SEVENTH
ANNUAL 

PrincipalComponents, 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) 2439830 email: jguerci@trg1.saic.com Jameson S. Bergin Information Systems Laboratory Abstract A major advantage of principalcomponents (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 degreesoffreedom (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 occursa problem that appears evident in many realworld 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 PCCMT 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 spacetime adaptive radar
are included to demonstrate the practical utility of the PCCMT approach. 
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