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This paper proposes a training-based channel estimation scheme for achieving quality-of-service discrimination between legitimate and unauthorized receivers in wireless multiple-input multiple-output (MIMO) channels. The proposed method has applications ranging from user discrimination in wireless TV broadcast systems to the prevention of eavesdropping in secret communications. By considering a wireless MIMO system that consists of a multiple-antenna transmitter, a legitimate receiver (LR) and an unauthorized receiver (UR), we propose a multi-stage training-based discriminatory channel estimation (DCE) scheme that aims to optimize the channel estimation performance of the LR while limiting the channel estimation performance of the UR. The key idea is to exploit the channel estimate fed back from the LR at the beginning of each stage to enable the judicious use of artificial noise (AN) in the training signal. Specifically, with knowledge of the LR's channel, AN can be properly superimposed with the training data to degrade the UR's channel without causing strong interference on the LR. The channel estimation performance of the LR in earlier stages may not be satisfactory due to the inaccuracy of the channel estimate and constraints on the UR's estimation performance, but can improve rapidly in later stages as the quality of channel estimate improves. The training data power and AN power are optimally allocated by minimizing the normalized mean-square error (NMSE) of the LR subject to a lower limit constraint on the NMSE of the UR. The proposed DCE scheme is then extended to the case with multiple LRs and multiple URs. Simulation results are presented to demonstrate the effectiveness of the proposed DCE scheme.