A remark on the definition of correlation coefficient by propagation modeling

Spatial correlation is an important index to evaluate performance of multi-antenna systems. Low correlation leads to good diversity performance [1] and large channel capacity [2]. The equations of spatial correlation are derived from Bessel function [3], radiation patterns [4]-[6], S-parameters [6], and the channel matrix [7]. Although the values of the correlation coefficient are different according to the derivation methods, previous researches have not focused on the issue. This paper clarifies applicable conditions for the equation of each correlation coefficient. Then, we reveal that under Rayleigh fading environments, the spatial correlation is properly evaluated by the equation based on three-dimensional radiation patterns, however, under environments with strong direct waves, the equation based on the channel matrix should be used for the evaluation.