calculated using existing models based on the value of R This gives path attenuation A 0.01 (in db) for radio path lengths of up to 22 km. This is tested at different frequencies for all the twelve geographical areas [Fashuyi, 2006]. In this paper, only a lower frequency of 10 GHz and a higher frequency of 40 GHz will be shown for 4 locations situated at different climatic regions in South Africa. This is to really observe how these models behave at different rain rate values and different frequencies. [14] Figure 1 shows the plots of rain attenuation for Cape Town. Cape Town is located in Mediterranean region of South Africa with an average R 0.01 of mm/h over a period of 5-years. Out of these three models, the ITU-R model gives the lowest attenuation values at both frequencies (10 GHz and 40 GHz). At 10 GHz, the ITU-R and Crane Global curves get closer as the path length increases while that of Moupfouma increases. Looking at the 40 GHz plots, the Moupfouma model behaves in a different way: as the path length increases, while the ITU-R model and the Moupfouma 4of15

5 Figure 3. Rain attenuation prediction models for terrestrial line-of-sight links for Durban. model plots get closer the Crane plot gives the highest rain attenuation along the radio link paths. [15] Figure 2 shows the A 0.01 plots for Pretoria, which is situated in the temperate region of South Africa. At 10 GHz and 40 GHz, ITU-R model gives the lowest attenuation values over the propagation path. At 40 GHz, ITU-R attenuation values are still very low as compared to the other two remaining models, while the Moupfouma model gives the highest attenuation values for Pretoria, and the results of the Crane Global model tend to be very close to the Moupfouma model. [16] Figure 3 shows the attenuation plots for Durban which lies in the Coastal Savannah region of South Africa with an average R 0.01 of mm/h. At both frequencies (10 GHz and 40 GHz), the ITU-R model gives the lowest attenuation values, while the Moupfouma model gives the highest attenuation prediction along the propagation paths. Finally, Figure 4 shows the plots for Brandvlei which is in the desert region of South Africa, with an average R 0.01 of 53.9 mm/h. At 10 GHz, the ITU-R model gives the lowest attenuation values along the propagation path. The Crane Global model (which tends to give the highest attenuation values here) intersects with that of the Moupfouma model at path lengths of 11 and 12 km, and bends a little bit more downward than that of the Moupfouma plots. At 40 GHz, the Crane Global gives the highest attenuation values along the entire propagation length. The ITU-R model gives the lowest attenuation plots up to a path length of 18 km. 5. Prediction of Rain Attenuation Model for South Africa From Measurements [17] In this section, the signal attenuation measurements over a period of one year in Durban by Naicker [2006] are utilized to model rain attenuation on a terrestrial line-of-sight links in South Africa Link Setup [18] The line-of-sight link was established between the Howard College and the Westville campuses of the University of KwaZulu-Natal, Durban. The transmitter station was setup on the roof of the Science building at the Westville campus on the azimuth angle of and about 178 m above sea level and the receiver station on the roof the Electrical Engineering building at Howard College campus on the azimuth angle of and about 145 m above sea level [Naicker, 2006; Naicker and Mneney, 2006]. These heights were able to provide sufficient clearance for the link. The path clearance from the first Fresnel ellipsoid and the line-of- 5of15

