  This paper studies the problem of estimating a covariance matrix from
correlated sub-Gaussian samples. We consider using the correlated sample
covariance matrix estimator to approximate the true covariance matrix. We
establish non-asymptotic error bounds for this estimator in both real and
complex cases. Our theoretical results show that the error bounds are
determined by the signal dimension $n$, the sample size $m$ and the correlation
pattern $\textbf{B}$. In particular, when the correlation pattern $\textbf{B}$
satisfies $tr(\textbf{B})=m$, $||\textbf{B}||_{F}=O(m^{1/2})$, and
$||\textbf{B}||=O(1)$, these results reveal that $O(n)$ samples are sufficient
to accurately estimate the covariance matrix from correlated sub-Gaussian
samples. Numerical simulations are presented to show the correctness of the
theoretical results.
