Three-dimensional geometrical channel modeling with different scatterer distributions

The problem of three dimensional (3D) stochastic geometrically-based channel modeling with non-uniform scatterer distributions is addressed for multistory indoor environments. To this end, we consider a geometrical channel model, where scatterers are assumed to be Gaussian or Rayleigh distributed about the receiver within a spheroid having the transmitter and the receiver located at its focal points. Closed-form expressions are obtained for the joint and marginal probability density functions (PDFs) of the angle of arrival (AOA) in both the elevation and azimuth planes and the time of arrival (TOA). The analytically-derived PDFs of the AOA and TOA obtained for Gaussian and Rayleigh scatterer distributions are compared against those obtained from ray-tracing simulation of a typical indoor office environment. The standard deviation values of Gaussian and Rayleigh scatterer distributions are chosen to provide the best possible approximation to the PDFs of the AOA and the TOA obtained from simulation. Our results clearly indicate that the analytically-derived PDFs of the AOA and the TOA for Gaussian and Rayleigh scatterer distributions are in much closer agreement with those obtained from ray-tracing simulation than for uniform scatterer distribution.