Asymptotic analysis of blind cyclic correlation-based symbol-rate estimators

Philippe Ciblat, Philippe Loubaton, Erchin Serpedin, Georgios B. Giannakis

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This paper considers the problem of blind symbol rate estimation of signals linearly modulated by a sequence of unknown symbols. Oversampling the received signal generates cyclostationary statistics that are exploited to devise symbol-rate estimators by maximizing in the cyclic domain a (possibly weighted) sum of modulus squares of cyclic correlation estimates. Although quite natural, the asymptotic (large sample) performance of this estimator has not been studied rigorously. The consistency and asymptotic normality of this symbol-rate estimator is established when the number of samples N converges to infinity. It is shown that this estimator exhibits a fast convergence rate (proportional to N-3/2), and it admits a simple closed-form expression for its asymptotic variance. This asymptotic expression enables performance analysis of the rate estimator as a function of the number of estimated cyclic correlation coefficients and the weighting matrix. A justification for the high performance of the unweighted estimator in high signal-to-noise scenarios is also provided.

Original languageEnglish (US)
Pages (from-to)1922-1934
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2002

Bibliographical note

Funding Information:
Manuscript received April 2, 2000; revised February 7, 2002. This work was supported by a DGA/CNRS Fellowship. P. Ciblat is with the Département Communications et Electronique, Ecole Nationale Supérieure des Télécommunications, 75634 Paris Cedex 13, France (e-mail: P. Loubaton is with the Laboratoire Système de Communication, Université de Marne-la-Vallée, Marne-la-Vallée, France (e-mail: E. Serpedin is with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77845 USA (e-mail: G. B. Giannakis is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: Communicated by J. A. O’Sullivan, Associate Editor for Detection and Estimation. Publisher Item Identifier S 0018-9448(02)05336-1.


  • Cumulant
  • Cyclostationary
  • Estimation
  • Frequency
  • Spectrum estimation
  • Symbol rate


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