  This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz
structured covariance matrix. In this regard, an equivalent reformulation of
the MLE problem is introduced and two iterative algorithms are proposed for the
optimization of the equivalent statistical learning framework. Both the
strategies are based on the Majorization Minimization (MM) paradigm and hence
enjoy nice properties such as monotonicity and ensured convergence to a
stationary point of the equivalent MLE problem. The proposed framework is also
extended to deal with MLE of other practically relevant covariance structures,
namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz.
Through numerical simulations, it is shown that the new methods provide
excellent performance levels in terms of both mean square estimation error
(which is very close to the benchmark Cram\'er-Rao Bound (CRB)) and
signal-to-interference-plus-noise ratio, especially in comparison with state of
the art strategies.
