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

TL;DR

Numerical and simulation results reveal that the system error performance is greatly improved by combining the detection information of distributed receivers and that the solutions to the formulated suboptimal convex optimization problems achieve near-optimal global error performance.

Abstract

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.

Figures (7)

• Figure 1: An example of a cooperative MC system with $K=5$, where the transmission from the TX to the RXs is represented by solid arrows and the decision reporting from the RXs to the FC is represented by dashed arrows.
• Figure 2: Average global error probability $\overline{Q}_{ \textnormal{FC}}$ of different fusion rules versus the decision threshold at RXs $\xi_{ \textnormal{RX}}$ with $K\!=\!3$ in the perfect reporting scenario.
• Figure 3: Optimal average global error probability $\overline{Q}_{ \textnormal{FC}}^{\ast}$ of different fusion rules versus the number of cooperative RXs $K$ in the perfect reporting scenario.
• Figure 4: Average global error probability $\overline{Q}_{ \textnormal{FC}}$ of different fusion rules versus the decision threshold at RXs $\xi_{ \textnormal{RX}}$ with $K=3$ in the noisy reporting scenario.
• Figure 5: Expected average global error probability $\overline{Q}_{ \textnormal{FC}}$ versus the decision threshold at RXs $\xi_{ \textnormal{RX}}$ and the decision threshold at the FC $\xi_{ \textnormal{FC}}$ with $K = 3$ in the noisy reporting scenario for \ref{['fig:a']} OR rule, \ref{['fig:b']} AND rule, and \ref{['fig:c']} majority rule. In \ref{['fig:a']}--\ref{['fig:c']}, '$\blacklozenge$' is the optimal $\overline{Q}_{ \textnormal{FC}}$ achieved by $\xi_{ \textnormal{RX}}^{\ast}$ and $\xi_{ \textnormal{FC}}^{\ast}$, obtained by exhaustive search, and '$\blacksquare$' is the approximated $\overline{Q}_{ \textnormal{FC}}$ achieved by $\xi_{ \textnormal{RX}}^{\circ}$ and $\xi_{ \textnormal{FC}}^{\circ}$.

Theorems & Definitions (4)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4