  We establish the optimal diversity-multiplexing (DM) tradeoff of coherent
time, frequency and time-frequency selective-fading MIMO channels and provide a
code design criterion for DM-tradeoff optimality. Our results are based on the
analysis of the "Jensen channel" associated to a given selective-fading MIMO
channel. While the original problem seems analytically intractable due to the
mutual information being a sum of correlated random variables, the Jensen
channel is equivalent to the original channel in the sense of the DM-tradeoff
and lends itself nicely to analytical treatment. Finally, as a consequence of
our results, we find that the classical rank criterion for space-time code
design (in selective-fading MIMO channels) ensures optimality in the sense of
the DM-tradeoff.
