Some properties of ordered eigenvalues of a Wishart matrix: application in detection test and model order selection

High resolution methods for estimation of parameters in signal processing (bearing angles in array processing or frequencies in spectral analysis for example) can suffer from a bad selection of the model order. This paper proposes an algorithm based on the properties of the eigenvalues of the covariance matrix. In the noise only case, this matrix is a Wishart matrix. For white noise the profile of ordered eigenvalues fits an exponential law. The proposed algorithm uses this property and looks for a mismatch between the observed profile and the model in order to detect the presence of a signal. Under estimation may result from the occurrence of small signal eigenvalues. Performances is greatly improved by the use of deflation for recursive detection-estimation test. Results of simulations are provided in order to show the capabilities of the algorithm.