A Three-Dimensional Angular Scattering Response Including Path Powers

Abstract

In this paper the angular power spectrum exhibited under a three-dimensional (3-D) Gaussian scatter 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 scatter distribution in space, which means that the angular power field at the base unit need not be due to a scatter distribution centered exactly at the mobile. Derivations are provided for the angular and power domains and as shown by conditioning the distance, the angular field reduces to the von-Mises Fisher distribution. Most importantly, this work undertakes the problem of a Gaussian angular power spectrum observed in radio propagation channel measurements and provides a formal theoretical framework of the experimental investigations found in literature. The proposed model denotes that a Gaussian scatterer distribution in space gives rise to a Gaussian angular power spectrum and a Gaussian angular power density in the azimuth and elevations fields. The proposed 3-D spatial channel model might be used for evaluating the performance of current and future multi-element wireless communication networks