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This detector is an alternative to the multiple-symbol detector that has been considered almost exclusively in the past. In this new configuration, the receivers do not perform chip-level precompensation as in conventional scheme but bit-level postcompensation. That is, the bit-level autocorrelation operation is first implemented with the \u201craw\u201d chip sample, and then the carrier frequency offset effect (CFOE) embedded in the achieved statistic is compensated. Correspondingly, the cumulative error in the detection metric is decreased so much that the pervasive error floor for the conventional MSDD scheme is suppressed. Also, complexity efficient estimators for the MSDD scheme are reinvestigated, analyzed, and summarized. Simulation results demonstrate that this new detection strategy may achieve rather more encouraging gain from differential and spread spectrum coding than the conventional single differential coherent detection (SDCD) scheme. The pervasive error floor is also eliminated as compared with conventional MSDD scheme even if the most simple estimator is configured under large bit observation length. 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