Analytical spatial correlation analysis based on the hierarchical angle model for uniform linear and circular antenna arrays

In this study, an analytical analysis of normalised spatial correlation based on a hierarchical angle model for uniform linear array (ULA) and uniform circular array (UCA) over clustered narrowband multiple-input multiple-output channels is presented. The clustered channel has independent multiple paths, each of which is a cluster consisting of a number of independent subpaths, constructing a hierarchical angle structure. Unlike most of existing analysis methods that employ various simplification to the hierarchical angle, in this study, the hierarchical angle is expressed as a function of bivariate random variables. This formulation can include the simplified models as special cases. Assuming the angle of departure and angle of arrival of each subpath are independent, a closed-form spatial correlation expression between transmit and receive antennas of ULA or UCA is derived. Simulation results show that the theoretical spatial correlation matches well with the simulated one with channel data generated from the 3GPP spatial channel model for different scenarios.