  We establish the optimal diversity-multiplexing (DM) tradeoff of coherent
time, frequency, and time-frequency selective-fading multiple-input
multiple-output (MIMO) channels and provide a code design criterion for DM
tradeoff optimality. Our results are based on the new concept of the "Jensen
channel" associated to a given selective-fading MIMO channel. While the
original problem seems analytically intractable due to the mutual information
between channel input and output 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. We formulate a
systematic procedure for designing DM tradeoff optimal codes for general
selective-fading MIMO channels by demonstrating that the design problem can be
separated into two simpler and independent problems: the design of an inner
code, or precoder, adapted to the channel statistics (i.e., the selectivity
characteristics) and an outer code independent of the channel statistics. Our
results are supported by appealing geometric intuition, first pointed out for
the flat-fading case by Zheng and Tse, IEEE Trans. Inf. Theory, 2003.
