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This paper proposes a joint carrier recovery and blind decision feedback equalizer (DFE) based on stop-and-go MCMA and decision-direct least-mean-square (SG-MCMA-DD-LMS) algorithm. The equalizer initially operates in modified constant modulus algorithm (MCMA) mode under stop-and-go principle to compensate the channel distortion and acquire phase offset. When the channel eye is opened equalizer switches to decision-direct least-mean-square (DD-LMS) mode to decrease the mean square error (MSE) further and carrier recovery begins to work at the same time. Simulations show that the proposed scheme could achieve distorted channel equalization and larger carrier acquisition in fast time-varying channels.