On the statistics of eigenvectors of sample covariance matrices

Eigenvectors of sample covariance matrices are used in a variety of estimation algorithms, especially for temporal and spatial spectrum analysis. The second order statistics of these eigenvectors are needed in the performance analysis of such algorithms. Formulas for the second order statistics of the eigenvectors have been derived in the statistical literature and are widely used in works on performance analysis. We point out some difficulties in using these results, due to the non-uniqueness of the definition of eigenvectors, and show that the second order statistics of eigenvectors evaluated by Monte-Carlo simulations may not match the theoretical results. We also propose a solution to the problem.