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In this paper, we propose a semi-blind state-space based receiver that jointly performs channel estimation and data detection in MIMO systems subject to fast frequency-selective fading. To accomplish these two tasks, we first define state equations representing the dynamics of channel and transmitted signals. Then, we obtain the state vector by concatenating the transmitted signals and the channel coefficients. This choice of state vector leads to a nonlinear observation equation and hence to the use of the extended Kalman filter (EKF) to estimate the states variables. We then develop the EKF and show that the proposed receiver is a generalization of many similar receivers for SISO channels. We also develop a reduced complexity version of the proposed algorithm. Simulation results show the performance gains of the proposed receiver when compared to other commonly used receivers.