A new look into the issue of the Cramér-Rao Bound for delay estimation of digitally modulated signals

The Cramer-Rao bound (CRB) with its modifications is a well known lower bound on the variance of any unbiased estimator of an unknown parameter. Focusing on the estimation of the time-delay experienced by a digitally modulated signal, we first introduce an approximation of the modified Cramer-Rao bound (MCRB) as a function of the spectral properties of the modulated signal, irrespective of the specific format of the digital modulation. In particular, we show the equivalence of the MCRB for single carrier modulation and for multicarrier modulation. As a corollary, it is shown that multicarrier signals with uneven power distribution and/or non-contiguous frequency allocation bear a smaller MCRB than equally spaced and powered modulations.