Spatial-correlation-coefficient at the basestation, in closed-form explicit analytic expression, due to heterogeneously Poisson distributed scatterers

This letter analytically derives, for stochastically located scatterers, closed-form expressions of the uplink received-signal's spatial-correlation-coefficient across the basestation antenna array's spatial aperture, explicitly as a function of 1) the basestation's interantenna spacing, and 2) each scatterer-cluster's distance and spatial angle from the basestation. This rigorous analytical derivation is based on idealized geometric relationships among the mobile transmitter, the basestation's receiving antennas, and the scatterers (whose spatial distribution is modeled as Poisson-distributed with a multi-Gaussian heterogeneous intensity).