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Principal-Components, Covariance Matrix Tapers, and the Eigenvalue Spreading Problem

Joseph R. Guerci
Science Applications International Corporation
4001 N. Fairfax Drive, Suite 400
Arlington, VA 22203
tel: (703) 243-9830
email: jguerci@trg1.saic.com

Jameson S. Bergin
Information Systems Laboratory

Abstract A major advantage of principal-components (PC) techniques is the potential for significant reduction in the sample support requirements to achieve adequate interference mitigation. Specifically, if the dominant interference (e.g., clutter and/or jamming) is confined to a rank K subspace, then it has been previously established that a reduction in sample support requirements by a factor of approximately K/2N can be realized over traditional sample matrix inverse (SMI) methods, where N is the total number of adaptive degrees-of-freedom (DOFs). This can be of significant practical benefit in environments where the requisite i.i.d. stationarity assumption is taxed (e.g., heterogeneous land clutter). Unfortunately this advantage is essentially lost in those situations were eigenvalue spreading occurs-a problem that appears evident in many real-world data sets and is justifiable based on physical modeling of the environments.

In this paper, a new approach to adaptive interference mitigation is presented based on the recognition that many eigenvalue spreading mechanisms (e.g., internal clutter motion, clutter scintillation, and jammer/clutter diffuse multipath) are effectively modeled as a covariance matrix tapering (CMT) of the interference covariance matrix associated with the "unspread" dominant eigenvalues. In particular, a combined PC-CMT approach is described which, for reasonable eigenvalue spreading environments, essentially restores the K/2N sample support reduction factor. For modest spreading environments, restoration is readily achieved by first estimating the covariance matrix associated with the K dominant eigenvectors, then applying a CMT to account for the remaining eigenvalues. For more severe spreading situations, a simultaneous estimation of the CMT and principal components is indicated for which a novel inverse tapering eigenvalue compression algorithm is offered. Several examples of interest to airborne space-time adaptive radar are included to demonstrate the practical utility of the PC-CMT approach.

Presentation (pdf format)



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