On the estimation of the covariance eigenspectrum of array sample observations

In this paper, we propose an estimator of the eigenspectrum of the array observation covariance matrix that builds upon the well-known power method and is consistent for an arbitrarily large array dimension. Traditional estimators based on the eigendecomposition of the sample covariance matrix are known to be consistent provided that the number of observations grow to infinity with respect to any other dimension in the signal model. On the contrary, in order to avoid the loss in the estimation accuracy associated with practical finite sample-size situations, a generalization of the conventional implementation is derived that proves to be a very good approximation for a sample-size and an array dimension that are comparatively large. The proposed solution is applied to the construction of a subspace-based extension of the Capon source power estimator. For our purposes, we resort to the theory of the spectral analysis of large dimensional random matrices, or random matrix theory. As it is shown via numerical simulations, the new estimator turns out to allow for a significantly improved estimation accuracy in practical finite sample-support scenarios.