Analysis on Asymptotic Orthogonality for Very Large Arrays

In this paper, we analyze the existence of asymptotic orthogonality in various propagation environments for very large arrays in different geometrical configurations. It is rigorously proved that: 1) in the case of spatially uncorrelated channels, asymptotic orthogonality exists for arrays in any geometrical configuration; 2) in the case of line-of-sight (LoS) propagation, asymptotic orthogonality exists for uniform linear arrays (ULA) and uniform planar arrays (UPA) but not for uniform circular arrays (UCA); 3) in the case of spatially correlated channels, asymptotic orthogonality exists for ULA and UPA only when there is no overlap between dominant virtual paths.