  In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the
multiple-antenna (MIMO) static half-duplex relay channel. A general expression
is derived for the DMT upper bound, which can be achieved by a
compress-and-forward protocol at the relay, under certain assumptions. The DMT
expression is given as the solution of a minimization problem in general, and
an explicit expression is found when the relay channel is symmetric in terms of
number of antennas, i.e. the source and the destination have n antennas each,
and the relay has m antennas. It is observed that the static half-duplex DMT
matches the full-duplex DMT when the relay has a single antenna, and is
strictly below the full-duplex DMT when the relay has multiple antennas.
Besides, the derivation of the upper bound involves a new asymptotic study of
spherical integrals (that is, integrals with respect to the Haar measure on the
unitary group U(n)), which is a topic of mathematical interest in itself.
