# Diffusive Mobile Molecular Communications Over Time-Variant Channels

## TL;DR

This paper models the time-variant behavior of diffusive molecular communication channels considering nano-machine mobility, providing an analytical expression for error probability that accounts for stochastic movements in a fluid environment.

## Contribution

It introduces a formalism to model time-variant channels in molecular communication considering nano-machine mobility and derives an analytical error probability expression.

## Key findings

- Analytical expression accurately predicts error probability.
- Channel behavior can be modeled by adjusting the diffusion coefficient.
- Simulation results verify the analytical model's accuracy.

## Abstract

This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are subjected to Brownian motion in addition to the diffusive motion of the information molecules used for communication. Due to the stochastic movements of the transmitter and receiver nano-machines, the statistics of the channel impulse response change over time. We show that the time-variant behaviour of the channel can be accurately captured by appropriately modifying the diffusion coefficient of the information molecules. Furthermore, we derive an analytical expression for evaluation of the expected error probability of a simple detector for the considered system. The accuracy of the proposed analytical expression is verified via particle-based simulation of the Brownian motion.