Arrival Modeling and Error Analysis for Molecular Communication via Diffusion with Drift

TL;DR

This paper analyzes the accuracy of Poisson and Gaussian approximations for the binomial distribution of molecule arrivals in diffusion-based molecular communication with drift, providing guidelines for model selection based on system parameters.

Contribution

It offers a detailed comparison of Poisson and Gaussian models for molecular arrival processes, establishing regions where each approximation is more accurate based on RMSE and error probabilities.

Findings

Poisson approximation is better for small numbers of molecules and short distances.

Gaussian approximation performs well for large numbers of molecules and longer distances.

Numerical simulations confirm the theoretical boundaries for model accuracy.

Abstract

The arrival of molecules in molecular communication via diffusion (MCvD) is a counting process, exhibiting by its nature binomial distribution. Even if the binomial process describes well the arrival of molecules, when considering consecutively sent symbols, the process struggles to work with the binomial cumulative distribution function (CDF). Therefore, in the literature, Poisson and Gaussian approximations of the binomial distribution are used. In this paper, we analyze these two approximations of the binomial model of the arrival process in MCvD with drift. Considering the distance, drift velocity, and the number of emitted molecules, we investigate the regions in which either Poisson or Gaussian model is better in terms of root mean squared error (RMSE) of the CDFs; we confirm the boundaries of the region via numerical simulations. Moreover, we derive the error probabilities for continuous communication and analyze which model approximates it more accurately.