Spatial correlation from multipath with 3D power distributions having rotational symmetry

In this paper we give a general expression for the 3D spatial correlation experienced between two sensors in 3D-space for the class of normalized power distributions (representing farfield multipath sources) having a rotational symmetry about their mean direction axis. A general expansion for the 3D spatial correlation is presented and interpreted in terms of an associated eigenfunction equation. This enables us to develop closed-form coefficient expressions for the spatial correlation for a number of distributions such as the Gauss-Weierstrass kernel based distribution and the previous known results for the von Mises-Fisher power distribution. Analytical results generated fully account for the effect of varying in the relative orientation between the sensors in 3D and the power distribution mean direction which can be arbitrarily oriented. The results provide information on placement of sensors to reduce correlation effects.