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Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ datamatrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations.The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbfY^*_n$ when $p$ increase with $n$ has been considered by some authors recently.This model has known an increasing popularity due to its widely applications inmulti-user multiple-input single-output (MISO) systems and robust signalprocessing. In this paper, for more convenient applications in practice, wewill investigate the spectral distribution of $\mathbf S_n$ under milder momentconditions than existing work. We also discuss a potential application insample classification.

On singular value distribution of large dimensional data matrices whose columns have different correlations