Maximum likelihood estimation of structured persymmetric covariance matrices

In this paper we address estimation of the structured covariance matrix of a Gaussian process. To this end we assume that the aforementioned quantity is the sum of a positive semidefinite hermitian and persymmetric term, which accounts for the interference, plus a matrix proportional to the identity and representative of the internal noise covariance. Under these constraints we devise the maximum likelihood estimator of the overall disturbance covariance matrix and remarkably show that exploiting persymmetry, in conjunction with the others structural covariance informations, can lead to a significant reduction in the number of training data required for ensuring satisfactory performances.