In this paper, the challenging problem of joint channel estimation and data detection for multiple-input\r\nmultiple-output orthogonal frequency division multiplexing systems operating in time-frequency dispersive channels\r\nunder unknown background noise is investigated. Based on two different but equivalent signal models, two\r\nexpectation-maximization algorithm-based iterative schemes for joint data detection and channel and noise variance\r\nestimation are proposed. The first scheme jointly detects data and estimates the channel and noise variance, but the\r\ncomputational complexity is high, owing to the simultaneous detection and estimation for all antennas. To reduce\r\nthe computational complexity, a complexity-reduced scheme that is detecting data and estimating channel for only\r\none antenna during each iteration and holding the unknown quantities of other antennas to their last values is\r\nproposed, whose performance only slightly degrades compared to the first scheme. Moreover, both schemes are\r\nderived as closed-form expressions, and therefore, our proposed schemes are free of exhaustive search. Simulation\r\nresults demonstrate quick convergence of the proposed algorithm, and after convergence, the performance of the\r\nproposed algorithm is close to that of the optimal channel estimation and data detection case, which assumes full\r\ntraining and perfect channel state information.
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