The effect of rain on radio signals and the importance of an accurate prediction of rain attenuation models on terrestrial radio links cannot be overemphasized in radio communication studies. For these reasons, this study has employed a semi-empirical approach for the formulation of the rain attenuation prediction models. This approach has involved knowledge of the scattering properties of raindrops, raindrop size distributions, rain rates, and signal level measurements recorded at 19.5 GHz on a horizontally polarized terrestrial radio link. The impact of the rain attenuation statistics on terrestrial radio links has also been investigated.
Firstly, empirical rain attenuation models were predicted based on the signal level measurements from the 19.5 GHz horizontally polarized 6.73 km terrestrial radio link in Durban. The link was set up for a period of one year, and 1-minute rain rates recorded alongside with the signal level measurements. From the link, non-rain faded average signal levels for each month was determined and the time series for different features of rains (light, moderate, and heavy rains) and their received signal levels are also analysed. With the average non-rain faded signal level, the rain attenuation of the different features of rains are estimated and the monthly rain attenuation models depicting the month-to-month attenuation variability were estimated statistically.
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The rain attenuation models depicting the measured upper and lower attenuation bounds for the average year along the 6.73 km line-of-sight link were predicted. These empirical rain attenuation models were compared with six different established rain attenuation models: The ITU-R model [ITU-R 530, 2007]; the global Crane [Crane, 1980: 1996]; the Moupfouma model [Moupfouma, 1984]; Garcia and Peiro model [Garcia-Lopez and Peiro, 1983]; the CETUC [Perez Garcia and da Silva Mello, 2004]; and new CETUC model [da Silva Mello et al., 2007]. This comparison are analysed quantitatively by calculating the root mean square (rms) percentage error between these six different established rain attenuation models and the measured attenuation bounds.
From the rms percentage error analysis, it was seen that, the Garcia and Peiro model has the lowest rms percentage error for the minimum measured attenuation bound then followed by the ITU-R model. For the average measured attenuation bound, the CETUC models give the lowest rms percentage error, and then followed by the ITU-R model. For the maximum measured attenuation bound, the global Crane model [Crane, 1980; 1996] gives the lowest rms percentage error, and then followed by the ITU-R model. The ITU-R model has given the lowest rms percentage error when calculated for all the measured rain attenuation bounds. With these observations, the ITU-R model [ITU-R 530, 2007] can reasonably be adopted to predict the rain attenuation in Durban and its environs.
The theoretical rain attenuation models for different drop-size distribution models proposed in this study were based on the interaction between raindrop particles, and the propagating incident electromagnetic wave. The scattering amplitudes for 14 different raindrop sizes were calculated by using the Mie scattering theory for dielectric spheres with the assumption that the shape of the raindrop is spherical. The extinction cross-section of the spherical raindrops were calculated from the forward scattering amplitudes, and modeled with a power-law relationship. The power law model from the extinction cross-section was integrated mathematically over different established drop-size distributions to propose different rain attenuation models for specific attenuation and path attenuation estimations on terrestrial radio links.
These models were used to compute the specific rain attenuation for four locations situated in different climatic rain zones in South Africa. To validate these theoretical models, they were compared with the experimental signal level measurement recorded in Durban. For the purpose of cross referencing, they were also compared with the ITU-R rain attenuation model. The results showed that the theoretical attenuation model developed from the negative exponential drop-size
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distribution of Joss et al. thunderstorm rain type [Joss et al. 1968] , lognormal drop-size distribution of Adimula-Ajayi tropical thunderstorm rains, and tropical shower rains [Adimula and Ajayi, 1996] gave the best fits for the minimum, average and maximum measured attenuation, respectively with the use of the chi-square statistic. The attenuation values predicted by the average theoretical attenuation model were also compared with the attenuation values predicted from the Moupfouma [1997] theoretical model.
It was observed that the Moupfouma theoretical attenuation model developed from oblate spheroidal raindrops [Moupfouma, 1997] and the predicted theoretical average attenuation model formulated from spherical raindrops reasonably describe the measured average attenuation. It was also observed that both models predicted almost the same rain attenuation values, despite the differences in the formulation of each theoretical model. Thus, it can be stated that, whether rain attenuation is modeled with a spherical or an oblate spheroidal drop, the same rain attenuation might be expected along a terrestrial link if the approach employed in this work is used; though the results may be influenced by the drop-size distribution used in the calculation of the path attenuation. Thus, the major parameter that needs to be known if this approach is to be applied to various geographical locations around the world for the estimation of rain attenuation is to know the raindrop size distribution governing the location. Since the attenuation models proposed in this work have been formulated from different raindrop-size distributions, these proposed models can be used directly to determine the attenuation caused by rain.
In this regard, preliminary raindrop size distributions for different rain types based on measurements carried out in Durban have been estimated. These distributions are estimated for the different rain types by measuring the percentage error between the distributions and the raindrop size measurement. From the error analysis, negative exponential distribution gives the highest percentage of error for all the rain types, lognormal drop-size gives the lowest percentage error for drizzle, widespread, and shower rain types, and gamma drop-size distribution gives the lowest percentage error for thunderstorm rains. Therefore, with this analysis the lognormal drop- size distribution can be employed to predict the drizzle, widespread, and shower rain types, while the gamma drop-size distribution is better suited for the thunderstorm rain types.
As a result of the rapidly varying nature of rain, the characteristics and the variations associated with rain attenuation statistics in South Africa were analyzed. This analysis took four geographical locations situated in four different climatic rain zones in South Africa as case
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studies. The analysis employed the ITU-R rain attenuation model on a 5-year rain rate data obtained from the four geographical locations to estimate the cumulative distributions of the rain attenuation. These attenuation distributions are estimated on a monthly, seasonal, and an average year basis. From these distributions, fade margin values are derived for various percentages of link availability. The fade margins give the necessary allowance needed on a terrestrial link to accommodate any impairment that may occur due to rain, and also estimate the outage probability of a radio link.
The analysis of the seasonal attenuation distributions in each of the four geographical locations are observed to be linked to their climatic characteristics. High attenuation distributions were observed in the coastal (Durban) and the temperate (Pretoria) climates as well as the summer and the autumn seasons. This resulted in large fade margins for different level of link availability.
Cape Town is an exception to this pattern due to its mediterranean nature of climate and its location. The monthly attenuation distributions tend to highlight the propagation characteristics of each month distinctively without averaging them over the seasons. From these distributions, it is seen that some summer or autumn months may not require a large fade margins as other months in the seasons (as shown in Durban and Brandvlei monthly distributions). It is also observed that the average attenuation distributions over the entire 5 years in each of the four locations may not be adequate for fade margin design as it underestimates the peak month’s fade margin. Thus, this may not be able to accommodate the fades that may occur in months of high rain rates.