Spatiotemporal First-Arrival Modeling and Parameter Estimation in Drift-Diffusion Molecular Channels

TL;DR

This paper derives a joint distribution for first arrival time and position in drift-diffusion channels, enabling improved parameter estimation and signal detection through spatiotemporal analysis in molecular communication.

Contribution

It introduces a closed-form joint distribution capturing spatiotemporal coupling, and proposes Drift Shift Keying for enhanced detection in molecular channels.

Findings

Estimation accuracy scales with spatial dimension.

Lateral drift can be recovered via a closed-form MLE.

Joint receivers outperform timing-only receivers in detection.

Abstract

We derive a closed-form joint distribution of the first arrival time (FAT) and first arrival position (FAP) in drift-diffusion molecular communication (MC) channels. In contrast to prior studies that analyze FAT or FAP in isolation, our framework explicitly captures the spatiotemporal coupling inherent in multidimensional transport. Building on this derivation, we compute the Fisher information matrix (FIM) and demonstrate that estimation accuracy for diffusivity scales proportionally with the spatial dimension, enabling increased sensitivity in higher-dimensional environments. Furthermore, we show that lateral drift -- which is unobservable from timing data alone -- can be recovered via a closed-form Maximum Likelihood Estimator (MLE) with a simple physical interpretation. Leveraging this spatial degree of freedom, we propose Drift Shift Keying (DSK), proving that joint receivers can reliably detect signals that are undetectable to timing-only receivers due to identical marginal FAT distributions. These results highlight the significant potential of spatiotemporal processing for future nanoscale communication and sensing.