  This paper considers the problem of selecting either routes that consist of
long hops or routes that consist of short hops in a network of multiple-antenna
nodes, where each transmitting node employs spatial multiplexing. This
distance-dependent route selection problem is approached from the viewpoint of
energy efficiency, where a route is selected with the objective of minimizing
the transmission energy consumed while satisfying a target outage criterion at
the final destination. Deterministic line networks and two-dimensional random
networks are considered. It is shown that when 1) the number of hops traversed
between the source and destination grows large or 2) when the target success
probability approaches one or 3) when the number of transmit and/or receive
antennas grows large, short-hop routing requires less energy than long-hop
routing. It is also shown that if both routing strategies are subject to the
same delay constraint, long-hop routing requires less energy than short-hop
routing as the target success probability approaches one. In addition,
numerical analysis indicates that given loose outage constraints, only a small
number of transmit antennas are needed for short-hop routing to have its
maximum advantage over long-hop routing, while given stringent outage
constraints, the advantage of short-hop over long-hop routing always increases
with additional transmit antennas.
