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

  • Angela Quinlan1Email author,

    Affiliated with

    • Jean-Pierre Barbot2,

      Affiliated with

      • Pascal Larzabal2 and

        Affiliated with

        • Martin Haardt3

          Affiliated with

          EURASIP Journal on Advances in Signal Processing20062007:071953

          DOI: 10.1155/2007/71953

          Received: 29 September 2005

          Accepted: 4 June 2006

          Published: 4 October 2006

          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.

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          Authors’ Affiliations

          (1)
          Department of Electronic and Electrical Engineering, University of Dublin
          (2)
          SATIE Laboratory, École Normale Supérieure de Cachan
          (3)
          Communications Research Laboratory, Ilmenau University of Technology

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          Copyright

          © Angela Quinlan et al. 2007

          This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.