An Efficient Analytical Evaluation of the Electromagnetic Cross Correlation Green’s Function in MIMO Systems

In this paper, we completely eliminate all numerical integrations needed to compute the far-field envelope cross correlation (ECC) in multiple-input-multiple-output (MIMO) systems by deriving accurate and efficient analytical expressions for the frequency-domain cross correlation Green's functions (CGFs), the most fundamental electromagnetic kernel needed for understanding and estimating spatial correlation metrics in multiple-antenna configurations. After deriving the analytical CGF for the most general 3-D case, we propose an efficient algorithm for fast CGF-based correlation matrix calculations in MIMO systems valid for arbitrary locations and relative polarizations of the constituent elements. We finally include some numerical examples involving 8 × 8 and 16 × 16 massive MIMO arrays of small dipoles to validate the proposed analytical CGF-based algorithm, which demonstrate almost 98% reduction in computational time with respect to the conventional numerical integration-based procedure.