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Most communication systems use some form of feedback, often related to channel state information. In this paper, we study diversity multiplexing tradeoff for both frequency division duplex (FDD) and time division duplex (TDD) systems, when both receiver and transmitter knowledge about the channel is noisy and potentially mismatched. For FDD systems, we first extend the achievable tradeoff region for 1.5 rounds of message passing to get higher diversity compared to the best known scheme, in the regime of higher multiplexing gains. We then break the mold of all current channel state based protocols by using multiple rounds of conferencing to extract more bits about the actual channel. This iterative refinement of the channel increases the diversity order with every round of communication. The protocols are on-demand in nature, using high powers for training and feedback only when the channel is in poor states. The key result is that the diversity multiplexing tradeoff with perfect training and <formula formulatype="inline"> <tex Notation="TeX">$K$</tex></formula> levels of perfect feedback can be achieved, even when there are errors in training the receiver and errors in the feedback link, with a multiround protocol which has <formula formulatype="inline"><tex Notation="TeX">$K$</tex></formula> rounds of training and <formula formulatype="inline"> <tex Notation="TeX">$K-1$</tex></formula> rounds of binary feedback. The above result can be viewed as a generalization of Zheng and Tse, and Aggarwal and Sabharwal, where the result was shown to hold for <formula formulatype="inline"><tex Notation="TeX">$K=1$</tex></formula> and <formula formulatype="inline"><tex Notation="TeX">$K=2$</tex> </formula>, respectively. For TDD systems, we also develop new achievable strategies with multiple rounds of communication between the transmitter and the receiver, which use the reciprocity of the forward and the feedback channel. The multiround TDD protocol achieves a diversity-multiplexing tradeoff which uniformly dominates its FDD counterparts, where no channel reciprocity is available.

Bits About the Channel: Multiround Protocols for Two-Way Fading Channels