An Analytical Formula of Spatial Correlation Based on the Hierarchical Angle Structure for 3GPP Spatial Channel Model

In this paper, an analytical expression of normalized spatial correlation of a hierarchical angle structure for 3GPP Spatial Channel Model (SCM) is derived. Most of the existing formulas of the normalized spatial correlation were derived by simplifying the angle structure. In the paper, the hierarchical angle is considered as a function of multiple random variables, which can include those simplified angle structures as special cases. A closed-form expression of the probability density function of the hierarchical angle for uniform linear array is developed that can yield the analytical formula of normalized spatial correlation. Computer evaluation shows that the derived formula matches well with the simulated correlations generated from the 3GPP SCM.