  Suppose that $\mathbf X_n=(x_{jk})$ is $N\times n$ whose elements are
independent real variables with mean zero, variance 1 and the fourth moment
equal to three. The separable sample covariance matrix is defined as
$\mathbf{B}_n = \frac1N\mathbf{T}_{2n}^{1/2} \mathbf{X}_n \mathbf{T}_{1n}
\mathbf{X}_n' \mathbf{T}_{2n}^{1/2}$ where $\mathbf{T}_{1n}$ is a symmetric
matrix and $\mathbf{T}_{2n}^{1/2}$ is a symmetric square root of the
nonnegative definite symmetric matrix $\mathbf{T}_{2n}$. Its linear spectral
statistics (LSS) are shown to have Gaussian limits when $n/N$ approaches a
positive constant.
