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

H. Steendam, M. Moeneclaey
2001 IEEE Communications Letters  
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, here we derive a simple expression for the limit of the CRB at low
more » ... e ratio (SNR), which is a relevant benchmark for timing recovery algorithms operating at small 0 .
doi:10.1109/4234.901818 fatcat:iecw2dajcnbe3bz2rstoiuvsx4