| Summary: | The elevation angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula> is relevant for the Low Earth orbit (LEO) satellite communications since it is always changing its relative position with respect to fixed Earth stations (ES’s), and this affects the link length and received power, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>R</mi></msub></semantics></math></inline-formula>. This article provides a new methodology to compute the probability density function (PDF) and cumulative distribution function (CDF) of the elevation angle, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>, for diverse ES locations. This methodology requires as input parameters an ES latitude, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, an orbit inclination value, <i>i</i>, and an orbit altitude, <i>h</i>. The elevation angle is characterized through a well known random variable, which facilitates the computation of the first and second-order statistics, and helps to determine the expected value and measures of dispersion of the angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula> for a particular ES location. The proposed methodology allows an easy and quick calculation of the elevation angle’s CDF, facilitating comparisons against CDF’s of more ES’s located at different latitudes, and longitudes, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>; as well as the comparisons of CDF’s of the elevation angle produced by different orbits. Extensive simulation results are summarized in a small table, which allows computation of the elevation angle’s CDF and PDF for multiple ES locations without requiring of simulations and statistical fitting. Finally, the proposed methodology is validated through an extensive error analysis that show the suitability of the obtained results to characterize the elevation angle.
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