Efficient Methods for Computing Wave Propagation Over a Spherical Earth With an Exponential Refraction Index

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Efficient methods for computing ground-wave propagation over a smooth spherical earth with an exponential refraction index are presented. The methods are based on a residue series, which is valid for large distances near and beyond the radio horizon. The previous solution, which also uses a residue series, involves extensive numerical calculations that are time consuming. Here, it is shown that it is possible to reduce the number of numerical calculations considerably. By using approximate expressions, it is possible to remove many of the time-consuming calculations and still get very good results, which are shown in several examples.