Model Order Selection for Short Data: An Exponential Fitting Test (EFT)
1 Department of Electronic and Electrical Engineering, University of Dublin, Trinity College, Ireland
2 SATIE Laboratory, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, Cachan Cedex 94235, France
3 Communications Research Laboratory, Ilmenau University of Technology, P.O. Box 100565, Ilmenau 98684, Germany
EURASIP Journal on Advances in Signal Processing 2007, 2007:071953 doi:10.1155/2007/71953Published: 4 October 2006
High-resolution methods for estimating signal processing parameters such as bearing angles in array processing or frequencies in spectral analysis may be hampered by the model order if poorly selected. As classical model order selection methods fail when the number of snapshots available is small, this paper proposes a method for noncoherent sources, which continues to work under such conditions, while maintaining low computational complexity. For white Gaussian noise and short data we show that the profile of the ordered noise eigenvalues is seen to approximately fit an exponential law. This fact is used to provide a recursive algorithm which detects a mismatch between the observed eigenvalue profile and the theoretical noise-only eigenvalue profile, as such a mismatch indicates the presence of a source. Moreover this proposed method allows the probability of false alarm to be controlled and predefined, which is a crucial point for systems such as RADARs. Results of simulations are provided in order to show the capabilities of the algorithm.