6 Figure 4. Rain attenuation prediction models for terrestrial line-of-sight links for Brandvlei. sight path are shown in Figure 5, with an effective earth radius factor value of 4/3. [19] The link is horizontally polarized and centred at an operating frequency of 19.5 GHz. The length of the link is 6.73 km and two Oregon Scientific WMR928N wireless professional weather stations were used along the path at both the receiver and the transmitter end to record the 1-minute rainfall rate, outdoor temperature, relative outdoor humidity, outdoor dew point temperature, outdoor pressure, wind speed and wind direction under the link [Naicker, 2006; Naicker and Mneney, 2006]. [20] A valuline 1 WR42/R220 parabolic antennae of diameter 0.6 m are used at both the receiving and the transmitting stations. The antennae can operate within the GHz and GHz bands and provide a gain of 38.6 dbi and a 3 db beam width of 1.9 degrees at 19.5 GHz [Naicker, 2006; Naicker and Mneney, 2006]. These parabolic antennae are protected by a weatherproof material called radome which prevents ice and freezing rain from accumulating directly onto the metal surface of the antenna (see wiki/radome). (A radome allows a relatively unattenuated electromagnetic signal between the antenna inside the radome and outside equipment.) The cabling consists of FSJ1-50A superflexible coaxial cable which produces an attenuation of 22 db per 100 m. At the transmitter, an agilent E8251A signal generator is used to provide the source signal and this can operate between 250 KHz-20 GHz. This is used in conjunction with an agilent 83018A microwave system amplifier which can operate from 0.5 GHz to 25 GHz and provide a gain of up to 27 db (see USeng/nav/ /pd.html). This setup produces unmodulated continuous wave signals at the operating frequency of 19.5 GHz. [21] At the receiver, another agilent 83018A power amplifier is used to produce additional gain before feeding the signal into the Rhodes & Schwarz FS1Q40 spectrum analyser. More details on the link setup at the receiver and the transmitter end can be seen in [Naicker, 2006; Naicker and Mneney, 2006]. The terrestrial link parameters are shown in Table 2. [22] The expected noise power in the receiver when no signal is transmitted lies between 80.5 to 80.2 dbm. This defines the noise floor. This is determined from the noise temperature of the antenna T A of 206 K (with an estimated efficiency of 63.4%, equivalent background temperature of 150 K [Pozar, 1988], and a maximum physical temperature of 303 K), the transmission line 6of15

7 Figure 5. The path profile for the 6.73 km terrestrial line-of-sight link from the Howard College campus to the Westville campus [Naicker, 2006; Naicker and Mneney, 2006]. noise temperature of 93.4 K (with an attenuation of 22 db per 100 m); 83018A Agilent Amplifier (with a gain of 27 db, and noise figure of about 9.5 db at 19.5 GHz (see nav/ /pd.html) with noise temperature of K; thus resulting in total receiver noise temperature of K, or a noise power of 80.2 dbm [Pozar, 1988]. At the lower temperature of 287 K, the noise power is 80.5 dbm. In the measurements, this value varied from 79.5 dbm to 82 dbm. [23] Calculating for the power received P r we have: P r ¼ P t FSL þ G rant þ G tan t Losses ¼ 20 dbm 135 db þ 38:6 dbi 2:2 db 1dB ¼ 41 dbm where P t = Power transmitted (taken as 100 mw = 20 dbm); FSL = Free space loss; G rant = Receive antenna gain; = Transmit antenna gain. G tan t ð15þ Thus the power received P r expected at the receiver end of the link when a transmitting power of 100 mw is employed between Howard College and Westville campuses should be 41 dbm when there is no rain to cause any rain attenuation. Table 2. Terrestrial Link Parameters for the LOS SHF System a Parameter Path length Height of transmitting antenna above the ground Altitude of transmitter station Height of receiving antenna above the ground Altitude of receiver station Carrier frequency Bandwidth under investigation Transmitting power Transmitting/receiver antenna gain Transmitting/receiver antenna beam width b Free space loss Total cabling and connection losses Clear air attenuation Receiver bandwidth a From Naicker [2006]. Description 6.73 km 24 m 178 m 20 m 145 m 19.5 GHz 200 MHz mw 38.6 dbi 1.9 degrees 135 dbm 2.2 db 1 db 100 khz 1 GHz b The beam width of an antenna is the angle enclosing the main lobe or twice the angle between the boresight direction and a reference power on the main lobe of the antenna pattern [Pozar, 1988]. 7of15

