An Analytical Model for Molecular Communication over a Non-linear Reaction-Diffusion Medium

TL;DR

This paper introduces an analytical perturbation-based model for non-linear reaction-diffusion chemical equations in molecular communication, enabling easier analysis and optimization without extensive simulations.

Contribution

It develops an analytical approximation method for non-linear reaction-diffusion equations using perturbation theory, simplifying the modeling process in molecular communication systems.

Findings

Approximate solutions track true solutions for small time or reaction rates

Optimal molecule release timing depends on reaction rate and time interval

Analytical model reduces reliance on numerical simulations

Abstract

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. In this paper, we provide an analytical technique for modeling the non-linearity of chemical reaction equations based on the perturbation method. The perturbation method expresses the solution in terms of an infinite power series. An approximate solution can be found by keeping the leading terms of the power series. The approximate solution is shown to track the true solution if either the simulation time interval or the reaction rate is sufficiently small. Approximate solutions for long time intervals are also discussed. An illustrative example is given. For this example, it is shown that when the reaction rate (or the total time interval) is low, instead of using a continuous release waveform, it is optimal for the transmitters to release molecules at two time instances.