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In this paper, we focus on the design of iterative receivers for OFDM coded systems in unknown broadband MIMO fading channels. The MIMO fading model is described by the environmental parameters such as mean angle of arrival, angular spread, antenna spacing, multiple clustered paths and Doppler shift. First, an expectation-maximization (EM)-based iterative receiver is presented for OFDM coded MIMO system without outer channel coding. The EM procedure is initialized by exploiting the time-domain correlation of the MIMO channels. When there is a mismatch on carrier frequency between the transmitter and receiver ends, which degrades the receiver performance, we also provide a scheme for frequency offset correction in MIMO systems. We further investigate a turbo-based EM receiver for OFDM coded MIMO system by adding interleaving and deinterleaving operators and outer channel coding. The receiver performance is proved to be greatly improved. For both systems, with and without outer channel coding, the performance degradation due to the spatial-domain correlation and/or frequency offset is presented in simulations.