Half-Space Modeling with Reflecting Surface in Molecular Communication

Molecular communications is a technique emulated by researchers, which has already been used by the nature for millions of years. In Molecular Communications via Diffusion (MCvD), messenger molecules are emitted by a transmitter and propagate in the fluidic environment in a random manner. In biological systems, the environment can be considered a bounded space, surrounded by different structures, such as tissues and organs. The propagation of molecules is affected by these structures in the environment, which reflect the molecules upon collision. Hence, understanding the behavior of MCvD systems near reflecting surfaces is important for modeling molecular communication systems analytically. However, deriving the channel response of MCvD systems with an absorbing spherical receiver requires solving the diffusion equation in 3-D space in the presence of a reflecting boundary, which is extremely challenging. Therefore, derivation of the channel response in a bounded environment has remained one of the unanswered questions in the literature. In this paper, a method to model molecular communication systems near reflecting surfaces is proposed, and an analytical closed-form solution for the channel response is derived.