### Abstract

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, using an appropriate electromagnetic analysis, can accurately predict the path-loss exponent for the propagation of radio waves in a cellular wireless communication scenario.

Original language | English (US) |
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Article number | 6387779 |

Pages (from-to) | 17-43 |

Number of pages | 27 |

Journal | IEEE Antennas and Propagation Magazine |

Volume | 54 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2012 |

### Keywords

- Norton surface wave
- Propagation
- Sommerfeld formulation
- cellular wireless communication
- ground wave
- imperfect ground
- land mobile radio cellular systems
- land mobile radio propagation factors
- macro modeling
- path loss exponent
- surface wave

### ASJC Scopus subject areas

- Condensed Matter Physics
- Electrical and Electronic Engineering

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## Cite this

*IEEE Antennas and Propagation Magazine*,

*54*(6), 17-43. [6387779]. https://doi.org/10.1109/MAP.2012.6387779