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.

翻译：本文推导了[14]所研究的“一般信息加噪声”型非中心协方差矩阵的极限谱分布的分析性质。通过定义其Stieltjes变换的方程，证明了该极限分布在远离零点处具有连续导数，且导数在其为正的区域内解析，并给出了其支撑集的判定准则。此外，我们将[14]的结果推广至允许底层随机矩阵行数与列数之比的所有可能取值。