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Perfect channel state information (CSI) is always assumed in work on multiple-input, multiple-output (MIMO) precoding theoretical analyze. In this paper, we investigate the effect of imperfect channel state information on the performance of MIMO broadcast channel (MIMO-BC). We show that even with moderate channel estimation error, the system performance degrade significantly. So, we propose a Frobenius norm based power allocation scheme to guarantee the user's QoS. Simulation results show that this scheme enhances the user's outage performance and reduces the sensitivity to the imperfect CSI.