Multiple-access channel capacity region with incomplete channel state information

In this work we provide an information-theoretic analysis of a Gaussian multiple-input multiple-output multiple access channel (MIMO MAC) with imperfect channel knowledge at the receiver. In particular we derive inner and outer bounds for the rate region of the MIMO MAC when the inputs are Gaussian. In the case where the channel knowledge at the receiver is obtained through training signals, we derive the structure of the optimum training signals for all users under a definite and semi-definite rank constraint. Numerical results show that the bounds we derive can be quite tight. Finally, we also investigate the low-SNR regime, specifically analyzing the minimum required energy per information bit and the wideband slope region.