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In this paper, we resort to the expectation-maximization (EM) algorithm to tackle the inter-carrier interference (ICI) problem, caused by time-variant multipath channels, for both orthogonal frequency division multiplexing (OFDM) systems and bit-interleaved coded modulation (BICM)/OFDM systems. We first analyze the ICI in frequency domain with a reduced set of parameters, and following this analysis, we derive an EM algorithm for maximum likelihood (ML) data detection. An ML-EM receiver for OFDM systems and a TURBO-EM receiver for BICM/OFDM systems are then developed to reduce computational complexity of the EM algorithm and to exploit temporal diversity, the main idea of which is to integrate the proposed EM algorithm with a groupwise ICI cancellation method. Compared with the ML-EM receiver, the TURBO-EM receiver further employs a soft-output Viterbi algorithm (SOVA) decoder to exchange information with a maximum a posteriori (MAP) EM detector through the turbo principle. Computer simulation demonstrates that the two proposed receivers clearly outperform the conventional one-tap equalizer, and the performance of the TURBO-EM receiver is close to the matched-filter bound even at a normalized maximum Doppler frequency (MDF) up to 0.2.