A statistical-physical model of interference in diffusion-based molecular nanonetworks

Molecular nanonetworks stand at the intersection of nanotechnology, biotechnology, and network engineering. The research on molecular nanonetworks proposes the interconnection of nanomachines through molecule exchange. Amongst different solutions for the transport of molecules between nanomachines, the most general is based on free diffusion. The objective of this paper is to provide a statistical-physical modeling of the interference when multiple transmitting nanomachines emit molecules simultaneously. This modeling stems from the same assumptions used in interference study for radio communications, namely, a spatial Poisson distribution of transmitters having independent and identically distributed emissions, while the specific molecule emissions model is in agreement with a chemical description of the transmitters. As a result of the property of the received molecular signal of being a stationary Gaussian Process (GP), the statistical-physical modeling is operated on its Power Spectral Density (PSD), for which it is possible to obtain an analytical expression of the log-characteristic function. This expression leads to the estimation of the received PSD probability distribution, which provides a complete model of the interference in diffusion-based molecular nanonetworks. Numerical results in terms of received PSD probability distribution and probability of interference are presented to compare the proposed statistical-physical model with the outcomes of simulations.