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.

This paper is first in the open literature of wireless landmobile radiowave cellular communication to derive via thorough mathematics explicit closed-form expressions for the uplink received-signal's spatial-correlation-coefficient function across the basestation antenna-array's aperture. This rigorous analytical derivation is based on geometric relationships among the mobile transmitter, the basestation's receiving antennas, and the scatterers. The derived spatial-correlation-coefficient functions are expressed explicitly in terms of the base-station's interantenna spacing and in terms of each scatterer-cluster's distance and spatial angle from the base-station. The scatterers' spatial distribution is herein modeled as stochastic, Poisson-distributed with multiGaussian intensity over a two-dimensional space. This nonhomogeneous stochastic spatial distribution accommodates better the field variability in the scatterers' spatial locations than would deterministic spatial distributions (like the uniform-ring, the uniform-disc, or the Gaussian spatial distributions) that currently dominate the literature.