  The diversity-multiplexing tradeoff of the dynamic decode-and-forward
protocol is characterized for the half-duplex three-terminal (m,k,n)-relay
channel where the source, relay and the destination terminals have m, k and n
antennas, respectively. It is obtained as a solution to a simple, two-variable,
convex optimization problem and this problem is solved in closed form for
special classes of relay channels, namely, the (1,k,1) relay channel, the
(n,1,n) relay channel and the (2,k,2) relay channel. Moreover, the tradeoff
curves for a certain class of relay channels, such as the (m,k,n>k) channels,
are identical to those for the decode-and-forward protocol for the full duplex
channel while for other classes of channels they are marginally lower at high
multiplexing gains. Our results also show that for some classes of relay
channels and at low multiplexing gains the diversity orders of the dynamic
decode-and-forward protocol protocol are greater than those of the static
compress-and-forward protocol which in turn is known to be tradeoff optimal
over all {\em static} half duplex protocols. In general, the dynamic
decode-and-forward protocol has a performance that is comparable to that of the
static compress-and-forward protocol which, unlike the dynamic
decode-and-forward protocol, requires global channel state information at the
relay node. Its performance is also close to that of the decode-and-forward
protocol over the full-duplex relay channel thereby indicating that the
half-duplex constraint can be compensated for by the dynamic operation of the
relay wherein the relay switches from the receive to the transmit mode based on
the source-relay channel quality.
