  Extremely large-scale array (XL-array) communications can significantly
improve the spectral efficiency and spatial resolution, and has great potential
in next-generation mobile communication networks. A crucial problem in XL-array
communications is to determine the boundary of applicable regions of the plane
wave model (PWM) and spherical wave model (SWM). In this paper, we propose new
PWM/SWM demarcations for XL-arrays from the viewpoint of channel gain and rank.
Four sets of results are derived for four different array setups. First, an
equi-power line is derived for a point-to-uniform linear array (ULA) scenario,
where an inflection point is found at $\pm \frac{\pi}{6}$ central incident
angles. Second, an equi-power surface is derived for a point-to-uniform planar
array (UPA) scenario, and it is proved that $\cos^2(\phi)
\cos^2(\varphi)=\frac{1}{2}$ is a dividing curve, where $\phi$ and $\varphi$
denote the elevation and azimuth angles, respectively. Third, an accurate and
explicit expression of the equi-rank surface is obtained for a ULA-to-ULA
scenario. Finally, an approximated expression of the equi-rank surface is
obtained for a ULA-to-UPA scenario. With the obtained closed-form expressions,
the equi-rank surface for any antenna structure and any angle can be well
estimated. Furthermore, the effect of scatterers is also investigated, from
which some insights are drawn.
