Low-SNR limit of the Cramer-Rao bound for estimating the time delay of a PSK, QAM, or PAM waveform

Author

Steendam, Heidi ; Moeneclaey, Marc

Author_Institution

Dept. of Telecommun. & Inf. Process., Ghent Univ., Belgium

Volume

5

Issue

1

fYear

2001

Firstpage

31

Lastpage

33

Abstract

In this letter we consider the Cramer-Rao bound (CRB) for the estimation of the time delay of a noisy linearly modulated signal with random data symbols and random carrier phase. Because of the presence of the nuisance parameters (i.e., data symbols and carrier phase), a closed-form expression of this CRB is very hard to obtain for arbitrary PSK, QAM or PAM constellations and a band-limited transmit pulse. Instead, we derive a simple expression for the limit of the CRB at low signal-to-noise ratio (SNR), which is a relevant benchmark for timing recovery algorithms operating at small E/sub s//N/sub 0/.

Keywords

delay estimation; phase shift keying; pulse amplitude modulation; quadrature amplitude modulation; synchronisation; Cramer-Rao bound; PAM constellation; PSK constellation; QAM constellation; band-limited transmit pulse; closed-form expression; low signal-to-noise ratio; low-SNR limit; noisy linearly modulated signal; nuisance parameters; random carrier phase; random data symbols; time delay estimation; timing recovery algorithms; Closed-form solution; Delay effects; Delay estimation; Phase estimation; Phase modulation; Phase noise; Phase shift keying; Quadrature amplitude modulation; Signal to noise ratio; Timing;

fLanguage

English

Journal_Title

Communications Letters, IEEE

Publisher

ieee

ISSN

1089-7798

Type

jour

DOI

10.1109/4234.901818

Filename

901818