8 Figure 6. The average nonrain faded signal values for 10 months in Rain Rate and Signal Level Measurements Recorded Along the 6.73 km Link [24] The signal level measurement and its corresponding 1-minute rain rate statistics were recorded along the 6.73 km link at 19.5 GHz over a period of ten calendar months in Durban for the year 2004: February, March, April, May, June, August, September, October, November and December. This data was analyzed, processed and the average signal level for the nonrainy days for each month was determined. There were no rains in the months of May, June, and August, (which are winter months in Durban) therefore, the signal variations recorded for those three months are assumed to be due to other attenuating factors like k-factor fading, multipath fading, water vapor, and fog. [25] The nonrain faded average was determined from all the received signal level data for nonrainy days in each month and averaged over the month in question. Figure 6 shows the monthly values of the average signal level for the nonrainy days, which can also be referred to as the nonrain faded average values. It is seen that the actual signal levels are 1 4 db below the expected freespace level of 41 dbm. Several factors contribute to this; k-factor fading arises due to the fact that the value of the k used in the design is 1.33, while the median value of k-factor for Durban is 1.21, with a value of k = 0.5, exceeded 99.9% of the time [see Odedina and Afullo, 2005; Afullo and Odedina, 2006]. The worst month for k-factor fading is February (with value of k 0.2 exceeded 99.9% of the month), while the month of August has k-factor value exceeded 99.9% of the time of 0.9. Note also that the median value of k for August is 1.27 as opposed to the 1.21 for February [Afullo and Odedina, 2006]. Thus, this type of fading may contribute db over the path (see clearance of the first Fresnel zone, Figure 5, and results in Odedina and Afullo [2005] and Afullo and Odedina [2006]). [26] On the other hand, due to the rugged, hilly, and nonflat nature of the intervening terrain, multipath fading need not be a major contributor to signal variation, and may be limited to below 1 db. Water vapor attenuation is another contributor with highest contribution in summer with an average pressure of about 27 mb (see Table 3), giving an average attenuation of 0.34 db/km, or 2.2 db over the 6.7 km path. On the other hand in winter, the average water vapor pressure is about 13 mb (see Table 3), resulting in attenuation of about 0.13 db per km, and 0.9 db over the 6.7 km path [Ajayi et al., 1996]. Thus, water vapor attenuation contributes about 1 db in winter and 2.2 db in summer. Due to the coastal nature of Durban, as well as the industries, fog attenuation is also a 8of15

9 Table 3. Average Water Vapor Recorded for Durban in 2004 at 19.5 GHz Months Water Vapor, mb Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Average over mb the year contributor. At the operating frequency of the link of 19.5 GHz, an average attenuation of 0.1 db/km is expected, resulting in a value of 0.7 db along the propagation path [Hall et al., 1996]. This thus accounts for the attenuation during nonrainy days Rain Attenuation Prediction Models Along the 6.73 km at 19.5 GHz [27] The rain attenuation was modeled for the months that had rains in the year This was done for the months of February, March, April, September, October, November and December. The actual rain attenuation measurements recorded for these months are plotted for varying rain rates. Logarithmic and power estimation models are then used to obtain an analytical fit for the measurement data. The three rain attenuation models, namely, ITU-R model, Crane Global model and the Moupfouma model, are also applied on the link for d = 6.73 km and f = 19.5 GHz. The predicted attenuation values for each month are then compared with the measurements, as displayed in Figures 7 13, where y refers to path attenuation (in db) and x refers to the rain rate (in mm/h). [28] Figure 7 shows the rain attenuation plots for February in Durban. The attenuation values predicted from these other models tend to be lower than the ones from the actual measurements for this month. From the measurements, the path attenuation is seen to increase as the rain rate increases until it gets to a rain rate of above 20 mm/h, and at this point, there is slight downward trend of the actual attenuation measurement curve. The highest rain rate measured in this month is 21 mm/h and its corresponding signal attenuation value is db. Similarly, in Figure 8 which shows the attenuation plots for the month of March, it is seen that the maximum rain rate recorded is 19 mm/h, and the attenuation measured at this point is db. For this month, the attenuation predicted by the Crane model is close to the measured Figure 7. Rain attenuation for Durban in February: measurement and models at 19.5 GHz. 9of15

10 Figure 8. Rain attenuation for Durban in March: measurement and models at 19.5 GHz. Figure 9. Rain attenuation for Durban in April: measurement and models at 19.5 GHz. 10 of 15

11 Figure 10. Rain attenuation for Durban in September: measurement and models at 19.5 GHz. Figure 11. Rain attenuation for Durban in October: measurement and models at 19.5 GHz. 11 of 15

12 Figure 12. Rain attenuation for Durban in November: measurement and models at 19.5 GHz. Figure 13. Rain attenuation for Durban in December: measurement and models at 19.5 GHz. 12 of 15

