Ergodic Capacity of Multi-User MIMO Systems Using Pilot-Based Channel Estimation, Quantized Feedback and Outdated Feedback as Well as User Selection

We derive the ergodic channel capacity of a closed-loop MIMO broadcast system under both random user selection (RUS) and semi-orthogonal user selection (SUS) principles, when considering the effects of channel estimation errors, channel state information (CSI) quantization errors and CSI feedback-delay. We intend to answer the question of "How many simultaneous users should be active in a time slot in order to achieve the maximum sum-rate in a MIMO broadcast system?". It is shown that we should refrain from supporting full-rank transmissions due to the excess inter-user interference caused by imperfect CSI at both the receiver and transmitter under RUS. By contrast, full-rank transmissions may be feasible under the SUS principle. An approximate ergodic capacity equation is also derived for RUS, and then an adaptive-rank transmission strategy is derived, which is capable of maximizing the achievable ergodic capacity.