MELT—Maximum-Likelihood Estimation of Low-Rank Toeplitz Covariance Matrix

In this letter, we develop a low-complexity algorithm named maximum-likelihood estimation of low-rank Toeplitz covariance matrix (MELT) to solve the maximum-likelihood estimation of a low-rank Toeplitz covariance matrix. Our derivation of MELT is based on the technique of majorization-minimization (MM), in which we design and optimize a novel tight upper-bound function. MELT is an iterative algorithm, and its each iterative step is a closed-form update, which can be implemented efficiently by fast Fourier transforms. As MELT is based on MM, it enjoys nice properties such as monotonicity and guaranteed convergence to a stationary point. Finally, we numerically show that the performance of MELT is much better than some of the algorithms currently available in the literature.