Electromagnetic Macro Modeling of Propagation in Mobile Wireless Communication: Theory and Experiment

The objective of this paper is to illustrate that electromagnetic macro modeling can properly predict the path-loss exponent in mobile cellular wireless communication. This represents the variation of the path loss with distance from the base-station antenna. Specifically, we illustrate that the path-loss exponent in cellular wireless communication is three, preceded by a slow-fading region, and followed by the fringe region, where the path-loss exponent is four. The sizes of these regions are determined by the heights of the base-station transmitting antennas and the receiving antennas. Theoretically, this is 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. 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 is also derived by applying a saddle-point method to the semi-infinite integrals, and this is shown to not provide the correct path-loss exponent that matches measurements. The various approximations used to evaluate the Sommerfeld integrals are described for different regions. It is also important to note that Sommerfeld´s original 1909 paper had no error in sign. However, Sommerfeld overlooked the properties associated with the so-called “surface-wave pole.” Both accurate numerical analyses, along with experimental data, are provided to illustrate the above statements. In addition, Okumura´s experimental data, and extensive data taken from seven different base stations in urban environments at two different frequencies, validate the theory. Experimental data revealed that a macro modeling of the environment, - sing an appropriate electromagnetic analysis, can accurately predict the path-loss exponent for the propagation of radio waves in a cellular wireless communication scenario.