Spatial Bandwidth Asymptotic Analysis for 3D Large-Scale Antenna Array Communications

TL;DR

This paper analyzes the spatial bandwidth of large-scale 3D antenna arrays in LOS channels, providing approximations for the spatial degrees-of-freedom and exploring how array orientation affects multiplexing capabilities.

Contribution

It introduces new approximations for spatial bandwidth in 3D LOS channels and evaluates their impact on spatial multiplexing under various orientation constraints.

Findings

Approximations accurately model spatial bandwidth in the radiative region.

Array length and bandwidth product estimate channel DOF.

Constrained 2D orientations can outperform 3D orientations in multiplexing.

Abstract

In this paper, we study the spatial bandwidth for line-of-sight (LOS) channels with linear large-scale antenna arrays (LSAAs) in 3D space. We provide approximations to the spatial bandwidth at the center of the receiving array, of the form $C R^{-B}$, where $R$ is the radial distance, and $C$ and $B$ are directional-dependent and piecewise constant in $R$. The approximations are valid in the entire radiative region, that is, for $R$ greater than a few wavelengths. When the length of the receiving array is small relative to $R$, the product of the array length and the spatial bandwidth provides an estimate of the available spatial degree-of-freedom (DOF) in the channel. In a case study, we apply these approximations to the evaluation of spatial multiplexing regions under random orientation conditions. The goodness-of-fit of the approximations is demonstrated and some interesting findings about the DOF performance of the channel under 3D and 2D orientation restrictions are obtained, e.g., that, under some conditions, it is better to constrain the receiving array orientation to be uniform over the unit circle in the 2D ground plane rather than uniform over the 3D unit sphere.