Maximum likelihood estimation of spectral moments at low signal to noise ratios

A maximum likelihood (ML) estimator of spectral moments of a zero-mean complex Gaussian vector process, immersed in independent additive Gaussian white noise is proposed. The covariance function is assumed known in advance, apart from a vector of parameters which are related with the spectral moments. Since the maximization of the log-likelihood function yields a highly cumbersome algorithm, a more manageable objective function is considered. This objective function provides estimates consistent with probability one, and that are asymptotically efficient, which are the asymptotic properties of the ML estimator. For finite sample sizes, and signal to noise ratio (SNR) tending to zero, the results are similar to the ML results. Statistical characterization and simulation examples are presented.<>