Diversity–Multiplexing Tradeoff in MIMO Channels With Partial CSIT

The diversity-multiplexing (D-M) tradeoff in a multi antenna channel with optimized resolution-constrained channel state feedback is characterized. The concept of
minimum guaranteed multiplexing gain
in the forward link is introduced and shown to significantly influence the optimal D-M tradeoff. It is demonstrated that power control based on the feedback is instrumental in achieving the D-M tradeoff, and that rate adaptation is important in obtaining a high diversity gain even at high rates. A criterion to determine finite-length codes to be tradeoff optimal is presented, leading to a useful geometric characterization of the class of
extended approximately universal codes
. With codes from this class, the optimal D-M tradeoff is achievable by the combination of a feedback-dependent power controller and a single code-book for single-rate or two codebooks for adaptive-rate transmission. Finally, lower bounds to the optimal D-M tradeoffs based on Gaussian coding arguments are also studied. In contrast to the no-feedback case, these random coding bounds are only asymptotically tight, but can quickly approach the optimal tradeoff even with moderate codeword lengths.