  In this paper, we consider abnormality detection via diffusive molecular
communications (MCs) for a network consisting of several sensors and a fusion
center (FC). If a sensor detects an abnormality, it injects into the medium a
number of molecules which is proportional to the sensed value. Two transmission
schemes for releasing molecules into the medium are considered. In the first
scheme, referred to as DTM, each sensor releases a different type of molecule,
whereas in the second scheme, referred to as STM, all sensors release the same
type of molecule. The molecules released by the sensors propagate through the
MC channel and some may reach the FC where the final decision regarding whether
or not an abnormality has occurred is made. We derive the optimal decision
rules for both DTM and STM. However, the optimal detectors entail high
computational complexity as log-likelihood ratios (LLRs) have to be computed.
To overcome this issue, we show that the optimal decision rule for STM can be
transformed into an equivalent low-complexity decision rule. Since a similar
transformation is not possible for DTM, we propose simple low-complexity
sub-optimal detectors based on different approximations of the LLR. The
proposed low-complexity detectors are more suitable for practical MC systems
than the original complex optimal decision rule, particularly when the FC is a
nano-machine with limited computational capabilities. Furthermore, we analyze
the performance of the proposed detectors in terms of their false alarm and
missed detection probabilities. Simulation results verify our analytical
derivations and reveal interesting insights regarding the trade-off between
complexity and performance of the proposed detectors and the considered DTM and
STM schemes.
