Estimation of large toeplitz covariance matrices and application to source detection

In this paper, performance results of two types of Toeplitz covariance matrix estimators are provided. Concentration inequalities for the spectral norm for both estimators have been derived showing exponential convergence of the error to zero. It is shown that the same rates of convergence are obtained in the case where the aggregated matrix of time samples is corrupted by a rank one matrix. As an application based on this model, source detection by a large dimensional sensor array with temporally correlated noise is studied.