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The paper deals with the problem of blind carrier synchronization in orthogonal frequency division multiplexing (OFDM) systems when the transmitted signal is encoded using space-time block codes (STBC). In this context, the carrier synchronism is critical to guarantee the orthogonality of the OFDM subcarriers and minimize the intercarrier interference (ICI). The paper adopts the maximum likelihood (ML) principle to design optimal second-order estimators of the carrier frequency-offset. Most STBC are found to correlate the sequence of received symbols. When this correlation is observable, second-order techniques are able to improve their performance considerably and take benefit from the STBC structure. Different STBC schemes have been studied, and we conclude that: 1) orthogonal full-rate STBCs preserve the symbols uncorrelation; 2) to exploit the STBC correlation, the channel normally needs to be known at the receiver; 3) for some redundant STBC, the correlation can be taken into account, even if the channel is random. Besides the STBC consideration, we also show that channel knowledge is required in order to exploit the frequency selectivity of the OFDM channel for carrier synchronization.