13 Table 4. Rain Attenuation Models for the Rainy Months in the Year 2004 in Durban, South Africa, for a 6.73 km Path Calendar Months Predicted Model Feb A = Ln(R) Mar A = 1.399R Apr A = R Sep A = Ln(R) Nov A = Ln(R) Dec A = R attenuation, while the ITU-R and Moupfouma models underestimate the attenuation. The power estimation model and the logarithmic estimation model derived from the measurements overlap the Crane model curve. [29] The other plots are shown for April (Figure 9); September (Figure 10); October (Figure 11); November (Figure 12); and December (Figure 13). The corresponding best-fit models (based on chi-square statistic) are given in Table 4. From the measurements, one observes that the highest rain rate recorded during the attenuation measurements occurred in the summer months of September and October in Durban, with rain rates of 79 mm/h and 73 mm/h, respectively. It is also observed that, as the rain rate goes above 18 mm/h, a drop in the signal attenuation is observed. That is, as the rain rates exceed about 18 mm/h, the rain attenuation no longer increases, but rather decreases. This is to say, the lower rain rates extend uniformly along the 6.73 km propagation path, but at higher rain rate, the rain may not be able to cover the entire propagation path length. The reason behind this may be explained by the fact that the higher the rain rate, the smaller the rain cell radius, as experimentally determined by Bonati [Pawlina-Bonati, 1999; Pawlina and Binaghi, 1998]. Therefore, the rain attenuation recorded at these high rain rates reflects a corresponding diminution of the effective path length. Note that, the effective path length is introduced to incorporate the effect of nonuniformity of rain along any propagation path length. The longer the path, the less likely it is that rain will extend the full length of the propagation path. Thus the effective length d eff, decreases as the rain rate rises above 18 mm/hr, due to the corresponding decrease in rain cell radius. This therefore reduces the actual signal attenuation due to rain. [30] Figure 14 shows the measured maximum, average, and minimum rain attenuation values per rain rate for the entire year along the 6.73 km path at 19.5 GHz. The maximum and minimum plots define an attenuation bound for the given rain rates. In this figure, it is Figure 14. Rain attenuation for Durban along the 6.73 km link at 19.5 GHz for the year 2004: Maximum, minimum and average measured values versus the three models. 13 of 15

