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In this paper, an approximate maximum-likelihood (ML) receiver for differential space-time block codes is investigated. The receiver is derived from the ML criterion and is shown to mitigate error floor occurring in a conventional differential receiver very well. Because the receiver employs knowledges of signal-to-noise ratio (SNR) and fading rate, we study mismatched cases when these parameters are not accurate. It is shown that the receiver is more sensitive to the mismatched parameters when the fading rate is high. Then, a union bound on the bit error probability is derived. The bounds show good agreement with the simulation results at high fading rate and at high SNR. Finally, a modified receiver, denoted as multistage receiver, is proposed to compensate the so-called intrablock interference caused by the time-varying characteristic of the channel within a transmission block. The multistage receiver offers further reduction of error floor of about half order of magnitude as compared with an approximate ML receiver.