Half-Space Modeling with Reflecting Surface in Molecular Communication
Abstract: In Molecular Communications via Diffusion (MCvD), messenger molecules are emitted by a transmitter and propagate randomly through the fluidic environment. In biological systems, the environment can be considered a bounded space, surrounded by various structures such as tissues and organs. The propagation of molecules is affected by these structures, which reflect the molecules upon collision. Deriving the channel response of MCvD systems with an absorbing spherical receiver requires solving the 3-D diffusion equation in the presence of reflecting and absorbing boundary conditions, which is extremely challenging. In this paper, the method of images is brought to molecular communication (MC) realm to find a closed-form solution to the channel response of a single-input single-output (SISO) system near an infinite reflecting surface. We showed that a molecular SISO system in a 3-D half-space with an infinite reflecting surface could be approximated as a molecular single-input multiple-output (SIMO) system in a 3-D space, which consists of two symmetrically located, with respect to the reflecting surface, identical absorbing spherical receivers.
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