# An Efficient Analytical Evaluation of the Electromagnetic Cross-Correlation Green's Function in MIMO Systems

## TL;DR

This paper derives exact analytical expressions for the electromagnetic Green's function in MIMO systems, enabling fast and accurate calculation of spatial correlation without numerical integrations.

## Contribution

It introduces a comprehensive analytical formulation for the electromagnetic Green's function in 3D MIMO systems, eliminating the need for numerical integration.

## Key findings

- Analytical expressions significantly reduce computation time.
- Applicable to arbitrary antenna locations and polarizations.
- Enhances accuracy of spatial correlation estimates.

## Abstract

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 (CGF), the most fundamental electromagnetic kernel needed for understanding and estimating spatial correlation metrics in multiple-antenna configurations. The analytical CGF is derived for the most general three-dimensional case, which can be used for fast CGF-based correlation matrix calculations in MIMO systems valid for arbitrary locations and relative polarizations of the constituent elements.