  In this paper an optimal relay selection algorithm with non-negligible
probing time is proposed and analyzed for cooperative wireless networks. Relay
selection has been introduced to solve the degraded bandwidth efficiency
problem in cooperative communication. Yet complete information of relay
channels often remain unavailable for complex networks which renders the
optimal selection strategies impossible for transmission source without probing
the relay channels. Particularly when the number of relay candidate is large,
even though probing all relay channels guarantees the finding of the best
relays at any time instant, the degradation of bandwidth efficiency due to
non-negligible probing times, which was often neglected in past literature, is
also significant. In this work, a stopping rule based relay selection strategy
is determined for the source node to decide when to stop the probing process
and choose one of the probed relays to cooperate with under wireless channels'
stochastic uncertainties. This relay selection strategy is further shown to
have a simple threshold structure. At the meantime, full diversity order and
high bandwidth efficiency can be achieved simultaneously. Both analytical and
simulation results are provided to verify the claims.
