Analytical Derivation of the Impulse Response for the Bounded 2-D Diffusion Channel

TL;DR

This paper derives the impulse response of bounded 2-D and 3-D diffusion channels in molecular communication, providing analytical solutions and extending existing models to unbounded environments.

Contribution

It presents the first analytical derivation of the impulse response for bounded 2-D diffusion channels and extends the model to 3-D environments, filling gaps in existing literature.

Findings

Derived joint distribution of molecules on the receiver over time and angle.

Analyzed channel characteristics using the derived distribution.

Provided a method to obtain the unbounded 2-D channel solution from bounded solutions.

Abstract

This paper focuses on the derivation of the distribution of diffused particles absorbed by an agent in a bounded environment. In particular, we analogously consider to derive the impulse response of a molecular communication channel in 2-D and 3-D environment. In 2-D, the channel involves a point transmitter that releases molecules to a circular absorbing receiver that absorbs incoming molecules in an environment surrounded by a circular reflecting boundary. Considering this setup, the joint distribution of the molecules on the circular absorbing receiver with respect to time and angle is derived. Using this distribution, the channel characteristics are examined. Furthermore, we also extend this channel model to 3-D using a cylindrical receiver and investigate the channel properties. We also propose how to obtain an analytical solution for the unbounded 2-D channel from our derived solutions, as no analytical derivation for this channel is present in the literature.