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In cellular systems, a basestation and mobile stations need to be synchronized before data exchange. Since the basestation clock reference is more accurate, a mobile station typically derives its clock reference from the basestation. But the carrier frequency offset due to Doppler shift may have harmful effects on the local clock derivation. This letter proposes a joint clock and frequency synchronization technique between a basestation and a mobile station, which is effective even with Doppler shift. We derive the joint estimation algorithm by analyzing the phase and the amplitude distortion caused by the sampling frequency offset and the carrier frequency offset. Simulation results showing the effectiveness of the proposed algorithm will also be presented.