Bounds for Eigenvalues of Spatial Correlation Matrices With the Exponential Model in MIMO Systems

It is important to understand the properties of spatial correlation matrices in multiple-input multiple-output (MIMO) systems. In this paper, we derive new bounds for the maximum and minimum eigenvalues of spatial correlation matrices characterized by the exponential model. The new upper bounds for the maximum and minimum eigenvalues are tighter than the previously known bounds. Moreover, the new lower bound for the minimum eigenvalue, which has not yet been derived in the literature as a function of the number of antennas, is also tight. In order to predict the behavior of these bounds, we investigate the gap between the lower and upper bounds. These bounds are directly applicable to the analysis of wireless communication scenarios, such as uniform planar arrays and ill-conditioned channels, which are expected to be widely used for massive MIMO systems.