A Three-Dimensional Angular Scattering Response Including Path Powers

In this paper, the angular power spectrum exhibited under a three-dimensional (3-D) Gaussian scattering distribution at fixed observation points in space is investigated. Typically, these correspond to the mobile and base units, respectively. Unlike other spatial channel models, the derived model accounts for the distance to each scatterer from the observation point, and transforms distances into power values under the assumption of free-space propagation. The proposed 3-D spatial channel model follows a non-central approach in terms of the scatterer distribution in space, which means that the angular power field at the base unit need not be due to a scatterer distribution centered exactly at the mobile. Derivations are provided for the angular and power domains. As shown, by conditioning the distance, the angular field reduces to the von-Mises Fisher distribution. Most importantly, this work provides a theoretical backup to the Gaussian angular power spectrum observed in radio propagation channel measurements, introducing a formal theoretical framework consistent with the experimental investigations found in literature. More specifically, our findings show that a Gaussian scatterer distribution in space gives rise to a Gaussian-like angular power spectrum and a Gaussian angular power density in the azimuth and elevations fields. By introducing the notion of distance into the framework, the proposed 3-D spatial channel model can be used to evaluate performance of current and future multi-element wireless communication networks.