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Interference alignment (IA) has evolved as a powerful technique in the information theoretic framework for achieving the optimal degrees of freedom of interference channel. In practical systems, the design of specific interference alignment schemes is subject to various criteria and constraints. In this paper, we propose novel transceiver schemes for the MIMO interference channel based on the mean square error (MSE) criterion. Our objective is to optimize the system performance under a given and feasible degree of freedom. Both the total MSE and the maximum per-user MSE are chosen to be the objective functions to minimize. We show that the joint design of transmit precoding matrices and receiving filter matrices with both objectives can be realized through efficient iterative algorithms. The convergence of the proposed algorithms is proven as well. Simulation results show that the proposed schemes outperform the existing IA schemes in terms of BER performance. Considering the imperfection of channel state information (CSI), we also extend the MSE-based transceiver schemes for the MIMO interference channel with CSI estimation error. The robustness of the proposed algorithms is confirmed by simulations.