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.