Using the duality of multiple input multiple output broadcast (MIMO BC) and MIMO multiple access (MIMO MAC), a lower bound and an upper bound of mutual information of MIMO BC systems with imperfect channel estimation are investigated. The gap between two bounds is considerably tight especially at high SNR region. The point-to-point MIMO system is a special case of our results. In the limit where the channel can be estimated perfectly, the mutual information converges to the case without errors. The effect upon the sum capacity of zero-forcing (ZF) precoding MIMO BC systems with channel estimation errors is also studied, which indicates that the sum capacity monotonously decreases as the covariance of channel estimation errors increases. At high SNR region, with fixed covariance of channel estimation errors, the multiplexing gain tends to be zero and the sum capacity will converge to a constant value as SNR increases.
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