2.7 Summary

We have summarized results on the capacity of MIMO channels for both single- and multi-user systems. The great capacity gains predicted for such systems can be realized in some cases, but realistic assumptions about channel knowledge and the underlying channel model can significantly mitigate these gains. For single-user systems the capacity under perfect CSI at the transmitter and receiver is relatively straightforward and predicts that capacity grows linearly with the number of antennas. Backing off from the perfect CSI assumption makes the capacity calculation much more difficult, and the capacity gains are highly dependent on the nature of the CSI/CDI, the channel SNR, and the antenna element correlations. Specifically, assuming perfect CSIR, CSIT provides significant capacity gain at low SNRs but not much at high SNRs. The insight here is that at low SNRs it is important to put power into the appropriate eigenmodes of the system. Interestingly, with perfect CSIR and CSIT, antenna correlations are found to increase capacity at low SNRs and decrease capacity at high SNRs. Finally, under CDIT and CDIR for a zero-mean spatially white channel, at high SNRs the capacity grows relative to only the double-log of the SNR with the number of antennas as a constant additive term. This rather poor capacity gain would not typically justify adding more antennas. However, at moderate SNRs the growth relative to the number of antennas is less pessimistic.

We also examined the capacity of MIMO broadcast and multiple-access channels. The capacity region of...