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.

翻译：本文研究了三维空间中线性大规模天线阵列（LSAA）在视距（LOS）信道下的空间带宽。我们给出了接收阵列中心处空间带宽的近似表达式，其形式为 $C R^{-B}$，其中 $R$ 为径向距离，$C$ 和 $B$ 依赖于方向且在 $R$ 上分段恒定。该近似在整个辐射区域（即 $R$ 大于几个波长的范围）内有效。当接收阵列长度相对于 $R$ 较小时，阵列长度与空间带宽的乘积可提供信道中可用空间自由度（DOF）的估计值。在案例研究中，我们将这些近似应用于随机取向条件下的空间复用区域评估。我们验证了近似拟合优度，并获得了关于三维和二维取向限制下信道自由度性能的一些有趣发现，例如：在某些条件下，将接收阵列取向限制为二维地平面单位圆上的均匀分布，比限制为三维单位球面上的均匀分布更优。