Mobile channels are often modeled using a well-defined Rice process. The statistics of its wrapped phase (i.e., phase values in $[-\pi,\pi)$), such as the mean, variance, and probability density function (pdf), are known. The absolute phase is the accumulated phase change over an observation interval. It can be calculated from the wrapped phase but contains more information. Its applications include channel characterization and cognitively tracking mobile users. However, there is little knowledge about the statistics of the absolute phase. In this thesis, the theory of the absolute phase is developed. The absolute phase is defined formally, and various formulations, based on unwrapping and on other methods from FM receiver analysis, are presented. These formulations lay a basis for analyzing the statistics of the absolute phase for a well-defined Rice process. The statistics of the absolute phase is affected by scattering directionality of the channel. New theoretical results are developed for the mean, variance and pdf of the absolute phase in isotropic scattering. The mean of the absolute phase is then derived for directional scenarios with scattering modeled by the von Mises distribution. The smooth transition of the von Mises distribution to the uniform distribution enables this mean to include isotropic scattering as a special case. Development of the absolute phase will foster new techniques in mobile communications. An example in isotropic scattering is a new Rice factor estimator which uses only the absolute phase. Since no amplitude is involved, the receiver structure can be simplified. This estimator achieves comparable performance, when the Rice factor is small, to existing estimators which require amplitude or both amplitude and phase. To demonstrate and confirm the new theoretical results, a channel simulation technique, based on the inverse discrete Fourier transform, is extended to include both isotropic and directional scattering. The simulation and theoretical results are in good agreement.
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