  Consider a sensor network made of remote nodes connected to a common fusion
center. In a recent work Blum and Sadler [1] propose the idea of ordered
transmissions -sensors with more informative samples deliver their messages
first- and prove that optimal detection performance can be achieved using only
a subset of the total messages. Taking to one extreme this approach, we show
that just a single delivering allows making the detection errors as small as
desired, for a sufficiently large network size: a one-bit detection scheme can
be asymptotically consistent. The transmission ordering is based on the modulus
of some local statistic (MO system). We derive analytical results proving the
asymptotic consistency and, for the particular case that the local statistic is
the log-likelihood (\ell-MO system), we also obtain a bound on the error
convergence rate. All the theorems are proved under the general setup of random
number of sensors. Computer experiments corroborate the analysis and address
typical examples of applications including: non-homogeneous Poisson-deployed
networks, detection by per-sensor censoring, monitoring of energy-constrained
phenomenon.
