A 2-D spectral estimation approach for source detection in array processing

The source detection problem in array processing is studied in the case where the two-parameter (2-D) process y(m,n) representing the signal on the sensor n, sampled at time m, is stationary. In this case the spectral measure of y is a singular measure carried by straight lines that are related to the directional parameters of the sources. As in the well-known Pisarenko method, it is shown that the spatiotemporal covariance matrix is singular. The author evaluates its rank and shows that its Cholevsky decomposition makes it possible to find the number of sources and the support of the spectral measure of y (i.e. the directional parameters of the sources)