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The problem of joint oscillator phase noise (PHN) estimation and data detection for multi-input multi-output (MIMO) systems using bit-interleaved-coded modulation is analysed. A new MIMO receiver that iterates between the estimator and the detector, based on the expectation-maximisation (EM) framework, is proposed. It is shown that at high signal-to-noise ratios, a maximum a posteriori (MAP) estimator can be used to carry out the maximisation step of the EM algorithm. Moreover, to reduce the computational complexity of the proposed EM algorithm, a soft decision-directed extended Kalman filter-smoother (EKFS) is applied instead of the MAP estimator to track the PHN parameters. The numerical results show that by combining the proposed EKFS-based approach with an iterative detector that employs low-density parity check codes, PHN can be accurately tracked. The simulations also demonstrate that compared to the existing algorithms, the proposed iterative receiver can significantly enhance the performance of MIMO systems in the presence of PHN.