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

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

doi:10.1109/TIT.2002.1013133

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

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

Electrical and Computer Engineering

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114 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	1922-1934
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	48
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2002.1013133
State	Published - 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: philippe.ciblat@enst.fr). P. Loubaton is with the Laboratoire Système de Communication, Université de Marne-la-Vallée, Marne-la-Vallée, France (e-mail: loubaton@univ-mlv.fr). E. Serpedin is with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77845 USA (e-mail: erchin@spcom.tamu.edu). G. B. Giannakis is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: geor-gios@ece.umn.edu). Communicated by J. A. O’Sullivan, Associate Editor for Detection and Estimation. Publisher Item Identifier S 0018-9448(02)05336-1.

Keywords

Cumulant
Cyclostationary
Estimation
Frequency
Spectrum estimation
Symbol rate

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abstract = "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.",

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N2 - 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.

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

Abstract

Bibliographical note

Keywords

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