Analysis of the limiting spectral distribution of large dimensional General information-plus-noise type matrices

TL;DR

This paper analytically characterizes the limiting spectral distribution of large non-central covariance matrices of the information-plus-noise type, extending previous results to all aspect ratios and detailing the distribution's support and properties.

Contribution

It provides a comprehensive analysis of the spectral distribution for a broader class of matrices, including all ratios of rows to columns, with explicit support criteria.

Findings

Distribution has a continuous derivative away from zero

Derivative is analytic where positive

Support determination criterion established

Abstract

In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in [14] to allow for all possible ratios of row to column of the underlying random matrix.