Diffusion Channel Characterization for A Cuboid Container: Some Insights into The Role of Dimensionality and Fluid Boundaries

Dimensionality of the fluid environment plays a crucial role in characterizing the diffusive channel. It is generally believed that increasing the dimensionality of the fluid medium should negatively affect the hitting probabilities as the degrees of freedom of propagating molecules have been enhanced. This paper has twofold objectives, it provides the diffusion channel characterization of a molecular communication (MC) system in an enclosed cuboid geometry and then studies the effect of dimensionality and the size of the receiver on the obtained channel statistics. The motility probability distribution function (PDF) of the molecules in a constrained cuboid environment with five reflecting and one absorbing wall is derived. The first hitting time (FHT) PDF and the hitting probabilities of the molecules to the absorbing wall are deduced from the same. A comparative analytical study of the derived FHT PDF against the diffusion channel statistics of various bounded and unbounded environments is presented. The comparison quantitatively establishes that an MC system with suitably configured fluid boundaries and transmitter and receiver arrangement can completely eliminate the effect of dimensionality and the size of the receiver on the hitting probabilities. The study may be of use in designing practically efficient and economic MC systems.