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This paper focuses on the derivation of the distribution of diffusedparticles absorbed by an agent in a bounded environment. In particular, weanalogously consider to derive the impulse response of a molecularcommunication channel in 2-D and 3-D environment. In 2-D, the channel involvesa point transmitter that releases molecules to a circular absorbing receiverthat absorbs incoming molecules in an environment surrounded by a circularreflecting boundary. Considering this setup, the joint distribution of themolecules on the circular absorbing receiver with respect to time and angle isderived. Using this distribution, the channel characteristics are examined.Furthermore, we also extend this channel model to 3-D using a cylindricalreceiver and investigate the channel properties. We also propose how to obtainan analytical solution for the unbounded 2-D channel from our derivedsolutions, as no analytical derivation for this channel is present in theliterature.

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