  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 coding was used to maximize diversity gain.
Assuming a low-rate feedback link from the destination to each relay stage and
the source, this paper proposes end-to-end antenna selection strategies as an
alternative to distributed space-time coding. One-way (where only the source
has data for destination) and two-way (where the destination also has data for
the source) multi-hop relay channels are considered with both the full-duplex
and half duplex relay nodes. End-to-end antenna selection strategies are
designed and proven to achieve maximum diversity gain by using a single antenna
path (using single antenna of the source, each relay stage and the destination)
with the maximum signal-to-noise ratio at the destination. For the half-duplex
case, two single antenna paths with the two best signal-to-noise ratios in
alternate time slots are used to overcome the rate loss with half-duplex nodes,
with a small diversity gain penalty. Finally to answer the question, whether to
code (distributed space-time code) or not (the proposed end-to-end antenna
selection strategy) in a multi-hop relay channel, end-to-end antenna selection
strategy and distributed space-time coding is compared with respect to several
important performance metrics.
