On the Second-Order Statistics of the EVD of Sample Covariance Matrices—Application to the Detection of Noncircular Or/and NonGaussian Components

This correspondence presents an asymptotic analysis of the eigenvalue decomposition (EVD) of the sample covariance matrix associated with independent identically distributed (i.i.d.) non necessarily circular and Gaussian data that extends the well known analysis presented in the literature for circular and Gaussian data. Closed-form expressions of the asymptotic bias and variance of the sample eigenvalues and eigenvectors are given. As an application of these extended expressions, the statistical performance analysis of the widely used minimum description length (MDL) criterion applied to the detection of the number of noncircular or/and non-Gaussian sources impinging on an array of sensors is considered with a particular attention paid to uncorrelated rectilinear sources.