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Keynote talk #3: The physics and mathematics of cellular wireless propagation

The objective of this presentation is to illustrate that an electromagnetic macro modeling can properly predict the path loss exponent in a 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 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. 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 semiinfinite 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. In addition, Okumura's experimental data and extensive data taken from seven different base stations in urban environments 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. It is also shown that an electromagnetic macro modeling of the environment can provide simulation results comparable to the data as one would obtain in an actual drive test measurement for a cellular environment. The input parameters for the electromagnetic model can be generated using only the physical parameters of the environment like the height of the transmitting and receiving antennas over the ground, their tilts toward the ground, and the electrical parameters of the ground. Such analysis can provide realistic plots for the received power versus separation distance between the receiving and the transmitting base station antennas. The novelty of the electromagnetic analysis technique proposed in this paper lies in its ability to match the simulation and measurement results without any statistical or empirical curve fitting or an adhoc choice of a reference distance. This illustration is made using real data measured for cellular networks in western India and Srilanka.