Degrees of Freedom in 3D Linear Large-Scale Antenna Array Communications—A Spatial Bandwidth Approach

For wireless communications using linear large-scale antenna arrays, we define a receiving coordinate system and parameterization strategy to facilitate the study of the impact of three-dimensional position and rotation of the arrays on the achievable spatial degrees of freedom (DoF) in line-of-sight (LOS) channels. An analytical framework based on spatial bandwidth analysis is developed, under which three elementary problems corresponding to three basic orthogonal receiving directions are investigated. For each of them, accurate, simple, and interpretable closed-form approximations for the achievable spatial DoF are derived, and the spatial region where a sufficient amount of spatial DoF is expected available is determined. The expressions can easily be integrated into large-scale system-level simulations. Some interesting and surprising observations are made from simulation studies based on the analytical results. For instance, the spatial bandwidth is shown to be approximately constant in almost the entire spatial multiplexing region. Moreover, in significant parts of this region, the optimal receive array orientation is not parallel with the transmitting array.