14 observed that the Crane, Moupfouma and ITU-R attenuation curves all fall within the maximum and minimum bounds up to a rain rate of 50 mm/h. Beyond this, only the ITU-R prediction stays within the bound up to 65 mm/h, while the Crane and Moupfouma plots exit and overpredict the expected attenuation. For rain rates below 30 mm/h, the Moupfouma and ITU-R plots overlap but fall below the measured average; while the Crane plot falls on the measured average plot up to 20 mm/h. Thus while on a month-to-month basis the three attenuation models appear inaccurate, on a yearly or longer-term basis, they fall within the measurement bounds for low to medium rain rates. 6. Conclusions [31] The different existing attenuation models for predicting rain induced attenuation on terrestrial line-ofsight links are studied in this paper. From the path rain attenuation predictions obtained from the ITU-R model, Crane Global model, and the Moupfouma models at different frequencies and propagation path lengths, ITU-R model gives the lowest attenuation values on all the geographical locations in South Africa, for all frequencies between 10 and 40 GHz. The Moupfouma model gives the highest attenuation prediction for the lower frequency of 10 GHz for the four regions, while the Crane Global model gives high attenuation predictions for the lower rainfall regions of Cape Town and Brandvlei at the higher frequency of 40 GHz. [32] From the measurement over 19.5 GHz along the 6.73 km link, it is seen that while there are different models depicting month-to-month attenuation variability, the final plot over the entire year indicates that, for rain rates up to 50 mm/h, all the three attenuation models fall within the measured attenuation bounds. They can thus be used to reasonably estimate rain attenuation for low to medium rain rates. However, beyond this, only the ITU- R model stays within the bound. Longer measurements are therefore needed to further buttress this conclusion. References Afullo, T. J., and P. K. Odedina (2006), On the k-factor distribution and diffraction fading for southern Africa, SAIEE Res. J., 97(2), Ajayi, G. O., S. Feng, S. M. Radicella, and B. M. Reddy (Eds.) (1996), Handbook on Radiopropagation Related to Satellite Communications in Tropical and Subtropical Countries, pp. 2 14, ICTP Press, Trieste. Crane, R. K. (1980), Prediction of attenuation by rain, IEEE Trans. Commun., 28(9), Crane, R. K. (1996), Electromagnetic Wave Propagation Through Rain, chap. 1 4, John Wiley, New York. Crane, R. K. (2003), Propagation Handbook for Wireless Communication System Design, chap. 2, CRC Press, New York. De Miranda, E. C., M. S. Pontes, and L. A. R. da silva Mello (1998), Statistical modelling of the cumulative probability distribution function of rainfall rate in Brazil, in Proceedings of URSI CLIMPARA, April, pp , Ottawa, Ont., Canada. Fashuyi, M. O. (2006), A study of rain attenuation on terrestrial paths at millimetric wavelengths in South Africa, MSc. thesis, Univ. of KwaZulu-Natal, Durban, S. Africa, Feb. Fashuyi, M. O., P. A. Owolawi, and T. J. O. Afullo (2006), Rainfall rate modelling for LOS radio systems in South Africa, SAIEE Res. J., 97(1), Green, H. E. (2004), Propagation impairment on Ka-band SATCOM links in tropical and equatorial regions, IEEE Antennas Propag. Mag., 46(2), Gunn, R., and G. D. Kinzer (1949), The terminal velocity of fall for water droplets in stagnant air, J. Meteorol., 6, Hall, M. P. M., L. W. Barclay, and M.T. Hewitt (1996), Propagation of Radiowaves, chap. 1 4, IEE Press, London. ITU-R (2001), Propagation prediction techniques and data required for the design of terrestrial line-of-sight systems, Recommend , ITU-R P Ser., pp , Int. Telecommun. Union, Geneva. ITU-R (2003), Characteristics of precipitation for propagation modelling, Recommend , 2, 3, 4, ITU-R P Ser., Int. Telecommun. Union, Geneva. Laws, J. O., and D. A. Parsons (1943), The relationship of raindrop size to intensity, Eos Trans. AGU, 24, Moupfouma, F. (1984), Improvement of rain attenuation prediction method for terrestrial microwave links, IEEE Trans. Antennas Propag., 32(12), Moupfouma, F., and J. Tiffon (1982), Raindrop size distribution from microwave scattering measurements in equatorial and tropical climates, Electron. Lett., 18, Naicker, K. (2006), Rain attenuation modelling for line-of-sight terrestrial links, MSc. thesis, Univ. of Kwazulu-Natal, Durban, Sept. Naicker, K., and S. H. Mneney (2006), Propagation of measurements and multipath channel modelling for line-of-sight links at 19.5 GHz, SAIEE Res. J., 97(2), Odedina, P. K., and T. J. Afullo (2005), Effective Earth radius factor determination and its application in southern Africa, in Proceedings of IASTED International Conference on Antennas, Radar, and Wave Propagation, July, pp , Banff, Canada. Olsen, R. L., D. V. Rogers, and D. B. Hodge (1978), The ar b relation in the calculation of rain attenuation, IEEE Trans. Antennas Propag., 26(2), Pawlina, A., and M. Binaghi (1998), Rain distribution along the path: New statistics of cells and cells separations from radar data, in Proceedings of URSI Commission F Open Symposium on Climatic Parameters in Radiowave Propagation Prediction, pp , Ottawa, Canada. Pawlina-Bonati, A. (1999), Essential knowledge of rain structure for radio applications based on available data and models, in Proceedings of 3rd Regular Workshop on Radio Communi- 14 of 15

15 cation in Africa, October, edited by J. S. J. Daka and T. J. O. Afullo, pp , Gaborone, Botswana. Pozar, D. M. (1988), Microwave Engineering, 2nd ed., chap. 12, John Wiley, New York. Segal, B. (1986), The Influence of Rain-gage Integration Time on Measured Rainfall-Intensity Distribution Functions, J. Atmos. Oceanic Technol., 3, Zhang, W., and N. Moayeri (1999), Power-Law Parameters of Rain Specific Attenuation, Rep. IEEE, WG, 1 8. T. J. Afullo and M. O. Fashuyi, School of Electrical, Electronic, and Computer Engineering, University of KwaZulu- Natal, Durban, 4000 South Africa. (afullot@ukzn.ac.za) 15 of 15