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In this paper, we propose a reduced-complexity iterative algorithm for joint maximum a posteriori (MAP) detection and the cochannel interferences (CCIs) suppression in orthogonal frequency-division multiplex (OFDM)-based spatial multiplexing systems, also known as multiple-input-multiple-output systems. The receiver employs an iterative architecture in which each iteration stage consists of channel/covariance estimation for CCIs and MAP detection, which suppresses interference while detecting the data. The interference suppression is performed in the MAP detection by whitening the interferences through a combination of the estimated covariance with the conventional MAP detection metric. Moreover, a complexity-reduction scheme is proposed for implementing an iterative MAP receiver without incurring performance degradation. Extensive simulations have demonstrated that the proposed scheme dramatically improves the performance compared to that of an iterative MAP scheme without interference suppression. The receiver complexity is significantly reduced with negligible performance degradation. Furthermore, it also can effectively suppress not only synchronous CCIs, but also all kinds of asynchronous CCIs without any a priori information on the CCIs.