On Toeplitz and Kronecker structured covariance matrix estimation

A number of signal processing applications require the estimation of covariance matrices. Sometimes, the particular scenario or system imparts a certain theoretical structure on the matrices that are to be estimated. Using this knowledge allows the design of algorithms exploiting such structure, resulting in more robust and accurate estimators, especially for small samples. We study a scenario with a measured covariance matrix known to be the Kronecker product of two other, possibly structured, covariance matrices that are to be estimated. Examples of scenarios in which such a problem occurs are MIMO-communications and EEG measurements. When the matrices that are to be estimated are Toeplitz structured, we show our algorithms to be able to achieve the Cramér-Rao Lower Bound already at very small sample sizes.