Analytically-derived explicit closed-form spatial-correlation function for the landmobile uplink with scatterers located stochastically as nonhomogeneous 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 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.