Bounds on Eigenvalues of a Spatial Correlation Matrix

TL;DR

This paper derives tighter bounds on the extreme eigenvalues of spatial correlation matrices in massive MIMO systems, aiding in the analysis of wireless communication performance.

Contribution

It introduces new upper and lower bounds on the eigenvalues of exponential model-based spatial correlation matrices, improving accuracy over previous bounds.

Findings

New upper bound on maximum eigenvalue is tighter than previous bounds.

Lower bound on maximum eigenvalue closely matches the true value in most cases.

Upper bound on minimum eigenvalue is also shown to be tight.

Abstract

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.