The true Cramer-Rao bound for estimating the time delay of a linearly modulated waveform

Abstract
In this contribution we consider the Cramer-Rao bound (CRB) for the estimation of the time delay of a noisy linearly modulated signal with random data symbols. In spite of the presence of the nuisance parameters (i.e., the random data symbols), we obtain a closed-form expression of this CRB for arbitrary PSK, QAM or PAM constellations and a bandlimited square-root Nyquist transmit pulse.