We consider a fixed data rate slow-fading MIMO channel with a long-term power constraint P at the transmitter. A relevant performance limit is the delay-limited capacity, which is the largest data rate at which the outage probability is zero. It is well known that if both the transmitter and the receiver have full channel state information (CSI) and if either of them has multiple antennas, the delay-limited capacity is non-zero and grows logarithmically with P. Achieving even a positive delay-limited capacity, however, becomes a difficult task when the CSI at the transmitter (CSIT) is imperfect. In this context, the standard partial CSIT model where the transmitter has a fixed finite bit of quantized CSI feedback for each channel state results in zero delay-limited capacity. We show that by using a variable-length feedback scheme that utilizes a different number of feedback bits for different channel states, a non-zero delay-limited capacity can be achieved if the feedback rate is greater than 1 bit per channel state. Moreover, we show that the delay-limited capacity loss due to finite-rate feedback decays at least inverse linearly with respect to the feedback rate. We also discuss the applications to ergodic MIMO channels.
