  Multi-hop relay channels use multiple relay stages, each with multiple relay
nodes, to facilitate communication between a source and destination.
Previously, distributed space-time codes were proposed to maximize the
achievable diversity-multiplexing tradeoff, however, they fail to achieve all
the points of the optimal diversity-multiplexing tradeoff. In the presence of a
low-rate feedback link from the destination to each relay stage and the source,
this paper proposes an end-to-end antenna selection (EEAS) strategy as an
alternative to distributed space-time codes. The EEAS strategy uses a subset of
antennas of each relay stage for transmission of the source signal to the
destination with amplify and forwarding at each relay stage. The subsets are
chosen such that they maximize the end-to-end mutual information at the
destination. The EEAS strategy achieves the corner points of the optimal
diversity-multiplexing tradeoff (corresponding to maximum diversity gain and
maximum multiplexing gain) and achieves better diversity gain at intermediate
values of multiplexing gain, versus the best known distributed space-time
coding strategies. A distributed compress and forward (CF) strategy is also
proposed to achieve all points of the optimal diversity-multiplexing tradeoff
for a two-hop relay channel with multiple relay nodes.
