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Half-Space Modeling with Reflecting Surface in Molecular Communication

Anil Kamber, H. Birkan Yilmaz, Ali Emre Pusane, Tuna Tugcu

TL;DR

This work addresses the diffusion-based molecular communication problem in a bounded 3-D half-space by introducing the method of images to derive a closed-form half-space channel response. By showing that a SISO system near an infinite reflecting boundary is equivalent to a SIMO system with two symmetric absorbing receivers, the authors circumvent the intractable diffusion equation under reflecting boundary conditions. They extend the approach to two parallel mirrors and validate accuracy across multiple topologies using GPU simulations, highlighting the importance of time-step choice for near-boundary accuracy. The findings offer a tractable framework for modeling MCvD in biologically bounded environments and could enable improved localization and communication performance in nanonetworks operating near tissues or organs.

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.

Half-Space Modeling with Reflecting Surface in Molecular Communication

TL;DR

This work addresses the diffusion-based molecular communication problem in a bounded 3-D half-space by introducing the method of images to derive a closed-form half-space channel response. By showing that a SISO system near an infinite reflecting boundary is equivalent to a SIMO system with two symmetric absorbing receivers, the authors circumvent the intractable diffusion equation under reflecting boundary conditions. They extend the approach to two parallel mirrors and validate accuracy across multiple topologies using GPU simulations, highlighting the importance of time-step choice for near-boundary accuracy. The findings offer a tractable framework for modeling MCvD in biologically bounded environments and could enable improved localization and communication performance in nanonetworks operating near tissues or organs.

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.
Paper Structure (12 sections, 28 equations, 10 figures, 11 tables)

This paper contains 12 sections, 28 equations, 10 figures, 11 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Methodology
  4. Method of Images
  5. Channel Response
  6. Two Parallel Infinite Reflecting Surfaces
  7. Performance Evaluation
  8. Infinite Reflecting Surface
  9. Finite Reflecting Surface
  10. Bounded Space with Two Infinite Reflecting Surface
  11. Effect of $\sqrt{2D\Delta t}$ on RMSE Performances
  12. Conclusion

Figures (10)

  • Figure 1: Half-space MCvD system with an infinite reflecting surface.
  • Figure 2: Approximated SIMO system when the infinite reflecting surface is omitted.
  • Figure 3: MCvD system between two infinite reflecting surfaces.
  • Figure 4: Approximated SIMO system when the two infinite reflecting surfaces are omitted.
  • Figure 5: Visualizations of Topology 0 and Topology 1.
  • ...and 5 more figures