The true Cramer-Rao bound for phase-independent carrier frequency estimation from a PSK signal

This contribution considers the Cramer-Rao bound (CRB) related to phase-independent carrier frequency estimation from a noisy PSK signal. Instead of estimating the frequency jointly with the carrier phase, we treat the phase as a nuisance parameter. Ideal symbol timing is assumed. Both cases of known data (training sequence) and random data are considered. We show that frequency estimation irrespective of the carrier phase yields a larger CRB than does joint frequency and phase estimation; the penalty resulting from the former strategy vanishes with increasing observation interval.