Spherical Statistics and Spatial Correlation for Multielement Antenna Systems

The well-known assumption of horizontal plane wave propagation is investigated and evidence suggests that elevation plays a crucial role in defining the spatial correlation between signals on adjacent antenna array elements. To augment previously published studies, an explicit relationship between the distribution of scatterers in three-dimensional (3D) space and the spatial correlation is formulated. A novel approach is taken for modeling of the distribution of scatterers in space. More specifically, the distribution of scatterers is modeled by the 3D von Mises-Fisher (vMF) distribution. In addition, a closed-form expression is derived for the harmonic coefficients of the vMF density. The main derivation expresses the spherical harmonic coefficients associated with an arbitrary mean direction on the sphere. Further, a closed-form expression for the spatial correlation function (SCF) is derived, based on the spherical harmonic expansion (SHE) of plane waves as well as the harmonic coefficients of the expanded vMF density. A novel approach is proposed for including the effect of directional antenna responses in the SCF. Finally, the SCF is evaluated under the existence of multiple scatterer clusters in the channel.