We follow [279] for this development. Define an *M* × *N* complex matrix as

where (*X*_{ij})_{1≤i≤M, 1≤j≤N} are (a number of MN) i.i.d. complex Gaussian variables . **x**_{1}, **x**_{2}, …, **x**_{N} are columns of **X**. The covariance matrix **R** is

The empirical covariance matrix is defined as

In practice, we are interested in the behavior of the empirical distribution of the eigenvalues of for large *M* and *N*. For example, how do the histograms of the eigenvalues (λ_{i})_{i=1, …, M} of behave when *M* and *N* increase? It is well known that when *M* is fixed, but *N* increases, that is, is small, the large law of large numbers requires

In other words, ...

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