Title :
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
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;
Journal_Title :
Communications Letters, IEEE
DOI :
10.1109/4234.901818
