Target Detection in Clustered Mobile Nanomachine Networks

TL;DR

The paper develops an analytical framework for target detection in diffusion-based molecular networks with clustered initial NM deployments modeled by Poisson cluster processes (MCP and TCP). It derives exact detection probabilities using the probability generating functional, provides bounds and approximations via swept-volume analyses, and compares PCP deployments to PPP, revealing clustering-induced coverage gaps. It also extends to single-cluster deployments and spherical targets, with validation through particle-based simulations that confirm accuracy and reveal design trade-offs. The findings offer practical guidance for optimizing nanoscale molecular communication systems in biological environments, including parameter choices for diffusion, clustering, and target geometry.

Abstract

This work focuses on the development of an analytical framework to study a diffusion-assisted molecular communication-based network of nano-machines (NMs) with a clustered initial deployment to detect a target in a three-dimensional (3D) medium. Leveraging the Poisson cluster process to model the initial locations of clustered NMs, we derive the analytical expression for the target detection probability with respect to time along with relevant bounds. We also investigate a single-cluster scenario. All the derived expressions are validated through extensive particle-based simulations. Furthermore, we analyze the impact of key parameters, such as the mean number of NMs per cluster, the density of the cluster, and the spatial spread, on the detection performance. Our results show that detection probability is greatly influenced by clustering, and different spatial arrangements produce varying performances. The results offer a better understanding of how molecular communication systems should be designed for optimal target detection in nanoscale and biological environments.

Figures (8)

• Figure 1: Schematic diagrams of (a) MCP and (b) TCP. Crosses ($\times$) represent cluster centers (parent points), and red dots (${\rm o}$) represent daughter points (NMs).
• Figure 2: Variation of the detection probability over time $t$ for different values of $\bar{m}$ in (a) MCP and (b) TCP. The probability of detection over time of PCP deployed NMs shows a higher detection probability when $t$ and $\bar{m}$ are increased. The parameter values are $a=3\,\mu$m, $r=10\,\mu$m, $\sigma=10\,\mu$m, $\lambda_{\mathrm{Pa}}=1\times10^{-6}$ clusters/$\mu$m$^{3}$, $D=100\,\mu$m$^{2}$/s, and $\Delta t=10^{-3}$ s.
• Figure 3: Variation of the detection probability over time $t$ for (a) MCP and (b) TCP. The probability of detection increases with cluster density. The parameter values are $a=3\,\mu$m, $r=10\,\mu$m, $\sigma=10\,\mu$m, $\bar{m}=5$, $D=100\,\mu$m$^{2}$/s, and $\Delta t=10^{-3}$ s.
• Figure 4: Variation of the detection probability over time $t$ versus (a) the cluster radius $r$ for MCP and (b) the spread parameter $\sigma$ for TCP. Increasing $r$ in MCP and $\sigma$ in TCP enhances the detection probability; however, the accuracy of the approximate expression degrades as NMs are distributed farther from the cluster centers. The parameter values are $a=4\,\mu$m, $\lambda_{\mathrm{Pa}}=5\times10^{-7}$ clusters/$\mu$m$^{3}$, $D=100\,\mu$m$^{2}$/s, $t=5$ s, and $\Delta t=10^{-3}$ s.
• Figure 5: A comparison of target detection probabilities for MCP and TCP distributed NMs shows that both methods have similar detection rates when NMs are near cluster centers. However, TCP performs better at higher values of $\sigma$. The parameters are $a = 3 \, \mu m$, $\lambda_\mathsf{p} = 1 \times 10^{-6} \, \text{Clusters}/\mu m^{3}$, and $D = 100 \, \mu m^2/s$.

Theorems & Definitions (18)

• Theorem 1
• Corollary 1
• proof
• Corollary 2
• proof
• Lemma 1
• Theorem 2
• proof
• Lemma 2
• Corollary 3