Compressive spectral estimation for nonstationary random processes

  • Authors:

  • Alexander Jung;Georg Taubock;Franz Hlawatsch

  • Affiliations:

  • Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Gusshausstrasse 25/389, A-1040, Austria;Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Gusshausstrasse 25/389, A-1040, Austria;Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Gusshausstrasse 25/389, A-1040, Austria

  • Venue:
  • ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
  • Year:
  • 2009

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Abstract

We propose a “compressive” estimator of the Wigner-Ville spectrum (WVS) for time-frequency sparse, underspread, nonstationary random processes. A novel WVS estimator involving the signal's Gabor coefficients on an undersampled time-frequency grid is combined with a compressed sensing transformation in order to reduce the number of measurements required. The performance of the compressive WVS estimator is analyzed via a bound on the mean square error and through simulations. We also propose an efficient implementation using a special construction of the measurement matrix.