Dispersion-Domain Detection for Mobile Molecular Communication Under Multiplicative Geometry Uncertainty

TL;DR

This paper introduces a dispersion-domain detection method for mobile molecular communication that accounts for geometry uncertainty and mobility, providing stable detection thresholds and improved performance.

Contribution

It proposes a novel dispersion-domain statistic $T_k^{(\Delta)}$ that normalizes for geometry gain uncertainty, enabling reliable detection in mobile molecular communication systems.

Findings

The proposed statistic achieves threshold stability across gain variations.

Simulation results support the effectiveness of the method under mobility and interference.

Gaussian approximations facilitate ROC and BER analysis for the detection scheme.

Abstract

Mobile molecular communication (MC) links with counting receivers are sensitive to transmitter--receiver geometry especially when nodes are mobile. We study binary detection from within-symbol count observations with unknown finite-memory inter-symbol interference (ISI) and a block-constant multiplicative geometry gain. Under a mixed-Poisson view mobility and geometry uncertainty can randomize the latent received intensity and create extra-Poisson dispersion. We propose a profiled dispersion-domain statistic $T_k^{(\Delta)}$ formed after profiling the deterministic mean shape. The statistic subtracts the intrinsic Poisson component and normalizes by the squared profiled mean to target threshold stability under the stated multiplicative-gain model. Activity gating makes conditional and gate-integrated false-alarm probabilities explicit. We characterize $T_k^{(\Delta)}$ using a time-series central-limit-theorem (CLT)-motivated Gaussian working approximation with long-run-variance dependence correction yielding Gaussian-approximate receiver operating characteristic (ROC)/bit-error-rate (BER) formulas and separability design metrics. Simulations with symbol-dependent active-Brownian mobility and finite-memory ISI support the proposed mechanism show empirical threshold stability over the tested gain range and indicate usefulness when mean-domain differences are weak unreliable or intentionally suppressed.