Eigenvalues Of Covariance Matrix For Two-Source Array processing

Abstract : This report begins with a survey of narrowband direction-finding algorithms in element space. Then it discusses a simple stress measure to direction-finding algorithms applied to scenarios with two sources. Eigenvalue weighting appears in some noise subspace methods, in parametric signal subspace fitting methods, and in nonparametric subspace adaptive nulling beamforming. For a two-source array-processing scenario, normalized large and small eigenvalues are reduced to forms depending only on a real triplet. Presented also are some easy-to-remember formulas that enable one to exercise 'back-of-envelope' assessment of scenarios. The small eigenvalue is shown to diminish qualitatively and quantitatively for two arrival scenarios increasingly stressed with high temporal and/or spatial correlations. The special case of equal-strength signal arrivals also important in low angle radar tracking, shares many rich structures. The equal-strength case also has several additional unique features for signal eigenvalue ratio which is important in direction finding.