Average-Instantaneous, Unimodal and Multimodal Scattering Responses in Spatial Gaussian Channels

The long-standing problem of identifying the scattering mechanism that triggers the observance of a heavy-tailed power azimuth spectrum is undertaken using a geometry-based stochastic approach. More specifically, the unimodal power azimuth spectrum (PAS) and joint power angular scattering response (PASR) are derived under the 2-D Gaussian scattering model. At first, it is formally shown that, under free-space propagation, a Gaussian scatter distribution in 2-D space gives rise to an angular power spectrum that may be well modeled by the Gaussian function. Numerical results are presented for higher path-loss exponents, where it is shown that heavy-tailed functions such as the Lorentzian and Laplacian functions provide good fits to the derived spectrum. To complement earlier research works in this area, a recently introduced geometry-based stochastic model is extended in order to express the instantaneous multimodal PASR, which significantly contributes to the estimated correlation statistics as shown in the paper. The 2-D spatial channel model developed herein, allows the distance from the observation point to vary, which enhances the validity of the derived PAS and PASR. Statistical results are provided for various distances from the observation point in order to facilitate any potential practical use of the derived 2-D model. Finally, an analytical expression for the correlation experienced between two antenna patterns is derived under the proposed model.