  In this paper, the error performance achieved by cooperative detection among
K distributed receivers in a diffusion-based molecular communication (MC)
system is analyzed and optimized. In this system, the receivers first make
local hard decisions on the transmitted symbol and then report these decisions
to a fusion center (FC). The FC combines the local hard decisions to make a
global decision using an N-out-of-K fusion rule. Two reporting scenarios,
namely, perfect reporting and noisy reporting, are considered. Closed-form
expressions are derived for the expected global error probability of the system
for both reporting scenarios. New approximated expressions are also derived for
the expected error probability. Convex constraints are then found to make the
approximated expressions jointly convex with respect to the decision thresholds
at the receivers and the FC. Based on such constraints, suboptimal convex
optimization problems are formulated and solved to determine the optimal
decision thresholds which minimize the expected error probability of the
system. Numerical and simulation results reveal that the system error
performance is greatly improved by combining the detection information of
distributed receivers. They also reveal that the solutions to the formulated
suboptimal convex optimization problems achieve near-optimal global error
performance.
