## 1. Introduction

[2] Rain affects the design of any communication system that relies on the propagation of electromagnetic waves. Above a certain threshold of frequency, the attenuation due to rain becomes one of the most important limits to the performance of line-of-sight (LOS) microwave links. Rain attenuation, which is the dominant fading mechanism at these frequencies, is based on nature, which can vary from location to location and from year to year. Daily rainfall accumulations, universally recorded on hourly basis, are also fairly widely available by national weather bureaus.

[3] *Rogers and Olsen* [1976] employ Mie scattering theory and Laws and Parsons (LP) drop size distribution (DSD) to obtain plots of specific attenuation *γ* (dB/km) against frequency (from 1 to 1000 GHz) for rain rate, varying from 0.25 mm/h to 150 mm/h. For each of the nine values of rain rate, the effect of rain temperature on specific attenuation is also shown at two temperatures, namely 273°K and 293°K. *Ajayi and Ofoche* [1983] determined that the use of 1-min rain rates gives the best agreement with the *International Telecommunication Union Radiocommunication Sector* (*ITU-R*) [2005] stipulations for the design of microwave radio links. This was then used to estimate the signal outages at 0.01% of the time on radio communication links, since it defines the rainfall rate recommended by *ITU-R* [2005] to evaluate the availability of terrestrial and satellite radio links.

[4] *Ajayi and Olsen* [1985] have shown that the LP and MP distributions overestimate the number of drops in the small and large diameter regions; and that the lognormal model gives a better fit to the measured drop size data at Ile-Ife, Nigeria (a tropical climate). *Moupfouma and Tiffon* [1982] used measurement data over a 33.5-km 7 GHz terrestrial radio link in the Congo (equatorial region of Africa) to propose a new rain drop size distribution, and also confirmed that the MP distribution overestimates the number of small drops while it underestimates the larger ones for this region. Similar conclusions have been made by O. Massambani and C. A. M. Rodriguez (Una distribuicao gamma de tamanhos de gotas de nuvens, paper presented at V Congresso Brasileiro de Meteorologia, Ministério da Agricultura, Pecuária e Abastecimento, Brazil, 1988) and O. Massambani and C. A. M. Rodriguez (Specific attenuation as inferred from drop size distribution measurements in the tropics, paper presented at URSI Commission F Open Symposium, Rutherford Appleton Laboratory, Rio de Janeiro, Brazil, 3–7 December, 1990), making use of the data obtained in Brazil.

[5] To determine specific attenuation due to rain using Mie computations, *Olsen et al.* [1978] employed the Ray method to determine the refractive index for water at various temperatures and frequencies. However, the Ray data are regarded as inaccurate especially at frequencies above 10 GHz [*Mätzler*, 2002a]. On the other hand Mätzler developed MATLAB functions based on the formulation of *Bohren and Huffman* [1983]: he used the more accurate dielectric model of Liebe to determine the refractive index of water for computation of Mie parameters [*Mätzler*, 2002a]. The parameters required were the interaction cross sections by rain per unit volume of a rainy atmosphere, i.e., the propagation coefficients for rain extinction, *γ*_{ext}, scattering, *γ*_{sca}, absorption, *γ*_{abs}, backscattering, *γ*_{b}, and the asymmetry parameter 〈cos θ〉 [see *Mätzler*, 2002a, 2002b, 2002c]. Here, 〈cos θ〉 (D) is the effective cosine of the scattering angle, and is a function of *D*, the rain drop size. In his approach, Mätzler computed the coefficients *γ*_{j}, {j = ext, abs, sca, b} from the corresponding Mie efficiencies *Q*_{j} and the drop size distributions using Marshall Palmer (MP), Joss-Thunderstorm (JT), Joss-Drizzle (JD) and Laws and Parsons (LP) distributions of N(D), from the equations [see *Mätzler*, 2002b]:

These coefficients are used in radiative transfer theory, as in, for example, the works of *Chandrasekhar* [1960] and *Meador and Waver* [1980]. In this presentation we determine propagation coefficients, *γ*_{j}, due to rain in Botswana for four selected stations from the corresponding Mie efficiencies *Q*_{j} and the drop size distribution based on lognormal distribution for tropical and subtropical countries, as presented by *Ajayi et al.* [1996]:

Here *μ* is the mean of ln (*D*), *σ* is the standard deviation, *N*_{t} is the total number of the drops per cubic meter per mm. We use R_{0.01} = 68.9 mm/h for Gaborone, R_{0.01} = 137.06 mm/h for Selebi-Phikwe, R_{0.01} = 86.87 mm/h for Francistown and R_{0.01} = 64.4 mm/h for Kasane, for Botswana, in southern Africa, as determined b C. T. Mulangu et al. (Rainfall rate distribution for LOS radio system in Botswana, paper presented at 10th Southern Africa Telecommunication, Networks and Application Conference (SATNAC), Ericsson, Mauritius, September 2007). We also discuss the variability of the propagation coefficients due to rain with temperature for Gaborone, Selebi-Phikwe, Kasane and Francistown, comparing the same with the results of *Rogers and Olsen* [1976], *Ajayi and Adimula* [1996], and *Moupfouma and Tiffon* [1982]. Since our work is based on the procedures presented by the various works of Mätzler, the brief theoretical basis that follows is based purely on *Mätzler* [2002a, 2002b].