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Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to accurately estimate the covariance matrix from $n$-dimensional independent Gaussian samples. However, in many practical applications, the received signal samples might be correlated, which makes the classical analysis inapplicable. In this paper, we develop a non-asymptotic analysis for the covariance matrix estimation from correlated Gaussian samples. Our theoretical results show that the error bounds are determined by the signal dimension $n$, the sample size $m$, and the shape parameter of the distribution of the correlated sample covariance matrix. Particularly, when the shape parameter is a class of Toeplitz matrices (which is of great practical interest), $O(n)$ samples are also sufficient to faithfully estimate the covariance matrix from correlated samples. Simulations are provided to verify the correctness of the theoretical results.
We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The cova
Obtaining channel covariance knowledge is of great importance in various Multiple-Input Multiple-Output MIMO communication applications, including channel estimation and covariance-based user grouping. In a massive MIMO system, covariance estimation
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We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac mixture dens