Geometric characterization of eigenvalues of covariance matrix for two-source array processing

For a two-source array processing scenario, the normalized eigenvalues expressions λ₁ and λ₂ are reduced to forms depending only on a real triplet: phase-dependent variable ξ, phase-independent variable η, and power ratio π ₁/π₂. (ξ, η) is confined to an isosceles-like region. This isosceles-like region is characterized along with the many-to-one mapping from the Cartesian product of the temporal and spatial correlation unit-disks onto this region. The behavior of the eigenvalues and their ratio as functions of the real triplet with respect to array processing are also discussed. A characterization is given of Speiser´s (1989) eigenvalue bounds specialized to the two source scenario