On spatial correlation and effect of mutual coupling for multiple antennas under 3D environment

For evaluating the spatial correlation (SC) of multiple antennas under three-dimensional (3D) environment, the power angle spectrum of arrival signal is modeled as von Mises-Fisher (vMF) distributions on the sphere coordinate. On this basis, a closed-form expression and an approximate expression of SC for different multiple antenna arrays are derived. The mutual coupling (MC) and its impact on the received signal vector are analyzed, and the general expressions of SC with MC is derived. Simulation results validate that the proposed analytical expressions consistent with the numerical ones. In addition, spatial correlation coefficient with MC waves around the one without MC when the angle spread is small and the uniform rectangular array has the least effect caused by MC.