Spatial Correlation Modeling and RS-LS Estimation of Near-Field Channels with Uniform Planar Arrays

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.