## 1. Introduction

[2] Recent advances in radio communication systems have put pressure on engineers to develop microwave systems operating at higher-frequency bands. The reliability of such systems may be severely impaired due to rain induced attenuation at such frequencies. Therefore, it is necessary to establish a model capable of predicting the behavior of these systems in the presence of rain. In the calculation of rain attenuation for high-frequency radio communication systems, a high degree of accuracy is needed because overprediction of a propagation effect can result to costly overdesign of a system while in the other hand; under prediction can result into a system that is unreliable [*Olsen*, 1999].

[3] An electromagnetic wave propagating through a region containing raindrops suffer two attenuating mechanisms. Part of its energy is absorbed by raindrops and transformed into heat and another part is scattered in all directions, which may introduce unwanted or interfering signals into the communication receiver that may mask the desired signal [*Medeiros Filho et al.*, 1986; *Crane*, 1996; *Cermak et al.*, 2005]. The solution of these scattering problems is mostly obtained for simple raindrop geometry such as sphere [*Medeiros Filho et al.*, 1986]. However, this assumption is not obviously true especially for raindrops with higher diameters [*Cermak et al.*, 2005], which assumes a flattened shape at the bottom and rounded at the top which becomes more pronounced as the rain diameter increases [*Pruppacher and Pitter*, 1971]. This makes the raindrops to be model as oblate spheroids with the scattering problem solution being studied by several authors [*Oguchi*, 1973; *Morrison and Cross*, 1974; *Uzunoglu et al.*, 1977]. Rain consists of drops of various sizes [*Medeiros Filho et al.*, 1986; *Cermak et al.*, 2005], and therefore the prediction of rain attenuation depends considerably upon the raindrop-size distribution and the forward scattered electromagnetic wave of the raindrops [*Medeiros Filho et al.*, 1986; *Jiang et al.*, 1997].

[4] The approach of this work is similar to the work performed by *Moupfouma* [1997], but differs in two ways. First, while Moupfouma obtains his scattering amplitudes from oblate spheroidal raindrop calculated by *Uzunoglu et al.* [1977] and *Morrison and Cross* [1974] who used the Ray complex refractive index in their simulations, in this presentation, the scattering amplitudes are calculated from spherical raindrop using the Liebe model [*Liebe et al.*, 1991] to compute the refractive index of the rain (water) drop, a method also employed by *Mätzler* [2002b] and more recently by *Mulangu and Afullo* [2009]. Second, while Moupfouma develops his rain attenuation coefficients from the imaginary part of the scattering amplitudes from the oblate spheroidal raindrop, in this paper we determine the rain attenuation coefficients from the real part of the extinction cross sections of the spherical raindrops, which is calculated from the real part of the spherical scattering amplitudes.

[5] In this work, the raindrops are assumed to be spherical so that the Mie scattering solution [*Mie*, 1908] is used for the calculation of the forward scattering amplitudes for the spherical raindrops at various frequencies. Based on the calculated forward scattering amplitudes, extinction cross-section coefficients are computed and these are used to generate power law models. The negative exponential, lognormal and Weibull raindrop-size distribution models are integrated over the power law model to formulate theoretical rain attenuation models. These models are used with the rain rate at *R*_{0.01} determined for 4 locations in different climatic rain zones in South Africa [*Fashuyi*, 2006] to compute the specific rain attenuation in these geographical locations. These locations are Brandvlei, Cape Town, Durban and Pretoria located in the M, N, P and Q climatic zones, respectively, as determined by *Fashuyi et al.* [2006] and *Owolawi and Afullo* [2007].

[6] The 1 year experimental results obtained from the horizontally polarized signal level measurements recorded in Durban for maximum, average and minimum attenuation values over a 6.73 km path at 19.5 GHz [*Fashuyi and Afullo*, 2007] are compared with the theoretical results obtained from the proposed rain attenuation models. The best theoretical model with a suitable raindrop-size distribution for all the seasons is used to estimate the seasonal cumulative distribution of rain attenuation for Durban.