Bounds on Eigenvalues of a Spatial Correlation Matrix

It is critical to understand the properties of spatial correlation matrices in massive multiple-input-multiple-output (MIMO) systems. We derive new bounds on the extreme eigenvalues of a spatial correlation matrix that is characterized by the exponential model in this paper. The new upper bound on the maximum eigenvalue is tighter than the previously known bound. Moreover, numerical studies show that our new lower bound on the maximum eigenvalue is close to the true maximum eigenvalue in most cases. We also derive an upper bound on the minimum eigenvalue that is also tight. These bounds can be exploited to analyze many wireless communication scenarios including uniform planar arrays, which are expected to be widely used for massive MIMO systems.