## 1 Introduction  
Satellite communication remains an invaluable tool in today's wireless communication systems. This is majorly due to its several merits, especially, the cost-effectiveness and ability to offer the widest coverage when compared to inter-terrestrial links [1, 2, 3]. In fact, a constellation of three satellites in the geostationary elliptical orbit (GEO) can provide efficient near-global communication coverage [4, 5, 6, 7]. Transmission of radio signalsat frequencies above 10 GHz has several advantages which are able to fulfil modern requirements such as wider spectrum availability, high data transfer rate, and smaller antenna size [8]. Conservation and optimum utilization of frequency is an important factor that must be considered in any satellite communication system because as frequency increases, attenuation due to atmospheric disturbances also increases. To optimize frequency usage in a communication network, frequency reuse is often adopted so that more than one channel per carrier frequency can be transmitted in a communication network. Frequency reuse in satellite communication is enabled by polarization, a method that allows two orthogonally polarized radio waves to be transmitted at a single frequency. Polarization in the context of antenna and radio wave propagation describes how the orientation of an antenna's electric field wave vector aligns relative to the direction of propagation of the electromagnetic waves [9; 10]. In radio communication links operating above 10 GHz, frequency reuse in orthogonal polarizations is limited by cross-polarization, a phenomenon where part of a signal originally transmitted in a specific polarization leaks into an orthogonal polarization. Cross-polarization causes a singularly polarized signal to be propagated in two opposite directions, i.e., right hand circular polarization (RHCP) and left hand circular polarization (LHCP) for circularly polarized signal; horizontal and vertical polarization for linearly polarized signal. The reason behind cross-polarization of radio signals in the atmosphere is the presence of hydrometeors such as rain, mist, cloud, snow, and ice. However, rain remains the major cause of severe attenuation and the greatest threat to radio waves propagating at frequencies above 10 GHz in the tropical and subtropical regions [11; 12; 13]. These regions experience high-intensity rainfall and longer rainy season compared to other regions. Heavy raindrops are more frequent, leading to scattering and absorption of radio waves [11]. Cross-polarization arises because raindrops are generally non-spherical and can be canted at various angles, causing the polarization plane of electromagnetic waves to rotate and resulting in cross-polarization [14]. The degradation of received signal strength from a singularly polarized wave's quality due to cross-polarization effects is known as CPA. Several studies have shown that cross-polarization occurs because of differential attenuation and differential phase shift between two orthogonal polarizations usually caused by interactions between radio signals and raindrops. Raindrops contribute significantly to the cross-polarization effect when the rain droplet diameter is comparable to the wavelength of radio waves [15; 16; 17]. Cross-polarization also increases with increasing frequency, thereby making higher frequency signals more vulnerable. Rain height is a portion along the propagation path shown in Figure 1, where raindrops have significant effects on radio waves, resulting in rain-induced attenuation. It is a function of the melting layer and rain region. The ice region has negligible impacts on radio waves because ice crystals possess very low permittivity and tangent loss [18; 19]. Rain heights vary temporally and spatially due to non-uniformity of climate, weather, geological, and topographical formations of satellite-earth receiver stations.