Capacity-approaching rate function for layered multiantenna architectures

The simultaneous use of multiple transmit and receive antennas can unleash very large capacity increases in rich multipath environments. Although such capacities can be approached by layered multiantenna architectures with per-antenna rate control, the need for short-term feedback arises as a potential impediment, in particular as the number of antennas - and, thus, the number of rates to be controlled - increases. What we show, however, is that the need for short-term feedback in fact vanishes as the number of antennas and/or the diversity order increases. Specifically, the rate supported by each transmit antenna becomes deterministic and a sole function of the signal-to-noise ratio of transmit and receive antennas, and the decoding order, all of which are either fixed or slowly varying. More generally, we illustrate - through this specific derivation - the relevance of some established random code-division multiple-access results to the single-user multiantenna problem.