Two Models for Noisy Feedback in MIMO Channels
  Two distinct models of feedback, suited for FDD (Frequency Division Duplex) and TDD (Frequency Division Duplex) systems respectively, have been widely studied in the literature. In this paper, we compare these two models of feedback in terms of the diversity multiplexing tradeoff for varying amount of channel state information at the terminals. We find that, when all imperfections are accounted for, the maximum achievable diversity order in FDD systems matches the diversity order in TDD systems. TDD systems achieve better diversity order at higher multiplexing gains. In FDD systems, the maximum diversity order can be achieved with just a single bit of feedback. Additional bits of feedback (perfect or imperfect) do not affect the diversity order if the receiver does not know the channel state information. 
Vaneet Aggarwal and Gajanana Krishna and Srikrishna Bhashyam and   Ashutosh Sabharwal