Abstract
The objective of this paper is to illustrate the physics associated with the propagation of mobile wireless communication signals. It is shown that an electromagnetic macro model can predict the nature of the path loss exponent in a mobile cellular wireless communication without the use of a statistical model which is devoid of basic physics. Hence this paper makes it possible to analyze propagation of wireless signals in any environment without introducing an adhoc reference distance in the model. Invariably, the reference distance chosen for the model is incorrect as the cell is located in the near field as opposed to be in the far field. In addition, the use of a two ray model provides a path loss exponent of 4 and not 3 which is the actual value within a cell as first described by Okumura in his classic paper. 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. The size of these regions is determined on the heights of the base station transmitting antennas and the receiving antennas. These principles are illustrated by using the analysis of radiation from a vertical electric dipole situated over a horizontal imperfect ground plane which was first presented by Sommerfeld in 1909. When the Sommerfeld integrals are evaluated using a modified saddle point method for field points moderate to far distances away from the source point, through moderate to large values of the numerical distance, the correct path loss exponents can be obtained. Okumura's experimental data are analyzed using the Sommerfeld formulation.