A Generalized Analysis of Three-Dimensional Anisotropic Scattering in Mobile Wireless Channels-Part I: Theory

Abstract

In this paper, we present a generalized theoretical analysis for multipath scattering in mobile wireless channels where scattered power arrives into three dimensions (3-D). Moreover, multipath power can arrive into any arbitrary number of discrete angular sectors under an anisotropic propagation regime. A new expression for the azimuth and elevation angle of arrival (AOA) joint distribution of the arriving multipath power is presented. In the general case of multi-modal arrival, we show that the azimuth and elevation AOA are statistically dependent. The latter issue is further investigated by providing certain conditions for statistically independent azimuth and elevation AOA. Due to space limitations, in a follow up paper, a parameterized case study will be analyzed with multi-modal arrival into four angular sectors.

Spatial Channel Degrees of Freedom for Optimum Antenna Arrays

“…In this paper, 3D directional, 3D isotropic, and 3D omnidirectional propagation scenarios [19]- [22] are considered for holistically analyzing both standardized and arbitrarilyshaped antenna array topologies. The directional scenarios are modeled via 3D restricted uniform and 3D Gaussian AOA distributions.…”

“…A 3D restricted uniform AOA has unlimited flexibility to theoretically model any propagation scenario, as arbitrary scattering can be modeled by the summation of weighted uniformly distributed elementary solid-angle contributions [12], [19], whereas a 3D Gaussian AOA is a very classical model for directional propagation [21]. 3D omnidirectional scenarios, accounting for propagation in urban environments, include the pairs uniform-restricted uniform [19] and uniform-Gaussian [20], [22] AOA distributions on azimuth-elevation planes, respectively. By leveraging the JAEbased approach, we derive a closed-form SCF for 3D restricted uniform scenarios similar to the one in [10] employing the 3D AOA model of [19].…”

“…3D omnidirectional scenarios, accounting for propagation in urban environments, include the pairs uniform-restricted uniform [19] and uniform-Gaussian [20], [22] AOA distributions on azimuth-elevation planes, respectively. By leveraging the JAEbased approach, we derive a closed-form SCF for 3D restricted uniform scenarios similar to the one in [10] employing the 3D AOA model of [19]. Extending the GHQ-based method presented in [14], which applies in 2D scenarios, we derive a novel closed-form SCF for 3D directional Gaussian scenarios.…”

Generic stochastic modeling of vehicle-to-vehicle wireless channels

“…Finally, we assume statistical independence between the azimuth and elevation AODs and AOAs. Such assumption can be valid only when multipath propagation results from a single cluster, or under specific assumptions for the azimuth and elevation AODs and AOAs in multi-clustered scenarios [63]. Based on the above assumptions, the joint PDF in equation (23) …”

“…First, we have analytical solutions for the PSDs at the Tx and Rx sides and moreover, there is a theoretical flexibility to incorporate any 3-D scattering scenario by considering AOD and AOA PDFs composed by weighted uniform contributions in different sectors (having the form of equation (27), see [63] and [64]). Then, the PSDs contributed by each sector can be analytically determined as in equation (34) and taking into account the relevant azimuth quadrant as described above.…”