  A nano abnormality detection scheme (NADS) in molecular nano-networks is
studied. This is motivated by the fact that early detection of diseases such as
cancer play a crucial role in their successful treatment. The proposed NADS is
in fact a two-tier network of sensor nano-machines (SNMs) in the first tier and
a data-gathering node (DGN) at the sink. The SNMs detect the presence of
competitor cells (abnormality) by variations in input and/or parameters of a
nano-communications channel (NCC). The noise of SNMs as their nature suggest is
considered correlated in time and space and herein assumed additive Gaussian.
In the second step, the SNMs transmit micro-scale messages over a noisy micro
communications channel (MCC) to the DGN, where a decision is made upon fusing
the received signals. We find an optimum design of detectors for each of the
NADS tiers based on the end-to-end NADS performance. The detection performance
of each SNM is analyzed by setting up a generalized likelihood ratio test.
Next, taking into account the effect of the MCC, the overall performance of the
NADS is analyzed in terms of probabilities of misdetection and false alarm. In
addition, computationally efficient expressions to quantify the NADS
performance is derived by providing respectively an approximation and an upper
bound for the probabilities of misdetection and false alarm. This in turn
enables formulating a design problem, where the optimized concentration of SNMs
in a sample is obtained for a high probability of detection and a limited
probability of false alarm. The results indicate that otherwise ignoring the
spatial and temporal correlation of SNM noise in the analysis, leads to an NADS
that noticeably underperforms in operations.
