  This paper presents a framework to evaluate the probability that a decision
error event occurs in wireless sensor networks, including sensing and
communication errors. We consider a scenario where sensors need to identify
whether a given event has occurred based on its periodic, noisy, observations
of a given signal. Such information about the signal needs to be sent to a
fusion center that decides about the actual state at that specific observation
time. The communication links -- single- or multi-hop -- are modeled as binary
symmetric channels, which may have different error probabilities. The decision
at the fusion center is based on OR, AND, K-OUT-OF-N and MAJORITY Boolean
operations on the received signals associated to individual sensor
observations. We derive closed-form equations for the average decision error
probability as a function of the system parameters (e.g. number of sensors and
hops) and the input signal characterization. Our analyses show the best
decision rule is closely related to the frequency that the observed events
occur and the number of sensors. In our numerical example, we show that the AND
rule outperforms MAJORITY if such an event is rare and there is only a handful
number of sensors. Conversely, if there is a large number of sensors or more
evenly distributed event occurrences, the MAJORITY is the best choice. We
further show that, while the error probability using the MAJORITY rule
asymptotically goes to 0 with increasing number of sensors, it is also more
susceptible to higher channel error probabilities.
