On the Eigenstructure of the Signal-Only Tempo-Spatial Covariance Matrix of Broad-Band Sources Using a Circular Array

In this correspondence we deal with the eigenstructure of the signal-only part of the data covariance matrix for broad-band sources. It is well known that, unlike the narrow-band case, all eigenstructure parameters (the matrix rank, eigenvalues, and eigenvectors) depend on source spectral and spatial parameters, as well as on the relation between sources. We prove that, when using a two-dimensional equally spaced circular array with flat-spectrum broad-band sources, the eigenstructure of the signal-only tempo-spatial covariance matrix (TSCM) has properties similar to the narrow-band case. Most importantly, the effective rank of the TSCM depends only on the number of sources. Consequently, we suggest an alternative approach for the resolving of frequency/location ambiguity in the broad-band case that may lead to an effective eigenstructurebased parameter estimation algorithms (MUSIC type).