A generalized model for the spatial characteristics of the cellular mobile channel

In this paper, we present an intensive study of the spatial characteristics of the cellular mobile channel for pico-cell, microcell, and macrocell environments. We review the previous physical channel models and make appropriate comments/corrections wherever needed. We find that almost all physical channel models proposed so far are specific to particular cellular environments and that no general model exists in the literature. Thus, we propose a generalized physical channel model, referred to as the eccentro-scattering model, and derive the expressions for the probability density function (pdf) in an angle of arrival (AoA) of the multipath signals at a base station (BS) for the pico-cell, microcell, and macrocell environments using the two most commonly used scatterers' distributions, i.e., uniform and Gaussian. The derived formulas, in closed form, can be further used in designing beamwidth and channel tracking algorithms and assessing the performance of smart antennas. We discuss the relations between the results obtained for different cellular environments in the uniform and the Gaussian scattering and investigate the effects of the standard deviation of the scatter density and size of the scattering disc on the pdf of AoA at the BS. Previous work on the AoA statistics considering either the shape of the scattering regions or the distribution of scatterers within that region can more easily be reproduced using the provided general formula. We prove that assuming the scatterers to be either uniformly or Gaussian distributed in sparsely populated areas gives almost the same distribution of AoA of multipaths at the BS.