ML estimation of covariance matrix for tensor valued signals in noise

In many signal processing algorithms the estimation of signal co-variance matrices is a key task. In many applications using tensor representation for the signals provides significant benefits in deriving new algorithms and revealing interesting signal properties. It is natural to model many signals in MIMO communications, physics, principal component analysis, or medical imaging using tensors. It is of high interest to develop signal processing algorithms for such problems. For some tensor-valued signals the covariance matrix may be approximated by a structured covariance with a Kronecker-product structure. This type of signals are referred to as separable. When the observed signals are contaminated by additive Gaussian noise, the separability property is lost and one ends up with shifted Kronecker-structured covariance matrices. In this paper, an iterative Maximum Likelihood (ML) estimator for covariance matrices of tensor-valued signals where covariance matrices have a shifted Kronecker-structure is proposed. The proposed algorithm is applied to wideband MIMO channel sounding measurements needed in realistic MIMO channel modeling.