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3D Stochastic Geometry Model for Large-Scale Molecular Communication Systems

Information delivery using chemical molecules is an integral part of biology at multiple distance scales and has attracted recent interest in bioengineering and communication. The collective signal strength at the receiver (i.e., the expected number of observed molecules inside the receiver), resulting from a large number of transmitters at random distances (e.g., due to mobility), can have a major impact on the reliability and efficiency of the molecular communication system. Modeling the collective signal from multiple diffusion sources can be computationally and analytically challenging. In this paper, we present the first tractable analytical model for the collective signal strength due to randomly-placed transmitters, whose positions are modelled as a homogeneous Poisson point process in three-dimensional (3D) space. By applying stochastic geometry, we derive analytical expressions for the expected number of observed molecules at a fully absorbing receiver and a passive receiver. Our results reveal that the collective signal strength at both types of receivers increases proportionally with increasing transmitter density. The proposed framework dramatically simplifies the analysis of large-scale molecular systems in both communication and biological applications.