Abstract
The objective of this paper is to illustrate that an electromagnetic macro modeling can properly predict the path loss exponent in a mobile cellular wireless communication [1]. Specifically, we illustrate that the path loss exponent in a cellular wireless communication is three preceded by a slow fading region and followed by the fringe region where the path loss exponent is four. Theoretically this will be illustrated through the analysis of radiation from a vertical electric dipole situated over a horizontal imperfect ground plane as first considered by Sommerfeld in 1909 [2,3]. To start with, the exact analysis of radiation from the dipole is made using the Sommerfeld formulation. The semi-infinite integrals encountered in this formulation are evaluated using a modified saddle point method for field points moderate to far distances away from the source point to predict the appropriate path loss exponents. The reflection coefficient method can also be derived by applying a saddle point method to the semi-infinite integrals and it is shown not to provide the correct path loss exponent. The various approximations used to evaluate the Sommerfeld integrals are described for different regions [3]. It is also important to note that Sommerfeld's original 1909 paper had no error in sign [1]. However, Sommerfeld overlooked the properties associated with the pole. Both accurate numerical analyses along with experimental data are provided to illustrate the above statements. Both Okumura's experimental data [4,5] and experimental data taken from different base stations in urban environments [6-8] at two different frequencies will validate the theory. Experimental data reveal that a macro modeling of the environment using an appropriate electromagnetic analysis can accurately predict the path loss exponent for the propagation of radio waves in a cellular wireless communication scenario.