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We consider the carrier frequency offset estimation in a digital burst-mode transmission affected by phase noise. The corresponding Cramer-Rao lower bound is analyzed for linear modulations under a Wiener phase noise model and in the hypothesis of knowledge of the transmitted data. Even if we resort to a Monte Carlo average, from a computational point of view the evaluation of the Cramer-Rao bound is very hard. We introduce a simple but very accurate approximation that allows to carry out this task in a very easy way. As it is shown, the presence of the phase noise produces a remarkable performance degradation of the frequency estimation accuracy. In addition, we bound and we also gain some important hints on the estimators to be used in this scenario.