Near-Field Spatial Correlation for Multi-path XL-Array Communications with Partial Visibility

For extremely large-scale array (XL-array) communications, the scatterers and/or user equipments (UEs) may be located in the near-field region and only visible to some portions of the XL-array. This paper studies the near-field spatial correlation function (S-CF) of multi-path XL-array communications with mixed line-of-sight (LoS) and non-LoS (NLoS) links. The generic near-field non-uniform spherical wave (NUSW) characteristic and the partial visibility property are considered. For the LoS link, a novel near-field S-CF is derived, which is in terms of the correlation of UE's visibility and location. It is found that the near-field S-CF depends on the UE's angle of arrival (AoA) and distance, which differs from the far-field result that only depends on the UE's AoA. For the NLoS links, we derive a novel integral expression for the near-field S-CF in terms of the correlation of the scatterers' visibility and location distribution. The near-field result is shown to depend on the scatterers' partial visibility and the power location spectrum (PLS) characterized by the AoAs and distances of scatterers, in contrast to the far-field model, which relies on the power angular spectrum (PAS). The result demonstrates that the near-field S-CF of the LoS/NLoS component no longer exhibits spatial wide-sense stationarity (SWSS) and is more generic than the far-field model. To gain further insights, we consider a specific scatterer's location distribution, namely the multi-ring scatterer model. Numerical results show the necessity of modeling near-field S-CF for XL-array communications with partial visibility.