Subspace leakage analysis of sample data covariance matrix

Subspace based methods provide a good compromise between performance and complexity. However, these methods are exposed to performance breakdown at the low SNR and/or small sample size region. It has been known for a long time that a major reason for such performance breakdown is the subspace swap phenomenon. However, in some scenarios such as the case of closely spaced sources, the breakdown happens before the subspace swap occurs. The reason is identified to be the intersubspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, we formally define the notion of subspace leakage which can be used as a measure for performance analysis and comparison of different methods used for estimating the signal and noise subspaces. We further study the statistical properties of the subspace leakage for the case of sample data covariance matrix.