Analytical results on the performance of some eigen-assisted array processors: two correlated source case

Analytic results on the performance of eigen-assisted methods in the presence of two correlated sources are presented. Based on the assumption that two narrowband sources are incident on an equispaced array, the two largest eigenvalues of the array correlation matrix, and their corresponding eigenvectors, are derived. The effects of correlation of sources and signal-to-noise ratio on the eigenvalue distribution and signal detection are studied. The effects of these factors on the two corresponding eigenvectors and the resolution of the eigen-assisted processors are examined. When correlation between the sources is not strong, the performance of the processor is shown to be affected by correlation very slightly. As a special case, it is proved that those methods reduce to classical delay-and-weight (or DFT) methods when the two sources are coherent (if no preprocessing is applied). This analytical result is then used to explain the well-known experimental phenomenon that when sources are coherent, the performance of these processors degrades severely