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.

翻译：本研究致力于开发一种分析框架，以研究基于扩散辅助分子通信的纳米机器网络在三维介质中检测目标的能力，该网络采用集群化初始部署。通过利用泊松簇过程对集群纳米机器的初始位置进行建模，我们推导出目标检测概率随时间变化的解析表达式及其相关边界。同时，我们探究了单集群场景。所有推导出的表达式均通过广泛的基于粒子的仿真得到验证。此外，我们分析了关键参数（如每簇纳米机器的平均数量、簇密度和空间扩散范围）对检测性能的影响。结果表明，检测概率受集群化影响显著，不同的空间布局会产生不同的性能表现。这些结果为如何在纳米尺度及生物环境中设计分子通信系统以实现最优目标检测提供了更深入的理解。