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

Clarke's scattering model, one of the most widely accepted channel models f or the land mobile environment, is a two-dimensional (2-D) model because of the assumption of horizontal traveling plane waves. By introducing a nonze ro elevation angle of the arriving wave, a three-dimensional (3-D) model is more general and accurate, especially for the urban environment. Though th e 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, f rom 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 a nd n are positive integers, for both the symmetrical and asymmetrical proba bility density function (PDF) of the elevation angle (EA), is proposed. Amo ng 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 PSD's in closed form associated with m and n equal to one and three are derived in particu lar, and the autocorrelation functions are obtained numerically, Since a fa mily of functions rather than a single function is proposed for the PDF of the EA, it provides certain flexibility in application and covers a nide ra nge 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 th e received signal.