A 3-D fading channel model with asymmetrical PDF of elevation angle

Power spectral density (PSD) of the signal received in a mobile radio environment is tightly related to the distribution of the arriving angles of the waves. One of the most widely accepted model, Clarke´s scattering model, is a two dimensional (2-D) model because of the assumption of horizontal travel of plane waves. By introducing a non-zero elevation angle (EA) of the arriving wave, the 3-D model is more general and suitable especially for urban environments. A family of functions with two positive integer parameters, {m,n}, for both symmetrical and asymmetrical probability density function (PDF) of the EA, has been proposed in a previous paper. Among these functions, those with odd m and n lead to analytical solutions for the PSD of the received signal. In this paper, it is pointed out that when m and n are even, though the PSD of signal has no analytical solution, it can be represented by the elliptic integrals