  In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed
for a cooperative diffusion-based molecular communication (MC) system. In this
system, the transmitter (TX) sends a common information symbol to multiple
receivers (RXs) and a fusion center (FC) chooses the TX symbol that is more
likely, given the likelihood of its observations from all RXs. The transmission
of a sequence of binary symbols and the resultant intersymbol interference are
considered in the cooperative MC system. Three ML detection variants are
proposed according to different RX behaviors and different knowledge at the FC.
The system error probabilities for two ML detector variants are derived, one of
which is in closed form. The optimal molecule allocation among RXs to minimize
the system error probability of one variant is determined by solving a joint
optimization problem. Also for this variant, the equal distribution of
molecules among two symmetric RXs is analytically shown to achieve the local
minimal error probability. Numerical and simulation results show that the ML
detection variants provide lower bounds on the error performance of simpler,
non-ML cooperative variants and demonstrate that these simpler cooperative
variants have error performance comparable to ML detectors.
