  Extremely large aperture arrays (ELAAs) can offer massive spatial
multiplexing gains in the radiative near-field region in beyond 5G systems.
While near-field channel modeling for uniform linear arrays has been
extensively explored in the literature, uniform planar arrays-despite their
advantageous form factor-have been somewhat neglected due to their more complex
nature. Spatial correlation is crucial for non-line-of-sight channel modeling.
Unlike far-field scenarios, the spatial correlation properties of near-field
channels have not been thoroughly investigated. In this paper, we start from
the fundamentals and develop a near-field spatial correlation model for
arbitrary spatial scattering functions. Furthermore, we derive the lower
dimensional subspace where the channel vectors can exist. It is based on prior
knowledge of the three-dimensional coverage region where scattering clusters
exists and we derive a tractable one-dimensional integral expression. This
subspace is subsequently employed in a reduced-subspace least squares (RS-LS)
estimation method for near-field channels, thereby enhancing performance over
the traditional least squares estimator without the need for having full
spatial correlation matrix knowledge.
