### 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 |
---|---|

Pages (from-to) | 1922-1934 |

Number of pages | 13 |

Journal | IEEE Transactions on Information Theory |

Volume | 48 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Information Systems

### Cite this

*IEEE Transactions on Information Theory*,

*48*(7), 1922-1934. https://doi.org/10.1109/TIT.2002.1013133

**Asymptotic analysis of blind cyclic correlation-based symbol-rate estimators.** / Ciblat, Philippe; Loubaton, Philippe; Serpedin, Erchin; Giannakis, Georgios B.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 48, no. 7, pp. 1922-1934. https://doi.org/10.1109/TIT.2002.1013133

}

TY - JOUR

T1 - Asymptotic analysis of blind cyclic correlation-based symbol-rate estimators

AU - Ciblat, Philippe

AU - Loubaton, Philippe

AU - Serpedin, Erchin

AU - Giannakis, Georgios B.

PY - 2002/7

Y1 - 2002/7

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.

AB - 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.

KW - Cumulant

KW - Cyclostationary

KW - Estimation

KW - Frequency

KW - Spectrum estimation

KW - Symbol rate

UR - http://www.scopus.com/inward/record.url?scp=0036649558&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036649558&partnerID=8YFLogxK

U2 - 10.1109/TIT.2002.1013133

DO - 10.1109/TIT.2002.1013133

M3 - Article

AN - SCOPUS:0036649558

VL - 48

SP - 1922

EP - 1934

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 7

ER -