We derive new Cramer-Rao lower bounds (CRBs) for the estimation of carrier phase and frequency offset from an unmodulated carrier or from a M-PSK data signal. The new CRBs are obtained formally from the exact likelihood function for the carrier phase and frequency offset, build from a block of received phase samples, and are applicable for a general alphabet size M. The bounds are compared with other previously obtained bounds (which also take into account the effect of random phase modulation) and with the performance of some popular feedforward algorithms for carrier phase and frequency offset estimation.
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Tavares et al. (2001) studied this question.
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