Spatial correlation characterization of a uniform circular array in 3D MIMO systems

Abstract : —In this paper, we consider a uniform circular array (UCA) of directional antennas at the base station (BS) and the mobile station (MS) and derive an exact closed-form expression for the spatial correlation present in the 3D multiple-input multiple-output (MIMO) channel constituted by these arrays. The underlying method leverages the mathematical convenience of the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre polynomials. In contrast to the existing results, this generalized closed-form expression is independent of the form of the underlying angular distributions and antenna patterns. Moreover, the incorporation of the elevation dimension into the antenna pattern and channel model renders the proposed expression extremely useful for the performance evaluation of 3D MIMO systems in the future. The simulation results not only verify the derived analytical expression but also highlight the dependence of the spatial correlation on channel and array parameters. An interesting interplay between the mean angle of departure (AoD), angular spread and the positioning of antennas in the array is demonstrated.