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

• Published in: IEEE transactions on wireless communications Vol. 23; no. 4; pp. 2638 - 2652
• Main Authors: Ding, Liqin, Zhang, Jiliang, Strom, Erik G.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antenna arrays; Antennas; Approximation; Bandwidth; Bandwidths; degree-of-freedom; Degrees of freedom; Eigenvalues and eigenfunctions; Frequency measurement; Goodness of fit; Ground plane; Large-scale antenna array; Line of sight communication; Multiplexing; Orientation; Receiving; Space division multiplexing; spatial bandwidth; spatial multiplexing; Three-dimensional displays; Wireless communication
• ISSN: 1536-1276; 1558-2248; 1558-2248
• DOI: 10.1109/TWC.2023.3301034

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 <inline-formula> <tex-math notation="LaTeX">C R^{-B} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula> is the radial distance, and <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">B </tex-math></inline-formula> are directional-dependent and piecewise constant in <inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula>. The approximations are valid in the entire radiative region, that is, for <inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula> greater than a few wavelengths. When the length of the receiving array is small relative to <inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula>, 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.