Fourth-order spatial correlation-coefficient across the uplink receiver's spatial aperture analytically derived in closed form

This paper is first in the open literature (to the authors' best knowledge) on wireless channel fading to derive the uplink received signal's fourth-order spatial-correlation coefficient function across a receiving sensor-array's aperture. This derivation is mathematically rigorous and is based on idealized geometric relationships among the mobile transmitter, the base-station's receiving antennas, and the scatterers of the channel. The scatterers' spatial locations are modeled as Poisson distributed, with a Gaussian intensity over a two-dimensional space. This scatterer model has previously been empirically verified to produce faithful expressions for the second-order spatial correlation coefficient. The final formula is in closed form, explicit in terms of the simple geometric model's few independent parameters.