Analysis of Eigenspace Dynamics with Applications to Array Processing.

摘要

For an N-element array (Fig.1(a)), methods such as beamforming and singular value decomposition rely on estimation of the sample covariance matrix, computed from M independent data snapshots. As M , the sample covariance is a consistent estimator of the true population covariance. However, this ideal condition cannot be met in most practical situations,1-2 in which large-aperture arrays operate in the presence of fast maneuvering interferers, or with towed/drifting arrays strongly affected by deformation or array-depth perturbations. The long-term goal of this effort is the development of physically motivated models to statistically describe the eigenstructure (eigenvalues and eigenvectors) of sample covariance matrices in sample-starved settings, and the use of those models for performance analysis and improvement of array processing methods. To this end, mathematical tools developed in the context of Random Matrix Theory (RMT)3-6 (mostly focused in the regime N~M) and High Dimension, Low Sample Size (HDLSS) array processing7-8 (which considers N>>M) are applied to obtain statistical descriptions of sample eigenvalues/eigenvectors and how those quantities differ from the (true) population eigenpairs. Additional long-term goals are exploiting the information carried by sample eigenvectors for the improvement of estimators of the sample covariance matrix (i.e., signal versus noise subspaces), and for quantifying local stationary in array data (Fig.1 (b)).