On the achievable sum-rate of correlated mimo multiple access channel with imperfect channel estimation

We study upper and lower bounds on the achievable sum-rate of a correlated MIMO MAC with channel estimation error at the receiver when the correlation information is available to the users' transmitters, and prove that, for Gaussian input signals with arbitrary input covariance matrices, the gap between these bounds does not exceed a limiting value at any input transmit power. We further prove that in systems with uniform input power utilization over the transmit antennas, the gap between the mutual information bounds increases monotonically as the input power of each user increases. Furthermore, we show that in the absence of correlation, the gap between the mutual information bounds is maximum for beamforming and minimum for uniform input power allocation over the transmit antennas. We further prove that utilizing the input power of each user towards the directions of the eigenvectors of its transmit correlation matrix maximizes the mutual information lower bound. Moreover, we derive the transmit directions that maximize the mutual information lower and upper bounds in an uncorrelated MIMO MAC with delayed feedback from the receiver to the transmitters, and characterize the power allocation of this system in terms of its beamforming range. Numerical simulations are conducted to corroborate our theoretical results.