For millimetre-wave communication systems, rain is a serious cause of attenuation and is the critical factor hindering system performance. Knowledge of the specific attenuation is invaluable to determine the path lengths, operating frequency and fade margins required for communication systems. Since the specific attenuation is heavily dependent on the DSD, the effect of the various DSDs on link availability needs to be examined and hence is the subject of this research.
During rain events, a large fade margin may often be required. It would be uneconomical to implement such margins since they are only needed for a fraction of the time. A cumulative distribution model of the fade depth and duration due to rain will thus be a valuable tool for a systems designer. With such models the system designer can then determine the appropriate fade margin and resulting outage period for the link.
The conversion of rain rate to specific attenuation is a crucial step in the analysis of the total path attenuation and hence radio-link availability. It is now common practice to relate the specific attenuation and the rain rate using the simple power law relationship.
The power-law parameters are then used in the path attenuation model, where the spatial variations of rainfall are estimated by a path-integration of the rain rate. These power law parameters are strongly influenced by the DSD. There exists, fundamentally two forms of DSD. One form corresponds to the distribution of raindrops present in a unit
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volume of air, while the other corresponds to the distribution arriving at a surface of unit area. For the evaluation of the specific attenuation, we are interested in the former, while ground-based measurement devices often provide the latter. To convert between these two forms the terminal velocity of raindrops in air is required.
Many models for the DSD have been suggested in literature, from the traditional exponential, to the gamma, lognormal and Weibull distributions. The type of DSD varies depending on the geographical location and rainfall type. An important requirement of DSDs is that they are consistent with rain rate. i.e. the DSD must satisfy the rain-rate integral equation. Thus before application in the specific attenuation calculations, normalisation needs to be performed to ensure the consistency.
The specific attenuation was evaluated for spherical raindrops using the following theoretical and empirical drop size distributions
• LP - Laws and Parsons (1943), three exponential DSDs, namely
• MP - Marshall Palmer (1948),
• JD - Joss-Drizzle (Joss et al. 1968), and
• JT - Joss-Thunderstorm(Joss et aI. 1968), two gamma DSDs, namely
de Wolf-de Wolf(2001), and
AU - (Atlas and Ulbrich 1974, cited Jiang et aI. 1997), four lognormal DSDs (Adimula and Olsen 1996), namely
• CS (continental shower),
• TS (tropical shower),
• CT (continental thunderstorm), and
• TT (tropical thunderstorm), and the Weibull DSD,
• WB - Sekine et al. (1987).
Once the specific attenuation (dB/km) has been evaluated for necessary frequency and rain-rate range, the parameters for the power-law relation are determined. These parameters are then used to determine the path attenuation. Rain exhibits significant spatial and temporal variation. Hence the rain-rate profile along the propagation path is also required. Crane (1980) developed an attenuation model to convert the point rain- rate to a path-averaged rain rate. The only required inputs are the power-law parameters for the specific attenuation and the rain rate.
Using the above model, for a given radio-link path and frequency of interest, it is possible to determine the path attenuation for any given rain rate. Knowledge of the cumulative distributions of the fade depth and durations due to the rain are now needed.
Depending on the link availability requirements, communication system designers may need the fade depth exceeded for 0.1,0.01 or 0.001%of the time.
To perform this task knowledge of the surface-point rain rate is a prerequisite. Long term statistics of rain rates of short integration time are needed. Even an integration time of 5 minutes is insufficient to account for the substantial temporal and spatial variability of rain. Fortunately, truly instantaneous rain rates are not necessary since rapid fluctuations in the rain rate will not necessarily translate into equivalent fluctuations in
attenuation due to the spatial averaging over the propagation path. For application in rain attenuation statistics, I-minute rain rates have been found to be the most desirable, to remove variations due to rain gauge limitations, such as small sampling area and contamination due to atmospheric turbulences (Crane 1996). Hence I-minute rates have been adopted as the standard for the evaluation of rain attenuation by researchers and the International Telecommunications Union (ITU).
In this study several models for the determining the surface-point I-minute cumulative rain-rate distributions for South Africa were examined. An extreme-value model (Lin 1976; Seeber 1985) was examined for South Africa. Using the measurements of the rainfall extremes in WB36 (Department of Transport, 1974) and the conversion ratio of Ajayi and Ofoche (1983) it is possible to obtain I-minute rain-rate distributions, as shown in this study. In the absence of reliable long-term data the global rain-rate climate models (Crane 1980; ITU-R P.837) can be used and were also examined. The ITU global rain-rate model provides superior results over the Crane global model and utilises bilinear interpolation to resolve distributions within each climatic zone.
Unfortunately, the ITU model is less reliable in regions that display characteristics of two climatic types. Thus whenever possible, one should make use of available rainfall data to augment the global rainfall models. The models discussed thus far are based on the lognormal distribution. Such models are very reliable for the higher probabilities (0.01% and higher). For the lower probabilities (less than 0.01%), the gamma models are better suited. The Moupfouma (1987) lognormal model and the Moupfouma and Martin (1995) gamma models for temperate and tropical/subtropical regions have also been considered.
Finally, each rain-rate model is then used to evaluate the cumulative distributions of the fade depth and duration due to rain. For each rain-rate model, the effect of the choice of DSDs on link availability can then be examined. For microwave and millimetre-wave
communication systems, the fade margin required to maintain system reliability is often too large and uneconomical to implement, since they are only needed for a fraction of the time. The cumulative distribution model of the fade depth and duration due to rain will thus be a valuable tool for a systems designer. With such models the system designer can then determine the appropriate fade margin and resulting outage period for a given radio-link path.
6.1 Summary of Dissertation
The numerical calculation of the scattering and attenuation of electromagnetic waves by rain requires detailed knowledge of the microphysical properties of raindrops such as raindrop size, fall velocity and drop-size distribution (DSD). This is the focus of Chapter 2 of this dissertation.
Firstly the fall velocity of raindrops is examined using the Gunn and Kinzer (1949) measurements of the terminal velocity at sea level and several analytical descriptions thereof are discussed in Section 2.2. Itis shown that a polynomial model of order 3 can provide good approximate of the terminal velocity at sea level. Thereafter models for arbitrary atmospheric conditions are examined, concluding with the Best (1950) model for variation with height in the S.T. and LC.A.N. standard atmospheres. The terminal velocity is essential for evaluating the consistency of DSD with rain rate and in the normalisation procedure.
The size and shape of a raindrop is required for the calculations of the scattering and extinction cross section of a single raindrop. A brief preamble to raindrop scattering is given in Section 2.3. Mie scattering calculations are extremely computationally complex for non-spherical shapes, such as for spheroidal and realistically raindrops (e.g.
Pruppacher and Pitter 1971), hence the classical approach of using spherical raindrops