Delay-limited capacity of MIMO channels with limited feedback

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 bits 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 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.