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 multimodal truncated Laplacian power azimuth spectrum that impinges on antenna elements exhibiting a directive radiation pattern that is widely used in standardization 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.