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The effect of a training-based linear minimum mean squared error (LMMSE) channel estimator on the sum mutual information of the multiple-input multiple-output (MIMO) multiple access channel (MAC) is investigated. The contribution of the present work consists in relating information-theoretic bounds on the sum mutual information with practical system parameters that impact on the training-based LMMSE MIMO channel estimator. The unboundness of the sum mutual information and conservation of the multiplexing gain are shown for a block fading channel model even in the presence of channel estimation errors. Then, as an application of the bounds, mutual information-maximizing power allocation strategies under total energy constraints are considered.