Eigenspace dynamics of sample covariance matrices
Jorge E. Quijano, Lisa M. Zurk · The Journal of the Acoustical Society of America · 2013
Estimation of the sample covariance matrix is a challenge in array processing, particularly with large-aperture arrays operating in dynamic environments affected by fast maneuvering interferers and background noise. Minimizing the impact of time-dependent variations in the underlying signal statistics requires short observation intervals, thereby reducing the number of snapshots available for covariance estimation. Distinguishing between true variations in the received signal statistics and artifacts introduced by insufficient samples is still an open field of research. Recent developments in random matrix theory (RMT) have provided mathematical foundations to understand the behavior of sample eigenvalues and eigenvectors, and how they deviate from their population counterparts due to the lack of snapshot support. Similarly, expressions have been obtained to describe the “distance” between an initial eigenspace (spanned by p eigenvectors), relative to a subsequent eigenspace (spanned by q eigenvectors). In this paper, simulations corresponding to a horizontal array operating in a realistic environment are used to investigate RMT-based metrics that quantify time-dependent eigenspace stability. This research develops mathematically justifiable methods for proper data segmentation into intervals that exhibit local stationarity, providing data-driven higher bounds for the number of snapshots available for the computation of sample covariance matrices.