Mutual Information of Block-Faded MIMO Multiple Access Channels with Channel Estimation Error

In this paper, 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. Adhering to the classical channel estimation philosophy, the overarching contribution of the present work consists in bridging pure information-theoretic bounds on the sum mutual information with practical system parameters that are inherent to the LMMSE channel estimator. The unboundness of the mutual information and conservation of the multiplexing gain is shown and, interestingly, the increase of the mutual information loss with respect of the perfect channel knowledge case with the increasing of the signal-to-noise-ratio (SNR) is revealed, with a close-form expression for the value bounding the loss for asymptotically high SNRs.