Convex Optimization of Distributed Cooperative Detection in Multi-Receiver Molecular Communication

Abstract

In this paper, the error performance achieved by cooperative detection among K distributed receivers in a diffusion-based molecular communication system is analyzed and optimized. In this system, the receivers first make local hard deci- sions 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 report- ing, are considered. Closed-form expressions are derived for the expected global error probability of the system for both report- ing 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 prob- lems 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 detec- tion information of distributed receivers. They also reveal that the solutions to the formulated suboptimal convex optimization problems achieve near-optimal global error performance.