Cramér-Rao lower bound and EM algorithm for envelope-based SNR estimation of nonconstant modulus constellations

  • Authors:

  • Wilfried Gappmair;Roberto López-Valcarce;Carlos Mosquera

  • Affiliations:

  • Institute of Communication Networks and Satellite Communications, Graz University of Technology, Austria;Department of Signal Theory and Communications, University of Vigo, Spain;Department of Signal Theory and Communications, University of Vigo, Spain

  • Venue:
  • IEEE Transactions on Communications
  • Year:
  • 2009

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Abstract

Signal-to-noise ratio (SNR) estimation for linearly modulated signals is addressed in this letter, focusing on envelope-based estimators, which are robust to carrier offsets and phase jitter, and on the challenging case of nonconstant modulus constellations. For comparison purposes, the true Cramér-Rao lower bound is numerically evaluated, obtaining an analytical expression in closed form for the asymptotic case of high SNR values, which quantifies the performance loss with respect to coherent estimation. As the maximum-likelihood algorithm is too complex for practical implementation, an expectation-maximization (EM) approach is proposed, achieving a good tradeoff between complexity and performance for medium-to-high SNRs. Finally, a hybrid scheme based on EM and moments-based estimates is suggested, which performs close to the theoretical limit over a wide SNR range.