EURASIP Journal on Advances in Signal Processing 
Volume 2007 (2007), Article ID 71953, 11 pages
doi:10.1155/2007/71953
Research Article

Model Order Selection for Short Data: An Exponential Fitting Test (EFT)

Angela Quinlan,1 Jean-Pierre Barbot,2 Pascal Larzabal,2 and Martin Haardt3

 1Department of Electronic and Electrical Engineering, University of Dublin, Trinity College, Ireland
2SATIE Laboratory, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, Cachan Cedex 94235, France
3Communications Research Laboratory, Ilmenau University of Technology, P.O. Box 100565, Ilmenau 98684, Germany
Received 29 September 2005; Revised 31 May 2006; Accepted 4 June 2006

Recommended by Benoit Champagne

Abstract

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.