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In this work, we propose and analyze a two-way training system that exploits the fact that most wireless nodes are capable of both transmitting and receiving signals. That is, the underlying channel is by design a two-way channel, even if only one of the nodes has data to communicate. For half-duplex nodes with one antenna at the source node and M antennas at the destination node, we show that a novel training system can double the maximum diversity order of the system. The key departure from existing work is that (a) all resources used to obtain channel information at the source and destination are accounted for, and (b) channel estimates at the source and destination are mismatched and noisy. We further derive the full diversity-multiplexing tradeoff which demonstrates a diversity order gain at almost all multiplexing gains due to information at the source, even when that information is based on noisy estimates and subjected to full resource accounting.