A three-dimensional scattering model for fading channels in land mobile environment

Clarke's (1968) scattering model, one of the most widely accepted channel models for the land mobile environment, is a two-dimensional (2-D) model because of the assumption of horizontal traveling plane waves. By introducing a nonzero elevation angle of the arriving wave, a three-dimensional (3-D) model is more general and accurate, especially for the urban environment. Though the concept of the 3-D model has been proposed already, there is still a lack of satisfying results regarding the distribution of the elevation angle, from both theoretical analysis and field measurement, and the power spectral density (PSD) of the received signal. In this paper, a family of functions with two parameters, {m,n}, where m and n are positive integers, for both the symmetrical and asymmetrical probability density function (PDF) of the elevation angle (EA), is proposed. Among these functions, those with odd m and n lead to analytical solutions of the PSD of the received signal in addition to satisfying other requirements for a PDF of the EA previously proposed in literature. The PSDs in closed form associated with m and n equal to one and three are derived in particular, and the autocorrelation functions are obtained numerically. Since a family of functions rather than a single function is proposed for the PDF of the EA, it provides certain flexibility in application and covers a wide range of environments. Another contribution of this paper is a new expression which directly relates the PDF of the EA in the 3-D model to the PSD of the received signal.