Geometric Characterization of Eigenvalues of Covariance Matrix for Two-SourceArray Processing

摘要

For a two-source array processing scenario, normalized eigenvalues' expressionslambda sub 1 and lambda sub 2 are reduced to forms depending only on a real triplet: phase-dependent, variable xi, phase-independent variable eta, and a certain power ratio is confined to an isosceles-like region. We characterize: (1) this isosceles-like region and the many-to-one mapping from the Cartesian product of the temporal and spatial correlation unit-disks onto this region; (2) the behavior of the eigenvalues and their ratio as functions of the real triplet with respect to array processing, and; (3) a characterization of Speiser's eigenvalues bounds specialized to the two source scenario.