Closed-Form Expressions for the Correlation Coefficient of Directive Antennas Impinged by a Multimodal Truncated Laplacian PAS

This paper addresses the derivation of a closed-form expression for the correlation coefficient of a pair of antenna elements at the base station. The closed-form expression is derived for the case of a multi-modal, truncated Laplacian Power Azimuth Spectrum which impinges on antenna elements exhibiting a directive radiation pattern that is widely used in standardisation bodies. To avoid numerical instability, an approximation for small Azimuth Spreads is presented. The proposed closed-form expression, along with its approximation, is successfully validated against the numerical computation of the correlation coefficient.