Near-Field Spatial Correlation for Extremely Large-Scale Array Communications

Abstract

Extremely large-scale array (XL-array) communications correspond to systems whose antenna sizes are so large that the scatterers and/or users may no longer be located in the far-field region. By discarding the conventional far-field uniform plane wave (UPW) assumption, this letter studies the near-field spatial correlation of XL-array communications, by taking into account the more generic non-uniform spherical wave (NUSW) characteristics. It is revealed that different from the far-field channel spatial correlation which only depends on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power angular spectrum</i> (PAS), the near-field spatial correlation depends on the scattered power distribution not just characterized by their arriving angles, but also by the scatterers’ distances, which is termed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power location spectrum</i> (PLS). A novel integral expression is derived for the near-field spatial correlation in terms of the scatterers’ location distribution, which includes the far-field spatial correlation as a special case. The result shows that different from the far-field case, the near-field spatial correlation no longer exhibits <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spatial stationarity</i> in general, since the correlation coefficient for each pair of antennas depends on their specific positions, rather than their relative distance only. To gain further insights, we consider a generalized one-ring model for scatterer distribution, where the ring center may be flexibly located. Numerical results are provided to show the necessity of the near-field spatial correlation modelling for XL-array communications.