Estimation of kronecker structured channel covariances using training data

The problem of estimating second order statistics for MIMO channels is treated. It is assumed that the so called Kroneckermodel holds. This implies that the channel covariance is the Kronecker product of two covariance matrices associated with the transmit and receive array, respectively. The proposed estimator uses training data from a number of signal blocks to compute the estimate. This is in contrast to methods that assume that the channel realizations are directly available, or possible to estimate almost without error. It is also demonstrated how methods that make use of the training data indirectly via channel estimates can be biased. An estimator is derived that can, in an asymptotically optimal way, use, not only the structure implied by the Kronecker assumption, but also linear structure on the transmit- and receive covariance matrices. The performance of the proposed estimator is analyzed and numerical simulations illustrate the results and also provide insight into the small sample behavior of the proposed method.