A Novel Quantification of 3D Directional Spread from Small-Scale Fading Analysis

The directional dispersion of multipath energy arriving at the receiver is an important quantity, as increasing it leads to lower correlation between spatial diversity elements. The `RMS angular spread´ metric, commonly used to measure this, is only applicable for relatively small angles in the 2-D plane. The quantification of the 3-D directional spread is not straighforward, and must be justified analytically by showing its relation to spatial selectivity, and hence spatial correlation. In this paper, an analysis of the second order moments of spatial fading has been used to define a spatial covariance matrix, which fully describes the second order moments of the directional energy distribution. An eigenvalue decomposition of this matrix has been used to propose a concise quantification of directional spread that is applicable for arbitrary distribution of multipath rays or clusters in 3-D directions. The effect of array orientation has also been investigated.