Stochastic Modeling of Narrowband Fading Channels with Three Dimensional Diffuse Scattering

Abstract

This chapter studies a composite stochastic model, in which the diffuse component arises from three dimensional (3-D) multipath scattering. That case occurs especially in dense scattering environments, in which the tall obstacles cause arrival of multipath power in the elevation plane, besides that arriving in the azimuth one. Also the multipath components are assumed to arrive at the mobile receiver in specific angular sectors at the azimuth receiver’s plane. The last is physically justified by multipath power blocking due to the channel obstacles (shadow fading), or/and lack of scattering objects at specific angular directions, or/and directional antennas utilization. An extended Suzuki model, where the Rician process for the diffuse scattering component is multiplied by a lognormal one, is considered as an appropriate composite model. The most important metrics of the model are presented, according to its assumptions. More specifically, from the closed form autocorrelation function, the Doppler power spectral density (PSD) of the diffuse component can be analytically derived. Afterwards exact solutions for the envelope and phase probability density functions (PDF’s) are presented. Exact solutions are also derived for the second order statistics, i.e. the level crossing rate (LCR) and the average duration of fades (ADF’s). An efficient deterministic simulation scheme will be presented, which implements the analytical model on a digital computer. Finally a curve fitting of the LCR to real world data, drawn from channel measurements, will demonstrate the flexibility and usefulness of the extended Suzuki model.