In frequency non-selective fading channels the multipath components can arrive at the mobile receiver via a three dimensional (3-D) scattering mechanism. That case occurs especially in urban environments, in which the tall buildings and other obstacles cause an arrival of multipath energy in the elevation plane, besides that arriving in the azimuth one. Another issue, which is a matter of investigation, is that the multipath energy may arrive at the mobile receiver in specific angular sectors. This is caused when a part of energy is blocked by the channel obstacles, or no multipath energy arrives from certain directions, due to lack of scattering objects in those directions, or directional antennas are employed. In this paper we propose a model which takes into account both 3-D multipath scattering and partial arrival of multipath energy. The proposed model assumes that the multipath components arrive at specific angular sectors in the azimuth receiver's plane, whereas in the elevation plane the angles of arrival are of continuous nature. Moreover a specular component with constant amplitude also exists. From the closed form autocorrelation function, the Doppler power spectral density (PSD) of the model is analytically derived Afterwards the probability density function (PDF) of the envelope and phase are analytically calculated. What follows are the second order statistics, level crossing rate (LCR) and average duration of fades (ADF's), in closed form.
Karadimas, P., Vagenas, E. D., & Kotsopoulos, S. A. (2008). A Small Scale Fading Model with Sectored and Three Dimensional Diffuse Scattering. In 2008 5th IEEE Consumer Communications and Networking Conference (943-947). https://doi.org/10.1109/ccnc08.2007.218