Analytically-derived explicit closed-form spatial-correlation function for the landmobile uplink with scatterers located stochastically as non-homogeneous poisson

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 inter-antenna 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 a multi-Gaussian intensity over a two-dimensional space. This non-homogeneous 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.