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In this paper, a new data-aided joint phase and frequency estimator, which has very low computational complexity, is proposed and its variances of phase and frequency estimates are derived. To estimate the phase and frequency offset, first of all, the overall observation interval is divided into same length sub-intervals, and then phase estimates are independently computed based on symbols of the each sub-intervals. To be continue the sequence of computed phase estimates, proper integer multiples of $2{\pi}$ are added to (or subtracted from) the computed phase estimates, which is called linearized phase estimate. The phase offset of the proposed joint estimator is estimated by averaging the linearized phase estimates and the frequency offset by averaging the differences between consecutive linearized phase estimates. The variance of the proposed phase offset estimate is same to MCRB of phase if there is no frequency offset, but it is smaller than MCRB of phase if there is frequency offset. However, the variance of the proposed frequency offset estimate is bigger by at least 0.5 dB than MCRB of frequency with the same observation interval.
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