  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 previous 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.
